WORKS OF
PROFESSOR MILO S. KETCHUM
PUBLISHED BY THE
McGRAW-HILL BOOK COMPANY
THE DESIGN OF STEEL MILL BUILDINGS and the Cal-
culation of Stresses in Framed Structures, Third Edition
Cloth, 6^x9 ins., pp. 562 +xvi, 66 tables and 270 illustra-
tions in the text. Price, $5.00 net, postpaid.
THE DESIGN OF WALLS, BINS AND GRAIN ELEVA-
TORS, Third Edition
Cloth, 6J^xp ins., pp. 556+xiv, 40 tables, 304 illustrations
in the text and two folding plates. Price, $ 5.00 net, postpaid
THE DESIGN OF HIGHWAY BRIDGES OF STEEL, TIM-
BER AND CONCRETE, Second Edition.
In Press. Price $ 5.00 net, postpaid.
THE DESIGN OF MINE STRUCTURES
Cloth, 6)^x9 ins., pp. 46o+xvi, 65 tables, 265 illustrations
in the text and 7 folding plates. Price, $5.00 net, postpaid.
STRUCTURAL ENGINEERS' HANDBOOK, Second Edition
Flexible, 6^x9 ins. pp. 95o + xvi, 260 tables, 400 illustra-
tions in the text. Price, $6.00 net, postpaid.
SPECIFICATIONS FOR STEEL FRAME MILL BUILDINGS
Paper, 6^x9 ins., pp. 32. Reprinted from " The Design of
Steel Mill Buildings." Price, 25 cents.
SURVEYING MANUAL. A Manual of Field and Office
Methods for the Use of Students in Surveying
By Professors William D. Pence and Milo S. Ketchum.
Leather, 4^*7 ins., pp. 388+xii, 10 plates and 140 illustra-
tions, and 130 pages of tables. Price, $2.50 net, postpaid.
OFFICE-COPY BOOKLET
For use with Pence and Ketchum's "Surveying Manual."
Tag board, 4^x7 ins., pp. 32, ruled in columns and rectangles.
Price, $1.50 per dozen or 75 cents per half dozen.
Tables of contents of the different books follow the index.
STRUCTURAL ENGINEERS' HANDBOOK
DATA FOR THE DESIGN AND CONSTRUCTION
OF STEEL BRIDGES AND BUILDINGS
BY
MILO S. KETCHUM, C.E.
M. AM. Soc. C. E.
PROFESSOR-IN-CHARGE OF CIVIL ENGINEERING, UNIVERSITY OF PENNSYLVANIA; SOMETIME DBAN
OF THE COLLEGE OF ENGINEERING AND PROFESSOR OF CIVIL ENGINEERING,
UNIVERSITY OF COLORADO; CONSULTING ENGINEER
SECOND EDITION
TENTH THOUSAND
Total Issue. 22.000
(Printed 1919)
} McGRAW-HILL BOOK COMPANY, INC.
239 WEST THIRTY-NINTH STREET, NEW YORK
\\ LONDON: HILL PUBLISHING COMPANY. I. it..
6-8 BOUVERIE STREET. 1
1918
COPYRIGHT, 1914, 1918
BY MILO S. KETCHUM
PRESS OF
THE NEW ERA PRIMING COMPANY
LANCASTER. PA.
PREFACE
The aim in writing this book has been to give data, details and tables for the design and
construction of steel bridges and buildings. The book is written for the structural engineer and
for the student or engineer who has had a thorough course in applied mechanics and the calcu-
lation of stresses in structures. To this end data and tables that will be of service to the designing
and constructing engineer have been given, rather than predigested data and designs that might
be used by the untrained. The book is intended as a working manual for the engineer, draftsman
and student and covers data, details and tables for the design of the structures ordinarily met
with. Swing and movable bridges, cantilever and suspension bridges require special treatment
and have not been considered. As the book is intended to supplement the present books on
stresses the calculation of stresses in bridges and buildings has been only briefly considered.
The calculation of stresses' in retaining walls, bins, stand-pipes, and other structures not ordinarily
covered in text-books on stresses have been given in compact form. Great care has been used
to give examples of structures that represent standard practice. With a few exceptions the draw-
ings of details of structures have been especially prepared for this book from actual working plans.
The book is a source book and is not a treatise, and is intended to furnish data and details that
are available only to a few engineers; and standard specifications for tnatcrialsand workmanship
that are available only in transactions of societies and in special treatises.
The tables giving properties of columns, top chords, plate girders and struts have b»i
culated especially for this book, and are original in material and arrangement. In calculating
the tables only those sections which comply with standard specifications have been given. The
tables have been calculated by the use of calculating machines and have been checked with great
care. The values will be found to be correct to one unit in the last place given. Properties of
Carnegie and Bethlehem sections are given in a compact form for easy reference. The tangents
of the angle of the axis giving the least radius of gyration, given in the tables giving properties
of Carnegie angles, were taken from Cambria Steel. With the exception of a few special I beams
and channels the tables may be used for Cambria, Pcncoyd and Jones & Laughlin angles, 1 beams
and channels. The American Bridge Company standards for eye-bars, loop-bars, clevises, pins,
and other structural details are given. Tables of logarithms, function of angles and tables that
are easily available have not been included.
The size of the book and the size of the type page were selected for the reasons that they give
a book of standard size with a type page large enough so that each table can come squarely on one
page, and large enough so that complete plans of structures can be given. A large clear type was
selected for both the text and for the tables. The paper has been selected with the idea of dear*
ness of the printed page.
This book is a result of many years' work, during which time the author has written four
books on structural engineering. In writing this book the author has drawn «»n his other books.
although much of the material given on steel mill buildings and highway bridges is new, and the
Structural Engineers' Handbook supplements the author's other books.
Data and details have been obtained from many sources, to which credit has been gi\
the body of the book. The author is under special obligation to many engineers, to whkh special
acknowledgment cannot be made on account of lack ol space.
vi PREFACE
In writing this book the author has been assisted by several of his former students. Credit
is due to Mr. I. C. Crawford, Instructor in Civil Engineering, for assistance in calculating tables
and reading proof; to Mr. C. S. Sperry, Instructor in Engineering Mathematics, for assistance in
calculating tables; to Professor H. C. Ford, of Iowa State College, and Mr. T. A. Blair, Instructor
in Civil Engineering, for assistance in preparing the drawings; and especially to Mr. W. C. Hunt-
ington, Assistant Professor of Civil Engineering, for assistance in arranging and calculating tables,
reading proof and assistance in other ways.
The author will appreciate notices of errors and suggestions for the improvement of future
editions.
M. S. K
BOULDER, COLORADO.
August 23, 1914.
PREFACE TO SECOND EDITION
In this edition details of steel windows and doors, data on cement and gypsum tile roofs,
solutions for bending moments in mill building columns and stresses in stiff frames have been added
to Chapter I, and Chapter III, Steel Highway Bridges, has been rewritten and enlarged. All
known errors have been corrected. Duties required of the author as Assistant Director in Charge
of Construction of the U. S. Government Explosives Plant, Nitro, West Virginia, have made it
impossible to complete a more thorough revision that was planned.
M. S. K.
U. S. GOVERNMENT EXPLOSIVES PLANT "C,"
NITRO, WEST VIRGINIA,
May 12, 1918.
PART I.
TABLE OF CONTENTS
DATA AND DETAILS FOR THE DESIGN AND CONSTRUCTION OF Srwo. BRIDGES AMD
BUILDINGS.
CHAPTER I.
STEEL ROOF TRUSSES AND MILL BUILDING*.
Definitions •»
Data for Design 3
Weight of Roof Trusses 3
Weight of Purlins, Girts, Bracing and
Columns 4
Weight of Roof Covering 4
Snow Loads 4
Wind Loads 5
Miscellaneous Loads 7
Stresses in Roof Trusses and Mill Buildings 7
Design of Steel Mill Buildings 7
General Principles of Design 7
Steel Frame Buildings 9
Types of Roof Trusses 9
Saw Tooth Roof Trusses 9
Transverse Bents 9
Roof Arches 14
Pitch of Roof 14
Pitch of Truss T 14
Spacing of Trusses and Transverse Bents. 14
Truss Details 15
Details of Roof Framing 15
Columns 15
Corrugated Steel 15
Fastenings for Corrugated Steel 19
Louvres, Ridge Roll, 24
Gutters, Purlins, Cornice 26
96
28
2&
28
3«
3«
3»
3*
38
43
43
Roof Coverings ....
Corrugated Steel Roofing
Anti-Condensation Lining
Slate Roofing
Tile Roofing
Tin Roofing
Tar and Gravel Roof
Shop Floors
Windows and Skylights. .
Ventilators
Wooden Doors
Steel Doors..
Examples of Steel Frame Buildings 44
Ketchum's Modified Saw Tooth Roof. . 44
Steel Transformer Building . 49
Steel Frame Building with Plaster Walls 53
Steam Engineering Building 53
Steel Windows 54*
Steel Doors 54f
Cement Roofing Tile 54m
Gypsum Roofing Tile . . . 54m
Bending Moments in Columns 540
Stresses in Rigid Frames 54p
General Specifications for Steel Frame
Buildings 55
References. . . 68
CHAPTER II. STEEL OFFICE BUILDINGS.
Skeleton Construction 69
Fire Resisting Construction 69
Loads 70
Dead Loads 70
Weights of Steel in Tall Buildings. . . 70
Live Loads 7°
Wind Loads 72
Snow Loads 72
Minimum Roof Loads 74
Live Loads on Columns 74
Loads on Foundations 75
Pressure on Foundations 75
Pressure on Masonry 75
Calculations of Wind Load Stresses 76
Allowable Stresses 79
Details of Framework. . . .
Floor Plan
Columns
Column Schedule. .
Column Details. . .
Column Bases
Anchors
Foundations. .
Spacing of Columns.
Floor Panels. .
Spandrel Sections
Wind Bracing
Examples of Steel Office Building*.
85
85
•M
94
94
94
94
98
99
loo
too
101
Specifications for Steel Office Building*. . . 103
References lo6
vu
TABLE OF CONTENTS.
CHAPTER III. STEEL HIGHWAY BRIDGES.
Types of Truss Bridges 107
Types of Structure .• no
Loads in
Weights of Bridges in
Weights of Standard Bridges 112
Live Loads I I2c
Impact I I2c
Concentrated Live Loads H2d
Distribution of Concentrated
Loads i I2e
Uniform Live Loads I I2f
Wind Loads Ii2h
Highway Bridge Floors H2h
Reinforced Concrete Floors. Ii2h
Buckle Plates 1 12]
Plank Floors. . . H2k
Highway Bridge Floors.
Wearing Surface for Floors Ii2m
Stringers 1 120
Floor Beams I I2p
Calculation of Stresses 115
Allowable Stresses 115
Short Span Steel Bridges 115
Beam Bridges 1 16
Plate Bridges 122
Low Riveted Truss Bridges 122
High Truss Steel Bridges 128
Shoes and Pedestals 135
Fence and Hub Guards 136
General Specifications for Steel Highway
Bridges 137
References 147
CHAPTER IV. STEEL RAILWAY BRIDGES.
Types of Steel Bridges 149
Weights of Railway Bridges 151
Loads 152
Cooper's Conventional System of Wheel
Concentration 153
Equivalent Uniform Loads 159
Uniform Loads and One or Two Excess
Loads '. 160
Maximum Stresses 160
Criteria for Maximum Stresses 1 60
Kinds of Stress 161
Impact Stresses 161
Impact Formulas 161
Launhardt-Weyrauch Formulas 162
Cooper's Method 162
Impact Tests 162
Calculation of Stresses 164
Moments, End Shears and Floorbeam
Reactions 164
Moment Diagram 164
Shears in Bridges 164
Moments in Bridges 164
Shears and Moments in a Plate Girder 173
Material 173
Allowable Stresses 173
Economic Design of Railway Bridges. ... 174
Details of Railway Bridges 175
Sections for Chords and Posts 175
Floors 176
Waterproofing Bridge Floors 178
Floorbeam Connections 184
Pedestals and Shoes 184
Examples of Plate Girders 184
Examples of Truss Bridges 185
Specifications for Railway Bridges 1 88
Clearances 201
Types of Bridges 202
Spacing of Trusses 202
Ties T 202
Live Loads 203
Impact 205
Wind Loads 205
Centrifugal Force 205
Unit Stresses 206
Alternate Stresses 206
Net Sections 206
Plate Girders 206
Compression Flanges 206
Counters 206
Minimum Angles 206
Expansion 206
Rollers 206
Stringer Connection Angles 206
Camber of Plate Girders 206
Web Stiffeners 207
Camber of Trusses 207
Rigid Members 207
Eye-Bars 207
Miscellaneous Specifications 207
General Specifications for Steel Railway
Bridges 208
Instructions for the Design of Railway
Bridges 219
References 224
TABLE OF CONTENTS.
CHAPTER V. RETAINING WALLS.
I nt reduction 225
C.ilculation of the Pressure on Retaining
Walls 225
R.inkine's Theory 226
Rankine's Formulas 226
Coulomb's Theory 227
Algebraic Method 227
Graphic Method 229
Cain's Formulas 230
Wall with Loaded Filling 230
Stability of Retaining Walls 231
Overturning 231
Sliding 231
Crushing 231
General Principles of Design 232
Design of Retaining Walls 234
Design of Masonry Retaining Wall
Data
Coefficients of Friction
Angles of Rcpoae
Allowable Pressures on Foundation*
Allowable Pressures on Masonry. .
Weight and Strength of Masonr
Weights of Materials
Examples of Retaining Walls.
Concrete Retaining Walls
Methods of Constructing Forms . .
Ingredients in (On. r
Mixing and Placing Concrete. . .
Specifications for Concrete Retaining
Walls
References. .
234
236
,j6
236
236
237
237
237
237
237
240
24,
CHAPTER VI. BRIDGE ABUTMENTS AND PIERS.
Introduction 245
Types of Abutments 245
Stability of Bridge Abutments without
Wings 245
Design of Concrete Abutments 245
Principles of Design 248
Empirical Design 248
Design of Bridge Piers 248
Allowable Pressures on Foundations 249
Waterway for Bridges 250
Dun's Drainage Table 250
Preparing the Foundations 250
Rock 250
Hard Ground 250
Soft Ground 253
Examples of Railway and Highway Bridge
Abutments 254
N. Y. C. & H. R. R. R. Standard Abut-
ments 254
CHAPTER VII. TIMBER
Definitions 277
Structural Timber 277
Definitions.' 277
Standard Defects 278
Piles and Pile Driving 279
Specifications for Timber Piles 281
Guard Rails and Guard Timbers 281
Timber Trestles 281
Pile Trestles 281
N. Y., N. H. & H. R. R. Pile Trestle. ... 282
Illinois Central R. R. Standard Abut-
ments 254
Cooper's Standard Abutments 254
Examples of Railway and Highway Bridge
Piers 255
N. Y. C. & H. R. R. R. Standard Piers. . 255
Illinois Central R. R. Standard Pier*. . . . 255
Cooper's Standard Piers 255
Steel Tubular Piers 255
Specifications for Steel Tubular Piers. . 257
Cylinder Piers for Highway Bridge. . . . 260
Cylinder PUTS for Railway Bridge*. . . . 262
Masonry and Concrete Definitions and
Specifications. . . . 266
Definitions 266
Specifications for Stone Masonry 269
Specifications for Plain and Reinforced
Concrete and Sterl Reinforcement. . . 272
References . 276
BRIDGES AND TRESTLES.
N. Y , N. H. & H. R. R- Frame Trestle. . 283
Illinois Central R. R. Frame Trestle 284
Illinois Central R. R. Pile Ballasted
Trestle. . - »«4
Frame Trestles
Timber Howe Trusses. . - *88
Highway Bridges and Trestles . 292
Specifications for Pile and Frame Trades 292
References *9*
TABLE OF CONTENTS.
CHAPTER VIII. STEEL BINS.
Stresses in Bin Walls 299
Stresses in Shallow Bins 299
Algebraic Solution 299
Pressure of Bituminous Coal 303
Pressure of Anthracite Coal 304
Pressure of Sand 305
Pressure of Ashes 306
Tables of Pressures on Vertical Bin Walls 302
Stresses in Shallow Bins, Graphic Solution 307
Hopper Bin, Level Full 307
Stresses in Framework 307
Hopper Bin, Top Surface Heaped 307
Stresses in Suspension Bunkers 309
Stresses in Deep Bins 311
Data for Design of Bins 311
Weight of Materials 311
Angle of Repose of Materials 311
Angle of Friction on Bin Walls 312
Self Cleaning Hoppers 312
Design of Bins 312
Flat Plates 312
Buckle Plates 315
Types of Bins 316
Suspension Bunkers 316
Hopper Bins .. 316
Circular Bins 317
Examples of Bins 317
Steel Suspension Coal Bunkers 317
Steel Hopper Ore Bins 318
Steel Hopper Coal Bins 318
References 318
CHAPTER IX. STEEL GRAIN ELEVATORS.
Introduction 319
Stresses in Grain Bins 319
Stresses in Deep Bins 319
Janssen's Solution 319
Data for Design of Steel Grain Bins 321
Coefficients of Friction of Wheat on Bin
Walls 321
Ratio of Lateral to Vertical Pressures of
Wheat 321
Hyperbolic Logarithms 322
German Practice in Design of Grain Bins. 324
Load on Bin Walls 324
Experiments on the Pressure of Grain in
Deep Bins 325
Rectangular Steel Bins 326
Circular Steel Bins 326
Rivets in Horizontal Joints 326
Stresses Due to Wind Moment 327
Stiffeners 327
Steel Country Elevator 329
Independent Steel Elevator 329
Costs of Steel Grain Elevators 337
References 338
CHAPTER X. STEEL HEAD FRAMES AND COAL TIPPLES.
Types of Head Works for Mines 339
Methods of Hoisting 339
Hoisting from Deep Mines 341
Hoisting Ropes 341
Strength of Wire Rope 342
Working Load on Hoisting Rope 342
Bending Stresses in Wire Rope 344
Safe Working Stresses in Round Wire
Ropes 345
Safe Working Stresses in Flat Wire Rope. 346
Cages, Skips, Sheaves, Safety Hooks. . . 346
Examples of Steel Head Frames 346
Diamond Steel Head Frame 347
New Leonard Steel Head Frame 347
Tonopah-Belmont Steel Head Frame . . 348
Data on Steel Head Frames 350
Estimate of Weight of Steel Head Frame. 352
Coal Tipples 352
Sizing Coal 352
Types of Coal Tipples 352
Examples of Steel Coal Tipples 352
W. P. Rend Steel Coal Tipple 352
Spring Valley Shaft No. 5 Steel Coal
Tipple 355
Phillip's Mine Steel Coal Tipple 356
Data on Steel Coal Tipples 360
Specifications for Steel Head Frames and
Coal Tipples, Washers and Breakers. 361
References 363
TABLE OF CONTENTS.
CHAPTER XI. STEEL STAND-PIPES AND ELEVATED TANKS ON Towns.
Data for Design 365
Formulas for Stresses in Stand-Pipes 365
Formulas for Stresses in Elevated Steel
Tanks 366
Stresses in a Circular Girder 367
Stresses in Columns 368
Details of Steel Tanks 369
Properties of Water-tight Joints 370
I )etails of Steel Towers 375
Examples of Steel Stand-Pipes and Ele-
vated Water Tanks on Towers 375
Railway \\at.-rTanks. .
aed Tank and Tower for Jackson.
J75
373
Standard Elevated Tank on a Tower. . . 377
Standard Steel Stand -I',; - 378
Specifications . 378
d Specifications for Elevated
Tanks on Towers and for Stand- Pipe* 379
( .< IK ral S|Mt-ifications for Steel Water and
Oil Tanks .387
References 387
CHAPTER XII. STRUCTURAL DRAFTING.
Plans for Structures 389
General Plan 389
Stress Diagram 389
Shop Drawings 389
Foundation or Masonry Plan 389
Erection Diagram 389
Falsework Plans 389
Bills of Material 389
Rivet List 389
List of Drawings 389
Structural Drawings 390
Methods 390
Rules for Shop Drawings 391
Size of Sheet 391
Title 392
Scale 392
Views Shown 392
Lettering 398
Conventional Signs 399
Marking System 399
Shop Bills 399
Field Rivets 400
General Notes 400
Erection Plan 400
Subdivisions '400
Plate Girder Bridges; General Rules 400
Deck Plate Girder Spans 400
Through Plate dirtier Spans.
Truss Bridges; General Rules. . .
Riveted Truss Bridges. .
Pin-connected Truss Bridge*
Order of Detailing Truss Spans. .
Office Buildings and Steel Frame Buildings
Floor Plans
Column Schedule
Columns
Riveted Girders
Beams
Erection Plan for Mill Buildings. . .
Detail Notes
Points to be Observed in Order to Facili-
tate Erection. . .
Ordering Material. . .
Bridge Work
Building Work
Shapes and Plates Most Easily Obtained.
Stock Material
Lengths and Wi.lt hs of Shape* and Plate*
Maximum Lengths of Shape*
Maximum Lengths of Plates
Design Drawings for St«t -1 Structure*. . . .
I V-ii;ns of Mill Buildings.
Designs of Plate Girders. . . ,
Designs of Truss Bridge*
CHAPTER XIII. ESTIMATES OF STRUCTURAL STBKL,
General Instructions 425
Mill Buildings 425
Office Buildings 426
Truss Bridges 426
Instructions for Taking off Material 426
Classification of Material 426
Rivet Heads 4*7
401
401
401
402
409
402
403
403
404
406
410
4'5
413
416
4'7
4I8
418
41'*
4*1
4*3
Material*..
K-.tim.ite of ('<••.(. i - '
Cost of Material - 4**
Cost of Fabrication of Structural Seed. . . 4*9
Cost of I>raftin«. • 4*9
Actual Cost of Drafting -4*9
Cost of Mill DctaiU. 43°
TABLE OF CONTENTS.
Card of Mill Extras 430
Extras on Round and Square Bars. ... 431
Miscellaneous Extras 431
Mill Orders 432
Cost of Shop Labor. . , 433
Shop Cost of Steel Frame Buildings. . . 433
Columns 433
Roof Trusses 433
Eave Struts 433
Plate Girders 433
Shop Cost of Bins and Stand-Pipes . . . . 434
Shop Costs of Individual Parts of
Bridges 434
Eye-bars 434
Chords, Posts and Towers 434
Pins 434
Floorbeams and Stringers 434
Shop Costs of Steel Bridges 435
Shop Costs of Steel Tubular Piers 435
Shop Cost of Combination Bridge Metal 435
Shop Cost of Howe Truss Bridge Metal 436
Cost of Erection of Steel Frame Office and
Mill Buildings and Mine Structures. . 436
Cost of Placing and Bolting 436
Cost of Riveting 436
Actual Costs of Erection 436
Cost of Erection of Steel Bridges 437
Hauling 437
Falsework 437
Erection of Tubular Piers 437
Placing and Bolting 437
Riveting 437
Number of Field Rivets in Steel Spans. 437
Actual Cost of Erection 438
Transportation 438
Freight Rates 438
Cost of Painting 438
Miscellaneous Costs 439
Mill Building Floors 439
Timber Floors on Tar Concrete Base. . 439
Concrete Floors 439
Creosoted Timber Block Floor 439
Roofing for Mill Buildings 439
Corrugated Steel Roofing 439
Tar and Gravel Roofing 440
Tin Roofing 440
Slate Roofing 440
Tile Roofing 440
Windows 440
Skylights 440
Circular Ventilators 4.40
Waterproofing 440
Chain 440
Nails 440
Gas Pipe 440
Steel Railroad Rails 440
Wire Rope 440
Manila Rope 440
Hardware and Machinist's Supplies 440
References 440
CHAPTER XIV. ERECTION OF STRUCTURAL STEEL.
Methods of Erection 441
Plate Girders and Short Riveted Spans 441
Truss Bridges 441
Cantilever and Arch Bridges 441
High Viaducts 441
Roof Trusses, Mill and Office Buildings 441
Elevated Towers and Tanks 442
Erection Tools 443
Design of Erection Tools 443
Hoists 443
Winches and Crabs 443
Hoisting Rope 443
Manila Rope 443
Knots in Manila Rope 444
Wire Rope 446
Hoisting Tackle 447
Rigging 447
Efficiency of Tackle 451
Chains 460
Jacks 460
Miscellaneous Tools 460
List of Tools 460
American Bridge Company List 460
Actual Lists of Tools 460
Erection of Truss Bridges 466
Riveting 467
Derricks and Travelers 470
Gin Pole 470
Guy Derricks 472
"A" Derrick 472
Stiff-Leg Derrick 472
Boom Travelers 472
Viaduct Travelers 472
Gallows Frame 472
Through or Gantry Travelers 472
Derrick Cars 473
Falsework 473
Piles 476
TABLE OF CONTENTS.
I >t sign of Falsework 479
TrawliT fur Krection of Armory 479
Instructions for the Erection of Structural
1 1 479
S|- < in, .it ions for the Erection of Railway
Bridw*. . . . ^gj
Instructions f«r tin- Inspection of Bridge
Erection. . . 4*5
CHAPTER XV. ENGINEERING MATERIALS.
Iron and Steel 487
Definitions 487
Classification 487
Cast Iron 488
Definitions 488
Malleable Castings 488
Strength of Cast Iron 488
Specifications for Gray- Iron Castings. . . 488
Wrought Iron 490
Method of Manufacture 490
Specifications for Wrought-Iron Bars. . . 490
Specifications for Wrought-Iron Plates . 492
Steel 493
Manufacture of Steel 493
Strength of Steel 494
Formulas for Tensile Strength 495
Special Steels 495
Specifications for Structural Steel for
Buildings 497
Specifications for Structural Steel for
Bridges 499
Specifications for Structural Nickel Steel 502
Specifications for Boiler Rivet Steel . . . 505
Specifications for Billet-Steel Reinforce-
ment Bars 5°7
Specifications for Rail-Steel Reinforce-
ment Bars 5°9
Specifications for Steel Castings 510
Corrosion of Iron and Steel 5'3
Paint 5^3
Oil Paints
Linseed Oil.
Lead
Zinc
Iron oxide. .
Carbon
Mixing Paint .
Proportions
Covering Capacity.
Applying tlu- Paint
Cleaning the Surface. .
Shop Coat
Finishing Coat .
Asphalt Paint
Coal Tar Paint
Cement and Cement Paint .
Portland Cement Paint. . 517
Instructions for the Mill Inspection of
Structural Steel. . . V7
Instructions for the Inspection of the
Fabrication of Strd Bridges. . 5"*
Misrrllunrous Metals. ... 5IQ
Alloys 5»9
Timber S*>
Stone Masonry 5*°
Concrete • 5*°
Working Stresses for Reinforced Con-
crete 5*°
Specifications for Portland Cement 5"
S>4
SU
SU
5U
S»4
SIS
S»5
S'S
S'S
S«S
516
Si*
5«6
S«6
516
CHAPTER XVI. STRUCTURAL MECHANICS.
General Nomenclature 525
Reinforced Concrete Nomenclature. . . . 526
Definitions 5^7
Forces 527
Moment of Forces 5^7
Couple 527
Stress 527
Unit Stress 527
Ultimate Stress 527
Tension 537
Compression 527
Shear. . 5*7
Axial Stresses. .
Simple Stress.
\VorkingSrres8 5*7
Factor of Safety
Strain
Elasticity.
Elastic Limit
Yield Point.
Modulus of EI*M
ShrarinK M.Klulusof ElMtfcfcy...
Poiason's Ratio
Rupture Strength
TABLE OF CONTENTS.
Ultimate Deformation 528
Work or Resilience of a Bar 528
Stresses due to Sudden Loads 528
Impact 529
Stresses in Beams 529
Neutral Surface 529
Neutral Axis 529
Reactions 529
Vertical Shear 529
Bending Moment 529
Relations between Shear and Bending
Moment 529
Formulas for Flexure 529
Resisting Shear 529
Resisting Moment 530
Moment of Inertia 53°
Section Modulus 530
Deflection of Beams 530
Simple and Combined Stress S31
Elastic Deformation. . 532
Stresses in Riveted Joints. 532
Stresses in Thin Pipes 532
Stresses in Beams 533
Stresses in Columns 533
Torsion of Shafts 533
Stresses in Hooks 533
Stresses in Plate Girders 534
Eccentric Stress 534
Flexure and Direct Stress 534
True Stress 534
Stresses in Thick Pipes 534
Stresses in Rollers 534
Stresses in Flat Plates 535
Work or Resilience 535
Centroid or Center of Gravity 535
Moment of Inertia 535
Product of Inertia 535
Cantilever Beams, Stresses and Deflections
Load at Free End 536
Uniform Load 536
Load at any Point 536
Variable Load 536
Simple Beams, Stresses and Deflections . . 537
Load at Center . 537
Load at any Point 537
Two Equal Symmetrical Loads 537
Uniform Load ! 538
Triangular Load 538
Triangular Load, Maximum at Center . 538
Triangular Load, Maximum at End — 538
Trapezoidal Load 538
Overhanging Beam, Stresses and Deflec-
tions 539
Uniform Load, Overhanging one Sup-
port 539
Load at any Point, Overhanging one
Support 539
Uniform Load, Overhanging both Sup-
ports 539
Two Exterior Loads, Overhanging bcth
Supports 539
Beam Fixed at one End, Supported at
other End, Stresses and Deflections. . 540
Load at any Point 540
Uniform Load 540
Load at Center 540
Beam Fixed at Both Ends, Stresses and
Deflections 541
Uniform Load 541
Load at Center 541
Load at any Point 541
Moving Loads 542
Maximum Shears 542
Maximum Moments 542
One Load 542
Two Loads 542
Three Loads 542
Four Loads 542
Two Unequal Loads 542
Three Loads, Two Equal 542
Continuous Beams, Uniform Loads 543
Moments at Supports 544
Shears at Supports 544
Continuous Beams, Concentrated Loads . . 545
Moments and Reactions of Beams of
Two and Three Spans 545
Reinforced Concrete Beams, Stresses in. . 546
Rectangular Beams, Reinforced for
Tension only 546
Slabs, 12 inches wide 546
T-Beams 546
Rectangular Beam, Reinforced for Ten-
sion and Compression 546
Shear 547
Bond 547
Stirrups 547
Columns 547
Working Stresses 547
Safe Loads in Reinforced Concrete Slabs. 547
Moments of Inertia and other Properties
of Sections 548
Stresses in Framed Structures 552
Loads 552
TABLE OF CONTENTS.
Methods of Calculation 552
Graphic Resolution 552
<ttv>M-s in Roof Trusses 552
Dead Load Stresses 553
Snow Load Stresses 553
Wind Load Stresses 553
Stresses in a Transverse Bent 556
Stresses in Bridge Trusses 558
Dead Load Stresses in a Camel Back
Truss by Graphic Resolution 558
Dead Load Stresses in a Petit Truss by
Graphic Resolution 558
Stresses in a Warren Truss by Algebraic
Resolution 558
Stresses in a Pratt Truss by Algebraic
Resolution 559
Stresses in a Deck Baltimore TRIM by
Algebraic Resolution . 559
Stream in a Through Baltimore Trim
by Algebraic Resolution . 560
Stresses in a Camel Back TRIM by Alge*
braic Moments. ... . 560
Stresses in a Warren Truss by Graphic
Moments . 561
Stresses in a Petit TniM by Algebraic
Moments . 562
Stresses in a Through Pratt Truss for
Cooper's E 60 Loading. . . 562
Stresses in a Portal of a Bridge 563
Stresses in a Trestle Bent 563
CHAPTER XVII. THE DESIGN OF STEEL DETAILS.
Members in Tension 571
Loop Bar 572
Bar with Clevises 572
Eye-Bar 573
Angle in Tension 573
Built-up Tension Member 574
Unriveted Pipe 575
Members in Compression 575
Single Angle Strut 575
' Double Angle Strut 576
Two Angles Starred 578
Plate and Angle Column 579
Expansion Rollers 579
Members in Flexure 579
I-Beam 580
Two I-Beams with Separators 580
Plate Girders 581
Pins and Pin Packing 584
The List of Tables in Part 1 1 follows page
The Index to Part I follows the Structural
Corrugated Steel Roofing.. . . 586
Bearing Plates . 586
Combined Flexure and Direct Strew 586
Eye-Bar 586
End-Post 587
Column of a Transverse lk-nt 590
Floorbeam 59O
End Connections for Tension and Com-
pression Members . 59*
Strut or Tie • 593
Pin-connected Top Chord 593
End Connections for I-Beams. . . 595
Eccentric Riveted Connections. . . 595
Web Splice 596
Riveted Joint in Cylinder, Pipe or Joint 597
Formulas for Riveted Joints c - -
Design of Lacing Bars ; '
600, Part 1.
Tables in Part II
STRUCTURAL ENGINEERS' HANDBOOK
Introduction. — The book is divided into two parts which are self contained. Part I include*
a discussion of the design of structures and gives data and details for the design of steel bridges
and buildings. Part II contains tables for structural design and include* table* giving the proper-
ties of rolled sections, properties of built-up sections for chords, columns, struts, plate girders,
etc., and data for standard structural details.
PART I.
DATA AND DETAILS FOR THE DESIGN AND CONSTRUCTION OP STEEL BRIDGES
AND BUILDINGS.
Introduction. — The discussion in Part I has been limited to steel bridges and buildings and
other simple steel structures; no reference being made to swing and movable bridges, cantilever
and suspension bridges. The design of a bridge includes the design of the substructure as well as
the superstructure, so that the design of retaining walls and bridge abutments has been briefly
discussed. Timber trestles and bridges are required for temporary structures and for the erection
of steel structures, and a brief discussion of timber trestles and bridges is therefore properly
included.
The design of a structure requires not only a knowledge of the properties of materials and the
ability to calculate the stresses, but also a knowledge of local conditions and requirements, of
economic design, of details of construction, of methods of erection, methods of fabrication and
their effect on cost, and of many other matters which limit the design. The most economical
structure for any given conditions is the one which will give the greatest service for the least
money, quality of service and the life of the structure being given proper consideration. Financial
limitations often limit the design and the problem then is to design a structure that will give
satisfactory service with the money available.
To design a satisfactory structure when limited by financial considerations is a problem that
requires the exercise of the highest possible skill on the part of the m^im-fr. H«- must be able to
select an economical type of structure; he must make an accurate estimate of the loads to be carried
by the structure; he must be able to calculate the stresses with accuracy; he must make the de-
tailed design with due reference to ease of obtaining the material, the cost of shop work, and the
cost of erection.
The shop cost of steel structures varies with the type of structure, the sue and weight of the
members and upon the make-up of the members and the details. By using fewer and larger mem-
bers, by using rolled beams and columns in the place of built-up plate girders and columns, and by
using tie plates in the place of lacing, the shop cost per pound of a railroad bridge may be materially
reduced. If the simplification of the design is carried too far the reduction in shop cost will result
in a material increase in the weight of the bridge, and in an increase in the cost of the bridge.
with a. decrease in efficiency. The details of the design of a structure should be worked out with
reference to ease and economy of erection as well as ease and low cost of fabrication. While the
standardizing of connections so that multiple punches may be used may result in a considerable
2 I
2 STRUCTURAL ENGINEERS' HANDBOOK.
saving in shop cost, it often results in a material increase in the weight of the details of the struc-
ture, and in the number of field rivets, so thac the efficiency of the structure is not increased,
and the final cost of the structure is not reduced. The author has in mind a case where to change
the details of a plate girder so that multiple punches might be used required the addition of details
equal to 5 per cent of the weight of the span and the addition of 25 per cent to the number of field
rivets, with no increase in efficiency.
The best results are obtained when the structural engineer prepares carefully worked out
detail drawings (not shop drawings) in which the efficiency of the structure, ease of fabrication
and ease of erection are given due consideration. The shop drawings may then be prepared by
the bridge company to take the greatest possible advantage of improved shop methods without
decreasing the efficiency of the structure, or increasing the total weight, or increasing the cost of
erection.
Part I is divided into seventeen chapters, of which the first eleven chapters cover different
types of structures, and the last six chapters cover subjects which apply to all types of steel con-
struction. While the aim has been to present the largest possible amount of information in the
limited space, each subject presented is discussed briefly in a logical order.
While the author has drawn on his other books in the various chapters, the reader will find
much new material on the subjects covered in the other books, especially in Chapter I, Steel Roof
Trusses and Mill Buildings, and Chapter III, Steel Highway Bridges, so that this book supple-
ments the author's other books on structures. Each chapter is self-contained, the illustrations
and tables being numbered independently of the other chapters. As far as possible the different
subjects are discussed fully in each chapter, thus reducing cross-references. The most of the
cross-referencing is made through the index, which together with the table of contents will be
found invaluable to the reader.
CHAPTER I.
STEEL ROOF TRUSSES AND MILL BUILDINGS.
Definitions. — The following definitions will assist the reader in a study of roof trusses and
steel frame buildings.
Truss. — A truss is a framed structure in which the members are so arranged and fastened
at their ends that external loads applied at the joints of the truss will cause only direct utresses
in the members. In its simplest form a truss is a triangle or a combination of triangles. In thu
chapter it will be assumed (i) that the structure is not constrained by the reactions, (2) that the
axes of the members meet in a common point at the joints, and (3) that the joints have friction-
less hinges.
Transverse Bent. — A transverse bent consists of a truss supported at the ends on column*
and braced against longitudinal movement by knee braces attached to the lower chord of the
truss and to the columns.
Purlin. — A beam that rests on the top chords of roof trusses and supports the »hca thing
that carries the roof covering, or supports the roof covering directly, or supports rafters.
Rafter. — A beam that rests on the purlins and supports the sheathing, or may support sub-
purlins. Rafters are not commonly used in mill buildings.
Sub-purlin. — A secondary system of purlins that rest on the rafters and arc spaced so a* to
support the tile or slate covering directly without the use of sheathing.
Sheathing. — A covering of boards or reinforced concrete that is carried on the purlins or
rafters to furnish a support for the roof covering.
Girt. — A beam that is fastened to the columns to support the side covering either directly
or to support the side sheathing.
Monitor Ventilator. — A framework at the top of the roof that carries fixed or movable louvres.
or sash in the clerestory.
Clerestory. — The clear opening in the side framework of a monitor ventilator of a building.
also the clear opening on the side of a building.
Louvres. — Slats made of metal or wood which are placed in the clerestory of a monitor
ventilator to keep out the storm. Louvres may be fixed or movable. The opening of a monitor
ventilator is also called a louvre.
Panel. — The distance between two joints in a roof truss or the distance between purlins.
Bay. — The distance between two trusses or transverse bents.
Pitch. — The pitch of a truss is the center heighc of the truss divided by the span where the
truss is symmetrical about the center line.
Other terms are defined when they are first used.
DATA FOR THE DESIGN OF ROOF TRUSSES AND STBKL FRAME BUILDING*.
Weight of Roof Trusses.— The weight of roof trusses varies with the span, the distance
between trusses, the load carried or capacity of the truss, and the pitch.
The empirical formula
where
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
W = weight of steel roof truss in pounds;
P = capacity of truss in pounds per square foot of horizontal projection of roof (30 to 80 lb.);
A = distance center to center of trusses in feet (8 to 30 ft.) ;
L = span of truss in feet;
was deduced by the author from the computed and shipping weights of mill building trusses of
the Fink type.
Weight of Purlins, Girts, Bracing, and Columns. — Steel purlins will weigh from i£ to 4 lb.
per sq. ft. of area covered, depending upon the spacing and the capacity of the trusses and the
snow load. Girts and window framing will weigh from i| to 3 lb. per sq. ft. of net surface. Brac-
ing is quite a variable quantity. The bracing in the planes of the upper and lower chords will
vary from | to I lb. per sq. ft. of area. The side and end bracing, eave struts and columns will
weigh about the same per sq. ft. of surface as the trusses.
Weight of Roof Covering. — The weight of corrugated iron or steel covering varies from
1 5 to 3 lb. per sq. ft. of area. The weight of corrugated steel is given in Table I. The approxi-
mate weight per square foot of various roof coverings is given in the following table:
Corrugated steel, without sheathing I to 3 lb.
Felt and asphalt, without sheathing 2
Tar and Gravel Roofing, without sheathing 8 to 10 "
Slate, ?V in. to j in., without sheathing 7 to 9
Tin, without sheathing I to i£ "
Skylight glass, & in. to 5 in., including frames 4 to 10 "
White pine sheathing I in. thick 3
Yellow pine sheathing I in. thick 4
Tiles, flat 15 to 20 "
Tiles, corrugated 8 to 10 "
Tiles, on concrete slabs 30 to 35 "
Plastered ceiling 10 "
The actual weight of roof coverings should be calculated if possible.
Snow Loads. — The annual snowfall in different localities is a function of the humidity and
the latitude and is quite a variable quantity. The amount of snow on the ground at one time
is still more variable. The snow loads given in Fig. I were proposed by the author in "The Design
of Steel Mill Buildings" in 1903 and have been generally adopted.
35 40 45
Latitude in Degrees
FIG. i. SNOW LOAD ON ROOFS FOR DIFFERENT LATITUDES, IN POUNDS PER SQUARE FOOT.
One of the heaviest falls of snow on record occurred at Boulder and Denver, Colorado on
Dec. 5 and 6, 1913, when 36 inches of snow weighing 9 lb. per cu. ft. fell during two days. Many
WIND LOADS. 5
ll.it roofs were loaded with a snow load of more than 30 Ib. per sq. ft. and roofs with a pitch of one-
half carried the full snow load of 27 Ib. per sq. ft. of horizontal projection.
A high wind may follow a heavy sleet and in designing the trusses the author would recom-
mend the use of a minimum snow and ice load as given in Fig. I for all slopes of roofs. The
m.ixiinuni stresses due to the sum of this snow load, the dead and wind loads; the dead and wind
loads; or of the maximum snow load and the dead load being used in designing the members.
Wind Loads. — The wind pressure, P, in pounds per square foot on a flat surface normal to
the direction of the wind for any given velocity, V, in miles per hour is given quite accurately
by the formula
P = 0.004 Vs (2)
The pressure on other than flat surfaces may be taken in per cents of that given by formula
(2) as follows: 80 per cent on a rectangular building; 67 per cent on the convex side of cylinders;
115 to 130 per cent on the concave side of cylinders, channels and flat cups; and 130 to 170 per
cent on the concave sides of spheres and deep cups.
Recent German specifications for design of tall chimneys specify wind loads per square foot
as follows: 26 Ib. on rectangular chimneys; 67 per cent of 26 Ib. on circular chimneys; and 71
per cent of 26 Ib. on octagonal chimneys.
The official specifications for the design of steel framework in Prussia have recently been
amplified in the matter of wind pressures. For the wind-bracing, as a whole, the wind pressure
on the whole building is to be taken as 17 Ib. per sq. ft. For proportioning individual frame
members, girts, studs, trusses, etc., a higher value of wind pressure must be assumed, viz., 28 to
34 Ib. per sq. ft.
It would seem that 30 Ib. per square foot on the side and the normal component of a hori-
zontal pressure of 30 Ib. on the roof would be sufficient for all except exposed locations. If the
building is somewhat protected a horizontal pressure of 20 Ib. per square foot on the sides is
certainly ample for heights less than, say 30 feet.
Wind Pressure on Inclined Surfaces. — The wind is usually taken as acting horizontally
and the normal component on inclined surfaces is calculated.
FIG. 2.
The normal component of the wind pressure on inclined surfaces has usually been computed
by Hutton's empirical formula
Pn = P'smA*-Meo"-1 (3)
where Pn equals the normal component of the wind pressure, P equals the pressure per square
foot on a vertical surface, and A equals the angle of inclination of the surface with the horizontal,
Fig. (2).
The formula due to Duchemin
p .. p 2 sin A . .
F l + sin' A
where Pn, P and A are the same as in (3), gives results considerably larger for ordinary roofs
than Hutton's formula, and is coming into quite general use.
The formula
P, = P. A/45 (5)
6
STEEL ROOF TRUSSES AND MILL BUILDINGS .
CHAP. I.
where Pn and P are the same as in (3) and (4), and A is the angle of inclination of the surface
in degrees (A being equal to or less than 45°), gives results which agree very closely with Hutton's
formula, and is much more simple.
Hutton's formula (3) is based on experiments which were very crude and probably erroneous.
Duchemin's formula (4) is based on very careful experiments and is now considered the most
reliable formula in use. The Straight Line formula (5) agrees with experiments quite closely
and is preferred by many engineers on account of its simplicity.
The values of Pn as determined by Hutton's, Duchemin's and the Straight Line formulas
are given in Fig. 3, for P equals 20, 30 and 40 Ib.
It is interesting to note that Duchemin's formula with P equals 30 pounds gives practically
the same values for roofs of ordinary inclination as is given by Hutton's and the Straight Line
formulas with P equals 40 pounds.
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FORMULAS
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Straight Line fc£A.(A i45°)
f%* Normal Pressure.lbs-per sqft-
^Horizontal" « ••
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X^iqle Exposed Roof makes with Horizontal in Degrees, A.
3. NORMAL WIND LOAD ON ROOF ACCORDING TO DIFFERENT FORMULAS.
Duchemin has also deduced the formula
PK = P
2 sin2 A
i + sin2 A
where PA in (6) equals the pressure parallel to the direction of the wind, Fig. 2; and
p p 2 sin A -cos ^4
'
i + sin2
(6)
(7)
where Pj in (7) equals the pressure at right angles to the direction of the wind, Fig. 2. PI may
be an uplifting, a depressing or a side pressure. With an open shed in exposed positions the
uplifting effect of the wind often requires attention. In that case the wind should be taken
normal to the inner surface of the building on the leeward side, and the uplifting force determined
DESIGN OF STEEL MILL BUILDINGS. 7
by using formula (7). If the gables are closed a deep cup is formed, and the normal pressure
should be increased 30 to 70 per cent.
That the uplifting force of the wind is often considerable in exposed localities is made evident
1>\ the fact that highway bridges are occasionally wrecked by the wind.
The wind pressure is not a steady pressure, but varies in intensity, thus producing excessive
vilir.it ions which cause the structure to rock if the bracing is not rigid. The bracing in mill
buildings should be designed for initial tension, so that the building will be rigid. Rigidity is
of more importance than strength in mill buildings.
Miscellaneous Loads. — Data on the weights of materials are given in Chapter II. The
weights and other data for hand cranes are given in Table 133 and of electric cranes are given
in Tabli- 130, Part II.
Minimum Loads. — For minimum loads to be calculated on roofs see § 27, "Specifications for
Stri-1 Frame Buildings" in the last part of this chapter.
STRESSES IN ROOF TRUSSES AND MILL BUILDINGS.— For the calculation of the
stresses in roof trusses and in the framework of steel frame mill buildings, see the author's " The
Design of Steel Mill Buildings."
DESIGN OF STEEL MILL BUILDINGS.
General Principles of Design. — The general dimensions and the outline of a mill building
will be governed by local conditions and requirements. The questions of light, heat, venti-
lation, foundations for machinery, handling of materials, future extensions, first cost and cost
of maintenance should receive proper attention in designing the different classes of structures.
One or two of the above items often determines the type and general design of the structure.
Where real estate is high, the first cost, including the cost of both land and structure, causes
the adoption in many cases of a multiple story building, while on the other hand where the site
is not too expensive the single story shop or mill is usually preferred. In coal tipples and shaft
houses the handling of materials is the prime object; in railway shops and factories turning out
heavy machinery or a similar product, foundations for the machinery required, and convenience
in handling materials are most important; while in many other classes of structures such as weaving
sheds, textile mills, and factories which turn out a less bulky product with light machinery, and
which employ a large number of men, the principal items to be considered in designing are light,
heat, ventilation and ease of superintendence.
Shops and factories are preferably located where transportation facilities are good, land is
cheap and labor plentiful. Too much care cannot be used in the design of shops and factories
for the reason that defects in design that cause inconvenience in handling materials and workmen,
increased cost of operation and maintenance are permanent and cannot be removed.
The best modern practice inclines toward single floor shops with as few dividing walls and
partitions as possible. The advantages of this type over multiple story buildings are (i) the
light is better, (2) ventilation is better, (3) buildings are more easily heated, (4) foundations for
machinery are cheaper, (5) machinery being set directly on the ground causes no vibrations in
the building, (6) floors are cheaper, (7) workmen are more directly under the eye of the superin-
tendent, (8) materials are more easily and cheaply handled, (9) buildings admit of indefinite
extension in any direction, (10) the cost of construction is less, and (n) there is less danger from
damage due to fire.
The walls of shops and factories are made (i) of brick, stone, or concrete; (2) of brick, hollow
tile or concrete curtain walls between steel columns; (3) of expanded metal and plaster curtain
walls and glass; (4) of concrete slabs fastened to the steel frame; and (5) of corrugated steel fastened
to the steel frame.
The roof is commonly supported by steel trusses and framework, and the roofing may be
slate, tile, tar and gravel or other composition, tin or sheet steel, laid on board sheathing or on
concrete slabs, tile or slate supported directly on the purlins, or corrugated steel supported on
board sheathing or directly on the purlins. Where the slope of the roof is flat a first grade tar
8 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
and gravel roof, or some one of the patent composition roofs is used in preference to tin, and on a
steep slope slate is commonly used in preference to tin or tile. Corrugated steel roofing is much
used on boiler houses, smelters, forge shops, coal tipples, and similar structures.
Floors in boiler houses, forge shops and in similar structures are generally made of cinders;
in round houses brick floors on a gravel or concrete foundation are quite common; while in buildings
where men have to work at machines the favorite floor is a wooden floor on a foundation of cinders,
gravel, or tar concrete. Where concrete is used for the foundation of a wooden floor it should be
either a tar or an asphalt concrete, or a layer of tar should be put on top of the cement concrete
to prevent decay. Concrete or cement floors are used in many cases with good results, but
they are not satisfactory where men have to stand at benches or machines. Wooden racks on
cement floors remove the above objection somewhat. Where rough work is done, the upper or
wearing surface of wooden floors is often made of yellow pine or oak plank, while in the better
classes of structures, the top layer is commonly made of maple. For upper floors some one of
the common types of fireproof floors, or as is more common a heavy plank floor supported on
beams may be used.
Care should be used to obtain an ample amount of light in buildings in which men are to
work. It is now the common practice to make as much of the roof and side walls of a trans-
parent or translucent material as practicable; in many cases fifty per cent of the roof surface is
made of glass, while skylights equal to twenty-five to thirty per cent of the roof surface are very
common. Direct sunlight causes a glare, and is also objectionable in the summer on account of
the heat. Where windows and skylights are directly exposed to the sunlight they may best be
curtained with white muslin cloth which admits much of the light and shades perfectly. The
"saw tooth" type of roof with the shorter and glazed tooth facing the north, gives the best light
and is now coming into quite general use.
Plane glass, wire glass, factory ribbed glass, and translucent . fabric are used for glazing
windows and skylights. Factory ribbed glass should be placed with the ribs vertical for the
reason that with the ribs horizontal, the glass emits a glare which is very trying on the eyes of
the workmen. Wire netting should always be stretched under skylights to prevent the broken
glass from falling down, where wire glass is not used.
Heating in large buildings is generally done by the hot blast system in which fans draw the
air across heated coils, which are heated by exhaust steam, and the heated air is conveyed by
ducts suspended from the roof or placed under the ground. In smaller buildings, direct radiation
from steam or hot water pipes is commonly used.
The proper unit stresses, minimum size of sections and thickness of metal will depend upon
whether the building is to be permanent or temporary, and upon whether or not the metal is
liable to be subjected to the action of corrosive gases. For permanent buildings the author
/
would recommend 16,000 Ib. per square inch for allowable tensile, and 16,000 — 70- Ib. per
square inch for allowable compressive stress for direct dead, snow and wind stresses in trusses
and columns; / being the center to center length and r the radius of gyration of the member,
both in inches. For wind bracing and flexural stresses in columns due to wind, add 25 per cent
to the allowable stresses for dead, snow and wind loads. For temporary structures the above
allowable stresses may be increased 20 to 25 per cent.
The minimum size of angles should be 2" X 2" X I", and the minimum thickness of plates
2 in., for both permanent and temporary structures. Where the metal will be subjected to
corrosive gases as in smelters and train sheds, the allowable stresses should be decreased 20 to 25
per cent, and the minimum thickness of metal increased 25 per cent, unless the metal is fully
protected by an acid-proof coating (at present the best paints do little more in any case than
delay and retard the corrosion).
The minimum thickness of corrugated steel should be No. 20 gage for the roof and No. 22
for the sides; where there is certain to be no corrosion Nos. 22 and 24 may be used for the roof
and sides respectively.
STEEL FRAME MILL BUILDINGS.
<J
Steel Frame Mill Buildings. — The framework of a steel frame mill building consists of a
scries of tr.uisverse bents, which carry the purlins on the tops of the trusses, and girts on the
sides of the columns to carry the covering, Fig. 4. The framework is braced by diagonal bracing
in the planes of the roof and the sides of the building, and in the plane of the lower chords. A
transverse bent consists of a roof truss supported at the ends on columns and is braced against
endwise movement by means of knee braces. The framing plan for a steel frame mill building
is shown in Fig. 4. Steel mill buildings are also made with end trusses in place of the end framing
shown in Fig. 4.
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7 ^
••
'-G'rf -.
f \
SIDE ELEVATION
Truss-*
END FRAMING
f- Pur I in
'-Truss
.- i. Struf
I-/ Sfrut
.- Pur fin
,Do
sOo
'•Do
&RAC1N6 A-A
PLAN LOWER CHORD PLAN UPPER CHORD
FIG. 4. FRAMEWORK FOR A STEEL MILL BUILDING.
Types of Roof Trusses. — Several types of roof trusses are shown in Fig. 5. These trusses
have been subdivided so that the purlins will come at the panel points, and will not have a spacing
greater than 4 ft. 9 in., the greatest spacing allowed for corrugated steel roofing when laid without
sheathing. The Fink trusses shown in (a) to (g) are commonly used in steel frame buildings
and are very economical. The other types of trusses need no explanation.
Different methods of lighting and ventilating buildings through the roof are shown in Fig. 6.
Saw Tooth Roofs. — The common type of saw tooth roof is shown in (m) Fig. 6. The glazed
leg faces the north and permits only indirect light to enter the building, thus doing away with
the glare and varying intensity of light in buildings where direct sunlight enters. In cold climates
the snow drifts the gutters nearly full and causes loss of light and also leakage from the over-
flowing gutters. The modified saw tooth roof shown in (n) was designed by the author, to obviate
the defects in the common type of saw tooth roof. The modified saw tooth roof permits the
use of a greater span and more economical pitch than the common form shown in (m).
Transverse Bents. — A number of the common forms of transverse bents are shown in Fig. 7.
Transverse bents (a), (b), (d), and (A) are used for boiler houses, shops, etc., while (c), (e), (/)
10
STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
(3) 30FT-SPAN (b) 40 FT- SPAN
(c) 50 FT- SPAN
(d) 60 FT- SPAN
(e) 80 FT SPAN
(F) MODIFIED FINK
(g) CAMBERED FINK
FINK TRUSSES
(h) HOWE
(i) HYBRID
(j) PRATT
(k) MODIFIED PRATT
W QUADRANGULAR (m) CAMEL BACK
FIG. 5. TYPES OF ROOF TRUSSES.
TYPES OF ROOF TRUSSES.
11
^--Louvres
Glass of Louvres
'Glass
Glass or Louvres
, , u c
(a) MONITOR AND SKYLIGHTS
(b) DOUBLE MONITOR
(c) SKYLIGHTS
Glass - </N> • Glass
•*-G/ass or Louvres
>^ Glass
ft) MONITOR AND SKYLIGHTS
Glass -
r—GIass
Circular Vent f labor
-Glass
(e) SKYLIGHTS
(f) SKYLIGHTS
-Glass
(k) SKYLIGHTS
(I) ROOF WITH SAW TOOTH SKYLIGHT
North End
Glass-*
South End North End
South End
(m) SAW TOOTH ROOF (MAWS SHED) (n) KETCHUN'S MODIFIED SAW TOOTH ROOF
FIQ. 6. ROOF TRUSSES SHOWING METHODS OF LIGHTING AND VENTILATING.
12
STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
- Glass
(a) BEHT WITH FINK TRUSS
(e) SIDE SHED AND CRANE
-Glass
<- Glass or Louvres
tf
r Traveling Craned
<- Glass
vv.
\
X
X
(b) BENT WITH TRIANGULAR TRUSS
#2 5/cif 5AE95 WITH CRANE
<- Glass or Louvres
/1/N\
* 'Glass
CAy\/v
5
V/V"\/\7
SIDE SHEDS WITH CRANE
Traveling Crdne
(d) BENT WITH DOUBLE MONITORS 00 BENT MTH CRANE
FIG. 7. TYPES OF TRANSVERSE BENTS.
ROOF ARCHES.
13
i Wefghb one arch
£0,000 Jbs-
>%y«ss> X^<w,
LIVE STOCK PAVILION
.'X// ^e/' members
are 2 L3 •
• — —
—Y ~ir~V^" ^ \Arches 39 6 centers- ^r
v i^ 1 H/ * Li. -. _^./L
\
1
^ . rre/e?nt one arch
i- 64,00 01 bs-
-ir -i ..n •/
-Jl"i , / // '
THREE HINGED ARCH, 5r- Louis COLISEUM'
/O'll [
^y
Web members
are 41? •
Weight one arch
30,000 Ibs-
K
HINGED ARCH, GOVERNMENT BUILDING
ST- Louis, Mo*
•-M
FIG. 8. ROOF ARCHES.
14 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
and (g) are used for shops or buildings where the main part of the building is required to be covered
by a crane and side sheds are used for lighter work.
Roof Arches. — Roof arches are used where a large clear floor space is required as in coliseums,
exposition buildings and train sheds, Fig. 8. The arches are braced in pairs and carry the roof
covering. Arches may have one, two or three hinges, or may be made without hinges. Three-
hinged arches are statically determinate structures, while the stresses in all other arches are
statically indeterminate. Arches without hinges are used for domes. Three-hinged roof arches
have been commonly used in America, although the two-hinged roof arch is more economical
and has many advantages. Arches may have a horizontal tie as in the Chicago Stock Pavilion
and the Government Building, or the horizontal reactions may be carried by the foundations
as in the St. Louis Coliseum, Fig. 8. For the calculation of the stresses in three-hinged and two-
hinged roof arches, see the author's "The Design of Steel Mill Buildings."
Pitch of Roof. — The pitch of a roof is given in terms of the center height divided by the span;
for example a 6o-ft. span truss with | pitch will have a center height of 15 ft. The minimum
pitch allowable in a roof will depend upon the character of the roof covering, and upon the kind
of sheathing used. For corrugated steel laid directly on. purlins, the pitch should preferably be
not less than j (6 in. in 12 in.), and the minimum pitch, unless the joints are cemented, not less
than £. Slate and tile should not be used on a less slope than J and preferably not less than |.
The lap of the slate and tile should be greater for the less pitch. Gravel should never be used
on a roof with a greater pitch than about £, and even then the composition is very liable to run.
Asphalt is inclined to run and should not be used on a roof with a pitch of more than, say, 2 in.
to the foot. If the laps are carefully made and cemented a gravel and tar or asphalt roof may be
practically flat; a pitch of f to I in. to the foot is, however, usually preferred. Tin may be used
on a roof of any slope if the joints are properly soldered. Most of the patent composition roofings
give better satisfaction if laid on a roof with a pitch of 5 to j. Shingles should not be used on a
roof with a pitch less than J, and preferably the pitch should be | to f.
Pitch of Truss. — There is very little difference in the weight of Fink trusses with horizontal
bottom chords, in which the top chord has a pitch of i, |, or £. The difference in weight is quite
noticeable, however, when the lower chord is cambered; the truss with the ^ pitch being then
more economical than either the i or the j pitch. Cambering the lower chord of a truss more
than, say, 1-40 of the span adds considerable to the weight. For example the computed weights
of a 6o-ft. Fink truss with a horizontal lower chord, and a 6o-ft. Fink truss with a camber of 3 ft.
in the lower chord, showed that the cambered truss weighed 40 per cent more for the j pitch and
15 per cent more for the | pitch, than the truss having the same pitch with horizontal lower
chord. It is, however, desirable for appearance sake to put a slight camber in the bottom chords
of roof trusses, for the reason that to the eye a horizontal lower chord will appear to sag if viewed
from one side.
In deciding on the proper pitch, it should be noted that while the f pitch gives a better slope
and has a less snow load than a roof with i or -5 pitch, it has a greater wind load and more roof
surface. Taking all things into consideration \ pitch is probably the most economical pitch for a
roof. A roof with \ pitch is, however, very nearly as economical, and should preferably be used
where corrugated steel roofing is used without sheathing, and where the snow load is large.
Spacing of Trusses and Transverse Bents. — The weight of trusses and columns per square
foot of area decreases as the spacing increases, while the weight of the purlins and girts per square
foot of area increases as the spacing increases. The economic spacing of the trusses is a function
of the weight per square foot of floor area of the truss, the purlins, the side girts and the columns,
and also of the relative cost of each kind of material. For any given conditions the spacing
which makes the sum of these quantities a minimum will be the economic spacing. It is desirable
to use simple rolled sections for purlins and girts, and under these conditions the economic spacing
will usually be between 16 and 25 ft. The smaller value being about right for spans up to, say,
60 ft., designed for moderate loads, while the greater value is about right for long spans, designed
for heavy loads.
TRUSS DETAILS. 15
Calculations of a scries of simple Fink trusses resting on walls and having a uniform span
of 60 ft. and different sparing Ravr ilu 1< a^i weight \*T square foot of horizontal projection of
tin roof for a spacing of 18 ft., and the least wri^ht of trusses and purlins combined for a spacing
of 10 ft. The weight of trusses per square foot was, however, more for the lo-ft. spacing than
for the l8-ft. spacing, so that the actual cost of the steel in the roof was a minimum for a spacing
of about 1 6 ft.; the shop cost of the trusses per Ib. being several times that of the purlins. Local
conditions and requirements usually control the spacing of the trusses so that it is not necessary
that we know the economic spacing very definitely.
For long spans the economic spacing can be increased by using rafters supported on heavy
purlins, placed at greater distances than would be required if the roof were carried directly by the
purlins. This method is frequently used in the design of train sheds and roofs of buildings where
plank sheathing is used to support slate or tile coverings, or where the tiles are supported by
angle sub-purlins spaced close together as shown in Fig. 13.
Truss Details. — Riveted trusses are commonly used for mill buildings and similar structures.
For ordinary loads the chord sections are commonly made of two angles, Fig. 10. For heavy
loads the chords may be made of two channels, Fig. 12. Where the purlins are not placed at the
panrl jxrints the upper chord must be designed for flexure as well as for direct stress. Two angles
with a vertical plate make an excellent section where the chord must take both direct and flexural
stress. Trusses supported on masonry walls should have one end supported on sliding plates
for spans up to 70 ft., for greater lengths of span rollers or a rocker should be used. Shop drawings
of a steel roof truss are given in Fig. 10. Details of the end connections of trusses resting on walls
and fastened to columns are given in Fig. 1 1. Details of truss joints are given in Fig. II. Wher-
ever possible, truss joints should be so designed that the joint will not be eccentric.
Details of Roof Framing. — Roof trusses and transverse bents should be braced transversely
with vertical framework and bracing to give the roof framing lateral stability. The bracing may
be placed in the center line of the building as in Fig. 12, or at the quarter points as in Fig. 4;
long span trusses should be braced at both the center and the quarter points. Details of roof
framing giving methods of bracing roof trusses and transverse bents are given in Fig. 4, Fig. 41,
and Fig. 42.
Details of a roof truss and roof framing to carry a Ludowici tile roof without sheathing, are
shown in Fig. 13. The tiles are carried on sub-purlins, the sub-purlins are supported by rafters,
which are in turn supported by the purlins.
Columns: — The common forms of columns used in mill buildings are shown in Fig. 14. For
side columns with light loads column (g) composed of four angles laced is very satisfactory, while
for side columns that take bending and heavy loads column (/) composed of four angles and a
plate is the most satisfactory column. Columns (a), (b), (c), (d), (e) and (j) are used to carry
heavy loads. The I beam and the angle columns are used for end and corner columns, respec-
tively. Details of a four angle laced column and a four angle and plate column are shown in
Fig. 15. Details of a heavy column and a light column made of two channels laced are shown
in Fig. 1 6.
CORRUGATED STEEL. — Corrugated steel is rolled to U. S. standard gage. The weights
of flat steel and corrugated steel for different gages and thickness are given in Table I. Corru-
gated siding and roofing is rolled as shown in Fig. 17. The special corrugated steel in (b) Fig. 17
is commonly used for roofing, and the corrugated steel in (c) is used for siding.
The standard stock lengths vary by single feet from 4 ft. to 10 ft. Sheets can be obtained
as long as 12 ft., but are special and cost 5 per cent extra and will delay the order.
The purlins for corrugated steel without sheathing should be spaced for a load of 30 Ib. per
sq. ft. on the roof; and the girts for 25 Ib. per sq. ft. on the sides, as given in Fig. 18.
The details of corrugated steel as given in Fig. 19 are standard with the McClintic-Marshall
Construction Company and the American Bridge Company.
16
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
I
Q
W
H
W
H
W
Q
TRUSS DETAILS.
(d) 5IWng P/afe
(b)
FIXED ENDS
(e) Rocker
EXPANSION ENDS
COLUMN CONNECTIONS
I I
=5j m
DETAILS OF POOF TRUSS CONNECTIONS
FIG. ii. DETAILS OF TRUSS CONNECTIONS AND JOINTS.
18
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
. 25'0'C.tcC.of Trusses NEWS.
Half Transverse Section.
FIG. 12. ROOF TRUSS AND TRANSVERSE BENT SHOWING TRANSVERSE BRACING.
I
Section fl-B
FIG. 13. DETAILS OF A ROOF COVERED WITH LUDOWICI TILE.
CORRUGATED STEEL.
19
Fastenings for Corrugated Sheeting. — Corrugated steel is fastened to purlins and girts usually
by the following fasteners.
Straps. — These are made of No. 18 U. S. gage steel, f of an in. wide. These straps pass
around the purlins and are riveted to the sheets at both ends by jV' diameter rivets, f in. long;
or, they may be fastened by bolts. Order one strap and two rivets, or bolts, for each lineal foot
of ^irt or purlin, to which the corrugated steel is to be fastened, and add 20 per cent to the number
of rivets for waste, and 10 per cent to the straps or the bolts. One thousand rivets will weigh
6 Ib. ; one bundle of hoop steel will weigh 50 Ib. and contains 400 lineal feet.
Z Channels
Laced
(a)
n
^Channels
2 Plates
CO
2 Channels
I I Beam
(d)
K
4 Z Bars.
I Plate
fe)
4 Angles
I Rate
(f)
II Beam
(h)
I Angle
(U
H
Gray
(I)
4 Angles
Box Laced
(m)
4 Angles
Box Laced
(n)
4 Angles
Starred
(O)
FIG. 14. TYPES OF COLUMNS FOR STEEL MILL BUILDINGS.
Clinch Rivets or Nails. — These are special rivets or nails made of No. 9 Birmingham gage
wire, which clinch around the edge of the angle iron or channel and are used for fastening the steel
sheathing to steel purlins or girts. They are of the lengths shown on page 24.
20
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
~ Center Koof Truss
$&&'
! ,' .'Back oFL5 on truss
i
tp^p5%
j
-^T
>^!
'x^
s
*•*
V
^'^o
^ .1 :x
rtN: ^
3/
^
.8?
^ '
l\
A
*§.
^J)i
*«»
. vT^
*^-
\S '
oX
§
Vs . /•
>
V|
^
~i»! >
\
1 * ////• ''
^ ^//-?r
m
X A
\\t
;Vi, i^
•^fetE
s>ii?fe>t'^
\SKt~
<£?^f-"
^
\ —
kF
rvi ^
s^ifl**«' «
• -> : ^T
y
HE
"^' !
"^i '
{
H^'o'i0 |
Q
* ''3
iX| |
N
^
fea
j 1
,1
^
* \
} j
KJ
h«a
>
&
1 J 1
*<j
> 'o^
^ ^
"If !
1
>v
^ <N.
$
it it
^
^5
jX^
I'J
s
', e^
\v
N \
^
W^NS
^%W
'1
^N
> 1
^s ,1
^ «i\S
NX
t "& ^ >
!^i>
1 19
! ' %
4
M
S Ml
^^ss*
•>|lf|s:|l
\ M—
X
M^, QQ ^ ^ *^J "vJi ^
^ ^ \ ^ ^ ^Si ^*
<.
ffl
fl
L '
1 /Faced \
^-----^
IU1
=6
?vx/
!~» // ,tf 7! . u j
Ysfa&r CT
|H»»«» ^f« «M Q J
ic ^r.v 2
•> i T "^ ^~
v^fei^
^p3
^i / ft 'i
|4-5
' N^ ll-
X I //,///
'Mi*!. ///
^•- *i ^^ o
1 S *
•N -t; en
» fif
FIG. 15. DETAILS OF MILL BUILDING COLUMNS.
MILL BUILDING COLUMNS.
21
'~5/<7<f //'*J^
FIG. 16. DETAILS OF MILL BUILDING COLUMNS.
22
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Order two rivets to each lineal foot of purlin or girt to which the corrugated steel is to be
fastened and add 10 per cent for waste.
Clips and Bolts. — These are used for fastening corrugated steel to steel purlins or girts. Clips
ace made of No. 16, 13 in. steel, about 2\ in. long, and are slightly crimped at one end, to go over
Corrugated Roof Steel
Side Lap 2 Corrugations
— CoversZ/f- *i* - Covers £/£ "
i . .__**_
"iTO
~>re corrugating
» after "
(a)
Special Cor- Roof Steel
Side Lap \k Corrugations
— Covers 24*- »{< - Covers Z4"
i* 2k "-1 I* -30 "w/tfe he fore corrugating
~- y7~ " - affer
End Lap for Roof 6"
(b)
Corrugated Siding Steel
Side Lap I Corrugation
— Covers 24"-^*- Covers 24 " - - — —*
|* £d "w/tfe before corrugaffng
**Z6" " after »
End Lap forS/'afes -4 "
(CJ
FIG. 17. DETAILS OF CORRUGATED STEEL.
= Tofal safe load.
Working stress* 12000 /fa.
h'Depfh of corrugation, ins.
* b/ictfh of sheett ins.
t-Th left ness of sheet ; ins. .
I • Clear »pon, in 5.
50an,L>in ft.
FIG. 1 8. SAFE LOADS FOR CORRUGATED STEEL.
CORRUGATED STEEL DETAILS.
23
flange of the purlin. The bolts are of the same diameter, and have the same head as the clinch
. pi th.it they are supplied with threads and nut, and are about I in. long. These clips
1 bolts should not be used excepting in special cases, where the regular fastenings cannot be
sily applied.
If If side laps of roofing are to bt
riveted, use closing rivets spaced
not more than M>*c. to c.
Straps every 4'0
24net 24net
^X^
Side L3p for Poof
Roof sheet turned up
behind Vent, end sheet
Finish of Yent. End
&!^
"^'Bottom
f" Hanging
Gutter
\
Box Cornice Gutter
and
Truss Pnchor
Laps for Gab. CorrStee/J/ding \
Closm0Kivet ^low ^'end /ap for siding \
6ab/e finish
Od- clinch nails
50- lib- Spaced
"'centers
]&
Sable Finish with Brick Wa//
M
Flashing turned into
{•joints of brick and pepped
\ about every 2'-6'
\ ^-Pur/in
^flng/e Spacer
Gab/e finish with Parapet Ivy//
Ridge Roll W 24 gsge,
or same gage 35 roofing
in 6"0' fe/ytfts. /H/ow
for 3" lap •
Allow 10 %fbr waste
of steel straps and dips •
_ V Table for dind) Rivets, W 10 Wire
Sheeting attached to Edve Struts
ROOFIHG- 27? wide, one ectae up undone down, 3/?d side Jap of /i corruga-
' ?'
tion M// 'conr
Purlin Leg
2'
&
3
&i
Length
4"
5"
6'
7'
Wperlb-
4S
58
33
27
rrnt iftsr&/ t-*-r * • — • ' '
Alto* 6" end lap for roofs of 6"pitch, 8'for roofs of4"pitch, 3" for roofs Spaced 6'apart-
U-— /.Z.-* ^^_ :t. . L - - 9 /_. _ .._.•*./ ^*/_ * • ^» • r*'* • » t
, ,
of less fan 4"pitch; and '/ay tr/th Slaters' Cement' /fsida laps are to be
riveted, vse c/osiff? r/'wts 12 "apart •
S/DIH6 - ?6"m'(/e, both edges Je>m trith s/de lap of one corrugation, M'/f cover
24- /)/foir4fffbrend/ap- Closing rivets in stde lap /2/fcenters.
- ust/3//ymade same gage as s/d/'ng, can be obtained in Following
extreme sizes:
= 48
,*
' W28- 4O'* 96" Order sbeetsin S'O'/engtbs-
" "
Closing Rivets
Standard Corrugated Roofing and Sid/ng can be obtained 48"x 152" varying
fy 6" Corrugations approximately 2$ ;*•£*•
FIG. 19. STANDARD DETAILS FOR CORRUGATED STEEL.
Diameter
r
3*
ie
i'
16
*'
Length
a*
f
i*
~z
S*
3*
~4
Mper/b-
200
166
142
125
24
STEEL ROOF TRUSSES AND MILL BUILDINGS.
TABLE OF CLINCH NAILS.
CHAP. I.
L Purlin leg
3"
4"
s"
6"
7"
Length
5"
6"
7"
8"
9"
No. per Ib
•?2
29
23
21
18
L Purlin leg
3"
4"
s"
6"
7"
Length
6"
7" or 8"
9"
10"
ii"
No. per Ib
2Q
21
18
16
14
In cases where flashing, cornice work, and several thicknesses of metal are to be fastened at
one point, rivets or bolts, other than standard lengths given will be needed. Closing rivets \ in.
long and bolts i| in. long will usually answer in these cases.
If side laps of corrugated steel are to be riveted, rivets should be ordered, one for each lineal
foot of side lap, plus 20 per cent for waste.
If corrugated steel is to be fastened to wooden purlins or timber sheathing, order 8d barbed
nails for roofing and for siding. These nails should be spaced one foot apart, for both end and side
laps; add 20 per cent for waste. Ninety-six 8d barbed nails weigh I Ib.
Corrugated steel for roofing should be laid with two corrugations side lap if standard or 13
'corrugations side lap if special, and 6 in. end lap. Corrugated steel for siding should have one
corrugation side lap and 4 in. end lap,
Louvres. — Weights of Shiffier louvres of black iron or steel are as follows:
Gage No.
20
22
Weight per Square Feet.
2.7 Ib.
2.O Ib.
The weight is obtained from Fig. 20, as follows:
T^l 45
"cj *s r~^^j
£* |g
3 ^ H £ £
.s i O .x\ "O
§
* LJ
FIG. 2Q. LOUVRES.
Louvres are estimated in square feet = 2h X length.
To get weight multiply area by (1.7 X weight per sq. ft. of flat of material used).
Ridge Roll. — Ridge roll is ordinarily of same gage as roofing and black or galvanized to cor-
respond with same. Ridge roll is usually made from an 18 in. flat sheet.
WEIGHT OF RIDGE ROLL.
Gage No.
Weight, Ib. per lineal ft.
2O
22
24
2.4)
2.0 > Black Iron or Steel.
1.6)
CORRUGATED STEEL SHEETS.
25
TABLE I.
CORRUGATED SHEETS. AMERICAN SHEET AND TIN PLATE COMPANY STANDARD.
DESCRIPTION OF CORRUGATED SHEETS
AREAS OF CORRUGATED SHEETS
Corrugations
Width. Inches
Nominal Actual
Depth,
Approx.
Inches
Num-
ber per
Sheet
Width, Inches
Full
Sheet
Covers
Ap-
prox.
Sq. Ft. in i Sheet
Corrugations
2"
1 1". »'
Sheets in 100 Sq. Ft.
Corrugations
5" *">$"> U", I
4*
1
6
9
10
ii
20
26
28
26
26
26
25
25
24
24
24
24
24
24
Standard lengths 5, 6, 7, 8, o and i<
imum length, 12 feet for 5 to ij"
10 feet. Max-
corrugation.
60
72
84
96
108
1 20
144
11.67
14.00
18.67
2I.OO
23-33
28.00
10.83
13.00
I5-I7
17-33
I9-SO
21.67
26.OO
10.42
12.50
14.58
16.67
18.75
20.83
25.OO
8.57
7-14
6.12
5.36
4.76
4.29
3-57
9-23
7.69
6.59
5-77
5-13
4.62
3-85
9.60
8.00
6.86
6.00
S-33
4.80
4.00
CORRUGATED SHEETS. — Painted.
Weights in Pounds per 100 Square Feet.
Thickness, U. S. Standard Gage and Decimals of an Inch
.038
163
163
163
I63
170
.034
ISO
I52
IS6
.031
136
136
136
136
I42
.028
123
123
123
123
128
24
.025
no
no
no
1 10
114
114
96
96
96
96
26
.019
83
83
83
83
86
86
27
.017
76
76
79
79
2S
.016
68
66
66
68
7^
72
CORRUGATED SHEETS. — Galvanized.
Weights in Pounds per 100 Square Feet.
Thickness, U. S. Standard Gage and Decimals of an Inch
•038
I78
I78
I78
I78
I8S
•034
22
.031
157
.028
I38
138
138
138
.025
124
124
124
I24
129
129
.022
III
III
III
III
26
.OI9
98
98
98
98
IOI
IOI
.017
91
91
91
91
94
94
.Ol6
85
85
85
85
87
87
The weights per 100 square feet given in preceding tables do not include allowances for end
or side laps. The following table gives the approximate number of square feet of sheeting neces-
sary to cover an area of 100 square feet and is based on sheets of standard width, 96 inches long.
If longer or shorter sheets are used, the number of square feet required will vary accordingly.
SQUARE FEET OF CORRUGATED SHEETS TO COVER 100 SQUARE FEET.
End Lap, Inches
Side Lap
I Corrugation .
no
116
123
in
117
124
112
118
125
"3
"9
126
114
120
127
"5
121
128
26
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Gutters. — Eave or valley gutters should always be galvanized. Valley gutters should be
No. 20 gage. Eave gutters and conductors should be No. 22 gage. Gutters should be sloped not
less than I in. in 15 ft.
WEIGHTS OF -EAVE GUTTERS AND CONDUCTORS OF GALV. IRON OR STEEL.
Span of Roof.
Size of Gutter.
Wt. per ft.
Size and Spacing
of Conductor.
Wt. per lin. ft.
No. 22.
up to 50'
50' to 70'
70' to 100'
6", No. 22
7", No. 22
8", No. 22
1.8 Ib.
1.9 Ib.
2.1 Ib.
4 in. every 40' o"
5 in. every 40' o"
5 in. every 40' o"
1.5 Ib.
2.1 Ib.
2.3 Ib.
Details of conductors and downspouts are given in Fig. 21.
Adjusbgble
hanger every
4 Feet-
Adjustable hanger
every 3 Feet for
Type
Area
Drained
5<j-Fb-
Size
of
Gubder
Conductors
D Id Ki-
lns-
Spaced
Ft-
WJ
0 bo! 200
1 ZOO to I 8 00
1800 bo 24 00
6"
7"
8"
4
5
5
40
40
40
N?2
and
#23
0 to2400
2400 bo £600
5600bo4800
4"*8"
5"x6"
5"*JO"
5
6
6
40
40
40
Eave and ]/a/fey Gutbers
usual/y N-??0 orsame gsge
5Jope one inch in Fifteen
Feel;.
Order in £ Feet lengths-
Conductors usua/fy N-??£
or ^a me gage as siding*
FIG. 21. DETAILS OF CONDUCTORS AND DOWNSPOUTS. AMERICAN BRIDGE COMPANY.
Purlins. — Details of connections for purlins used for a corrugated steel roof are given in Fig.
22.
Cornice. — For details of cornice see the author's " The Design of Steel Mill Buildings."
ROOF COVERINGS. — Mill buildings are covered with corrugated steel supported directly
on the purlins; by slate, tile or cement tile supported by sub-purlins; or by corrugated steel,
slate, tile, cement tile, shingles, gravel or other composition roof, or some one of the various pat-
ented roofings supported on sheathing. The sheathing is commonly made of a single thickness
PURLIN DETAILS FOR CORRUGATED STEEL ROOF.
27
fStf
MM >-"
T l
Note 'Make due allowance in P and H for angles which overrun
ANGLE PUPLJNS
Leg
H
Clip
Angle-
*2
CHANNEL PURL/MS
Purlin Clip Angle
Channel pur/ins over 7"
deep to have Flange g/so
attached to rafters-
ir
4*5
4*5
4*5
2"
H
3
3
3
3|
31
1 Beam purlins over 7" deep are usually bolted dfrect to rafter-
l&EAM PUQL1N5
4*5
4*3
5*%
A /?
/
-t— -f
Win Clip Angk
T ^T
Zee Bar purlins over 5" to have flange punched for connection to rafter-
I BAR PURLINS
4*3
P
Purfms or gfrts should extend, v/heris possible, over two or more bays with joints
staggered- Where pur/ins act as struts, use c/fp with four holes •
Where purlins are punched for nai/fng scrips, space holes about 5'0* apart - Bolt
purlins to clips and clips to trusses unless otherwise specified-
FIG. 22. DETAILS OF PURLINS FOR CORRUGATED STEEL ROOF. AMERICAN BRIDGE COMPANY.
28 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
of planks, I to 3 inches thick. The planks are sometimes laid in two thicknesses with a layer of
lime mortar between the layers as a protection against fire. In fireproof buildings the sheathing
is commonly made of reinforced concrete. Concrete slabs are sometimes used for a roof covering,
being in that case supported directly by the purlins, and sometimes as a sheathing for a slate or
tile roof.
The roofs of smelters, foundries, steel mills, mine structures and similar structures are com-
monly covered with corrugated steel. Where the buildings are to be heated or where a more
substantial roof covering is desired slate, tile, tin or a good grade of composition roofing is used,
or the roof is made of reinforced concrete. For very cheap and for temporary roofs a cheap com-
position roofing is commonly used. The following coverings will be described in the order given;
corrugated steel, slate, tile, tin, and tar and gravel. A slate roof on reinforced concrete sheath-
ing is shown in Fig. 45 and in Fig. 46.
CORRUGATED STEEL ROOFING. — Corrugated steel roofing is laid on plank sheathing or
is supported directly on the purlins. Corrugated steel roofing should be kept well painted with a
good paint. Where the roofing is exposed to the action of corrosive gases as in the roof of a smelter
reducing sulphur ores, ordinary red lead or iron oxide paint is practically worthless as a protective
coating; better results being obtained with graphite and asphalt paints. Tar paint, made by
mixing tar, Portland cement and kerosene in the proportions of 16 parts of tar, 4 parts of Portland
cement, and 3 parts of kerosene, by volume, is an excellent protection against corrosive gases in
smelters and similar structures. Galvanized corrugated steel is quite extensively used. To pre-
vent the condensation of vapor on the inside of the metal roof, corrugated steel roofing should
be laid on sheathing or should have anti-condensation lining.
Corrugated steel sheets covered with an asbestos preparation can now be obtained on the
market.
Anti-Condensation Lining. — Anti-condensation lining, shown in Fig. 23, consists of asbestos
felt supported on wire netting that is stretched tight and supported by the purlins. Anti-con-
densation lining is put on according to two systems.
Berlin System, (5) Fig. 23. — (i) Lay galvanized wire netting, No. 19, 2-in. mesh, trans-
versely to the purlins with edges about i| in. apart so that when laced together with No. 20 brass
wire the netting will be stretched smooth and tight. When the purlins are spaced more than 4 ft.
apart stretch No. 9 galvanized wire across the purlins about 2 ft. centers to hold up the netting.
(2) On the top of the wire netting place a layer of asbestos paper weighing 14 Ib. per square
of 100 sq. ft., and on this place a layer of asbestos paper weighing 6 Ib. per square. All holes in
the paper must be patched when laid.
(3) On top of the asbestos paper lay two thicknesses of Neponset building paper.
Note. — The asbestos and building paper should lap 3 in. and break joints 12 in. The corru-
gated steel is fastened with the usual connections. Use tin washers on corrugated steel bolts
where there is danger of breaking or tearing the lining.
Wire netting, No. 19 gage, 2-in. mesh comes in bundles 6 ft. wide and 150 ft. long, containing
900 sq. ft. Asbestos comes in rolls 36 in. wide and is sold by the pound. No. 20 brass wire is
bought by the pound, 272 lineal ft. weigh one pound. Neponset building paper conies in rolls
36 in. wide and 250 ft. or 500 ft. long. Do not cut a roll. Add 10 per cent for laps of asbestos
and building paper.
Minneapolis System, (6) Fig. 23. — (i) Lay wire netting, No. 19, 2-in. mesh, transversely to
the purlins, with edges I J in. apart, so that when laced together with No. 20 brass wire the netting
will be stretched smooth and tight.
(2) On the top of the netting lay asbestos paper weighing 30 Ib. to the square of loo sq. ft.,
allowing 3 in. for laps. For important work lay one or two thicknesses of building paper on top
of the asbestos.
(3) Lay the corrugated steel and fasten to purlins in the usual manner.
Note. — If wood purlins are used the wire netting may be fastened to the nailing strips with
| in. staples. Where the purlins are more than 2 ft. 6 in. centers place a line of ^ in. bolts between
purlins, about 2 ft. centers, with washers I in. X 4 in. X | in. to prevent netting from sagging.
' * SLATE ROOFING. — Roofing slates are usually made from f to \ inches thick; ^ inch
being a very common thickness. Slates vary in size from 6 in. X 12 in. to 24 in. X 44 in.; the
sizes varying from 6 in. X 12 in. to 12 in. X 18 in. being the most common.
ROOFING, VENTILATORS, AND ANTI-CONDENSATION LINING.
29
One Layer Sheathing Paper,
Two Plies Tarred Felb, -
. _- _.-
0) SLATE ROOF
Pitch
--Paper
~~5heathiny
Section A- A
(2) TAR AND 6RAVEL ROOF-
For 30 and Apron Me ka,
over, use N-??0 3^ut
9*9*'
UnderZO
Variable-
.-\ J^/Biam- oF Stack
K--- --->! Diam- of Flashing
\
(3} CIRCULAR VENTILATOR
--f
^j Give pitch
5: oF RooF on
91
^ Ventilator
Detai/s-
Apron and
Flashing shipped
in 2 or more
pieces, depend-
ing on the size*
(4) STACK FLASH INS
YYYYYYYY
T YYTYYY Y WI9 Galv Wire Netting
wvVvvv\ •>!'„..!. , , . -XA
mesh, laced with
N?- 20 Brass Wire-
14 Ib- Asbfstos Paper-
6 Ib- Asbestos Paper-
\/\, Two thicknesses of
J^J Neponset Bldg- Paper-
Corrugated Stee/-
(5) ANTl- CONDFHSA TIOH ROOFIH6
BERLIH SYSTEM
50 Ib- Asbestos
Paper-
Corrugated Sheeting
Use I"*4**j" Clips
2 '0 centers, mid tray
between Purlins-
(6)AHTI-COHDEHSATION ROOFING
MINNEAPOLIS SYSTEM
J
FIG. 23. DETAILS OF ROOFING, VENTILATORS AND ANTI-CONDENSATION LINING.
30
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Slates are laid like shingles as shown in Fig. 23. The lap most commonly used is 3 inches;
where less than the minimum pitch of \ is used the lap should be increased. The number of slates
of different sizes required for one square of 100 sq. ft. of roof for a 3-in. lap are given in Table II.
The weight of slates of the various lengths and thicknesses required for one square of roofing,
using a 3-in. lap is given in Table III. The weight of slate is about 174 Ib. per cu. ft. The weight
of slate per superficial sq. ft. for different thicknesses is given in Table IV.
TABLE II.
NUMBER OF ROOFING SLATES REQUIRED TO LAY ONE SQUARE OF ROOF WITH 3-lN. LAP.
Size in Inches.
No. of Slate in
Square.
Size in Inches.
No. of Slate in
Square.
Size in Inches.
No. of Slate in
Square.
6 X 12
533
8 X 16
277
12 X 20
141
7 X 12
457
9 X 16
246
14 X 20
121
8 X 12
400
10 X 16
221
II X 22
137
9X 12
355
12 X 16
184
12 X 22
126
10 X 12
320
9X 18
213
14 X 22
108
12 X 12
266
10 X 18
192
12 X 24
114
7X14
374
ii X 18
174
14 X 24
98
8 X 14
327
12 X 18
160
16 X 24
86
9 X 14
291
14 X 18
137
14 X 26
89
10 X 14
261
10 X 20
169
i6X 26
78
12 X 14
218
II X 20
J54
TABLE III.
THE WEIGHT OF SLATE REQUIRED FOR ONE SQUARE OF ROOF.
Length in
Weight in pounds, per square, for the thickness.
Inches.
1"
A"
i"
4
3"
8
\"
f"
i"
i"
12
483
724
967
H50
1936
2419
2902
3872
H
460
688
92O
1370
1842
2301
2760
3683
16
445
667
890
1336
1784
2229
2670
3567
18
434
650
869
1303
1740
2174
2607
348o
20
425
637
851
1276
1704
2129
2553
3408
22
418
626
836
1254
1675
2093
2508
335°
24
412
617
825
1238
1653
2066
2478
3306
26
407
610
815
1222
1631
2039
2445
3263
TABLE IV.
WEIGHT OF SLATE PER SQUARE FOOT.
Thickness — in.
i
A
i
f
i
5
3
I
Weight — Ib
1.81
2.71
3.62
5-43
7-25
9.O6
10.87
14. c
The minimum pitch recommended for a slate roof is J; but even with steeper slopes the rain
and snow may be driven under the edges of the slates by the wind. This can be prevented by
laying the slates in slater's cement. Cemented joints should always be used around eaves, ridges
and chimneys.
Slates are commonly laid on plank sheathing. The sheathing should be strong enough to
prevent deflections that will break the slate, and should be tongued or grooved, or shiplapped, and
dressed on the upper surface. Concrete sheathing reinforced with wire mesh, expanded metal
or rods is now being used quite extensively for slate and tile roofs, and makes a fireproof roof, see
ROOFS FOR MILL DUILDINGS. 31
32 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
it will lay 168 sq. ft. For flat seam roofing, using £ in. locks, a box of 20 X 28 tin will lay about
399 sq. ft., and for standing seam, using f in. locks and turning i j and if in. edges, making i in.
standing seams, it will lay about 365 sq. ft.
TAR AND GRAVEL ROOF.— Tar and gravel roofs are called three-, four-, five-ply, etc.,
depending upon the number of layers of roofing felt. Tar and gravel roofs may be laid upon timber
sheathing or upon concrete slabs. For details of a tar and gravel roof see Fig. 23. The following
specifications are taken from the author's " Specifications for Steel Frame Buildings."
Specifications for Five-Ply Tar and Gravel Roof on Timber Sheathing. — The materials used
in making the roof are I (one) thickness of sheathing paper or unsaturated felt, 5 (five) thick-
nesses of saturated felt weighing not less than 15 (fifteen) Ib. per square of one hundred (100)
sq. ft., single thickness, and not less than one hundred and twenty (120) Ib. of pitch, and not
less than four hundred (400) Ib. of gravel or three hundred (300) Ib. of slag from f to f in. in size,
free from dirt, per square of one hundred (100) sq. ft. of completed roof.
The material shall be applied as follows: First, lay the sheathing or unsaturated felt, lapping
each sheet one in. over the preceding one. Second, lay two (2) thicknesses of tarred 'felt, lapping
each sheet seventeen (17) in. over the preceding one, nailing as often as may be necessary to
hold the sheets in place until the remaining felt is applied. Third, coat the entire surface of this
two-ply layer with hot pitch, mopping on uniformly. Fourth, apply three (3) thicknesses of felt,
lapping each sheet twenty-two (22) in. over the preceding one, mopping with hot pitch the full
width of the 22 in. between the plies, so that in no case shall felt touch felt. Such nailing as is
necessary shall be done so that all nails will be covered by not less than two plies of felt; fifth,
spread over the entire surface of the roof a uniform coating of pitch, into which, while hot, imbed
the gravel or slag. The gravel or slag in all cases must be dry.
Specifications for Five-Ply Tar and Gravel Roof on Concrete Sheathing.— The materials
used shall be the same as for tar and gravel roof on timber sheathing, except that the one thick-
ness of sheathing paper or unsaturated felt may be omitted.
The materials shall be applied as follows: First, coat the concrete with hot pitch, mopped
on uniformly. Second, lay two (2) thicknesses of tarred felt, lapping each sheet seventeen (17)
in. over the preceding one, and mop with hot pitch the full width of the 17-in. lap, so that in no
case shall felt touch felt. Third, coat the entire surface with hot pitch, mopped on uniformly.
Fourth, lay three (3) thicknesses of felt, lapping each sheet twenty-two (22) in. over the preceding
one, mopping with hot pitch the full width of the 22-in. lap between the plies, so that in no case
shall felt touch felt. Fifth, spread the entire surface of the roof with a uniform coat of pitch,
into which, while hot, imbed gravel or slag.
Cost of Five-Ply Tar and Gravel Roofing.* — The cost of a round house roof in the middle
west, based on 1912 prices and containing 500 squares of five-ply tar and gravel roofing, was as
follows.
Cost per square of 100 sq. ft. not including fixed charges or profit ,*not including sheathing.
Sheathing paper, 5 Ib $o. 12
Pitch, 155 Ib. at 60 cents per 100 Ib 0.93
Felt, 85 Ib. at $1.65 per 100 Ib 1.40
Nails and caps 0.05
Cleats for flashing 0.05
Gravel (about one-seventh yard) 23
Labor, including hauling, board and railroad fare 1.15
Total cost per square $3-93
SHOP FLOORS. — Floors for industrial plants may be placed on a foundation resting directly
on the ground or may be self supporting. Several examples of shop floors that rest on the ground
are shown in Fig. 25. Standard specifications for a cement floor and for a wood floor on a tar
concrete base follow.
The following specifications are from the author's " Specifications for Steel Frame Buildings."
Specifications for Cement Floor on a Concrete Base. Materials. — The cement used shall
be first-class Portland cement, and shall pass the standards of the American Society for Testing
Materials. The sand for the top finish shall be clean and sharp and shall be retained on a No. 30
sieve and shall have passed the No. 20 sieve. Broken stone for the top finish shall pass a \ in.
*Am. Ry. Eng. Assoc., Vol. 14, p. 852.
FLOORS FOR MILL BUILDINGS.
33
s. ivm and shall be retained on the No. 20 screen. Dust shall be excluded. The sand for the
base shall U rl.-an ami sharp. The aggregate for the base shall be of broken stone or gravel and
shall pass a J in. ring.
Base. -On a thoroughly tamped and compacted subgrade the concrete for the base shall be
laid .UK! thoroughly tamped. The base shall not be less than 2\ in. thick. Concrete for the
hall IK- thoroughly mixed with sufficient water so that some tamping is ri-quired to bring
the moisture to the surface. If old concrete is used for the base the surface shall be roughened
" Lirn* Mortar. '?" Plank
TIMBER FLOOR ON CINDERS
,' I Matched Mapfe, Longitudinal
» " , Transverse!.
fit
fix Tonguedde Grooved Mapfe
—• —
^•Cinders ' ^ **4 " W-P- Nailing 5 trip
(t>) TIMBER FLOOR ON CINDERS
,r",
f/z P/Bnk, Longitudinal
'"?- PJank, Transverse
\ rR>* Concrete oF Tar orAspha/l;
*"3* 'Concrete
(c) TIMBER FLOOR ON TAR CONCRETE
f I' Mapfe, Longitudinal
/ ,'*>" Hemlock, Diagonaf
f f £ Hemlock, Transverse
J^ \? RooFing Pitch
"-Compacted Earth
(d) TIMBER FLOOR ON TAR CONCRETE
,*•/ Pitch and Sand, I :$•
( ;'4"*4"x8 "Map/e Block, fain Vertical
*~-4? Port /and Cement Concrete-
(e) TIMBER FLOOR ON CONCRETE
tl" Wearing Surface, /•'£ Port/and
Cement Mortar
^6" Tar - Grave/ Concrete
(F) TIMBER BLOCKS ON TAR CONCRETB
'&" A'n" /"
( *~~" ' — *^ Concrete-J^
Cinders, well drained
? Portland Cement Corrcretefl&6
(g) CONCRETE FLOOR
FIG. 25. EXAMPLES OF
• ' ' ... ..'... y
'— Tin Gutter
(h) CONCRETE SHOP FLOOR
GROUND SHOP FLOORS.
and thoroughly cleaned so that the new mortar will adhere. The roughened surface of old con-
crete shall then be thoroughly wet so that the base will not draw water from the finish when the
latter is applied. Before scrubbing the base with grout the excess water shall be removed.
Finish. — With old concrete the surface of the base shall first be scrubbed with a thin grout
of pure cement, rubbed in with a broom. On top of this, before the thin coat is set, a coat of
finish mixed in the proportions of one part Portland cement, one part stone broken to pass a J in.
ring, and one part sand shall be troweled on using as much pressure as possible, so that it will
take a firm bond. After the finish has been applied to the desired thickness it should be screeded
and floated to a true surface. Between the time of initial and final set it shall be finished by
4
34
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
skilled workmen with steel trowels and shall be worked to a final surface. Under no condition
shall a dryer be used, nor shall water be added to make the material work easily.
Specifications for Wood Floor on a Tar Concrete Base. Floor Sleepers. — Sleepers for
carrying the timber floor shall be 3 in. X 3 in. placed 18 in. c. to c. After the subgrade has been
thoroughly tamped and rolled to an elevation of 4^ in. below the tops of the sleepers, the sleepers
shall be placed in position and supported on stakes driven in the subgrade. Before depositing
the tar concrete the sleepers must be brought to a true level.
Tar Concrete Base. — The tar concrete base shall be not less than 4.5 in. thick and shall be
laid as follows: First, a layer three (3) in. thick of coarse, screened gravel thoroughly mixed with
tar, and tamped to a hard level surface. Second, on this bed spread a top dressing i| in. thick
of sand heated and thoroughly mixed with coal tar pitch, in the proportions of one (i) part pitch
to three (3) parts tar. The gravel, sand and tar shall be heated to from 200 to 300 degrees F.,
and shall be thoroughly mixed and carefully tamped into place.
Plank Sub-Floor. — The floor plank shall be of sound hemlock or pine not less than 2 in.
thick, planed on one side and one edge to an even thickness and width. The floor plank is to be
toe-nailed with 4 in. wire nails.
Finished Flooring. — The finished flooring is to be of maple of clear stock, £ in. finished thick-
ness, thoroughly air and kiln dried and not over 4 in. wide. The flooring is to be planed to an even
thickness, the edges jointed, and the underside channeled or ploughed. The finished floor is to
be laid at right angles to the sub-floor, and each board neatly fitted at the ends, breaking joints
at random. The floor is to be final nailed with 10 d. or 3 in. wire nails, nailed in diagonal rows
16 in. apart across the boards, with two (2) nails in each row in every board. The floor to be
finished off perfectly smooth on completion.
The finished flooring is not to be taken into the building or laid until the tar concrete base
and sub-plank floor are thoroughly dried.
,»
,--i Tar
Flooring
Z"FIoc
•ing
^~Tie Rott
(a) BRICK ARCH FLOOR
Corrugated Jren '"-Tie Rod
(b) CORRU6ATED IRON FLOOR
(c) RE1HFORCED CONCRETE FLOOR
(</} REINFORCED CONCRETE FLOOR
(F)
PEHCOYD CORRUGATED FLOORING (g) Z BAR FLOOR
(h) ANGLE & PLATE
FLOOR
d) "BUCKEYE "FIREPROOF FLOORING (/) MULTIPLEX STEEL PLATE FLOOR
FIG. 26. EXAMPLES OF SHOP FLOORS ABOVE GROUND.
Shop floors above ground may be made of timber resting on beams, of brick arch construc-
tion, (a) Fig. 26, of concrete with corrugated steel arch centers as shown in (6), of reinforced con-
TIMBER FLOORS.
35
crete as shown in (c) and (d), of steel filled with concrete as shown in («), (/), (g), (A), or of
concrete reinforced with Buckeye flooring as shown in (*') or Multiplex flooring as shown in (j).
Timber Floors. — The Yellow Pine Manufacturers Association has calculated the safe
span of yellow pine when used for mill floors with fiber stresses of 1,200 to 1, 800 Ib. per sq. in.
for live loads of 100 to 300 Ib. per sq. ft. in addition to the weight of the floor, Table V. In the
line in. irked " Deflection " is given the span which has a maximum deflection of one thirtieth of
an inch per foot of span for the various live loads. • The modulus of elasticity of timber was taken
as 1 ,684,800 Ib. per sq. in. The table may be used for any kind of timber by using the proper
working stress. The maximum spans for fiber stresses less than 1,200 Ib. per sq. in. may be found
as follows: Required the maximum safe span for a timber floor 2\ in. thick for a fiber stress of
800 Ib. per sq. in. and a live load of 150 Ib. per sq. ft. The span is approximately the same as for
a fiber stress of 1,200 Ib. per sq. in. and a live load of 225 Ib. per sq. ft., = 6 ft. II in.; or for a
fiber stress of 1,600 Ib. per sq. in. and a live load of 300 Ib. per sq. ft., = 6 ft. n in.
TABLE V.
ALLOWABLE SPAN FOR TIMBER. FLOORS.
YELLOW PINE MANUFACTURERS ASSOCIATION.
Thick-
ness in
Inches.
Stress per
Square Inch.
Pounds.
SPAN IN FEET.
Live Load in Pounds Per Square Foot.
ICO
125
150
175
200
225
250
275
300
If
,2OO
,300
,500
,600
,800
Deflection
6' 4"
6' 7"
7' i"
7; <;
I' 1"
4 8
5' 8"
5' 11"
6' 4"
6' 7"
7' o"
4' 4"
S' 3"
, „
5' 10"
6' o"
4' 10"
5' o"
5' S"
S' 7"
4' 6"
4' 9"
5' i"
S' 3"
4' 4"
4' 6"
4' 10"
5' o"
4' i"
4' 3"
A' 7"
1' 8"
4/ //
3' n"
4- 1"
!•£
3' 9"
3' 10"
4' 2"
4' 4"
6' 5"
4' i"
5' n"
3' n"
£j?
!• *»
5' o"
3' Si"
5- Sr
3' 3"
2l
,200
,300
,500
,600
,800
Deflection
10' I"
10' 6"
9' i"
9' 6"
8' 4"
8' 8"
7' 9"
8' i"
£3
6' n"
7' 2"
6' 6"
6' 10"
6' 3"
6' 6"
6' o"
6' 3"
11' 3"
n' 8"
10' 6"
9' 4"
9' 8"
8' 8"
8' 11"
8' 2"
8' 5"
7' 8"
7' 11"
if
7' o"
7' 2"
7' 8"
5' S"
6' 11"
7' 4"
S' 3"
12' 4"
/ si"
n' 2"
6' ii*"
10' 3"
6' 7"
9' 6"
6' 3"
8' 11"
6' o"
8' 5"
5' 9i"
5' 7"
M
1,200
1,300
1,500
1, 600
1, 800
Deflection
n' 3"
10' 7"
10' o"
9' 5"
9' o"
8' 7"
8' 3"
11' 8"
12' 7"
13' o"
13' 9"
9' o"
II O"
II' 10"
12' 3"
13' o"
8' 7"
10' 5"
II' 2"
n' 6"
12' 3"
8' 3"
9' 10 "
10' 7"
10' II"
11' 7"
7' Hi"
9' 4"
10' o"
10' 4"
II' 0"
7' 8"
8' n"
9' 7"
9' u"
10' 6"
7' Si"
8' 7"
9' 2"
9' 6"
10' I"
7' 3"
.
10' 2j"
9' 6*"
4f
1,200
1,300
1,500
1, 600
1, 800
Deflection
12' 7"
il' u"
11' 4"
10' 10"
10' 5"
13' 2"
14' i"
12' 5"
13' 4"
12' 9"
11' 4"
12' 2"
n' 8"
H 7
& I-
J3 9
14' 8"
10' I"
13 2
14' 2"
9' 9"
12 7
'i- J-
12' 9"
9' 2i"
12' II"
12' I"
n' Si"
10' II"
Si
1,200
1,300
1,500
1, 600
i, 800
Deflection
IS' 3"
14' 5"
13' 9"
13' 2"
12' 7"
15' 10"
15' o"
14' 4"
13' 8"
13' i"
17' i"
i/ 7"
18' 8"
II' Oj"
16' i"
16' 8"
17' 8"
10' 8"
15' 10"
16' 10"
10' 4"
14' 8"
IS' 2"
16' i"
10' 9"
14' i"
14' 7"
15' s"
10' 9"
13' 7"
12' 8i"
12' oi"
11' 6"
Waterproofing. — For methods of waterproofing floors, walls, etc., see methods of waterproofing
bridge floors in Chapter IV.
36
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
DIMENSIONS FOR GLAZED WOOD SASH
QUALITY OF GLASS
"B" American Single Strength
"B" American Double Strength
IO"*I2"
I2"*/2"
10"* /4"
I2"*]4"
10"* 16".
I2"*16"
14"* 16"
All sash to be I j' thick, except Sliding Sash, Pivoted Sash, dnd Single Sash (or one
half oF Double Sash) exceeding 4'6"high or 4'0"wide, which should be made fjr" thick-
TopRai/s ?/'• Stiles ?£"• Bottom Rail 5"- Muntins %"•
Pivoted Sash, 4 lights high or over, co have one Horizontal Muntin I? thick ; al/
other Sash, 6 lights high or over, to have one Horizontal Muntin I ^" thick'
Pivoted Sash, 4 lights wide or over, to have one Vertical Muntin Ij "thick- all
other Sash, 6 lights wide or overt bo have one Vertical Muntin /j> "thick •
for Pivoted Sash 4 and 5 lights high or wide, add Ig" to Figures given in above tables-
FIG. 27. DIMENSIONS AND DATA FOR GLAZED WOOD SASH. •
AMERICAN BRIDGE COMPANY.
GLAZED WOOD SASH.
37
Height
of
6/ass
No-of
Lights
High
Spacing
H
\ -"1
v£ $
.rl
co >C;
^3 7^
*^
ir
^t*
Width
of
Glass
No-of
Lights
Wide
Spacing
W
Spxing
D.
Width
of
Glass
No-oF
Lights
Wide
Spxing
W
Spxfy
D
12"
12
/2
12
12
/2
14
J4
14
/4
14
14
2
3
4
5
6
7
2
3
4
5
6
7
4-2
5-21
6-2$
7-4$s
3-4
4-8
W
10'
10
10
10
10
3
4
5
6
4-4%
6-2$
?/p7*
22s
3Jj
4-10
5-ti
12
12
12
12
12
2
3
4
5
6
2'H?
4-0?
5-01
6-1
26g
3-7*
4-71
5-8
W = Width of Single Pivoted, fixed or Counter-
balanced Window- Width iof 'Continuous Window ;
=No- of Windows *Dr -f-^i'+Zf^C^Clesr^nce^'
8-4$
9-6J
Jltr*
'*> '<> — ^ ^ \y\\\
21*'* D H' ^tfj"
f/eight
of
Glass
No-of
Lights
High
Spacing
rf
^
,
Width
of
6/ass
No-of
Lights
Wide
Spacing
Spacing
D
Width
of
Glass
No-of
Lights
Wide
Spxing
W
Spxfy
D
• "iy^j * **
T
nee H" Girt Spacing foi
^balanced Windows-
r
12"
/2
12
12
/2
/4
14
14
14
/4
4
6
8
10
12
4
6
8
10
12
5'3f
7-4
9-4*
15-8L2
H/i
8-4
fO-6%
13-li
10"
10
10
10
10
4
6
8
10
12
4'6f
6-3
79f%
4'lf
5-10
7-6%
9-3^
12"
12
12
12
12
4
6
8
10
12
7-35
13-7*1
6-10
8-10$.
10-lli
W* Width of Single Sliding Window- Mdthof Cont*
K W-- ---H
1 1 w^
|i
L
B
^-f^^lM
* a
\ ^ 3 "
^•/^ U -
D ,j j
Height
of
Glass
No-of
Lights
High
Spacing
H
ceH" Girt Spacing for Double
sighted ftfndows-
*" il'i'"
v 4r//
'\
r
Width
of
Glass
No-of
Lights
Wide
Spxing
W
Width
of
Glass
No-of
Lights
Wide
W
12"
12
12
12
12
14
14
14
14
/4
4
6
8
10
12
4
6
8
10
12
5'5f
7-6%
9-6^
8-6s
10-IO's
10"
10
10
to
10
2
4
5
6
3-1-
3-fl%
6-8
12"
12
12
12
12
2
3
4
5
6
4-k
6-6^
7-8
W= Width of Single Dwb/eHwy Weighted Window-
^ ^
V*
\
as -^S -"• -"- ' J- TT
T
-•f==-fi-c-----A~s-.---!itm?; j-U
15 10a
FIG. 28. DIMENSIONS FOR GLAZED WOOD SASH.
AMERICAN BRIDGE COMPANY.
38
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
WINDOWS AND SKY LIGHTS. — Mill and mine buildings should have an ample amount
of glazing in the form of windows and sky lights. Plane glass is made in two thicknesses, single
strength approximately ^ in. thick, and double strength approximatley f in. thick. Plane
DOUBLE HUM WEIGHTED MHDOWS
rr
;*?!
-vA*jL /JP
jg-W
7*f»
. LJtitxr*/ farting Strip ft? Parting Strip
rMuntin "g
1 \
f t
DDDE
Use steel window post only when qirts. connect at side
TYPEB-
7j',3''l'',Z»,J."
r'f KBf&is.
J\
i?
/// ,///, _ rii/ i '* ft- » '*
% */f Ltt-Scnifilf t ,,,•
/< ' ^,,~v 5* \0vtto out of woodwork +3; to 4 !
J — f KOUnu — l* — . _ *r o_ vi
f /f^fl7 steef window post is used\
\\~. .) [ omit for Type A
--V yVhen steel 'window -post is not used, f]f*$'
FIG. 29. DATA FOR DOUBLE HUNG WEIGHTED WINDOWS.
AMERICAN BRIDGE COMPANY.
glass is graded as AA, A, and B. The AA grade being the best and the B grade the poorest.
Wire glass is T8^ in. or \ in. thick and may be obtained with a smooth surface, with factory ribs
or prisms. For ordinary windows double strength glass gives very satisfactory results. For
sky lights and where windows are liable to be broken, wire glass should be used. The best
COUNTERBALANCED WINDOWS.
fxlfLsgScrtw^
#*5**6'Bhck
j'^" Parting
Strip —
1 4
I
^
*j c
I
I
» 1
^; \
%
^»
^
5
x>
i....11-
— L
TYPEA
i
/i'ffi
COUNTERBALANCED WINDOW*
J ^-ft-^Stop
r*t
1
DDDD
DDO
DDDD
run
DDD
DDD
voir*
££"
Stile
(x
*o
--Muntin
"Parting
Strip
Girb
§
of woodwork +j
Use steel windyw posts only
when girts connect at side • x
Jt
ii'isVtfi* TYPEB'
/ZiZfJj/I
^Drip \OuttooutoFw<x/wrt+j
/'-£ Round"''
J*2
^P7:-1
J JS. x "-*
/? '* width angle for TypeB
(When steel window post is used\
11 X J \omit For Type A •
— ^ ^ A .# 0
When steel window post is not used, fe*/? forTypesA&B*
DlMENSIOHS FOR WOOD FRAMES FOR TRIPLE HUNG COUNTERBALANCED WINDOW-
Height
oF 6ldss
Ho-Lights
High
Spacing
H
Height
oF6/ass
No-Lights
High
Spacing
H '
/2'
12
J2
/2
/2
6
9
12
IB
/8
r*P
10-6%
/3-7$
16-8i
20-1
14"
14
14
/4
14
6
9
12
!5
IS
8'BJf
/2-0^
K-7i
19-2?
25 -f
Distance Hin table is Girt Spacing
For Triple Hung Counterbalanced Win-
dows • For width see sheet giving width
oF ordinary Counterbalanced Windows*
FIG 30. DATA FOR COUNTERBALANCED WINDOWS.
AMERICAN BRIDGE COMPANY.
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
— r ,„ i i /*?Aa0WUi
5f ^ ^U$e steel window posts only w/ten girts connect at s/cte-i
\>n?it for Type A
When steel window post is not i/sedj /•? *Iz For Types A & B
DATA FOR SPACING BETWEEN STEEL WINDOW POSTS-
For Fixed, Pivoted and Counterbalanced Windows •
Glass I0"orl2"n
Muntins (each) %'tl
Stiles (each) 2$
Sash Clearance £"
Jambs (each) /%
Nailing Pieces (esch) Ij
Frame Clearance 4
For Sliding Windows use above data except no Sash Clearance, and add 2$ for meeting rail1
FIG. 31. DATA FOR PIVOTED WINDOWS. AMERICAN BRIDGE COMPANY.
FIXED SASH WITH MONITORS. 41
glass for glazing windows in industrial plants is " factory ribbed glass " with twenty-one rib* to
the inch, the ribs being placed on the inside of the window. This glass is considerably more ex-
pensive than plane glass but is much more satisfactory.
Translucent fabric made by imbedding wire cloth in a translucent material made of linseed
oil, is also used for glazing in industrial buildings. Translucent fabric will be charred by a live
coal but is practically fire-proof. It shuts off part of the light, making it possible for men to work
under it without shading.
CONTINUOUS PIVOTED
AHD FIXED SASH
•i'*?} Bolts
every 3 Feet
every 5 Feet
Note •• If sash are fixed continue stops a//
around except across si// on outside • I~z fourxP every 3 /*•
FIG. 32. DATA FOR CONTINUOUS PIVOTED AND FIXED SASH IN MONITORS.
AMERICAN BRIDGE COMPANY.
The amount of glazed surface required in mill buildings depends upon the use to which the
building is put, the material used in glazing, the location and the angle of the windows and sky
lights, and the clearness of the atmosphere. It is common to specify that not less than 10 per
cent of the exterior surface of mill buildings and 25 per cent of the exterior surface of machine
shops should be glazed. Many industrial plants have as much as 60 per cent of the exterior
walls of glass.
42
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
CONTINUOUS FIXED SASH-
,'Corrugated Steel
JSirb
W0-/2 Blue round
head screw 2% fong
with washer.
220
~TWr
i ^
---
^
1
l
~s
. i
k!
s3>'
3*|
* 1
^'
<o|
n '
•fcj
J(j if'SfSili
1 5cren,
I
^
$
&fA.
—J-^
&*\ft
<
^H
iJ
crew-*
ILJkJI
i^1^ i-^"^ r^
^~
'Varies
\-t w*
.5^5^
^1
UL
Note • 5} Us can be obtained
in lengths from /4ft •
toJ6ft-
'/^, 6"centers-
"(ja/vdnized Steel Flashing-
Glass
Sash Top Rail
Sash Bottom Raff
Muntins (each)
Sash Clearance
DATA FOR SPACING BETWEEN GIRTS
For Fixed, Pivoted and Sliding Windows-
f?"or/4* Sil/ and Head (each)
£4 Top Nailing Piece
3 " Bottom Nailing Piece
Block
Frame Clearance
It"
r
f
For Counterbalanced use above data except no Sash Clearance, and 'add I 2 For meeting rail-
FIG. 33. DATA FOR CONTINUOUS FIXED SASH.
AMERICAN BRIDGE COMPANY.
VENTILATORS AND DOORS.
43
Details of glazed sash and window frames as adopted by the American Bridge Company
are given in Fig. 27 to Fig. 34.
VENTILATORS. — Mill buildings may be ventilated by means of monitor ventilators, or by
means of circular ventilators. Details of a circular ventilator as designed by the American Bridge
Company are shown in (3) Fig. 23. Details of a standard monitor steel louvre ventilator are
shown in Fig. 35. The sides of the monitor ventilator in Fig. 42 were fitted with louvres which
were to be closed in cold weather. Buildings of this type should have glazed sash so that when
the ventilators are closed the light will not be cut off. Data for estimating louvre slats are given
in Fig. 20.
CONTINUOUS SLIDING SASH
j *2y LagScrewr,
/1W6" Block' \?\ .> ±
iL*~ T* 'ft.-- ^1- -~. ^--NN.
7^ /'/.
pi Stop-'
*'
~*:for&y Strip
|
•5^
^-1
^i
«*!
i...y
f—
,
4
x-5£//
<---*-~
-
-y%//?
E
c:£''-> "*
i
_oji"o _
1 i
1
/
Flashing*
fffffflfj
• ~ - , _ ^ 'j'-'
¥*jr stop* &£?*M ,„ ,r
' nrnrnn f ^/y
^'fcrd-
woodStr/p
<lZ"*74-"s;lt
FIG. 34. DATA FOR CONTINUOUS SLIDING SASH.
AMERICAN BRIDGE COMPANY.
WOODEN DOORS. — Wooden doors are usually constructed of matched pine sheathing
nailed to a wooden frame as shown in Fig. 36. These doors are made of white pine. Doors up
to four feet in width should be swung on hinges; wider doors should be made to slide on an over-
head track or should be counter-balanced and raise vertically. Sliding doors should be at least
4 in. wider and 2 in. higher than the clear opening.
44
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
9kukl'0"
r—
SECTION A-A
LOU WES
Maximum length unsupported 7fO"
Use tt-0-?? U'S- Gage un/ess specified*
Order 5heets //"wide and a/Sow ? "enj fsp .
Punch ~f ho/es in steel work, sr?d bifl
^ ' diameter x / long round head store bolts*
FIG. 35. DETAILS OF A STEEL MONITOR LOUVRE VENTILATOR.
AMERICAN BRIDGE COMPANY.
" Sandwich " doors are made by 'covering a wooden frame with flat or corrugated steel.
The wooden framework of these doors is commonly made of two or more thicknesses of | in.
dressed and matched white pine sheathing not over 4 in. wide, laid diagonally and nailed with
clinch nails. Care must be used in handling sandwich doors made as above or they will warp
out of shape. Corrugated steel with I J in. corrugations makes the neatest covering for sandwich
doors.
For swing doors use hinges about as follows: For doors 3 ft. X 6 ft. or less use 10 in. strap or
10 in. T-hinges; for doors 3 ft. X 6 ft. to 3 ft. X 8 ft. use 16 in. strap or 16 in. T-hinges; for doors
3 ft. X 8 ft. to 4 ft. X 10 ft. use 24 in. strap hinges.
STEEL DOORS. — Details of a steel sliding door are shown in Fig. 37. Details of a swing-
ing steel door are shown in Fig. 38. Steel doors should be covered with corrugated steel-, prefer-
ably with I y in. corrugations.
Details of the track for a sliding door are shown in Fig. 39.
EXAMPLES OF STEEL MILL BUILDINGS.— The following examples will illustrate the
practice in the design of steel mill buildings.
Example of Ketchum's Modified Saw Tooth Roof. — The modified form of saw tooth
roof shown in (n) Fig. 6, was proposed by the author in the first edition of " The Design
of Steel Mill Buildings " (1903). This form of saw tooth roof has been used in the paint
shops of the Plank Road Shops of the Public Service Corporation of New Jersey, Newark, N. J.
WOODEN DOORS.
45
X Quarter round
/•ailed' with brudi
-Mi
f-
"si
fi
LJ For Joo£» «i0_to^-0_wjdc|
all door* over tt'o'wlde to hare two or mare center (tile*
Section A-A
bf
TTI
Meeting strips for Meeting strip fop
double sliding doors, double swing door*.
Doors in u y be either slid* or .wing-. Sliding door* should
be 4'wlder mid 8 higher than clear opening between jambs.
All doors uudcr6'-0'wlde to hare l*b stiles and rails.
All door* over 0-0 wide to hove 1\' stiles and rolls.
All stiles and rails to be halved or mortised uud tenoned
together.
Doors to be uiuJv of w Kite pine
Irdoorn ore to be eorcrcd with tin or sheet metal they «re
to be made of two or more tlilt-kncssc* of ,H matched whit*
pine- slieuthlne not over 4'wlde, laid dlttconallj aad put
together with wrought nails well clinched.
De»lgn for door up to Design for doors over 3-O"x 7^O*
3'-O"x 7^O" and up to 6-0 wide
FIG. 36. DETAILS OF WOODEN DOORS. AMERICAN BRIDGE COMPANY.
46
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
The building proper is 135 ft. wide by 354 ft. long. The main trusses are of the modified saw
tooth type with 44 ft. spans and a rise of j, and are spaced 16 ft. centers. The general details of
one of the main trusses are shown in Fig. 40. The building has an independent steel framing with
Jamb to run I?"
!nto ground and
•-^•••i"
Corr- Sheeting to be fastened to I 4. angle frame top and bottom*
Corrugated Steel to be of same gage as siding*
Rivets on inside frame, N-°-5 wire- r/oles for fastening inside to outside
frame for H-5 wire •
Rivets on outside frame ? inch • Inside frame to be shipped bolted in place •
Jf desired bo cheapen construct/on of door, omit side and center angles of inside frame-
FIG. 37. DETAILS OF A SLIDING STEEL DOOR. AMERICAN BRIDGE COMPANY.
brick curtain walls on the exterior. Pilasters 24 in. by 20 in. are placed 16 ft. apart under the ends
of the trusses, the intermediate curtain walls being 12 in. thick. The roof is a 5 ply slag roof laid
on tongued and grooved spruce sheathing, which is spiked to 2 in. X 5 in. spiking strips, which are
bolted to 8 in. channel purlins spaced 6 ft. centers.
STEEL SWINGING DOOR.
47
Holes
Center angfe
fnside frame
a £*JLffjL*
Round
5/iding Bar-''
i Round
Sliding
OUTSIDE FR^ME
I'O
'ff^l VffsveFKA*
'<>"•>' ±._. \si?4"xJ.'pr.
'o/es about:
6 apart
I
&
11
Ft
Section A-A
i^Jl
Lp- j, * T
rf«~* -S^'1
r I!
Itri "*^i
s.
31
£"I
C/ffJ.
"1
£jh ^
^ ] °Q
^i
Nj
r1 <>
n | •
J'y//7x!
XT!
^2 1 '
Bf^S-r— •*
Hofes in
[t'imhc £rtf^
r
4 Bar
jallfP5 1 VI
hinges, to
he drilled
in the Field-
(loose)
\ u__^
^.nmpectr/' \ ±" L^^^^f6i^
J>"X%"x8rO"-' £>/>' outside Frjme
6"*i"PIdt;e Hinge
with^'Rod-
Corrugated Steel bo be same gsge as siding ••
Rivets on inside Frame, N-°-5 wire • Ho/es For Fastening inside Frame to
outer Frame, N-°-5 wire •
fiivets on outer Frame £" diameter- fns/de Frame to be shipped bo/ted in place •
Corrugated SteeJ to be nVeted in F/'e/dtotop and bottom ang/es oF inside Frame-
IF desired to cheapen construction oFdoor, omit side and center ang/es oF inside Frjme-
FIG. 38. DETAILS OF A SWINGING STEEL DOOR. AMERICAN BRIDGE COMPANY.
48
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
"**/]*"
H
Center Bracket-^ "** '
'Corr. Steel — -
r^&j
^At*,
Flashing 8J(
Vr- "»&--
nu»
"2 Carriage Bolt
"V-
\ 1
vvMt
if
$
l*j __
jefel
i
^^ t «1 f
U-.?Z*^I«-.7/''^i /* \
g> b
?^^! I
^
•^
^5$ i
\ ;•> N; i 0 ! i' '•; 1J Section through Track
2^S«J3Si J -1 i \*>i
I
^\
,i .t i ^
— (n^
a s shown ^5
^
^^j-.a ^
N
*-.
2Thickr
and i.
t J Mfe^
4 Bolts-' / \ : Notch Door
/ \
fi*x-s.D'\
\ ^'O ck /
S ^ v J ^\ X
^ S|v& O ^~~^ O | ^<
I
r/^
*
1
" ;~^
/?/<?/(? ^
</$3K>
^ tf
^
^ ^"Slotted r/o/e for
^ Lateral Adjustment
^
•1
^H
1} pair consists of 2 Hangers
v/th Ldteralfic/justment-
\ets and / Center Bracket
'<?jj(?5 ofg"D$H Sheathing laid diagonally
•overedw/th *24 Sheet Steel. NOTE
com
2En
for 8 foot Track- Packed with screws
for Hanger. Track comes in 4, 0, 8, and
10 foot lengths. Furnish 2 Center
Brackets For 10 foot Track.
FIG. 39. DETAILS OF A TRACK FOR A SLIDING DOOR.
CCMM
finished floor Level -s-*f> /•'•? ;J Portland Cement Concrete
FIG. 40. MODIFIED SAW TOOTH ROOF, PAINT SHOP, PUBLIC SERVICE CORPORATION.
A STEEL TRANSFORMER BUILDING.
49
A Steel Transformer Building. — The framework of a steel frame transformer building is shown
in Fig. 41 and Fig. 42. The trusses are Fink trusses with the members made of angles placed
to back. The main columns carrying the roof trusses are made of four angles laced, the
SECT/ON
APX^/AV />v PLANE OF BOTTOM CHORD BRACING IN PLANE OF TOP CHOW
FIG. 41. PLANS OF A TRANSFORMER BUILDING.
section being I-shaped, each flange being composed of two angles placed back to back with the
long legs outstanding, and the web consisting of lacing. The columns in the end of the building
are made of 9 in. I-beams. The main purlins are made of 5 in. channels @ 6J lb., while the girts
5
50
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
ELEVATION'
FIG. 42. PLANS OF A TRANSFORMER BUILDING.
are 4 in. channels @ 5J Ib. The purlins are spaced less than 4 ft. 9 in., which is a maximum spac-
ing where corrugated steel roofing is used without sheathing. The steel framework is braced in
the plane of the top chord and the sides and ends of the building by means of diagonal rods f in.
in diameter. The crane girder beams in the plane of the lower chord brace the building longi-
tudinally, the diagonal bracing being composed of angles.
A STEEL TRANSFORMER BUILDING.
51
60-0* -----------
<
END ELEVATION
"*~J
}./;ji-7'6^^{j^!3i-7/6%J«<-5.}tf^-<9^^^ *g«
U I6-O'- ->*<- - 16'-0*- - H« - -16-0"- ->*< - - 16'-0*- -x*- -/6'-O"- ->|
}< 80-0" >*
5//>5 ELEVATION
FIG. 43. CORRUGATED STEEL PLANS FOR TRANSFORMER BUILDING.
Corrugated, Steel Covering. — The plans for the corrugated steel covering on the roof and sides
are shown in Fig. 43 and Fig. 44. The corrugated steel for the roof is No. 22 gage steel with 2j
in. corrugations, while the corrugated steel for the sides is No. 24 gage steel with 2\ in. corrugations.
The flashing and ridge roll are made of No. 22 flat sheet steel.
52
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Corrugated Steel List for Building
Rectangular Sheets Beveled Sheets as per Sketch
No- J-5-56 Length Marks
55
95
95
56
40
190
48
62
87
7
7
IZ
81
28
87
**
4'-fO
6 ';?>',
9'-6\
?,,$»
4-0"
4'-9'
4 -IO'
5-.Z.
5-3'
5 "-4"
6'-0'
9L 8'
9' -10"
No. U-55-G Length Marks
24-
*
4-5i'
6'-0"
4'- 8"
5'- 4"
2~°",
10'- 0"
8'-8'
7-4"
/ £* IR
2*3
2
2
ZZ«ZR
2*4Z*4R
52* 5R
4*64
4-*!
4*8
Z*/0
2*11
6f?
4*7R
4«8f?
Z*10R
a*iif?
Z*IZR
84 //near/ feet
Rrdae Ro/I-
*?ZF/af5fe<sf.
JOO tinea/ feef
Hashing
55.
etfone coaf Reef least.
Sheets £6" wftfe
/300//n. ft 60 "Pou/ fry Netting- Corrvgaf/ons Z?"
/Corru
t'Fbt//fry Nefftng
METHOD OF FASTENING
STEEL AHD LINING ON ROOF
METHOD OF FASTEN/MS
5TEEL ON THE 5 WE 5
-WireNeffing
-L.wvresAfo.20
•-Steel
FINISH AT COK NEK
LOUVRES
FIG. 44. CORRUGATED STEEL LIST AND DETAILS FOR TRANSFORMER BUILDING.
STEEL FRAME BUILDING WITH PLASTER WALLS.
53
To prevent the condensation of moisture on the inside of the steel roof and the resulting
dripping, anti-condensation lining was used, as is shown in Fig. 44. This lining was constructed as
follows: ( i.ilv.ini/xl wire poultry netting was fastened to one eave purlin, was passed over the ridge,
stivti'hed tight and fastened to the other eave purlin. The edges of the wire were woven together
1>\ inrans of wire clips. On the wire netting was laid two layers of asbestos paper rV in. thick,
and on top of the asbestos was laid two layers of tar paper. The corrugated steel was then laid on
top of the roof in the usual way and was fastened to the purlins by means of long soft iron wire
n.iiU spaced as shown in Fig. 44. To prevent the lining from sagging stove bolts A in. in diam-
i ti-r with I in. X J in. X 4 in. flat washers on the lower side were placed between the purlins.
The author would recommend that the purlins be spaced not to exceed 2 ft. 6 in. and the stove
bolts omitted.
.• ~"r
ZT Concrete— *
Expanded
Metal
I
r r* P * i z
n - — •
JJ C ll 01
|» K S l' 0' »
'^
: »?'-
i
E
£
t /
2 »
I
«
t0 V
•y-O
•
N
m
'?$
M
1
r4
10
i sifC'
S 2k" L
— ra
IV Plaster-'
Expanded.'
Metal '
5tone I8"«i8"«izm
Brick
Concrele
k -37re" i .---••
FIG. 45. STEEL FRAME BUILDING WITH PLASTER WALLS.
Steel Frame Building with Plaster Walls. — The steel frame building shown in Fig. 45 was
svered with expanded metal and plaster walls and roof constructed as follows: The side walls
ere made by fastening f in. channels at 12 in. centers to the steel framework and then covering
lis framework with expanded metal wired on. The expanded metal was then covered on the
Jtside with a coating of cement mortar composed of one part Portland cement and two parts
ind, and on the inside with a gypsum plaster, making the walls about 2 in. thick. The roof con-
sists of a 2\ in. concrete slab reinforced with expanded metal, this slab being covered with 10 in. X
12 in. slate nailed directly to the concrete.
Steam Engineering Building. — Details of a transverse bent of the steam engineering building
at the Brooklyn Navy Yard are given in Fig. 46.
The main columns are spaced 48 ft. centers while the main trusses are spaced 16 ft. centers.
The intermediate trusses are carried on heavy trusses rigidly fastened to the main columns. The
crane girders are carried on crane columns that arc fastened to the main columns by light lacing.
This method of supporting heavy crane girders is the most satisfactory method yet proposed.
The building is well lighted with glass in the side walls, and sky lights in the roof. More than 60
per cent of the area of the external walls and roof is glazed. Many other interesting details can
be obtained from the drawings.
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Skrtefioof
Nailed ft i
FIG. 46. STEAM ENGINEERING BUILDING, BROOKLYN NAVY YARD.
STEEL WINDOWS AND DOORS.
54a
FIG. 47. TYPES OF STEEL WINDOWS.
54d
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
1
i
STEEL WINDOWS AND DOORS.
54e
Details of window sash as taken from the catalogs of the " Fenestra " windows, made by the
troit Steel Products Company, Detroit, Mich.; the " Lupton " windows, made by the David
•Pulley
FixedSash-
ifleeting
\Rails
SlidingSash-
Sill
(c) Vertical 5ection,Counter- . (d) Vertical Section, (e) Horizontal Sect,
weighted W/ndow 2 5a$h High. Horizontal Sliding Sash.
4?£>. (b) Vertical Section, Counter-
''•% balanced Window 2 Sash High, d|f
/"
(a) Vertical Section, Counter-
balanced Window 3 5ash High.,
K
.-,
N£
if 1 &' W ' 3— i
rluHionandJambftSash) /j ,.
-tto//ionarrdJwt>(l5ash) Side and Top Kii/
/•<J v 15" '
-wbzazn—i J!«&~M*-I-
/!" &£a£*&.\
Bottom Rail and Si//
bullion
» A '',
S||
^!
1
...i
i .J;
L£;
-1
fluntirj
Botto/n/foif .fleeting /fails Weathering]
^ { i ' 'r t •"'
J| JL (Bronze Weathering-
1
w /f/'A^ Bron2e ^feathering tlullion with Copper Weathering Meeting Rail (2 Sash)
(f)yert/cal5/iding5ash, Type A. (g) Vertical S/id/ng Sash, Typed. (h) Vertical Sliding Sash, Type C.
FIG. 53. DETAILS OF STEEL SASH.
»( (f) is "Lupton," (g) is " United Steel Sash," and (h) is "Fenestra '"
Lupton Son Company, Philadelphia, and United Steel Sash " made by the Trussed Concrete
Co., Youngstown, Ohio, are shown in Fig. 49 to Fig. 52. While each company uses different
sections the details are essentially the same and may be used interchangeably as far as the
f(
54f
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
designing engineer is concerned. Details of counterbalanced sash, are shown in (a) to (c) and
details of a horizontal sliding sash are shown in (d) and (e), Fig. 53. The details of the sections
used by the different firms may be determined by observing that in Fig. 53 (f) is " Lupton " (g)
is " United Steel Sash," and (h) is "Fenestra." Details of construction, and details of operating
Continuous^ £ 3 I J, <// '**/ ^ttomof
.kJLJ. &}?/ / Storm Pane!
(3) Vertical Section (b) Vertical Section (c)Yert.Sect. Fixed f3ne/.(d)5tormfene/
Top Hung Monitor Sash Continuous Sawtooth Sash Top Hung Monitor 5as/?
= (Fixed Panel For standard s^sh, height ^4',5,'or 6'. Units are
=/ iJtormrane/ designed for ?0' truss spacing. The rar/m5cm/ts,h0ir-
erer, can be combined to fitany/enqth ofro/r. Sfanobrrf
mvnt/'n spacing •= S3 '& 'if. 6/ass width =23$, he/ghc. =
Horiz.5ect. Continuous Top Hung 5ash
End Member, Storm
^i "^ N 3"
Top Supporting i_ _ ^H< 76
Member Interior Vertical fluntin Bottom Member, Storm Panel Endflember
FIG. 54. DETAILS OF "UNITED STEEL SASH" VENTILATORS AND SKYLIGHTS.
devices and hardware can be obtained from the various catalogs. Details of "United Steel Sash''
monitor ventilators and skylights are shown in Fig. 54. Details of "Lupton" monitor ventilators
and skylights are shown in Fig. 55. The details shown in Fig. 54 and Fig. 55 are very complete.
For address of other companies manufacturing steel windows, see Sweet's "Architectural Catalog"
published by Sweet's Catalog Service, New York.
STEEL DOORS. — Steel doors built up out of special steel sections are made by several firms.
Details of "Lupton" tubular steel doors manufactured by David Lupton Sons Company,
STEEL WINDOWS AND DOORS.
54g
liiadelphia, Pa., arc shown in Fig. 56. These doors are hinged to swing one way or slide horizon-
Is . Hie lower part of the door is filled with No. 12 gage steel, while the upper part is commonly
1 with wire glass set in steel sash and steel frames. "Lupton" doors have the frames welded.
Details of "Fenestra" tubular steel doors made by the Detroit Steel Products Company,
troit, Mich., are shown in Fig. 57. The doors are hinged to swing one way, or slide horizontally.
Vertical Section ft
Top Hung Doub/e /fur) Sash
- Fixed --
» Horiz. Sect. Endoffyf). Swing 5ash
*— -Fixed— -;.
Horiz. Sect, [ndoffoft. Fixed Sash
Horn. Sect. Center Hunq Sash.
FIG. 55. DETAILS OF "LUPTON" STEEL MONITOR VENTILATORS AND SKYLIGHTS.
ecial tubular sliding doors can be made 10 ft. wide and 25 ft. high, or with double doors for an
;ning 20 ft. wide and 25 ft. high. " Fenestra " doors have the frames riveted. Steel doors are
made by the Trussed Steel Concrete Company.
Diagrammatic sketches of several types of doors are shown in Fig. 58. These sketches repre-
snt different types of doors shown in the catalog of J. Edward Ogden Co., New York, N. Y. This
>mpany is prepared to furnish door hardware and mechanical parts of the doors shown, or will
apply the doors complete. The following data have been taken from, the Ogden catalog.
54h
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
^
a
A
&
&
T^
t
r.
",
~*
", *'.
I
•>,,
'••
',
( ?•
D
\
\
« #
:.
:
77
'/
'*
''
B\
5
%/'
X_£
SX
1 %
SECTIOH B-B
HORIZOffTAL 5fCTIO/i\^^
hinged doors. Frames^^
should be built in walls. ' ••
Steel Plate \
^-VERTICAL DETAIL ATlnPosr.
a=|!=ffl _
HORIZONTALSECTIOf1,s/iding \
doors. Weathering members \
\idesandconnectionat
'ting stiles
SECTionD-D
VERTICAL SECTION. HORIZOHTAL SECTIOM.
Heavy steel jamb and casing are made for
any tvall thickness.
SECTIOH C-C
Single leaFdoors uptolOFt.w/deby25ft.hiqhdrerr>3de.) Tubeslfx^g" for doors up to4x8'.0thfrsjli*!(3f
TUBULAR STEEL DOOR-TYPE A. TUBULAR STEEL DOOR- TYPEB
FIG. 56. DETAILS OF "LUPTON" TUBULAR STEEL DOORS.
Doors upto
do not requi
UsetiorSt-F&me. To facilitate weathering '.Inside \,
'
^, doors should be hunon
inside oF building. Irout-
side,proper housing For
— -"4}= r^H1- track must be provided.
5lidinqdoors can be
made as large as 7 Ft. wide
by 12 ft high with good
results.
i£VAT/on DOUBLE DOOR
to swing out
-Concrete
! Width of Opening
HORIZONTAL SECTIOH
fL£WT/on DOUBLE DOORS VERTICAL SECTION
*-~CZEQlSE3I2-4r
VERTICAL SECT/OH
DOUBLE DOORS -SIDE HUHG
5/nqle Doors have simi/er details
TO HoRI70fiTAL5fCTIOrf
>\t«-
DOUBLE SLIDING EXTERIOR DOORS
Sinqle Doors have simi/ardetai/s
FIG. 57. DETAILS OF "FENESTRA" TUBULAR STEEL DOORS.
STEEL WINDOWS AND DOORS.
54i
..-—>*.
i(ld)
Two- SECTION DOOR
^ Shelf asm 4 may replace supporting chain
wA"V '/-v/w sy/'/w
tta)
MULTI-SECTION DOOR; 3,4, or £ SECTIONS.
I: vs/A'sss \'M'//M'//.'.'/.»ss/.'//.:w/.'.-6: t:
/x
f; Door may be placed on ovts/de
:of building to pror/de anop/.
^ WT^
SINGLE-SECTION DOOR
SINGLE-SECTION DOOR
(Sa)
_
ly 'I
"Say
@ One-Hal f of daor projects
°T outside to form wdter shed.
TURN-OVER DOOR
CANOPY DOOR
(7*)
t
?•:: ~*
(Ib)
(7d)
\(7c)
T /V^s operated independently
WssSir'r/7?. Ws.WSSSt
DOUBLE-LEAF VERTICAL-SLIDING DOOR
(Sa)
w
(SO
^7.T,r/ r.'.-7s '"'•', •!'•'//? '.'',•/' '.'WS *y,lsflvW£
SINGLE-LEAF VERTICAL-SLIDING DOOR
ffl) i
Doors For passage of "Loao 'i. .•>
- -Doors for passage of load— i ,'•>
CRANERUHWAY DOOR; SWIN6IN6 iNWARb
CRAME RUNWAY DooRS;Sw/N6/N6Ourn'AfiD
58. DIAGRAMMATIC SKETCHES OF DOORS. COMPILED FROM CATALOG OF ]. EDWARD OGDEN
COMPANY.
54j
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
Two-section Doors. — Doors may be made of wood frame with a sheet-steel covering, or with a
steel frame with a sheet-steel covering; the upper section may be glazed with j in. wire glass set in
metal frames. Details of doors 20 ft. wide and 22 ft. high are shown as constructed with wood
frames, and also with steel frames. Counterweights are commonly made equal to one-half the
total weight of the door.
Sorless
\-&y&taaa: •&&%- Sheet Metal' ^ j
(Cement Mortar 'Ppf • '.Cement^rlortaf <
• with -Corbel. =5;
<*&&%>
¥$4''^
xtf
fm&F
MS? *sc/>9s*
/%?7yf5 fly ^ FOR SLOPIH6 ROOFS. ' ,
Extreme Dimensions, ?6x5I'!Expt>sed,24x4£."Th/ckness£t.
Standard pur/in spacing 4'-Q". Spacing can be wriedfry/ff \
3LIO%4ty"5pec;alti/efore3veccurseM%r!f.lfthe]
standard spacing can not be used the short course is -
""
Tiles withl4x24"Mre-g/dssinsetsarefnadeFors/(y//4>ht:5. (
fft/getile, ridge rent/ fetor tile, hip ridge tile, sawtooth ridge
t/le,and flashing tile are made.Metal gutters are used
with standard tilesfcut to fit) in hlpKilley construction.
Tiles require no fastening topurlinsJointsmadenster-tight
with elastic cement. Exposed side of tile isred^nders/Je,
Is white. Minimum pitch of roof is one-Fifth. Safe/oad
pForft'bay.Saqrodsshyse two lines fcrbaysorer/S1. Mebl Thimbie^^t^,
For Downspout)
FIG. 59. DATA FOR "BONANZA" CEMENT TILE.
Single-Section Doors. — Doors may be made with wood frames or with steel frames. Details
of a door 27 ft. 9 in. wide and 19 ft. 6 in high are shown.
STEEL WINDOWS AND DOORS.
54k
Multi-Section Door. — This door is especially adapted for locations where there is little ceiling
space. Doors may be made with wood frames or with steel frames. Details of doors 18 ft. 3 in.
•ide and 22 ft. 2 m. high are shown.
> J-
Arrange pur/ins to suit standard ti/e by spacing 4) Std ' Ridqe
^ purlins 3-$' todW. When necessary, vary faV"n/{ *« Copinq.lengtl)
oer- j ca'u- * tile 24 to 60 /Ofig t&ry/flg
RoofFinishatfndofBldq. ^4*
"0'c.toc.
'
~£ Corrugated Iron
RooffaisrtatfndofBuildirHj
BottomEndof\ !
course above \ <•"••••••'••• •/—v-'---/-"-"/--\
Section of Jointand toll HermeticallySea/ed
with Elastic Cement during Erection
y^ ^/ ^/ Lt....-.f---.f* , ' •
large Ridge Tile and Framing Special Tile showing Method £*^i
of carrying Ventilator 'lller"^
/-, iJboLine oFChannel Purlins
^•Jili-cT'^ -»^. L. «7
/%> Gutter and Framing
.^JifhfbinhFSaddle-^
•^•T^T^a
SectionB-B'
Gutterlileare forfa"^' forf, Standard FlashinqTile with Steel and Hbodtek
''
Dow Spevt " .
High Point oFkddle
Loosefo//-'
' General Arrangement oF Gutter and Supporb
JSIK NOTES OH TILE FOR SLOPING ROOFS
Overall lenqth.52"F.xpoSed,M'x4S'Thickness,i'
FlabSlao^./r Weight.Mlkpersq.ft.lilesper/OOsqft., ffj.
HighfointofSadd/e-a. •&// Standard purlin spacing 4L0" Spacing can be
varied From 3- fto4!0i'5pecial tile for S-0"
f
space at ridge or moator using special tilt Zf'k 60
long myirxfWTi/ewithglassjnset node for
/> t t , n c i- ^Composition sky/ight.Tilesreguire no Fastening to purlins.
0o*n5povt-,r={ CowSpout-^Yl Mninwmpitchofnvfisonf-sMSafe/oad
6utters an'd Yd/leys of Flat Slabs covered with Composition.
FIG. 60. DATA FOR FEDERAL CEMENT TILE.
Turn-Over Door. — This door is used for small openings. There is no operating winch, the door
being operated by hand.
Canopy Door. — This door protects the entrance when open. The minimum headroom above
the door is 16 inches. This is a modification of the single-section door.
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
^Concrete -^ f E/ast/c Cement f,- RooFinqTfle
\
1
i
i J
I
w ^r
Tp
Horizontal Set.
jri:
I *l
-.tionoFWbll
r f
<n
if/or. Joint-}
' YerticalJo/m
i
/ ^Composition Roofing
longitudinal Section oFFIatTile
:JvidthZW,\
Transverse Section of FlatTile
Length5L0"orless. Width?-0'! Thick. £ "
'z. Section Weiqht I6lb./sq. Ft. Reinforcement-?-^
"s bdrshnqitudina//ydndt1o./6£xp.r1etdl.
.
Pur/ins for total load ofM*6<f. ft. 5-O'Tile,
Horizontal Mnt Election Showing Joints Yertical Section /fa?0'-7'h/f*??'*?4'#"Jx/#*
CtMEfiTWALL PLATES MOHITOR END WALLS FLAT CEMENT RMFINGTILE
Standard J-0"\-
Cement Tile ,(jl .
^•'Truss ^^^ ^
Top Plan Book ile
Composition Roofing- -f.
Under side pot/shed
\ lO'-O'L toe. tn/sxsorpur/ins I
Thickness 3','airspdce/j, ,
Min.pitchg. Weight ?5lb./sq. Ft.
fie waterproofinq required.
CEMENT HOLLOW PITCHED TILE
j Weight 25 /k/sq. Ft J
Composition Roofing-
, .tt ^^6'of Jess c.toc. Standard 5'^.
\ J-^i* Thickness 3; Wall
Each course of 5 'tile substituted for4'tile
increases A /W for j pitch, l-ffirj pitch,
RBNFWKfD OWSUMtiMfTlLE. CEttEHT HOLLOW FLAT SLAB
P^C — „ it=r- - -' : •.xr-ftf1"' O.-.F ii|(
WIDTHS OF BUILDING FOR 5TANDAKDTUE ROOF
WHEL Pu/?LIHSFORPmOBA/tTlLEl?00F5
Total Load 50 lb./sq.f {.including WeightjF too f
HarRarters
Total load 50lb.fa.Ft.. fei
jtfkemr 100 sq.ft.
•T-fofterslW*-'"'--71"-
j- \btli M«F 51 1/Sfft.
DETAILS FOR PYWBAR GYPSUM ROOF TILE 5--Purlinspac.M£aremmumtm sections.
5
Truss5pac!nq, Ft.
5
Truss Spacing, Ft.
Ft.
10
12
14
16
IS
20
22
ft
Ft.
10
K
14
16
18
20
H14
2.5
3
3.5
4
4.5
5
4'
4
d
4-
5
5
i"
5
5
5
5
t>
5"
5
6
b
b
1
ff
6
t>
7
7
7
6'
7
7
7
8
8
r
7
S
8
9
9
7"
8
S
3
9
10
f
9
9
10
10
12
5.5
6
b.5
7
7.5
8
5'
5
b
6
b
6
6"
i>
7
7
7
7
7"
7
7
8
8
8
S"
S
8
9
9
9
9"
9
9
IS
IS
10
ff
10
ID
10
10
//
ff'ff
////
1212
1212
1212
I?I5
FIG. 61. DATA FOR FEDERAL CEMENT TILE (UPPER PART), AND DATA FOR PYROBAR GYPSUM
TILE (LOWER PART).
Single-Leaf Vertical-Sliding Door. — These doors require adequate headroom. Details of a
door 8 ft. wide and 8 ft. high are shown. These doors are often placed in pairs, where one counter-
weight and one winch will serve for both doors.
Double-Leaf Vertical-Sliding Doors. — The two sections of these doors are equipped with sep-
arate guides and are operated separately. Details of a door 20 ft. wide and 18 ft. high are shown.
Crane Runway Doors. — These doors may swing inward or outward. The doors may be
STEEL WINDOWS AND DOORS. 54m
operated by the crane operator or from the floor. Additional doors should be provided for the
lo.nl, .iiul for the crane cage where necessary. Folding and sliding doors are also made by the
Kinm'ur Manufacturing Company, Columbus, Ohio.
Rolling Steel Doors. — Rolling steel doors are made by several firms. The J. G. Wilson
Corporation, New York, manufactures rolling steel doors that may be operated by hand with
widths of 3 ft. to 6 ft. and heights of 6 ft. to 14 ft.; widths of 6 ft. to 10 ft. and heights of 13 ft.
to 17 ft.; widths of 10 ft. to 15 ft., and heights of 13 ft. to 15 ft. Doors operated by gear have
heights up to 21 ft. and widths up to 20 ft. The Kinnear Manufacturing Co., Columbus, Ohio,
manufactures rolling steel doors with widths of 3 ft. to 20 ft., and heights of 6 ft. to 18 ft. For
additional details and the names and addresses of other manufacturers of steel doors, see Sweet's
Architectural Catalog, published by Sweet's Catalog Service, New York, N. Y.
CEMENT ROOFING TILE. — Cement tile are made of Portland cement and clean, sharp
sand and are reinforced with steel rods.
Data for "Bonanza" cement tile, manufactured by the American Cement Tile Mfg. Co.,
Pittsburgh, Pa., are given in Fig. 59. The exposed surface of the tile is Indian red in color, while
the underside has a cement finish. The least desirable slope of roof is a pitch of one-fifth. Data
for Federal Cement tile, manufactured by the Federal Cement Tile Co., Chicago, 111., are given in
Fig. 60, and in the upper part of Fig. 61. Cement roofing tile have been very extensively used for
industrial plants. The cement tile have the following advantages: (a) are fire resisting; (b)
require very simple roof construction; (c) require no sheathing; (d) are non-conductors, (e) may
be erected rapidly; (f) the first cost is low for a permanent type of roof; (g) maintenance is low.
Gypsum Roofing Tile. — Gypsum roofing tile made by the United States Gypsum
Company, Chicago, are sold under the trade name of Pyrobar Gypsum Roof Tile. The tile
are 12 in. wide and 30 in. long, and weigh 13 Ib. per sq. ft. Data taken from the catalog for rafters
and purlins for Pyrobar Gypsum Roof Tile are given in the lower part of Fig. 61. Gypsum roof
tile have recently been used on buildings for the Navy Department at Norfolk, Va. The follow-
ing advantages of gypsum roof slabs were given by L. M. Cox, U. S. N., Engineering News, Jan.
25i 1917- (a) Light weight; (b) rapid construction; (c) roof slab is non-conductor and non-con-
densing; (d) is fire resisting; (e) shows few cracks; (f) low cost of maintenance. Gypsum roofing
tile are made by several firms, and are also made at the building site.
STRESSES IN MILL BUILDING COLUMNS CARRYING CRANE LOADS.— The stresses
produced in columns of mill buildings by crane loads eccentrically applied depend upon the method
used in bracing the structure against lateral forces. If the kneebraces are omitted or only very
small kneebraces are used, the columns are practically hinged at the top and the lateral thrust due
to the eccentric crane loads must be carried to the ends of the building by the lateral bracing in the
planes of the chords of the trusses. Proper bracing must then be provided in the end bents.
If rigid kneebraces are provided the columns may be considered as fixed at the top and a
transverse bent may be considered as carrying its load directly to the foundations. The lateral
load will in reality be distributed between the direct path down the columns and the indirect path
along the lateral bracing in the planes of the chords to the end bents. The portion carried by each
route will depend upon the relative rigidity of the routes. Since the transverse bent is much more
rigid than the lateral bracing, all of the load may be considered as carried by the transverse bent.
In Fig. 62 three cases are considered.
Case I. Columns Hinged at Base and Top. — This case is statically determinate. The
lateral thrust is taken by the bracing in the plane of the chords and by the bracing in the end bents.
Case n. Columns Hinged at Base and Fixed at Top. — Columns with constant cross-section. —
The formulas for rigid frames were used, making the ratio of the moment of inertia of the truss to
the moment of inertia of the column equal to infinity. The formula is sufficiently accurate when
this ratio becomes as small as four, and is on the safe side. The distance h is measured to a point
one-half way between the foot of the knee-brace and the top of the column.
Case m. Columns Hinged at the Base and Fixed at Top. Columns with variable cross-
sections. — In this case the column has a different cross-section above and below the attachment
of the crane girder. The formulas for rigid frames were used, making the ratio of the moment of
54n
STEEL ROOF TRUSSES AND MILL BUILDINGS.
inertia of the truss to the moment of inertia of the column equal to infinity. The formula is
sufficiently accurate with a ratio of four and is on the safe side.
Case IV. Columns Fixed at Base and Fixed at Top. — Formulas for Case II and Case III
may be used, the value of h being taken as the distance from the point of contraflexure to a point
midway between the foot of the kneebrace and the top of the column. The point of contraflexure
may be calculated by formula (4), page 556.
Stresses in Rigid Frames. — Formulas for stresses in rigid frames with pin-connected
columns, for different loadings are given in Fig. 63. Formulas for the general case are given
in the second column, while formulas for special- cases are given in the third column. The
formulas are very much simplified where the columns and the top girder have the same moment
of inertia.
CASE I. COLUMNS HINGED AT BASE AND TOP: CONSTANT OR VARIABLE CROSS-SECTION.
A
d
.H'
•Hd
r/fe
H'd-
Pe-'M
CASE 2. COLUMIiSHlHGEDATBASE AfiD FlXED ATTop:C/?05S-5ECTWrt CONSTANT.
CASE 3. COLUMNS HINGED AT BASE AND FIXED ATTOP: CROSS-SECTION VARIABLE.
H
p
i r . ii
i-e
^ h e'J
cf :
Y y
FIG. 62. STRESSES IN MILL BUILDING COLUMNS CARRYING CRANE LOADS.
STEEL WINDOWS AND DOORS.
5-io
GEHERAL CASE
Pat> ksi,h
(2M)' * Tt'l
. i/. Pa
*~
u.
. 3P
. kj,h
' Ttl
OEHERAL CASE
H-wb f6ac±bJ3Hb)l,._Ilh
4 ' tttfk+l) ' 4'Z
TOPFULL Y LOADED; b-l
H-
4h(2k+3)' 1,1
y-v - £?
H V*
GENERAL CASE
frto
T
LOAD'ATB; a=h
"f
y=y=PJ]
"A 'o
M0=Pa-Hh; Hc=-Hh
GENERAL CASE
v-y _w(b'-a2) kj,h
A D~~~n — //
MB=V0l-Hh; Mc=-Hh
5iDE FULLY LoADfD;c=h
H=wh.6±5k
" 3 2k+3
ysy=*!l2- k-1'^
* * 21 ' *l
GfHEKAL CASf.
LOAD OH OHE SIDE-; fio
Me=Pe-Hh; Mc=-
GEHERAL CASE
LOADSATTOPja=h
u-3(Pe+P'e).L_Lh
'
t.eea&;t, {
VA and V0 are the same
as in general case.
For sides, M8=Mc=Hh
GENERAL CASE
H-(P-P')Zkh+3(Pa+PaJ-6Ph
Zh(2k+3)
y-y -Pa-Pa', j I,h
H=P(2kh+3a)
FIG. 63. STRESSES IN RIGID FRAMES.
54p
STEEL ROOF TRUSSES AND MILL BUILDINGS.
STANDARD LAG SCREWS, HOOK BOLTS AND WASHERS.
AMERICAN BRIDGE COMPANY.
LAG SCREWS
Length
Diameter
Diam
B"
16
\
J6
I
9.
16
i
I
Min
Length I
ft"
Ji
fi
/i
2
2
Max-
'.ength
6"
6
8
10
12
12
12
12
12
12
12
12
No-Thread
perinch
5
4
3
Length of Lag
Screw & Head
Length
of Screw of Head
3
3*
4
4i
5
*t
6
7
8
9
10
11
12
Length
1"
'*
2
2i
3
3*
5
5
5
Heads are the same as for square head bolts
Threaded portion is not tapered except at point:
BEAM CLAMP
/ Cored Ho/e
5/ze
Dimensions 0fC/3Mp\ Weight
in Ibs-
18"
15
12
l&B
C
7"
8
D
0-4
0-4
0-4
0-4
0-4
OGEE WASHERS
16 Recess for naif lock •
5ize
Bolt
Dimensions of Washer
A B C D £ R r
ff
H
4
4
II"
16
73
1£>
J/
32
31
5"
Weight
in Pounds
0-4
0-7
1-0
SKEWBACK WASHERS
Used
With
Dimensions of Washers
M
H
4"
If
fi
i*.
'4
2
D
I"
/
/
R
4%
Weight
if? Pounds
1-2
1'8
2-5
2-7
3-0
ftooK BOLTS, % or? .
V
In biffing Hook Bolts give dimensions A,
5 &L; all other dimensions are standard-
Unless otherwise specified, 5" will
be made "- Hex- nuts furnished-
CAST/ROff CUP
54
GENERAL SPECIFICATIONS FOR STEEL FRAME BUILDINGS.*
BY
MILO S. KETCHUM,
M. Am. Soc. C. E.
THIRD EDITION.
1914.
GENERAL DESCRIPTION.
1. Height of Building. — The height of the building shall be the distance from the top of the
masonry to the under side of the bottom chord of the truss.
2. Dimensions of Building. — The width and length of the building shall be the extreme dis-
tance out to out of framing or sheathing.
3. Length of Span. — The length of trusses and girders in calculating stresses shall be con-
sidered as the distance from center to center of end bearings when supported, and from end to
end when fastened between columns by connection angles.
4. Pitch of Roof. — The pitch of roof for corrugated steel shall preferably be not less than
J (6 in. in 12 in.), and in no case less than £. For a pitch less than £ some other covering than
corrugated steel shall be used.
5. Spacing of Trusses. — Trusses shall be spaced so that simple shapes may be used for
purlins. The spacing should be about 1 6 ft. for spans of, say, 50 ft. and about 20 to 22 ft. for
spans of, say, 100 ft. For longer spans than 100 ft. the purlins may be trussed and the spacing
may be increased.
6. Spacing of Purlins. — Purlins shall be spaced not to exceed 4 ft. 9 in. where corrugated
steel is used, and shall be placed at panel points of the trusses.
7. Form of Trusses. — The trusses shall preferably be of the Fink type with panels so sub-
divided that panel points will come under the purlins. If it is not practicable to place the purlins
at panel points, the upper chords of the trusses shall be designed to take both the flexural and
direct stresses. Trusses shall preferably be riveted trusses.
Trusses supported on masonry walls shall have one end supported on sliding plates for spans
up to 70 ft., for greater lengths of span rollers or a rocker shall be used. No rollers with a
diameter less than 3 in. shall be used.
All field connections of the steel framework shall be riveted except the connections for purlins
and girts, which may be field bolted.
8. Bracing. — Bracing in the plane of the lower chords shall be stiff; bracing in the planes of
the top chords, the sides and the ends may be made adjustable.
9. Proposals. — Contractors in submitting proposals shall furnish complete stress sheets,
general plans of the proposed structures giving sizes of material, and such detail plans as will
clearly show the dimensions of the parts, modes of construction and sectional areas.
10. Detail Plans. — The successful contractor shall furnish all working drawings required by
the engineer free of cost. Working drawings will, as far as possible, be made on standard size
sheets 24 in. X 36 in. out to out, 22 in. X 34 in. inside the inner border lines.
11. Approval of Plans. — No work shall be commenced or materials ordered until the working
drawings are approved in writing by the engineer. The contractor shall be responsible for dimen-
sions and details on the working plans, and the approval of the detail plans by the engineer will
not relieve the contractor of this responsibility.
•
LOADS.
12. The trusses shall be designed to carry the following loads:
13. DEAD LOADS. Weight of Trusses. — The weight of trusses per sq. ft. of horizontal
projection, up to 150 ft. span shall be calculated by the formula
where W = weight of trusses per sq. ft. of horizontal projection;
P = capacity of truss in pounds per sq. ft. of horizontal projection;
L = span of the truss in feet;
A = distance between trusses in feet.
* Reprinted from the author's " The Design of Steel Mill Buildings."
55
56 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
14. Weight of Covering. Corrugated Steel. — The weight of corrugated steel shall be taken
from Table I.
When two corrugations side lap and six in. end lap are used, add 25 per cent to the above
weights; when one corrugation side lap and four in. end lap are used, add 15 per cent to the above
weights to obtain weight of corrugated steel laid. For paint add 2 Ib. per square. The weight
of covering shall be reduced to weight per sq. ft. of horizontal projection before combining with
the weight of trusses.
15. Slate. — Slate laid with 3 in. lap shall be taken at a weight of 1\ Ib. per sq. ft. of inclined
roof surface for ^ in. slate 6 in. X 12 in., and 6£ Ib. per sq. ft. of inclined roof surface for ^ in.
slate 12 in. X 24 in., and proportionately for other sizes.
16. Tile. — Terra-cotta tile roofing weighs about 6 Ib. per sq. ft. for tile I in. thick; the actual
weight of tile and other roof coverings not named shall be used.
17. Sheathing and Purlins. — Sheathing of dry pine lumber shall be assumed to weigh 3 Ib.
per ft. and dry oak purlins 4 Ib. per ft. board measure.
1 8. Miscellaneous Loads. — The exact weight of sheathing, purlins, bracing, ventilators,
cranes, etc., shall be calculated.
19. SNOW LOADS. — Snow loads shall be taken from the diagram in Fig. i.
20. WIND LOADS. — The normal wind pressure on trusses shall be computed by Duch-
emin's formula, Fig. 3, with P = 30 Ib. per sq. ft., except for buildings in exposed locations,
where P = 40 Ib. per sq. ft. shall be used.
21. The sides and ends of buildings shall be computed for a normal wind load of 20 Ib. per
sq. ft. of exposed surface for buildings 30 ft. and less to the eaves; 30 Ib. per sq. ft. of exposed
surface for buildings 60 ft. to the eaves, and in proportion for intermediate heights.
22. Mine Buildings. — Mine, smelter and other buildings exposed to the action of corrosive
gases shall have their dead loads increased 25 per cent.
23. Concentrated Loads. — Concentrated loads and crane girders shall be considered in
determining dead loads.
24. Purlins. — Purlins shall be designed to carry the actual weight of the covering, roofing
and purlins, but shall always be designed for a normal load of not less than 30 Ib. per sq. ft.
25. Girts. — Girts shall be designed for a normal load of not less than 25 Ib. per sq. ft.
26. Roof Covering. — Roof covering shall be designed for a normal load of not less than 30
Ib. per sq. ft.
27. Minimum Loads. — No roof shall, however, be designed for an equivalent load of less
than 30 Ib. per sq. ft. of horizontal projection.
28. Loads on Foundations. — The loads on foundations shall not exceed the following in
tons per sq. ft. :
Ordinary clay and dry sand mixed with clay 2
Dry sand and dry clay 3
Hard clay and firm coarse sand 4
Firm coarse sand and gravel 5
Shale rock 8
Hard rock 20
For all soils inferior to the above, such as loam, etc., never more than one ton per sq. ft.
29. Stresses in Masonry. — The allowable stresses in masonry shall not exceed the following:
Tons per Sq. Ft. Lb. per Sq. In.
Common brick, Portland cement mortar 12 168
Hard burned brick, Portland cement mortar 15 210
Rubble masonry, Portland cement mortar 10 140
First class masonry, crystalline sandstone or limestone 25 350
First class masonry, granite 30 420
Portland cement concrete, 1-3-5 2O 280
Portland cement concrete, 1-2-4 3° 42°
30. Pressures on Masonry. — The pressure of column bases, beams, etc., on masonry shall
not exceed the following in pounds per sq. in.
Brick work with cement mortar 250
Rubble masonry with cement mortar 250
Portland cement concrete, 1-2-4 500
First class dimension sandstone or limestone 400
First class granite 500
SPECIFICATIONS. 57
31. Loads on Timber Piles. — The maximum load carried by a pile shall not exceed 40,000
lb., or 600 lb. per sq. in. of its average cross-section. The allowable load on piles driven with a
drop hammer shall be determined by the formula P = - - . Where P = safe load on pile
in tons; W = weight of hammer in tons; h = free fall of hammer in ft.; s = average penetration
for the last six blows of the hammer in in. Where a steam hammer is used, tV '8 to be used in
place of unity in the denominator of the right hand member of the formula.
Piles shall have a penetration of not less than 10 ft. in hard material, such as gravel, and not
less than 15 ft. in loam or soft material.
PROPORTION OF PARTS.
32. Allowable Stresses. — In proportioning the different parts of the structure the maximum
stresses due to the combinations of the dead and wind load; dead and snow load; or dead, minimum
snow and wind load are to be provided for. Concentrated loads where they occur must be pro-
vided for.
33. Tensile Stress. — Allowable Unit Tensile Stresses for Structural Steel. For direct dead,
snow and wind loads.
Lb. per Sq. In.
Shapes, main members, net section 16,000
Bars 16,000
Bottom flanges of rolled beams 16,000
Shapes, laterals, net section 20,000
Iron rods for laterals 20,000
Plate girder webs, shear on net section 10,000
Shapes liable to sudden loading as when used for crane girders 10,000
Expansion rollers per lineal inch 600 X d
where d — diameter of roller in inches.
Laterals shall be designed for the maximum stresses due to 5,000 pounds initial tension and
the maximum stress due to wind.
34. Compressive Stress. — Allowable Unit Compressive Stress for Structural Steel. For
direct dead, snow and wind loads
S = 16,000 — 70 -
where S = allowable unit stress in lb. per sq. in;
/ = length of member in inches c. to c. of end connections;
r = least radius of gyration of the member in inches.
35. Plate Girders. — Top flanges of plate girders shall have the same gross area as the tension
flanges.
36. Shear in webs of plate girders shall not exceed 10,000 lb. per sq. in. of net section.
^ 37. Alternate Stress. — Members and connections subject to alternate stresses shall be
designed to take each kind of stress.
38. Combined Stress. — Members subject to combined direct and bending stresses shall be
proportioned according to the following formula:
^S=P- + -
re 5 = stress in lb. per sq. in. in extreme fiber;
P = direct load in lb.;
A = area of member in sq. in.;
Af = bending moment in in-lb.;
yi = distance from neutral axis to extreme fiber in inches;
/ = moment of inertia of member;
/ = length member, or distance from point of zero moment to end of member in inches;
E = modulus of elasticity = 30,000,000. lb. per sq. in.
When combined direct and flexural stress due to wind is considered, 50 per cent may be
added to the above allowable tensile and Compressive stresses.
39 Stress Due to Weight of Member. — Where the stress due to the weight of the member or
due to an eccentric load exceeds the allowable stress for direct loads by more than 10 per cent, the
section shall be increased until the total stress does not exceed the above allowable stress for
t loads by more than 10 per cent.
ioE
58
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
The eccentric stress caused by connecting angles by one leg when used as ties or struts shall
be calculated, or only one leg will be considered effective.
40. Rivets. — Rivets shall be so spaced that the shearing stress shall not exceed 11,000 Ib.
per sq. in.; nor the pressure on the bearing surface (diameter X thickness of piece) of the rivet
hole exceed 22,000 Ib. per sq. in.
Rivets in lateral connections may have stresses 25 per cent in excess of the above.
Field rivets shall be spaced for stresses two-thirds those allowed for shop rivets.
Field bolts, when allowed, shall be spaced for stresses two-thirds those allowed for field
rivets.
Rivets and field bolts must not be used in direct tension. Where it is necessary that con-
nections take tension turned bolts shall be used.
41. Pins.— Pins shall be proportioned so that the shearing stress shall not exceed 11,000 Ib.
per sq. in.; nor the pressure on the bearing surface (diameter X thickness of piece) of the pin
hole exceed 22,000 Ib. per sq. in.; nor the extreme fiber stress due to cross bending exceed 24,000
Ib. per sq. in. when the applied forces are assumed as acting at the center of the members.
42. Plate Girders. — Plate girders shall be proportioned by the moment of inertia of their
net section or on the assumption that | of the gross area of the web is available as flange area,
and the shear is resisted by the web. The distance between centers of gravity of the flange areas
shall be considered as the effective depth of the girder.
43. Web Stiffeners. — The web of plate girders shall have stiffeners at the ends and inner
edges of bearing plates, and at points of concentrated loads, and also at intermediate points where
the thickness of the web is less than ^fo.of the unsupported distance between flange angles, not
farther apart than the depth of the full web plate with a maximum limit of 5 ft. Stiffeners shall
be designed as columns for a length equal to one-half the depth of the girder. Stiffener angles
must have enough rivets to properly transmit the shear.
44. Compression flanges of plate girders shall have at least the same sectional area as the
tension flanges, and shall not have a stress per sq. in. on the gross area greater than 16,000 — 150 r ,
where / = unsupported distance, and b = width of flange, both in inches. Compression flanges
of plate girders shall be stayed transversely when their length is more than thirty times their
width.
45. Rolled Beams. — Rolled beams shall be proportioned by their moment of inertia. The
depth of rolled beams in floors shall not be less than -fa of the span. Where rolled beams or
channels are used as roof purlins the depths shall not be less than -fa of the span.
46. Timber. — The allowable stresses in timber purlins and other timber shall be taken from
the following table.
ALLOWABLE WORKING UNIT STRESSES IN TIMBER, IN POUNDS PER SQUARE INCH.
Kind of Timber.
Trans-
verse
Loading,
S.
End
Bear-
ing.
Columns
Under 10
Diam-
eters, C.
Bearing
Across
Fiber.
Shear.
Modulus of
Elasticity,
£.
Parallel
to Grain.
Longitu-
dinal
Shear in
Beams.
White Oak
,20O
,300
,OOO
,OOO
,2OO
I,20O
I,3OO
I,OOO
I, COO
1,200
I,OOO
I, COO
800
800
1,000
45°
300
2OO
2OO
35°
2OO
1 80
IOO
160
1 80
no
1 2O
70
IOO
no
I,I5O,OOO
I,6lO,OOO
1,130,000
1,480,000
I,5IO,OOO
Long Leaf Yellow Pine. . .
White Pine and Spruce. . .
Western Hemlock
Douglass Fir
Columns may be used with a length not exceeding 45 times the least dimension. The unit
stress for lengths of more than 10 times the least dimension shall be reduced by the following
formula:
p = c-±i
ioo a
where C = unit stress, as given above for short columns;
P = allowable unit stress in Ib. per sq. in. ;
/ = length of column in inches;
d = least side of column in inches.
SPECIFICATIONS. 59
COVERING.
47. Corrugated Steel.-yCorrugated steel shall generally have 2$ in. corrugations when used
for roof and sides of buildings, and li in. corrugations when used for lining buildings. The
minimum gage of corrugated steel shall be No. 22 for roofs, No. 24 for sides, and No. 26 for lining.
The gage of corrugated steel in U. S. standard gage and weight per sq. ft. shall be shown
on the general plan.
48. Spacing Purlins and Girts. — The span, or center to center distance of purlins, shall not
rxrivd the distance given in Fig. 18 for a safe load of 30 Ib. per sq. ft. Corrugated steel sheets
shall preferably span two purlin spaces. Girts shall be spaced for a safe load of 25 Ib. per sq. ft.
in Fig. 1 8.
49. End and Side Laps. — Corrugated steel shall be laid with two corrugations side lap and
six inches end lap when used for roofing, and one corrugation side lap and four inches end lap
when used for siding.
50. Fastening. — Corrugated steel shall be fastened to the purlins and girts by means of
galvanized iron straps J in. wide by No. 1 8 gage, spaced 8 to 12 in. apart; by clinch nails spaced
8 to 12 in. apart; or by nailing directly to spiking strips with 8d barbed nails, spaced 8 in. apart.
Spiking strips shall preferably be used with anti-condensation lining. Bolts, nails and rivets
shall always pass through the top of corrugations. Side laps shall be riveted with copper or
galvanized iron rivets 8 to 12 in. apart on the roof and I J to 2 ft. apart on the sides.
51. Corrugated Steel Lining. — Corrugated steel lining on the sides shall be laid with one
corrugation side lap and four in. end lap. Girts for corrugated steel lining shall be spaced for a
safe load of 25 Ib. per sq. ft. as given in Fig. 18.
52. Anti-condensation Lining. — Anti-condensation roof lining shall be used to prevent
dripping in engine houses and similar buildings, and shall be constructed as follows: Galvanized
wire poultry netting is fastened to one eave purlin and is passed over the ridge, stretched tight
and fastened to the other eave purlin. The edges of the wire are woven together and the netting
is fastened to the spiking strips, where used, by means of small staples. On the netting are laid
two layers of asbestos paper ^ in. thick and two layers of tar paper. The corrugated steel is
then fastened to the purlins in the usual way; ^ in. stove bolts with I in. X i in. plate washers
on the lower side are used for fastening the side laps together and for supporting the lining; or
the purlins may be spaced one-half the usual distance where anti-condensation lining is used and
the stove bolts omitted.
53. Flashing. — Valleys or corners around stacks shall have flashing extending at least 12 in.
above where water will stand, and shall be riveted or soldered, if necessary, to prevent leakage.
4 Flashing shall be provided above doors and windows.
'54. Ridge Roll. — All ridges shall have a ridge roll securely fastened to the corrugated steel.
55. Corner Finish. — All corners shall be covered with standard corner finish securely fastened
to the corrugated steel.
56. Cornice. — At the gable ends the corrugated steel on the roof shall be securely fastened to a
finish angle or channel connected to the end of the purlins, or, where molded cornices are used,
to a piece of timber fastened to the ends of the purlins.
57. Gutters. — Gutters and conductors shall be furnished at least equal to the requirements
of the following table:
Span of Roof. Gutter. Conductor.
Up to 50 ft. 6 in. 4 in. every 40 ft.
50 ft. to 70 ft. 7 in. 5 in. every 40 ft.
70 ft. to 100 ft. 8 in. 5 in. every 40 ft.
Gutters shall have a slope of at least i in. in 15 ft. Gutters and conductors shall be made
of galvanized steel not lighter than No. 24.
58. Ventilators. — Ventilators shall be provided and located so as to properly ventilate the
building. They shall have a net opening for each 100 sq. ft. of floor space as follows: not less
than one-fourth sq. ft. for clean machine shops and similar buildings; not less than one sq. ft.
for dirty machine shops; not less than four sq. ft. for mills; and not less than six sq. ft. for forge
shops, foundries and smelters.
59. Shutters and Louvres. — Openings in ventilators shall be provided with shutters, sash,
or louvres, or may be left open as specified.
Shutters must be provided with a satisfactory device for opening and closing.
Louvres must be designed to prevent the blowing in of rain and snow, and must be made
stiff so that no appreciable sagging will occur. They shall be made of not less than No. 20 gage
galvanized steel for flat louvres, and No. 24 gage galvanized steel for corrugated louvres.
60. Circular Ventilators. — Circular ventilators, when used, must be designed so as to prevent
down drafts. Net opening only shall be used in calculations.
60 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
61. Windows. — Windows shall be provided in the exterior walls equal to not less than 10 per
cent of the entire exterior surface in mill buildings, and of not less than 25 per cent in machine
shops, factories, washeries, concentrators, breakers and similar buildings.
Window glass up to 12. in. X 14 in. may be single strength, over 12 in. X 14 in. the glass
shall be double strength. Window glass shall be A grade except in smelters, foundries, forge
shops and similar structures, where it may be B grade. The sash and frames shall be constructed
of white pine. Where buildings are exposed to fire hazard the windows shall have wire glass set
in metal sash and frames.
62. Skylights. — At least half of the lighting shall preferably be by means of skylights, or
sash in the sides of ventilators.
Skylights shall be glazed with wire glass, or wjre netting shall be stretched beneath the
skylights to prevent the broken glass from falling into the building. Where there is danger of
the skylight glass being broken by objects falling on it, a wire netting guard shall be provided
on the outside.
Skylight glass shall be carefully set, special care being used to prevent leakage. Leakage
and condensation on the inner surface of the glass shall be carried to the down-spouts, or outside
the building by condensation gutters.
63. Windows in sides of buildings shall be made with counterbalanced sash, and in venti-
lators shall be made with sliding or swing sash. All swinging windows shall be provided with a
satisfactory operating device.
64. Doors. — Doors are to be furnished as specified and are to be provided with hinges, tracks,
locks and bolts. Single doors up to 4 ft. and double doors up to 8 ft. shall preferably be swung
on hinges; large doors, double and single, shall be arranged to slide on overhead tracks, or may be
counterbalanced to lift up between vertical guides.
Steel doors shall be firmly braced and shall be covered with No. 24 corrugated steel with I J
in. corrugations.
The frames of sandwich doors shall be made of two layers of f in. matched white pine, placed
diagonally, and firmly nailed with clinch nails. The frame shall be covered on each side with a
layer of No. 26 corrugated steel with ij in. corrugations. Locks and all other necessary hard-
ware shall be furnished for all windows and doors.
(Sections 65 to 77 cover specifications for tar and gravel roofing and concrete and wood floors
which have already been given.)
DETAILS OF CONSTRUCTION.
78. Details. — All connections and details shall be of sufficient strength to develop the full
strength of the member.
79. Pitch of Rivets. — The pitch of rivets shall not exceed 6 in., or sixteen times the thickness
of the thinnest outside plate in the line of stress, nor forty times the thickness of the thinnest
outside plate at right angles to the line of stress. The pitch shall never be less than three diameters
of rivet. At the ends of compression members the pitch shall not exceed four diameters of the
rivet for a length equal to twice the width of the member.
80. Edge Distance. — The minimum distance from the center of any rivet hole to a sheared
edge shall be i£ in. for £ in. rivets, i j in. for f in. rivets, i| in. for f in. rivets, and I in. for 5 in.
rivets, and to a rolled edge i}, i|, i and f in., respectively. The maximum distance from the
edge shall be eight (8) times the thickness of the plate.
81. Maximum Diameter. — The diameter of the rivets in angles carrying calculated stresses
shall not exceed j of the width of the leg in which they are driven, except that f in. rivets may
be used in 2 in. angles.
82. Diameter of Punch and Die. — The diameter of the punch and die shall be as specified
in § 147.
83. Net Sections. — The effective diameter of a driven rivet will be assumed the same as
its diameter before driving. In deducting the rivet holes to obtain net sections in tension members,
the diameter of the rivet holes will be assumed as | inch larger than the undriven rivet.
84. Minimum Sections. — No metal of less thickness than ? in. shall be used except for
fillers; and no angles less than 2" X 2" X i". The minimum thickness of metal in head frames,
rock nouses and coal tipples, coal washers and coal breakers shall be j^ in., except for fillers.
No upset rod shall be less than f in. in diameter. Sag rods may be as small as f in. diameter.
85. Connections. — All connections shall be of sufficient strength to develop the full strength
of the member. No connections except for lacing bars shall have less than two rivets. All field
connections except lacing bars shall have not less than three rivets.
86. Flange Plates. — The flange plates of all girders shall not extend beyond the outer line
of rivets connecting them to the angles more than 6 in. nor more than eight times the thickness
of the thinnest plate.
SPECIFICATIONS. 61
87. Web Stiffeners. — Web stiffeners shall be in pairs, and shall have a close fit against flange
angles. The stiffeners at the ends of plate girders shall have filler plates. Intermediate stiffeners
may have fillers or be crimped over the flange angles. The rivet pitch in stiffeners shall not be
greater than 5 in.
88. Web Splices. — Web plates shall be spliced at all points by a plate on each side of the
wi-li, capable of transmitting the shearing and bending stresses through the splice rivets.
89. Net Sections. — Net sections must be used in calculating tension members and in deducting
the rivet holes they shall be taken i in. larger than the nominal size of rivet.
90. Pin connected riveted tension members shall have a net section through the pin hole
25 per cent in excess of the required net section of the member. The net section back of the
pin hole in line of the center of the pin shall be at least 0.75 of the net section through the pin
hole.
91. Upset Rods. — All rods with screw ends, except sag rods, must be upset at the ends so that
the diameter at the base of the threads shall be & inch larger than any part of the body of the bar.
92. Upper Chords. — Upper chords of trusses shall have symmetrical cross-sections, and shall
preferably consist of two angles back to back.
93. Compression Members. — All other compression members for roof trusses, except sub-
struts, shall be composed of sections symmetrically placed. Sub-struts may consist of a single
section.
94. Columns. — Side posts which take flexure shall preferably be composed of 4 angles laced,
or 4 angles and a plate. Where side posts do not take flexure and carry heavy loads they shall
preferably be composed of two channels laced, or of two channels with a center diaphragm.
95. Posts in end framing shall preferably be composed of I-beams or 4 angles laced. Corner
columns shall preferably be composed of one angle.
96. Crane Posts. — The cross-bending stress due to eccentric loading in columns carrying
cranes shall be calculated. Crane girders carrying heavy cranes shall be carried on independent
columns.
97. Batten Plates. — Laced compression members shall be stayed at the ends by batten
plates, placed as near the end of the member as practicable and having a length not less than the
greatest width of the member. The thickness of batten plates shall not be less than -fa of the
distance between rivet lines at right angles to axis of member.
98. Lacing. — Single lacing bars shall have a thickness of not less than fa, and double bars
connected by a rivet at the intersection of not less than fa of the distance between the rivets
connecting them to the member; they shall make an angle not less than 45 degrees with the axis
the member; their width shall be in accordance with the following standards, generally:
Size of Member. . Width of Lacing Bare.
For 15 in. channels, or built sections with 3$ and 4 in. angles.. .2j inches (| in. rivets).
For 12, 10 and 9 in. channels, or built sections with 3 in. angles. . .2} inches (J in. rivets).
For 8 and 7 in. channels, or built sections with 2\ in. angles.. . .2 inches (f in. rivets).
For 6 and 5 in. channels, or built sections with 2 in. angles i \ inches (i in. rivets).
I Where laced members are subjected to bending, the size of lacing bars or angles shall be cal-
lated, or a solid web plate shall be used.
99. Pin Plates. — All pin holes shall be reinforced by additional material when necessary, so
as not to exceed the allowable pressure on the pins. These reinforcing plates must contain enough
rivets to transfer the proportion of pressure which comes upon them, and at least one plate on
each side shall extend not less than 6 in. beyond the edge of the batten plate.
100. Maximum Length of Compression Members. — No compression member shall have a
length exceeding 125 times its least radius of gyration for main members, nor 150 times its least
radius of gyration for laterals and sub-members. The length of a main tension member in which
the stress is reversed by wind shall not exceed 150 times its least radius of gyration.
101. Maximum Length of Tension Members. — The length of riveted tension members^ in
horizontal or inclined position shall not exceed 200 times their radius of gyration except for wind
bracing, which members may have a length equal to 250 times the least radius of gyration. The
horizontal projection of the unsupported portion of the member is to be considered the effective
length.
102. Splices. — In compression members joints with abutting faces planed shall be placed as
near the panel points as possible, and must be spliced on all sides with at least two rows of rivrts
on each side of the joint. Joints with abutting faces not planed must be fully spliced.
103. Splices. — Joints in tension members shall be fully spliced.
104. Tension Members.— Tension members shall preferably be composed of angles
shapes capable of taking compression as well as tension. Flats riveted at the ends shall not I
used.
62
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
105. Main tension members shall preferably be made of 2 angles, 2 angles and a plate, or 2
channels laced. Secondary tension members may be made of a single shape.
106. Eye-Bars. — Heads of eye-bars shall be so proportioned as to develop the full strength
of the bar. The heads shall be forged and not welded.
107. Pins. — Pins must be turned true to size and straight, and must be driven to place by
means of pilot nuts.
The diameter of pin shall not be less than f of the depth of the widest bar attached to it.
The several members attached to a pin shall be packed so as to produce the least bending
moment on the pin, and all vacant spaces must be filled with steel or cast iron fillers.
1 08. Bars or Rods. — Long laterals may be made of bars with clevis or sleeve nut adjustment.
Bent loops shall not be used.
109. Spacing Trusses. — Trusses shall preferably be spaced so as to allow the use of single
pieces of rolled sections for purlins. Trussed purlins shall be avoided if possible.
no. Purlins and Girts. — Purlins and girts shall preferably be composed of single sections —
channels, angles or Z-bars, placed with web at right angles to the trusses and posts and legs turned
down.
in. Fastening. — Purlins and girts shall be attached to the top chord of trusses and to columns
by means of angle clips with two rivets in each leg.
112. Spacing. — Purlins for corrugated steel without sheathing shall be spaced at distances
apart not to exceed the span as given for a safe load of 30 lb., and girts for a safe load of 25 Ib.
as given in Fig. 18.
113. Timber Purlins. — Timber purlins and girts shall be attached and spaced the same as
steel purlins.
114. Base Plates. — Base plates shall never be less than f in. in thickness, and shall be of
sufficient thickness and size so that the pressure on the masonry shall not exceed the allowable
pressures in § 30.
115. Anchors. — Columns shall be anchored to the foundations by means of two anchor
bolts not less than i in. in diameter upset, placed as wide apart as practicable in the plane of the
wind. The anchorage shall be calculated to resist one and one-half times the bending moment
at the base of the columns.
1 1 6. Lateral Bracing. — Lateral bracing shall be provided in the plane of the top and bottom
chords, sides and ends; knee braces in the transverse bents; and sway bracing wherever necessary.
Lateral bracing shall be designed for an initial stress of 5,000 lb. in each member, and provision
must be made for putting this initial stress into the members in erecting.
117. Temperature. — Variations in temperature to the extent of 150 degrees F. shall be
provided for. •
MATERIAL AND WORKMANSHIP.
MATERIAL.
1 1 8. Process of Manufacture. — Steel shall be made by the open-hearth process.
1 19. Schedule of Requirements.
Chemical and Physical
Properties.
Structural Steel.
Rivet Steel.
Steel Castings.
r>i. i. -\/s / Basic.. .
Phosphorus Max. < A • j
Sulphur maximum
0.04 per cent
0.08 " "
0.05 " "
0.04 per cent
0.04 " "
0.04 " "
0.05 per cent
0.08 " "
0.05 " "
Ultimate tensile strength
Pounds per square inch
Desired
60,000
1,500,000*
Desired
50,000
1,500,000
Not less than
65,000
Elongation: min. % in 2". . .
Character of fracture
Ult. tensile strength
22
Silky
Ult. tensile strength
Silky
18
Silky or fine granular
Cold bends without fracture.
180° flatf
180° flatj
90°, d = 3*
The yield point, as indicated by the drop of beam, shall be recorded in the test reports.
* See paragraph 128.
t See paragraphs 129, 130 and 131.
j See paragraph 132.
SPECIFICATIONS. 63
1 20. Allowable Variations. — If the ultimate strength varies more than 4,000 Ib. from that
<lrMinl, a rrtrst shall be made on the same gage, which, to be acceptable, shall be within 5,000
Ib. of thr (Irsircd ultimate.
121. Chemical Analyses. — Chemical determinations of the percentages of carbon, phos-
phorus, sulphur and manganese shall be made by the manufacturer from a test ingot taken at
thr time of the pouring of each melt of steel and a correct copy of such analysis shall be furnished
to the t ni;iiH t r or his inspector. Check analyses shall be made from finished material, if called
for by the purchaser, in which case an excess of 25 per cent above the required limits will be
allowed.
122. Form of Specimens. PLATES, SHAPES AND BARS. — Specimens for tensile and bending
tests for plates, shapes and bars shall be made by cutting coupons from the finished product,
which shall have both faces rolled and both edges milled to the form shown by Fig. I ; or with
both edges parallel; or they may be turned to a diameter of J in. for a length of at least 9 in.,
with enlarged ends.
• 123. RIVETS. — Rivet rods shall be tested as rolled.
124. PINS AND ROLLERS. — Specimens shall be cut from the finished rolled or forged bar, in
such manner that the center of the specimen shall be I in. from the surface of the bar. The
specimen for tensile test shall be turned to the form shown by Fig. 2. The specimen for bending
test shall be i in. by J in. in section.
i*"- ! Not less than o" „!
I i-y i yiu !
-About 18"-
FlG. I.
Abjom a"
FIG. 2.
125. STEEL CASTINGS. — The number of tests will depend on the character and importance
of the castings. Specimens shall be cut cold from coupons molded and cast on some portion of
one or more castings from each melt or from the sink heads, if the heads are of sufficient size.
" ie coupon or sink head, so used, shall be annealed with the casting before it is cut off. Test
imens shall be of the form prescribed for pins and rollers.
126. Annealed Specimens. — Material which is to be used without annealing or further
treatment shall be tested in the condition in which it comes from the rolls. When material is to
be annealed or otherwise treated before use, the specimens for tensile tests representing such
material shall be cut from properly annealed or similarly treated short lengths of the full section
of the bar.
127. Number of Tests. — At least one tensile and one bending test shall be made from each
melt of steel as rolled. In case steel differing f in. and more in thickness is rolled from one melt,
a test shall be made from the thickest and thinnest material rolled.
128. Modifications in Elongation. — For material less than fV m- a°d more than | in. in
thickness the following modifications will be allowed in the requirements for elongation:
(a) For each tV in. in thickness below & in., a deduction of 2\ per cent will be allowed from
the specified elongation.
(6) For each \ in. in thickness above } in., a deduction of i per cent will be allowed from
the specified elongation.
(c) For pins and rollers over 3 in. in diameter the elongation in 8 in. may be 5 per cent less
than that specified in paragraph 1 19.
129. Bending Tests. — Bending tests may be made by pressure or by blows. Plates, shapes
and bars less than i in. thick shall bend as called for in paragraph 1 19.
64
STEEL ROOF TRUSSES AND MILL BUILDINGS.
CHAP. I.
130. Thick Material. — Full-sized material for eye-bars and other steel i in. thick and over,
tested as rolled, shall bend cold 180 degrees around a pin the diameter of which is equal to twice
the thickness of the bar, without fracture on the outside of bend.
131. Bending Angles. — Angles f in. and less in thickness shall open flat and angles | in. and
less in thickness shall bend shut, cold, under blows of a hammer, without sign of fracture. This
test will be made only when required by the inspector.
132. Nicked Bends. — Rivet steel, when nicked and bent around a bar of the same diameter
as the rivet rod, shall give a gradual break and a fine, silky, uniform fracture.
133. Finish. — Finished material shall be free from injurious seams, flaws, cracks, defective
edges, or other defects, and have a smooth, uniform, workmanlike finish. Plates 36 in. in width
and under shall have rolled edges.
134 Stamping. — Every finished piece of steel shall have the melt number and the name of
the manufacturer stamped or rolled upon it. Steel for pins and rollers shall be stamped on the
end. Rivet and lattice steel and other small parts may be bundled with the above marks on an
attached metal tag.
135. Defective Material. — Material which, subsequent to the above tests at the mills, and
its acceptance there, develops weak spots, brittleness, cracks or other imperfections, or is found
to have injurious defects, will be rejected at the shop and shall be replaced by the manufacturer
at his own cost.
136. Allowable Variation in Weight. — A variation in cross-section or weight of each piece of
steel of more than 2| per cent from that specified will be sufficient cause for rejection, except in
case of sheared plates, which will be covered by the following permissible variations, which are to
apply to single plates.
137. When Ordered to Weight. — Plates I2| Ib. per square foot or heavier:
(a) Up to 100 in. wide, 2| per cent below or above the prescribed weight.
PLATES J INCH AND OVER IN THICKNESS.
Thickness
Ordered, in.
Nominal
Weight, Ib.
Width of Plate.
Up to 75 in.
75 in. and up to
100 in.
100 in. and up to
115 in.
Over 115 in.
'~4<
5-i6
3~8*
7-16
1-2
9-l6
5-8
Over 5-8
I0.2O
12.75
I5-30
17.85
20.40
22.95
25-SO
IO p
8
7
6
5»
4
3*
er ce
nt
14 p
12
IO
8
fa
6
5
sr ce
nt
18 p
16
13
IO
9
81
8
6£
er ce
nt
17 per
13
12 '
II '
10 '
9 '
:ent
PLATES UNDER \ INCH IN THICKNESS.
Thickness
Ordered, in.
Nominal Weights
Ib. per sq. ft.
Width of Plate.
Up to 50 in.
50 in. and up to
70 in.
Over 70 in.
1-8 up to 5-32
5-32 " " 3-16
3-16 " " 1-4
5. 10 to 6.37
6.37 " 7-65
7.65 " 10.20
10 per cent
8J " "
~ « "
15 per cent
12! " "
10 " "
20 per cent
17 " "
IS " "
(6) One hundred in. wide and over, 5 per cent above or below.
138. Plates under 12 1 Ib. per sq. ft.:
(a) Up to 75 in. wide, 2§ per cent above or below.
(&) Seventy-five in. and up to 100 in. wide, 5 per cent above or 3 per cent below.
(c) One hundred in. wide and over, 10 per cent above or 3 per cent below.
139. When Ordered to Gage. — Plates will be accepted if they measure not more than .01
in. below the ordered thickness.
140. An excess over the nominal weight, corresponding to the dimensions on the order,
will be allowed for each plate, if not more than that shown in the preceding tables, one cubic inch
of rolled steel being assumed to weigh 0.2833 Mb.
SPECIFICATIONS. (>")
SPECIAL METALS.
141. Cast-iron. — Except where chilled iron is specified, castings shall be made of tough gray
iron, with sulphur not over o.io per cent. They shall be true to pattern, out of wind and free
from llaws and excessive shrinkage. If tests are demanded they shall be made on the " Arbitra-
tion M.i r " of the American Society for Testing Materials, which is a round bar, I J in. in diameter
and 15 in. long. The transverse test shall be on a supported length of 12 in. with load at middle.
The minimum breaking load so applied shall be 2,900 lb., with a deflection of at least fa in. before
rupture.
142. Wrought-Iron Bars. — Wrought-iron shall be double-rolled, tough, fibrous and uniform
in character. It shall be thoroughly welded in rolling and be free from surface defects. When
1 in specimens of the form of Fig. I, or in full-sized pieces of the same length, it shall show
an ultimate strength of at least 50,000 lb. per sq. in., an elongation of at least 18 per cent in 8 in.,
with fracture wholly fibrous. Specimens shall bend cold, with the fiber through 135°, without
sign of fracture, around a pin the diameter of which is not over twice the thickness of the piece
ted. When nicked and bent the fracture shall show at least 90 per cent fibrous.
WORKMANSHIP.
143. General. — All parts forming a structure shall be built in accordance with approved
drawings. The workmanship and finish shall be equal to the best practice in modern bridge
works.
144. Straightening Material. — Material shall be thoroughly straightened in the shop, by
methods that will not injure it, before being laid off or worked in any way.
145. Finish. — Shearing shall be neatly and accurately done and all portions of the work
exposed to view neatly finished.
146. Rivets. — The size of rivets, called for on the plans, shall be understood to mean the
actual size of the cold rivet before heating.
147. Rivet Holes. — When general reaming is not required, the diameter of the punch for
material not over f in. thick shall be not more than fa in., nor that of the die more than J in. larger
than the diameter of the rivet. The diameter of the die shall not exceed that of the punch by
iore than i the thickness of the metal punched.
148. Planing and Reaming. — In medium steel over f of an in. thick, all sheared edges shall
planed and all holes shall be drilled or reamed to a diameter of f of an in. larger than the punched
holes, so as to remove all the sheared surface of the metal. Steel which does not satisfy the
drifting test must have holes drilled.
149. Punching. — Punching shall be accurately done. Slight inaccuracy in the matching of
les may be corrected with reamers. Drifting to enlarge unfair holes will not be allowed. Poor
tching of holes will be cause for rejection by the inspector.
150. Assembling. — Riveted members shall have all parts well pinned up and firmly drawn
ether with bolts before riveting is commenced. Contact surfaces to be painted (see § 182).
151. Lacing Bars. — Lacing bars shall have neatly rounded ends, unless otherwise called for.
152. Web Stiffeners. — Stiff eners shall fit neatly between flanges of girders. Where tight
ts are called for the ends of the stiffeners shall be faced and shall be brought to a true contact
aring with the flange angles.
153. Splice Plates and Fillers. — Web splice plates and fillers under stiffeners shall be cut to
t within i in. of flange angles.
154. Web Plates. — Web plates of girders, which have no cover plates, shall be flush with
e backs of angles or be not more than \ in. scant, unless otherwise called for. When web plates
spliced, not more than i in. clearance between ends of plates will be allowed.
I55- Connection Angles. — Connection angles for girders shall be flush with each other and
rrect as to position and length of girder. In case milling is required after riveting, the removal
more than fa in. from their thickness will be cause for rejection.
156. Riveting. — Rivets shall be driven by pressure tools wherever possible. Pneumatic
mmers shall be used in preference to hand driving.
157. Rivets shall look neat and finished, with heads of approved shape, full and of equal size.
iey shall be central on shank and grip the assembled pieces firmly. Recupping and calking
ill not be allowed. Loose, burned or otherwise defective rivets shall be cut out and replaced,
n cutting out rivets great care shall be taken not to injure the adjacent metal. If necessary
" iev shall be drilled out.
158. Turned Bolts. — Wherever bolts are used in place of rivets which transmit shear, the
holes shall be reamed parallel and the bolts turned to a driving fit. A washer not less than i in.
thick shall be used under nut.
159. Members to be Straight. — The several pieces forming one built member shall be straight
and fit closely together, and finished members shall be free from twists, bends or open joints.
6
66 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
160. Finish of Joints. — Abutting joints shall be cut or dressed true and straight and fitted
close together, especially where open to view. In compression joints depending on contact
bearing the surfaces shall be truly faced, so as to have even bearings after they are riveted up
complete and when perfectly aligned.
161. Field Connections. — All holes for field rivets in splices in tension members carrying
live loads shall be accurately drilled to an iron templet or reamed while the connecting parts are
temporarily put together.
162. Eye-Bars. — Eye-bars shall be straight and true to size, and shall be free from twists,
folds in the neck or head, or any other defect. Heads shall be made by upsetting, rolling or forg-
ing. Welding will not be allowed. The form of heads will be determined by the dies in use at
the works where the eye-bars are made, if satisfactory to the engineer, but the manufacturer shall
guarantee the bars to break in the body with a silky fracture, when tested to rupture. The
thickness of head and neck shall not vary more than TJ- in. from the thickness of the bar.
163. Boring Eye-Bars. — Before boring, each eye-bar shall be properly annealed and carefully
straightened. Pin holes shall be in the center line of bars and in the center of heads. Bars of the
same length shall be bored so accurately that, when placed together, pins -^ in. smaller in diam-
eter than the pin holes can be passed through the holes at both ends of the bars at the same
time.
164. Pin Holes. — Pin holes shall be bored true to gage, smooth and straight; at right angles
to the axis of the member and parallel to each other, unless otherwise called for. Wherever pos-
sible, the boring shall be done after the member is riveted up.
165. The distance center to center of pin holes shall be correct within -£$ in., and the diameter
of the hole not more than -fa in. larger than that of the pin, for pins up to 5 in. diameter, and -£% in.
for larger pins.
1 66. Pins and Rollers. — Pins and rollers shall be accurately turned to gage and shall be
straight and smooth and entirely free from flaws.
167. Pilot Nuts and Field Rivets. — At least one pilot and one driving nut shall be furnished
for each size of pin for each structure; and field rivets 15 per cent plus 10 rivets in excess of
the number of each size actually required.
1 68. Screw Threads. — Screw threads shall make tight fits in the nuts and shall be U. S.
standard, except above the diameter of if in., when they shall be made with six threads per in.
169. Annealing. — Steel, except in minor details, which has been partially heated shall be
properly annealed.
170. Steel Castings. — All steel castings shall be annealed.
171. Welds. — Welds in steel will not be allowed.
172. Bed Plates. — Expansion bed plates shall be planed true and smooth. Cast wall plates
shall be planed top and bottom. The cut of the planing tool shall correspond with the direction
of expansion.
173. Shipping Details. — Pins, nuts, bolts, rivets, and other small details shall be boxed or
crated.
174. Weight. — The weight of every piece and box shall be marked on it in plain figures.
175. Finished Weight. — Payment for pound price contracts shall be by scale weight. No
allowance over 2 per cent of the actual total weight of the structure as computed from the shop
plans will be allowed for excess weight.
ADDITIONAL SPECIFICATIONS WHEN GENERAL REAMING AND PLANING ARE REQUIRED.
176. Planing Edges. — Sheared edges and ends shall be planed off at least J in.
177. Reaming. — Punched holes shall be made with a punch j^ in. smaller in diameter than
the nominal size of the rivets and shall be reamed to a finished diameter of not more than YS in-
larger than the rivet.
178. Reaming after Assembling. — Wherever practicable, reaming shall be done after the
pieces forming one built member have been assembled and firmly bolted together. If necessary
to take the pieces apart for shipping and handling, the respective pieces reamed together shall be
so marked that they may be reassembled in the same position in the final setting up. No inter-
change of reamed parts will be allowed.
179. Removing Burrs. — The burrs on all reamed holes shall be removed by a tool counter-
sinking about ik in.
TIMBER.
1 80. Timber. — The timber shall be strictly first-class spruce, white pine, Douglas fir, Southern
yellow pine, or white oak timber; sawed true and out of wind, full size, free from wind shakes,
large or loose knots, decayed or sapwood, wormholes or other defects impairing its strength or
durability.
SPECIFICATIONS. 67
PAINTING.
181. Painting. — All steel work before leaving the shop shall be thoroughly cleaned from all
loose scale and rust, and be given one good coating of pure boiled linseed oil or paint as specified,
\vrll worked into all joints and open spaces.
182. In riveted work, the surfaces coming in contact shall each be painted (with paint)
bffure being riveted together.
183. Pieces and parts which are not accessible for painting after erection shall have two
coats 01 paint.
184. The paint shall be a good quality of red lead or graphite paint, ground with pure linseed
oil, or such paint as may be specified in the contract.
185. After the structure is erected the iron work shall be thoroughly and evenly painted
with two additional coats of paint, mixed with pure linseed oil, of such quality and color as may
selected. Painting shall be done only when the surface of the metal is perfectly dry. No
lint ing shall be done in wet or freezing weather unless special precautions are taken. The two
jld coats of paint shall be of different colors.
1 86. Machine finished surfaces shall be coated with white lead and tallow before shipment
before being put out into the open air.
INSPECTION AND TESTING AT MILL AND THE SHOPS.
187. The manufacturer shall furnish all facilities for inspecting and testing weight and the
quality of workmanship at the mill or shop where material is fabricated. He shall furnish a
suitable testing machine for testing full-sized members if required.
1 88. Mill Orders. — The engineer shall be furnished with complete copies of mill orders, and
no materials shall be ordered nor any work done before he has been notified as to where the orders
have been placed so that he may arrange for the inspection.
189. Shop Plans. — The engineer shall be furnished with approved complete shop plans, and
must be notified well in advance of the start of the work in the shop in order that he may have an
inspector on hand to inspect the material and workmanship.
190. Shipping Invoices.— Complete copies of shipping invoices shall be furnished the engineer
with each shipment.
191. The engineer's inspector shall have full access, at all times, to all parts of the mill or
lop where material under his inspection is being fabricated.
192. The inspector shall stamp each piece accepted with a private mark. Any piece not so
marked may be rejected at any time, and at any stage of the work. If the inspector, through an
oversight or otherwise, has accepted material or work which is defective or contrary to the speci-
fications, this material, no matter in what stage of completion, may be rejected by the engineer.
193. Full Size Tests. — Full size tests of any finished member shall be tested at the manu-
facturer's expense, and shall be paid for by the purchaser at the contract price less the scrap value,
if the tests are satisfactory. If the tests are not satisfactory the material will not be paid for and
the members represented by the tested member may be rejected.
ERECTION.
194. Tools. — The contractor shall furnish at his own expense all necessary tools, staging and
material of every description required for the erection of the work, and shall remove the same
when the work is completed.
All field connections in the trusses and framework shall be riveted. Connections of purlins
and girts may be bolted.
195. Risks. — The contractor shall assume all risks from storms or accidents, unless caused
by the negligence of the owner, and all damage to adjoining property and to persons until the
work is completed and accepted.
196. The contractor shall comply with all ordinances or regulations appertaining to the
work.
197. The erection shall be carried forward with diligence and shall be completed promptly.
68 STEEL ROOF TRUSSES AND MILL BUILDINGS. CHAP. I.
REFERENCES. — For data on windows and glazing; paints and painting; foundations, and
additional data and examples of roof trusses and steel mill buildings, see the author's " The
Design of Steel Mill Buildings." This book also contains a full treatment of algebraic and graphic
statics; and the calculation of stresses in simple framed structures, in the transverse bent, the
two-hinged arch, etc.; also contains 24 problems in algebraic and graphic statics illustrating the
methods of calculating the stresses in roof trusses and other framed structures.
CHAPTER II.
STEEL OFFICE BUILDINGS.
Skeleton Construction. — Skeleton construction is a building where all external and internal
loads and stresses are transferred from the top of the building to the foundations by a skeleton or
framework of steel or reinforced concrete. In steel skeleton construction the framework con-
sists of columns, floorbeams, girders, trusses, and diagonal and transverse bracing. The steel
trusses have riveted connections and all connections in the steel framework should be riveted.
Fire Resisting Construction. — To protect the structural steel from fire the framework is
covered with materials that are slow heat conducting or "fireproof material." The steel frame-
work may be fireproofed with reinforced concrete, brick, tiles of burnt clay, or terra cotta. The
windows on exposed sides and elevator enclosures are glazed with wire glass set in metal frames or
are protected with fire shutters. Doors and other exposed openings are protected with fire doors
or shutters. The interior finish, doors, etc. should be of metal and every precaution should be
taken to prevent the spread of fire. Reinforced concrete fireproofing is usually made of the
following thickness: For columns, trusses, girders or other very important members at least 2
inches of concrete outside of the metal reinforcement ; for ordinary beams or long span floor slabs
or arches, I \ inches of concrete outside of the reinforcement, and for short span floor arches and
slabs, partitions and walls at least I inch outside the metal reinforcement. Fireproofing of brick,
tile or terra cotta is usually made with a thickness of not less than 4 inches for columns and the
main framework. Metal flanges should be protected with not less than 2 inches of fireproofing
at any point.
TABLE I.
WEIGHTS OF BUILDING MATERIALS, ETC.
POUNDS PER CUBIC FOOT.
[ Material.
Weight.
Material.
Weight.
Brick, pressed and paving
ICQ
Hemlock
2C,
" common building
1 2O
\Vhite pine
2C,
" soft building
ICO
30
Granite
1 70
Yellow pine
4.O
Marble
I7O
\Vhite oak
1O
Limestone
160
Mortar
IOO
Sandstone . .
ICO
Stone concrete
ISO
Cinders
4.O
no
Slag
l6o-l8o
Common brick work
IOO-I2O
Granulated furnace slag
e-i
Rubble masonry, sandstone
I^O-IIO
Gravel
1 2O
limestone
I4O
Slate
I7C
granite
IS°
Sand, clay and earth (dry)
IOO
Ashlar sandstone
140-1 qo
" " " " (moist)
1 2O
limestone
ICO
Coal ashes
AC
granite
165
Paving asphaltum
IOO
Cast iron
4. co
Plaster of Paris
HO
Wrought iron
480
Glass
160
Steel
400
Water
62*
Lead
711
Snow freshly fallen
Copper rolled
490
" packed
12
Brass
523
" wet
co
Plaster, ceiling 10 to 15 Ib. per sq. ft. .
Spruce
2C
70
STEEL OFFICE BUILDINGS.
CHAP. II.
For details and data on fireproofing and fireproofing materials, see Freitag's "Fire Prevention
and Fire Protection," and Kidder's "Architects and Builders Pocket Book."
LOADS. — The loads coming on office buildings may be grouped under the following headings:
(i) dead loads; (2) live loads; (3) wind loads; (4) snow loads; (5) miscellaneous loads.
Dead Load. — The "dead load" includes the weight of the structure, and other permanent
fixtures and machines. A formula for the weight of roof trusses is given in Chapter I. The
weights of materials are given in Table I. The actual weights of all dead loads should be calcu-
lated. The minimum weight of a fireproof floor should be taken at not less than 75 Ib. per sq. ft.
of floor surface. In office buildings a minimum of 10 Ib. per sq. ft. should be added for movable
partitions.
WEIGHT OF STEEL IN TALL BUILDINGS.— The weight of the steel framework for tall
steel buildings varies with the height, the column spacing, the floor loads and other conditions.
The weights of steel per cubic foot for several tall steel buildings are given in Table II. In calcu-
lating the weight per cubic foot only the part of the building above the curb was considered.
TABLE II.
WEIGHT OF STEEL IN TALL BUILDINGS, POUNDS PER CUBIC FOOT.
Building.
Plan
Sq. Ft.
Height.
Weight of
Steel, Lb.
per Cu. Ft.
Reference.
Stories.
Ft.
307
543
220
775
580
309
176
I4S
Park Row Building, New York. .
Hotel Astor (addition), New
York
15,000
21,306
9,018
3,952
13,231
31,000
42,686
5,000
S5,ooo
39,5oo
94,000
7,500
26
9
39
18
13
55
7
12
25
10
12
3-6
2.6
3-i
2.6
2-3
3A
3-6
2.1
2.8
2.0
3-o
2.8
Eng. News, Oct. 8, 1896
Eng. Record, Oct. 14, 1911
Eng. Record, Feb. n, 1911
Eng. Record, April i, 1911
Eng. Record, May 27, 1911
Eng. Record, May 27, 1911
Eng. News, July 27, 1911
Eng. News, July 25, 1912
Eng. Record, May 11, 1912
Eng. Record, Mar. 30, 1912
Eng. Record, July 9, 1910
Designed by the author
Banker's Trust Building. New
York
Underwood Building, New York .
Hotel Rector, New York
Woolworth Building, New York.
Municipal Building, New York. .
Poole Bros. Printing, Chicago.. .
Merchants & Mfgs. Exchange,
New York
Hotel McAlpin, New York
Curtis Building, Philadelphia . . .
Office Building, Denver
Live Loads. — The live loads on floors are commonly given in pounds per square foot. The
minimum live loads in pounds per square foot as required by the buildings laws of several cities
are given in Table III.
Mr. C. C. Schneider, M. Am. Soc. C. E., in his "General Specifications for Structural Work of
Buildings" gives the following requirements for live loads on floors.
"Table IV gives the 'live' load on floors, to be assumed for different classes of buildings.
These loads consist of: (a) A uniform load per square foot of floor area; (b) A concentrated
load which shall be applied to any point of the floor; (c) A uniform load per linear foot for girders.
The maximum result is to be used in calculations. The specified concentrated loads shall also
apply to the floor construction between the beams for a length of 5 ft."
LIVE LOADS.
71
TABLE III.
FLOORS AND ROOFS.
MINIMUM LIVE LOADS, POUNDS PER SQUARE FOOT.
By Building Laws of Various Cities.
American Bridge Company.
Kind of Building.
§ •*
*3 HI
2 o>
*"*
New York.
1006.
•32
•o o,
rt M
n
iS
3
OS
Pittsburgh,
1913-
(Proposed.)
cti M
|s
fi
u
Jf .
3 O
•33
35
San Fran-
cisco, 1910.
Apartments
50
100
125
60
70
60
50
50
80
IOO
80
IOO
40
60
60
Public Rooms* and Halls . ....
Assembly Halls
90
1 20
125
125
IOO
125
75
125
125
Fixed Seat Auditoriums .
75
125
75
IOO
IOO
IOO
IOO
Movable Seat Auditoriums
Churches
90
125
ISO
150
150
125
5°
Dance Halls
200
2OO
20O
150
Drill Rooms
Riding Schools
Theaters
T
60
75
60
IOO
40
'2s
60
Dwellings
50
IOO
50
70
40
60
Public Rooms*
Hotels
60
70
60
70
50
5°
60
IOO
60
First Floors
Corridors
80
80
Office Floors
IOO
IOO
125
Public Rooms*
Manufacturing
1 20
120
1 20
150
125
I2S
125
IOO
125
Light Factories '. . .
150
Mercantile
Heavy Storehouses
150
150
1 20
150
IOO
250
125
200
125
2OO
70
2OO
125
250
125
250
60
150
Retail Stores
125
250
IOO
IOO
IOO
IOO
5°
150
150
70
.150
Warehouses
ISO
75
150
Offices
75
150
60
First Floor
Corridors
IOO
60
80
200
80
Schools (Class Rooms)
60
125
75
90
300
75
75
70
70
40
75
IOO
75
125
150
75
Assembly Rooms — Halls
Sidewalks
200
IOO
Stables — Carriage Houses
IOO
40
IOO
Area less than 500 sq. ft
Stairways and Landings
70
70
40
80
80
40
40
30||
Fire Escapes
Roofs — Flatt
5°
30
3°
30||
40
20
3°
50}
5°§
5o§
25
25
25
40
30
20
Horizontal Projection Steep Roofs
Superficial Surface
Wind Pressure .
30
20
3°
2O
* Area greater than 500 square feet,
f First Floors 200.
J Slopes less than 20 degrees.
§ Dead and live, except for one story steel frame buildings, corrugated iron roofs, 35 pounds.
|| High Buildings, built up districts, 35 pounds; 14 stories or over, 25 pounds at tenth story, z\
pounds less each story below.
Figures for manufacturing establishments do not include machinery.
72
STEEL OFFICE BUILDINGS.
TABLE IV.
TABLE OF LIVE LOADS, SCHNEIDER'S SPECIFICATIONS.
CHAP. II.
Classes of Buildings.
Live Loads in Pounds.
Distributed
Load.
Concentrated
Load.
Load per
Linear Ft. of
Girder.
Dwellings, hotels, apartment-houses, dormitories, hos-
pitals
40
50
60
80
Floor ico
Columns 50
80
300
from 1 20 up
" 300 "
" 200 "
2 OOO
5 ooo
5 ooo
5 ooo
Y 5 ooo
8 ooo
10 ooo
Special
u
C The actu
1 engines, bo
-j etc., shall b<
no case less
[ per sq. ft.
500
I 000
I OOO
I OOO
I OOO
I OOO
I OOO
Special
n
al weights of
ilers, stacks,
: used, but in
than 200 Ib.
Office buildings, upper stories
Schoolrooms, theater galleries, churches
Ground floors of office buildings, corridors and stairs in
public buildings
Assembly rooms, main floors of theaters, ballrooms, f
gymnasia, or any room likely to be used for drilling •<
or dancing (_
Ordinary stores and light manufacturing, stables and
carriage-houses
Sidewalks in front of buildings
Warehouses and factories
Charging floors for foundries
Power houses, for uncovered floors
"If heavy concentrations, like safes, armatures, or special machinery, are likely to occur on
floors, provision should be made for them. For structures carrying traveling machinery, such
as cranes, conveyors, etc., 25 per cent shall be added to the stresses resulting from such live load,
to provide for the effects of impact and vibration.'-'
Mr. Schneider's method for live loads is the most rational method yet proposed. In the
design of floor slabs when using this method the author has used an equivalent distributed load
equal to twice the distributed loads in Table IV, and has omitted the concentrated load and load
per lineal foot of girders.
The floor loads on warehouses and the recommended floor loads per sq. ft. have been tabu-
lated by the American Bridge Company in Table V.
Wind Loads. — The wind loads required by different cities are given in Table III.
Schneider's specifications for wind load are as follows:
"The wind pressure shall be assumed as acting in any direction horizontally: First. — At 20
Ib. per sq. ft. on the sides and ends of buildings and on the actually exposed surface, or the vertical
projection of roofs; Second. — At 30 Ib. per sq. ft. on the total exposed surfaces of all parts com-
posing the metal framework. The framework shall be considered an independent structure,
without walls, partitions or floors."
Additional data on wind loads are given in Chapter I.
Snow Loads. — The snow loads on roofs are given in Fig. I, Chapter I.
Schneider's specifications require "A snow load of 25 Ib. per sq. ft. of horizontal projection
of the roof for all slopes up to 20 degrees; this load to be decreased I Ib. for every degree of increase
of slope up to 45 degrees, above which no snow load is to be considered. The above snow loads
are minimum values for localities, where snow is likely to occur. In severe climates these snow
loads should be increased in accordance with the actual conditions existing in these localities."
FLOOR LOADS.
73
HOU
y.
.i>i
>' 9 wu
w^ 3 a
_J rt ^3
« g P !£
"• 8 J
c
u
M
HEff 3
$5 £
•8(5?(2E,2
Weights
per
Cubic Foo
of Space,
Pounds.
"8.- -
W
a X
eco
Liv
|8*g1
fwl
Weights
per
Cubic Foo
of Space,
Pounds.
•00 1O O «0 JJ">O °5 MO WO O OOOOO I^.«to0 QOOO u» 25^J °S"
l^tM lO'f tOfO^t M M«CO«>-'fOC1flM«(O«'OfTr «OM« C1tO>i
• « • 10 to <O toiO-OO *tv><O<O « (OO M ro^-fO oooooo OOO
lO'fwMMOO
to >-l >rt d >O <« O 00 00 « 00 fO O t^ fl O O t- W>O«
-
c <->•» K Oi.b S.h.ts 3 SJ3 3 >> e c
8 5 8 % 2 « *
« TJ -3 0,^5 a «
OOO'tMOOOOOOOOfOiflvOOOO
N rf >o Mrot»O^t**'O<'>O»OMOON
fOfOWfOfOrOMWfONPOf*)MNfOCt«
••O Tj-O MO OOO O O OOO «
OvOO O >O 1^ t M "> •* 'tO ffl
?°
HI (1
eo <o oo co o 10 10 u>« v> v>oo >o lO'C oo o
«oooo oooooooooooo oooo 1000 <ooo ao -oooo
O 00 fO Ol <O Tf O 00 00 *O O 00 V) fO M >/>00
-1
MUUU
74
STEEL OFFICE BUILDINGS.
CHAP. II.
Minimum Roof Loads. — Schneider's specifications contain the following:
" In climates corresponding to that of New York, ordinary roofs, up to 80 ft. span, shall be
proportioned to carry the minimum loads in Table VI, per square foot of exposed surface, applied
vertically, to provide for dead, wind and snow loads combined:
TABLE VI.
MINIMUM LOADS ON ROOFS.
( On boards, flat slope, i to 6, or less 50 Ib.
Gravel or Composition Roofing j On boards, steep slope, more than I to 6 45
I On 3-in. flat tile or cinder concrete 60
Corrugated sheeting, on boards or purlins 40
ci t f On boards or purlins 50
{ On 3-in. flat tile or cinder concrete .*. . 65
Tile, on steel purlins 55
Glass 45
"For roofs in climates where no snow is likely to occur, reduce the foregoing loads by 10 Ib.
per sq. ft., but no roof or any part thereof shall be designed for less than 40 Ib. per sq. ft."
LIVE LOADS ON COLUMNS. — Schneider's specifications require that:
"For columns, the specified uniform live loads per square foot, Table IV, shall be used,
with a minimum of 20,000 Ib. per column.
"For columns carrying more than five floors, these live loads may be reduced as follows:
"For columns supporting the roof and top floor, no reduction;
"For columns supporting each succeeding floor, a reduction of 5 per cent of the total live
load may be made until 50 per cent is reached, which reduced load shall be used for the columns
supporting all remaining floors."
The Chicago Building Ordinance (1911) requires that live loads on walls, columns and piers
be taken as follows:
" (a) The full live load (see Table III) on roofs of all buildings shall be taken on walls, piers,
and columns.
" (b) The walls, piers and columns of all buildings shall be designed to carry the full dead
loads and not less than the proportion of the live load given in Table VII.
TABLE VII.
PERCENTAGE OF LIVE LOAD FOR COLUMNS.
Chicago Building Ordinance (1911).
Floor . .
16.
IS-
H-
13-
12.
II.
IO.
9-
8.
7-
6.
5-
4-
3-
2.
I.
17 16 15 14 13 12 ii
5
85 per cent
80 85
75 80 85
70 75 80 85
65 70 75 80 85
60 65 70 75 80 85
55 60 65 70 75 80 85
50 55 60 65 70 75 80 85
50 50 55 60 65 70 75 80 85
50 50 50 55 60 65 70 75 80 85
50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 50 50 50 50 55 60 65 70 75 80 85
50 50 50 50 50 50 50 50 50 50 55 60 65 70 75 80 85
" (c) The proportion of the live load on walls, piers, and columns on buildings more than
seventeen stories in height shall be taken in same ratio as the above table.
" (d) The entire dead load and the percentage of live load on basement columns, piers and
Walls shall be taken in determining the stress in foundations."
FOUNDATIONS.
75
,
LOADS. ON FOUNDATIONS. — Schneider's specifications require that:
"The live loads on columns shall be assumed to be the same as for the footings of columns.
The areas of the bases of the columns shall be proportioned for the dead load only. That founda-
tion which receives the largest ratio of live to dead load shall be selected and proportioned for the
combined dead and live loads. The dead load on this foundation shall be divided by the area
thus found and this reduced pressure per square foot shall be the permissible working pressure to
be used for the dead load for all foundations."
PRESSURE ON FOUNDATIONS. — The following allowable pressures may be used in
the absence of definite data. No important structure should be built without the making of
careful tests of the bearing power of the soil upon which it is to rest.
The loads on foundations should not exceed the following in tons per square foot:
Ordinary clay and dry sand mixed with clay 2
Dry sand and dry clay . , 3
Hard clay and firm, coarse sand 4
Firm, coarse sand and gravel 5
Shale rock 8
Hard rock 20
"or all soils inferior to the above, such as loam, etc., never more than one ton per square foot.
The Chicago Building Ordinance (1911) requires that:
" (a) If the soil is a layer of pure clay at least fifteen feet thick, without admixture of any
foreign substance other than gravel it shall not be loaded to exceed 3,500 Ib. per sq. ft. If the
soil is a layer of pure clay at least fifteen feet thick and is dry and thoroughly compressed, it may be
loaded not to exceed 4,500 Ib. per sq. ft.
" (b) If the soil is a layer of firm sand fifteen feet or more in thickness, and without admixture
of clay, loam or other foreign substance, it shall not be loaded to exceed 5,000 Ib. per sq. ft.
" (c) If the soil is a mixture of clay and sand, it shall not be loaded to exceed 3,000 Ib. per
sq. ft.
"Foundations shall in all cases extend at least four feet below the surface of the ground
upon which they are built, unless footings rest on bed rock."
. PRESSURE ON MASONRY. — The allowable stresses in masonry and pressures of beams,
girders, column bases, etc. on masonry as given in Table VIII represent good practice.
TABLE VIII.
ALLOWABLE STRESSES IN MASONRY AND PRESSURES OF BEARING PLATES.
Kind of Masonry.
Safe Stresses in
Masonry, Lb. per
Sq. In.
Safe Pressures of Walls,
Plates and Columns on
Masonry, Lb. per Sq. In.
Common Brick, Portland Cement Mortar
I7O
2CO
Hard burned brick, Portland Cement Mortar
Rubble Masonry, Portland Cement Mortar
210
1 7O
300
2 SO
First Class Masonry, Sandstone
280
•JCQ
First Class Masonry, Crystallized Sandstone
4.OO
>3
6OO
First Class Masonry, Limestone
1OO
COO
First Class Masonry, Granite
4.OO
600
Portland Cement Concrete, 1-2-4
4.OO
600
Portland Cement Concrete, 1-3-5
1OO
4.OO
BEARING POWER OF PILES.— The maximum load carried by a pile should not exceed
40,000 Ib. Piles should be driven not less than 10 ft. in hard material, nor less than 20 ft. in soft
material if the pile is to be loaded to full bearing. The safe load should not exceed that given by
the Engineering News formula (i), Chapter XIV.
THICKNESS OF WALLS.— The minimum thickness of curtain walls in steel skeleton
buildings should be 12 in. for brick or concrete and 8 in. for reinforced concrete.
76
STEEL OFFICE BUILDINGS.
CHAP. II.
Schneider's specifications give the following empirical rule for calculating the. thickness of
walls in buildings several stories in height.
"The minimum thickness of walls will be given by the formula
t = L/4 + (Hi + H2 + - • • + Hn)/6
where / = minimum thickness of wall in inches, L = unsupported length in feet, which shall be
assumed as not less than 24 ft. ; and Hi, H2, H3, etc. the heights of stories in feet beginning at the
top. Cellar walls are to be 4 in. thicker than the first story walls."
The Chicago Building Ordinance (1911) contains the following:
" (a) Brick, stone, and solid concrete walls, except as otherwise provided, shall be of the
thickness in inches indicated in the following table:"
THICKNESS OF WALLS.
Chicago Building Ordinance (1911).
Basement.
Stories.
I
2
3
4
S
6
7
8
9
IO
ii
12
One-story
12
16
16
20
24
24
24
24
28
28
28
32
12
12
16
20
2O
2O
2O
24
24
28
28
28
12
12
16
20
2O
2O
24
24
28
28
28
12
16
16
20
20
2O
24
24
24
28
12
16
16
20
20
20
24
24
24
16
16
16
20
20
24
24
24
16
16
16
20
20
20
24
16
16
16
20
20
2O
16
16
20
20
2O
16
16
16
20
16
16
16
16
16
16
Two-story
Three-story
Four-story
Five-story
Six-story
Seven-story
Eight-story
Nine-story
Ten-story
Eleven-story
Twelve-story
WATERPROOFING. — For methods of waterproofing walls, floors, etc., see methods of
waterproofing bridge floors in Chapter IV.
CALCULATION OF WIND LOAD STRESSES.— (i) The wind load on the sides of the
steel frame in a building in which the wind bracing is all in the outside walls of the building will
be carried to the ends of the building by means of bracing in the plane of each floor or by the floor
slabs where the floors are made of reinforced concrete, and the loads will then be transferred to
the foundations by means of bracing in the planes of the ends of the building. In calculating the
stresses in the bracing in the end panels it is usual to assume that the wind load carried by each
braced bent, consisting of two columns, together with the floor girders and wind bracing, is equal
to the total wind load divided by the number of braced panels in the plane. This was the method
used in calculating the stresses in the Singer Tower, New York. (2) As usually constructed the
interior columns have brackets and only part of the wind load will be transferred to the ends or
sides of the building, the remainder of the wind load will be transferred to the foundations by
portal action and flexure in the columns and beams. It is not possible to determine the proportion
of the wind load that will be taken by the main framework and by the ends of the building, as the
stresses in the framework are statically indeterminate. During erection and before the floors
have been put in place, or with types of floors which do not increase the rigidity of the building in
horizontal planes, the wind loads will all be taken by the framework normal to the side of the
building upon which the wind blows. This wind load is commonly taken as 30 Ib. per sq. ft. of
all framework exposed. When rigid floors have been put in place and the building is completed
the wind load will be taken by the end transverse frames and the intermediate transverse frames,
in proportion to the relative rigidity of the two frameworks. In a long narrow building with
efficient wind bracing in the intermediate framework, practically all the wind load will be taken
directly to the foundations by the transverse intermediate bents; while in the direction of the
length of the building, practically all the wind load will be carried by the bracing in the sides of
the building. For a building as long as wide with rigid floors and efficient transverse framework
STRESSES IN TALL BUILDINGS. 77
ami efficient wind bracing in the ends and sides of the building, it would appear reasonable to
usMiinr that in the completed building one-half the wind load will be taken by the intermediate
transverse framework, and one-half-will be transferred by means of the floors to the ends of the
building and then transferred to the foundations by means of wind bracing in the ends of the
building. The author's specifications permit reinforced concrete floors to be considered as assisting
in transferring wind loads in finished buildings, but most specifications require that the steel
framework be required to carry all the wind loads in the completed structure.
The transverse intermediate framework usually consists of columns and floor girders, in
which the floor girders have brackets or knee braces at the ends to increase the rigidity of the
framework. It will be seen that it is not only impossible to calculate the amount of wind load
that is taken by each intermediate transverse framework, but that the intermediate transverse
framework is itself statically indeterminate. In addition to being statically indeterminate it is
not possible to determine the sizes of the columns and floor girders until after the wind stresses
are determined. With a given framework in which the sizes of the members and the loads are
given the stresses may be calculated by taking into account the deformations of the structure or
by the "Theory of Least Work." From the above it can easily be seen that an exact solution of
th • wind stresses in a tall steel frame building is impracticable and that an approximate practical
solution must be used. Three approximate methods for calculating the wind stresses in tall
steel frame buildings are described by Mr. R. Fleming in Eng. News, March 13, 1913. The third
method described by Mr. Fleming, and known as the " Continuous Portal Method," follows the
method of the continuous portal given in the author's " Design of Steel Mill Buildings" and is the
method in most common use. This method will now be described and some of its limitations
will be shown.
Problem. — A transverse intermediate frame bent consisting of four columns with bracketed
floor girders will be taken as in Fig. I. The wind loads are assumed as acting in the planes of the
floors as shown. It will be assumed: (i) That the framework is rigid, that is the columns and
floor girders do not change their lengths. (2) That each of the four columns takes one-fourth
of the shear. (3) That the points of contra-flexure in the columns are midway between the floors.
(4) .That the vertical components of the stresses in the columns vary as the distance from the
center of the building, or center of gravity of the columns.
The shear in each column between the 6th floor and the roof will be 1,000 Ib. The shear in
each column between the 5th and 6th floors will be 2,500 Ib. The shear in each column between
the 4th and 5th floors will be 4,000 Ib. The shears in the other columns are shown in Fig. I.
The bending moments at the tops of each column between the 6th floor and the roof is M =
+ i ,000 Ib. X 6 f t. = + 6,000 ft.-lb. To calculate the vertical stresses in the columns in the top
story take moments about a plane cutting the columns in the points of contra-flexure. Then
since the stresses vary as the distance from the center of the building,
Fi X 24 ft. + F2 X 8 ft. - F, X 8 ft. - F« X 24 ft.
= 4,000 Ib. X 6 ft.
= 24,000 ft.-lb.
Now
Fi = - F« = 3F2 = -3F,,
and
F«(3 X 24 + 8 + 8 + 3 X 24) ft. = 24,000 ft.-lb
F, =lb. = i5olb. = -F,
Ft = 450 Ib. = - F*.
The bending moment in the floor girder at the top of column No. i must be M = — 6,000
ft.-lb., and will be equal to the vertical stress in column No. I multiplied by the distance to the
aint of contra-flexure. The point of contra-flexure in floor girder 2-3 will be at the center of
78
STEEL OFFICE BUILDINGS.
CHAP. II.
^£
-,6000
'^+6000
+Z/000
+150M"
teMDm MOMENT D/AGRAMS FOR 5™ AND 6™ FLOODS AND
-6000 -4800 -6000
^-+15000
1000
4000-
5500-
7000
3000
1
<5E
(1000) ^
1000
-?/000
00)
-39000
^--
,4000
57000
-
5500
75000
9000
¥KL.
-3IZOO
-45600
-$0000
-105600
^
4000-
-57000
-75 000
g
9000-*
1
4000
' — "JT
6000
J» 4.^/3^1
-^Fhor
6000
£™±4»nn
"-l^'Floor
-J32000 indicates tending moment fn ft-lbs* (£000) indicates direct stress in Jbs*
FIG. i. WIND STRESSES IN A TALL BUILDING.
ALLOWABLE STRESSES.
79
tin- p.iiu'l, while the point of contra-flexure in floor girder 3-4 will be 13 ft. 4 in. from column
N<>. 4. The bending moments at the top of column No. 2 will be M » *> + 6,000 ft.-lb.; in the
right end of floor girder 1-2 will be Mi-t = — 450 Ib. X 2 ft. 8 in. = — 1,200 ft.-lb.; in the left
end of floor girder 2-3 will be Mt-t = — 600 Ib. X 8 ft. = — 4,800 ft.-lb. It will be seen that
the sum of the bending moments equals zero and the point is in equilibrium. The bending
niomrnt-i at the tops of columns No. 3 and No. 4 are calculated in the same manner. The direct
st iv>s in floor girder 3-4 is 4,500 Ib., in floor girder 2-3 is 3,000 Ib., and in floor girder 1-2 is 1,500 Ib.
In the plane of the 6th floor the bending moments at the foot of the columns between the
6th floor and the roof will be M = -f- 6,000 ft.-lb., while the bending moments in the columns
below the 6th floor will be M = 2,500 Ibi X 6 ft. = + 15,000 ft.-lb. The bending moments in the
floor girders are calculated as for the roof girders. It will be seen that the sum of the bending
moments at each intersection of columns and floor girders equals zero and the structure is in
static equilibrium. The remainder of the vertical stresses, horizontal stresses and bending
moments are easily calculated in the same manner.
Limitation of Method. — When the transverse framework consists of more than four bays
(five columns) the solution above locates the point of contra-flexure of the leeward floor girder
in the second panel, and the method fails, as the point of contra-flexure in the girder must not
fall outside of the girder. For a wide building the shears cannot be taken equal.
Distribution of Shears. — In the above solution it is assumed that the shear is taken equally
by the columns. If the columns do not have the same cross-section this assumption will not be
correct. If the columns do not have the same cross-section the condition that the deflection of
the points of contra-flexure in each story are equal will require that the shears in the columns
be in proportion to the moments of inertia of the cross-sections of the columns.
For buildings having a greater width than four bays the most consistent method is to calcu-
late the shear in the outside columns so that the points of contra-flexure in the floor girders will
not fall outside the girder, the remainder of the shear being equally divided among the inside
columns.
ALLOWABLE STRESSES.— The allowable stresses in the steel framework of high buildings
should be taken the same as for steel frame buildings in Chapter I. It is usual to add 25 per cent
to the live load stresses due to cranes and vibrating machinery to provide for impact.
Comparison of Compression Formulas. — The standard formula for the design of compression
members adopted by the Am. Ry. Eng. Assoc., is used by the author in his "Specifications for
Steel Frame Buildings" in Chapter I, and by the building ordinance of Chicago. The A. R. E. A.
formula is
P = 16,000 — 70//r (i)
where P = unit stress in Ib. per sq. in.; / = length and r = least radius of gyration of the column
in inches. The maximum value of P is taken as 14,000 Ib.
The American Bridge Company's Formula. — The American Bridge Company has adopted
the following formula for the design of compression members.
Axial compression of gross sections of columns, for
ratio of l/r up to 120 19,000 — ioo//r
with a maximum of 13,000
Ratio.
Amount.
Ratio.
Amount.
60
I3OOO
130
6500
70
12000
I40
6000
80
1 1000
150
5SOO
90
1 0000
160
5000
ICO
9000
170
4S00
no
8000
180
4000
120
7000
190
3500
80
STEEL OFFICE BUILDINGS.
CHAP. II.
where / = effective length of members in inches,
r = corresponding radius of gyration of section in inches.
For ratios of l/r up to 120, and for greater ratios up to 200, use the amounts given in the
preceding table. For intermediate ratios, use proportional amounts.
A comparison of several compression formulas is given in Table IX.
TABLE IX.
COMPARISON OF COMPRESSION FORMULAS.
ALLOWABLE UNIT STRESSES IN POUNDS PER SQUARE INCH.
American Bridge Company.
1
A. R. E. Ass'n.
Chicago.
Ketchum.
Gordon.
New York.
Philadelphia.
Boston.
r
A. B. Co.
1
12,500
„ 1
16,250
16,000
il 12 '
15,200-58—.
il V '
I 1 P '
14,000 max.
' 36,000 r2
' ii.ooor1
' 20,000 rz
O
5
10
IS
20
25
3°
35
40
45
SO
55
60
65
70
75
80
85
90
95
ICO
105
no
"S
1 20
T?C
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
13 ooo
12 5OO
12 OOO
II 500
II OOO
10 500
IO OOO
9 Soo
9 ooo
8 500
8 ooo
7 500
7 ooo
6 7co
14 ooo
14 ooo
14 ooo
14 ooo
14 ooo
14 ooo
13 900
13 55°
13 200
12 850
12 500
12 I5O
II 8OO
II 450
II IOO
10 750
10 400
10 050
9 700
9 350
9 ooo
8 650
8 300
7 950
7 600
7 2CO
12 500
12 490
12 460
12 42O
12 365
12 285
12 I9S
12 OCX)
II 970
II 835
II 690
II 530
II 365
II 185
II OOO
10 810
10 615
10 410
10 205
9 995
9 785
9 570
9 35S
9 HO
8 930
8 7IC
15 200
14 910
14 620
H 33°
14 040
13 750
13 460
13 170
12 880
12 590
12 3OO
12 OIO
II 72O
II 430
II 140
10 850
10 560
10 270
9 980
9 690
9 400
9 no
8 820
8 530
8 240
16 250
16 215
16 loo
is 925
15 680
IS 375
15 020
14 620
14 185
13 725
13 240
12 74S
12 240
II 740
II 240
10 750
10 275
9 810
9 360
8 930
8 510
8 115
7 740
7 38o
7 035
6 7IC
16 ooo
15 980
15 920
15 820
15 690
IS SiS
IS 31°
IS °75
H 815
H 530
14 220
13 900
13 560
13 2IO
12 850
12 490
12 I2O
II 755
II 39O
II O2S
10 670
10 315
9 97°
9 630
9 3°o
fJO
6 500
6 QOO
8 cio
6 4.OC
11 c
6 250
6 ceo
8 -?oo
6 IK
6 ooo
6 200
8 OQC
c 84.0
r 7CO
c 8co
7 8qo
1 CO
C CQO
c coo
7 600
c 2CO
7 4.0?
1 60
C OOO
7 ^oc
i6c
A 7C.O
7 1 2O
1*70
A COO
6 Q-K
T7C
A 2CO
, 733
6 7CC
1 8O
4 ooo
6 c8o
i8c
•5 7CO
V, JUW
6 4.IO
•? coo
f *
6 24.O
roe
-? 2CO
6 080
200
3 ooo
"> 920
FLOOR PLAN OF STEEL OFFICE BUILDING.
TABLE IX. — Continued.
81
Name of Formula.
Abbreviation.
Maximum Ratio of 1/r.
Main Members.
Bracing Struts.
American Bridge Company
A. B.
A. R. E. A.
C.
K.
G.
N. Y.
P.
B.
120
ICO
120
125
1 2O
140
1 2O
- 2OO
1 2O
ISO
ISO
American Railway Engineering Association
Chicago Building Law
Ki'tchum's Specifications
Gordon .
\i \v York Building Law
Philadelphia Building Law
Boston Building Law
i
i r
\
\
i
1
i [
f
i
|
i
1
i
1
i
i
ij.
53
i 04 r
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54
•
I...,"
-.co/./e
65
T.Cof./7
53
j
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O*V |
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;
6~
0.
9'
0"
66
*
53
i
**^' ^
i
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A
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I21&40*
67
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H
53
i
H
Si 69 +
70
tS
l$*
\Co/.2t
i
22
•
* — i
Co/.22
22
+
Co/.23
1 f M / * 9 f\
\ /f fa jr&*\
*~du//d/rrg Line
E
5L0
/5'0"
'-Floor Line
fill WallP/dtes standard.
Top of Plate Girders in Wall
/'above F/oorLine.
FIG. 2. FLOOR PLAN OF STEEL OFFICE BUILDING.
82
STEEL OFFICE BUILDINGS.
CHAP. II.
H*
*47 Z'9V 7' 6" IO'IO%" 7i"
8
*£0' 3 £•$ ' 76$ ' 10 JO 2 8
7+
1
*53^ 3'9^" 7'8"^ 10' II" 7$
*i
1
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7$
#58? 3'3s" 7>/*« tOrl/f 7$
8}
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Fhnge hyles both sides [<?=3j
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f i ' T ' T * T
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3
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6
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howi n-tMt
47
2
1
3
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BO
1
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53
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61
1
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7£
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t&ff* 3' 6" 7' 6" II '6" 14 '6$* '. 8"
7
5
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gf
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T i ; i
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P/5 6'*I2}**9'0* (ord-9'0")
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1 30 5//-^/-5J 3 6-P'Seps- /"°X6$ - \ Bolted
re
3
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3
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"\3Bo!bs%"x8". f
' 2 Is 6 "x 12} *x g'O" (on/- 6"09.
ft Girders f 3 G-P-Seps- /"0*6%"' 1 AJ#«</
1 3^0/65 i*x^*. r
FIG. 3. DETAILS OF FLOORBEAMS FOR A STEEL OFFICE BUILDING.
CAST IRON SEPARATORS FOR BEAMS AND CHANNELS.
83
CASTIROH BEAM
Beams
Separators
Bolts y
For 5" 4 "& 3 Beams
use 1" gas pipe 2>4 f
tively-
Size
Weioht
per
Foot-
Dlst-
c-toc
of
Bems
Out to
Out
of
Flange
w
h.
d
t
Weight
Each
Incna*
Weight.
For/"
Width
Length
Weight
'Mid-
ing
Nub
Incrsaa
Weight
forl"
Length
24"
J/S*
/oo
95S90
85
80
8*"
8
t
g
8
16%
15k
15%.
15%.
15
8"
7*
7*
7k
7to
20
20
20
20
12"
12
12
12
12
1
31*
28
28
29
29
3-6*
3*6
5-6
3-6
3-6
10
fO
9k
9k
3-5
3-5
3-3
3-3
0-2S
0-25
0-25
0-25
0-25
'\
$" Cored Holes.
20"
IOO&95
90
85&80
8
7k
7to
14%
14k
7
6%
6%
16
16
16
12
12
!2
2
22
22
2-9
2-9
2-9
10
9
3-5
3-3
3-2
0-25
0-25
0-25
20"
75
70
65
7k
7
7
14
15k
6%
6k
16
16
16
12
12
12
2
22
21
21
2-9
2-9
2-9
9
9
8k
3-2
3-2
0-25
0-25
0-25
•>,--!
/'" ITS'
> \*- *X3 *^
18"
90
SS
80
75
8
8
8
8
154
15
7*
7*2
14
/4
14
14
9
9
9
9
*»
20
21
21
21
2-5
2-5
2-5
2-5
10
10
10
10
3-5
3-5
3-5
3-5
0-25
0-2B
0-25
0-2B
./sff
70&65
60
55
7
7
7
13
6'/4
6k
14
14
14
9
9
9
5/8
IS
/9
19
2-5
2-5
2-5
9
8k
8k
3-2
3-2
3-2
0-25
0-2B
0-25
15"
IOO&95
90
85
74
7k
7k
14
6%
6k
6k
//
7k
7k
7k
k
to
12
12
12
1-6
1-6
1-6
9k
9k
9k
3-3
3-3
0-25
0-25
0-25
ft! -
15"
80&75
70<f65
60
7
7
13%.
12k
6
£*
|
7*
7k
7k
to
k
12
12
11
1-6
1-6
1-6
9
9
8
3-2
3-2
3-0
0-25
0-25
0-25
fei L-^-J
/5"
55
50S45
42
6k
6k
12%.
12
6
//
7k
7k
7k
k
to
k
II
12
12
1-6
f-6
1-6
8
8
8
3-0
3-0
3-0
0-25
0-25
0-25
12"
55
BO
6
6
11%
Ilk
sb
5%
8%
a*
5
5
ft
9
9
f&
8
8
3-0
3-0
0-25
0-25
12"
45
40&35
31-5
6
6
6
II
5%
5k
5k
8*
8%
8%
5
5
5
to
9
9
9
A3
7*
7k
7k
2-9
2-9
2-9
0-25
0-25
0-25
10*
40
35
30
25
5k
5k
Sk
S'/z
10%.
/Ok
rok
/o
4*
4%
5
5
7k
7k
7*
I
6
6
7
7
1
7k
7
7
T
1-4
1-4
1-4
1-4
0-13
0-J3
0-13
/ Cored Hole
„. 'X
9K
35
30
25
21
5
S
5
5
10
9k
9k
4*
4%.
4k
4k
6k
6k
6k
6k
h
A
to
5
5
5
5
0-9
0-9
0-9
0-9
7
6k
6k
6k
1-4
1-3
1-3
1-3
0-13
0-13
0-13
0-13
1 I «
'/ Radius ^
d"
25-5
23
20-5&I8
4k
4k
9
8k
4
4
4
5k
5k
5k
to
to
4
4
4
0-8
0-8
0-8
6
6
6
1-2
0-13
0-/S
0-13
7"
20
17-5
15
4k
4k
4k
8k
8%.
8%.
4
4
4%
5
5
5
1
4
4
4
0-7
0-7
0-7
6
6
6
1-2
A?
0-15
0-13
0-13
\
'/"' M/
£#' ' '*' '
h*—
6"
1725
14-75
12-25
4
4
4
7*
7k
7k
3k
3k
3*
4k
4k
4k
*
4
4
4
0-6
0-6
0-6
5k
Sk
5k
1-2
1-2
0-13
0-15
0-13
FIG. 4. CAST IRON SEPARATORS FOR BEAMS AND CHANNELS.
AMERICAN BRIDGE COMPANY.
(For details of separators for Bethlehem beams, see Part II.)
34
STEEL OFFICE BUILDINGS.
CHAP. II.
r
(I) 4 ANGLES (2) 4 ANGLES
J PLATE 5 PLATES
(3) 8 ANGLES (4) ? CHANNELS
5 PLATES I PLATE, 4 ANGLES
3 E
1
J
1
r
L
r
L
/> CHANNELS (/o) 8 ANGLES ff/J BETHLEHEM (/2) H COLUMN
6 PLATES 7 PLATES H COLUMN 2 PLATES
ir
x /
w
L
(17) 6 KAY
LJ
4 7- BARS (14) 4 Z-BARS (/$} 2 CHANNELS (l6) 2 CHANNELS
J PLATE 3 PLATES I I-BEAM I I-BEAM
HU__. J! _
LARIMER (19) 4 ANGLES (?o) BANGLES
LACED 5 PLATES
FIG. 5. TYPES OF COLUMNS FOR STEEL BUILDINGS.
DETAILS OF FRAMEWORK.
85
DETAILS OF FRAMEWORK. — The framework of a steel skeleton building consists of
floorbcams and floor girders which carry the floor loads to the columns, of columns which carry
i In- loads to the foundations and of foundations which transfer the loads to the earth; the columns
art- brart-d transversely and longitudinally by wind bracing and by means of the floor girders,
and the roof is carried on trusses or on roof beams or purlins. There is in addition miscellaneous
framing to carry the outside walls and the cornice, and the framing around elevators, etc. For
additional details, see Chapter XII, Structural Drafting.
I—
Pocf
I7th'r~/oor
16th -Floor
I5th-Floor
/4^-f/oor
115
115
82
116
•8
^
115
NOTE '--Figures in
^/ denote sheet numbers.
FIG. 6. COLUMN SCHEDULE.
.
Floor Plan. — The floor is carried on floorbeams to the floor girders and by the floor girders
to the columns. A detail plan of a section of a floor plan of a steel skeleton building is shown in
Fig. 2. The floorbeams, girders and columns are numbered as shown.
Details of floorbeams for an eight story steel office building are given in Fig. 3. For addi-
tional details of rolled beams and bracing, see Chapter XII. Details of cast separators are given
in Fig. 4.
Columns. — Details of steel columns that are commonly used in steel skeleton buildings are
given in Fig. 5. The built-H columns made of 4 angles and I plate or of 4 angles and 3 or 5 plates
86
STEEL OFFICE BUILDINGS.
CHAP. II.
1
= 11
I
* ,jJ|
5?"
]
i'l
A "^
-->
c- --
i ,.. ^
51
i ^
o
tx
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i* >j
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ti
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4'
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Y , J Ul
VD
R
P
^JcCC
i
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* 16' A j
r 1?" 'i
lO'CHANNEL COLUMNS
with IP'S 14'Cov.Pb.
I2"CHANNEL COLUMNS
withl4"&l6'Cov.Pb.
^'CHANNEL COLUMNS
wHhl6"&l8"Cov.Pls.
-f ^
*1*
i
r»i
j*
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w ,n
(ri
(0
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||
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" Distance B=Webt(^'to^
distance C in even ind
y Q> [p* *^
6 1 1
=oj,l"i j,
V A
m S
Tj
iR
ti
(l o
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^ i j.
Varies Va'ri
| Constant
i C (Constant)
9'CHANNEL COLUMNS
withlO"&ie'Cov.Pb.
&"CHANNEL COLUMNS
withlo"&12"Cov.Pls.
PLATE & ANGLE
COLUMM5
FIG. 7. DETAILS OF COLUMNS. AMERICAN BRIDGE COMPANY.
DETAILS OF COLUMNS.
87
-
i ;
Si
CJ
>_:£]11
-/*"
'4
/£>'/£/ & without Covers Covers
with Reinforcing 16" and 16" bo 12
Reinforcing Web Plates Web P/ates over
FIG. 8. DETAILS OF COLUMNS. AMERICAN BRIDGE COMPANY.
88
STEEL OFFICE BUILDINGS.
CHAP. II.
wrr-
^fff ffH5-
4i :4
ii
>i
4-^\
-
14
i,>yv'^!&'
a£i£i£a
— >i
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4- 4-
-
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i tr ^ *•
!j! ^J3j
i //^ i
k >)
/// / if)" tit i
Web lo Web
Covers 18" Covers
Angles 8"*8" Angles 6"* 6"and 6*4" Angles
FIG. 9. DETAILS OF COLUMNS. AMERICAN BRIDGE COMPANY.
r// _ /x/
5*3?
DETAILS OF COLUMNS.
_
U --- w
Web
Covers
Anyfes
.12" \ \ /Of
M -M K---f*«
I8"if Web 14" and I?" Web 10" f
18" Covers /4" Covers 12"
8"*8" Angles 6"*6"an(f 6*4" Angles 5*3?
FIG. 10. DETAILS OF COLUMNS. AMERICAN BRIDGE COMPANY.
90
STEEL OFFICE BUILDINGS.
CHAP. II.
T"
H
T
1-
i
1
p -
i
1 1]
Vr>*~
"i-
.
4-
? l
1
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-6-
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JJ
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•i"~.-n'^i r
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Covers 14 Angles 6x4
Light Columns
Loads under 40,000-lb5.
Filler-
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li-U-i- J-
hy jTjjj; jii
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..J
3i:
Fin.
-6-
fin.
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-6- ' -6-
V
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m
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tftl
-f~"ifj r*irf*"3 tijfrj
Weblfi" CoverTlS" AnqbTxS"
.pi 'LJJJJL - - „.. L
lll'-M >JZ'-M 'It! ' ""
T
lftcol.toPI&L-col
t
H
FIG. ii. DETAILS OF COLUMN SPLICES. AMERICAN BRIDGE COMPANY.
DETAILS OF COLUMN SPLICES.
91
7rt"TT TtT
-f- : -f
£4$
Fin.
HJ.
El Channels 10"
U?!.j Covers 12"
ft- Channeb 10
Covers 12
•rt*t"
Fillera-
-4..-I— j-L_
lll.if Channels 12"
U£J Covers 14"
1
T
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32
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Fillers --<
Cl-
Channels
i^Pi Cover5_ 14"
TJ
1
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-,--r.-Jrr:
H"
f!H fin.
141 Channels 12 (
L..!4.".:J Covers 14'
ii i . ; '--^i
jljJL jf Channels 15 (i
L....!^..j Covers 16"
Filler-
•ut
f-4-
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Channeb 15
. _
Covers 16
5PLICK 5hown on these sheeb
are to be used only where Columns
are supported near splice. All other
cases are special.
SPLICE FILLERS are to vary in
thickness by even jj .
CLEARANCE at one side of Column
(after packinq has been considered)
I C_ ft"L I"
to vary From 0 cog .
FIG. 12. DETAILS OF COLUMN SPLICES. AMERICAN BRIDGE COMPANY.
92
STEEL OFFICE BUILDINGS.
CHAP. II.
Dimensions in inches
COLUMN BASES, CAST /POM
Drill holes in cap plate tosvft cofumn-
Core two drain holes (one each side)
j? o'fameterin lower end of hub •
Core holes 2 "diameter in baseplate-
Thickness of hub rib "6 "applies only
to bases used with channel columns •
For plate & angle columns, hub rib "6"
C_* ^ /sco be increased when necessary •
Base
Pfdte.
Height
C
Hub
Cap
Plate
Ribs
Edge
Rib
Esti-
mated
Weight
inlbs-
Bearing Capacity
Thoi/s
Ibs
sq-Ft-
Lbs
per
sq-in
Total
Thous
Lbs-
A
5
Diam
D
Thick
E
6
H
J
Cor.
K
Int-
L
Oist-
M
0
p
2'0"
1"
9"
9"
1"
1"
f'6"
1"
1"
/"
4"
490
30
208
/20
2-0
//
9
9
1
1
f-6
1
1
I
4
530
50
350
200
2-3
fi
9
9
1
1
1-6
/
1
I
4j
<t
\
590
30
208
150
2-3
9
9
I
I
1-6
,i
I
I
4?
5>
\
630
50
350
250
2-6
4
9
9
/
1
1-8
/
/
1
5
5
^5
730
30
208
/88
2-6
/i
9
9
fi
fi
1-8
fi
I
1
5
^
=§
830
50
350
312
2-9
/i
f-3
9
fi
fi
1-8
fi
I
1
si
1/40
30
208
226
2-9
2
1-3
9
fi
fi
1-8
fj
I
1
5^
1270
50
350
378
!>-0
,L
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1-3
fO
fi
fi
1-9
fi
1
f
6
/"
?f
1260
30
20&
270
3-0
1-3
10
fi
fi
1-9
/I
fi
fi
6
1
^~4
1400
40
275
360
3-0
7J
1-3
10
fi
fi
1-9
fi
fi
/•#
6
fi
3
1460
50
350
450
3-6
fj
1-3
II
fi
fi
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fif
fi
7
I
24
1790
30
208
368
3-6
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11
fi
fi
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fi
f?
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fi
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1 890
40
275
490
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fi
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fi
fi
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2140
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350
612
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fi
fi
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fi
fi
fi
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fi
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2620
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208
480
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fi
fi
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fi
fi
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fi
3i
3030
40
27$
640
4-0
2
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11
/I
/|
2-1
^
fi
fi
8
fi
4
3250
50
350
800
4-6
/$.
'4
1-9
12
fi
fi
2-3
'4
fi
fi
9
fi
3*2
3560
30
208
608
4-6
2
1-9
12
/I
/I
2-3
2
/I
/I
9
fi
4
4040
40
275
810
4-6
^i
1-9
12
2
2
2-3
2%
/I
/I
9
fi
4i
4290
50
350
1012
4-9
/I
1-9
13
fi
/?
2-5
/I
fi
fi
9?
fi
3?
3880
30
208
676
4-9
2
1-9
13
j%
/^
2-5
2
/j.
f*
-9?
/i
4
4400
40
275
902
4-9
2i
1-9
13
*2
2
2-5
2i
(i
^
9z
/i
4i
4720
50
350
1128
FIG. 13. CAST IRON COLUMN BASES. AMERICAN BRIDGE COMPANY.
CAST IRON COLUMN BASES.
93
u 'COLUMN BASES, CAST IRON- C
K W
V/~~v '
—A'
Base
Plate
Height
Hub
Cap
Plate
Ribs
Edge
Rib
Esti-
mated
bearing Capacity
Thous
Lbs-
Total
A
B
C
Diam
D
Thid
E
Rib
6
"
J
Cor-
K
/nt-
L
Dist-
M
0
P
Weight
in Ibs-
Ibs
per
stj-in-
Thous-
Lbs-
sq-ft
&
/|"
2 '5'
15"
/*"
'4
ft"
2'5
fi>"
ff
ff
I'O?
I-
3/
5590
50
208
750
5-0
2
2-5
15
2
'4
2-5
/—
/i
n
1-0$
fj
4
5850
40
275
I 000
5-0
%4
2-5
15
2-j.
2
2-5
2
2
/4
1-0$
/?
4-k
6550
50
550
1 2 BO
5-6
/|
2-5
/3
$
ft
2-5
fi
i3
>4
I±
H4
/^
3j
6/90
30
208
908
5-6
2
2-5
15
2
/|
2-5
/j-
2
/I
/V|
/?
4
70/0
40
275
J 210
5-6
?i
2-5
/3
24
2
2-5
2
24
/"/I
/i
5
7780
50
550
1 512
6-C
2
2-9
15
2
It
2-5
/£
1%
/?
1-5
/?
4
8250
50
208
1 080
6-0
2%
2-9
15
2%
14
2-5
2
2
/|
/-5
It
4i
9 280
40
275
/440
6-0
2i
2-9
15
?J
2
2-5
2
2*
fi
1-5
1?
5
9 830
50
550
/800
COLUMN SECTIONS
Channel Column P/dte&Ang/e Column Channel Column P/ate 5 Angle Column
One Cover Plate One Cover P/ate Two Cover Plates Two Cover P/ates
§
Channel Column Plate & Angle Column Channel Column Plate & Angle Column
Three Cover Plates Three Cover P/ates Four Cover Plates Four Cover Plates
FIG. 14. STEEL COLUMN SECTIONS AND CAST IRON COLUMN BASES. AMERICAN BRIDGE COMPANY.
94
STEEL OFFICE BUILDINGS.
CHAP. II.
as given in (i) and (2) are the most satisfactory columns for usual conditions. The Bethlehem
H columns in (n) and (12) make very satisfactory columns. While the Bethlehem H columns
require the driving of less rivets than are required to fabricate built-H columns, the extra cost
required to drill from the solid in heavy Bethlehem H columns makes the final cost of the two
types of columns practically the same for average conditions. Columns made of two channels
laced are deficient in lateral rigidity and should only be used for light loads. Z-bars are difficult
to obtain from the rolling mill and Z-bar columns should not be used unless it is knpwn that
Z-bars can be obtained. Additional sections are given in Fig. 14.
Column Schedule. — A column schedule should be prepared as in Fig. 6. The column schedule
should give the length, area of cross-section and the composition of every column in the building.
For the use of the shop draftsmen the dead load, wind load and eccentric stresses should be given
for each column.
Column Details. — Standard details for channel columns and for plate and angle columns are
given in Fig. 7. Details of channel columns are given in Fig. 8. Details of plate and angle
columns are given in Fig. 9 and Fig. 10. Details of column splices are given in Fig. 1 1 and Fig. 12.
Details of a column used in the Singer Building are shown in Fig. 27.
Column Bases. — Details of cast iron column bases as designed by the American Bridge
Company are given in Fig. 13 and Fig. 14. Intermediate sizes may be obtained by interpolation.
/ \ ,**!
I tinlJ 1 '•«?**/«'"'*«-./'
it~», n ^gf-yfLfM i.Siv*«^ A
° °'
Sectional Side Elava+ion.
FIG. 15. CAST STEEL BASE.
FIG. 1 6. BUILT STEEL COLUMN BASE.
Details of a cast steel column base used in the Singer Building are shown in Fig. 15. Details
of a built steel column base designed by Mr. E. W. Stern, Consulting Engineer, are shown in Fig. 16
Mr. Stern considers the built steel column base as cheaper and more reliable than a cast steel
base; and cheaper and very much more reliable than a cast iron base. In addition the base is
easily set and readily grouted. After setting, the base is grouted with I to 2 Portland cement
mortar. Bases of this design have been used for loads up to 1,600 tons.
Anchors. — Details of anchors are given in Fig. 17. Anchors for columns in tall buildings
should be calculated for the actual conditions.
FOUNDATIONS. — The foundation for a tall building will depend upon the height of the
structure, the total load on the foundation, the character of the soil, and the requirements of the
design and may be briefly described as follows.
(1) Ordinary wall or pier foundations built on the natural soil.
(2) Walls and columns supported by timber grillage resting on the soil.
(3) Walls and columns supported on grillages made of steel beams or bars encased in concrete
and resting on the soil.
(4) Piles of timber or concrete driven to rock or to a sufficient depth to carry the loads without
settlement.
(5) Caissons as constructed in Chicago by excavating in an open well or shaft, curbing it
with timber, and then filling the well with concrete.
(6) Caissons as constructed in New York by sinking steel cylinders, or steel and timber
caissons, or reinforced concrete caissons, usually by the pneumatic process and filling the shaft
with concrete. The first type of foundation, where the soil is compressible, can only be used for
DETAILS OF ANCHORS AND ANCHOR BOLTS.
95
"
/4 for2>j legs
1" fort" % 2? legs
y for 2" legs
These wall connec-
WALL ENDS tons an to k used oo
$?. ties in upper and lower
chords of roof trusses •
Washers 5'*i'-5"
Jong for 2>^" legs •
Washers 4"*{"-
4" long for all others -
'SWall
!7"Walf
2l"Wall
Where wall
extends above
truss, use an
angle anchor
1 as shown'
BUILT-IN ANCHOP BOLTS
When bolts are separated less than
width of washer, use washer with two holes-
GOVERNMENT AncHOfi ANGLE ANCHOR .
*
i |i ---i • »'y"~-' K*
jj- 5hmdloose\ j
~W* I Vft
^Rodl'9'long
Weight
I'.."...! 21s 6"*f*$-l±' long-
life
. SWEDGE BOLTS
Diamtt\L.ength Weight
withnut
Inches
Ft-&ln-
0-9
1-0
f-0
I'b*
2-5*
3-/*
6-/*
Screw Bolt Split Bolt Hacked Bolt-
FIG. 17. DETAILS OF ANCHORS AND ANCHOR BOLTS.
AMERICAN BRIDGE COMPANY.
96
STEEL OFFICE BUILDINGS.
CHAP. II.
LofLne
-TMullicn
Spandrel Section Between Cols 2— and3-FloorPiers
TMulhon
Typical Spoindrel Section
East andWestWalls andCourts
BuildindLne
loor Spandrel Section Typical Spandrel Section
MaidenLcme and Cedar St. Fronts
TMut/iori
Typical Spandrel Sections Spandrel Section BetweenCols.No.l4andL7
East and WestWal Is and Courts MaidenLane and Cedar StFronts Maiden LaneEntrance
FIG. 1 8. DETAILS OF WALL CONSTRUCTION, UNITED FIRE COMPANY'S BUILDING, NEW YORK.
(Eng. Record, Dec. 9, 1911.)
WIND BRACING.
97
(9)DtA60HAL5RACING (b) KNEE BRACE (c) PQKTAL BRAC/N6 (d) BRACKETS
FIG. 19. TYPES OF WIND BRACING.
Maiden Lane Street Front
FIG. 20. WIND BRACING IN UNITED FIRE COMPANY'S BUILDING.
(Eng. Record, Dec. 9, 1911.)
STEEL OFFICE BUILDINGS.
CHAP. II.
buildings of four to six stories, but may be used for buildings of twelve to fifteen stories where the
supporting power of the soil is considerable as in Denver. With high buildings the footings
become so large as to be very expensive and also encroach upon the basement area.
Timber grillage and timber piles must be kept permanently wet or the life of the foundation
will be very short. Many of the early tall buildings in Chicago were carried on timber grillages
and on timber piles, but the settlement of the structures was so great that the method was aban-
doned for the method of concrete wells.
Steel grillage foundations have been much used for high buildings. With steel grillage the
foundations may be made very shallow so that the basement is not encroached upon.
Bracket B 9
Bracket 85
Bracket B 20
FIG. 21. DETAILS OF WIND BRACING IN UNITED FIRE COMPANY'S BUILDING.
(Eng. Record, Dec. 9, 1911.)
In cities like Chicago and New York where real estate is so valuable that basements are
often made three or four stories in depth, and where nearby disturbances due to excavations and
tunneling would cause settlement it has been found necessary to carry the foundations to rock
by means of wells or pneumatic caissons. In Chicago the wells commonly vary from 5 ft. to
12 ft. in diameter and are sunk in the open and are lined with timber curbing. After bed rock is
reached the well is filled with concrete.
For a description of the sinking of the foundations for buildings in New York City, see a paper
entitled "Foundations for the New Singer Building, New York City" by Mr. T. Kennard Thom-
son, Consulting Engineer, in Trans. Am. Soc. C. E., Vol. 63, June, 1909.
SPACING OF COLUMNS. — The spacing of columns in steel frame buildings varies from
about II ft. to 24 ft., depending upon the height of the building, the floor loads, the type of floor
FLOOR PANELS.
QQ
ami i <t In -r conditions. For buildings a few stories in height it is economical to space the columns
closely together, while in high buildings a spacing of 16 ft. to 20 ft. will commonly be found eco-
nomical. The columns in the Singer Tower in Fig. 22 were spaced 12 ft. centers; the columns in
tlu- (Guaranty Trust Company's New York Building, 162 ft. high were spaced about 16 ft. by 16
ft. and 21 ft. 6 in. by 19 ft. 9 in.; the columns in the Woolworth Building, New York, were spaced
.it -listances varying from 18 ft. 6 in. by 18 ft. 6 in. in the main part to a maximum of 28 ft. by
28 ft. in the tower.
'
FIG. 22. TYPICAL FLOOR PLAN OF SINGER TOWER.
FLOOR PANELS. — For the long span system, floor girders connect the columns forming a
square or rectangle, the floor slabs being supported on the floor girders. For the short span
system, floorbeams are carried by the floor girders and the spans for the flooring are reduced. The
spacing of the floorbeams will depend upon the type of floor, but it will commonly be found eco-
nomical to use an even number of floorbeams giving an odd number of short spans in each panel.
A common arrangement is to use two floorbeams which divide each panel into three short spans.
100
STEEL OFFICE BUILDINGS.
CHAP. II.
SPANDREL SECTIONS. — The design of the curtain walls that are supported by the spandrel
beams will depend upon the material of which the wall is built, the amount and character of the
ornamentation, and the details of the windows. The details of the wall construction in the
United Fire Company's Building, New York, are given in Fig. 18. The spandrel masonry is carried
by the wall girders and by horizontal angles bracketed from their outer faces. The angles in the
outer flanges of the wall girders are often wider than those in the inner flanges to give additional
support to the masonry, and both they and the detached spandrel angles have holes through their
horizontal flanges to receive vertical expansion and wedge bolts to hold the stone or terra-
cotta. The mullions over the windows are made of 3 in. by 4 in. tees.
mm mm
,,6-4v...... i* ~-i*'4i i
no 4* — *i
•V54
fwifropu rlT.l._.SJ J Jj 1
" " '"* *
J ----- -2 — I — '— x --- \ --- -_dt_^J.
L. „.. _____ ....... ,„._.. _ _„ __. __ .... .......
FIG. 23. FOUNDATION PLAN OF SINGER BUILDING.
The details of the spandrel walls should be worked out by the architect and the engineer
working together if the best results are to be obtained.
WIND BRACING. — The arrangement of the wind bracing in a steel frame building will
depend upon the size and height of the building, upon the arrangement of the columns and the
space that may be occupied by the wind bracing. Several types of wind bracing are shown in
Fig. 19. Where space permits the diagonal bracing is the most effective. Diagonal bracing can
only be used in solid walls or partitions. Knee braces (b) and portal bracing (c), can be used
in outside walls where there is sufficient space above and below windows. Brackets (d) are
used where the vertical clearance is limited and in wind bracing transversely through the building.
Details of wind bracing of the United Fire Company's Building, New York, are given in Fig. 20
and Fig. 21. The building is 130 ft. 6 in. by 173 ft. 6 in. in plan and 25 stories in height. The
columns are of Bethlehem H sections two stories in height. The floor panels are chiefly 15 ft.
6 in. by 24 ft. 3 in. The columns rest on grillages which rest on pneumatic piers.
Details of the wind bracing in the Singer Building are given in Fig. 24, Fig. 25, and Fig. 26.
SINGER BUILDING.
101
SINGER BUILDING.* — The Singer Building consists of a main portion approximately 75(1. by
1 16 ft. in pi. HI and 14 stories high, and a tower 60 ft. by 60 ft. in plan and 41 stories high with a
four tier lantern which rises to a total height of 612 ft. The building is of skeleton steel con-
FIG. 24. DIAGRAM OF WIND BRACING, SINGER BUILDING.
struction, fireproofed with terra-cotta tiling and provided with terra-cotta floor systems surfaced
with cement. The columns are carried on concrete footings sunk by the pneumatic process to a
depth of 90 feet. The columns are spaced 12 ft. centers and are connected at right angles by
* Engineering News, Vol. 58, pp. 595 to 598.
102
STEEL OFFICE BUILDINGS.
CHAP. II.
1
i II
) 2
4- 3
5
11
17
10
16
22
28
-
•
9
15
21
27
8
14.
20
'l
1
3 I
3 2
5
FIG. 25. PLAN OF WIND BRACING,
SINGER BUILDING.
FIG. 26. DETAILS OF WIND BRACING,
SINGER BUILDING.
FIG. 27. COLUMN IN SINGER BUILDING.
SPECIFICATIONS. 103
Birders and floorbeams. A typical floor plan of the tower is shown in Fig. 22. The columns are
in. uli- of two channels, reinforced with plates where necessary. Details of a typical column are
shown in Fig. 27. The wind bracing of the steel frame is shown in Fie. 24. A plan of the wind
bracii;;; in the tower is shown in Fig. 25. The panels that have heavy full lines were wind braced
to the 33d story on the exterior and to the 36th story on the interior. Heavy dotted lines indi-
cate wind bracing to the I4th story. Fine lines indicate no diagonal bracing. Circles on diagonal
intersections represent anchor bolts. In designing the bracing the loads were distributed as
follows: — It will be noticed that in a north and south direction there are 1 1 lines of wind bracing
in the tower, nearly symmetrically placed. It was therefore assumed that on each story eacn
line of X-bracing took -fa of the total wind pressure of 30 Ib. per sq. ft. The loads on the bracing
in an cast and west direction were distributed in a similar manner. The details of the X-bracing
-re shown in Fig. 26. Each of the 12 ft. square towers was assumed to act independently and
me uplift of the columns was provided for.
SPECIFICATIONS FOR STEEL OFFICE BUILDINGS.
BY
MILO S. KETCHUM,
M. Am. Soc. C. E.
1914.
I. Design. — In all steel frame or skeleton buildings the stresses due to external and internal
s and wind stresses shall be transmitted to the foundation by the steel framework, no reliance
ing placed on the strength of the walls and partitions. Beams and girders shall have riveted
connections to the steel columns. All columns shall be of structural steel with their different
rs riveted together and shall be riveted to the beams and girders connecting to them.
2. LOADS. — The structure shall be designed to carry the following loads.
3. Dead Loads. — The dead load shall consist of the weight of all permanent construction
and fixtures, such as walls, roofs, interior partitions, and fixed or permanent appliances. The
weights of different materials shall be assumed as given in Table I. The minimum weight of
fireproof floors to be assumed in designing the floor system shall be 75 Ib. per sq. ft. The actual
weight of floors shall be used in designing columns. The minimum weight of movable partitions
11 be taken as 10 Ib. per sq. ft.
4. Live Loads. — The live load shall consist of movable loads and loads due to machinery
other appliances.
The live loads required by Schneider's specifications and given in Table IV shall be used
for the different classes of buildings. The maximum stresses due to any one of the three systems
of loads shall be used in the design. Floor slabs for office buildings may be designed for a uniform
load equal to twice the distributed load given in the second column of Table IV, and the effect
of the concentrated load may be neglected. The concentrated load and load per linear foot of
girder shall be considered in the design of all beams and girders. Flat roofs of office buildings,
hotels, etc. that can be loaded by crowds of people shall be designed as the floors.
5. Impact. — For structures carrying traveling machinery such as cranes or conveyors, or
machinery such as printing presses, 25 per cent shall be added to the stresses resulting from live
load to provide for impact and vibrations.
6. Snow Loads. — The snow loads on roofs shall be taken the same as for steel frame mill
buildings, Fig. I, Chapter I.
7. Wind Loads. — All structures shall be designed to resist the horizontal wind pressure on
the surface exposed above surrounding buildings as follows.
a. The wind pressure on roofs shall be taken as the normal component, calculated by Duchem-
in's formula, Fig. 3, Chapter I, of 30 Ib. per square foot on the vertical projection of the roof.
b. The wind pressure on the sides and ends of buildings except as otherwise provided in the
following paragraph shall be assumed as 20 Ib. per square foot acting in any direction horizontally.
c. In designing the steel or reinforced concrete framework of fireproof buildings the frame-
work shall be designed to resist a wind pressure of 30 Ib. per square foot acting on the total exposed
surface of all parts composing the framework or a horizontal wind pressure of 20 Ib. per square
foot acting in any direction horizontally on the sides and ends of the completed building. The
strerfgth of reinforced concrete floors may be considered in calculating the strength of the frame-
work in the completed structure. The framework before the structure has been completed shall
104 STEEL OFFICE BUILDINGS. CHAP. II.
be self-supporting without walls, partitions or floors. In no case shall the overturning moment
due to wind pressure exceed 75 per cent of the resisting moment of the structure. In the calcu-
lations for wind bracing the working stresses for dead and live loads may be increased 25 per
cent providing the sections are not less than required for dead and live loads. Chimneys shall
be designed to resist a wind pressure of 20 Ib. (§ of 30 Ib.) per square foot acting on the vertical
projection of the chimney. Curtain walls carried on the framework of steel or reinforced concrete
buildings shall be designed to resist a horizontal pressure of 30 Ib. per square foot acting hori-
zontally on the outside of the entire surface of the wall.
8. Minimum Loads on Roofs. — Roofs shall be designed for the minimum loads specified by
Schneider and given in Table VI.
9. Live Loads on Columns. — For columns carrying more than five floors, the live load may
be reduced as follows:
For columns supporting the roof and top floor no reduction.
For columns supporting each successive floor a reduction of 5 per cent of the total live load
may be made until 50 per cent is reached, which reduction of the load shall be used for the columns
supporting all remaining floors. No column shall, however, be designed for a live load of less
than 20,000 Ib. The above reduction is not to apply to the live load on columns of warehouses,
and similar buildings which are liable to be fully loaded on all floors at the same time.
10. Loads on Foundations. The loads on foundations shall not exceed the following in
tons per square foot:
Ordinary clay and dry sand mixed with clay 2
Dry sand and dry clay 3
Hard clay and firm, coarse sand 4
Coarse sand and gravel 5
Shale rock 8
Hard rock 20
For all soils inferior to the above, such as loam, etc. never more than I ton per square foot.
The loads on foundations shall be assumed to be the same as for the footings of columns.
The area of the bases of the foundation shall be proportioned for the dead load only as follows.
That foundation which has the largest ratio of live load to dead load shall be selected and pro-
portioned for the combined dead and live loads. The dead load on this foundation shall be
divided by the area thus found, and this reduced pressure per square foot shall be the permissible
pressure to be used for the dead loads of all foundations.
11. Pressure on Masonry and Wall Plates. — The maximum pressure on masonry and wall
plates shall not be greater than the values given in Table VIII.
12. Bases. — Structural steel columns shall rest on either cast iron, cast steel or built steel
bases proportioned so as to distribute entire load of the column on the concrete or masonry founda-
tion. Columns carrying wind stresses shall be firmly anchored with at least two anchor bolts
to a mass of concrete whose weight is at least i| times the up-lift in the column. All columns
shall be properly secured to the bases.
13. Shape of Foundations. — Foundations under columns shall be symmetrical except under
wall columns, where the center line of the column must lie within the middle third of the founda-
tion. In this case the average intensity of the pressure on the soil shall not exceed one-half the
safe load allowed for a symmetrical section. In cases where the wall column load exceeds the
above safe loads the column must rest upon a steel or reinforced concrete girder or cantilever
having a column or columns at the inner end. The foundation shall then be designed for the
combined loads.
14. Rolled Beams. — The depth of rolled beams in floors shall be not less than one-twentieth
of the span, and if used as roof purlins not less than one-thirtieth of the span. In case of floors
subject to shocks and vibrations the depth of beams and girders shall be limited to one-fifteenth
of the span. If shallower beams are used the sectional area shall be increased until the maximum
deflection is not greater than that of a beam having a depth of one-fifteenth of the span, but the
depth of such beams shall in no case be less than one-twentieth of the span.
15. Expansion. — Provision shall be made for expansion and contraction corresponding to a
variation of temperature of 150 degrees Fahr. where necessary. Expansion rollers shall not be
less than 4 inches in diameter.
16. Cast Iron. — The allowable stresses in cast iron shall be as follows:
Compression = 12 ooo Ib. per sq. in.
Tension = 2 500 Ib. per sq. in.
Shear = i 500 Ib. per sq. in.
17. Steel Columns. — Columns shall be of rolled or built sections. No wall column or column
with eccentric loads shall be used which does not have at least one solid plate or web of metal in or
SPECIFICATIONS. 105
parallel to the plane of eccentric stress. Columns shall have a minimum length equal to two
storii •>•: and splices on adjacent columns shall preferably be made at different stories unless the
building i> -\ mmrtrir.il about a middle line of columns, in which case for ease in construction
similarly situated columns may be made alike. Columns shall be designed so as to provide for
ive connections for floorbeams, girders and brackets. The splices shall be strong enough
lit the bending stresses and make the columns practically continuous for their entire length.
Tin- split os of columns shall be riveted.
1 8. Roof Trusses. — Roof trusses shall be of steel and may have either pin or riveted con-
nections, and shall be of such design that the stress in each member may be calculated. Roof
trusses shall be braced in pairs and each pair of trusses shall be rigidly connected by lateral and
transverse bracing. Purlins shall be made of shapes, or riveted plate or lattice girders. Trussed
purlins will not be allowed. Main members of trusses shall be designed so that the neutral axes
of intersecting members skall meet in a common point, or if this is not possible the eccentric
M rt-sses shall be calculated and provided for.
19. Floorbeams. — Floorbeams shall generally be rolled steel beams and shall be riveted to the
floor girders by means of connection angles. Floor girders may be rolled beams or plate girders
and shall be riveted to columns by means of connection angles. Shelf angles may be provided
for convenience during erection.
The flange plate's of all girders shall be limited in width so as not to extend beyond the outer
line of rivets connecting them to the angles, more than 4 inches, or more than 8 times the thickness
of the thinnest plate. For fireproof floors, floorbeams shall generally be tied together with tie
rods at intervals not to exceed 8 times the depth of the beams. Tie rods are not required with
reinforced concrete floors where the reinforcement is rigidly fastened to all outside beams and
girders. Holes for tie rods, where the construction of the floor permits, shall be spaced 3 inches
above the bottom of the beam.
Where more than one rolled beam is used to form a girder, they shall be connected by cast
n or steel separators and bolts spaced at intervals of not more than 5 feet. All beams having a
ith of 12 inches and more shall have at least 2 bolts to each separator.
20. Wall Plates. — Bearing stones of granite, crystalline sandstone, or metal plates shall be
d to reduce or distribute the pressure on the wall under the ends of wall beams, girders and
sses.
21. Wall Anchors. — The wall ends of beams, girders, and columns shall be anchored securely
give rigidity to the structure.
22. Minimum Thickness of Metal. — No plate or rolled section, having a thickness of less
n } in. shall be used except for fillers.
23. Bracing. — Lateral, longitudinal and transverse bracing shall preferably be composed of
id members.
24. Material. — All parts of the structure shall be of rolled steel except column bases, bearing
tes, separators or minor details which may be of cast iron or cast steel. The steel shall be
made by the open-hearth process. All rolled steel, cast steel and cast iron shall comply with the
"Specifications for Structural Steel for Buildings" adopted by the American Society for Testing
Materials and printed in Chapter XV.
25. Stresses. — All parts of the structural framework shall be designed for the same unit
stresses as for steel frame buildings given in sections 32 to 46 inclusive of "Specifications for
Steel Frame Buildings" in Chapter I.
26. Details of Construction. — The details of construction shall comply with the specifications
for steel frame buildings given in sections 78 to 117 inclusive of "Specifications for Steel Frame
Buildings," in Chapter I.
27. Workmanship. — The workmanship shall be equal to the best practice in modern bridge
works and shall comply with sections 143 to 186 inclusive of "Specifications for Steel Frame
Buildings" in Chapter I.
28. Inspection and Testing at Mill and Shop. — The specifications are the same as given in
sections 187 to 193 inclusive in "Specifications for Steel Frame Buildings" in Chapter I.
ERECTION.
29. Tools. — The contractor shall furnish at his expense all necessary tools, derricks, hoists,
staging and material of every description required for the erection of the work, and shall remove
same when the work is completed.
30. Risks. — The contractor shall assume all risks from storms or accidents, unless caused by
the negligence of the owner, and all damage to adjoining property and to persons until the work
is completed and accepted.
31. The contractor shall comply with all ordinances or regulations appertaining to the work.
32. Details of Erection. — The structural steel and iron work shall be erected as rapidly as
the progress of the other work on the building will permit. Bases, bearing plates and ends of
106 STEEL OFFICE BUILDINGS. CHAP. II.
girders which require to be grouted, shall be supported exactly at the proper level by means of
steel wedges. Structural steel and ironwork shall be set accurately to the established lines and
levels. The steel and iron must be plumb and level before riveting is commenced and must be
kept in position until final completion. Temporary bracing shall be provided to resist the stresses
due to derricks and other erection equipment. Elevator shafts shall be plumbed from top to
bottom with piano wire. Riveted connections shall be carefully drawn up before riveting is
commenced. Not less than one-third the holes shall be filled with field bolts, drawn up tight.
All field connections shall be riveted. Pneumatic hammers shall be used in driving field rivets.
Rivets must have a sufficient length to completely fill the holes and to form full heads. Rivets
must be tight with full concentric heads. Loose or imperfect rivets must be cut out and redriven,
recupping or calking will not be permitted. Holes which will not admit a cold rivet must be
reamed. Where bolts are permitted, washers not less than £ in. thick shall be used under the
nuts, the nuts shall be drawn tight and the threads checked with a chisel. Connections to cast
iron and for separators in steel beams may be bolted.
REFERENCES.— For the details of the design of tall buildings the following books may be
consulted: Kidder's "Architects and Builders Pocketbook"; Freitag's "Fire Prevention and
Fire Protection"; Freitag's "Architectural Engineering"; Ketchum's "The Pesign of Steel Mill
Buildings."
For a full discussion of foundations for steel office buildings, see Jacoby and Davis, " Founda-
tions of Bridges and Buildings," published by McGraw-Hill Book Co.
CHAPTER III.
STEEL HIGHWAY BRIDGES.
Definition. — A truss is a framework composed of individual members so fastened together
that loads applied at the joints produce only direct tension or compression. The triangle is the
only geometrical figure in which the form is changed only by changing the lengths of the sides.
In its simplest form every truss is a triangle or a combination of triangles. The members of the
iss are either fastened together with pins, pin-connected, or with plates and rivets, riveted.
Types of Truss Bridges. — The bridge in Fig. I consists of two vertical trusses which carry
the floor and the load; of two horizontal trusses in the planes of the top and bottom chords, re-
spectively, which carry the horizontal wind load along the bridge, and of cross-bracing in the planes
of the end-posts, called portals, and in the planes of the intermediate posts, called sway bracing.
ftrtal —
*X, U10°
FIG. i. DIAGRAMMATIC SKETCH OF A THROUGH PRATT TRUSS HIGHWAY BRIDGE.
The floor is carried on joists or stringers placed parallel to the length of the bridge, and which are
supported in turn by the floorbeams. The names of the different parts of the bridge are shown
in Fig. i. The main ties, hip verticals, counters and intermediate posts are together called
"webs." The bridge shown in Fig. i, is a through pin-connected highway bridge of the Pratt
type, the traffic passing through the bridge. In a deck bridge the roadway floor is carried on top
of the main trusses. The bridge shown has square abutments; if the abutments are not at right
107
108
STEEL HIGHWAY BRIDGES.
CHAP. III.
angles to the center line the bridge is called a "skew" bridge. Short span highway and railway
bridges have low trusses and no top lateral system nor portals, as in Fig. 2. In a railway bridge
the loads are carried to the panel points by stringers resting on or riveted to the floorbeams.
V
*lii
Plate Beam Hang*r End View
iiyi;iiiiiiiiimi|
4*6 felloe Guard
II I U I I I I I I I | I ' '
m#fe?*
LIXJ.uJ-L.lj j_i_UJJ
Quarter lop Plan
Quarter Bottom Plan.
*-- -Floor beam
Cross Section
FIG. 2. PLAN OF A Low OR "PONY" TRUSS HIGHWAY BRIDGE.
The simplest type of bridge is the beam bridge, (a) Fig. 3. Beam bridges commonly consist
of I beams which span the opening, and are placed near enough together to carry the floor of the
(a) B>eam Bridge.
(a/) L ow Warren Truss.
pfe
I
(b) Beam L eg Bridge, (e) Low Pratt Truss. Half Hip.
(c) Truss L eg Bridge. (f) L ow Pratt Truss. Full 5 I ope.
FIG. 3. TYPES OF SHORT SPAN HIGHWAY BRIDGES.
bridge. Where foundations are relatively expensive the beams may be carried on posts as in
(b), Fig. 3. A truss leg-bridge is shown in (c), Fig. 3. Types (b) and (c) unless constructed with
great care make inferior structures and are not to be recommended. A Warren truss is a combi-
TYPES OF TRUSS BRIDGES.
109
nation of isosceles triangles as shown in (d), Fig. 3 and in (c) and (d), Fig. 4. The Pratt truss
has its vertical web members in compression while its diagonal web members are in tension, as
shown in (b), Fig. 4. The Warren truss is commonly built with riveted joints while the Pratt
truss is usually built with pin-connected joints. The Warren low truss with riveted joints as
shown in (d) is generally preferred in place of the low Pratt truss in either (e) or (f), Fig. 3. The
Howe truss has its vertical web members in tension, and its inclined web members in compression
as shown in (a), Fig. 4. The upper and lower chords and the inclined members of a Howe truss
commonly made of timber, while the vertical tension members are iron or steel rods or bars.
(a) THROUGH HOWE TRUSS
(b) THROUGH PRATT TRUSS
/KXXXXXV
(c) THROUGH WARREN TRUSS
(d) QUAOKANGULAR THROUGH WARKEN TRUSS
THROUGH WHIPPLE TRUSS
(F) CAMEL BACK TRUSS
THROUGH BALTIMORE TRUSS
(h) K-TRUSS
(i) THROUGH PETIT TRUSS (j)K-TRUSS
FIG. 4. TYPFS OF HIGH TRUSS STEEL BRIDGES.
The Whipple truss, (e) Fig. 4, is a double intersection Pratt truss. This truss was designed
give short panels in long spans which have a considerable depth. The stresses in the Whipple
truss are indeterminate for moving loads, and its use has been practically abandoned, the Balti-
more truss, (g) Fig. 4 being used in its place. The quadrangular Warren truss with riveted joints
is used by the American Bridge Company as a standard truss for through highway bridges, with
spans of from 80 to 170 ft. Like the Whipple truss its stresses are indeterminate for moving loads.
For spans of from, say, 170 to 240 ft. it is quite common to use pin-connected trusses of the
Pratt type having inclined chords as in (f), Fig. 4. The K-bracing in (h) or (j) is more economical
of material and gives smaller secondary stresses than the subdivided bracing in (g) and (i), and
is rapidly replacing both forms of bracing shown.
The Baltimore truss, (g) Fig. 4, is a Pratt truss with parallel chords in which the main panels
have been subdivided by an auxiliary framework. The auxiliary framework may have struts
as in (g), or ties as in (i), Fig. 4. The Baltimore truss with inclined upper chords, (i) Fig. 4, is
110
STEEL HIGHWAY BRIDGES.
CHAP. III.
called a Petit truss. Baltimore and Petit trusses are statically determinate for all conditions
of loading; are economical in construction and satisfactory in service, and have almost entirely
replaced the Whipple truss for long span bridges.
The types of simple bridge trusses described above are those that are in the most common
use, although quite a number of other types of trusses have been used and abandoned.
Beams and Plate Girders. — For spans of, say, 30 ft. and under rolled beams are often used to
carry the roadway, while for spans from about 30 to 100 ft. plate girders are used for city bridges.
When the roadway is carried on top of the girders, the bridge is called a deck plate girder bridge,
and when the roadway passes between the girders, the bridge is called a through plate girder
bridge as in Fig. 19.
(3) SMNG BRIDGE, CENTER BEARING fa) smN6 &RIDGEt TURNTABLE BEARINQ
FIG. 5. SWING BRIDGES.
Swing Bridges. — Swing bridges may be made of plate girders or trusses,, and may turn on a
center pivot as in (a), or on a turntable supported on a drum as in (b), Fig. 5. The center pivot
swing bridge has two spans continuous over the pivot support, while the turntable swing bridge
has three spans ordinarily continuous over the middle supports.
Steel Arches. — Steel arch bridges are made (i) with three hinges, (2) with two hinges, and
(3) without hinges, and may have solid webs, or spandrel or open webs.
Cantilever Bridges. — A cantilever bridge consists of two anchor spans, which support a
suspended or channel span. The shore ends of the anchor spans are anchored to the shore piers
and are supported on the river piers.
Suspension Bridges. — In a suspension bridge the roadway is supported by hangers attached
to the main cables. Stiffening trusses are placed above the plane of the roadway to assist in
distributing the live loads and for the purpose of increasing the rigidity of the structure.
Simple truss bridges, beam and plate girder bridges, only, will be considered in this book.
TYPES OF STRUCTURE.— The types of structure for steel highway bridges as recommended
by the author are given in section 3, " General Specifications for Steel Highway Bridges," printed
in the last part of this chapter.
The following data will show present standard practice.
Illinois Highway Commission. — The types of highway bridge recommended by the commis-
sion are as follows:
Concrete Bridges. — For culverts requiring a waterway of 12 square feet or less, plain or rein-
forced concrete arch culverts or square culverts, reinforced concrete pipes or double strength cast-
iron pipe.
For culverts having an area of more than 12 square feet, and for bridges having a span up to
30 ft., reinforced concrete slabs, plain or reinforced concrete arches.
For spans of 30 ft. to 65 ft., reinforced concrete through or deck girders, plain or reinforced
concrete arches.
For spans greater than 65 ft., plain or reinforced concrete arches.
Steel Bridges. — For spans of 12 ft. to 45 ft., steel I-beams; for spans of 30 ft. to loo ft., plate
girders or riveted pony trusses; for spans of go ft. to 160 ft., riveted trusses with parallel chords;
for spans of 160 ft. and more, riveted or pin-connected trusses with parallel or inclined upper chords.
Iowa Highway Commission. — The types of highway bridges recommended by the commission
are as follows:
Concrete Bridges. — Box culverts for spans up to 16 ft.; slab bridges for spans from 14 ft. to
25 ft.; arch culverts and bridges for spans of 6 ft. and over; girder bridges for spans of from 24 ft.
to 40 ft.
Steel Bridges. — Steel I-beams up to 32 ft. span; plate girders, 20 ft. to 80 ft. span; low truss
30 ft. to loo ft. span ; high truss 100 ft. span and over, riveted up to 140 ft. span.
TYPES OF BRIDGES. Ill
Massachusetts Public Service Commission. — The types of highway bridge recommended by
the commission are as follows:
Sttel Bridges. — For spans up to 20 ft., wooden stringers or rolled beams; for spans from 20 ft.
to 40 ft., rolled beams or plate girders; for spans from 40 ft. to 70 ft., plate girders; for spans from
70 it. to 100 ft., plate girders or riveted trusses; for spans from loo ft. to 125 ft., riveted trusses; for
span* from 125 ft. up, riveted or pin trusses.
Wisconsin Highway Commission.— The types of highway bridge recommended by the com-
mission are as follows:
Concrete Bridges. — Spans of i| ft. to 10 ft., slab culverts and bridges; spans 10 ft. to 18 ft.,
slab bridges; spans 10 ft. to 40 ft., through girders.
Steel Bridges. — Spans 10 ft. to 38 ft., rolled beams; spans 35 ft. to 80 ft., Warren riveted low
trusses or plate girders; spans 80 ft. to 135 ft., Pratt riveted high trusses; spans over 135 ft., riveted
high trusses with curved chords.
WIDTH OF ROADWAY.— The following data will show standard practice.
Illinois Highway Commission. — The widths of roadways are specified for State Aid Routes,
'rincipally Traveled Roads, and Secondary Roads.
On Designated State Aid Routes. — Bridges up to and including 10 ft. span, 20 to 30 ft. roadway;
ridges over 10 ft. up to and including 60 ft. span, 1 8 to 24 ft. roadway; bridges over 60 ft. span,
16 to 20 ft. roadway.
On Principally Traveled Roads. — Bridges and culverts 10 ft. or less in span, 20 to 30 ft. road-
iray; bridges over 10 ft. and up to and including 60 ft. span, 16 to 20 ft. roadway; bridges over 60
t. span, 1 6 to 1 8 ft. roadway.
On Secondary Roads. — Bridges and culverts 10 ft. or less in span, 18 to 24 ft. roadway; bridges
jr 10 ft. span, 16 ft. roadway.
Culverts Under Fills. — The length of the barrel of the culvert shall have a length that will
jrmit of side slopes of ij horizontal to i vertical, and a top width of 20 to 30 ft. on State Aid
Dutes, 20 to 30 ft. on Principally Traveled Roads, and 1 8 to 24 ft. on Secondary Roads.
Iowa Highway Commission. — The widths of roadway for highway bridges as recommenedd
jy the commission are as follows:
Concrete Bridges. — For box or arch culverts with spans of 2 ft. to 16 ft., 24 ft. roadway for
junty roads, and 20 ft. for township roads; for slab bridges with spans over 16 ft. span, 20 ft.
idway for county roads, and 18 ft. for township roads; for girder bridges over 16 ft. span, 20 ft.
idway ; for arches over 16 ft. span, 24 ft. roadway for county roads, and 20 ft. for township roads,
"he slopes on fills shall be I \ horizontal to i vertical.
Steel Bridges. — A roadway of 20 ft. on county roads, for all spans, and 18 ft. on township roads
)r all spans. The minimum legal width of rpadway is 16 ft.
Association of State Highway Departments. — The following minimum widths of concrete
ridges are recommended.
For First Class Roads. — Culverts under 12 ft. span, 24 ft. roadway; slab bridges over 12 ft.
in, 20 ft. roadway; all other spans 20 ft. roadway.
For Second Class Roads. — Culverts under 12 ft. span, 20 ft. roadway; slab bridges over 12 ft.
in, 18 ft. roadway; all other spans, 18 ft. roadway.
For Third Class Roads. — Culverts under 12 ft. span, 20 ft. roadway; slab bridges over 12 ft.
in, 1 8 ft. roadway; longer bridges, 16 ft. roadway.
The above widths of concrete bridges have been adopted by the Wisconsin Highway Com-
sion.
LOADS. — The loads carried by a bridge consist of (i) fixed or dead loads, (2) the moving or
live load, and (3) miscellaneous loads.
The dead load consists of the weight of the structure and is always carried by the bridge; the
live load consists of the moving load which the bridge is built to carry, while the miscellaneous
loads include wind loads, snow loads, etc. Data on dead loads are given in the " Specifications for
Steel Highway Bridges " in the last part of this chapter.
WEIGHTS OF BRIDGES.— The weight of a bridge is composed of (i) the weight of the steel
in the steel framework, consisting of the vertical trusses, the upper and lower lateral systems, the
floorbeams, the portals and sway bracing; (2) the weight of the joists and the fence; and (3) the
weight of the floor covering.
112 STEEL HIGHWAY BRIDGES. CHAP. III.
WEIGHTS OF STEEL HIGHWAY BRIDGES.— The following data may be used in calcu-
lating the dead loads in the design of highway bridges or as a basis for preliminary estimates.
AMERICAN BRIDGE COMPANY.— Standard Steel Highway Bridges with Timber Floor.
Timber floor, 3-in. plank on roadway and 2-in. plank on footwalks. Live loads for floor and its
supports, 100 Ib. per sq. ft. of floor surface, or 6 tons on two axles 10 ft. centers and 5 ft. gage, or a
15-ton road roller. For trusses 100 Ib. per sq. ft. of roadway up to a span of 75 ft., 75 Ib. per sq. ft.
of roadway for spans of 168 ft. and over, and proportional for intermediate spans. No allowance
is made for impact. Designed for allowable stresses given in specifications in the latter part of this
chapter. Let W = weight of the structural steel per lineal foot of span; L = length of span in feet,
b = width of roadway in feet (without sidewalks).
1. Steel Through Plate Girders. — Through plate girder spans 36 ft. to 70 ft., roadway 20 ft.
wide, without sidewalks, but including stringers. The weight of structural steel per lineal foot
of span is
W = 300 + 3.8L. (i)
For sidewalks with steel joists add about 12 Ib. per sq. ft. of sidewalks.
2. Steel Low Riveted Truss Spans, with Timber Floor. — For low truss spans 36 ft. to 102 ft.,
with timber floors, the weight of structural steel per lineal foot of span, not including the weight
of the stringers and the railing, is given approximately by the formula for a i6-ft. roadway
W = 100 + 2.oL. (2)
and for a 2O-ft. roadway
W = 150 + 1.7 L. (3)
3. Steel Low Riveted Truss Spans, with Reinforced Concrete Floors. — For low truss spans
36 ft. to 102 ft., with reinforced concrete floors, 5 in. thick with 6 in. of gravel at center and 3 in.
of gravel at curb, the weight of structural steel per lineal foot of span, not including the weight of
the stringers and the railing, is given approximately by the formula for a i6-ft. roadway
W = 150 + 3-5L. (4)
and for a 2O-ft. roadway
W = 185 + 3.5!*. (5)
4. Steel High Truss Spans, with Timber Floor. — For high truss spans 104 to 204 ft., with
timber floors the weight of structural steel per lineal foot of span, not including the weight of the
stringers and the railing, is given approximately by the formula for a i6-ft. roadway
W = 250 + i.sL. (6)
and for a 2O-ft. roadway
W = 285 + 1.2 L. (7)
IOWA HIGHWAY COMMISSION.— Steel Highway Bridges with Reinforced Concrete
Floor. — Reinforced concrete floor slabs 6 in. thick for all spans in which stringers are used. Slabs
for stringerless floors 1\ in. thick for 8-ft. span, 8 in. thick for g-ft. span, and 85 in. .thick for xo-ft.
span. Live loads for the floor and its supports a uniform live load of 100 Ib. per sq. ft., and a 15-ton
traction engine with two-thirds of the load on the rear axle; axles spaced n ft. centers, and rear
wheels spaced 6 ft. centers. Rear wheels 22 in. wide. The trusses are to be designed for the
uniform loads given in Table I. No allowance is made for impact.
Let W = weight of structural steel in Ib. per lineal foot of span; L = length of span in feet;
b = width of span in feet (without sidewalks).
i. Steel Beam Spans. — The weight of steel beam spans from 16 ft. to 32 ft. and with i6-ft.,
i8-ft., and 2O-ft. roadway are given in Table IX.
WEIGHTS OF STEEL HIGHWAY BRIDGES. 112a
2. Steel Low Truss Spans, with Stringers. — For low truss highway bridges with spans of
ft. to s.s ft., not including the weight of the fence or the steel stringers, the weight of structural
T liiir.il foot of span for a i6-ft. roadway is
W = 235 + 2.35^- (8)
ami tor .in l8-ft. roadway is
W = 240 -f 2.40!,. (9)
3. Steel Low Truss Spans, without Stringers. — For low truss highway bridges with spans of
35 ft. to 100 ft., not including the weight of the fence or steel floorbeams, the weight of the struc-
tural steel per lineal foot of span for a i6-ft. roadway is
W = 200 -f 4,L. (10)
for an i8-ft. roadway is
W = 225 + 4.25 L. (u)
4. Steel High Truss Spans, with Stringers. — For high through truss highway bridges with
ins of from 90 ft. to 150 ft., not including the weight of fence or the steel stringers, the weight of
structural steel per lineal foot of span for a i6-ft. roadway is
W = 245 + 2.45!,. (12)
for an i8-ft. roadway is
W = 270 + 2.7 L. (13)
WISCONSIN HIGHWAY COMMISSION. Steel highway bridges with reinforced con-
te floor. — Reinforced concrete floor slabs 6 in. thick for all spans. Live loads for the floor and
supports a 1 5-ton road roller with two-thirds of the load on the rear axle, axles 10 ft. centers,
rolls 4 ft. 10 in. centers, rear rolls 20 in. wide. The trusses designed for the loads given in
Table I. No allowance is made for impact. Let W = weight of structural steel in Ib. per lineal
: of span, L = length of span in feet; b = width of roadway in feet (without sidewalks).
1. Steel Beam Spans. — Weight of steel beam spans from 10 ft. to 38 ft. and for i6-ft., l8-ft.
2o-ft. roadway are given in Table X.
2. Steel Through Plate Girders. — The weight of the structural steel in through plate girder
iway bridges from 35 ft. span to 80 ft. span including floorbeams spaced 3 to 2\ ft. apart, is
sn approximately by the following formula. For a i6-ft. roadway
W = 300 + ZL. (14)
an i8-ft. roadway
W = 300 + 3-25£- (15)
for a 2O-ft. roadway
W = 320 + *L. (16)
3. Steel Low Truss Spans, with Stringers. — The weight of the structural steel in low truss
el highway bridges with spans of 35 ft. to 85 ft. span, not including1 the weight of the fence or
: steel stringers, is given approximately by the formula. For a i6-ft. roadway
W = 80+3.5!,. (17)
and for an l8-ft. roadway
W = 80 + *L. (18)
4. Steel High Truss Spans, with Stringers. — For high through truss steel highway bridges
with spans of from 90 ft. to 150 ft., not including the weight of the fence or the steel joists, the
weight of structural steel per lineal foot of span is given approximately by the formula. For a
i6-ft. roadway
W = 180 + 2L. (ig)
and for an i8-ft. roadway
W = 240 + 2L. (20)
S'
112b STEEL HIGHWAY BRIDGES. CHAP. III.
ILLINOIS HIGHWAY COMMISSION. Steel highway bridges with reinforced concrete
floor. — Reinforced concrete floor slabs 4 in. thick with a wearing surface assumed to weigh not
less than 50 Ib. per sq. ft. Live load for floor and its supports a 1 5-ton traction engine, supported
on two axles spaced 10 ft. apart, with two thirds of the load on the rear axle; or a uniform live load
of 125 Ib. per sq. ft. The trusses designed for the loads given in Table I. No allowance is made
for impact.
Let W = weight of steel in Ib. per lineal foot of span, L = span of bridge in feet, b = width of
roadway in feet (without sidewalks).
1. Steel Low Truss Spans, with Stringers. — The weight of the structural steel in low truss
steel highway bridges with spans of 50 ft. to 85 ft., not including weight of the fence or the steel
stringers, is given approximately by the formula. For a i6-ft. roadway, b = 16 ft.
W = 235 + 2.35!,. (21)
and for an i8-ft. roadway, b = 18 ft.
W— 240 + 2.4-L. (22)
2. Steel High Truss Spans, with Stringers. — The weight of structural steel in high truss steel
highway bridges with spans of 90 ft. to 160 ft., not including the weight of fence or the steel string-
ers, is given approximately by the formula. For a i6-ft. span, b = 16 ft.
W = 140 + \L. (23)
and for an l8-ft. span, b = 18 ft.
W = 1 80 + 4.5 L. (24)
The weights given by formulas (21) to (24) are for bridges with concrete floors weighing
loo Ib. per sq. ft. Calculations by Mr. Clifford Older, Bridge Engineer, Illinois Highway Com-
mission, show that a variation of the weight of the floor of 10 Ib. per sq. ft. makes a similar variation
in the weight of the structural steel, including the joists, of 4.35 per cent for a 50-ft. span, of 3.75
per cent for a i6o-ft. span, and proportional for intermediate spans. For the structural steel, not
including the joists, an average value of 4 per cent may be used for each decrease of 10 Ib. per sq.
ft. of floor surface.
BOSTON BRIDGE WORKS STANDARDS.*— The weights of steel highway bridges
designed by the Boston Bridge Works are as follows:
Through truss highway bridges without sidewalks designed for a live load of 80 Ib. per sq. ft.
for the trusses, 100 Ib. per sq. ft. and a 6-ton wagon for the floor The weight, w, of steel in Ib.
per sq. ft. of area covered by the floor, not including joist or fence, for a span of L ft., is
w = 5 + L/g.s (25)
The weight of through truss highway bridges with two sidewalks is
w = 2.8 + L/ii.3 (26)
The sidewalks were 5 or 6 ft. wide, and the clear roadways were 1 6 to 20 ft. The total area
covered by the roadway and sidewalk floors is to be used in calculating the weight of steel.
Weights of Steel Highway Plate Girder Bridges. — The weights of highway plate girder
bridges as designed by the Boston Bridge Works for the live loads shown are as follows.
Deck plate girder highway bridges without sidewalks designed for a live load of 100 Ib. per
sq. ft. for girders, 100 Ib. per sq. ft. and a 6-ton wagon for the floor. The weight, w, of steel in
Ib. per sq. ft. of area covered by the floor, not including joist or fence, for a span of L ft., is
w = 2.5 + L/34 (27)
* Published by permission of John C. Moses, Chief Engineer.
LIVE LOADS. 112c
The weight of deck plate girder highway bridges with sidewalks is
w - 2.5 + Z./4-4 (28)
The weight of through plate girder highway bridges without sidewalks is
w = 3 + L/4.25 (29)
The weight of through plate girder highway bridges with sidewalks is
v> = 3-3 + L/5.6 (30)
Weight of Electric Railway Bridges. — The Boston Bridge Works gives the following formula
for the weight of electric railway bridges, where W = total weight of steel in Ib. per lineal foot of
bridge and L is the span of the bridge in feet.
Beam bridges
W = 50 + 5L (31)
Light truss bridges
W = 200 + o.8L (32)
Heavy truss bridges
W = 250 + i.5L (33)
The beam bridges were designed for 3O-ton cars; the light truss bridges were designed for
-ton cars or 1,500 Ib. per lineal foot of bridge, and the heavy truss bridges were designed for
•ton cars, or 2,000 Ib. per lineal foot of bridge.
LIVE LOADS. — The live loads for highway bridges are usually assumed to consist of a uni-
live load for the trusses and a uniform live load or a concentrated moving load for the floor
its supports. A few highway bridge specifications require that trusses be designed for a con-
itrated moving load as well as for a uniform live load, and also that the floor and its supports be
jsigned for a concentrated moving load and that the portion of the floor of the bridge not covered
by the concentrated load be covered with a uniform live load. In calculating the stresses in the
truss members the uniform live load is commonly assumed as applied in full joint loads at joints
on the loaded chord. Moving loads and loads suddenly applied produce stresses that are greater
than the static stresses due to stationary loads or to loads gradually applied. This increase in
stress due to moving loads or due to loads suddenly applied is called impact stress.
IMPACT. — The effect of impact or increase in live load stresses over the stresses due to the
same loads gradually applied, is very much less for highway bridges than for railway bridges.
Experiments made by Professor F. O. Dufour and recorded in Journal of Western Society of Engi-
neers, June, 1913, show that the effect of impact on steel truss highway bridges with concrete floors
is very small. The effect of impact on steel truss bridges with plank floors is considerably larger
than for bridges with concrete floors. The maximum impact percentages do not occur with maxi-
mum static stresses. Experiments made at the University of Colorado under the author's direction
show that the effect of impact on highway bridges is very much less than for railway bridges.
The specifications of the highway commissions of Illinois, Iowa, Michigan, Nebraska and
Wisconsin do not add impact for highway bridges.
The allowance for impact of the Massachusetts Railway Commission is as follows: For
stringers, floorbeams and hangers, when loaded with a 2O-ton auto truck, 50 per cent; for all other
loads, floorbeams and stringers, 25 per cent; floorbeam hangers, 40 per cent; counters, 40 per cent;
for all other members in trusses, and for main girders the percentage shall be 26$ minus one-
twelfth the loaded length in feet, with a maximum of 25 and a minimum of 10 per cent.
Mr. J. A. L. Waddell in "Bridge Engineering" specifies that highway bridges shall be designed
for the impact allowance, / = ioo/(»Z, + 200), where L is the loaded length of the bridge in feet
that produces maximum stress and n is the total clear width of the roadway and footwalks divided
by twenty. The above impact allowance is made for motor-truck loadings but not for road-roller
loadings.
112d STEEL HIGHWAY BRIDGES. CHAP. III.
The specifications for steel bridges prepared by the U. S. Office of Public Roads, and the
specifications for steel bridges of the West Virginia Highway Commission and the Oregon Highway
Commission specify the impact factor, / = ioo/(L + 300), where L is the loaded length of the
bridge in feet that produces maximum stress in the member.
The Montana Highway Commission specifies 25 per cent impact.
The Department of Public Roads of Kentucky requires no impact allowance for bridges with
concrete floors, and 25 per cent for bridges with wooden floors.
The Utah Highway Commission specifies 25 per cent impact for floors, and 15 per cent for
trusses.
For concrete highway bridges the impact allowance varies from no impact allowance, as
specified by the highway commissions of Illinois, Iowa, Michigan, Nebraska and Wisconsin; an
allowance of 15 per cent of the live load, as specified by the highway commission of West Virginia,
to an allowance of 50 per cent of the live load, as specified by the U. S. Office of Public Roads.
Watson's "General Specifications for Concrete Bridges," third edition, 1916, uses an impact al-
lowance of 7 = i5o/(L + 300), where L is the loaded length of the bridge in feet that produces
maximum stress.
Ketchum's Specifications for Impact. — The author has adopted the following impact factors
for concrete bridges and steel bridges.
(a) For concrete arches with spandrel filling on culverts with a minimum filling of one foot,
no allowance for impact.
(b) For concrete slab and girder bridges and trestles, and arches without spandrel filling, 30
per cent for impact.
(c) For steel bridges the following allowance for impact. For the floor and its supports in-
cluding floor slabs, floor joist, floorbeams and hangers, 30 per cent.
For all truss members other than the floor and its supports, the impact increment shall be
7 = ioo/(L + 300), where L = length of span for simple highway spans (for trestle bents, towers,
movable bridges, arch and cantilever bridges, and for bridges carrying electric trains, L shall be
taken as the loaded length of the bridge in feet producing maximum stress in the member).
CONCENTRATED LIVE LOADS. — Traction engines weighing 20 tons are quite common in
the west and northwest. The heaviest motor truck in common use has a capacity of 75 tons and
a total weight of 13 tons, with nearly 10 tons on the rear axle. With an overload of 50 per cent,
which is not unusual, this truck would carry 14 tons on the rear axle. The maximum road roller
weighs 20 tons.
The highway commissions of the different states have adopted concentrated live loads as fol-
lows: Illinois specifies a 15-ton traction engine; Iowa specifies a 15-ton traction engine for bridges
with reinforced concrete floors; Wisconsin specifies a 15-ton road roller; Michigan specifies an i8-ton
road roller; Nebraska specifies a 2o-ton traction engine; Minnesota specifies a 2o-ton traction
engine; New York specifies a 1 5-ton road roller; all loadings to be used without impact.
Utah specifies an i8-ton road roller with 25 per cent impact; Oregon specifies a 15-ton road
roller for medium traffic and a 2O-ton road roller for heavy traffic; Ohio specifies a 15-ton concen-
trated load with l6f per cent impact; Montana specifies a 2O-ton traction engine with 25 per cent
impact; the Massachusetts Railway Commission specifies a 2O-ton motor truck with 14 tons on the
rear axle, with an allowance of 50 per cent for impact on the floor and its supports; Mr. J. A. L.
Waddell in "Bridge Engineering" specifies for class A bridges an i8-ton motor truck with impact
allowance as given above.
For additional data see article entitled "Concentrated Live Loads for Highway Bridges,"
by Milo S. Ketchum, printed in University of Colorado Journal of Engineering, October, 1916.
Ketchum's Specifications for Concentrated Moving Loads. — The author has adopted the
following specifications for moving concentrated loads.
(a) That highway bridges on main roads or near towns or cities shall be designed to carry
a 2O-ton motor truck with axles spaced 12 ft. and wheels with a 6-ft. gage, with 14 tons on rear axle
and 6 tons on front axle. The truck to occupy a space 10 ft. wide and 32 ft. long. The rear wheels
to have a width in inches equal to the total load in tons (20 in. for a 2o-ton truck).
(b) That bridges not on main roads shall be designed for a 1 5-ton motor truck with axles
spaced 10 ft. and wheels with a 6-ft. gage, and occupying a space IO ft. wide and 30 ft. long, with
10 tons on rear axle and 5 tons on front axle, and with rear wheels 15 in. wide.
(c) To provide for impact and vibration and unevenness of road surface thirty (30) per cent
is to be added to the maximum live load stresses. Only one motor truck is to be assumed to be on
a bridge at one time.
CONCENTRATED LIVE LOADS. 112e
Motor trucks have narrower tires and are driven at greater speeds than traction engines, and
thrn-fore not only produce greater static stresses in the floor, but should have a greater impact
allowance. In view of the above, it would not appear to be necessary to consider any road rollers
or traction engines now in use in addition to the above motor-truck loadings.
DISTRIBUTION OF CONCENTRATED LOADS.— In designing floor slabs, floor stringers
and floorbeams it is necessary to know the distribution of the concentrated loads.
Concrete Floor Slabs. — Tests of the distribution of concentrated loads on concrete floor slabs
have been made by the Ohio Highway Commission, the results of which are given in Bulletin No.
28, published by the Commission; by Mr. W. A. Slater at the University of Illinois and described
in Proceedings of American Society for Testing Materials, Vol. XIII, 1913, and by A. T. Goldbeck
and E. B. Smith, described in Journal of Agricultural Research, Vol. VI, No. 6, Department of
Agriculture, Washington, D. C., May 8, 1916.
Ohio Tests. — The following conclusions drawn from the Ohio tests are of interest:
" The percentage of reinforcement has little or no effect upon the distribution to the joists, so
long as safe loads on the slabs are not exceeded.
"The outside joists should be designed for the same total live load as the intermediate joists.
" The axle load of a truck may be considered as distributed over 12 ft. in width of roadway.
"The safe value for ' effective width 'of a slab, where the total width of slab is greater than
1.33 L + 4 ft. is given by the formula, e = O.6L + 1.7 ft., where e = effective width (width over
which a single concentrated load may be considered as uniformly distributed on a line down the
middle of the slab parallel to the supports) and L = span in feet. '
Slater Tests. — It was recommended that where the total width of slab is greater than twice
the span, the effective width be taken as e = 42/3 + d, where x is the distance from the concen-
ited load to the nearest support, and d is the width at right angles to the support over which the
id is applied. While the depth of slab and the amount of longitudinal reinforcement had little
Feet on the distribution, it was recommended that the latter be limited to I percent.
Goldbeck and Smith Tests. — Tests were made on three slabs, each slab being 32 ft. wide, 16 ft.
in, and with effective depths of 10.5 in., 8.5 in. and 6 in., respectively. All slabs were made of
1-2-4 Portland cement concrete, and were reinforced with 0.75 per cent of mild steel.
The following conclusions were drawn from these tests:
(1) The effective width decreases as the effective depth increases; the effective width for safe
ids being 75.7 percent; 81.1 percent, and 109.3 percent of the span, for the slabs having effective
jpths of 10.5 in., 8.5 in. and 6 in., respectively.
(2) For slabs in which the ratio of the width of the slab is not less than twice the span length,
ic effective width may be taken as
e = 0.7 L (34)
icre e is the effective width and L is the span length.
(Additional tests by Goldbeck, Proceedings American Concrete Institute, 1917, show that
lula (34) may be used when the width of the slab is not less than the span.)
Watson's " General Specifications for Concrete Bridges," third edition, 1916, specifies that con-
itrated loads on reinforced concrete slabs may be assumed as distributed over a distance of 4 ft.
right angles to the supports, and a distance parallel to the supports equal to 2 ft. plus three-
iths of the span of the slab.
The State Highway Department of Ohio uses the following distribution of concentrated loads
floor slabs.
For spans less than 6 ft. the percentage, p, of the wheel load carried by one foot in width of
ib for a span in feet, /, is given by the formula
p = 42 - 47 (35)
vhile for spans greater than 6 ft. the percentage, p', of the wheel load carried by one foot in width
Df slab for a span in feet, /, is given by the formula
p' = 20 - o.4/ (36)
For a span of 5$ ft., from formula (35), p = 20 per cent, and the concentrated load is assumed
as carried by a slab 5 ft. wide, applied on a line parallel to the supports.
For a span of 10 ft., from formula (36), p' = 16 per cent, and the concentrated load is assumed
as carried by a slab 6.67 ft. wide, applied on a line parallel to the supports.
!
112f
STEEL HIGHWAY BRIDGES.
CHAP. III.
Floor Stringers and Floorbeams. — The Illinois Highway Commission specifies that longi-
tudinal stringers be spaced not more than 2%-ft. centers, and that each stringer be designed for 20
per cent of the rear axle load concentrated at the center of the span when a concrete sub-floor is
used, and 25 per cent of the rear axle load when a plank floor is used. Transverse stringers or
floorbeams, spaced not more than 2|-ft. centers, shall be designed to carry 40 per cent of the rear
axle load distributed over the middle 10 ft. of the stringer. Floorbeams shall be designed for
maximum stresses due to concentrated load.
The Iowa Highway Commission specifies that one-third of a wheel load be assumed as carried
by one joist, when a concrete floor slab is used, and that one-half of a wheel load be assumed as
carried by one joist, when a plank floor is used.
The Massachusetts Railway Commission specifies that the wheel load on plank floors be dis-
tributed over a width in feet equal to the thickness of the floor in inches, with a maximum distri-
bution of 6 ft. With solid floors each wheel load is assumed as distributed over a width of 6 ft.
Watson's "General Specifications for Concrete Bridges," third edition, 1916, specifies that
the part of the concentrated load carried by one stringer shall be found by dividing the stringer
spacing by the gage distance of the concentrated load. With a gage distance of 6 ft. this gives
one-third the total load for a stringer spacing of 2 ft. ; one-half the total load for a stringer spac-
ing of 3 ft. ; the total load for a stringer spacing of 6 ft.
Ketchum's Specifications for Distribution of Concentrated Loads. — From a study of the
various tests and specifications, the author has adopted the following rules for calculating the
stresses in slabs, stringers and floorbeams:
l< 3->t
t \ /
h \*1../
A
,'
i
_i
! 4 \ / '
!
\ i.
i
! ! « V • '
i
/ry V*i ^
,/ »^ !-«--->- /
i
A 7 »
j
j
/
V / \
^ i
FiG.6.
FIG. 7.
(a) The distribution of concentrated wheel loads for bending moments in reinforced concrete
slabs with longitudinal girders shall be calculated by the formula,
e = f (/ + c)
(37)
with a maximum limit of 6 ft. for e, where e = effective width (distance that the load may be con-
sidered as uniformly distributed on a line down the middle of the slab parallel to the supports),
/ = span, and c = width of tire of wheel, all distances in feet. See Fig. 6.
(b) The distribution of concentrated wheel loads for bending moments in reinforced concrete
slabs with transverse girders shall be calculated by the formula
e = 2//3 + c
(38)
with a maximum limit of 6 ft. for e, where e = effective width, / = span, and c = width of tire of
wheel as defined in paragraph (a). See Fig. 7.
(c) The distribution of concentrated wheel loads for bending moments in slabs of girder
bridges in which the span of the bridge is not less than the width of bridge center to center of
girders, shall be calculated for spans of 9 ft. or over by the formula
e = 2//3
(39)
with a maximum limit of e = 12 ft., where e = effective width, and / = span as defined in para-
graph (a).
UNIFORM LIVE LOADS.
(d) The effective width for shear in beams carrying concentrated loads shall be taken the same
as for bending moment as calculated by formula (37) or formula (38), with a minimum effective
width of 3 ft. and a maximum effective width of 6 ft.
Tin- total shear for an effective width of 3 ft. shall be considered as punching (pure) shear.
Tin- total slu-ar for an effective width of 4.5 ft. and over shall be considered as beam shear (a
measure of diagonal tension), for effective widths between 3 ft. and 4.5 ft. the total shear shall be
divided proportionally between punching shear and beam shear. Beam shear shall be used in
calculating bond stress and as a measure of diagonal tension.
(e) In the design of longitudinal joists or stringers with concrete floors, the fraction of the
concentrated load carried by one stringer for spacings 6 ft. or less will be taken equal to the stringer
spacing in feet divided by 6 ft.; with plank floors the fraction of the concentrated load carried by
one stringer for spacings 4 ft. or less will be taken equal to the stringer spacing in feet divided
by 4 ft., the maximum in each case being the full load. Outside stringers are to be designed for
the same load as intermediate stringers.
(/) In the design of transverse stringers or floorbeams with concrete floors, the fraction of the
concentrated load carried by one floorbeam for floorbeams spaced 6 ft. or less, will be taken equal
to the floorbeam spacing divided by 6 ft. For floorbeams spaced 6 ft. or over the entire reactions
are assumed as carried by one floorbeam. Axle loads are assumed as distributed on a line 12 ft.
long.
UNIFORM LIVE LOADS FOR TRUSSES. — The uniform live loads for trusses of steel high-
way bridges as specified by the highway commissions of Illinois, Iowa and Wisconsin, the American
Concrete Institute, 1916, and the uniform loads as specified by the author for classes DI and Dz
are given in Table I. The DI and D2 loadings are to be taken as proportional for intermediate
spans, and are to be increased for impact.
It will be seen that the DI loadings with impact added are practically the same as the Illinois
idings; while the D2 loadings with impact added are practically the same as the Iowa and Wis-
consin loadings.
TABLE I.
UNIFORM LIVE LOADS FOR HIGHWAY BRIDGES.
Illinois High-
way Commis-
sion.
Iowa High-
way Commis-
sion.
Wisconsin High-
way Commission.
American Concrete Institute,
1916.
Ketchum's Specifications, 1918.
Class A.
Class B.
Class Da.
Class D,.
• £
"O •
£
TJ •
£
.£
£
•a" .
£
.£
•a .
£
£
•d" •
i
9
J*
a
&
3^
i
a r-
c
I
K
1
a"
i
j£
en
3
en
3
en
3
en
3
en
3
en
3
en
3
Up to 50
125
Up to 50
IOO
Up to 40
125
Up to 80
125
Up to 80
IOO
30
«5
3°
IOO
50-100
IOO
50-100
90
SO
120
80-100
IIO
80-100
90
50
106
SO
90
100-150
IOO
100-150
80
75
106
100-125
IOO
100-125
80
80
85
80
75
150-200
85
150-200
70
IOO
93
125-150
90
125-150
75
IOO
80
IOO
71
Over 200
85
200-250
50
150
60
150-200
85
150-200
65
160
68
1 60
60
Over 250
SO
1 80 and over
SO
Over 200
80
Over 200
60
200 and
60
200 and
So
over
over
Class DI and Dt bridge loadings to be increased for impact.
UNIFORM LIVE LOADS FOR FLOORS.— The Illinois Highway Commission specifies that
stringers and floorbeams for spans of 50 ft. and less shall be designed for a uniform live load of 125
Ib. per sq. ft., and of spans over 50 ft. in length for a uniform live load of 100 Ib. per sq. ft., or a
15-ton concentrated load for all spans. No allowance is made for impatt.
The Iowa Highway Commission specifies a live load of 100 Ib. per sq. ft. or a 15-ton traction
engine for class "A" floors, and a live load of 100 Ib. per sq. -ft., or a lo-ton traction engine for class
" B " floors (plank floors). No allowance is made for impact.
The Wisconsin Highway Commission specifies that floor systems and spans under 40 ft. be
designed for a 1 5-ton road roller. No allowance is made for impact.
H2h STEEL HIGHWAY BRIDGES. CHAP. III.
The Michigan Highway Commission specifies that the floor and its supports be designed for
an i8-ton road roller, or 100 Ib. per sq. ft. No allowance is made for impact.
The floor systems for Di bridges are to be designed for 125 Ib. per sq. ft. or a 2o-ton auto truck;
while D2 bridges are to be designed for 100 Ib. per sq. ft. or a 1 5-ton auto truck. An impact factor
of 30 per cent is to be added both for the uniform loads and for the auto truck.
WIND LOADS FOR HIGHWAY BRIDGES.— The Illinois Highway Commission specifies a
wind load of 25 Ib. per sq. ft. on the vertical projection of both trusses and the floor system, but in
no case shall the wind be less than 300 Ib. per lineal foot on the loaded chord nor less than 150 Ib.
per lineal foot on the unloaded chord.
The Iowa Highway Commission specifies 150 Ib. per lineal foot on the unloaded chord and
300 Ib. per lineal foot on loaded chord, all loads considered as moving loads.
The Wisconsin Highway Commission specifies 150 Ib. per lineal foot on the unloaded chord
and 300 Ib. per lineal foot on the loaded chord; 150 Ibs. of the latter being considered a moving
load.
Cooper's 1909 specifications require that highway bridges be designed for a lateral force of
150 Ib. per lineal foot on the unloaded chord and a lateral force of 300 Ib. per lineal foot on the
loaded chord, 150 Ib. of the load on the loaded chord being treated as a moving load. For spans
exceeding 300 ft. add in each case above 10 Ib. for each additional 30 ft.
The author's specifications for wind loads are given in " General Specifications for Steel High-
way Bridges" given in the latter part of this chapter.
DESIGN OF HIGHWAY BRIDGE FLOORS. Types of Floors.— The choice of floor for a
highway bridge depends upon the traffic, the cost, including first cost and cost of maintenance, and
the climate. A highway bridge floor consists of a sub-floor which has the necessary strength to
carry the loads and a wearing surface. Plank floors and reinforced concrete slabs without wearing
surface have the sub-floor and wearing surface combined. A highway bridge floor should have
a strength and a weight appropriate to the structure of the bridge, and should be well drained.
The wearing surface should be waterproof, capable of resisting wear and should be as smooth as
possible without being slippery. For proper drainage the wearing surface should have a longi-
tudinal grade of not less than I in 50 or a transverse slope of not less than I in 12. Sub-floors for
highway bridges are made (i) of reinforced concrete; (2) of buckle plates or other steel sections,
and (3) of timber. The most common wearing surfaces for highway bridge floors are (a) concrete,
(b) bituminous concrete, (c) asphalt, (d) creosoted timber blocks, (e) brick, (/) stone block, (g)
macadam, (h) gravel or earth. The different types of sub-floors and wearing surfaces for highway
bridges will be described in some detail.
Reinforced Concrete Floor Slabs. — Reinforced concrete floor slabs on steel highway bridges
may be supported on joists or stringers and floorbeams, or by the floorbeams alone. Stringers
are used for beam bridges and are commonly used for truss bridges, while the stringerless floor is
commonly used on plate girder bridges. The sub-floor slabs are commonly calculated to carry
the dead load due to the weight of the slab and of the wearing surface, and a live load consisting
of a uniform load per square foot or a concentrated moving load. The thickness of reinforced
concrete slabs in short spans is commonly determined by the concentrated moving load. The
stresses in reinforced concrete slabs due to a concentrated load will depend upon the distribution
of the load over the slab. The different methods for the distribution of concentrated loads in use
in different specifications have been described and the specifications adopted by the author have
already been given.
Design of Reinforced Concrete Floor Slabs. — The live loads and the distribution of loads on
floor slabs as specified by the author are given on pages H2d and H2f. The concrete should be
a 1-2-4 Portland cement concrete that will give a compressive strength of not less than 2,000 Ib.
per sq. in. when tested in cylinders 8 in. in diameter and 16 in. long after having been stored for
28 days in moist air. Allowable compression in slabs, 650 Ib. per sq. in.; allowable tensile stress
in steel, 16,000 Ib. per sq. in., modulus of elasticity of steel to be taken as 15 times the modulus of
elasticity of concrete, allowable shear as a measure of diagonal tension 40 Ib. per sq. in.; punching
shear 120 Ib. per sq. in., bond stress in slabs 120 Ib. per sq. in.
REINFORCED CONCRETE FLOOR SLABS.
1121
The thickness of floor slabs when supported on longitudinal joists or stringers is given in
T.i! ilc II and the thickness of floor slabs when supported on cross floorbeams (stringerless floor)
is given in Table III. The reinforcing steel for reinforced concrete floor slabs is given in Table
IV. The reinforcement given in the table is to be placed at the bottom of slabs calculated as
simply supported and at top and bottom of slabs calculated as continuous or partially continuous.
TABLE II.
THICKNESS OF REINFORCED CONCRETE FLOOR SLABS, USED WITH JOISTS.
Simply Supported, Reinforcement on Under Side Only.
Fully Continuous, Reinforcement on Both Sides.
Span,
Ft.
la-Ton Truck.
15-Ton Truck.
20-Ton Truck.
Span,
Ft.
ia-Ton Truck.
i5-Ton Truck.
20-Ton Truck.
Weight of Wearing Surface. Lb. per Sq. Ft.
Weight of Wearing Surface, Lb. per Sq. Ft.
o
too
o
too
o
ioo
o
zoo
0
100
o
100
2
3
4
I
in.
Si
i
6i
6i
in.
I*
6i
6|
7
in
Si
oj
6
6;
7<
i
in.
si
61
6J
'*
in.
si
6i
7
7f
81
in.
Si
6i
7i
8
8i
2
3
4
I
in.
4i
i
in.
4i
1
6
in
4J
5
5!
5^
6
in.
4f
i
6
61
in.
4l
Si
6
6i
6J
in.
4!
si
61
6i
7
Center of reinforcing i in. from face of slab. Impact 30 per cent.
Reinforced as in Table IV.
TABLE III.
THICKNESS OF REINFORCED CONCRETE FLOOR SLABS, USED WITHOUT JOISTS.
Simply Supported, Reinforcement on Under Side Only.
Partially Continuous, Reinforcement on Both Sides.
Span,
Ft.
1
\
8
9
10
12-Ton Truck.
i5-Ton Truck.
20-Ton Truck.
Span,
Ft.
12-Ton Truck.
i5-Ton Truck.
ao-Ton Truck.
Weight of Wearing; Surface, Lb. per Sq. Ft.
Weight of Wearing Surface, Lb. per Sq Ft.
o
in.
i
61
7
7
7i
8
8i
100
o
zoo
0
ICO
o
100
0
100
o
100
in.
Si
61
6}
jl
71
W
8f
9l
in.
6
6i
6|
\\
81
8J
9l
in.
6
6i
7
1
7i
81
H
9l
10
in.
6i
7i
8
81
8f
9l
10
10)
in.
6i
7*
81
8i
9
9i
iol
III
2
3
4
6
7
8
9
10
in.
sl
IJ
6
61
6|
6!
7i
n
in.
si
IJ
61
6i
6|
7l
8 .
8i
in.
i!
61
6i
64
6i
7i
8
8i
in.
Si
6
61
6i
£i
8
8i
9
in.
si
64
6i
**•
8
8i
9
9i
in.
H
7
?!
81
9
9i
10
Center of reinforcing I in. from face of slab for slabs less than J\ in. thick.
Center of reinforcing il in. from face of slab for slabs J\ in. and over, in thickness.
Impact 30 per cent, of live load.
Reinforced as in Table IV.
Examples of Reinforced Concrete Floor Slabs. — The reinforced concrete floor slabs used by
the Wisconsin Highway Commission are given in Fig. 14, Fig. 15, Fig. 21 and Fig. 22. The floor
slabs used by the Iowa Highway Commission are given in Fig. 12, Fig. 13, Fig. 17, and Fig. 24.
'For a stringerless floor the slabs used by the Iowa commission agree very closely with the values
given in Table III.
STEEL HIGHWAY BRIDGES.
CHAP. III.
TABLE IV.
REINFORCEMENT FOR REINFORCED CONCRETE FLOOR SLABS.
The reinforcement given in this table is to be used at the bottom of slabs figured as simple
supported, and at the top and bottom of slabs figured as continuous or partially continuous over
the supports. Longitudinal reinforcement ^ in. round or square bars spaced two feet centers.
Total
Thick-
Concrete
Outside
Center
Area of
Steel per
Foot
Weight
of Slab,
Lb. per
Spacing of Bars in Inches.
Round.
Square.
In.
Sq. In.
Sq. Ft.
fin.
iln.
fin.
iln.
fin.
Jin.
{In.
Jin.
5
I
0.370
63
^
61
IO
4*
8
124
5?
I
0.416
69
3i
A
9
4
7i
III
6
I
0.462
75
2f
5
8
3l
6|
IO
6£
I
0.508
81
4
4f
7i
3i
6
9i
7
I
0-554
88
2i
4i
6i
3
Si
8^
7i
ii
0.578
94
2i
4
6*
3
Si
8
8
ii
0.624
IOO
2
3l
6
2f
4f
7h
8^
ii
0.670
1 06
2
34
Si
8
2i
4*
7
10
9
ii
O.7l6
"3
3i
si
7i
4i
&
9i
9i
ij
0.762
."9
3
41
7
4
6
9
10
ii
0.809
125
*f
4?
61
3f
si
8|
ii
ii
O.9OI
138
2*
4
6
3i
Si
7|
12
ii
0-993
150
3j
si
3
4!
6|
Interpolate for intermediate slabs.
The Illinois Highway Commission for stringer spacings of about 25 ft. uses a concrete sub-
floor 4 in. thick, with a 4 in. concrete wearing surface, or a 3 in. creosoted timber block wearing
surface. The concrete sub-floor, 4 in. thick, is reinforced on the under side with £ in. square bars,
spaced 6 in. centers and centers I in. above lower edge. Transverse reinforcement consists of
f in. square bars spaced 12 in. centers. The concrete is specified as 1-2-3^ mix, and is designed
for a stress of 800 Ib. per sq. in.
The West Virginia Highway Commission specifies 1-2-4 concrete and a minimum thickness
of slab of 5 in. to the center of the tension reinforcement.
The Ohio Highway Commission specifies concrete slabs for different stringer spacings as
follows: 5 in. slab for 2 ft. spacing; 6 in. slab for 3 ft. spacing; 6 in. slab for 4 ft. spacing.
Specifications for highway bridges of the state of Nebraska specify slabs made of concrete of
a 1-2-4 mix, 6 in. thick reinforced with £ in. round bars spaced 6 in. centers. The bottom of the
concrete to be i inch below top of joists.
The standard reinforced concrete floor used by the Michigan Highway Commission is shown
in Fig. 8. The slab is 6| in. thick at the center and 6 in. thick at the curb. The details of the
floor are shown in the cut.
Buckle Plates. — Buckle plates are made by "dishing" flat plates as in Table 55, Part II.
The width of the buckle W or length L, varies from 2 ft. 6 in. to 5 ft. 6 in. The buckles may be
turned with the greater dimension in either dimension of the plate. Several buckles may be put
in one plate, all of which must be of the same size and be symmetrically placed. Buckle plates
are made i in., fV in., | in. and ^ in. thick. Buckle plates should be firmly bolted or riveted
around the edges with a maximum spacing of 6 inches, and should be supported transversely
between the buckles. The process of buckling distorts the plates and an extra width should be
ordered, and the plate should be trimmed after the process is complete. The buckle plates are
usually supported on the tops of the stringers, but may be fastened to the bottoms of the stringers.
The space above the buckles is filled with concrete which carries the wearing surface. Buckle
plates are now seldom used except for special floors and heavy floors where the weight of a rein-
forced concrete floor would be too great, or where it is necessary to cut down the clearance.
PLANK FLOORS.
112k
Plank Floors. — As long as an excellent grade of timber was available and the concentrated
loads were not excessive, timber floors were quite satisfactory when properly constructed. Plank
floors should be of white oak, long leaf yellow pine or similar timber, laid transversely. Where
two layers of plank are used the lower layer is laid diagonally. Planks should be from 8 in. to
12 in. wide and not less than 3 in. thick. To carry modern auto trucks the plank should have a
minimum thickness in inches of three halves the spacing of the stringers in feet. Planks should
Concrete per /in ft. of roadway* 6. 36 cubic yards. Reinforcement = 63. 5 pounds.
Pour this half of Floor first , Pour this half of floor last
Construction Joint" i_
5ecTioriA-A SECT ion B-B
Use this detail only when traFFic is to be maintained during construction. Otherwise
use detail given below. Other notes same as for detail shown below.
&' Bridge and RpadwaylT-0 belweena/rds 6"^
*i^i-rj J-^. (A-~bars]l"<ti8"<t LOT ~t& $L 6'} Jd---i«s-j
J'\ fy-bars I
1 -*k; 1 1 i-y..v.-.i
: l'-3" \ Drain t—F/oorbeam
SECTIOttA-A
bw
5KTIOHB-B
<T\ ,, "c"'"1 "";," -<^A
\316 fE^bars.'TopoFGurb I^Z-FlyTsrPaperJointoyer/^FIbms^ i
,"""t' "7" — ^LJ: ±i : '- — L
\ Stringer
'•J- Tar Paper Joint
— ^"Searing P/dte
5ECTion on &OF ROADWAY
OcfiERAL HOTES SURFACE TREATrlEHT OF ROADWAY
Concrete l:?:4mix, class CZ.
Reinforcements "round, medium open
hearth steel. H
Drain-l"x2"tdperedout£onexh$Kle.
Thoroughly clean surface and spread with coal tar heated
to tWorSWF.usinqratl&stjqallonspersq.yd. While tar is
still hot cover surface with? "of clean, coarse, sharp sand.
Tar must not be app/iedwhen concrete is damp.
Concrete per /in. ft.of roadway = 0.36 cubic yards,
ffeinforcement per /in. ft. ofro3dway=57.8pour?ds.
FIG. 8. REINFORCED CONCRETE FLOOR, MICHIGAN HIGHWAY COMMISSION.
laid from J in. to \ in. apart so that water will not be retained, but will run through and will
give the planks an opportunity to dry out. Where more than one layer of planks is used a liberal
coating of coal tar to the upper side of the lower planks and to the lower side of the upper planks
will materially prolong the life of the floor. The timber in floors made of more than one layer of
planks should be creosoted. Each plank should be solidly spiked to each joist with spikes having
a length not less than twice the thickness of the plank, or 6-in. spikes for 3-in. plank and 8-in.
spikes for 4-in. plank. Where steel joists are used, spiking strips about 3 in. by 8 in. are bolted to
the tops of all joists, or spiking strips 4 in. by 6 in. are bolted to the sides of three lines of joists
STEEL HIGHWAY BRIDGES.
CHAP. III.
under each plank length. When the latter method is used the floor planks are fastened to the
intermediate joists by bending spikes, driven through the floor plank, around the upper flanges of
the joist. For specifications for plank floors, see the author's "General Specifications for Steel
Highway Bridges."
The thickness of plank for different loadings and spans calculated for the allowable stresses
required by the author's specifications are given in Table V.
Laminated Timber Floor. — Highway bridge floors are sometimes made by placing 2 in. by
4 in., 2 in. by 6 in., or 3 in. by 8 in. timbers on edge and spiking them together. A waterproof
wearing surface is placed on top of the laminated base.. The safe spans for a laminated timber
floor may be taken the same as for planks 12 inches wide.
The Oregon Highway Commission uses laminated wood floors made of 3 in. by 8 in. timbers
placed on edge and spiked together at intervals of not less than 18 in. " The timbers shall prefer-
ably be long enough to extend the full width of the roadway, and in no case shall more than two
lengths be used in the width of roadway. Every fifth timber shall project £ in. above the inter-
vening four pieces, to furnish a grip for the waterproof wearing surface."
A laminated floor made of 2 in. by 4 in. pine timbers placed on edge and spiked together was
used for reflooring 23d Street Bridge, Denver, Colorado. The laminated timber base is covered
with an asphalt paving i^ inches thick.
TABLE V.
THICKNESS OF 12-iNCH FLOOR PLANK.
For 8-inch plank add 23 per cent to the thickness of plank.
Thickness in Inches, Actual Size, No Impact.
Spacing of Joists,
In.
io-Ton Auto Truck.
12-Ton Auto Truck.
15-Ton Auto Truck.
20-Ton Auto Truck.
12
2
2
2
2
IS
18
21
24
27
2f
2f
22
2|
3
II
4
3f
3
3*
35
3t
3t
3°
s!
4
4f
L|
33
36
4*
41
4f
4*
si
Allowable Stresses. — Bending stress, 1,500 lb. per sq. in.; bearing across fiber, 400 lb; per sq. in.
Minimum thickness of plank allowed by Ketchum's specifications is 3 in.; maximum spacing
of joists is 30 in.
Creosoted Timber Floor. — Creosoted timber may be used as a sub-floor for a creosoted timber
block wearing surface, for a bituminous wearing surface, or may carry a gravel or earth fill, or may
have no wearing surface.
Specifications for Creosoted Timber. — Timber used for all creosoted floor timbers except
blocks shall be first-class oak, long-leaf yellow pine or Oregon fir. It shall be cut from live trees and
Shall be straight grained, free from shakes, large or loose knots, decayed wood, worm holes or other
defects that will impair its strength or durability. It shall be sawed straight and true and shall
be full size. All timber shall be impregnated with at least 12 lb. of creosote oil per cubic foot of
timber. The creosote oil shall be a pure coal-tar product free from any adulteration. It shall be
free from any tar or any petroleum oil or petroleum residue. The specific gravity at 100° F. shall
be at least 1.03, but not more than 1.07. The creosote oil shall comply with the specifications of
the American Railway Engineering Association for creosote oil. The timber shall be impregnated
with creosote oil by the full cell process. The details of the treatment shall comply with the
specifications of the American Railway Engineering Association for the treatment of ties with
creosote oil.
HIGHWAY BRIDGE FLOORS. 112m
The timbers for the sub-floor shall be surfaced on one side and one edge, and shall not vary
moiv than ^ in. from the specified thickness. The timbers shall be laid with the surfaced side
tluwii with tight joints, and shall be fastened to the outside spiking strips with two 6-in. lag screws
;it i-.irli end of each plank, and to the intermediate stringers with two spikes in each stringer, the
length of the spikes to be at least twice the thickness of the floor planks. The fellow guard shall
be bolted to the stringers with |-in. bolts spaced not more than 5 ft. centers.
WEARING SURFACES FOR HIGHWAY BRIDGE FLOORS.— The wearing surface of a
highway bridge floor should satisfy the usual conditions for a pavement and in addition should
not have an excessive weight; as an increase in dead load on the bridge increases the necessary
amount of steel in the floor supports and the trusses and increases the total cost. The most
common wearing surfaces will be briefly described.
Concrete. — A concrete wearing surface is laid on top of the concrete slab by the Illinois High-
way Commission as follows: — The wearing surface shall have a thickness of not less than 4
inches. The lower 2 in. of the wearing surface shall be made of concrete mixed in the proportions
of one part Portland cement, 2 parts clean sand and 4 parts clean gravel or broken stone that will
pass a I J-in. ring. The concrete shall be thoroughly mixed in a batch mixer to a jelly-like consis-
tency and shall be placed immediately on the sub-floor slab. Upon this concrete layer shall be
immediately laid a 2-in. layer of mortar made by mixing one part Portland cement and 2 parts of
clean, coarse sand. The mortar shall be mixed to a jelly-like consistency in a batch mixer and
shall be immediately placed upon the freshly laid concrete. Before the mortar has begun to set
it shall be finished off with a wood float, and before it has hardened it shall be roughened by brush-
ing with a stiff vegetable brush or broom.
The concrete slab and the concrete wearing surface are commonly laid in one operation,
the wearing surface being finished up as for a concrete pavement.
Creosoted Timber Blocks. — The blocks shall be made of prime sound long-leaf yellow pine
or Oregon fir and shall contain no loose knots, worm holes or other defects, and shall be well manu-
factured. No wood averaging less than 6 rings to the inch, measured radially from the center of
the heart shall be used. The blocks shall have a depth as specified, but the depth shall not be less
than 3 in. The blocks shall be from 6 to 10. in. long. The width shall be from 3 to 4 in., but the
blocks in any contract shall have the same width. A variation of -fa in. in depth and J inch in
width will be permitted. The width shall be greater or less then the depth by not less than J in.
The blocks shall be impregnated with creosote oil by the full cell process. The creosote oil and the
method of creosoting timber blocks shall be the same as specified for creospted timber. All creo-
soted timber blocks shall contain not less than 16 Ib. of creosote oil per cubic foot of timber.
Laying Creosoted Timber Blocks. — When the creosoted timber blocks are laid on a creosoted
timber base, a layer of tar paper shall be laid on the timber base. When creosoted timber blocks
are laid on a concrete floor slab, a layer of dry cement mortar made by mixing dry one part of
Portland cement and four parts of clean dry sand shall be spread on the dry floor slab. The cement
cushion shall be rolled to a thickness of | in. As the blocks are laid on the concrete slab the sand
and cement shall be moistened by sprinkling and the blocks shall be laid before the cement has
had time to set. The blocks shall be laid at right angles to the length of the bridge in parallel
lines, with the grain vertical. The blocks shall break joints at least 3 in. Two lines of blocks
shall be laid next to the curb with the long dimension of the block parallel to the bridge, and the
remainder of the blocks shall be laid at right angles to those blocks. The blocks shall be laid with
open joints, J-in. open joints transversely, J-in. open joints longitudinally. Expansion joints not
less than I in. thick the full depth of the block shall be provided along each curb, and transverse
joints not less than \ in. thick shall be provided every 50 ft. in length of the bridge. These joints
shall be kept closed until the blocks are all laid, and the space is then to be filled with a bituminous
filler. After the blocks have been laid they shall be tamped or rolled to firm bearing. All defect-
ive, broken, damaged or displaced blocks shall be removed and replaced with sound blocks. All
joints and expansion joints shall then be filled to a depth of two-thirds the depth of the block with
a satisfactory bituminous filler. The filler shall not be brittle at o° F. nor flow at 120° F. The
filler shall be applied at a temperature of not less than 300° F. After the first application has
set the joints shall be filled to the proper height with a second coat. Joints shall be filled only in
dry weather, when the temperature is not less than 50° F. Before the second coat has hardened
a layer of sand J in. thick shall be spread on the surface and shall be swept into the joints.
Bituminous Wearing Surface Floors. — Bituminous wearing surface floors may be laid on a
creosoted timber sub-floor or on a concrete sub-floor.
112n STEEL HIGHWAY BRIDGES. CHAP. III.
Bituminous Wearing Surface on Timber Sub-Floor. — The bituminous wearing surface may
be put on hot by the standard method, or by a cold process. The specifications adopted in 1917
by the Illinois Highway Commission are as follows:
Bituminous Wearing Surface — Hot Penetration Method. Illinois Highway Commission.
Asphalt. — The asphalt used for bituminous wearing surface shall conform to the following
requirements: Asphalt shall have a specific gravity at 25° C. of not less than 0.97 nor more than
unity. It shall be soluble in cold carbon disulphide to the extent of at least 98 per cent. Of the
total bitumen, not less than 22 per cent nor more than 30 per cent shall be insoluble in 86° B.
naphtha. When 20 grams (in a tin dish 2| in. in diameter and £ in. deep with vertical sides) are
maintained at a temperature of 163° C. for 5 hours in a N. Y. testing laboratory oven, the evapora-
tion loss shall not exceed 2 per cent and the penetration shall not have been decreased more than
25 per cent. The fixed carbon shall not exceed 16 per cent by weight. The penetration as de-
termined with the Dow machine using a*No. 2 needle, 100 g. weight, 5 seconds time, and a tem-
perature of 25° C. shall be not less than 30 nor more thah 50. The asphalt shall contain not to
exceed 6 per cent by weight of paraffine scale.
Aggregate. — The aggregate shall consist of screened gravel, which shall have been approved
by the engineer, dry, free from dust, dirt and clay, and graded in size from f in. to £ in.
Cleaning Sub-Planking. — Before placing the wearing surface, the sub-planking shall be thor-
oughly cleaned from all foreign material and the cracks shall be filled and the plank covered to a
depth of approximately | in. with asphalt of the character herein specified, which shall be applied at
a temperature of not less than 400° F. The sub-planking shall be dry when the asphalt is applied.
Placing Wearing Surface. — The gravel shall be spread on the asphalt covering while the same
is hot and in a quantity which will just cover the asphalt. The thickness must not exceed that
which will be formed by a single layer of the gravel pebbles.
Upon the material thus spread, -there shall be poured hot asphalt until the interstices are all
filled, the asphalt being at a temperature of not less than 400° F.
Upon the layer of asphalt thus poured there shall be spread a second layer of gravel which shall
not exceed the thickness of a single layer of pebbles, but which must be spread in sufficient quantity
to cover completely the layer of asphalt.
Upon the layer of gravel thus spread there shall be poured hot asphalt until all the interstices
are filled, the asphalt having a temperature of not less than 400° F.
Finish. — The surface shall then be covered with a layer of pebbles just sufficient to cover th$
asphalt, the pebbles to be well rolled or tamped into the asphalt and the surface finally covered
with coarse sand sufficient to take up any free asphalt. After the surface has stood for one day,
it may be opened to traffic.
Bituminous Wearing Surface — Cold Mixing Method, using an Asphalt Emulsion. Illinois
Highway Commission.
Asphalt Emulsion. — The emulsion shall consist of asphalt, water and fatty or resin soap thor-
oughly emulsified. It shall conform to the following requirements:
Total bitumen Not less than 60.0 per cent
Specific gravity of dehydrated material Not less than i.ooo
Penetration of dehydrated material, 25° C., 100 gm., 5 sec 150 to 200
Total Bitumen. — The total bitumen shall be considered as being 100 minus the sum of the
percentages of water, of fatty or resin acids, of organic matter insoluble in carbon disulphide other
than fatty or resin acids from the soap, or mineral matter (ash), and of ammonia.
For percentages of water, fatty or resin acids, organic matter insoluble in carbon disulphide,
mineral matter (ash), and ammonia, see United States Department of Agriculture Bulletin 314,
p. 41.
Specific Gravity. — Standardized pycnometers, United States Department of Agriculture
Bulletin 314, p. 4.
Penetration— A.. S. T. M. Stand. Test D 5-16.
Aggregate. — The aggregate shall consist of crushed stone chips uniformly graded from f in.
down to dust with all dust removed, to which shall be added sufficient sand to fill all remaining
voids, but not to exceed 20 per cent of the volume of the aggregate.
Cleaning Sub- Planking. — Before placing the wearing surface, the sub-planking shall be
thoroughly cleaned from all foreign material and all cracks shall be filled with wood strips or oakum.
Mixing Materials. — The aggregate and the asphalt emulsion shall be mixed cold in the pro-
portions of I gal. of emulsion to I cu. ft. of aggregate. To facilitate mixing, water to the extent of
20 per cent may be added to the emulsion. The proportions given above for mixing the aggregate
and the emulsion are based on the undiluted emulsion. The mixing shall be done on a tight
mixing board or in a batch concrete mixer, and shall continue until all particles of the aggregate
are thoroughly coated.
HIGHWAY BRIDGE FLOORS. 112o
Placing Wearing Surface. — After mixing, the material shall be spread upon the roadway in
sufficient cjuantity to provide a thickness of J in., after rolling or tamping.
Finish. — After the material has been rolled or tamped smooth and to a uniform thickness of
I in., the surface shall be given a paint coat of the emulsion applied at the rate of J gal. per sq. yd.,
and then shall be covered with coarse sand sufficient to take up any free asphalt and to fill all voids
in the surface. After the surface has stood for one day, it may be opened to traffic.
Bituminous Pavement on Concrete. — A bituminous wearing surface may be laid as on the
creosoted plank sub-floor, or the wearing surface may be laid according to the following standard
method. The concrete shall be dry and thoroughly clean. A bituminous wearing surface two
indies thick is applied as follows: The aggregate consists of broken stone or gravel passing a
oiK'-inch screen with the dust screened out to which is added sand equal to about one-quarter to
one-half the volume of the stone. The aggregates shall be heated and mixed with the bituminous
matt rial in a mechanical mixer or by hand with hot shovels. The asphalt shall be mixed not less
than 20 gallons to the cubic yard of aggregate at a temperature of 350° to 400° F. The mixture
shall be applied hot to the concrete surface and shall be raked with hot hoes or rakes and is rolled
with a roller weighing not less than 5 tons. After the surface has been rolled a layer of hot asphalt
shall be applied and a layer of coarse sand rolled into hot asphalt.
Examples of Highway Bridge Floors. — The following examples of highway bridge floors
specified by different highway commissions are of interest.
The Illinois Highway Commission uses the following standard floors: (l) A reinforced con-
crete sub-floor 4 in. thick, and a concrete wearing surface 4 in. thick, weight 100 Ib. per sq. ft.;
(2) a reinforced concrete sub-floor 4 in. thick and a creosoted timber block wearing surface 3 in.
thick, weight 65 Ib. per sq. ft.; (3) a creosoted plank sub-floor 3 in. thick and a wearing surface of
creosoted timber blocks 3 in. thick, weight 32 Ib. per sq. ft.; and (4) a creosoted timber ship lap
floor 3 in. thick and a wearing surface of creosoted timber blocks 3 in. thick, weight 26 Ib. per sq. ft.
The Michigan Highway Commission uses the following surface treatment on concrete floor
slabs. The surface of the concrete is thoroughly cleaned and $ of a gallon per sq. yd. of coal tar
heated to a temperature of 250° to 350° F. is spread over the slab. While the tar is hot the surface
is evenly covered with a layer £ in. thick of clean, sharp, coarse sand.
I The Wisconsin Highway Commission does not specify a wearing coat on top of concrete floor
slabs.
The Iowa Highway Commission uses either a 3 in. fill of gravel or a creosoted block floor 3 in.
thick. Concrete slabs are covered with a bituminous coating made by applying 5 of a gallon per
sq. yd. of hot tar to the clean dry slab. A layer of coarse dry sand is heated and sifted on top of
the tar.
Cost of Floors. — The costs of highway bridge floors were estimated by Mr. Clifford Older,
bridge engineer, Illinois Highway Commission in 1915 as follows: Concrete in sub-floors including
reinforcing steel, $12.00 per cu. yd.; concrete wearing surface, 4 in. thick, $0.90 per sq. yd.;
•eosoted sub-plank (i2-lb. treatment) in place, $70 per thousand feet B. M.; creosoted blocks 3
in. thick, in place, $1.80 per sq. yd.; bituminous gravel wearing surface, f in. thick, $0.60 per sq.
d. The weights and costs of the Illinois Highway Commission standard floors were as follows:
oncrete sub-floor 4 in. thick and concrete wearing surface 4 in. thick, weighs 100 Ib. per sq. ft.,
and costs $2.95 per sq. yd.; concrete sub-floor 4 in. thick, and creosoted blocks 3 in. thick, weighs
65 Ib. per sq. ft., and costs $3.25 per sq. yd.; creosoted plank sub-floor 3 in. thick, and creosoted
blocks 3 in. thick, weighs 32 Ib. per sq. ft., and costs $4.10 per sq. yd.; creosoted plank fub-floor
3 in. thick, and bituminous wearing surface j in. thick, weighs 26 Ib. per sq. ft., and costs $3.00
per sq. yd.
DESIGN OF STRINGERS. — Stringers or joists support the floor and in turn are supported
the floorbeams. The joists may be supported on the tops of the floorbeams or may be framed
into the floorbeam by the use of connection angles. Where concrete floors are used the steel joists
should either be supported on the tops of the floorbeams or if framed into the floorbeams should
have the upper flanges of the beams coped so that the tops of the joists will be on the same level
as the floorbeams. The loads carried by the joists are (i) the dead load which is made up of the
weight of the joists, the floor slab and the wearing surface; (2) a uniform live load, or a concen-
trated moving load. The uniform live load and the concentrated moving loads are the same as the
loads used in designing the floor slabs, but the distribution of the concentrated load is not the same.
112p
STEEL HIGHWAY BRIDGES.
CHAP. III.
The distribution of the moving concentrated load to the joists as specified by different highway
commissions and others, and by the author have already been given.
Steel Stringers. — The sizes of steel I-beams of minimum weights required for stringers with
different spacings to carry a dead load of 100 Ib. per sq. ft. and a 2o-ton auto truck with 30 per cent
impact or a live load of 125 Ib. per sq. ft. with 30 per cent impact are given in Fig. 9; and to carry
a dead load of 100 Ib. per sq. ft. and a 1 5-ton auto truck with 30 per cent impact or a live load of
loo Ib. per sq. ft. with 30 per cent impact are given in Fig. 10. The sizes of steel I-beams of mini-
mum weights required to carry a dead load of 100 Ib. per sq. ft. and a 1 5-ton auto truck without
impact or a live load of 100 Ib. per sq. ft. without impact are given in Fig. 1 1. The steel stringers
used by the Wisconsin Highway Commission to carry a 15-ton road roller without impact, and the
steel stringers used by the Iowa Highway Commission to carry a 1 5-ton traction engine without
impact are practically the same as those given in Fig. u.
Timber Joists. — The sizes of timber stringers or joists for different spacings and spans to
carry a 2O-ton auto truck are given in Table VI ; to carry a 1 5-ton auto truck in Table VII, and to
carry a lO-ton auto truck in Table VIII. The timber joists were designed for the following unit
stresses, to be used without impact: Allowable bending stress, 1,500 Ib. per sq. in.; allowable
bearing across the grain, 400 Ib. per sq. in.; allowable longitudinal shear in beams, 140 Ib. per sq. in.
The maximum spacings of timber joists for short spans are determined by the longitudinal shear.
TABLE VI.
SPACING OF TIMBER STRINGERS OR JOISTS.
Calculated for 2O-ton Auto Truck, Without Impact.
Nominal Size of
Joists, In.
Maximum Spacing in Feet for Different Spans in Feet.
6
8
10
12
14
16
18
20
3 X 10
0.7
0.9
0.8
i.i
I.O
i-3
2.O
i-5
2.2
0-7
0.9
0.8
I.I
I.O
i-3
2.0
i-5
2.2
0.6
0.8
0.7
I.O
0.8
I.I
i-7
i-5
2.2
I.O
1.5
i-3
2.0
«-3
1.2
i-7
1.2
I.O
i-5
4 X 10
3 X 12
0.8
I.i
I.O
1-3
2.O
1-5
",.2
4X 12
1 X 14. .
I.O
i-3
2.0
I-S
2.2
4 X 14. .
6 X 14
4 X 16
6 X 16
The proportion of the concentrated live load carried by one joist shall be taken equal to the
spacingof the joists in feet divided by four feet.
Joists were designed for allowable stresses as follows: Cross-bending, 1,500 Ib. per sq. in.; bear-
ing across the grain 400 Ib. per sq. in.; longitudinal shear 140 Ib. per sq. in.
Spacing of joists for spans to left of heavy line are determined by longitudinal shear.
DESIGN OF FLOORBEAMS.— The floor loads may be carried to the floorbeams by means
of stringers or joists, or the loads may be carried to the floorbeams directly by the floor slabs.
The loads carried by the floorbeams consist of (i) the dead load which is the weight of the floor
system; (2) a uniform live load; or a concentrated moving load. The uniform live loads are the
same as the uniform live loads used in designing the floor slabs an9 stringers, but the distribution
of the concentrated moving load is not the same as for either the floor slabs or the stringers. The
distribution of the moving concentrated load to floorbeams as specified by different highway com-
missions and others, and by the author have already been given.
TIMBER STRINGERS.
TABLE VII.
SPACING OF TIMBER STRINGERS OR JOISTS.
Calculated for 15-ton Auto Truck, Without Impact.
113
Nominal Size of
Joins. In.
Maximum Spacing in Feet for Different Span* in Feet.
6
8
to
xa
M
16
18
•
3 X 10
4 X 10
I.O
1-3
I.I
1.6
* 1.4
1.9
2.8
2.1
3-i
I.O
i-3
i.i
1.6
«4
1.9
2.8
2.1
3-i
0.8
i.i
0.9
I.O
1-4
1.2
1.2
1.6
2.4
2.1
3-i
I.O
I.O
1.4
2.O
1.8
2.7
1.2
1.8
1.6
2.4
I.I
1.6
'•5
2.2
3 X 12. . .
i.i
1.6
1.4
1.9
2.8
2.1
3-1
4 X 12
-i x 14.
i-4
1.9
2.8
2.1
3-1
4 X U. .
6 X 14
4 X 16
6 X 16
The proportion of the concentrated live load carried by one joist shall be taken equal to the
spacing of the joists in feet divided by four feet.
Joists were designed for allowable stresses as follows: Cross-bending, 1,500 Ib. per sq. in.; bear-
ing across the grain, 400 Ib. per sq. in.; longitudinal shear, 140 Ib. per sq. in.
Spacing of joists for spans to left of heavy line are determined by longitudinal shear.
TABLE VIII.
SPACING OF TIMBER STRINGERS OR JOISTS.
Calculated for lo-ton Auto Truck, Without Impact.
Nominal Size of
Joists In.
Maximum Spacing in Feet for Different Spans in Feet.
6
8
IO
12
'4
16
18
"20"
3 X 10
1-4
2.O
1.8
2.4
2.O
2.8
4.1
3-2
4-7
1.4
2.O
1.8
2.4
2.O
2.8
4-i
3-2
4-7
1.2
i-7
I.O
1.4
o-9
1.2
I.J
1.8
I.O
I.I
I-S
i-5
2.1
3-i
2.8
4.1
I.O
1-4
1.4
1-9
2.8
21
3.6
1.2
1.2
1-7
2.5
2.2
3-3
4X 10
3 X 12.
1.8
2.4
2.O
2.8
4.1
3-2
4-7
i-5
2.O
4X 12
3 X 14. .
2.O
2.8
4-1
3-2
4-7
1.8
2.4
3-5
3-2
4-7
4 X U- .
6 X 14
4 X 16
6 X 16
The proportion of the concentrated live load carried by one joist shall be taken equal to the
spacing of the joists in feet divided by four feet.
Joists were designed for allowable stresses as follows: Cross-bending, 1,500 Ib. per sq. in.; bear-
ing across the grain, 400 Ib. per sq. in.; longitudinal shear, 140 Ib. per sq. in.
Spacing of joists for spans to left of heavy line are determined by longitudinal shear.
Steel I-Beam Floorbeams. — The sizes of steel I-beams required for floorbeams for panel
lengths of 10 ft. to 24 ft. and widths center to center of trusses or girders of 15 ft. to 26 ft. to carry
a dead load of 100 Ib. per sq. ft., and a 2o-ton auto truck with 30 per cent impact, or a uniform live
load of 125 Ib. per sq. ft. with 30 per cent impact are given in Fig. 9; while the floorbeams required
to carry a 15-ton auto truck with 30 per cent impact, or a uniform live load of 100 Ib. per sq. ft.
with 30 per cent impact are given in Fig. 10. It will be noted that the uniform live load controls
for wide roadways or for long panels.
9
114
STEEL HIGHWAY BRIDGES.
CHAP. III.
24*1*80*
LlVELOAD:20-Tonautotrucki-30%impad,orl?5lt>.
persq. Ft.t30%imp3ct. DEADLOAfrlOOIbptrsq.ft.
12 Id 16 18 20 22 24
Psnel Length in Feet.
2345
Spacing inFeet.
FIG. 9. BENDING MOMENTS IN FLOORBEAMS AND STRINGERS FOR ao-TON AUTO TRUCK.
(30 PER CENT IMPACT). CONCRETE FLOOR.
24"lx80*'
LiVELoWfrTonautotrvcktXZimpacLorlWIb.
2 3 4
Spacing in feet.
10 12 14 /6 18 20 22 24
Panel Length in Feet.
FIG. 10. BENDING MOMENTS IN FLOORBEAMS AND STRINGERS FOR IS-TON AUTO TRUCK.
(30 PER CENT IMPACT). CONCRETE FLOOR.
DESIGNS OF FLOORBEAMS AND STRINGERS.
115
For a bridge 17 ft. center of trusses and 18 ft. panels, from Fig. 9 the required floorbeam
is a 24 ;n. I @ 80 lb., while from Fig. 10 the required floorbeam is a 20 in. I @ 70 Ib.
The sizes of steel I-beams required for floorbeams for panel lengths of 10 ft. to 24 ft., and
widths center to center of trusses or girders of 15 ft. to 26 ft. to carry a dead load of 100 lb. per sq.
ft. and a 15-ton auto truck without impact, or a uniform live load of 100 lb. per sq. ft. without im-
pact are given in Fig. II. These are practically the floorbeams required by the specifications of
thr Illinois, Iowa, and Wisconsin Highway Commissions. Steel stringers for the same loading
are given in Fig. n.
The bending moments for the design of built-up floorbeams may be obtained from Fig. 9,
Fig. 10, or Fig. 1 1.
24'hSO*
UVCLOAD:l5-Tonavtotruck(noimpad),orMlt>.
persq.Ft.(noimpact).DEADLQAD:IOO/hpfrsa.Ft.
10 12 14 16 18 20 22
Panel Length in Feet. '
2345
Spacing in feet.
FIG. ii. BENDING MOMENTS IN FLOORBEAMS AND STRINGERS FOR IS-TON AUTO TRUCK.
(No IMPACT.) CONCRETE FLOOR.
CALCULATION OF STRESSES. — For the calculation of the stresses in highway bridges,
see the author's "The Design of Highway Bridges," also see Chapter XVI.
ALLOWABLE STRESSES.— For allowable stresses to be used in the design of steel highway
bridges, see "General Specifications for Steel Highway Bridges," printed in the last part of this
chapter.
SHORT-SPAN STEEL HIGHWAY BRIDGES.— The term short-span highway bridges
will be assumed to include beam, low truss and plate girder bridges.
116
STEEL HIGHWAY BRIDGES.
CHAP. III.
BEAM BRIDGES. — Beam bridges are made by placing steel I-beams side by side with the
ends resting on the abutments. The roadway floor may be made of planks laid transversely on
the tops of the beams, or of reinforced concrete. The spacing of the beams depends upon the load
to be carried and upon the thickness of the floor planks or floor slabs and varies from 2 to 4 ft.
Timber joists should not be spaced more than 2\ ft. centers. A common rule for the thickness
of oak floor planks is that the plank shall have at least one and one-half inch in thickness for each
foot of spacing of the joists or stringers. The outside beams should be the same size as the inter-
mediate beams. It is commonly specified that rolled beams shall have a depth not less than •$•$ the
span.
Note-.-NumberofRsilmq Posts
varies with length of Span.
v Tar paper - three layers %// with concretes
r ~ ' after-jojstsareinp/jce
L:.t!:;:...j::::;:^K
ii-
i ConcreteSlabfithick - Bottom I "oe/ow tops of joists
Transverse :„ D? ~? '
ir)3l:-z "'terbet-exhpairof joists- '
{3" Fill ^center r
three layers after joists are placed '
HALF SEC TIONA T ABUTMENT HALF INT SECTION
*-^r
\^3ar paper- thrt
v&ysrs
"•;/
•f/// ' withconcrvte
afterjo/stsjreflbce
T/^/,
L_ . -u
! j
Clear
Curb--*
PLAN OF ANGLE RAiuno ON WING WALLS
lt>Ft
20"
28-
W-
10 '25
1542
1542
1542
w_ww_
IO'I5
IMF5 l?>?0-5 WMW
I5-33
16V 9
IIV
10,000
?0,.00ff
V,WU x*\
co O
hote:-Abovf bble is for 3 16ft- rofdwsyFor
18 ft 31^^ ft roadways, <sdd one line joists-
Hote:- This design to be usedonly with
concrete substructures shown-
5£CT/W BELOW CWCRETE FLOOR.
i i «*-*— — r*° ?
snoot . loomM
3 ^::n=5^
15 TON ENGINE
Assumed Live Load: -
Engines per diagram-
STANDARD &EAM SPAMS
Concrete Slab Floor
IOWAHI6HWAY COMMISSION.
FIG. 12. BEAM BRIDGES.
Standard steel beam bridges with concrete floor as designed by the Iowa Highway Commission
are given in Fig. 12 and Fig. 13. The spans vary from 16 ft. to 32 ft. The details are shown in_the
cuts. Quantities for beam bridges with angle fence as shown in Fig. 12 are given in Table IX.
A standard steel beam bridge as designed by the Wisconsin Highway Commission is shown in
Fig. 14. Data and quantities for beam spans from 10 ft. to 38 ft. are shown in Table X.
BEAM BRIDGES.
117
^V3«7W> 5tft>, Bottom I'Attnr tq> of Jo/sis
~ '~y/ ters - It'c-toc-
Wirf
Rflnferffmtnt in
tf'c-toc
Hor. 5-j: fi'rs- not thru HALF INT- SfCWti
HALF SECTION AT ABUTMEHT
Note: Out SK*> Is to it \
raised // * stew Art^e
with mesh
r.lj. DATA FOB STAHMRD BCAN SPANS -pwctfTf FLXR
Hole:- Add or subtract ont I for axh 2ft.
chanqt of
For hsndrjil oner m'rtfs jdd 1.9 yd's. con-
crete jnd . ISO lo- rsin forcing ptr bridqt .
STANDARD BEAM 5PM15
Concrete Floor £ Hdnt/r<?il
IOWA HIGHWAY Co/mission
FIG. 13. BEAM BRIDGES.
The minimum sizes of I-beams for different loadings and for different spacings and spans and
with a concrete and a plank floor have been calculated by the author and are given in Table XI
and Table XII.
Floor planks may be spiked to spiking strips on the tops of the beams, or to spiking strips
bolted on the sides of the I-beams. The floor planks are spiked to these spiking strips, and are
fastened to the other beams by clinching spikes, which have been driven through the planks,
around the top flanges of the beams.
118
STEEL HIGHWAY BRIDGES.
CHAP. III.
The maximum span for beam bridges should be 30 ft. Riveted truss bridges or plate girders
should be used for spans of 30 ft. and upwards for country bridges, and plate girders for heavy city
bridges. Riveted bridges for spans of, say 40 ft., are more economical than plate girder bridges
and will give fully as great a length of service if properly designed and constructed. The ends of
beam bridges should always be supported on masonry abutments.
TABLE IX.
ESTIMATED QUANTITIES FOR STANDARD BEAM SPANS. IOWA HIGHWAY COMMISSION.
Structural Steel.
Reinforced Concrete Floor.
Span,
Ft.
Roadway.
16 Ft. Roadway.
18 Ft. Roadway.
20 Ft. Roadway.
i6Ft.
i8Ft.
20 Ft.
Concrete.
Steel.
Concrete.
Steel.
Concrete.
Steel.
Ib.
Ib.
Ib.
cu. yd.
Ib.
cu. yd.
Ib.
cu. yd.
Ib.
16
3,370
3,780
3,800
5-6
600
6-3
680
7-0
740
18
4,280
4,810
4,820
6.2
670
7.0
750
7-7
820
20
4,720
5,300
5,320
6.8
730
7-6
830
8-5
9OO
22
6,340
7,130
7,150
7-4
800
8-3
9OO
9.2
990
24
6,840
7,690
7,710
8.0
870
9-o
980
IO.O
1,070
26
7,330
8,240
8,260
8.6
930
9-7
1,050
10.7
1,150
28
10,570
11,870
11,880
9.2
1,000
10.4
1,120
"•5
1,230
30
11,240
12,620
12,640
9.8
1, 060
II.O
I,20O
12.2
1,310
32
11,910
13,370
13,390
10.4
1,130
11.7
I,27O
13.0
1,390
Standard angle railing for wing walls as shown in Fig. 12.
Rails /s 2\" X 2?" X i" X s'-g". Top of rail 3'-z" above grade. Post /s 3" X 3" X I"
V A'--)"
•*• 4 3 •
Weight of rails and posts for one wing = 90 Ib.
TABLE X.
STEEL I-BEAM BRIDGES. WISCONSIN HIGHWAY COMMISSION.
Channels on outside. Weight includes railing.
16 Feet Roadway.
18 Ft. Roadway.
20 Ft. Roadway.
Span,
Ft.
STo. Beams
Size
Weight
No. Beams
Size
Weight
No. Beams
Size
Weight
and
I-Beams,
Structural
and
I-Beams,
Structural
and
I-Beams,
Structural
Channels.
In. Lb.
Steel, Lb.
Channels.
In. Lb.
Steel, Lb.
Channels.
In. Lb.
Steel, Lb.
10
8
8— 1 8
I,9OO
9
8— 1 8
2,120
IO
8— 18
2,335
12
8
8— 1 8
2,20O
9
8— 1 8
2,450
10
8— 18
2,70O
H
8
9 — 21
2,800
9
9 — 21
3,130
IO
9 — 21
3,465
16
8
9 — 21
3,185
9
9 — 21
3,560
10
9 — 21
3,93°
18
8
10 — 25
4,030
9
10 — 25
4,505
10
10 — 25
5,000
20
7
12—315
4,810
8
12—31!
5,6OO
9
12—31!
6,285
22
8
12—312
6,050
9
12—31^
6,790
IO
I2—3l|
7,545
24
8
12— 31!
6,435
9
12—315
7,350
10
12—31!
8,160
26
7
15—42
8,275
8
15—42
9,420
9
15—42
10,570
28
8
15—42
10,045
9
15—42
11,275
10
15—42
12,510
30
8
15—42
10,715
9
15—42
12,025
10
15—42
13,350
32
7
18—55
12,050
8
18—55
13,930
9
18—55
15,750
34
7
18—55
12,825
8
18—55
15,760
9
18—55
16,685
36
8
18—55
15,530
9
18—55
17,570
IO
18—55
19,615
38
8
18—55
16,350
9
18-55
18,405
IO
18-55
20,655
i6-ft. Rdwy. i8-ft. Rdwy. zo-ft. Rdwy.
Weight in Ib. of reinforcing per lineal foot .... 40 44 48
Cu. yd. concrete per line;
il foot
0.32 0.36 0.40
BEAM BRIDGES.
119
TABLE XI.
DEPTH IN INCHES OF I-BEAMS FOR DIFFERENT SPACINGS AND SPANS REQUIRED TO CARRY ZO-TON,
15-ToN AND IO-TON AUTO TRUCKS AND 30 PER CENT IMPACT. DEAD LOAD 100 LB.
PER SQ. FT. MINIMUM WEIGHTS OF I-BEAMS ARE USED.
Concrete Floor.
Span. Ft.
90-Ton Auto Truck.
15-Ton Auto Truck.
io- Ton Auto Truck.
Spacing, Ft.
Spacing, Ft.
Spacing, Ft.
a
3
4
a
3
4
a
3
4
IO
12
16
18
20
22
24
26
28
30
8
9
IO
IO
12
12
12
IS
IS
IS
IS
IO
10
12
12
IS
IS
IS
IS
18
18
18
12
12
IS
IS
IS
18
18
18
18
20
20
7
8
9
9
10
IO
12
12
IS
IS
IS
9
9
IO
12
12
IS
IS
IS
IS
1 8
18
10
10
12
12
IS
IS
is
18
18
18
20
6
7
8
8
9
9
IO
10
12
12
12
8
8
9
10
IO
12
12
12
IS
IS
IS
9
9
IO
12
12
12
IS
IS
IS
18
18
The proportion of the concentrated live load carried by one joist shall be taken equal to the
spacing of the joists divided by six feet when reinforced concrete floor is used.
The outside beams to be the same as the intermediate beams.
TABLE XII.
DEPTH IN INCHES OF I-BEAMS FOR DIFFERENT SPACINGS AND SPANS REQUIRED TO CARRY 20-
TON, 15-TON AND 10-TON AUTO TRUCKS AND 30 PER CENT IMPACT. MINIMUM
WEIGHTS OF I-BEAMS ARE USED.
Plank Floor.
Span, Ft.
ao-Ton Auto Truck.
i5-Ton Auto Truck.
lo-Ton Auto Truck.
Spacing, Ft.
Spacing, Ft.
Spacing, Ft.
4
2
4
4
a
4
4
a
4
IO
12
14
16
8
9
9
IO
9
IO
IO
12
IO
10
12
12
7
8
8
9
8
9
9
10
9
9
10
12
6
7
7
8
7
7
8
8
7
8
9
9
18
IO
12
IS
9
10
12
8
9
10
20
12
12
IS
IO
12
12
9
9
IO
22
12
IS
IS
IO
• 12
IS
9
10
12
24
12
IS
15
12
12
IS
9
IO
12
26
28
30
IS
IS
IS
IS
IS
18
18
18
18
12
12
12
IS
is
is
IS
IS
IS
IO
12
12
12
12
12
12
IS
IS
The proportion of the concentrated live load carried by one joist shall be taken equal to the
spacing of the joists divided by four feet when timber floor is used.
The outside beams to be the same as the intermediate beams.
120
STEEL HIGHWAY BRIDGES.
CHAP. III.
HIGHWAY PLATE GIRDER BRIDGE.
121
bv. ...... !sdj
122 STEEL HIGHWAY BRIDGES. CHAP. III.
PLATE GIRDERS. — Plate girders are frequently used for highway bridges. Where the
conditions will permit deck plate girder bridges are to be preferred to through plate girder bridges
for highway service. The details of plate girders when used for highway bridges are essentially
the same as when used for railway bridges, which see.
Details of a steel through plate girder highway bridge as designed by the Wisconsin High-
way Commission are shown in Fig. 15. Standard plans have been prepared for spans from 35
ft. to 80 ft., varying by 5-ft. intervals, and for i6-ft., i8-ft. and 2O-ft. roadway. Spans of 35 ft.
to 60 ft. inclusive have webs 60 in. by ^ in.; the 65-ft. and yo-ft. spans have webs 66 in. by ^
in.; the 75-ft. spans have a web 66 in. to 72 in. by f in., while the 8o-ft. spans have a web 72 in.
to 78 in. by f in. For weights of plate girder bridges, see first part of this chapter.
Details of a log-ft. span through-plate girder highway bridge built over the D. L. & W. R. R.
tracks in Jersey City, N. J., are given in Fig. 16. The girders were designed for a live load of 100
Ib. per sq. ft. on roadway and sidewalk; while the roadway floor was designed for a live load of 100
Ib. per sq. ft. and two 12,000 Ib. axle loads spaced 10 ft. apart with an allowance of 25 per cent for
impact. The expansion end is carried on 4-in. rollers. The concrete has a minimum thickness of
4 in. and is covered with i| in. of binder and 2 in. of asphalt. Each main girder weighed 1 12,000
Ib. ; and the total weight of steel in the bridge was about 403,000 Ib.
LOW RIVETED TRUSS BRIDGES.— Low riveted bridges are made with either Warren or
Pratt trusses, the Warren truss usually being preferred. The upper chords should be made of two
angles and a plate, two channels laced, or two channels with a top cover plate and lacing on the
bottom side of the member. The lower chord and the web members are made of two angles placed
in the same relative positions as in the upper chords.
Details of a low riveted truss bridge with a reinforced concrete floor carried on steel stringers
or joists, as designed by the Iowa Highway Commission are shown in Fig. 17. The commission
has prepared standard plans for spans from 35 ft. to 85 ft. and with i6-ft. and i8-ft. roadway.
Spans over 65 ft. in length have one end supported on rockers. Spans 65 ft. or less in length have
one end supported on sliding plates.
Details of a low riveted truss bridge with a reinforced concrete floor carried directly on the
floorbeams, as designed by the Iowa Highway Commission, are shown in Fig. 18. The commission
has prepared standard plans for spans from 35 ft. to IOO ft. and with i6-ft. and i8-ft. roadway.
Spans more than 65 ft. in length have one end supported on rockers. Spans 65 ft. or less in length
have one end supported on sliding plates. The reinforced concrete floor slabs have a thickness of
75 in. for an 8-ft. span, of 8 in. for a 9-ft. span, and of 8£ in. for a lo-ft. span. The slabs are rein-
forced top and bottom with f in. square bars spaced 9 in. centers and i| in. from face of slab.
Transverse bars £ in. sq. are spaced about 2 ft. centers with one bar over the floorbeam.
Details of a low riveted truss bridge with a reinforced concrete floor as designed by the Michi-
gan Highway Commission are given in Fig. 19. The Commission has prepared standard plans
for spans from 50 ft. to too ft. by 5-ft. intervals.
The riveted low truss highway bridge with an inclined upper chord shown in Fig. 20 is built
by the American Bridge Company for locations requiring an artistic and serviceable bridge at a
moderate cost. This bridge has been built with six panels and with spans of 90, 96 and 102 ft.
The bridge in Fig. 20 has a 2O-ft. roadway and was designed for a dead load of 930 Ib. per lineal
foot of bridge, and a live load of 2,400 Ib. per lineal foot of bridge. The total weight of the steel
in this bridge, exclusive of joists and fence is, approximately, 57,000 Ib. The floorbeams are rolled
I-beams and are riveted below the chords. The top chords are made of two channels with a top
cover plate, the lower edges of the channels being fastened together with tie plates — lacing is much
better practice. The bottom chord is composed of two angles, with tie plates — tie plates are all
right for this member. The web members are made of 2 or 4 angles laced, as shown. Rods, not
shown, are used for the lower lateral system.
Details of a low riveted truss bridge with a reinforced concrete floor as designed by the Wis-
consin Highway Commission are given in Fig. 21. Standard plans have been prepared for spans
from 35 ft. to 85 ft., and with i6-ft. and i8-ft. roadway. One end of all spans is carried on sliding
plates as shown.
LOW TRUSS HIGHWAY BRIDGES.
123
•Weephole with perforated*
•» '
15-Ton Engine.
•ri
i/ 6 concrete slab, botbm I" below tops ofjoiscs
' -•- .Wp'*^*5*
-j ReinForcement\!ran^' \Bot. same. Staqqer with top
\Lonq. f'sq. between adjacent joists.
HalF5ection.
£fj "bolts withjvund heads, about /8c.coc.
Section through End Floorbearm
('
Cast Iron5hoe-Fixed End.
5j& jliePb. StressSheetsOeneralDetails
5TANDARD70'xl6'LOWTRU555PAH
Concrete Floor onSkeelJoists
IOWA HIGHWAY COMMISSION
FIG. 17. Low TRUSS SPAN WITH STRINGERS.
Depth and Panel Length of Low Trusses. — The depths and number of panels in Iowa High-
ly Commission low truss bridges with joists are as follows: 35 ft. and 40 ft. span, 3 panels, 6 ft.
ep; 45 ft. and 50 ft. spans, 3 panels, 6$ ft. deep; 60 ft. and 65 ft. span, 4 panels, 7 ft. deep; 70 ft.
!n, 5 panels, 7 ft. deep; 80 ft. and 85 ft. span, 5 panels, 8 ft. deep. For low truss bridges without
rists, 35 ft. span, 4 panels, 6 ft. deep; 40 ft. span, 5 panels, 6 ft. deep; 45 ft. span, 5 panels, 6J ft.
ep; 50 ft. and 55 ft. span, 6 panels, 6J ft. deep; 60 ft. span, 7 panels, 7 ft. deep; 65 ft. and 70 ft.
span, 8 panels, 7 ft. deep; 75 ft. span, 9 panels, 7J ft. deep; 80 ft. span, 10 panels, 8 ft. deep; 85 ft.
span, 10 panels, 8J ft. deep; 90 ft. span, 10 panels, 9 ft. deep; 95 ft. span, 10 panels, 9$ ft. deep;
100 ft. span, 10 panels, 10 ft. deep.
124
STEEL HIGHWAY BRIDGES.
CHAP. III.
NOTE •.fair/forcing bars to be spaced and @
wired in position before concrete ispoured.
;i bar over each Floorbeam. .1* ,* •
-3 per panel
t #
lOWWtmAL 5iort OF FLOOR. ^ i
34PI.;1 '\spaced/8c.toc.
vw » ..
* f
/ Weep Me with perforated coyer
L
— Standard Specifications
*
(L?A{?.c.-f.r.u.tt?-5
ASSUMED LOAD/NO HALFSECTIOH
DeadMO'perft. of truss.
Live,9Q*pers<j.ft.ofnadwy
or engine as per diagram.
Kaph./H \ji
JS3|OXi|SMJ0 /$&''' &W /J^l" ff^c&clresses \ (Bradebare
WfW'Wm T" '*<WM Cast Iron Masonry PI. l?xttl!/r ** omittedon spans
Qajfiffi. /u \K/& lessthanlf!)
al Details
CAST lRon5Hocs- FIXED Eno. 1
ConcreteSldb Floor
lowd Highway Commission
FIG. 1 8. Low TRUSS SPAN WITHOUT STRINGERS.
The depths and number of panels in Wisconsin Highway Commission low truss bridges with
joists are as follows: 35 ft. span, 3 panels, \\ ft. deep; 40 ft. span, 3 panels, 5 ft. deep; 45 ft. span,
3 panels, 5! ft. deep; 50 ft. span, 4 panels, 5^ ft. deep; 55 ft. span, 4 panels, 6 ft. deep; 60 ft. span,
4 panels, 6| ft. deep; 65 ft. span, 5 panels, 7 ft. deep; 70 ft. span, 5 panels, 75 ft. deep; 75 ft. span,
5 panels, 8 ft. deep; 80 ft. span, 5 panels, 8| ft. deep; 85 ft. span, 6 panels, 9 ft. deep.
LOW TRUSS HIGHWAY BRIDGE.
125
\
a
\
^L 4'3*f ', conn, same <ys /<?ts.\
AH lat's IL 4'*$"*}". 1 rivet at \
int'sect. 3 rivets at end
&'
PART PLAN
HALF SECT/ON
'Connect bterjls 60 f/'r bhts\ -.
Top of
•Specifications: Mich. Stete Hiohwy DepL.
1916 Edition.
Life Lojd : /8 T. roller or /Off /6 per sq. ft.
Desd Lox/: Weight of steel p/vs /350 Ib.
per /in. ft. for ^ "concrete floor.
Raint: One shop jr?d two f/'e/d costs.
First to 6e red , second, qreen <?nd
third, 6teck. fiaint to ee fond mi
IB Ib. pare red /e^d to one <?j//0n
Unseed, 0r^t?t/?er pjint <spproved oy
Michtojn Stete Higtinay Commissioner.
Resmina: A// hales for f/e&/ rivets except
for teter<3/s to be drilled or reamed
to iron template or resmed true
while pieces <3rv bo/ted together.
Connections : A// fie/d connections sf&l/ of
made tv/th riffts.
Pi vets : To fa * " unless noted.
Traffic: To be maints/ned dt/rino, erection
unless otherwise hand/ed /n manner
by fityhnay Commissioner.
Sections of ffou/K3/e/?t strength
y be substituted on approval.
All ousset plates g "
Estimated tveifhc 63,000 Iff.
in Shoes
PI. /"
2 Side Pis. i
2 Outs. 1*6 S3,
„ Pis.}"
? Fillers, *
Railfnp jnd Connections,
Pedestals and Shoes
STANDARD ffl FT. L0w
WOW Kox/wy
'Michigan H/yhwy fommission
FIG. 19. Low TRUSS SPAN WITH STRINGERS.
126
STEEL HIGHWAY BRIDGES.
CHAP. III.
o
U
M
O
Q
a
PQ
o
a
u
Q
M
w
o
Q
3
CQ
STEEL HIGHWAY BRIDGES.
127
{Ill
1 5 i
^ i %: ^
r*i
45 il
»
S fv; -5
111>J5
i
128
STEEL HIGHWAY BRIDGES.
rlgtholes ?.,„
CHAP. III.
gjx.xxjjgi.xxxx
SHOES-EXPANSION tno
Ca5t5teel
mFloorbeamsJ-afatt*
WJ*sts,Ui*3,Ttxl&
9"MI*
FIG. 23. DETAIL PLANS OF THROUGH HIGH TRUSS SPAN.
COMMISSION.
WISCONSIN HIGHWAY
HIGH TRUSS STEEL HIGHWAY BRIDGES.— Through truss bridges with spans of from
80 to 170 ft., are built with parallel chords and preferably with riveted joints. For spans of from
1 60 to 220 ft. bridges are usually built of the Pratt type with inclined upper chord (camel-back)
trusses. Above 220 ft., bridges are usually built with the Petit type of truss. The above limits
are approximate only. For long span bridges the inclined chord truss with K-bracing is rapidly
taking the place of the Petit truss. High truss pin-connected bridges should never be built with
less than five panels.
Types of bridge adopted in the American Bridge Company's standards are as follows:
Pratt, pin-connected trusses 80 to 168 ft. span
Pratt, riveted trusses. .- 80 to 168 ft. span*
Warren, quadrangular, riveted trusses 80 to 152 ft. span'
Inclined chord Pratt (camel-back), pin-connected trusses 168 to 220 ft. span-
Petit trusses, pin-connected 220 ft. span and over
Examples of High Truss Highway Bridges. — Details of a high truss steel highway bridge as
designed by the Wisconsin Highway Commission are shown in Fig. 22 and Fig. 23. Standard plans
have been prepared for spans of 90 ft. to 150 ft., varying by 5-ft. intervals, and a roadway of 16 ft.
and 1 8 ft. All spans have one end carried on rockers as shown. These designs have been worked
out very economically by Mr. M. W. Torkelson, bridge engineer, and represent the extreme econ-
omy of design that will conform to good practice.
Details of a high truss steel highway bridge as designed by the Iowa Highway Commission are
given in Fig. 24. Standard plans have been prepared for spans of 90 ft. to 150 ft. varying by
5-ft. intervals, and a roadway of 16 ft. and 18 ft. All spans have one end carried on rockers as
shown. The designs are well worked out with the exception of the collision strut in the first panel,
which should be omitted.
STEEL HIGH TRUSS HIGHWAY BRIDGES.
129
130
STEEL HIGHWAY BRIDGES.
CHAP. III.
111
STEEL RIVETED HIGHWAY BRIDGES.
131
I I
I $
&.- •£
^> -t? •£ < &V • "S **
*^si< v> ^:
kCV I •* « tJ
^c§^^ .^
-svl vl * J^S^ X>
^fl^ll
«§;¥.
^
IIP ; • u i : - LT:
^ZHaiJt in ends oF each board-
4"*6'xl'0' Block-, Sxfi'xlM'Wftee/fatf^ .
1
- 1
•13^Ep
LI K 0 !•! i! \
i , >.i ,, v
! L! I! U !l
f\ ;i rt !! ft i
: u ;: y
\\ Li :: ^ i! :
ELJLj !- " ;
fl t! ", ! n ;
L_M_il__y •• :
n u i ij n •
;j (j | ;; |! ji
:: w: u :i ;
:• L :i L: •! :
^o\l
tO-Jfx.txJ-'
I
I
N%>
i
^
i
O
3
N-
^^^
\..
\,
•^.
*\
^
^
»
hH
^v
•»^
^
^
1
^
§
^
JQ
vr\
PLAH AHD SECTION
>
^
^
^
•*.
•*?
I
JoJsf 4*x/4*S
INTERMEDIATE Joi.
Kx
"'"
\ — i
y
D
G
X
^
>
5
2
O
p^!>f *
.f7^
132
STEEL HIGHWAY BRIDGES.
CHAP. III.
lihp
..^, ^\ ifliio i 'S »
vx S !
^Ji
PIN-CONNECTED HIGHWAY BRIDGE.
133
O^ff^y^f&il^'im^^ r T.r
! S/Xlfffjfftf&tW !!;ffl| j Piigg J^T
1 — atef — » — 1 1 v — i — mo* — I i anwE^ss ifi^.i
Q S3^?tf
i ! i
• :::: : - K;
k-i|-;lkFfelFI-
:§il -^ .1 f-:
'in ! "-*! JL_..«"tS!>f ' ! >>
STEEL HIGHWAY BRIDGES.
CHAP. III.
SHOES AND PEDESTALS. 135
The details of a riveted truss highway bridge for light country traffic designed by Mr. H. S.
Crocker, Consulting Engineer, Denver, Colo., are given in Fig. 25 and Fig. 26. The details of a
Pin-connected truss highway bridge designed for country traffic are given in Fig. 27, Fig. 28 and
ig. 29. Both of these bridges represent standard practice in the design of steel highway bridges
for light country traffic. For additional examples of steel highway bridges, see the author's
"The Design of Highway Bridges."
Economic Depth and Panel Length of Trusses. — The economic depth and panel length of
trusses is not capable of mathematical calculation. The minimum depth is determined by the
required clear head room, which varies from \2\ to 15 ft. Short panel lengths give heavy trusses
and light floor systems; while long panels give light trusses and heavy floor systems. For ordinary
conditions it is not economical to use panel lengths less than 15 ft. for short spans nor more than
25 ft. for long spans. The minimum depth for through spans is about 16 feet where the floor-
beams are placed below the lower chords. To make a stiff structure, the depth should be suffi-
cient to permit the placing of the floorbeams above the lower chords and to permit of efficient portal
and sway bracing. Experience has shown that the most economical conditions occur when the
angle 9, the tangent of which is the panel length divided by the depth, is about 40 degrees. The
top chord points of bridges with inclined chords should be approximately on a parabola passing
through the pin at the hip.
Depth and Panel Length of High Trusses. — The depths and number of panels in Iowa High-
way Commission high truss riveted bridges are as follows: Pratt, riveted trusses, go-ft. span, 5
panels, 20 ft. deep; loo-ft. and no-ft. spans, 6 panels, 20 ft. deep; i2O-ft. span, 7 panels, 20 ft.
deep; i4O-ft. span, 8 panels, 21 ft. deep. The depths and number of panels in Wisconsin Highway
Commission high truss riveted bridges are as follows: go-ft. and 96-ft. span, 6 panels, 18 ft. deep;
ico-ft. span, 6 panels, 20 ft. deep; io5-ft. span, 7 panels, 20 ft. deep; i2O-ft. span, 8 panels, 20 ft.
jp; 128-ft. span, 8 panels, 21 ft. deep; i4O-ft. span, 8 panels, 20 ft. deep at hip and 27 ft. deep at
iter; i5O-ft. span, 8 panels, 20 ft. deep at hip and 28 ft. deep at center.
The depths and number of panels in American Bridge Company's high truss bridges are as
allows: Riveted and pin-connected trusses with parallel chords, 8o-ft. to go-ft. span, 5 panels,
pth equal to panel length; 90- to i2O-ft. span, 6 panels, depth equal to panel length; i2O-ft. span
i4O-ft. span, 7 panels, depth equal to panel length, I2o-ft. to i68-ft. span, 8 panels, ratio of
:pth to panel length 1. 1. For bridges with inclined chords with spans of 162 ft. to 180 ft., 9
inels, and ratios of depth to panel length of l.o, 1.16, 1.25 and 1.29; i^o-ft. to 22O-ft. span, 9
.nels, and ratios of depth to panel length of l.o, 1.24, 1.28 and 1.43. For Petit trusses, 24O-ft.
276-ft. span, 12 panels, and ratios of depths to panel length of l.o, 1.4, 1.6 and 1.7; 294-1!. to
22-ft. span, 14 panels, and ratios of depth to panel length of i.o, 1.36, 1.60, 1.8 and 2.0.
SHOES AND PEDESTALS. — The bridge rests on shoes or pedestals, the loads being trans-
red to the shoes in pin-connected bridges by means of pins, and through the riveted joints in
iveted bridges. The shoes at the expansion ends of the bridge are placed on smooth sliding plates
bridges of less than, say, 65-ft. span, and on nests of rollers or rockers for spans of greater
igth. The action of the rollers under the expansion ends of riveted bridges will be much more
itisfactory if the shoes are pin-connected to the truss the same as for pin-connected trusses,
lollers should be made with as large diameters as practicable in order to reduce the pressure on
ic base plate and also to reduce the resistance to movement. Experience shows that even for
jht bridges rollers smaller than 3 in. diameter are practically worthless. To economize space,
jmental rollers, as shown in Fig. 35, Chapter IV, are often used for heavy spans.
It is usual to specify that a movement produced by a variation of 150 degrees Fahr. be pro-
dded for. The coefficient of expansion of steel is approximately 0.0000067 per degree Fahr.,
lich makes it necessary to provide for approximately one inch of movement for each 80 ft. of
ridge span.
Where both bridge seats are of ihe same height, the fixed end is carried on cast iron pedestal
blocks. The blocks are usually made with recesses (honeycombed) to reduce the weight.
The Illinois, Iowa and Wisconsin Highway Commissions use rockers in the place of rollers
for highway bridges. Detail* of rockers are shown in Fig. 17, Fig. 18, Fig. 23, and Fig. 24. The
specifications of the Illinois Highway Commission contain the provision that rockers shall be made
of cast iron as specified. They shall have a thickness of not less than 2\ in. for spans of 45 ft. or
less, and a thickness of 3 in. for spans exceeding 45 ft. in length, but in no case shall the unit com-
pressive stress exceed 9,000-40 l/r Ib. per sq. in. All rockers shall have bearing surfaces turned to
a uniform radius and smooth surface and shall be provided with two 2-in. holes through the web to
facilitate handling.
136
STEEL HIGHWAY BRIDGES.
CHAP. III.
'Yfosher
^^7-OOx.Kr-H:
FENCE FOR ^3^ ST- VIADUCT,
DENVER, COLORADO-
J'GasPfjpe-iC^
r£> " kwwztf
20^ ST- VIADUCT,
DENVER, COLORADO-
Swtion A-B.
ELECTRIC LIGHT POLE,
I&ST- V/ADUCT, DENVER, COLO*
FIG. 30. STEEL FENCE FOR HIGHWAY BRIDGES.
FENCE AND HUB GUARDS. — The fence on steel bridges is commonly made of two lines
of channels or two lines of angles with angle posts. Posts should not be spaced farther apart than
8 ft. to 10 ft.
A gas pipe railing with gas pipe posts is in frequent use. The posts should be spaced not more
than 8 ft. apart. Details of the fence and light poles for the 2Oth St. Viaduct, and the fence on
23d St. Viaduct, Denver, Colo., designed by Mr. H. S. Crocker, consulting engineer, are shown in
Fig. 30.
GENERAL SPECIFICATIONS FOR STEEL HIGHWAY BRIDGES.*
BY
MILO S. KETCH UM,
M. Am. Soc. C. ET.
THIRD EDITION,
1918
PART I. DESIGN.
GENERAL DESCRIPTION.
1. Classes. — Bridges under these specifications are divided into eight classes, as follows;
Class A. — For city traffic.
Class B. — For suburban or interurban traffic with heavy electric cars.
Class C. — For country roads with ordinary traffic and light electric cars.
Class DI. — For country roads with heavy traffic.
Class Dj. — For country roads with light traffic.
Class Ei. — For heavy electric street railways only.
Class Ej. — For medium electric street railways only.
Class E3. — For light electric street railways only.
2. Material. — All parts of the structure shall be of rolled steel, except the flooring, floor
joists and wheel guards, when wooden floors are used. Cast iron or cast steel may be used in the
machinery of movable bridges, for wheel guards, and in special cases for bed plates.
3. Types of Truss. — The following types of bridges are recommended:
Spans up to 30 ft. — Rolled beams.
Spans from 30 to 80 ft. — Riveted plate girders, or riveted low trusses for classes A, B, Ei,
Ej and E3; and riveted low trusses for classes C, Di and D2.
Spans 80 to 1 60 ft. — Riveted or pin-connected high trusses.
Spans 160 to 200 ft. — Pin-connected trusses of the Pratt type with inclined chords.
Spans over 200 ft. — Pin-connected trusses of the Petit type or K-type.
4. Length of Span. — In calculating the stresses the length of span shall be taken as the
distance between centers of end pins for pin-connected trusses, centers of end bearing plates for
riveted trusses and for girders, and center to center of trusses for floorbeams.
5. Form of Trusses. — The form of truss shall preferably be as given in paragraph 3. In
through trusses the end vertical suspenders and the two panels of the lower chord at each end
shall be made rigid members if the wind load produces a reversal of stress in the lower chord. In
through bridges the floorbeams shall be riveted above or below the lower chord pins.
6. Lateral Bracing. — All lateral and sway bracing shall preferably, and all portal bracing
must be, made of shapes capable of resisting compression as well as tension, and shall have riveted
connections. Low trusses and through plate girders shall be stayed by knee braces or gusset
plates at each floorbeam.
7. Spacing of Trusses. — For bridges carrying electric cars the clear width from the center of
the track shall not be less than 7 ft. at a height exceeding one foot above the track where the
tracks are straight, and an equivalent distance when the tracks are curved. The distance between
centers of trusses shall in no case be less than one-twentieth of the span between the centers of
end-pins or shoes, and shall preferably not be less than one-twelfth of the span.
8. Head Room. — For classes A, B, C, Di, Ei, E2 and E3 the clear head room for a width of
eight (8) ft. on each track, or eight (8) ft. on the center line of the bridge shall not be less than
15 ft., and for class D2 not less than I2| ft.
9. Footwalks. — Where footwalks are required, they shall generally be placed outside of the
trusses and be supported on longitudinal beams resting on overhanging steel brackets.
10. Handrailing. — A strong and suitable handrailing shall be placed at each side of the bridge
and be rigidly attached to the superstructure.
n. Trestle Towers. — Trestle bents shall preferably be composed of two supporting columns,
two bents forming a tower; each tower thus formed shall be thoroughly braced in both directions
and have struts between the feet of the columns. The feet of the columns must be secured to
an anchorage capable of resisting one and one-half times the specified wind forces (§89).
* Reprinted from the author's "The Design of Highway Bridges."
137
138 STEEL HIGHWAY BRIDGES. CHAP. III.
Each tower shall have a sufficient base, longitudinally to be stable when standing alone,
without other support than its anchorage. Tower spans for high trestles shall not be less than
30 ft.
12. Proposals. — Contractors in submitting proposals shall furnish complete stress sheets,
general plans of the proposed structures, and such detail drawings as will clearly show the dimen-
sions of all the parts, modes of construction and sectional areas.
13. Drawings. — Upon the acceptance and the execution of the contract, all working drawings
required by the engineer shall be furnished free of cost (§168).
14. Approval of Plans. — No work shall be commenced or materials ordered until the working
drawings have been approved by the engineer in writing.
FLOOR SYSTEM.
15. Floorbeams. — All floorbeams shall be rolled or riveted steel girders, rigidly connected
to the trusses at the panel points, or may be placed on the top of deck bridges at panel points.
Floorbeams shall preferably be square to the trusses or girders.
16. Joists and Stringers. — All joists and stringers of bridges of classes A, B, EI, E2 and E3
shall be of steel. Joists for classes C, Di and D2 may be either of wood or steel as specified.
Steel joists shall be securely fastened to the cross floorbeams, and steel stringers shall preferably
be riveted to the webs of floorbeams by means of connection angles at least -fa in. thick.
17. End Spacers for Stringers. — Where end floorbeams cannot be used, stringers resting on
masonry shall have cross-frames at their ends. These frames shall be riveted to girder or truss
shoe where practicable.
1 8. Wooden Joists. — Wooden floor joists shall be spaced not more than 2| ft. centers, and
shall lap by each other so as to have a full bearing on the floorbeams, and shall be separated | in.
for free circulation of air. Their width shall not be less than 3 in., or one-fourth the depth in
width. The proportion of the concentrated live load carried by one joist shall be taken equal to
the spacing of the joists in feet divided by four feet. No impact shall be considered in the design
of wooden joists, planks or ties. Oak, longleaf yellow pine and Oregon fir shall be designed for a
safe bending of 1,500 Ib. per sq. in., bearing across the fiber of 400 Ib. per sq. in., and shearing along
the grain of 140 Ib. per sq. in. Outside joists shall be designed for the same live loads as the inter-
mediate joists.
19. Steel Joists. — Steel I-beams when used as joists shall have a depth of not less than one-
thirtieth of the span, and one-twentieth of the span when used as track stringers. The proportion
of the concentrated live load carried by one joist shall be taken equal to the spacing of the joists
in feet divided by four feet when timber flooring is used, and divided by six feet when a reinforced
concrete or other rigid floor is used. Outside joists shall be designed for the same live loads as the
intermediate joists.
20. Floor Plank. — For single thickness the roadway planks shall not be less than 3 in. thick
nor less than one-eighth of the distance between centers of joists, and shall be laid transversely with
y in. openings and securely spiked to each joist. All plank shall be laid with heart side down.
When an additional wearing surface is required it shall be i^ in. thick, and the lower planks of a
minimum thickness of 3 in. shall be laid diagonally with £ in. openings.
21. Footwalk plank shall be not less than 2 in. thick nor more than 6 in. wide, spaced with
5 in. openings.
All plank shall be laid with heart side down, shall have full and even bearing on and be firmly
attached to the joists.
22. Wheel Guards. — Wheel guards of a cross-section of not less than 6 in. by 4 in. shall be
provided on each side of the roadway. They shall be spliced with half-and-half joints with 6 in.
lap, and shall be bolted to the stringers or joist with f in. bolts, spaced not to exceed 5 ft. apart.
23. Solid Floor. — For bridges of classes A and B a solid floor, consisting of wooden blocks,
brick, stone, asphalt, etc., on a concrete bed is recommended. For this case the floor shall con-
sist of buckle plates or corrugated sections or reinforced concrete slabs, and a waterproof
concrete (bitumen or cement) bed not less than 3 in. thick for the roadway and 2 in. thick for the
footwalk, over the highest point to be covered, not counting rivet or bolt heads. The floor shall
be laid with a slope of at least one inch in 10 ft.
Reinforced Concrete Floor.— See specifications for reinforced concrete floor on page 112 h,
and distribution of loads on page 112 f.
24. Buckle plates shall not be less than -& in. thick for the roadway and j in. thick for the
footwalk. The crown of the plates shall not be less than 2 in.
25. For solid floor the curb holding the paving and acting as a wheel guard on each side of
the roadway shall be of stone or steel projecting about 6 in. above the finished paving at the gutter.
The curb shall be so arranged that it can be removed and replaced when worn or injured. There
shall also be a metal edging strip on each side of the footwalk to protect and hold the paving in
place.
SPECIFICATIONS. 139
26. Drainage. — Provision shall be made for drainage clear of all parts of the metal work.
27. Floor of Classes EI, Ez, and Et. — The floors of classes EI, Eif and EI shall consist of
cross-tics not loss than 6 in. by 6 in. for stringers spaced 6J ft.; and larger for greater spacings,
they shall be spaced with openings not exceeding 6 in., shall be notched down \ in., and secured
to the supporting stringers by J in. bolts spaced not over 6 ft. apart. The ties shall extend the
full width of the bridge on deck bridges, and every other tie shall extend the full width in through
tni(l<vs to carry the footwalk. Ties shall be designed for the same allowable unit stresses as
wooden joists.
There shall be guard timbers not less than 6 in. by 6 in., or 5 in. by 7 in., on each side of
each track, with their inner faces not less than 9 in. from the center of the rail. They shall be
notched I in. over every tie, and shall be spliced over a tie with a half-and-half joint with 6 in.
lap. Each guard timber shall be fastened to every third tie and at each splice with a f in. bolt.
All heads or nuts on the upper faces of ties or guards shall be countersunk below the surface of
the wood.
PART II. LOADS.
28. Dead Load. — The dead load will consist of (r) the weight of the metal, and (2) the weight
of the timber in the floor, or of the material other than steel. In determining the dead load the
weight of oak or other hard wood shall be taken at 4^ Ib. per foot board measure, and the weight
of pine or other soft woods at 3^ lb. per foot; the weight of asphalt at 130 Ib., of concrete and
paving brick at 150 Ib., and of granite at 160 lb per cu. ft.
The rails, fastenings, splices and guard timbers of street railway tracks shall be assumed to
weigh not less than 100 lb. per lineal foot of track.
29. Live Load. — The bridges of different classes shall be designed to carry, in addition to
icir own weight and that of the floor, a moving load, either uniform or concentrated, or both, as
:ified below, placed so as to give the greatest stress in each member.
Class A. For City Traffic. — For the floor and its supports, on any part of the roadway or
each of the street car tracks, a concentrated load of 24 tons on two axles 10 ft. centers and 5 ft.
ige (assumed to occupy 12 ft. in width for a single line or 22 ft. for a double line), and upon
ic remaining portion of the floor, a load of 125 lb. per sq. ft. and a concentrated load as for class
Sidewalks a load of 100 lb. per sq. ft.
Loads for the trusses as per Table I.
Class B. For Suburban or Interurban Traffic. — For the floor and its supports, on any part
the roadway, a concentrated load of 12 tons on two axles lo-ft. centers and 5-ft. gage (assumed
occupy a width of 12 ft.), or on each street car track a concentrated load of 24 tons on two
Jes lo-ft. centers; and on the remaining portion of the floor, a load of 125 lb. per sq. ft. and a
jncentrated load as for class DI. Sidewalks a load of 100 lb. per sq. ft.
Loads for the trusses as per Table I.
Class C. For Highway and Light Interurban Traffic. — For the floor and its supports, on
ly part of the roadway, a concentrated load of 12 tons on two axles lo-ft. centers and 5-ft. gage
ssumed to occupy a width of 12 ft.), or on each street car track r concentrated load of 18 tons
two axles xo-ft. centers; and upon the remaining portion of the floor, a load of 125 lb. per sq. ft.
id a concentrated load as for class DI. Sidewalks a load of 100 lb. per sq. ft.
Loads for the trusses as per Table I.
Class DI. Heavy Country Bridges. — For the floor and its supports, a load of 125 lb. per sq .ft.
total floor surface or a 2o-ton motor truck with axles spaced 12 ft. and wheels with a 6-ft. gage,
nth 14 tons on rear axle and 6 tons on front axle. The truck to occupy a space 10 ft. wide and
ft. long. The rear wheels to have a width of 20 in.
Loads for the trusses as per Table I. No bridge, however, to be designed for a load of less
an 1,000 lb. per lineal foot of bridge.
Class Dt. Oridnary Country Bridges. — For the floor and its supports, a load of 100 lb. per
1. ft. of total floor surface or a 1 5-ton motor truck with axles spaced 10 ft. and wheels with a 6-ft.
ige, and occupying a space 10 ft. wide and 30 ft. long, with 10 tons on rear axle and 5 tons on
jnt axle, and with rear wheels 15 in. wide.
Loads for the trusses as per Table I. No bridge, however, to be designed for a load oi less
in 800 lb. per lineal foot of bridge.
Class EI. For Heavy Electric Railways Only. — On each track a series of concentrations
insisting of two pairs of trucks, the axles of the pairs being spaced 5 ft. centers, while the distance
etween centers of interior axles is 10 ft., the pairs of trucks being spaced 15 ft. centeVs. The
des are loaded with a load of 40,000 lb., making a total of 160,000 lb. Or a uniform load of 6,000
>. per lineal foot for all spans up to 50 ft., reduced to 4,500 lb. per lineal foot for spans of 200 ft.
id over, and proportionately for intermediate spans.
140
STEEL HIGHWAY BRIDGES.
CHAP. III.
Class £2- For Medium Electric Railways Only. — On each track a series' of concentrations
consisting of two pairs of trucks, the axles of the pairs being spaced 5- ft. centers, while the distance
between centers of interior axles is 10 ft., the pairs of trucks being spaced 15-ft. centers. The
axles are loaded with a load of 25,000 lb., making a total load of 100,000 Ib. Or a uniform load
of 3,500 lb. per lineal foot for all spans up to 50 ft., reduced to 2,000 lb. per lineal foot for spans
of 200 ft. and over, and proportionately for intermediate spans.
Class EZ. For Light Electric Railways Only. — On each track a series of concentrations
consisting of two pairs of trucks, the axles of the pairs being spaced 5-ft. centers, while the distance
between centers of interior axles is 10 ft., the pairs of trucks being spaced 15-ft. centers. The
axles are loaded with a load of 20,000 lb. making a total load of 80,000 lb. Or a uniform load of
2,500 lb. per lineal foot for all spans up to 50 ft., reduced to 1,500 lb. per lineal foot for spans of
200 ft. and over, and proportionately for intermediate spans.
TABLE I.
LIVE LOADS FOR THE TRUSSES
Class A.
Class B.
Class C.
Class Di.
Class D2.
Span in Feet.
j.'S
m
fc2*8
S.§.s,g
.gfa.s?
a « gw
t.'o
p, o « .
. "o .;
• «* MB
l!|1
•Ju-jj
6-6.8'
ag.s,g
«'P
•C° v
&||
ftl
h ° «
S 4J 0
&§^
"fa 3
^ UM
lp
IJJJ
t/3 fa
ill
Ipl
f> fa
l|^
lUi
tfl fa
3 >5 IH
ly
c«fa
° 3 g
(^ fffS
(AH
Up to
3O
i, 800
I2S
1, 800
I2C
1, 8OO
I2C
I2C
ICO
80
i, 800
105
. 1, 800
85
I,2OO
85
85
71
160
1,440
88
1,440
68
I, O8O
68
68
60
200
and over
1,200
80
I,2OO
60
I, COO
60
60
5°
Loads for intermediate spans to be proportional.
30. Wind Loads. — The lateral bracing in the unloaded chords of truss bridges shall be designed
for a lateral wind load of 150 lb. per lineal foot of bridge, considered as a moving load. The lateral
bracing in the loaded chords of truss bridges shall be designed for a lateral wind load of 300 lb. per
lineal foot of bridge, considered as a moving load. For spans over 300 ft. each of the above load-
ings shall be increased 10 lb. for each 20 ft. increase in span. In highway bridges not carrying
electric cars the end-posts of through and deck bridges and the intermediate posts of through
bridges shall be designed for a combination (i) of the dead load stresses and the total live load
stresses; or (2) of the dead load stresses, the live load stresses, the impact and centrifugal stresses,
and one-half the total wind load stresses. In low truss bridges and plate girders not carrying
electric cars the wind load on the unloaded chord may be omitted and the lateral bracing be de-
signed for a lateral wind load of 300 lb. per lineal foot treated as a moving load. In bridges with
sway bracing one-half of the wind load may be assumed to pass to the lower chord through the
sway bracing.
31. In trestle towers the bracing and columns shall be designed to resist the following lateral
forces, in addition to the stresses due to dead and live loads: The trusses loaded or unloaded, the
lateral pressures specified above; and a lateral pressure of 100 lb. for each vertical lineal foot of
trestle bent.
32. Temperature. — Stresses due to a variation in temperature of 150 degrees shall be pro-
vided for (§81).
33. Centrifugal Force of Train. — Structures located on curves shall be designed for the
centrifugal force of the live load acting at the top of the rail. The centrifugal force shall be calcu-
lated by the following formula: C = (0043— 0.003 D) W'D; where C = centrifugal force in lb.;
W ' = weight of train in lb. ; and D = degree of curvature.
34. Longitudinal Forces. — The stresses produced in the bracing of the trestle towers, in any
members of the trusses, or in the attachments of the girders or trusses to their bearings, by sud-
denly stopping the maximum electric car trains on any part of the work must be provided for;
the coefficient of friction of the wheels on the rails being assumed as 0.20.
35. All parts shall be so designed that the stresses coming upon them can be accurately
calculated.
SPECIFICATIONS. 141
PART III. UNIT STRESSES AND PROPORTION OF PARTS.
^6. Unit Stresses. — All parts of the structure shall be proportioned so that the sum of the
maximum stresses shall not exceed the following amounts in Ib. per sq. in., except as modified by
§45 and §48.
Impact. — The dynamic increment of the live load stress shall be added to the maximum live
lo.ul Musses as follows:
For the floor and its supports including floor slabs, floor joist, floorbeams and hangers, 30
per cent.
For all truss members other than the floor and its supports, the impact increment shall be
/ = loo/(L + 300), where L = length of span for simple highway spans (for trestle bents, towers,
movable bridges, arch and cantilever bridges, and for bridges carrying electric trains, L shall be
taken as the loaded length of the bridge in feet producing maximum stress in the member).
Impact shall not be added to the stresses produced by longitudinal, centrifugal and lateral or
wind forces.
37. Tension. — Axial tension on net section 16,000
The lengths of riveted tension members in horizontal or inclined positions shall not exceed
200 times their radius of gyration about the horizontal axis. The horizontal projection of the
unsupported portion of the member is to be considered as the effective length.
38. Compression. — Axial compression on gross section 16,000 — 7O'//r
with a maximum of 14,000 Ib.; where "/" is the length of member in inches and "r" is the least
radius of gyration in inches.
No compression member, however, shall have a length exceeding 100 times its least radius of
gyration for main members or 120 times for laterals for classes A, B, C, Ei, Ej, and Es; or 125 times
its least radius of gyration for main members or 150 times for laterals for classes DI and Dz.
39. Bending. — Bending: on extreme fibers of rolled shapes, built sections and girders;
net section 16,000
on extreme fibers of pins 24,000
40. Shearing. — Shearing: shop driven rivets and pins 12,000
field driven rivets and turned bolts 10,000
plate girder webs; gross section 10,000
41. Bearing. — Bearing: shop driven rivets and pins .". 24,000
field driven rivets and turned bolts 20,000
granite masonry and Portland cement concrete 600
sandstone and limestone 400
expansion rollers; per linear inch 6ood
where "d" is the diameter of the roller in inches.
Rivets shall not be used in direct tension, except for lateral bracing where unavoidable; in
irhich case the value for direct tension on the rivet shall be taken the same as for single shear.
. 42. Alternate Stresses. — Members subject to alternate stresses of tension and compression
lall be proportioned for the stresses giving the largest section. If the alternate stresses occur
succession during the passage of one train, as in stiff counters, each stress shall be increased by
per cent of the smaller. The connections shall in all cases be proportioned for the sum of the
resses.
43. Angles in Tension. — When single-angle members subject to direct tension are fastened by
leg, only seventy-five per cent of the net area shall be considered effective. Angles with lug
igle connections shall not be considered as fastened by both legs.
44. Net Section. — In members subject to tensile stresses full allowance shall be^made for
uction of section by rivet-holes, screw-threads, etc. In calculating net area the rivet-holes
aall be taken as having a diameter | in. greater than the normal size of rivet.
45. Long Span Bridges. — For long span bridges, where the ratio of the length to width of
in is such that it makes the top chords acting as a whole, a longer.column than the segments of
ic chords, the chord shall be proportioned for the greater length.
46. Wind Stresses. — The stresses in truss members or trestle posts from assumed wind forces
not be considered except as follows:
1. When the direct wind stresses per square inch in any member exceed 25 per cent of the
stresses due to dead and live loads in the same member. The section shall then be increased
until the total unit stress shall not exceed by more than 25 per cent the maximum allowable
stress for dead and live loads.
2. When the wind stress alone or in combination with a possible temperature stress can
neutralize or reverse the stresses in the member.
When both direct and flexural stresses due to wind are considered 50 per cent may be added
to allowable stresses for dead and live loads, provided the area thus obtained is not less than re-
quired for dead and live loads alone, or for dead, live and direct wind loads designed as in §46.
47. Combined Stresses. — Members subjected to direct and bending stresses shall be designed
so that the greatest fiber stress shall not exceed the allowable unit stress on the member.
142 STEEL HIGHWAY BRIDGES. CHAP. III.
48. Stress Due to Weight and Eccentric Loading. — If the fiber stress due to weight and
eccentric loading on any member exceeds 10 per cent of the allowable unit stress on the member
such excess must be considered in proportioning the member. See §46.
49. Counters. — Counters in bridges carrying electric cars shall be designed so that an increase
of the live load of 25 per cent will not increase the stress in the counters more than 25 per cent.
50. Design of Plate Girders. — Plate girders shall be proportioned either by the moment of
inertia of their net section; or by assuming that the flanges are concentrated at their centers of
gravity, in which case one-eighth of the gross section of the web, if properly spliced, may be used
as flange section. The thickness of web plates shall be not less than & in., nor less than 1/160 of
the unsupported distance between flange angles.
Compression Flanges. — In beams and plate girders the compression flanges shall have the
same gross section as the tension flanges. Through plate girders shall have their top flanges
stayed at each end of every floorbeam, or in case of solid floors, at distances not exceeding 12 ft., by
knee braces or gusset plates. The stress per sq. in. in compression flange of any beam or girder
shall not exceed 16,000 — 2oo-l/b, when flange consists of angles only or if cover consists of flat
plates, or 16,000— 150 l/b if cover consists of a channel section, where / = unsupported distance
and b = width of flange.
51. Web Stiffeners. — There shall be web stiff eners, generally in pairs, over bearings, at points
of concentrated loading, and at other points where the thickness of the web is less than ^ of the
unsupported distance between flange angles. The distance between Stiffeners shall not exceed
that given by the following formula, with a maximum limit of six feet (and not greater than the
clear depth of the web): d = t (12,000 — 5)740.
Where d = clear distance, between Stiffeners of flange angles ; t = thickness of web ; 5 = shear
per sq. in.
The Stiffeners at ends and at points of concentrated loads shall be proportioned by the formula
of paragraph 38, the effective length being assumed as one-half the depth of girders. End Stiffeners
and those under concentrated loads shall be on fillers and have their outstanding legs as wide as
the flange angles will allow and shall fit tightly against them. Intermediate Stiffeners may be
offset or on fillers, and their outstanding legs shall be not less than one-thirtieth of the depth of
girder, plus 2 in.
52. Flange Rivets. — The flanges of plate girders shall be connected to the web with a sufficient
number of rivets to transfer the total shear at any point in a distance equal to the effective depth
of the girder at that point combined with any load that is applied directly on the flange. The
wheel loads, where the ties rest on the flanges, shall be assumed to be distributed over three ties.
53. Depth Ratios. — Trusses shall preferably have a depth of not less than one-tenth of the
span. Plate girders and rolled beams, used as girders, shall preferably have a depth of not less
than one-twelfth of the span. If shallower trusses, girders or beams are used, the section shall be
increased so that the maximum deflection will not be greater than if the above limiting ratios had
not been exceeded. For steel joists and track stringers, see § 19.
54. Low Trusses. — Riveted low trusses shall have top chords composed of a double web mem-
ber with cover plate. The top chords shall be stayed against lateral bending by means of brackets
or knee braces rigidly connected to the floorbeam at intervals not greater than twelve times the
width of the cover plate. The posts shall be solid web members. The floorbeams shall be riveted,
preferably above the lower chord. Pin-connected low truss bridges shall not be used.
55. Rolled Beams. — Rolled beams shall be designed by using their moments of inertia. The
webs of rolled beams and plate girders shall be assumed to take all the shear.
PART IV. DETAILS OF DESIGN.
GENERAL REQUIREMENTS.
56. Open Sections. — Structures shall be so designed that all parts will be accessible for in-
spection, cleaning and painting.
57. Water Pockets. — Pockets or depressions which would hold water shall have drain holes,
or be filled with waterproof material.
58. Symmetrical Sections. — Main members shall be so designed that the neutral axis will be
as nearly as practicable in the center of section, and the neutral axes of intersecting main members
of trusses shall meet at a common point.
59. Counters. — Rigid counters are preferred; and where subject to reversal of stress shall
preferably have riveted connections to the chords. Adjustable counters shall have open turn-
buckles.
60. Strength of Connections. — The strength of connections shall be sufficient to develop the
full strength of the member, even though the computed stress is less, the kind of stress to which
the member is subjected being considered.
61. Minimum Thickness. — The minimum thickness of rnetal shall be ^ in. in classes A, B,
C, Ei, E2 and E3, except for fillers; and j in. in classes DI and D2, except for fillers and webs of chan-
nels. Webs of channels for classes DI and D2 may have a minimum thickness of 0.20 in. The
minimum angle shall be 2 in. x 2 in. x j in. The minimum rod shall have an area of at least
I sq. in., in all classes except DI and D2, which shall have no rods less than f in. in diameter. Webs
of plate girders shall not be less than ^ in.
62. Pitch of Rivets. — The minimum distance between centers of rivet holes shall be three
diameters of the rivet; but the distance shall preferably be. not less than 3 in. for |-in. rivets,
SPECIFICATIONS. 143
2\ in. for |-in. rivets, and 2 in. for |-in. rivets. The maximum pitch in the line of stress for
iiienilHTs composed of plates and shapes shall be 16 times the thickness of the thinnest outside
pl.ite or 6 in. Fur angles with two gage lines and rivets staggered, the maximum shall be twice
the above iii each line. Where two or more plates are used in contact, rivets not more than 12 in.
ap.nt in either direction shall be used to hold the plates well together. In tension members com-
pnM-d of two angles in contact, a pitch of 12 in. will be allowed for riveting the angles together.
<>.V Edge Distance. — The minimum distance from the center of any rivet hole to a sheared
edge shall be I J in. for |-in. rivets, I J in. for j-in. rivets, and i{ in. for f-in. rivets, and to a rolled
edge i}, ij and i in., respectively. The maximum distance from any edge shall be eight times
the thickness of the plate, but shall not exceed 6 in.
64. Maximum Diameter. — The diameter of the rivets in any angle carrying calculated stress
shall not exceed one-quarter the width of the leg in which they are driven. In minor parts j-in.
rivets may be used in 3-in. angles, J-in. rivets in 2j-in. angles, and |-in. rivets in 2-in. angles.
65. Long Rivets. — Rivets carrying calculated stress and whose grip exceeds four diameters
shall be increased in number at least one per cent for each additional -fa-in. of grip.
66. Pitch at Ends. — The pitch of rivets at the ends of built compression members shall not
exceed four diameters of the rivets, for a length equal to one and one-half times the maximum
width of member.
67. Compression Members. — In compression members the metal shall be concentrated as
much as possible in webs and flanges. The thickness of each web shall be not less than one-
thirtieth of the distance between its connections to the flanges. Cover plates shall have a thickness
not less than one-fortieth of the distance between rivet lines.
68. Minimum Angles. — Flanges of girders and built members without cover plates shall
have a minimum thickness of one-twelfth of the width of the outstanding leg.
69. Batten Plates. — The open sides of all compression members shall be stayed by batten
plates at the ends and diagonal lattice-work at intermediate points. The batten plates must be
placed as near the ends as practicable, and shall have a length not less than the greatest width of
the member or I $ times its least width.
70. Lattice Bars. — The latticing of compression members shall be proportioned to resist
the shearing stresses corresponding to the allowance for flexure for uniform load provided in the
column formula in paragraph 38 by the term 70 l/r. They must not be less in width than I J in.
for members 6 in. in width, ij in. for members 9 in. in width, 2 in. for members 12 in. in width,
2j in. for members 15 in. in width, nor 2\ in. for members 18 in. and over in width. Single lattice
bars shall have a thickness not less than one-fortieth, or double lattice bars connected by a rivet
at the intersection, not less than one-sixtieth of the distance between the rivets connecting them
to the members. They shall be inclined at an angle not less than 60° to the axis of the member for
single latticing, nor less than 45° for double latticing with riveted intersections.
71. Spacing of Lattice Bars. — Lattice bars shall be so spaced that the portion of the flange
included between their connection shall be as strong as the member as a whole. The pitch of
tlu; lattice bars must not exceed the width of the channel plus nine inches.
72. Rivets in Flanges. — Five-eighths-inch rivets shall be used for latticing flanges less than
in. wide; f-in. for flanges from 2^ to 35 in. wide; J-in. rivets shall be used in flanges 3$ in. and
er, and lattice bars with two rivets shall be used f9r flanges over 5 in. wide.
73. Splices. — In compression members joints with abutting faces planed shall be placed as
iear the panel points as possible, and must be spliced on all sides with at least two rows of rivets
ireach side of the joint. Joints with abutting faces not planed shall be fully spliced. Joints in
;nsion members shall be fully spliced.
74. Pin Plates. — Where necessary, pin-holes shall be reinforced by plates, some of which
lust be of the full width of the member, so the allowed pressure on the pins shall not be exceeded,
nd so the stresses shall be properly distributed over the full cross-section of the members. These
einforcing plates must contain enough rivets to transfer their proportion of the bearing pressure,
md at least one plate on each side shall extend not less than 6 in. beyond the edge of the nearest
itten plate.
75. Riveted Tension Members. — Riveted tension members shall have an effective section
through the pin-holes 25 per cent in excess of the net section of the member, and back of the pin
at least 75 per cent of the net section through the pin-hole.
76. Pins. — Pins shall be long enough to insure a full bearing of all the parts connected upon
the turned body of the pin. The diameter of the pin shall not be less than J of the depth of any
eye-bar attached to it.* They shall be secured by chambered Lomas nuts or be provided with
washers if solid nuts are used. The screw ends shall be long enough to admit of burring the
threads.
77. Filling Rings. — Members packed on pins shall be held against lateral movement.
78. Bolts. — Where members are connected by bolts, the turned body of these bolts shall be
long enough to extend through the metal. A washer at least J in. thick shall be used under the
* The allowable bearing stress = | allowable tensile stress.
144 STEEL HIGHWAY BRIDGES. CHAP. III.
nut. Bolts shall not be used in place of rivets except by special permission. Heads and nuts shall
be hexagonal.
79. Indirect Splices. — Where splice plates are not in direct contact with the parts which
they connect, rivets shall be used on each side of the joint in excess of the number theoretically
required to the extent of one-third of the number for each intervening plate.
80. Fillers. — Rivets carrying stress and passing through fillers shall be increased 50 per cent
in number; and the excess rivets, when possible, shall be outside of the connected member.
81. Expansion. — Provision for expansion to the extent of | in. for each 10 ft. shall be made
for all bridge structures. Efficient means shall be provided to prevent excessive motion at any
one point (§32).
82. Expansion Bearings. — Spans of 60 ft. and over resting on masonry shall have turned
rollers or rockers at one end; and those of less length shall be arranged to slide on smooth surfaces.
83. Fixed Bearings. — Movable bearings shall be designed to permit motion in one direction
only. Fixed bearings shall be firmly anchored to the masonry (§87).
84. Rollers. — Expansion rollers shall be not less than 3 in. in diameter for spans of 100 feet
and less, and shall be increased I in. for each 100 ft. additional. They shall be coupled together
with substantial side bars, which shall be so arranged that the rollers can be readily cleaned.
85. Bolsters. — Bolsters or shoes shall be so constructed that the load will be distributed over
the entire bearing.
86. Pedestals and Bed Plates. — Built pedestals shall be made of plates and angles. All
bearing surfaces of the base plates and vertical webs must be planed. The vertical webs must be
secured to the base by angles having two rows of rivets in the vertical legs. No base plate or web
connecting angle shall be less in thickness than J in. The vertical webs shall be of sufficient height
and must contain material and rivets enough to practically distribute the loads over the bearings
or rollers. t
Where the size of the pedestal permits, the vertical webs must be rigidly connected trans-
versely.
87. All the bed-plates and bearings under fixed and movable ends must be fox-bolted to the
masonry; for trusses, these bolts must not be less than ij in. diameter; for plate and other girders,
not less than £ in. diameter.
The details of cast iron or cast steel shoes shall be subject to the special approval of the en-
gineer.
88. Wall Plates. — Wall plates may be cast or built up; and shall be so designed as to distrib-
ute the load uniformly over the entire bearing. They shall be secured against displacement.
89. Anchorage. — Anchor bolts for viaduct towers and similar structures shall be long enough
to engage a mass of masonry the weight of which is at least one and one-half times the uplift (§i i).
90. Inclined Bearings. — Bridges on an inclined grade without pin shoes shall have the sole
plates beveled so that the masonry and expansion surfaces may be level.
91. Camber. — Truss spans shall be given a camber by making the panel length of the top
chords, or their horizontal projections, longer than the corresponding panels of the bottom chord
in the proportion of YS in. in 10 ft. Plate girder spans need not be cambered.
92. Eye-bars. — The eye-bars composing a member shall be so arranged that adjacent bars
shall not have their surfaces in contact; they shall be as nearly parallel to the axis of the truss as
possible, the maximum inclination of any bar being limited to one inch in 16 ft.
PART V. MATERIALS AND WORKMANSHIP.
MATERIAL.
93. Process of Manufacture. — Steel shall be made by the open-hearth process and shall
comply with the standard specifications of the Am. Ry. Eng. Assoc.
(Sections 94 to 117 inclusive cover the Am. Ry. Eng. Assoc. Specifications for steel, see
specifications for railroad bridges, Chapter IV.)
118. Timber. — The timber shall be strictly first-class spruce, white pine, Douglas fir, Southern
yellow pine, or white oak bridge timber; sawed true and out of wind, full size, free from wind
shakes, large or loose knots, decayed or sapwood, wormholes or other defects impairing its strength
or durability.
WORKMANSHIP.
119. General. — All .parts forming a structure shall be built in accordance with approved
drawings. The workmanship and finish shall be equal to the best practice in modern bridge works.
1 20. Straightening Material. — Material shall be thoroughly straightened in the shop, by
methods that will not injure it, before being laid off or worked in any way.
121. Finish. — Shearing shall be neatly and accurately done and all portions of the work
exposed to view neatly finished.
122. Size of Rivets. — The size of rivets, called for on the plans, shall be understood to mean
the actual size of the cold rivet before heating.
SPECIFICATIONS. 145
1123. Rivet Holes. — When general reaming is not required the diameter of the punch shall
In- IMMIV t li.m fa in. greater than the diameter of the rivet; nor the diameter of the die more than
$ in. griMtrr t han the diameter of the punch. Material more than J in. thick shall be sub-punched
and reamed or drilled from the solid.
124. Punching. — All punching shall be accurately done. Drifting to enlarge unfair holes
will not be allowed. If the holes must be enlarged to admit the rivet, they shall be reamed.
r matching of holes will be cause for rejection.
125. Sub-punching and Reaming. — Where reaming is required, the punch used shall have a
ianu'ter not less than A m- smaller than the nominal diameter of the rivet. Holes shall then be
reamed to a diameter not more than ^ in. larger than the nominal diameter of the rivet. All
reaming shall be done with twist drills. (§140.)
126. Reaming After Assembling. — When general reaming is required it shall be done after
the pieces forming one built member are assembled and firmly bolted together. If necessary to
take the pieces apart for shipping and handling, the respective pieces reamed together shall be
marked that they may be reassembled in the same position in the final setting up. No inter-
nge of reamed parts will be allowed.
127. Edge Planing. — Sheared edges or ends shall, when required, be planed at least i in.
128. Burrs. — The outside burrs on reamed holes shall be removed.
129. Assembling. — Riveted members shall have all parts well pinned up and firmly drawn
ither with bolts, before riveting is commenced. Contact surfaces to be painted.
130. Lattice Bars. — Lattice bars shall have neatly rounded ends, unless otherwise cabled for.
131. Web Stiff eners. — Stiffeners shall fit neatly between flanges of girders. Where tight
fits are called for, the ends of the stiffeners shall be faced and shall be brought to a true contact
bearing with the flange angles.
132. Splice Plates and Fillers. — Web splice plates and fillers under stiffeners shall be cut to
fit within J in. of flange angles.
133. Web Plates. — Web plates of girders, which have no cover plates, shall be flush with
the backs of angles or project above the same not more than J in., unless otherwise called for.
When web plates are spliced, not more than J in. clearance between ends of plates will be allowed.
134. Connection Angles. — Connection angles for floorbeams and stringers shall be flush
with each other and correct as to position and length of girder. In case milling (of all such angles)
is needed or is required after riveting, the removal of more than ^ in. from their thickness will be
cause for rejection.
135. Rivets. — Rivets shall be driven by pressure tools wherever possible. Pneumatic
hammers shall be used in preference to hand driving.
136. Riveting. — Rivets shall look neat and finished, with heads of approved shape, full and
of equal size. They shall be central on shank and grip the assembled pieces firmly. Recupping
and calking will not be allowed. Loose, burned or otherwise defective rivets shall be cut out and
replaced. In cutting out rivets, great care shall be taken not to injure the adjacent metal. If
necessary, they shall be drilled out.
137. Turned Bolts. — Wherever bolts are used in place of rivets which transmit shear, the
holes shall be reamed parallel and the bolts turned to a driving fit. A washer not less than i in.
thick shall be used under nut.
138. Members to be Straight. — The several pieces forming one built member shall be straight
and fit closely together, and finished members shall be free from twists, bends or open joints.
139. Finish of Joints. — Abutting joints shall be cut or dressed true and straight and fitted
close together, especially where open to view. In compression joints, depending on contact
bearing, the surfaces shall be truly faced, so as to have even bearings after they are riveted up
plete and when perfectly aligned.
140. Field Connections. — Holes for floorbeam and stringer connections shall be sub-punched
id reamed according to paragraph 125, to a steel templet one inch thick. (If required, all
other field connections, except those for laterals and sway bracing, shall be assembled in the shop
and the unfair holes reamed; and when so reamed, the pieces shall be match-marked before being
taken apart.)
141. Eye-bars. — Eye-bars shall be straight and true to size, and shall be free from twists, folds
in the neck or head, or any other defect. Heads shall be made bv upsetting, rolling or forging.
Welding will not be allowed. The form of heads will be determined by the dies in use at the
works where the eye-bars are made, if satisfactory to the engineer, but the manufacturer shall
guarantee the bars to break in the body when tested to rupture. The thickness of head and
neck shall not vary more than ^ in. from that specified.
142. Boring Eye-bars. — Before boring, each eye-bar shall be properly annealed and care-
fully straightened. Pin-holes shall be in the center line of bars and in the center of heads. Bars
of the same length shall be bored so accurately that, when placed together, pins ^ in. smaller in
diameter than the pin-holes can be passed through the holes at both ends of the bars at the same
time without forcing.
11
146 STEEL HIGHWAY BRIDGES. CHAP. III.
143. Pin-Holes. — Pin-holes shall be bored true to gages, smooth and straight; at right angles
to the axis of the member and parallel to each other, unless otherwise called for. The boring shall
be done after the member is riveted up.
144. Variation in Pin-Holes. — The distance center to center of pin-holes shall be correct
within £i in., and the diameter of the holes not more than -fa in. larger than that of the pin, for
pins up to 5-in. diameter, and ^ in. for larger pins.
145. Pins and Rollers. — Pins and rollers shall be accurately turned to gages and shall be
straight and smooth and entirely free from flaws.
146. Screw Threads. — Screw threads shall make tight fits in the nuts and shall be U. S.
standard, except above the diameter of if in., when they shall be made with six threads per inch.
147. Annealing. — Steel, except in minor details, which has been partially heated, shall be
properly annealed.
148. Steel Castings. — All steel castings shall be annealed.
149. Welds. — Welds in steel will not be allowed.
150. Bed Plates. — Expansion bed plates shall be planed true and smooth. Cast wall plates
shall be planed too and bottom. The cut of the planing tool shall correspond with the direction
of expansion.
151. Pilot Nuts. — Pilot and driving nuts shall be furnished for each size of pin, in such
numbers as may be ordered.
152. Field Rivets. — Field rivets shall be furnished to the amount of 15 per cent plus ten
rivets in excess of the nominal number required for each size.
153. Shipping Details. — Pins, nuts, bolts, rivets and other small details shall be boxed or
crated.
154. Weight. — The weight of every piece and box shall be marked on it in plain figures.
155. Finished Weight. — Payment for pound price contracts shall be by scale weight. No
allowance over 2 per cent of the total weight of the structure as computed from the plans will be
allowed for excess weight.
SHOP PAINTING.
156. Cleaning. — Steel work, before leaving the shop, shall be thoroughly cleaned and given
one good coating of pure linseed oil, or such paint as may be called for, well worked into all joints
and open spaces.
157. Contact Surfaces. — In riveted work, the surfaces coming in contact shall each be painted
before being riveted together.
158. Inaccessible Surfaces. — Pieces and parts which are not accessible for painting after
erection, including tops of stringers, eye-bar heads, ends of posts and chords, etc., shall have a
good coat of paint before leaving the shop.
159. Condition of Surfaces. — Painting shall be done only when the surface of the metal is
perfectly dry. It shall not be done in wet or freezing weather, unless protected under cover.
160. Machine-finished Surfaces. — Machine-finished surfaces shall be coated with white
lead and tallow before shipment or before being put out into the open air.
INSPECTION AND TESTING AT THE SHOP AND MILL.
161. Facilities for Shop Inspection. — The manufacturer shall furnish all facilities for inspecting
and testing the weight and quality of workmanship at the shop where material is manufactured.
He shall furnish a suitable testing machine for testing full-sized members, if required.
162. Starting Work in Shop. — The purchaser shall be notified well in advance of the start
of the work in the shop, in order that he may have an inspector on hand to inspect material and
workmanship.
163. Copies of Mill Orders. — The purchaser shall be furnished complete copies of mill orders,
and no material shall be rolled, nor work done, before the purchaser has been notified where the
orders have been placed, so that he may arrange for the inspection.
164. Facilities for Mill Inspection. — The manufacturer shall furnish all facilities for inspecting
and testing the weight and quality of all material at the mill where it is manufactured. He shall
furnish a suitable testing machine for testing the specimens, as well as prepare the pieces for the
machine, free of cost.
165. Access to Mills. — When an inspector is furnished by the purchaser to inspect material
at the mills, he shall have full access, at all times, to all parts of mills where material to be inspected
by him is being manufactured.
1 66. Access to Shop. — When an inspector is furnished by the purchaser, he shall have full
access, at all times, to all parts of the shop where material under his inspection is being manu-
factured.
SPECIFICATIONS. 147
167. Accepting Material or Work. — The inspector shall stamp each piece accepted with a
private mark. Any piece not so marked may be rejected at any time, and at any stage of the
work. If the inspector, through an oversight or otherwise, has accepted material or work which
is defective or contrary to the specifications, this material, no matter in what stage of completion,
may be rejected by the purchaser.
168. Shop Plans. — The purchaser shall be furnished complete shop plans (§13).
169. Shipping Invoices. — Complete copies of shipping invoices shall be furnished to the
purchaser with each shipment.
FULL-SIZED TESTS.
170. Test to Prove Workmanship. — Full-sized tests on eye-bars and similar members, to
prove the workmanship, shall be made at the manufacturer's expense, and shall be paid for by
the purchaser at contract price, if the tests are satisfactory. If the tests are not satisfactory, the
members represented by them will be rejected.
171. Eye-bar Tests. — In eye-bar tests, the fracture shall be silky, the elongation in 10 ft.,
including the fracture, shall be not less than 15 per cent; and the ultimate strength and true
elastic limit shall be recorded (§141).
ERECTION.
172. If the contractor erects the bridge he shall, unless otherwise specified, furnish all staging
and falsework, erect and adjust all metal work, and shall frame and put in place all floor timbers,
guard timbers, trestle timbers, etc., complete ready for traffic.
173. The contractor shall put in place all stone bolts and anchors for attaching the steel
work to the masonry. He shall drill all the necessary holes in the masonry, and set all bolts with
neat Portland cement.
174. The erection will also include all necessary hauling from the railroad station, the un-
loading of the materials and their proper care until the erection is completed.
175. Whenever new structures are to replace existing ones, the latter are to be carefully taken
awn and removed by the contractor to some place where the material can be hauled away.
176. The contractor shall so conduct his work as not to interfere with traffic, interfere with
work of other contractors, or close any thoroughfare on land or water.
177. The contractor shall assume all risks of accidents and damages to persons and properties
rior to the acceptance of the work.
178. The contractor must remove all falsework, piling and other obstructions or unsightly
iterial produced by his operations.
PAINTING AFTER ERECTION.
.179. After the bridge is erected the metal work shall be thoroughly cleaned of mud, grease
1 other material, then thoroughly and evenly painted with two coats of paint of the kind specified
/ the engineer, mixed with linseed oil. All recesses which may retain water, or through which
water can enter, must be filled with thick paint or some waterproof cement before the final painting.
The different coats of paint must be of distinctly different shades or colors, and one coat must
be allowed to dry thoroughly before the second coat is applied. All painting shall be done with
round brushes of the best quality obtainable on the market. The paint shall be delivered on the
work in the manufacturer's original packages and is subject to inspection. If tests made by the
inspector shows that the paint is adulterated, the paint will be rejected and the contractor shall
pay the cost of the analyses, and shall scrape off and thoroughly clean and repaint all material
that has been painted with the condemned paint. The paint shall not be thinned with anything
whatsoever; in cold weather the paint may be thinned by heating under the direction of the
inspector. No turpentine nor benzine shall be allowed on the work, except by the permission of
the inspector, and in such quantity as he shall allow. The inspector shall be notified when any
painting is to be done by the contractor, and no painting shall be done until the inspector has
approved the surface to which the paint is to be applied. Paint shall not be applied out of doors
in freezing, rainy, or misty weather, and all surfaces to which paint is to be applied shall be dry,
clean and warm. In cool weather the paint may be thinned by heating, and this may be required
by the inspector.
REFERENCES. — For the calculation of stresses in bridge trusses and plate girders, for
details of bridges, for the design of bridge details, and for additional examples of highway
bridges, see the author's " The Design of Highway Bridges."
CHAPTER IV.
STEEL RAILWAY BRIDGES.
TYPES OF STEEL BRIDGES. — The same types of trusses are used for railway as for high-
way bridges, Fig. 4, Chapter III. Beam bridges are used for short spans, and plate girders up to
spans of about 125 ft. Riveted truss spans are used for spans of 100 ft. and upwards. Pin-con-
nected truss spans are still used for long span bridges and by a few railroads for spans of 150 ft.
and upwards. Many railroads are building riveted trusses for spans of more than 200 ft., and
riveted truss spans of 300 ft. are not uncommon. The new terminal bridge over the Missouri
River at Kansas City, Mo., has riveted trusses with a span of 425 ft. 6$ in. The Norfolk & West-
ern R. R. has constructed a double track bridge over the Ohio River with a span of 520 ft., which
is riveted with the exception of four bottom chord panel points, which have pin joints. The
lengths and types of railway bridges as used by different railroads are given in Table XII in the
latter part of this chapter. The longest simple truss span is 668 ft. and is in the Municipal Bridge
over the Mississippi River at St. Louis, Mo. The maximum practical length of simple span truss
bridges made of carbon steel is about 550 feet; while with nickel steel it is practical to build simple
truss spans up to 750 feet and economical to build simple truss spans up to 700 feet. The pro-
posed Metropolis Bridge over the Ohio River will be a double track simple truss bridge with a
in of 720 feet.
Portal --,
FIG. i. DIAGRAMMATIC SKETCH OF A RAILWAY TRUSS BRIDGE.
149
150 STEEL RAILWAY BRIDGES. CHAP. IV.
'Cross Girder' Tower Span Intermediate -Span Tower Span Cross Girder?
Trestle dent
(a)
Tower
(b)
FIG. 2. RAILWAY STEEL TRESTLE.
TABLE I.
DATA ON RAILROAD BRIDGES DESIGNED UNDER COMMON STANDARD (HARRIMAN LINES)
SPECIFICATIONS C. S. 1006.
SINGLE TRACK BRIDGES.
DOUBLE TRACK BRIDGES.
Length
of
Span,
Ft.
Distance
Center to
Center of
Trusses or
Girders,
Ft.-In.
Dist. C. to C. of
Chords or B. to
B. of Angles,
Ft.-In.
°1
II
Total
Weight,
Lb.
Length
of
Span,
Ft.
Distance
Center to
Center of
Trusses or
Girders,
Ft.-In.
Dist. C. to C. of
Chords or B. to
B. of Angles,
Ft.-In.
ll
Total
Weight,
Lb.
3°
40
1°
60
70
80
90
IOO
Th
13-6
15-6
T6
1 6-0
16-6
16-6
16-6
16-6
rough Plate Gird
4~ °5
5-0*
5- 8i
6-4^
7- oj
8- o£
8- 6*
9- o|
:rs
3
4
6
7
8
9
10
27,500
41,900
56,600
79,600
105,100
132,300
161,350
198,500
50
60
70
80
90
Tr
29-6
29-6
29-6
30-0
3O-O
rough Plate Gird
8-oJ
9-o|
9-6^
lo-oj
io-6£
;rs
4
6
7
8
142,000
173,000
22I,OOO
277,000
317,200
20
30
40
1°
60
70
80
90
IOO
7-0
7-0
7-0
7-0
7-0
8-0
8-0
9-0
9-0
Deck Plate Girdei
i- 8
4- oj
4-1 if
S-i if
6-5f
8-3f
8- 8f
9- if
9-3f
3
4
8
8
10
10
IO
12
12
I2,8oo
14,900
23,800
34,300
47,500
68,000
87,800
113,200
137,800
IOO
no
125
140
T
30-6
30-6
30-6
irough Rivet Spa
30-0
30-0
31-0
n
4
4
5
360,000
400,000
472,600
IOO
no
125
140
150
T
16-6
16-6
16-6
17-0
17-0
hrough Rivet Spa
29- o
29- o
30- o
31-0
31-0
n
4
4
6
6
165,000
185,000
220,000
273,000
311,000
150
160
1 80
200
r
30-6
30-6
Ihrough Pin Spar
33-°
40-0
i
6
7
633,000
932,200
150
1 60
1 80
2OO
i
17-0
17-0
17-0
17-0
Through Pin Spar
31- o
32- o
33- o
32-& 38
i
6
6
7
7
304,000
348,000
417,000
485,000
WEIGHTS OF RAILWAY BRIDGES.
151
A diagramatic sketch of a truss railway bridge is shown in Fig. I. The names of the different
iiit-iiil>ers are shown on the diagram. The floor may be carried on two or more stringers. Two
M i in^ri ^ .ire commonly used for an open timber floor and two or four stringers for a ballasted floor.
A railway steel trestle is shown in Fig. 2. Steel trestles are commonly built with the inter-
mi diute spans equal to twice the tower spans; 60 feet and 30 feet, and 80 feet and 40 feet being
common lengths of span.
Swing, movable, cantilever and suspension bridges will not be considered in this chapter.
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•/^
/
•
/7tt
'/
20 30 40 50 60 70 80 00 100
Span in Feet.
0 50 100 150 WO 150 300
Span in Feet.
IG. 3. WEIGHT OF SINGLE TRACK DECK
PLATE GIRDER SPANS, CONCRETE BALLAST
FLOOR. CHICAGO, MILWAUKEE & ST.
PAUL RY.
FIG. 4. WEIGHT OF SINGLE TRACK RIVETED
DECK TRUSS SPANS. CHICAGO, MIL-
WAUKEE & ST. PAUL RY.
WEIGHTS OF RAILWAY BRIDGES.— The weights of railway bridges vary with the
loading, the specifications, the span, the width, the type of floor, and with the design. The weights
of the total structural steel in single track bridges of different types as designed and built by the
Chicago, Milwaukee & St. Paul Ry. are given in Fig. 3 to Fig. 10, inclusive.
Weights of single track plate girder spans as designed and built by the Illinois Central Rail-
road are given in Fig. n, Fig. 12 and Fig. 13; weights of single track through bridges are given in
Fig. 14, weights of signal bridges are given in Fig. 15, and weights of single track draw spans are
given in Fig. 16. Weights and other data for railway bridges designed by the Harriman Lines,
under "Common Standard Specification 1006" (approximately equal to Cooper's E 55), are given
in Table I.
Weights of single track steel viaducts as designed by the McClintic-Marshall Construction
Co. are given in Fig. 17.
152
STEEL RAILWAY BRIDGES.
CHAP. IV.
For the relative weights of railway bridges built of carbon and of nickel steel, see paper
entitled " Nickel Steel for Bridges," by Mr. J. A. L. Waddell, M. Am. Soc. C. E., printed in Trans.
Am. Soc. C. E., Vol. 63, 1909.
0 10 20 30 40 50 00 70 80
Span in Teet.
FIG. 5. WEIGHT OF SINGLE TRACK THROUGH
PLATE GIRDER SPANS. TYPE C4 (FLANGES
OF 2 ANGLES AND COVER PLATES, Two
STRINGERS). CHICAGO, MILWAUKEE
& ST. PAUL RY.
0 10 W 30 40 50 00 70 80 90
in FeeL
FIG. 6. WEIGHT OF THROUGH PLATE GIRDER
SPANS^ TYPE Cs (FLANGES OF 2 ANGLES
AND COVER PLATES, SHALLOW FLOOR,
4 STRINGERS). CHICAGO, MIL-
WAUKEE & ST. PAUL RY.
LOADS. — The dead load of a railway bridge is assumed to act at the joints the same as in a
highway bridge. The dead joint loads are commonly assumed to act on the loaded chord, but
may be assumed as divided between the panel points of the two chords, one-third and two-thirds
of the dead loads usually being assumed as acting at the panel points of the unloaded and the
loaded chords, respectively, see discussion of specifications in the last part of this chapter.
The live load on a railway bridge consists of wheel loads, the weights and spacing of the
wheels depending upon the type of the rolling stock used. The locomotives and cars differ so
much that it would be difficult if not impossible to design the bridges on any railway system for
the actual conditions, and conventional systems of loading, which approximate the actual con-
ditions, are assumed. The conventional systems for calculating the live load stresses in railway
bridges that have been most favorably received are: (i) Cooper's Conventional System of Wheel
Concentrations; (2) the use of an Equivalent Uniform Load; and (3) the use of a uniform load
and one or two wheel concentrations. In addition to these some railroads specify special engine
loadings. The three Methods will be briefly described.
COOPER'S LOADINGS.
153
Cooper's Conventional System of Wheel Concentrations. — In Cooper's loadings two con-
locomotives are followed by a uniformly distributed train load. The typical loading
for Cooper's Class £40, £45, E 50, E 55 and E 60, are shown in Fig. 18. The loads on the
(Irivi-rs in thousands of pounds and the uniform train load in hundreds of pounds are the same as
the class number. The wheel spacings are the same for all classes. The stresses for Cooper's
loadings calculated for one class may be used to obtain the stresses due to any other class loading.
For example, the live load stresses in any truss due to Cooper's Class E 60 are equal to f of the
stresses in the same truss due to Class E 40 loading. The E 50, E 55 and E 60 loadings are those
most used for steam railways in the United States. In bridges designed for Class E 40 loading
and under the floor system must in addition be designed for two moving loads of 100,000 Ib. each,
spaced 6 ft. apart on each track. The special loads for Class E 50 are 120,000 Ib. with the same
/J?/0
^
:::!:::
...|. —
^^
j|
•^ I/O •
\ mn -
iiiiilliii
"§ 00 •
:::;:::
1
^ fin -
jiljiij:
5 W
{§ 70.-
.C; xr/o
^ 0<y '
•1^-
^ 40 •
^ •?<? I
^ o/,B
HfeHII ] o y^
^^? :
10 •
n ;
iiigg •/
/ Ct
'50 "
'jn/e £55
ZO 30 40 50 60 70 80 90 100
Span in Feet.
IG. 7. WEIGHT OF SINGLE TRACK DECK
.ATE GIRDER SPANS. OPEN TIMBER FLOOR.
TYPE A4 (FLANGES OF 6 ANGLES WITH-
OUT COVER PLATES). CHICAGO, MIL-
WAUKEE & ST. PAUL RY.
ZO 20 40 50 00 70 80 90 100
Span in Feet.
FIG. 8. WEIGHT OF SINGLE TRACK DECK
PLATE GIRDER SPANS. TIMBER BALLAST
FLOOR. TYPE A4 (FLANGES OF 6 ANGLES
WITHOUT COVER PLATES). CHICAGO,
MILWAUKEE & ST. PAUL RY.
spacing. The American Railway Engineering Association has adopted Cooper's loadings, except
that the special loads are spaced 7 ft. The live loads used by several prominent railroads are
given in Table XVI. The heaviest locomotives in use on American railroads as given in Bulletin
No. 161, November 1913, of the Am. Ry. Eng.Assoc., by Mr. ]. E. Greiner, Consulting Engineer,
are given in Table II. The maximum stresses in terms of the maximum stresses for E 50 loading
for spans between 100 ft. and 10 ft. are given in the last two columns. The ratios for spans
greater than 100 ft. are less than for those given. The larger ratio is for short spans so that by
increasing the special concentrated loads a bridge designed for an E 50 loading will safely carry
the heaviest engines now in use.
154
STEEL RAILWAY BRIDGES.
CHAP. IV.
0 25 50 75100 125 150 175 200
Span in feet.
FIG. 9. WEIGHT OF SINGLE TRACK THROUGH
RIVETED TRUSS SPANS. CHICAGO,
MILWAUKEE & ST. PAUL RY.
. 26
^ U
\ 22
1 to
\ &
^s 14-
£;
^ IZ
•§ 10
i *
f§ 2
ffiffl
I 11
1 ._
|
•--^- •-
|
--• :^--
2
J. —
'.I
.i ..
f^i
---'/ '-
„ , T .....
f+ -^'- --
:::::::« ::::
° E '55 Load.
•HO "
! Curve E55
/ " FtO
// '
I j" ji i11"*"" " "
JaOTll 1
Span in Feet.
FIG. 10. WEIGHT OF SINGLE TRACK THROUGH
PIN CONNECTED TRUSS SPANS. CHI-
CAGO, MILWAUKEE & ST. PAUL RY.
TABLE II.
HEAVIEST LOCOMOTIVES AND RELATIVE STRESSES PRODUCED FOR SPANS OF 10 FT. TO 100 FT.
Class.
Engine Alone.
Double Header.*
Proportional
Stress.
Weight in
i.ooo Lb.
Wheel
Base, Ft.
Propor-
tional
Weight.
Weight in
1,000 Lb.
Wheel
Base, Ft.
Weight
per Ft., Lb.
From
To
E cot. .
225.0
214.8
244.7
26o.I
262.0
267.0
270.0
305-0
334-5
361.0
478.0
493-0
616.0
300.4
320.0
23.00
30.79
34-25
26.50
27.08
29-83
35-20
35-00
30.66
43-50
59.80
40.17
65.92
3850
44.22
1. 00
.96
.09
.16
•17
.19
.20
1.36
1.49
1. 60
2.12
2.19
2.74
i-33
1.42
710.0
728.4
807.5
860.4
817.4
8O2.O
865.4
960.0
473-8
1,074.0
703.6
588.0
841.6
600.8
640.0
104.0
127.76
132.92
131.81
130.15
127.00
142.48
150.00
64.56
161.00
99.70
82.58
105.82
86.50
102.84
6,830
5,700
6,070
6,520
6,280
6,320
6,070
6,400
7>340
6,670
7,060
7,130
7,950
6,950
6,220
I.OO
0.83
0.88
o-99
I.OO
0.96
0.93
1.02
0.98
I.OO
I.OI
1.26
1.15
0.83
0.84
.00
•15
•03
.14
.14
.07
.08
.16
:ii
.14
•34
•33
0.98
o-93
Atlantic
Prairie
Consolidation
12 Wheel
Decapod
Pacific
Mikado
12 Wheel Articulated]: .
10 Coupled
20 Wheel Articulated t .
16 Wheel Articulatedj .
24 Wheel Articulatedj .
12 Wheel Electric Motor
16 Wheel Electric Motor
* Weight and wheel base for articulated engines are given for one engine and tender,
f Given for comparison,
t Mallet Type.
WEIGHTS OF PLATE GIRDERS.
155
Lotv/rot
N
\i--l
-r-*
i^
ri>i
He of Pail
oof Masonry
I-
'owed by
Span
Total
FndSfar
A
B
c
******
eo'o'
85'0'
90' 0'
95'0"
lOO'O1
IIO'O'
2070
2200
255-0
2464
2600
2800
2'2l'
??*,'
v#
2'4i'
5'/0$'
5 ' ioy
yiof
I7'6'
17'6'
I7'6'
17'6'
I7'6'
149000 Joy
165000 '
180000 •
200000 '
222000 •
250000 •
\A j<.
*
r~ ' r
Shear in thousands of pounds ptr rai
Loading- 2-J8875 ton f/y/nes fbl,
6, OOOlbs ptr foot uniform Joad-
Span
Total
£',-,/ <\v
A
B
c
»****»>
Span
Weight of one Wwhtofone ffe/f/ff of
WO*
bB'O"
40'0'
SO'O'
SS'O'
60'0'
6B'0'
70'0'
75'0"
98-0
108-0
118-0
129-0
159-0
148-0
158-0
170-0
ltt-0
194-0
?'?£
2' 2%
?'/r
rrt
IS'O"
16' 0'
I7'0'
/7'6*
I7'6'
I7'6'
I7'6"
I7'6"
/7'P
I7'6»
40 000 Ibs-
48000 '
58 000 '
68000 '
77000'
88000 "
58000 -
IIIOOO t
120000 »
135000 »
WO" to 50' 0"
55'0gto80'0'
8B'0' to IIO'O'
0-72 W 0-59 W 0-56 W
0-27W 0-48W 0-47W
0-5/tT 0-67IY 0-58P
2'2f
2'2i'
ri"
W
2'H'M
I-Beams, /8"@ 65 Ibs-
ERECTOK'S HOTE:-
ff~ Total tve/ght of one single track span with
tm> light girders-
DATA OH THROWn1 PLATE 6/PDEP SPANS
I- BEAM FLOODS
FIG. ii. WEIGHTS OF THROUGH PLATE GIRDER SPANS.
ILLINOIS CENTRAL RAILROAD.
i "K . , Hb**"*W
Span
Total
A
5
C
******
Lor Iron ~^f
I.I^IJ LLll^
? of Masonry
BO'O*
8B'0"
215-4
728-1
W
A1 II*
Jt IL
|»
17'6'
I7'6'
154 200 Ibs
mooo •
— i* '
Shear in thousands of pounds per rail-
90'0'
2406
5'4r('
4'i/i'
I7'6'
189600 '
Load/ny - Z-/8875 ton cngtnes, fo//owed
95'0'
2547
3V|"
Jtf/J
*
I7'6'
210000 '
by 6000 Ibs- per foot umfbrn? fosd
lOO'O"
2672
y&
4'lli'
i> at *
I7'6'
2?4SW '
Span
Total
A
B
C
Weight of 5psn
IIO'O'
2956
4 1/4
17 6
Weight of one.
Ifo^tefeof Might of
K'O"
100-5
3' 2j"
y i&'
IS' 6'
45 000 Ibs
Lighttiirder
fffjyy&n/fr one Floor
55'0'
111-9
3' 34'
3* 3V
I6'6'
56000 •
50'0' to50'0"
0-24 n-
0-42 W 0-54 #
40'0"
122-B
3' 5%°
3'3^'
17V
64400 •
BB'O1 toSO'O'
0-25W
0-46ff O-BOff
4B'0"
152-6
3'3|'
3'3f/
I7'6"
71000 >
85'0 to IIO'O'
0-28W
0-Blff 0-45W
BO'O"
142-8
3'3|'
3'3i
I7'6'
81200 •
ERECTOR'S HOTE:-
5B'0*
155-4
5'4tf
yioi
I7J6'
95900 •
ff- Total ftvyht ofonty/y/f tryckspsn mth
60'0'
161-1
5'4i"
yio?
l/'6'
105800 •
two /qtrt gtrdtrs-
65'0"
174-9
5'4i'
5' 10%'
17'6'
116000 •
DATA
OH
70'0'
187-4
3V|"
5'/0%'
I7'6"
128000 »
THROUGH PLATE
GIWEP 50WS
7B'0'
201-9
3Vi'
4' 11$
I7'6'
14 B 700 •
5TP1HOEI? FLOOR
FIG. 12. WEIGHTS OF THROUGH PLATE GIRDER SPANS.
ILLINOIS CENTRAL RAILROAD.
156
STEEL RAILWAY BRIDGES.
•CHAP. IV.
Total
*»
A
B
c
We/ght of Span
ifBdS? of J?3ll
WO"
94-0
4'IOi'
4'IO?6"
7'0"
18000/bs
Lowlron-^ _,[_ JL ByTcpoftfaenry
15'0'
40'0"
4B'0"
SO'O'
IOM
115-B
123-5
/X-5
S'2i'
5'tt"
6'ti"
5' 2\
ro"
7'0"
7'0"
7I0"
22 000 •
78000 •
54000 ;•
40 000 »
Shear in thousands of pounds per rail-
Loading ~?-J88'7£ ton er?g/n<?$, fol/owed
by 6000 Its- per foot vmform /ojrf
5B'0"
141-0
71/"
7V/"
7'0"
46000 •
ERECTION NOTE:-
60'0"
150-0
7' 4"
7'IOi"
7'0"
B7000 •
In a// spans, 30'0" to eO'C"//? length, one
65'0"
165-0
8' 6"
9'0i"
S'O"
62000 "
girder mil 'weigh 457» of total tre/ght of spsr?
70 '0"
176-0
9 '4"
yjo?
8'0"
68000 »
'In all spans 65'0" to //O'O in kryth, one
7S'0"
/89-0
9'6i"
10' Of
S'O"
78000 '
girder W tve/'fA 46 -5 per cent of tote/ weyht
SO'O"
202-0
9'8i'
II' 4?
S'O"
90000 •
of span.'
8B'0"
2/6-0
/O'O"
my
9' 0'
100000 '
WO"
228-0
I0'2%
I/ '9$'
9'0"
1/4000 •
DATA OH
95'0"
242-0
/0'2i"
II' 9i*
9'0"
/ 50000 *
DECK PLATE GIRDER
lOO'O"
2&0
I0'4i'
11' Hi'
9'0"
/BOOOQ »
SPANS
//O'O"
295-0
tf'tf"
ff'3i'
VS"
275000 »
FIG. 13. WEIGHTS OF DECK PLATE GIRDER SPANS.
ILLINOIS CENTRAL RAILROAD.
SPANS
ISO'O" TO JffO'O" ioo\ | , , 1 1 1 1 1 1 1 1 , 1 1
IN LENGTH -r
as?|llllllljl —••_,'•-••-
^iiimiiii —•>•'-'- \ llll'llll
:::;;:!:: /
SPANS
-..•'-'- WO'TO eoo'o' ^im!|Mi'i,.
,--'- 1HLEH6TH -- \":\
lilHHHl ^'niiiiiiiJiiiii ^:a'':
j2oo :::::;;•:::
i™ •^IIIIIIIIIILLUI ;=•'"
ooo ::::".:•'.:.: :
/somrr •-••''•"-- Ilii''''''''''' soo
600 800
k
jy loo IIIIIIIIIHIIMI 450, n 1 1 1 1 1 1 II 1 II 1
It! ZOO 400
I "mHw-'F-'
I:::::;;;:::::::::::::::::::: 40004200 4400
:::;fff -ti: : 5400 w JMP
*•---- - Loading-2- 18875 ton engines
2800 3000 3200 kllonfd by 6000 Ibs- per foot
^Q ' *
-£• fsi-vJ
^o «»
f f) Lf 7~ I • C
m 2400 2600 famx curve wyhts 85 per cent-
WEIGHTS OF SINGLE TRACK
THROUGH PIN OR RIVETED SPANS
5 OF 'POUNDS
;:;;; ; . >-- ^
^
600 SOO 1000 1200 1400 1600 1SOO 2000
WEIGHT IN THOUSAND
FIG. 14. WEIGHTS OF SINGLE TRACK THROUGH SPANS
ILLINOIS CENTRAL RAILROAD.
WEIGHTS OF DRAW SPANS AND SIGNAL BRIDGES.
157
e'O" Cltar.
11111 Illlllllll Hill Illlllllllll't. mil III
e:
:;::; ::::;:::;:;:::;:::::::!!:::;::::::::::::::::::::::::
I? iili ::!!!!:!:::!!!!::::
iiiiiiiiSiiiiiiiiiiiiiiiSiiiiiisllliSiiiiiiiiiiiiiiiiiiiiiii
:::::::::!!::ii::::::::::::::::::i::::::::ui
26000 28000
14000 16000
2ZCOO- 24000
Mote *• All 'spans figured to carry a signdl
18000 2QOOO neighing 2000 pounds over each track
W' Weight of one span and two bents
0-62Hf"ffejght of or* span
flti W= Weight of tno bents-
WEIGHTS OF 5/6NAL BRIDGES
dooo ioooa 12000
WEIGHT IN POUNDS
FIG. 15. WEIGHTS OF SIGNAL BRIDGES.
ILLINOIS CENTRAL RAILROAD.
Aim inn mil iimiirii mil mil mil
liiiiliiiiiiitliiiii'.iiiiiiiiiiiiilimi
IIIW%IIIIIIIIIIIIIIIIIIIII
liiiiiiiliir.iiiiiiiiiiiiiiini
130
1000
800
Loading- 2-188-75 ton engines followed by
6000 Ibs-per foot uniform had .
For Double Track Spans
hcrvase curve freights SSptr cent-
WEIGHTS OF SINGLE TRACK
DRAW SPANS •
200
400
600
HEIGHTS IN THOUSANDS OF POUNDS
FIG. 16. WEIGHTS OF SINGLE TRACK DRAW SPANS.
ILLINOIS CENTRAL RAILROAD.
158
STEEL RAILWAY BRIDGES.
CHAP. IV.
WEIGHT OfS/N6LE 7WCK J?.£ WADUGT, TOWE2S.
Coopers EBOLoadipj A.&E.ZM. W. Spec's -1900.
30'S 30' Spans
Weight of 30 ft.Span complete =14400
c
D
<£
"o
to
130
120
110
100
00
80
70
60
50
40
30
20
10
25' 35° 45' 55' 65'
Height . of . Towers (from cap to base.)
40'X40' and 30'560' Spans'
Weight of 60ft.5pan complete =40200
• -30fb. • " =15300
• =22100
90'
-g^ Height of Towers (from cap bo base.)
-> om 40'580'Spans
- - 4- - 4- 44-
..-
200 --•
190 :
180 "-'-,
wfeicrhhof 80ft ^nan comolpte =77000*
-^ _..^tff_.
— •* "*
j /^ CL O Cl t ^ ^
— x *"
^TW 1 C * * ~"^ 0 I C/ VX
^ ^ **
I I
^. ^
I7fi -
*• **
^ •"
\ £\C\
I j
tf •*
\ OL/
" ^ •*•
I ^iC\
\pV.s ^ •• *"
\ *S\J
1 ' AVT^^ j_» •• *"" ^
1 A C\
Y^C ^ l_j - *" ""
l*rL/
C "1"oV^ — L— •* *" "^
1 O f\
1 OL/
I ^C\
V* • *•'••*
IbW
L. -• s
no -------
= :[!:±::::::::: :::::::E:: :::::::::::::
900^
50' 60' 70' 80' 90' I00r
Height of Towers (from cap to base)
FIG. 17. WEIGHT OF STEEL VIADUCTS. MCCLINTIC-MARSHALL CONSTRUCTION Co.
COOPER'S CONVENTIONAL ENGINE LOADINGS.
159
OOOO o o cm zo OOOO noon
Class
E-40
t $' 'J/ic^ir^i^
UniFormLoid
11
4000lb-
perlirr-Ff-
E-45
I 1111
§ § §5
a
4SOOIb-
per /it?- ff-
£•50
1 1111 I
I 1 |1 |l
SOOOlk.
per I in- ff-
E-55
111
1111
S*S ^ *<\ *<\
**c^ *<% Vc\ Wv
SSOOIb-
l-SO
1 1111
11 11 1
11
1111
6000/b-
per/ifr-ff-
FIG? 1 8. COOPER'S CONVENTIONAL ENGINE LOADINGS.
(Loads for one track.)
Equivalent Uniform Load System. — The equivalent uniform load for calculating the stresses
trusses and the bending moments in beams, is the uniform load that will produce the same
bending moment at the quarter points of the truss or beam as the maximum bending moment
produced by the wheel concentrations. The equivalent uniform loadings for different spans for
Cooper's E 40 loading are given in Fig. 19. The equivalent uniform loading for E 60 loading
will be f the values for E 40 in Fig. 19. In calculating the stresses in the truss members select
"? 8500
E 8000
S 7500
•o
"*" 7000
Both
O
"?
8
1 Load
m O
V O
88
•£ 5000
D
•£ 4500
j>
.% 4000
?00
u
20 40 60 60 \00 120 140 \W) \QQ 200 220 240 260
5pan of Bridge in Feet
FIG. 19. EQUIVALENT UNIFORM LIVE LOAD FOR COOPER'S £40 LOADING.
(Loads for one track.)
the equivalent load for the given span, and calculate the chord and web stresses by the use of
equal joint loads, as for highway bridges. In designing the stringers for bending moment take a
loading for a span equal to one panel length, and for the maximum floorbeam reaction take a
160 STEEL RAILWAY BRIDGES. CHAP. IV.
loading for a span equal to two panel lengths. It is necessary to calculate the maximum end
shears and the shears at intermediate points by wheel concentrations, or to use equivalent uni-
form loads calculated for wheel concentrations. The calculated values of the moment, M,
shear, S, and floorbeam reaction, R, for Class E 60 are given in Table III. The equivalent
uniform load method has been advocated very strongly by Mr. J. A. L. Waddell who has de-
scribed its use in detail in his " De Pontibus." Live load stresses as calculated by the method
of equivalent uniform loads are too small for the chords and webs between the ends of the truss
and the quarter points, and are too large between the quarter points. The stresses obtained
for the counters are too large. The live load stresses calculated by the method of equivalent
uniform loads are sufficiently accurate for all practical purposes. Even though the equivalent
uniform load method is simple to apply and gives results which are sufficiently accurate, it is now
seldom used.
Uniform Load and One or Two Excess Loads. — A uniform load is used and to provide for
the wheel concentrations one or two excess loads are assumed to run on top of the uniform load.
This method is now rarely used. In a paper entitled "Rolling Loads on Bridges," published in
Bulletin No. 161, Am. Ry. Eng. Assoc., November 1913, Mr. J. E. Greiner, Consulting Engineer,
found that thirty-eight of the thirty-nine most important railroads in the country used a system
of wheel concentrations, and one road used a uniform load with a single excess load; the method
of equivalent uniform loads was not used.
MAXIMUM STRESSES. — The conditions of live loading for maximum stresses in beams
and trusses are as follows.
Uniform Live Load on Beam or Girder. — For bending moment the span should be fully
loaded. For shear the longer segment of the span should be loaded.
Equal Joint Loads. — For bending moment (chord stresses) the bridge should be fully loaded.
For shear (web stresses in trusses with parallel chords) the longer segment. of the truss should be
loaded for maximum stress, and the shorter segment of the truss should be loaded for maximum
counter stress (minimum stress).
Point of Maximum Bending Moment in a Beam. — The maximum bending moment in a
beam loaded with moving loads will come under a heavy load when this load is as far from one
end of the beam as the center of gravity of all the moving loads then on the beam is from the other
end of the beam.
Wheel Loads, Bridge with Parallel Chords. — The maximum bending moment at any joint
in the loaded chord will occur when the average load on the left of the section is equal to the
average load on the entire span.
The maximum bending moment at any joint in the unloaded chord of a symmetrical Warren
truss will occur when the average load on the entire span is equal to the average load on the left
of the section, one-half of the load on the panel under the joint being considered as part of the
load on the left of the section.
The maximum shear in any panel of a truss will occur when the average load on the panel is
equal to the average load on the entire bridge.
Wheel Loads, Bridge with Inclined Chords. — The criterion for maximum bending moment
in a bridge with vertical posts is the same as for bridges with parallel chords.
For web members the criterion is that
P/L = P,(i + ale)ll (I)
where P = total load on the bridge;
P2 = load on the panel in question;
L = span of bridge;
/ = panel length;
a = distance from left, abutment to left end of panel in question;
e — distance from left abutment to intersection of top chord section of the panel produced
and the lower chord. (The intersection is to the left and outside of the span.)
IMPACT STRESSES. 161
KINDS OF STRESS. — Bridges must be designed for the stresses due to (i) dead load;
(2) live or moving load; (3) wind load; (4) snow load; (5) impact stresses; (6) temperature stresses;
(7) rentrifugal stresses, and (8) secondary stresses not taken into account in the calculations.
In addition t<> the above it is necessary in determining the allowable stress in any member to take
into account imperfections in materials and workmanship, possible increase in live loads, fatigue
of metals, the frequency of the application of the stress, corrosion and deterioration of materials,
etc. The structure should be so designed that no part will be ever stressed beyond the elastic
limit. The allowable stresses for dead load are usually taken at about 60 to 70 per cent of the
clastic limit; for an elastic limit of 30,000 lb., the allowable working stresses for dead loads alone
would then vary from 18,000 to 21,000 lb. per sq. in.
IMPACT STRESSES. — As a load moves over the bridge it causes shocks and vibrations
whereby the actual stresses are increased over those due to the static load alone. It is shown
in mechanics of materials that a load suddenly applied to a bar or beam will produce stresses
twice the stresses produced by the same load gradually applied. A bridge is a complex structure
and it is not possible to determine the exact effect of the moving loads. It has been found by
experiment that the ultimate strength for repeated loads is much less than for dead loads. In a
bridge it will be seen that the dead load is a fixed load and that the live load is a varying load.
For stresses of one kind Professor Launhardt has proposed the following formula:
/ Min^tressN
\ Max. stress /
vhere P is the allowable working stress required, and S is the allowable working stress for live
ids, varying from zero to the maximum stress. For stresses of opposite kinds Professor Wey-
luch has proposed the following formula:
• p _ o / Min. stress \
\ 2 Max. stress /
irhere P and 5 are the same as for the Launhardt formula, the maximum and minimum stresses
eing taken without sign. For columns and struts the allowable stresses as given by formulas
i) and (3) are to be reduced by a suitable column formula.
There are three methods in common use for taking account of impact and fatigue: (l) Impact
armulas; (2) Launhardt- Weyrauch formulas, and (3) Cooper's Method.
(i) Impact Formulas. — The formula in most common use is given in the form
^here 7 = impact stress to be added to the static live load stress, S = the static live load stress,
= the length in feet of the portion of the bridge that is loaded to produce the maximum stress
the member, and a and b are constants expressed in feet. The American Railway Engineering
ciation specifies for railway bridges, a = b = 300 ft. Mr. J. A. L. Waddell specifies a = 400
and 6 = 500 ft. for railway bridges; and a = 100 ft., and b = 150 ft. for highway bridges.
7or the names of several roads using A. R. E. A. impact formula, see Table XVI.
For highway bridges the American Bridge Company specifies that the maximum live load
ess shall be increased 25 per cent to cover impact and vibration.
Mr. C. C. Schneider, M. Am. Soc. C. E., specifies that for electric railway bridges
7 = 5- i5o/(L + 300) (5)
In the Osborn Engineering Company's 1901 specifications for railway and for highway
bridges the impact is calculated by the formula
7 = 5- 5/(S + D) (6)
12
162 STEEL RAILWAY BRIDGES. CHAP. IV.
where 5 is the static live load stress and D is the dead load stress. This method is used by the
Illinois Central R. R.
(2) Launhardt-Weyrauch Formulas. — Formula (2) is used for determining the allowable
stress for stresses of one kind and formula (3) is used for determining the allowable stress for
stresses of different kinds. This method is used in Thatcher's Specifications, in Common Standard
Specifications (Harriman Lines), and specifications of Pennsylvania Lines West of Pittsburgh.
(3) Cooper's Method. — Cooper uses formula (2) and calculates the area for the dead load
and the area for the live load stress separately. For dead loads from formula (2) we have P — 28,
while for live loads the range of stress is from zero to the maximum, and P = S.
For a reversal of stress Cooper designs the member to take both kinds of stress, but to each
stress he adds eight-tenths of the lesser of the two stresses,
IMPACT TESTS. — The American Railway Engineering Association has made an exhaustive
series of tests to determine the effect of impact on railway bridges. The following summary is
taken from the Proceedings of Am. Ry. Eng. Assoc., Vol. 12, Part 3.
(1) With track in good condition the chief cause of impact was found to be the unbalanced
drivers of the locomotive. Such inequalities of track as existed on the structures tested were of
little influence on impact on girder flanges and main truss members of spans exceeding 60 to 75
ft. in length.
(2) When the rate of rotation of the locomotive drivers corresponds to the rate of vibration
of the loaded structure, cumulative vibration is caused, which is the principal factor in pro-
ducing impact in long spans. The speed of the train which produces this cumulative vibration is
called the "critical speed." A speed in excess of the critical speed, as well as a speed below the
critical speed, will cause vibrations of less amplitude than those caused at or near the critical speed.
(3) The longer the span length the slower is the critical speed and therefore the maximum
impact on long spans will occur at slower speeds than on short spans.
(4) For short spans, such that the critical speed is not reached by the moving train, the
impact percentage tends to be constant so far as the effect of counterbalance is concerned, but
the effect of rough track and wheels becomes of greater importance for such spans.
(5) The impact as determined by extensometer measurements on flanges and chord members
of trusses is somewhat greater than the percentages determined from measurements of deflection,
but both values follow the same general law.
(6) The maximum impact on web members (excepting hip verticals) occurs under the same
conditions which cause maximum impact on chord members, and the percentages of impact for
the two classes of members are practically the same.
(7) The impact on stringers is about the same as on plate girder spans of the same length
and the impact on floorbeams and hip verticals is about the same as on plate girders of a span
equal to two panels.
(8) The maximum impact percentage as determined by these tests is closely given by the
formula
T _ IO°
(7)
i +
20,600
in which I = impact percentage and / = span length in feet.
(9) The effect of differences of design was most noticeable with respect to differences in the
bridge floors. An elastic floor, such as furnished by long ties supported on widely spaced stringers,
or a ballasted floor, gave smoother curves than were obtained with more rigid floors. The results
clearly indicated a cushioning effect with respect to impact due to open joints, rough wheels and
similar causes. This cushioning effect was noticed on stringers, hip verticals and short span
girders.
(10) The effect of design upon impact percentage for main truss members was not sufficiently
marked to enable conclusions to be drawn. The impact percentage here considered refers to
variations in the axial stresses in the members, and does not relate to vibrations of members
themselves.
(n) The impact due to the rapid application of a load, assuming smooth track and balanced
loads, is found to be from both theoretical and experimental grounds, of no practical importance.
(12) The impact caused by balanced compound and electric locomotives was very small and
the vibrations caused under the loads were not cumulative.
(13) The effect of rough and flat wheels was distinctly noticeable on floorbeams, but not
on truss members. Large impact was, however, caused in several cases by heavily loaded freight
cars moving at high speeds.
MAXIMUM MOMENTS, SHEARS AND FLOORBEAM REACTIONS. 163
TABLE III.
MAXIMUM MOMENTS, M; END SHEARS, S; AND FLOORBEAM REACTIONS, R; PER RAIL, FOR
GIRDERS.
Cooper's E6o Loading (A. R. E. A.).
Loading Two E 60 Engines and Train Load of 6,000 Pounds per Foot or Special Loading
Two 75,000 Pound Axle Loads 7 Ft. C. to C.
Moments in Thousands of Foot-Pounds. Shears and Floorbeam Reactions in Thousands of
Pounds.
Results for One Rail. Results from Special Loading marked*. A. R. E. A. Impact Formula.
Span
I..
Ft.
Maximum
Moments
M.
Moment
Impact
M'.
End
Shear
S.
End
Shear
Impact
S'.
Floorbeam
Reaction
R.
Floorbeam
Impact
R'.
Span
Lt
Ft.
Maximum
Momenta
M.
Moment
Impact
M'.
End
Shear
S.
End
Shear
Impiirt
S'.
5
*46-9
* 46.1
*37-S
*36-9
*37-5
*36-3
50
1426.3
1222.6
130.8
112. 1
6
* S6.2
*S5-i
*37-5
*36.8
40.0
38.5
51
1474-7
1260.4
132.5
II3.2
7
* 65.6
* 64.2
38.6
37-7
47.1
45-o
52
1522.8
1297.8
I34-I
114.3
8
* 7S-Q
* 73-o
*42.2
*41.2
52.5
49-8
53
IS7I.O
I335-I
135-7
II5.3
9
* 844
* 82.0
*45-8
*44-5
56.7
53-5
54
1621.5
1374-2
137-4
116.4
10
* 93-7
* 90-7
*48.8
*47-2
60.0
56-3
55
1675.2
I4I5.7
139.0
II7.5
ii
*io3.o
* 99-5
*Si.i
*49-3
65.5
61.0
56
1728.0
H56.7
140.6
118.5
12
I2O.O
"5-4
*53-2
*5i-i
70.0
64.8
57
1781.9
1497.4
142.2
"9-5
13
142.5
136.6
55-4
53-i
73-9
68.0
58
I834.5
1537-4
143.8
I2O-5
14
165.0
157.6
57-8
55-2
78.2
71-5
59
1891.4
1580.6
145-4
I2I-5
f*
187.5
178.6
60.0
57-2
82.0
74-5
60
1949.4
1624.5
147.0
122-5
16
2IO.O
199.3
63.8
60.6
85-3
77.1
61
2007.5
1668.3
148.6
123-5
17
232.5
22O.O
67.1
63-5
88.2
79-2
62
2064.3
I7I0.8
150.2
124.5
is
255-0
240.5
70.0
66.0
91.0
81.3
63
2123.4
1754-9
152.0
125.6
19
280.0
263.2
72.6
68.3
94-3
83-7
64
2183.3
1799-4
153-8
126.8
20
309-5
290.5
75-o
70.3
98-3
86.7
65
2246.3
1846.3
155-7
128.0
21
339-0
3l6.8
77-i
72.1
101.9
89-4
66
2309.3
1893.0
157-5
I29.I
-22
368.5
343-3
79.1
73-7
105.2
91.7
67
2378.3
1943.2
159.6
130.5
23
398-2
369-8
80.9
75-1
108.2
93-8
68
2435-4
I985-3
161.7
I3I.8
24
427.8
396.1
83.1
76.9
110.9
95-6
96
2498.4
2031.2
163.8
133.2
25
457-5
422.3
85-2
78.6
II3-5
97-3
70
2561.3
2076.8
165.8
134-4
26
487.2
448.3
87.1
80.2
116.6
99.4
7i
2624.5
2122.2
167.7
135-6
27
516.9
474-2
88.9
81.6
1 20. i
101.8
72
2688.0
2168.0
170.0
I37-I
28
548.3
SOi-5
90.6
82.9
123.4
104.0
73
2750.9
2212.5
172.2
138.5
29
582.0
530.7
92-3
84.2
126.5
106.0
74
2818.5
2260.7
174.4
139.9
3°
615.8
559-8
94-6
86.0
129.4
107.8
75
2888.6
2310.9
176.5
I4I.2
3i
649.3
588.5
96.6
87-5
132.7
IIO.O
76
2958.0
2360.1
178.6
142.5
32
683.2
617.3
98.6
89.1
136.5
112.5
77
3028.6
2410.0
180.6
143-7
33
716.9
645.8
100.4
90-5
140.0
114.8
78
3096.6
2457.6
182.5
144.8
34
750.6
674.2
IO2.I
91.7
143.2
116.7
79
3168.2
2507.8
184.4
146.0
35
784.5
702.5
103.8
93-0
146.4
118.7
80
3240.7
2558.5
186.3
I47.I
36
823.0
734-9
105.9
94-6
H9-3
120.4
81
33II-4
2607.4
188.4
148.4
37
861.6
767.0
107.8
96.0
152.2
122. 1
82
3385.1
2658.4
190.4
H9-5
38
900.0
798.8
109.7
97-4
155.6
124.2
83
3459-6
2709.8
192.3
150.6
39
940.0
831.8
III.4
98.6
158.8
I26.O
84
3534-6
2761.4
194.2
I5I.7
40
9834
867.7
II3.I
99-8
162.0
127.9
85
3610.4
2813.3
196.1
152.8
4i
1027.0
903.5
II5.2
IOI.1
86
3689.4
2867.4
198.1
154.0
42
1070.4
938.9
II7.2
J
102.8
87
3766.5
2919.8
2OO.I
I55.I
41
1113.9
Q74.2
IIQ.O
1 04. 1
88
3846.0
2973.7
2O2.I
156.3
44
1157.4
s 1 "T""*
1009.4
7
120.8
T
IOC.1
89
3924.3
3026.5
2O4.O
157.3
45
I2OI.I
IO4.4.. 4.
122. C
••""J • J
io6.c
Viaduct
7
oo
4OOC.8
3081.4
205.8
158.3
46
12444
T^ T
IO78.9
mm»y
124.2
* vv/*3
IO7.7
Span
7^
QI
.fW J «
4084.4
3133.8
2O7.7
1594
47
1287.9
nn.4
T
I2C.Q
• •**/ • f
108.8
3o'-6o'
7
02
4164.0
J J J
3186.7
2O9.7
J' T
160.5
48
I HI. 4.
* J T
1147.8
J J
I27.C
lOQ.q
j
170.2
S
01
4.24.6.6
~ ~
1241.6
f
2II.6
., •>
161.5
49
J J * T
1178.3
1184.8
* I J
I2Q.2
*v-ft-y
III. I
if
sj
04.
4128.0
J ~
1205-4
211. C
162.6
j 1 j
* S **
:^T
TJ ~v
J ~ S J T
J J
164
STEEL RAILWAY BRIDGES.
CHAP. IV.
TABLE III.— Continued.
MAXIMUM MOMENTS, M; END SHEARS, S; AND FLOORBEAM REACTIONS, R; PER RAIL, FOR
GIRDERS.
Cooper's E6o Loading (A. R. E. A.)-
Span
L,
Ft.
Maximum
Moments
M.
Moment
Impact,
M'.
End
• Shear
S.
End
Shear
Impact
S'.
Floorbeam
Reaction
R.
Floorbeam
Impact
R'.
Span
L,
Ft.
Maximum
Moments
M.
Moment
Impact
M'.
End
Shear
S.
End
Shear
Impact
S'.
95
4408.4
3348.2
215.4
163.6
Viaduct
no
C82Q.6
4.261;. c
24.1.O
177 8
96
44.QO.7
3402.0
217.2
164.1;
Span
III
5Q17.4
4111.Q
24.4.. 8
178 7
97
4571.1;
1456.O
219.2
165.6
4o'-6o'
112
6040.0
4.108.1
246.6
I7Q C
Q8
4.6CQ.8
3CI2.4.
221.2
166.7
IQ7.2
111
6148.2
4466 o
248 1
180 3
on
J.74.^.8
'K66.7
221.1
167.7
114.
6258 o
AC14. 8
250 o
181 2
IOO
4.830.0
3622. c
225.O
168.8
Viaduct
lie
6366.8
4.6O2.5
251 8
182 o
IOI
4.016.0
3678.?
226.8
160.7
Span
TT<S
64.78.0
4.671.6
251.6
182.9
I O2
SOO4..O
1714..4.
228.6
170.6
4o'-8o'
117
6586.1
4.718.2
255.1
183.6
IO1
"ill?.?
3808.1
230.4
171.?
™ ,
236.5
TT8
6696.6
4806.1
257.O
184.4
I O4.
5212.8
1870.0
212.1
172.5
IIQ
6808.3
4.874.. 7
258.8
18; 1
IOC
5106.1;
1010.7
21 A. I
177.4.
1 20
6921.6
4Q4.4..O
260.5
186.1
*
IOO
C4.OI.1
•3QQI. I
21 5. Q
1 74.. -2
121
7Oio.tr
5OOQ Q
262.2
1 86 9
1 07
54QQ.2
4.O51.4
2-37.7
175.2
122
714.1.8
5O78 C
264 o
l87 7
1 08
5617.0
4I1O.I
210.4
•'}••
I76.O
121
7260.1
5I48.Q
26C.7
188.4
IOQ
5727.6
42OI.I
24.1.2
176.0
124.
7176.4.
52IQ.I
267.4
189.2
125
7495-2
5290.7
269.1
I9O.O
CALCULATION OF STRESSES. — For the calculation of stresses in railway bridges, see
the author's "The Design of Highway Bridges;" Johnson, Bryan & Turneaure's "Framed Struc-
tures," Part I; Marburg's "Framed Structures," Part I; Spofford's "Theory of Structures"; or
other standard textbook.
Moments, End Shears and Floorbeam Reactions. — The maximum bending moments and
end shears, for Cooper's E 60, and A. R. E. A. special loadings, for girders up to 125 ft. span are
given in Table III. The maximum moments occur at a point near the center of the girder.
Maximum floorbeam reactions are given for stringers up to 40 ft. span. The table also gives
the impact stress calculated for A. R. E. A. impact formula (4).
The maximum moments, end shears, quarter-point shears, center shears, and maximum
floorbeam reactions for girders up to 75 ft. span are given in Table IV.
Moment Diagram. — A diagram giving the position of the wheels in Cooper's E loadings that
will produce maximum moment in a beam or at a panel point in a truss is given in Table Va.
The condition for maximum shear in the first panel is the same as for bending moment at Li,
which value may be obtained from Table Va. Other loadings for maximum shear must be cal-
culated by means of the criterion given above.
A moment diagram for Cooper's E 60 loading is given in Table Vb, and brief instructions
for use of the table are given on the page opposite Table Vb.
Shears in Bridges. — Shears in the panels of the loaded chords of spans with 3 to 9 panels,
for Cooper's E 50 loading, are given in Table VI, Table VII, and Table VIII. To obtain the
shears for E 60 loading multiply the tabular values by f . The stresses in the web members of a
Pratt truss are equal to the shears X sec 0, where 6 is the angle that each web member makes with
a vertical line. The tables were calculated by the McClintic-Marshall Construction Company.
Moments in Bridges. — Bending Moments in beams and girders and at points in the loaded
chord of bridges, are given in Table IX and Table X. The bending moments for an E 60 loading
will be equal to the tabular values X f .
For example, the bending moment for an E 50 loading, at joint L\, in an 8 panel truss of 2OO-ft.
span from Table X, is 6,787 thousand ft.-lb. For an E 60 loading the bending moment at joint
Li is 6,787 X 6/5 = 8,145 thousand ft.-lb., which checks the value calculated from Table Vb
on the page opposite Table Vb. The tables were calculated by the McClintic-Marshall Con-
struction Company.
Elevated Trestle Span Reactions. — The floorbeam reactions and the maximum reactions of
the intermediate and tower spans of elevated railway trestles may be calculated from Table IX
and Table X, as follows:
Required the end reactions for a 40 ft. tower span and an 80 ft. intermediate span. Take a
span equal to 40 + 80 = 120 ft., and calculate the bending moment at a point 40 ft. from the
left end. In Table IX, take a 6-panel bridge with 20 ft. panels, the bending moment at L2 is
MAXIMUM SHEARS, MOMENTS AND FLOORBEAM REACTIONS. 165
r^4° +
5i255 thousand ft.-lb. Then the reaction, R
- RX 6/5
-197.1 thousand Ib. For E 60,
cluvks the value in Table III.
40
197.1 X 6/5
= M x 3/8°
x 3/8°
236.5 thousand Ib., which
TABLE IV.
MAXIMUM END SHEARS, QUARTER-POINT SHEARS, CENTER SHEARS; MAXIMUM MOMENTS, AND
FLOORBEAM REACTIONS FOR GIRDERS.
Cooper's E6o Loading (A. R. E. A.).
Moments in Thousands of Foot-Pounds. Shears and Floorbeam Reactions in Thousands of
Pounds.
Results for One Rail. Results from Special Loading marked*.
Span
L,
Ft.
End
Shear.
Quarter
Point
Shear.
Center
Shear.
Maximum
Moment.
Floorbeam
Reaction.
Span
L.
Ft.
End
Shear.
Quarter
Point
Shear.
Center
Shear.
Maximum
Moment.
10
*48.8
30.0
*l8.8
* 93-7
6o.O
45
122.5
75-3
35-2
1201.1
II
*SI-I
*32-4
*l8.8
*io3.o
65-5
46
124.2
76.1
35-6
1244.4
12
*S3-2
*34-4
*i8.8
I2O.O
7O.O
47
125.9
77-i
36.0
1287.9
13
55-4
*36.o
*i8.8
142.5
73-9
48
127-5
78.2
36.3
1331-4
H
57-8
*37-S
19.3
165.0
78.2
49
129.2
79-2
36.8
1378.3
IS
60.0
*38.8
*20.O
187-5
82.0
So
130.8
80.2
37-2
1426.3
16
63.8
*39-9
*2I.I
2IO.O
85-3
Si
132.5
81.2
37-8
1474.7
J7
67.1
41.1
*22.I
232.5
88.2
52
I34-I
82.2
38.3
1522.8
18
70.0
42.6
*22-9
255-0
91.0
53
135-7
83.1
38.7
1571.0
19
72.6
43-8
*23-7
280.0
94-3
54
137-4
84.1
39-2
1621.5
20
75.0
45-0
*244
309-5
98.3
55
139.0
85.2
39-6
1675.2
21
77-i
47.2
*25-O
339-0
101.9
56
140.6
86.3
40.0
1728.0
22
79.1
49.2
*25.6
368.5
105.2
57
142.2
87-3
40.4
1781.9
23
80.9
50.8
*26.I
398.2
108.2
58
143.8
88.3
40.8
1834-5
H
83.1
S2-S
*26.6
427.8
110.9
59
H5-4
89-3
4i-3
1891.4
25
85.2
54.0
*27.0
457-5
"3-5
60
147.0
90.2
41.8
1949.4
26
87.1
SS-4
*27-4
487.2
116.6
61
148.6
91.1
42-3
2007.5
27
88.9
S6.7
*27.8
516.9
1 20. i
62
150.2
92.0
42.8
2064.3
28
90.6
57-9
*28.I
548-3
123.4
63
152.0
92-9
43-2
2123.4
29
92.3
59.0
*28.s
582.0
126.5
64
153-8
93-8
43-7
2183.3
30
94.6
60.0
*28.8
615.8
129.4
65
155-7
94-7
44.1
2246.3
31
96.6
61.2
*29-I
649.3
132.7
66
I57-S
95.6
44-6
2309.3
32
98.6
62.4
*29-3
683.2
136.5
67
159.6
96-5
45-o
2378.3
33
100.4
63.6
*2g.6
716.9
140.0
68
161.7
97-4
45-4
2435-4
34
IO2.I
64.7
*29.8
750.6
143.2
69
163.8
98.3
45-7
2498.4
1C
103.8
6e.7
•3Q 1
784. ?
70
165.8
OQ.2
4.6.2
2c6i.i
6
IOC.O
vj*/
66.7
JW'J
1O.Q
/UTO
823.0
/ **
71
*";>•"
167.7
• 7s
IOO.I
•f.V.4
46.6
j j
2624.C
37
AVO-:/
IO7.8
***^/
67. c
j y
•IIC
86l.6
72
* / /
I7O.O
IOI.O
T
47.1
T J
2688.0
8
IOO.7
W '3
68.3
J *O
12.0
QOO.O
/
71
• / ***
172.2
IOI.Q
*T f ""
47. c
2750.9
J
•IO
7 /
II 1.4.
WU.J
60.0
j ••*
•J2.C
yv^w.w
Q4.O.O
/ J
74
174.4
7
IO2.8
~/ J
48.0
2818.5
J 7
4O
* * * 'T
111. 1
vy.w
70. 2
j*'j
•Ji.O
J^MMH
081.4.
/ T
7S
/ T T
176.?
101.6
T
48.4
2888.6
•f V
4.1
* * J • *
IK. 2
1 v..
71 1
j j w
•J-I C
y^j -f-
IO27.O
/ j
* / w J
• J
T T
42
* * j •*•
117. 2
/ * • j
72.1
jj'j
•J1.Q
IO7O.4.
41
/ •**
IIQ.O
/ *" j
7-1.1
j j *y
14..4.
*w/ W*T
I I 11.0
T J
44.
* *y«w
I2O.8
I j j
74. 1
JT T"
14. 8
* * * J'7
IIC7 4.
TT
/T'J
JT'U
• * J/'T
166
STEEL RAILWAY BRIDGES.
CHAP. IV.
u
IS
155
1=5
155
115
155
155
155
155
S V)
II
S 5
Bi
K \j
155
*
^
i •§
&*
k ><
»o ^>
Ni
'
,*•&*? V «
H I §.8 S'S
MOMENT
£
, i
=3iJ G
*
0
^u g
•5 J o
._
.5 rt
^2'S ^^
^~3§
=>^^^^
^.GT) ° rt
-S^s
O 3 f
2^-
> o
Jag
<U en S <U
a.S
*5
om ea
ts of all
about h
f moment
f valu
each li
ed lin
of mo
te mo
t
,
on
ep
gh
ul
-1-1 O
85 J
o •*
-1-1 o
§8
1^"
13 M
^"G
H.*
g S o-o M<3
o S I? c o «
Ita- S 03
n
on,
s o
n lef
line
e st
to ri
Calc
ee
me
y w
f mo
ques
mati
eel o
ped
of th
heel
i. —
-szl
a) .Z ?
151*8
.-a^^g
^§--Ss
oa§i§
^ taoilj: <u
_ C a) +j J3
115 s:
*C ffl pC .— ! Jj
> a-^- rt
3G2S1
Q;sfct^
^™ c iu ( J
y rt n) g"2 G"
fcuO r i i-. *-« fii
*Tj C^ " Q rt r;
o -a « -3 ~
. o -
d ^ G
N rt
S^+j
•* G
MOMENT TABLE FOR COOPER'S E 60 LOADING
167
w
< $
H 2
H
^fe 1^
-f^c--
H*l
— i— i— -
fc* Ms
r^i NS
-i-\-
jfii
Ht-i-"-
N
N
tx
MOMENT TABLE
COOPER'S E-60 LOADING
Two ?/5 TON ENGINES + 6000 LBS-PER FOOT-
N
MOMENT JN THOUSAND FOOT POUNDS FOR ONE RAIL
LOADS IN THOUSANDS OF POUNDS FOJ? ONE RAIL •
I
1
§
168
STEEL RAILWAY BRIDGES.
CHAP. IV.
TABLE VI.
MAXIMUM SHEARS IN TRUSS BRIDGES FOR COOPER'S £50 LOADING.
SHEARS FOR THROUGH SPANS
COOPER'S E-50 LOADING
Shears in Thousands oF Pounds For
One Rail
Number
of
Panels
in
Bridge
fcnek
Length oF Panel
I2'0"
/Z'6"
I3'0"
I3'6"
I4rO"
14'6"
tfo"
I5'6"
16'0'
/6'6"
17'0"
I?1?
18'0tt
/S'6"
3
LoL,
51-6
53-0
54-3
55-9
57-4
58-7
60-0
61-5
63-0
64-3
65-6
66-9
68-2
69-5
4
LoL,
71-6
73-6
75-5
77-6
79-6
81-6
83-6
85-5
87-3
89-0
90-6
92-6
94-5
96-4
Uz
34-4
55-6
36-7
37-7
38-6
39-6
40-6
41-7
42-7
43-9
45-0
46-1
47-2
48-3
uu
7-9
8-4
S-9
9-4
9-8
10-3
10-7
lf-2
11-7
12-2
//-/
13-1
13-5
/3-9
5
LoL,
89-2
91-4
93-6
96-4
99-2
102-3
105-4
108-6
111-8
II5-J
118-3
12J-5
124-6
127-5
L,LZ
53-8
55-5
//•/
58-7
60-3
61-9
63-4
64-8
66-2
67-7
69-/
70-S
724
74-0
LzL;
25-9
26-9
27-8
28-7
29-5
30-4
31-2
32-0
52-8
33-6
34-3
35-1
35-8
36-6
6
LoL,
106-7
110-5
114-3
///•/
///•/
127-1
131-0
134-9
138-8
142-7
146-5
150-2
153-!
157-5
L.Lz
72-1
74-2
76-3
7/7
79-8
82-2
84-6
86-9
90-1
93-0
95-8
W-5*
ion
103-6
/2/3
4*4
44-9
46-3
47-7
49-1
£0-4
51-7
52-9
54-0
55-3
56-5
57-6
5g-6
59-7
kU
20-z
2H
Z/-9
Z2-6
23-3
24-1
24-8
25-6
26-3
27-0
27-6
28-3
2f-9
29-6
7
LoL,
127-5
152-0
!36-5
141-4
146-2
150-9
155-5
160-1
J64-6
169-0
173*3
177-5
m-6
///</
L,LZ
89-0
92-0
95-0
9M
102-6
106-f
109-6
113-0
1/6-4
1/9-7
////
126-4
129-6
132-8
LZL3
59-6
WO
64-3
65-9
67-4
69-3
//•/
73-1
75-0
77-4
79-7
82-1
#44
86-6
LSL4
56-1
37-4
3H
39-t
41-0
42-2
43-4
444
45-4
46-5
47-5
48-5
49-4
50-4
L+LS
i6-i
16-9
17-7
18-4
19-0
19-7
£0-3
Z/-0
?/-6
22-2
22-8
Z3-4
24-0
24-6
8
LoL,
147-2
152-3
157-4
162-9
JW4
173-6
17M
183-8
/88-7
/93-6
W-4
203i
207-8
212-5
L,LZ
m-4
112-6
1/6-7
1Z/-0
125-5
129-5
133-7
/37-8
14/-8
/45-7
149-5
153-2
156-9
160-5
LzL?
76-8
793
8Z?
S5-0
87-8
90-9
93-9
96-8
99-6
1026
W5-6
108-5
1//-4
114-2
L,U
52-0
53-7
55-3
56-7
58-1
59-8
61-4
63-/
648
66-7
68-5
70-4
72-2
740
L4Ls
30-5
31-7
32-8
33-9
35-0
36-1
37-1
38-0
38-9
39-9
40-9
41-7
42-5
43-4
LSL6
i3-i
13-S
J4-5
15-1
15-7
16-4
/7-0
J7-6
18-1
18-7
19-2
19-8
206
20-8
9
LoL,
1M4
1720
177-6
183-5
189-4
195-1
200-9
206-4
21/-8
2/7-5
222-7
228-0
233-2
238-4
L,L2
IZfiZ
132-9
137-5
142-5
147-4
152-f
156-8
161-3
/65-7
170-/
174-5
178-8
183-0
1872
LzL*
95-4
99-2
102-9
106-4
109-8
112-9
1/6-6
120-4
124-1
127-6
131-0
154-4
137-7
141-0
ku
67-4
69-8
7Z-?
74-8
77-3
80'1
82-7
85-2
87-6
90-1
92-5
94-9
97-3
99-9
L*LS
45-5
46-8
48-3
49-6
50-i
52-4
53-8
55-4
56-9
58-6
60-2
61-9
63-5
65-3
LsL6
Z6-2
27-3
m
Z9-5
30-3
31-3
32-3
33-1
33-9
34-S
35-7
36-5
37-Z
38-0
MAXIMUM SHEARS IN PRATT TRUSSES.
169
TABLE VII.
MAXIMUM SHEARS IN TRUSS BRIDGES FOR COOPER'S ESO LOADING.
SHEARS FOR THROUGH SPANS
COOPER'S E-50 LOADING
Shears In Thousands oF Pounds For
One Rail.
Humbec
oF
Panels
in
Bridge
Panels
Length oF Panel
I9'0"
I9'6"
20'0'
20'6°
21'0"
2I'6"
22'0"
2?'6"
25'(f
25'6"
?4'0"
24'6"
25'0'.
25'6n
3
LoL,
70±
72-0
73-2
4
LoL,
98-2
100-7
103-0
105-6
108-2
110-7
l/tt
1/5-5
117-7
120-0
122-2
IZ4-4
126-5
I?#-7
Uz
49-}
50-5
51-3
52-2
53-1
54-0
54-9
55-8
56-7
574
58-Z
59-0
59-7
606
LtU
14-5
14-7
15-0
15-3
15-6
15-9
162
16-5
16-7
17-0
17-?
17-5
17-8
1S-1
5
LoL,
130-4
133-5
136-6
159-8
I4&
146-0
149-0
152-0
154-9
157-8
160-5
163-3
166-0
168-8
L,L2
75-6
77-4
79-1
80-9
82-6
84-4
86-1
88-0
89-9
91-7
93-5
95-1
96-6
93-3
LZL3
37-5
38-1
38-8
59-6
40-3
40-9
41-6
42-3
4Z-9
43-7
44-5
45-0
45-5
46-3
6
LoL,
161-1
1644
168-1
171-7
175-2
173-8
182-5
185-8
189-2
192-6
195-9
199-2
ZOf-5
205.9
L,L2
106-1
/DM
111-0
113-6
116-0
113-5
120-S
123-2
1254
127-9
150-1
1324
134-5
136-8
LzL,,
60-7
62-1
633
65-1
66-6
68-Z
69-6
71-5
72-9
74-5
75-9
77-4
73-6
80-Z
LsL4
50-2
50-8
31-4
32-1
32-8
35-4
340
34-5
35-0
35-5
36-0
36-6
37-1
376
7
LoL,
1/9-7
195-9
197-8
201-7
205-5
209-6
213-7
217-9
221-8
225-8
229-7
233-6
2374
2414
L,L2
155-9
159-0
142-0
145-0
147-9
150-9
153-7
156'!
159-3
16Z-1
164-8
167-6
170-3
173-2
LZLZ
JM
91-0
95-1
95-4
97-5
99-6
101-6
105'8
105-8
107-9
109-8
111-8
113-6
115.6
L3L4
£&
52-4
53-4
54-5
55-5
56-7
57-3
59-3
60-6
6Z-1
63-4
64-7
65-3
67-1
L4LS
25-1
//•/
?6-3
26-9
27-4
23-0
&5
29-0
29-4
29-9
ZO-Z
30-S
31-3
31-3
8
LoL,
217-1
221-7
22&
23M
235-2
259-9
244-5
248-9
2534
258-0
262-5
267-1
Hl-5
276-0
Uz
164-1
167-7
171-3
174-8
173-2
181-7
185-0
188-4
191-7
195-1
198-3
Z01-7
2043
208-3
L2LZ
117-0
119-8
122-5
125-1
127-6
130-5
132-9
135-4
137-8
140-3
142-7
145-2
J47-5
150-0
L3L4
75-8
77-8
79-8
81-7
83-6
85-5
87-5
89-2
91-0
92-8
94-5
96-3
93-0
99-8
L4LB
44-Z
45-2
46-1
47-1
48-0
49-0
49-9
51-0
52-1
53-1
54-1
55-3
56-4
57-4
LSL6
21-5
ZI-9
22-4
?&
Z3-4
?£•$
?4-4
24-9
25-3
25-7
26-0
26-S
Z6-9
Z7-3
9
LoL,
245-6
248-8
253-9
259-0
264-0
fftt
274-2
279-4
284-5
Z89-7
Z94-9
Z99-9
504-9
310-0
LLZ
191-4
195-4
199-5
205-5
207-2
ZIf-5
215-6
219-4
223-3
227-2
Z51-0
234-9
258-8
2X8
LzL*
144-2
147-4
150-6
155-8
156-9
160-0
163-0
166-0
169-0
J7ZO
175'0
177-9
180-8
133-8
L3L4
102-4
104-9
107-3
109-7
1/20
1/4-3
116-6
118-9
////
123'4
125-5
Iffl
J?9-4
J3Z-0
ULs
67-0
68-6
70-1
7/7
73-3
74-9
76>4
7/-0
79-5
81-2
tt-8
84-3
85-8
87-4
LSL6
38-7
59-6
404
41-3
4?'/
45-0
43-9
44-9
45-S
46-7
47-6
4t-6
49-6
AV
17U
STEEL. RAILWAY BRIDGES.
CHAP. IV.
TABLE VIII.
MAXIMUM SHEARS IN TRUSS BRIDGES FOR COOPER'S ESO LOADING.
SHEARS FOR THROUGH SPANS
COOPER^ E-50 LOADING
Shears in Thousands of Pounds For
One Rail.
Humber
oF
Panels
In
Bridge
Panels
Length of Pane/
Z6W
26W
27-'0"
27-6"
28-0"
2^6"
29^0"
29V'
30-0"
&0"
32-'0"
33-0"
34-'0"
55^0"
3
LoL,
4
LoL,
130-9
133-1
135-2
137-3
139-3
J4/-5
143-6
145-8
/47-9
L,LZ
61-3
62-1
62-9
fog
64'6
65-6
66-5
67-4
68-3
LzLs
18-4
18-6
J8-9
/9-/
194
19-6
J9-8
ZO-1
ZO-3
b
UL,
17/-4
174-1
176-7
179-4
181-9
184-5
187-0
189-6
192-0
197-1
2024
207-5
212-6
2/7-6
L,LZ
IOO-I
10/-9
105-6
105-4
107-1
108-9
1/0-6
//Z-3
1/4-0
1/7-3
JZO-3
/&&
126-5
129-5
LZLS
46-9
47-7
4&3
49-0
49-6
50-5
5/-3
52-/
52-8
54-3
55-8
57-3
59-1
60-8
6
LoL,
20M
212-2
2/5-4
218-6
221-8
2249
228-0
23H
234-2
240-3
246-6
252-8
259.1
265-3
L,LZ
139-0
14/3
143$
145-8
J4S-0
150-3
152-4
154-6
156-7
160-8
165-1
169-3
173-3
177-3
LzL2
81-5
83>0
84-3
85-7
87-0
88-4
89-6
91-1
92-4
95-0
97-5
mo
102-5\
105-1
L3L4
38-1
38-6
39-/
39-6
40-0
40-5
41-0
41-7
4?-4
4Z-6
45-1
46-3
47-8
49-3
7
LoL,
245-2
249-1
252-8
256-6
260-4\
264-1
267-7
27/-4
275-0
282-3
289-6
297-1
304-6
312-0
L,L?
175-9
178-8
181-5
J84-4
187-0
JS9-9
192-5
195-4
197-9
203-3
20S-5
213-8
218-8
224-0
LzL3
117-4
119-3
///•/
123-0
124-8
126-6
128-3
130-2
131-9
135-3
138-8
142-5
146-0
149-6
L3L4
W3
69-6
70-8
72-0
73-t
74-3
75-4
76-7
77-8
80-f
82-4
84-5
86-6
88-8
L4LS
32.1
32-6
33-0
334
33-2
34-3
34-6
35-f
35-6
36-5
37-5
38-5
39-8
41-0
8
L0L,
280-4
2144
mi
293-6
297-9
302-3
30M
310-9
315-0
3233
332-0
340-6
349-3
357-9
L,L,
21/-6
2/5-1
2/1-4
22/-8
225-0
221-4
2S/-7
235-9
238-2
244-6
251-0
257-3
263-8
270-0
LzL3
152.3
I54>7
157-0
/59-4
/6/-7
164-0
166-1
161-5
170-8
175-4
1X0-1
1W
1S9-3
193-9
L*L4
WI-4
103-1
104-6
106-3
W7-9
/09-5
1/1-0
112-6
114.-1
117-3
120-3
123-3
126-3
129-3
L4LS
58-4
593
60-5
ei-6
62-6
63-7
64-8
65-9
66-9
68-9
70-8
72-8
74-8
76-7
LsL6
27-6
28-0
22-4
28-8
?9-I
29-5
29-9
30-4
30-8
31-5
32-5
33-3
34-3
35-2
9
LoL,
315-0
320-1
3254
530-0
554-9
539-9
344-7
349-7
354-5
364-1
373-8
583-5
593-5
403-5
L,L2
246-7
250-6
2545
258-5
262-4
266-3
270-2
274-0
277-8
285-4
293-0
300-5
308-0
315-5
LZL3
186-7
ISM
192-4
195-3
19M
200-9
203-8
206-7
209.5
2/5-3
221-0
22f-8
232-5
258-Z
L3L*
134-1
136-3
138-4
/40-5
142-5
144-6
146-6
148-6
J50-6
154-8
158-8
162-7
166-6
170-5
L4L5
88-9
90-4
91-8
93-3
94-8
96-Z
97-6
99-0
100-4
103-1
105-8
108-6
111-3
114-0
LsLt
51-5
52-4
53-3
54-2
55-0
.55-9
56-8
57-6
5S-4
60-3
62-0
63-8
65-5
67-2
MAXIMUM BENDING MOMENTS IN PRATT TRUSSES.
171
TABLE IX.
MAXIMUM BENDING MOMENTS IN PRATT TRUSS BRIDGES FOR COOPER'S £50 LOADING.
&MDIN6 MOMENT5 FOR THROUGH SPANS
COOPER'S E-50 LOADING
Moments //? Thousands of Foot- Pounds for
One Rail-
Hualxr
Panels
in
Bridge
Pane/
Point
Length of Pane/
8L0"
9'-0"
/o'-o*
J/W
/?'-0'
l?'-6"
/3'-0"
J3L6'
I4'-0"
I4W
/5'-0"
&6"
3
L,
325
392
464
542
6/9
66/
707
755
803
850
900
952
4
L,
435
532
652
745
859
9/6
982
/046
///5
1/83
/254
1524
Lt
569
681
821
964
1//0
//89
1269
/ 552
1441
/529
/624
/720
5
L,
540
662
792
929
1071
1/40
/?I7
1298
1389
/480
1580
/679
Lt
790
964
1148
1361
1574
/675
1792
/9/0
2047
2/77
2309
2439
V
L,
641
783
930
1 095
1280
/375
1445
!600
!7?4
1840
/964
ZM9
Lt
J008
J166
/465
17/0
1997
2/35
2289
2445
26/6
2792
2984
3/74
L*
J/JO
/35I
1617
1924
2240
2407
2581
2760
2946
3/38
3337
5538
7
L
729
892
1 080
1292
1530
/645
/775
1906
2047
2/85
233/
2479
U
1Z/5
1475
/748
2070
2441
2642
2849
3050
3263
3485
3722
3957
U
J425
J739
Z086
2465
2879
3100
3332
3560
3802
4040
431?
4595
8
L,
SI5
/02I
1254
1500
1766
/900
2047
2200
2358
2516
2680
2845
Lz
1397
170!
2046
2490
2933
3165
3405
3645
3898
4/60
4436
47/0
U
/715
2/00
2529
2991
3498
3775
4078
4383
47/0
5040
5380
57?0
1-4
1819
Z240
2699
32 03
3742
4025
4344
468/
5034
5398
5768
6/47
\
L,
92?
1163
1418
1698
1997
2145
2309
2475
265/
2827
30/0
3195
It
1576
1955
2404
2888
3400
3670
3946
4224
45//
4804
5/07
5420
L5
1933
2435
2986
3571
4/94
4531
4886
B24/
56/6
5993
6390
6790
t±
2J27
2598
3186
3860
4588
4970
5370
5770
6/86
66/0
7047
7485
16'-0'
!6'-6"
nW
17'-6n
/8'-0"
J8'-6"
/9'-0"
19-6"
20'-0"
20'-6"
2/'-0'
2/'-6"
3
L,
1008
1060
1115
1170
1228
J285
1346
1404
1464
4
L,
1396
1463
1539
/6/4
J70/
1776
1868
1958
206/
2/66
2273
2580
Lz
1819
1923
2023
2134
2240
2349
2465
2581
270/
282/
2946
3074
5
L,
I7S8
1895
2009
2123
2242
2355
2477
2600
273/
2864
3001
3/38
L2
2580
2724
2fS0
5030
3190
3350
3518
3685
3943
4/44
4347
4555
b
L,
2220
2351
24M
2626
2769
29/0
3062
32/0
3562
3516
3678
3840
U
3372
3569
3775
3978
4194
44/5
4650
4885
5255
550/
5750
5998
U
3742
3952
4170
4422
4681
4948
52/5
5487
5746
6028
632/
66/7
'I
L,
2633
2786
2945
3104
3268
3434
3605
3778
3955
4/50
43/7
4505
U
4203
4450
4705
4958
5218
5480
5746
6025
6326
66/3
69/4
7215
U
4198
5200
5509
5815
6/35
6460
6 gOO
7140
7646
7990
8347
8710
8
L,
3018
3189
3372
3553
374/
3930
4125
4320
4525
4727
4939
5150
Lz
4994
5280
5576
5873
6180
6487
6806
7125
7458
7805
8/62
8520
L,
6072
6430
6806
7180
7575
7985
8569
8780
9234
9650
10070
/05/5
(*
6516
6915
7351
7740
8164
8595
9043
9490
9943
10396
/0862
113/7
\\
L,
3388
3582
3785
3 987
4/98
44W
4629
4850
5079
5508
5545
57SO
L2
5747
6074
6414
6755
7108
7463
7830
8198
8578
8970
9578
9790
/3
7204
7620
8054
8496
8959
94/5
9892
W372
lOttO
1/375
1/900
12425
U
7966
8460
8910
9490
10 010
10530
1/065
/1605
12172
/2735
13310
/38SO
172
STEEL RAILWAY BRIDGES.
CHAP. IV.
TABLE X.
MAXIMUM BENDING MOMENTS IN PRATT TRUSS BRIDGES FOR COOPER'S £50 LOADING.
BINDING MOMENTS FOR Tn#ou6H 5PANS
COOPED E-50 LOADING
Moments In Thousands oF Foot-Pounds For
One fell*
//i/mfor
Panels
in
Bridge
fene/
Point
Length oF Pane/
22-0"
22W
2$'-0'f
23'-6"
Z4W
?4!-6'f
2&0*
?5L6"
26'-0"
?6L6"
27W
27+6"
3
L,
4
L,
2490
2597
2708
28/9
2955
5046
3163
3282
3402
3526
5649
5774
u
5205
3538
3470
3607
3743
3883
4025
4/70
4344
450/
4681
4858
5
//
3278
3418
5562
3705
3852
3999
4150
4301
4456
46/f
4770
4929
Li
4767
4978
5193
54/5
5640
5865
6093
637/
6552
67S3
70/4
7250
6
L,
4008
4175
4349
4522
4700
4873
506/
5245
5435
5622
58/6
60/0
Lz
6? 50
6501
6756
70/f
7270
7525
7794
8068
8352
3654
8960
9268
U
692f
7228
7558
7850
8166
8491
882/
9155
9490
9m
/0/70
W5/4
7
L,
4702
4897
5/00
5303
55/2
572/
5956
605!
6373
6595
6825
705/
Lz
7530
7845
8/73
8503
8842
9/82
9550
9875
10236
JO 600
10980
//357
Li
9073
9448
9826
/0207
10609
1/017
//444
1/870
/2312
12752
13203
/3655
8
it
5373
5594
5829
606f
6300
6540
6787
7035
7289
7540
7306
8069
Lz
8890
9260
9640
W030
10430
/0852
11244
f/655
/2080
/2508
12950
15392
Ls
10993
1/475
1/976
/2472
/298/
13490
/40/0
14528
15065
/5605
16/63
167/8
U
11805
12283
12790
13289
13795
14300
/4820
J5340
15875
/64/3
16965
/75/4
9
L,
6050
6280
6542
6804
7074
7344
7622
7900
8/88
8477
8774
9070
L2
/02/6
10640
1/082
11525
//9S5
12448
12925
13400
13890
14580
/4888
/5400
u
12978
13555
/4J/8
14705
15308
159/0
16528
17/45
17778
184/4
/9070
19730
L4
14472
/506S
15684
16300
16930
17560
18205
/8850
195/5
20/80
20870
21557
28'0"
28!6"
29'0"
29'6!f
30'0"
3/'0'f
32'0'f
33'0"
34'0"
35'0"
56'0"
37'0*
3
- //
4
//
5900
405!
4/65
4300
4456
L2
5054
52/5
5398
5580
5768
5
• //
5092
5255
5422
5589
5760
61/3
6477
6849
7229
76/7
Lz
7492
7736
79U
8252
8482
8985
9496
100/2
1059!
11/92
6
L,
6208
6402
66/2
68/7
7026
7449
789!
8346
88/2
92M
Lz
9580
9897
J02/S
/0547
/0880
//J57
/2248
/297X
/3728
/45/0
L*
10862
/1 208
1/565
1/925
/??96
/5040
/3796
f4565
15341
/6/45
7
L,
7286
7521
7762
8003
8250
8751
9267
9805
/0556
/0920
Lz
11742
12125
12520
/29/8
15550
J4I64
15016
15894
/68/0
17755
Ls
14 112
14571
/5059
15507
15984
16965
17963
18979
200/2
2/073
8
L,
8538
8608
8887
9165
9450
/0029
10622
//259
1/874
12525
/3/30
13873
Lz
15850
14508
/4780
15250
/5730
/6721
/7732
18768
19850
20959
22092
25247
Lz
/7285
17852
J845/
190/0
/9600
208/2
22052
233/2
2460!
2Z32/
27271
28652
L*
/S075
18655
192/0
/9795
20406
21635
^2895
24/97
25550
26905
28311
29726
9
L,
9m
9686
9996
W3/0
/0.655
//289
J/962
/26f6
13576
f4//4
14S7I
15644
Lz
15950
16460
17005
17547
/8JOO
19244
204/6
21616
22855
24144
25425
26793
/3
20405
21080
2/771?
2246/
23/68
24605
2608!
2759f
29J35
307/0
32527
33983
L*
22260
2Z&5
23678
24405
25170
26707
28282
29908
31572
53289
55051
36826
MATERIAL AND ALLOWABLE STRESSES.
173
SHEARS AND MOMENTS IN A PLATE GIRDER BRIDGE.— The maximum shears
and moments in an 86 ft. span deck girder railway bridge are shown in Fig. 20. In calculating the
maximum live load shears the girder was divided into sections about 7 ft. in length and the maxi-
mum shears were calculated as in a truss bridge. The maximum bending moments were also
r.ilrul.itrd for the same points in the girder. The make-up of the tension flange and the rivet
spacing is shown in Fig. 20.
The stress diagram for a 60 ft. span single track deck plate girder bridge is shown in Fig. 21.
3622000
5 56 611 Max Moment
'460
Max Shear 167370
Curvtoffiax
Dead Shear-16120
Pitch staggered
Curve of Max
Moments
Cross Frame —
I, Alignment Tangent
1 1 Scate o f Shears l'= 150000*
1 1 Scale of Moment* l"= 1800000
'rfGIZO Dead Shear
\ i:
117700
I42}0(T^: (|
Effective Span 'G5'-O"- 1.-J&/67370 Max Shear
• t MI t a I * * rf .
Curve of flax
Shears
Hfe^'-tf1
j< — - atf'-<?
FIG. 20. SHEARS AND MOMENTS IN A RAILWAY PLATE GIRDER.
MATERIAL. — Open-hearth carbon steel complying with the specifications of the Am. Ry.
Eng. Assoc. as given in the last part of this chapter is commonly used for bridges up to spans
of 500 to 550 feet. For spans of more than 500 or 550 feet to about 650 feet carbon and nickel
steel are used, or nickel steel alone is used. For spans of 650 to 750 feet nickel steel alone should
be used. For an exhaustive discussion of the use of nickel steel in the construction of bridges see
article entitled "Nickel Steel for Bridges" by Mr. J. A. L. Waddell, M. Am. Soc. C. E., in Trans.
Am. Soc. C. E., Vol. 63, 1909. An excellent discussion of the design of large bridges is given in
"Design of Large Bridges with Special Reference to the Quebec Bridge" by Ralph Modjeski,
Consulting Engineer, in Journal Franklin Institute, September, 1913.
ALLOWABLE STRESSES.— The allowable stresses on carbon steel as adopted by the Am.
Ry. Eng. Assoc. are given in the specifications in the last part of this chapter. Out of 39 railroads
in the United States 24 were using the Am. Ry. Eng. Assoc. specifications for allowable unit
stresses in 1913. For additional data on unit stresses, see Table XVI.
174
STEEL RAILWAY BRIDGES.
J«^«5|JFP
j.y gj^^NVS^^^S^
?! -&^ + ^
EN •« s »NBfp-5 s. ^
mi ,*SA**JH«^«^
V^^pP^H^I
fe§%8fc?S94«|45!
ECONOMIC DESIGN OF RAILWAY BRIDGES.— Pin-connected truss bridges have
been used for railroads on account of the ease of erection, ease in calculating the stresses, and the
simplicity of details which give small secondary stresses. The present practice in railway bridge
design is to use plate girders for spans up to about 115 ft., and riveted truss bridges for longer
spans; pin-connected bridges being used only for very long spans and for spans of 200 ft. and over
where there is some special reason such as ease of erection or low cost. The author would recom-
mend pin-connected truss bridges for all spans of 200 ft. and over for the following reasons: —
(i) the weight of a pin-connected truss bridge with eye-bars is less than the weight of a riveted truss
bridge of the same span and capacity, and while the shop cost per pound of pin-connected truss
bridges
DESIGN OF RAILWAY BRIDGES. 175
is slightly higher than for riveted truss bridges, the total cost erected of the structural
strrl in the- pin-connected bridge is less than the steel in the riveted bridge. (2) The pin-con-
mvii-d t russ bridge can be erected in less time at a very much less cost than the riveted truss bridge.
(3) The secondary stresses in the pin-connected truss bridge are smaller than in the riveted truss
Initial' and the structure is more efficient. (4) With the present ballasted floors the vibration
and impact stresses are no greater in a pin-connected truss bridge than in a riveted truss bridge.
i\< ted tension members are difficult to design and are expensive of material and labor. Eye-
arc ideal tension members in which the material is used efficiently. For the above reasons
author predicts that the pin-connected bridge for spans of 200 ft. and over will regain its
as a standard type of railroad bridge.
The Pratt truss with parallel chords is used for pin-connected spans up to about 250 ft.,
iile riveted truss spans are made with Pratt or Warren trusses; double and triple intersection
isses are also used for riveted trusses. For long span bridges the subdivided Pratt truss with
inclined chords (Petit truss) is generally used. The width center to center of trusses should not
be less than one-twentieth of the span, and preferably not less than one-eighteenth. The height
the center should be from one-fifth to one-seventh of the span; the Municipal Bridge at St.
iris has a center height of one-sixth of the span. The height at the ends should be only sufficient
an effective portal. The most economical inclination of diagonals is very nearly 40 degrees,
that in a Petit truss the panel length should be about 0.42 times the height. For the most
momical web system the panels should vary in length as the depth varies, but this increases
ic weight of the floor and also increases the shop cost and cost of erection, so that constant panel
:ngths are commonly used. One railroad specification requires that panel lengths shall not
exceed 35 feet. For truss bridges of the Pratt type with two stringers and an open timber floor
E-~ present practice is to use a panel length of 22} to 27^ ft., with 25 ft. as an average. Increasing
length of the panels increases the weight of the floor system, and decreases the weight of the
sses. The economical panel lengths for bridges with ballasted floor is less than for bridges with
open timber floor. Riveted truss bridges with triple-intersection web members, Fig. 41, are
made with very short panels.
With the increase in the size of the sections in a bridge great care must be taken in detailing
to use details that will develop the full strength of the members. Increased details increase the
shop cost and for this reason there is a tendency for bridge companies to cut down details and to
change details so as to simplify shop work even at the expense of added weight in order to obtain
a low pound price. For this reason detail drawings, not necessarily shop drawings, should always
be made by the designing engineer. The author has in mind a case where to change the details
a plate girder so that multiple punches might be used required the addition of details equal to
per cent of the weight of the span and the addition of 25 per cent to the number of field rivets,
:h no increase in efficiency. It is needless to say the change was not made.
An empirical rule for calculating the economical depth of plate girder spans is to make the
area of the flanges equal to the area of the webs. The actual depths of plate girders are commonly
slightly less than the depth given by the above rule. The minimum thickness of f inch for plate
girder webs should be used only for stringers with short spans, and the thickness of the web
lould be increased as the span and depth of the girder increases. For the depths and spacing of
.te girders designed undor Common Standard Specifications 1006, see Table I.
DETAILS OF RAILWAY BRIDGES.— It is very important that the details of railway
idges be worked out with great care. A few standard details will be briefly described.
Sections for Chords and Posts. — Chord sections are shown in (a) to (i) in Fig. 22. Sections
and (b) are used for light chords and (c), (d) and (e) for heavy chords. Sections (a) and (d) are
also made by turning the angles in, as in section (i). Sections (f) to (i) are used for chord sections,
for intermediate posts and for columns. Sections (n) and (p) to (t) are used for column sections.
Chord sections, posts and columns with diaphragms or webs at right angles to each other as in
I to (e), (n), and (p) to (t) give much better results under actual service than laced sections as
(f) to (i) and (o). Sections (j) to (m) and (o) are used for struts and braces.
176
STEEL RAILWAY BRIDGES.
CHAP. IV.
Floors. — Bridges may have open timber floors as in Fig. 23, or ballasted floors as in Fig. 24,
or in Fig. 25. For track elevation and for bridges crossing over streets, buildings, and similar
locations and for ballasted floors, the bridge floor is waterproofed and the water falling on the
floor is carried to the ground through properly arranged drains.
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FIG. 22. TYPES OF COLUMNS AND TOP CHORD SECTIONS.
Details of the standard timber floors used by the Southern Pacific R. R., the Union Pacific
R. R. and other Harriman Lines are given in Fig. 23. For additional details of open timber floors
see Fig. I and Fig. 2, Chapter VII. The American Railway Engineering Association in 1912
TIMBER FLOORS.
177
13
178 STEEL. RAILWAY BRIDGES. CHAP. IV.
recommended that guard timbers be used on all open-floor bridges, also that guard rails be used
on all bridges, and that the guard rails should extend at least 50 ft. beyond the end of the bridge.
For additional details see Chapter VII, "Timber Bridges and Trestles."
Details of a ballasted floor with a reinforced concrete slab deck, and a ballasted floor with a
timber deck, as designed and used by the Chicago, Milwaukee & St. Paul Ry. are given in
Fig. 24. The reinforced concrete slabs are made either at the bridge site or at some other con-
venient location and are hoisted into place after the concrete has gained sufficient strength.
The Chicago, Burlington & Quincy R. R. uses reinforced concrete slabs for a ballasted deck
on deck girders that differ from the Chicago, Milwaukee & St. Paul slabs in Fig. 24, in the following
details. The reinforced concrete slabs are 14 ft. long in place of 13 ft.; and are 5 ft. wide in place
of 3 ft. 7 in. The top of the slabs and the edges of the slabs are painted with tar paint (made of
1 6 parts coal tar, 4 parts Portland cement, and 3 parts kerosene). The edges of the reinforced
concrete slabs are beveled and after the slabs are laid the joint between the slabs is packed with
oakum for a depth of I in. at the bottom and the remainder of the joint is filled with I to 3 Portland
cement mortar. Where the reinforced concrete deck, is placed on a deck girder with cover plates,
a strip of No. 22 gage lead 3 in. wider than the cover plate is placed on top of the cover plate and
forced down over the rivet heads. After the slabs have been put in place and blocked up to the
proper elevation the space between the lead sheet and the slab is filled with I to 3 Portland cement
mortar. The minimum thickness of the mortar joint is one'inch. Cinders or slag are not used
for ballast on reinforced concrete slab decks.
A standard reinforced concrete floor for a through plate girder bridge as designed by the
Chicago, Burlington & Quincy R. R. is shown in Fig. 25. The concrete is 1:2:4 Portland
cement concrete. The upper surface of the concrete slab is painted with coal tar paint, the same
as the deck slabs. Zinc sheets, No. 22 gage and 8 in. wide are placed on the tops of the floorbeams.
A steel plate ballasted floor on a through riveted truss bridge is shown in Fig. 41.
WATERPROOFING BRIDGE FLOORS.— The problem of waterproofing bridge floors is a
difficult one and has been worked out in great detail by the engineers of many railroads, and by
the American Railway Engineering Association. For a very full discussion of the problem, see
the proceedings of the American Railway Engineering Association, especially Volume 14, 1913,
and Volume 15, 1914. The following extracts from the report of a committee of the American
Railway Engineering Association presented at the annual meeting of the society in March, 1914,
are of value.
The methods of waterproofing are stated as follows: —
"The ordinary methods of waterproofing are.
" (i) Coatings: (a) Linseed oil paints and varnishes, (b) Bituminous; asphalt and coal tar.
(c) Liquid hydrocarbons, (d) Miscellaneous compounds, (e) Cement mortar.
" (2) Membranes: Felts and burlaps in combination with various cementing compounds.
" (3) Integrals: (a) Inert fillers, (b) Active fillers.
" (4) Watertight concrete construction."
The conclusions reached in the report are as follows: —
" (i) Watertight concrete may be obtained by proper design, reinforcing the concrete against
cracks due to expansion and contraction, using the proper proportions of cement and graded aggre-
gates to secure the filling of the voids and employing proper workmanship and close supervision.
" (2) Membrane waterproofing, of either asphalt or pure coal tar pitch in connection with felts
and burlaps, with proper number of layers, good materials and workmanship and good working
conditions, is recommended as good practice for waterproofing masonry, concrete and bridge floors.
" (3) Permanent drainage of bridge floors is essential to secure good results in waterproofing.
" (4) Integral methods of waterproofing concrete have given good results. Special care is
required to properly proportion the concrete, mix thoroughly and deposit properly so as to have
the void-filling compounds do the required duty; if this is neglected the value of the compound is
lost and its waterproofing effect is destroyed. Careful tests should be made to ascertain the
proper proportions and effectiveness of such compounds. Integral compounds should be used
with caution, ascertaining their chemical action on the concrete as well as their effect on its
strength; as a general rule, integral compounds are not to be recommended, since the same results
as to water-tightness can be obtained by adding a small percentage of cement and properly grading
the aggregate.
STANDARD BALLASTED FLOORS.
f
179
6'-6
'-"
6'-6
""'"
j Track Tie \6"x8"*8'-0'ri
(Handling Rod \
Web Groove • j ' 5tfrrup Bars*
JyJynfa*. f§§t °{L the_ Missouri River _
.. i7'6' for Girders West of the Missouri River „
r^ ~ — — — — — — — — — — — 7— — — — -^— - — — — — — ^^
SECTION OF STANDARD CONCRETE FLOOR
BILL OF MATERIAL FOR *>'-?" SLAB
Ho-
Size
Length
Remarks
I
15
fir a
4
1^0'
farsA"kenfin bottom of sbb
7
3///7
7
ll'-6"
Straight in fop ofsbb-
15
I"D
*>'-3"
Longitudwsf-
8
tiro
?
IOL0*
5tim//>
Z
3 I'O
4
4Y
Handling Rods Uo.
Z
Z"
1-0"
Fibre Pipes, for j//bt/f end $/3b
/•%
((/•Yds- of Concrete
SECTION AT CEHTER OF TRACK
Weight of Floor Section -Concrete •
Ves6"x8"x8¥,I5"ctrs- = I Berlin- ft of track
footfawriy Sfotf
f/0
Z-100
'» rt » tt
» » » »
Weight of one Slab = 3'S6 tons-
Total =5570 per lin- ft- of track
JLQ*- -H
Track Ties \ 6"x8*x8L0" 1 Guard Rail 8**l2"-~\
Z*r ^t^^^^^v^/^/'^^^^^^^1^^'1^'^^'
(4 polt jz^-Q- 6- Washer K.---/-/ on curve or tangent j^
Creosote J Tie
S**JO**J4'-0*
'•* IH 8-0 "for Girders Ea_sr_of_ the_ Missouj _
_ Wjst_of_the_ Missoj/r^River^
~CR~05S~~5ECTION ~
^Lug Washer
Weight of Floor Section- Timber
Track Ties, 15" centers - 115 per lineal foot oF track
15-5 cu- ft- of Gravel @ HO* = 1485* » » M « »
Floor Ties ®4**$'M- = 650* » » » » » TIMBER BALLAST
Guard Rails @4z*0-M' - 70 * » » » » » _
Z- 100* Rails «= 65* » » » » „ FLOOR
Total c Z565* per lineal foot of track
FIG. 24. STANDARD BALLASTED FLOORS. CHICAGO. MILWAUKEE & ST. PAUL RY.
STANDARD
180
STEEL RAILWAY BRIDGES.
CHAP. IV.
"(5) Surface coatings, such as cement mortar, asphalt or bituminous mastic, if properly
applied to masonry reinforced against cracks produced by settlement, expansion and contraction,
may be successfully used for waterproofing arches, abutments, retaining walls, reservoirs and
similar structures; for important work under high pressure of water these cannot be recommended
for all conditions.
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SECT/OHAL ELEVATION
SECTION S-B
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DETAIL OF APRON PLATE
Materials:- 6501m. ft- N? tf Sheet Zinc , 8\
135 Gal/on s Tar Paint-
Port/and Cement Concrete, /•'?•' 4 •
REIHFORCED COHCRETE FLOOR
FOR THROUGH
C'5-SQ'R-R
SECTIONAL PLAN A- A-
FIG. 25. REINFORCED CONCRETE FLOOR FOR THROUGH PLATE GIRDER BRIDGE.
C. B. & Q. R. R.
"(6) Surface brush coatings, such as oil paints and varnishes, are not considered reliable or
lasting for waterproofing of masonry."
The membrane method of waterproofing bridge floors will be shown by describing the standard
methods of waterproofing in use by two railroads.
CHICAGO, MILWAUKEE & ST. PAUL RY. SPECIFICATIONS FOR WATERPROOFING.
The specifications of the Chicago, Milwaukee & St. Paul Ry. for waterproofing are as follows-.
The necessary provision for drainage and expansion must be made in designing the structure.
The waterproofing should never be compelled to resist hydrostatic pressure, and the membrane
should always be protected by a layer of concrete.
(1) Preliminary. — Fill all openings and pockets in the concrete except expansion joints
with cement mortar, and round off all sharp corners. Wherever waterproofing stops on a vertical
surface the end should be flashed into a groove in the concrete.
(2) Preparing the Surface. — Thoroughly clean and dry the concrete surface using wire
brushes and being careful to remove all the laitance. If necessary use hot sand to dry the con-
crete. Apply a coat of gasolene to the clean dry surface and follow with a coat of cold primer,
spreading the primer evenly with a brush. Omit the primer where tar paper is to be placed and
over expansion joints.
(3) Laying the Burlap. — After the primer coat has completely dried, apply a coat of pure
hot asphalt, and mop until the layer has a thickness of | in. While the asphalt is still hot begin
laying the burlap. Lay the first strip of burlap transverse to the drainage at the lowest point.
Lay the strips shingle fashion, as for tar and gravel roofs, and parallel to the first strip working
WATERPROOFING BRIDGE FLOORS. 181
I to the summit and exposing one-third of each width of burlap to the weather. Press each
ip firmly into the asphalt, then mop well with pure melted asphalt taking care to thoroughly
unite the burlap and to fill all cracks and blow holes. Lap the joints in the strips 6 in. On
this three-ply layer of burlap spread a continuous layer of hot asphalt mopping well until a layer
of I in. is obtained. See (f) Fig. 26.
(4) Summit Joints. — After the work has been brought up to the desired point from both
sides interl.ip in order the strips which reach across the joint, mopping asphalt between burlap
surfaces. Place a strip of burlap along the joint for a closing strip; and complete by laying the
UPJKT i in. of asphalt as before described. See (g) Fig. 26.
(5) Longitudinal Joints. — If possible the waterproofing should be laid in one run the full
idth transverse to the drain slope of the surface to be waterproofed. The ends of the burlap
rips should be (lashed into recesses in the walls, curbs or parapets as shown in (e) Fig. 26. Where
ngitudinal joints are necessary cut the burlap long enough to extend 12 in. beyond the primed
id asphalted surface of the concrete and use care as the strips are laid that the 12 in. strip is
pt free from asphalt. When the succeeding section is to be waterproofed fold back the projecting
rips of burlap over the completed waterproofing and bring the new up against the completed
portion of the waterproofing, interlapping the projecting ends of the burlap with the new burlap
as the work progresses, (f) Fig. 26. On concrete trestle or subway slabs longitudinal joints in
the waterproofing should preferably be on the center line of the slabs. If it is necessary to place
joints in the waterproofing over joints in the slabs special care should be taken.
(6) Expansion Joints. — Lay two continuous strips of tar paper 36 in. wide over the expansion
joint, being careful to see that no asphalt gets between or under the two strips of tar paper. Then
mop the top strip with hot asphalt and carry the waterproofing over the top of the paper the
same as if no joint existed. See (b) and (h) Fig. 26.
(7) Concrete Protection. — After the i in. layer of asphalt on top of the burlap has become
cold, spread a f in. layer of concrete evenly over the surface. Then press a layer of expanded
metal into the concrete, and cover the metal with a layer of concrete i in. thick making the total
thickness of the concrete I J in., and trowel the concrete smooth. Protect the concrete from the
sun for 24 hours after laying. The joints in the expanded metal should be lapped 6 in. See (d)
. 26.
(8) Materials. — Burlap. — The burlap is to be treated 8 oz. open mesh furnished in widths
36 in. to 42 in.
Concrete. — The concrete is to be I part Portland cement, 2 parts torpedo sand, and 3 parts
>ne or gravel that will pass a i in. ring.
Mortar. — The mortar is to be I part Portland cement and 2 parts washed torpedo sand.
Primer. — The primer is made by pouring hot asphalt in 80 per cent gasolene until mixture
will spread readily with a brush.
Asphalt. — Pure asphalt conforming to accepted specifications is to be used. Before using
the asphalt heat it in a suitable kettle to a temperature not exceeding 450° F. The temperature
is to be taken with a thermometer. Asphalt heated above 450 degrees F. or giving off yellow
fumes is to be discarded as overheated.
Expanded Metal. — The expanded metal is to be equivalent to Northwestern Expanded
Metal Go's. "2j in. No. 16 Regular" expanded metal.
Tar Paper. — The tar paper will be furnished in rolls 36 in. wide.
CHICAGO, BURLINGTON & QUINCY R. R. SPECIFICATIONS FOR WATERPROOF-
ING.— The specifications of the Chicago, Burlington&Quincy R. R. for waterproofing are as follows:
(1) Description. — The waterproofing shall consist of a mat of 4-ply of burlap and i-ply of
felt thoroughly saturated and bonded together with waterproofing asphalt and covered with one
inch of sand and asphalt mastic.
(2) Preparing the Surface. — The surface of the concrete shall be smooth, clean and dry.
Upon this surface apply a coat of primer, which shall be thin enough to penetrate the concrete
and form an anchorage for the waterproofing. No waterproofing shall be done when the temperature
is less than 60 degrees F.
(3) Applying the Burlap. — After the priming coat has dried, a heavy coat of waterproofing
asphalt heated to a temperature of 400 degrees F. shall be applied with mops the width of the
burlap, and while the asphalt is still hot a layer of burlap shall be bedded in it. The burlap
shall be laid just behind the mopping and shall be swept free from folds and pockets with a broom.
The surface of the burlap shall be heavily mopped with waterproofing asphalt. Three more ply
of burlap shall be laid in the same manner, making a 4-ply burlap mat all thoroughly saturated
and bonded together.
The top of the burlap mat shall be heavily mopped with asphalt and one layer of felt saturated
with asphalt shall be laid on the burlap and the edges of the felt lapped at least 3 inches and sealed
f'i asphalt. The top of this felt shall also be mopped with waterproofing asphalt.
(4) Mastic Protection. — The burlap and felt mat shall be covered with one inch of asphalt
tic laid in one layer, the mastic to be composed of one part waterproofing asphalt and four
182
STEEL RAILWAY BRIDGES.
CHAP. IV.
parts fine gravel graded from £ in. to fine sand. The top of the mastic shall be leveled off with
wooden floats and mopped with waterproofing asphalt.
(5) Expansion Joints. — At all expansion joints in the concrete a fold to allow for the ex-
pansion of the structure shall be formed by laying the burlap and felt over a one-inch pipe; the
pipe being removed as the mat is being completed.
(6) Splices and Flashing. — Where the work is stopped before being completed at least 3 feet
of burlap at the end and one-half the width of the burlap at the side shall be left exposed to form a
splice.
Special care shall be taken to seal the waterproofing at the sides and ends of the bridge. The
burlap and mastic shall be carried up the parapet walls at the sides and the ends of the burlap
shall be concreted into a recess in the walls so that no water can enter. The burlap shall be
carried down over the back-walls at the ends of the bridge to cover all construction joints and
shall run into a line of tile to facilitate the escape of the water.
(7) Materials. — Burlap. — The burlap is to be 8 oz. open mesh high grade burlap saturated
with an asphalt meeting the specifications for waterproofing asphalt. It shall come in rolls
which shall be placed on end for shipment and storage, and shall not stick together in the roll.
Felt. — The felt shall be a good quality of wool felt saturated and coated with an asphalt
meeting the specifications for waterproofing asphalt. It shall come in rolls which shall be placed
on end for shipment and storage, and shall not stick together in the roll. It shall not weigh less
than 15 Ib. per 100 sq. ft.
Primer. — The primer shall be an asphaltic compound of approved quality and capable of
adhering firmly to the concrete.
Waterproofing Asphalt.— The waterproofing asphalt shall meet the following requirements.
1. The specific gravity of the asphalt desired shall be greater than 0.95 at 77 degrees F.
2. The flowing point shall not be less than 100 degrees F. nor more than 140 degrees F.
3. The flash point shall not be lower than 450 degrees F.
Broken
Stone
Filling \
Abutment
**~~Drain Tile
Mortar-'' Corners of Slab \
(b) SECTION OF EXPANSION JOINT AT
OFFSET IN WATERPROOFING SURFACE
Concretet\ Expanded Mefak 3 Layers ef Burlap.
* ~-U • • • * ..... i t i . i . L . . . J
Woun</i>ff Corners
\Round off Slope-' W'— Mortar \
| D J
(c) SECTION OF FIXED JOINT AT OFFSET
IN WATERPROOFING SURFACE-
Surface of Waterproofing to
conform to surface of Hase--^ \
^- Groove
Asphalt'' fe) TRANSVERSE SECTION OF SLAB-
3 Layers of Burhp-~^
3 Layers of Burlap — '
i \
1 !
II "-Burlap
J| j j / Layers or\\ Tar Papery (
(f) LONGITUDINAL SECTION OF WATERPROOFING (g) DETAIL OF SUMMIT (h) SECTION OF EXPANSION JOINT
FIG. 26. STANDARD METHOD OF WATERPROOFING BRIDGE FLOORS. C. M. & ST. P. RY.
4. The penetration at 80 degrees F. for a period of 30 seconds shall be at least 15 millimeters
and must not exceed 20 millimeters. This penetration to be measured with a Vicat needle weighing
300 grams, one end being one millimeter in diameter for a distance of 6 centimeters.
5. When heated to a temperature of 325 degrees F. for 7 hours the loss in weight shall not
exceed 2 per cent and the penetration of the residue at 80 degrees F. and for the period of 30
seconds using the same instrument as described above shall not be reduced more than 50 per cent.
6. The total soluble in carbon bisulphide shall not be less than 99 per cent.
7. The total soluble in 88 degree naptha shall not be less than 70 per cent.
8. The total inorganic matter or ash shall not exceed one per cent.
9. Cold Test.
a. A cube of the asphalt one inch on edge shall be soft and malleable at a temperature of
zero degrees F.
DETAILS OF FLOORBEAMS.
183
— j
-
184
STEEL RAILWAY BRIDGES.
CHAP. IV.
b. A film of the asphalt having a thickness not less than •& inch shall be so pliable at zero
degrees F. that it can be bent in a radius of 2 inches. The total time consumed in the bending
of this film shall not exceed 3 seconds.
10. The asphalt shall not be affected by any of the following solutions, after being immersed
in them for a period of 3 days: — (a) a 25 per cent solution of sulphuric acid; (b) a 25 per cent
solution of hydrochloric acid; (c) a 20 per cent solution of ammonia.
FLOORBEAM CONNECTIONS.— The details of floorbeam connections depend upon the
clearance, depth of truss, length of panels and type of floor. A standard type of floorbeam con-
nection for a pin-connected truss of 150 ft. span is shown in Fig. 28, and details of the lower lateral
connection are shown in Fig. 27. Details of a floorbeam connection for a pin-connected truss with
"
f^^^&6±m*fa§!
IHTERMEDIATE FLOOR BEAM
FIG. 29. INTERMEDIATE FLOORBEAM CONNECTION. A. T. & S. F. RY.
four stringers is shown in Fig. 29. Details of a floorbeam for a riveted truss bridge are shown in
Fig. 40. Details of an end floorbeam are shown in Fig. 40. Details of the standard end floorbeam
of the A. T. & S. F. Ry. are shown in Fig. 30. The end floorbeam in Fig. 30 is supported directly
on the end pin, and gives a very satisfactory solution of a difficult problem and requires the driving
of a minimum number of field rivets.
PEDESTALS AND SHOES. — Details of standard cast steel pedestals and shoes as designed
by the Chicago, Milwaukee & St. Paul Ry. are shown in Fig. 31, Fig. 33, and Fig. 34. Details
of segmental rollers are shown in Fig. 32, and Fig. 35. Details of expansion bearings for plate
girders are shown in Fig. 36, and Fig. 37. Details of a built-up end shoe with circular rollers
are shown in Fig. 40. Details of a built-up end shoe and segmental rollers are shown in Fig. 41.
EXAMPLES OF PLATE GIRDERS. — Details of an 8s-ft. span single track deck railway
plate girder bridge as designed for the Kansas City, Mexico & Orient R. R., by Mr. Ira G.
Hedrick, Consulting Engineer, are shown in Fig. 36. The upper flanges are made of four angles
EXAMPLES OF TRUSS BRIDGES.
185
without cover plates, so that the ties may be of uniform thickness and there will be no rivet heads
to iiiUTlVrv with placing the ties. The lower flanges arc made of angles with cover plates. These
plans represent the most modern practice in the design of deck plate girder railway bridges.
^*i **d u^
4a $ "JB
L° EHD FLOOR BEAM
lP~l^$< : 5
tfX P + »WA7'TJ* 12 ?!
|:| tji*^!&£ij*j |
FLOOR teAH STRUT
END FLOOR BEAM
FIG. 30. END FLOORBEAM CONNECTION. A. T. & S. F. RY.
Details of a 6o-ft. span single track through railway plate girder bridge as designed for the
larriman Lines are shown in Fig. 37. The details of the bearings are shown. Rollers are used
ar the expansion ends of spans of 75 ft. and over. Data on standard plate girder bridges designed
ider Common Standard Specifications 1006 are given in Table I.
EXAMPLES OF TRUSS BRIDGES.— The marking diagram for a truss railway bridge is
down in Fig. 38. The lower chord joints are marked Lo, L\, Lt, etc., while the upper chord
)ints are marked Ui, Uz, etc. In detailing a truss an inside view of the left end of the farther
iss is shown; this is marked right as shown. Details of a single track through riveted truss
186
STEEL RAILWAY BRIDGES.
3
CHAP. IV.
Finish"^
Material -Cast Iron.
TYPICAL FIXED IA/D PEDESTAL
Fo£ TWJSES M TO/50 FT. SP/M
'a f~ Cast Iron.
'ED£ND PED,
FOB Tj?US5E5/50T0200FlSPAN
FIG. 31. PEDESTALS. CHICAGO, MILWAUKEE & ST. PAUL RY.
m-^
i 7 / " i / */ /
^_ ^l Jt A. A- A
1 1 -/? J
rlateriaf-Cdst Steef.
TmcffL £oaE£ BED DETAILS
FIG. 32. ROLLERS. CHICAGO, MILWAUKEE & ST. PAUL RY.
TwtCBL END POLLEZ DETAILS
Intermedf'ate Coffers are same except
that Spurs are omitted and ends are
6eve/ed on corners.
SHOE DETAILS.
187
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FIG. 33. SHOE DETAILS. CHICAGO, MILWAUKEE & ST. PAUL RY.
T
T \ Ifr iP
rP=Dfam.Pin
HALF VIEW
x^
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'&CorectHo/ey\ ^ ^
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II
TW/CGL r/XED SHOE DETAILS
FIG. 34. SHOE DETAILS. CHICAGO, MILWAUKEE & ST. PAUL RY.
•^
kj
1
il
I
188
STEEL RAILWAY BRIDGES.
CHAP. IV.
bridge designed for the Kansas City, Mexico & Orient R. R., by Mr. Ira G. Hedrick, Consulting
Engineer, are shown in Fig. 39 and Fig. 40. The end-posts and top chords are made of two 15
inch channels with a cover plate, and the lower chords, the posts and the main ties are made of
two channels with the flanges turned in. The total weight of the steel in the span was 303,000 Ib.
•g
CIV.
^ [f
M-
, irfl
:.TD | |
; IB
cr::
>K
&>vj"
v v
13
cir:
For End Rollers
ff*3f fo/tf dr/vint/ Fit
/"Elastic Lock Nut.
/z>r Infaatdiaft Rollers
&'*&* Turned Pin,
driving Fit, with
ROLLER NE5T shoulder <?5 shown-
FIG. 35. DETAILS OF SEGMENTAL ROLLERS FOR GIRDERS.
CHICAGO, MILWAUKEE & ST. PAUL RY.
Details of a double track through riveted truss bridge designed for the Chicago & North-
western Ry. are given in Fig. 41. The bridge has a span of 170 ft., the trusses are spaced 29 ft.
I in. centers, and the bridge has a vertical clearance of 22 ft. 6 in. This bridge has trusses with
triple intersection webs, and has a ballasted track carried on a steel plate trough floor. This
bridge was designed for a dead load of 4,570 Ib. per lineal foot for each truss and an E 50 live load.
There is a top lateral system of multiple X-bracing made with pairs of angles latticed, and sway
bracing of transverse top chord struts and portals.
Detail shop drawings of the end-post of a pin-connected truss bridge are given in Fig. 42, and
the detail shop drawings of the end section of the top chord of the same bridge are given in Fig. 43.
The standard methods of detailing compression members are shown.
Details of a single track pin-connected truss bridge designed by Mr. Ralph Modjeski for the
Northern Pacific R. R. are given in Fig. 44, Fig. 45 and Fig. 46.
SPECIFICATIONS FOR RAILWAY BRIDGES.— To determine the present practice in
the design of railway bridges the author has made a study of the latest available specifications.
As a basis for comparison the sixteen specifications given in Table XI, were selected as being
representative of the best practice. Several other prominent railroads have adopted the speci-
fications of the American Railway Engineering Association, so that the sixteen specifications cover
the major part of the railroad mileage in North America. The standard specifications of the
Chicago, Milwaukee and St. Paul Ry., the New York, New Haven and Hartford R. R., and
the Canadian Society of Civil Engineers, all adopted in 1912, are based on the standard speci-
DECK PLATE GIRDER BRIDGE.
189
190
STEEL RAILWAY BRIDGES.
CHAP. IV.
5» ,TS 3* .y % s
te»|5hS
J? Vfi^ ^S . . J* V> ^
MARKING DIAGRAM FOR TRUSS BRIDGES.
191
1
2
£3
as
3
~
192
STEEL RAILWAY BRIDGES.
CHAP. IV.
THROUGH RIVETED TRUSS BRIDGE.
193
-?-/-. — -i-J ^» ^^
TF1*~1 — rr'7 ». T~iTt*Z. "> ?'~VS
wfeU ii [Km
194
STEEL RAILWAY BRIDGES.
CHAP. IV.
PartSeciional Elevation
through End Pin
a Girder?"
Floor Plan
Section of Floor
(BortomGhoni t Section^perTrough
V |ii'a'.i I/*'*- SWtbP/s/di'xi'
l:.'3v :. *;'.:! 2CwPt*iit*S
t:.'5«.' :.•*•.:! 0^—0^ ,/^j' .
Brunei Point Trcx/ghs
Section perTrough Section D-D
ZWebP/s /ai'xj^
.DajtaTffotl
•ITJs'xl'Pi
Section E-E Intermeiote Trough
• IS'Si'--
Lon^itudmol Floor Section
FIG. 41. CHICAGO & NORTHWESTERN RAILWAY BRIDGE.
DRAWINGS OF END-POST.
firh-j-__^L._i-_
195
2
H
o
u
•*
d
196
STEEL RAILWAY BRIDGES.
CHAP. IV.
1
^
3T
^
so
I
^ ^
v?^ ^J
Ox X
1$ £ ^
^ .| v
^ d? %'tt;
v^-^^&^
^f$; ' i^^o
^i t^llijli
,^i ^ |^^^.
qjjl
L;^
^
>
/
o
X
u
I
Th
6
-rf.,,-.- . —
p-
198
STEEL RAILWAY BRIDGES.
CHAP. IV.
V5i
<M
01
^>!
*!
"ih.es
T*-sT
^J*
vV>^
?!
W&6**&
2 Fillers 6"*
2L*6*4"x§"
Jj>jJ_c;fo_c-^ oF^Trusses^
SI
IRe!nForcingPI-45xj'
this side
-H-
I
}$£ i ?$pKcttyt&'*}*
i it ' 2 IP 3~7 x3? * "g * shear
* •?>" *' n" > *' n" <
• 4_-2>?_ i 4-0 : 4^0_ '
>7/4Z^ IHTBMED1ATE SECT/ON
[git
Nofe:- 6"f6 turned bolfs af top of each
Stringer connect/on-
fffJs of f/o<?r beams to be Faced-
z"5faf?c/3rd F/oor Bo/fs, one fo every
spf/'ce in guard timber-
's 5fc/-H0oA, one every third fie, fo
each stringer-
•i *lO*-Boat Spikes, one to every fie
except af gi/ffrcF f imber splic
Cooper's £-50
HALF END ELEVATION
Rivets to be j diameter-
.NORTHERN PACIFIC RY-
STANDARD PLAN
I 50 FT- THROUGH SPAN .
KALPH MODJESKI,
FIG. 45. SINGLE TRACK THROUGH PIN-CONNECTED RAILWAY BRIDGE.
SINGLE TRACK THROUGH PIN-CONNECTED BRIDGE.
WWff
JMIMMMM*
DOUBLE FIXED END
1ft!)
-Face*'
ifff * *" *" ""•*'*" ff
Note:- 6--J6 turned bolts at top of each stringer connection-
"Washer
5TKitf6£R BRACKET
f?
t-% Turned Bolts Req'tf-
STRINGERS
EXPAHSIOH EHD
BILL OF TRACK MATERIAL
FOR ONF5PAN
Material
N2
Rtfi
Size
Length
Mark
Cross Ties
///
9"* If"
I?L0"
6uard Timber
//
6*8*
20-0"
St</-Flftrgo/t
16
ff"
lW
B-K
HookBo/ff
8S
|V/>.
M"
C-V.
Boatfyikes
///
i'fo-
O-JO"
Cooper 's E~50 L oadfng •
Note:- Holes to be punched with % Jia/nefer
die, and reamed fojj diameter aFter assembling-
Rivefs to be £ "diamefer-
Totaf weight oF one span including track,
toffs and bearings =3/5,490 Ibs-
HORTHERH PACIFIC Ry.
STANDARD PLAN
150 FT- THROUGH SPAN •
#ALPH MODJESKI, Etf&NfER-
FIG. 46. SINGLE TRACK THROUGH PIN-CONNECTED RAILWAY BRIDGE.
200
STEEL RAILWAY BRIDGES.
CHAP. IV.
fications of the American Railway Engineering Association; the specifications in each case differing
from the specifications of the American Railway Engineering Association only in requirements
for clearances, and in minor clauses, and clauses required to cover individual practice, and local
conditions of the individual roads.
TABLE XL
RAILWAY BKIDGE CLEARANCES
Specification
a
3'
h
c
<J
e
e'
f
f
';~r
vj
/•Americ3n Ry- Eng-Assoc-, 1910
rto"
14-0"
6L0"
JO-6"
12-0"
40"
?-AT&S-F-Ry-5ystem, 1902
?&*
I4L0"
7-0"
IOL.0"
J9-0"
40'
3- Baltimore & 'Ohio, 1904
22-0"
140'
6'-0"
IOW
WO"
40"
4-fiosfonfi Maine (In CdnsJa), 191?
tf'O"
100"
s-r
ti'-O"
19-0"
4-0"
S-Chi-Mil-SSt-P-R-R; I9IZ
rt-o"
I510"
7L0"
/l-O"
19-0"
?-6"
6- Chi- Rock Islsnd&PacW, 1906
r#f
00"
7*0"
f/Y
IS'-6"
40"
!A
Ifiij —
oFfoil
" ^T
yU 1
^_-J^<?5(?
of Rail
7- Common Standard, 1909
24L0"
15-0"
6-0"
l/^O"
19-0"
4-0"
$• Cooper, 1906
21-0"
140"
tf-0"
2-0"
9-JIIinois Central, J9/J
tf-'O"
I6W
S'O"
1/!0"
IS'O"
40"
10- fan-City, Mexico & Orient, 1907
rto"
I5L0"
W
IW
/9-0"
46"
Il-Lehigh Valley, 1911
2?-'o"
140*
^o"
11-0"
IM"
4^0"
For Double Track
12- Hew York Central 1910
tf-'O"
15-0"
S'O"
I/'O"
15-0"
4-0"
add d/sfartce c-to c-
!3-NewYorl(,Neir Haven & Hart ford,
(In Canada) 1912
220"
IM"
W'
M"
ItW
4*0"
oF tracks fo above
Figures 4 c, <?/?</</•
ttreimd-LineslfostoF Pittsburgh,^
?/J6"
MO"
6L0"
/M"
IM"
4-0"
15- National Lines of Mexico, 1907
tf-'O"
15-0"
6!0"
I/'O"
ISL0"
4-0"
16- Cansdian Society fivi/fngi/ietrs, 1312
??-6"
I6'-0"
7-0"
10V
//-r
3'-3>"
3
F Car-±
tS\\\\\\\
\
\
\
^— — -- -^
\
XXXXXXXXXXXXXXXXXNNXXXXX^XNXNXXXNXXXX^
t gJ^^—^^A
,^^ .-«4 $5~~~ f_~ T' ~=-"r^^T7^N
"jT jC'ic " s
~---3
SfelM
-TT:I
~~'^K
\\\\\\\\i
^ 4. ^/^/vi^^^vxxvvvvwvxvvvxvvivw^vvv^^
- _J
,_.— ~-
<j!
* zzzzzzzszzzzzzzzz
"" • —
(""•
\
& = Distance c- to c- of Trucks J
\
A- Total Lenafh of Car
-^ ^! ^i
i| s:|M ^ ] .
* ^i
_.i.Ti...i
FIG. 47. CLEARANCE DIAGRAM.
The present practice is to use the specifications of the American Railway Engineering Associ-
ation as a basis for specifications and to add such additional clauses as may be necessary to cover
.the practice of the individual railroad. Several railroads have adopted the specifications of the
American Railway Engineering Association and issue supplementary instructions to cover their
individual practice; see standards of Chicago, Milwaukee & St. Paul Ry. which follow the
A. R. E. A. specifications in this chapter. The specifications of the American Railway Engineering
COMPARISON OF RAILWAY BRIDGE SPECIFICATIONS.
201
Association are reprinted in the last part of this chapter. To show the present practice in the
• if railway bridges as given in the sixteen different specifications the most important vari-
ations from the American Railway Engineering Association Specifications will be briefly discussed.
Tin- sections in the specifications of the American Railway Engineering Association will be referred
to by mi'iilier.
§2. Clearances. — The clearances for through single track bridges on tangent are given in
Table XI. The clearances on curves differ considerably. Standard formulas for calculating
bridge clearances on curves are as follows:
AI'D
Formulas: —
A* t t^
a= - (nearly)
«= .00002181 jA* -D
b = .00002 1817 5s -D
c = .00002 1 81 7 L*'D
s = - X h = o.2e-h (c. to c. rails
0
«= 5 ft. nearly)
Nomenclature, Fig. 47: —
D = degree of curve
R = radius of curve, in feet
w = clearance width on tangent
a = mid-ordinate to chord of length A
b = mid-ordinate to chord of length B
c = mid-ordinate to chord of length L
e — amount of superelevation in feet which is
taken up in floor of span
h — height of car or distance from top of upper
flange or chord, whichever is least G = \- a — b -\ —
s = additional clearance required on account 2
of superelevation jf = H!_i_j_L-£.-i-5
G = outside clearance from center line of bridge 2 2
H = inside clearance from center line of bridge For Standard Car
A = 8o'-o" B = 6o'-o"
a = o.i 3961*
b = .07854!)
Mp
G = — h (.06109 + -ooooi 0909 U}D
H = 1- (.07854 + .OOOOIOQOQL*)D
2
+ 0.26 -h
The following specifications indicate the present practice of several railroads.
New York Central Lines. — Single-track through bridges on curves shall have the location of
trusses or girders and the width between clearance lines as shown in Figs. 48 and 49.
CLEARANCE
ClfAMHCE Line-
CENTER LM/_ ±QF_T#ACK
1CT
">£"
CLEAKAHCE xf LIHE -«
FIG. 48.
L_EH6TH_ OF 5PAH_
FIG. 49.
lateral clearance from center line of track required by. clearance diagram for tangent aline-
ment.
middle ordinate of curve for a chord equal to span length.
X = addition for overhang of a car 85 ft. long, with trucks 60 ft. c. to c. ; to be taken as one inch
for each degree of curve.
Y = addition in inches (on the inside of the curve only) on account of the superelevation of the
outer rail, to be taken as follows:
For heights from 15 ft. to 22 ft. above the top of rail; Y = 3 inches per inch of superelevation.
For heights from 3 ft. 9 in. to 15 ft. above top of rail; Y = s-h/5 (to use with W = 7 ft.
6 in.).
For heights from top of rail to 3 ft. 9 in. above; Y = s(h + l-5)/4.
s = superelevation in inches.
h = height above top of rail in feet.
202
STEEL RAILWAY BRIDGES.
CHAP. IV.
Cooper's Specifications. — The additional clearance for curves is to be as follows: 0.85.0
= inches on each side; 1.70!) = inches between track; where D = degree of curve.
N. Y., N.H. & H. R. R. — The additional clearances on curves will be as follows: i.oo X D
= inches on each side; 1.75.0 = inches between tracks, where D = degree of curve.
Types of Bridges. — The present practice is to use plate girders for spans up to no or 120 ft.,
riveted trusses for spans of from 100 to 200 or 250 ft., and pin-connected trusses for spans of
about 200 ft. and upwards. Riveted truss bridges of 300 and 400 ft. span are not uncommon.
The types of bridges and minimum lengths of span as given in twelve specifications are given in
Table XII.
TABLE XII.
TYPES OF BRIMES AHD LENGTHS OF SPAH-
Specification
Rolled
Beams
. Ft-
Plate
Girders
Ft-
Riveted
Trusses
Ft-'
PinConnecfed
Trusses
Ft-
2- A-T$5-F-Ry System, 1902
26toS4
26 to 106
I06tol50
150 and up
6- Baltimore & Ohio, 1904
30
30 to I/O
WO to 150
I50andup
6- Chi',Rock Island £Pac-M',/906
19
19 to 110
I00to200
200andup
7- Common Standard, 1909
19
19 to 100
100 to 150
150 and up
8- Cooper, 1906
20
20tol20
I20tol50
I50and up
9 -Illinois Central, 191 f
21
21 to 100
IOOtff/50
150 and up
10- Kansas City, Mexico ^Orient, 1907
20
20to/00
W0to250
250and up
II- Lehigh Valley, 1911
25
25tol/0
110 to 160
I60andup
12- New York Central, 1910
25
25tollO
I/O to 180
180 and up
14'Pems- Lines WestoFPiftsl>tirgh,l906
tolOO
I00to250
250andup
15- National 'Lines oF Hex/co,l907
30
25 to SO
SOtolBO
150 and up
17 Department of Railways oF Canada,!^
IS
18 to 100
100to200
200 to 600
§3. Spacing of Trusses. — The present practice is not to put requirements for spacing of
trusses, lengths of span, types of bridge, etc., in the specifications but to prepare office standards
for the use of engineers and draftsmen. Data on spacing stringers, girders and trusses are given
in Table XIII. The spacings for Illinois Central R. R. deck girders are given in Figs, n, 12 and
13, and of Common Standard Bridges in Table I.
The Chicago, Milwaukee and St. Paul Ry. spaces girders 7 ft. 6 in. west of the Missouri
River, and 8 ft. east of the Missouri River. The Northern Pacific R. R. spaces stringers 8 ft.
for spans of 150 to 200 ft. ; and deck girders 8 ft. for 80 ft. spans.
§5. Ties. — The present practice is to calculate the size of stringers for the specified fiber
stress. Fifteen specifications require that the wheel load be considered as carried by three ties,
and one specification by four ties. Data on ties are given in Table XIV.
The Illinois Central R. R. uses ties on deck girders as follows:
Deck Spans.
Distance Centers.
Ties.
60 ft. and under
60 ft. to 80 ft.
80 ft. to ico ft.
ICO ft. tO IIO ft.
7ft.
8ft.
9ft.
9lft.
8 in. X 8 in. X 10 ft.
8 in. X 10 in. X 12 ft.
10 in. X 10 in. X 12 ft.
IO in. X 12 in. X 12 ft.
Dead Loads. — Data on dead loads are given in Table XV.
COMPARISON OF RAILWAY BRIDGE SPECIFICATIONS.
208
TABLE XIII.
SPACING OF GIRDERS AND TRUSSES
Specification
6ir<Jers
Trusses
Stringers
Deck Girders
Deck
Through
/•American Py Eng-Assoc-, 1910
Span/tO
Span/W
Span/ZO
$• Baltimore & Ohio 1904-
M'
not less than 6-'6"
not less than I0!0"
Span/W
6-Ctiic3go,Itocklsl3rrJ&kc-g-J?;1906
7-'0"
up to 60 Ft; 7W
MFtto80Ft;8-'0"
Span/ZO
7 Common Standard, I9Q9
7-'0"
up to 60 Ft-, 7-0"
60 ft- to 80 Ft, 8-0"
M ft to 100 Ft, Mf
100Ft-tollOFt,10-V
l/OFHotiOFf;l?-V
l50ft-toI50Ft;!4!0"
S- Cooper, 1906
M"
not less than &6'
9- Illinois Centra! 1911
4stri),gers
i>pacedZ-6"
upto60Ft;7-'0"
60'Ftto80Ft;8'0"
SOFttolOOFt; 9-0"
100 ft to 110 Ft, 9-6"
100 Ft-tollOFt; 10^0"
llOFt-toI50ft;/£'0"
l$Oftfo]50ft;l4J0'
IO-KansCify,Mexico& Orient, 1907
7-'0"
uptoSOft-J-'O"
overSOFf-,^0"
Span/ZO
ll'Lthfgff M/ey, 1911
W
vp to 75 Ft; 6-'6"
fefrto/MhjW
lOOFttolttftJ'MO
tf-New York Central, 1910
e-'f
up to 75 Ft-, 6-6" n
over 75 ft-, 7-6"
Span/15
M-Pema-LinesWesfofftttshrgfrjm
&",
for 4 stringers
, . 7 /nil
outer pair 7-0 ,
• Z'A"
innerpa/r^O
6'-6"
17- Department if Railways of Canada,/ 908
s-'o"
Single Track, S-'O"
Double Track, 6' 6'
iWor^Span-
Span/rO
§7. Live Loads. — Data for live loads are given in Table XVI. The type of engine is given
in the second column and the weight in thousands of pounds of a single engine without tender
is given in the third column; the special loadings and the spacing of the loads are given in the
fourth and fifth columns; the impact formulas are given in the sixth column; the allowable tensile
stresses are given in the seventh column, and the equivalent loading is given in the last column.
The equivalent loading is found by multiplying the loading in the second column by 16,000 and
dividing by the allowable tensile strength. The present standard loading on trunk lines is Cooper's
E 60 loading.
The C. M. & St. P. Ry. uses E 60 followed by a train load of 7,000 Ib. per lineal foot of track
on ore roads; while the Duluth & Iron Range R. R. uses E 60 followed by a train load of 8,000 Ib.
per lineal foot of track.
In a paper entitled "Rolling Loads on Bridges" published in Bulletin No. 161, Am. Ry.
Eng. Assoc., November 1913, Mr. J. E. Greiner, Consulting Engineer, has tabulated the live
loads of 39 railroads, including all but one of the roads in Table XVI. Of the 39 roads thirteen
are building bridges equal to E 60; four equal to E 57; seven equal to E 55; one equal to E 53;
ten equal to E 50; two equal to E 47; one equal to E 45, and one equal to E 65.
Of the 39 roads considered 26 roads use the impact formula of the Am. Ry. Eng. Assoc.;
and 24 roads use a tensile stress of 16,000 Ib. per sq. in. The highest tensile stress is 18,000 Ib.
204
STEEL RAILWAY BRIDGES.
CHAP. IV.
TABLE XIV.
DATA ON TIES ON BRIDGES.
Specifications.
Minimum Size and Spacing of Ties.
Data for Design.
Size.
Length.
Maximum Spacing.
Fiber Stress, Lb .
per Sq. In.
Impact,
Per Cent.
' i Am Ry. Eng. Assoc.
IO ft.
12 ft.
9ft.
10 ft.
10 ft.
6 in.
12 in. centers
6 in.
6 in.
6 in.
2,OOO
1,400
I,OOO
2,OOO
2,OOO
100
none
none
IOO
IOO
2. A. T. &St. F. R. R..
3 B. & O. R. R
8 in. X 8 in.
8 in. X 8 in.
4 B. & M. R. R
5 C M. & St. P. Ry. . .
6 C R I. & P. R. R.
7. Common Standard ...
8 Cooper
8 in. X 10 in.
4 in.
I,OOO
I,5OO
2,OOO
none
none
IOO
9. Illinois Central R. R.
10. K. C., M. & O. R. R.
ii. L. V. R. R
("6" X 8" flat
-< Four lines of
( stringers)
8 in. X 10 in.
10 ft.
10 ft.
13 in. centers
on edge
6 in.
12 N. Y. Central Lines .
13. N. Y., N. H. & H.
R. R
10 ft.
6 in.
2,OOO
IOO
14. Penna. W. of Pitts-
burgh
15. Nat. L. of Mexico . . .
4 in.
1,000
1,800
none
IOO
16. Can. Soc. C. E
TABLE XV.
DATA ON DEAD LOADS.
Specifications.
Weight in Lb.
Timber.
Ballast.
Concrete.
Rails and
Fastenings.
Total Weight of
Floor, Lb.
2. A., T. & S. F. R. R
3 B & O R R.
4i
3
Timber Ballasted
Deck 1,400
130
ISO
ISO
IOO
ISO
150
4 B & M R R
IOO
IOO
5 C M & St. P. Ry. .
a
7. Common Standard
Soo>
400 mm.
8 Cooper
41
4t
Creosoted 5
110
IOO
9. Illinois Central R. R
10. K. C, M. &O. R. R....
ISO
IOO
400
IS°
600
ii.'Lehigh Valley R.-R
12. N. Y. Central R. R
13. N. Y., N. H. & H. R. R.
14. Penna. W. of Pittsburgh
15. Nat. L. of Mexico
4|
4i
4i
150
150
150
170
150
150
1 20
IOO
400
4
4
IOO
1 20
17. Dept. of R. R. of Canada
600
per sq. in. and the lowest is 15,000 Ib. per sq. in. Of the 39 roads considered all except one use a
concentrated system of engine loadings; one road, the Pennsylvania Lines West of Pittsburgh,
uses a uniform load of 5,500 Ib. per lineal foot of track and an excess load of 66,000 Ib. on one
axle; no road is using an equivalent uniform load. For data on the heaviest locomotives in service
and the relative stresses due to these locomotives compared with E 50 loading see Table II.
Mr. Greiner's conclusion is that E 50 bridges will safely carry all loads that can be carried
without increasing the present vertical and horizontal clearances.
COMPARISON OF RAILWAY BRIDGE SPECIFICATIONS.
2C5
TABLE XVI.
LIVE LOADS FOR RAILWAY BRIDGES.
Specification.
Engine.
Special Loads.
Impact.
Tensile Unit Stress
inLb.
Equivalent
Loading in
Terms of
Tensile
Strew.
Type.
Weight
in i.ooo
Lb.
Weight
per
Track.
Two
Loads,
Lb.
Sp.ii iiu;
of Two
!><>.ii!s,
Ft.
2. A., T. & S. F.
R. R.
Consol.
£50
E6o
JEss1
XE601
ESS
ESS
ESS
E4S
E6o
E6o
E6o
Excess5
E6o
291.0
225.0
270.0
247.5
270.0
247-S
247.5
247-S
202.5
270.0
270.0
270.0
Cooper
A. R. E. A.
it
«
«
«
Launhardt
LL
E6o
£50
E6o
/ESS1
\E6o»
ESS
ESS1
ESS4
£40
E6o
ES3
E6o
£65
ESS
3. B. &O. R. R....
4. B. & M. R. R. . .
5. C. M. & St. P.
Ry
6o,OOO
65,000
68,750
75,000
68,750
l6,OOO
l6,OOO
l6,OOO
l6,OOO
/ . min. \
8, coo I i -\ 1
6
7
7
7
6. C. R. I. & P.
R. R.
7. Common
9. Illinois Central
R R
V max./
16,000
18,000
16,000
18,000
16,000
(. min. \
I -1 1
10. K. C., M. & O.
R. R
56,250
75,000
72,000
65,000
7
7i
7
6
LL + DL
A. R. E. A.
«
M
((
Launhardt
Cooper
u. Lehigh Valley
R. R
12. N. Y. Central...
13. N. Y., N. H. &
H. R. R
14. Penna. W. of
Pittsburgh
15. Nat. L. of Mex..
270.0
75,000
S
1 max./
1. C. M. & St. P. Ry. uses E 55 east of the Missouri River and E 60 west.
2. A uniform train load of 7,000 Ib. per lin. ft. on ore roads.
3. A uniform train load of 5,000 Ib. per lin. ft.
4. A uniform train load of 6,000 Ib. per lin. ft.
5. Train load of 5,500 Ib. per lin. ft. and excess load of 66,000 Ib.
§9. Impact. — Ten of the sixteen specifications use the impact coefficient as given in section 9,
3OO/(L + 300). Three specifications follow Cooper's method of using dead load unit stresses
jual to twice the live load unit stresses, with different stresses for different members. Two
:ifications use Launhardt's formula, P = S [ I H '• 1 where P = allowable unit
\ max. stress /
ss, and 5 = allowable unit stress for live load alone. One specification uses the impact
. , _ Live Load Stress
Live Load Stress + Dead Load Stress
In the paper referred to in section 7, Mr. Greiner found that 26 roads used the A. R. E. A.
jrmula for impact.
§10 & ii. Wind Loads. — The wind loads given in the different specifications are variable
and space will not permit going into detail. Most of the specifications require that the moving
wind load on the loaded chord be considered as applied at 6 or 7 ft. above the top of the rail.
§13. Centrifugal Force. — Five of the sixteen specifications have the same requirement as in
section 13. The centrifugal force of a body moving in a circular path is C = W- J^/32 '2R,
where W = weight of live load per lineal foot; V = velocity of tram in feet per second, and
R = radius of curve in feet. For a speed of 60 — 2\D, C = 0.039^ for a I degree curve; C =
0.071 W for a 2 degree curve; C = 0.117^ for a 4 degree curve, and C = 0.143 W" for a 10 degree
curve. Five specifications require that the centrifugal force be applied at 5 to ^\ feet above the
rail. Two specifications take the centrifugal force as C = o.o^W-D, where W = equivalent
weight of live load per lineal foot, and D = degree of curve; one takes C = O.O2W-D, and two
take C = 0.045 W-D. The K. C. M. & O. R. R. takes C - W- V/32-2/?, where W = equiva-
lent weight of live load per lineal foot, V = velocity of train in feet per second (calculated for 50
miles per hour), and R = radius of curve in feet. This gives C = o.O2gW-D.
206 STEEL RAILWAY BRIDGES. CHAP. IV.
§14. Unit Stresses. — For a comparison of the tensile unit stresses see Table XVI.
§22. Alternate Stresses. — Four of the sixteen specifications use the same specification as in
section 22. Six specifications use Cooper's specification. "All members and their connections
shall be designed to resist each kind of stress. Both of the stresses shall, however, be considered
as increased by 0.8 of the least of the two stresses." One specification increases each stress by
0.60 of the lesser stress, one by 0.70, and two by 0.75. One specification uses Weyrauch's formula,
P = S ( I — m' — ) . where P = allowable unit stress for alternate stresses, and 5
\ 2 max. stress /
= allowable unit stress for live loads alone.
§26. Net Sections. — Section 26 is standard. In addition the method of calculating the
net area of a riveted tension member is given in several specifications.
Cooper requires that "The rupture of a riveted tension member is to be considered as equally
probable, either through a transverse line of rivet holes or through a zigzag line of rivet holes, where
the net section does not exceed by 30 per cent the net section along a transverse line."
The Baltimore & Ohio R. R. requires that "The greatest number of rivet holes that can be
cut by a transverse plane, or come within one inch of the plane is to be deducted in calculating
the net section."
The New York Central Lines require that "The net section of riveted members shall be the
least area which can be obtained by deducting from the gross sectional area the areas of holes cut
by any plane perpendicular to the axis of the member and parts of the areas of other holes on one
side of the plane, within a distance of 4 inches, and which are on other gage lines than those of the
holes cut by the plane, the parts being determined by the formula: A (i — pi\), in which A = the
area of the hole, and p = the distance in inches of the center of the hole from the plane."
The Canadian Society of Civil Engineers requires "There shall be deducted from each member
as many rivets as there are gage lines, unless the distance center to center of rivets measured in
the diagonal direction is 40 per cent greater than their distance center to center of gage lines."
§29. Plate Girders. — Seven of the sixteen specifications require that plate girders be pro-
portioned either by the moment of inertia of their net section; or by assuming that the flanges
are concentrated at their centers of gravity; in which case one-eighth of the gross section of the
web, if properly spliced, may be used as flange section. Six specifications require that the bending
moment all be taken by the flanges. Two specifications require that the bending moment be
taken by the flanges and that one-eighth of the gross section of the web be taken as flange area.
One specification requires that plate girders with stiffeners be designed on the assumption that
the flanges take all the bending moment, and that for plate girders without stiffeners one-eighth of
the web may be considered as flange area.
§30. Compression Flanges. — Two specifications require that the flange angles shall contain
at least one-half of the area of the flange. The specifications uniformly require that the com-
pression flange shall have the same gross area as the tension flange.
§36. Counters. — Eight specifications require that counters be stiff members. Eight speci-
fications permit adjustable counters and laterals.
§45. Minimum Angles. — Five specifications give 3!" X 3" X I" as the minimum angle.
Two specifications give 3" X 2|" X f " as the minimum angle. One specification requires that
the vertical leg be not less than 3!". One specification requires that connection angles for stringers
and floorbeams be not less than 4" X 4" X f"; one specification 3!" X 35" X f ", and one
specification 6" X 4" X f ".
§59. Expansion. — Six specifications require that provision be made for an expansion of | in.
for each 10 ft. of span. Five specifications require that provision be made for a range in tempera-
ture of 150 degrees F. ; one for 180 degrees F. Three specifications require that provision be
made for an expansion of I in. in 100 ft.; one for an expansion of i in. in 70 ft.
§62. Rollers. — Six specifications require that rollers be at least 6 in. in diameter. Five
specifications permit rollers 4 in. in diameter. One specification permits rollers 3 in. in diameter.
Cooper requires that rollers for spans up to 100 ft. be 4! in., and that the diameter be increased
i in. for each 10 ft. increase in span over 100 ft. The New York Central R. R. requires that rollers
shall not have a less diameter in inches than 3 + 0.03 (span in feet).
§68. Stringer Connection Angles. — One specification requires that connection angles of
stringers and floorbeams be not less than 4" X 4" X f"; one specification 3?" X 3?" X £",
and one specification 6" X 4" X f ".
§77. Camber of Plate Girders. — Four specifications require that plate girders more than
50 ft. long be cambered ^ in. per 10 ft. of length. Two specifications require full camber. Two
specifications require a camber of T^ the span. Two specifications require a camber of y^ the
span. One specification requires a camber of | in. per 10 ft. of length, one specification requires
a camber of j^ in. per 15 ft. of length. Four specifications do not require that plate girders be
cambered.
COMPARISON OF RAILWAY BRIDGE SPECIFICATIONS. 207
§79. Web Stiffeners. — Seven specifications have the same specification as given in section 79-
Two >|K (itir.it ion> require that stiffeners be spaced not to exceed depth of girder. The Baltimore
The New York Central Lines require that stiffeners be spaced not to exceed depth of
h r or § ft. 6 in.; near ends of girders the spacing shall not exceed one-half the depth of girder
or .} ft. 6 in.
The New York Central Lines require that stiffeners shall have an outstanding leg not less
than 2 inches plus 5^ the depth of the girder.
The Chicago, Milwaukee & St. Paul Ry. requires that stiffeners bearing against 6" X 6"
flange angles shall be 5" X 3*" X f"; and against 8" X 8" flange angles shall be 6" X 3*" X |".
§8 1. Camber of Trusses. — Six specifications require full camber as stated in section 81. Six
specifications require that the upper chords be increased J in. for each 10 ft. One specification
requires that the upper chord be increased i in. for each 15 ft. Two specifications require that
a be cambered T»W the span. One specification requires that trusses be cambered rfco the
span.
§82. Rigid Members. — All specifications require that hip verticals and the two end panels
of bottom chords (two at each end) be stiff members. The Common Standard specifications
(Harriman Lines) require that the bottom chords of bridges of less than 150 ft. span be stiff
members. The Illinois Central R. R. requires that bridges with 6 panels or less shall have stiff
lower chords. The New York Central Lines limit the specification for rigid members to spans
less than 300 ft.
§83. Eye-bars. — Nine specifications permit bars to be out of line i in. in 16 ft. as in section 83.
le specification permits bars to be out of line I in. in 8 ft.
Miscellaneous. — The following specifications are of interest.
Initial Stress. — Four of the sixteen specifications require that diagonals and struts be designed
for an initial stress of 10,000 Ib. in each diagonal.
Collision Strut. — Two of the sixteen specifications require collision struts.
Fastening Angles. — Two specifications require that angles .must be fastened by both legs,
iree specifications require that angles be fastened by both legs or only one leg will be considered
fective. One specification requires that 75 per cent of the net area be considered effective where
igles are fastened by one leg, and 90 per cent of the net area be considered effective where angles
fastened by both legs.
Calculating Dead Load Stresses. — One specification requires that all the dead load be con-
sidered as coming on the loaded chord. Two specifications require that three-fourths of the dead
id be considered as coming on the loaded chord and one-fourth on the unloaded chord. Two
ecifications require that two-thirds of the dead load be considered as coming on the loaded chord
id one-third on the unloaded chord. Two specifications require that the floor load shall be
wumed as taken by the loaded chord, and the remainder of the dead load to be divided equally
jtween the chords. The other specifications do not state where the dead load shall be applied.
Minimum Bar. — Three specifications require that the minimum bar shall have not less than
sq. in. cross section. One specification permits a minimum bar I } in. square. One specification
jquires that an increase of 80 per cent in the live load shall not increase the stress in the counters
lore than 80 per cent. One specification has a similar clause with 70 per cent variation.
Paint. — The shop coat of paint as required by several specifications is as follows:
The New York Central Lines use red lead paint mixed by the following formula: — too Ib.
sure red lead; 4 gallons pure open-kettle-boiled linseed oil; and not to exceed one-half pint of
irpentine-japan drier.
The Boston & Maine R. R. and the New York, New Haven & Hartford R. R. use red lead
lint made by mixing 32 Ib. of red lead to one gallon of linseed oil.
The A. T. & S. F. Ry. gives steel work a shop coat of linseed oil; while the C. R. I. & P.
1. R. uses linseed oil with 10 per cent of lamp black.
The Illinois Central R. R. uses red lead paint for a shop coat.
The Pennsylvania Lines West of Pittsburgh use a shop coat of pure linseed oil.
The Common Standard specifications require a shop coat of red lead.
GENERAL SPECIFICATIONS FOR STEEL RAILWAY BRIDGES.*
American Railway Engineering Association.
Fourth Edition.
STANDARD SPECIFICATIONS.
PART FIRST— DESIGN.
I. GENERAL.
1. Materials. — The material in the superstructure shall be structural steel, except rivets,
and as may be otherwise specified.
2. Clearances. — When alinement is on tangent, clearances shall not be less than shown on
the diagram; the height of rail shall, in all cases, be assumed as 6 in. The width shall be increased
so as to provide the same minimum clearances on curves for a car 80 ft. long, 14 ft. high, and 60 ft.
center to center of trucks, allowance being made for curvature and superelevation of rails.
3. Spacing Trusses. — The width center to center of girders and trusses
shall in no case be less than one-twentieth of the effective span, nor less than
is necessary to prevent overturning under the assumed lateral loading.
4. Skew Bridges. — Ends of deck plate girders and track stringers of
skew bridges at abutments shall be square to the track, unless a ballasted
floor is used.
5. Floors. — Wooden tie floors shall be secured to the stringers and shall
be proportioned to carry the maximum wheel load, with 100 percent impact,
distributed over three ties, with fiber stress not to exceed 2,000 Ib. per sq. in.
Ties shall not be less than 10 ft. in length. They shall be spaced with not
more than 6-in. openings; and shall be secured against bunching.
II. LOADS.
6. Dead Load. — The dead load shall consist of the estimated weight of
the entire suspended structure. Timber shall be assumed to weigh 4^ Ib. per -r Oc\o :t
ft. B. M.; ballast 100 Ib. per cu. ft., reinforced concrete 150 Ib. per cu. ft., ' I
and rails and fastenings, 150 Ib. per linear ft. of track.
t/. Live Load. — The live load, for each track, shall consist of two typical engines followed
by a uniform load, according to Cooper's series, or a system of loading giving practically equivalent
strains. The minimum loading to be Cooper's £-40, and the special loading, the diagram as
shown in the following diagrams, that which gives the larger strains to be used.
f8. Heavier Loading. — Heavier loadings shall be proportional to the above diagrams on the
same spacing.
9. Impact. — The dynamic increment of the live load shall be added to the maximum computed
-7QQ
live load strains and shall be determined by the formula I = S , — ,
L, -J- 3OO
where I = impact or dynamic increment to be added to live-load strains.
5 = computed maximum live-load strain.
L = loaded length of track in feet producing the maximum strain in the member. For
bridges carrying more than one track, the aggregate length of all tracks producing
the strain shall be used.
Impact shall not be added to strains produced by longitudinal, centrifugal and lateral or
wind forces.
10. Lateral Forces. — All spans shall be designed for a lateral force on the loaded chord of
200 Ib. per linear foot plus 10 per cent of the specified train load on one track, and 200 Ib. per
linear foot on the unloaded chord; these forces being considered as moving.
* Adopted by the American Railway Engineering Association,
t See Addendum, clause (a).
208
SPECIFICATIONS. 209
ii. Wind Force. — Viaduct towers shall be designed for a force of 50 Ib. per sq. ft. on one
and onr-li.il! times tin- vertical projection of the structure unloaded; or 30 Ib. per sq. ft. on the
.X.HIH Miriuce plus 400 Ib. per linear ft. of structure applied 7 ft. above the rail for assumed wind
I. 'in MM train when the structure is cither fully loaded or loaded on either track with empty cars
" to weigh 1,200 Ib. per linear ft., whichever gives the larger strain.
1111 s§ §§ § 1111 §§ %§
S <a ^ "^ §§§§ § ^ <^ ^ ^ ^<^^<i Tram Load **> K>
"» ^ ^ ^ S&SS ^ ^J5^5^ 4000 It. per Ft. (~\C\
OOOO ^oon^-n OOOO noon v; ;/;;;/;//;», \J\J
Special Loading
12. Longitudinal Force. — Viaduct towers and similar structures shall be designed for a
longitudinal force of 20 per cent of the live load applied at the top of the rail.
13. Structures located on curves shall be designed for the centrifugal force of the live load
applied at the top of the high rail. The centrifugal force shall be considered as live load and be
derived from the speed in miles per hour given by the expression 60 — 2\D, where "D" = degree
of curve.
III. UNIT STRESSES AND PROPORTION OF PARTS.
14. Unit Stresses. — All parts of structures shall be so proportioned that the sum of the maxi-
mum stresses produced by the foregoing loads shall not exceed the following amounts in pounds
sq. in., except as modified in paragraphs 22 to 25:
15. Tension. — Axial tension on net section 16,000
16. Compression. — Axial compression on gross section of columns 16,000 — 70 —
irith a maximum of 14,000
here "/" is the length of the member in inches, and "r" is the least radius of
gyration in inches.
ct compression on steel castings 16,000
17. Bending. — Bending: on extreme fibers of rolled shapes, built sections,
rders and steel castings; net section 16,000
extreme fibers of pins 24,000
. 18. Shearing. — Shearing: shop driven rivets and pins 12,000
eld driven rivets and turned bolts 10,000
plate girder webs; gross section 10,000
19. Bearing. — Bearing: shop driven rivets and pins 24,000
field driven rivets and turned bolts 20,000
expansion rollers; per linear inch 6oo<f
where "d" is the diameter of the roller in inches.
on masonry 600
^20. Limiting Length of Members. — The lengths of main compression members shall not
eed 100 times their least radius of gyration, and those for wind and sway bracing 120 times
ir least radius of gyration.
21. The lengths of riveted tension members in horizontal or inclined positions shall not
exceed 200 times their radius of gyration about the horizontal axis. The horizontal projection
of the unsupported portion of the member is to be considered as the effective length.
22. Alternate Stresses. — Members subject to alternate stresses of tension and compression
shall be proportioned for the stresses giving the largest section. If the alternate stresses occur
in succession during the passage of one train, as in stiff counters, each stress shall be increased by
50 per cent of the smaller. The connections shall in all cases be proportioned for the sum of the
stresses.
23. Wherever the live and dead load stresses are of opposite character, only two-thirds of the
load stresses shall be considered as effective in counteracting the live load stress.
24. Combined Stresses. — Members subject to both axial and bending stresses shall be pro-
portioned so that the combined fiber stresses will not exceed the allowed axial stress.
25. For stresses produced by longitudinal and lateral or wind forces combined with those
from live and dead loads and centrifugal force, the unit stress may be increased 25 per cent over
15
210 STEEL RAILWAY BRIDGES. CHAP. IV.
those given above; but the section shall not be less than required for live and dead loads and
centrifugal force.
26. Net Section at Rivets. — In proportioning tension members the diameter of the rivet holes
shall be taken |-in. larger than the nominal diameter of the rivet.
27. Rivets. — In proportioning rivets the nominal diameter of the rivet shall be used.
28. Net Section at Pins. — Pin-connected riveted tension members shall have a net section
through the pin-hole at least 25 per cent in excess of the net section of the body of the member,
and the net section back of the pin-hole, parallel with the axis of the member, shall be not less than
the net section of the body of the member.
29. Plate Girders. — Plate girders shall be proportioned either by the moment of inertia of
their net section; or by assuming that the flanges are concentrated at their centers of gravity;
in which case one-eighth of the gross section of the web, if properly spliced, may be used as flange
section. The thickness of web plates shall be not less than T£ff of the unsupported distance
between flange angles (see 38).
30. Compression Flange. — The gross section of the compression flanges of plate girders shall
not be less than the gross section of the tension flanges; nor shall the stress per sq. in. in the
compression flange of any beam or girder exceed 16,000 — 200 -r , when flange consists of angles
only or if cover consists of flat plates, or 16,000 — 150^-, if cover consists of a channel section,
where / = unsupported distance and b = width of flange.
31. Flange Rivets. — The flanges of plate girders shall be connected to the web with a sufficient
number of rivets to transfer the total shear at any point in a distance equal to the effective depth
of the girder at that point combined with any load that is applied directly on the flange. The
wheel loads, where the ties rest on the flanges, shall be assumed to be distributed over three
ties.
32. Depth Ratios. — Trusses shall preferably have a depth of not less than one-tenth of the
span. Plate girders and rolled beams, used as girders, shall preferably have a depth of not less
than one-twelfth of the span. If shallower trusses, girders or beams are used, the section shall
be increased so that the maximum deflection will not be greater than if the above limiting ratios
had not been exceeded.
IV. DETAILS OF DESIGN.
GENERAL REQUIREMENTS.
33. Open Sections. — Structures shall be so designed that all parts will be accessible for
inspection, cleaning and painting.
34. Pockets. — Pockets or depressions which would hold water shall have drain holes, or be
filled with waterproof material.
35. Symmetrical Sections. — Main members shall be so designed that the neutral axis will be
as nearly as practicable in the center of section, and the neutral axes of intersecting main members
of trusses shall meet at a common point.
36. Counters. — Rigid counters are preferred; and where subject to reversal of stress shall
preferably have riveted connections to the chords. Adjustable counters shall have open turn-
buckles.
37. Strength of Connections. — The strength of connections shall be sufficient to develop the
full strength of the member, even though the computed stress is less, the kind of stress to which
the member is subjected being considered.
38. Minimum Thickness. — The minimum thickness of metal shall be f-in., except for
fillers.
39. Pitch of Rivets. — The minimum distance between centers of rivet holes shall be three
diameters of the rivet; but the distance shall preferably be not less than 3 in. for f-in. rivets and
25 in. for f-in. rivets. The maximum pitch in the line of stress for members composed of plates
and shapes shall be 6 in. for f-in. rivets and 5 in. for f-in. rivets. For angles with two gage lines
and rivets staggered the maximum shall be twice the above in each line. Where two or more
plates are used in contact, rivets not more than 12 in. apart in either direction shall be used to
hold the plates well together. In tension members, composed of two angles in contact, a pitch
of 12 in. will be allowed for riveting the angles together.
40. Edge Distance. — The minimum distance from the center of any rivet hole to a sheared
edge shall be i| in. for f-in. rivets and I J in. for f-in. rivets, and to a rolled edge I \ in. and l| in.,
respectively. The maximum distance from any edge shall be eight times the thickness of the
plate, but shall not exceed 6 in.
SPECIFICATIONS. 211
41 . Maximum Diameter. — The diameter of the rivets in any angle carrying calculated stress
sh.ill inn r\. cv<l Din- -quarter the width of the leg in which they are driven. In minor parts J-in.
rivri-^ may be used in 3-in. angles, and J-in. rivets in 2}-in. angles.
4^. Long Rivets. — Rivets carrying calculated stress and whose grip exceeds four diameters
>hall In- iniTiMsi-d in number at least one per cent for each additional A-in. of grip.
43. Pitch at Ends. — The pitch of rivets at the ends of built compression members shall not
r\ivrd four diameters of the rivets, for a length equal to one and one-half times the maximum
width of nu'inber.
44. Compression Members. — In compression members the metal shall be concentrated as
much as possible in webs and flanges. The thickness of each web shall be not less than one-
t hirt it-t h of the distance between its connections to the flanges. Cover plates shall have a thickness
nut less than one-fortieth of the distance between rivet lines.
45. Minimum Angles. — Flanges of girders and built members without cover plates shall have
a minimum thickness of one-twelfth of the width of the outstanding leg.
46. Tie-Plates.— The open sides of compression members shall be provided with lattice and
shall have tie-plates as near each end as practicable. Tie-plates shall be provided at intermediate
points where the lattice is interrupted. In main members the end tie-plates shall have a length
not less than the distance between the lines of rivets connecting them to the flanges, and inter-
mediate ones not less than one-half this distance. Their thickness shall not be less than one-
fiftieth of the same distance.
47. Lattice. — The latticing of compression members shall be proportioned to resist the
shearing stresses corresponding to the allowance for flexure for uniform load provided in the
column formula in paragraph 16 by the term 70 - . The minimum width of lattice bars shall be
2j in. for J-in. rivets, 2} in. for f-in. rivets, and 2 in. if f-in. rivets are used. The thickness shall
not be less than one-fortieth of the distance between end rivets for single lattice, and one-sixtieth
for double lattice. Shapes of equivalent strength may be used.
48. Three-fourths-inch rivets shall be used for latticing flanges less than 2$ in. wide, and
|-in. for flanges from 2 J to 3 J in. wide; $-in. rivets shall be used in flanges 3$ in. and over, and
lattice bars with at least two rivets shall be used for flanges over 5 in. wide.
49. The inclination of lattice bars with the axis of the member shall be not less than 45 degrees,
and when the distance between rivet lines in the flanges is more than 15 in., if single rivet bar is
used, the lattice shall be double and riveted at the intersection.
50. Lattice bars shall be so spaced that the portion of the flange included between their
connections shall be as strong as the member as a whole.
51. Faced Joints. — Abutting joints in compression members when faced for bearing shall be
spliced on four sides sufficiently to hold the connecting members accurately in place. All other
joints in riveted work, whether in tension or compression, shall be fully spliced.
52. Pin Plates. — Pin-holes shall be reinforced by plates where necessary, and at least one
plate shall be as wide as the flanges will allow and be on the same side as the angles. They shall
contain sufficient rivets to distribute their portion of the pin pressure to the full cross-section of
the member.
53. Forked Ends. — Forked ends on compression members will be permitted only where
unavoidable; where used, a sufficient number of pin plates shall be provided to make the jaws of
twice the sectional area of the member. At least one of these plates shall extend to the far edge
of the farthest tie-plate, and the balance to the far edge of the nearest tie-plate, but not less than
6 in. beyond the near edge of the farthest plate.
54. Pins. — Pins shall be long enough to insure a full bearing of all the parts connected
upon the turned body of the pin. They shall be secured by chambered nuts or be provided with
washers if solid nuts are used. The screw ends shall be long enough to admit of burring the
threads.
55. Members packed on pins shall be held against lateral movement.
56. Bolts. — Where members are connected by bolts, the turned body of these bolts shall be
long enough to extend through the metal. A washer at least J-in. thick shall be used under the
nut. Bolts shall not be used in place of rivets except by special permission. Heads and nuts
shall be hexagonal.
57. Indirect Splices. — Where splice plates are not in direct contact with the parts which
they connect, rivets shall be used on each side of the joint in excess of the number theoretically
required to the extent of one-third of the number for each intervening plate.
58. Fillers. — Rivets carrying stress and passing through fillers shall be increased 50 per cent
in number; and the excess rivets, when possible, shall be outside of the connected member.
59. Expansion. — Provision for expansion to the extent of i-in. for each 10 ft. shall be made
for all bridge structures. Efficient means shall be provided to prevent excessive motion at any
one point.
212 STEEL RAILWAY BRIDGES. CHAP. IV.
60. Expansion Bearings. — Spans of 80 ft. and over resting on masonry shall have turned
rollers or rockers at one end; and those of less length shall be arranged to slide on smooth surfaces.
These expansion bearings shall be designed to permit motion in one direction only.
61. Fixed Bearings. — Fixed bearings shall be firmly anchored to the masonry.
62. Rollers. — Expansion rollers shall be not less than 6 in. in diameter. They shall be
coupled together with substantial side bars, which shall be so arranged that the rollers can be
readily cleaned. Segmental rollers shall be geared to the upper and lower plates.
63. Bolsters. — Bolsters or shoes shall be so constructed that the load will be distributed over
the entire bearing. Spans of 80 ft. or over shall have hinged bolsters at each end.
64. Wall Plates. — Wall plates may be cast or built up; and shall be so designed as to distribute
the load uniformly over the entire bearing. They shall be secured against displacement.
65. Anchorage. — Anchor bolts for viaduct towers and similar structures shall be long enough
to engage a mass of masonry the weight of which is at least one and one-half times the uplift.
66. Inclined Bearings. — Bridges on an inclined grade without pin shoes shall have the sole
plates beveled so that the masonry and expansion surfaces may be level.
FLOOR SYSTEMS.
67. Floorbeams. — Floorbeams shall preferably be square to the trusses or girders. They
shall be riveted directly to the girders or trusses or may be placed on top of deck bridges.
68. Stringers. — Stringers shall preferably be riveted to the webs of all intermediate floorbeams
by means of connection angles not less than 5-in. in thickness. Shelf angles or other supports
provided to support the stringer during erection shall not be considered as carrying any of the
reaction.
69. Stringer Frames. — Where end floorbeams cannot be used, stringers resting on masonry
shall have cross frames near their ends. These frames shall be riveted to girders or truss shoes
where practicable.
BRACING.
70. Rigid Bracing. — Lateral, longitudinal and transverse bracing in all structures shall be
composed of rigid members.
71. Portals. — Through truss spans shall have riveted portal braces rigidly connected to the
end posts and top chords. They shall be as deep as the clearance will allow.
72. Transverse Bracing. — Intermediate transverse frames shall be used at each panel of
through spans having vertical truss members where the clearance will permit.
73. End Bracing. — Deck spans shall have transverse bracing at each end proportioned to
carry the lateral load to the support.
74. Laterals. — The minimum sized angle to be used in lateral bracing shall be 3! by 3 by f-in.
Not less than three rivets through the end of the angles shall be used at the connection.
75. Lateral bracing shall be far enough below the flange to clear the ties.
76. Tower Struts. — The struts at the foot of viaduct towers shall be strong enough to slide
the movable shoes when the track is unloaded.
PLATE GIRDERS.
77. Camber. — If desired, plate girder spans over 50 ft. in length shall be built with camber at
a rate of rVm- Per IO ft. °f length.
78. Top Flange Cover. — Where flange plates are used, one cover plate of top flange shall
extend the whole length of the girder.
79. Web Stiffeners. — There shall be web stiffeners, generally in pairs, over bearings, at points
of concentrated loading, and at other points where the thickness of the web is less than -^ of the
unsupported distance between flange angles. The distance between stiffeners shall not exceed
that given by the following formula, with a maximum limit of six feet (and not greater than the
clear depth of the web) :
d = — (12,000 — s),
40
Where d = clear distance, between stiffeners of flange angles.
t = thickness of web.
5 = shear per sq. in.
The stiffeners at ends and at points of concentrated loads shall be proportioned by the formula
of paragraph 16, the effective length being assumed as one-half the depth of girders. End stiffeners
and those under concentrated loads shall be on fillers and have their outstanding legs as wide as
the flange angles will allow and shall fit tightly against them. Intermediate stiffeners may be
SPECIFICATIONS.
213
or on fillers, and their outstanding legs shall be not less than one-thirtieth of the depth of
er plus 2 in.
80. Stays for Top Flanges. — Through plate girders shall have their top flanges stayed at
rial of rvery tloorbeam, or in case of solid floors, at distances not exceeding 12 ft., by knee
braces or gusset plates.
TRUSSES.
81. Camber. — Truss spans shall be given a camber by so proportioning the length of the
members that the stringers will be straight when the bridge is fully loaded.
82. Rigid Members. — Hip verticals and similar members, and the two end panels of the
bottom chords of single track pin-connected trusses shall be rigid.
83. Eye-bars. — The eye-bars composing a member shall be so arranged that adjacent bars
shall not have their surfaces in contact; they shall be as nearly parallel to the axis of the truss as
possible, the maximum inclination of any bar being limited to one inch in 16 ft.
84. Pony Trusses. — Pony trusses shall be riveted structures, with double webbed chords, and
shall have all web members latticed or otherwise effectively stiffened.
PART SECOND— MATERIALS AND WORKMANSHIP.
V. MATERIAL.
85. Steel. — Steel shall be made by the open-hearth process.
86. Properties. — The chemical and physical properties shall conform to the following limits:
Elements Considered.
Structural Steel.
Rivet Steel.
Steel Castings.
Phosphorus, max.. { ^£yf" '
Sulphur, maximum
0.04 per cent
0.06 per cent
0.05 per cent
0.04 per cent
0.04 per cent
0.04 per cent
0.05 per cent
0.08 per cent
0.05 per cent
Ultimate tensile strength.
Pounds per square inch
Desired.
60,000
1,500,000*
Desired.
50,000
1,500,000
Not less than
65,000
15 per cent
f Silky or fine
\ granular
90° d = 3*
Elong., min. %, in 8", Fig. I {
Elong., min. %, in 2", Fig. 2. .
Character of Fracture
Ult. tensile strength
22
Silky
180° flatf
Ult. tensile strength
Silky
180° flatt
Cold Bends without Fracture.
The yield point, as indicated by the drop of beam, shall be recorded in the test reports.
87. In order that the ultimate strength of full-sized annealed eye-bars may meet the
juirements of paragraph 163, the ultimate strength in test specimens may be determined by
ic manufacturers; all other tests than those for ultimate strength shall conform to the above
juirements.
8. Allowable Variations. — If the ultimate strength varies more than 4,000 Ib. from that
sired, a retest shall be made on the same gage, which, to be acceptable, shall be within 5,000 Ib.
the desired ultimate.
89. Chemical Analyses. — Chemical determinations of the percentages of carbon, phosphorus,
sulphur and manganese shall be made by the manufacturer from a test ingot taken at the
time of the pouring of each melt of steel, and a correct copy of such analysis shall be furnished
to the engineer or his inspector. Check analyses shall be made from finished material, if called
for by the purchaser, in which case an excess of 25 per cent above the required limits will be
permitted.
90. Specimens. — Plate, shape and bar specimens for tensile and bending tests shall be made
by cutting coupons from the finished product, which shall have both faces rolled and both edges
milled to the form shown by Fig. I ; or with both edges parallel; or they may be turned to a diameter
of |-in. for a length of at least 9 in., with enlarged ends.
91. Rivet rods shall be tested as rolled.
* See paragraph 96. f See paragraphs 97, 98, and 99. J See paragraph 100.
214
STEEL RAILWAY BRIDGES.
CHAP. IV.
92. Pin and roller specimens shall be cut from the finished rolled or forged bar, in such manner
that the center of the specimen shall be one inch from the surface of the bar. The specimen for
tensile test shall be turned to the form shown by Fig. 2. The specimen for bending test shall be
one inch by 3-in. in section.
93. For steel castings the number of tests will depend on the character and importance of
the castings. Specimens shall be cut cold from coupons molded and cast on some portion of one
or more castings from each melt or from the sink heads, if the heads are of sufficient size. The
coupon or sink head, so used, shall be annealed with the casting before it is cut off. Test specimens
to be of the form prescribed for pins and rollers.
-
«•? i Not less ilrin 9" ( „!
| r t t • • * f • ••
— f
Abput *''
—it
» About' 18" • •*
FIG. i
FIG. 2.
94. Specimens of Rolled Steel. — Rolled steel shall be tested in the condition in which it
comes from the rolls.
95. Number of Tests. — At least one tensile and one bending test shall be made from each
melt of steel as rolled. In case steel differing f-in. and more in thickness is rolled from one melt,
a test shall be made from the thickest and thinnest material rolled.
96. Modification in Elongation. — A deduction of i per cent will be allowed from the specified
percentage for elongation, for each f-in. in thickness above f-in.
97. Bending Tests. — Bending tests may be made by pressure or by blows. Plates, shapes
and bars less than one inch thick shall bend as called for in paragraph 86.
98. Thick Material. — Full-sized material for eye-bars and other steel one inch thick and
over, tested as rolled, shall bend cold 180 degrees around a pin, the diameter of which is equal to
twice the thickness of the bar, without fracture on the outside of bend.
99. Bending Angles. — Angles f-in. and less in thickness shall open flat, and angles |-in. and
less in thickness shall bend shut, cold, under bl Jws of a hammer, without sign of fracture. This
test shall be made only when required by the inspector.
100. Nicked Bends. — Rivet steel, when nicked and bent around a bar of the same diameter
as the rivet rod, shall give a gradual break and a fine silky uniform fracture.
101. Finish. — Finished material shall be free from injurious seams, flaws, cracks, defective
edges or other defects, and have a smooth, uniform and workmanlike finish. Plates 36 in. in
width and under shall have rolled edges.
102. Melt Numbers. — Every finished piece of steel shall have the melt number and the
name of the manufacturer stamped or rolled upon it. Steel for pins and rollers shall be stamped
on the end. Rivet and lattice steel and other small parts may be bundled with the above marks
on an attached metal tag.
103. Defective Material.— Material which, subsequent to the above tests at the mills, and
its acceptance there, develops weak spots, brittleness, cracks or other imperfections, or is found
to have injurious defects, will be rejected at the shop and shall be replaced by the manufacturer at
his own cost.
104. Variation in Weight. — A variation in cross-section or weight of each piece of steel of
more than 2| per cent from that specified will be sufficient cause for rejection, except in case of
sheared plates, which will be covered by the following permissible variations, which are to apply
to single plates, when ordered to weight:
105. Plates \2\ Ib. per sq. ft. or heavier:
(a) Up to 100 in. wide, 2\ per cent above or below the prescribed weight.
(b) One hundred inches wide and over, 5 per cent above or below.
SPECIFICATIONS.
106. Plates under I2| Ib. per sq. ft.:
(a) Up to 75 in. wide, 2j per cent above or below.
(b) Seventy-five inches and up to 100 in. wide, 5 per cent above or 3 per cent below.
(c) 'One hundred inches wide and over, 10 |« r . < nt alxwc or 3 prr rent U-low.
107. Plates when ordered to gage will be accepted if they measure not more than o.oi in.
below the ordered thickness.
108. An excess over the nominal weight, corresponding to the dimensions on the ord>
be allowed for each plate, if not more than that shown in the following table, one cu. in. of rolled
steel being assumed to weigh 0.2833 ^-:
Thickness
Ordered.
Nominal
Weights.
Width of Plate.
Up to 75".
75" and up to
1 00".
100" and up to
115".
Over us".
i-in
A
i
A
Over |
ch
IO.2O 11
12-75
I5-30
17.85
20.40
22.95
25-50
).
10 per
8
I
\k
ji
cent
14 per
12
10
8
6}
6
5
cent
18 per
16
13
10
i»
8
6J
cent
17 per
13
12
II
IO
9
cent
109. Cast-iron. — Except where chilled iron is specified, castings shall be made of tough gray
iron, with sulphur not over o.io per cent. They shall be true to pattern, out of wind and free from
flaws and excessive shrinkage. If tests are demanded, they shall be made on the "Arbitration
Bar" of the American Society for Testing Materials, which is a round bar ij in. in diameter and
15 in. long. The transverse test shall be made on a supported length of 12 in. with load at middle.
The minimum breaking load so applied shall be 2,900 ID., with a deflection of at least ^ in. before
rupture.
no. Wrought-Iron. — Wrought-iron shall be double-rolled, tough, fibrous and uniform in
character. It shall be thoroughly welded in rolling and be free from surface defects. When tested
in specimens of the form of Fig. I, or in full-sized pieces of the same length, it shall show an ultimate
strength of at least 50,000 Ib. per sq. in., an elongation of at least 18 per cent in 8 in., with fracture
wholly fibrous. Specimens shall bend cold, with the fiber, through 135 degrees, without sign of
fracture, around a pin the diameter of which is not over twice the thickness of the piece tested.
When nicked and bent, the fracture shall show at least 90 per cent fibrous.
VI. INSPECTION AND TESTING AT THE MILLS.
111. Mill Orders. — The purchaser shall be furnished complete copies of mill orders, and no
material shall be rolled nor work done before the purchaser has been notified where the orders have
been placed, so that he may arrange for the inspection.
112. Facilities for Inspection. — The manufacturer shall furnish all facilities for inspecting
and testing the weight and quality of all material at the mill where it is manufactured. He shall
furnish a suitable testing machine for testing the specimens as well as prepare the pieces for the
machine, free of cost.
113. Access to Mills. — When an inspector is furnished by the purchaser to inspect material
at the mills, he shall have full access, at all times, to all parts of mills where material to be inspected
by him is being manufactured.
VII. WORKMANSHIP.
114. General. — All parts forming a structure shall be built in accordance with approved
drawings. The workmanship and finish shall be equal to the best practice in modern bridge works.
Material arriving from the mills shall be protected from the weather and shall have clean surfaces
before being worked in the shops.
115. Straightening. — Material shall be thoroughly straightened in the shop, by methods that
will not injure it, before being laid off or worked in any way.
116. Finish. — Shearing and chipping shall be neatly and accurately done and all portions of
the work exposed to view neatly finished.
117. Size of Rivets. — The size of rivets, called for on the plans, shall be understood to mean
the actual size of the cold rivet before heating.
216 STEEL RAILWAY BRIDGES. CHAP. IV.
118. Rivet Holes. — When general reaming is not required, the diameter of the punch shall
not be more than rs-'m. greater than the diameter of the rivet; nor the diameter of the die more
than |-in. greater than the diameter of the punch. Material more than f-in. thick shall be
sub-punched and reamed or drilled from the solid.
119. Punching. — Punching shall be accurately done. Drifting to enlarge unfair holes will
not be allowed. If the holes must be enlarged to admit the rivet, they shall be reamed. Poor
matching of holes will be cause for rejection.
120. Reaming. — Where sub-punching and reaming are required, the punch used shall have a
diameter not less than ^-in. smaller than the nominal diameter of the rivet. Holes shall then be
reamed to a diameter not more than r^-in. larger than the nominal diameter of the rivet. (See
I35-)
121. Reaming after Assembling.* — [When general reaming is required it shall be done after
the pieces forming one built member are assembled and so firmly bolted together that the surfaces
shall be in close contact. If necessary to take the pieces apart for shipping and handling, the
respective pieces reamed together shall be so marked that they may be reassembled in the same
position in the final setting up. No interchange of reamed parts will be permitted.]
122. Reaming shall be done with twist drills and without using any lubricant.
123. The outside burrs on reamed holes shall be removed to the extent of making a i^-in.
fillet.
124. Assembling. — Riveted members shall have all parts well pinned up and firmly drawn
together with bolts, before riveting is commenced. Contact surfaces to be painted. (See 152.)
125. Lattice Bars. — Lattice bars shall have neatly rounded ends, unless otherwise called for.
126. Web Stiffeners. — Stiff eners shall fit neatly between flanges of girders. Where tight
fits are called for, the ends of the stiffeners shall be faced and shall be brought to a true contact
bearing with the flange angles.
127. Splice Plate and Fillers. — Web splice plates and fillers under stiffeners shall be cut to
fit within f-in. of flange angles.
128. Web Plates. — Web plates of girders, which have no cover plates, shall be flush with
the backs of angles or project above the same not more than f-in., unless otherwise called for.
When web plates are spliced, not more than j-in. clearance between ends of plates will be allowed.
129. Floorbeams and Stringers. — The main sections of floorbeams and stringers shall be
milled to exact length after riveting and the connection angles accurately set flush and true to
the milled ends f[or if required by the purchaser the milling shall be done after the connection
angles are riveted in place, milling to extend over the entire face of the member]. The removal
of more than ^-in. from the thickness of the connection angles will be cause for rejection.
130. Riveting. — Rivets shall be uniformly heated to a light cherry red heat in a gas or oil
furnace so constructed that it can be adjusted to the proper temperature. They shall be driven
by pressure tools wherever possible. Pneumatic hammers shall be used in preference to hand
driving.
131. Rivets shall look neat and finished, with heads of approved shape, full and of equal
size. They shall be central on shank and grip the assembled pieces firmly. Recupping and
calking will not be allowed. Loose, burned or otherwise defective rivets shall be cut out and
replaced. In cutting out rivets, great care shall be taken not to injure the adjacent metal. If
necessary, they shall be drilled out.
132. Turned Bolts. — Wherever bolts are used in place of rivets which transmit shear, the
holes shall be reamed parallel and the bolts shall make a driving fit with the threads entirely
outside of the holes. A washer not less than |-in. thick shall be used under nut.
133. Members to be Straight. — The several pieces forming one built member shall be straight
and fit closely together, and finished members shall be free from twists, bends or open joints.
134. Finish of Joints. — Abutting joints shall be cut or dressed true and straight and fitted
close together, especially where open to view. In compression joints, depending on contact
bearing, the surfaces shall be truly faced, so as to have even bearings after they are riveted up
complete and when perfectly aligned.
135. Field Connections. — Holes for floorbeam and stringer connections shall be sub-punched
and reamed according to paragraph 120, to a steel templet not less than one inch thick. $[If
required, all other field connections, except those for laterals and sway bracing, shall be assembled
in the shop and the unfair holes reamed; and when so reamed the pieces shall be match-marked
before being taken apart.]
136. Eye-Bars. — Eye-bars shall be straight and true to size, and shall be free from twists,
folds in the neck or head, or any other defect. Heads shall be made by upsetting, rolling or
forging. Welding will not be allowed. The form of heads will be determined by the dies in use
* See Addendum, clause (d).
f See Addendum, clause (f).
j See Addendum, clause (e).
SPECIFICATIONS. 217
at i In- works where the eye-bars arc made, if satisfactory to the engineer, but the manufacturer
sli.ill Kii.uMiit.-r tin- liars to break in tin- body when tested to rupture. 1 he tin. knew of head
and in-rk shall not vary more than iVin. from that specified. (See 163.)
1.^7. Boring Eye-Bars. — Before boring, earh eye-bar shall In- proj>erly anm-aled and carefully
Mi.iijitened. 1'in-holes shall be in the renter line of bars and in tin- o-nter of head*. Ban of
in- length -^lull be bored so accurately that, when placed together, pins A-in. smaller in
dianu-tiT than the pin-holes can be passed through the holes at both ends of the bars at the tame
tiiiu- without forcing.
138. Pin-Holes. — Pin-holes shall be bored true to gages, smooth and straight; at right angles
to tin- a\i-> of tin- nii-inbiT and parallel to each other, unless otherwise called for. The boring
shall bo done alter (hi- memU-r is riveted up.
139. The distance center to center of pin-holes shall be correct within ^y-in., and the dianu-ter
of the holes not more than sVin. larger than that of the pin, for pins up to 5-in. diameter, and ^-
in. for larger pins.
140. Pins and Rollers. — Pins and rollers shall be accurately turned to gages and shall be
straight and smooth and entirely free from flaws.
1.4.1. Screw Threads. — Screw threads shall make tight fits in the nuts and shall be U. S.
standard, except above the diameter of if in., when they shall be made with six threads per inch.
142. Annealing. — Steel, except in minor details, which has been partially heated, shall be
properly annealed.
143. Steel Castings. — Steel castings shall be free from large or injurious blowholes and shall
be annealed.
144. Welds. — Welds in steel will not be allowed.
145. Bed Plates. — Expansion bed plates shall be planed true and smooth. Cast wall plates
shall be planed top and bottom. The finishing cut of the planing tool shall be fine and correspond
with the direction of expansion.
146. Pilot Nuts. — Pilot and driving nuts shall be furnished for each size of pin, in such
numbers as may be ordered.
147. Field Rivets. — Field rivets shall be furnished to the amount of 15 per cent plus ten rivets
in excess of the nominal number required for each size.
148. Shipping Details. — Pins, nuts, bolts, rivets and other small details shall be boxed or
crated.
149. Weight. — The scale weight of every piece and box shall be marked on it in plain figures.
150. Finished Weight. — Payment for pound price contracts shall be by scale weight. No
allowance over 2 per cent of the total weight of the structure as computed from the plans will be
allowed for excess weight.
VIII. SHOP PAINTING.
*I5I. Cleaning. — Steel work, before leaving the shop, shall be thoroughly cleaned and given
one good coating of pure linseed oil, or such paint as may be called for, well worked into all joints
and open spaces.
152. Contact Surfaces. — In riveted work, the surfaces coming in co/itact shall each be painted
before being riveted together.
.153. Inaccessible Surfaces.— rPieces and parts which are not accessible for painting after
erection, including tops of stringers, eye-bar heads, ends of posts and chords, etc., shall have an
additional coat of paint before leaving the shop.
154. Condition of Surfaces. — Painting shall be done only when the surface of the metal
is perfectly dry. It shall not be done in wet or freezing weather, unless protected under cover.
155. Machine-Finished Surfaces. — Machine-finished surfaces shall be coated with white
lead and tallow before shipment or before being put out into the open air.
IX. INSPECTION AND TESTING AT THE SHOPS.
156. Facilities for Inspection. — The manufacturer shall furnish all facilities for inspecting
and testing the weight and quality of workmanship at the shop where material is manufactured.
He shall furnish a suitable testing machine for testing full-sized members, if required.
157. Starting Work.— The purchaser shall be notified well in advance of the start of the work
in the shop, in order that he may have an inspector on hand to inspect material and workmanship.
158. Access to Shop.— When an inspector is furnished by the purchaser, he shall have full
access, at all times, to all parts of the shop where material under his inspection is being manu-
factured.
159. Accepting Material.— The inspector shall stamp each piece accepted with a private mark.
Any piece not so marked may be rejected at any time and at any stage of the work. If the m-
* See Addendum, clause (b).
218 STEEL RAILWAY BRIDGES. CHAP. IV
spector, through an oversight or otherwise, has accepted material or work which is defective 01
contrary to the specifications, this material, no matter in what stage of completion, may b<
rejected by the purchaser.
1 60. Shop Plans. — The purchaser shall be furnished complete shop plans.
161. Shipping Invoices. — Complete copies of shipping invoices shall be furnished to tnt
purchaser with each shipment. These shall show the scale weights of individual pieces.
X. FULL-SIZED TESTS.
162. Eye-Bar Tests. — Full-sized tests on eye- bars and similar members, to prove the work-
manship, shall be made at the manufacturer's expense, and shall be paid for by the purchaser al
contract price, if the tests are satisfactory. If the tests are not satisfactory, the members repre-
sented by them will be rejected.
163. In eye-bar tests, the minimum ultimate strength shall be 55,000 Ib. per sq. in. The
elongation in 10 ft., including fracture, shall be not less than 15 per cent. Bars shall generally
break in the body and the fracture shall be silky or fine granular, and the elastic limit as indicated
by the drop of the mercury shall be recorded. Should a bar break in the head and develop the
specified elongation, ultimate strength and character of fracture, it shall not be cause for rejection,
provided not more than one-third of the total number of bars break in the head (see 136).
ADDENDUM TO GENERAL SPECIFICATIONS FOR STEEL RAILWAY BRIDGES.
POINTS TO BE SPECIFICALLY DETERMINED BY BUYERS WHEN SOLICITING PROPOSALS FOR STEEL
RAILWAY BRIDGES.
When general detail drawings are not furnished for the use of bidders specific answers shoulc
be given to questions a, b and c, below.
Specific answers should also be given to questions d, e and f if the class of work described ir
any of the paragraphs there referred to is desired. If these features are not specifically demanded
the unbracketed paragraphs will be construed to define the kind of work desired.
(a) What class of live load shall be used? (Pars. 7 and 8.)
(b) Shall linseed oil or paint be used? If paint, what kind? (Par. 151.)
(c) Shall contractor furnish floor bolts?
Sd) Shall general reaming be done? (Par. 121.)
e) Shall field connections be assembled at the shop? (Par. 135.)
f) Shall floor connection angles be milled after riveting? (Par. 129.)
INSTRUCTIONS FOR THE DESIGN OF RAILWAY BRIDGES.*
The following instructions for the design of the details of railway bridges have been prepared
y the engineering department of the Chicago, Milwaukee & St. Paul Railway, 1912.
RIVETS AND RIVET SPACING. — I. For conventional signs, actual sizes of heads and
of field rivets for various grips, see Fig. 10, Chap. XII, and Table 109, Part II.
2. Size. — Rivets for steel bridge work shall usually be \ in. diameter, except where limited
y si/i- of m.iti-rial. In very heavy work, where rivets of long grip are required, such as in the
ruins of draw spans, I in. rivets are preferable.
3. Flattened. — Rivet heads are not to be flattened to less than f in. high.
4. Countersunk. — Where heads less than | in. high are required, they shall be countersunk.
'lu- conventional signs for countersunk rivets mean that rivets shall be countersunk and chipped.
Vhrre chipping is not required, it should be so noted on the drawing. Countersunk rivets should
whenever possible.
5. Clearance of Heads. — In determining clearance the heights of heads should be assumed
jws:
Full head j in. rivet Jin. high
Full head 1 in. rivet | in. high
Full head f in. rivet A in- high
Head flattened to f in. rivet \ in. high
Countersunk, not chipped i in. high
6. Spacing. — In spacing rivets the use of fractions smaller than J in. should be avoided,
unavoidable, locate in such a way as to cause the least number of repetitions.
Locate splices and stiffeners with a view to keeping the rivet spacing as regular as possible.
7. Stagger and Clearance. — For distances center to center of staggered rivets and clearance
jired for driving, see standards. In special cases where the prescribed clearances are im-
sible, allow at least \ in. clearance for f in. and I in. rivets and A in. for f in. rivets, from the
of the rivet head to the nearest surface or other obstruction.
In the connection of cross-frames to girders, and in small lug angles and detail angles, rivets
be spaced so that they will not interfere with each other in driving.
In girder flange angles, the rivets in the "flange" legs should stagger at least I in. with rivets
he "web" legs, but should be staggered uniformly.
RIVETED CONNECTIONS. — i. Grouping. — Rivets should be grouped to insure that
line of applied stress passes as near as possible through the center of the group of rivets which
that stress. Where the eccentricity is marked, the stress on the extreme rivet due to this
itricity shall be computed and when properly combined with the direct stress shall not exceed
illdwable stress per rivet.
2. Gusset Plates. — Gusset plates shall have such a thickness as will on any section develop,
;nding and shear, the full stress which has been transmitted to it by the rivets outside the
ML.
3. Clearance. — The clearance between chords and web members entering same and other
ir riveted connections shall be not less than f in. in heavy structures and tV m- m light
tures.
PINS AND PIN PACKING. — i. Pins. — Pins shall be proportioned to carry the reactions
he stresses in all the members meeting at a point at unit stresses specified. In computing
ling moment on pins, assume each load concentrated at its center of bearing.
2. Pin Packing. — Observe the following rules regarding arrangement of eye-bars and pin
s:
(1) Arrange pin packing so as to reduce bending moment on pin to minimum.
(2) Leave at least ^g in. clearance between adjacent surfaces.
(3) Provide an additional clearance in the length of the pin of not less than \ in.
(4) When two or more pin plates are riveted together, allow fa in. for each plate, in addition
J its nominal thickness.
(5) Where hinge plates are used allow | in. clearance between hinge plates and faces of con-
ecting members.
(6) Adjacent surfaces of eye-bars composing a member shall have a clearance of f in. to
How for painting.
(7) All eye-bars are to lie in planes as nearly as possible parallel to the center line of truss,
10 divergence exceeding one inch in 16 ft. being permitted.
* Prepared by the engineering department of the Chicago, Milwaukee & St. Paul Ry.;
fir. C. F. Loweth, Chief Engineer, and Mr. J. H. Prior, Office Engineer.
219
220 STEEL RAILWAY BRIDGES. CHAP. IV.
(8) Where distance between adjacent surfaces is f in. or more, filler rings shall be provided
to prevent lateral motion, but the aggregate length of such filler rings shall be , in. less than the
neat length required, after making necessary allowances for packing.
(9) The neat grip of pins shall be the distance out to out of outside surfaces after making
allowances for clearance.
(10) The ordered length of pins between shoulders shall exceed the neat grip by the following
allowances:
For pins of 3^ in. diam. or less, allow j in.
For pins of 3! in. diam. to 6 in. diam., allow | iiv
For pins of 6| in. diam. to 91 in. diam., allow f in.
GIRDER WEBS. — Width of Web Plates. — On deck girders the web must usually project
f in. above the back of the top flange angles, to receive the notches in the track ties, except for
concrete deck floors where the slabs rest on a top cover plate. In other cases, where no cover
plates are required, the web must be flush with the top flange angles. At the bottom flange in
all cases, and at the top flange where cover plates are required, the web may be set back i in.
Web plates shall not be ordered in widths having a fraction of an inch less than £ in.
Thickness. — Web plates should have a minimum thickness of ^ in. At web splices \ in.
clearance between ends of web plates shall be allowed.
Web Splices Location. — Web splices for girders, when required, should preferably be placed
near the third or quarter points, and never when avoidable at the point of maximum moment.
Size. — Web splices should be of sufficient width to take two lines of rivets through each
section of the web spliced. When not under floorbeam connection angles, f in. clearance may be
allowed top and bottom.
Moment Splices. — In addition there should be splice plates on the vertical legs of the flange
angles, designed to splice the portion of the web covered by the flange and where thus spliced, the
resisting moment on the web may be taken as equivalent to that of | of its gross area considered
as flange section.
Where the splice plates on the flange angles are omitted, the rivets in the flange angles for a
distance of one foot either side of the splice may be considered as part of the group of splicing rivets,
and account shall be taken of the longitudinal shearing stress on these rivets as well as the stress
due to the splice.
Riveting. — The riveting shall, where practicable, be such as to develop the full strength of
the web, and shall always be such as to develop the actual moment carried by the web at any point;
this being determined by multiplying the total moment on the section by the ratio of | of the gross
web section to the total flange area, including this web equivalent. Splices shall also be designed
to carry the total shear on the section due to the assumed loading.
GIRDER FLANGES. — i. Composition. — At least £ of the area of the flange section should
consist of angles, or else the maximum size of the latter be used, and in no case should the center
of gravity of the flange come above the flange angles. For location of center of gravity for various
types of flange and sizes of material, see Table 88, Part II.
2. Composition of flanges shall preferably be as follows:
(1) 6" X 6" angles without cover plates.
(2) 6" X 6" angles with 14 in. or 16 in. cover plates.
(3) 8" X 8" angles with 17 in. or 18 in. cover plates.
(4) 8" X 8" angles with 2 or 4-6" X 4" angles, without cover plates. (Type A4.)
Thickness of flanges without cover plates shall not be less than TV the width of the outstanding
leg of the angle.
3. Net Section. — The riveting in the tension flanges shall be computed according to method
shown in Tables 109 to 113, Part II. Where the spacing of flange rivets is not known in advance,
about the following allowances shall be made. In detailing flange riveting, where there is not a
considerable excess of flange section, endeavor to keep within these allowances:
(1) Flange angles without cover plates and without lateral bracing connections, each angle —
one hole out.
(2) Flange angles without cover plates, but with lateral connections, each angle — if holes
out.
(3) Flange angles with cover plates, each angle— two holes out.
(4) Cover plates — two holes out.
4. Cover Plates. — Cover plates shall have the same thickness or shall diminish in thickness
from the flange angle out. In determining length of cover plates, the curve of maximum moments
shall be established and plates shall be made I ft. longer at each end than the theoretical require-
ment.
5. Flange Splices. — Flanges shall never be spliced unless it is impossible to get material of
the required length. Where flange splices occur the following requirements shall be observed:
INSTRUCTIONS TO DRAFTSMEN, C. M. & ST. P. RY. 221
(1) Splices shall always be located at points where there is an excess of flange section.
(2) No two parts of the ilaii^e shall be spliced within 2 ft. of each other.
(3) Flange angles shall be spliced with a splice angle of equal section riveted to both legs of
the angle spliced. Where this is impossible, the largest possible splice angle shall be used, and the
difference made up by a plate riveted to the vertical leg of the opposite angle.
(4) In splicing cover plates where one or more plates intervene between the splice plate and
the cover plate which it splices, the requirement of paragraph 57 of the A. R. E. A. Specifications
for Design shall be-observed.
(5) Rivets in splice plates and angles shall be located as close together as possible, in order
that the transfer may take place in a short distance.
(6) No allowance shall be made for abutting edges of spliced members of the compression
flange.
6. Flange Riveting. — Rivets connecting flange to the web shall be sufficient to resist at any
point the longitudinal shear combined with any load that is applied directly to the flanges. The
wheel loads where ties rest directly on the flanges shall be assumed to be distributed over 3 ft.
The pitch of rivets between flange and web at any section may be computed by the formulas:
For through girders, p = R • d/S.
D
For deck girders, p
P = longitudinal spacing of rivets in inches;
R = value of one rivet in bearing or double shear in pounds;
d = distance center to center of flanges in inches;
S = total maximum shear in pounds at the section, reduced in the ratio of the net area of
flange angles and plates to the net area of flange plus J the gross web section.
W = one wheel load plus 100 per cent impact.
7. Maximum Spacing. — Maximum spacing of rivets between flanges and web shall be:
Top flange, deck girders 3^ in.
Top flange, through girders f 4 J in.
For convenience in shop work, spacing of rivets in top and bottom flanges shall be exactly
alike where possible.
8. Rivets in Cover Plates. — Where it is necessary to compute spacing of rivets connecting
cover plates to flange angles, the following formula may be used:
p = n • R • d/S X Ala
where R = value of one rivet in single shear or bearing;
n = number of rivets on one transverse line through cover plates and flanges;
a = total area of cover plates at section;
A = area of entire flange at section;
S and d, as in section 6, "Flange Riveting."
The pitch as computed by this formula shall be diminished 15 per cent for every cover plate
more than one. Rivets in cover plates shall preferably stagger half way with the rivets in the verti-
cal legs of the flange angles. The maximum spacing shall be 6 in.
9. Circular Ends. — For through spans with circular ends, the end angles should be spliced near
the ends, as the full length angles cannot be handled in making the bends.
Rivets through cover plates on circular ends must be spaced close enough to draw the plates
tight against the angles. The smaller the radius, the closer rivets should be spaced.
10. Overrun of Angles. — In plate girders whose top flange is composed of four or more angles,
about I in. should be allowed between the edges of angles to allow for overrun.
11. Gage in Cover-Plates.— On girders which are similar, but which have webs of different
thickness, the gage in the angles should be left the same and the gage in the cover plate varied to
suit the web thickness.
GIRDER STIFFENERS. — Intermediate Stiff eners. — Intermediate stiff eners, except at con-
centrated load, may be offset, and shall bear tightly against top and bottom flange. The ordered
length of offset stiffener angles shall be the finished length plus the thickness of each angle over
which it is offset.
Size of Stiffeners. — In general, the minimum size of stiffeners bearings against 6" X 6"
flange angles shall be 5" X 3$" X I", and against 8" X 8" flange angles shall be 6" X 3i"
X I".
Field riveted stiffeners at floorbeams of through girders may have J in. clearance at the top.
Fillers under end stiffeners and under concentrated loads must bear on bottom flange, but may
have i in. clearance at top.
222 STEEL RAILWAY BRIDGES. CHAP. IV.
Rivets in Stiff eners.— Rivets in stiffener angles may have the maximum spacing, except that:
(a) Rivets in end stiffeners and stiffeners at concentrated loads shall develop the full computed
stress in the stiffeners.
(b) Spacing of rivets in end stiffeners, intermediate stiffeners, and web splices shall be identi-
cal, except that rivets in any line may be omitted where possible without exceeding the maximum
specified pitch, in order to minimize shop work of punching.
Holes for Hand-Hooks. — All stiffeners on deck girders with concrete decks and ballast floors
should have holes punched in the outstanding legs for inserting hand-hook to support a person
inspecting bridge. Holes should be jf in. diameter and located 6 in. from top flange on shallow
girders and 6 ft. from bottom flange on deep girders. Gage line of hole to be l| in. from outer
edge of angle.
STRINGERS AND FLOORBEAMS. — I. Stringers. — Stringers for through girder spans
may be either I-beams or built girders. Where I-beams are used two stringers shall be placed
under each rail. Depth of stringers shall depend on available distance from base of rail to "low
bridge"; depth shall be preferably £ to i, but not less than TV, the panel length.
2. Floorbeams. — Depth of floorbeams shall be such as to allow stringers to be framed readily
into the web, and not less than | of the distance center to center of girders or trusses.
3. Stringer Connections. — Stringers shall be riveted to webs of floorbeams with f in. con-
nection angles. Connection angles are to be faced to provide uniform bearing against webs of
floorbeams. Make stringers yj in. short at each end for clearance in erecting.
4. Floorbeams for Through Girders. — The gusset plates connecting floorbeams to main
girders shall, wherever possible, extend to the top of the girder and shall have an angle riveted
along the edge, to form an effective stay for the top flange of the main girder, and they shall also
form the webs of the end portions of the floorbeams, extending out toward the center as far as the
clearance line will allow, and being there spliced to the main web.
5. Floorbeams for Truss Bridges. — Floorbeams for truss spans shall preferably be riveted to
the vertical posts or hangers, extending the connection angle above the top flange where necessary
to secure sufficient rivets. When it is necessary to cut away the lower corner of the floorbeam to
clear the chord, special care shall be taken to so reinforce the web as to carry the end shear into
the connection angles.
TRUSS AND TOWER MEMBERS. — i. Top Chord and End-post. — The top chord and
the inclined end-post shall usually consist of two built channels, with a thin cover plate on top
and with bottom flanges latticed. The bottom flanges shall be made heavier than the top, in
order that the gravity axis may come as close as possible to the center line of the webs.
2. Verticals and Rigid Tension Members. — Intermediate posts shall usually consist of two
rolled or built channels latticed. Hip verticals and similar members and the two end panels
of the bottom chords of single track pin-connected trusses shall be rigid, and may consist either
of two rolled or built channels latticed; or of four angles latticed to form an I-section.
3. Eye-bars. — Eye-bars shall be used for all bottom chord members and main diagonals that
do not require to be stiffened in pin-connected trusses. Dimensions of heads shall be according
to manufacturers shop standard. Length of eye-bars shall be given on the drawings, center to
center of pin holes, and also back to back of pin holes.
4. Eccentricity. — The line of applied force must coincide with the gravity axes of built
members or else the member must be designed for combined direct stress and flexure due to the
eccentricity of the applied load.
5. Bending Due to Weight. — Bending moment in the top chord and end-post due to weight
p
of member may be computed by the approximate formula, -r db M-c/I, where P = total direct
A
stress in the member; A = gross area of the section of the member; M = bending moment at the
section of the member in in.-lb.; c = distance to extreme fiber; and / = moment of inertia of the
section of the member, and the stress from such bending shall be deducted from the average
compressive stress allowed by the column formula.
6. Bending in End-posts. — In computing stresses in the end-post of through pin-connected
trusses, due to wind force, where the end-post consists of two built or rolled channels, if the product
of the wind reaction in the top chord times one-half the distance from the foot of the post to the
lowest connection of the portal bracing does not exceed the product of the dead load stress in one
of the channels composing the end-post times the distance center to center of the bearings of the
channels on the pin, the post may be considered fixed-ended and the point of contra-flexure
assumed midway between the foot of the post and the lower connection of the portal bracing.
Otherwise it must be considered pin-connected. The end-posts of riveted through trusses shall
be considered as fixed-ended columns.
7. Over-run of Angles. — Where side plates are used on chord sections placed between the
flange angles, at least | in. clearance should be allowed between the edges of the plate and the
angles to allow for over-run of angles.
INSTRUCTIONS TO DRAFTSMEN, C. M. & ST. P. RY. 223
8. Clearance for Riveting. — When flanges of angles and channels of built members are turned
in, 5i in. opi-nin^ U-i wt-.-n c.l-r-, ot aiu.K •-, or ili.uin.l-, is required torivet the tic platcaand lacing.
LATERAL AND SWAY BRACING.— i. Minimum Sizes.— The minimum size of ai
to In- and in br.u-inus shall be 3i" X 3" X J". Not less than three rivets shall be used in the
connection.
2. Effective Section. — Where single angles are used for bracing members without lug angler
connecting the outstanding leg to the gusset plates, not more than 80 per cent of the net section, if
in U-IIM .HI, >h.ill be considered as effective.
\Vlu n- single angles, used for bracing members, have lug angles connecting their outstanding
legs to the gusset plates, and where the center of the group of connecting rivets in the gusset
plates fall close to the gravity line of the angle, in plan, 90 per cent of the net section may be
considered effective.
3. Double Diagonal Systems. — In double diagonal systems the shear due to wind force shall
be considered as carried wholly by one diagonal in tension, but the maximum value of IJr — 120,
specified for bracing members, shall not be exceeded. In assuming "r" the connection of di-
agonals at their intersection may be considered as offering support against deflection in the plane
of the system, but not against deflection perpendicular thereto.
4. Bending at Connections. — Connections between bracing members and chords shall be
designed to avoid as far as possible any bending stress in main truss members.
5. Allowance for Draw. — For diagonal bracing of one or two angles the following draw
should be allowed:
For lengths up to 10 ft. No Allowance,
from 10 to 21 ft. Allow & in.
from 21 to 35 ft. Allow | in.
over 35 ft. Allow ^ m-
The use of thirty-seconds of an inch should be avoided but the above allowances should not be
varied by more than ^j in.
LATERAL BRACING. — i. Lateral Bracing. — Lateral bracing shall be in general as follows:
(1) Deck girders and top flanges of stringers 15 ft. long and over; single diagonal system with
transverse struts, composed of single angles. Slope of diagonals 45° to 60° with axis of bridge.
(2) Through girders: Do'uble diagonal system of same panel length as floor system, com-
posed of single angles; floorbeams to act as the transverse struts of the system.
(3) Trusses, loaded chord: Double diagonal systems of same panel length as floor systems,
composed of single angles, or double angles back to back; floorbeams to act as the transverse
struts of the system.
(4) Trusses, unloaded chord: Double diagonal systems of same panel length as floor system
with transverse struts at panel points; all composed of two or four angles laced to form a channel
or I-section, of depth equal to depth of chords.
2. Traction Stresses. — The lateral system in the plane of the loaded chord of truss spans and
of through girder spans shall be effectively riveted to the stringers at intersections, and the diagonal
shull be designed to transmit the traction for one panel length of track to the panel point; one
diagonal for each stringer considered acting in tension.
3. Clipping Angles for Clearance. — The vertical leg of laterals should be clipped -at the end
when there is a possibility that the square corner would interfere in any way with putting in the
laterals or riveting up. This is to be particularly looked out for at floorbeam connections of
through girder spans and in top laterals of Type A4 girder spans.
4. Squaring of Holes in Connections. — Where laterals are riveted to stringers the holes
should be squared with the stringers, if possible. At the intersection of diagonals, the holes in
splices with two lines c'
5. Tie Plates and
bars, they should bedet
6. Lateral Plates €3 and C4 Spans.— The lateral plates of Type C3 and Type C4 girder
spans (flanges two angles and cover plates) should not be shop riveted to the girders, as it is
impossible to put in floorbeam connection angles when this is done.
TRANSVERSE BRACING. — I. Transverse bracing shall be used as follows:
(1) At intervals of not more than 15 ft. on deck girder spans. Intermediate frames shall be
of minimum material. End frames shall be designed to carry to the abutment the total lateral
forces acting on the top flange. End frames of skew deck gilders shall be placed at the end
of the short girder, and at right angles to same. Top and bottom lateral diagonal braces shall
be used to stay the end of the long girder.
(2) As spacers for stringers resting on masonry where end floorbeams cannot be used. These
frames shall be riveted to girders or truss shoes where practicable.
(3) As spacers for stringers at all expansion points.
(4) At end panel of through truss spans, having vertical truss members. These frames
shall be as deep as clearance will permit.
224 STEEL RAILWAY BRIDGES. CHAP. IV.
(5) Through truss spans shall have riveted portal braces rigidly connected to the end-posts
and top chords. They shall be as deep as clearance will allow, and shall be designed to carry to
the abutment the total wind force acting on the top chord.
(6) At panel points of deck truss spans, having vertical members. Intermediate frames
shall be designed to carry \ the panel concentration of wind and centrifugal force to the bottom
chord and the end frame shall be designed to carry f the total wind and centrifugal force acting
on the top chord to the abutment.
Frames for (i), (2) and (3) shall consist of single angle struts, top and bottom and double
diagonals. Frames for (4) may consist of knee braces attached to the top lateral struts, but pre-
ferably where clearance permits, of light open webbed girder. Portal frames shall consist of open
webbed girders, with knee braces connections to inclined posts. Frames for (6) shall consist of
double diagonals running between floorbeams and lower lateral struts and composed of two angles
back to back, or of two or four angles laced.
2. Diaphragms for Twin Deck Spans. — Diaphragms connecting two pairs of twin girders
are to be omitted on shallow spans. Where the girders exceed 3 ft. 6 in. in depth, diaphragms shall
be added for rigidity. They shall be connected to girders with field bolts.
3. End Cross Frames and Diaphragms. — In the design and location of end cross frames and
diaphragms their shape and position shall be such as to give access to the space between the
girders for inspection, painting and the placing of anchor bolts.
REFERENCES. — For the calculation of the stresses in railway bridges and for additional
details and the details of design, the following books may be consulted: Merriman & Jacoby's
"Roofs and Bridges," Part I, Stresses; Part II, Graphic Statics; Part III, Bridge Design; Part IV,
Higher Structures; Johnson, Bryan and Turneaure's "Framed Structures," Part I, Stresses,
Part II, Statically Indeterminate Structures and Secondary Stresses ; Part III, Design (in prep-
aration); Marburg's "Framed Structures," Part I, Stresses; Spofford's "Theory of Structures,"
stresses in structures; DuBois's "Framed Structures"; Burr and Falk's "Design and Construction
of Metallic Bridges"; Skinner's "Details of Bridge Design," Parts I, II, III; Moore's "Design
of Plate Girders"; Ketchum's "The Design of Highway Bridges, "-stresses, details and design.
CHAPTER V.
RETAINING WALLS.
Introduction. — A retaining wall is a structure which sustains the lateral pressure of earth or
some other granular mass which possesses some frictional stability. The pressure of the material
supported will depend upon the material, the manner of depositing in place, and upon the amount
of moisture, and will vary from zero to the full hydraulic pressure. If dry clay is loosely deposited
behind the wall it will exert full pressure, due to this condition. In time the earth may become
consolidated and cohesion and moisture make a solid clay, which may cause the bank to shrink
away from the wall and there will be no pressure exerted. On the other hand all cohesion may
be destroyed by the vibration of moving loads or by saturation, and the maximum theoretical
pressures may occur. The pressures due to a dry granular mass, a semi-fluid, without cohesion,
of indefinite extent, the particles held in place by friction on each other, will be considered. The
effect of cohesion and of limiting the extent of the mass is considered in the author's "The Design
of Walls, Bins and Grain Elevators."
Nomenclature. — The following nomenclature will be used:
^ = the angle of repose of the filling.
<t>' = the angle of friction of the filling on the back of the wall.
6 = the angle between the back of the wall and a horizontal line passing through the heel of the
wall and extending from the back into the fill.
8 = angle of surcharge, the angle between the surface of the filling and the horizontal; & is
positive when measured above and negative when measured below the horizontal.
2 = the angle which the resultant earth-pressure makes with a normal to the back of the wall.
X = the angle between the resultant thrust, P, and a horizontal line.
h = the vertical height of the wall in feet.
d = the width of the base of the wall in feet.
t> = the distance from the center of the base to the point where the resultant pressure, E, cuts
the base. -
P = the resultant earth-pressure per foot of length of wall.
£ = the resultant of the earth-pressure and the weight of the wall.
w = the weight of the filling per cubic foot.
W = the total weight of the wall per foot of length of wall.
PI = the pressure on the foundation due to direct pressure.
fa = the pressure on the foundation due to bending moments.
P = the resultant pressure on the foundation due to direct and bending forces.
y = the depth of foundation below the earth surface.
Calculation of the Pressure on Retaining Walls. — To fully .determine the pressure of the
filling on a retaining wall it is necessary that the resultant of the pressure be known (a) in amount,
(b) in line of action, and (c) in point of application. Many theories have been proposed for
finding the pressure, each differing somewhat as to the assumptions and results. All theories
for the design of retaining walls that have any theoretical basis come in two classes: (i) the Theory
of Conjugate Pressures, due to Rankine, and commonly known as Rankine's Theory, and (2)
the Theory of the Maximum Wedge, probably first proposed by Coulomb, and commonly known
as Coulomb's Theory. Rankine's Theory determines the thrust in amount, in line of action, and
in point of application. In Coulomb's Theory, with the exception of Weyrauch's solution, the
line of action and point of application must be assumed, thus leading to numerous solutions of
16 225
226
RETAINING WALLS.
CHAP. V.
more or less merit. All solutions based on the theory of the wedge assume that the resultant
thrust is applied at one-third the height for a wall with a level or inclined surcharge, as is given
by Rankine; but the resultant is assumed as making angles with a normal to the back of the
wall varying from zero to the angle of repose of the filling. In Rankine's solution the resultant
pressure is parallel to the plane of the surcharge for a vertical wall with a level or positive surcharge.
(i) RANKINE'S THEORY. — In this theory the filling is assumed to consist of an incom-
pressible, homogeneous, granular mass, without cohesion, the particles are held in position by
friction on each other; the mass being of indefinite extent, having a plane top surface, resting
on a homogeneous foundation, and being subjected to its own weight. The principal and conju-
gate stresses in the mass are calculated, thus leading to the ellipse of stress. In the analysis it
is proved (a) that the maximum angle between the pressure on any plane and the normal to
the plane is equal to the angle of internal friction, and (b) that there is no active upward component
of stress in a granular mass. Both of these laws have been verified by experiments on semi-
fluids. Ra'nkine deduced algebraic formulas for calculating the resultant pressure on a vertical
wall with a horizontal surcharge, and on a vertical wall with a surcharge equal to 5, an angle
equal to or less than the angle of repose. The general case is best solved by constructing the
ellipse of stress by graphics, or Weyrauch's algebraic solution may be used. The author has
extended Rankine's solution in "The Design of Walls, Bins and Grain Elevators," so that it is
perfectly general.
Rankine's Formulas. — With a vertical wall and a horizontal surcharge, Fig. i, the total
resultant pressure is
„ , ,, i — sin <t> , .
P = \-W-W j r— 7 (i)
I + sin <£
where w is the weight of the filling in Ib. per cu. ft., h is the depth of the wall in feet, <f> is the angle
of repose of the filling, and P is the resultant pressure on the wall in pounds. The resultant
pressure, P, will be horizontal.
D
FIG. i.
For a vertical wall with surcharge at an angle 5, Fig. 2, the pressure is given by the formula
(2)
P = %w-h?-cos d
Where 8 is equal to 4>, formula (2) becomes
P =
cos S — \ cos2 5 — cos2
cos 5 + Vcos2 5 — cos2 <f>
cos<(>
(3)
The resultant pressure, P, is parallel to the inclined top surface for a vertical wall with a level
or a positive surcharge (many authors have incorrectly assumed that the resultant pressure is
always parallel to the top surface of the surcharged filling).
Inclined Retaining Wall. — The pressure on an inclined retaining wall may be calculated by
means of the ellipse of stress — see the author's "The Design of Walls, Bins and Grain Elevators."
COULOMB'S THEORY.
227
The pressure on an inclined retaining wall may also be calculated by means of the graphic solution
shown in Fig. 3 if the direction of the thrust be known. From Rankine's theory we know that
the resultant pressure on a vertical retaining wall is always parallel to the top surface where the
stirrhar^e is K-vel or is inclined upwards away from the wall. The pressure on a retaining wall
inclined away from the filling may then be calculated as follows:
FIG. 3. PRESSURE ON AN INCLINED RETAINING WALL.
In Fig. 3 the retaining wall A CDB sustains the pressure of a filling having an angle of repose
^, and sloping up away from the top of the wall at an angle 5. Calculate P' the pressure on the
plane E-B by means of formula (2). P' acts at a point \EB above B and is parallel to the
top surface DE. Let the weight of the triangle of filling DBE be G, which acts through the
center of gravity of the triangle and intersects P' at point O. Then Pt, the resultant of P'
and G, will be the resultant pressure at O, and makes an angle z with a normal to the back of the
wall, and an angle, X = 0 + z — 90° with the horizontal.
(2) COULOMB'S THEORY. — In this theory it is assumed that there is a wedge having
the wall as one side and a plane called the plane of rupture as the other side, which exerts a maxi-
mum thrust on the wall. The plane of rupture lies between the angle of repose of the filling and
the back of the wall. It may coincide with the plane of repose. For a wall without surcharge
(horizontal surface back of the wall) and a vertical wall the plane of rupture bisects the angle
between the plane of repose and the back of the wall. This theory does not determine the direc-
tion of the thrust, and leads to many other theories having assumed directions for the resultant
pressure.
Algebraic Method. — In Fig. 4, the wall with a height h, slopes toward the earth, being in-
clined to the horizontal at an angle Q, and the earth has a surcharge with slope S, which is not
greater than <£, the angle of repose. It is required to find the pressure P against the retaining
wall, it being assumed that the resultant pressure makes an angle z with the back of the wall.
It is assumed that the triangular prism of earth above some plane, the trace of which is the
line A E, will produce the maximum pressure on the wall and on the earth below the plane, and
that in turn the prism will be supported by the reactions of the wall and the earth. Let OW
represent the weight of the prism ABE, the length of the prism being assumed equal to unity,
let OP be the reaction of the wall, and OR be the reaction of the earth below.
Now the forces OW, OP, and OR will be concurrent and will be in equilibrium; OP and OR
will therefore be components of OW. When the prism ABE is just on the point of moving OP
228
RETAINING WALLS.
CHAP. V.
will make an angle with a normal to the back of the wall equal to z (different authorities assume
values of z from zero to <j>', the angle of friction of earth on masonry, or <j>, the angle of repose of
earth); while OR will make an angle with the normal to the plane of rupture AE equal to <f>.
Let P represent the pressure OP against the wall, W represent the weight of the prism of earth,
and w the weight. per cu. ft.
I*--.
FIG. 4.
In the triangle OWR angle WOR = x - <j>, and angle ORW = 9 + <t>+z-x. Through E
draw E N, making the angle AEN = 9 + <]> + z — x with A E. Then the triangle A E N is
similar to triangle ORW, and
P_
W
EN
AN'
and
P = W
EN
AN
But W equals warea triangle ABE = %w-AB- BE- sin (0 — 5), and
AB-BE-EN
P =
(0 - 5)
(4)
Now P varies with the angle x, and will have a maximum value for some value of x, which
may be found by differentiating (4) and placing the result equal to zero.
Differentiating and substituting in (4) and reducing we have
sin2 (0 - 0)
P =
sin2 6 • sin (0 +
sin (z + &) • sin
sin (0 + z) • sin (0
_=«Y
-*))
which is the general formula for the pressure on a retaining wall.
Now if z in (5) is made equal to <£', the angle of repose of earth on the wall,
sin2 (6 — 0)
P = \w-W
sin2 0- sin (0 + <t>') I i
which is Cain's formula (20) in another form.
sin (0 + 0')-sin (0 — 5)
sin (0 + 0') • sin (0
-*)V
-I)/
(5)
(6)
(7)
GRAPHIC METHOD.
If t in (5) is made equal to «, and 8 made equal to 90°,
COS*0
/sill 10 -f d.-MH (0 - A,V
\" co*'« J
(8)
which is Rankine's formula (2) in another form.
If 2 in (5) is made equal to zero,
sin1 (8 - 0)
(9)
which gives the normal pressure on a wall.
If 0 in (9) = 90°,
If 6 in (10) - 0°,
/ i I sin 0- sin (0 -g)\*
\ V cos 5 /
P = Jwft*
(i -f sin #)* '
tan2 (45° - i«j
I — sin <b
do)
(II)
(12)
which is Rankine's formula (i) for a vertical wall without surcharge.
Graphic Method. — If the angle 2, the angle between the back of the wall and a normal to
the wall, is known, the resultant pressure on a wall may be calculated by a graphic method.
Fig. 5, based on the "theory of a wedge of maximum thrust." The graphic method will be
described— the proof of the method is given in "The Design of Walls, Bins and Grain Elevators."
FIG. 5.
In Fig. 5 the retaining wall AB sustains the pressure of the filling with a surcharge i and
an angle of repose <f>. It is required to calculate the resultant pressure P.
The graphic solution is as follows: Through B in Fig. 5 draw BM making an angle with BF,
the normal to AD, equal to X = 0 + x — 90°, the angle that P makes with the horizontal. With
230 RETAINING WALLS. CHAP. V.
diameter AD describe arc A CD. Draw M C normal to AD and with A as a center and a radius
AC describe arc CN. Then A N = y, AM = b and y = Vo^>. Draw EN parallel to BM.
With N as a center and radius E N, describe arc ES. Then A E is the trace of the plane of
rupture, and P = area SEN-w.
Cain's Formulas.* — Professor William Cain assumes that the angle z is equal to <£', the
angle of friction of the filling on the back of the wall. By substituting in (5) we have for a
Vertical Wall With Level Surface, 5 = o.
where
Vsin (<f> + <t>') • sin <f>
cos</>'
If $ = </>', then n = V 2 sin <f>, and
, -M
(i + sm ^> i/2)a
If <£' = o, then
P = ^-A2-tan2(45° - (IS)
Fer/icoJ Wctf Witt Surcharge = 5.
.
n + i / cos </>'
where
Vsin (<f> -|- «ft') • sin (</> — 5)
cos 0' • cos 5
If 5 = 4,
P = ?w-hZ^j-T' (J7)
If <f>' = o, and 5 = <f>,
p = ^wffi'cos* <i> (18)
Inclined Wall With Horizontal Surface.
P = \wh*( sin(g~.^ \*-. L (I9)
where
Vsin (<ft + </>Q-sin <t>
sin (<£' + (?)-sin<?
Inclined Wall With Surcharge = d.
where
Vsin (<^> + (/>Q-sin (<^>
sin («' + »)• sin (9 -
— 5)
8)
Wall With Loaded Filling. — In Fig. 6, the filling is loaded with a uniformly distributed load.
Calculate hi by dividing the loading per sq. ft. by w. Let h + hi = H. Then the resultant
pressure for a wall with height H, will be
Pz = %w-H*-K (21)
and the resultant pressure for a wall with height hi, will be
Pi = i«> •*!»•.£ (22)
* Professor Rebhann makes the same assumptions and uses the graphic method of Fig. 5.
STABILITY OF RETAINING WALLS. 231
The pressure on the wall AD will be
P = Pt - P, = \w(H* - hS)K (23)
and the point of application is through the center of gravity of ADGE, which makes
t
yi ~ * ~
A • L oading per sq. ft+Hr
DA
)*
I H*+ Hh,-2h?
FIG. 6.
Walls With Negative Surcharge. — For the calculation of the pressures on retaining walls with
negative surcharge, 5 negative, see the author's " The Design of Walls, Bins and Grain Elevators,"
second edition.
STABILITY OF RETAINING WALLS.— A retaining wall must be stable (i) against
overturning, (2) against sliding, and (3) against crushing the masonry or the foundation.
The factor of safety of a retaining wall is the ratio of the weight of a filling having the same
angle of internal friction that will just cause failure to the actual weight of the filling. For a
factor of safety of 2 the wall would just be on the point of failure with a filling weighing twice
that for which the wall is built.
1. Overturning. — In Fig. 7, let P, represented by OP', be the resultant pressure of the earth,
and \V, represented by OW, be the weight of the wall acting through its center of gravity. Then
E, represented by OR, will be the resultant pressure tending to overturn the wall.
Draw 05 through the point A. For this condition the wall will be just on the point of
overturning, and the factor of safety against overturning will be unity. The factor of safety
for E = OR will be
/o = SWIRW (25)
2. Sliding. — In Fig. 7 construct the angle Hi G equal to <f>', the angle of friction of the masonry
on the foundation. Now if E passes through I, and takes the direction OQ, the wall will be on
the point of sliding, and the factor of safety against sliding, /«, will be unity. For E = OR, the
factor of safety against sliding will be
/. = QM'/RM (26)
Retaining walls seldom fail by sliding.
The factor of safety against sliding is sometimes given as
/?
/. = jj tan *'. (27)
where H is the horizontal component of P. Equations (26) and (27) give the same values only
where the resultant P is horizontal.
3. Crushing. — In Fig. 7 the load on the foundation will be due to a vertical force F, which
produces a uniform stress, p\ = Fid, over the area of the base, and a bending moment = F-b,
which produces compression, fa, on the front and tension, fa, on the back of the foundation.
232
RETAINING WALLS.
CHAP. V.
The sum of the tensile stresses due to bending must equal the sum of the compressive stresses,
= $p2d. These stresses act as a couple through the centers of gravity of the stress triangles on
each side, and the resisting moment is
M' = \p*-d'ld =
(28)
FIG. 7.
FIG. 8.
But the resisting movement equals the overturning moment, and
and
6F-b
(29)
The total stress on the foundation then is
P = pi =*= pz = pi(i ="= 6bfd) (30)
Now if b = \d, we will have
p = 2pi, or o.
In order therefore that there be no tension, or that the compression never exceed twice the
average stress, the resultant should never strike outside the middle third of the base.
If the resultant strikes outside of the middle third of a wall in which the masonry can take
no tension, the load will all be taken by compression and can be calculated as follows:
In Fig. 8 the resultant F will pass through the center of gravity of the stress diagram, and
will equal the area of the diagram.
F = \p-a
and
2F
which gives a larger value of p than would be given if the masonry could take tension.
General Principles of Design. — The overturning moment of a masonry retaining wall of
gravity section depends upon the weight of the filling, the angle of internal friction of the filling,
the surcharge, and the height and shape of the wall. The resisting moment depends, upon the
GENERAL PRINCIPLES OF DESIGN. 233
weight of the masonry, the width of the foundation, and the cross-section of the wall. The most
economical section for a masonry retaining wall is obtained when the back slopes toward the
filling. In cold localities, however, this form of section may be displaced by heaving due to the
action of frost, and it is usual to build retaining walls with a slight batter forwards. The front of
the wall is usually built with a batter of from i in. to I in. in 12 in. In order to keep the center
of gravity of the wall back of the center of the base it is necessary to increase the width of the
wall at the base by adding a projection to the front side. Where the wall is built on the line
of a right of way it is sometimes necessary to increase the width of the base by putting the pro-
jection on the rear side, making an L-shaped wall. The weight of the filling upon the base and
back of the wall adds to the stability of the wall. Where the wall is built to support an em-
bankment expensive to excavate, it is often economical to make the wall L-shaped, with ah the
projection on the front side.
In calculating the thrust on retaining walls great care must be exercised in selecting the
proper values of w and </>, and the conditions of surcharge. It will be seen from the preceding
discussion that the value of the thrust increases very rapidly as 0 decreases, and as the surcharge
increases. Where the wall is to sustain an embankment carrying a railroad track, buildings,
or other loads, a proper allowance must be made for the surcharge.
The filling back of the wall should be deposited and tamped in approximately horizontal
layers, or with layers sloping back from the wall; and a layer of sand, gravel or other porous
material should be deposited between the filling and the wall, to drain the filling downwards.
To insure drainage of the filling, drains should be provided back of the wall and on top of the
footing, and "weep-holes" should be provided near the bottom of the wall at frequent intervals
to allow the water to pass through the wall. With walls from 15 to 25 ft. high, it is usual to use
"weepers" 4 in. in diameter placed from 15 to 20 ft. apart. The "weepers" should be connected
with a longitudinal drain in front of the wall. The filling in front of the wall should also be
carefully drained.
The permissible point at which the resultant thrust may strike the base of the foundation
will depend upon the material upon which the retaining wall rests. When the foundation is
solid rock or the wall is on piles driven to a good refusal, the resultant thrust may strike slightly
outside the middle third with little danger to the stability of the wall. When the retaining wall,
however, rests upon compressible material the resultant thrust should strike at or inside the center
of the base. Where the resultant thrust strikes outside of the center of the base, any settlement
of the wall will cause the top to tip forward, causing unsightly cracks and local failure in many
cases, and total failure where the settlement is excessive. Where extended footings are used it
may be necessary to use some reinforcing steel to prevent a crack in the footing in line with the
face of the wall.
Plain masonry walls should be built in sections, the length depending upon the height of the
wall, the foundation and other conditions.
Under usual conditions the length of the sections should not exceed 40 ft., 30 ft. sections
being preferable, and in no case should the length of the section exceed about three times the
height. Separate sections should be held in line and in elevation, either by grooves in the masonry
or by means of short bars placed at intervals in the cross-section of the wall, fastened rigidly in
one section and sliding freely in the other. The back of the expansion joints should be water-
proofed with 3 or 4 layers of burlap and coal tar pitch. The burlap should be about 30 in. wide,
and the pitch and the burlap should be applied as on tar and gravel roofs. The joints between
the sections of a retaining wall on the front side should be from fc to J of an in. in width, and
should be formed by a V-shaped groove made of sheet steel and fastened to the forms while the
concrete is being placed. Where there is danger of the water in the filling percolating through
the wall or in an alkali country, the surface of the back of the wall should be coated with a water-
proof coating. The most satisfactory waterproof coating known to the author is a coal tar
paint made by mixing refined coal tar, Portland cement and kerosene in the proportions of 1 6
parts refined coal tar, 4 parts of Portland cement and 3 parts of kerosene oil. The Portland
234 RETAINING WALLS. CHAP. V.
cement and kerosene should be mixed thoroughly and the coal tar then added. In cold weather
the coal tar may be heated and additional kerosene added to take account of the evaporation.
This paint not only covers the surface but combines with it, so that two or three coats are some-
times required. While the surface of the concrete should be dry, coal tar paint will adhere to
moist or wet concrete. In building retaining walls in sections, the end of the finished section should
be coated with coal tar paint to prevent the adhesion to the next section.
For methods of waterproofing masonry, see methods of waterproofing bridge floors in Chap-
ter IV.
DESIGN OF RETAINING WALLS.— The design of masonry retaining walls will be
illustrated by the design of the retaining walls for West Alameda Avenue Subway, taken from
the author's "The Design of Walls, Bins and Grain Elevators," second edition.
Design of Retaining Walls for West Alameda Avenue Subway, Denver, Colorado. — The
height of the walls varied from 8 ft. to 29 ft. 3 in., while the foundation soil varied from a compact
gravel to a mushy clay. The design of the maximum section, which rests on a compact gravel,
will be given. The concrete was mixed in the proportion of i part Portland cement, 3 parts sand
and 5 parts screened gravel. Crocker and Ketchum, Denver, Colo., were the consulting engineers.
The wall is shown in Fig. 9 and in Fig. 10.
The following assumptions were made: Weight of concrete, 150 Ib. per cu. ft.; weight of
filling, w = 100 Ib. per cu. ft.; angle of repose of filling, if : i (<£ = 33° 40'); surcharge, 600 Ib.
per sq. ft., equivalent to 6 ft. of filling; maximum load on foundation, 6,000 Ib. per sq. ft.
Solution. — After several trials the following dimensions were taken: Width of coping 2 ft.
6 in., thickness of coping i ft. 6 in., batter of face of wall % in. in 12 in., batter of back of wall
3^ in. in 12 in., width of base 15 ft. 2§ in. (ratio of base to height = 0.52), front projection of
base 4 ft., other dimensions as shown in Fig. 9. The calculations were made for a section of the
wall one foot in length.
The property back of the wall will probably be used for the storage of coal, etc., and it was
assumed that the surcharge came even with the back edge of the footing of the wall. The resultant
pressure of the filling on the plane A-2 was calculated by the graphic method of Fig. 5 and Fig. 6,
and was found to be P' = 17,290 Ib. The weight of the filling in the wedge back of the wall is
W = 16,435 lb-> acting through the center of gravity of the filling. The resultant of P' and
W is P = 23,850 Ib. = the resultant pressure of the filling on the back of the wall. The weight
of the masonry is W = 33,144 Ib., acting through the center of gravity of the wall, and the re-
sultant of P and W is E = 52,510 Ib. = the resultant pressure of the wall and the filling upon
the foundation. The vertical component of E is F = 49,580 Ib., and cuts the foundation, b = 2.1
ft. from the middle.
1. Stability Against Overturning. — The line OD in this case is nearly parallel to the line QW
which brings the point 5 in Fig. 9 at a great distance from the point W. The factor of safety
against overturning was calculated on the original drawing and found to be/o > 25.
2. Stability Against Sliding. — The coefficient of friction of the masonry on the footing will
be assumed to be tan <f>' = 0.57 and <£' = 30°. Through 0, Fig. 9, draw OQ, cutting the base of
wall 5/1 at 6, and making an angle <£' = 30° with a vertical line through 6. Then the factor of
safety against sliding will be
/. = QM'/RM = 2.5
This is ample as the resistance of the filling in front of the toe will increase the resistance
against sliding.
3. Stability Against Crushing. — In Fig. 9 the direct pressure will be pi = 49,580/15.21
= 3,220 Ib. per sq. ft.
The pressure due to bending will be
pi = ± 6F-bfd2 = ± (6 X 49,580 X 2.i)/23i.4 = ± 2,700 Ib. per sq. ft., and the maximum
pressure is
p = 3,220 + 2,700 = + 5.92O Ib. per sq. ft.
DESIGN OF RETAINING WALLS. 235
and the minimum pressure is
p =• 3,220 — 2,700 - + 520 Ib. per sq. ft.
The allowable pressure was 6,000 Ib. per sq. ft., so that the pressure is safe for a compact gravel.
Where the walls were supported on the mushy clay it was necessary to extend the projection of
the footing on the front side and to bring the resultant F to the center of the wall.
FIG. 9. RETAINING WALL, WEST ALAMEDA AVENUE SUBWAY.
4. Upward Pressure on Front Projection of Foundation. — Where projections are used on the
foundations of retaining walls it may be necessary to reinforce the base to prevent the projection
breaking off in line with the face of the wall. The bending moment of the upward pressure about
the front face of the wall from Fig. 9 is
M = M5.920 + 4.120) X 4 X 2.1 X 12
= 506,000 in-lb.
The tension on the concrete at the bottom of the footing will be
/ = M -c/I = M -d/2l = (506,000 X 27)7157,464
= 88 Ib. per sq. in.
Since the ultimate strength of the concrete in tension is approximately 200 Ib. per sq. in.,
236
RETAINING WALLS.
CHAP. V.
no reinforcing is required. However, f in. D bars were placed 18 in. centers and 3 in. from the
bottom of the foundation.
Data. — The coefficients of friction of various materials are given in Table I. The angles of
repose of different materials are given in Table II. The conditions of surface and amount of
moisture cause wide variations in the coefficients. Additional data for the design of retaining
walls are given in Tables III to VI.
TABLE I.
COEFFICIENTS OF FRICTION.
Materials.
Coefficients.
Materials.
Coefficients.
Dry masonry on dry masonry. . .
O.6 to 0.7
Masonry on dry clay
0.5 to 0.6
Masonry on masonry with wet
Masonry on moist clay
O.11
mortar
O.7C
Karth on earth
0.25 to i.o
Timber on stone
O.J.
Hard brick on hard brick
O.7
Iron on stone
0.3 to 0.7
Concrete blocks on concrete
Timber on timber
• O.2 to 0.5
blocks . .
o.6t;
TABLE II.
ANGLES OF REPOSE, <j>, FOR MATERIALS.
Materials.
<t>
Materials.
*
Earth, loam
30° to 4C°
Clay. .
2q° to 4C°
Sand dry.
2C° to -K0
Gravel
30° to 40°
Sand, moist
30° to 4?°
Cinders
25° to 40°
Sand, wet
iq° to lo0
Coke
1O° to 4C°
TABLE III.
ALLOWABLE PRESSURE ON FOUNDATIONS.
Material.
Pressure in Tons per Sq. Ft.
Soft clay
I to 2
Ordinary clay and dry sand mixed with clay
2 to 3
Dry sand and clay
3 to 4
Hard clay and firm, coarse sand
J «•" 2
4 to 6
Firm, coarse sand and gravel
6 to 8
Bed rock
15 and up.
TABLE IV.
ALLOWABLE PRESSURE ON MASONRY.
Materials.
Pressure in Tons per Sq. Ft.
Common brick, Portland cement mortar
12
Paving brick, Portland cement mortar
15
Rubble masonry, Portland cement mortar
12
Sandstone, first class masonry
2O
Limestone, first class masonry
25
Granite first class masonry
30
Portland cement concrete, 1—2— 4 . . . .
2;
Portland cement concrete, 1—3—6
2O
EXAMPLES OF RETAINING WALLS.
237
TABLE V.
WEIGHT, SPECIFIC GRAVITY AND CRUSHING STRENGTH OF MASONRY.
Materials.
Weight in Pound*
per Cubic Foot.
Specific Gravity.
Crushing Strength in
Pound* per Square Inch.
Sandstone
ICQ
2.A.
4 ooo to i c ooo
Limestone
7
160
li
Trap
1 80
2.Q
IQ OOO to 33 OOO
Marble
i6c
2 7
8 ooo to 20 ooo
Granite
165
2.7
8 ooo to 20 ooo
Paving brick, Portland cement
ICO
2 4.
2 OOO to 6 OOO
Stone concrete, Portland cement
140 to 150
2.2 to 2.4
2 500 to 4 ooo
Cinder concrete, Portland cement
1 12
1.8
I OOO to 2 COO
TABLE VI.
WEIGHT OF DIFFERENT MATERIALS.
Materials.
Wt. per Cu. Ft.. Lb.
Materials.
Wt. per Cu. Ft.. Lb.
Loam, loose
7C. to QO
Sand, wet
1 10 to 1 20
Loam, rammed
90 to 100
Gravel
1 20 to 135
Sand, dry
90 to no
Soft flowing mud
105 to 1 20
For specifications for concrete, plain and reinforced, see Chapter VI.
EXAMPLES OF RETAINING WALLS.— Details of six masonry retaining walls with a
gravity section are given in Fig. 10. These retaining walls represent the best practice. Details
of four reinforced concrete retaining walls are given in Fig. n. For additional examples see
the author's "The Design of Walls, Bins and Grain Elevators."
The contents of standard concrete retaining walls, as designed by the Illinois Central Rail-
road, are given in Fig. 12.
Concrete Retaining Walls. Methods of Constructing Forms. — Forms for a retaining wall
may be built in sections, or may be built up each time they are used. The former method is
much the cheaper, especially for plain concrete walls where the sections between expansion joints
are of equal length. The forms used on the C. B. & Q. R. R. walls shown in Fig. 13 are shown
in Fig. 14. The studs, coping and bottom forms for the face, and the back forming are sectional,
while ordinary sheeting is used between the coping and bottom forms. No attempt was made
to use sectional forms on the face of the wall, because the sections soon become badly warped,
making a rough wall. The concrete had a tendency to lift the forms and they were tied to bars
imbedded in the footings as shown. The sectional forms were 12 ft. o in. long, while the studs
were spaced 3 ft. o in. center to center.
The forms for the Illinois Central R. R. retaining wall shown in Fig. 10 are shown in Fig. 15.
The forms were built in sections 54 ft. long. The forms were cross-braced by J in. rods spaced
7 ft. 8J in. center to center as shown. When the forms were taken down the ends of these rods
were unscrewed, the main portion of the rod being left in the wall. The forms were made of
2 in. plank surfaced on the inside.
The forms used by the Chicago and Northwestern Ry. on track elevation in Chicago are
shown in Fig. 16. The forms were built in sections 35 ft. long. The 2 in. X 8 in. braces were
used to hold the sides of the forms apart and were removed as the concrete was put in place. The
2 in. pipe used to cover the rod bracing was old boiler flues and rejected pipe.
Ingredients in Concrete. — The proportions of concrete materials should be stated in terms
of the volume of the cement. The volume of one barrel or four bags of cement is taken as 3.8
cu. ft., and the sand and aggregate are measured loose. Concrete mixed one part cement, 2 parts
sand, and 4 parts stone is commonly called 1:2:4 concrete. The proportions should be such
238
RETAINING WALLS.
CHAP. V.
_^JL_JL
t~ «'<-J
//^ PENN'AVE-5UBWAY RETAININ6 WALL (2) H'Y'C- SH-R-fi-R- RETAINING WALL
CENTRAL R-R- RETAINING WALL
M—
(4)WESTALAMEDA AVENUE SUBWAY
RETAIN/NG WALL
-tf"«w
(6) KANSAS C/TY TERMINAL RAILWAY
(5) C-B-&Q-R-R-RETAINING WALL RETAINING WALL
FIG. 10. EXAMPLES OF MASONRY RETAINING WALLS.
REINFORCED CONCRETE RETAINING WALLS.
9" 'Ground Surface
£ V"ia- '111 i !• | s
r^^iEif* J 'f cor- tors 6*t
't'o'tfriwttf 47* \
SECT/ON
FRONT ELEVATION
L;..;.j JJJJJ.
SECTION
A// reinforcing bars
are high elastic limit
corrugated rounds'
REAR ELEVATION
(I) SLAB RETAINING WALL, ILLINOIS CENTRAL R-R- (?)SLA& RETAIWNG WALL, &PRUGATED BAR Co-
*.„, f'Q" All bars are corrugated rounds^
^^ Horiz.- bars in rear face 5'"" ~~
SECT/ON FRONT ELEVATION SECTION KEM ELEVAT/ON
(*>) COUNTERFORT RETAINING WALL (4) COUNTERFORT RETAINING WALL
ILLINOIS CENTRAL R-R- CORRUGATED BAR Co*
FIG. ii. EXAMPLES OF REINFORCED CONCRETE RETAINING WALLS.
240
RETAINING WALLS.
CHAP. V.
that there should be more than enough cement paste to fill the voids in the sand, and more than
enough mortar to fill the voids in the stone. With voids in sand and stone varying from 40 to 45
per cent, the quantities of the ingredients are closely given by Fuller's rule, where
c = number of parts of cement;
5 = number of parts of sand ;
g = number of parts of gravel or stone.
Then — - - — — = p = number of barrels of Portland cement required for one cu. yd. concrete.
\ s
— -
= number of cu. yd. sand required for one cu. yd. concrete.
- --- - - -— = number of cu. yd. gravel or stone required for one cu. yd. concrete.
gjj-
**
55
H-HEI6HT, TOP Of WALL TO GROUND
^ ^ £ ,
WALL
^
— •
•
^*
^
,*"
*^
*-^
.
^
•**
M —
^
^^
^
*
^"
^
A
^
•"•*
^
•^
0
x!
x
•^
^.
x
P!
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16 17 18 19 ZO 21 ZZ Z5 24
CONTENTS OF
RETAINING WALL5
B
ill cases not affected by live load
or surcharge •
all cases affected 'by live fod 'or
surcharge
>ng Pressure- J-5 Tons per
square foot •
/
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// 12 K 14 1
Use mil A in i
Use Wall Bin
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Average Foot
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1 Z 3 4 £ 6 7531
CUBIC YARDS PER LINEAL FOOT
FIG. 12. CONTENTS OF CONCRETE RETAINING WALLS, ILLINOIS CENTRAL RAILROAD.
The materials for one cu. yd. of I : 2 : 4 concrete will then be: Portland cement 1.57 barrels,
sand 0.44 cu. yd., gravel or stone 0.88 cu. yd.
The proportions for plain walls commonly vary from r : 2| : 5 to I : 3 : 6, while the pro-
portions for reinforced walls vary from i : 2 : 4 to I : 2| : 5.
Mixing and Placing Concrete. — For mixing concrete a batch mixer in which the materials
can be definitely proportioned and thoroughly mixed is to be preferred. In cold weather the
concrete materials should be heated by the addition of boiling water to the mixer. To prevent
scalding the cement the sand, aggregate and hot water should first be placed in the mixer and,
after giving it several turns to remove the frost, the cement should be added and the mixing
completed.
The author uses the following specifications for placing concrete in cold or freezing weather.
"When the temperature of the air during the time of mixing and placing is below 40° Fah. the
water used in mixing the concrete shall be heated to such a temperature, that the temperature
of the concrete when deposited in the forms shall not be less than 60° Fah. Care shall be used
not to scald the cement."
Where the wall is in a cut and the materials can be delivered on the bank, the mixer may be
installed on the bank above and the concrete wheeled or chuted to place. Concrete should not
be chuted in freezing weather. In building the West Alameda Avenue Subway retaining walls,
De
SPECIFICATIONS FOR CONCRETE RETAINING WALLS.
241
MVIT, Colo., the gravel and sand were taken from the cut, the concrete waa mixed in mixers
installed at the foot of movable towers, and the concrete was raised in a skip elevator and chuted
into place.
On railroad work the mixer may be mounted on a flat car, the materials may be delivered on
other cars, and the concrete is dumped or chuted directly into place.
FIG. 13. RETAINING WALL, C. B.
& Q. R. R.
FIG. 14. F OEMS FOR RETAINING WALL, C.
B. & Q. R. R.
SPECIFICATIONS FOR CONCRETE RETAINING WALLS.— The following extracts
have been taken from the specifications prepared by Crocker and Ketchum, Consulting Engineers,
for the concrete retaining walls for the West Alameda Avenue Subway, Denver, Colo.
16. MATERIALS. Cement. — The cement shall be furnished by the Companies on board
cars or in store houses at the site of the work as required. The cement shall be Portland, and
shall meet the requirements of the Standard Specifications of the American Society for Testing
Materials.
17. Concrete Aggregate. — The fine aggregate shall pass a screen with J in. mesh, while the
coarse aggregate shall all be retained on a screen with J in. mesh and all shall pass a screen with
3 in. mesh. The sand and gravel shall be obtained from the excavation of the open cut of the
Subway. The Consulting Engineers reserve the right to change the proportions of sand and
screened gravel (§34 and §35) from time to time, as may be necessary to secure a dense concrete
of desired consistency. Payment to trie Contractor for the screening will be made on the basis
of unit price per cubic yard of gravel measured after screening.
1 8. Water. — The water used in mixing concrete shall be clean and reasonably clear, free
from acids and injurious oils, alkalies or vegetable matter.
19. Lumber. — Lumber for forms shall have a nominal thickness of 2" before surfacing, and
shall be of a good quality of Douglas fir or Southern long leaf yellow pine. Lumber used for
forms of face work shall be dressed on one side and both edges to a uniform thickness and width.
Lumber for backing and other rough work may be unsurfaced and of an inferior grade of the
kinds above specified.
20. Reinforcing Steel. — All reinforcing steel shall be plain bars, and shall comply with the
specifications for structural steel as given in the Standard Specifications of the American Railway
Engineering Association.
21. EXCAVATION. — The subway is being excavated by the Companies but the contractor
shall make all necessary excavations for wall and pedestal footings, and shall furnish all necessary
sheeting and supports and bracing to hold the forms in place during the construction of the work.
17
242
RETAINING WALLS.
CHAP. V.
The cost of the necessary sheeting and supports shall be included in the unit price for excavation.
The Contractor shall provide all pumps and other equipment incidental to such excavation.
22. All excavation shall be measured in vertical prisms whose end areas are of sufficient
size to include the footing courses, and the sheeting surrounding the same. "Wet excavation"
shall include all excavation below the surface of standing water in open pits.
23. CONCRETE. Machine Mixing. — Machine mixers, preferably of the batch type, shall
be used except where the volume of concrete to be mixed .is not sufficient to warrant their use.
The requirements are that the product delivered shall be of the specified proportions and con-
sistency, and thoroughly mixed.
« *r M ^
FIG. 15. FORMS FOR ILLINOIS CENTRAL
R. R. RETAINING WALL.
. -^b. ?' ' Concrete Footing
FIG. 1 6. FORMS FOR C. & N. W. RY.
RETAINING WALL.
24. Mixing by Hand. — When it is necessary to mix by hand the mixing shall be done on water
tight platforms of sufficient size to accommodate men and materials for the progressive and
rapid mixing of at least two batches of concrete at the same time. Batches shall not exceed one-
half yard. The mixing shall be done as follows: The fine aggregate shall be spread evenly upon
the platform, then the cement upon the fine aggregate and these mixed thoroughly until of an
even color. Then add the coarse aggregate which, if dry, shall first be thoroughly wet down.
The mass shall then be turned with shovels until thoroughly mixed and all the aggregate covered
with mortar, the necessary amount of water being added as the mixing proceeds.
25. Consistency. — The material shall be mixed wet enough to produce a concrete of such
consistency that it will flow into the forms and about the metal reinforcement, and which on the
other hand can be conveyed from the place of mixing to the forms without the separation of the
coarse aggregate from the mortar.
26. Retempering. — Retempering mortar or concrete, i. e., remixing with water after it has
partially set will not be permitted.
SPECIFICATIONS FOR CONCRETE RETAINING WALLS. 243
27. Placing of Concrete.-^-Conctete after the addition of water to the mix, shall be handled
rapidly from the place of mixing to the place of final deposit, and under no circumstances shall
concrete be used that has partially set before final placing.
28. The concrete shall be deposited in such a-manner as will prevent the separation of the
ingredients and permit the most thorough compacting. It shall be compacted by working with
a straight shovel or slicing tool kept mqying* up and down until all the ingredients have settled
in their proper place, and the surplus water i» forced to the surface. All concrete must be de-
posited in horizontal layers of uniform thickness throughout. Temporary planking shall be placed
at rnds of partial layers so that the concrete shall not run out to a thin edge. In placing concrete
it shall not be dropped through a clear space of over 6 ft. vertical, For greater heights a trough
or other suitable device must be used to deliver the concrete in place, and in depositing each
batch this trough or other device must first be carefully filled with concrete and then as fast as
concrete is removed at the bottom it shall be replenished at the top.
29. The work shall be carried up in alternate sections of approximately 32 ft. in length as
shown on the plans, and each section shall be completed without intermission. In no case shall
work on a section stop within 18 in. of the top.
30. Before depositing concrete, the forms shall be thoroughly wetted, except in freezing
weather, and the space to be occupied by the concrete cleared of debris..
31. Expansion Joints. — Expansion joints shall be provided (sections were approximately
32 ft. long) as shown on the plans. The wall shall be constructed in alternate sections, the ends
of the sections being formed by vertical end forms, the section being completed as though it were
the end of the structure. Before placing the remaining sections the end forms shall be removed
and the surface of the concrete shall be painted with coal tar paint, composed of sixteen (16)
parts coal tar, four (4) parts Portland cement and three (3) parts kerosene oil. The expansion
joints shall be finished on the exposed side by the insertion in the forms of a metal mold that will
give a groove i in. wide, I in. deep and shall have a draft of I in. The wall sections shall be
locked together by means of bars as shown on the plans.
32. Forms. — Forms shall be substantial and unyielding and built so that the concrete shall
conform to the design, dimensions and contours, and so constructed as to prevent the leakage of
mortar. Where corners of the masonry and other projections liable to injury occur, suitable
moldings shall be placed in the angles of the forms to round or bevel them off. Material once
used in forms shall be cleaned before being used again.
33. The forms must not be removed within 36 hours after all the concrete in that section
has been placed; in freezing weather they must remain until the concrete has had sufficient time
to become thoroughly set.
34. Proportioning. — In proportioning concrete, a barrel or 4 sacks of Portland cement shall
be assumed to contain 3.8 cu. ft., while the sand and gravel shall be measured loose in a measuring
vessel. The proportions required for concrete are as follows:
For footings, walls of retaining walls, abutments, and pedestals, one (i) part Portland cement,
three (3) parts sand and five (5) parts gravel. For bridge seats and copings, one (i) part Portland
cement, two (2) parts sand and four (4) parts gravel.
35. The tops of the bridge seats, pedestals, and copings, shall be finished with a smooth
surface composed of one (i) part Portland cement and two (2) parts sand applied in a layer I in.
thick. This must be put in place with the last course of concrete.
36. Water-Proofing. — The expansion joints in the retaining walls and abutments shall be
water-proofed as follows: After the forms have been removed and the concrete is thoroughly
dried, the back of the wall for a distance of 18 in. on each side of the expansion joints shall be
mopped with hot refined coal tar pitch. A layer of burlap shall then be placed so as to cover the
expansion joints, and the burlap shall be mopped with coal tar pitch. In the same manner two
additional layers of burlap shall be applied, making a 3-ply water-proofing.
37. Reinforcing Bars. — Reinforcing bars, where used, shall be placed 3 in. clear from the
outside surface of the concrete, and shall be placed in the position shown on the plans. Care
must be taken to insure the coating of the metal with mortar, and a thorough compacting of
concrete around the bars. All reinforcing bars shall be clean and free from all dirt or grease.
38. Freezing Weather. — Concrete shall not be mixed or deposited at a freezing temperature,
unless special precautions are taken to avoid the use of materials containing frost or covered
with ice, and means are provided to prevent the concrete from freezing. Where the temperature
of the air during the time of mixing and placing concrete is below 40° Fahr. the water used in
mixing the concrete shall be of such a temperature, that the temperature of the concrete when
delivered in the forms shall not be lower than 60° Fahr. Special precautions shall be taken not
to scald the cement.
39. Placing in Water. — Concrete shall not be deposited under water except on the approval
of the Consulting Engineers. Where water is encountered without current, but in such quantity
that it cannot be lowered to the required depth and maintained there, or where such lowering
244 RETAINING WALLS. CHAP. V.
would cause further difficulty, concrete may be deposited through troughs or other device in the
manner designated above.
40. Cleaning Up. — Upon the completion of any section of the work the Contractor shall
remove all debris caused by his operations and leave the work ready for backfilling.
REFERENCES. — For the design of reinforced concrete retaining walls, examples of plain
and reinforced concrete retaining walls, details of construction, and the theory of reinforced
concrete, see the author's "The Design of Walls, Bins and Grain Elevators." For a discussion of
the theory of the pressures in granular materials and semi-fluids, see Chapter VIII, Bins, and
Chapter IX, Grain Elevators; also see the author's "The Design of Walls, Bins and Grain Ele-
vators."
CHAPTER VI.
BRIDGE ABUTMENTS AND PIERS.
Introduction. — An abutment is a structure that supports one end of a bridge span and at the
same time supports the embankment that carries the track or roadway. An abutment also
usually protects the embankment from the scour of the stream.
A pier is a structure that supports the ends of two bridge spans. Piers must be designed
so as not to interfere with the flow of the stream, and care must be used to prevent undermining
the pier by the scour of the stream.
TYPES OF ABUTMENTS.— Masonry abutments may be classified under four heads,
Fig. i, (a) straight or "stub" abutments; (6) wing abutments; (c) U abutments; (d) T abutments.
(a) The standard straight abutment of the N. Y. C. & H. R. R. R., shown in Fig. I, is an
excellent example of an abutment of this type. The earth fill is allowed to flow around the ends
of the abutment as shown. Straight abutments should not be used where the water will wash
the fill away.
(6) A standard wing abutment of the N. Y. C. & H. R. R. R. is shown in Fig. i. The length
of the wings is determined by the width of the roadway, the allowable slope of the sides of the
embankment and the angle of the wings. The angle that the wings make with the face of the
abutment ordinarily varies from 30 degrees to 45 degrees for standard conditions. For skew
bridges and for unusual conditions the angle of the wing is variable.
(c) A standard U abutment of the N. Y. C. & H. R. R. R. is shown in Fig. I. This is a
wing abutment with the wings making an angle of 90 degrees with the face of the abutment.
The wings are tied together by means of old railroad rails as shown. The wing walls run back
into the fill, which flows down in front of the wings. If the slope is liable to be washed away by
the scour of the stream the wings should be extended farther into the bank.
(d) A standard T abutment of the South Bend and Michigan Southern Railway for a skew
span is shown in Fig. I. The T abutment is essentially a straight abutment with a stem running
back into the fill; the stem carries the roadway, supports the abutment, and prevents water from
finding its way along the back of the abutment. A T abutment may be considered as a U abut-
ment with the two wings in one.
STABILITY OF BRIDGE ABUTMENTS WITHOUT WINGS.— A bridge abutment
must be stable (i) against overturning, (2) against sliding, and (3) against crushing the material
on which the abutment rests, or the masonry in the abutment. The problem of the design of a
bridge abutment is essentially the same as the design of a retaining wall, for which see Chapter V.
The method of design will be shown by giving the calculations for a straight concrete abutment
for West Alameda Avenue Subway, Denver, Colo.
Design of Concrete Abutment for West Alameda Avenue Subway, Denver, Colorado. — The
height of the abutment is 21 ft. 6 in. from the bottom of the footing to the top of the bridge seat,
and 25 ft. o| in. to the top of the back wall. The following assumptions were made: Weight of
concrete, 150 Ib. per cu. ft.; weight of filling, w = 100 Ib. per cu. ft.; angle of repose of the filling,
ii to i (<f> = 33° 42'); surcharge 800 Ib. per sq. ft., equivalent to 8 ft. of filling; maximum load
on foundation 6,000 Ib. per sq. ft.
Solution. — After several trials the dimensions given in Fig. 2 were taken. The stability of
the abutment was investigated for two conditions: (a) with a full live and dead load on the bridge
and on the filling, and (6) with no live load on the bridge and no surcharge coming on the filling
above the wall, it being assumed that a locomotive is approaching the bridge from the right, and
245
246
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI.
Brfy* S*at} fB*s* *f R*H
Vf\ *StJtS J* Cft^cr^ — jt/*tf f
.X- ,^1 i _ -.-_ >/C' P,'' Slope — ^-JL o_/. /'/./o
" sj'0"^?r7~~ "i^V '• fYT-* //v .^ZZIIElZ^-.i V
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Alf corners
and edges to
be rounded bo
.
PLAN
STANDARD W/NG ABUTMENT
N-Y-C-&H-R-R-R-
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PLAN
STANDARD STRAIGHT (STUB) ABUTMENT
N-Y-C-&rf-R-R-R*
Bridge 5t
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t*i k
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MICHIGAN SOUTHERN R-R- —rrf, J- ^->
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5/pf ELEVATION SECT/ON A~ A
FIG. i. TYPES OF MASONRY ABUTMENTS.
/^/^v
STABII.H Y OF BRIDGE ABUTMENTS.
247
ached the point 2 in (b), Fig. 2. The weight of the girders and the live load was assumed as
uniformly distributed over a length of the abutment equal to the distance between track centers,
and one lineal foot of wall was investigated.
Case (a). — The pressure of the filling on the plane 5-2 was calculated as in Chapter V,
Fig. 9, and is P' = 14,700 lb., acting through the center of gravity of the trapczoid 2-3-4-5.
The weight of the filling and surcharge is Wt + Wi =» 14,900 lb., which when combined with P'
t he resultant pressure of the filling on the wall = P = 20,900 lb. The pressure P is then
combine-el with the weight of the wall, W\ = 29,800 lb.. and with the dead load and live load
from the girder = 12,820 lb., giving the resultant pressure on the foundation, E — 59,400 lb.,
and acting, b = 1.4 ft. from the center of the wall, and F = 57,500 lb.
i. Stability Against Overturning. — The resultant E is nearly vertical and well within the
middle third, so that the wall is amply safe against overturning.
/£=" "Fill
Wj-" Surcharge
Concrete /50 Ibs/cu.ft.
Far/h 100"-"
f=>=?0900
(b)
FIG. 2. ABUTMENT FOR WEST ALAMEDA AVENUE SUBWAY, DENVER, COLO.
2. Stability Against Sliding. — Assuming that <£' = 30°, then the coefficient of friction will
be tan <j>' — 0.57. Using the definition of factor of safety given in equation (27) Chapter V. the
resistance of the wall against sliding will be 57.500 X 0.57 = 32,765 lb. The sliding force is
P' = 14,700 lb., and the factor of safety is 32,765/14,700 = 2.23, which is ample.
3. Pressure on Foundation. — The pressure on the foundation will be p = F/d * 6F-b/d*
= + 5>74° a°d + 1,700 lb. per sq. ft., which is safe.
4. Upward Pressure on Front Projection of Foundation. — The base will be investigated on
the plane 7-8 to see that the upward pressure .will not break off the front projection of the founda-
tion. The bending moment of the upward pressure about the front face of the wall in (a), Fig. 2,
will be
248 BRIDGE ABUTMENTS AND PIERS. CHAP. VI.
M = i(5.740 + 4.690)4 X 2.1 X 12
= 525,672 in-lb.
The tension on the concrete at the bottom of the footing will be
_ M-c _ M-d _ 525,672 X 27
/ 2! 157,464
= 92 Ib. per sq. in.
The footing is safe, but f in. D rods were placed 18 in. centers and 3 in. from the bottom of
the foundation.
Case (b). — The solution is the same as for (a) except that the live load from the girder = 9,980
Ib., and the surcharge load 1-2-5-6 = Wa = 6,620 Ib. were omitted. The wall is safe for over-
turning. The factor of safety against sliding is from equation (27) Chapter V, /, = 41,500
X 0.57/14,700 = 1.6, which is safe. The pressure on the foundation is safe.
The back wall was placed after the bridge seats were finished. To bond the back wall to
the abutment, \ in. D rods 4 ft. long, spaced 18 in. centers, were placed in two rows 3 in. from
the back and front face, one-half of the length of the rod being imbedded in the main wall.
PRINCIPLES OF DESIGN. — To prevent tension on the back side of the footing and to
make sure that the maximum compression on the front side of the footing shall not be greater
than twice the average pressure, the resultant of the thrust of the filling, the weight of the masonry,
the weight of the bridge and the live load must strike within the middle third of the base. Where
the abutment rests on rock or solid material where settlement will not occur, it will not be serious
if the resultant strikes a little outside of the middle third, providing the allowable pressure on the
foundation is not exceeded. When the abutment is on compressible material where settlement
will take place, the resultant of the pressures should strike at or back of the center of the base, so
that the abutment will not tip forward in settling. It is standard practice to use piles in the
foundation for abutments resting on compressible soil.
For the design of wing walls see the design of Retaining Walls, Chapter V.
In addition to the requirements for stability abutments should satisfy the following additional
requirements.
(a) The abutment should protect the bank from scour, (b) The abutment should prevent
the embankment drainage from washing away the bank, (c) The abutment should be easily
drained.
Empirical Design. — A common rule is to make the minimum thickness of the main part of
the abutment not less than -fa the height above any section; and project the footings on each
side as may be required. Empirical methods of design often give unsatisfactory results and are
not to be recommended.
DESIGN OF BRIDGE PIERS. — Bridge piers must be designed (i) for the total vertical
load due to the dead load of the span and the live load on the span, and the weight of the pier;
(2) for wind pressure on the pier and the bridge; (3) to withstand floating drift and ice; and (4)
to take the longitudinal thrust due to stopping a car or train on the bridge, and due to temperature
when the rollers do not move freely. The wind pressures are calculated as specified in speci-
fications for bridges, and are assumed to act in the vertical line of the center of the pier; on the
top chord of the truss; the bottom chord of the truss; 6 or 7 feet above the base of the rail; and at
the center of gravity of the exposed part of the pier. The total wind moment is then calculated
about the leeward edge of the base of the pier, and the maximum stresses on the foundation due
to direct load and wind are calculated in the same manner as the calculation of the pressures of
abutments.
The effect of the current of the stream and of floating ice and drift are difficult to calculate.
The pressure of a flowing stream on an obstruction is given by the formula
F2
P = m-w-a- —
ALLOWABLE PRESSURES ON FOUNDATIONS.
wlu-rc P — the total pressure on the surface; m •« a constant; v> •• weight of a cubic foot of
w.itrr; a — area of wetted surface normal to the current in square feet; » — velocity of current
in l.vt per second; and g = acceleration due to gravity - 32.2 feet. The value of m varies with
the shape and the dimensions of the pier. Weisbach's Mechanics gives the following data: —
For a prism three times as long as broad, m «• 1.33. For a pier five or six times as long as broad
and with a cutwater having plane faces and an angle of 30 degrees between the cutwater faces,
m =» 0.48. For a square pier, m = 1.28, and for a circular pier, m — 0.64.
The maximum pressure due to floating ice will be the crushing strength of the ice, which
varies from 400 to 800 Ib. per sq. in. The principal danger from floating ice and drift is that
the current of the stream will be deflected downward and will gouge out the material around
and under the pier and cause failure. To prevent this it is quite common to build piers with a
" break- water," "starkwater," "cutwater," or nose that will deflect drift and ice, or to put in a
pile protection on the upstream side of the pier. If the water can get under the pier the buoyancy
of the water must be considered in calculating the stability of the pier. If there is danger of
scouring then it is well to deposit large stones and riprap around the base of the pier.
Batter. — Piers and abutments are seldom battered more than one inch to one foot of vertical
height, or less than one-half inch to the foot, although high piers are sometimes battered only
one-fourth inch to one foot.
ALLOWABLE PRESSURES ON FOUNDATIONS.— The allowable pressures on founda-
tions depend upon the material, the drainage, the amount of lateral support given by the adjacent
material, the depth of the foundation, and other conditions, so that it is not possible to give data
that will be more than an aid to the judgment. If properly designed a moderate settlement of
some particular structure may do no harm, while a less settlement in another structure may be
disastrous. Professor I. O. Baker gives the values in Table I in his " Masonry Construction."
TABLE I.
SAFE BEARING POWER OF SOILS.*
Kind of Material.
Safe Bearing Power in Tons per Square Foot.
Min.
Max.
Rock hardest in thick layers in bed
300
25
IS
5
4
2
I
8
4
2
0.5
30
20
IO
6
4
2
10
6
4
i
Rock equal to best ashlar masonry
Rock equal to best brick
Rock equal to poor brick
Clay in thick beds, always dry
Clay in thick beds, moderately dry
Clay soft
Gravel and coarse sand, well cemented
Sand compact and well cemented
Sand clean, dry
Quicksand, alluvial soils, etc
Present practice is more nearly given by the values in Table II. Foundations should never
be placed directly on quicksand.
TABLE II.
ALLOWABLE BEARING ON FOUNDATIONS.
Kind of Material.
Tons per Square Foot.
Soft clay or loam .*
I
Ordinary clay and dry sand mixed with clay
2
Dry sand and dry clay
l
Hard clay and firm, coarse sand
4
Firm, coarse sand and gravel
6
Shale rock
8
Hard rock
20
Baker's " Masonry Construction," John Wiley & Sons.
250 BRIDGE ABUTMENTS AND PIERS. CHAP. VI.
Mr. E. L. Corthell gives the summary of the pressures on deep foundations in Table III.
TABLE III.
ACTUAL PRESSURES ON DEEP FOUNDATIONS.*
Actual Pressures which Showed No Settlement.
Material.
Number of
Examples.
Pressure in Tons per Square Foot.
Maximum.
Minimum.
Average.
Fine sand
IO
33
IO
16
5
' 54
7-75
8-5
6.2
8.0
I2.O
2.25
2.4
2-5
i-5
2.O
3-o
4-5
5-i
4-9
2.9
5.08
8.7
Coarse sand and gravel
Sand and clay
Alluvium and silt
Hard clay
Hard pan
Actual Pressures which Showed Settlement.
Fine sand
3
5
2
3
7-0
5-6
7.6
74
1.8
4-5
1.6
1.6
5-2
5-2
3-3
Clay
Alluvium and silt
Sand and clay
The data in Table III shows that great care must be used in determining on the allowable
pressure for any particular foundation, and that safe values for the bearing power of soils should
only be used as an aid to the judgment of the engineer.
WATERWAY FOR BRIDGES.— The clear waterway for bridges should be ample; great
care should be used to prevent floating logs and debris from clogging up the opening. The neces-
sary waterway depends upon the character and sizeof the runoff area, the slope and size of the stream
and upon other local conditions. The "Dun Drainage Table," Table IV, will be of assistance in
assisting the judgment of the engineer in determining on the proper waterway for any bridge.
Many formulas have been proposed for determining the waterway of culverts and bridges.
The formula best known to the author is that proposed by Professor A. N. Talbot. It is
A = cVjtfi
where A = area of the required opening in sq. ft. ;
M = area of drainage basin in acres;
c = a coefficient varying with the slope of the ground, slope of the drainage area, character
of the soil and character of vegetation.
Professor Talbot gives the following values of c : c = f to i for steep and rocky ground;
c = \ for rolling agricultural country, subject to floods at times of melting snow, and with the
length of valley 3 to 4 times its width; c = f to £ for districts not affected by accumulated snow
and where the length of the valley is several times its width.
PREPARING THE FOUNDATIONS.— The preparation of the site of the abutment or
pier will depend upon the conditions and character of the material.
Rock. — Where the water can be excluded, the rock should be cleared of all overlying material
and disintegrated rock. The surface is then leveled up either by cutting off the projections or
by depositing a layer of concrete.
Hard Ground. — The material should be excavated well below the frost and scour line. Where
the foundations cannot be carried low enough to prevent undermining, piles should be driven at
about 25 to 3 ft. centers over the foundation.
* " Allowable Pressures on Deep Foundations " by E. L. Corthell, John Wiley & Sons.
WATERWAY FOR BRIDGES.
251
TABLE IV.
THE DUN DRAINAGE TABLE.*
Atrhison, Topcka & Santa Fe Railway System.
Areas Drained in
Square Miles.
AKKAS OK \\-.\TKKWAY.
Areas Drained in
Square Mile*
AREAS OF WATERWAY.
•O
L
9
J!
.I*
*!,* .
Sg^S
<jj4 j a
s s^u
£4
2{»i
•l«
xr> ^
Fli
PERCENTAGE or
COLUMN a.
1
9
PntCEMtAGK OV
COLUMN a.
.2
§
1
*t
ll
£
H
1
IJ
J
s
~ ~
1
1.
If
i
2
3
4
5
6
7
8
i
a
S
6
7
8
.01
.02
.03
.04
.05
.06
.07
.08
.09
.IO
.IS
.30
.25
•30
•35
.40
•45
•SO
•55
.60
.65
.70
.75
.80
.85
.00
•95
I.O
i.i
1.2
1-3
1-4
1-5
1.6
1.7
1.8
1-9
2.0
2.2
24
2.6
2.8
3-0
3-2
3-4
3-6
3-8
4.0
4-2
4-4
4.6
4.8
5-0
5-5
6.0
6.5
7-0
7-S
8.0
8.5
9-0
9-5
IO
2.0
4-0
6.0
7.5
9.0
10.5
12.0
13-5
IS
16
25
32
38
44
51
S6
62
66
70
74
78
ft]
85
88
91
94
97
IOO
IIO
1 20
130
140
ISO
160
170
1 80
IOO
' 200
220
240
260
280
300
321
340
3S7
373
388
403
417
430
443
455
483
509
533
556
579
601
622
641
660
679
1-24 in.
1-24
1-30
1-36
1-42
1-42
1-48
2-36
2-36
2-36
2-48
3-42
3-48
2 I B
2 2 "
21 3 ".
3l 3
3 3 "
3i 3 "
3 4 "
D 2i 3 "
" 2$ 3 "
"3 3 "
"3 4 "
6 4 A
6 5 "
6 Si"
8 4l"
8 s "
8 6 "
8 6 "
8 6| "
10 4i "
10 S "
10 5l "
10 6 "
10 61 "
10 61 "
10 61 "
12 5 "
12 S "
12 6 "
12 7 "
12 8 "
14 61 "
14 7 "
16 61 "
16 7 "
16 71 "
16 8 '
18 7 '
18 8 '
18 9i '
20 8 '
20 9 '
20 9l '
22 81 '
22 9 '
24 81 '
24 9 '
28 7 '
28 7l '
28 8 '
28 81 "
28 9 "
28 9l "
28 10 "
32 7i "
32 8 "
33 9 '
33 x 10 '
33 X II
33 xill '
33 X 13 '
32 XI2| '
33 x 13 '
&
S
I
i
&
•o
1
S,
1
1
w
•3
1
*> ^
&R
ss
l|
IS
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0-3
II
1
H
|
-o
6
1
«
3
3
1
04
•s
1
z
«•*
CU
OH
II
14
11
££
•o"3
II
ll
M
J
3
105
105
105
105
105
105
105
105
105
105
105
105
105
ios
105
105
IOS
105
105
IOS
IOS
105
105
105
105
105
105
105
105
IOS
105
105
105
105
ios
«
1
1
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
98
97
97
97
97
97
97
97
97
97
97
97
97
97
93j
93
93
n
13
13
»4
11
17
18
19
2O
33
364
38
30
33
34
36
38
40
45
50
55
60
6S
70
75
80
85
00
95
IOO
IIO
120
130
I4O
ISO
1 60
170
1 80
IOO
2OO
22O
240
200
280
300
325
350
375
400
450
500
550
000
700
800
000
I, OOO
2,000
3,000
4,000
5.000
710
740
775
80$
83$
86$
800
920
94$
970
1.01$
1, 060
1,100
1,140
1,180
1,220
I.3SS
1, 20O
1.320
1, 3 SO
I.43S
1. 510
1.580
1.650
1,720
I.78O
1,840
1,900
1,060
2,015
2,065
2,120
2,220
2.315
2,405
2,500
2,580
2,665
2.745
3,830
3.OOO
3.970
3.HS
3,245
3.370
3.495
3.615
3.770
3.000
4.035
4.165
4.385
4.610
4.825
5.030
5.420
S.Soo
6.080
6.380
8.820
10,640
12,160
13.500
i
i
$
i
s
•3
i
k
s
1
$
•5
1
u
So
II
}|
•s?
It
Ed
3
1
1
•3
5
1
«
1
9
S
I
•s
1
i
H
n
u
^
|5
zl
105
10$
10$
10$
10$
10$
10$
10$
105
10$
10$
IIO
IIO
IIO
IIO
IIO
IIO
IIO
IIO
IIO
IIO
IIO
US
US
11$
11$
US
"S
11$
US
IIS
120
120
120
135
13$
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
130
93
93
93
93
93
•94
94
94
94
94
94
94
93
93
93
93
93
91
91
91
91
89
89
89
88
88
88
86»
86J
86J
M|
8$
8$
8$
83
83
82
83
80
So
79
79
77
77
76
76
74
74
73
Bi
70
681
67
6S
63
59
56
The above classification by states is for convenience only, and merely denotes the general characteristics of
topography and rainfall.
Column 2 in this table is prepared from observations of streams in Southwest Missouri, Eastern Kansas.
Western Arkansas and the southeastern portions of the Indian Territory. In all this region steep, rocky slopes
prevail and the soil absorbs but a small percentage of the rainfalls. It indicates larger waterways than are required
in Western Kansas and level portions of Missouri. Colorado. New Mexico and Western Texas.
* American Railway Engineering Association, Vol. 12, p. 484.
elaborate report on Runoff and Waterways for Culverts.
This report also contains an
252
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI
i^lllfl*iilll
* ^CA^Si S ^-«
alftJtezi
^ 5^J SJg £
il^-ril
3 ^^^ S: S
•S ^ ^?'g « § ^
lie--, rail? %*J1!
ftlf
^5 */ T »,^7^i-tV^ ^ ^15"^__^
>S <S\ vv'vsvl \ l.c> « o, PSTr-K-T*"
,<i!i.sM%i-£ §« >,-
I jlfiMJ * "
^ ^ I ^,U &*aua9futityS#l
PREPARING THE FOUNDATIONS.
Soft Ground. — The materials should be excavated to a solid stratum or piles spaced about
zj to 3 ft. ivnters should be driven over the foundation to a good refusal. The piles should be
nit oil Ix low low water level to carry a timber grillage, or concrete may be deposited around the
lu .ids of the piles. Where water cannot be excluded it will be necessary to use one of the following
mi -tluxls: open caisson, crib, coffer dam, or pneumatic caisson.
In using an open caisson the masonry is built up or the concrete is deposited in a water tight
box built of heavy timbers or of reinforced concrete, the caisson being sunk as the pier is built up.
•si?.
To suit superstructure, but not less
than y-u 'for girders and trusses
or 2-6 'for solid floor.
nt For high back walls.
Ifbackwallisleu than 5'0'
hiqh to be Class A Concrete,
to be used -.vhere soft
maler'at is found Where
of rails to be 6 from
bottom.
• -Number ofpiks, if required,
to be determined by character of underlying
material.
Foundation to suit local conditions, but not to
be/ess than4'-0 "deep unless good rock /:
nil exposed corners % edges to be rounded to
I inch radius.
TYPE A. \^'v;jL..j 4~...|....J £' j! TYPE B. other porous material.
Flaring Wings. JL~ -j— -^ j^ r-"^ !| Straight Wings.
To be used at crossings of Streams U-^j— -4- ft; -«4*- Tobe used at Street and
and at other places where this •&!»... J..- .^15 Highway crossings where
type is desirable. igj :(| flaring wings are not desir-
RngltflisysualfyJO butmaybe -%j PLAN. \ able, fit Streets arnf Highways M of bat-
-varied to yuit locdi conditions. ^ >w ten's usually placed on building line
ten's usually pkced on building li
FIG. 4. MASONRY ABUTMENTS, N. Y. C. & H. R. R. R.
The caisson is commonly floated into place and then is sunk on piles which have been sawed off
to receive it, or on a solid rock foundation. The sides of timber caissons are usually removed
after the pier is completed.
Timber cribs are made of squared timbers placed transversely and longitudinally, and bolted
together so as to form a solid structure with open pockets. The crib is sunk by loading the
pockets with stone. No timber should be left above the low water mark in open caissons or cribs.
A coffer dam is usually made by driving two rows of sheet .piling around the pier, the space
between the rows of piling being filled with clay puddle. For small depths a single row of sheet
piling is often sufficient. Where the depth is too great for one length of sheet piling, additional
rows are driven inside the first. Steel sheet piling is now much used for difficult foundations.
Steel sheet piling can be driven through ordinary drift and similar material, is not limited in
depth, and is practically water tight when used in a single row. It can be drawn and used again.
It is almost impossible to shut off all the water with a coffer dam, and pumps should be provided.
Pneumatic caissons should only be used under the direction of experienced engineers and
will not be considered here.
For details of sinking piers see Jacoby & Davis' " Foundations of Bridges and Buildings ",
McGraw-Hill Book Company.
254
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI,
EXAMPLES OF RAILWAY BRIDGE ABUTMENTS.— Standard stone masonry abut-
ments designed by the Baltimore & Ohio Railway are shown in Fig. 3. These abutments are
to be used for deck and through girder spans. The plans are worked out in detail and give data
for different conditions.
Standard designs for a straight abutment and for a wing abutment designed by the N. Y. C.
& H. R. R. R, are shown in Fig. 4. Data for different conditions are given on the plans. The
quantity of masonry and of old railroad rails required for the N. Y. C. & H. R. R. R. abutments
shown in Fig. 4 are given in Fig. 5. The wings are the length required for a flare of 30 degrees and
a side slope of roadway of 15 to I.
d
14
'18
v
&
30
TT
rv /or Skewed Abutments multiply
w»v quantity from curve by Secant
Vulk of Angle of Shew.
\isfii
\ \ s \.\.
y_\Vs vs~r
flng/e
Secant
tM\ $K ;
£ of Bridge \Vi\W
5°
10
20
30 •
55
^
45
50
55
60
70
75
1.004
1.015
1.035
1.064
1.103
I.I5S
1.221
1.305
1.414
1.556
1.743
2.000
2.366
2.924
3.864
. ! .5 !i S T
1 M\ s \ ^v£%
^ "^~^'ij\\ calculated from'
[ t v \ ^ ife
> kE\\\ Abutment, of
\ V\ s^ NS NSI
J^, ^wij^/i^K/xf.
f u\ \ ii -X
^ ^^C. "^
* V ^A \
S S ^ S^o ^
UJiVi \
>vv '^Hr,
\ ^ yjg-T N
S s ' s s N 1>S%
\ V i|tg. sv
\ "s^ S>Sf^x^_.
;: : ; is ss
"\ S->s "ti?^
--\ -p jy
Sv S\ S>x SSft-io%>
; A i&t!
"S- S"^ NS^ SvKT4»
\ \ fi-f
s S s N s ^4- -btHtf^VX
L i 5 tmt
"NN s^s S-v ^'Hs
\— v \r\i^
Ss '-s^ <". Vs^
>s>
yl L H k.%
SNS ^$s ^Vs>
>Sss
\ L f\ 1
!S!Ii 1 's>s*
^^
'-s
v*,
JOO 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600
Cubic Yards of Masonry
Old Pails in Foundation - 65* l Pails spaced 10 "to 12' c. to c.
Weight in Tbns-2 Abutments- Straight k/ings.
H
9
10
II
12
13
14
15
16
17
Id
13
20
2!
22
23
24
25
26
27
28
23
30
1 Track
6.3
7.0
7.8
8A
9.2
10.0
10.8
11.5
12.4
13.2
14.0
15.0
16.0
17.0
18.0
190
20.0
21.0
22.0
23.2
24.4
25.6
2Tracks
9.0
9.8
10.6
//.4
12.2
/3.2
/4.0
15.0
16.0
17.0
18.0
13.0
20.0
21.0
22.0
23.2
24.4
25.6
26.8
28.0
29.2
30.5
3 •
11.4
12.2
13.2
14.2
15.0
16.2
17.2
18.2
10.2
20.2
21.4
22.5
23.6
24.8
26.0
27.2
28.4
23.6
31.0
32.3
33.6
35.0
4 "
13.5
14.5
15.5
16.5
17.5
18.6
19.6
20.8
22.0
23.1
24.2
25.5
268
28.0
20.4
30.6
32.0
33.4
35.0
36.2
316
32.0
NOTE '-H equals distance from top of
foundgtion to Base of Pail.
Quantities shown by curves are /VET.
•Foundation based on depth of 4 feet,
FIG. 5. QUANTITIES IN MASONRY ABUTMENTS, N. Y. C. & H. R. R. R.
The quantity of concrete in single track railway bridge abutments as designed by the Illinois
Central R. R. are given in Fig. 6. The quantities in double track abutments may be calculated
as shown in Fig. 6.
Cooper's Standard Abutments — The abutment in (a), Fig. 7, is from Cooper's "General
Specifications for Foundations and Substructures of Highway and Electric Railway Bridges."
The length, /, and the thickness, a, for highway and single track electric railway bridges are as
RAILWAY HKIlx.l. I'IKRS.
and are proportional for interim -i li.it r spans. These abutments may be made of either
fir>t -class stone masonry, or first-class Portland cement concrete.
For double track electric railway bridges add one foot to the value of a in Fig. 7. The mini-
mum thickness of the wall at any point is to be 0.4 of the height. The length of the wing walla
will be determined l>y local conditions.
/
u
^ /
a I
c^
^ 1—
fc %
^ Bast of Rail,
T
40 '•
ni " "
'. *
, ' ' '
£
||
,
!
*\50 ^^
TOO 800 300 1000
jte •- Carve shots number of cubic yanA,
m one single trxk abutment with
straight stepped or 30* wing tralb.
ith of Abutment
jngle track abutment) + c-J
k- per foot of abutment
ridth
4H\ ..,, :::.
"*• ,." N
-^
^ *r
u* r
,..,,:!.! ^^ _^; ^a?
<s
,1 ' - - . F~- AJJ,'t,~r,^t W,.
uj
S
, ' X-( 'Contents of*
/ r - Nn- pf rti- y
200 300 </• Additional A
(^
^
OHTEHTSOF H lo,0. /£
"0" ZO'tT 50'0" 40'0'
^
BBD6C ABUTMENTS c 2-so 3
84 S-60 10-20 16 -X
0
/T- CONTENTS IN CUBIC YARDS
FIG. 6. QUANTITIES IN MASONRY ABUTMENTS, ILLINOIS CENTRAL RAILROAD.
The abutment without wing walls in (ft), Fig. 7, has the same dimensions as the abutment
with wing walls. The width for single track electric railways may be taken as 14 ft., double
track 26 ft. The approximate cubical quantities in abutments without wing walls are given in
Fig. 7-
RAILWAY BRIDGE PIERS. — Standard piers for railway bridges as designed by the
N- Y. C. & H. R. R. R. are shown in Fig. 8. Dimensions and data for different spans and heights
of piers are given on the plans. The quantities of masonry in the standard plans shown in Fig. 8
are given in Fig. 9, for deck spans and for through spans.
Quantities of masonry in piers for deck plate girder spans are given in Fig. 10 and for through
girder and truss spans in Fig. II. These piers were designed and the estimates were prepared by
the bridge department of the Illinois Central Railroad.
Illinois Central Railroad Pier. — Details of a concrete pier designed and built by the Illinois
Central Railroad are shown in Fig. 12. The pier rests on timber piles spaced as shown. The
"starkwater" is reinforced with an 8 in. I beam.
Cooper's Standard Masonry Piers. — The masonry pier in Fig. 13 is from Cooper's "General
Specifications for Substructures of Highway and Electric Railway Bridges." The length, /, and
the thickness, a, for highway and single track electric railway bridges are given in Fig. 13. These
piers may be made of either first-class stone masonry, or first-class Portland cement concrete.
For double track electric railway bridges add one foot to /, and 6 inches to a. The width,
w = center to center of trusses, and may ordinarily be taken 14 ft. for single track, and 26 ft.
for double track through bridges. Where drift and logs are liable to injure the pier the nose
of the cut-water should be protected with a steel angle or plate. The approximate cubical con-
tents of the piers are given in Fig. 13.
STEEL TUBULAR PIERS.— Steel tubular piers are made of steel plates riveted together
and filled with concrete. Where the piers are founded on soft material, piles are driven in the
256
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI.
bottom of the tube, the piles being sawed off below the water line. The piles should extend at
least two diameters of the tube above the bottom. The tubes are braced transversely by means
of struts and tension diagonals above high water and by diaphragm bracing below high water.
Where the piers will be subject to blows from floating drift or logs they should be protected by a
timber cribwork or other device.
Cooper's Standards. — The tubular piers in Fig. 14 are from Cooper's "General Specifications
for Foundations and Substructures for Highway and Electric Railway Bridges." Cooper specifies
j WaFfr***
Ground,
OF MASONRY ABUTMENTS
WJTH WING WALLS
Distance, a
Span, Feet
Length, I.
2'6"
2' 8"
5'0"
5'4"
3' 6"
50
100
I5O
200
250
w + 4'0"
w+5'0"
W+5'3"
w+6'6"
w+7'0"
Section A~B
(a) HIGHWAY ABUTMENT WITH WWG WALLS
iv - center to center oF trusses,
/4 ft • For sing/e track, 26 Ft- For
double track-
s
1
~3T
/
\ \ \
-^"m
\ &
*H
-I
r'!
APPROXIMATE QUANTITIES IN Cu> YDS-
OF ONE MASONRY ABUTMENT
WITHOUT WING WALLS
_t
Ground.
a-?00ff.5pari
jjj--:--- ----;[ At 'any 'po/'nt mm/mum
^a-75~ff~5pan &**»•» ''&**.
Span
Feet
Roadway
Depth Footing Below Grade
10'
15'
20'
25r
50'
12 Feet
20
59
67
100
145
100
20 Feet
E, 5 ingle T-
E, Double T-
28
21
26
56
44
72
95
75
120
145
112
185
206
J60
260
12 Feet
&
45
77
116
165
500
20 Feet
E, Single T-
E,Doul>leT-
51
25
49
63
BO
84
106
85
141
161
128
210
227
181
296
(I?) HIGHWAY ABUTMENT WITHOUT WIHG WALLS
FIG. 7. MASONRY ABUTMENTS FOR ELECTRIC RAILWAY AND HIGHWAY BRIDGES.
COOPER'S STANDARDS.
a minimum thickness of f in. for plates below and | in. above the high water. The minimum size
of tubular piers are as given in Fig. 14.
A steel tubular pier with a timber crib protection is given in Fig. 14. The crib is filled with
loose rock.
A steel oblong pier, as designed by Cooper, is given in Fig. 15. The center of the truss is to
come a/2 + one ft. from the end of the pier. The width c, as specified by Cooper, is given in
Fig- 15-
American Bridge Company Standards. — The American Bridge Company's standard tubular
piers are shown in Fig. 16. The minimum diameters for a height of 15 feet to carry a single span,
STEEL TUBULAR PIERS FOR HIGHWAY BRIDGES.
257
ami data on piers, pier beams and pier bracing are given in Fig. 16. In calculating the weight of a
pin- add one foot to the length of each tube. The weight of the concrete in two tubes is given
in Fig. 1 6. The concrete is assumed to fill the tube, and the space occupied by piles should be de-
durti-d. The number of piles required for different diameters of tubes is given. The number of
pilrs m|iiiied for large tubes agrees quite closely with Cooper's Specifications, but the number
for small tubes is very much less.
Pier Beams. — The sizes of pier beams required for different panel lengths and clear distance
between tubes in feet are given in Fig. 16. The pier beam should be assumed as one foot longer
than the clear distance between the tubes, in calculating the weight of the beams.
PLAN
Up stream end to At
same as down stream
except wnere starkwttr
is necessary.
Fer square crossings*-
V/hert sp/icingr ofrai/s in
Piers over 30-0 "hig>/> to Foundation to suit /oca/ conditions^ foundation is necessary thest
but must be not /ess than 4-0 dey>, to be ful/y boJ ted with two
un/ess pood roc* is found. any/ebars, breahnfjowts.
foundation to be c/ass S concrete
/'•3:6 without rubb/e, un/ess /oca/
conditions maJce stone cheaper.
Number of pi/es, if reyu/red,
to be determined by character
ef under/yiny maferia/.
FIG. 8. MASONRY PIERS, N. Y. C. & H. R. R. R.
. urse.
fl/so corM course to be
wed w/rtn the c/vtanct
from top of starkwater
for skew crossings
incsuse ft if necessary
Pier Bracing. — The piet bracing for piers supporting the ends of two spans are given in
Fig. 16. If the spans are unequal in length, enter the table with one-half of the algebraic sum
of the spans. For example, for a pier carrying a 75 ft. and a 125 ft. span, enter the diagram with a
span of loo ft. Steel tubular piers should never be used for end abutments carrying a fill.
In calculating the weight of the diagonal bars the length of the bar should be multiplied by
the weight per foot as obtained from a handbook, and the details for one bar added to the product.
In calculating the weight of the struts add one foot to the clear length.
Pier Caps. — Tubular piers may be capped with steel plate caps, may be finished with con-
crete, or may have a stone pedestal block. The weights given in Fig. 16 do not include the
weights of steel caps.
Specifications for Steel Tubular Piers for Highway and Electric Railway Bridges. — The
plates for the tubes shall be not less than 1 in. thick for tubes up to 30 in. \n diameter, not loss
than ^ in. for tubes from 30 to 48 in. in diameter, and not less than | in. for tubes from 48 to
72 in. in diameter. Where the plates are in contact with the soil the thickness shall be increased
at least ^ in. For A in- plate and less use { in. rivets; for | in. plate and over use I in. rivets.
The horizontal seams shall be single lap joints riveted with a pitch of 4 diameters of rivet,
while the vertical seams shall preferably be butt riveted with single riveting spaced 4 diameters
of rivet, up to 48 in. diameter of tubes, and double riveting with 3 in. spacing for tubes of larger
diameter.
18
258
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI.
^ - }—
" — Old Raffs in Foundation in Tons '8/0 ofj
flasonry in Foundation^ in Cubic Yards
when Foundation is 4 ~0' deep.
fingle
5"
10
15
20
25
30
35
40
45
50
55
60
65
70
75
Secant
1.004
1.015
1.035
1.064
1.103
1.155
1.221
1.305
1.414
1.556
1.743
2.000
2366
2.924
3M4
For Skewed Piers multiply
quantity from Curve by
Secant of ftngle of Skew.
For Skew Cress
ings increase ft
ifnecesssry.
For each additional fool in width of Pier
add to Masonry in Cubic Yards
Foundation
24-
Body IVa//
12
10
202428 Seat
/823
24 33 42 51 \W
17
2& 33 40 47
2834
1.0
1.9
3.8
DECK BRIDGE.
'•- -Quantities shown by curves are Nt
and calculated from pier shown hereof}.
Foundation based on depth of 4-0 "
for Piers without starkwater use
'quantities given by broken line curves.
Masonry in Foundation Masonry in Body Wall
0 100 200 300 j
!.. / Cabic^rds oF Masonry
\ I i_l I II I
Tracks !/ 2 3 4\ \J_
flasonry in Foundation
0 100 200
flasonry in Body \Va//
300 400
500'
Cubic Yards oF flasonry
FIG. 9. QUANTITIES IN MASONRY PIERS, N. Y. C. & H. R. R. R.
QUANTITIES IN MASONRY PIERS.
260
III J^BaxofMI
. - '
i. .1
. • * ' • •
e • ' •— J""'^
. * ( • *
T , • ' ,* '
* :::::::::::;
tl^J-V., -:-'--
> %s
Q PIER A Pic/iB ...-,;.
!<•
*t /T , ..<.'-.
^ **
VM 10}
v§ I'""!'
Si
Note-- Curve shorn number of 'cubic yards
K ;•;» <(,»
Hi/, „ ' , '
*& sure- 1-5 tons per #?• ft'
"or Additional Width of Pier-
Xm (Contents of single track per) + cd-
c-No-cu yds per ft of per- d- Additional iridth-
Jk. ..!••..'.
^ / „' '
« " " 7 ;
k> £#
tffKSSDgP
H ZO'O" K'O' 40'0' SO'O"
RDIfMSF DIFDS
Pier A B A 6 A. B A B
C 4-00 5-00 6-SO 8-00 10-00 12-00 IZ-SO 15-00
150 /-CONTENTS IN CUBIC YARDS
FIG. 10. QUANTITIES IN MASONRY PIERS FOR DECK GIRDERS, ILLINOIS CENTRAL
RAILROAD.
esf
— >
i
f of Pail
X.~/fumter of ci/b/c yardf in one siny/e track, pffr.
Gtrcfers or trusses-15'0" to /t'O'c- to c- rooting Ptoft/rt'J-S tam/si-ft"
For AJdit/onaf Width of Pter :-
X~( Con tents of Stngit Trick P/er)+c-d
C--tfo-offU-yds-f>erft--ofp*n d-AoV/hoffaf trtdtA-
i T— -||-
=^te
m
4
5»t- ^
^.i
7/£ffA
«w
to
ro"
SPANS JSO'0'08 UWfK
SPANS OY£# /SO'O'
H
ZO'O
WO*
40/0'
SO'O'
?0'0*
SO'O*
40'0
/_
PwB
Pier
A
S
A
ft
A
B
A
B
A
B
A
9
A
B
A B
C
S-B
w
8-0
9-0
'.-•
0 15-5
H*
/#•/
7-/
8-2
..v
12-C
' ISO
W
/7-0 21-0
VALUES OF X
fOG SPANS WO" TO 400'0'
/V
L£N6TH
H
JO'O"
40'0*
SO'O'
60'0'
70'0*
SO'O"
90'0"
IOOW
A
B
A
B
A
B
A
B
A
0
A
B
A
B
A
a
ZO'01
SO'O'
SO'O'
500"
IZI
tot
•>I4
4/0
J41
244
264
470
IZI
Z08
314
410
/4i
244
}64
470
Of
2/9
HO
4/S
149
2BS
570
477
127
219
$20
4IS
149
215
J70
477
ao
221
X7
4/7
/52
257
572
477
1M
224
525
420
160
260
575
490
147
277
at
in
169
265
516
482
151
754
540
424
190
no
590
4t4
H
J?S'0'
WO'
ns'o'
ZOO'O"
:^~ J
^r s '
< V .''
400'0*
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
ZO'O'
XW"
40V
SO'O'
00
252
)4Z
4/5
/9f
S10
4)0
590
//4
£06
MS
SOI
278
}$6
4S2
601
zst
i20
420
54*
280
M4
f?0
648
275
}28
448
S7S
124
400
fSO
70}
261
M6
4&
550
m
404
545
7/0
270
540
455
576
571
425
570
726
as
570
410
tot
&/
467
652
795
nt
599
5/5
64S
570
5f6
(75
tsz
tfote:- -P/frs ftr all spans, ZW'O'ar more in
length drrdrsq vw 'for Pi/e /vi/nobtM/rs
CONTENTS Of
5IHGLE TRACK, THPOUGH 5MH PIERS
FIG. n. QUANTITIES IN MASONRY PIERS FOR THROUGH SPANS, ILLINOIS CENTRAL
RAILROAD.
The bracing of piers shall be designed to take all the wind forces specified to come on the
bridge. Diaphragm webs are to be used up to well above high water for piers located in the
stream or where floating materials may find lodgment. Oblong piers shall be braced against
inside and outside pressure. Piers exposed to injury from floating logs and drift shall be pro-
tected.
The tubes should be painted inside and out with two coats of red lead and linseed oil, or
other prescribed paint.
260
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI.
The materials and workmanship shall comply with the specifications for the highway bridge
superstructure.
Erection. — Where the bottom will permit, the tubes shall be sunk well below possible scour
by loading the tube and excavating the material from the inside. For this purpose a clamshell
bucket is very effective. Driving the tube with a pile driver will cut off the rivets in the horizontal
seams and will not be permitted. After the tube is sunk, piles are to be driven inside of the
steel shell, as closely together as possible, using care to get no pile nearer than 4 to 6 in. to the
steel shell. The piles shall be driven to a good refusal, and the tops sawed off below the low
water mark and reaching at least 2. diameters of the tube above the bottom. The space inside the
tubes shall then be filled with concrete well tamped. Concrete should not be deposited in running
water if possible to prevent it.
l'-0
7-0'
*-:rr;H
V __3p§Spr
\AoF Girder-^ \,/tof6ir0er/
PILE PLAN
PLAN
MASONRY PIEK
ILLINOIS CEHTRAL R-R-
7, .... \Concrete,
Quantities \ „., ^
FIG. 12. DETAILS OF ILLINOIS CENTRAL RAILROAD PIER.
Where piers are founded on rock, the tubes are to be anchored to the rock and then filled
with concrete. Or cribs may be sunk on the rock and the tube set in a pocket in the crib and
resting on the rock. The space outside the tube is then filled with concrete and the tube is filled
with concrete in the usual manner.
Cylinder Piers for Highway Bridge, Trail, B. C.* — Steel cylinder piers were used for a steel
highway bridge designed by Waddell and Harrington, Consulting Engineers, and built across
the Columbia River at Trail, B. C. The main spans are 172 ft. 8 in long and are carried on
piers made of two steel cylinders filled with concrete. The steel cylinders are 9 ft. in diameter
at the bottom and 6 ft. in diameter at the top, and are 86 ft. long. The cylinders are made of
* Engineering News, Dec. 5, 1912.
MASONRY PIERS FOR HIGHWAY BRIDGES.
201
, K /
-TJ5» 1
DIM fusions FOK MASOHKY
PICK £OK HI6HWAY AND
SMSLE TRACK EutcTRic
RAILWAY BRIMCS
W&ffferfo ctnrtr oF _, — — ,
frvsse3sJ4'0*for siffgfefrack pt- / *j
HIGHWAY
Distance
a
Span
Fttt
Length
?'*"
50
#'4'0"
t'10*
75
w'4'6'
2>'2U
100
w+5'0'
W
150
w+5'9'
4' 4"
200
w+6'6'
4' JO"
250
w+7'0'
5'4"
ZOO
»+7'6"
For double trsck Electric
Railway bridges add 12H
to Land 6* toa*
APPROXIMATE CONTENTS IN CUBIC YARDS OF ONE MASONRY PIER
Spans
Feet
Roadway
Depth oF Pier from Top oF Coping
to Bottom of Footing in Feet-
JO
15
20
25
30
100
12 Feet
20 Feet
F., Single T-
F., Double T-
29
38
31
50
44
59
46
75
60
82
62
102
77
108
80
132
94
136
100
166
150
/2 Feet
20 Feet
E, Single T-
E, Doub/e T-
34
46
37
58
5f
70
54
86
70
95
74
118
90
125
96
152>
III
157
120
19f
200
12 Feet
20 Feet
E, Sing/e /"•
E, Double T-
39
53
43
66
58
80
63
99
80
109
86
135
J03
143
1/2
174
128
178
140
217
250
/2 Feet
20 Feed
E, Single T-
E, Double T-
44
61
48
73
66
91
74
109
90
/23
98
149
116
160
127
192
145
199
159
238
ZOO
/2 Feet
20 Feet
E, Single T-
E, Double T.
49
68
54
80
73
101
80
120
100
137
109
164
130
177
142
210
162
220
178
260
FIG. 13. MASONRY PIERS FOR ELECTRIC RAILWAY AND HIGHWAY BRIDGES.
COOPER'S STANDARDS.
262
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI
plates | in. thick and are connected by a double plate web diaphragm, each diaphragm made
of rs in. plates spaced 24 in. apart and 25 ft. high, and reaching from below low water to above
high water. The diaphragms were covered and filled with concrete. The cylinders are spaced
21 ft. centers. The piers were sunk by the pneumatic process.
Hiqh Wate
Low U£r/eA-£
Timber Crib work
Stream
*>^2
&ect Rock'
(b) CRIB CONSTRUCTION FOR
STEEL TUBULAR PJERS
Sps>n
in
Feeb
Highway & Single Track Electric
Railway
Double Track Electric Railway
Minimum
Top, <f
Diameter
Bob- D-
Number of"
Piles-
Minimum
Top d
Diameter
Bot D
Number oF
Piles
50
75
too
J25
J50
!75
200
250 ,
2 '10"
5r4"
3'£"
4'0"
4'4'r
4'g*
5'0"
5'e"
5'4"
3'9"
4'2"
4'7"
5' 0"
5' 6"
5'/0"
6'4"
4
5
£
8
9
10
//
J2
5' 4"
£']0"
4'6"
4'/0'r
5'2"
5' 6"
$'/0"
6'4'r
4'4"
5'**
B'O"
6'4"
7'0"
7'6"
t'O*
3'0"
8
/O
JO
12
12
15
15
19
FIG. 14. STEEL TUBULAR PIERS FOR ELECTRIC RAILWAY AND HIGHWAY BRIDGES.
COOPER'S STANDARDS.
STEEL CYLINDER PIERS FOR RAILWAY BRIDGES.— Steel cylinder piers have been
used for the foundations of several important bridges, Table V, by the Chicago and Northwestern
Railway. Mr. W. H Finley, Asst. Chief Engineer, gives the following advantages of steel cylinder
piers over masonry piers.*
(i) "Where it is desired to provide for future second track, cylinder foundations will cost
very little more for double track than for single track.
* Engineering News, Oct. 24, 1912.
STEEL CYLINDER PIERS FOR RAILWAY BRIDGES.
(2) "Cylinder piers can be constructed under traffic with less trouble than any other type.
(3) "Cylinder piers permit of rapid sinking by open dredging where the material is. favorable
and Minken logs are not liable to be encountered. Air pressure can be applied readily and cheaply
if it IK-COIIU-S necessary."
Details of the cylinder piers for the Oxford Mill Pond bridge arc shown in Fig. 17, and details
of the steel shells for the base of the piers are shown in Fig. 18. The bridge is 481 feet long and
consists of 30 ft. and 60 ft. spans resting on piers made of two steel cylinders and a steel shell for
the base, filled with concrete.
•L SHffener
-L
- -Plate
MINIMUM SIZES OF STEEL OBLONG PIERS
COOPER'S STANDARDS
Width 3
jpan
in
Feet
Highway and
Single Track
Electric Railway
Double Track
Electric
Railway
50
2'IO"
3>'4"
75
Z'4"
4'0"
too
*>' 8"
4'6"
125
4'0"
4' 10"
150
4' 4"
5'2"
175
4'8lf
5'6"
?00
5'0"
5' 10"
250
5'6"
6'4"
OdL ONG 5TEEL PlERS
FIG. 15. STEEL OBLONG PIERS FOR ELECTRIC RAILWAY AND HIGHWAY BRIDGES.
COOPER'S STANDARDS.
TABLE V.
DATA ON SEVERAL STEEL CYLINDER PIERS USED BY THE CHICAGO AND NORTHWESTERN
RAILWAY.
Bridge.
£
U>
Number of
Cylinders
in Pier.
Steel Cylinder Piers.
Steel Caisson Piers.
Diameter
of Piers.
Thickness of
Metal, In.
Height of
Pier, Ft.
No. of Piles
in One
Cylinder.
£
5
•ci
%
£
Thickness of
Metal, In.
Height of
Caisson, Ft.
No. of Piles.
Top,
Ft.
Bot-
tom,
Ft
Boone Viaduct
300
]46
\46
Mo
\6o
J3Q
\6o
150
I7S
70
4 (Tower)
3
2
2
2
2
2
IO
si
6
10
8
8
12
:ii
1
A
1
A
f
1
70
34
3°
34
92
97
43
*
t
Lake Butte Des Morts Via-
duct.,
Buffalo Lake Viaduct
Oxford Mill Pond Viaduct. .
IO
29*
i
I9l
49
t
30
Pckin Bridge
* Rests on Sandstone.
t Hard Clay.
t Rests on Hard Shale.
264
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI.
Cap A
Cap 5
CYLMDER PIERS
MINIMUM DIAMETER OF
STEEL TUBULAR PIERS
FORA HE/GHT OF 15 FEET
TO CAKRYA SINGLE 5 PAH
Span
feet
Diameter
Inches
25
18
50
21
75
24
100
27
125
50
150
33
J75
56
200
42
Increase diameter 5 "for each additional 5 feet in height-
STEEL TUBULAR PIERS
AMERICAN BRIDGE COMPANY STANDARDS
All quantities for One Pair of Tubes
Pi/es
No-Fiii
One
Tube
Hiam-
of
Tube
Weight per Vert- Ft- of 2 Tubes
Cu-Y<f-
per
Vert-Ft-
z«
16
i"
4
£''
16
3"
a
7"\ /"
Te \ 5
15"
75"
97*
1/9*
142'
' I/-**
164
Isr
'0-091
I
18
88
114
J40
167
194
220
0-15!
I
21
102
J3I
162
194
225
255
0-173
I
24
1/7
150
/85
22!
255
290
0-232
I
27
130
167
206
247
284
524
0-296
I
50
143
185
227
271
3/5
557
0-364
I
33
157
205
250
500
547
595
0-446
1
36
172
222
275
526
577
429
0-524
2
59
185
240
295
552
408
463
0-614
2
42
200
257
5/6
578
437
497
0-712
3
45
215
275
539
405
469
552
0-820
3
48
227
235
562
412
500
568
0-930
4
54
529
405
485
563
636
U78
5
60
565
449
5*9
621
705
1-454
6
£6
495
595
6S4
780
1-758
7
72
558
643
743
845
2-094
8
78
698
805
9/7
2-45B
10
84
749
866
984
2-gfO
15
PIER BEAMS
FOR VARIOUS PANEL LENGTHS
AND CLEARANCES BETWEEN BEAMS-
Span
Length
Clearances for Various Sizes oFT Beams
8"T
18*
9"!
21*
IO"I,
25'
12":
31?
/2"I
40*
15"!
42*
15*1
50*
IS*I
55*
12V
13-0
14-0
15-0
16-0
17-0
18-0
19-0
20-0
21-0
9'6"
9-0
10V
10-6
10-0
9-9
9-6
9-0
I2'3"
11-9
11-3
I/-0
10-9
/0-5
10-0
9-9
9-6
9-5
J5'0'
14-5
15-9
15-5
13-0
12-6
12-3
12-0
!/-£>
11-3
/6'9"
16-0
15-6
15-0
14-6
14-0
15-6
15-5
15-0
12-6
I9'5"
18-6
17-9
/7-0
16-6
16-0
15-6
15-5
14-9
14-6
20'0"
19-5
18-6
18-0
J7-3>
16-9
16-5
16-0
15-6
15-5
23'611
22-6
21-9
21-0
20-5
19-9
19-5
18-9
18-5
17-9
PIER BRACING
Supped Size, Wt-perft-
tidDi* and
tance Details I Rod
25
50'
75'
too
125'
1-KottO* 17%t- I7*ft> I7"/Ft- I7*/ft- !7*/Ft-
Oet3ih,I-Rod 30
Det3ik,l-Rod45
5TRUTS:-Sizes deWts-per Ft-
For forious Roadways
!7*/ft- !7*/fb //%•• //%-• ffVfo
I-MCS" tfVft- I9*/Ft-
14'0
16'0
18'0
17*/Fb !7*/Ft !9*/ft- /9*/ft- t?*/ft-
20'0"
FIG. 1 6. STEEL TUBULAR PIERS FOR HIGHWAY BRIDGES,
AMERICAN BRIDGE COMPANY.
STEEL CYLINDER PIERS FOR RAILWAY BRIDGES.
^LlHi., —Base__of_Ra;/, 0.6% Grade
CLof Future Track
C.L. of Present Track
Longitudinal Elevation Cross Sectional Elevation
FIG. 17. STEEL TUBULAR PIERS, OXFORD MILL POND BRIDGE, CHICAGO &
NORTHWESTERN RAILWAY.
f<
-- •-.. v^- .« »„
l9'-6*C.-h>e. of Cylinder Piers
Too -of Shell
>j
1
S Field
All Side Ptfffts «fi i
"
OK
Hatf fop Plan
C. L. between Tract's
To of Shell
Bottom Bar 6*W
~~29'-6~-—»
Side Eleva-1-ion
->1
Verficol Section A-B.
FIG. 18. STEEL SHELL FOR BASE OF CYLINDER PIERS OF THE OXFORD MILL
BRIDGE, CHICAGO & NORTHWESTERN RAILWAY.
MASONRY AND CONCRETE DEFINITIONS AND SPECIFICATIONS .
CLASSIFICATION OF MASONRY.*
Kind.
Material.
Description.
Manner of
Work.
Dressing.
Joints or Beds.
Face or Surface.
Dimension
Coursed
Smooth
( Smooth
\ Rock-faced
Bridge and Retaining
Stone
. Ashlar. . . .
f Coursed 1
] Broken- [
[ coursed j
f Smooth
s Fine pointed
[ Rough pointed
f Smooth
\ Rock-faced
Wall
Rubble
f Reinforced
Uncoursed
f Rough pointed
\ Scabbled
Rock-faced
Concrete. .
Plain
[ Rubble
'Stone
f Ashlar
[ Rubble
Coursed. . .
Uncoursed
Smooth
Fine pointed
Rough pointed
Scabbled
f Smooth
\ Rock-faced
Rock-faced
Arch
• Concrete. .
/ Reinforced
\ Plain
f English
Brick
No. I
) Bond
j Flemish
( Bond
Culvert
( Stone
Rubble
Dry
Reinforced
Uncoursed
/ Rough pointed
\ Scabbled
Rock-faced
I Concrete . .
Plain
Rubble
Dry. .
Stone
Rubble
Uncoursed
DEFINITIONS.*
Masonry, Bridge and Retaining Wall. — Masonry of stone or concrete, designed to carry
the end of a bridge span or to retain the abutting earth, or both.
Masonry, Arch. — That portion of the masonry in the arch ring only, or between the intrados
and the extrados.
Masonry, Culvert. — Flat-top masonry structure of stone or concrete, designed to sustain the
fill above and to permit the free passage of water.
Masonry, Dry. — Masonry in which stones are built up without the use of mortar.
CONCRETE.
Concrete. — A compact mass of broken stone, gravel or other suitable material assembled
together with cement mortar and allowed to harden.
Reinforced Concrete. — Concrete which has been reinforced by means of metal in some form,
so as to develop the compressive strength of the concrete.
Rubble Concrete. — Concrete in which rubble stone are imbedded.
BRICK.
Brick. — No. I. — Hard burned brick, absorption not exceeding 2 per cent by weight.
CEMENT.
Cement. — A material of one of the three classes, Portland, Natural and Puzzolan, possessing
the property of hardening into a solid mass when mixed with water.
* Adopted by Am. Ry. Eng. Assoc., Vol. 7, 1906, pp. 596-601, 619; Vol. 12, 1911.
266
MASONRY DEFINITIONS. 267
Portland Cement.— This term shall be applied to the finely pulverized product resulting
fiom the r.tlcin.ition to incipient fusion of an intimate mixture of properly proportioned argif-
l.uvous and r.ih .in MUS materials, and to which no addition greater than 3 per cent has been made
•.lent t<> '-.ill inution.
Natural Cement. — This term shall be applied to the finely pulverized product resulting from
the calcination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic
acid gas.
Puzzolan Cement, as Made in North America. — An intimate mixture obtained by finely
pulverizing together granulated basic blast furnace slag and slacked lime.
COURSES AND BOND.
Coursed. — Laid with continuous bed joints.
Broken Coursed. — Laid with parallel, but not continuous, bed joints.
Uncoursed. — Laid without regard to courses.
English Bond. — That disposition of bricks in a structure in which each course is composed
entirely of headers or of stretchers.
Flemish Bond. — That disposition of bricks in a structure in which the headers and stretchers
alternate in each course, the header being so placed that the outer end lies on the middle of a
stretcher in the course below.
DRESSING.
Dressing. — The finish given to the surface of stones or to concrete.
Smooth. — Having surface, the variations of which do not exceed one-sixteenth inch from the
pitch line.
Fine Pointed. — Having irregular surface, the variations of which do not exceed one-quarter
inch from the pitch line.
Rough Pointed. — Having irregular surface, the variations of which do not exceed one-half
inch from the pitch line.
Scabbled. — Having irregular surface, the variations of which do not exceed three-quarters
inch from the pitch line.
Rock-Faced. — Presenting irregular projecting face, without indications of tool mark.
DESCRIPTIVE WORDS.
Abutment. — A supporting wall carrying the end of a bridge or span and sustaining the pressure
of the abutting earth. The abutment of an arch is commonly called a bench wall.
Arris. — The external edge formed by two surfaces, whether plain or curved, meeting each
other.
Ashlar. — A squared or cut block of stone with rectangular dimensions.
Backing. — That portion of a masonry wall or structure built in the rear of the face. It must
be attached to the face and bonded with it. It is usually of a cheaper grade of work than the face.
Batter. — The slope or inclination of the face or back of a wall from a vertical line.
Bed. — The top and bottom of a stone. (See Course Bed; Natural Bed; Foundation Bed.)
Bed Joint. — A horizontal joint, or one perpendicular to the line of pressure.
Bench Wall. — The abutment from which an arch springs.
Bond. — The mechanical disposition of stone, brick or other building blocks by overlapping
to break joints.
Build. — A vertical joint.
Centering. — A temporary support used in arch construction. (Also called centers.)
Clamp. — An instrument for lifting stone so designed that its grip on the surface of the stone
is increased as the load is applied. That portion engaging the stone is of wood attached to a steel
shoe, which in turn is hinged to the shank of the clamp in such a manner as to adjust itself to the
surface of the body lifted.
Coping. — A top course of stone or concrete, generally slightly projecting, to shelter the masonry
from the weather, or to distribute the pressure from exterior loading.
Course. — Each separate layer in stone, concrete or brick masonry.
Course Bed. — Stone, brick or other building material In position, upon which other material
is to be laid.
Cramps. — Bars of iron having the ends turned at right angles to the body of the bar which
enter holes in the upper side of adjacent stones.
Culvert. — A small covered passage for water under a roadway or embankment.
Dimension Stone. — (i) A block of stone cut to specified dimensions.
Dimension Stone. — (2) Large blocks of stone quarried to be cut to specified dimensions.
268 BRIDGE ABUTMENTS AND PIERS. CHAP. VI.
Dowels. — (a) Straight bars of iron which enter a hole in the upper side of one stone and also
a hole in the lower side of the stone next above.
Dowel. — (b) A two-piece steel instrument used in lifting stone. The dowel engages the
stone by means of two holes drilled into the stone at an angle of about 45 degrees pointing toward
each other. The dowel is not keyed in place.
Draft. — A line on the surface of a stone cut to the breadth of the chisel.
Expansion Joint. — A vertical joint or space to allow for temperature changes.
Extrados. — The upper or convex surface of an arch.
Intrados. — The inner or narrow concave surface of an arch.
Face. — The exposed surface in elevation.
Facing. — In concrete: (i) A rich mortar placed on the exposed surfaces to make a smooth
finish.
(2) Shovel facing by working the mortar of concrete to the face.
Final Set. — A stage of the process of setting marked by certain hardness. (See Cement
Specifications.)
Flush. — (Adj.) Having the surface even or level with an adjacent surface.
Flush. — (Verb.) (i) To fill. (2) To bring to a level. (3) To force water to the surface
of mortar or concrete by compacting or ramming.
Footing. — A projecting bottom course.
Form. — A temporary structure for giving concrete a desired shape.
Foundation. — (i) That portion of a structure usually below the surface of the ground, which
distributes the pressure upon its support. (2) Also applied to the natural support itself; rock,
clay, etc.
Foundation Bed. — The surface on which a structure rests.
Grout. — A mortar of liquid consistency which can easily be poured.
Header. — A stone which has its greatest length at right angles to the face of the wall, and
which bonds the face stones to the backing.
Initial Set. — An early stage of the process of setting, marked by certain hardness. (See
Cement Specifications.)
Joint. — The narrow space between adjacent stones, bricks or other building blocks, usually
filled with mortar.
Lagging. — Strips used to carry and distribute the weight of an arch to the ribs or centering
during its construction.
Lewis. — A four-piece steel instrument used in lifting stone. (The lewis engages the stone
by means of a triangular-shaped hole into which it is keyed.)
Lock. — Any special device or method of construction used to secure a bond in the work.
Mortar. — A mixture of fine aggregate, cement or lime and water used to bind together the
materials ot concrete, stone or brick in masonry or to cover the surface of the same.
Natural Bed. — The surfaces of a stone parallel to its stratification.
Parapet. — A wall or barrier on the edge of an elevated structure for protection or ornament.
Paving. — Regularly placed stone or brick forming a floor.
Pier. — An intermediate support for arches or other spans.
Pitch. — (Verb.) To square a stone.
Pitched. — Having the arris clearly defined by a line beyond which the rock is cut away by
the pitching chisel so as to make approximately true edges.
Pointing. — Filling joints or defects in the face of a masonry structure.
Retaining Wall. — A wall for sustaining the pressure of earth or filling deposited behind it.
Voussoirs. — The individual stones forming an arch. They are always of truncated wedge
form.
Ring Stones. — The end voussoirs of an arch.
Riprap. — Rough stone of various sizes placed compactly or irregularly to prevent scour by
water.
Rubble. — Field stone or rough stone as it comes from the quarry. When it is of a large or
massive size it is termed block rubble.
Rubbed. — A fine finish made by rubbing with grit or sand stone.
Set. — (Noun) The change from a plastic to a solid or hard state.
Slope Wall. — A wall to protect the slope of an embankment or cut.
Soffit. — The under side of a projection.
Spall. — (Noun). A chip or small piece of stone broken from a large block.
Spandrel Wall. — The wall at the end of an arch above the springing line and extrados of the
arch and below the coping or the string course.
Stretcher. — A stone which has its greatest length parallel to the face of the wall.
Wing Wall. — An extension of an abutment wall to retain the adjacent earth.
SPECIFICATIONS FOR STONE MASONRY.*
GENERAL.
i. Standard Specifications. — The classification of masonry and the requirements for cement
and concrete shall be those adopted by the American Railway Engineering Association.
Engineer Defined. — Where the term "Engineer" is used in these specifications, it refers
to the cn^iiu •>. T actually in charge of the work.
GENERAL REQUIREMENTS.
3. Stone. — Stone shall be of the kinds designated and shall be hard and durable, of approved
quality and shape, free from seams, or other imperfections. Unseasoned stone shall not be used
where liable to injury by frost.
4. Dressing. — Dressing shall be the best of the kind specified.
5. Beds and joints or builds shall be square with each other, and dressed true and out of
wind. Hollow beds shall not be permitted.
6. Stone shall be dressed for laying on the natural bed. In all cases the bed shall not be
less than the rise.
7. Marginal drafts shall be neat and accurate.
8. Pitching shall be done to true lines and exact batter.
9. Mortar. — Mortar shall be mixed in a suitable box, or in a machine mixer, preferably of
the batch type, and shall be kept free from foreign matter. The size of the batch and the pro-
portions and the consistency shall be as directed by the engineer. When mixed by hand the sand
and cement shall be mixed dry, the requisite amount of water then added and the mixing continued
until the cement is uniformly distributed and the mass is uniform in color and homogeneous.
10. Laying. — The arrangement of courses and bond shall be as indicated on the drawings, or
as directed by the engineer. Stone shall be laid to exact lines and levels, to give the required bond
and thickness of mortar in beds and joints. .
11. Stone shall be cleansed and dampened before laying.
12. Stone shall be well bonded, laid on its natural bed and solidly settled into place in a full
bed of. mortar.
13. Stone shall not be dropped or slid over the wall, but shall be placed without jarring stone
already laid.
14. Heavy hammering shall not be allowed on the wall after a course is laid.
15. Stone becoming loose after the mortar is set shall be relaid with fresh mortar.
16. Stone shall not be laid in freezing weather, unless directed by the engineer. If laid,
it shall be freed from ice, snow or frost by warming; the sand and water used in the mortar shall
be heated.
17. With precaution, a brine may be substituted for the heating of the mortar. The brine
shall consist of one pound of salt to eighteen gallons of water, when the temperature is 32 degrees
Fahrenheit; for every degree of temperature below 32 degrees Fahrenheit, one ounce of salt shall
be added.
1 8. Pointing. — Before the mortar has set in beds and joints, it shall be removed to a depth of
not less than one (i) in. Pointing shall not be done until the wall is complete and mortar set;
nor when frost is in the stone.
19 Mortar for pointing shall consist of equal parts of sand, sieved to meet the requirements,
and Portland cement. In pointing, the joints shall be wet, and filled with mortar, pounded in
with a "set-in" or calking tool and finished with a beading tool the width of a joint, used with a
straight-edge.
BRIDGE AND RETAINING WALL MASONRY — ASHLAR STONE.
20. Bridge and Retaining Wall Masonry. Ashlar Stone. — The stone shall be large and
well proportioned. Courses shall not be less than fourteen (14) in. or more than thirty (30) in.
thick, thickness of courses to diminish regularly from bottom to top.
21. Dressing. — Beds and joints or builds of face stone shall be fine-pointed, so that the
mortar layer should not be more than one-half (}) in. thick when the stone is laid.
22. Joints in face stone shall be full to the square for a depth equal to at least one-half the
height of the course, but in no case less than twelve (12) in.
* Adopted by American Railway Engineering Association.
269
270 BRIDGE ABUTMENTS AND PIERS. CHAP. VI.
i
23. Face or Surface. — Exposed surfaces of the face stone shall be rock-faced, and edges pitched
to the true lines and exact batter; the face shall not project more than three (3) in. beyond the
pitch line.
24. Chisel drafts one and one-half (i£) in. wide shall be cut at exterior corners.
25. Holes for stone hooks shall not be permitted to show in exposed surfaces. Stone shall
be handled with clamps, keys, lewis or dowels.
26. Stretchers. — Stretchers shall not be less than four (4) ft. long and have at least one and a
quarter times as much bed as thickness of course.
27. Headers. — Headers shall not be less than four (4) ft. long, shall occupy one-fifth of face
of wall, shall not be less than eighteen (18) in. wide in face, and, where the course is more than
eighteen (18) in. high, width of face shall not be less than height of course.
28. Headers shall hold in heart of wall the same size shown in face, so arranged that a header
in a superior course shall not be laid over a joint, and a joint shall not occur over a header; the
same disposition shall occur in back of wall.
29. Headers in face and back of wall shall interlock when thickness of wall will admit.
30. Where the wall is three (3) ft. thick or less, the face stone shall pass entirely through.
Backing shall not be permitted.
*3i-a. Backing. — Backing shall be large, well-shaped stone, roughly bedded and jointed;
bed joints shall not exceed one (i) in. At least one-half of the backing stone shall be of same
size and character as the face stone and with parallel ends. The vertical joints in back of wall
shall not exceed two (2) in. The interior vertical joints shall not exceed six (6) in. Voids shall
be thoroughly filled withy Mded {n cement mor^
T concrete.
3i-b. Backing shall be j headers and stretchers, as specified in paragraphs 26 and 27, and
( heart of wall filled with concrete.
32; Where the wall will not admit of such arrangement, stone not less than four (4) ft. long
shall be placed transversely in heart of wall to bond the opposite sides.
33. Where stone is backed with two courses, neither course shall be less than eight (8) in.
thick.
34. Bond. — Bond of stone in face, back and heart of wall shall not be less than twelve (12)
in. Backing shall be laid to break joints with the face stone and with one another.
35. Coping. — Coping stone shall be full size throughout, of dimensions indicated on the
drawings.
36. Beds, joints and top shall be fine-pointed.
37. Location of joints shall be determined by the position of the bed plates, and be indicated
on the drawings.
38. Locks. — Where required, coping stone, stone in the wings of abutments, and stone
on piers, shall be secured together with iron clamps or dowels, to the position indicated on the
drawings.
BRIDGE AND RETAINING WALL MASONRY — RUBBLE STONE.
39. Dressing. — The stone shall be roughly squared, and laid in irregular courses. Beds shall
be parallel, roughly dressed, and the stone laid horizontal to the wall. Face joints shall not be
more than one (i) in. thick. Bottom stone shall be large, selected flat stone.
40. Laying. — The wall shall be compactly laid, having at least one-fifth the surface of back
and face headers arranged to interlock, having all voids in the heart of the wall thoroughly filled
with I con.crete-
' \ suitable stones and spalls, fully bedded in cement mortar.
ARCH MASONRY — ASHLAR STONE.
41. Arch Masonry, Ashlar Stone. — Voussoirs shall be full size throughout and dressed true
to templet, and shall have bond not less than thickness of stone.
42. Dressing. — Joints of voussoirs and intrados shall be fine-pointed. Mortar joints shall
not exceed three-eighths (f) in.
f smooth.
43. Face or Surface. — Exposed surface of the ring stone shall be \ rock faced, with a marginal
( draft.
44. Number of courses and depth of voussoirs shall be indicated on the drawings.
45. Voussoirs shall be placed in the order indicated on the drawings.
* Paragraphs 3i-a and 3i-b are so arranged that either may be eliminated according to
requirements. Optional clauses printed in italics.
SPECIFICATIONS FOR STONE MASONRY. 271
f concrete.
46. Backing. — Backing shall consist of j large stone, shaped to fit the arch bonded to the spandrel
(. and laid in full bed of mortar.
47. Where waterproofing is required, a thin coat of mortar or grout shall be applied evenly
for a finishing out, upon which shall be placed a covering of approved waterproofing mutt-rial.
4,s. Out i TS >hull not be struck until directed by the engineer.
41). Bench Walls, Piers, Spandrels, etc. — Bench walls, piers, spandrels, parapets, wing walls
ami copings shall be built under the specifications for Bridge and Retaining Wall Masonry,
Ashlar Stone.
ARCH MASONRY — RUBBLE STONE.
50. Arch Masonry, Rubble Stone. — Voussoirs shall be full size throughout, and shall have
bond not less tli.iu thickness of voussoirs.
51. Dressing. — Beds shall be roughly dressed to bring them to radial planes.
52. Mortar joints shall not exceed one (i) in.
53. tface or Surface. — Exposed surfaces of the ring stone shall be rock-faced, and edges
pitched to true lines.
54. Voussoirs shall be placed in the order indicated on the drawings.
[ concrete.
55. Backing. — Backing shall consist of j large stone, shaped to fit the arch, bonded to the span-
[ drel, and laid in full bed of mortar.
56. Where waterproofing is required, a thin coat of mortar or grout shall be applied evenly
for a finishing coat, upon which shall be placed a covering of approved waterproofing material.
57. Centers shall not be struck until directed by the engineer.
58. Bench Walls, Piers, Spandrels, etc. — Bench walls, piers, spandrels, parapets, wing walls
and copings shall be built under the specifications for Bridge and Retaining Wall Masonry,
Rubble Stone.
CULVERT MASONRY.
59. Culvert Masonry. — Culvert Masonry shall be laid in cement mortar. Character of
stone and quality of work shall be the same as specified for Bridge and Retaining Wall Masonry,
Rubble Stone.
60. Side Walls. — One-half the top stone of the side walls shall extend entirely across the
wall.
61. Cover Stones. — Covering stone shall be sound and strong, at least twelve (12) in. thick,
or as indicated on the drawings. They shall be roughly dressed to make close joints with each
other, and lap their entire width at least twelve (12) in. over the side walls. They shall be doubled
under high embankments, as indicated on the drawings.
62. End Walls, Coping. — End walls shall be covered with suitable coping, as indicated on
the drawings.
DRY MASONRY.
63. Dry Masonry. — Dry Masonry shall include dry retaining walls and slope walls.
64. Retaining Walls. — Retaining Walls and Dry Masonry shall include all walls in which
rubble stone laid without mortar is used for retaining embankments or for similar purposes. _
65. Dressing. — Flat stone at least twice as wide as thick shall be used. Beds and joints
shall be roughly dressed square to each other and to face of stone.
66. Joints shall not exceed three-quarters (J) in.
67. Disposition of Stone. — Stone of different sizes shall be evenly distributed over entire
face of wall, generally keeping the larger stone in lower part of wall.
68 The work shall be well bonded and present a reasonably true and smooth surface, free
from holes or projections.
69. Slope Walls. — Slope Walls shall be built of such thickness and slope as directed by the
engineer. Stone shall not be used in this construction which does not reach entirely through the
wall. Stone shall be placed at right angles to the slopes. The wall shall be built simultaneously
with the embankment which it is to protect.
SPECIFICATIONS FOR PLAIN AND REINFORCED CONCRETE AND STEEL
REINFORCEMENT.*
CONCRETE MATERIALS.
1. Cement. — The cement shall be Portland and shall meet the requirements of the standard
specifications.
2. Fine Aggregates. — Fine aggregate shall consist of sand, crushed stone or gravel screenings,
graded from fine to coarse, and passing when dry a screen having I in. diameter holes; it shall
preferably be of hard siliceous material, clean, free from dust, soft particles, vegetable loam or
other deleterious matter, and not more than 6 per cent shall pass a sieve having 100 meshes per
linear inch.
3. The fine aggregate shall be of such quality that mortar composed of one part Portland
cement and three parts fine aggregate by weight when made into briquettes shall show a tensile
strength at least equal to the strength of I : 3 mortar of the same consistency made with same
cement and standard Ottawa sand.f
4. Coarse Aggregates. — Coarse aggregate shall consist of material such as crushed stone or
gravel which is retained on a screen having j in. diameter holes and having gradation of sizes from
the smallest to the largest particles; it shall be clean, hard, durable and free from all deleterious
matter. Aggregates containing dust, soft or elongated particles shall not be used.
5. Water. — The water used in mixing concrete shall be free from oil, acid, and injurious
amounts of alkalies or vegetable matter.
STEEL REINFORCEMENT.
6. Manufacture. — Steel shall be made by the open-hearth process. Rerolled material will
not be accepted.
7. Plates and shapes used for reinforcement shall be of structural steel only. Bars and
wire may be of structural steel or high carbon steel.
8. Schedule of Requirements. — The chemical and physical properties shall conform to the
following limits:
Elements Considered.
Structural Steel.
High Carbon Steel.
T>I i ( Basic. .
0.04 per cent
o 04 per cent
rnosphorus, max. . < . . ,
0.06 per cent
0.06 per cent
Sulphur, maximum
0.05 per cent
0.05 per cent
Ultimate tensile strength in pounds
inch
per square
Desired
60,000
Desired
88,000
Elong min per cent in 8 in Fig I
1
i,5oo,oooj
1,000,000
Character of Fracture
'1
Ult. tensile strength
Silky
Ult. tensile strength
Silky or finely
Cold Bends without Fracture
180° flat
granular
1 80° d = 4t§
9. Yield Point. — The yield point for bars and wire, as indicated by the drop of the beam,
shall be not less than 60 per cent of the ultimate tensile strength.
10. Allowable Variations. — If the ultimate strength varies more than 4,000 Ib. for structural
steel or 6,000 Ib. for high carbon steel, a retest shall be made on the same gage, which, to be ac-
ceptable, shall be within 5,000 Ib. for structural steel, or 8,000 Ib. for high carbon steel, of the
desired ultimate.
* Adopted by the American Railway Engineering Association.
t This sand may be obtained from the Ottawa Silica Company at a cost of 2 cts. per Ib.
f. o. b. cars, Ottawa, 111.
J See paragraph 15.
§ "d = 4/" signifies "around a pin whose diameter is four times the thickness of the specimen."
272
SPECIFICATIONS FOR PLAIN AND REINFORCED CONCRETE. 273
11. Chemical Analyses. — Clu-mical determinations of the percentages of carbon, phosphorus,
sulphur and manganese shall be made by the manufacturer from a test ingot taken at the time
of tlu- pouring of each melt of steel, and a correct copy of such analysis shall be furnished to the
fii^iiu'i-r or his inspector. Check analysis shall be made from finished iu.iti-ri.il, if railed for liy
tin- railroad company, in which case an excess of 25 per cent above thi- required limits will be
allowed.
12. Form of Specimens. — Plates, Shapes and Bars: Specimens for tensile and bending
tests for plates and shapes shall be made by cutting coupons from the finished product, which
shall have both faces rolled and both edges milled to the form shown by Fig. i; or with both edges
parallel; or they may be turned to a diameter of J in. with enlarged ends.
13. Bars shall be tested in their finished form.
uf.
iW i
i . . ±
•— »
FIG. i.
14. Number of Tests. — At least one tensile and one bending test shall be made from each melt
of steel as rolled. In case steel differing f in. and more in thickness is rolled from one melt, a
test shall be made from the thickest and thinnest material rolled.
15. Modifications in Elongation. — For material less than ^ in. and more than } in. in thick-
ness the following modifications will be allowed in the requirements for elongation:
(a) For each -fa in. in thickness below ^ in. a deduction of 2\ will be allowed from the speci-
fied percentage.
(b) For each \ in. in thickness above \ in., a deduction of i will be allowed from the specified
percentage.
16. Bending Tests. — Bending test may be made by pressure or by blows. Shapes and bars
less than one inch thick shall bend as called for in paragraph 8.
17. Thick Material. — Test specimensone inch thickand over shall bend cold 1 80 degrees around
a pin, the diameter of which, for structural steel, is twice the thickness of the specimen, and for high
carbon steel, is six times the thickness of the specimen, without fracture on the outside of the bend.
1 8. Finish. — Finished material shall be free from injurious seams, flaws, cracks, defective
edges or other defects, and have a smooth, uniform and workmanlike finish.
19. Stamping. — Every finished piece of steel shall have the melt number and the name of
the manufacturer stamped or rolled upon it, except that bar steel and other small parts may be
bundled with the above marks on an attached metal tag.
20. Defective Material. — Material which, subsequent to the above tests at the mills, and its
acceptance there, develops weak spots, brittleness, cracks or other imperfections, or is found to
have injurious defects, will be rejected and shall be replaced by the manufacturer at his own cost.
21. Reinforcing steel shall be free from excessive rust, loose scale, or other coatings of any
character, which would reduce or destroy the bond.
WORKMANSHIP.
22. Unit of Measure. — The unit of measure shall be the cubic foot. A bag containing not
less than 94 Ib. of cement shall be assumed as one cubic foot of cement. Fine and coarse aggre-
gates shall be measured separately as loosely thrown into the measuring receptacle.
23. Relation of Fine and Coarse Aggregates. — The fine and coarse aggregates shall be used
in such relative proportions as will insure maximum density.
19
274
BRIDGE ABUTMENTS AND PIERS.
CHAP. VI
24. Proportions. — The proportions of materials for the different classes of concrete shall be
as follows:
Class.
Use.
Cement.
Aggregates.
Fine.
Coarse.
Note: — This blank to be filled for each contract.
25. For plain concrete, a proportion of i : 9 (unless otherwise specified) shall be used, i. e.,
one part of cement to a total of nine parts of fine and coarse aggregates measured separately; for
example, I cement, 3 fine aggregate, 6 coarse aggregate.
26. For reinforced concrete a proportion of I : 6 (unless otherwise specified) shall be used,
i. e., one part of cement to a total of six parts of fine and coarse aggregates measured separately;
for example, I cement, 2 fine aggregate, and 4 coarse aggregate.
27. Mixing. — The ingredients of concrete shall be thoroughly mixed to the desired con-
sistency, and the mixing shall continue until the cement is uniformly distributed and the mass
is uniform in color and homogeneous.
28. Measuring Proportions. — The various ingredients, including the water, shall be measured
separately, and the methods of measurement shall be such as to secure the proper proportions at
all times.
29. Machine Mixing. — A machine mixer, preferably of the batch type, shall be used, wher-
ever the volume of the work will justify the expense of installing the plant. The requirements
demanded are that the product delivered shall be of the specified proportions and consistency
and thoroughly mixed.
30. Hand Mixing. — When it is necessary to mix by hand, the mixing shall be on a watertight
platform of sufficient size to accommodate men and materials for the progressive and rapid mixing
of at least two batches of concrete at the same time. Batches shall not exceed one-half cubic
yard each. The mixing shall be done as follows: The fine aggregate shall be spread evenly upon
the platform, then the cement upon the fine aggregates, and these mixed thoroughly until of an
even color. The water necessary to mix a thin mortar shall then be added and the mortar spread
again. The coars'e aggregates, which, if dry, shall first be thoroughly wetted down, shall then
be added to the mortar. The mass shall then be turned with shovels or hoes until thoroughly
mixed and all the aggregate covered with mortar. Or, at the option of the engineer, the coarse
aggregate may be added before, instead of after, adding the water.
31. Consistency. — The materials shall be mixed wet enough to produce a concrete of such
consistency that it will flow into the forms and about the metal reinforcement, and which, on
the other hand, can be conveyed from the place of mixing to the forms without separation of the
coarse aggregate from the mortar.
32. Retempering. — Retempering mortar or concrete, i e., remixing with water after it has
partially set, will not be permitted.
33. Placing of Concrete. — Concrete after the completion of the mixing shall be handled
rapidly to the place of final deposit and under no circumstances shall concrete be used that has
partially set before final placing.
34. The concrete shall be deposited in such a manner as will prevent the separation of the
ingredients and permit the most thorough compacting. It shall be compacted by working with
a straight shovel or slicing tool kept moving up and down until all the ingredients have settled in
their proper place and the surplus water is forced to the surface. In general, except in arch work,
all concrete must be deposited in horizontal layers of uniform thickness throughout.
35. In depositing concrete under water, special care shall be exercised to prevent the cement
from floating away and to prevent the formation of laitance.
36. Before depositing concrete the forms shall be thoroughly wetted (except in freezing
weather) or oiled, and the space to be occupied by the concrete cleared of debris.
37. Before placing new concrete on or against concrete which has set, the surface of the latter
shall be roughened, thoroughly cleansed of foreign material and laitance, drenched and slushed
with a mortar consisting of one part Portland cement and not more than two parts fine aggregate.
38. The faces of concrete exposed to premature drying shall be kept wet for a period of at
least three days.
SPECIFICATIONS FOR PLAIN AND REINFORCED CONCRETE. 275
39. Freezing Weather. — Concrete shall not be mixed or deposited at a freezing temperature,
i.il |>i(( u.niniis, approved by the enginn r, .m i.ik< -n to avoid the use of materials
i ,.vtic<l with ire crystals or containing frost ana to provide HUMUS to prevent the concrete from
ing.
Tin author has used the following specification for depositing concrete in freezing weather: —
When the temperature of the air is below 40° F. during the time of mixing and placing concrete, the
water used in mixing concrete shall be heated to such a temperature that the temperature of the concrete
mixture shall not be less than 60° when it reaches its final position in the forms. Care shall be used
that the cement shall not be injured by boiling water.
40. Rubble Concrete. — Where the concrete is to be deposited in massive work, clean, large
stums, evenly distributed, thoroughly bedded and entirely surrounded by concrete, may Be
used, at the option of the engineer.
1 1 . Forms. — Forms shall be substantial and unyielding and built so that the concrete shall
conform to the designed dimensions and contours, and so constructed as to prevent the leakage
of mortar.
42. The forms shall not be removed until authorized by the engineer.
43. For all important work, the lumber used for face work shall be dressed to a uniform thick-
ness and width; shall be sound and free from loose knots and secured to the studding or uprights
in horizontal lines.
44. For backings and other rough work undressed lumber may be used.
45. Where corners of the masonry and other projections liable to injury occur, suitable mold-
ings shall be placed in the angles of the forms to round or bevel them off.
46. Lumber once used in forms shall be cleaned before being used again.
47. The reinforcement shall be carefully placed in accordance with the plans, and adequate
means shall be provided to hold it in its proper position until the concrete has been deposited
and compacted.
DETAILS OF CONSTRUCTION.
48. Splicing Reinforcement. — Wherever it is necessary to splice the reinforcement otherwise
than as shown on the plans, the character of the splice shall be decided by the engineer on the
basis of the safe bond stress and the stress in the reinforcement at the point of splice. Splices
shall not be made at points of maximum stress.
49. Joints in Concrete. — Concrete structures, wherever possible, shall be cast at one opera-
tion, but when this is not possible, the resulting joint shall be formed where it will least impair
the strength and appearance of the structure.
50. Girders and slabs shall not be constructed over freshly formed walls or columns without
permitting a period of at least four hours to elapse to provide for settlement or shrinkage in the
supports. Before resuming work, the tops of such walls or columns shall be cleaned of foreign
matter and laitance.
51 A triangular-shaped groove shall be formed at the surface of the concrete at vertical
joints in walls and abutments.
52 Surface Finish. — Except where a special surface finish is required, a spade or special
tool shall always be worked between the concrete and the form to force back the coarse aggre-
gates and produce a mortar face.
53. Top Surfaces. — Top surfaces shall generally be " struck" with a straight edge or floated
after the coarse aggregates have been forced below the surface.
54. Sidewalk Finish. — Where a "sidewalk finish" is called for on the plans, it shall be made
by spreading a layer of I : 2 mortar at least } in. thick, troweling the same to a smooth surface.
This finishing coat shall be put on before the concrete has taken its initial set.
276 BRIDGE ABUTMENTS AND PIERS. CHAP. VI.
REFERENCES. — Plain masonry and concrete abutments and piers, only, have been con-
sidered in this chapter. The following books may be consulted for additional information.
Baker's " Masonry Construction," John Wiley & Sons, gives a full discussion of the design
of masonry, plain and reinforced concrete abutments and piers, and the different methods of
constructing abutments and piers.
Fowler's " Ordinary Foundations," John Wiley & Sons, gives a full discussion of the design
and construction of abutments and piers, with special attention given to the coffer dam process.
Jacoby and Davis' " Foundations of Bridges and Buildings," McGraw-Hill Book Co., gives
a full discussion of the design and construction of abutments and piers.
Bulletin 140 of the Am. Ry. Eng. Assoc. has an article on the Design of Railway Bridge Abut-
ments by Mr. J. H. Prior, Asst. Engineer, C. M. & St. P. Ry. This article describes in detail
the standard plain and reinforced concrete abutments used by the C. M. & St. P. Ry.
CHAPTER VII.
TIMBER BRIDGES AND TRESTLES.
Definitions. — The following definitions have been adopted by the American Railway Engi-
mvring Association.
Wooden Trestle. — A wooden structure composed of upright members supporting simple
horizontal members or beams, the whole forming a support for loads applied to the horizontal
members.
Frame Trestle. — A structure in which the upright members or supports are framed timbers.
Pile Trestle. — A structure in which the upright members or supports are piles.
Bent. — The group of members forming a single vertical support of a trestle, designated as
pile bent where the principal members are piles, and as framed bent where of framed timbers.
Post. — One of the vertical or battered members of the bent of a framed trestle.
Pile. — (See definition under subject of Piles and Pile Driving.)
Batter. — A deviation from the vertical in upright members of a bent.
Cap. — A horizontal member upon the top of piles or posts, connecting them in the form of a
bent.
Sill. — A lower horizontal member of a framed bent.
Sub-Sill. — A timber bedded in the ground to support a framed bent.
Intermediate Sill. — A horizontal member in the plane of the bent between the cap and sill
to which the posts are framed.
Sway Brace. — A member bolted or spiked to the bent and extending diagonally across its
face.
Longitudinal Strut or Girt. — A stiff member running horizontally, or nearly so, from bent to
bent.
Longitudinal X-Brace. — A member extending diagonally from bent to bent in a vertical or
battered plane.
Sash Brace. — A horizontal member secured to the posts or piles of a bent.
Stringer. — A longitudinal member extending from bent to bent and supporting the ties.
Jack Stringer. — A stringer placed outside of the line of main stringers.
Tie. — A transverse timber resting on the stringers and supporting the rails.
Guard Rail. — A longitudinal member, usually a metal rail, secured on top of the ties inside
of .the track rail, to guide derailed car wheels.
Guard Timber. — A longitudinal timber framed over the ties outside of the track rail, to
maintain the spacing of the ties.
Packing Block. — A small member, usually wood, used to secure the parts of a composite
member in their proper relative positions.
Packing Spool or Separator. — A small casting used in connection with packing bolts to
secure the several parts of a composite member in their proper relative positions.
Drift Bolt. — A piece of round or square iron of specified length, with or without head or
point, driven as a spike.
Dowel. — An iron or wooden pin, extending into, but not through, two members of the struc-
ture to connect them.
Shim. — A small piece of wood or metal placed between two members of a structure to bring
them to a desired relative position.
Fish-Plate. — A short piece lapping a joint, secured to the side of two members, to connect
them end to end.
Bulkhead.— A wall of timber placed against the side of an end bent to retain the embankment.
STRUCTURAL TIMBER.
Definitions. — The following definitions have been adopted by the American Railway Engi-
neering Association.
Timber. — A single stick of wood of regular cross-section.
Cross-Section. — A section of a stick at right angles to the axis.
True. — Of uniform cross-section. Defects are caused by wavy or jagged sawing or consist
of trapezoidal instead of rectangular cross-sections.
277
278 TIMBER BRIDGES AND TRESTLES. CHAP. VII.
Axis. — The line connecting the centers of successive cross-sections of a stick.
Straight. — Having a straight line for an axis.
Out of Wind. — Having the longitudinal surfaces plane.
Full Length. — Long enough to "square" up to the length specified in the order.
Corner. — The line of intersection of the planes of two adjacent longitudinal surfaces.
Girth. — The perimeter of a cross-section.
Side. — Either of the two wider longitudinal surfaces of a stick.
Edge. — Either of the two narrower longitudinal surfaces of a stick.
Face. — The surface of a stick which is exposed to view in the finished structure.
Sapwood. — A cylinder of wood next to the bark and of lighter color than the wood within.
It may be of uneven thickness.
Heartwood. — The older and central part of a log, usually darker in color than sapwood.
It appears in strong contrast to the sapwood in some species, while in others it is but slightly
different in color.
Springwood. — The inner part of the annual ring formed in the earlier part of the season,
not necessarily in the spring, and often containing vessels or pores.
Summerwood. — The outer part of the annual ring formed later in the season, not necessarily
in the summer, being usually dense in structure and without conspicuous pores.
Decay. — Complete or partial disintegration of the cell walls, due to the growth of fungi.
Sound. — Free from decay.
Solid. — Without cavities; free from loose heart, wind shakes, bad checks, splits or breaks,
loose slivers, and worm or insect holes.
Wane. — A deficient corner due to curvature or to taper of the log.
Square Cornered. — Free from wane.
Knot. — The hard mass of wood formed in a trunk at a branch, with the grain distinct and
separate from the grain of the trunk.
Cross-Grain. — The gnarly mass of wood surrounding a knot, or grain injuriously out of
parallel with the axis.
Wind Shake. — A crack or fissure, or a series of them, caused during growth.
STANDARD DEFECTS OF STRUCTURAL TIMBER.*
The standard defects included in the following list are mostly such as may be termed natural
defects, as distinguished from defects of manufacture. The latter have usually been omitted,
because the defects of manufacture are of minor significance in the grading of structural timber:
Sound Knot. — A sound knot is one which is solid across its face and is as hard as the wood
surrounding it. It may be either red or black, and is so fixed by growth or position that it will
retain its place in the piece.
Loose Knot. — A loose knot is one not firmly held in place by growth or position.
Pith Knot. — A pith knot is a sound knot with a pith hole not more than f in. in diameter f
in the center.
Encased Knot. — An encased knot is one which is surrounded wholly or in part by bark or
pitch. Where the encasement is less than | in. in width on each side, nor exceeding one-half the
circumference of the knot, it shall be considered a sound knot.
Rotten Knot. — A rotten knot is one not as hard as the wood surrounding it.
Pin Knot. — A pin knot is a sound knot not over \ in. in diameter.
Standard Knot. — A standard knot is a sound knot not over \\ in. in diameter.
Large Knot. — A large knot is a sound knot, more than I } in. in diameter.
Round Knot. — A round knot is one which is oval or circular in form.
Spike Knot. — A spike knot is one sawn in a lengthwise direction. The mean or average
diameter shall be taken as the size of these knots.
Pitch Pockets. — Pitch pockets are openings between the grain of the wood, containing more
or less pitch or bark. These shall be classified as small, standard and large pitch pockets.
Small Pitch Pocket. — (a). — A small pitch pocket is one not over | in. wide.
Standard Pitch Pocket. — (b). — A standard pitch pocket is one not over f in. wide nor over
3 in. in length.
Large Pitch Pocket. — (c).^A large pitch pocket is one over f in. wide, or over 3 in. in length.
Pitch Streak. — A pitch streak is a well-defined accumulation of pitch at one point in the
piece. When not sufficient to develop a well-defined streak, or where the fiber between grains,
that is, the coarse grained fiber, usually termed "spring wood," is not saturated with pitch, it
shall not be considered a defect.
* Adopted by Am. Ry. Eng. Assoc., Vol. 8, 1907.
t Measurements which refer to the diameter of knots or holes shall be considered as the mean
or average diameter in all cases.
PILES AND PILE DRIVING. 279
Shakes. — Shakes are splits or checks in timber which usually cause a separation of the
\\ci<nl Ixiw.i n annual rings.
Ring Shake. — An o|x-ning between annual rings.
Through Shakes.— A shake which extends Ix-tween two faces of a timber.
Rot, Dote and Red Heart. — Any form of decay which may be evident either as a dark red
discolorat i. m not found in the sound wood, or by the presence of white or red rotten spots, shall be
omMcli ivd as a defect.
Wane. — (See definition under the subject of Structural Timber.)
Note. — See additional definitions of defects under Structural Timber.
, PILES AND PILE DRIVING.*
The following definitions and the principles of Pile Driving have been adopted by the Ameri-
can Railway Engineering Association.
Pile. — A member usually driven or jetted into the ground and deriving its support from the
underlying strata, and by the friction of the ground on its surface. The usual functions of a
pile are: (a) to carry a superimposed load; (b) to compact the surrounding ground; (c) to form a
wall to exclude water and soft material, or to resist the lateral pressure of adjacent ground.
Head of Pile. — The upper end of a pile.
Foot of Pile. — The lower end of a pile.
Butt of Pile. — The larger end of a pile.
Tip of Pile. — The smaller end of a pile.
Bearing Pile. — One used to carry a superimposed load.
Screw Pile. — One having a broad-bladed screw attached to its foot to provide a larger bearing
area.
Disc Pile. — One having a disc attached to its foot to provide a larger bearing area.
Batter Pile. — One driven at an inclination to resist forces which are not vertical.
Sheet Pile. — Piles driven in close contact in order to provide a tight wall, to prevent leakage
of water and soft materials, or driven to resist the lateral pressure of adjacent ground.
Pile Driver. — A machine for driving piles.
Hammer. — A weight used to deliver blows to a pile to secure its penetration.
Drop Hammer. — One which is raised by means of a rope and then allowed to drop.
Steam Hammer. — One which is automatically raised and dropped a comparatively short
distance by the action of a steam cylinder and piston supported in a frame which follows the pile.
Leads. — The upright parallel members of a pile driver which support the sheaves used to
hoist the hammer and piles, and which guide the hammer in its movement.
Cap. — A block used to protect the head of a pile and to hold it in the leads during driving.
Ring. — A metal hoop used to bind the head of a pile during driving.
Shoe. — A metal protection for the point or foot of a pile.
. Follower. — A member interposed between the hammer and a pile to transmit blows to the
latter when below the foot of the leads.
PILE-DRIVING — Principles of Practice. — (i) A thorough exploration of the soil by borings,
or preliminary test piles, is the most important prerequisite to the design and construction of
pile foundations.
(2) The cost of exploration is frequently less than that otherwise required merely to revise
the plans of the structure involved, without considering the unnecessary cost of the structures
due to lack of information.
(3) Where adequate exploration is omitted, it may result in the entire loss of the structure,
or in greatly increased cost.
(4) The proper diameter and length of pile, and the method of driving depend upon the result
of the previous exploration and the purpose for which they are intended.
(5) Where the soil consists wholly or chiefly of sand, the conditions are most favorable to
the use of the water jet.
(6) In harder soils containing gravel the use of the jet may be advantageous, provided
sufficient volume and pressure be provided.
(7) In clay it may be economical to bore several holes in the soil with the aid of the jet before
driving the pile, thus securing the accurate location of the pile, and its lubrication while being
driven.
(8) In general, the water jet should not be attached to the pile, but handled separately.
(9) Two jets will often succeed where one fails; in special cases a third jet extending a part
of the depth aids materially in keeping loose the material around the pile.
(10) Where the material is of such a porous character that the water from the jets may be
* For an elaborate bibliography on " Piles and Pile Driving" see Am. Ry. Eng. Assoc., Vol. 10.
280 TIMBER BRIDGES AND TRESTLES. CHAP. VII.
dissipated and fail to come up in the immediate vicinity of the pile, the utility of the jet is uncer-
tain, except for a part of the penetration.
(n) A steam or drop hammer should be used in connection with the water jet, and used to
test the final rate of penetration.
(12) The use of the water jet is one of the most effective means of avoiding injury to piles
by overdriving.
(13) There is danger from overdriving when the hammer begins to bounce. Overdriving is
also indicated by the bending, kicking or staggering of the pile.
(14) The brooming of the head of a pile dissipates a part, and in some cases all, of the energy
due to the fall of the hammer.
(15) The weight or the drop of the hammer should be proportioned to the weight of the
pile, as well as to the character of the soil to be penetrated.
(16) The steam hammer is more effective than the drop hammer in securing the penetration
of a pile without injury, because of the shorter interval between blows.
(17) Where shock to surrounding material is apt to prove detrimental to the structure, the
steam hammer should always be used instead of the drop hammer. This is especially true in the
case of sheet piling which is intended to prevent the passage of water. In some cases also the
jet should not be used.
(18) In general, the resistance of piles, penetrating soft material, which depend solely upon
skin friction, is materially increased after a period of rest. This period may be as short as fifteen
minutes, and rarely exceeds twelve hours.
(19) In tidal waters the resistance of a pile driven at low tide is increased at high tide on
account of the extra compression of the soil.
(20) Where a pile penetrates muck or a soft yielding material and bears upon a hard stratum
at its foot, its strength should be determined as a column or beam; omitting the resistance, if any,
due to skin friction.
(21) Unless the record of previous experience at the same site is available, the approximate
bearing power may be obtained by loading test piles. The results of loading test piles should
be used with caution, unless their condition is fairly comparable with that of the piles in the
proposed foundation.
(22) In case the piles in a foundation are expected to act as columns the results of loading
test piles should not be depended upon unless they are sufficient in number to insure their action
in a similar manner, and they are stayed against lateral motion.
(23) Before testing the penetration of a pile in soft material where its bearing power depends
principally, or wholly, upon skin friction, the pile should be allowed to rest for 24 hours after
driving.
(24) Where the resistance of piles depends mainly upon skin friction it is possible to diminish
the combined strength, or bearing capacity, of a group of piles by driving additional piles within
the same area.
(25) Where there is a hard stratum overlying softer material through which the piles are to
pass to a firm bearing below, the upper stratum should be removed by dredging or otherwise,
provided it would injure the piles to drive through the stratum. The material removed may be
replaced if it is needed to provide lateral resistance.
(26) Timber piles may be advantageously pointed, in some cases, to a 4-in. or 6-in. square
at the end.
(27) Piles should not be pointed when driven into soft material.
(28) Shoes should be pfovided for piles when the driving is very hard, especially in riprap or
shale, and should be so constructed as to form an integral part of the pile.
(29) The use of a cap is advantageous in distributing the impact of the hammer more uni-
formly over the head of the pile, as well as to hold it in position during driving.
(30) The specification relating to the penetration of a pile should be adapted to the soil which
the pile is to penetrate.
(31) It is far more important that a proper length of pile should be put in place without
injury than that its penetration should be a specified distance under a given blow, or series of
blows.
SPECIFICATIONS FOR TIMBER PILES.*
RAILROAD HEART GRADE.
1. This grade includes white, burr, and post oak, longicaf pine, Douglas fir, tamarack, Eastern
white ami ml cedar, chestnut, Western cedar, redwood and cypress.
2. Piles shall be cut from sound trees; shall be close grained and solid, free from defects, such
as injurious ring shakes, large and unsound or loose knots, decay or other defects, which may
materially impair their strength or durability. In Eastern red or white cedar a small amount of
In ut rot at the butt, which does not materially injure the strength of the pile, will l>c allo .
3. Piles must be butt cut above the ground swell and have a uniform taper from butt to tip.
Short bends will not be allowed. A line drawn from the center of the butt to the center of the
tip shall lie within the body of the pile.
4. Unless otherwise allowed, piles must be cut when sap is down. Piles must be peeled soon
after cutting. All knots shall be trimmed close to the body of the pile.
5. For round piles the; minimum diameter at the tip shall be nine (9) in. for lengths not
exceeding thirty (30) ft.; eight (8) in. for lengths over thirty (30) ft. but not exceeding fifty (50)
ft., and seven (7) in. for lengths over fifty (50) ft. The minimum diameter at one-quarter of the
length from the butt shall be twelve (12) in. and the maximum diameter at the butt twenty (20) in.
6. For square piles the minimum width of any side of the tip shall be nine (9) in. for lengths
not exceeding thirty (30) ft.; eight (8) in. for lengths over thirty (30) ft. but not exceeding fifty
(50) ft., and seven (7) in. for lengths over fifty (50) ft. The minimum width of any side at one-
quarter of the length from the butt shall be twelve (12) in.
7. Square piles shall show at least eighty (80) per cent heart on each side at any cross-section
of the stick, and all round piles shall show at least ten and one-half (loj) in. diameter of heart
at the butt.
RAILROAD FALSEWORK GRADE.
8. This grade includes red and all other oaks not included in R. R. Heart grade, sycamore,
sweet, black and tupelo gum, maple, elm, hickory, Norway pine, or any sound timber that will
stand driving.
9. The requirements for size of tip and butt, taper and lateral curvature are the same as for
R. R. Heart grade.
10. Unless otherwise specified piles need not be peeled.
11. No limits are specified as to the diameter or proportion of heart.
12. Piles which meet the requirements of R. R. Heart grade except the proportion of heart
specified will be classed as R. R. Falsework grade.
GUARD RAILS AND GUARD TIMBERS.— In 1912 the American Railway Engineering
Association made an investigation of the use of guard rails and guard timbers for timber trestles
and bridges and adopted the following report based on replies from 61 railroads.
1. It is recommended as good practice to use guard timbers on all open-floor bridges, and
same shall be so constructed as to properly space the ties and hold them securely in their places.
2. It is recommended as good practice to use guard rails to extend beyond the end of the
bridges for such a distance as required by local conditions, but that this length in any case be not
less than fifty feet; that guard rails be fully spiked to every tie and spliced at every joint, the guard
rail to be some form of metal guard rail.
3. It is recommended that the guard timber and guard rail be so spaced in reference to the
track rail that a derailed truck will strike the guard rail without striking the guard timber.
4. The height of the guard rail to be not over one inch less in height than the running (track)
rail.
TIMBER TRESTLES. — The details of the design of timber trestles depends upon the loading,
the details of the floor system, the available timber and upon the designer. The length of panels
varies from 12 ft. to 16 ft., with 14 ft. as a fair average panel length.
Pile Trestles. — The details of the standard pile trestle with open floor of the N. Y., N. H. &
H. R. R. are given in Fig. I. The number and arrangement of the piles in the bents are shown.
The bents are 12 ft. center to center. The stringers are 24 ft. long and are placed to span two
panels and to break joints. The tops of the caps are covered with No. 20 flat galvanized iron to
protect the trestle from fire. The details of washers, packing blocks, drift bolts, etc., are shown
on the plans.
* Adopted, Am. Ry. Eng. Assoc., Vol. 10, 1909.
281
282
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
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288
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284
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
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FIG. 3. PLANS OF TIMBER FRAME TRESTLE. ILLINOIS CENTRAL RAILROAD.
j!0tt jlo" -- , jlQ" fLQ"
r7'*ISl 'Stringers, 10 per Pwef-
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2 ^Ma dALLAST FLOOR TRESTLE •
ILLINOIS CENTRAL RAILROAD
FIG. 4. PLANS OF TIMBER TRESTLE WITH BALLASTED DECK.
.Nails, ?0 Nails per P/ank
PLAN
TIMBER HOWE TRUSS THROUGH BRIDGE.
286
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
wvi/vi/vfa/i^' '*• i
glSIMsdl^a. ^sb
flngleB/odB~3J83 ;
Material- Cast Iron
ILJI'
j^MM^J.
«* — *-*-.-.— «»—--~— i-— .™«ifr"-"v*f — i
't'/ifMlfi/ift /V *" flaterial-Castlron
fing/e Slock" B 3m
Material-Cast Iron t _
It'-Q"l0j!0jf-O'l'
jJW/MM ^ JM
-js-jtiL* iHr/4*
^Mjl
! V? 'dflliLl
^i;-^--. I «aM
N
SSi-^
f
Lateral finale Block
83/93
Material-Cast Iron
B 3/90 A with fins. Separating Washer
83/90 omit Fins. dark "Pz'
Material-Cast Iron Material-Cast Iron
Jif^M^MJL •** //'
\f¥~\3?6\ z?T ^^
^nar^nprt^^' ^^* •
«], I J^/14^4 /^| t*. __^[r^....,v
f//^
s%
KSf^L'
-4-"
6wJn?fhwnMrk"BCf" \ ^ \ &
M-^«».^~fe5L
I //'/ ! g j-'|
sfeza-^L/- ^ -SRJ^- -ns
Hl_^K^
-.:
Lateral finale Block
83194.
Material-Cast Iron
finale Block B3I3I
tlaterial- Cast Iron '
^i
NIQ}-
t
i
I
I
i
j
i
^IfcL,
Cast Iron Packing Washer
for Lateral Rods
llsj& ''"These ccm$rs.rnust fie square^ !fejr/aj
//?/'' //??'
Lateral ' fing/e Block
51365
Material-Cast Iron.
C-r—
,^._..^.^
^/77/? C3 ~,
FIG. 6. IRON DETAILS FOR 150 FT. SPAN, HOWE TRUSS SPAN.
C. M. & P. S- RY.
IRON DETAILS FOR TIMBER HOWE TRUSS BRIDGE.
! Material 9i\ Cast Iron Washer B3I99
1C5>-VL**^>I-*V-^ ° ^-s-^^ z <S>[-(TV ° 7TI v^Oi
Clamp Block BM0/*0jhm Clamp Block
• • Bm/Lopp.haqd fork B 3090
Material-Cast Iron\ Materialist Iron
62020"} ones above except for Lateral fingfe Block B3I95f)
bosses as shown. Material-Cast Iron
• $£' ' m • $f i'-o£
/*
,ji j i'- ffTi 4
J5 f% fiff "^BM2^JS|r"
X
f^f----^^- ^i^^anatyL
!^A^*^nt ^®
Lateral Angle Block B3/96 Lateral ffngle Block BMM *0-0» ,
Material -Cast Iron Material -Cast Iron lp°ql ^*l
•T Sffw/eNubT. M Square Nuts M ^^ — L—i^J
^,1 t r'r>! ilnl !~rd Padfnq Washer For Bottom Chord
^— k ta^ . i-LTL 1 LTH y MdrkB325I
V?
JPiyhtHand Threads.
tlaterial-Cast Iron
General Notes.:-
'V
/^77 «y/^ or twist with inside corners: square and
at right angles to Lne longitudinal axis oftht
member. Ihe surfaces ofooth cbmps and wedges
must be finished wAene catted for. The workmanship
and finish shall conform to the best practice in
modem bridge shops.
FIG. 7. IRON DETAILS FOR 150 FT. SPAN, HOWE TRUSS SPAK.
C. M. & P. S. RY.
288
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
Frame Trestles. — The details of the standard frame trestle with open floor of the N. Y.,
N. .H. & H. R. R. are given in Fig. 2. The bents are spaced 12 ft. center to center. The floor
system is the same as for pile trestles. The frame trestle may be supported on a pile foundation,
upon timber sub-sills (mudsills) or on concrete pedestals. Timber sub-sills soon decay and
should be used only for temporary trestles. Other data and details are shown on the plans.
The plans of a standard frame trestle designed and built by the Illinois Central Railroad are
given in Fig. 3. The bents are spaced 14 ft. centers, while the stringers are 28 ft. long and cover
two panels. The details of the track and the guard rails are not shown. A complete bill of
timber and iron for one bent and one panel of the floor are given in Fig. 3. The standard frame
trestle may be carried on mudsills (sub-sills) as shown in Fig. 3, or on piles or concrete pedestals
as shown in Fig. 2.
Detail plans of a pile trestle with ballasted deck are given in Fig. 4.
TIMBER HOWE TRUSSES.— Plans of a standard 150 ft. span Howe truss designed and
erected by the C. M. & P. S. Ry. are shown in Fig. 5, Fig. 6, and Fig. 7. This bridge was designed
for Cooper's E 55 Loading, with the allowable unit stresses as given in the American Railway
Engineering Association Specifications for Timber Bridges and Trestles. The bill of lumber is
given in Table I; the bill of castings and bolts is given in Table II; the bill of upset vertical rods
is given in Table III, and the bill of lateral rods is given in Table IV. The following additional
specifications were given on the plans.
TABLE I.
BILL OF TIMBER FOR ONE 150 FT. HOWE TRUSS SPAN.
No. of
PCS.
Size, In.
Length, Ft.-In.
Location.
No. of
PCS.
Size, In.
Length, Ft.-In.
Location.
2
10 X 14
12-6
Top Chord.
8
8X8
28-31
Diag. Posts.
2
" " "
18-3!
11 it
2
12 X 14
22-O
Portal.
2
(( ft tf
24-Of
ti it
4
6 X 12
I4-O
"
2
ft If ((
29-10!
ti it
2
8 X 10
9-0
Bott. Laterals.
2
If ( ff
35-7*
it it
2
ti ti it
8-7
>
2
ff ( ff
4i-5
it it
2
it tt it
1 8-0
12
ff C ff
46-3
it ft
2
ft tt it
17-9
2
ff ( (C
47~2i
ii it
4
tt it it
8-8
2
tf i ff
S2-Ilf
tt t
2
8X8
17-4
16
4 X 14
2-4*
ti i
2
it it ii
8-1
12
11 It it
2-8
ti i
2
ti ii it
8-9
4
<( « 11
s-il
ii t
4
6X8
17-0
132
3 X 14
I-O
" '
8
ft tt ft
8-5
4
10 X 18
20-3!
Bott. Chord.
4
6X6
8-5
4
" " "
3i-ioi
ti it
2
tt ti tt
17-1
2
ii it «
43-4i
» ii
I
it tt tt
17-8
2
it .it «
54-" 1
it ii
2
ft tt ft
8-9
t
IO
« ft <(
57-8J
it ii
H
it ii ii
8-10
Top Late als.
4
ft ft it
66-Sf
it ti
6
11 it ii
17-11
4 •
« ff 11
83-3
it ti
4
it tf it
9-2
8
4 X 18
2-42
it ti
2
it tt it
9-5
8
11 it ft
2-8
ii 11
2
tt ft ii
1 8-6
16
10 X 10
7-0
Corbels.
2
ii ii ii
9~3
12
12 X 16
28-3!
Diag. Posts.
2
if if ti
18-3
8
14 X 16
ii (i
ii i
I
tf ft ft
19-1
8
14 X 14
U 11
ti i
56
12 X 22
22-0
Floorbeams.
8
12 X 14
11 ft
ti i
4
8 X 12
23-2f
Stringers.
8
12 X 12
28-sf
ii i
42
ft ft ft
17-3?
ii
2
10 X 12
11 11
ti i
4
ft ft ft
ii-7l
ii
8
10 X 10
11 It
ii i
4
ft ft ft
17-Sl
it
8
8 X 10
II If
ii i
*34
8 X 10
10-0
Ties.
4
8 X 10
28-4!
ii i
21
6X8
16-0
Guard Rail.
4
8X8
II II
it it
21
4X8
1 6-0
ft tf
Lengths given for Top and Bottom Laterals are longer than finished lengths.
BILL OF CASTINGS AND BOLTS FOR HOWE TRUSS BRIDGE.
TABLE II.
BILL OF CASTINGS, BOLTS, ETC. FOB ONE 150 FT. HOWE TRUSS SPAN.
No. of
tab
Description.
Mark.
No. of
PCS.
Description.
Mark.
Angle Blocks
63189
18
Dowels { in. X o ft.~9 in.. .
20
Biioo
176
Dowels } in. X o ft.-j in.
4.
ii it
BlIQI
27?
Spikes 9 in. X i in
16
it ii
'. 5 1< >i
22?
8 in. X I in
2
ii it
63202
27?
" 14 in. X i in.. .
12
Lateral Angle Blocks
BlIQI
II?
Drift Bolts j in. X i ft. 8 in..
it ii ii
BiiQiA
24.
Bolts I in. X i ft.-nj in.
12
ii ii ii
Biicu
Sq. H & N 2\ in. thd
12
ii ii ii
BIIQ?
24
Bolts i in. X i ft.~7J in.
8
ii ii ii
83196
Sq. H & N 2\ in. thd
10
Clamp Blocks
BlOQO
56
Bolts J in. X 5 ft.-6} in.
6
BioqoA
Sq. H & N 2j in. thd. . .
1C.
it ii
B309iR
12
Bolts | in. X 4 ft.~4J in.
•I
ii ii
B3CX)iRA
Sq. H & N 2J in. thd
1C
ii ii
B3O9iL
8
Bolts { in. X 4 ft.-j in.
•7
ii ii
B3O9iLA
Sq. H & N 2j in. thd
4
72
WasheYs for Lateral Rods. . . .
ii ii i
B 3199
BlIQ7
142
Bolts J in. X 3 ft.-8J in.
Sq. H & N 2$ in. thd. . . .
72
64.
ii <i <
ii it i
63198
BiioSA
24
Bolts J in. X 3 ft.~9l in.
Sq. H & N 2J in. thd
O. G. Washers for 2j in. Bolts
60
Bolts | in. X 3 ft.~4 in.
ii ii .]
Sq. H & N 2\ in. thd
II II T
16
Bolts } in. X I ft.-gj in.
i ii 5
Sq. H & N 2j in. thd.
i <i j
56
Bolts f in. X 2 ft.~3J in.
^
' " 1
Sq. H & N 2\ in. thd
8
< II 3
72
Bolts } in. X 2 h.-Jt in.
16
1 II 1
Sq. H & N 2} in. thd
48
I
2
Bolts } in. X 2 ft.~4i in.
122
' " I
Sq. H & N 2| in. thd
2*6
II II 3
4
Bolts } in. X 2 ft.-6J in.
A8
Slot \Vashers for i in Bolts
Sq. H & N 2j in. thd
4°
•722
ll ll II 7 II II
8
Bolts } in. X 2 ft.-ioj in.
4 TO
II II II 3 II II
Sq. H & N 2\ in. thd
4
6 in. X 4 in. X i in. X 38 ft.-
5} in Guard Angles
Gi
8
Bolts } in. X 3 ft.-2j in.
Sq. H & N 2j in. thd
4
6 in. X 4 in. X i in. X
G»
48
Bolts f in. X 3 ft.-$} in.
Sq. H & N 2i in. thd
4.24.
Packing Washers
63251
8
Bolts i in. X 4 ft.-l} in.
4*J
3ft
it ii
p.
Sq. H & N 2j in. thd
0
152
ii ii
P
8
Bolts f in. X 4 ft.~3| in.
III
ii ii
p.
Sq. H & N 2\ in. thd
410
16
Clamps
c,
16
Bolts J in. X 4 ft.~4i in.
8
Wedges
W
Sq. H & N 2\ in. thd
i6
Bearing Plates
BP
64
Bolts } in. X I ft.-3i in.
12
BCi
Sq. H & N 2\ in. thd
16
ii ii
BC2
64
Recess Washers
4.
Angle Blocks
B3i9oA
100
Special Bolts J in. X i ft
63 195 A
I
Dowels I in X o ft —II in
Lateral Angle Blocks
BiiqiA
steel
2
Angle Blocks
20
290
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
sill! «"
^^^^^^J^^^^^^^^i^^^^^^^^^^
S» Vx V\ vi^C^rv?^V.*vV^^^^*?^^vs^\.^v^v^^»^^^V^\NcwV?^>^r^
TIMBER HOWE TRUSS DECK BRIDGE.
291
••:
«l
292
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
"Outer 6 in. X 8 in. Guard Rails are notched for ties, spiked to each tie with one 9 in. X f in.
spikes. Each tie to be spiked to stringers with $ in. X 14 in. spikes. Stringers drift-bolted to
floorbeams with f in. X 18 in. drift bolts. All f in., £ in. and I in. bolts to be provided with one
O. G. and one slot washer. All contacts of wood and wood to be painted with white lead. Corbels
to be creosoted. All holes bored in chord sticks to be creosoted. Inner 4 in. X 8 in. Guard
Rails bolted at center and ends of each piece, spiked to each tie not bolted, with one 8 in. X f in.
spike and spliced. The 6 in. X 4 in. X 2 in. guard rail is bolted at ends and at intervals of not
over 3 ties with f in. special bolts. Leave | in. opening between ends of Guard Rail angles.*'
The detail plans of a timber Howe truss railway bridge with an 80 ft. span are given in Fig. 8
and Fig. 9. This bridge was designed for Cooper's E 55 loading for the allowable stresses given
in the specifications of the American Railway Engineering Association. The details and a bill
of materials are given on the plans.
TABLE III.
BILL OF UPSET VERTICAL RODS FOR ONE 150 FT.
HOWE TRUSS SPAN.
TABLE IV.
BILL OF LATERAL RODS FOR ONE 150
FT. HOWE TRUSS SPAN.
No. of PCS.
Length. Ft.-In.
Section
"A"
Diam., In,
Diameter of Upsets.
No. of PCS.
Length,
Ft.-In.
Diameter of
Rod "A,"
In.
Length of
Thread
"T," In.
U. S. Std..
In.
Ry. Eng.
& M.of
W.f In.
12
12
12
16
12
40
30-10^
30-10
30- 8
30- 92
3°- 7?
30- 6f
2f
2*
3
3
a!
2
3!
3i
3l
zf
a}
2*
3l
3
li
al
a|
2
2
2
2
2
2
2
2
2
4
4
22-9f
23-4i
23-4
24-S
24-4!
24-4J
'iA— 1%
2}
at
1
I
1
if
if
if
ij
j|
1?
42
4*
4*
4
4
4
4
4
Diameter of Upset "U" based on number of threads per
inch.
Length of upsets "M" to be in accord with shop stand-
ards.
23-2?
23-if
23-if
22-5 J
HIGHWAY TIMBER TRESTLES AND BRIDGES.— Details of a highway crossing of
the Illinois Central Railroad are given in Fig. 10 and Fig. n.
A combination timber and iron bridge is shown in Fig. 12; while a short span timber highway
bridge is given in Fig. 13.
For additional details of timber highway bridges, see the author's " The Design of High-
way Bridges."
SPECIFICATIONS FOR WORKMANSHIP FOR PILE AND FRAME TRESTLES TO
BE BUILT UNDER CONTRACT.*
•I. Site. — The trestle to be built under these specifications is located on the line of
Railroad at .' County of State of
2. General Description. — The work to be done under these specifications covers the driving,
framing and erection of a track wooden trestle about ft. long and
an average of ft. high.
GENERAL CLAUSES.
3. The contractor shall furnish all necessary labor, tools, machinery, supplies, temporary
staging and outfit required. He shall build the complete trestle ready for the track rails, in a
workmanlike manner, in strict accordance with the plans and the true intent of these specifica-
tions, to the satisfaction and acceptance of the engineer of the railroad company.
4. The workmanship shall be of the best quality in each class of work. Details, fastenings
and connections shall be of the best method of construction in general use on first class work.
* Adopted by American Railway Engineering Association.
HIGHWAY CROSSING.
5. Holes shall be bored for all bolts. The depth of the hole and the diameter of the auger
to be specified by the engineer.
(.. I iMiniiiK sh.ill be accurately fitted; no blocking or shimming will be allowed in making
joints. Timbers shall be cut off with the saw; no axe to be used.
7. Joints and points of bearing, for which no fastening is shown on the plans, shall be fastened
as specified by the engineer.
,'„'«•
rJMStnnpr r&dmciny
* '
i— - 14-0"-^- 14-0"-
'•0'+-I4'-0'+~I4'-0-
''Jif**- -Slept Hoi
-l2>l2*l8-0"Cap
3>8'*20!0"0race
>8 "16 -0 *CollarBrac»
Showing roadway -for dbvMt
Zandf.
Showing roadway fo
track crossing.
FIG. 10. HIGHWAY CROSSING. ILLINOIS CENTRAL RAILROAD.
8. The engineer or his authorized agents shall have full power to cause any inferior work
to be condemned, and taken down or altered, at the expense of the contractor. Any material
destroyed by the contractor on account of inferior workmanship or carelessness of his men is to
be replaced by the contractor at his own expense.
294
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
9. Figures shown on the plans shall govern in preference to scale measurements; if any
discrepancies should arise or irregularities be discovered in the plans, the contractor shall call
on the engineer for instructions. These specifications and the plans are intended to co-operate,
and if any question arises as to the proper interpretation of the plans or specifications, it shall be
referred to the engineer for a ruling.
t
I Lag Screws
6 long
-4*10
Detail of Joint "
Detail of Hanger.
Ca5lIron-2-Req'cL
Hotes forty Lag 3cre*^\ A
bent Plate R*i*M0'
Z-focl..
devef Washfr-Casf Iron.
12-Req'ct.
^w<?/ ftr<r/^ <?/?»/ of rod to Zcdamefer.
Length of upset 8". Thread &?
FIG. ii. DETAILS OF HIGHWAY CROSSING. ILLINOIS CENTRAL RAILROAD.
10. The contractor shall, when required by the engineer furnish a satisfactory watchman to
guard the work.
11. On the completion of the work, all refuse material and rubbish that may have accumu-
lated on top or under and near the trestle, by reason of its construction, shall be removed by the
contractor.
COMBINATION HIGHWAY BRIDGE.
.ft
296
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
.« \ \
^ Hole for T,e Rod ^
-*p/i^i^-
1^'r
h-
"C .
\®
1
fl 1 if
*~ Hole if for Laf.
A
\-J-^>
I-6**I6-I8-0"
-Capl0"xiz"-20'-0*
A
A
.. 13-4'c toe —————
V
^y
' * / *
r
7*\~1 X. '
* vj \ I" ftl
1
" r«-
7; Counter* °
IgHo/g} 4
FIG. 13. DETAILS OF A TIMBER HIGHWAY BRIDGE.
DETAIL SPECIFICATIONS.
12. Piles. — Piles shall be carefully selected to suit the place and ground where they are to
be driven. When required by the engineer, pile butts shall be banded with iron or steel for
driving, and the tips with suitable iron or steel shoes; such shoes will be furnished by the railroad
company.
13. — Piles shall be driven to a firm bearing, satisfactory to the engineer, or until five blows
of a hammer weighing 3,000 lb., falling 15 feet (or a hammer and fall producing the same mechan-
ical effect), are required to cause an average penetration of one-half Q) in. per blow, except in
soft bottom, where special instructions will be given.
14. — Batter piles shall be driven to the inclination shown by the plans, and shall require but
slight bending before framing.
15. — Butts of all piles in a bent shall be sawed off to one plane and trimmed so as not to
leave any horizontal projection outside of the cap.
1 6. — Piles injured in driving, or driven out of place, shall either be pulled out or cut off,
and replaced by new piles.
17. Caps. — Caps shall be sized over the piles or posts to a uniform thickness and even bearing
on piles or posts. The side with most sap shall be placed downward.
1 8. Posts. — Posts shall be sawed to proper length for their position (vertical or batter), and
to an even bearing on cap and sill.
19. Sills. — Sills shall be sized at the bearing of posts to one plane.
20. Sway Braces. — Sway bracing shall be properly framed and securely fastened to piles or
posts. When necessary for pile bents, filling pieces shall be used between the braces and the
piles on account of the variation in size of piles, and securely fastened and faced to obtain a
bearing against all piles.
21. Longitudinal Braces. — Longitudinal X-braces shall be properly framed and securely
fastened to piles or posts.
SPECIFICATIONS. 297
22. Girts. — Girts shall be properly framed and securely fastened to caps, sub-nib, posts or
piles, .is the plans may require.
23. Stringers. -Striii^-rs shall be sized to a uniform height at supports. The edges with
most sap shall bo placed downward.
24. Jack Stringers. — Jack stringers, if required on the plans, shall be neatly framed on
caps, .iin 1 their tops shall be in the same plane as the track stringers.
• 25. Ties. — Ties shall be framed to a uniform thickness over bearings, and shall be placed
with tlu- rough side upward. They shall be spaced regularly, cut to even length and line, a*
calk-cl for on the plans.
26. Guard Rails. — Timber guard rails shall be framed as called for on the plans, laid to line
and to a uniform top surface. They shall be firmly fastened to the ties as require* I.
27. Bulkheads. — Bulkheads shall be of sufficient dimensions to keep the embankment clear
of the caps, stringers and ties, at the end bents of the trestle. There shall be a space not less
than two (2) in. between the back of end bent and the face of the bulkhead. The projecting
ends of the bulkhead shall be sawed off to conform to the slope of the embankment, unless other-
wise specified.
28. Time of Completion. — The work shall be completed in all its parts on or before . .
A. D. 19....
29. Payments. — Payments will be made under the usual regulations of the railroad company.
SPECIFICATIONS FOR METAL DETAILS USED IN WOODEN BRIDGES AND TRESTLES.
30. Wrought-iron. — Wrought-iron shall be double-rolled, tough, fibrous and uniform in
character. It shall be thoroughly welded in rolling and be free from surface defects. \Vlu-n
tested in specimens of standard form shall give an ultimate strength of at least 50,000 Ib. per sq.
in., ah elongation of 18 per cent in 8 in., with fracture wholly fibrous. Specimens shall bend cola,
with the fiber, through 135 degrees, without sign of fracture, around a pin the diameter of which
is not over twice the thickness of the piece tested. When nicked and bent, the fracture shall show
at least 90 per cent fibrous.
31. Steel. — Steel shall be made by the open-hearth process and shall be of uniform quality.
It shall contain not more than 0.05 per cent sulphur; if made by the acid process it shall contain
not more than 0.06 per cent phosphorus, and if made by the basic process not more than 0.04
per cent phosphorus. When tested in specimens of standard form, or full sized pieces of the
same length, it shall have a desired ultimate tensile strength of 60,000 Ib. per sq. in. If the
ultimate strength varies more than 4,000 Ib. from that desired, a retest shall be made on the
same gage, which to be acceptable, shall be within 5,000 Ib. of the desired ultimate. It shall
have a minimum percentage of elongation in 8 in. of - -r and shall bend cold with-
^ ult. tens, strength
out fracture 180 degrees flat. The fracture for tensile tests shall be silky.
32. Castings. — Except where chilled iron is specified, castings shall be made of tough gray
iron, with sulphur not over o.io per cent. They shall be true to pattern, out of wind and free
from flaws and excessive shrinkage. If tests are demanded, they shall be made on the "Arbi-
tration Bar" of the American Society for Testing Materials, which is a round bar 1} in. in diameter
and 15 in. long. The transverse test shall be made on a supported length of 12 in., with load at
middle. The minimum breaking load so applied shall be 2,900 Ib., with a deflection of at least
xV in. before rupture.
33. Bolts. — Bolts shall be of wrpught-iron or steel, made with square heads, standard size, the
length of thread to be 2 J times the diameter of bolt. The nuts shall be made square, standard size,
with thread fitting closely the thread of bolt. Threads shall be cut according to U. S. standards.
34. Drift Bolts. — Drift bolts shall be of wrought-iron or steel, with or without square head,
pointed or without point, as may be called for on the plans.
35. Spikes. — Spikes shall be of wrought-iron or steel, square or round, as called for on the
plans; steel wire spikes, when used for spiking planking, shall not be used in lengths more than
6 in.; if greater lengths are required, wrought or steel spikes shall be used.
36. Packing Spools or Separators. — Packing spools or separators shall be of cast-iron, made
to size and shape called for on plans; the diameter of the hole shall be J in. larger than diameter
of packing bolts.
37. Cast Washers. — Cast washers shall be of cast-iron. The diameter shall be not less than
3i times the diameter of bolt for which it is used, and its thickness equal to the diameter of bolt;
the diameter of hole shall be i in. larger than the diameter of the bolt.
38. Wrought Washers. — Wrought washers shall be of wrpught-iron or steel, the diameter
shall be not less than 3 \ times the diameter of bolt for which it is used, and not less than J in
thick. The hole shall be \ in. larger than the diameter of the bolt.
39. Special Castings. — Special castings shall be made true to pattern, without wind, free from
flaws and excessive shrinkage, size and shape to be as called for by the plans.
298
TIMBER BRIDGES AND TRESTLES.
CHAP. VII.
WORKING UNIT-STRESSES FOR STRUCTURAL TIMBER EXPRESSED IN POUNDS PER SQUARE
INCH.*
Note. — The working unit-stresses given in Table V are intended for railroad bridges and
trestles. For highway bridges and trestles the unit-stresses may be increased twenty-five (25)
per cent. For buildings and similar structures, in which the timber is protected from the weather
and practically free from impact, the unit stresses may be increased fifty (50) per cent. To
compute the deflection of a beam under long-continued loading instead of that when the load is
first applied, only fifty per cent of the corresponding modulus of elasticity given in the table is
to be employed.
TABLE V.
UNIT STRESSES FOR STRUCTURAL TIMBER EXPRESSED IN POUNDS PER SQUARE INCH.
AMERICAN RAILWAY ENGINEERING ASSOCIATION.
Kind of Timber.
Bending.
Shearing.
Compression.
Ratio of Length of
Stringer to Depth.
Extreme
Fiber
Stress.
Modulus
of
Elasticity.
Parallel
to Grain.
Longitudi-
nal Shear
in Beams.
Perpen-
dicular
to Grain.
Parallel to
Grain.
in ;n
v i!
is
(3 MM
c/3 a M
1
ij
&
Average
Ultimate.
£ %
Average
Ultimate.
$ *-*
w 'g
09
>'3
-1
Douglas fir
6lOO
6500
5600
4400
4800
42OO
4600
5800
5000
4800
42OO
5700
I2OO
1300
IIOO
900
IOOO
800
900
IIOO
900
900
800
IIOO
1,510,000
I,6lO,000
1,480,000
I,I3O,OOO
I,3IO,OOO
I,I9O,OOO
I,22O,OOO
1,480,000
800,000
1,150,000
86o,OOO
I,I5O,OOO
690
720
710
400
600
590*
670
630
300
500
170
1 80
170
IOO
150
130
170
160
80
1 20
270
300
330
1 80
170
250
260
27°t
no
1 20
130
70
70
IOO
IOO
IOO
630
520
340
290
370
440
400
340
470
920
3IO
260
170
ISO
1 80
ISO
2 2O
22O
170
230
450
3600
3800
3400
3000
3200
26oof
3500
3300
3900
2800
3500
I2OO
I30O
IIOO
IOOO
IIOO
800
IOOO
I20O
9OO
IIOO
900
I3OO
900
980
830
750
830
600
75°
900
680
830
680
980
1300(1-^-3)
\ 6o^/
1100 V 6od)
13001 i — ~^ — •} I
\ OOa/
10
IO
IO
IO
12
Longleaf pine . . .
Shortleaf pine. . .
White pine
Spruce
Norway pine. . . .
Tamarack
Western hemlock
Redwood
Bald cypress. . . .
Red cedar . .
White oak
840
2IO
270
no
Note. — These unit stresses are for a green condition of timber and are to be used without in-
creasing the live load stresses for impact.
REFERENCES. — For additional details and information the following references may be
consulted :
Foster's " A Treatise on Wooden Trestle Bridges," John Wiley & Sons, gives data and
details of the design of timber trestles.
Jacoby's " Structural Details ; Design of Heavy Framing," John Wiley & Sons, gives data
and details of the design of timber trestles and timber structures, and is the best book on tim-
ber construction. Every engineer interested in the design of timber structures should have a
copy of Jacoby's " Structural Details."
* Adopted, Am. Ry. Eng. Assoc., Vol. 10, 1909.
t Partially air-dry. / = length in inches. d = least side in inches.
CHAPTER VIII.
STEEL BINS.
Stresses in Bin Walls. — The problem of the calculation of pressures on bin walls is similar
to the problem of the calculation of pressures on retaining walls; but in the case of bin walls the
material is limited in extent and the condition of static equilibrium is disturbed by drawing the
material from the bottom of the bin. For plane bin walls where the plane of rupture cuts the
free surface of the material (shallow bins), the formulas developed for retaining walls are directly
applicable if friction on the wall is considered. The graphic solution will be found the simplest
and most direct for any particular case. The following analyses of the calculations of stresses in
bins have been abstracted from the author's "The Design of Walls, Bins and Grain Elevators,"
second edition.
STRESSES IN SHALLOW BINS.— The problem of the calculation of the pressures on
bin walls is the same as the problem of the calculation of pressures on retaining walls. The forces
acting on bin walls depend upon the weight, angle of repose, moisture, etc., of the material, which
are variable factors, but are less variable than for the filling of retaining walls.
Algebraic Solution. — The same nomenclature will be used as in retaining walls except that P'
will be used to indicate the pressure obtained by means of Cain's formulas when z = $', N' will
indicate the normal component of P', and N will indicate the normal pressure on the wall when
<f>' = o. This analysis applies to shallow bins, only.*
Case i. Vertical Wall, Surface Level. Angle z = </>'. Fig. i.
D/ _ .. L« COS1*
(,)
N' = P'-COS*' (2)
If </>' = <t>
P' = jw ft* COS * (3)
JV' = P'-cos0 (4)
_£
II/L
^ x»
FIG. i.
If <(>' = o, which corresponds to a smooth wall,
N - iw-A'.tan' (45° - */*) (5)
* A shallow bin is one where the plane of rupture cuts the free surface of the filling.
299
300
STEEL BINS.
CHAP. VIII.
TABLE I.
CONSTANTS FOR STEEL PLATE BINS, CASE i.
Material.
<t>
Degrees.
*'
Degrees.
W
Lb. Per
Cu. Ft.
P'
Lb.
Nf
Lb.
2V
Lb.
Bituminous coal
3C.
18
CO
6.I3A2
c,.8-?A2
67C.A2
Anthracite coal
27
. 16
W
8.73A2
8.3QA2
Q 77 A2
Sand
34
18
QO
n.5oA2
lO.Q^A2
1 2. 72 A2
Ashes
4°
31
4O
4.O2A2
1.44A2
4 3 4 A2
Cose 2. Vertical Wall, Surface Surcharged at Angle 8. Angle z = <j>'. Fig. 2.
P' = 2
') sin («-«)
If
If
( , + / a
\ \
cos<£'-cos5
N' = P'-cos
5 = <f>
P> = iw.h*<2!
N' = P'-cos<j>' =
</>' = o
FIG. 2.
TABLE II.
CONSTANTS FOR STEEL PLATE BINS, CASE 2. S = <£.
(6)
(7)
(8)
(9)
(10)
Material.
*
Degrees.
<t>'
Degrees.
W
Lb. Per
Cu. Ft.
P'
Lb.
2V'
Lb.
2V
Lb.
Bituminous coal
-2C
18
CO
17 6cF
16 7cA2
16 7cA2
Anthracite coal
27
16
C2
21 AC/t2
20 50 A2
20 5oA2
Sand
34
18
oo
•J2 CoA2
30 ooA2
30 90 A2
Ashes
AO
•3 T
yj 7o/i2
II 77 A2
II 71 A2
Casej. Vertical Wall, Surcharge Negative = 5. Angle 2 = <f>'. Fig. 3.
P' = iw.^_ ™s* +
CQ
cos <j>' • cos 5
' = P'-cos<f>'
(II)
(12)
If
STRESSES IN SHALLOW BINS.
0' - o
tf-htK
FIG. 3.
TABLE III. *
CONSTANTS FOR STEEL PLATE BINS, CASE 3. 6 = — 4>.
301
(13)
Material.
*
Degrees.
*'
Degrees.
W
Lb. Per
Cu. Ft.
P»
Lb.
Nf
Lb.
N
Lb.
Bituminous coal
M
18
?O
4.40A1
4.27**
5.13**
Anthracite coal
27
16
12
6.64^*
6.38A*
7-64A*
Sand
•74.
18
QO
8.44A1
S.ooA*
9.6iA»
Ashes
4.O
•Ji
4.O
2.8sA»
2.4SA1
3- 23 A1
Case 4. Wall Sloping Outward. 0 < 90° + <*>'. Surface Level. Fig. 4.
sin* (6 — <t>)
f =
in (</> + 0') sin 0V
- + g) rin
FIG. 4.
Case 5. Wall Sloping Outward. 6 < 90° + <*>'• Surface Surcharged. Fig. 5.
sin* (6 - *)
P'
sm
sn 0 -
(M)
(15)
JV - P'-cos*'
(16)
(17)
302
STEEL BINS.
CHAP. VIII.
Case 6. Wall Sloping Outward. 6 > 90° + <£'. Surface Level. Fig. 6.
P = §w/f2-tan2 (45° -
+ tan4 (45°
tan 9
(18)
(19)
() = .E-cos z
r = £ • sin 2
FIG. 6.
For a wall sloping outwards, and sloping surface the use of formulas is cumbersome and the
calculations can be more easily made by graphic methods as explained on succeeding pages.
Tables of Pressure on Vertical Bin Walls. — The normal pressure on vertical bin walls as
calculated by the preceding formulas for bituminous coal, anthracite coal, sand, and ashes are
given in Table IV, Table V, Table VI, and Table VII, respectively. 4 In the tables column I gives
the normal pressure for a smooth vertical wall and horizontal surcharge, while column 4 gives
the normal pressure on a rough wall with an angle of friction = <£'. Column 2 gives the normal
pressure for a smooth vertical wall and a surcharge = tf>, while column 5 gives the normal pressure
on a rough wall with an angle of friction = </>'. Column 3 gives the normal pressure for a smooth
vertical wall and a negative surcharge = — <£, while column 6 gives the normal pressure on a
rough wall with an angle of friction = <f>'. It will be seen that the pressures in columns 2 and 5
are identical. For a vertical wall with 8 = <j>, the normal pressures as given by Rankine's and
Cain's formulas are identical.
These tables have been taken from the author's "The Design of Walls, Bins and Grain
Elevators." The tables of pressures and the formulas were first published in a modified form
by Mr. R. W. Dull, in Engineering News.
I'KLSSIKK 01 Bill MI.NOI >, COAL.
The total pressures are given for a wall one foot long in all cawc.
Note. — These tables apply to shallow bins only (bins where the plane of rupture cut* the
free surface of the filling). For the calculation of the stresses in deep bins (bins where the plane
of rupture cuts the side of the bin) see Chapter IX, Steel Grain Elevators.
TABLE IV.
TOTAL PRESSURE IN POUNDS FOR DEPTH "h" FOR BITUMINOUS COAL.
WALL ONE FOOT LONG.
w =50 lb., <t> = 35°.
Smooth Wall. «' - o.
Rough Wall. Angle of Friction - *' - IB*.
i
a
3
4
5
6
Depth, h.
_
_
In Feet.
IF
- x«^<p
IP"
IF
It
IP*
<t>' = o
6 = <t>
S = — <f>
<t>' = 18°
« = 0
4- _* ,
I
6-75
16.75
5.83
5-83
16.75
4-27
2
27
67
20.5
23.32
67
17.1
3
60.75
150.75
46.2
52.47
150.75
38.4
4
108
268
82
93-4
268
68.3
5
168.75
418.75
128
H5-7
418.75
107
6
243
603
184.5
209.4
603
156
7
333
821
257
286
821
209
8
432
1,072
328
373
1,072
273
9
547
i,357
415
472
1,357
346
10
675
i,675
513
583
1,675
427
ii
817
2,027
615
70S
2,027
516
12
972
2,412
738
840
2,412
615
13
1,141
2,831
866
985
2,831
722
H
1,323
3,283
1,005
1,143
3,283
838
3,769
1,152
1,312
3,769
960
16
1,728
4,288
1,311
1,492
4,288
1,093
17
1,951
4,841
1,480
1,685
4,841
1,232
18
2,187
5,427
i, 660
1,889
5,427
1,382
19
2,437
6,047
1,852
2,105
6,047
1,541
20
2,700
6,700
2,052
2,332
6,700
1,708
21
' 2,977
7,387
2,262
2,571
7,387
1,883
22
3,267
8,102
2,483
2,821
8,102
2,067
23
3,57i
8,861
2,560
3,084
8,861
2,259
24
3,888
9,648
2,810
3,358 .
9,648
2,460
25
4,219
10,469
3,206
3,644
10,469
2,669
26
4,563
",323
3,468
3,941
11,323
2,887
27
4,923
12,211
3,740
4,250
12,211
3, "3
28
5,292
13,142
4,022
4,570
13,142
3,348
29
5,677
14,087
4,314
4,903
14,087
3,591
3°
6,075
15,075
4,617
5,247
15,075
3.843
304
STEEL BINS.
CHAP. VIII.
TABLE V.
TOTAL PRESSURE IN POUNDS FOR DEPTH "h" FOR ANTHRACITE COAL.
WALL ONE FOOT LONG.
w = 52 lb., <t> = 27°.
Smooth Wall, *' = o.
Rough Wall, Angle of Friction = <j>' = 16°.
i
2
3
4
5
6
Depth, h,
^j
-XTi
in Feet.
Tf." ' Y"*"~*
ik
.sT (D
— .-. -— *i — ir-p
It
IP
IF
Tf^
iJr
IP
5' = o
6 = 0
5 = — <{>
<j>' = 16°
5 = <t>
8 = — <j>
I
9-75
20.5
7.64
8-39
20.5
6.38
2
39-o
82.0
30.6
33-5
82.0
25-5
3
87.8
184.5
68.8
75-5
184.5
57-5
4
156
328
122.2
134-2
328
IO2.O
5
244
513
191
2IO
513
159-5
6
3SI
738
267
3O2
738
230
7
478
1,005
374
411
1,005
313
8
624
1,312
489
536
1,312
4O2
9
790
1,661
619
680
1,661
517
10
97S
2,050
764
839
2,050
638
ii
1,180
2,481
925
1,014
2,481
773
12
1,405
2,952
I,IOO
I,2O9
2,952
920
13
1,648
3,465
1,290
I,4l8
3,465
i, 080
H
1,910
4,018
i,497
1,643
4,018
1,250
15
2,193
4,6i3
1,720
1,887
4,6i3
i,436
16
2,500
5,248
1,953
2,H5
5,248
1,636
17
2,808
5,945
2,207
2,421
5,945
i,845
18
3,160
6,642
2,47i
2,718
6,642
2,064
19
3,521
7,400
2,758
3,030
7,400
2,310
20
3,902
8,200
3,053
3,350
8,200
2,554
21
4,303
9,041
3,372
" 3,700
9,041
2,820
22
4,718
9,922
3,701
4,061
9,922
3,086
23
5,i56
10,845
4,040
4,438
10,845
3,372
24
5,611
11,808
4,398
4,833
1 1, 808
3,68o
25
6,097
12,813
4,770
5,244
12,813
3,985
26
6,600
13,858
5,160
5,672
13,858
4,52i
27
7,112
H,945
5,56o
6,1 16
14,945
4,650
28
7,638
16,072
5,979
6,578
16,072
5,000
29
8,202
17,241
6,421
7,056
17,241
5,370
30
8,775
18,450
6,880
7,55i
18,450
5,742
PRESSURE OF SAND.
105
TABLE VI.
TOTAL PRESSURE IN POUNDS FOR DEPTH "h" FOR SAND.
WALL ONE FOOT LONG.
w = 90 lb.,
34*
Smooth Wall. <f>' - o.
Rough Wall. Angle of Friction - * - 18°.
i
a
3
4
5
6
Depth, h,
in Feet.
~"JT ""Vv *-*>/•/>
If
IP
~\~ V'»m
if
IP
<t>' = 0
a = <t>
«=—</>
<t>' = 18°
6 = 0
6 = - 0
I
12.72
30.9
9.6l
10.93
30.9
8
2
50.8
123.6
38.4
43-7
123.6
32
3
II4.S
278
86.40
98.5
278
72
4
203.7
494
II3.8
175
494
128
5
318
772
240
273
772
200
6
458
I,H3
346
394
1,113
288
7
624
1,515
471
535
1,515
392
8
8lS
1,980
6lS -
700
1,980
512
9
1,030
2,500
778
885
2,500
648
10
1,272
3,090
961
1,093
3,090
800
ii
1,540
3,740
I,l62
i,345
3,740
968
12
1,833
4,450
1,383
1,575
4,450
1,152
13
2,150
5,230
1,624
1,848
5,230
1,352
H
2,495
6,060
1, 880
2,160
6,060
1,568
IS
2,862
6,960
2,160
2,460
6,960
1, 800
16
3,256
7,910
2,460
2,798
7,910
2,048
17
3,676
8,930
2,777
3,159
8,930
2,312
18
4,121
10,012
3,"4
3,541
10,012
2,592
19
4,592
",155
3,469
3,946
",155
2,888
20
5,088
12,360
3,844
4,372
12,360
3,200
21
5,6io
13,627
4,238
4,820
. 13,627
3,528
22
6,156
H,956
4,651
5,290
14,956
3,872
23
6,729
16,346
5,084
5,782
16,346
4,232
24
7,327
17,798
5,535
6,296
17,798
4,608
25
7,950
19,313
6,006
6,831
»9,3I3
5,000
26
8,599
20,889
6,496
7,389
20,889
5,408
27
9,273
22,526
7,006
7,x,s
22,526
5,832
28
9,972
24,225
7,534
8,569
24,225
6,272
29
10,698
25,987
S.OS2
9,192
25,987
6,728
30
11,448
27,810
8,649
9,837
27,8lO
7,200
21
306
STEEL BINS.
CHAP. VIII.
TABLE VII.
TOTAL PRESSURE IN POUNDS FOR DEPTH "h" FOR ASHES.
WALL ONE FOOT LONG.
w — 40 lb., (t> = 40°.
Smooth Wall, <t>' = o.
Rough Wall, Angle of Friction = <t>' = 31°.
i
2
3
4
5
6
Depth, h,
^ffj.
^ff.L
in Feet.
-^ i"'""
Tf^-
TTN£
~f "V""">
TIP**1
"*~Tv*
h U
h k
h rx
h h-
h U
h L
J-.J:
>._ir
i-JT
±JL
jL-L
jL_L~
<£' = O
5 — (j>
5 = - 4>
4>' = 31°
8 = 0
d = — <t>
I
4-35
"•73
3-23
3-44
n-73
2-45
2
17.4
47
12.9
13.76
47
9.80
3
39-2
105.7
29.01
30.96
105.7
22.05
4
69.6
1 88
3i-7
55-04
188
39-20
5
108.7
294
80.8
86
294
61.2
6
156.4
423
116
124
423
88.2
7
213
576
158
1 68
576
120
8
278
75i
207
220
751
157
9
352
952
261
279
952
199
10
435
i,i73
323
344
1,173
245
ii
526
1,420
391
416
1,420
296
12
626
1,690
465
495
1,690
353
13
735
1,985
546
58i
1,985
414
H
852
2,300
634
674
2,300
480
IS
978
2,640
726
774
2,640
550
16
1,113
3,010
828
88 1
3,010
627
17
i,257
3,400
934
994
3,400
708
18
1,408
3,803
1,045
I,H5
3,803
794
19
1,527
4,240
i,l65
1,242
4,240
884
20
1,740
4,700
1,290
1,376
4,700
980
21
1,920
5,i8i
1,423
1,517
5,i8i
,080
22
2,100
5,677
1,561
1,665
5,677
,186
23
2,300
6,215
1,706
1,820
6,215
,296
24
2,506
6,756
1,860
1,981
6,756
,411
25
2,720
7,33i
2,017
2,150
7,33i
,53i
26
2,940
7,929
2,180
2,325
7,929
,656
27
3,165
8,55i
2,352
2,508
8,55i
,786
28
3,4o6
9,196
2,530
2,697
9,196
,921
29
3,660
9,865
2,718
1 2,893
9,865
2,060
30
3,915
io,557
2,910
3,096
io,557
2,205
STRESSES IN SHALLOW BINS.
307
STRESSES IN SHALLOW BINS, Graphic Solution.— The graphic solution will be given
for two cases which frequently occur in prat 1 1
Graphic Solution. Hopper Bin, Level Full. '-The calculation of Btresses in bin* by means
of graphics will be illustrated by the following problem taken from "The Design of Walls, Bins
and Grain Hk-vators." A cross-section of the bin shown in Fig. 7 is filled with coal weighing 58
Ib. per cu. ft., and having an angle of repose * - 30°. The total pressure on the plane A-H is
Pi - JwA»
I — sin <t>
- 3,130 Ib.
I -j- sin <j>
acting horizontally through a point 12 ft. below the top surface. Now, to find the pressure Pt
on the plane G-A, produce PI until it intersects the line O» - the weight of triangle AHG - 10,440
J_£ ^f Surface of t
_yi\~£ •$ i I Material-'
'F~m?i
$ ?*• ^
f
-Oaf a -
Weiqh 1 of Coal Sdlbs. per ct/. ft.
Angle of Rtpoje #*50T
FIG. 7.
Ib. at 0, and by constructing O-i = P» = 10,860 Ib. P» is parallel to £ in Fig. 7. The normal
pressure on A-g is 9,900 Ib. Now A-i = 9,900 Ib. acts through the center of gravity of triangle
AG^, and is equal to the area of AG$ X w. The normal unit pressure at A is 733 Ib. per sq. ft.,
and the normal unit pressure at B is 320 Ib. per sq. ft. The normal pressure on A B acts through
the center of gravity of the shaded area, and is N = 7,850 Ib. Also by construction E = 8,600 Ib.
The pressure on bottom A-F is equal to 18 X 58 = 1,044 Ib. per sq. ft. The pressure on the
wall C-B is
I — sin
n i .,
PI = \w n*
— ; — : — -
I + sin <t>
620 Ib.
Calculation of Stresses in Framework. — The loads on the bin walls are carried by a transverse
framework as shown in Fig. 8, spaced 17 ft. o in. center to center. The loads at the joints act
parallel to the pressures as previously calculated, and the loads can be calculated in the same
manner as for a simple beam loaded with & similar loading. The stresses are calculated by graphic
resolution and by algebraic moments as shown in Fig. 8 and Fig. 9.
Hopper Bin, Top Surface Heaped. — The bin in Fig. 10 is heaped at the angle of repose,
^ = 30°. To calculate the pressure on side A-B, proceed as follows: Locate points G and H,
* The calculations are made for a section of the bin one foot long.
308
STEEL BINS.
CHAP. VIII.
^K>C~'*
i*5&
-Data-
We/phf ofCaa/ 58 Ibs.per cu. ft
Any/e of Repose <fi = 50."
Bin 1 7~0 "fang'.
FIG. 8.
Algebra/'c Moments.
Center of Moments, £. .
Stress GD.
-6D* 6.5 '-3520 x8'=P
Stress FG.
•Sfress
Left Side
Cen ter of Mom enfs ,f~.
Stress GH.
- GHx. /O '-3520x/8-7040xlO-65000xl3.5 '= 0
Stress GE»
-6Cx./Ol+433Ox8l-3KOxl8-7040x.lO'
-G50OOX/3.5-0 OE=-97700
Center of Moments, <?.
Stress ED.
.5= 0
ED = +2560
Stress FC.
Stress AF.
AFx/0 '+8l20Ox3-G50OOx/0.5
-3520 x 8'= O AF-+46700
FIG. 9.
STRESSES IN SUSPENSION BUNKERS.
309
and calculate the horizontal pressure PI - 7,680 lb., acting on the plane H-K at \HK above //.
Pressure Pi was calculated by the graphic method. Produce Pi until it intersects at O the line
of action of the weight of the triangle GHK acting through the center of gravity of the triangle.
From O lay off 0-1 — W «• 19,900 lb., acting downwards, and from I lay off 1-2 •• P\ — 7,680
lb., acting to the left. Then 0-2 - Pt - 21,300 lb. Now Pt - area triangle 6'CH-w, and
%,c*>
•^^'j*4000.'-5-!-^7^ ;<
*»» .- I «'„
Surcharge- +.50.
FIG. 10.
£ = areaS'- B-A-s'-w = 1 1,340 \b. Force £ acts through the center of gravity of area 8-B-A-$.
The horizontal pressure on plane C-B = 1,400 lb. = area s'e'n'-w. The vertical pressure on
the left-hand side of the bottom A-F is 7,480 lb., acting through the center of gravity of the
pressure polygon. The vertical unit pressure at A is 1,412 lb. per sq. ft.
STRESSES IN SUSPENSION BUNKERS.— The suspension bunker shown in (a) Fig. 11,
carries a load which varies from zero at the support to a maximum at the center. If the bunker
is level full the loading from the supports to the center varies nearly as the ordinatcs to a straight
line, while if the bunker is surcharged the straight line assumption for loading is more nearly
correct.
We will, therefore, assume that the loading of the bunker in (a) is represented by the tri-
angular loading varying from p = zero at each support to a maximum of p — P at the center.
Let / = one-half the span in feet;
S = the sag in feet;
// = the horizontal component of the stress in the plate in lb. per lineal foot of bin;
w = weight of bin filling in lb. per cu. ft. ;
310.
STEEL BINS.
CHAP. VIII.
T = maximum tension in plate in Ib. per lineal foot of bin;
V — reaction of the bunker in Ib. per lineal foot of bin;
C = capacity of bunker in cu. ft. per lineal foot of bin;
B = origin of coordinates.
FIG. ii.
Now if the right-hand half of the bunker be cut away as in (6) and moments be taken about
A, the moment will be
M = H-S (20)
If the bunker be assumed as an equilibrium polygon drawn by using a force polygon, the bending
moment at the center is equal to the pole distance multiplied by the intercept 5. Therefore H
must be equal to the pole distance of the force polygon.
The following equations are deduced in the author's "The Design of Walls, Bins and Grain
Elevators."
Equation of the curve of the bunker
Capacity of bunker level full
C =
(22)
In calculating P for any given bunker, since P is the maximum pressure for a triangular
loading
P - £f (23)
for a bunker level full
P = %S-w (24)
also
,, C-w-l
(25)
DATA FOR DESIGN OF BINS.
311
, for a bin level full
(26)
:'wVl + ol
The length of the curve of a suspension bunker is given in Table VIII.
TABLE VIII.
LENGTH OF ONE-HALF CURVE, L.
Sag ratio - Sll.
Length, L.
Sag ratio - S/l.
Length. L.
I. 06378/
I.I3686/
I.220Q2/
I.28307/
1.3665 iJ
I
1.4S7221
i.6ii3i/
I.7iao6J
i.8s8is/
The curve may be constructed graphically as follows: In (c) Fig. n it is required to pass
the curve through the points A and B. The loads I, 2, 3, 4, etc., are laid off in the force polygon
(d), and a pole 0 is taken. The equilibrium polygon A-B' is then constructed in (c). Now we
know from graphic statics that if two poles be taken for the force polygon in (d), and corresponding
equilibrium polygons be drawn through A, the strings meeting on the same load will intersect on a
line through A parallel to the line 0-0'. Now D is determined by the intersection of rays D-B'
and D-B. The true curve is then easily constructed and pole 0' is located.
If the bunker is surcharged by vertical walls as shown in (e) the curve is extended until it
meets the slope of the material, and the span and sag are to be used as shown.
Deep Bins. — For the calculation of the stresses in deep bins, see the calculation of the stresses
in grain bins, Chapter IX.
For methods of calculating the stresses in hopper bins with the top surface surcharged, and
the calculation of the stresses in bin bottoms and circular girders, see the author's "The Design
of Walls, Bins and Grain Elevators."
Angle of Repose. — The angle of repose and the weights of different materials are given in
Table IX.
DATA. — For angles of internal friction, see Table IX, and for angles of friction on bin walls,
see Table X.
TABLE IX.
WEIGHT AND ANGLE OF REPOSE OF COAL, COKE, ASHES AND ORE.
Material.
Weight Lb.
per Cu. Ft.
Angle'of Repose
0 in Degrees.
Authority.
Bituminous coal
SO
35
Link Belt Machinery Co.
Bituminous coal
47
35
Link Belt Engineering Co.
Bituminous coal
47 to c6
Cambria Steel.
Anthracite coal
C2
27
Link Belt Machinery Co.
Anthracite coal
"J2.I
27
Link Belt Engineering Co.
Anthracite coal fine
27
K. A. Muellenhoff.
Anthracite coal
52 to 56
Cambria Steel.
Slaked coal
45
Wellman-Seaver-Morgan Co.
Slaked coal
<;•*
37*
Gilbert and Barth.
Coke
21 tO 12
Cambria Steel.
Ashes
40
40
Link Belt Machinery Co.
Ashes, soft coal , . . . .
4O to 4.C
Cambria Steel.
Ore soft iron
35
Wellman-Seaver-Morgan Co.
312
STEEL BINS.
CHAP. VIII.
Coal, ore, etc., will give an angle of <f> = 40° if the material is dry, but if the material is wet
the angle of repose may be increased to nearly 90°.
Angle of Friction on Bin Walls. — The values in Table X may be used in the absence of more
accurate data.
TABLE X.
ANGLE OF FRICTION OF DIFFERENT MATERIALS ON BIN WALLS.
Material.
Steel Plate.
<t>' in Degrees.
Wood Cribbed.
^' in Degrees.
Concrete.
<t>' in Degrees.
Bituminous coal
18
•K
•jc
Anthracite coal
16
2C
27
Ashes
"?!
4.O
AO
Coke
2<;
4O
4.O
Sand
18
•so
•7Q
Panels 12'-6*
Typicotf Section through fixfofs*
FIG. 12. COKE AND STONE BINS, LACKA WANNA STEEL Co.
Self-cleaning Hoppers. — In order to have hoppers self-cleaning when the material is moist
it is necessary to have the hopper bottoms slope at an angle considerably in excess of the angle of
repose <£ or angle of friction </>'.
DESIGN OF BINS.
Ore pockets on the Great Lakes arc made with hopper bottoms at an angle of 48° 40' to
50° 45', but the majority are at an angle of 49° 45'. Bituminous coal will slide down a steel
chute at an angle of 40° and a wooden chute at an angle of 45°. Anthracite coal will slide down a
Mr« -1 chute at an angle of 30° and down a wooden chute at an angle of 35°.
.t_
FIG. iv{. ELEVATION CIRCULAR STEEL ORE BIN FOR OLD DOMINION COPPER MINING Co.
DESIGN OF BINS. — Bins are usually subjected to sudden loads and vibrations and should
be designed for two-thirds the allowable unit stresses for dead loads given in §§ 33 to 41, inclusive,
in "Specifications for Steel Frame Buildings," Chapter I.
Bins are made of timber, of structural steel, or of concrete, or the different materials may
be used in combination.
FLAT PLATES. — The analysis of the stresses in flat plates supported or fixed at their edges
is extremely difficult. The following formulas by Grashof may be used: The coefficient of lateral
contraction is taken as \. For a full discussion of these formulas based on Grashof "s "Theorie
Der Elasticitat und Festigkeit" see Lanza's Applied Mechanics.
I. Circular plate of radius r and thickness t, supported around its perimeter and loaded with w
314
STEEL BINS.
CHAP. VIII.
per square inch. — Let / = maximum fiber stress, v = maximum deflection, and E = modulus of
elasticity,
(28)
128 t*
189 wr*
256 E-P
(29)
.A' f • — r
# -//*
/ </ (f
~ -Csk. Alt. Hole}- set &oHom section.
t!4j dfa. ofSo/f circle an CJ. Hopper.
I* —}0'di'am. opening.
Section "a-er*
Section at Bendi/nt.
FIG. 14. DETAILS FOR CIRCULAR BINS FOR OLD DOMINION COPPER MINING Co.
2. Circular plate built in or fixed at the perimeter.
f = 45
3 64
= _
256 E
(30)
3. Rectangular plate of length a breadth b, and thickness t, built in or fixed at the edges and
I'l.AlKS.
Ill',
carrying a uniform load w per square inch. — Let /a be the unit stress parallel to a, ft be the unit
stress parallel to b, and a > b.
2(0*
For a square plate o =• b,
(a*
, w-a*
f — .
4*
w-a*
(33)
(34)
(35)
The strength of plates simply supported on the edges is about f the strength of plates fixed.
Plates riveted or bolted around the edges may be considered as fixed.
For a diagram giving the safe loads on flat plates, see the author's " The Design of Walls,
Bins and Grain Elevators," also see Part II.
Buckle Plates. — Buckle plates are made by "dishing" flat plates as in Table 59, Part II.
The width of the buckle W, or length L, varies from 2 ft. 6 in. to 5 ft. 6 in. The buckles may be
turned with the greater dimension in either direction of the plate. Several buckles may be. put
- l*6ranolHh!c
--2? Concrete
-Mre
>5 Cms Section of ^
• doff. Chord,
IT
-6alv.Corr.Steel '
Detail showing method of fastening
Concrete lining to bunker pttte
FIG. 15.
Crois Section of Bunker House
On line 'A- A'
Note:~5tre3in given in thousands of pounds
COAL BUNKERS, RAPID TRANSIT SUBWAY, NEW YORK, N. Y.
in one plate, all of which must be the same size and symmetrically placed. Buckle plates are
made \ in., ^ in., f in. and -j^ in. in thickness. Buckle plates should be firmly bolted or riveted
around the edges with a maximum spacing of 6 in., and should be supported transversely between
the buckles. The process of buckling distorts the plate and an extra width should be ordered and
the plate should be trimmed after the process is complete.
316
STEEL BINS.
CHAP. VIII.
Strength of Buckle Plates. — The safe load for a buckle plate with buckles placed up, is approxi-
mately given by the formula
W = 4f-R-t (36)
where W = total safe uniform load in Ib. per inch of width of plate;
/ = safe unit stress in Ib. per sq. in.;
R = depth of buckle in in.;
t = thickness of plate in in.
Where buckle plates are riveted and the buckle placed down the safe load is from 3 to 4 times
that given above.
TYPES OF BINS. — The most common types are (i) the suspension bunker, (2) the hopper
bin, and (3) the circular bin.
Suspension Bunkers. — Suspension bunkers are made by suspending a steel framework from
two side members, the weight of the filling causing the sides to assume the curve of an equilibrium
polygon. The stresses in the plates of a true suspension bunker are pure tensile stresses. Steel
suspension bunkers are commonly lined with a concrete lining about 1 1 to 35 in. thick, reinforced
with wire fabric, to protect the metal of the bin.
........... -65-0" ..........
llevarthn
FIG. 1 6. COAL BUNKERS, RAPID TRANSIT SUBWAY, NEW YORK, N. Y.
Hopper Bins. — Hopper bins may be made of timber, steel, or reinforced concrete. A steel
coke and stone bin, erected by the Lacka wanna Steel Company, is shown in Fig. 12. These bins
were divided into panels 12 ft. 6 in. center to center, with double partitions at each panel point,
leaving a clear length of 1 1 ft. 6 in. The bins are lined throughout- with f in. plates. All rivets
in the floor are countersunk. The gates at the bottom of the bin are cylindrical and are revolved
KXAMI'U.S 01 STKF.L BINS.
317
by a system of shafting and gears. There is an opening in the side of the drum, and when the
drum is revolved this opening comes opposite the opening in the bottom of the bin and the drum
is filled. The drum is then revolved and the material is dumped into the larries.
Circular Bins. — Circular bins are made of both steel and reinforced concrete. A circular
ore bin with a hemispherical bottom is shown in Fig. 13 and Fig. 14.
EXAMPLES OF BINS. Steel Coal Bin for Rapid Transit Subway. — A cross-section of a
I,ooo-ton suspension bunker built by the Rapid Transit Subway, New York City, is shown in
Fin. 15 and Fig. 16. The bunker is supported on posts and is covered by corrugated steel. The
bin is lined with a layer of concrete 3$ in. thick, reinforced with expanded metal. The details of
construction are plainly shown in the cuts.
Plan of Hoppers and
Hopper Bottoms
\General Elemti'on ofHopptrs £ Botfoms
S8n
I
^ W'4>'"4 'Faces Co/3-~*
* Sectional Elevation at 'M'
FIG. 17. HOPPER BIN CANANEA CONSOLIDATED COPPER Co., CANANEA, MEXICO.
318
STEEL BINS.
CHAP. VIII.
Ore Bins for Cananea Consolidated Copper Company. — Detail drawings of a hopper ore
bin built by the Cananea Consolidated Copper Company are shown in Fig. 17. The ore is coarse
and heavy and is dumped from cars on the top of the bins. The ore is drawn off through gates
on the bottom and is carried away on a conveyor. The side plates are J in. thick and are stiffened
with channels spaced about 4 ft. apart. The hopper plates are f in. thick and are stiffened with
10 in. channels.
"^ :<-i-.
3>'^
HalF Half
End View Cross Section
Longitudinal Section
at Center
FIG. 1 8. STEEL COAL BINS AT COKETON, W. VA.
Steel Coal Bins for Davis Coal and Coke Co. — The steel coal bin shown in Fig. 18 was designed
by the American Bridge Company for the Davis Coal and Coke Co. for the coke ovens at Coketon,
W. Va. The framework is made of structural steel and is covered with corrugated steel. The
bin is lined with 3 in. oak plank spiked to timber spiking pieces which are bolted to the steel
beams. The bin is carried on plate girders each having a web plate 96 in. X f in., and top and
bottom flanges of two angles 6" X 6" X A"- The bin is filled by a belt conveyor passing over
the top of the bin, as shown in Fig. 18. The coal is drawn from the bins through gates into cars
and is hauled to the coke ovens. The capacity of the bin is 300 tons.
References. — For the design of reinforced concrete bins, and for additional data and examples,
see the author's "The Design of Walls, Bins and Grain Elevators."
CHAPTER IX.
STEEL GRAIN ELEVATORS.
Introduction. — Grain elevators, or "silos," as they arc called in Europe, may be divided into
two classes according to the arrangement of the bins and elevating machinery: (a) elevators
which are self contained, with all the storage bins in the main elevator or working house; and
(6) elevators having a working house containing the elevating machinery, while the storage is in
bins connected with the working house by conveyors. The working house is usually rectangular
in shape, with square or circular bins; while the independent storage bins are usually circular.
With reference to the materials of which they are constructed, elevators may be divided
into (i) timber; (2) steel; (3) concrete; (4) tile, and (5) brick. Steel grain elevators, only, will
be considered in this chapter. For a complete treatise on the design of grain elevators, see the
author's "The Design of Walls, Bins and Grain Elevators."
STRESSES IN GRAIN BINS.— The problem of calculating the pressure of grain on bin
walls is somewhat similar to the problem of the retaining wall, but is not so simple. The theory
of Rankine will apply in the case of shallow bins with smooth walls where the plane of rupture
cuts the grain surface, but will not apply to deep bins or bins with rough walls. (It should be
remembered that Rankine assumes a granular mass of unlimited extent.)
Stresses in Deep Bins. — Where the plane of rupture cuts the sides of the bin the solution for
shallow bins does not apply.
Nomenclature. — The following nomenclature will be used:
<f> = angle of repose of the filling;
<f>' = the angle of friction of the filling on the bin walls;
It, = tan 0 = coefficient of friction of filling on filling;
n' = tan <(>' = coefficient of friction of filling on the bin walls;
x = angle of rupture;
w = weight of filling in Ib. per cu. ft. ;
V = vertical pressure of the filling in Ib. per sq. ft.;
L = lateral pressure of the filling in Ib. per sq. ft. ;
A = area of bin in sq. ft.;
U = circumference of bin in ft.;
R = A/U = hydraulic radius of bin.
Janssen's Solution. — The bin in (a) Fig. i, has a uniform area A, a constant circumference U,
and is filled with a granular material weighing w per unit of volume, and having an angle of repose
<t>. Let V be the vertical pressure, and L be the lateral pressure at any point, both V and L
being assumed as constant for all points on the horizontal plane. (More correctly V and L will
be constant on the surface of a dome as in (6).)
The weight of the granular material between the sections of y and y + dy = A-w-dy; the
total frictional force acting upwards at the circumference will be = L- U'tan 4>'-dy\ the total
perpendicular pressure on the upper surface will be = V-A; and the total pressure on the lower
surface will be = ( V + d V)A.
Now these vertical pressures are in equilibrium, and
V-A - (V + dV)A + A-wdy - L-U-ten+'-dy = o
and
= (w-
(i)
319
320
STEEL GRAIN ELEVATORS.
CHAP. IX.
Now in a granular mass, the lateral pressure at any point is equal to the vertical pressure
times k, a constant for the particular granular material, and
L = k-V
Also let A/U = R (the hydraulic radius), and tan $' = /»'.
Substituting the above in (i) we have
dV =
Now let
k-V A .
-R^dy
and
w-w-K
Surface of \
Material-* '
y
L-U'dy.
c: x
I:
(c)
FIG. i.
Integrating (3) we have
log (w> — n- V) = — n-y + C
Now if y = o, then F = o, and C = log w, and (4) reduces to"
w - n-V
and
where e is the base of the Naperian system of logarithms. Solving for F we have
V = - (i - «-»•»)
w
Substituting the value of n from (2), we have
Now if h be taken as the depth of the granular material at any point we will have
F = j^- (i
Also since
(2)
(4)
(5)
(6)
(7)
DATA FOR DESIGN OF STEEL GRAIN BINS.
L - k-V
L - ~ (i -
321
(8)
Now if w is taken in Ib. per cu. ft., and R in ft., the pressure will be given in Ib. per sq. ft.
For (Itvp bins with a depth of more than two and one-half diameters the last term of the
right hand member of (8) may be omitted, and
L'
w-R
(9)
Now both i/ and k can only be determined by experiment on the particular grain and kind of
bin. For wheat and a wooden bin, Janssen found /*' = 0.3 and k = 0.67, making k-n' = 0.20.
Jamieson found by experiment that for wheat k = 0.6, and he found values in Table I for //
with wheat weighing 50 Ib. per cu. ft. and having <f> = 28°, n = 0.532:
TABLE I.
COEFFICIENTS OF FRICTION // FOR WHEAT ON BIN WALLS.
JAMIESON.
Wheat Weighing 50 Ib. per cu. ft., and Angle of Repose </> = 28 Degrees.
Materials.
Coefficient of Friction.
Wheat on wheat
O. C-t2
Wheat on steel trough plate bin
O 468
Wheat on steel flat plate, riveted and tie bars
O.'i'rc to O 4.OO
Wheat on steel cylinders, riveted
O.l6i; to O 17C
Wheat on cement-concrete, smooth to rough
0.400 to 0.425
Wheat on tile or brick, smooth to rough
0.400 to 0.425
Wheat on cribbed wooden bin
o 420 to o 450
Pleisner obtained the values of y! as given in Table II, and of k as given in Table III.
TABLE II.
COEFFICIENTS OF FRICTION OF GRAIN BIN WALLS. PLEISNER.
Bins.
Coefficient of Friction it' = tan <t>'.
Wheat.
Rye.
Cribbed bin
0-43
0.58
0.25
0.45
0.71
0-54
0.78
0-37
0.55
0.85
Ringed cribbed bin .
Small plank bin
Large plank bin
Reinforced concrete bin
TABLE III.
VALUES OF k = LfV FOR WHEAT AND OTHER GRAINS IN DIFFERENT BINS. PLEISNER.
Bins.
fc - LIV.
Wheat.
Rye.
Rape.
Flax-seed.
Cribbed bin
0.4 to 0.5
0.4 to 0.5
0.34 to 0.46
0-1
0-3 to 0.35
0.23 to 0.32
0.3 to 0.34
0.3 to 0.45
0.23 to 0.28
0.3
Ringed cribbed bin
Small plank bin. ...
0.5 to O.6
0.5 to 0.6
Large plank bin
Reinforced concrete bin ....
22
322
STEEL GRAIN ELEVATORS.
CHAP. IX.
TABLE IV.
HYPERBOLIC OR NAPERIAN LOGARITHMS.
N.
Log.
N.
Log.
N.
Log.
1. 00
o.oooo
3-65
1.2947
6.60
1.8871
1.05
0.0488
3-70
1.3083
6.70
I.902I
l.IO
0.0953
3-75
1.3218
6.80
1.9169
1-15
0.1398
3.80
1-3350
6.90
I-93I5
1. 20
0.1823
3-85
1.3481
7.OO
1-9459
1.25
0.2231
3-90
1.3610
7.20
1.9741
1.30
0.2624
3-95
1-3737
740
2.0015
i-35
0.3001
4.00
1-3863
7.6o
2.0281
1.40
0-3365
4-05
1-3987
7.80
2.0541
1.45
0.3716
4.10
1.4110
8.00
2.0794
1.50
0.4055
4-iS
1.4231
8.25
2.II02
i-SS
0.4383
4.20
I-43SI
8.50
2.I4OI
1.60
0.4700
4-25
1.4469
8-75
2.1691
i.6S
0.5008
4-30
1.4586
9.00
2.1972
1.70
0,5306
4-35
1.4701
9-25
2.2246
i -75
0.5596
4.40
1.4816
9-50
2.2513
i. 80
0.5878
4-45
1.4929
9-75
2.2773
i.8S
0.6152
4-50
1.5041
IO.OO
2.3O26
1.90
0.6419
4-55
1-5151
II.OO
2-3979
i -95
0.6678
4.60
1.5261
I2.OO
2.4849
2.OO
0.6931
4-65
1-5369
I3.OO
2.5649
2.O5
0.7178
4.70
I-5476
I4.OO
2.6391
2.IO
0.7419
4-75
1.5581
15.00
2.708l
2.IJ
0.7655
4.80
1.5686
16.00
2.7726
2. 2O
0.7885
4-85
1.5790
17.00
2.8332
2.25
0.8109
4.90
1.5892
18.00
2.8904
2.3O
0.8329
4-95
1-5994
19.00
2-9444
2-3S
0.8544
5.00
1.6094
20.00
2-9957
2.40
0.8755
5-05
1.6194
2I.OO
30445
2-4S
0.8961
5.10
1.6292
22.OO
3.0910
2.50
0.9163
5-iS
1.6390
23.OO
3-1355
2-55
0.9361
5-20
1.6487
24.OO
3.1781
2.6O
0.9555
5.25
1.6582
25.0O
3.2189
2.65
0.9746
5-30
1.6677
26.OO
3-2581
2.70
0.9933
5-35
1.6771
27.OO
3.2958
2-75
1.0116
5-40
1.6864
28.00
3-3322
2.80
1.0296
5-45
1.6956
29.OO
3-3673
2.85
1-0473
5-50
1.7047
3O.OO
3.4012
2.9O
1.0647
5-55
1.7138
3I.OO
3-4340
2-95
1.0818
5.60
1.7228
32.00
34657
3.00
1.0986
5-65
I-73I7
33.OO
3-4965
3-oS
1.1154
5-70
I-740S
34-oo
3.5264
3.10
1.1314
5-75
1.7492
35.00
3-5553
3-iS
1.1474
5.80
1-7579
40.00
3.6889
3.20
1.1632
5-85
1.7664
45-oo
3.8066
3-2S
1.1787
5-90
1-7750
50.00
3.9120
3-3°
I-I939
5-95
I-7834
60.00
4-0943
3-3S
1.2090
6.00
1.7918
70.00
4-2485
3-4°
1.2238
6. o
1.8083
80.00
4.3820
3-45
1.2384
6.2O
1.8245
90.00
4-4998
3-SO
1.2528
6.30
1.8405
IOO.OO
4.6052
3-55
1.2669
6.40
1-8563
3.60
1.2809
6.50
1.8718
It will be seen in (8) that the maximum lateral pressure in a bin which must be used in the
design of deep bins, is independent of k, and that therefore an exact determination of k is not very
important. In calculating the values of V and L in (7) and (8), it is necessary to use a table of
PRESSURES IN STEEL GRAIN BINS.
n.itural or hyperbolic logarithms. A brief table of hyperbolic logarithms is given in Table IV.
To find the hyperbolic logarithm of any number, using a table of Brigg's or common logarithms,
use tht- rrlat ion: The hyperbolic or Naperian logarithm of any number ™ common or Brigg's
logarithm X 2.30259.
The author has calculated the lateral pressures on steel plate bins, Fig. 2.
Ca/cufafec/ •
Pressures
Wheat 50 lbs.cu.ft.
//* fan 4*0.552
' 3 45 67
Pressure in Ibs.per sq. in.
FIG. 2. LATERAL PRESSURE IN STEEL PLATE GRAIN BINS CALCULATED BY JANSSEN'S
FORMULA.
To use Fig. 2 to calculate the pressures in rectangular bins, calculate the pressure in a circular
or square bin which has the same hydraulic radius, R (R = area of bin •*• perimeter of bin), as
the rectangular bin.
It will be seen in Fig. 2 that the pressure varies as the diameters, where the height divided
by the diameter is a constant. By using this principle the pressure for any other diameter within
the limits of the diagram may be directly interpolated.
Problem I. Required the lateral pressure at the bottom of a cement lined bin, 10 ft. in
diameter and 20 ft. high, containing wheat weighing 50 Ib. per cu. ft. Assume /*' = 0.416, and
k = 0.6, also R will = 2\ ft., w = 50 Ib., h = 20 ft., and Jfe-/ = 0.25.
Now from (8)
5Q X 2.5
0.416
300(1 - <
(j _ g-0.26 x M/2.8)
Now from Table IV the number whose hyperbolic logarithm is 2.00 is 7.40, and
L = 300 ( I ) ,
V 7-40 9
= 260 Ib. per sq. ft.,
= 1.8 Ib. per sq. in.
324 STEEL GRAIN ELEVATORS. CHAP. IX.
German Practice. — Janssen's formula is given in Hutte Des Ingenieurs Taschenbuch, as
the standard formula for the design of grain bins. For wheat Janssen found that // = 0.3, and
k = 0.67, so that n'-k = 0.20. Using these values and changing to English units, we have for
wheat,
V = HL* (Z
0.2 v
or if d = diameter or side of bin, then
V = \wd(i
L = k-V
which is the German practice.
Load on Bin Walls. — The walls of a deep bin carry the greater part of the weight of the
contents of the bin. The total weight carried by the bin walls is equal to the total pressure, P,
of the grain on the bin walls, multiplied by the coefficient of friction fj.' of the grain on the bin
walls.
From formula (8) the unit pressure on a unit at a depth y will be
L = —~ (i - £-*.f*'.y/*) (10)
and the total lateral pressure for a depth y, per unit of length of the perimeter of the bin, will be
P = JJ L-dy = £—-£ (i -
w-R I" R R
, ,p~l
J
Now the last term in (n) is very small and may be neglected for depths of more than two
diameters, and
_ w-R f R "1 , N , .
: ~" y ~ fcpp*0*-)
The total load per lineal foot carried by the side walls of the bin will be
' = w-R y ~ (aPProx-) (13)
For the total weight of grain carried by the side walls multiply (13) by the length of the cir-
cumference of the bin.
Formulas (12) and (13) may be deduced as follows: — The grain carried by the sides of the
bin will be equal to the total weight of grain in the bin minus the pressure on the bottom of the
bin. If P is the total side pressure on a section of the bin one unit long, then
P-U'ii,1 = w-A-y - A-V (a)
= w-A-y - W'A'
K" (J.
and solving (6)
= ~n~ L y ~ £v J (approx-}
and the total load carried on a section of the bin one unit long will be found by multiplying P in
(ii) by /i', and
EXPERIMENTS ON THE PRESSURE OF GRAIN IN DEEP BINS. 326
PV -w-j^y-^d- r**'*/*) I
- w R [ y - -~r] (approx.) (13)
I
For example take a steel bin 10 ft. in diameter and 100 ft. deep; weight of wheat, 10-50
I). IM r cu. ft.; angle of friction of wheat on steel, / - 0.375; angle of repose of grain on grain,
i - tan 28° = 0.532 (M does not occur in formula (13) but may be used in calculating an approxi-
mate value of * = (i - sin 28°)/(i + sin 28°) = 0.37 which is a close approximation to k - 0.4
which will be used). Then the load carried by the side walls per lineal foot will be from (13)
P V = 50 X 2.5 f 100 ±£
* L 0.4 x 0.375
— 10,416 lb.
he total load on the entire bin walls will be
P V X 31-416 = 327,635 lb.
'he total weight of wheat in the bin is
5° X 78.5 X ioo = 392,700 lb.
and the total load carried by the bottom of the bin is
392,700 - 327,635 = 65,065 lb.
and the pressure on the bottom = V = 65,065/78.54 = 830 lb. per sq. ft. From formula (7) we
find that V = 830 lb. per sq. ft.
EXPERIMENTS ON THE PRESSURE OF GRAIN IN DEEP BINS.— The laws of pressure
of grain and similar materials are very different from the well known laws of fluid pressure. Dry
wheat and corn come very nearly filling the definition of a granular mass assumed by Rankine in
deducing his formulas for earth pressures. As stored in a bin the grain mass is limited by the
bin walls, and Rankine's retaining wall formulas are not directly applicable.
If grain is allowed to run from a spout onto a floor it will heap up until the slope reaches a
certain angle, called the angle of repose of the grain, when the grain will slide down the surface
of the cone. If a hole be cut in the bottom of the side of a bin, the grain will flow out until the
opening is blocked by the outflowing grain. There is no tendency for the grain to spout up as
in the case of fluids. If grain be allowed to flow from an orifice it flows at a constant rate, which
is independent of the head and varies as the diameter of the orifice.
Experiments by Willis Whited,* and by the author at the University of Illinois, with wheat
have shown that the flow from an orifice is independent of the head and varies as the cube of the
diameter of the orifice. This phenomenon can be explained as follows: The wheat grains in
the bin tend to form a dome which supports the weight above. The surface of this dome is
actually the surface of rupture. When the orifice is opened the grain flows out of the space below
the dome and the space is filled up by grains dropping from the top of the dome. As these grains
drop others take their place in the dome. Experiments with glass bins show that the grain from
the center of the bin is discharged first, this drops through the top of the dome, while the grain
in the lower part of the dome discharges last.
The law of grain pressures has been studied experimentally by several engineers within
recent years. A brief resume of the most important experiments is given in the author's "The
Design of Walls, Bins and Grain Elevators," where after a careful study of all available experi-
ments the author reached the following conclusions: —
I. The pressure of grain on bin walls and bottoms follows a law (which for convenience will
be called the law of "semi-fluids"), which is entirely different from the law of the pressure of fluids.
* Proc. Eng. Soc. of West. Penna., April, 1901.
326 STEEL GRAIN ELEVATORS. CHAP. IX.
2. The lateral pressure of grain on bin walls is less than the vertical pressure (0.3 to 0.6 of
the vertical pressure, depending on the grain, etc.), and increases very little after a depth of 2\
to 3 times the width or diameter of the bin is reached.
3. The ratio of lateral to vertical pressures, k, is not a constant, but varies with different grains
and bins. The value of k can only be determined by experiment.
4. The pressure of moving grain is very slightly greater than the pressure of grain at rest
(maximum variation for ordinary conditions is, probably, IO per cent).
5. Discharge gates in bins should be located at or near the center of the bin.
6. If the discharge gates are located in the sides of the bins, the lateral pressure due to moving
grain is decreased near the discharge gate and is materially increased on the side opposite the
gate (for common conditions this increased pressure may be two to four times the lateral pressure
of grain at rest).
7. Tie rods decrease the flow but do not materially affect the pressure.
8. The maximum lateral pressures occur immediately after filling, and are slightly greater
in a bin filled rapidly than in a bin filled slowly. Maximum lateral pressures occur in deep bins
during filling.
9. The calculated pressures by either Janssen's or Airy's formulas agree very closely with
actual pressures.
10. The unit pressures determined on small surfaces agree very closely with unit pressures
on large surfaces.
11. Grain bins designed by the fluid theory are in many cases unsafe as no provision is made
for the side walls to carry the weight of the grain, and the walls are crippled.
12. Calculation of the strength of wooden bins that have been in successful operation shows
that the fluid theory is untenable, while steel bins designed according to the fluid theory have
failed by crippling the side plates.
RECTANGULAR STEEL BINS.— For the calculation of the stresses in and the design of
rectangular steel bins, see the author's " The Design of Walls, Bins and Grain Elevators,"
Second Edition.
CIRCULAR STEEL BINS. — In the designing of steel grain bins particular attention should
be given to the horizontal joints, and to the strength of the bin to act as a column to support the
grain. To calculate the thickness of the metal the horizontal pressure L is obtained from Jan-
ssen's formula, and then the thickness may be found by the formula
L-d
1 = ^ (<4}
where / = thickness of the plate in in. ;
L = horizontal pressure in Ib. per sq. in.;
d = diameter of bin in in.;
S = working stress in steel in Ib. per sq. in.;
/ = efficiency of the joint.
The unit stress S may be taken at 16,000 Ib. per sq. in., and / will be about 57 per cent for a
single riveted lap joint, 73 per cent for a double riveted lap joint, and 80 per cent for double
riveted double strap butt joints. For the efficiency of riveted joints, see Table I la, Chapter XI.
The allowable stresses given for the design of steel mill buildings should be used in design.
These allowable stresses are as follows: Tension on net section 16,000 Ib. per sq. in.; shear on
cross-section of rivets 11,000 Ib. per sq. in.; bearing on the projection of rivets (diameter X thick-
ness of plate) 22,000 Ib. per sq. in. Compression in columns P = 16,000 — "joljr where P = unit
stress in Ib. per sq. in. , / = length of member and r = radius of gyration of the member, both in inches.
Rivets in Horizontal Joints. — The side walls carry a large part of the weight of the grain in
the bin and this should be considered in designing the horizontal joints. The weight of the
grain supported by the bin above any horizontal joint can be calculated as shown in the following
example. Assume a steel plate bin 25 ft. in diameter, and it is required to calculate the grain
DESIGN OF STEEL GRAIN BINS.
327
supported by the bin walls above a horizontal joint 75 ft. below the top of the grain. From
filiation (13) the grain carried by the bin walls |x r liiu-.il foot of circumference of bin, where
w — 50 Ib. per cu. ft.; M' ™ 0.375; k «- 0.40, also R «• 25/4 — 6.25, and
50 X 6.25
10,415 Ib.
75 -
6.25
0.4 X 0.375
The weight of the steel bin above the joint may be taken as 1,250 Ib. per lineal foot of joint.
The horizontal riveting should then be designed for a shear of 11,665 Ib. per lineal foot of joint.
Assume that the plates are | in. thick and the rivets } in. in diameter. For allowable stresses of
16,000 Ib. per sq. in. in tension, 11,000 Ib. per sq. in. in shear, and 22,000 Ib. per sq. in. in com-
pression; then, Tablell4,Part II, the value of a j in. shop rivet in single shear = 4,860 Ib., and a
field rivet is f of 4,860 = 3,240 Ib., and in compression = 6,190 Ib. for shop rivets and = 4.127
Ib. for field rivets. For a lap joint therefore the spacing should not be greater than 3,240 X 12
-T- 11,665 = 3.25 in., requiring but one row of rivets.
Stresses in a Steel Bin Due to Wind Moment. — If M is the moment due to the wind acting
on the bin above the horizontal joint, then the stress per lineal foot of joint due to wind moment
be
** (approx.) and 5 = — « (15)
2!
but / =
where all dimensions are in feet. For a wind load of 30 Ib. per sq. ft. on two-thirds of the tank
(20 Ib. per sq. ft. on the entire surface of the tank) the wind stress will be S = 2,865 Ib. per lineal
foot. The spacing therefore should not be greater than 3,240 X 12 -5- (11,665 -f- 2,865) = 2f in.
Stiffeners. — In large circular steel bins the thin side walls are not sufficiently rigid to support
the weight of the grain and it is necessary to supply stiffeners. For this purpose angles or Z-bars
may be used. Experience has shown that bins' in which the height is equal to or greater than
about 2$ times the diameter do not need stiffeners. There is at present no rational method for
the design of these stiffeners or the stiffeners in plate girders. In Fig. 9 will be seen the details
of a steel bin of the Independent Steel Elevator with Z-bar stiffeners. Angle stiffeners were
used in the bins of the Electric Elevator, Minneapolis, Minn.
c w'-e" -H<- w'-o'- *K M'-I'- -H
FIG. 3. PLAN OF STEEL STORAGE BINS FOR A STEEL ELEVATOR.
Circular steel bins are used for storage in large elevators and may be used for a complete
elevator as in Fig. 3. The space between the bins is sometimes used for auxiliary storage. The
circular bin walls are stiffened by means of vertical channels, and the auxiliary bins are cross-braced
with steel rods. Complete details of circular steel bins for the Independent Elevator, Omaha,
Neb., are shown in Fig. 9.
328
STEEL GRAIN ELEVATORS.
CHAP. IX.
EXAMPLES OF STEEL GRAIN ELEVATORS.
829
Steel Country Elevator. — General plans of a steel grain elevator for the Manhattan Milling
Co., designed and conMrm ttd by the Minneapolis Steel & Machinery Co., Minneapolis, Minn.,
are given in Kig. 4. This elevator could easily be changed to a shipping elevator by putting in a
wagon dump. Grain is run from the cars into the boot of the receiving leg, and is then elevated
and conveyed by a screw conveyor to the large storage bins, or is run into the temporary storage
bins, then cleaned and elevated and conveyed to the storage bins by the screw conveyor. The
1'ins are built of steel plates, and the working house is built of steel framework covered with cor-
rugated steel. This elevator has a capacity of 76,300 bushels but the scheme can be used for a
30,000 to 40,000 bushel elevator for either shipping or for milling purposes.
THE INDEPENDENT STEEL ELEVATOR, OMAHA, NEB. General Description.—
This elevator consists of a steel working house having a bin capacity of 240,000 bushels and 8 steel
storage bins having a storage capacity of 100,000 bushels each, making a total storage capacity of
1,040,000 bushels.
The steel working house is 64 ft. X 70 ft., with 14 ft. sheds on two ends and one side, as
shown in Fig. 5. The sub-story of the building is 26 ft. The bins are 64 ft. 4 in. high, as shown
in Fig. 6, and are supported on steel columns, as shown in Fig. 6 and Fig. 7. The spouting story
is 24 ft. 6 in. high; the garner and scale story is 26 ft. 6 in. high; and the machinery story is 13
ft. 8 in. high. The walls below and above the bins are covered with No. 24 corrugated steel laid
with ij corrugations side lap and 3 in. end lap. The roof is covered with No. 22 corrugated steel
laid directly on the steel purlins with 2 corrugations side lap and 6 in. end lap.
On the first or working floor the floor between the tracks is made of J in. plate bolted to the
beams, while the remainder of this floor is made of concrete filled in above concrete arches which
rest on the flanges of the beams with a finish ij in. thick of Portland cement mortar consisting
of one part cement to one part clean, sharp sand. The concrete is composed of one part Portland
cement, two parts sand, and five parts crushed stone.
-p=— ^==
V { "-Outside ofCorr. Iron "&&*
l^O'ln C/ear todase offai/.
FIG. 5. PLAN OF INDEPENDENT ELEVATOR.
The floor of the cupola throughout the different floors and in the gallery leading over the
bins is made of No. 24 corrugated steel resting on steel framework, and covered with 3 in. of •m-
crete and a one-inch finish of one to one Portland cement mortar troweled smooth. All doors
are of the rolling steel type. The window frames were made of 2 in. X 6 in. timbers and are
covered with No. 26 sheet steel. All windows are provided with I f in. checked rail sash and are
glazed with double strength glass.
Painting. — All steel work of every description was painted with one coat oxide of iron paint
at the. shop and a second coat after erection. The tank plates and corrugated steel were painted
on the exterior surface only after erection.
Bins. — The eight steel storage bins are 44 ft. in diameter and 80 ft. high, have a capacity of
100,000 bushels and rest on separate concrete foundations. The bins are constructed of steel
plates stiffened with Z-bars, as shown in Fig. 9. The bins are covered with a steel plate roof,
Fig. 12, supported on roof trusses, as shown in Fig. 1 1 and Fig. 13. A conveyor gallery 10 ft.
330
STEEL GRAIN ELEVATORS.
CHAP. IX.
FIG. 6. TRANSVERSE SECTION OF WORKING HOUSE OF INDEPENDENT ELEVATOR.
IM>I:I'I;M)I;NT STI.KI. C.KAIN KU.YATOK.
881
*T§i — VTrr^nT^, >..-
J^KI^.*****^^ j
4i -fi<-1* i
FIG. 7. LONGITUDINAL SECTION OF WORKING HOUSE OF INDEPENDENT ELEVATOR.
332
STEEL GRAIN ELEVATORS.
CHAP. IX.
wide and 8 ft. high extends from the working house over the bins. A conveyor tunnel extends
from the working house under the bins. The rivet spacing in the circular bins is shown in Fig. 9.
The bins in the working house are arranged as shown in Fig. 8, and are constructed of plates,
as shown in Fig. 6 and Fig. 7. The bins, 14 ft. X 16 ft., are braced in the corners with angle
braces spaced 5 ft. centers vertically, and of the sizes shown in Fig. 8. The large bins are also
braced with f and f-in. round rods spaced 5 ft. apart as shown. All the smaller bins are braced
with f-in. round rods spaced 2 ft. 6 in. apart as shown. Vertical angles in the sides of the bins
are provided, as shown in Fig. 6, Fig. 7, and Fig. 8.
Connection of Rods erf
Interior Bin Walls.
FIG. 8. PLAN OF BINS IN WORKING HOUSE OF INDEPENDENT ELEVATOR.
INDKl'KNDKM Ml.l.l. (,!<AI.\ ELEVATOR
888
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f_V»T*v - -Ho.'loi',o1s®-^.fi 3 •*v,//-/*i*
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334
STEEL GRAIN ELEVATORS.
CHAP. IX.
EQUIPMENT. — There are two stands of receiving elevators with receiving pits on either
side. These elevators have' 22-inch 6-ply belts and 20 in. X 7 in. X 7 in. buckets spaced 14 in.
apart; the receiving pits are covered with steel grating, and a pair of Clark's automatic grain
shovels are located at each unloading place. These elevators are driven with an electric motor
of 100 H. P., each elevator being driven with a clutch and pinion so that the elevator may be
stopped and started at will.
There is one stand of shipping elevators constructed in the same manner, having a 26-in.
6-ply belt and 2 lines of 12 in. X 7 in. X 7 in. buckets spaced 14 in. apart.
* VV*^ *? ^V
L-These rods same length as those opposite
K le'-io*—-
Conveyor Supports spaced ' //-6*-1 '—?l>-4®5j* ,
j*- 29-5*--' -.-- •*)* 46'-0*- - - *1
Section along i of Conveyor Tunnel.
FIG. 10. DETAILS OF BIN BOTTOMS AND CONVEYORS UNDER BINS, INDEPENDENT
ELEVATOR.
There are two stands of cleaning elevators with 14-in. 6-ply belts with 12 in. X 6 in. X 6 in.
buckets spaced 12 in. apart.
There are also two screenings elevators with 9-in. 5-ply belts with 8 in. X 5 in. X 5 in.
buckets spaced 12 in. apart.
The shipping, screenings, and cleaner elevators are driven from a line shaft which is driven
by a zoo H. P. motor, each elevator being driven by a core wheel and pinion.
Three scale hoppers, having a capacity of 1,800 bushels, are located in the cupola, and three
garner hoppers of 1,800 bushels capacity are located above the scale hoppers.
The main line shaft on the first floor is driven by a 170 H. P. motor.
A car puller capable of moving 25 loaded cars is provided.
Elevators. — The boots of the receiving and shipping elevators rest in water-tight steel boot
tanks made of iVin. steel plates. The elevator boots are made of i^-in. steel plates, the boot put
INDEPENDENT STEEL GRAIN ELEVATOR.
leys having a vertical adjustment of 8 inches. The elevator cases arc made of No. 12 steel up to
the liins, and of A-in. plates in the bins, and No. 14 steel above the bins. The cases are strength-
riu-il by angles at the corners. The elevator heads are made of No. 14 steel. At each receiving
i-lrv itor is a large elevator pit extending from the leg back to the center of the track. This pit
is constructed of beams and i'« -in. plates and is covered with a grating of I } X J-in. bars spaced
ij in. apart.
The elevator buckets are " Buffalo" buckets; those for the receiving elevators are 20 in. X 7
in. X 7 in.; for the shipping elevators two lines of 12 in. X 7 in. X 7 in. buckets; for the cleaning
elevators one line of 12 in. X 6 in. X 6 in. buckets; and for the screenings elevator one line of
8 in. X 5 in. X 5 in. buckets. The buckets in the receiving, shipping and cleaning elevators
are spaced 14 in. apart, while those in the screenings elevator are spaced 12 in. apart.
The elevator belts in the receiving elevators are 22 in. wide and 6-ply, the shipping belts
are 26 in. wide and 6-ply; the cleaning belts are 14 in. wide and 6-ply, and the screenings belts
are 9 in. wide and 5-ply. The belting is made of 32 ounce duck and is first-class.
Roof Framing Plan for Tanks.
FIG. ii. FRAMING FOR ROOF OF CIRCULAR BINS, INDEPENDENT ELEVATOR.
Spouts. — The building is provided with a complete system of spouts. The general distrib-
uting spouts from the scales to the shipping spouts are double-jointed Mayo spouts. There are
three shipping spouts which are provided with telescoping bottom sections. All bin bottoms
are provided with a revolving spout with a cut-off gate operated with a rack and pinion, with
cords leading to within reaching distance of the floor.
Conveyors. — The conveyor belt leading from the working house over the bins is a 36 in.
4-ply conveyor belt, is carried on disc rolls consisting of 3 straight-faced 6-in. pulleys and 2 special
discs; the discs run loose on the shafts, which are iA-in. diameter and are spaced 5 ft. centers.
The return rolls are 5-in. straight-faced rolls spaced 15 ft. centers. At each point in the elevator
where grain is loaded onto the belt there are two pairs of special concentrating rolls. Movable
336
STEEL GRAIN ELEVATORS.
CHAP. IX.
__t_
Punch Holes in Pli,
to fit 'Holes in Trusses.
til
«3£
|||
.ftfffa.
imicfe
-lV*f
\^
j^^
^^S^-S^* . 'JT— « -
Section "DO'
if -"Da^i. • <; 26I ^'M'4 Oeiail of flan Ho/e Door,
View -DP Showing <5f>ouf.
FIG. 12. DETAILS OF STEEL ROOF FOR STEEL BINS FOR INDEPENDENT ELEVATOR.
INDKl'HNDKNT STKKI. (-KAIN KU-.VAI < )K.
337
trippers provided with spouts are provided, so that grain may be discharged on either side of the
belt. Tin- t-iit ire conveyor is carried on a steel framework. The conveyor belt is driven by a
40 II. P. motor. The conveyor in the tunnel leading from the storage tanks to the working
house is of the same type as the conveyor above the bins, and is supported on a steel framework,
except that the top or carrying rolls are all of the concentrating types, as shown in Fig. 10. The
coucriitr.it ing rollers arc composed of two straight-faced rolls from the main shaft, and two
concentrating rolls meeting at an angle of 45° to the straight rolls. The lower conveyor is driven
by a rope drive from the main line shaft in the working house.
FIG. 13. DETAILS OF STEEL ROOF TRUSS FOR STEEL BINS, INDEPENDENT ELEVATOR.
Scale Hoppers. — There are three scale hoppers of 1,800 bushels capacity, each mounted
on a Fairbanks-Morse and Company's scales, having a capacity of 84,000 lb., and have steel
frames. The hoppers have fs-in. steel plate sides, and {-in. plate bottoms, stiffened with angle
irons, and are tied together with tie rods. Each hopper is provided with a 22-in. cast iron outlet
with a steel plate cut-off gate.
Garners. — A steel garner hopper is placed directly over each scale hopper. The garners
have a capacity of 1,800 bushels, and are constructed with A-in. side plates and }-in. bottom
plates. The bottoms of the garners are hoppered to four openings, which are provided with gates
sliding on steel rollers.
Cleaning Machines. — A large size cleaning machine and a large size oat clipper are provided.
These machines are connected with a large dust collector which discharges the dust from the
cleaning machines and from the sweepings outside of the building.
Car Puller. — A car puller having a capacity of 25 loaded cars is provided. The car puller
has two drums, each provided with 400 ft. of f-in. crucible steel cable.
Shovels. — A pair of Clark automatic grain shovels, with all necessary counterweights, sheaves, .
scoops, etc., are provided.
The total weight of steel in the elevator is 1,700 tons; approximately 900 tons in the working
house, and 800 tons in the circular bins and conveyors.
The total cost was $205,000, of which the 8 steel bins and conveyors cost $80,000.
COST OF STEEL GRAIN ELEVATORS.— The following costs of steel grain elevators have
been taken from the author's " The Design of Walls, Bins and Grain Elevators," which also gives
costs of reinforced concrete and tile bins, and timber grain elevators. The total cost of the steel
grain elevator of the working house type, constructed by the Great Northern Railway at
Superior, Wis., was 39.65 cts. per bushel of storage. The elevator had a storage capacity of
3,100,000 bushels, and the steel weighed 7 lb. per bushel of storage capacity. The Independent
23
338 STEEL GRAIN ELEVATORS. CHAP. IX.
Elevator cost gj cts. per bushel storage capacity for the steel bins.and 54 cts. per bushel storage
capacity for the working house. A steel country elevator having four steel tanks, 17 \ ft. diam-
eter and 30 ft. high, with an interspace bin and a conveyor shed, and having a storage capacity
of 30,000 bushels, weighed 3 Ib. per bushel of storage capacity. The shop cost and cost of erec-
tion of the structural steel was $15.00, and $19.00 per ton, respectively.
References. — For the design of reinforced concrete grain bins and elevators, and for additional
data and examples, see the author's "The Design of Walls, Bins and Grain Elevators."
CHAPTER X.
STEEL HEAD FRAMES AND COAL TIPPLES.
Types of Head Works for Mines. — The design of the head works for a mine depends upon
the material which is to be hoisted, upon the depth of the mine, the inclination of the shaft, the
rate of hoisting, the amount to be hoisted at one time, the treatment of the ore or coal after being
hoisted, and upon the material used in the construction of the structure. Head works for mines
may be divided into three classes: (i) head frames; (2) rock houses; (3) coal tipples.
The first head frames were constructed of timber; the most common type being the 4-post
head frame. The square or rectangular mine tower was cross-braced and the sheave supports
were made of heavy timber. The back brace was inclined and was placed between the hoisting
rope and the line of the resultant of the stress in the hoisting rope.
•Sheave
FIG. i.
Steel head frames vary in design to suit local conditions and the ideas of the designer. The
A-frame in Fig. I is the most satisfactory type where conditions permit of its use. It is simple
in design and economical of material; the stresses are statically determinate, and it can be easily
and effectively braced, making a very rigid frame. The 4-post frame in Fig. 2 is the type to use
when it is necessary to hoist from several compartments of a shaft not in a single line. It is also
used for coal tipples and double compartment shafts. The 4-post frame is not so economical of
material as the A-frame; is more difficult to brace effectively, partly for the reason that part of
the bracing in the tower must be omitted to permit the dumping of the ore or coal, and in addition
the stresses are statically indeterminate. The frame shown in Fig. 3 is a modification of the
A-frame used for an inclined shaft. Several early head frames in the coal fields of Pennsylvania
were built on the lines of the frame shown in Fig. 4. This type of frame has no points of merit
and is practically obsolete.
For an elaborate discussion of the design of head frames, coal tipples, and other mine struc-
tures, see the author's "The Design of Mine Structures."
METHODS OF HOISTING.— In hoisting from inclined or vertical shafts, the hoisting
engine is placed at some distance from the mouth of the shaft, the cable passes up over the sheave
at the top of the head frame and into the shaft. The rope, if round, is carried on a smooth or a
grooved hoisting dium, and if flat, is carried on a hoisting reel. The maximum working load on
the rope occurs when the loaded skip or cage is being hoisted from the bottom of the shaft. The
working load then consists of the skip or cage, the load, the accelerating force, the weight of the
339
340
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
rope itself, and the friction of the rope on the sheave and drum and of the skip or cage in the
guides.
With round ropes the hoisting drum for deep mines is commonly made conical, the small
diameter being used when the load is at the bottom of the shaft. Flat ropes are wound on a reel,
5heave
^Sheave
FIG. 3.
so that the small diameter is used when the load is at the bottom of the shaft, the diameter of
the reel increasing as the rope is wound up. The required height of the head frame depends
upon (i) the room required for screening, crushing and handling the coal or ore; (2) the speed
of hoisting — with rapid hoisting it is necessary to have a height from the landing to the sheaves
-"Shesve
r Ho/'s tin (f Drum
FIG. 5.
of from two to three times the height of the cage or skip or a full revolution of the drum to prevent
over winding, and (3) the desired location of the hoisting engine. ' With a given height of head
frame h, the distance d. Figs, i to 5, depends upon the diameter of the sheave, the diameter of
the rope, and whether the rope is round or flat. The sheave should be as large as can conveniently
METHODS OF HOISTING.
341
be used, as the larger the sheave the longer the life of the hoisting rope. The inertia of a large,
heavy ^tn ,i\. , however, with rapid hoisting may kink the rope and cause excessive wear. The
Ix-mling stresses in flat ropes for a sheave of given diameter are less than in round ropes having
equul strength, but the life of flat ropes is less than for round ropes. Flat ropes are wound on
reels which are at all times in line with the head frame sheave, while round ropes are wound
on a drum so that the horizontal angle between the center line of the sheave and the cable is
continually changing. The distance, d, for flat ropes can then be less than for round ropes.
J60-0
h- .................... '
FIG. 6. GILBERTON STEEL HEAD FRAME.
Hoisting from mine shafts is commonly done in two compartments of the shaft at the same
time, the unloaded skip or cage descending as the loaded skip or cage ascends. This is known as
hoisting in balance or counterbalance. There is a considerable saving in power in hoisting in
balance. To hoist in balance it is necessary to take ore from one level with both skips unless the
Whiting system is used. When a round rope winds off the drum it makes an angle with the
groove in the sheave on the head frame and the friction increases the tension in the cable and
also reduces its life. To reduce the friction and wear the hoisting engines are placed at a con-
siderable distance back from the head frame.
The head frame may be placed so that the sheaves are parallel, as in Figs. I to 4, or so that
the sheaves are in tandem, as in Figs. 5 and 6. With the latter method it is necessary to place
the hoisting engine farther from the shaft than where the sheaves are in parallel. Where the
hoisting engine is placed well back from the shaft it becomes necessary to support the hoisting
rope on idlers, as shown in Fig. 6. Where mines have three compartment shafts, ore is commonly
hoisted from but two compartments, the third compartment being used for pumps, pipes, etc.
This arrangement makes it necessary to place the head sheaves so that they will not be sym-
metrical with the center line, bringing heavier working stresses on one side of the head frame
than on the other side.
Hoisting from Deep Mines. — In deep mines the rope in the mine becomes a large part of
the load and various methods have been used to counterbalance the weight of the rope. Four
methods for obviating the difficulty just mentioned have been used: (i) the Koepe system;
(2) the Whiting system; (3) modifications of (i) and (2), and (4) by the use of a taper rope. These
methods are described in the author's "The Design of Mine Structures."
HOISTING ROPES. — Round hoisting ropes are commonly made of six strands, each of
which is formed by twisting nineteen wires together, the strands being wound around a hemp
342
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
center. Wire strands are twisted around the core either to the right or the left, and the resulting
rope is either "right lay" or "left lay." The twist may be long or short; the shorter twist forms a
more flexible rope, while the longer twist forms a more rigid rope. Wire rope is made of iron,
open-hearth steel, crucible steel, and plough steel. The strength of the wire from which the
rope is made is about as follows: iron wire, 40,000 to 100,000 Ib. per sq. in.; open-hearth steel
wire, 50,000 to 130,000 Ib. per sq. in.; crucible steel wire, 130,000 to 190,000 Ib. per sq. in.; and
plough steel wire, 190,000 to 350,000 Ib. per sq. in. Hoisting ropes are usually made of crucible
cast steel or plough steel.
Flat wire rope is composed of several round ropes whose diameter is equal to the required
thickness of the flat rope, laid side by side and sewed together with iron or annealed cast steel
wire. The round ropes are alternately of right and left lay or twist, have four strands without
either hemp or wire center. The number of wires in each strand is usually seven, but may be
nineteen. The chief drawbacks to the use of flat wire rope are its first cost and the rapid wear
of the sewing wires.
Flat ropes and reels are used to a limited extent in the western part of the United States, while
round ropes are generally used in hoisting coal and in the deep copper and iron mines in Michigan.
Strength of Wire Rope. — The dimensions, weight and strength of round crucible steel hoisting
rope are given in Table I, while similar data for plough steel hoisting rope are given in Table II.
The strengths of wire rope given by the different makers differ somewhat.
TABLE I.
CAST STEEL HOISTING ROPE. ULTIMATE STRENGTH, WORKING STRENGTH AND WEIGHT OF
WIRE ROPE COMPOSED OF 6 STRANDS AND A HEMP CENTER, 19 WIRES
TO THE STRAND.
Diameter,
In.
Approximate
Circumference ,
In.
Weight per
Ft., Lb.
Safe Working
Load, for Hoist-
ing, L, Lb.
Approximate Break-
ing Stress, Lb.
Safe Working
Stress for D'rect
Pull, 5, Lb.
Minimum Size
of Drum or
Sheave, Ft.
2f
81
H-95
456,000
76,000
10
7}
9-85
03
380,000
66,300
9£
2j
7f
8.00
JJ
3I2,OOO
52,OOO
8i
2
6}
6.30
to
248,000
41,300
8
If
5*
4-85
60
I92,OOO
32,OOO
7i
If
5
4-iS
a
l68,OOO
28,OOO
6|
If
^i
44
3-55
u
Jo
144,000
24,000
5f
If
4i
3.00
1
124,000
2O,700
Ij
4
2.45
co
100,000
16,700
5
l|
3i
2.00
I.
84,000
I4,OOO
4i
I
3
I.S8
>-l
68,000
II,3OO
4t
7
8
2f
1. 2O
•rf
52,000
8,700
3
4
2j
0.89
o
38,800
6,300
3
I
2
O.62
60
27,200
4,500
2i
T6
If
O.5O
.s
22,000
3,700
If
1
2
If
0-39
o
17,600
2,900
If
A
I?
O.3O
J
13,620
2,300
f
If
O.22
CJ
10,000
1,670
I
I
0.15
6,800
I,I7O
2
3
i6
3
4
O.IO
4,800
800
\
Working Load on Hoisting Rope. — The stresses in a hoisting rope are the sum of the stresses
due to (i) the weight of the rope, (2) the friction of the rope, (3) the bending of the rope over the
head sheave, (4) the live load, and (5) the impact due to starting and stopping the load. The
stresses due to bending are discussed in the next section. The stresses due to impact vary from
zero to twice the working load if the hoisting cable is taut, and to several times the working load
STRENGTH OF STEEL WIRE ROPE.
Mfl
TABLE II.
PLOUGH STEEL HOISTING ROPE. ULTIMATE STRENGTH, WORKING STRENGTH AND WEIGHT OF
WIRE ROPE COMPOSED OF 6 STRANDS AND A HEMP CENTER, 19 WIKI •.-,
TO THE STRAND.
Diameter, In.
Approxim.it>-
(. irrumfiT-
ence, In.
Weight
per Ft.. Lb.
Safe Working
Load for
Hoisting, L,
Lo.
Approximate
Breaking •
Strew, Lb.
Safe Working
Stress for
Direct Pull.
5, Lb.
Minimum
Size of Drum
or Sheave. Ft.
ai
8
11-95
550,000
91,700
14 *
ai
7
9.85
458,000
76,300
12$
2\
7
8.00
I
372,000
62,000
II
2
6:
6.30
E
*->
280,000
47,700
9l
if
s!
4.85
do
224,000
37,300
H
c
'
5
4.15
K3
a
188,000
31,300
7l
IT
4*
3-55
J
164,000
27,300
7
ii
4i
3.00
I
144,000
24,000
6!
I{
4
2-45
03
116,000
19,300
6
ii
Si
2.OO
II
94,000
15,700
5
i
3
I.58
76,000
12,700
4i
1
ai
1. 2O
~
58,000
9,700
4
$
2'
I
0.89
0
46,000
7,700
3i
1
•>
2
O.62
w
31,000
5,170
ai
A
l|
I
0.50
6O
24,600
4,100
a
i
ii
0.39
O
20,000
3,300
2
ij
0.30
u
16,000
2,700
ij
f
ii
t
O.22
*4-«
i
11,500
1,900
If
A
i
0.15
CO
7,600
1,270
If
*
i
0.10
5,300
890
I
TABLE III.
CAST STEEL FLAT HOISTING ROPE. ULTIMATE STRENGTH, WORKING STRESS AND WEIGHT OF
FLAT WIRE ROPE COMPOSED OF 4 STRANDS, 7 WIRES TO THE STRAND.
Width and
Thickness, In.
Weight in Lb.
jer Lineal Foot.
Safe Working
Load for
Hoisting, L,
Lb.
Approximate
Breaking
Stress, Lb.
Safe Working
Stress for Di-
rect Pull, S.
Lb.
Approximate Diame-
ter in Inches of Round
Cast Steel Rope of
Equal Strength.
f xsi
3-90
IIO,OOO
18,300
lA
f xs
3-40
IOO,OOO
16,700
ij
f.x4i
3.12
94,000
15,700
iA
f X4
2.86
86,000
14,300
ii
f X3i
2.50
«
76,OOO
12,700
i
1
s X 3
2.00
6o,OOO
IO,OOO
f X 2i
1.86
0 60
56,000
9,300
|Xa
1.19
"fcc^i
36,000
6,OOO
C c
iX7
5.90
'•%£
178,000
29,700
if
iX6
5.10
i i
I54,OOO
25,700
ixsi
4.82
<2><-'i
144,000
24,000
Ii
ixs
4.27
rt **
I28,OOO
21,300
if
ix4i
4.00
C/3 ||
I2O,OOO
2O,OOO
i X4
3-30
IOO,OOO
16,700
1}
iX3i
2.97
9O,OOO
15,000
ii
iX3
2.38
72,OOO
I2,OOO
i
344 STEEL HEAD FRAMES AND COAL TIPPLES. CHAP. X.
if the cable is slack. If a descending cage should stick and then drop, the stress will be equal
to the kinetic energy developed and will be very large. The load due to starting a cage suddenly
from the bottom of a shaft may be taken as
K = 2W+R+F (i)
where K = stress in Ib. at the sheave at the instant of picking up the load;
W = gross load in Ib.;
R = weight of rope in Ib. ;
F = friction in Ib., = (W + K)f, where / = coefficient of friction, which may be taken
at O.OI to 0.02 for vertical shafts and from 0.02 to 0.04 for inclined shafts with the rope supported
on rollers. The working load should not be greater than K plus the stress due to bending, and
should not exceed ^ of the ultimate strength of the rope, or f of the ultimate strength for direct pull.
For inclined shafts with angle of inclination with horizontal = 0, the stress in the rope due
to starting the cage is
K'.= (2W + R) sine +f(W+ R) cos 0 (2)
Bending Stresses in Wire Rope. — The stresses due to bending will depend upon the diameter
of the rope, the make-up of the rope, the angle through which the rope is bent, and the diameter
of the sheave. The unit stress due to bending in a round hoisting rope may be obtained from
formula (3), the form of which is due to Rankine ("Machinery and Mill Work," p. 533).
5 = 1, 894,000 -p (3)
where D = the diameter of the sheaves in inches, and d = the diameter of the rope in inches.
The area of the steel in a round hoisting rope is approximately a = 0.4^2, and the total bending
stress in a round rope will be
d3
Sb = S-a - 757,600 ^ (4)
Now the direct breaking strength of a crucible steel round rope is closely
U = 6o,ooodz (5)
Where bending stress is considered, the safe working load should not exceed I of the ultimate
strength, and the safe working load, L, should not exceed
d3
L = 20,oood2 — 757,6oo— (6)
The safe working loads for crucible steel round ropes based on formula (6) are given in Fig. 7.*
For plough steel ropes the ultimate strength is U = 7O,oood2, and
L = 26,700^ — 757,600 j: (6')
Mr. William Hewitt in "Wire Rope," published by the Trenton Iron Company, gives the
following formula for bending, f
S> = Ea (7)
where E = the modulus of elasticity of steel, a = the area of the rope in sq. in., D = the diameter
of the sheave in inches, d' — the diameter of the individual wires in inches, and C = a constant
* Redrawn from a diagram prepared by Mr. E. T. Sederholm, Chief Engineer, Allis-Chalmers
Company.
t Also see Engineering News, May 7, 1896.
WORKING STRESSES IN ROUND WIRE ROPE.
65,000
60,000
840
5teel Hoistinq Ropes with six
strands oF nine teen wires each.
Total unit stress equals direct
stress plus bendinq stress or
equals 50,000 Ibs.per sq.in.
Working unit stress equals 50,000
minus bendinq stress.
Bendinq stress in rope equa/s:
3*1,894,000 J-
Safe Working Load in rope
equals :
d=diam. oF rope in inches .
D =diam. oFdrum in inches.
/ Z 3 4 5 d 78 9 10 II IZ 13 14 15
Diameter of Drum In Feet
FIG. 7. SAFE WORKING STRESSES, L, IN CRUCIBLE STEEL, ROUND HOISTING ROPE.
depending upon the rope, and varies from 9.27 for haulage rope to 27.81 for tiller rope. For
standard hoisting rope, C = 15.45. Substituting E = 29,000,000,
c = 0.4 d1, and d' — — , we have
D-d
Since d is very small as compared with the values of D used in hoisting, formulas (4) and (8)
give practically the same results.
346
STEEL HEAD FRAMES AND COAL TIPPLES
CHAP. X.
The bending stresses in crucible steel flat ropes are given in Fig. 8.
Cages and Skips. — For details of cages and skips, see the author's "The Design of Mine
Structures."
Hal Steel Hoisting Ropes, Four
strands oF seven wires each.
Total unit stress equals direct
stressplus bending stress or
equals 50,000 Ibs per sq.in.
Working unit stress equals 50,000
minus bendinq stress.
Bending stress in rope equals
~ 14, 200,00 O'd
K
d^diam. of each wire in inches
-.05575 fors S. 0615 for f rope.
CJ L *
R- Radius of hub in inches.
7
W/'/.
36,000
U,000
28,000
26,000
24,000
Z?,000
J?,000
10,000
8,000
6,000
4,000
2,000
50 36 42 43 54 60 66 7Z
Diameter of fee/ Hubs jn Inches
FIG. 8. SAFE WORKING STRESSES, L, IN CRUCIBLE STEEL, FLAT HOISTING ROPE.
Sheaves and Safety Hooks. — For details and data on sheaves, safety hooks, etc., see the
author's "The Design of Mine Structures."
EXAMPLES OF STEEL HEAD FRAMES.— The detail plans for three steel head frames
taken from the author's "The Design of Mine Structures" are excellent examples of steel head
frames. Data on 16 steel head frames are given in Table V.
EXAMPLES OF STEEL HEAD FRAMES.
347
Steel Head Frame for the Diamond Mine. — The details of the steel head frame of the
mini are shown in Fig. 9. The Diamond head frame is 100 ft. high from the collar
<>(' (lu- shaft to the center of the sheaves. The shaft is 2,800 ft. deep. The sheaves are 10 ft.
in ili.imrUT and carry a 7 in. X i in. flat rope. The ore is hoisted in self-dumping skips with a
capacity of 7 tons and weighing 3$ tons, and is dumped into hoppers from which it is run directly
into cars which pass beneath the head frame. The main front columns and back braces are
3/DE EiEVflT/OM
h- 38-0----*
fwNT ELEWT/ON
FIG. 9. STEEL HEAD FRAME FOR DIAMOND MINE, Bun/r BY THE GILLETTE-HERZOG MFG. Co.
made of built-up sections consisting of one cover plate 20 in. X ^t in., two plates 1 8 in. X A in.,
4 angles 3$ in. X 3$ in. X i in., with lacing bars on the inner side 4 in. X I in. The main diagonal
bracing is made of two channels laced. The total weight of the structural steel in the head frame
proper was 292,000 lb., while the steel work in the bins weighed 26,000 Ib. At 40 cts. per hour
the cost of shop labor on the structural steel was 1.09 cts. per lb. The cost of erection, everything
being riveted, was $11.20 per ton.
Steel Head Frame for the New Leonard Mine. — The steel head frame shown in Fig. 10 was
built by the American Bridge Company for the New Leonard mine of the Boston & Montana
Copper Company, Butte, Montana. The head frame is of the A-type, and is 140 ft. high from
348
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
the collar of the shaft to the center of the sheaves. The mine has a four compartment shaft, two
of the compartments being used for hoisting ore. The mine is now 1,697 ft. deep, but the head
frame was designed for an ultimate depth of 3,500 ft. The ore is hoisted in five-ton self-dumping
skips with a single deck cage above the skip. The skips weigh 7,500 Ib. each. Four-deck cages
are used for hoisting men. The hoisting rope is i| in. in diameter, a round hoisting rope being
an innovation in the Butte district. The rate of hoisting is 2,800 ft. per minute. The skip ore
bins have a capacity of 150 tons. From the skip ore bins the ore runs into railroad ore bins (not
shown in Fig. 14), 26 ft. 9 in. wide by 150 ft. long, with a capacity of 1,500 tons. The sheaves are
12 ft. in diameter, and are placed 5 ft. 10 in., center to center.
The main posts are made of two channels 12 in. @ 205 Ib., with a cover plate 16 in. wide
and ^g in. and | in. thick, with lacing on the inner side. The back braces for the lower two
panels are made of channels 12 in. @ 30 Ib., with a plate 16 in. X f in.; the third section is made
of two channels 12 in. @ 30 Ib., with a plate 16 in. X TS in., while the two upper sections are
made of channels 12 in. @ 2o| Ib., laced on both sides. The main struts and diagonal braces are
made of two channels, with battens top and bottom. The skip guides are made of two channels
12 in. @ 20^ Ib. The main girder at the top of the back brace consists of one plate 36 in. X 1 in., and
four angles 4 in. X 4 in. X I in. The skip bins are supported on columns made of two channels
10 in. @ 15 Ib., laced on both sides. Where two channels are used for a section, the flanges are
turned out. The New Leonard head frame is one of the highest in the country, and is one of the
best designed frames that has been constructed. The shipping weight of the structural steel in
this head frame was 346,425 Ib.
Tonopah-Belmont Steel Head Frame. — The Belmont shaft of the Tonopah-Belmont Mining
Co., Tonopah, Nevada, is at present 1,420 ft. deep. It has three compartments, one for the
ladder-way and pipes and two for hoisting. Double-deck cages of the Leadville type are used
for hoisting, but the use of skips is contemplated later. The head frame, Fig. u, is of the A-type,
and the height is 75 ft. from the base to the center of the sheaves. The hoisting drum is placed
100 ft. from the center of the shaft.
TABLE IV.
ESTIMATE OF WEIGHT OF 75-FT. STEEL HEAD FRAME, TONOPAH-BELMONT MINING Co.
Member.
Weight in Lb.
Total Weight,
Lb.
Detail? in
Per Cent of
Main Members.
Main Members.
Details.
Back braces
9,170
3,590
5,440
2,936
1,790
2,627
3,263
J,466
8,065
6,673
4,150
2,790
1,250
2,582
440
1,015
2,179
613
2,279
414
13,320
6,380
6,696
5,518
2,230
3,642
5,442
2,079
io,344
7,087
43
77
23
82
25
I9
67
43
28
6
Front posts
Girders
Diaphragms
Channels
Angle struts
Channel struts
Stringers
Angle bracing
Steel girders
Total
45,026
17,712
62,738
39-4
The sheave wheels are of the bicycle pattern with a diameter of 84 in. at the center of the
rope groove, and an over all diameter of 91 in. Each wheel has 16 spokes of if in. rolled iron
rods. The spokes are cast at their inner ends into two rings 16 in. in diameter and 3 in. wide,
so that they form integral parts of the hub, which is 12 in. in diameter and 16 in. long, while the
outer ends are cast into bosses on the inside of the ring. The rolled steel shafts are 16 in. in
diameter at the central portion with bearings 5 in. in diameter, and are 12 in. long. The rope
grooves are turned in hard maple blocks fastened in a recess in the rim. The total weight of
the sheaves is 2,950 Ib. each.
u,
9
i
£
^.
\
3
*
w
X
o
I
C<\ (V
> «:
* ' &
/$
,VV<Y *
350
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
The head frame is designed so as to give a factor of safety of 8 when there is on each sheave
a load of 100,000 Ib. The head frame is sufficiently strong and rigid to permit of hoisting loads
of 7 tons from a depth of 2,000 ft. at a speed of 1,000 ft. per minute without appreciable vibration
during the most severe period of starting and acceleration.
TABLE V.
DATA ON STEEL HEAD FRAMES.
Description.
Depth of
Mine, Ft.
°"e
£§"
Mg J
%**
Diameter of
Sheaves,
Ft. In.
<~ y «
O.S1-1
& " 3?
HI
Method of
Hoisting.
Weight of
Weight of
Ore, Lb.
Rate of
Hoisting.
Weight of
Head Frame,
Lb.
Skip,
Lb.
Cage,
Lb.
Ft.
per
Min.
Tons
per
Day.
I
2
3
4
5
6
7
8
9
10
ii
12
13
H
15
16
Sibley Mine, Ely, Minn.. .
High Ore, Butte, Mont.. .
Diamond, Butte, Mont.. .
New Leonard, Butte,
Mont
726
(de-
signed
for
2,000)
2,800
2,800
1,679
/de-
signed
for
3,500)
225
I4O-O
100-0
IOO-O
140-0
76-0
55-0
90-0
75-o
60-0
50-0
50-0
70-0
55-o
58-8
"9-3
97-o
I2-O
IO-O
IO-O
I2-O
6-0
5-o
7-0
7-0
7-0
7-0
7-0
IO-O
7-0
IO-O
12-0
IO-O
If
7X£
7X£
ii
i*
3iXi
if
i
ij
7Xi
it
Vxi
i*
7X§
Skips
Skips
Skips
Skips
Skips
5,000
7,000
7,000
7,Soo
3,700
3,500
14,000
14,000
I4,OOO
IO,OOO
6,700
15,200
work-
ing
load
10,000
2,OOO
I,OOO
I,OOO
2,8OO
I,2OO
I,2OO
576,663
292,OOO
3l8,OOO
346,425
79,000
Inland Steel Co., Hibbing,
Minn
Elkton, Elkton, Colo
Cia. Minera de Penoles,
Bermejillo, Mex
1,000
1,420
1,700
2,000
Skips
5,ooo
80,000
63,000
35,250
42,000
42,200
79,000
45,000
74,700
839,000
117,000
Tonopah-Belmont, Tono-
pah, Nev. .
I,OOO
I,OOO
2,OOO
500
Copper Queen, Bisbee,
Ariz
Skips
Cages
Skips
Skips
Skips
Skips
Skips
Skips
5,990
I,2OO
3,700
2,400
Union Shaft, Virginia, Nev.
Speculator, Butte, Mont..
Basin & Bay State, Basin,
Mont
Steward, Butte Mont
10,000
14,000
1 68
cu. ft.
14,000
Anaconda, Butte, Mont. .
Quincy Rock House, No.
2, Hancock, Mich
St.Lawrence,Butte,Mont.
2,400
6,000
(in-
chned
57°)
2,100
7,000
10,000
7,000
I,OOO
I,OOO
I,2OO
2,400
I,2OO
The head frame was built by the Koken Iron Works, St. Louis, Mo., was made of structural
steel furnished under standard specifications, and was fully riveted up in place with pneumatic
hammers. The shipping weight of the structural steel was 63,000 Ib.
The hoist is placed loo ft. from the shaft, and is a Wellman-Seaver-Morgan double drum
electric hoist with drums having 64 in. diameter and a face 36 in. wide between flanges. The
hoist is designed to operate in or out of balance and is capable of handling a load of 12,000 Ib.
at a speed of 1,000 ft. per minute. The hoisting rope is a six strand, nineteen wire, plow-steel
rope, I in. in diameter, that weighs 1.58 Ib. per ft., and each rope is 1,700 ft. long. The diameter
TONAPAH-BELMONT STEEL HEAD FRAME.
801
352 STEEL HEAD FRAMES AND COAL TIPPLES. CHAP. X.
of the drum at the hoist is 64 in., but the rope winds twice around the drum, so that the diameter
is 66 in. near the end of the lift. With proper allowance for bending stresses the working stresses
under the most severe conditions do not exceed the working load of 7.6 tons as given by the manu-
facturers of the wire rope.
Estimate of Weight of a Steel Head Frame. — A summary of a detailed estimate of the 75 ft.
steel head frame built by the American Bridge Company at Tonopah, Nev., is ;given in Table IV.
The details are 39.4 per cent of the weight of the main members. The rivet heads are 4.1 per cent
of the weight of the structure.
For additional examples of steel head frames, see the author's "The Design of Mine Struc-
tures."
COAL TIPPLES. — The design of a coal tipple depends upon the quality of the coal, upon
whether the coal is hoisted from the shaft or is taken from a drift or tunnel, and upon the work
that it is necessary to do in order to prepare the coal for the market. The coal tipple for a bitumi-
nous mine in which the coal is hoisted from a shaft, consists of a head frame and a shaker structure
or tipple proper where the coal is weighed and screened. A coal tipple for an anthracite mine
ordinarily consists of a head frame with storage bins into which the coal is run without crushing
or screening; the coal being prepared for market in a separate breaker building. Where bituminous
coal is dirty or contains a large amount of refuse material it is sometimes cleaned in a washer
building, or is broken, sized and cleaned in a coal breaker.
With a double compartment shaft the shaking structure, or tipple proper, is usually placed
with its axis at right angles to the center line of the two compartments. The hoisting ropes
may be either parallel to the axis of the tipple, in which case the head sheaves are parallel; or
may be placed at right angles to the axis of the tipple, in which case the sheaves are placed in
tandem. The coal may be run through rotary screens, or over shaking screens as is now the
common practice. Shaking screens are usually divided into sections and are driven by eccentrics
placed 1 80 degrees apart. The shaking screens do not ordinarily weigh more than two to three
tons empty or four to six tons when loaded, but are driven with a velocity of 100 to 150 strokes
per minute, with a length of stroke of from 4 to 12 in. and the shaking motion makes it necessary
to design the shaker structure with great care in order to reduce the vibration. The best modern
practice in the design of coal tipples is to make the head frame and the tipple, or shaker structure,
entirely separate and independent units.
Sizing Coal. — The object in sizing coal is to separate the dirt and slack from the coal, and
to obtain a product that can be burned more advantageously than unsized coal. A compact
coal will not admit the air and will burn on the surface, and it is therefore an advantage to have
the lumps of approximately equal size. The sizes and names of the different grades of coal differ
considerably in different localities.
Types of Coal Tipples. — Coal tipples may be classed under three types, depending upon the
manner in which the coal is brought to the tipple; (i) hoisting in cages or skips from vertical or
slightly inclined shafts; (2) cage hoisting on an incline either from a shaft, or on a bridge, or from a
tunnel; (3) conveyor hoisting either from the mine or from a head bin into which the coal has
been dumped from cars or skips.
The design and operation of coal tipples will be illustrated by describing three steel coal
tipples, (i) Steel Coal Tipple for the W. P. Rend Coal Company — vertical hoisting with self
dumping cages and shaking screens; (2) Spring Valley No. 5 Steel Coal Tipple — vertical hoisting
in cages, with Ramsey transfer and shaking screens; and (3) Phillip's Coal Tipple — vertical
hoisting with self dumping cages dumping into a storage bin.
Steel Coal Tipple for W. P. Rend Coal Company.— The steel coal tipple for the W. P. Rend
Coal Company, Rendville, 111., has the head frame covering four tracks, with provision for four
extra tracks on the opposite side of the center line of the head frame. The steel head frame is
79 ft. 6 in. from the collar of the shaft to the center of the sheaves. The sheaves are 8 ft. in
diameter and carry a i f in. hoisting cable.
COAL TIPPLE FOR W. P. REND COAL COMPANY.
24
354
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
•^
E>w/tty
flmerican Bridge
Designedly
W.Morjva,
Chicago.
H
-4
|L^|
>
|»l J
-i I sj
H
. i
EXAMPLES OF STEEL COAL TIPPLES.
Operation of Coal Tipple. — Detail plans of the shaking screens and tipple equipment are
>h..u 11 in Fig. 12. The coal is raised from the mine in self dumping cages and is dumped into two
\v»-ii;li hoppers having a capacity of four tons each. From the weigh hoppers the coal passes
through a dump chute, and may be run directly into cars on the track or may be run over shaking
M-riviis. The first section of the shaking screens is 29 ft. 9 in. long, the top deck, having a length
of 16 ft., has f in. round perforations; the middle, having a length of 18 ft., has 2 in. round perfora-
tiim>, the l>ottom plate being solid. The upper deck of screens sloping toward the head frame
has perforations 3J in. to 2 in. round; the second deck has perforations 2j in. to 3 in. round; the
third plate deck has perforations f in. round, the bottom deck being solid. The coal passing
over the 2 in. and 3J in. round perforations of the main screen may be run back over the shaking
screens just described, or may be run over the second shaking screen 27 ft. 4 in. long and 8 ft. widf.
This shaking screen has a length of 8 ft. with perforations 6 in. in diameter. By making different
combinations of the screens different grades of coal can be obtained, as is shown in Fig. 12. The
shaking screens are carried on rollers 12 in. in diameter, which are operated by eccentric connecting
rods with a 12 in. stroke. These rollers give the shaking screens a motion in two directions and
give much more satisfactory results than the earlier method of suspending the shaking screens
from overhead supports. .The capacity of the tipple is 2,500 tons in eight hours.
The tipple was designed and constructed by the Wisconsin Bridge & Iron Company, and
the tipple equipment was furnished by the Link-Belt Company.
Steel Coal Tipple at Spring Valley Shaft No. 5. — The steel coal tipple constructed at Spring
\ alley shaft No. 5, Spring Valley, Illinois, is one of the best examples of steel tipple construction
for bituminous mines. The stSel tipple building is 187 ft. long, 36 ft. wide and 35 ft. from the
track level to the level part of the main tipple floor. The steel head frame is 75 ft. and 85 ft.
6 in. from the track level to the centers of the sheaves, respectively. The sheaves are 10 ft. in
{1-4*3.
-ftf-
5iD£ ELEVQTION. FMNT ELEVATION.
FIG. 14. STEEL HEAD FRAME, SPRING VALLEY COAL TIPPLE, SHAFT No. 5.
356
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
diameter and are placed tandem with the hoisting rope, and at right angles to the axis of the
main tipple building. The hoisting rope is crucible steel if in. in diameter. The steel tipple
building and head frame are covered with No. 18 galvanized corrugated steel carried on steel
purlins. Detail plans of the tipple structure are given in Fig. 13 and of the head frame in Fig. 14.
The head frame and tipple building are fully braced and make a very rigid structure. The main
track floor of the tipple is level over the first five panels on the left of the structure, the remainder
of the floor having a pitch of 4 in. in 17 ft. The tipple floor is covered with 4 in. planking spiked
to 4 in. nailing strips which are carried on I-beam joists. The weight of the structural steel,
including the corrugated steel but not including tipple equipment, was 415,530 Ib.
\wfo//ofPP~-^ Levet--^ . KkhfperB^ofl?-'0'orli%-^ _, ~~^p^j^,a &_ _ V> . „.,
^J_eve/-^ Pitch 4'~pef fay or ?°/o 1 ^ — ^2^'^iMchc7r^^^^y'.
ELfvfiTioN or TOP LINE or'PniL "~^l
^-..iy.,._/^l^.-y^^^j^ W ff ifff
-\ -fe;_ T :i^?ur^lf T'- jT^p-y-j ~j-
- i "1 i i t l\ ^"1 I "T^ i "f
FIG. 15. PLAN OF TIPPLE TRACKS, SPRING VALLEY No. 5 COAL TIPPLE.
Operation of Tipple. — The detail track plan is shown in Fig. 15; the operation of the Ramsey
transfer is shown in Fig. 16, and the arrangement of the shaking bar screens is shown in Fig. 17.
Two coal cars containing if tons each are hoisted on the shaft cage. The loaded cars are pushed
off the cage and two empty cars are pushed on the cage by means of a steam pusher, as shown in
Fig. 16. From the cage platform the loaded cars run by gravity on a if per cent grade to the
dumps, where the coal is dumped by Phillips automatic tipples or dumps. After dumping, the
cars pass to the right by gravity on the 10 per cent descending grade and are stopped by a 2 per
cent ascending grade and a short piece of track. The cars then return by gravity, and may either
be switched to the outside tracks or run back on the transfer tracks. The empty cars are run on
the platform of the Ramsey transfer and are raised by a steam cylinder a height of 4 ft. 7 in. to
the level of the floor of the shaft cage, and are ready to be shoved on the cage by the steam pusher.
The coal is dumped by the Phillips tipple dumps into one of two weigh hoppers 5 ft. wide,
as shown in Fig. 17. After the coal is weighed it runs out of the weigh hopper on a converging
chute having a slope of 30 degrees with the horizontal. From the converging chute the coal
runs over shaking bar screens 6 ft. 6 in. wide, the bars being placed | in. apart. The fine coal
passing through this screen runs over a f in. shaking bar screen and is chuted into the cars. The
slack passing through the f in. bar screen is run directly into the cars. From the | in. shaking
bar screen the lump coal passes through a converging chute and over a bar screen 5 ft. 6 in. wide
with the bars spaced 5 in. apart, from which the lump coal is run into cars. It will be noted that
five grades of coal are obtained: mine run coal; lump coal passing over the 5 in. screen; coal passing
the 5 in. screen and retained on a f in. screen; nut coal passing a f in. screen and retained on a f in.
screen, and slack.
The capacity of the coal tipple is from 1,800 to 2,000 tons per day. The tipple was designed
by Mr. W. Morava, Consulting Engineer, Chicago, 111., and was built by the American Bridge
Company in 1900.
Steel Coal Tipple for the Phillips Mine. — The steel coal tipple at the Phillips mine of the
H. C. Frick Coke Company is an excellent example of a modern coal tipple for handling bituminous
coal. Detail plans of the coal tipple are shown in Fig. 18. The steel head frame is of the 4-post
EXAMPLES OF STEEL COAL TIPPLES.
±*r
T"
358
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
EXAMPLES OF STEEL COAL TIPPLES.
808
360
STEEL HEAD FRAMES AND COAL TIPPLES.
CHAP. X.
type, and is 107 ft. from the collar of the shaft to the center of the sheaves. The main tower of
the head frame has six posts made of 4 Z's 3 in. X 2 fl in. X f in. with one plate 6 in. X f in. The
back braces consist of three columns having the same section as the main posts. The head frame
is fully cross-braced with angle struts, as shown in Fig. 22. The batter of the main tower columns
is I in. in 12 in., while the back brace makes an angle of 30 degrees with the vertical. The sheaves
are 10 ft. in diameter and are supported on I-beams, resting at the end nearest the engine house
on a built-up frame of angles and plates carried on two 15 in. I-beams, so as to make the necessary
clearance for the sheaves. The roof trusses above the sheaves carry two I-beams, on the lower
flanges of which are trolleys arranged for the attachment of chain blocks for placing and re-
placing the sheaves. The shipping weight of structural steel, including the corrugated steel, was
569,500 Ib.
TABLE VI.
DATA ON STEEL COAL TIPPLES.
Depth of
Mine, Ft.
Height of
Head Frame,
Ft. In.
Diameter
Sheaves,
Ft. In.
Size of Hoist-
ing Rope, In.
Method of
Hoisting.
Weight of
Cage Skip,
Lb.
Weight of
Coal, Lb.
Rate of
Hoisting.
Weight of Struc-
ture in Lb.
Ft.
per
Min.
Tons
per
Day.
Phillips Coal Tipple,
Pennsylvania
268
I,IOO
107-0
66-0
65-9
, 74-3
85-6
\ 83-0
/ 95-0
79-6
90-0
IO-O
14-0
IO-O
IO-O
I2-O
8-0
9-0
r3
ls
2
If
If
Self
dump-
ing
cages
4,000
work-
d each
rtment
6 tons
per
min.
569,500
Philadelphia & Read-
ing, Gilberton
4O,OOO
ing loa
compa
2,300
Cars
2,000
2,000
200
tons
per
hour
2,500
l8o,OOO
5OO,OOO
[Head
j Frame 100,000
[ Shaker 56,000
355,400 Struc-
tural steel
16,800 Corru-
gated steel
171,200 Struc-
tural steel
31,300 Corru-
gated steel
117,200 Struc-
tural steel
10,300 Corru-
gated steel
Cardiff No. 2, Cardiff,
111
Spring Valley No. 5,
Spring Valley, 111. . .
Cars
Self
dump-
ing
cages
Cars
Cars
Cars
2,000
8,000
Alberta Railway & Ir-
rigation Co., Leth-
bridge, Alta
|ooo
Rend Tipple, Rend-
ville, 111. . .
Carbon Tipple, Car-
bon Montana
R. F. C. Co. Tipple,
Adontana .
Gebo Tipple, Montana
The coal is hoisted in self-dumping cages which dump the coal into distributing chutes, in
which it runs by gravity to the bins having a capacity of 800 tons. The coal, being all used for
making coke, is not screened or weighed.
The storage bins are built with a steel framework and are lined with \ in. buckle plates on
the sides, and have a f in. plate floor. The sides are supported by the 15 in. I-beams @ 42 Ib.,
spaced 3 ft. 5i in. center to center. The inclined bottom framing consists of girders having 48
in. X | in. web plates and flanges composed of two angles 6 in. X 6 in. X TS in., and are tied together
with ties consisting of two angles 8 in. X 8 in. X f in. and one plate 17 in. X 2 in. at the bottom,
SPECIFICATIONS FOR STEEL MINE STRUCTURES.
and 15 in. I -brains @ 42 Ib. at the top, the girders being spaced 3 ft. sJ in. center to center. The
in. tin M<lr ninU-rs are composed of two I-beams 15 in. @ 42 Ib., and one channel 15 in. @ 33 Ib.
Tin- || in. pl.itr floor is carried on 12 in. I-bcams spaced about I ft. 6 in. centers. The steel plate
floor is placed at a slope of 8 in. in 12 in., and it is stated that 95 per cent of the coal can be with-
dr.iwn from the bin. The bins discharge through vertical gates in the sides into motor-driven
larrirs, which run to the coke ovens. The vertical gates arc raised by rack and pinion and chain
\\hrt 1>.
Data on ten steel coal tipples are given in Table VI. For additional examples and data on
steel coal tipples, see the author's "The Design of Mine Structures."
SPECIFICATIONS FOR STEEL HEAD FRAMES AND COAL TIPPLES, WASHERS
AND BREAKERS.*
PART II.
BY
MILO S. KETCHUM,
M. Am. Soc. C. E.
1912
GENERAL DESCRIPTION.
198. Types of Structure. — The structure shall be of a type that will give maximum rigidity
and strength. The structure shall be of a type in which the stresses can be calculated either by
statics or by taking into account the deformations of the members.
199. Bracing. — All bracing shall be stiff, and shall be riveted together at all intersections to
give maximum rigidity.
200. Proposals. — Contractors in submitting proposals shall furnish complete stress sheets,
general plans of the proposed structures, giving sizes of material, and such detail plans as will
clearly show the dimensions of the parts, modes of construction and sectional areas.
201. Detail Plans. — The successful contractor shall furnish all working drawings required
by the engineer free of cost. Working drawings will, as far as possible, be made on standard
size sheets 24 in. X 36 in. out to out, 22 in. X 34 in. inside the inner border lines.
202. Approval of Plans. — No work shall be commenced or materials ordered until the working
drawings are approved in writing by the engineer. The contractor shall be responsible for dimen-
sions and details on the working plans, and the approval of the detail plans by the engineer will
not relieve the contractor of this responsibility.
LOADS.
203. The structures shall be designed to carry the following loads without exceeding the
permissible unit stresses.
204. Dead Loads. — The dead loads shall consist of the weight of the head sheaves, sheaves,
blocks and girders, the weight of the structure, and all concentrated machinery and equipment
loads.
205. Working Loads. — The working loads on head frames for, vertical shafts shall be taken
as equal to
K = 2W+± R + (W + R)f (i)
where K = the working stress in Ib. at the head sheave at the instant of picking up the load;
W = the gross load of the cage or skip and the load of ore or coal in Ib. ; R = the weight of the
rope from the head sheaves to the bottom of the shaft in Ib. ; and / = coefficient of friction of the
rope, skip and sheaves, which may be taken at o.oi to 0.02 for vertical shafts and 0.02 to 0.04 for
inclined shafts with ropes supported on rollers.
206. For inclined shafts the working load shall be taken as
K' = (aW + R) sin 6+ f(W +R) cos 9 (2)
where 9 = the angle of inclination of the shaft with the horizontal.
* From Specifications for Steel Mine Structures as printed in the author's "The Design of
Mine Structures." Part I is "Specifications for Steel Frame Buildings" as printed in Chapter I.
362 STEEL HEAD FRAMES AND COAL TIPPLES. CHAP. X.
207. Breaking Load. — The head frame shall be designed for a load in one or all of the hoisting
ropes equal to the breaking stress of the hoisting rope as given in the manufacturer's catalog.
208. Machinery Loads. — The stresses due to machinery, crushers, tipple equipment, etc.,
shall be considered the same as the stresses due the working or live load.
209. Wind Loads. — Where the head frame or tipple is enclosed the wind load shall be assumed
as 30 Ib. per sq. ft. of exposed surface acting horizontally. Where the framework is open the
wind load shall be taken as 50 Ib. per sq. ft. acting on the projection of the members of the head
frame or tipple. In calculating the stresses due to wind, the wind loads may be assumed as
applied at the joints of the structure. Where one side of the structure is open so that a deep cup
or pocket is formed the wind load shall be taken as not less than 60 Ib. per sq. ft. on the projection
of the cup-like surface.
210. Snow Loads. — Snow loads shall be taken the same as for steel frame buildings.
ALLOWABLE UNIT STRESSES.
211. Steel head frames, coal tipples, coal washers and breakers, and similar structures shall
be designed for the following allowable stresses.
212. Dead Load Stresses. — The allowable unit stresses for dead loads shall be the same as
for steel frame buildings given in "Specifications for Steel Frame Buildings." Snow loads shall
be considered as dead loads.
213. Working Load Stresses. — The allowable unit stresses for working loads shall be one-half
the allowable unit stresses for dead load stresses as given in "Specifications for Steel Frame
Buildings."
214. Bins. — Bins shall be designed for two thirds the allowable unit stresses for dead load
stresses as given in " Specifications for Steel Frame Buildings."
215. Breaking Load Stresses. — The allowable unit stresses for the maximum stresses due
to breaking one or all the hoisting ropes shall be equal to the allowable unit stresses for dead load
stresses, plus 50 per cent, equal to three times the allowable unit stresses for working loads. The
breaking loads and working loads for any shaft compartment or machine need not be assumed
as acting together.
216. Machinery Load Stresses. — The allowable unit stresses for the maximum stresses due
to machinery and moving loads shall be the same as the allowable unit stresses for working loads,
equal to one half the allowable unit stresses for dead load stresses.
217. Wind Load Stresses. — The allowable unit stresses when the wind load stress is com-
bined with the dead load stress plus twice the working load and machinery load stresses shall not
exceed the allowable unit stresses for dead loads by more than 25 per cent. If the sum of the
wind load unit stress, the dead load unit stress, and twice the working load and machinery load
unit stresses exceed the allowable unit stress for dead loads by more than 25 per cent the area of
the section shall be increased to reduce the actual stresses to within the prescribed limit. Wind
load stresses need not be combined with breaking load stresses.
218. Reversal of Stress. — Members subject to a reversal of stress due. to a combination of
dead load stresses and working load stresses shall be designed to take both tension and com-
pression, each stress being increased by one half the smaller of the two stresses. Members subject
to a reversal of stress due to wind stress combined with dead load stresses and working load
stresses, or breaking load stresses combined with dead load stresses shall be designed to carry
both stresses.
EQUIPMENT.
219. Skips and Cages. — Skips and cages shall be made of structural steel, as shown on the
detail drawings. They shall be provided with guide shoes and safety devices. For inclined
shafts the wheels shall have phosphor bronze bushings.
220. Safety Detaching Hooks. — All skips and c|ges shall be provided with effective detaching
hooks. The case shall be designed to take the stress due to a loaded cage or skip dropping a
vertical distance of two feet.
221. Bin Gates. — Unless otherwise specified all bin gates shall be of the undercut ^ type.
All gates shall be equipped with operating mechanism so that they can be opened in service by
one man.
222. Screens. — Fixed screens shall be made of bars as shown on the drawings and shall be
supported so that the bars will not be permanently deflected under the load. The screen bars
shall be placed at an angle so that they will screen the ore or coal without choking up.
223. Shaking screens shall be carried on rollers and be driven by eccentric connecting bars.
They shall be placed at proper slopes, and shall be provided with all necessary gates. Unless
otherwise specified the screens shall be made of structural steel.
224. Rotary screens shall be made of structural and machinery steel, and shall perform the
work required by the specifications.
SPECIFICATIONS FOR STEEL MINE STRUCTURES.
225. Coal Tipples or Dumps. — Coal tipples or dumps shall be provided as shown on the detail
plans or called for in tin- specifications.
226. Dumping Devices. — Where self-dumping skips or cages are used an efficient and satis-
l\n lory (lumping device shall be provided.
227. Head Sheaves. — The head sheaves shall be substantial with the top flanges turned
smooth and true to receive the hoisting rope. The sheave wheel shaft shall be of the best grade
of machinery steel of ample strength, carefully and truly made. The sheave boxes shall be lined
with the l>est quality of anti-friction metal and shall be adjustable to take up the wear. Unless
otherwise specified the sheave wheels shall have wrought iron spokes.
228. Landing Stage. — An efficient landing device shall be furnished.
DETAILS OF CONSTRUCTION.
229. Unless otherwise provided for the details of construction are to be the same as for
steel frame buildings.
230. Design. — In designing head frames, coal tipples, coal washers and breakers and similar
structures care shall be used to strongly brace the different parts of the structure in order that it
may be rigid. Preference shall be given to types of structures that are statically determinate.
Where 4-post head frames and other statically indeterminate structures are used the stresses shall
be calculated by taking account of the deformation and distortions of the members.* All bracing
is to be made of stiff members; the use of rods or bars will not be permitted, except for sag rods
and anchors. It is very important that head frames, coal tipples, coal washers and breakers and
similar structures be made very rigid.
231. Lengths of Compression Members. — The length of compression members in head
frames and shaker structures shall not exceed 100 times the least radius of gyration for main
members nor 140 times the least radius of gyration for secondary bracing.
232. Lengths of Tension Members. — The length of tension members in head frames shall
not exceed 150 times the least radius of gyration for main members, nor 200 times the least radius
of gyration for secondary bracing. The length of a tension member is to be taken as the distance
center to center of end connections.
233. Splices. — All splices in main members shall be designed to carry the full strength of
the member.
234. Reaming. — The rivet holes for all field splices shall be punched to a diameter ^ in. less
than the finished hole and shall be reamed to the required size with the members bolted in place
with an iron templet. All metal more than f in. thick shall be punched and reamed, or be drilled
from the solid.
235. Minimum Thickness of Metal. — The minimum thickness of metal in plates and sections
shall be fg in., except for fillers.
236. Erection. — All field connections shall be riveted. Before the riveting is begun all field
connections shall be fully drawn up with field bolts, in not less than one-half the holes of each
joint.
237. Materials and Workmanship. — All materials and workmanship shall comply with the
Specifications for Steel Frame Buildings unless otherwise specified.
238. Painting. — All steel work shall receive one coat of satisfactory graphite or carbon paint
at the shop. Before erecting all abraded spots shall be touched up, and all rivet heads shall be
painted as soon as accepted by the inspector. After the erection is complete all structural steel
work shall be given two coats of satisfactory graphite or carbon paint. The three coats of paint
shall be of different colors.
REFERENCES. — For additional data for the design of head frames, rock houses, coal tipples
and other mine structures, and for numerous examples of structures, see the author's ' The
Design of Mine Structures." This book gives the calculation of stresses in head frames, and also
gives a full discussion of the details of design of mine structures, including specifications, methods
of construction and costs.
* For the calculation of the stresses in mine structures, see the author's "The Design of Mine
Structures."
CHAPTER XI.
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS.
DATA FOR DESIGN. — The following data will be of assistance in the design of steel
stand-pipes and rlrv.nnl tanks on towers. For definitions of stand-pipes and elevated tanks
on towers, see the specifications in the latter part of this chapter.
Notation: —
h = distance in ft. of any point below the top of the stand-pipe or elevated tank;
d = diameter of the stand-pipe or elevated tank in feet;
r = radius of the stand-pipe or elevated tank in feet;
/ = thickness of the shell in inches at any given point;
P = hydrostatic pressure in Ib. per sq. in. at any point = 0.434/1;
S = stress per vertical lineal inch of stand-pipe;
s = unit stress in Ib. per sq. in. in vertical section of stand-pipe;
5' = stress per horizontal lineal inch of stand-pipe;
s' = unit stress in Ib. per sq. in. in horizontal section of stand-pipe;
S" = stress per lineal inch along a circumferential line, due to wind;
s" = unit stress in Ib. per sq. in. in circumferential line, due to wind.
Formulas for Stresses in Stand-Pipes. — The stress per lineal vertical inch of stand-pipe is
= 62^-d _
2 X 12
The stress per sq. in. is
s = 2.6h-dft (2)
The stress per horizontal lineal inch of stand-pipe due to the weight of stand-pipe W, is
S' = W/(i2ir'd) = o.026W/d (3)
The stress per sq. in. is
s' = o.026W/(d'f) (4)
For ordinary conditions the wind pressure is taken at 30 Ib. per sq. ft. acting on two-thirds
of the surface, or 20 Ib. per sq. ft. on the entire surface; while for exposed positions the wind pressure
may need to be taken as high as 45 Ib. per sq. ft. acting on two-thirds of the surface, or 30 Ib.
per sq. ft. on the entire surface. Recent Prussian specifications require that circular chimneys
be designed for two-thirds of 25 Ib. per sq. ft. At 30 Ib. per sq. ft. acting on two-thirds of the
surface (20 Ib. per sq. ft.) the bending moment at any distance h below the top, due to wind is
M = 20 X d-h X h X 12/2 = I2od-h* (5)
where M is in in.-lb.
The stress in the extreme fiber of the shell is
s" = M-yfl (6)
Now y — I2r, I = \ir(r\* — r*4) = t-*-r* (approx. — r is in ft.1 and / in in.) = /•T-rl-i2t (in in.4).
Substituting y and / in (6)
i.o6ft*/('-<f) (7)
365
366 STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
The stress per lineal inch will be
S" = I.o6h*/d
(8)
If the allowable stress in the net section of the plate is 12,000 Ib. per sq. in., and e = efficiency
of joint, then from (2)
t = 2. 6h-d/ (12,000 X e) (9)
where values of e for different conditions are given in Table I la.
Formulas for Stresses in Elevated Steel Tanks. — The stress per lineal vertical inch of plate
is the same as in stand-pipes
S = 2.6h-d (i)
and the unit stress in vertical joints is
5 = 2.6h-d/t (2)
Stresses on Radial Joints. — Spherical Bottoms. — In a hemispherical bottom the radial
stress per sq. in., TI, "will be one-half the stresses in a cylinder of the same radius and the same
internal pressure.
TI = 2.6h-d/(2t) = 2.6h-r/t (10)
In a segmental bottom (b) Fig. I , the stress 7Y will be
TF-cscfl T
2 X I2ir'b't 247TT1'/
Now W = 62.5&-7T-&2 = 62.5&-7r-ri2-sin20, and
(II)
(12)
which reduces to equation (10) for a hemispherical bottom when r\ — r.
- A
CONICAL BOTTOM
(b) 5EGMEHTAL BOTTOM
FIG. i.
STRESSES IN ELEVATED TANKS ON TOWERS. 367
Stresses on Radial Joints. Conical Bottoms. — In a conical bottom the stress per sq. in.
Ti" will be from (a) Fig. I,
Il'-i-si- 6
„ W CSC 9
2r,-T-l2/
Now
W =• 62.5* -TTi1,
and
= 2.6h-ri-cscO/t (15)
Stresses on Circumferential Joints. Conical Bottoms. — In (a) Fig. i» pass two horizontal
planes through the cone so that the intercept along the cone will be a unit in length. The tapered
ring cut away has a pressure of p' Ib. per lineal inch. This pressure p' may be resolved into a
pressure along the element of the cone, p\ = p' cot 9, and a Horizontal pressure, p* = p' esc 6.
The stress in circumferential joint will be •
Ti" = I2pt-ri/t = i2p'-ri-caceft
= 12 X o.434A-ri-csc0//
= 5.2/1 TI- csc 0/* (16)
which is twice the stresses in the radial joints.
Stresses in Circumferential Joints. — Spherical Bottoms. — The radial unit stress in a hemi-
spherical bottom is given by equation (12). Now in a segment of a spherical shell the curvature
is the same in all directions, and the unit stress on a circumferential joint will be the same as on
a radial joint, and
TV = 7Y = 2.6* T,// (17)
Connection Between Side and Bottom Plates. — With a conical bottom the inclined pull per
lineal inch at the bottom of the circular tank will be from (15)
TV" = 2.6* T csc 0. (18)
The compressive stress in the horizontal ring will be due to the horizontal components of the
inclined stresses and will be
P' = Ti" cos 6-r X 12
= 3i.2*-r*-cot 0 (19)
There are no inclined or compressive stresses in a hemispherical bottom unless the circular
shell and the hemispherical bottom are joined by an elliptical segment. If the radius of the
circular tank divided by the radius of the segment = 2, there will be no secondary stresses (see
"Stresses in Tank Bottoms," by Professor A. N. Talbot, The Technograph No. 16, p. 139).
Stresses in a Circular Girder. — The circular girder supports the weight of the tank, the
contents of the tank, and its own weight. The load is uniformly distributed along the girder.
The girder rests on or is supported by four or more columns, and transmits its load to them.
Let W = total load on girder in Ib. ;
r = radius of girder in in.;
n = number of posts;
a = 2ir/n = angle at center subtended by radii through two consecutive posts;
«' = angle subtended at center by any arc;
M = direct bending moment in the girder at any point in in.-lb. ;
T = torsional bending moment in girder at any point in in.-lb.;
5 = shear in girder at any point in Ib. ;
Pa = Pb, etc., = reactions of columns in Ib.
368
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XL
FIG. 2. CIRCULAR GIRDER.
•
Now in the author's "Design of Walls, Bins and Grain Elevators" it is proved that the
bending moment at the supports is
it W-r ( l I «\ , .
M i = I cot- I (20)
n \a 2 2)
and the maximum moment midway between the posts is
,,
= Mi -cos-
2
W-r
2n
2 sin2 —
4
(21)
The torsional moment is zero at the supports and midway between the columns, and is a
maximum at the points of zero bending moment at points between the columns.
The torsional moment is
„ ,, . , W-r . .. . W-a'-rf sin«'\
Tb = Mi'sm a.' (i — cos a') H ( I r- )
2n 4 \ a' J
Values of M and T are given in Table la.
(22)
TABLE la.
STRESSES IN CIRCULAR GIRDERS.
No. of
Posts.
Load on
Post, Lb.
Max. Shear,
Lb.
Bending Moment
at Posts, In-lb.
Bending Moment
Midway Between
Posts, In-lb.
Angular Distance
from Post to Point
of Max. Torsion.
Max. Torsional
Moment, In-lb.
4
r-4
W- 8
— O.O34I5/TT
-\-O.Olj62W-r
19° 12'
0.0053 W'r
6
W - 6
W - 12
— o.oi^&zW-r
+0.0075 1 /F-r
12 44
0.00151 W-r
8
W - 8.
W - 16
—o.oo%2jW-r
+o.oo4i6/iF.T
9 33
0.00063 W- r
12
W - 12
W - 24
— 0.003 65 JF- r
+0.00190 W-r
6 21
o.oooi85/F-r
Stresses in Columns. — The stresses in the columns will be due to the dead load and to the
wind moment. The vertical components of the dead load stress will be equal to W divided by
the number of columns, where W is the total weight of tank and the water. To calculate the
stresses due to wind moment in the columns proceed as follows: Calculate the wind force by
multiplying the exposed surface by the wind pressure, and assume the wind force as acting through
the center of gravity of the exposed surface. The pressure on circular tanks may be taken at
two-thirds of 30 Ib. per sq. ft. of the surface at right angles to the direction of the wind. To
calculate the stresses in the columns at any point pass a horizontal section through the columns
DETAILS OF STEEL TANKS.
as in Fig. 3. Then the maximum vertical stress in column I will occur on the leeward side when
the wind is blowing in tin- dine (ion i-i. If M is tin- wind moment about the axis A-B, the
moment of the stresses in the column about axis A-B will be equal to M. In a tower with 8
.columns as in Fig. 3 we have (stress i) X 2r + (stress 2) X 4r-cos 45° - M.
But Stress I is to Stress 2 as r is to r -cos 45°; and Stress I (zr + 2r) — M. Stress I — JW/4r,
ami Sm-iss 2 = o.jM/^r. In a 6 column tower the stress in the most remote post is M/y and
in each of the others is J M/y. In a 4 column tower the stress in each column is M/2r. If the
columns are vertical the maximum stresses will occur at the foot of the columns; if the columns
are inclined the stress should be calculated at both the top and the bottom. The maximum
stresses will be the sum of the dead and wind load stresses.
Having calculated the vertical components of the stresses in the columns, the stress in the
column will be equal to the vertical component multiplied by the secant of the angle between the
column and a vertical line.
A
\5
X
\
\
\
I
Wmcf
If the upward pull of the columns on the windward side is greater than the dead load when
the bin is empty the column must be anchored down. The masonry footing should have a
weight equal to at least one and one-half times the resultant upward pull.
DETAILS OF STEEL TANKS.— The standard plans in Fig. 10 and Fig. u and the Jack-
son, Minn., tank in Fig. 6, show the plates in alternate courses of different diameters, while the
standard details of the Chicago Bridge and Iron Co. in Fig. 8 shows the plates telescoped with
the edge of the plate for caulking on the inside so that it may be caulked from above. The stand-
ard specifications given in the last part of this chapter, also the specifications of the American
Railway Engineering Association in the last part of this chapter both require that the plates in
alternate courses be of different diameters as shown in Fig. 10, Fig. u, and Fig. 6.
Hemispherical or segmental bottoms are now quite generally used, the conical bottom being
rarely used on account of the difficulty in making a satisfactory connection to the tank cylinder.
Spherical tank bottoms are used to a limited extent.
The standard details of the Chicago Bridge and Iron Co. for circular water tanks and hemis-
pherical bottoms are given in Fig. 8, and the standard column details are shown in Fig. 9.
The properties for water tight joints together with shearing and bearing values of rivets are
given in Table I la. Standard plans for a 95,000 gallon tank on a 100 ft. tower are given in Fig. 10;
while standard plans for a stand-pipe 20 ft. in diameter and 90 ft. high are given in Fig. 1 1. Table
Ha and Fig. 10 and Fig. II were prepared by Mr. C. W. Birch-Nord to accompany the standard
specifications printed in Trans. Am. Soc. C. E., VoL 64, and partially reprinted in this chapter.
25
370
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
TABLE Ila.
PROPERTIES OF WATERTIGHT JOINTS.
Thickness
of plate
Number of
rows of
rivets
H"Kivets
^"Rivets
%"Kivets
l"nivets
Efficiency
of joints
in per cent
Pitch of
rivets
in inches
Effective
section of
plates
Efficiency
of joints
in per cent
Pitch of
rivets
in inches
Effective
section of
plates
Efficiency
of joints
in per cent
*s!
II J
£ .3
Effective
section of
plates
Efficiency
of joints
in per cent
Pitch of
rivets
in inches
Effective
section of
plates
f
1
43.7
11
0.121
2
70.7
2*
0.177
i.
16
1
39.5
n
0.124
47.1
21
0.147
2
65.4
21
0.205
70.5
3
0.220
1 1
2
61.3
2
0.230
66.6
24
0.250
70.7
31
0.265
3
70.8
o
0.2G5
75.6
5|
0.284
73.2
3}
0.274
3*
2
63.5
21
0.279
66.5
3
0.291
3
72.3
§
0.317
75.2
4
0.32S)
i
2
58.9
21
0.295
63.8
§
0.319
3
69.4
2J
0.347
72.6
3}
0.303
9
10
2
61.0
24
0.344
3
70.5
3|
0.397
16
2
72.0
§
0.315
72.3
31
0,316
3
82.2
3J
0.359
84.7
31
0.370
1
2
72.0
3i
0.360
72.3
31
0.362
3
80.8
g
0.405
82.8
31
0.415
A
16
2
72.0
3k
0.105
72.3
34
0.407
3
80.5
s
0.453
82.1
34
0.463
1
2
70.7
3
0.442
72.3
34
0.452
3
73.4
3
0.490
81.0
31
0.506
1*
2
68.3
21
0.469
72.3
31
0.498
3
75.7
S
0.522
80.3
31
0.552
1 *
2
66.4
|f
0.498
70.2
31
0.52(5
3
73.8
2*
0.553
78.0
31
0.585
13
2
68.3
31
0.555
. 16
3
76.5
31
0.614
i
2
66.5
3
0.582
3
74.1
3
0.647
II
2
Note:
70.1
; si
0.657
3
Heavy 1
grures indicate
70.5
3*
0.717
1"
2
economi
cal riveted joints
67.3
3*
0.673
3
74.7
3*
0.747
Ifote: The distances between rivets at caulked edges shall never exceed 10 times the thickness of platea
or straps. The thickness of each strap for butt joints shall never be less than half the thickness of
the plates plus ^ inch.
SHEARING AND BEARING VALUE OF RIVETS.
Diameter
of rivets,
in inches
Area in,
square
inches
Single Shear
at 9000 Ib.
per sq. in.
Bearing value for different thicknesses of plates, In inches, at 18000 Ib.per sq.in.
i"
JL"
16
r
_L"
is
*"
9"
16
**
OL"
16
J"
js"
1G
r
OS."
16
1"
i
0.3068
2761
2813
3516
4219
4922
5625
6328
7031
*
0.4418
3976
3375
4219
5063
5906
6750
7594
8438
9281
10125
1
0.6013
5412
3938
4922
5906
6891
7875
8859
98 14
10828
11813
12797
13781
1
0.7854
7069
4500
5625
0750
7875
9000
10125
11250
12375
13500
14625
15750
16875
18000
Single riveted Double riveted Triple riveted
lap joint lap joint lap joint
Double riveted
butt joint
KXAMl'LKS OF STKKL WATKK TANKS.
371
f Steel Xoof.
,'Tdr <f Gravel Roof
."In ''JZ'Spotfy
fa) 50, ooo GALLON RAILWAY
WATER TANK AND TOWER
65,000 GALLON STEEL
WATER TANK, HARRIMAN LINES
Ladder-
Devolving
Ladder
t
<-
V
<jd Drum
"Inlet
"Outlet
Botton
'Ground \
i
*
«•
tj
^
i ij
i
^
\
>
K
7/°/J
_i
-*
/L
i*]
*i*f
/*
4
P/s-
N
^
X
^
<^
^
s"
/ Pis-
^
Pis-
s
4rO--
__ __^
\ S*
76
Pfs-
\
%
%•
$'
P/s-
\.... '
fn* \
.. f
(c) 50,000 GALLON STEEL
WATER TANK, C-B-&Q-R-R.
FIG. 4. TYPICAL STEEL WATER TANKS. ,
\ Jntet— ^Vji-Y-.-.r^V.::*
(d) STEEL WATER TANK.
372 STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
^Galvanized
Jron /v/7/a/
L.
Capacity
JO 0,000 Odl-
'"**'* ft
Laced-
?-?" K8" Frame
^"*8"
/iding door
dose opening
the cornice
DETAIL OF TRAP DOOR
Cedsr Shingfes
"x 12" Block
ff Board
'<-----////>J//----
"~~Wooden
]+?& 4" Thick
DETAIL OF ROOF
*5*3*f.
Laced
ifBo/t^
\eddr Shingles
Frame
}oor in two
Sections. The upward
section to open upward •
The fower section to
open sideways-
Bolts, IO'3"Jong'
>2'tf ,
x j- Steel Hoops
6\
<--7';^^--. ,
^
ELEVAT/ON OF
AND TANK TOWER FOUNDATION
FIG. 5. ELEVATED TANK AND TOWER, JACKSON, MINN.
~ *2I
EXAMPLES OF STEEL TANKS ON TOWERS.
878
\ '•/ Rivets, S" Spaces
4f>l9t93,i thick
"Rivets, 2j "Spaces
, 2j>"5p3ces
4 Plates, thick
*,%* Rivets, ?i"Sp3ces
t... ' ~ < SiilSli* » f 4-" r ^
% Rivets^ Z-f
'. thick
T _i i r
k~«r r"f f
N "SV j £/V*£s, 3 "Spaces
\- i " Rivets, 2 j" Spaces
Sflates, " Me.
Rivets %", Pitch ?$•
Lap 3"- DETAIL OF PLATES
Note : Space j rivets /£ from edge off/ate- <j
- - - - -2'\JO"- - -
DETAIL OF INLET PIPE DETAIL OF
._ . . DETAIL OF COLUMN BASE
FROST PKOOFM6 LATERAL CONNECTION
FIG. 6. ELEVATED TANK AND TOWER, JACKSON, MINN.
374
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XL
2 Inside
Splice Plates
Place rdi/i'ng posts
tower posts and
at points midway
between tower posts
DETAIL OF
COL u MM
Brackets
on each post
Bars i*
DETAIL OF
LADDER
%"' Steps-
S 'Spaces^
4 "Spaces,
DETAIL OF
LATERAL CONNECT/OH
•Splice />/• J4x
bottom
DETAIL OF
COLUMN AND HORIZONTAL CIRCULAR GJRDER
FIG. 7. ELEVATED TANK AND TOWER, JACKSON, MINN.
EXAMPLES OF ELEVATED TANKS AND STAND-PIPES.
.'5 To
DETAILS OF STEEL TOWERS. — Steel towers are commonly made with four columns,
although eight or twelve columns are sometimes used for large elevated tanks. The columns of
u« commonly made of two channels, laced top and bottom; of two channels with top
cover plate and bottom lacing; of a built // section made of plates and angles, or a rolled H section.
Z-bars are now very difficult to obtain and the Z-bar column should not be used. The struts
are made of built channels, or of angles, or of plates and angles. The diagonal bracing is commonly
in.i.lo of rods with adjustable clevises or turnbuckles.
EXAMPLES OF STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS.— The
design of steel stand-pipes and elevated tanks on towers will be illustrated by describing several
typical examples.
-5"
8'\P/s-= Sketch *±
m*i'
I Row i* Rivets,
Pitch -2? "
DETAILS OF s"L
75,000 GALLON Sfffl TANK f
CHICAGO BRW&E AND IRON Co-
FIG. 8. DETAILS OF TANK AND HEMISPHERICAL BOTTOM. CHICAGO BRIDGE & IRON Co.
Railway Water Tanks. — Four typical examples of steel water tanks are shown in Fig. 4; the
50,000 gallon railway water tank in (a) Fig. 4 was designed by the American Bridge Company;
the 65,000 gallon water tank in (6) is a standard tank on the Harriman Lines; the 50,000 gallon
tank in (c) was designed by the C. B. & Q. R. R.; while (d) is a typical stand-pipe.
Elevated Tank and Tower for Jackson, Minn. — Details of the steel elevated tank and tower
designed by Mr. L. P. Wolff, Consulting Engineer, St. Paul, Minn., for Jackson, Minn., are shown
in Fig. 5, Fig. 6, and Fig. 7. A general plan and details of the foundations and the roof are shown
in Fig. 5. Details of the riveting of the tank plates; details of the columns, and details of the
frost proofing are shown in Fig. 6. Details of the circular girder, and the connections of the
columns are shown in Fig. 7. The tank has a hemispherical bottom with a conical sub-bottom.
376
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
N«w2S*w
fyj'jsyjf-
COLUMN
75,000 GALLON
STEEL TANK
FIG. 9. DETAILS OF COLUMN CONNECTIONS FOR ELEVATED TANK AND TOWER.
CHICAGO BRIDGE & IRON Co.
STANDARD PLAN OF ELEVATED TANK ON TOWER.
377
95000-GALLON TANK
ON 100-FOOT TOWER
General Note*:
Aofeul C»p«Hj of Tuk 9«,tOO Oil.
Wind lout 30 1I>.|MC tqxmioot
UnltStTmlDi,M»Url«l.»nd
Workmuublp uoordUw to
BpnU<»Uo« f«r
FlnUh
Detail of Expansion. Joint
Detail at Balcony
V
FIG. 10. STANDARD PLAN OF ELEVATED TANK ON TOWER, BY C. W. BIRCH-NORD.
(Trans. Am. Soc. C. E. , Vol. 64, 1909.)
378
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
The details work out very satisfactorily. Mr. Wolff has designed a number of elevated tanks
and towers following the standard details in the Jackson tank. The details of construction are
shown by the drawings.
STAND-PIPE
20 FT. IN DIAMETER
90 FT. HIGH
General Notes:
Actual capacity of Stand-pipe = 211 490 gaL
Wind load = 30 lb.p«r 8q.ft.onVj diameter
Ultimate strength In plate! =12 000 Ih.per BqJn.
Rivets: shear=9000 Ib.per sq.in.
Bearing on plate»=18 000 Ib.per sq.ln.
Material and workmanship according to
General Specifications for Elevated Steel
Tanie and Sund- Pipes.
FIG. ii.
STANDARD PLAN OF STAND-PIPE, BY C. W. BIRCH-NORD.
(Trans. Am. Soc. C. E., Vol. 64, 1909.)
SPECIFICATIONS.— The details of design of steel stand-pipes and elevated tanks on
towers are given in the specifications prepared by Mr. C. W. Birch-Nord and the specifications
of the American Railway Engineering Association. Both of these specifications are printed in
the last part of this chapter.
GENERAL SPECIFICATIONS FOR ELEVATED STEEL TANKS ON TOWERS, AND
FOR STAND-PIPES.*
PART I. DESIGN OF ELEVATED STEEL TANKS ON TOWERS.
Definition. — i. An elevated tank is a vessel placed on a tower in order to furnish a certain
required prrssun- head. The lank is filled through a riser or inlet pipe.
2. Klev.ited tanks are mostly used in connection with pumping stations, or are connected
directly to Artesian wells, in order to store water under pressure.
3. As practically all tanks are cylindrical, this specification will only have reference to those
of that shape.
Loads. — 4. The dead load shall consist of the weight of the structural and ornamental steel-
work, platforms, roof construction, piping, etc.
5. The live load shall be the contents of the tank, the movable load on the platforms and
roof, and the wind pressure.
6. The live load on the platforms and roof shall be assumed at 30 Ib. per sq. ft., or a 2OO-lb.
concentrated load applied at any point.
7. The wind pressure shall be assumed at 30 Ib. per sq. ft., acting in any direction. The
surfaces of cylindrical tanks exposed to the wind shall be calculated at two-thirds of the diameter
multiplied by the height. Similar assumptions may also be made for spherical and conical surfaces
by using the correct heights.
8. The live load on platforms and roof shall not be considered as acting together with the
wind pressure.
Unit Stresses. — 9. All parts of the structure shall be proportioned so that the sum of the dead
and live loads shall not cause the stresses to exceed those given in Table I.
TABLE I.
Tension in tank plates 12,000 Ib. per sq. in. of net area.
Tension in other part of structure 16,000 Ib. per sq. in. of net area.
Compression 16,000 Ib. per sq. in. reduced.
Shear on shop rivets and pins 12,000 Ib. per sq. in.
Shear on field rivets (tank rivets) and bolts 9,000 Ib. per sq. in.
Shear in plates 10,000 Ib. per sq. in. of gross area.
Bearing pressure on shop rivets and pins 24,000 Ib. per sq. in.
Bearing pressure on field rivets (tank rivets) 18,000 Ib. per sq. in.
Fiber strain in pins 24,000 Ib. per sq. in.
10. For compression members, the permissible unit stress of 16,000 Ib. shall be reduced by the
formula:
p = 16,000 — 70 l/r,
, where p = permissible working stress in compression, in Ib. per sq. in.:
/ = length of member, from center to center of connections, in inches;
r — least radius of gyration of section, in inches.
The ratio, l/r, shall never exceed 120 for main members and 180 for struts and roof construc-
tion members.
11. Stresses due to wind may be neglected if they are less than 25 per cent of the combined
dead and live loads.
12. Unit stresses in bracing and other members taking wind stresses may be increased to
20,000 Ib. per sq. in., except as shown in Section n.
13. The pressures given in Table II will be permissible on bearing plates.
TABLE II.
Brickwork with cement mortar 200 Ib. per sq. in.
Portland cement concrete 350 Ib. per sq. in.
First-class sandstone 400 Ib. per sq. in.
First-class limestone 500 Ib. per sq. in.
First-class granite 600 Ib. per sq. in.
* Condensed from Specifications by C. W. Birch-Nord, Assoc. M. Am. Soc. C. E., Trans.
Am. Soc. C. E., Vol. 64, pp. 548 to 563. The preliminary statement and the specifications for the
foundations have been omitted. These specifications have been adopted by the American Bridge
Company.
379
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
Details of Construction. — 14. The plates forming the sides of cylindrical tanks shall be of
different diameters, so that the courses shall lap over each other, inside and outside, alternately.
15. The joints for the horizontal seams, and for the radial seams in spherical bottoms, shall
preferably be lap joints.
16. For vertical seams double-riveted lap joints shall be used for |, &, and f in. plates. Triple
lap joints shall be used for ^ and f in. plates; double-riveted butt joints shall be used for •£$, f,
H and f in. plates; and triple-riveted butt joints for jf, I. if and I in. plates.
17. Rivets f in. in diameter shall be used for | in. plates; rivets f in. in diameter shall be
used for ^s m- plates; rivets I in. in diameter shall be used for f to f in. plates, inclusive. Rivets
I in. in diameter shall be used for j| in. and I in. plates.
Rivets shall be spaced so as to make the most economical seams (70 to 75 per cent efficiency).
A table of riveted joints is given in Table Ila.
1 8. In no case shall the spacing between rivets along the caulked edges of plates be more
than ten times the thickness of the plates. All rivets shall be entered from the inside of the
tank, and shall be driven from the outside, that is, new heads on rivets shall always be formed from
the opposite side of the plate on which the caulking is done.
19. Plates f in. thick, and not more than f in. thick, shall be sub-punched with a punch ^ in.
smaller in diameter than the nominal size of the rivets, and shall be reamed to a finished diameter
not more than YS m- larger than the rivet. Plates thicker than | in. shall be drilled.
20. The minimum thickness of the plates for the cylindrical part shall be f in. The thick-
ness of the plates in spherical bottoms shall never be less than that of the lower course in the
cylindrical part of the tank.
21. The facilities at the plant where the material is to be fabricated will be investigated
before the material is ordered.
22. All plates shall be sheared or planed to a proper bevel along the edges for caulking.
23. All plates shall be caulked along the beveled edges from the inside of the tank, and with a
round-nosed tool. The use of foreign material for caulking, such as lead, copper, filings, cement,
etc., will not be permitted.
24. The plates in tanks for the storage of oil shall be beveled on both sides for outside and
inside caulking.
25. The radial sections of spherical bottoms shall be made in multiples of the number of
columns supporting the tank, and shall be reinforced at the lower parts, where holes are made
for piping.
26. When the center of the spherical bottom is above the point of connection with the cylin-
drical part of the tank, there shall be provided a girder at said point of connection to take the hori-
zontal thrust. The horizontal girder may be made in connection with a balcony. This also
applies where the tank is supported by inclined columns.
27. The balcony around the tank shall be 3 ft. wide, and shall have a floor-plate J in. thick,
which shall be punched for drainage. The balcony shall be provided with a suitable railing,
3 ft. 6 in. high.
28. The upper parts of spherical bottom plates shall always be connected on the inside of the
cylindrical section of the tank.
29. In order to avoid eccentric loading on the tower columns, and local stresses in spherical
bottoms, the connections between the columns and the sides of the tank shall be made in such a
manner that the center of gravity of the column section intersects the center of connection between
the spherical bottom and the sides of the tank. Enough rivets shall be provided above this inter-
section to transmit the total column load.
30. If the tank is supported on columns riveted directly to the sides, additional material shall
be provided in -the tank plates riveted directly to the columns to take the shear. The shear may
be taken by providing thicker tank plates, or by reinforcement plates at the column connections,
while bending moments shall be taken by upper and lower flange angles. Connections to columns
shall be made in such a manner that the efficiency of the tank plates shall not be less than that
of the vertical seams.
31. For high towers, the columns shall have a batter of I to 12. The height of the tower
shall be the distance from the top of the masonry to the connection of the spherical bottom, or
the flat bottom, with the cylindrical part of the tank.
32. Near the top of the tank there shall be provided one Z-bar to act as a support for the
painter's trolley, and for stiffening the tank. Its section modulus shall not be less than Z?2/25O,
where D is the diameter of the tank in feet. If the upper part of the tank is thoroughly held by
the roof construction, this may be reduced.
33. On large tanks, circular stiffening angles shall be provided in order to prevent the plates
from buckling during wind storms. The distance between the angles shall be determined by the
formula:
d = 900 t*/D,
SPECIFICATIONS. 381
where d «• approximate distance between angles, in feet;
/ — thickness <>| tank plates, in inches;
D = diameter of tank, in fn-t.
34. The top of the tank will generally be covered with a conical roof of thin plates; and the
pitch shall be I to 6. For tanks up to 22 ft. in diameter, the roof elates will be assumeti to be
s< 1! supporting. If the diameter of the tank exceeds 22 ft., angle rafters shall be used to support
the roof plates, which are generally i in. thick.
1 Mates of the following thicknesses will be assumed to be self-supporting for various diameters:
•fj in. plate, up to a diameter of 18 ft.
\ in. plate, up to a diameter of 20 ft.
tV in. plate, up to a diameter of 22 ft.
Rivets in the roof plates shall be from J to -fg in. in diameter, and shall be driven cold. These
mvts iuvd not be headed with a button set.
35. A trap-door, 2 ft. square, shall be provided in the roof plate. Near the top of the higher
tanks, there shall be a platform with a railing, for the safety of the men operating the trap-door.
36. There shall be an ornamental finial at the top of the roof.
37. There shall be a ladder, I ft. 3 in. wide, extending from a point about 8 ft. above the
foundation to the top of the tank, and also one on the inside of the tank. Each ladder shal' be
made of two 2\ by f in. bars with \ in. round rungs I ft. apart. On large, high tanks, 30 fi. or
more in diameter, a walk shall be provided from the column nearest *the ladder to the expansion
joint on the riser or inlet pipe.
38. In designing a tank, a height of 6 in. shall be added to the required height of the tank
if an overflow pipe is not specified by the owner.
39. Each elevated tank shall be furnished with a riser or inlet pipe, the size of which shall be
determined by the rate at which the tank must be filled. The size of the riser pipe will be speci-
fied by the owner. The outlet pipe, in most cases, is not required, as the riser or inlet pipe will
serve the same purpose, but it shall be furnished if demanded by the owner.
40. AH pipes entering the tank shall have cast-iron expansion joints with rubber packing, and
facilities for tightening such joints. The expansion joint, generally, shall be fastened to the
bottom of the tank with bolts having lead washers. The tank plates shall be reinforced where the
pipes enter the tank.
41. All pipes entering the tank shall be thoroughly braced laterally with adjustable diagonal
bracing at the panel points of the tower.
42. The diagonal bracing in the tower shall preferably be adjustable, and shall be calculated
for an initial stress of 3,000 Ib. in addition to wind stresses, etc.
43. The size and number of the anchor-bolts in the tower shall be determined by the maxi-
mum uplift when the tank is empty. The anchor-bolts in the tower, where the maximum uplift
is greater than 10,000 Ib., shall be fastened directly to the columns with bent plates or similar
details. In all other cases it will be sufficient to connect the anchor-bolts directly to the base-
plates.
The tension in anchor-bolts shall not exceed 15,000 Ib. per sq. in. of net area. The minimum
section shall be limited to a diameter of ij in. The details shall be made so that the anchor-
bolts will develop their full strength, and, at the lower end, they shall be furnished with an anchor-
plate, not less than \ in. thick, to assure good anchorage to the foundation without depending on
the adhesion between the concrete and the steel.
44. The concrete foundation shall be assumed to have a weight of 140 Ib. per cu. ft., and
shall be sufficient in quantity to take the uplift, with a factor of safety of l^.
45. Three-ply frost-proof casing shall be provided, if necessary, around the pipes leading to
and from the tank. This casing shall be composed of two layers of f by 2j in. dressed lumber,
and each layer shall be covered with tar paper or tarred felt, and one outside layer of f by 2\ in.
dressed and matched flooring. The lumber shall be in lengths of about 12 ft. There shall be a
I in. air space between the layers of lumber, and wooden rings or separators shall be nailed to
them every 3 ft. (In very cold climates it is good practice to fill the space between the pipes and
the first layer of lumber with hay or similar material.) The frost casing may be square or cylin-
drical; it shall be braced to the tower with adjustable diagonal bracing, as described for pipes in
Section 41.
46. All detailed drawings shall be subject to the owner's approval before work is commenced.
47. For materials, workmanship, inspection, painting, and testing, see Part III; for founda-
tions, see Part IV.
PART II. DESIGN OF STAND-PIPES.
Definition.— I. A stand-pipe is a tank, generally cylindrical, used for the storage of water,
oil, etc. Its height, in most cases, is considerably greater than its diameter; it has a flat bottom,
and rests directly on its foundation.
382 STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XL
2. Stand-pipes are economical only in special cases: where their capacity is more important
than pressure, or where local conditions are such that an elevated tank is not required.
3. Stand-pipes for the storage of oil are an exception. These are generally of very large
diameter, while the height may not exceed 40 ft. ; they are usually referred to as tanks.
4. Stand-pipes are filled and emptied through pipes connected with their sides or bottom,
and are provided with manholes for cleaning purposes.
5. In cold climates roofs are generally omitted on stand-pipes used for water supply, on
account of the formation of ice. In warmer climates there may be roofs in order to prevent the
water from becoming a breeding place for mosquitos, flies, etc. Stand-pipes used for the storage
of oil or other fluids from which rain-water is to be excluded should always be roofed.
Loads. — 6. The.dead load shall consist of the weight of structural and ornamental steel work,
and the roof construction, if any.
7. The live load shall be the contents of the stand-pipe, the movable load on the eventual
roof, and the wind pressure.
8. The eventual live load on the roof shall be assumed at 30 Ib. per sq. ft., or a 200 Ib. con-
centrated load applied at any point.
9. The wind pressure shall be assumed at 30 Ib. per sq. ft. acting in any direction. The
surfaces of cylindrical stand-pipes exposed to the wind shall be calculated at two-thirds of the
diameter multiplied by the height.
10. The eventual live load on the roof, if the .stand-pipe is roofed, shall not be considered as
acting together with the wind pressure.
Stresses. — n. All parts of the structure shall be porportioned so that the sum of the dead
and live load stresses shall not exceed the stresses given in Table III.
TABLE III.
Tension in plates forming sides or bottom of stand-pipes 12,000 Ib. per sq. in. of net area.
Tension in roof construction 16,000 Ib. per sq. in. of net area.
Compression in roof construction 16,000 Ib. per sq. in. reduced.
Shear on shop rivets in roof, etc 12,000 Ib. per sq. in.
Shear on field rivets (in stand-pipe plates) and bolts 9,000 Ib. per sq. in.
Shear in plates 10,000 Ib. per sq. in.
Bearing pressure on shop rivets 24,000 Ib. per sq. in.
Bearing pressure on field rivets (in stand-pipe plates) 18,000 Ib. per sq. in.
12. For compression members in the roof construction, the permissible unit stress of 16,000
Ib. shall be reduced by the formula:
p = 16,000 — 70 l/r,
where p = permissible working stress in compression, in Ib. per sq. in.;
/ = length of member, from center to center of connections, in inches;
r — least radius of gyration of section, in inches. The ratio, l/r, shall never exceed 180.
13. Stresses due to wind may be neglected if they are less than 25 per cent of the combined
dead and live loads.
14. The average permissible pressures on masonry shall be as given in Table II, Part I.
Details of Construction. — 15. The plates forming the sides of the stand-pipe shall be of
different diameters, so that the courses shall lap over each other, inside and outside, alternately.
1 6. The joints for the horizontal seams in the sides, and for the bottom plates, shall pre-
ferably be lap joints.
17. For further information regarding riveted joints, etc., see Part I, Sections 16, 17, 18,
and 19.
1 8. The minimum thickness of the plates forming the sides shall be J in. and ^ in. for the
bottom plates, except for oil tanks on a sand foundation. The bottom plates for ordinary stand-
pipes shall be provided with tapped holes, if in. in diameter, with screw plugs, spaced at about
4 ft. centers, to permit of filling with cement grout on top of the foundation of the masonry while
the bottom part is being erected, in order to secure proper bearing.
19. Oil tanks of large diameter are generally set directly on a sand foundation, and do not
need any holes in the bottom plates for filling beneath with cement grout. In such cases, J in.
bottom plates will be sufficient.
20. The bottom plates shall be connected with the sides by an angle iron riveted inside the
stand-pipe. This angle iron shall be bevel sheared for caulking along both legs. For the caulking
of plates, see Part I, Sections 22 and 23.
21. On the side and near the bottom there shall be a 12 by 18 in. manhole of elliptical shape.
In the same manner, or on the bottom plates, flanges shall be provided for the connection of
SI'K( IKK ATIO.NS.
383
inli -t .in.l outlet pipes of the sizes specified by the owner. All openings in stand-pipes shall be
I >[.>!» -rly rvintoirrd by forged rings or plates.
22. For stiffening angles, etc., see Part I, Sections 32 and 33.
23. In cases where a roof is used see Section 5; Sections 34, 35, and 36 of Part I should also
be followed.
24. There shall be an outside ladder, I ft. 3 in. wide, extending from a point about 8 ft. above
thr found. ition to the top of the stand-pipe. The ladder shall be made of two 2\ by | in. bars with
I in. round rungs i ft. apart. An inside ladder will not be required. (In no case should inside
ladders be provided on stand-pipes in climates where ice will form. Owners of oil tanks often
spivii'y stairways to take the place of ladders.) All ladders shall be able to sustain a concentrated
load of at least 800 Ib.
25. Large stand-pipes for oil storage, the heights of which are very small compared with
their diameter, will generally be set directly on a sand foundation, and will not need any anchorage
whatever, as the overturning moment is very small in comparison with the resisting moment.
26. Stand-pipes of the ordinary type, for water storage, shall be set on concrete foundations,
and shall be anchored thoroughly thereto with anchor-bolts not less than ij in. in diameter,
set deep enough to take the necessary uplift, and provided with an anchor plate not less than i in.
thick in the masonry. All anchor bolts shall be connected directly to the sides of the stand-pipe
with bent plates or similar details. The unit stress in anchor-bolts shall not exceed 15,000 Ib.
per sq. in. of net area. See Part I, Section 43.
27. All detailed drawings shall be subject to the owner's approval before work is commenced.
28. For materials, workmanship, inspection, painting, and testing, see Part III; for founda-
tions, see Part IV.
PART III. MATERIALS, WORKMANSHIP, INSPECTION, PAINTING, AND TESTING.
Structural Steel. — i. The steel shall be made by the open-hearth process.
2. The chemical and physical properties shall conform to the following limits:
Elements considered.
Structural Steel.
Rivet Steel.
•n\ L ( Basic. .
0.04 per cent
0.04 per cent
rnosphorus, maximum < . • ,
0.06 " "
0.04 " "
Sulphur, maximum
o.oc " "
0.04. " "
Ultimate tensile strength, in pounds per square inch
Desired
60,000
Desired
50,000
Elongation' minimum percentage in 8 in Fig I
1,500,000
1,500,000
Elongation: minimum percentage in 2 in. Fig. 2
Ultimate tensile
strength
22
Ultimate tensile
strength
Character of fracture
Silky
Silky
Cold bends without fracture
i 80° flat
1 80° flat
The yield point, as indicated by the drop of beam, shall be recorded in the test reports.
3. If the ultimate strength varies more than 4,000 Ib. from that desired, a re-test shall be
made on the same gage, which to be acceptable, shall be within 5,000 Ib. of the desired ultimate.
4. Chemical determination of the percentages of carbon, phosphorus, sulphur, and manganese
shall be made by the manufacturer from a test ingot taken at the time of the pouring of each
melt of steel, and a correct copy of such analysis shall be furnished to the engineer or his inspector.
Check analyses shall be made from finished material, if called for by the purchaser, in which case
an excess of 25 per Cent above the required limits will be allowed.
5. Specimens for tensile and bending tests, for plates, shapes, and bars, shall be made by
cutting coupons from the finished product, which shall have both faces rolled and both edges
milled to the form shown by Fig. I ; or with edges parallel ; or they may be turned to a diameter
of } in. for a length of at least 9 in. with enlarged ends.
6. Rivet rods shall be tested as rolled.
7. Specimens shall be cut from the finished rolled or forged bar, in such manner that the
center of the specimen shall be I in. from the surface of the bar. The specimen for the tensile
test shall be turned to the form shown by Fig. 2. The specimen for the bending test shall be I in.
by $ in. in section.
8. Material which is to be used without annealing or further treatment shall be tested in the
condition in which it comes from the rolls. When material is to be annealed, or otherwise treated
384
STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XL
before use, the specimens for tensile test representing such material shall be cut from properly
annealed or similarly treated short lengths of the full section of the bar.
9. At least one tensile and one bending test shall be made from each melt of steel as rolled.
In case steel differing f in. and more in thickness is rolled from one melt a test shall be made
from the thickest and thinnest material rolled.
About i8;' *!
FIG. 2.
10. For material less than -fs in. and more than f in. in thickness, the following modifications
will be allowed in the requirements for elongation:
(a) For each YS in. in thickness below j^ in., a deduction of 2\ from the specified percentage
will be allowed.
(b) For each $ in. in thickness above f in., a deduction of I from the specified percentage
will be allowed.
n. Bending tests may be made by pressure or by blows. Plates, shapes, and bars less
than I in. thick shall bend as called for in Section 2.
12. Angles f in. and less in thickness shall open flat, and angles | in. and less in thickness
shall bend shut, cold, under blows of a hammer> without sign of fracture. This test will be made
only when required by the inspector.
13. Rivet steel, when nicked and bent around a bar of the same diameter as the rivet rod,
shall give a gradual break and a fine, silky, uniform fracture.
14. Finished material shall be free from injurious seams, flaws, cracks, defective edges, or
other defects, and have a smooth, uniform, workmanlike finish. Plates 36 in. in width and less
shall have rolled edges.
15. Every finished piece of steel shall have the melt number and the name of the'manufacturer
stamped or rolled upon it. Steel for pins shall be stamped on the end. Rivet and lattice steel
and other small parts may be bundled, with the above marks on an attached metal tag.
16. Material which, subsequent to the foregoing tests at the mills, and its acceptance there,
develops weak spots, brittleness, cracks, or other imperfections, or is found to have injurious
defects, will be rejected at the shop, and shall be replaced by the manufacturer at his own cost.
17. A variation in cross-section or weight of each piece of steel of more than z\ per cent from
that specified will be sufficient cause for rejection, except in cases of sheared plates, which will be
covered by the following permissible variations, which are to apply to single plates:
Plates weighing 12^ Ib. per sq. ft. or more:
(a) Up to 100 in. wide, 2§ per cent above or below the prescribed weight;
(b) 100 in. wide or more, 5 per cent above or below.
Plates weighing less than 12 J Ib. per sq. ft.:
(a) Up to 75 in. wide, z\ per cent above or below;
(&) 75 in., and up to 100 in. wide, 5 per cent above or 3 per cent below;
(c) 100 in. wide or more, 10 per cent above or 3 per cent below.
18. Plates will be accepted if their thickness is not more than o.oi in. less than that ordered.
19. An excess over the nominal weight, corresponding to the dimensions on the order, will
be allowed for each plate, if not more than that shown in Table IV, I cu. in. of rolled steel being
assumed to weigh 0.2833 Ib.
Cast Iron. — 20. Except where chilled iron is specified, castings shall be made of tough, gray
iron, with not more than o.io per cent of sulphur. They shall be true to patterns, out of wind,
and free from flaws and excessive shrinkage. If tests are demanded, they shall be made on the
SPECIFICATIONS.
TAI'.I.E IV.
Tliuknrss. in
Niiiniii.il \\Vi«ht in
I'oumU IKT Square
Foot.
Width of Plate*.
Up to 75 In.
75 In. and up to
100 In.
100 In. and up to
115 In.
A
10.20
12.75
10 p
8
cr ce
nt
14 pi
12
:r ce
nt
18 p
16
tree
nt
I
IS-3
17.85
I
IO
8
13
IO
A
20.4
22.95
,1
4
4
i
25-5
4
6
8
More than f
3i
5
6J
"Arbitration Bar" of the American Society for Testing Materials, which is round bar, ij in. in
(li.um'ter ami 15 in. long. The transverse test shall be made on a supported length of 12 in. with
the load at the middle. The minimum breaking load thus applied shall be 2,900 lb., with a
ck tk-ction of at least -fa in. before rupture.
Workmanship, Inspection* and Painting. — 21. All parts forming the structure shall be built
in accordance with approved drawings. The workmanship and finish shall be equal to the best
in modern shop practice.
22. All material shall be thoroughly straightened in the shop, by methods which will not
injure it, before being laid off or worked in any way.
23. The shearing shall be done neatly and accurately, and all portions of the work exposed
to view shall have a neat and uniform appearance.
24. The size of each rivet, called for by the plans, shall be understood to mean the actual
size of the cold rivet before it is heated.
25. All plates and shapes shall be shaped to the proper curve by cold rolling; heating or
hammering for straightening or curving will not be allowed.
26. Plates to be scarfed may be heated to a cherry-red color, but not hot enough to ignite a
piece of dry wood when applied to it. Most careful attention shall be paid to all scarfing.
27. All plates or shapes shall be punched before being bevel-sheared or planed for caulking.
28. All screw threads shall make tight fits in the nuts and turnbuckles, and shall be United
States Standard, except for diameters greater than if in., when they shall have six threads per
inch. The dimensions of screws of various sizes shall be as follows:
Diameter of screw ends I in. I f in. I J in. if and greater
Number of threads per inch 8 7 7 6
The minimum excess at the root of the thread over the body of the bar shall be 15 per cent.
The shape of the thread shall be U. S. Standard.
TABLE V.
STANDARD UPSETS FOR ROUND AND SQUARE BARS.
Round Bars.
Square Bars.
Bar.
Upset.
Bar.
Upset.
Diameter, in Inches.
Diameter, in Inches.
Side, in Inches.
Diameter, in Inches.
i
i
if
i
;
ij
I
i
If
li-
if
If
ii
ij
If
if
ij
2
:t
2
ii
» j
3
if
2|
if
ti
if
2}
i]
2f
2
2!
2
2}
26
386 STEEL STAND-PIPES AND ELEVATED TANKS ON TOWERS. CHAP. XI.
29. The diameter of the die used in punching rivet holes shall not exceed that of the punch
by more than ^ in. All rivet holes shall be punched, except as stated in Part I, Section 19.
30. All punched and reamed bolts shall be clean cuts, without torn or ragged edges. The
burrs on all reamed holes shall be removed by a tool, countersinking not more than ^ in. Any
parts of the structure in which difficulties may arise in field riveting, shall be assembled in the
shop and marked properly before shipment.
31. Rivet holes shall be accurately spaced; eccentrically located rivet holes, if not sufficient
to cause rejection shall be corrected by reaming, and rivets of larger size shall be used in the
holes thus reamed.
32. The use of drift-pins will be allowed only for bringing together several parts forming
part of the structure; force will not be allowed to be used in drifting under any circumstances.
33. The use of sledges in driving or hammering any part of the structure will not be allowed.
Care shall be taken to prevent material from falling, or from being in any way subjected to heavy
shocks.
34. Rivets shall be driven by pressure tools wherever possible. Pneumatic hammers shall
be used in preference to hand-driving. All rivet heads shall be concentric with the holes.
35. All caulking shall be done with a round-nosed tool, and only by experienced and skilled
men. Caulking around rivet heads will not be allowed. All leaky rivets shall be cut out and
replaced with new ones. All fractured material shall be replaced free of cost to the owner.
36. If the owner furnishes an inspector, he shall have full access, at all times to all parts of
the shop where material under his inspection is being manufactured.
37. The inspector shall stamp with a private mark each piece accepted. Any piece not thus
marked may be rejected at any time, and at any stage of the work. If the inspector, through
oversight or otherwise, has accepted material or work which is defective or contrary to these
specifications, this material, no matter in what stage of completion, may be rejected by the owner.
Painting and Testing. — 38. Before leaving the shop, all steel work excepting the laps in
contact on the tank work, shall receive one coat of approved paint or boiled linseed oil. All
parts which will be inaccessible after erection shall be well painted, except as stated before.
39. After the structure is erected and all seams have been caulked, it shall be tested for
water-tightness, and leaky places shall be caulked or marked. The water shall then be dis-
charged and the leaky seams shall be caulked. Leaky rivets shall be treated as per Section 35.
After the structure has been standing empty for 3 days it shall be retested, and then, if all joints
are water-tight, it shall be given one coat of approved paint both inside and outside of the tank or
stand-pipe. Painting in the open air shall never be done in wet or freezing weather. The owner
will select the color of the final coat of paint.
40. The contractor shall guarantee the tightness of the tank, or stand-pipe, against leakage,
when filled with the liquid it is designed to contain.
PART IV. FOUNDATIONS FOR ELEVATED TANKS ON TOWERS, AND FOR STAND-PIPES.
1. The average permissible pressure on the soil is as follows:
Soft clay I ton per sq. ft.
Ordinary clay 2 tons per sq. ft.
Dry sand and dry clay 3 tons per sq. ft.
Hard clay 4 tons per sq. ft.
Gravel and coarse sand 6 tons per sq. ft.
2. In all cases a thorough investigation of the ground and the site shall be made before
proceeding with the foundations.
3. All foundations shall be carried below the frost line, and the anchor-bolts shall be placed
deep enough to develop their full strength. '
4. In foundations for towers with inclined legs supporting elevated tanks care shall be taken
that the piers are constructed in such a manner, that the resultant of the vertical and horizontal
forces, due to direct loads, passes through the center of gravity of the piers.
5. Foundations, in general, shall be of concrete composed of I part Portland cement, 3 parts
sand, and 5 parts crushed stone or gravel. In special cases, where part of the foundation is
under water, the concrete shall be a I : 2 : 4 mixture.
Note. — For specifications for mixing and placing the concrete in the foundations, see Chap-
ter V.
SPECIFICATIONS. 367
GENERAL SPECIFICATIONS FOR STEEL WATER AND OIL TANKS.*
1. Scope of Specifications. — These specifications are intended for steel tanks requiring plates
not more than f in. thick.
2. Quality of Metal. — The metal in these tanks shall be open-hearth steel. The steel shall
conform in physical and chemical properties to the specifications of this Association for steel
3. Loading. — The weight of water shall be assumed to be 63 lb., crude oil 56 lb., and creosote
oil 66 lb. per cu. ft. Wind pressure, acting in any direction, shall be assumed to be, in pounds,
30 times the product of the height by two-thirds of the diameter of the tank in feet.
A. Unit Stresses. — Unit stresses shall not exceed the following:
(a) Tension in plates, 15,000 lb. per sq. in. on net section.
(b) Shear in plates, 12,000 lb. per sq. in. on net section.
(c) Shear on rivets, 12,000 lb. per sq. in. on net section.
(d) Bearing pressure on field rivets, 20,000 lb. per sq. in.
5. Cylindrical Rings. — Plates forming the shell of the tank shall be cylindrical am/ 01 aifferent
diameters, in and out, from course to course.
6. Workmanship. — All workmanship shall be first-class. All plates shall be beveled on all
edges for caulking after being punched. The punching shall be from the surface to be in contact.
The plates shall be formed cold to exact form .after punching and beveling. All rivet holes shall
be accurately spaced. Drift pins shall be used only for bringing the parts together. They shall
not be driven with enough force to deform the metal about the holes. Power riveting and caulking
should be used. A heavy yoke or pneumatic bucker shall be used for power driven rivets. Rivet-
ing shall draw the joints to full and tight bearing.
7. Caulking. — The tank shall be made water or oil tight by caulking only. No foreign
substance shall be used in the joints. For water tanks, the caulking shall preferably be done
on the inside of tank and joint only; but for oil tanks the caulking should be done on both sides.
No form of caulking tool or work that injures the abutting plate shall be used.
8. Minimum Thickness of Plates. — The minimum thickness of plates in the cylindrical
part of the tank shall not be less than } in. and in flat bottoms not less than & in. In curved
bottoms the thickness of plate shall be not less than that of the lower plate in the cylindrical part.
9. Horizontal and Radial Joints. — Lap joints shall generally be used for horizontal seams
and splices and for radial seams in curved bottoms.
10. Vertical Joints. — For vertical seams and splices, lap joints shall be used with plates not
more than f in. thick. With thicker plates, double butt joints with inside and outside straps
shall generally be used. The edge of the plate in contact at the intersection of horizontal and
vertical lap joints shall be drawn out to a uniform taper and thin edge.
11. Rivets, Rivet Holes, Punching and Pitch. — For plates not more than f in. thick, f in.
rivets shall be used. For thicker plates, f in. rivets shall be used. The diameter of rivet holes
shall be -fa in. larger than the diameter of the rivets used. The punching shall conform to the
specifications of this Association for such work on steel bridges. A close pitch, with due regard
for thickness of plate and balanced stress between tension on plates and shear on rivets, is desirable
for caulking.
12. Tank Support. — If the tank is supported on a steel substructure, the latter shall con-
'form to the specifications of this Association for the manufacture and erection of steel bridges,
except that allowance shall be made for wind pressure, but not for impact.
13. Painting. — In the shop the metal shall be cleaned of dirt, rust and scale and, except the
surfaces to be in contact in the joints of the tank, shall be given a shop coat of paint or metal
preservative selected and applied as specified by the company.
After being completely erected, caulked and cleaned of dirt, rust and scale, all exposed metal
work shall be painted or treated with such coat or coats of paint or metal preservative as shall
be selected by the railway company.
14. Plans and Specifications. — Under these specifications and in conformity thereto the
railway company shall cause to be prepared or shall approve detailed plans and specifications for
such tanks, herein specified, as it shall construct. Such plans and specifications shall cover all
necessary tank auxiliaries.
REFERENCES. Hazlehurst's " Towers and Tanks for Waterworks," second edition, 1904,
published by John Wiley & Sons, covers the design and construction of steel stand-pipes and steel
elevated tanks on steel towers, and supplements the data and discussion in this chapter. Con-
siderable data on the design and construction of stand-pipes and elevated tanks on towers for
railway service are given in the annual reports of the proceedings of the American Railway En-
gineering Association, particular reference is made to volume 1 1, part 2; volume 12, part 3, and
volume 13.
* Adopted, Am. Ry. Eng. Assoc., Vol. 13, 1912.
CHAPTER XII.
STRUCTURAL DRAFTING.
PLANS FOR STRUCTURES.
Introduction. — The plans for a structure must contain all the information necessary for the
design of the structure, for ordering the material, for fabricating the structure in the shop, for
erecting the structure, and for making a complete estimate of the material used in the structure.
Every complete set of plans for a structure must contain the following information, in so far as
the different items apply to the particular structure.
In writing this chapter- the instructions of many bridge companies have been consulted;
special credit being due the instructions prepared by the American Bridge Company, the Penn-
sylvania Steel Company, and the McClintic-Marshall Construction Company.
1. General Plan. — This will include a profile of the ground; location of the structure; ele-
vations of ruling points in the structure; clearances; grades; (for a bridge) direction of flow, high
water, and low water; and all other data necessary for designing the substructure and super-
structure.
2. Stress Diagram. — This will give the main dimensions of the structure, the loading, stresses
in all members for the dead loads, live loads, wind loads, etc., itemized separately; the total
maximum stresses and minimum stresses; sizes of members; typical sections of all built members
showing arrangement of material, and all information necessary for the detailing of the various
parts of the structure.
3. Shop Drawings. — Shop detail drawings should be made for all steel and iron work and
detail drawings of all timber, masonry and concrete work.
4. Foundation or Masonry Plan. — The foundation or masonry plan should contain detail
drawings of all foundations, walls, piers, etc., that support the structure. The plans should
show the loads on the foundations; the depths of footings; the spacing of piles where used; the
proportions for the concrete; the quality of masonry and mortar; the allowable bearing on the
soil; and all data necessary for accurately locating and constructing the foundations.
5. Erection Diagram. — The erection diagram should show the relative location of every part
of the structure; shipping marks for the various members; all main dimensions; number of pieces
in a member; packing of pins; size and grip of pins, and any special feature or information that
may assist the erector in the field. The approximate weight of heavy pieces will materially assist
the erector in designing his falsework and derricks.
6. Falsework Plans. — For ordinary structures it is not common to prepare falsework plans
in the office, this important detail being left to the erector in the field. For difficult or important
work erection plans should be worked out in the office, and should show in detail all members and
connections of the falsework, and also give instructions for the successive steps in carrying out
the work. Falsework plans are especially important for concrete and masonry arches and other
concrete structures, and for forms for all walls, piers, etc. Detail plans of travelers, derricks,
etc., should also be furnished the erector.
7. Bills of Material.— Complete bills of material showing the different parts of the structure
with its mark, and the shipping weight should be prepared. This is necessary in checking up
the material to see that it has all been shipped or received, and to check the shipping weight.
8. Rivet List. — The rivet list should show the dimensions and number of all field rivets,
field bolts, spikes, etc., used in the erection of the structure.
9. List of Drawings. — A list should be made showing the contents of all drawings belonging
to the structure.
389
390
STRUCTURAL DRAFTING.
STRUCTURAL DRAWINGS.
CHAP. XII.
METHODS. — The drawings for structural steel work differ from the drawings for machinery
in that (a) two scales are used, one for the length of the member or the skeleton of the structure,
and one for the details; (b) members are commonly shown by one projection; and (c) the drawings
are not to exact scale, all distances being governed by figures.
Two methods are used in making shop drawings.
FIG. i. TRUSS JOINT, COMPLETELY DETAILED.
(1) The first method is to make the drawings so complete that the templets can be made
for each individual piece on the bench. This method is used for all large trusses and members,
and where there is not room to lay the member out on the templet shop floor. The details for the
joint of a Fink roof truss completely detailed are shown in Fig. i. A joint of a roof truss of the
locomotive shop of the A. T. & S. F. Ry., at Topeka, Kansas, is completely detailed in Fig. 2.
(2) The second method is to give on the drawings only sufficient dimensions to locate the
position of each member, the number of rivets, and the sizes of members, leaving the details to
be worked out by the templet maker on the laying-out floor. Sufficient data should be given
to definitely locate the main laying-out points. The interior pieces should be located by center
lines corresponding to the gage lines of the angles, or center line of the piece, as the case may be.
The rivet spacing should be given complete for members detailed on different sheets, or where
it is necessary to obtain a required clearance, and other places where it will materially assist the
RULES FOR SHOP DRAWINGS.
891
tnnpli-t m.ikt T. The drawings should indicate the number and arrangement of the rivets in each
i ( mini linn, as well as the maximum, the usual and the minimum rivet pitch allowed. Sketch
details of the joint which was completely detailed in Fig. I are shown in Fig. 3, and the outline
details of a roof truss by the second method arc shown in Fig. 4.
i
\ \ \ \ \i\i-Wr «• /
&
FIG. 2. JOINT OF ROOF TRUSS COMPLETELY DETAILED.
(Section of Shop Details of Roof Truss.)
Members may be detailed in the position which they are to occupy, or they may be detailed
separately. For riveted trusses and riveted members the entire truss or member should be
detailed in position. The detail shop plans for a riveted brace are shown in Fig. 5. The field
rivets are shown by black and the shop rivets by open circles. The center lines are indicated by
dotted lines. Light full black lines are commonly used for dimension lines, while red dimension
lines are sometimes used but do not make as good blue prints as black lines.
RULES FOR SHOP DRAWINGS.— The following rules are essentially those in use by
the best bridge and structural shops.
Size of Sheet. — The standard size of sheet shall be 24 X 36 in. with two border lines i and I in.
from the edge respectively, see Fig. 6. Sheets 18 X 24 in. with two border lines } and I in.
392
STRUCTURAL DRAFTING.
CHAP. XII.
from the edge respectively, may also be used. For beam sheets, bills of material, etc., use letter
size sheets 85 X n in.
Title. — The title shall be arranged uniformly for each contract and shall be placed in the
lower right hand corner. The title shall contain the name of the job, the description of the
details on the sheet, the number of the sheet, spaces for approval and other information as shown
in Fig. 6.
Scale. — The scale of the lengths of the members or skeleton of the structure shall be J, or f ,
or I in. to I ft., depending upon the available space and the complexity of the member or structure.
Shop details shall as a rule be made f or I in. to I ft. For small details I f and 3 in. to I ft. may
be used; while for large plate girders § or f in. to I ft. may be used.
Views Shown. — Drawings shall be neatly and carefully made to scale. Members shall be
detailed in the position which they will occupy in the structure; horizontal members being shown
lengthwise, and vertical members crosswise on the sheet. Inclined members (and vertical members
FIG. 3. TRUSS JOINT, SKETCH DETAILED.
when necessary on account of space) may be shown lengthwise on the sheet, but then only with
the lower end on the left. Avoid notes as far as possible; where there is the least chance for
ambiguity, make another view.
In truss and girder spans, draw the inside view of the far truss, left hand end, Fig. 7. The
piece thus shown will be the right hand, and need not be marked right. In cases where it is
necessary to show the left hand of a piece, mark "left-hand shown" alongside the shipping mark.
Show all elevations, sections and views in their proper position, looking toward the member.
Place the top view directly above, and the bottom view directly below the elevation. The bottom
view should always consist of a horizontal section as seen from above.
In sectional views, the web (or gusset plate) shall always be blackened; angles, fillers, etc.,
may be blackened or cross-hatched, but only when necessary on account of clearness. In a plate
RULES FOR SHOP DRAWINGS.
891
uinlt r, for example, it is not necessary to blacken or cross-hatch all the fillers and stiffencrs in the
bottom view.
Holes for field connections shall always be blackened, and shall, as a rule, be shown in all
rlrv.it ions and sectional views. Rivet heads shall be shown only where necessary; for example,
at the ends of members, around field connections, when countersunk, flattened, etc. In detailing
members which adjoin or connect to others in the structure, part of the latter shall be shown in
TTT
-*
H
y
5
H
u
x
p
M
H
I
AilJL
394
STRUCTURAL DRAFTING.
CHAP. XII.
FIG. 5. SHOP DETAILS OF BRACE.
TOP CHORDS/* END POSTS
J50fOOT THMU6H Pfi/LROfiD BRIDGE
Qj?E60NMLWf)r$NfiV/6fffJON Co.
PORTLAND, OBZ.
IfldvTjLbii.Ml+hj&L ...Chief Enq'/neerfl.MSfYBridq'eCo.
^
^
**
*5
5
/I ^ j
Checked by £C.fu/Jer - L&te.....J9.-22-QQ.m
Order No. B.-782 Draw/np No...-835Q......
Sheet d of 15 . .
flpproved-.zi.&.JcujMTL^^ O.&fyN.Co.
\
*— t
X/l"
2 .'/ 1^ *
//// Rlfio Pnnf- /7/7 //4/r frnt>
L"
i
Cat Tracj'nffon this f/'ne
FIG. 6. STANDARD SHEET AND TITLE FOR STRUCTURAL DRAWINGS.
STRUCTURAL DETAILS.
806
396
STRUCTURAL DRAFTING.
CHAP. XII.
Vsjbfe
STRUCTURAL DETAILS.
J<3
*! it-*WI3
•
jW
398
STRUCTURAL DRAFTING.
CHAP. XII.
dotted lines, or in red, sufficiently to indicate the clearance required or the nature of the connection.
Plain building work is exempted from this rule.
A diagram to a small scale, showing the relative position of the member in the structure,
shall appear on every sheet, Fig. 8 and Fig. 9. The members detailed on the sheet shall be shown
by heavy black lines, the remainder of the structure in light black lines. Plain building work is
exempt from this rule.
CONVENTIONAL SIGNS FOR RIVCT5
Two Fulf I
+
Heads \
I
0
t •*
t
Near Side
(Visible)
a
^ §
£~t §L
Far Side
/9\
1 *§
(Not Visible)
W
3
doth
53
Sides
Two ff// Heads
•
Nearside
1 -^
(Visible)
m
> C-xs ^.
Far Side
A
^ l<
(Not Visible)
w
^ *s>
-~-~-
—
Sides
®
«*-^
Near Side
(Visible)
a
Far Side
(Not Visible)
0
Both
Sides
0
Near Side
(Visible)
a
Far Side
(Not Visible)
®
Both
0*
Sides
*^
Near Side
(Visible)
a
Far Side
^
(Not Visible)
vy
doth
~~*7
Sides
%2t
FIG. 10. CONVENTIONAL SIGNS FOR RIVETS.
When part of one member is detailed the same as another member, figures for rivet spacing
need not be repeated; refer to previous sheet or sheets, bearing in mind that these must contain
final information. It is not permissible to refer to a sheet, which in turn refers to another sheet. The
section, finished length, and the assembling mark for each member shall be shown on every sheet.
Main dimensions which are necessary for checking, such as c. to c. distances, story heights, etc.,
shall be repeated from sheet to sheet. Holes for field connections must always be located inde-
pendently, even if figured in connection with shop rivets; they shall be repeated from sheet to
sheet unless they are standard, in which case they shall be identified by a mark and the sheet
given on which they are detailed.
The quality of material, workmanship, size of rivets, etc., shall be specified on every sheet as
far as it refers to the sheet itself. Standard workmanship need not be specified on each sheet.
Lettering. — Engineering News lettering as developed by Reinhardt in his book on freehand
lettering shall be used on all drawings. Preferably main titles and sub-titles shall be vertical
and the remainder of the lettering inclined. The height of letters shall be as follows: Main titles —
capitals 15/50 in., small capitals 12/50 in.; sub-titles — capitals, full height lower case letters and
numerals 5/20 in., lower case letters 3/20 in. ; other lettering — capitals, full height lower case letters
and numerals 5/30 in., lower case letters 3/30 in. Where the drawing is crowded the body of the
lettering may be 5/40 in. and 3/40 in. respectively. The following pens are recommended : For
RULES FOR SHOP DRAWINGS.
899
t it U > Lconardt & Co.'s Ball-Pointed No. 5i6F; for all other lettering Hunt Pen Co.'g extra fine Shot
Point, No. 512. No pen finer than Gillott's No. 303 should be used. Light pencil guide lines
Mull he drawn for all lettering. All tracings shall be made on the dull side of the tracing cloth.
Kr.i-urcs shall be made with soft rubber pencil eraser and a metal shield. Rubber erasers con-
taining sand destroy the surface of the cloth and make it difficult to ink over the erased spot.
The use of knives or steel erasers will not be permitted. Tracings shall be cleaned with a very
soft rubber eraser, and not with gasolene or benzine, which destroy the finish of the tracing cloth.
All liiu-s shall preferably be made with black India ink; full lines to represent members, dash and
dot to represent center lines, and dotted lines (or full light black lines) to represent dimension
lines. If permitted by the chief draftsman red ink may be used for dimension and center lines.
The ends of dimension lines shall, however, always be indicated by arrows made with black
ink.
Conventional Signs. — Conventional signs for rivets are shown in Fig. 10. Countersunk
rivets project J in.; if less height of rivets is required, drawings shall specify that they are to be
chipped, or the maximum projection may be specified. Flattened heads project f in. to iV in-l
if less height of heads is required, they shall be countersunk. Metals in section shall be shown
as in Fig. n. Standards for rivets and riveting are given in Part II, which see.
Marking System. — A shipping mark shall be given to each member in the structure, and no
dissimilar pieces shall have the same mark. The marks shall consist of capital letters and num-
erals, or numerals only; no small letters shall be used except when sub-marking becomes absolutely
necessary. The letters R and L shall be used only to designate "right" and "left." Never use
the work "marked" in abbreviated form in front of the letter, for example say, 3 Floorbeams G4,
and not, 3 Floorbeams, Mk. G4. Whenever a structure is divided up into different contracts care
should be taken not to duplicate shipping marks. Pieces which are to be shipped bolted on a
5teel 5teel Cast Iron Cast Steel Bronze
FIG. ii. CONVENTIONAL SIGNS FOR METALS.
member shall also have a separate mark, in order to identify them should they for some reason
or another become detached from the main member. The plans shall specify which pieces are
to be bolted on for shipment, and the necessary bolts shall be billed. For standard marking
system for a truss bridge, see Fig. 7.
A system of assembling marks shall be established for all small pieces in a structure which
repeat themselves in great numbers. These marks shall consist of small letters and numerals
or numerals only; no capital letters shall be used; avoid prime and sub-marks, such as Maf. Pieces
that have the same assembling mark must be alike in every respect; same section, length, cutting
and punching, etc.
Shop Bills. — Shop bills shall be written on special forms provided for the purpose. When
the bills appear on the drawings as well, they shall either be placed close to the member to which
they belong or on the right hand side of the sheet. When the drawings do not contain any shop
bills, these shall be so written that each sheet can have its bill attached to it if desired; one page of
shop bills shall not contain bills for two sheets of drawings. In large structures which are sub-
divided into shipments of suitable size, both mill and shop bills must be written separately for
each shipment. In writing the shop bill bear in mind that it shall serve as a guide for the laying
out and assembling of the member, besides being a list of the material required. For this reason
members which are radically different as to material shall not be bunched in the same shop bill,
neither shall pieces which have different marks be bunched in the same item, even if the material
400 STRUCTURAL DRAFTING. CHAP. XII.
is the same. Bill first the main material in the member, and follow with the smaller pieces, begin-
ning at the left end of a girder, or at the bottom of a post or girder. On a column each different
bracket shall be billed complete by itself. Do not bill first all the angles and then all the flats;
for example when the end stiffeners in a girder are billed, the fillers belonging to them shall follow
immediately after the angles, and so on.
When machine-finished surfaces are required, the drawing and the shop bill shall specify the
finished width and length of the piece, the proper allowance for shearing and planing being made
in the mill bill. When the metal is to be planed as to thickness, the drawing and the shop bill
shall specify both the ordered and the finished thickness; one pi. 15 in. X f in. X I ft. 6 in. (planed
from 13/16 in.).
Field Rivets. — A " Bill of Field Rivets" shall be made for each structure. The " Bill of Field
Rivets" shall give in order the number, diameter, grip, length and the location of the rivets in
the structure. The number of field rivets to be furnished to the erector shall be the actual number
of each diameter and length required, plus 15 per cent, plus 10.
Field bolts shall be billed on " bill of rivets and bolts" only. Bill them similarly to field rivets,
and give the drawing number on which they are shown; 4 — bolts | in. X 2 in. grip, 3 in. U. H.
stringers "S" to floorbeam "F" drawing No. 13, 4 hex. (or 4 square) nuts for above bolts. Bill
of bolts and bill of field rivets shall be prepared and placed in the shop in time to be made with
other material.
General Notes. — Full information regarding the following points shall appear on the drawings,
where practicable as "General Notes." Loading , Specifications , Material
, Rivets , Open Holes , Reaming Requirements , Other Special
Requirements , Painting.
Erection Plan. — Make erection plans simultaneously with the shop plans, and keep same up
to date. The erection plans must show plainly the style of connections; joints in pin spans are to
be shown separately to a larger scale. For the erection plan of a truss bridge see Fig. 7. Shipping
bills showing the number of pieces, erection mark, and weight shall be made for each shipment.
Subdivisions. — Every contract embracing different classes of work shall have a subdivision
for each class. These subdivisions will be furnished by the chief draftsman. Drawings, shop
and shipping bills must be kept separate for each class.
PLATE GIRDER BRIDGES.— General Rules.— The plate girder span shall be laid out
with regard to the location of web splices, stiffeners, cover plates, and in a through span, floor-
beams and stringers, so that the material can be ordered at once. Locate splices and stiffeners
with a view of keeping the rivet spacing as regular as possible; put small fractions at the end of
girder. Stiffeners, to which cross-frames or floorbeams connect, must not be crimped, but shall
always have fillers. The outstanding leg shall not be less than 4 in., gaged 2f in.; this will enable
cross-frames or floorbeams to be swung into place without spreading the girders. The second pair
of stiffeners at the end of girder over the bed-plate shall be placed so that the plate will project
not less than I in. beyond the stiffeners.
Always endeavor to use as few sizes as possible for stiffeners, connection plates, etc., and
avoid all unnecessary cutting of plates and angles. For this purpose locate end holes for laterals
and diagonals so that the members can be sheared in a single operation. In spans on a grade,
unless otherwise specified, put the necessary bevel in the bed-plate and not in the base-plate.
In short spans, say up to 50 ft. put slotted holes for anchor-bolts in both ends of girders, f in.
larger diameter than the anchor bolts.
In square spans, show only one-half, but give all main dimensions for the whole span. In
skew spans show the whole span; when the panels in one-half of span are same as in the other
half, give the lengths of these panels, but do not repeat rivet-spacing, except where it differs.
In the small scale diagram, which shall appear on every sheet, unless span is drawn in full,
show the position of stiffeners, particularly those to which cross-frames or floorbeams connect.
Deck Plate Girder Spans. — On top of sheet show a top view of span, with cross-frames,
laterals and their connections complete, with the girders placed at right distances apart. Below
SHOP DRAWINGS FOR TRUSS BRIDGES. 401
tlii^ \ it ss -how the elevation of the far girder as seen from tin- inside, with all field holes in flange*
and stilfencr.-. indicated and blackened. At one end of the elevation show in red the bridge-Beat
and hack wall, i;ive figures for distance from base of rail to top of masonry, notch of ties, depth
of girder, thickness of base-plate and of bed-plate or shoe. When the other end of girder has a
diiU rent height from base of rail to masonry, give both figures at the one end, and specify "for
this end" and "for other end." If span has bottom lateral bracing, a bottom view (horizontal
section) shall be shown below the elevation. When no bottom laterals are required, show only
end or ends of lower flange of girder, giving detail of base-plate and its connection to the flange.
1 )i tail the bed-plate separately, never show it in connection with the base-plate.
Cross-frames shall, whenever possible, be detailed on the right hand of the sheet in line with
the elevation. The frame shall be made of such depth as to permit it being swung into place with-
out interfering with the heads of the flange rivets in the girders. Always use a plate, not a washer
with one rivet, at the intersection of diagonals. In skew spans it is always preferable to have an
uneven number of panels in the lateral system.
Through Plate Girder Spans. — Show on top of sheet an elevation of the far girder as seen from
inside; below this view show a horizontal section of span as seen from above with the lateral system
detailed complete. It is generally best to show floorbeams and stringers in red in this view and to
detail them on a separate sheet. The stiffeners in a through span should always be arranged so
that the floor system can be put in place from the center towards the ends. What is said under
" deck spans " about showing bridge-seat, back wall, detailing bed-plate separately, etc., applies
to through spans as well.
TRUSS BRIDGES.— General Rules.— Before any details are started all c. to c. lengths of
chords, posts, diagonals, etc., shall be determined, and sketches made of shoes, panel-points,
splices, etc., so that the material can be ordered as soon as required.
If not otherwise specified, camber shall be provided in the top chord by increasing the length
J in. for every 10 ft. for railroad bridges, and ^ in. for every 10 ft. for highway bridges. This
increase in length shall not be considered in figuring the length of the diagonals, except in special
cases, as directed by the engineer in charge. Half the increase in length shall be considered in
figuring the length of the top laterals. Particular attention must be paid to what is said under
"General Rules" about showing part of adjoining member in red, and about the small scale dia-
gram on every sheet.
For every truss bridge an erection diagram shall be made on a separate sheet, giving the ship-
ping marks of the different members and all main dimensions, such as c. to c. trusses, height of truss,
number and length of panels, length of diagonals, distance from base of rail to masonry, distance
.from center of bottom chord or pin to masonry, size and grip of pins (Fig. 7), also show in larger
scale the packing at panel points, state any special feature which the erector needs to look out for,
and give approximate weight of heavy and important pieces when their weight exceeds five tons.
If in any place it is doubtful whether rivets can be driven in the field, the erection diagram and
also the detail drawings shall state that "turned bolts may be used if rivets cannot be driven."
A list giving number and contents of drawings belonging to the bridge shall also appear on the
erection diagram sheet.
Riveted Truss Bridges. — In square spans, not too large, show the left half of the far truss as
seen from the inside and detail all members in their true position, making scale of the skeleton one-
half the scale of the details. In skew spans, not symmetrical, show the whole of the far truss. In
large spans detail every member separately. When detailing web members bear in mind that the
intersection point on the chord must not be used as a working point for a member which stops
outside of the chord. A separate working point, preferably the end rivet, shall be established on
the member proper, and shall be tied up with the intersection point on the chord.
The clearance between the chord and a web member entering same shall, whenever possible,
be not less than J in. in heavy and -fa in. in light structures.
Members shall be marked with the panel points between which they go, for example, end-
post Ly-Ui', hip vertical Ui-Li; top chord U\-Ut, etc., see Fig. 7.
27
402 STRUCTURAL DRAFTING. CHAP. XII.
Pin-connected Truss Bridges. — In pin-connected truss bridges detail the left half of the far
truss as seen from the inside, every member by itself. It is generally best to commence with the
end-post, showing it lengthwise on the sheet with the lower end to the left; then the first section
of the top chord, and so on. The packing at panel points shall, whenever possible, be so arranged
that, besides the customary allowance of & in. for every bar, a clearance of not less than f in. can
be provided between the two sides of the chord. When two or more plates are used, -55 in. should
in addition be allowed for each plate. Members shall be marked the same as for riveted truss
bridges, with the panel points between which they go, see Fig. 7.
Order of Detailing Truss Spans. — In making detail plans and bills of material the following
order shall be followed for truss spans.
1. General drawing; 7. Upper laterals;
2. End-posts; 8. Lower laterals;
3. Upper chords; 9. Floorbeams;
4. Lower chords; 10. Stringers;
5. Intermediate posts; n. Castings, bolts, eye-bars, pins, etc.
6. Sway bracing;
OFFICE BUILDINGS AND STEEL FRAME BUILDINGS.— Number of Drawings.— The
different sheets shall be numbered consecutively, whether large or small. No half numbers are
permissible except in emergency cases. It is always well to arrange the number so that the sheets
follow in the order in which the material is required at the building. The following is generally
a good order:
1. Floor plans for all floors;
2. Column schedule;
3. Cast-iron bases for columns;
4. Foundation girders;
5. Foundation beams;
6. First tier of columns;
7. Riveted girders, connecting to first tier of columns
8. Beams connecting to first tier of columns;
9. Miscellaneous material for above;
10. Second tier of columns, etc., etc.
Floor Plans. — Floor plans, Fig. 12, shall, as a rule, be made to a scale f in. to i ft. A separate
plan shall be made for each floor, unless they are exactly alike. Columns shall be marked consec-
utively with numerals, the word Col. always appearing in front of the numeral, for example,
Col. 20. The architect or engineer has generally on his drawing adopted a system of marking for
the columns, which should be adhered to, unless altogether too impracticable. Riveted girders
shall be indicated with two (2) fine lines when they have cover plates, and with four (4) fine lines
when they have no cover plates. They shall be marked consecutively with numerals, using the
same marks for girders which are alike. Beams and channels shall be indicated with one single
heavy line. They shall be marked the same as girders, with numerals, using same marks when
alike. Tie-rods shall be indicated with one single fine line; they need not have any marks. The
marking system shall be as uniform as possible for the different floors, i. e., a beam which goes
between Col. 2 and Col. 3 shall be marked with the same numeral throughout all the floors. All
figures necessary for making the details shall, as a rule, appear on the floor plan, care being taken
in writing same to leave room for the erection marks, which must be printed in heavy type above
the line or lines representing a beam or girder.
Column Schedule. — For every large building a schedule of the columns shall be made before
the details are started, see Fig. 13. Each column, even should several be alike, shall have a separ-
ate space, in which shall be given the material and the finished length. As soon as the detail
drawings for one tier of columns are finished the sheet numbers shall be inserted as shown on the
sample schedule, Fig. 13, making the schedule serve as an index for the column drawings.
SHOP DRAWINGS FOR OFFICE BUILDINGS.
403
Columns. — Columns shall, whenever possible, be drawn standing up on the sheets as they
npp<-.ir in the building. If it becomes necessary to draw them lengthwise on the sheet, the base
shall IK- to UH- left. Particular attention shall be paid to establishing a marking system for
brackets, splir.--pl.iu-s, etc. A summary of all these standard pieces shall be made for each tier
1
1
1
1
1
j
i
_ jV
53
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CoL/5
54
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1
53
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„ •_ ]5.~.0— ,JU
X
^~du/fd/n(f Line
,. —
f- Floor Line
-1-
(W Tie Rods Darn.
/?// Wall Plates standard.
Top of Plate Girders in Wall
/ above Floor Line.
FIG. 12. FLOOR PLANS FOR OFFICE BUILDINGS.
and sent to the shop as early as practicable, in order that they may be gotten out before the main
material is taken up. The material for the small pieces shall, as far as possible, be chosen from
stock sizes. Columns shall be marked with the numbers of the floors between which they go;
Col. 5 (1-3). The lower tier is best marked " Basement Tier." Standard details for columns are
given in Fig. 14 and Fig. 15.
Riveted Girders. — Girders shall be marked with the number of the floors, not with letters,
404
STRUCTURAL DRAFTING.
CHAP. XII.
unless requested; for example, 2d Floor, No. 5. What is said under columns about marking system
for standard pieces applies to girders as well. When a girder is unsymmetrical about the center
line, and a question may arise how to erect it, one end shall be marked with the number of the
column to which it connects, or with North, South, East or West. Girders must not be bunched
t-
O;
"S-i
t—
Poof
!7tf}-F/oor
16th -Floor
I5th-Floor
I4th-Floor
H5
115
-§
82
83
II5
*
NOTE '--Figures in
FIG. 13. COLUMN SCHEDULE FOR OFFICE BUILDINGS.
together for the different floors more than to meet the requirements in the field; but they must
correspond to the tiers of columns as they will be erected.
Beams. — Beams shall be drawn on the standard forms provided for the purpose. They
need not be drawn to scale, see Fig. 16 and Fig. 17. Beams shall be marked the same as girders
with the number of the floor; One 12" I @ 40 Ib. X i9'-3l", (Mark) 2d Floor No. 35. What
is said under girders about marking one end, when not symmetrical around the center line, and
about not bunching the different floors more than to meet the requirements in the field, applies
to beams as well.
Whenever possible use standard framing angles, Tables 117 and 118, Part II. If it is deemed
necessary to use 6 in. X 6 in. angles, punch both legs the same as the 6 in. leg of standard; in 3! in. X
3f in. or 4 in. X 3! in. angles, punch both legs the same as 4 in. leg of standard. It is not abso-
SHOP DRAWINGS FOR OFFICE BUILDINGS.
405
lin< K imp' i.iti\< tli, it the K-'K<'"f ''" fi.miing angles shall be standard as long as the vertical distance
1" t\\. i -n the holes and in the 6 in. leg the horizontal distance (2\ in.), are kept standard. Holes
for connection-^, tir-nxls, rtr., shall be located from one end of the beam, preferably the left. If
«MH- end rests on the wall and the other end is framed, then figure from the latter end, be it right
FIG. 14. STANDARD DETAILS FOR BETHLEHEM H -COLUMNS.
or left. This rule may be dispensed with in case of numerous holes regularly spaced in web or
flange for connection of shelf-angles, buckle-plates, etc. The allowed overrun at ends of beams
must always be indicated, either by giving figures or by showing wall bearing. Holes at the end
406
STRUCTURAL DRAFTING.
CHAP. XII.
t
FIG. 15. STANDARD DETAILS FOR BUILT-UP H-COLUMNS.
STANDARD DETAILS FOR ROLLED BEAMS.
407
jr
/Beam-B43-3rd-FI.
K KAi """^I4"
i*~ "'"/"*"'"" *^-« — — -^ .
'• I
»"
-1
ad
*
EHt H>- — -^ — ^'-*-
L^j- 4--+-*- v4j t-}-t f '
f-(?' i /^?2
"1
J
- „
3 Beams
Ho/es • D/am.
FIG. 1 6. STANDARD DETAILS FOR ROLLED BEAMS.
408
STRUCTURAL DRAFTING.
CHAP. XII.
of beam for anchors are best figured from wall end, not connecting them with other figures. The
distance between end holes in beams which connect through web or flange to columns, girders, etc.,
shall always be given. When framing angles are standard, do not give any figures for either shop
or field rivets, except the distance from bottom of beam to center of connection or to first holes in
framing angle, and the horizontal distance between field holes. When special framing angles are
used, the fact must be noted and figures given for gages, etc. For standard connection holes in
web of beam all figures required are the distance from bottom of beam to centre of connection or
to first hole and the horizontal distance between holes. Whenever possible use standard punching.
3 Separators for /8"W£
6 Hex dolts I *'*8' L Sl'l'L
l6irder-5?I-3rdfL
cut 35 shown !*—-- -•
i"*f '' ^K! cut n°t cr/fpped
/'/>'" c ./-// -/_// /In n
4/s6x4x/xOL7?"
/deam-B48-3rd-FI.
FIG. 17. STANDARD DETAILS FOR ROLLED BEAMS.
ERECTION PLAN FOR MILL BUILDINGS.— The preceding method for office buildings
will need considerable modification for steel frame mill buildings. The following method for
making erection plans lor steel frame mill buildings has been found very satisfactory.
If the points of the compass are known, mark all pieces on the north side with the letter, N,
those on the south with the letter, S, etc. Mark girts N.G.i; N.G.2; etc. Mark all posts with a
different number, thus: N.P.i; N.P.2; etc. Mark small pieces which are alike with the same
mark; this would usually include everything except posts, trusses and girders, but in order to
follow the general marking scheme, where pieces are alike on both sides of a building, change the
general letter; e. g., N.G.7 would be a girt on the north side and S.G.7 the same girt on south side.
Then in case the north and south sides are alike, only an elevation of one side need be shown, and
under it a note thus: "Pieces on south side of building, in corresponding positions have the same
STANDARD DETAILS FOR ANGLE STRUTS.
40'.)
5(57 :
\ Jl*
-4-
J
4'0'
' "
2 Struts 12 0
\M
ills 6"^o'4i'-d3 2 Pieces- <*n* *'*<?** <**
10 Braces 4'll*"
Same as K5 except as shown •
6 Braces 4'>
plOx"
12
l_
«rv
M - — -7 *4
FIG. 1 8. STANDARD DETAILS FOR ANGLE STRUTS.
410
STRUCTURAL DRAFTING.
CHAP. XII.
number as on this side, but prefixed by the letter, S, instead of the letter, N." Mark trusses
T.I; T.2; etc. Mark purlins R.I; R.2; etc.
The above scheme will necessarily have to be modified more or less according to circum-
stances; for example, where a building has different sections or divisions applying on the same order
number, in which case each section or division should have a distinguishing letter which should
prefix the mark of every piece. In such cases it will perhaps be well to omit other letters, such as
N., S., etc., so that the mark will not be too long for easy marking on the piece. In general,
however, the scheme should be followed of marking all the larger pieces, whether alike or not,
with a different mark. This would refer to pieces which are liable to be hauled immediately to
their places from the cars. But for all smaller pieces which are alike, give the same mark.
DETAIL NOTES. — Sections. — End views of sections shall be shown as in (a) Fig. 19, and
sections shall be cross-hatched or blackened as shown in (b) Fig. 19.
Assembling Note. — Covers, webs, flange angles, etc., must not be marked alike when it
would be necessary to turn them end for end, see (c) Fig. 19.
Rivet Spacing. — Rivet spacing must be tied up from end to end.
(a)
j'Sf
(c)
L2i
-i- ^'/
i *
s
i
*K
x-/r"'*
i
.
/f
(e)
FIG. 19.
Connection Plates. — In detailing connection plates wherever bevel for holes on lines "b,"
(d) and (e) Fig. 19, is different, spacing for holes on lines "a" should be made different to prevent
plates from being interchanged.
Writing Angles. — In writing angles give the longer leg first, l-L 6" X 4" X \" X io'-o|".
Writing Plates. — In writing plates the width of the plate is given in inches, the thickness in
inches, and the length in ft. and in.; 2-P1. 48" X f" X is'-of". A length of 9 in. should be
written o'-g" and not 9". The width of a plate is the dimension at right angles to the length
of the member, while the length of a plate is the dimension parallel to the length of the member
to which the plate is attached; except that for lacing bars, tie plates and other universal mill
plates 6 inches and less in width the least dimension is taken as the width of the member, and
for splice plates the width is the dimension at right angles to the splice.
Writing Sections. — Sections are written as follows: i-I 12" @ 40 Ib. X l6'-3l".
Miscellaneous. — Bevels may be shown as so many inches in 12", (a) Fig. 20; or where con-
venient the total lengths may be given as in (b) Fig. 20. The latter method is the better as it
assists the checker and the templet maker.
The maximum amount that one leg of an angle can be bent is 45°. For a greater bend than
45° a bent plate shall be used, (c) Fig. 20.
The center to center length of stiff laterals should be -not less than rs in. short.
Do not use 2 sizes of rivets in the same leg, or same angle, or same piece unless absolutely
necessary.
RULES TO FACILITATE ERECTION.
411
Where unequal legged angles arc used mark the width of one leg of the angle on the leg.
Where heavy laterals are spliced in the middle by a plate, ship the plate riveted to one angle
only.
Do not countersink rivets in long pieces unless absolutely necessary.
Do not draw any more of a member than necessary, and do not dimension the same piece
several times.
Revising Drawings. — When drawings have been changed after having been first approved,
tli.-y must be marked, Revised (give date of revision).
cvi
6"
(a)
9'-o"
(b)
FIG. 20.
Measuring Angles. — All measurements on angles are to be made from the back of the angle,
and not from the edge of the flange. The center to center distance between open holes should
always be given for each piece that is shipped separate, in order that the inspector can check the
piece.
Width of Angles. — The widths of the legs of angles are greater than the nominal widths,
unless the angle has been rolled with a finishing roll. The over-run for each leg is equal to the
nominal width of the leg plus the increase in thickness of leg made by spreading the rolls. For
example finishing rolls are used for rolling 3" X 3" angles with a thickness of \". The actual
length of the leg of a 3" X 3" angle is as follows: angle 3" X 3" X i", leg 3"; angle 3" X 3" X ft",
leg 3ft"; angle 3" X 3" X f", leg 3J"; angle 3" X 3" X i", leg 3J"; angle 3" X 3" X f",
leg 3t".
The over-run of Pencoyd angles are given in Table 27, Part II; and the over-run of Pennsyl-
vania Steel Company's angles are given in Table 28, Part II.
POINTS TO BE OBSERVED IN ORDER TO FACILITATE ERECTION.— The first
consideration for ease and safety in erection should be to so arrange all details, joints and con-
nections that the structure may be connected and made self-sustaining and safe in the shortest
time possible. Entering connections of any character should be avoided when possible, notably
on top chords, floorbeam and stringer connections, splices in girders, etc. When practicable,
joints should be so arranged as to avoid having to put members together by entering them on end,
as it is often impossible to get the necessary clearance in which to do this. In all through spans
floor connections should be so arranged that the floor system can be put in place after the trusses
or girders have been erected in their final position, and vice versa, so that the trusses or girders
can be erected after the floor system has been set in place. All lateral bracing, hitch-plates, rivets
in laterals, etc., should, as far as possible, be kept clear of the bottoms of the ties, it being expensive
to cut out ties to clear such obstructions. Lateral plates should be shipped loose, or bolted on
so that they do not project outside of the member, whenever there is danger of their being broken
off in unloading and handling. Loose fillers should be avoided, but they should be tacked on with
rivets, countersunk when necessary.
In elevated railroad work, viaducts and similar structures, where longitudinal girders frame
into cross girders, shelf angles should be provided on the latter. In these structures the expansion
412
STRUCTURAL DRAFTING.
CHAP. XII.
Xsf if f//
/ Clearance "b should 'be ab feast 4 and 2 iF possible-
Clearance "c" should be ab least, %"•
Clearance (td" should be jjl'plus £' for each additional
neb plate when more than two are in chord-
Clearance "e"
must be large
enough to per-
mit access to inside For
riveting-
At "X"cut Flanges
square as shown by Full line and not bevel-
ed 35 shown by dotted tine
s
u
h
Clearance "F" should be 3 when
possible but specifications may call For $ • . ^ - ^3.
*
Clearance "d M should never be less
&**¥
4+
f
-
b f
Clearance "g "should be about •% 9
never less • Clearance "k" should never be less thanl'f.
FIG. 21. CLEARANCE STANDARDS. AMERICAN BRIDGE COMPANY.
CLEARANCE STANDARDS.
413
Ixo-
18
p
1
Tfl
111
ffl
I--O O-Oj
4\ KK> Q- .
< /77 , /77
K— *-
Clearance "a" should never be less khan?
Clearance "b" should never be less than f'From center line bo each piece, and
where possible should bej> •
Clearance "h" should never be /ess than ^" and as a rule should be I •
Always give figure For distance nm"on detail For use oF checker •
When standard Framing angles are used, make "m"=6^M'
Clearances given should be allowed fn addition to overrun oF angles •
FIG. 22. CLEARANCE STANDARDS. AMERICAN BRIDGE COMPANY.
414
STRUCTURAL DRAFTING.
CHAP. XII.
Style 1.
" "
Style 2.
T
Thickness
of Bar
Single Lacing
O=4OT
2'- 1"
1-10H
1- 8
1- 6H
1- 3
1- OX
' 10V
C=5OT
2-1
Double Lacing
C=6OT
3'- 1H"
2- 9K
2- 6 ;
2- 2K
1- 3
0=76 T
2- 81%.
2- 4H
1-1 !%•
1- 6%
2 Rivet.
() -j
u
Width
of
Bar in
Inches
aK
a .
§ Rivet.
1
&»
For § Rivets. \
S"
f'Rivet
I-
Pi
^ feJSta
J c*a
-^
,iC
at
I
oo
UJ
Lengtn to be added to Distance C
For finished length A
V
3H"
3H
3H
For ordered length B
W
FIG. 23. STANDARDS FOR LACING BARS. AMERICAN BRIDGE COMPANY.
RULES FOR ORDERING MATERIALS. 416
joints should be so arrange. I th.it the rivets connecting the fixed span to the croaa girder can be
<lri\vn alt. i tin- c\pan,i.m span is in place. In viaducts, etc., two spans, abutting on a bent,
>h<.ul(I be so arranged that cither span ran be set in place entirely independent of the other. The
same thing applies to uinler spans of different depth resting on the same bent. Holes for anchor-
holts should be so arranged that the holes in the masonry can be drilled and the bolts put in place
after the structure has been erected complete.
In structures consisting of more than one span a separate bed-plate should be provided for
each shoe. This is particularly important where an old structure is to be replaced; if two shoes
were put on one bed plate or two spans connected on the same pin, it would necessitate removing
two old spans in order to erect one new one. In pin-connected spans the section of top chords
t the center should be made with at least two pin-holes. In skew spans the chord splices
should be so located that two opposite panels can be erected without moving the traveler. Tie
plates should be kept far enough away from the joints and enough rivets should be countersunk
inside the chord to allow eye-bars and other members being easily set in place. Posts with
channels or angles turned out and notched at the ends should be avoided whenever possible.
ORDERING MATERIAL.— Bridge Work. — Ordinarily plates less than 48 in. wide are
ordered U. M. (universal mill or edge plates), but when there is no need for milled edges and
prompt delivery is essential specify either U. M. or sheared. Never order widths in eighths.
Flats and universal (edge) plates over 4 in. in width should be ordered in- even inches, flats under
4 in. should be ordered by i in. variation in width. Flats J in. and under in thickness are very
difficult to secure from the mills and should be avoided if possible.
Rolling mills are allowed a variation of J in. in width of plates, over or under, and a variation
of | in. in length, over or under, from the ordered width or length. Rolling mills are allowed a
v.iri.ition of $ in. over or under the ordered length of beams, channels, angles, zees, etc. An
extra price is charged for cutting to exact length. See Chapter XIII.
Allow ^s in. in thickness for planing plates 2 ft. 6 in. square or less, J in. for plates more than
2 ft. 6 in. square, and j; in. for columns; chords and girders which have milled ends are ordered
1 in. longer than the finished dimensions.
Web plates should be ordered i in. less than the back to back of flange angles unless a less
clearance is specified. Web plates should preferably be ordered in even inches and the distance
back to back of angles made in fractions.
When angles, beams or channels are bent in a circle allow 9 in. to 12 in. for bending.
Bent plates should be ordered to the length of the outside of the bend.
out_to oyt___
FIG. 24. BEAMS BETWEEN COLUMNS.
Large gusset plates, large plates with angle cuts, etc., should be ordered as sketch plates,
when the amount of waste if ordered rectangular will exceed 20 per cent. Mills will not make re-
entrant cuts in plates or shapes.
In ordering lacing bars add A in- to the finished length and order in multiple lengths.
ORDERING MATERIAL.— Building Work. — Order beams in foundation neat length.
Order beams framing into beams f in. short for each end, see Fig. 24.
416 STRUCTURAL DRAFTING. CHAP. XII.
Order main column material f in. long for milling both ends (this takes care of permissible
variation in length of plus or minus f in. as well as the milling).
Order girder flange angles and plates I in. long.
Order girder web plates f in. short, where end connections are used.
Order girder web plates neat length, where end connections are not used.
Order girder web plates £ in. less in width than back of flange angles.
Order stiffener angles j in. long.
Order fillers under stiffeners neat length.
Add j^ in. to each lacing bar and order in multiple lengths.
SHAPES AND PLATES MOST EASILY OBTAINED.— The ease with which different
commercial sizes of shapes and plates may be obtained from the rolling mill varies with the mill
and with the demand. Where any section is in demand rollings are frequent and the orders are
promptly filled, while the order for a section not in demand may have to wait a long time until
sufficient orders have accumulated to warrant a special rolling.
The following list of plates and sections is fairly accurate, the list varying from time to time.
Plates. — Plates most easily obtained.
Width, Thickness, Width, Thickness,
In. In. In. In.
i| -fs and | 5 I and up
if YS and | 6 | and up
2 •£§ and \ 7 i and up
2| I and up 8 J and up
2? | and up 9 j and up
3 j and up 10 \ and up
3^ I and up 12 J and up
4 J and up 14 | and up
Over 14 in. in width it is immaterial what width of plate is specified.
Squares and Rounds. — Squares and rounds most easily obtained.
Rounds, f", f", 1", i", if, ij".
Squares, f", f , i", l\"y ij".
All other sizes are liable to cause delay.
Beams. — Sizes of I-Beams which can be obtained most readily.
Depth. Weight.
6" 12! Ib.
8" 18 Ib. 20§ Ib.
10" 25 Ib. 30 Ib.
12" 3iilb. 35 Ib. 40 Ib.
15" 42 Ib. 50 Ib. 60 Ib.
1 8" 55 Ib. 60 Ib. 70 Ib.
20" 65 Ib. 80 Ib.
24" 80 Ib. 90 Ib. loo Ib.
Sizes of I-Beams which may be used but for which prompt deliveries may not be expected.
Depth. Weight.
5" 9f Ib.
7" 15 Ib.
9" 21 Ib. 25 Ib.
Beams of weights different from the above can always be obtained from the mills but not so
readily as those given. Beams of minimum section can always be obtained more readily than
heavier sections.
SHAPES AND PLATES MOST EASILY OBTAINED. 417
Channels. — Channels which can be most readily obtained from the mills.
Depth. Weight.
6" 8 Ib.
8" II Jib. 18} Ib.
10" 15 Ib. 20 Ib. 25 Ib.
12" 2oi Ib. 25 Ib. 30 Ib.
15" 33 Ib. 40 Ib. 50 Ib.
Sizes which may be used but for which prompt deliveries cannot be expected.
Depth. Weight.
5" 6i Ib.
7" 9l Ib.
9" I3i Ib.
Channels of weights different than those given above can always be obtained at the mills
but not so readily as those given. Channels of minimum section can always be obtained more
readily than heavier sections.
Angles. — Angles most easily obtained from the mill.
Even legs.— 2j" X 2*"; 3" X 3": 3i" X 3*"; 4" X 4": 6" X 6".
Uneven legs.— 2\" X 2"; 3" X 2j"; 3*" X 3": 4" X 3"; 5" X 3*"; 6" X 4"-
Angles which may be used but for which prompt deliveries cannot be expected.
Even legs.— 2" X 2"; 2!" X 2j"; 5" X 5"; 8" X 8".
Uneven legs.— 3" X 2"; 3J" X aj": 4" X 3*"; 6" X 3*".
Angles 4" X 3i"; 5" X 4"; 7" X 3*" and 8" X 6" are very difficult to obtain.
To obtain prompt deliveries as few sizes and shapes as practicable should be used for any
contract. For example if 6" X 4" angles are used 6" X 3$" should be avoided, and vice versa.
Tees.— If possible the use of Tees should be confined to 3" X 3" X f " and 2" X 2" X A"i
and even these sizes are uncertain of delivery.
Zees. — The delivery of zees is uncertain and will depend upon special rollings, which do not
occur frequently. The following sizes are the most used, and are therefore most easily obtained.
Web. Thickness.
3" i", A" and |"
4" i", A" and |"
5" A", I" and \"
6" f", i", f", |", I" and i"
Stock Material. — The Pennsylvania Steel Company carries the following material in stock
in 30 ft. lengths for use in its structural plant.
Angles, Even Legs. Angles, Uneven Legs.
6" X 6" X A" and \" 6" X 4" X |", A" and i"
4" X 4" X |" and A" 5" X 3*" X f", A" and \"
3*" X 3i" X |" and A" 4" X 3i" X A" and \"
3" X 3" X A", I" and A" 3*" X 3" X A" and |"
3" X 2i" X A" and |"
Plates. Flats.
20" XI" and J" 7"Xi"
1 8" X I" and i" 6" X I" and i"
16" X I" and i" 3$" X I", i" and f"
15" X I" and i" 3" X f" and A"
14" X |" and \" 2J" X |" and A"
13" X I" and i" 2i" X A" and |"
12" X |", A" and V 2" X 1" and A"
10" X i" and A"
9" X |"
28
418
STRUCTURAL DRAFTING.
CHAP. XII.
Lengths and Widths of Plates. — The maximum sizes and lengths of shapes and plates
rolled by the Carnegie Steel Company and the Illinois Steel Company are given in Table I
Table VII, inclusive.
TABLE I.
MAXIMUM LENGTHS OF SHAPES; CARNEGIE STEEL Co.
Angles (Eneven Legs): —
8" X6" ....................... 80
7" X 3i" X i" to |" ............ 80
7" X 3i" X H" to A" .......... 85
6" X 4" X i" to f" ............. 85
6" X 4" X H" and under ....... 90
6" X 3J" X i" to |". . . ......... 80
6" X 3?" X H" ................ 85
6" X 3i" X f" and under ....... 90
5" X 4" ....................... 90
5"X3i"Xi" ................. 75
5" X 3J" X If" ................ 80
5" X 35" X f" and under ....... 90
I Beams: —
24" to 12" 75 ft.
10" to 5" 70 "
4" and 3" 5o "
Channels: — •
15" to 12" 75 ft.
10" standard 70 "
10" special 80 "
9" to 5" 70 "
4" and 3" So "
Tees: —
5" to i" Soft.
Zees: —
6" and 5" 70 ft.
4" XI" 65 "
4" X H and under 70 "
ft.
5"X3
70
Deck Beams: —
10" 45ft.
9" to 7" 65 "
6" 60 "
Bulb Angles: —
10" to 7" 65 ft.
6" 60 "
5".-.. 65 "
Angles (Even Legs): —
8" X 8" 120 ft.
6" X 6" X i" to |" 80 "
6" X 6" X H" and under 90 "
5" X 5" 85 "
4" X 4" 90 "
3i" X 35" 90 "
3" X 3" '...-. 75 "
2f" X2f" 50 "
2j" X 2\" 5° "
2i" X ~2\" 50 "
2" X2" 50 "
if" X if" to I" Xf" 50 "
90
50
55
60
65
70
42 X3"XH"
4k" X3" X f"
4i"X3" xir
4i"X3" X f"
*i" \/ -," V 9 "
4!" X 3" X \" and under. ... . . 80
4" x 3rr 90
A" V i" V 1 3// fie
4 X 3 X TIT 05
4" X 3" X I" and under 90
3*" X3" Xif" 60
32-"X3"Xf" 65
3t" X 3" X H" 70
32-" X 3" Xf" 75
3^" X 3" X i" and under 80
3i" X 2| X H" 55
3l" X 2^ X f" 60
3i" X 2i X TV 65
3i" X 2^ X J" 70
3^" X 2j X A" 80
3i" X 2^ X f" and under 90
3l" X2" 50
3" X2|"to if" X i" 50
TABLE II.
MAXIMUM LENGTHS OF MATERIAL; ILLINOIS STEEL Co. (SOUTH WORKS).
Angles: —
All angles 100 ft.
I Beams: —
All I Beams up to 15 75 ft.
15 I Beams 42 Ib. to 55 Ib. . 75 "
15 I Beams 60 Ib. to 75 Ib 62 "
15 I Beams 80 Ib 60 "
15 I Beams 90 Ib 50 "
15 I Beams 100 Ib : . 45 "
Channels: —
All Channels 75 ft.
In case it is absolutely essential to have any of the above material in lengths longer than
MAXIMUM SIZES OF SHEARED PLATES.
419
shown, it will be necessary to take the matter up with the mill to ascertain whether same can be
obtained.
For extreme lengths of material rolled at the Bay View (Milwaukee Works) follow list of
maximum lengths rolled by Carnegie, as the facilities for rolling all smaller sections are about
the same at both mills.
TABLE III.
MAXIMUM SIZES OF RECTANGULAR AND CIRCULAR PLATES; CARNEGIE STEEL Co.
SHEARED PLATES, ONE-FOURTH INCH AND OVER.
Thickness,
Widths and Lengths in Inches.
Diam..'
Inches.
Inches.
132
126
1 20
114
1 08
1 02
96
90
84
78
|
I "CO
200
2IO
2CO
280
•3OO
no
A
1 80
2OO
*3W
2^0
260
27C
AJW
•3QO
•J2C
j**»
•?8o
1 2O
P
200
220
2CO
*J«
26?
•7 JO
* f J
•7 rn
jvw
400
J*j
A.A.O
JOU
4.60
126
ft
190
200
240
*
265
*"^3
29O
J ivy
35°
j iw
380
440
Ty
465
^•w
475
132
i
220
230
260
280
300
360
4OO
450
475
500
132
I
22O
230
260
290
300
380
4OO
450
475 .
500
132
22O
230
27O
300
32O
360
380
420
440
480
134
i
2 2O
230
270
300
320
35°
380
420
440
480
134
• •
22O
230
270
29O
32O
350
380
420
440
480
»34
1
220
230
270
29O
32O
350
380
420
440
480
134
I
220
230
260
280
32O
350
380
420
440
480
134
i
2 2O
230
2SO
27O
3OO
320
35°
380
400
430
134
if
2OO
22O
230
250
280
300
320
35°
370
4°5
132
it
190
2OO
2IO
230
2SS
275
295
325
340
360
132
i*
1 80
190
2OO
2IO
240
250
275
300
315
34°
132
i|
175
1 80
190
2OO
225
240
260
285
300
320
132
2
I6S
170
1 80
190
210
230
245
270
280
300
130
2\
132
HS
ISO
160
170
190
200
230
240
260
130
Thickness.
72
66
60
54
50
48
42
36
3°
24
Diam.
i
350
350
380
400
4OO
430
400
400
380
380
no
A
380
400
450
460
460
500
450
45°
400
400
1 2O
!
490
500
540
540
540
540
500
500
480
480
126
r
520
S2S
S6o
S6o
S60
S60
560
560
5S
560
560
560
55°
550
550
55°
530
530
530
530
132
132
A
525
S6o
S60
560
560
560
55°
55°
53°
53°
132
520
560
560
560
560
560
560
560
530
500
134
H
500
530
540
540
560
560
560
540
530
500
134
|
490
500
540
540
560
560
560
54°
530
500
134
H
480
500
520
540
540
540
S6o
54°
520
480
134
i
480
500
52O
520
520
530
530
S30
500
480
134
i
460
480
500
520
520
520
500
480
470
460
134
ii
430
450
470
480
480
500
480
480
470
450
132
ii
380
400
42O
430
43°
450
460
460
450
440
132
il
360
380
400
420
430
440
440
420
420
420
132
1 1
34°
360
380
400
420
430
400
380
380
360
132
2
320
340
360
380
400
400
360
350
350
320
130
2*
280
300
32O
340
350
33°
300
300
250
200
130
Plates 48" wide and under can also be rolled on Universal Mills.
For greater length and Universal Mill Sizes, see Universal Mill Plate Table V.
Plates of greater dimensions than shown in above tables may be submitted for special
consideration.
420
STRUCTURAL DRAFTING.
CHAP. XII.
TABLE IV.
MAXIMUM SIZES OF RECTANGULAR AND CIRCULAR PLATES; CARNEGIE STEEL Co.
SHEARED PLATES, THREE-SIXTEENTHS INCH AND UNDER.
Thickness, Inches,
B W G
Widths and Lengths in Inches
Diam., Inches.
74
72
70
68
66
64
62
60
58
A
2OO
2 2O
240
250
270
290
310
320
330
77
No. 8
2OO
2IO
2IO
220
240
250
260
270
74
No. 9
160
I7O
1 80
200
200
220
2"?O
7O
No. 10
IAO
160
170
170
IQO
2OO
68
t
140
150
150
160
I7O
66
No. ii
140
150
150
160
1 7O
66
No. 12
1 20
130
130
140
ICQ
64
Thickness.
56
54
52
50
48
42
36
30
24
Diam.
A
340
350
360
370
360
360
360
360
360
77
No. 8
270
280
280
290
290
290
290
290
290
74
No. 9
230
240
240
250
250
250
250
250
250
70
No. 10
2 2O
2 2O
230
230
230
230
230
230
230
68
i
1 80
190
190
195
195
200
200
200
200
66
No. ii
1 80
190
190
195
195
200
200
200
200
66
No. 12
160
160
170
I76
1 80
1 80
1 80
1 80
180
64
TABLE V.
MAXIMUM SIZES OF RECTANGULAR UNIVERSAL PLATES; CARNEGIE STEEL Co.
UNIVERSAL MILL PLATES, ONE-FOURTH INCH AND OVER.
Thick-
ness,
Inches.
Widths and Lengths in Inches.
48-46
45-41
40-36
35-31
30-26
25-20
19-17
16-15
14-12
ii
io-6|
1
780
780
780
780
C4O
C4O
ft
600
600
600
660
720
/ v
840
/
840
840
/ "*•
840
OT^
600
^
60O
3
8
840
840
960
1140
1140
1140
1080
1080
1080
9OO
840
&
960
960
960
1140
1140
I20O
1080
1080
1080
9OO
840
1
960
960
1080
1 200
1200
I20O
1080
1080
1080
IO2O
840
A
960
960
1080
1 200
I2OO
I2OO
1080
1080
1080
IO2O
840
5.
960
960
1 020
1 200
I2OO
I2OO
1 020
1080
1080
IO2O
840
|
840
840
960
1080
I08O
I080
1 020
1 020
IO2O
9OO
840
1
780
840
840
960
960
960
960
960
960
9OO
840
I
720
720
720
840
840
840
900
960
960
9OO
840
it
6OO
600
660
708
72O
780
780
900
9OO
840
840
if
?4°
540
600
660
660
660
720
840
840
840
840
ii
480
528
54°
600
6OO
6OO
660
780
840
840
840
1}
480
504
528
540
540
54°
600
720
780
840
840
if
480
480
480
480
480
480
54°
660
72O
840
840
if
420
420
432
420
42O
420
480
600
660
72O
72O
a
420
420
432
420
42O
420
480
540
6OO
660
720
2
420
420
420
408
408
408
420
480
54°
. 600
72O
Plates of greater dimensions than shown in above tables may be submitted for special
consideration.
MAXIMUM SIZES OF UNIVERSAL PLATES.
421
TABLE VI.
MAXIMUM SIZES OF UNIVERSAL PLATES; ILLINOIS STEEL Co.
ThickncM,
Inches.
Width of Plate in Incbe*.
6
7
8
9
10 to 30
i
960
960
960
900
960
ni
960
960
960
960
960
1
960
960
960
960
960
A
960
960
960
960
960
*
960
960
960
960
960
I
960
960
960
960
960
i
960
960
960
960
960
i
810
960
960
960
960
l
75°
930
960
960
960
1
690
860
960
960
960
i.
640
800
910
960
960
H
600
740
850
960
960
i
560
700
800
900
960
itV
530
660
750
850
900
r*
500
620
710
800
850
irV
470
590
670
760
810
ij
450
560
640
720
770
i M-,
420
530
610
680
73°
II
400
580
650
690
irV
390
490
560
620
660
ii
37°
470
530
600
640
360
450
510
570
610
340
430
490
550
590
330
410
470
530
570
ij
320
400
460
510
55°
ijt
310
39°
440
490
530
i*
300
370
430
480
Jii
290
360
410
460
490
2
280
350
400
450
480
All plates both sheared and Universal Mill rolled by Illinois Steel Co., can exceed above lengths
by I ft. If longer lengths are necessary take up with the mill.
DESIGN DRAWINGS FOR STEEL STRUCTURES.
Drawings. — Designs shall be made on standard sized sheets. A scale of J in. to I ft. shall
be a minimum, a larger scale being used if practicable. Give such distances on both plan and
cross-section that the dimensions of either can be understood without reference to the other.
DESIGNS OF MILL BUILDINGS.
Loads. — All roof loads, snow loads, wind loads, floor loads, wheel loads and spacing for
cranes, and in case of bins, the weight per cubic foot and the angle of repose of the material shall
appear on the design drawings.
Diagrams. — Draw as many sections as are necessary to show all transverse bents and trusses,
a plan of lower chord bracing, and views to indicate framing and side views when necessary to
give location of doors and windows. When a sectional view is shown, always mark the location
of the sections on the plan. When two buildings frame into each other the design should always
indicate the framing for the connections, drawing additional sections if required.
422
STRUCTURAL DRAFTING.
CHAP. XII.
Stresses. — The stresses in all members of transverse bents, trusses and latticed and plate
girders, and the loads on all main building columns shall be given on the design drawings. Give
maximum bending moment and maximum shear in all crane girders, plate girders, and floor girders
and columns. Maximum shear and bending moment shall be given for all stringers or I-Beams
used as floor or crane girders.
Notes. — Material (whether O. H. (open-hearth) or Bessemer, soft, medium or structural
steel); specifications (name and date; size of rivets and holes, reamed or punched full size).
Angle Members. — In all cases where two unequal legged angles are used as main members,
show the direction in which the outstanding legs are turned by giving the dimension of the leg
appearing in elevation, or by exaggerating the longer leg.
TABLE VII.
MAXIMUM SIZES OF SHEARED PLATES; ILLINOIS STEEL Co.
Thickness,
Inches.
Width of Plate in Inches.
Diam.
1 2O
us
no
100
90
80
72
60
50
40
3°
A
240
2?O
28O
-?6o
360
7C
16
156
2OO
2OO
24O
T^
•?2O
j
•?2O
•21Q
J*-"-*
4.2O
j ^^
420
/ 3
T T C
A
144
156
J
200
25O
250
T
42O
j **w
420
j **~
480
J Jv
42O
T***
480
480
1 * J
I 2O
1
1 80
200
220
3OO
360
5OO
6OO
6OO
6OO
600
600
126
A
1 80
2IO
220
360
480
500
600
6OO
6OO
600
600
126
1
1 80
2IO
220
360
480
54°
6OO
6OO
6OO
600
600
126"
A
1 80
2IO
220
360
430
480
55°
6OO
600
600
600
126
5
8
1 80
2IO
220
360
4OO
430
500
580
6OO
600
600
126
tt
1 80
2IO
220
32O
350
4OO
450
530
6OO
600
600
126
!
1 80
2IO
220
3OO
32O
36O
410
480
570
600
600
126
tt
1 80
2IO
220
260
3OO
33°
380
440
530
600
600
126
1
1 80
210
220
250
280
310
350
4IO
50O
600
600
126
if
1 80
2OO
210
230
260
3OO
330
390
460
580
600
126
1 80
I9O
2OO
22O
240
27O
310
360
430
54°
600
126
I
160
170
1 80
190
22O
24O
280
320
390
480
600
124
i
t
144
ISO
160
1 80
2OO
2 2O
250
29O
350
440
580
122
i
2
144
ISO
160
1 80
2OO
22O
250
290
290
360
480
122
f
I2C
130
I4O
1 60
1 80
2IO
240
29O
^60
480
1 2O
2
J
1 20
130
I4O
160
190
2 2O
26O
j ^~
330
T.VW
440
"S
Sections. — Give sections of all members used in the structure. Whenever two or more
columns or other members in different locations have the same section, either note it, or mark the
section on each one. For a column of special make-up show a cross section.
Dimensions. — The following dimensions should be given: (i) Height of lower chord of
trusses from floor level; (2) elevation of top of crane rail with clearance; (3) distance c. to c. of
crane rail with clearance; (4) distance b. to b. of angles of all main columns; (5) pitch of trusses
or height of same at heel and slope of upper chord; (6) width and height of ventilator; (7) length
of bays; (8) distance c. to c. of building columns; (9) location and size of stacks ; (10) location and
size of openings and circular ventilators; (n) thickness of all walls, and relation to center line
of columns.
Windows. — Give size and number of lights and height of windows. Show location of all
windows. State whether pivoted, sliding, counter-balanced or fixed, and whether continuous.
State kind of glass.
Doors. — Give dimensions (width by height) and state whether wood or steel, swinging,
lifting, rolling or sliding. State style of track, hangers and latch.
DESIGN DRAWINGS. 423
Louvres. — Note depth on design, and whether wood or metal, fixed or pivoted. If metal
give gage and kind of same.
Corrugated Steel. — Give gage and kind of all corrugated sheeting, painted or galvanized;
method of fastening, lining, etc.
Gutters and Conductors. — Show gutters, conductors and downspouts where necessary and
give size and kind and thickness of metal, methods of fastening, etc.
Circular Ventilators. — Show location on design and note size and kind.
Roofing. — Give kind of roofing material, and thickness of sheathing when used.
Notes. — Note on design the section of: (a) Purlins and form where trussed; (b) girts; (c) sag
rods; (d) lateral bracing; (c) end columns; (f) window posts; (g) door posts.
Connections. — In making a design be sure that all clearances and connections with adjoining
structures are properly provided for and that all dimensions necessary for detailing of same are
given on the design.
DESIGNS OF PLATE GIRDER BRIDGES.
Loads. — Give assumed dead, live and wind loads, and show diagram of wheel loads.
Diagram and Views. — Show an elevation of girder with stiffeners, a plan with lateral bracing,
and a half end view and a half intermediate section.
Stresses. — Give maximum bending moments and maximum shears, maximum stresses,
required and actual net area of flanges, noting number of rivets deducted, and required net and
actual gross areas»of webs.
Dimensions. — The following dimensions should appear on all plate girder designs. Distance
b. to b. of end angles, or distance out to out of girders, c. to c. of bearings, back wall to back wall,
or c. to c. of piers, b. to b. of flange angles, spacing of girders and track stringers, base of rail to
masonry, end of steel to face of back wall, angle of skew if any, and grade of base of rail.
For girder bridges on curves give the curvature and super-elevation of outer rail and distance
from top of masonry to base of low rail. Give elevation of grade and of masonry on a vertical
line through center of end bearing.
Rivet Spacing. — Note on the elevation of girders the spacing of rivets connecting flange
angles to web, changing spacing at stiffener points. Give number of rivets in single shear for end
connections of all laterals and cross frames.
Shoes and Pedestals. — Give maximum reaction, required and actual area of masonry plate,
with allowable pressure on masonry. Note size of bed plate, and show in position with location
of holes for anchor bolts. Note size and number of rollers for expansion pedestal, and also whether
pedestal is built, cast iron or steel.
Expansion Points. — Mark fixed and expansion points and show whether pedestals or bearing
plate-* are to be used.
Stiffeners. — Show end and intermediate stiffeners on elevation of girder, giving sections and
stating whether fillers are used, or stiffeners crimped.
Super- elevation. — If the bridge be on a curve, show how the super-elevation of the outer
rail is to be cared for, whether by tapering ties, or changing height of pedestal or masonry plate.
Track. — Show track in place, noting such information as size and notching of ties and guard
timbers and manner of connecting timber deck to the girder. For through girder always show
clearance diagram with dimensions.
Notes. — (a) Material (whether O. H. (open-hearth) or Bessemer, soft, medium or structural
steel) ; (b) specifications (name and date) ; (c) size of rivets and holes, reamed or punched full size.
DESIGNS OF TRUSS BRIDGES.
Loads. — Always give the following assumed loads on the stress sheets.
Dead Loads. — (a) Weight of track in Ib. per lin. ft. of track; (b) weight of trusses and bracing
per lin. ft. of bridge; (c) weight of stringer and stringer bracing per lin. ft. of bridge; (d) weight
of floorbeams per lin. ft. of bridge.
424 STRUCTURAL DRAFTING. CHAP. XII.
Live Load. — (Diagram of wheel loads.)
Wind Load.
Diagrams. — In general, the design shall show an elevation of the truss, plan of top lateral
bracing, plan of bottom lateral bracing and stringer bracing, half end view showing portal, half
intermediate view, or as many intermediate views as are necessary to show intermediate sway
frames. The end view shall show track in place with information similar to that for plate girders.
The design of a pin-connected bridge shall show the sizes of pins and the arrangement of the
members at all panel points.
Stresses. — Give the stresses in all members of trusses as follows: D. L. (Dead Load); L. L.
(Live Load); I. (Impact); C. (Curvature); W. (Wind Stresses). Also total stresses.
Always use the minus sign for tensile stress and the plus sign for compressive stress. Compute
and give traction stresses for viaduct towers.
For stringers and floorbeams give the bending moment and shear and stresses in the same
manner as for plate girders.
General Dimensions. — The most important dimensions are, number of panels and length,
depth of truss at every panel point if upper chord is curved, distance c. to c. of trusses, distance
base of rail to masonry, distance center of end pin to masonry, distance c. to c. of end pins and
face to face of masonry, or c. to c. of piers. If the bridge be on a curve, give the degree and show
direction of curvature, the distance of base of low rail to masonry, and the super-elevation of
outer rail. Note that greater clearances are required on curves. Show the clearance line and line
of base of rail in the elevation of truss.
Compression Members.— Give the actual unit stress, the allowable unit stress, radius of
gyration, moment of inertia, actual and required area, eccentricity and cross-section.
Tension Members. — Give allowable and actual stresses, the required and actual net area.
For built sections give number of holes deducted for rivets in obtaining net area, and radius of
gyration.
Sections. — Give section of every member and thickness of all gusset plates. Always give
size of lacing bars, and state whether single or double lacing is required.
Built Sections. — On all built sections give depth of section, and in using plate and angle
sections, make the web | in. less in width than the depth of section.
Angles with Unequal Legs. — In any member composed of one or more angles with unequal
legs, show clearly the direction in which the long or short leg is turned.
Rivets. — Note the number of rivets to be used for end connections of all members, and give
the number of rivets in single shear required at end connection of track stringers.
Shoes or Pedestals. — Give maximum reaction, required and actual area of masonry plate,
with allowable pressure on masonry. Note size of bed plate, and show in position with location
of holes for anchor bolts. Note size and number of rollers for expansion pedestal, and also whether
pedestal is built, cast iron or steel.
Camber. — The amount of camber should be shown on the design.
Notes. — Same as for Plate Girders.
CHAPTER XIII.
ESTIMATES OF STRUCTURAL STEEL.
GENERAL INSTRUCTIONS.— When an estimate of the structural steel in a structure
is to be made the man in charge shall immediately examine all of the data furnished to see that
he has sufficient information to make a satisfactory estimate. He shall fill out the data sheet
completely, and then take off the quantities. Use only the standard estimate blanks for taking
off material. The author has found the estimate blank below very satisfactory.
CROCKER C& KETCHUM
Consulting Engineers
'
Feb.E5.19lg
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' Number each page consecutively, and when all the quantities are totaled prepare a summary
on the last page. Each sheet shall have the sheet number and also the total number of sheets
in the estimate, for example 9 of 20. This will prevent the loss of a page. After the estimate is
completely taken off another man shall check it. When checked the estimate shall be extended
by the checker, each sheet being immediately totaled up as extended. The extensions shall then
be checked by the original estimator, who also prepares a summary. The summary is then
checked by the checker and the estimate is complete.
The estimate should be practically a condensed bill of material of the work, and should be
so clearly made that a reference to the estimate will show at a glance the weight of all the principal
pieces. Main and secondary trusses, main columns, girders, crane gilders, etc., for buildings;
and trusses, girders, floorbeams, etc., for bridges should be taken off separately, thus — I truss,
6 required — and shall not be mixed together even though the correct weight is obtained. In
making an estimate the following order will be found convenient.
i. MILL BUILDINGS. — Trusses. — Top chords, lower chords, web members, purlin lugs,
gusset plates, connection plates, splice plates, eave strut connections, knee, braces and knee
brace connections.
Ventilator Trusses. — Rafters, posts, web members, gusset plates, connections to trusses and
purlin lugs.
425
426 ESTIMATES OF STRUCTURAL STEEL. CHAP. XIII.
Columns. — Column angles, web plate, base plate and angles, crane seat and cap. Base in-
cludes anchor bolts.
Crane Girders. — Flange angles, web plate, cover plates, end stiffeners, intermediate stiffeners,
fillers, knee braces and knee brace connections. Rails, splice bars, clips and crane stops.
Miscellaneous. — Eave struts, lattice girders, purlins, girts, ridge struts, lower chord struts,
column struts, rafter bracing, lower chord diagonals, reinforcing angles for purlins used as rafter
struts, and sag rods.
Miscellaneous Materials Not Structural Steel. — Corrugated steel roofing and siding, louvres,
flashing and ridge roll, gutters, conductors, downspouts, ventilators, stack collars. Windows,
doors, skylights, operating device, lumber, roofing, brick and concrete.
2. OFFICE BUILDINGS. — Floorbeams, girders, including all their connections not riveted
to other members. Floors should be estimated separately using a multiplier if two or more are
exactly alike.
Columns. — Columns including splices and connections riveted to the columns. If columns
are of Bethlehem "H" sections, it should be so noted on the estimate summary. Estimate columns
in tiers.
Miscellaneous, such as suspended ceilings, galleries, penthouses, lintels, curb-angles, canopies,
etc.
3. TRUSS BRIDGES. — Truss members should be taken off separately in order that the
estimate will show at a glance the weight of any main member. Never write off material for
the trusses thus, "5 — Truss — 4 Req'd."
n Stringers; floorbeams; pprtals; sway trusses; upper laterals; lower laterals: shoes, masonry
plates, anchor bolts, etc.
A convenient order can easily be arranged for other structures.
INSTRUCTIONS FOR TAKING OFF MATERIAL.— Quantity estimates shall give the
shipping weights, not shipping weights plus scrap. Pin plates, gusset plates, etc., shall be taken
off as equivalent rectangular plates. Large irregular plates or small irregular plates which occur
in larger numbers shall have the exact sizes shown in the estimate and should have their weights
accurately calculated. All quantity estimates shall be made out with black drawing ink.
The following colored pencils shall be used in estimating:
Black.— lr\ taking off quantities, all check marks on drawings or blue prints shall be made
with a black pencil.
Red. — In checking "quantities taken off" all check marks on drawings, blue prints and
data sheets shall be made with a red pencil.
Blue. — Blue pencils shall be used for checking extensions, also for making notes, corrections,
alterations or additions on white prints or tracings.
Yellow. — All alterations, corrections or additions, on blue prints at the time of estimating
shall be made with a yellow pencil.
All notes on blue prints or drawings in regard to alterations, corrections or additions shall be
dated and signed by the person in charge of the estimate. In general all work shall be taken off
in feet and inches. Lengths of bolts shall be given in feet and inches.
CLASSIFICATION OF MATERIAL.— In making the summary steel and iron should be
classified as follows:
Bars, including plates 6 in. wide and under, rounds up to 3 in. in diameter and squares up
to 3 in. on a side.
Plates (a) Flats over 6 in. wide up to and including 100 in., and ? in. thick and over.
(6) Flats over 100 in. wide up to and including no in.
(c) Flats over no in. wide up to and including 115 in.
(d) Flats over 115 in. wide up to and including 120 in.
(e) Flats over 120 in.
(/) Plates & in. thick,
(g) Plates | in. thick.
CLASSIFICATION OF MATERIAL. 427
(*) Plates checkered.
($') Plates buckle.
Angles (a) Having both legs 6 in. wide or under.
(b) Having either leg more than 6 in. in width.
(c) Having both legs less than 3 in. in width.
Channels and I- Beams
(a) Channels and beams up to and including 15 in. in depth.
(6) Over 15 in. in depth.
If Bethlehem sections are used distinguish between "Bethlehem Special I-Beams" and
"Girder Beams," and also regarding depths as above.
Zees.
Tees.
Rails (Separate rails under 50 Ib. per yd., rails over 100 Ib. per yd., and girder rails).
Rail Splices.
Iron Castings.
Steel Castings.
Nuts.
Clevises and Turnbuckles.
Pins, rounds from 3 in. diameter to 6| in. in diameter.
Forgings, rounds over 6J in. in diameter.
Bronze, Lead, etc.
Rivets and Bolts.
Rivet Heads. — Where the estimate is made from shop drawings the actual number of rivet
heads shall be determined. The weight of rivet heads in per cent of the total weight of the other
material is about as follows: Purlins, girts and beams, 2 per cent; trusses and bracing, 4 per cent;
plate girders and columns of 4 angles and I pi., 5 per cent; plate girders and columns with cover
plates, 6 per cent; box girders or channel columns with lacing, 7 per cent; trough floors, 8 to IO
per cent.
The rivet heads in highway bridges may be taken at 5 and 4 per cent of the total weight
of steel exclusive of fence and joists for riveted and pin-connected trusses, respectively.
Bolts are usually taken off in the estimate when they occur, and entered as rivets. When
bolts are under 6 in. in length, include bolts under the item " Bolts and Rivets." When over
6 in. in length, put the bolts under "Bars."
Miscellaneous Materials. — Corrugated Steel. — Always give the number of gage, whether
painted or galvanized, and whether iron or steel. This remark also applies to louvres, flashing,
ridge roll, gutters and conductors. State whether corrugated steel is for roofing or siding. Roofing
shall be estimated in squares of 100 sq. ft., adding three feet on each end of building to the distance
c. to c. of end trusses to allow for cornice. Allow one foot overhang at eaves. Siding shall be esti-
mated in squares of 100 sq. ft., adding one foot at each end of building to allow for corner laps.
Louvres shall be estimated in sq. ft. of superficial area, stating whether fixed or pivoted.
Flashing shall be estimated in lineal feet and shall be taken off over all windows where corru-
gated sheathing is used on the sides of building, and under all louvres and windows in ventilators.
Ridge roll shall be estimated in lineal feet, adding one foot to the distance center to center
of end trusses. Ridge roll is usually taken off the same gage as the corrugated steel roofing.
Gutters and conductors shall be estimated in lineal feet, the conductors usually being spaced
from 40 to 50 ft., depending upon the area drained.
Circular ventilators shall be estimated by number, giving diameter and kind, if specified.
Stack collars shall be estimated by number, giving diameter of stack.
Windows shall be estimated in sq. ft. of superficial area, taking for the width the distance
between girts. State whether windows are fixed, sliding, pivoted, counter-balanced or counter-
weighted. State kind and thickness of glass and give list of hardware, and any thing else of a
special nature.
428 ESTIMATES OF STRUCTURAL STEEL. CHAP. XIII.
Doors shall be estimated in sq. ft.; state whether sliding, lifting, rolling or swinging. Steel
doors covered with corrugated steel shall be estimated by including the steel frame under steel
and the covering with corrugated steel siding. State style of track, hangers and latch.
Skylights shall be estimated in sq. ft., giving kind of glass and frames.
Operating devices for pivoted windows or louvres shall be estimated in lineal feet.
Lumber shall be estimated in feet, board measure, noting kind. Note that lumber under
I in. in thickness is classified as I in. Above I in. it varies by j in. in thickness, and if surfaced
will be i in. less in thickness, i. e., if in. sheathing is actually if in. thick, but shall be estimated
as if in. Lumber comes in lengths of even feet?; if a piece 10 ft.-8 in. or n ft.-o in. is required, a
stick 12 ft.-o in. long shall be estimated. In using lumber there is usually considerable waste de-
pending upon the purpose for which it is intended. In estimating tongue and grooved sheathing
10 to 20 per cent shall be added for tongues and grooves and from 5 to 10 per cent for waste,
depending upon the width of boards and how the sheathing is laid.
Composition roofing or slate shall be estimated in squares of 100 sq. ft., allowing the proper
amount for overhang at eaves and gables and for flashing up under a ventilator or on the inside
of a parapet wall.
Tile roofing or slate shall be estimated in squares of 100 sq. ft., adding 5 per cent for waste.
Include in an estimate for tile roof, gutters, coping, ridge roll, plates over ventilator windows and
plates under ventilator windows, these being estimated in lineal feet. Flat plates for the ends
of ventilators shall be estimated in sq. ft.
Brick shall be estimated by number. For ordinary brick such as is used in mill building
construction, estimate 7 brick per sq. ft. for each brick in thickness of wall, i. e., a 9 in. wall is two
bricks thick and contains 14 brick for each sq. ft. of superficial area.
Always note whether walls are pilastered or corbeled and estimate the additional amount of
brick required. If walls are plain, no percentage need be added for waste, but if openings such
as arched windows occur add from 5 to 10 per cent.
Concrete shall be estimated in cubic yards. Walls or ceiling of plaster on expanded metal
shall be estimated in squares of 100 sq. ft., noting thickness and kind of reinforcement. Rein-
forced concrete floors shall be estimated in sq. ft. of floor area, noting thickness and kind of rein-
forcement. Paving of all kinds is estimated in square yards, but the concrete filling under the
pavement itself is estimated in cubic yards. Concrete floor on cinder filling is usually estimated
in square yards, specifying its proportions.
ESTIMATE OF COST. — The different types of framed steel structures vary so much with
local conditions and requirements that it is only possible to give data that may be used as a guide
to the experienced estimator. The cost of steel frame structures may be divided into (i) cost of
material, (2) cost of fabrication, (3) cost of erection, and (4) cost of transportation.
i. Cost of Material. — The price of structural steel is quoted in cents per pound delivered
f. o. b. cars at the point at which the quotation is made. Current prices may be obtained
from the Engineering News, Iron Age or other technical papers. The present prices (1914)
f. o. b. Pittsburgh, Pa., are about as follows:
TABLE I.
PRICES OF STRUCTURAL STEEL (1914) F. o. B. PITTSBURGH, PA., IN CENTS PER POUND.
Price in Cts.
Material. per Lb.
I-beams, 1 8 in. and over 55
I-beams and channels, 3 in. to 15 in 45
H-beams, over 8 in 60
Angles, 3 in. to 6 in. inclusive 45
Angles, over 6 in 50
Zees, 3 in. and over i .45
Angles, channels, and zees, under 3 in 1.40
COST OF DRAFTING. 429
Deck beams and bulb angles 1.75
Checkered and corrugated plates 1.75 to 1.90
1 Mates, structural, base 1.40
Plates, flange, base 1.50
Corrugated steel No. 22, painted 2.15
Corrugated steel No. 22, galvanized 3.00
Steel sheets Nos. 10 and 1 1 , black 1 .90
Steel sheets Nos. 10 and 1 1 , galvanized 2.35
Steel sheets No. 22, black 2.10
Steel sheets No. 22, galvanized 2.95
Bar iron, base 1 .65
Rivets 2.10
COST OF FABRICATION OF STRUCTURAL STEEL.— The cost of fabrication of
structural steel may be divided into (a) cost of drafting, (b) cost of mill details, and (c) cost of
shop labor.
(a) COST OF DRAFTING. — The cost of drafting varies with the character of the structure
and with the shop methods of the bridge company. There are two general methods in common
use for detailing steel structures, sketch details, and complete details (see Chapter XII). The
cost of drafting varies with the method of detailing and the number of pieces to be made from
one detail, and costs per ton may mean but little and be very misleading. The cost per standard
sheet (24 in. X 36 in.) is more nearly a constant and varies from $15 to $25 per sheet. The
following approximate costs, based on a total average charge of 40 cents per hour may be of value.
Mill and Mine Buildings. — Details of ordinary steel mill buildings cost from $2 to $4 per
ton; details for head works for mines cost from $4 to $6 per ton; details for churches and court
houses having hips and valleys, cost from $6 to $8 per ton; details for circular steel bins cost
from $1.50 to $3 per ton; details for rectangular steel bins cost from $2 to $4 per ton; details for
conical or hopper bottom bins cost from $4 to $6 per ton.
Bridges. — Details of steel bridges will cost from $i to $2 per ton where sketch details are
used and from $2 to $4 per ton where the members are detailed separately.
Actual Cost of Drafting. — The details of the Basin and Bay State Smelter, containing 270
tons, cost $2 per ton.
The costs of making shop details for steel structures as given in the Technograph No. 21,
1907, by Mr. Ralph H. Gage, are given in Table II.
TABLE II.
COST OF SHOP DRAWINGS.
Character of Building.
Average Cost per Ton.
Entire skeleton construction, i. e., loads all carried to the foundation by means
of steel columns
Interior portion supported on steel columns; exterior walls carry floor loads
and their own weight
Interior portion carried on cast iron columns; exterior waHs support floor loads
as well as their own weight
No columns and floorbeams resting on masonry walls throughout
Structure consisting mostly of roof trusses resting on columns
Structure consisting mostly of roof trusses resting on masonry walls
Mill buildings
Flat one-story shop or manufacturing buildings
Tipples, mining structures or other complicated structures
Malt or grain bins and hoppers
Remodeling and additions where measurements are necessary before details
can be made
$1.45
1.22
0.70
0.85
2.47
"I
2.56
0.74
4.88
2-47
1.87
430 ESTIMATES OF STRUCTURAL STEEL. CHAP. XIII.
Mr. Gage makes the following comments on the cost of drafting: "The cost of drafting
materials and blue prints was not included. There is always a noticeable decrease in cost of
the details when the plans for the ironwork are made and designed by an engineer and separated
from the general work. On the average it cost 35 per cent more to make shop drawings of the
structural steel when the data were taken from the architect's plans than when the data were
taken from carefully worked out engineer's plans. Inaccurate plans where the draftsman is
continually finding errors which must be referred to the architect materially increase the cost of
shop drawings."
(6) COST OF MILL DETAILS. — If material is ordered directly from the rolling mill the
price for the necessary cutting to exact length, punching, etc., is based on a standard "card of
mill extras."
CARD OF MILL EXTRAS.— If the estimate is to be based on card rates it will be necessary
to have the subdivisions a, b, c, d, e, f, r, etc., as follows:
a = o.i $cts. per Ib. This covers plain punching one size of hole in web only. Plain punching,
one size of hole in one or both flanges.
b = o.2^cts. per Ib. This covers plain punching one size of hole either in web and one flange
or web and both flanges. (The holes in the web and flanges must be of same size.)
c = o.^octs. per Ib. This covers punching of two sizes of holes in web only. Punching of
two sizes of holes either in one or both flanges. One size of hole in one flange and another size
of hole in the other flange.
d = o.$5cts. per Ib. This covers coping, ordinary beveling, riveting or bolting of connection
angles and assembling into girders, when the beams forming such girders are held together by
separators only.
e = o.^octs. per Ib. This covers punching of one size of hole in the web and another size of
hole in the flanges.
/ = o.i^cts. per Ib. This covers cutting to length with less vibration than + f in.
r = o.$octs. per Ib. This covers beams with cover plates, shelf angles, and ordinary riveted
beam work. If this work consists of bending or any unusual work, the beams should not be
included in beam classification.
Fittings. — All fittings, whether loose or attached, such as angle connections, bolts, separators,
tie rods, etc., whenever they are estimated in connection with beams or channels to be charged
at i.55cts. per Ib. over and above the base price. The extra charge for painting is to be added
to the price for fittings also. The base price at which fittings are figured is not the base price of
the beams to which they are attached but is in all cases the base price of beams 15 in. and under.
The above rates will not include painting, or oiling, which should be charged at the rate of
o.iocts. per Ib. for one coat, over and above the base price plus the extra specified above.
For plain punched beams where more than two sizes of holes are used, o.iscts. per Ib. should
be added for each additional size of hole, for example, plain punched beams, where three sizes of
holes occur would be indicated as: c + o.iscts., four sizes of holes; e + o.iocts. For example:
a beam with f in. and f in. holes in the flanges and f in. and f in. holes in the web should be
included in class e.
Cutting to length can be combined with any of the other rates, class d excepted, and would
have to be indicated; for example: Plain punching one size of hole in either web and one flange,
or web and both flanges, and cutting to length would be marked bf, which would establish a total
charge of o.4octs. per Ib.
Note to class d. — No extra charge can be added to this class for punching various sizes of
holes, or cutting to exact lengths; in other words; if a beam is coped or has connection angles
riveted or bolted to it, it makes no difference how many sizes of holes are punched in this beam,
the extra will always be the same, namely o.35cts. When beams have angles or plates riveted to
them, and same are not half length of the beam, figure the beams as class d, and the plates and
angles as beam connections.
Note to class r. — This rate of o.socts. per Ib. applies to all the material making up the riveted
beam. In case of assembled girders in which one of the beams should be classed as a riveted
beam, in making up the estimate, figure only the beam affected as included in class "r." When
beams have angles or plates riveted to them and same are half length or more than half length
of the beam, figure the beams as class "r," including the plates or angles and rivets. When
1 8 in., 20 in., or 24 in. beams are in "r" class keep the I's separate from the material (plates,
cast iron, separators, angles and nvets) which should go under heading, "15 in. I's and Under."
Beams should be divided as 15 in. I's and under, and 18 in., 20 in. and 24 in. I's. If there
are only one or two sizes of beams in any particular class, give exact sizes, instead of "15 in. I's
and Under."
COST OF MILL DETAILS. 431
In estimating channel roof purlins classify 7 in. channels and smaller as one punched; 8 in.
cli.niii.-l-, .mil larger as two punched, unless they are shown or noted otherwise, and keep separate
from i idirr U-a ins.
No extra charm- '"•l" 'Ir a.l.li-d to curved beams for riveting, cutting to length, etc.
Subdividing work into a larnt1 nmnlH-r of classes should t>e avoided; it is better to have too
few classes, radicr than too many.
Tin- only sulxliviMon necessary for cast iron columns are: I in. and over, and under I in.
Columns with ornamental work cast on must be kept separate.
Round and Square Bars. — In estimating round and square bars use the standard card for
rxt ras, Table III. It is not usual to enforce more than one-half the standard card extras for round
a n.l square bars.
Extras. — Shapes, Plates and Bars:
(Cutting to length)
Under 3 ft. to 2 ft., inclusive 0.25 ct. per Ib.
Under 2 ft, to l ft., inclusive 0.50 ct. per Ib.
Under i ft 1.55 ct. per Ib.
Extras — Plates (Card of January 7, 1902):
Base J in. thick, 100 in. wide and under, rectangular (see sketches).
Per too Lb.
Widths — 100 in. to 1 10 in $ .05
no in. to 115 in 10
1 15 in. to 120 in 15
120 in. to 125 in 25
125 in. to 130 in 50
Over 130 in l.oo
Gages under J in. to and including & in 10
Gages under r\ in. to and including No. 8 15
Gages under No. 8 to and including No. 9 25
Gages under No. 9 to and including No. 10 . . 30
Gages under No. 10 to and including No. 12 40
Complete circles 20
Boiler and flange steel 10
Marine and fire box 20
Ordinary sketches 10
(Except straight taper plates, varying not more than 4 in. in width at ends, narrowest end
not less than 30 in., which can be supplied at base prices.)
TABLE III.
STANDARD CLASSIFICATION OF EXTRAS ON IRON AND STEEL BARS.*
Rounds and Squares.
Squares up to 4$ inches only. Intermediate sizes take the next higher extra.
Per 100 Lb.
} to 3 in Rates.
I to Ji ' $0.10 extra.
to
1 i
and
.20
.40
•50
.70
i.oo
• 2.00
A , 2.50
3rV to 3^ 15
* This classification has been quite generally adopted, although several firms issue a special
card of extras.
432
ESTIMATES OF STRUCTURAL STEEL.
CHAP. XIII
3rV to 4 in.
4tV to 4!
4ft to 5
5| to |J
to 6
to 65
to 71
TABLE III.— Continued.
STANDARD CLASSIFICATION OF EXTRAS ON IRON AND STEEL BARS.
Flat Bars and Heavy Bands.
5
6|
6f
Flat Bars and Heavy Bands.
J
to
6 ii
1 V
1
to I
ii
i
I
to
6
V
i
and
ii
to
V
j
to
7 '
to
IF
x
and
TO
9
and
1
x
to
i
and
V
|
and-
ft
1
V
i
and
i
V
and i
.
V
1
2
x
i
and
5
3
V
i.
and
jL
i
to
6 in. '
v T-A
to i^
in. .
1
to
6 "
v TI
to 15
if
to
6 "
V T£
to 2\
«
^
to
6 "
X •*
to 4.
n
Light Bars and Bands.
I*
1^
I
to 6 in.
to 6 in.
to 1 3^ in.
in.
in.
in.
in.
in.
in.
in.
I to
H to
Hand
Hand
H and
T%and
i^and
*
I
o, 9 and ^ in. . .
, ii, 12 and i in.
8, 9 and ^g in. . .
ii, 12 and | in.
3, 9 and ^ in. . .
II, 12 and | in.
8, 9 and ^g in. .
, ii, 12 and | in.
8, 9 and tV m- • •
n, 12 and | in.
3, 9 and tV m
n, 12 and A
', 9 and 3
X Nos. 7,
X Nos. 10,
X Nos. 7, 1
X Nos. 10,
X Nos. 7, !
X Nos. 10,
X Nos. 7, ;
X Nos. 10,
X Nos. 7, i
X Nos. 10,
X Nos. 7, i
X Nos. 10,
X Nos. 10, ii, 12 and | in
X Nos. 7, 8, 9 and ^ in.. .
X Nos. 10, n, 12 and | in,
in.
m.
.25 extra.
•30
.40
•50
•75
i.oo
1-25
Per 100 Lb.
Rates.
$0.20 extra.
.40
•50
•50
.70
.90
1. 10
I.OO
1. 20
1.50
.10
.20
•30
.40
Per 100 Lb.
$0.40 extra.
.60
•50
.70
.70
.80
I.OO
1.20
1.20
1.30
1.30
1.50
1. 80
2.10
I.QO
2.40
Mill Orders. — In mill orders the following items should be borne in mind. Where beams butt
at each end against some other member, order the beams f in. shorter than the figured lengths
this will allow a clearance of \ in. if all beams come f in. too long. Where beams are to be built
into the wall, order them in full lengths, making no allowance for clearance. Order small plates
in multiple lengths. Irregular plates on which there will be considerable waste should be ordered
cut to templet. Mills will not make reentrant cuts in plates. Allow \ in. for each milling for
members that have to be faced. Order web plates for girders J to \ in. narrower than the distance
back to back of angles. Order as nearly as possible every thing cut to required length, except
where there is liable to be changes made, in which case order long lengths.
It is often possible to reduce the cost of mill details by having the mills do only part of the
work, the rest being done in the field, or by sending out from the shop to be riveted on in the field
connection angles and other small details that would cause the work to take a very much higher
SHOP COST OF STRUCTURAL STEEL. 433
Si.in.I.ini «.nu<( tions should be used wherever possible, and special work should be
avuiili-tl. I 01 additional notes on ordering material, see Chapter XII.
In i-stimatinu tin- ro>t «>f plain mad rial in a finished structure the shipping weight from the
structural *hop is wanted. The cost of material f. o. b. the shop must therefore include the cost
of \vasti-, paint material, and tin- freight from the mill to the shop. The waste is variable but
a^ an average may be taken at 4 per cent. Paint material may be taken as two dollars per ton.
Tin- cost of plain material at the shop would be
Average cost per Ib. f. o. b. mill, say 1-75 cts.
Add 4 per cent for waste 07
Add $2.00 per ton for paint material 10
Add freight from mill to shop (Pittsburg to St. Louis) 225 "
Total cost per pound f. o. b. shop 2.145"
To obtain the average cost of steel per pound multiply the pound price of each kind of material
by the percentage that this kind of material is of the whole weight, the sum of the products will
be the average pound price.
(c) COST OF SHOP LABOR. — The cost of shop labor may be calculated for the different
parts of the structure, or may be calculated for the structure as a whole. The following costs
are based on an average charge of 40 cents per hour and include detailing and shop labor. The
cost of fabricating beams, channels and angles which are simply punched or have connection
angles loose or attached should be estimated on the basis of mill details, which see.
SHOP COSTS OF STEEL FRAME BUILDINGS.— The following costs of different parts
of steel frame office and mill structures are a fair average.
Columns. — In lots of at least six, the shop cost of columns is about as follows: Columns
made of two channels and two plates, or two channels laced cost about 0.80 to 0.70 cts. per Ib.,
for columns weighing from 600 to 1,000 Ib. each; columns made of 4 angles laced cost from 0.80
to i.io cts. per Ib.; columns made -of two channels and one I-beam, or three channels cost from
0.65 to 0.90 cts. per Ib. ; columns made of single I-beams, or single angles cost about 0.50 cts. per
Ib.; and Z-bar columns cost from 0.70 to 0.90 cts. per Ib.
Plain cast columns cost from 1.50 to 0.75 cts. per Ib., for columns weighing from 500 to 2,500
Ib., and in lots of at least six.
Roof Trusses. — In lots of at least six, the shop cost of ordinary riveted roof trusses in which
the ends of the members are cut off at- right angles is about as follows: Trusses weighing 1,000 Ib.
each, 1.15 to 1.25 cts. per Ib.; trusses weighing 1,500 Ib. each, 0.90 to i.oo cts. per Ib.; trusses
weighing 2,500 Ib. each, 0.75 to 0.85 cts. per Ib.; and trusses weighing 3,500 to 7,500 Ib. 0.60 to
0.75 cts. per Ib. Pin-connected trusses cost from o.io to 0.20 cts. per Ib. more than riveted trusses.
Eave Struts. — Ordinary eave struts made of 4 angles laced, whose length does not exceed
20 to 30 ft., cost for shop work from 0.80 to i.oo cts. per Ib.
Plate Girders. — The shop work on plate girders for crane girders and floors will cost from
0.60 to 1.25 cts. per Ib., depending upon the weight, details and number made at one time.
TABLE IV.
SHOP COST OF CIRCULAR AND RECTANGULAR BINS AND STAND-PIPES, NOT INCLUDING
HOPPERS OR BOTTOMS.
Shop Cost in Cents per Lb.
Water Tight.
Bins.
t
0.90
0.8$
0.80
0.80
0-75
0.70
1
0.75
0.65
29
434:
ESTIMATES OF STRUCTURAL STEEL.
CHAP. XIII.
SHOP COSTS OF BINS AND STAND-PIPES. — Shop costs for circular and rectangular
bins and stand-pipes are given in Table IV, while shop costs for bin and elevated tank bottoms
are given in Table V. The shop cost of towers for elevated tanks are given in Table VI.
TABLE V.
SHOP COST OF BOTTOMS FOR CIRCULAR AND RECTANGULAR BINS AND STAND-PIPES.
Thickness of Material,
Flat Bottom, Cents
Spherical Bottom,
Conical Bottom, Cents
Hopper Bottom, Cents
In.
per Lb.
Cents per Lb.
per Lb.
per Lb.
J
1.50
4.00
3-50
2.50
A
1-45
4-IS
3.00
2.40
f
1.40
4.40
2-75
2.25
*
1-25
4.50
2.50
2.0O
TABLE VI.
SHOP COST OF TOWERS FOR ELEVATED TANKS AND BINS.
Weight of Tower and Bracing in Lb.
Shop Cost in Cents per Lb.
Adjustable Bracing.
Riveted Bracing.
10 ooo and less
1.30
1.25
I- IS
I.IO
1.20
I.IO
1.05
I.OO
10 ooo to 20 ooo
20 ooo to 50 ooo
50 ooo and up
SHOP COSTS OF INDIVIDUAL PARTS OF BRIDGES.— The cost of fabricating joists
and other similar members should be estimated on the basis of mill details, which see.
Eye-Bars. — The shop cost of eye-bars varies with the size and length of the bars and the
number made alike. The following costs are a fair average: Average shop costs of bars 3 in. and
less in width and f in. and less in thickness is from 1.20 to 1.80 cts. per lb., depending upon the
length and size. A good order of bars running 2\ in. X f in. to 3 in. X f in., and from 1 6 to 20
ft. long, with few variations in size, will cost about 1.20 cts. per lb. Large bars in long lengths
ordered in large quantities can be fabricated at from 0.55 to 0.75 cts. per lb. To get the total cost
of eye-bars the cost of bar steel must be added to the shop cost. Half card extras given in Table
III should ordinarily be added to the base price of plain steel bars.
Chords, Posts and Towers. — In lots of at least four, the shop cost is about as follows: Members
made of two channels and a top cover plate with lacing on the bottom side, or two channels laced
on both sides cost about i.oo to 0.85 cts. per lb. for pin-connected members weighing from 600
to 1,500 lb.; and about 0.80 to 0.70 cts. per lb. for members with riveted end connections. Mem-
bers made of four angles laced cost from 0.80 to i.io cts. per lb. for members with riveted ends.
Members made of two angles battened will cost about 0.50 cts. per lb. Angles used without end
connections should have their cost estimated on the basis of mill details, which see.
Pins. — The cost of chord pins will vary with the size, number and other requirements. The
shop cost of chord pins and nuts may be estimated at from 2.00 to 3.00 cts. per lb. Rollers will
cost practically the same as pins. Rolled rounds (pin rounds) are used for making pins and
rollers.
Latticed Fence. — The shop cost of light simple latticed fence made of two 2 in. X 2 in.
angles, with double lacing and about 18 in. deep, will be about 2.00 cts. per lb.; while the shop
cost of latticed fence, with ornamental rosettes OB ornamental plates, may be as much as 4.00 to
5.00 cts. per lb.
Floorbeams and Stringers. — Plate girders used for floorbeams and stringers will cost from
0.60 to 1.25 cts. per lb. depending upon the weight, details and number made at one time. Floor-
beams made of rolled I-beams will cost from 0.50 to 0.75 cts. per lb.
SHOP COSTS OF STEEL BRIDGES. 435
SHOP COSTS OF BRIDGES AS A WHOLE.— The cost will be taken up under the head
of pin-i-nmurtfd bridges, riveted bridges, plate girder bridges, combination bridge metal, and
Howe truss metal.
Shop Costs of Pin-connected Bridges. — The shop costs of pin-connected highway or railway
bridges, exclusive of fence and joists, are about as follows:
Bridges weighing 5,000 Ib. and less 1.30 cts. per Ib.
" " 5,000 to 10,000 Ib 1.20 " " "
" " 10,000 to 20,000 Ib i.oo " " "
20,000 to 40,000 Ib 0.90 '
44 " 40,000 to 60,000 Ib 0.80 '
44 44 60,000 to 100,000 Ib 0.75 " " "
41 " 100,000 to 150,000 Ib 0.70 " " "
44 <4 150,000 and up 0.65 " " "
These costs include detailing and one coat of shop paint. For reaming add 0.15 cts. per Ib.
Shop Costs of Riveted Truss Bridges. — The shop costs of riveted truss highway or railway
bridges, exclusive of fence and joists, are about as follows:
Bridges weighing 5,000 Ib. and less 1.15 cts. per Ib.
" 5,000 to 10,000 Ib i.oo " " "
44 " 10,000 to 20,000 Ib 0.90 " " "
44 4I 20,000 to 40,000 Ib 0.85 " " "
44 " 40,000 to 60,000 Ib 0.75 " " "
44 " 60,000 to 100,000 Ib 0.70 " " "
44 4< 100,000 to 150,000 Ib 0.65 " " "
150,000 Ib. and up 0.60" " "
These costs include detailing and one coat of shop paint. For reaming add 0.15 cts. per Ib.
Shop Costs of Plate Girder Bridges. — The shop costs of plate girder highway or railway
bridges, exclusive of fence and joists, are about as follows:
Spans weighing 10,000 Ib. and less 0.90 cts. per Ib.
14 " 10,000 to 20,000 Ib 0.85 " " "
" " 20,000 to 40,000 Ib 0.75 " " "
44 " 40,000 to 60,000 Ib 0.70 " " "
41 " 60,000 to 100,000 Ib 0.60 " " "
44 100,000 and up 0.50 " " "
These costs include detailing and one coat of shop paint. For reaming add 0.15 cts. per Ib.
Shop Costs of Tubular Piers and Culverts. — The shop costs of steel tubular pier shells and
steel culvert pipe are about as follows:
Tubes 18 in. to 24 in. diameter, J in. metal i.oo cts. per Ib.
44 24 in. to 30 in. diameter, J in. to f in. metal 0.75 to 0.65 "
44 30 in. to 48 in. diameter, J in. to f in. metal 0.70 to 0.60 " " "
" 48 in. to 72 in. diameter, J in. to i in. metal 0.65 to 0.50 " " "
44 72 in. and up f in. to | in. metal 0.50100.45 " " "
The above shop costs include detailing and one coat of shop paint. The necessary bracing
and rods for tubular piers are included.
Shop Cost of Combination Bridge Metal. — Where the bars and rods are standard and the
castings are made from standard patterns, the metal for combination bridges can be fabricated
at about the same cost per pound as for pin-connected spans weighing the same as the weight of
the metal in the combination bridges.
436 ESTIMATES OF STRUCTURAL STEEL. CHAP. XIII.
Shop Cost of Howe Truss Bridge Metal. — The shop cost of highway bridge castings made
from standard patterns, is from 1.50 to 2.00 cts. per Ib. The shop costs of the plates, rods and
other miscellaneous iron work will be from 2.00 to 2.50 cts. per Ib.
COST OF ERECTION OF STEEL FRAME OFFICE AND MILL BUILDINGS AND
MINE STRUCTURES. — In estimating the cost of erection of structural steel work it is best to
divide the cost into (a) cost of placing and bolting steel, and (b) cost of riveting. The cost will
be based on labor at an average price of $3.20 per day of 8 hours or 40 cts. per hour.
(a) Cost of Placing and Bolting. — The cost of placing and bolting mill buildings for ordinary
conditions may be estimated at from $6.00 to $8.00 per ton. The cost of placing and bolting up
steel office buildings may be estimated at from $5.00 to $9.00 per ton. The cost of placing and
bolting up steel bins may be estimated at from $10.00 to $15.00 per ton. The cost of placing
and bolting up head frames may be estimated at from $12.00 to $18.00 per ton.
(b) Cost of Riveting. — It will cost from 6 to 10 cts. per rivet to drive f or f in. rivets by
hand in structural framework where a few rivets are found in one place. A fair average is 7 cts.
per rivet. The same size rivets can be driven in tank work for from 4 to 7 cts. per rivet, with
5 cts. per rivet as a fair average.
The cost of riveting by hand is distributed about as follows:
3 men, 2 driving and I bucking up, at $3.50 per day of 8 hours $10.50
I rivet heater at $3.00 per day of 8 hours 3.00
Coal, tools, superintendence 1.50
Total per day $15.00
On structural work a fair day's work driving f in. or f in. rivets will be from 150 to 250,
depending upon the amount of scaffolding required. This makes the total cost from 6 to 10 cts.
per rivet.
On bin work when the rivets are close together and little staging is required the gang above
will drive from 200 to 400 rivets per day. This makes the total cost from about 4 to 7 cts. per rivet.
Rivets can be driven by power riveters for one-half to three-fourths the above, not counting
the cost of installation and air. The added cost for power and equipment makes the cost of
driving field rivets with pneumatic riveters about the same as the cost of driving field rivets by
hand.
Soft iron rivets f in. and under can be driven cold for about one-half what the same rivets
can be driven hot, or even less.
Cost of Erection. — Small steel frame buildings will cost about $10.00 per ton for the erection
of the steel framework, if trusses are riveted and all other connections are bolted. The cost of
laying corrugated steel is about $0.75 per square when laid on plank sheathing, $1.25 per square
when laid directly on the purlins, and $2.00 per square when laid with anti-condensation lining.
The erection of corrugated steel siding costs from $0.75 to $1.00 per square. The cost of erecting
heavy machine shops, all material riveted and including the cost of painting but not the cost of
the paint, is about $8.50 to $9.00 per ton. Small buildings in which all connections are bolted
may be erected for from $5.00 to $6.00 per ton. The cost of erecting the structural framework
for office buildings will vary from $6.00 to $10.00 per ton.
Actual Costs of Erection. — The cost of erecting the East Helena transformer building, 1897,
was $12.80 per ton, including the erection of the corrugated steel and transportation of the men.
The cost of erecting the Carbon Tipple was $8.80 per ton, including corrugated steel. The cost
of erection of the Basin & Bay State Smelter was $8.20 per ton, including the hoppers and corru-
gated steel.
The cost of erecting the structural steel work for the Great Northern Ry. Grain Elevator,
Superior, Wisconsin, was $13.25 per ton including the driving of all rivets. There were 10,600
tons of structural steel work, and 2,000,000 field rivets, or nearly 200 field rivets per ton of struc-
tural steel.
COST OF ERECTION OF STEEL BRIDGES. 437
Erection of Structural Steel for an Armory.* — The structural framework for the new armory
of the l:niviTMty of Illinois, consists of three-hinged arches having a span of 206 ft., and a o-ntrr
lu-inht of 94 ft. 3 in. The arches are spaced 26 ft. 6 in. centers and are braced in pairs. The total
weight of structural steel was 985 tons, and contained 15,400, J in. and 14,900, } in. or a total of
30,300 field rivets. The cost of erecting the structural steel, including field riveting was $9.55
|KT ton. The average cost of driving the field rivets was 13.1 cts. each.
COST OF ERECTION OF STEEL BRIDGES.— The cost of erection ordinarily includes:
(l) the cost of hauling the bridge to the bridge site; (2) the building of the falsework and the
placing of the steel in position; (3) the riveting up of the bridge, and (4) painting the steel and
the woodwork.
Hauling. — Transportation over country roads will ordinarily cost about 25 cts. per ton-
niilo, in addition to the cost of loading and unloading. In estimating the cost of hauling on any
particular job the length of haul, kind of roads, price of teams and labor, and the character of
the teams should be considered. The cost of loading on the wagons and unloading will depend
upon the local conditions, but will ordinarily be from 25 to 50 cts. per ton. For railroad bridges
the steel work may ordinarily be brought directly to the site by rail.
Falsework. — If piles are to be used the cost should be carefully estimated. The cost of the
piles in place will vary with the cost of piles and local conditions. Under ordinary conditions,
piles in falsework will cost from 25 to 50 cts. per lineal foot in place. The cost of the timber will
depend upon local conditions and upon what use is made of it after erection. The flooring plank
in highway bridges, and ties and guard timbers in railway bridges can often be used in the false-
work without serious injury. The cost of erecting the timber in the falsework will ordinarily be
from $6.00 to $8.00 per thousand ft. B. M.
Erection of Tubular Piers. — The cost of setting tubular piers for highway bridges will depend
upon the conditions. Tubes 36 in. in diameter and 20 ft. long have been set in favorable locations
for $25.00 per pair, not including the driving of the piles or the placing of the concrete. It is,
however, not safe to estimate the cost of setting tubes from 36 to 48 in. in diameter under even
favorable conditions at less than $2.00 per lineal foot of tube. When the cost of setting tubes is
estimated by weight, it should be figured at from $15.00 to $20.00 per ton, for ordinary conditions.
It will commonly cost from 25 to 50 cts. per lineal ft. to drive piles in tubes, in addition to the cost
of the piles, which will vary from 10 to 20 cts. per lineal foot. The concrete will commonly cost
from $6.00 to $8.00 per cu. yd. in place in the tube.
Placing and Bolting. — The cost of placing and bolting up riveted highway spans, and erecting
pin-connected highway spans, no rivets being driven, is about as follows:
• Highway spans from 30 to 60 ft $12.00 to $15.00 per ton.
" 60 to 100 ft. .• 10.00 to 12.00 " "
" loo to 150 ft 9.00 to 10.00 " "
" isoft. and up 8.00 " "
The cost of placing and bolting up railroad spans will depend so much upon the local con-
ditions and equipment that it is difficult to give general costs.
The cost of driving field rivets in pin-connected spans will vary from 7 to 12 cts. per rivet,
while the cost of driving field rivets in riveted trusses will vary from 6 to 10 cts. per rivet. The
number of rivets in riveted low truss highway bridges depends upon the number of panels and
the style of details, and will be about 155 to 200 for a three-panel bridge, and 400 to 500 for a
six-panel bridge. The number of rivets in through riveted highway bridges will be about 250 to
300 for a four-panel bridge, and 1,300 to 1,500 for a nine-panel bridge. Pin-connected bridges
ordinarily have about $ to J as many field rivets as a riveted bridge of similar dimensions.
The approximate number of field rivets in single track railway bridges, designed for E 55
loading, are given in Table VII.
* Engineering and Contracting, Aug. 6, 1913.
438
ESTIMATES OF STRUCTURAL STEEL.
CHAP. XIII.
TABLE VII.
NUMBER OF FIELD RIVETS IN RAILWAY BRIDGES, SINGLE TRACK, E 55 LOADING.
(HARRIMAN LINES.)
Plate Girders.
Through Truss Bridges.
Deck.
Through.
Riveted.
Pin- Connected .
Span, Ft.
Number of
Fieid Rivets.
Span, Ft.
Number of
Field Rivets.
Span, Ft.
Number of
Field Rivets.
Span, Ft.
Number of
Field Rivets.
30
40
SO
60
70
80
90
IOO
IOO
2OO
3OO
400
500
SCO
5OO
600
3°
40
1°
60
70
80
90
IOO
6OO
I,20O
I,30O
1,700
1,900
2,OOO
2,2OO
2,4OO
IOO
no
125
140
ISO
2,900
2,900
4,300
5,300
5,600
ISO
160
1 80
200
2^800
3,OOO
3,200
3,200
The field rivets on the 2Oth St. Viaduct, Denver, Colorado, cost 7 cts. each. The rivets
were driven by air riveters.
Actual Costs of Erecting Railway Bridges. — The cost of erecting railway bridges on the A. T.
& S. F. Ry. in 1907 are given in the report of the Assoc. of Ry. Supt. of B. & B. as follows: —
Trusses, 984 tons erected, cost $4.63 per ton.
Plate Girders, 2,784 tons erected, cost $5.49 per ton.
I-Beams, 2,837 tons erected, cost $2.88 per ton.
All girders and I-beams were erected with a steam wrecker and the through spans with a derrick
car. The reason for the plate girders costing more to erect than the through trusses was that
many of the plate girders were on second track where the old girders had to be cut apart and moved
to the outside and heavier girders put in their place. All rivets were driven by hand. For addi-
tional examples of actual costs, see Gillette's "Cost Data."
Transportation. — Fabricated structural steel commonly takes a "fifth-class rate" when
shipped in car load lots, and a "fourth-class rate" when shipped "local" (in less than car load
lots). The minimum car load depends upon the railroad and varies from 20,000 to 30,000 Ib.
Tariff sheets giving railroad rates may be obtained from any railroad company. The shipping
clerk should be provided with the clearances of all tunnels and bridges on different lines so that
the car may be properly loaded.
Freight Rates. — The freight rates (1913) on finished steel products in car load shipments from
the Pittsburgh District, including plates, structural shapes, merchant steel and iron bars, pipe
fittings, plain and galvanized wire, nails, rivets, spikes and bolts (in kegs), black sheets (except
planished), chain, etc., are as follows, in cts. per 100 Ib. in carload shipments; Albany, 16; Buffalo,
ii ; Boston, 18; Baltimore, 14!; Cleveland, 10; Columbus, 12; Cincinnati, 15; Chicago, 18; Denver,
Colo., 85!; Harrisburg, 14^; Louisville, 18; New York, 16; Norfolk, 20; Philadelphia, 15; Rochester,
nf ; Richmond, 20; Scranton, 15; St. Louis, 23; Washington, 14!.
COST OF PAINTING. — The amount of materials required to make a gallon of paint
and the surface of steel work covered by one gallon are given in Table VIII. Structural steel
should be painted with one coat of linseed oil, linseed oil with lamp-black filler, or red lead paint
at the shop; and two coats of first-class paint after erection. The two field coats should be of
different colors; care being used to see that first coat is thoroughly dry before applying the second
coat. Steel bridges and exposed steel frame buildings ordinarily require repainting every three
or four years.
The steel work in the extension to the i6th St. Viaduct, Denver, Colo., was painted with red
lead paint mixed in the following proportions, — 100 Ib. red lead, 2 Ib. lamp-black and 4.125 gallons
COST OF PAINTING.
439
of linseed oil. This mixture made 6 gallons of mixed paint of a chocolate color, and gave 1.455
gallons of paint for each gallon of oil.
TABLE VIII.
AVERAGE SURFACE COVERED PER GALLON OF PAINT.
PENCOYD HAND BOOK.
Paint.
Volume of Oil.
Pounds of
Pigment.
Volume and
Weight of
1'aint.
Square Feet.
Gal. Lb.
i Coat.
2 Coats.
Iron oxide (powdered)
I gal.
I gal.
I gal.
I gal.
I gal.
I gal. (turp.)
I gal.
8.00
24-75
22.40
25.00
I2.JO
17.50
1.2 «- l6.00
2.6 - 32.75
1.4 = 30.40
1.7 = 33.00
2.0 = 20.50
4.0 = 3O.OO
600
630
630
I°°
630
5'5
875
350
375
375
300
35°
310
\Vhite lead (ground in oil)
Graphite (ground in oil)
Black asphalt
Light structural work will average about 250 sq. ft., and heavy structural work about 150
sq. ft. of surface per net ton of metal, while No. 20 corrugated steel has 2,400 sq. ft. of surface.
It is the common practice to estimate $ gallon of paint for the first coat and f gallon for the
second coat per ton of structural steel, for average conditions.
The price of paint materials in small quantities in Chicago are (1914) about as follows:
Linseed oil, 50 to 60 cts. per gal.; iron oxide, i to 2 cts. per lb.; red lead, 7 to 8 cts. per lb.; white
lead, 6 to 7 cts. per lb.; graphite, 6 to 10 cts. per lb.
A good painter should paint 1,200 to 1,500 sq. ft. of plate surface or corrugated steel or 300
to 500 sq. ft. of structural steel work in a day of 8 hours; the amount covered depending upon the
amount of staging and the paint. A thick red lead paint mixed with 30 lb. of lead to the gallon
of oil will take fully twice as long to apply as a graphite paint or linseed oil. The cost of applying
paint is roughly equal to the cost of a good quality of paint, the cost per ton depending on the
spreading qualities of the paint. This rule makes the cost of applying a red lead paint with 30 lb.
of pigment per gallon of oil from two to three times the cost of applying a good graphite paint,
per ton of structural steel. For additional data on paints, see Chapter XV.
MISCELLANEOUS COSTS. — The following approximate costs will be of value in making
preliminary estimates. The cost of construction depends so much upon local conditions that
average costs should only be used as a guide to the judgment of the engineer.
MILL BUILDING FLOORS. — The following costs are for floors resting on a good compact
soil and do not include unusual difficulties.
Timber Floor on Pitch-Concrete Base. — The cost varies from about $1.25 per sq. yd. for a
2-in. pine sub-floor and a $-in. pine finish, to about$l.75 per sq. yd. for a 2-in. pine sub-floor and a
J-in. maple finish.
Concrete Floor on Gravel Sub-base. — The cost varies from $1.25 to $2.00 per sq. yd.
Creosoted Timber Block Floor. — Creosoted timber blocks 3 in. to 4 in. thick, laid on a 6-in.
concrete base, will cost from $2.50 to $3.50 per sq. yd.
ROOFING FOR MILL BUILDINGS.— The following costs include the cost of materials
and the cost of laying, but do not include the cost of the sheathing.
Corrugated Steel Roofing. — The weight of corrugated steel roofing and siding may be ob-
tained from Table I, Chapter I. The price of corrugated steel may be obtained from current
quotations in Engineering News or Iron Age. The cost of laying corrugated steel is about $0.75
per square when laid on plank sheathing, $1.25 per square when laid directly on the purlins, and
$2.00 per square when laid with anti-condensation lining. The erection of corrugated siding
costs from $0.75 to $1.00 per square. Asbestos paper costs from 3} to 4 cts. per lb. Galvanized
440 ESTIMATES OF STRUCTURAL STEEL. CHAP. XIII
wire netting, No. 19, costs 25 to 30 cts. per square of 100 sq. ft. Brass wire, No. 20, costs about 20
cts. per Ib. No. 9 galvanized wire costs about 3 cts. per Ib. For trimmings, flashing, ridge roll,
etc., add I ct. per Ib. to the base price of corrugated steel.
Tar and Gravel Roofing. — Four- or five-ply tar and gravel roofing, for average conditions,
costs from $3.75 to $4.00 per square, not including sheathing. Five hundred squares of 5-ply
tar and gravel roofing, in 1912, in the middle west, cost $3.93 per square, not including sheathing.
Tin Roofing. — Tin roofing costs from $7.00 to $9.00 per square, not including sheathing.
Slate Roofing. — Slate roofing costs from $7.00 to $i2.oo.per square, not including sheathing.
Tile Roofing. — The cost of tile roofing is variable, depending upon style of roof and location
and local conditions, and may vary from $13.00 to $30.00 per square, not including sheathing.
WINDOWS. — Windows with wooden frames and sash, and double strength glass, will cost
from 25 to 50 cts. per sq. ft. of opening. Windows with metal frames and sash and wire glass,
will cost from 45 to 55 cts. per sq. ft. of opening.
SKYLIGHTS. — Skylights with metal frames and sash and wire glass, will cost from 50 to
60 cts. per sq. ft. Skylights made of translucent fabric stretched on wooden frames, will cost
from 25 to 30 cts. per sq. ft. Louvres without frames, will cost about 25 cts. per sq. ft.
CIRCULAR VENTILATORS. — Circular ventilators will cost about as follows: — 12-in.,
$2.00; i8-in., $6.75; 24-in., $10.00; 36-in., $15.00 each, when ordered in lots of at least six.
ROLLING STEEL SHUTTERS.— Rolling steel shutters will cost $0.75 to $1.00 per sq. ft.
WATERPROOFING. — The following cos.ts for waterproofing engineering structures are
taken from the Proceedings of the American Railway Engineering Association, Vol. 12, 1911.
(1) Bridge floor, 6-ply felt and pitch, \z\ cts. per sq. ft., including protection over waterproofing.
(2) Trough bridge floor, 4-ply burlap and asphalt, 10 to 165 cts. per sq. ft. (3) Bridge floor, 3-ply
burlap and asphalt, and asphalt mastic, 16 cts. per sq. ft. (4) Concrete slab bridge floor, 5-ply
felt, i-ply burlap and pitch, 15^ cts. per sq. ft., including a 10 year guarantee.
MISCELLANEOUS MATERIALS.— The following prices are for small lots, f.o.b. Pittsburgh
(May, 1914).
Chain. — Standard chain, YS m-> 7 1 cts. per Ib.; f in., 3 cts. per Ib.; I in., 2.6 cts. per Ib.
For BB chain, add if cts. per Ib., and for BBB chain, add 2 cts. per Ib.
Nails. — Base price of nails, $2.00 per keg of 100 Ib. — 2od to 60 d nails are base; for xod to
i6d, add 5 cts. per keg; for 8d and gd, add 10 cts. per keg; for 6d and 7d, add 20 cts. per keg;
for 4d and 5d, add 30 cts. per keg; for 3d, add 45 cts. per keg, and for 2d, add 70 cts. per keg.
Gas Pipe. — Gas pipe costs about as follows: — Standard gas pipe I in. diam., black, 3§ cts.
per ft., glavanized, 5 cts. per ft.; 2 in. diam., black, "]\ cts. per ft., galvanized, n cts. per ft.; 3 in.
diam., black, 165 cts. per ft., galvanized, 23 cts. per ft.
Steel Railroad Rails. — Bessemer rails, $28 per gross ton (2240 Ib.); open-hearth, $30 per
gross ton.
Wire Rope. — The cost of steel wire rope is about as follows: — f in. rope, 10 cts. per lineal ft.;
| in. rope, 13 cts. per lineal ft.; I in. rope, 20 cts. per lineal ft.; if in. rope, 45 cts. per lineal ft.
Manila Rope. — Manila rope costs about 12 \ cts. per Ib. Sisal rope costs about 9 cts. per Ib.
HARDWARE AND MACHINISTS SUPPLIES.— Prices of hardware and machinists
supplies are for the most part quoted by giving a discount from standard list prices. The " Iron
Age Standard Hardware Lists," price $2.00, may be obtained from the Iron Age Book Department,
239, W. 39th St., New York. Discounts from these standard lists are given each week in Iron
Age. The base prices of structural materials are given in the first issue of each month of Engineer-
ing News, and are given in each issue of Iron Age.
REFERENCES. — For detailed estimates of steel mill buildings and additional data on the
cost of steel mill buildings see the authors " The Design of Steel Mill Buildings." For detailed
estimates of steel highway bridges and additional data on the cost of steel highway bridges, see
the author's " The Design of Highway Bridges." For data on the cost of retaining walls, bins and
grain elevators, see the author's " The Design of Walls, Bins and Grain Elevators." For data
on the cost of steel head frames, coal tipples, and other mine structures, see the author's " The
Design of Mine Structures."
CHAPTER XIV.
ERECTION OF STRUCTURAL STEEL.
METHODS OF ERECTION. — The method used in erecting a steel structure will depend
upon the type of structure, the size of the structure, the risk to be taken, as in bridge erection,
\vlu-ther the structure is to be erected without interfering with traffic, as in erecting a railroad
bridge to replace an existing structure, or in erecting a building over furnaces or working machinery,
the available tools, and local conditions. The tendency of modern structural steel erection
practice is, as far as possible, to use derrick cars for erecting railway bridges and locomotive cranes
for erecting mill buildings and other structures.
The methods of erection that may be used for erecting different steel structures are as follows.
Plate Girders and Short Riveted Spans. — Plate girders up to about 60 ft. span are very
commonly riveted up complete with cross frames and bracing, either at the shop oral the site, and
are placed in position on the abutments. With plate girders longer than 60 ft. and short riveted
trusses one girder or truss is placed in position at a time and the floorbeams and bracing are put
in place after the girders or trusses are in place. The girders or trusses may be swung into place
by a stiff-leg derrick or a guy derrick set up alongside the track or back of the abutment where
there is no track; by a derrick car, or may be hoisted into place by a gin pole. Where falsework
has been placed girders are picked up from the cars by two gallows frames, one near each end of the
span, or by one gallows frame and a derrick. Plate girders may also be put in place by sliding
into place either longitudinally or transversely, or by jacking and cribbing.
Truss Bridges. — Riveted trusses up to a span of 100 to 125 ft. may be riveted up on the
bank and be swung into place by a boom traveler or a derrick. The floorbeams and bracing
are then put in place and the span riveted up. Where falsework is required the bridge may be
erected by a gantry or outside traveler placed outside of the trusses, by a boom traveler running
on a track placed inside the trusses, or by a derrick car. The gantry or outside traveler is com-
monly used for long spans and for highway spans where no tracks are available. The boom
traveler is commonly used for elevated railway and highway viaducts. The derrick car is now
commonly used for erecting railway bridges and is sometimes used for erecting viaducts.
. Cantilever Bridges. — Cantilever bridges are commonly erected by means of an overhang
traveler running on the completed portion, the structure being built out from the shore. Canti-
lever bridges are sometimes erected on falsework in the same manner as simple trusses.
Arch Bridges. — Arches may be erected on falsework in the same manner as simple truss spans,
or may be cantilevered out from each abutment, the cantilever being supported by temporary
cables running over a tower placed back of the abutments.
High Viaducts. — High steel viaducts are commonly erected by means of an overhang or
boom traveler running on a track on top of the viaduct girders. The overhang or boom is long
enough to place a tower in advance with the traveler on the completed portion. Derrick cars
have also been used for erecting high steel viaducts. The towers and the girders may be erected
by means of gin poles. The tower bents may be bolted up before raising or may be erected and
bolted up in place.
Roof Trusses, Mill and Office Buildings. — Where there is sufficient room, roof trusses up
to 150 ft. span may be riveted or bolted up on the ground and may then be raised into position
by means of one or two gin poles. Two gin poles should be used for long trusses. Care should
be used not to cripple the lower chord. With light trusses, the lower chord members should be
stiffened by means of timbers or other stiff members temporarily bolted or lashed to the member.
Columns and beams in office buildings may be erected with stiff-leg or guy derricks, or "A"
441
442
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
derricks may be used for loads up to 5 tons. The bents of steel mill buildings may be erected in
the same manner. Roof arches and train sheds are sometimes erected by means of falsework,
which is moved as the erection proceeds. Boom-tower derricks running on tracks are found
(a) CRAB
(b) WINCH
^•—Boiler
(Spool, or
A Winch, or
\ A \N/ggerHe3d
(c) DERRICK CRAB (d) HOISTING ENGINE
FIG. i. HOISTS FOR STEEL ERECTION.
very convenient. Locomotive cranes are now used for erecting mill buildings and similar struc-
tures where tracks are available.
Elevated Towers and Tanks. — The towers for high tanks are commonly erected by means
of a gin pole. A gin pole long enough to erect the entire tower may be used, or short gin poles
may be lashed to the part of the tower already erected ; the gin poles being moved up as the erection
HOISTING ROPE.
proceeds. Steel tanks are commonly erected from a movable platform suspended inside the
tank. A movable swinging platform fur ih« riveters is also swung outside of the tank.
ERECTION TOOLS. — The tools and appliances used in the erection of structural steel vary
so much that it will only be possible to give a brief summary together with data not ordinarily
av.iil.iMr. Many of the tools and appliances used in the erection of structural steel are of standard
contruction and may be purchased direct from dealers, so that a detailed description is not neces-
sary.
Design of Erection Tools. — For the design of hoists, derricks, cranes, crane hooks, and other
tools used in bridge erection, see Hcss's " Machine Design, Hoists, Derricks, Cranes," published
by J. B. Lippincott Company.
Hoists. — Hoisting engines may have the boilers attached or may be detached. A self-con-
tained steam hoisting engine is shown in Fig. I. Gasoline or electric power may be used to
advantage where available. For light hoisting the 4-spool engine is commonly used. Data for
tho standard hoisting engines used by the American Bridge Company are given in Table I.
Winches and Crabs. — For light hoisting winches or crabs operated by hand power may be
used. A crab is attached to the mast or boom, while a winch is self-contained. Views of a crab
and of a winch are shown in Fig. I.
HOISTING ROPE. — Either manila rope or wire rope may be used for hoisting.
Manila Rope. — Only the very best new manila rope should be used for hoisting, as manila
rope rapidly deteriorates when used and commercial manila rope varies greatly in strength. The
weight, ultimate strengths and safe working loads for manila rope are given in Table II. Working
loads with a factor of safety of three should only be used with new rope of the best quality.
TABLE I.
STANDARD HOISTING ENGINES. AMERICAN BRIDGE COMPANY.
Ordinary
Rated
H.P.
Lead Line
Pull
Single Line
Average
Speed, Lb.
Weight
with Boiler,
Lb.
Drums.
Spools,
Size.
In.
Boilers.
Bed.
Diam.,
In.
Length ,
In.
Diam.,
In.
Length,
In.
Width,
Ft-In.
Length,
Ft-In.
Double Drum,
4 Spool
20 H. P.
35 H. P.
45 H. P.
60 H.P.
5,000
9,000
12,000
15,000
I2,OOO
I5,OOO
22,OOO
30,000
H
li
to
16
26
27
30
34
17
19
22
22
42
46
50
54
96
108
1 08
108
S-o
6-0
7-0
8-0
8-0
IO-O
II-O
I2-O
Double Drum,
4 Spool
6 Spool
8 Spool
TABLE II.
MANILA ROPE. ULTIMATE STRENGTH, WEIGHT AND WORKING STRESS OF BEST
MANILA ROPE.
Diameter, In.
Circumference
of Rope, In.
Weight loo Ft.
Rope, Lb.
Ultimate
Strength, Lb.
Working Load for Derricks.
Minimum Size
of Drum or
Sheave, In.
Used Rope,
Factor of 6, Lb.
New Rope,
Factor of 3, Lb.
|
!
i
it
ii
I*
2
2i
3
1-57
2-37
2.75
3-14
3-93
4.71
5.50
6.28
7.86
9.42
7
17
24
28
46
64
84
us
175
252
1, 800
4,OOO
5,400
7,200
11,200
16,000
21,600
28,500
45,000
64,200
300
670
900
I,2OO
1,870
2,670
3,600
4,750
7,500
IO,70O
600
1,340
1, 800
2,400
3,740
5,340
7,200
9,500
15,000
21,400
8
10
12
14
16
444
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
Knots in Manila Rope. — In a knot no
move in the same direction in case the rope
shown in Fig. 2 which has been taken from
1. Bight of a rope,
2. Simple or Overhang Knot.
3. Figure 8 Knot.
4. Double Knot.
5. Boat Knot.
6. Bowline, first step.
7. Bowline, second step.
8. Bowline, completed.
9. Square or Reef Knot.
10. Sheet Bend or Weaver's Knot.
11. Sheet Bend with a toggle.
12. Carrick Bend.
13. "Stevedore" Knot completed.
14. "Stevedore" Knot commenced.
15. Slip Knot.
"The bowline 7 is one of the most useful knots; it will not slip, and after being strained is
easily untied. Commence by making a bight in the rope, then put the end through the bight
and under the standing part as shown in Fig. 2, then pass the end again through the bight, and
haul tight.
"The square or reef knot 9 must not be mistaken for the 'granny' knot that slips under a
strain. Knots 8, 10 and 13 are easily untied after being under strain. The knot 13 is useful
when the rope passes through an eye and is held by the knot, as it will not slip, and is easily untied
after being strained.
TABLE III.
CRUCIBLE STEEL HOISTING ROPE. WEIGHT, ULTIMATE STRENGTH AND WORKING LOADS OF
WIRE ROPE COMPOSED OF 6 STRANDS AND A HEMP CENTER, 19 WIRES TO THE STRAND.
two parts which lie alongside of each other should
were to slip. A few of the more common knots are
C. W. Hunt Company's book on "Manila Rope."
1 6. Flemish Loop.
17. Chain Knot with toggle.
18. Half-hitch.
19. Timber-hitch.
20. Clove-hitch.
21. Rolling hitch.
22. Timber-hitch and Half-hitch.
23. Black-wall-hitch.
24. Fisherman's Bend.
25. Round Turn and Half-hitch.
26. Wall Knot commenced.
27. Wall Knot completed.
28. Wall Knot Crown commenced.
29. Wall Knot Crown completed.
Minimum Size of Drum or
Diameter,
In.
Approximate
Circumference,
In.
Weight per
Ft., Lb.
Approximate Break-
ing Stress, Lb.
Safe Working Stress
for Derricks, Factor
of 4, Lb.
Sheave.
Derricks, In.
Rapid Hoist-
ing, In.
I
If
O.22
IO,OOO
2,500
6
12
&
If
O.JO
13,600
3,400
7i
15
1
If
0-39
17,600
4,400
9
18
TV
If
O.5O
22,OOO
5,500
10
21
1
2
O.62
27,2OO
6,800
12
27
1
2*
0.89
38,800
9,700
H
36
1
2|
1. 2O
52,OOO
I3,OOO
18
42
3
I.S8
68,OOO
I7,OOO
20
48
1
3*
2.OO
84,000
2I,OOO
22
54
I
4
2-45
IOO,OOO
25,OOO
24
60
I
4t
3.00
124,000
3I,OOO
27
66
I
4f
3-55
144,000
36,000
30
69
"The timber-hitch, 19, looks as though it would give way, but it will not; the greater the
strain the tighter it will hold. The wall knot looks complicated; but is easily made by pro-
ceeding as follows: Form a bight with strand a and pass the strand b around the end of it, and
the strand c around the end of b, and then through the bight of a, as shown in the engraving 26.
Haul the ends taut, when the appearance is as shown in 27. The end of the strand a is now laid
KNOTS IN MANILA ROPE.
445
24 25 26 27 28 29
52
FIG. 2. KNOTS IN MANILA ROPE
446
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
over the centre of the knot, strand b laid over a, and c over b, wKen the end of c is passed through
the bight of a, as shown in 28. Haul all the strands taut, as shown in 29."
The efficiency of a knot will vary from 45 to 75 per cent.
TABLE IV.
PLOUGH STEEL HOISTING ROPE. WEIGHT, ULTIMATE STRENGTH AND WORKING LOADS OF WIRE
ROPE COMPOSED OF 6 STRANDS AND A HEMP CENTER, 19 WIRES TO THE STRAND.
Minimum Size of Drum
Diameter,
Approximate
Weight per
Approximate
Safe Working Stress
or Sheave.
In.
C ircurnf crcnce ,
In.
Foot, Lb.
Stress, Lb.
Factor of 4, Lb.
Derricks, In.
Rapid Hoisting,
In.
1
it
0.22
11,500
2,870
9i
18
0.30
l6,OOO
4,000
21
I
5|
0-39
2O,OOO
5,000
12
24
A
if
O.5O
24,600
6,150
14
27
I
2
0.62
31,000
7,750
14
33
f
1\
0.89
46,000
11,500
16
39
1
2j
1. 2O
58,000
14,500
18
48
i
3
1.58
76,000
19,000
20
54
if
3l
2.OO
94,000
23,500
24
60
ij
4
2-45
116,000
29,000
28
72
if
4l
3.00
144,000
36,000
32
81
il
4s
3-55
164,000
41,000
36
84
TABLE V.
DATA ON WOODEN BLOCKS FOR MANILA ROPE. AMERICAN BRIDGE COMPANY.
Type of Block.
Nomi-
nal
Size,
In.
Width
of Shell,
In.
Thickness
of Block,
In.
Ca-
pacity,
Tons.
Size of Line, In.
Outside
Diameter
of Sheave,
In.
Weight,
Lb.
Single with hook. . . .
8
8
12
12
12
14
14
H
14
16
16
16
16
20
20
2O
2O
16
20
si
si
8|
8|
81
I0i
iol
lol
lOj
III
III
III
III
14
14
14
14
8|
9l
«f
6f
Si
81
"1
6
8f
I3f
i6|
6|
iof
I3f
I7f
8j
12 ;
«7:
21;
i»
2
4
5
7
8
6
10
12
H
8
12
IS
20
IS
22
30
35
5
8
|
l\
I
l\
r.
i\
r,
i\
i.
Ij
I
i\
2 or
2 or
2 or
2 or
f.orii
I? or if c
i
:
2l
a!
*}
2|
ror i|
r 2 or 2j
4l
4l
7l
7l
71
9
9
9
9
10)
id
lof
10],
tai
I2J
12]
12}
8
9
IS
2O
45
70
95
70
US
ISO
190
90
140
190
270
170
230
360
430
So
95
Double with hook
Single with hook
Double with hook
Triple with hook
Single with hook
Double with hook
Triple with hook. . . .
Quadruple with shackle . .
Single with hook
Double with hook
Triple with hook
Quadruple with shackle. .
Single with hook
Double with hook
Triple with hook
Quadruple with shackle . .
16" snatch block.
20" snatch block
Wire Rope. — Wire hoisting rope is now used for heavy hoisting and in all cases where prac-
ticable. Wire rope is much more reliable, gives much greater service, and is much more eco-
HOISTING TACKLE.
447
nomical and satisfactory than manila rope. Data on crucible cast steel hoisting rope are given
in Table III; and data on plough steel hoisting rope are given in Table IV. A factor of safety
of 4 should be used for working loads only with derricks or hoists that are not in continuous
action. For pile driving and for continuous hoisting a factor of safety of 6 should be used for
working loads. Wire ropes used in hoisting are commonly |, j and { in. in diameter. The smaller
di.imi I«T> art used for guy lines. For standing guy lines a cheaper wire rope will usually be
found satisfactory. Bending stresses in wire ropes are given in Fig. 7, Chapter X.
HOISTING TACKLE. — Blocks for both manila rope and wire rope are made with wooden
shells and with steel shells. Blocks up to 12 to 15 tons capacity are commonly provided with
hooks; blocks for heavier loads are provided with shackles. Blocks should be well built with
adequate bearings and carefully worked out details. The common types of blocks are shown in
Fig. 3-
Data on wooden blocks for Manila rope as used by the American Bridge Company are shown
in Table V.
Data on steel blocks for wire rope as used by the American Bridge Company are shown in
Table VI.
TABLE VI.
DATA ON STEEL BLOCKS FOR WIRE ROPE. AMERICAN BRIDGE COMPANY.
Type of Block.
Width of
Shell. In.
Thickness
of Block,
In.
Capacity,
Tons.
Size of
Line, In.
Outside
Diameter of
Sheave, In.
Weight,
Lb.
Snatch with hook
17
21
21
21
21
21
t^vO 00 « •«*• O
ci 1-1 M
8
10
20
3°
40
60
f ar
;
1
1
I
idf
14
H
14
H
H
H
260
250
390
590
820
1,260
Single with shackle
Double with shackle
Triple with shackle
Quadruple with shackle
Six sheave with shackle
Rigging. — The rigging for lifting loads with wire rope are given in Fig. 4, and for manila
rope in Fig. 5. These data are based on experiments made by the American Bridge Company,
and have been adopted as standard by the American Bridge Company and the McClintic-Marshall
Construction Company.
TABLE VII.
RATIOS OF LOAD TO PULL IN LEAD LINE.
Work-
Manila Rope.
Diam. of
Rope, In.
ing
Load,
Lift per Unit Pull in Lead Line for Tackle with Parts as follows.
Lb.
I
2
3
4
S
6
7
8
9
10
ii
12
13
H
I
I,9OO
0.86
i-93
2-73
348
4.12
4.71
s-23
5-71
6.12
6.50
6.83
7.14
7-40
7.64
J
2,300
0.83
1.92
2.68
3-37
3-95
4.48
4.92
5-32
5.66
S-96
6.22
6.4S
6.64
6.82
I
3,IOO
0.87
i-93
2.74
3-SO
4.16
4-77
15.30
5.80
6.23
6.63
6.98
7.30
7-S8
7.8<;
I*
4,3CO
0.83
1.92
2.68
3-37
3.9S
4.48
4.92
•5-32
5-6S
S-96
6.21
6.44
6.63
6.8 1
ii
5,900
0.83
i-9i
2.67
3-36
3-93
4-4<;
4.89
«;.28
S.6i
S-9I
6.iS
6.38
6.<;6
6.73
ii
7,900
0.8 1
1.91
2.64
3-30
3.84
4-33
4.72
5-08
5-37
5.64
5-8S
6.04
6. 20
6.34
2
10,300'
0.82
1.91
2.65
3-32
3-«7
4-37
4.78
5-14
5-45
S-72
5 -94
6.IS
6.31
6.46
2!
13,100
0.80
1.90
2.63
3.28
3.80
4.28
4-<>s
5.00
5.27
5-52
S-72
5.90
6.04
6.17
Wire Rope.
i
16,600
0.86
i-93
2-73
3-47
4.11
4.70
5.20
5.68
6.08
6.46
6.78
7.08
7-34
7.58
448
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
(c) &)
BLOCK WITH SWIVEL HOOK BLOCK WITH SHACKLE
STEEL SHEAVE BLOCKS FOR W/KE ROPE
-Becket-'
(e) (F) (g)
WOODEN SHEAVE BLOCK WITH BECKET SNATCH BLOCKS WITH HOOKS
(!) (j) Ck) (I)
FALL LIHE BALL WEIGHTED SHEAVE STRAP SHEAVE BL OCKS
BLOCK
FIG. 3. BLOCKS FOR HOISTING.
LIFTING CAPACITY OF TACKLE.
449
Lift
LeadLine
Rigging
Lift
LeadLine
figgina
Tons
Pvll-Lbs-
j Wire Rope
Tons
Pu//-Lbs
£* W/re Kope
Doublt
/C\5/V
\
Double C
/CX5//aj/«C
10
5,700
4 Psrts
4 Parts
10
7,400
3 Parts |
2>Par>ts \
Double
Double^
Single O
\l
20
8,500
Triple
6 Part s
\
/QDouble
6 Parts
}
to
9,300
Triple C
5 Parts |
S
^f
Triple
y
Trip/e
Double C
Double \J
to
10,600
Quadruple
8 Parts
\
/OJripIe
S Parts
}
$0
II, 700
Quadruple C
7 Parts |
\
7 Parts \
Quadruple
0
Quadruple^
Trip/e C
Triple JC
40
JO, 700
/Q65ht3v'C,
1 5 Paris 1
40
15,400
Sfbrbs |
6 Sheared
Quadrupled
60
60
16,600
15 Parts 1
65heave^£,
Lift
Tons
Lead Line
PulI-Lbs-
Rigging
f"W/'re Rope
/O
7,500
Double C
3 Par -Is I
Single C
\
yOSrtf/eC
3 Parts \
Single \J
20
11,000
QoubJe
4 Parts
Double
j
\
/^Single
4 Parts
Doub/e ^
i
50
13.SOO
Triple
6 Parts
Triple
]
\
/Qfoub/e
6 Parts
Triple ^
j
40
15,000
Quadruple
8 Parts
Quadruple
]
\
/Q-Trtple
8 Paris
Quadruple^
}
60
19, 000
/OSShea/C
Jf Parts |
£J^r^G
Best Crucib/e Casb Steel Hoist -
//y Rope •' 6 Strand, /9 Wires to a
Strand and Hemp Core •
These values are on/y For tackle
as shown • //" the lead l/'ne is snatch-
ed or passes over additional sheaves,
capacity diminishes'
LIFTING CAPACITY OF TACKLE
STEEL SHELL BLOCKS
WJTH WIRE ROPE
FIG. 4.
30
450
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
t/ft
Tons
Rigging
li" Manila Rope
Lift
Tons
Rigging
/j Manila Rope
Lift
Tons
I? Manila Rope
Single
ZParts
Single
2Parts
Sing/e
2 Parts
Single
O^ing/e
? Parts
Single XJ
10
Triple
f Parts
Double
QDoub/e
5 Parts
Double N
Double
3 Parks
Single
Single Cj
2> Parts \
\J
3Parts
II
Triple
6Parts
Triple
6tert
Triple
Double
4 Parts
Double
4 Parts
Double
7
Double
12
6 Parts
Trip/e
Double
4 Parts
Double
4 Parts
Double
8
4 Parts
Double^
/3
Quadruple
SParts
Quadruple
SParts
Quadrupl
le^
8
Triple
6 Parts
Trip/e
6 Parts
Triple
Double
4 Parts
Double
Double
14
Quadruple
8 Parts
Quadruple
Lift
Tons
Rigging
2" Manila Rope
Trip/e
?
O^oub/e
Q
20
6 Parts
I
6 Parts
1
Trip/e
Z
Trip/e ^
o
22
Trip/e
6 Parts
!
6 Parts
\
Triple
"•
Trip/e
J
24
Qusdrup/e
8 Parts
1
O\ Tripled
7Pa>ts 1
Quadruple
Triple XJ
Quadruple
crf
<Z\7Jr//>/e
fl
26
8 Parts
\
8 Parts
1
Quadruple
"
Quadruple^
J
28
Q-Quadruple
9 Part s
8
Quadrupfe
X
12 "Blocks For 1^" Rope-
Capacity of Blocks
Single with Hook, 5 Tons-
Double with Hook, 7 Tons-
Trip/e with Hook, 8 Tons-
Approximate pulJ 'on lead line > 2 Tons*
14" Blocks for Ii "Rope-
Capacity of Blocks
Single m'th Hook, 6 Tons-
Double with Hook, fO Tons'
Triple with Hook, 12 Tons*
Quadruple with Shackle, 14 Tons*
Approximate pull on lead line, 3 Tons*
20" Blocks for 2" Rope-
Capacity of Slocf^s
Single with Shackfe, f5 Tons-
Double with Shackle, 22 Tons-
Triple with Shackle, 50 Tons-
Quadruple with Shackle, 35 Tons*
Approximate pu// on lead line, 5 Tons-
These values are only for tackle as shown- If lead
line is snatched or passes orer additional sheaves,
capacity diminishes*
LIFTING CAPACITY OF TACKLE
WOODEN SHELL BLOCKS WITH MANILA ROPE*
FIG. 5.
EFFICIENCY OF TACKLE.
461
Efficiency of Tackle. — The efficiency of rigging as calculated from tests made by the Ameri-
can Bridge Company is given in Table VII. The tables may be used in calculating the loads
that can IK- lifted by tackle as follows: —
Given pull in lead line, to find load lifted — Divide the pull by 1.20 each time line is snatched
or passes over sheaves other than those in tackle blocks; multiply quotient by ratio of load to
UM<| lim- pull, Table VII, and the result is the load lifted. For example, lead line pull of engine
— 10,000 lb.; rigging as follows: — 2 snatch blocks, 2 sheaves, and 7 parts of ij in. line in main
falls. Then Load lifted =
10,000
(1.20)*
pull in lead line, reverse above operation.
X 4.89 = 23,600 lb. If load to be lifted is given, to find
TABLE VIII.
DATA ON CHAINS. AMERICAN BRIDGE COMPANY.
Size.
Diatn. of
Bar. In.
Weight
per Foot
in Lb.;
Outside
Lengths of
Links in In.
Outside
Width of
Links in In.
Proof Test
in Lb.
Ultimate
Strength in
Lb.
Working
Load in Lb.
Factor of 3.
Working
Load in Lb.
Factor of 4.
|
2-5
2|
if
7,700
15,000
5,000
3,800
|
4.10
3
2i
12,000
23,000
7,600
5,700
$
6.70
3i
»f
I7,OOO
33,000
11,000
8,200
|
8.37
4
3
22,OOO
43,000
14,300
10,700
I
10.50
4f
3
29,OOO
56,000
18,600
14,000
If
13.62
s*
3'
37,000
71,000
23,600
17,700
li
16.00
si
4
46,000
88,000
29,300
22.OOO
if
19.25
6*
4
SS.ooo
106,000
35,300
26,500
l|
23.00
7
5;
66,000
126,000
42,000
31,500
I|
28.00
7i
si
74,000
141,000
47,000
35,200
c>"
o?
^ «^^J^^/f_|-V% Cham
,1"
IA^
Total Weight oF Chain = L'(t>20) + //•/
Hook** i" Hook Chain
— -H of" '•
i 04
•*----*
Total Weight oF Chain ~L'(f-*0) +24-4
u i it 7 4" Twin ^^ Hook Chain
Hook ** ^
*!•"
\**+-*A
~ 1
Tote/ Weight of Chain - Lf(6-?0) +48-5
Usual Length of L' is 8 feet>
Hook
FIG. 6. CHAINS.
452
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
si' /*v; /r
,'/r'
^ ij-
//" ^V 5"
^r /^
a
i jj./ i i;
/ 1*
> *i * i r*^
., — x i x. . — _ : +
( r*:r~)) J ^ [C3
its
Af
BAC
s^—1 ^KP *:t:
.-JL
/>//£ 7" HAMMER
Weight- Bibs-
^~^
rfvet&a for^ rivet-* fr* \\
^3^^/v ;
-KING OUT PUNCH YF" «;
A/
'HET BUSTER
tps n — -^ n
fMl U M !/
j
ffANDLE 60U6E
CUTTER
(!$ 6" ,*
I \*£i" .- * f* °
*fe ^ =J-t \
'
r/i
SET (SNAP) j RIVET SET (SNAP) f RIVET SET (SNAP)
?;
< J7*
a <?*
off
8 ,L"
?j.*
1^8
A1 "
°2 rL"
±1 //T
«»' */'
N I^V
x-~xv-» -*riH — i
_ ' + '. — ,
• ^ °*n^rfA<i©D
/TYJi* 1 »]
O\ tuj
SZ3"^@
/r-J
^-,'"x£"
//''
4 "RIVET 5ET(5NAP)
I" RIVET SET (SNAP)
Tf
'/i'
//r
2f
5" to 8"
1 r-a!
^>J_j-^4-r
;S^5]X0
( » ? "
J."
4 I
*\
vf
O-r
•*• i .3:
o-
^/%HEM9 /^Wi /*/
FIG. 7. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
TOOLS FOR STEEL ERECTION.
453
H 2 r) H r
J , / % SET CUPPERS / SET CUPPERS 5ET TRIMMER
Hr®
,3' 4'8"
t...
CONNFCTINCi flAff *-j>
£*! U-
OPO^ Me
£ ^ U?
I/* /5"
^v * *
t ' , /
3?' '%---/j' ;V'
- """^^ 2'fr
FORK WRENCHES
g
,
S <E
V
/f '-Too/Stee/ _.-/%
b tt t
!^r
SHACKLE BAR -g's? 'FORK WRENCHES
FIG. 8. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
454
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
f/4 for%"rivet- rj For privet ,' f 4" for %" rivets- fj~6
y/ifforj "rivet-]^" for %' rivet- *-!% for %" rivets /.-^
^-:::v;£_^ I K [o|:^:^"v.p f
7*c £" .
•/g ror-4 rivets
f or %" rivets-
>«J | d" \ /'#'
DOLLY
~\ £» i f>t£tl
I v i 2: 6
STRAIGHT DOLLY
0/am- of cup for privet- /%, for^-IJt rf£ for% "rivet, t£ Jvrf* ,Q'>
Depth of cup for% "rivet" j^', forj ff~ j" / f'jg for% rivet, ? for i / ^r
30"
Goose NECK DOLLY
rt
% "for? rivets J^f' P "~*!+->4 "to 8"
Ljjiv
~jf\9
HEEL DOLLY
% rorjr r/V(
?cs,jrorj-
r '^
fwy r/vets, j ror
?
^^
"for j"nvets, /£ forj'
•*A
iff 2>" - t. rt
h for% rivets, ]•%
s;
'A-/'
/rt) j
A V )
o
) * 9
»
X ^T^
NJcM
yjT
-*-T-\ '4r
& 1 l^-v\ * 1
"• ' i
-* 6 f ~)
VJ p »••• C
\ rf?
D
L£p3V
5^7/
l\l
.t_L_U-M_
J S'O"
1
I
•
«*'U
f«-- •
— n
Cti/5 /?^zz.y
^^ r*
CLUB DOLLY BEN'*
r
ir
?'6ff
s'o"
I +r*
*1
i
C )*• 1 1 )
j / j
t
//f* ,x ^*
l(^O
•*» 6? C^
>;00
i^4^2 p
t !
i , i)
' 'w Z^M •,
r. -k
REAMER WRENCH *~* 5/vz?
FIG. 9. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
TOOLS FOR STEEL ERECTION.
4-..1
i <i 'for i' "Rivet \ ^ij/2'ar/S1
Si
'^" Hole For Tap Bo/t
/W/ZK WITH DETAILS
HANDLE B
tf b^
* IT - *~n 2"j
"Si MV Z*
*-(J L.
-^ 7"
rf
IZ
* ^" w
-*« ,'-^\ MEDIUM KEY WRENCH
TS ?--' K-H
A'* Ray
/r
H*---
KEY WRENCH
5'0"
?i> tifZ.*--:-**-
~f '.
» I V%i-
S*>L
__t.kT
L£
rr^r
zl*
.0^
KEY WRENCH
FIG. 10. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
456
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
/3*
u/ ,7 (Hardened Steel Point
I fj
*
IL "t- - — =H-- ----^ %iV ~i
'4 -^-l-yd::or--. . . *•>
yf/K/fj- CLAMP HOOK
BLACKSMITH'S TOOLS
OLD MAN
>r' S"'f^
yl' ~£*'
RIVET PITCHING TONGS * RIVET STICKING TONGS
,* CORRUGATED IRON TOOLS
02
©
CORRUGATED IRON PUNCH
c
,j."
"ii"
CORRUGATED IRON HAMMER
CORRUGATED IRON RIVET SET
-'? /'2"
i i '
T.5 D
CORRUGATED IRON DOLLY
CORRUGATED IRON SHEARS
FIG. ii. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
Tool.s I ()R STKKL KKI-< I lo\.
457
•>*
2-'--*
10 "fye Bar Hook
2^"*] 3 Bars-
6" EYE BAR HOOK
w' ;^i/«
/"fin/t *'---?.
•Rounded
V-
I'Bo/t
PURCHASE Rms K« £YE BAR HooK
W--*-W
SHACKLES MTH PINS ^.^^ t
6 TON GIRDER HOOK FOR 14" QUADRUPLE & 20" SINGLE BLOCK "3" "•*?
7 x/ f5 TSv GIRDE R HOOK
4! !*-• --,7-- --;/ ™w SSTon 6/rJer Hook* 12 "*5i" flats, 5% <!> Rii
wb^V*^ ^**h ^'V^^N l5T°n^er^ok,8"-2^flats,2^
%W;v//r i>/v^x /%i5\
T^V^* > /'?J
r/*
(Tp» ^Shackle
HEAVY I BEAM HOOK LIGHT / BEAM HOOK
FIG. 12. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
458
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
j Octagonal Steel-'
turn in handle-^ ?*$&&¥* Bogs, /j " Diarn-
//r\ii/>
Va
3 Hole in head
c ft" J- S"
or I daor*
Handle of
3sh or hickory.
CARRYING HOOK
jt'
i".. f
Clevis* 5" ,/£**£
(?i 9} " \^:cf/3teA
* K-- |S-— >» ) -~.fr
STEEL WEDGE
OAK WEDGE-
4
for Double Nut Falsework
_3* ff Zj
4 Bolts, L =6rip +5' \4
i — -i \ for Single Nut Falsework lr~L
Bolts* L*6rip~
y z _^__ : |^ _/__;
* Square Nuts '' STANDARD FALSEWORK BOLTS Square Head & Hut
FIG. 13. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
0
TOOLS FOR STEEL ERECTION.
4.VJ
STANDARD GAUGE PUSH CAR
6
Roller A &
TIMBER BUGGY & DETAILS
— .^j i /jf
Handle 6 '"STANDARD DOUBLE RAIL JACK Handle G-
FIG. 14. TOOLS FOR STEEL ERECTION. AMERICAN BRIDGE COMPANY.
460
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
Chains. — Chains should be made of the best grade of double refined iron, and should be
fabricated with great care. Details of a f-in. ring chain; a |-in. hook chain, and of a f-in. twin
hook chain, as made for the American Bridge Company, are given in Fig. 6, and data on chains
are given in Table VIII.
Jacks. — Hydraulic and power lifting jacks of the necessary capacity should be provided.
Miscellaneous Tools; — In addition to the standard tools required by bridge carpenters and
by the blacksmiths many special tools are required by structural steel erectors. The most im-
portant special tools required in steel erection as used by the American Bridge Company are
STEAMBOAT JACK
TERRY OLD MAN
SHEAR FOR CORRUGATED STEEL STEAMBOAT RATCHET
FIG. 15. MISCELLANEOUS TOOLS FOR STEEL ERECTION.
given in Fig. 7 to Fig. 14. An improved "old man" as used by Terry and Tench is shown in Fig.
15. A corrugated rolling shear, and a steamboat jack and a steamboat ratchet are also shown
in Fig. 15. The special tools used by the Chicago Bridge and Iron Company for the erection of
elevated tanks are given in Fig. 16 and Fig. 17.
LIST OF TOOLS.— The tools required for any job will depend upon the size of the work,
the number of men employed, and upon local conditions. A complete list of the tools that are
commonly used by structural steel erectors is given in Table IX.
Actual lists of the tools used for the erection of a steel railway bridge, a steel highway bridge,
and a steel mill building are given in Table X, Table XI, and Table XII, respectively.
TOOLS FOR ERECTION OF ELEVATED TANKS.
481
1?"
M— — *M -H
*•—
•—*=>———
r^F ,* ,/*
"
WRENCHES
AUGER
"*"
4*orless
BAR DOLLY, Wt-26Ibs-
J.'jyr
H
DOLLY, Wt-26]bs-
5PRIN6 DOLLY. Wt-38Ibs
DOLLY-
FIG. 16. TOOLS FOR ERECTION OF ELEVATED TANKS. CHICAGO BRIDGE & IRON COMPANY.
462
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
GOUGE, Wt-2?lbs>
5"''
BACKING OUT PUNCH, We- 3 Ibs-
••«
-*_
//v
K~
DRIFT PINS
HAND CHISEL, Wt-1%
HAND CALKING TOOL
\ Hand Fuller is same
35 Hand Calking Too!
but point is rounded-
Diam-
Rivet
Dimensions in Inches
L
A
B
c
7"
|
|
16
8i
7i
n
%
£
a
i
~2
B
16
I
i
3
4-
7
ie
9
16
_7
16
B
16
5
16
5|
5"
,I$" For %" Rivet, tjffvrf'
I,- 1 "For •§ "Rivet, j " for f "•
/£
1 16\
%" for j" Rivet, %-Fori''
RIVET BUSTER, Wt-5Ibs- RIVET HAMMER, Wt-^lbs- HAND CHISEL, Wt-2Ibs-
FIG. 17. TOOLS FOR ERECTION OF ELEVATED TANKS. CHICAGO BRIDGE & IRON COMPANY.
LIST OF TOOLS FOR ERECTION OF STRUCTURAL STEEL.
TABLE IX.
LIST OF ERECTION TOOLS FOR STRUCTURAL STEEL.
AMERICAN BRIDGE COMPANY.
N.UUI-.
N.IHII-.
Adzes.
Air Chippers.
Air Compressors
Air Drills.
Air Pumps.
Air Reamers.
Air Receivers.
Anchors.
Angle Bars for R. R. Rails.
Anvils.
Auger Bits.
Augers (ship) H in- to 'tV m-
Axes.
Axes (Hand).
Backing Out Punches.
Balance Beams.
Bars, Chisel.
Bars, Claw.
Bars, Connecting.
Bars, Crow.
Bars, Pinch.
Bellows.
Bits for Braces.
Blacksmith Blowers.
Blacksmith Hand Tools.
Blocks (8, 10, 12, 14, 16, 18) in. Single.
Blocks (8, 10, 12, 14, 16, 18) in. Double.
Blocks (14, 16, 18, 20) in., 3 Sheave.
Blocks, 4 Sheave.
Blocks (8, 10, 12, 14, 16, 18, 20) in. (Snatch)
Gate.
Blocks (i, 2, 3, 4, 6) Sheave, Wire Rope.
Boats (give kind).
Boilers (only).
Boring Machines.
Braces (Carpenter).
Branding Irons.
Brushes (Paint).
Brushes (Wire).
Buckets.
Car Axles.
Cars, Camp.
Cars, Derrick.
Cars, Flat.
Cars, Lever.
Cars, Push.
Cars, Tool.
Car Wheels.
Center Punches.
Chains, (J, |, J, J) in. Hook & Ring, — ft. long.
Chains, I in. Hook & Ring, — ft. long.
Chains, J, f , J, I in., two rings, — ft. long.
Chisels, Cope.
Chisels, Framing.
Clevises.
Cold Chisels.
Currugated Iron Cutters.
Corrugated Iron Dolly Bars.
" Hammers.
" " Punches. "
Corrugated Iron Rivet Sets.
" Shears.
Crabs, Single Gear Iron Frame A — Flat.
Crabs, Double Gear Iron Frame A — Flat.
Crabs, Single Gear Wooden Frame A — Flat.
Crabs, Double- Gear Wooden Frame A — Flat.
Cutters, Handle.
Derricks.
Derrick Balls Overhauling.
Booms (Steel).
Booms (Wood).
Boom Bands, 2 Links.
Foot Blocks.
& Mast Angles.
Bearing Plates.
Pins.
Plates.
Foot Blocks.
Goose Necks.
Gudgeon Pins.
Masts (Steel).
Masts (Wood).
Mast Band.
Mast Band, one link.
Mast Seat.
Round Spiders.
Long Spiders, Two Guys.
" One Guy.
Diamond Points.
Do ly Bars, Bent.
Club.
Goose Necks.
Heel.
Spring.
Straight.
Drawing Knife.
Drilling Machine (Portable).
Drift Pins (&, ft, H, II) in. diameter.
Drills, Flat.
Drills (Stone).
Drills (Twist).
Engine and Boiler.
Eye Bolts.
Files.
Forges (not rivet).
Gauges (Track).
Gin poles (Wood) Gas Pipe, Shoes.
Grind Stone.
Guy Clamps.
Guy Rods.
Guy Wire.
Hammers (Chipping).
Hand Gouges.
Handle Gouges.
Handles — Hammer, Maul, Axe, Adze, Pick.
Hatchets.
Hook for I Beams — Large, Medium, Small.
Hooks, Cant.
Hooks for Eye-Bars.
Hooks, Girder.
464
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
TABLE IX. — Continued.
Name.
Name.
Hooks for Heavy Chord.
Hooks for holding on.
Hooks, Scaffold.
" Stringer.
" Timber.
Horse Powers.
Hose, Air Drill.
" Rubber.
" Steam.
Bands.
" Couplings.
Jacks, Hydr. — Capacity.
" Norton.
" Rail, Double.
" Rail, Single.
" Steamboat.
Steamboat 'Pull. _
" Steamboat Pushing.
" Screw.
" Track.
Kettles, Iron.
Ladles.
Lag Screws.
Ladders.
Lanterns.
Levels (Spirit).
Locks.
Marking Pot.
Mattocks.
Mauls, Spike.
Mauls, Steel (8, 9, 12, 16, 18, 20) Ib.
Nails.
Oars.
Oar Locks.
Oil Cans.
Old Man.
Picks.
Pike Poles.
Pile Hammers.
" Driver Leads.
" Rings.
" Ring Hooks.
Pins, Cotter.
Pipe Cutters.
Pipe, Iron.
Pipe Tongs.
Planes.
Plumb Bobs.
Pneumatic Bucker-up.
Pneumatic Hammer.
Pump, Boat, Galvanized Iron.
Pump, Centrifugal.
" Force.
" Steam.
Punch, Hydraulic.
Punch, Screw.
Purchase Rings.
Rails (Steel).
Rail Splice Plates.
Rail Buggies.
Rams.
Ratchets.
Reamers — re", if , if , ITS in.
Reamer Handles.
Rivet Busters.
Clamps.
Clamp Hooks.
Forges.
Gouges.
Hammers.
Sets for — |, |, f, |, i, in. Rivets (Hand).
Sets for — £, f, 5, |, I, in. Rivets (Pneu-
matic).
Set Cuppers.
Set Gouges, Standard.
Set Rivet Tongs.
Set Trimmers.
Spikes.
Rollers.
Roofing Sets.
Rope, Manila — f, I, ij, i|, 2 in.
Rope Lashing, Manila.
Rope Slings, Manila.
Rope, Wire Hoisting.
Saws, Crosscut.
Saws, Hand.
Saw Frames, Hack.
Saws, One Man.
Saw Sets (Crosscut).
Screw Drivers.
Shackles.
Sheaves, — in. dia.
Shovels.
Squares (Carpenter).
Stock and Dies.
Stoves.
Sulphur Pot.
Tape Lines.
Tarpaulins.
Timber Buggies.
Tool Boxes.
Steel, Octagon.
Steel, Round.
" Steel, Square.
Traveler Corner Irons.
" Plates.
Rods.
" Wheels, Standard.
Traveler Wheels.
" Wheel Boxes.
Travelers (Wood).
Travelers (Steel).
Turnbuckle Rods.
Tuyere Irons.
Valves.
Vises.
Wagons.
Wrenches, Chain.
Wrenches, Fork — |, f, &, f, in.
Wrenches, Key — large, medium, small.
Wrenches, Monkey.
Wrenches, S.
Wrenches, Stillson.
Wedges.
LIST OF TOOLS FOR ERECTION OF A STEEL BRIDGE.
TABLE X.
LIST OF TOOLS FOR ERECTION OF STEEL RAILROAD BRIDGE CONSISTING OF SEVERAL 75-FT. PLATE
C.IKDERS, A i8o-FT. THROUGH SPAN, AND AN SO-FT. VERTICAL LIFT SPAN, INTER-
NATIONAL FALLS, MINNESOTA. MINNEAPOLIS STEEL & MACHINERY Co.
Quantity.
Name and Size of Tool.
Quantity
Name and Size of Tool.
3
Augers, Ship, ^i in.
3
Forges, Complete.
2
Adz.
3
Files.
I
Axe, Hand.
2
Gouges, Hand.
2
Anvils.
3
Gouges, Handle.
3
Bars, Crow.
3
Hack Saws and Blades.
I
Bars, Claw.
i
Hammer, 7 Ib.
2
Bits, f in.
i
Hammer, Claw.
I
Box, Tool.
2
Hammers, Blacksmith, 5 Ib.
2
Braces.
16
Handles.
I
Brushes, Wire.
7
Hooks, Scaffold.
7
Brushes, Paint.
i
Hose, Air, f in., 700 ft.
i
Block, Steel, Snatch, IO in.
9
Hose, Water, J in. X 50 ft.
3
Block, Steel, Snatch, 12 in.
4
Jack, Screw, 2$ in. X 16 in.
3
Block, Steel, Snatch, Wire Rope, 12 in.
i
Jack, Track.
i
Block, Steel, Single, Wire Rope, 12 in.
2
Jack, Stone.
2
Block, Steel, Single, Wire Rope, 14 in.
I
Jack, Hydraulic, 15 ton.
2
Block, Steel, 4 Part, Wire Rope, 16 in.
2
Lanterns.
4
Block, Steel, Double, Wire Rope, 18 in.
I
Level.
4
Block, Steel, Double, Wire Rope, 12 in.
I
Man, Old.
2
Block, Steel, Triple, Wire Rope, 12 in.
4
Punches, Backing Out.
4
Block, Wood, Snatch, 10 in.
3
Punches, Screw (Frame).
2
Block, Wood, Snatch, 12 in.
i
Pipe Vise.
I
Block, Wood, Single, Tackle, 8 in.
i
Pick.
I
Block, Wood, Single, Tackle, 10 in.
12
Drift Pins, f in.
I
Block, Wood, Single, Tackle, 12 in.
10
Drift Pins, -f in.
6
Block, Wood, Double, Tackle, 8 in.
4
Drift Pins, f in.
4
Block, Wood, Double, Tackle, 10 in.
i
Pail, Water.
2
Block, Wood, Double, Tackle, 12 in.
2
Ratchets.
I
Block, Wood, Triple, Tackle, 12 in.
I
Receiver, Air, 30 in. X 60 in.
3
Block, Wood, Triple, Tackle, 14 in.
I,4OO ft.
Rope, Manila, I in., 7 pieces.
i
Block, Chain, 5 Ton.
1,300 ft.
Rope, Manila, ij in., 5 pieces.
1,200 ft.
Cable, Wire, $ in.
42O ft.
Rope, Manila, 2 in., I piece.
300 ft.
Cable, Wire, f in.
640 ft.
Rope, Manila, 2 in., I piece.
100 ft.
Cable, Wire, J in., galvanized.
275 ft.
Rope, Manila, 2 in., I piece.
2
Chains, f in., 23 ft. long.
565 ft-
Rope, Manila, I in., 2 pieces.
I
Chains, | in., 14 ft. long.
4
Rope, Manila, Lashings.
2
Chains, f in., 12 ft. long.
i
Stock and Dies, Blacksmith.
2
Chains, i in , 12 ft. long.
i
Stock and Dies, Pipe.
12
Clamps, Cable, i in.
6
Snaps, Rivet, f in.
IO
Clamps, Cable, f in.
6
Snaps, Rivet, f in.
8
Clamps, Cable, f in.
4
Snaps, Rivet, f in.
4
Clamps, Rivet.
3
Saws, Cross Cut.
2
Chisels, Round Nose.
2
Saws, Hand.
I
Chisels, Cold.
I
Shovels, No. 2.
5
Cutters.
4
Shovels, Snow.
3
Cant Hooks.
i
Square.
i
Compressor, Air.
13
Shackles
i
Derrick, 12 ton.
2
Trucks, Dolly.
i
Dolly, Timber.
3
Tongs, Blacksmith.
i
Dolly, Goose Neck.
4
Tongs, Heater
i
Dolly, Straight.
7
Wrenches, Bridge f in.
3
Dolly, Spring.
6
Wrenches, Bridge | in.
i
Dolly, Wedge.
2
Wrenches, Monkey
i
Dolly, Heel.
I
Heavy Traveler, 12 ton .
5
Drills, Twist, H in.
4
Rollers, 10 in. and 12 in.
6
Drills, Twist, f| in.
5
Pneumatic riveting guns.
6
Drills, Twist, H in-
2
28 in Turnbuckles.
i
Drills, l| m. X 4 ft.
2
Stoves.
2
Engine, Hoisting.
27
| in. X 8 in. Step bolts.
466
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
TABLE XL
LIST OF TOOLS FOR THE ERECTION OF SO-FT. SPAN HIGHWAY BRIDGE.
MINNEAPOLIS STEEL & MACHINERY Co.
Quan-
tity.
Name and Size of Tool.
Quan-
tity.
Name and Size of Tool.
2
Axes.
I
Man, Old.
2
Axes, Hand.
1 4
Punches, Backing out.
3
Bits, i in., f in., f in.
i
Pick.
i
Buster.
i
Pump.
i
Box, Tool.
4
Pins, Drift, f in.
i
Brace.
6
Pins, Drift, f in.
i
Brush, Paint.
2
Pails, Water.
2
Blocks, 10 in.
2
Pile Driver Leads.
I
Block, Single Tackle, 8 in.
I
Pile Driver Hammer.
I
Block, Single Tackle, 10 in.
I
Pile Driver Head Block.
4
Blocks, Double Tackle, 8 in.
I
Pile Driver Nipper
i
Chain, f in., 8 ft. long.
I
Ratchet.
i
Chain, % in., 7 ft. long.
124 ft
Rope, Manila, ij in.
i
Clamp, Rivet.
675 ft.
Rope, Manila, i in., 5 pieces.
i
Chisel, Hand.
2
Lashings, 15 ft.
i
Dolly, Timber.
Stock and Dies, Blacksmith.
4
Drills, Twist, H in.
Saw, Crosscut.
2
Files.
Saw, Hand.
2
Gouges, Handle.
Shovels, Short Handle
I
Hacksaw and Blades.
Shovels, Long Handle,
3
Hammers, 7 Ib.
Square.
3
Hammers, Claw.
Wrench, Bridge, f in.
i
Hammer, Machine.
6
Wrench, Bridge, f in.
3
Handles, 30 in.
2
Wrench, Bridge, ^ in.
i
Jack Screw, 12 in.
I
Wrench, Stillson, 10 in.
i
Level.
I
Wrench, Monkey, 12 in.
4
Wheel Barrows.
ERECTION OF TRUSS BRIDGES. — Truss bridge spans are usually erected on falsework.
The truss may be erected by means of a traveler or a derrick traveler or a derrick car. The usual
procedure where a traveler is used will be briefly described. After the falsework and traveler are
ready, lay out the center lines of the trusses on the falsework and locate the positions of the panel
points. At each panel point place the necessary blocking for camber. Then beginning at the
fixed end place the pedestals in position and place the lower chords and the floorbeams and stringers
in position and distribute the pins. If the floorbeams and stringers will be in the way they are
not placed until they are needed. The traveler is run to the center of the bridge and the center
panel on each side is erected. The upper chord section is hoisted and held a little above its final
position; the posts are raised, the diagonals are put in place and the pins are driven, or with a
riveted truss the joints are field bolted in about 50 per cent of the holes. The panel on the oppo-
site side is then erected and the top lateral struts and bracing are put in place, the floorbeams and
stringers are connected up and the lower laterals are put in place, so that the center tower is fully
braced. Great care must be used in erecting the middle tower to see that it is in exactly the
proper place. After the center panel is complete the traveler is moved toward the fixed end,
erecting the trusses one panel at a time. The traveler is then run back to the center and the
roller end of the trusses are erected. After the span is all connected up and all connections are
properly bolted up, the blocking is knocked out and the bridge is swung clear. The details of
erection vary with the type of truss and local conditions .and the above description is intended to
merely give an idea of the procedure. Truss bridges may also be erected by starting the
traveler at the fixed end.
Where a derrick car or a derrick traveler is used the erection is commonly started at the
fixed end.
RIVETING.
467
TABLE XII.
LIST OF ERECTION TOOLS FOR THE ERECTION OF A STEEL MILL BUILDING 60 FT. BY 150 FT. WITH
CORRUGATED STEEL COVERING; 43 TONS STEEL, 7 TONS CORRUGATED STEEL.
MINNEAPOLIS STEEL & MACHINERY Co.
Quantity.
Name and Size of Tool.
ijii.iiility.
N.uni- .in.l Si/c of Tool.
I
IO
8
700 ft.
i
i
I
23
7
2
6
3
i
i
i
i
i
3
i
i
Axe, Hand.
Bars, Crow.
Bars, Connecting.
Box, Tool.
Braces.
Brushes, Paint.
Block, Steel, Single, Wire Rope,
10 in.
Block, Steel, Double, Wire Rope,
10 in.
Block, Wood Snatch, 10 in.
Block, Wood, Single Tackle, 8 in.
Block, Wood, Double Tackle, 8 in.
Cable, J in., 3 pieces.
Chain, f in., 3 ft. long.
Chain, i in., 8 ft. long.
Chain, f in., 9 ft. long.
Clamps, Cable, f in.
Clamps, Cable, $ in.
Clamps, Rivet.
Chisels.
Cutters.
Crab, Small.
Dolly, Timber.
Dolly, Goose Neck, f in.
Dolly, Straight, | in.
Dolly, Spring, f in.
Dolly, Corrugated Steel.
Dolly, Jam, f in.
Drills, Twist, H in.
6
i
2
6
20
10
i
I,IOO ft,
4
i
3
i
i
4
2
I
2
I
I
15
20
8
i
2
Forge, Complete.
Gin Pole.
Gouges, Handle.
Hack Saw and Blades.
Hammer, Claw.
Hammer, Machine.
Handles, 30 in.
Man, Old.
Punches, Backing out.
Punches, Corrugated.
Pins, Drift, f in.
Pins, Drift, f in.
Ratchet.
Rope, Manila, f in., 8 pieces.
Rope, Manila, Lashings.
Stock and Dies, Blacksmith.
Snaps, Rivet, f in.
Saw, Hand.
Square.
Shackles.
Snips, Corrugated.
Tongs, Blacksmith.
Tongs, Heater.
Tongs, Pick-up.
Vise, Machinist.
Wrenches, Bridge, \
Wrenches, Bridge, j
Wrenches, Bridge, |
Wrenches, Bridge, j
Wrenches, Monkey.
In erecting the Municipal Bridge over the Mississippi River at St. Louis, sand boxes were
used for camber blocking in the place of the usual timber camber blocking.
The threads of pins should be protected by pilot nuts and pilot points when driving. Details
of standard pilot nuts are given in Table 99, Part II, and of standard pilotpoints in Table 100,
Part II.
RIVETING. — Field rivets may be driven by hand or with pneumatic riveters. Before
driving the rivets the parts to be riveted must be drawn up by means of erection bolts so that the
holes are fully matched and the surfaces of the metal are so close together that the metal from the
rivet will not flow out between the plates. The holes are brought in line and matched by the use
of drift pins, Fig. 7 and Fig. 17; care should be used not to injure the metal with the drift pin.
If the holes will not match they should be reamed. A gang for hand riveting consists of four
men, (i) a rivet heater, (2) a bucker-up, (3) a rivet driver, and (4) a man to catch and enter the
rivets, to assist in driving and to hold the rivet set (snap). The hot rivet is thrown by the rivet
heater with rivet-pitching tongs, Fig. 1 1 ; the rivet is caught in a bucket or keg and is put into the
rivet hole with the rivet-sticking tongs, Fig. II. The rivet is then bucked-up with a dolly, Fig. 9
or Fig. 10, and is upset with a rivet hammer, Fig. 7. After the rivet is upset to fill the hole a rivet
set (snap), Fig. 7, is held over the upset rivet and a few blows with the riveting hammer completes
the work. Field rivets are ordered with enough stock to furnish metal to fill the hole and to
form a perfect rivet head. If the rivet is too short, either the hole will not be filled or the rivet
468
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
head will be imperfect. If the rivet is too long the rivet set (snap) will force the metal out under
the edge of the rivet set (snap) making a bad looking job. The rivet should be heated uniformly
so that it will be upset for its entire length. Riveters prefer to use rivets with scant stock so that
ines j Guy Line rFdli 'Lines fGuyLine
'
Hook'
JL.
* Gas Pipe
G/N POLE, 8 TONS
*rBoom Lines
SHEAR LEGS
GUY DERRICK
1% Manila
•Front 5i//
Elevation Section B-B
"A" DERRICK, 3 TONS
clj: "Manila or j "wire fine
E/ewtion ~" Plan
STIFF LEG DERRICK, 12 TONS
" Manila or wire line
Elevation Section A-A
VIADUCT TRAVELER, REVOLVING MASTS
J2 TONS
Elevation Section A-A
BOOM TRAVELER WITH F/XED MASTS
12 TONS
FIG. 1 8. DERRICKS AND TRAVELERS.
the rivet can be upset and a perfect head formed with little labor. To drive a rivet properly the
rivet should be upset by striking it squarely on the end, as side blows will upset the rivet without
filling the hole.
DETAILS OF DERRICKS.
Where compressed air is available a pneumatic field riveter is used for driving rivets. Pneu-
matic tii-ltl rivi-ters are of two types: (a) jaw riveters that buck-up the rivet and form the head as
in shop riveters; and (6) a pneumatic gun that is held against the rivet by the riveter, the rivet
being bin -kccl-up with a dolly as in hand riveting or with a pneumatic dolly. The pneumatic gun
'Guy Lines^
"-Boom or Topping Lines
Boom Lines, ^
—5oom Lines
(Fall Lines or
** Hois ting L ines
GUY DERRICK
-Bull Wheel
GUY DERRICK WITH BULL WHEEL
-Boom Lines
r-Masb
fall Lines or
* Hois ting Lines '•
,-BulI Wheel
STIFF LES DERRICK W/TH BULL WHEEL
BULL WHEEL
FIG. 19. DETAILS OF DERRICKS.
is more convenient and is commonly used. A rivet snap is used in the air gun. Good rivets can
be driven by hand, but the work of the pneumatic riveter is more uniform and most specifications
for erection of structural steel call for its use. Several railroad bridge specifications now
require that hand driven field rivets be calculated for only four-fifths of the allowable stresses on
machine driven field rivets. While more rivets can be driven with an air gun than by hand, the
added expense for air makes the cost of driving nearly the same as for hand driven rivets.
470
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
Dollys for bucking-up rivets are made in many forms to suit the different conditions.
Straight, goose-neck, bent, heel and club dollys are shown in Fig. 9, a ring dolly is shown in Fig.
10, and a corrugated iron dolly in Fig. II. Dollys for use in erecting elevated tanks are shown
in Fig. 1 6, and include the bar dolly, the heel dolly, the combination dolly, and the spring dolly.
DERRICKS AND TRAVELERS.— Derricks and travelers are made in many different forms.
A few of the more common forms will be described.
-
Tons
Ties ]%
-Lateral Ties ?i"n
Elevation
STEEL VIADUCT TRAVELER
*4»^1 JL'W
!_-• -i W
Cross Section
/3" Manila
-5-?0" Sheaves
,tf/,6u If
rryi ;
t* - - --#<?'- ^55 5^£/b/?
Elevation*
STEEL DERRICK CAR
FIG. 20. DETAILS OF A VIADUCT TRAVELER AND A STEEL DERRICK CAR.
Gin Pole. — A gin pole, Fig. 18, is a timber or steel mast with four guys and a block at the
top through which the hoist line leads to a crab bolted near the bottom, or the hoist line may
run to the hoisting engine. The foot of a gin pole is supported by timbers which are shifted with
bars or on rollers. The gin pole should not be inclined more than a few degrees from the vertical,
and care must be used to prevent the bottom from kkking out with heavy loads. Gin poles
may be made of timber, gas pipe, or may be built structural steel masts. Gin poles are not
commonly made longer than 40 to 60 ft., but a trussed gin pole 120 ft. long has been used for
erecting elevated towers. The mast of a gin pole may be built up so that only two guys are
necessary, resulting in " shear legs" as in Fig. 18.
Each guy is fastened at its lower end to a "deadman" (a timber, or log, or beam buried in
the ground).
DETAILS OF A STIFF-LEG DERRICK.
471
f ^ ' i*^-~ r,- ' ' -
\ i i = / « vy .y7-rf-.fr,
&<&£'.*%: ™* :-"
FOOT BLOCK "H"
***^"
Counter Weight J/
'
MAST CAP "E"
Weight 165*
Lumber =
9./00 fard Feet.
Weight of Lumber- 56, 300 /6s. _
^<? » STANDARD I? Ton STIFF LK£B*KK
Tota/ Weight 46, 200 » American Bridge Comp3ny
FIG. 21. DETAILS OF A STIFF-LEG DERRICK.
472
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
Guy Derricks. — A guy derrick, Fig. 18 and Fig. 19, has a vertical mast guyed with three or
more guy lines, and has a boom which carries blocks and a fall line on the upper end. The boom
is raised and lowered with rigging called "topping lines" or "boom lines." The load is raised
by rigging called "fall lines" or "falls." The hoisting line may be run down the boom to a crab
or to the hoisting engine, or the hoisting line may be run through a "rooster" placed on top of the
mast and then to the hoisting engine. Guy derricks may be swung in a full circle, either by hand
or by means of a bull wheel operated by a line from the hoisting engine.
"A" Derrick. — The "A" derrick or "Jinniwink" derrick is shown in Fig. 18. "A" derricks
are used for light hoisting up to three to five tons. The "A" derrick is a simple form of the stiff-
leg derrick.
Stiff-Leg Derrick. — The stiff-leg derrick has a mast braced by "A" frames set at right angles
to each other, Fig. 18 and Fig. 19. The loads may be lifted and the boom raised and lowered
by means of a crab or by a hoisting engine. The stiff-leg derrick has a free swing of about 240
degrees. The mast may be turned by hand or by means of a bull wheel operated by a line from the
hoisting engine. Details of a 1 2-ton timber stiff-leg derrick are shown in Fig. 21. Stiff -leg
derricks of large capacity are now commonly made of structural steel. Details of a steel stiff-leg
derrick are given in Fig. 29.
— -c. to c. Oirders ^
FIG. 22. DETAILS OF A GALLOWS FRAME. AMERICAN BRIDGE COMPANY.
Boom Travelers. — The mast of a derrick may be supported by the framework of a traveler,
Fig. 1 8. The traveler may be made one or several stories in height. The booms may swing or
may be fixed to raise and lower in one plane, and may be used single or in pairs. Boom travelers
are commonly used in erecting train sheds, and structural steel buildings. Details of a steel boom
traveler are given in Fig. 28 and Fig. 29.
Viaduct Travelers. — An overhang traveler for erecting a high steel viaduct is shown in Fig. 20.
Gallows Frame. — A gallows frame or a transverse bent as shown in Fig. 22, is used for erecting
plate or riveted girders. The gallows frame is guyed fore and aft with steel cables. Gallows
frames are commonly used in pairs or a gallows frame is used with a stiff-leg derrick.
Through or Gantry Travelers. — A through or gantry traveler consists of two or three trans-
verse bents or "gallows frames" braced longitudinally and is carried on a track supported on the
falsework and placed outside of the trusses. The traveler has a clearance such that it can be
FAI.SI.WOKK.
473
TABLE XIII.
BILL OF TIMBER IN TRAVELER, FIG. 24.
No.
CroM Sec-
tion, In.
Length.
iM-h:.
No.
CroM Sec-
tion, In.
Length,
Ft- In.
5
10 X 12
28-0
Hoisting beams.
4
4X8
1 8-0
Platform cut to 9 ft.
4
12 X 12
38-0
Longitudinal.
4
6X 12
38-0
Sills.
2
8X 16
44-0
Caps.
2
8 X 12
32-0
Sheave beams.
2
8X 8
24-0
Chord.
IO
4X8
36-0
Longitudinals.
4
8 X 10
30-0
Leg*.
4
6X 8
36-0
Platform.
4
8 X 10
24-0
Legs.
10
3 X 8
36-0
Platform plank. •
4
6X 8
32-0
Legs batter.
i
6X 10
2O-O
* Blocks cut to 2 ft.
4
6X 8
22-O
Legs.
4
6X 10
28-0
Side braces.
8
4X 8
26-0
Web braces.
4
6 X 10
3O-O
Side braces.
4
3 X 8
16-0
Web braces.
2
4X6
16-0
Fillers cut to 8 ft.
4
3 X 8
I4-O
Web braces.
2
4X6
14-0
Fillers.
4
3 X 8
I2-O
Web braces.
I
3 X 8
12-0
Leg brace.
I
3X 8
2O-O
Web braces cut to IO ft.
2
6X 12
16-0
Fillers cut to 2 ft.
2
3X8
1 8-0
Leg braces cut to 9 ft.
2
8 X 10
16-0
Trucks cut to 8 in. X 9 in.
2
3 X 8
2O-O
Leg braces cut to 10 ft.
X4*t.
2
3 X 8
12-0
Leg braces cut to 6 ft.
I
i X 6
16-0
Fillers.
4
3 X 8
1 8-0
Leg braces platform.
4
3 X 8
20-0
Chord cut to 10 ft.
8
3 X 10
I2-O
Leg splices cut to 6 ft.
2
3 X 8
22-O
Leg brace cut to 1 1 ft.
8
3 X 8
12-0
Leg splices cut to 6 ft.
I
3 X 8
1 8-0
Leg brace cut to 4 ft. 6 in.
8
3X6
I2-O
Leg splices cut to 6 ft.
4
2X4
38-0
Sliding beam.
TABLE XIV.
BILL OF BOLTS IN TRAVELER, FIG. 24.
TABLE XV.
BILL OF IRONS IN TRAVELER, FIG. 24.
No.
Diameter, In.
Length, Ft-In.
No.
Name.
Dimensions.
2O
I3S
ICO
160
ISO
100
20
IO
IO
' IO
I
-IO
- 8
- 6
- 4
- 2
- O
o-io
o- 8
2- 0
i- 4
IO
4
4
2
2
16
8
4
8
2
2
Sheave Chocks. . . .
Bent Bars
loj in. Block Sheave.
3 in. X J in. X 2 ft. 9 in.
3 in. X i in. X 3 ft. 5 in.
3 in. X i in. X 2 ft. o in.
3 in. X i in. X 2 ft. o in.
3 in. X i in. X I ft. 10 in.
i\ in. diameter X 9 ft. 2 in.
14 in. diameter, 3 in. shaft.
Bent Bars
Bent Bars
Bent Bars
Scabs
Rods
Traveler Wheels. . .
Wheel Boxes
Rods
ij in. diameter X 6 ft. 6 in.
l\ in. diameter X 3 ft. 6 in.
Rods
run past the completed bridge or structure. Travelers may be made of timber or structural steel.
Outline plans for fouc standard timber travelers designed by the American Bridge Company are
given in Fig. 23, while the detail plans for traveler No. I are given in Fig. 24. The bill of lumber
for traveler No. I is given in Table XIII; the bill of bolts is given in Table XIV, and the bill of
irons in Table XV. Traveler No. I may be used for single track railway spans up to 250 ft.;
traveler No. 3 for single track spans up to 175 ft.; traveler No. 2 for double track spans up to
175 ft.; and traveler No. 4 for double track spans up to 250 ft.
Derrick Cars. — Derrick cars with a capacity up to 75 tons are in common use. The derrick
cars are usually self-contained and can move under their own power. The boom can be folded
back over the car out of the way when not in use. A sketch of a derrick car is shown in Fig. 20.
FALSEWORK. — Falsework for the erection of bridges is built up of bents made of three or
more posts or piles, braced transversely in the same manner as for permanent trestles. Framed
bents are carried on mudsills, or on piles where the foundation is inadequate or where the false-
work is in flowing water. Where piles can not be driven in running water or where there is danger
474
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
Weight of
Traveler =
25 tons-
Safe loads
For 240O Jbs
Fiber $ tress s
15,000 Ibs- ab
CROSS SECT/ON pounds
. points /, 2,3, 4,
5 or 6 , not app//'ed ^
simultaneously •
Traveler wheel
•figured for 30,000 \
t.^_
Weight of Traveler
=36 Tons-
/6"*S"
Safe Joads
for 2400 Ibs.
fiber stress,
25,000 Ibs-at
points / or 2 and
20,000 Jbs-ab
points 3, 4,5 or 6,
not applied ' s/'mt//-
taneous/y-
Trsve/er wheel
figured for 30,000
nrv
N +
/s
3--,
/
,?p"
A
A
pouno
A **•
/
>'
X
it ^-*-
,x
f
^
H-, •*' '
'*?
"~:;~JO"x 12" ,'/"* Z^
v/ „ ,.
<---//" -f/^
U'O"
»
/»
5
^
£
z
5
' ^ tvT
f
5
4
6
2
5
K/
jp-12**!*?
W<7*
?
4?
/
- r'' ' '4'0"
/ / i ;
/
4
^2*
+' ,-r-I2*x 14*
+ ^'
>,
'*.,
x
>
~*~
v_
/ *
V'<7
,/'''
>
3-'
>Z/4A
/'-'
r
'-x"^?"
/-;
3J
PLAN
?
,3'*/6
Weight of
Traveler =
22? Tons-
. f-3"*8"
SECT1ON\
/JO"*/2-} 2-4"* '8
•fO"*10"
Weight of Trsvefer
30 Tons'
h rti
"
rt i*
y
4J
'-5
i
4J
V? 4
^
'
i
i
J
\
/
j
i
2
A..
b. 4*1*
4
5
4
'Hi, -. -1}
Safe load for
2200 fbs. fiber
stress, 15,000
at points 1,2 or
4, /0,OOO/bs-
at points 5, and
30,000 Ibs -s&
point 3 • Loads
applied simu/tan- ^_\ CROSS SECT/ON
eousfy on/y 3t ^
, points number-
Traveler
wheel is
f/gured for
30, Off O Ibs.
PLAH
TRAVELER
b i?"*1
|
1 +M
' * 5*
3
4
3
S5 _ ^
\
'2
\
j
2
SI *s^
i
S
^ *0
./---
"t"
-/;
\
1 J
i
i
1
^
i
2
^4 J.
ih* A x
3
rf
3
>''ffi iti "^
\f V —
f ^ f
SaFe loads for
fiber stress of
2200 Ibs-,
15, 000 Ibs-tf
points 1,25,000
Ibs' at points 2.
3, 4 or 5' Loads
dpp/ied simultdn -
eousfy on/y at
po/nts numbered alike
Trave/er
figured for
30,000 Ibs.
PLAH
TRAVELER N° 4
FIG. 23. STANDARD TIMBER TRAVELERS. AMERICAN BRIDGE COMPANY.
• DETAILS OF A TIMBER BRIDGE TRAVELER.
475
§
u
< bi
£
3
H
u
o
5
1
u
H
-yff-fff.
476
ERECTION OF STRUCTURAL STEEL.
CHAP. XIV.
of flood, it may be necessary to use spread footings which are anchored in place. Where it is
practicable to obtain piles of sufficient length they may be used for the full height of the falsework.
The timber used in building falsework should be sound, strong, free from defects that will affect
its strength or interfere with its use. Since the structure is temporary, durability is not an
important element in selecting timber for falsework unless it is to be used several times.
For examples of timber trestles, see Chapter VII.
Plans of typical four-legged falsework as used by the American Bridge Company are shown
in Fig. 25. When trains are to be carried and 2-8 in. X 16 in. stringers are used under each rail,
bents must not be spaced over 18 ft. centers for the falsework as shown.
Zd'o'itotti-ayeler^rComtant^^
r6M--i^
'—•yim^m m>-
'*w\ wrwm*'
Var.^ (to ^ TrussesJVa_riab[e^ '^Jfar.\
;, This line oF stringers tobeused^
'<?• trusses are erected first--* '';
Y/ff-^X; 4x8'" -) ,'8'il6"i i ' \; ,'-^'8x1
*- Dotted lines denote sill to be used wnen necessary
The average maximum length of leg nottoexceed30-0.
8x16 stringers are to be ordered either ?6-0 or3?-0
to suit conditions.
This type of false work is designed Porheavy slnqle
track spans when trains are not carried and for '
sinqle track spans up to 250 when trains are carried.
' —Doffed fines denote ail/ to be used when necessary
FIG. 25.
OffiEWYORK
Piles. — Timber piles may be driven with a drop hammer, Fig. 26, or with a steam hammer.
A spool roller pile driver with a drop hammer is shown in Fig. 26. The hammer is raised to the
top of the leads by the hoisting engine; the hammer is then permitted to fall on the top of the
pile, dragging the hoisting rope down with it. The force of the blow of the hammer depends
upon the weight of the hammer, the height of free fall, and the resistance of the hammer in the
leads. By catching the hammer as it descends the operator can cushion the blow so that the safe
bearing power of a pile as calculated from the penetration may be very misleading.
Details of a pile driver are given in Fig. 27.
DETAILS OF STEEL ERECTION.
477
Tin- safe load on piles may be calculated by the Engineering News formula
p a2W-h
wlirrt- P — safe load on the pile in tons;
W — weight of hummrr in tons;
h — height of free fall of hammer in ft.;
s •• average penetration of the pile for last six blows.
(0
•Leads
PJ/« S Hammer Lines
'Rocker Front
< ^Center 6eyr
SPOOL ROLLER DRIVER
ORDINARY TRACK PJLS DRIVER
FIG. 26. TYPES OF PILE DRIVERS.
I? 'Shears
folts £ t unless otherwise noted-
STANDARD 4B'On
LAND PILE DRIVER
American Bridge Co
FIG. 27. DETAILS OF STANDARD PILE DRIVER.
AMERICAN BRIDGE COMPANY.
478
STEEL BOOM TRAVELER.
EN*. NEWS
Front Elevation
FIG. 28. TRAVELER USED IN ERECTION
4 Washer under lower
goose neck; '-•& /
Planff //
Side Elevation
OF ARMORY, UNIVERSITY OF ILLINOIS.
Triple Block-
ENS. NEWS
FIG. 29. STIFF-LEG DERRICK USED ON ERECTION TRAVELER FOR ERECTION OF ARMORY,
UNIVERSITY OF ILLINOIS. (Two of these derricks were used on front of traveler.)
INSTRUCTIONS FOR THE ERECTION OF STUCTURAL STEEL. 479
Piles should have a penetration of not less than 10 ft. in hard material and not less than 20 ft.
in soft material. For a steam hammer unity in the denominator in (l) should be replaced by -j^.
The following specification is commonly used for piles for heavy falsework.
All piles are to be spruce, yellow pine or oak, not less than 9 in. in diameter at the point and
not more than 14 in. in diameter at the butt. Piles are to be straight and sound, and free from
-i affecting their strength or durability. Piles are to be driven into hard bottom until they
do not move more than § in. under the blow of a hammer weighing 2,000 Ib. and falling 25 ft.
For specifications for falsework piles, see Chapter VII.
A track pile driver is shown in Fig. 26.
Design of Falsework. — Falsework should be designed to carry the necessary loads. Where
the falsework is required to carry traffic it should be designed for the same allowable stresses as
are permitted for timber trestles and bridges, Table V, Chapter VII. Where the falsework does
not carry traffic the allowable stresses may be fifty per cent in excess of those permitted for perma-
nent structures. Care should be used in the design to prevent crushing of timber across the
grain. For details of timber trestles see Chapter VII.
Traveler for Erection of Armory.* — The new armory for the University of Illinois is 276 ft.
by 420 ft. in plan, the main drill hall being covered by three-hinged arches with a span 206 ft.
centers of end pins, a center height of 94 ft. 3 in., and are spaced 26 ft. 6 in. The arches have a
horizontal tie of two 4 in. X t in. bars, and are braced together in pairs.
Each arch was shipped in eight segments, and the four sections for each half of the arch
were assembled and riveted up in horizontal position on the ground close to their final positions.
One side of the arch was then lifted into a vertical plane by a two-boom traveler, and its lower
end was fitted into the shoe and the shoe pin driven. The truss was then lowered on this pin
until its head rested on the ground, the arch segment being supported by guys at the sides. The
opposite segment of the arch was then raised and adjusted in the same way. The traveler was
then placed at the center of the arch, and the hoisting lines of the two booms were attached near
the ends of the two half-arches, which were then raised, the lower ends rotating on the shoe pins.
The arch was then held while the center pin was driven and the purlins were placed connecting it
to the adjacent arch.
The traveler, Fig. 28, consisted of a steel tower about 40 ft. square and 33 ft. high to the
working deck. On this deck were two 4O-ft. masts wj$h A-frames, each carrying a 9O-ft. boom, so
that the top of the boom could reach about 20 ft. above the top of the arches, the maximum
height from the ground to the hoisting block being 125 ft.
The traveler was supported on wood rollers on tracks of 16 X 16 in. timbers about 40 ft.
apart. The .upper part of the traveler was composed of two stiff-leg derricks of the type shown
in Fig. 29, with one stiff- leg and one sill removed from each, the masts being stepped on the
traveler frame and connected by bracing as shown. Each derrick had a lifting capacity of 15 tons,
and was operated by an engine of 8 H. P., the two engines being placed on a platform on the
lower sills of the traveler about 2 ft. from the ground.
INSTRUCTIONS FOR THE ERECTION OF STRUCTURAL STEEL.— The McClintic-
Marshall Construction Co. has issued the following instructions to foremen.
In Order to Avoid Accidents, as Far as Possible, be Guided by the Following:
I. See that Your Equipment is Sufficiently Strong. — It is your duty to see that the equip-
ment and tools you use for each part of the work are sufficiently strong to handle the same safely.
You should see that the derricks you use are amply strong for the loads to be lifted. The
goose neck and gudgeon pia are the critical points of a derrick. If you have any doubt about
the strength of the goose neck, provide heavy wire guys from gudgeon pin to sill at base of stiff
legs. Don't lift a ten ton load on a five ton derrick. The same thing applies to gin poles and
travelers. Don't overload your equipment and don't run any chances where life is endangered.
Be careful not to lift any but a light load on a derrick if the length of the boom exceeds seventy
times the least width or thickness of the boom; that is, if your boom is 12 in. X 14 in. the least
width is 12 in., you should not lift a heavy load on this boom if it is more than seventy feet in
length.
* Engineering News, Dec. n, 1913. The structural steel was fabricated and erected and the
traveler was designed by the Morava Construction Co., Chicago, Illinois.
480 ERECTION OF STRUCTURAL STEEL. CHAP. XIV.
See that travelers are well and carefully framed and erected, well braced and capable of
withstanding the greatest wind, and shocks from heaviest loads that are to be lifted.
See that the hooks, shackles and beckets on your blocks are amply strong, and don't allow a
gate block to be used without it being closed and hooked. Also see that your cables and chains,
as well as the rings and hooks in the same, are amply strong for the loads to be lifted.
Do not use old or worn line when there is any danger to men or material by so doing. Cut
out the use of manila line whenever possible. When you are obliged to use it be sure it is amply
strong. Use steel cable whenever possible, as it is safer, will last longer and is cheaper in the
long run. Be sure that the guy cables for gin poles, derricks, etc., are of sufficient size to with-
stand the tension to come upon them. Also that the cables are securely fastened by means of a
sufficient number of good, strong clamps well fastened, and also that dead men or other anchorages
are ample, and watch them when lifting heavy loads to see that guys do not cut dead men in two.
Keep gin pole guys as near at right angles to each other as possible, when only four are used.
You should be careful to see that the gas pipe or wooden scaffold you use is of proper size
and strength for the span and loads. If there is any question about the strength, test the same
by applying several times the load that will come upon it. See that plank you use for scaffolding,
etc., is the right kind of wood, preferably white or yellow pine, free from knots and shakes and
plenty strong, watching to see that it is thick enough for the span on which it is used.
Do not put heavy loads on light push cars. The frame is not only liable to crush but the
shafts, boxes or wheels may bend or break, upsetting the load and injuring the men.
2. See That Your Equipment is in Order. — In setting up your derricks see that they are
plumb, properly guyed and that the splices are brought into contact and bolted with tight-fitting
bolts. See that the goose-necks fit gudgeon pin closely and are not cracked or bent and that the
top of stiff-leg is tied down from the goose-neck to the sill to prevent lifting tendency. If the
timbers in the mast, boom, stiff-legs or sills are rotten, knotty or wind shaken, do not use them.
See that your gudgeon pin and pintle casting are well fastened to the mast, and if the mast is of
wood that the wood is not rotten or worn at these points.
You should see that all leads are as straight and direct as possible, as failure to provide good
leads reduces the efficiency of your power and equipment, as well as producing heavy wear on the
lines and is a frequent cause of accidents. Particular care should be exercised in securing good
leads for wire cable on account of liability of breaking the individual wire strands by sharp bends
or indirect leads. A broken individual wire is liable to lie across and cut the other wires of the
cable. When you use a wooden traveler see that the timbers are all in good condition and that
it is erected plumb and square and the joints are properly and securely bolted. More accidents
occur from the use of wooden derricks and wooden travelers than from any other cause, and for this
reason extreme care should be exercised to see that they are in good condition before using them.
When a traveler is used, see that it is properly erected and thoroughly bolted and all sway and
bracing rods tightened.
Do not use an iron gin pole if the sections are bent or dented seriously, or the splices do not
clamp the pole tightly and securely. Do not use a wooden gin pole unless the timber is in good
condition, well spliced with good long splices securely bolted.
See that your hoisting engine is in good order; that the shafts are not bent, the dogs, clutches
and brakes, including the friction, are in good condition and working order. The lever con-
trolling the winch heads should be straight and when thrown in should engage the ratchet fully.
See that winch head cannot slip off shaft. See that the boilers are cleaned frequently and kept in
good condition.
You should be particular to see that gas pipe scaffolding is not rusted on the inside and that
it is fastened so that it cannot roll or turn. Do not use any plank or timber for scaffolding that
is knotty, rotten or weather cracked, and allow no man to work on scaffold plank laid loose on
the supports. The plank should be fixed so that they cannot move or slide endwise, by using drop
bolts.
All cables should be in good condition and kept oiled or greased so that they will not rust;
if they are not in good condition, do not use them. All guy cables should be securely fastened
by means of a sufficient number of good clamps.
See that your chains and the rings and hooks in the same are not worn, cracked or bent
out of shape and that they are annealed at least once every three months in an annealing furnace,
if you are near one, or otherwise anneal them yourself by laying them down in a straight line and
building a good sized wood fire over them, heating slowly to a cherry red, then cover over thor-
oughly with ashes and heated dry dirt leaving them to cool slowly in the ashes and dirt. In laying
the chains down in a straight line do not lay one chain on top of another. Be particular to see
that the covering is ample so that air or moisture cannot cool the chains quickly or partially.
This annealing should be done on Saturday and chains not disturbed until Monday. Chains
used frequently every day should be annealed once a month.
See that your blocks are in good order and that the beckets, shackles and hooks are not
bent, cracked or out of shape, and that faces of blocks are in good condition, also that the sheaves
are not cracked or the flanges broken.
INSTRUCTIONS FOR ERECTION OF STRUCTURAL STEEL. 481
Sec tli.it all button sets (rivet sets) arc fastened to the air hammers.
See that Your Equipment and Tools are Properly Used. — In using a locomotive crane be
sun- that your track is pn.prily ballasted ami level and the- rails well spiked down. Do not lift a
tdnoays when the locomotive crane is standing on a curve, without using extra care. Use your
<-rs and mil clamps when lifting a heavy load.
1 'he l.i'ls that a locomotive crane is capable of handling safely for each radius are plainly
marked on the . T.IIK-; don't attempt to lift heavier loads with the crane.
that the booms of locomotive cranes, derrick cars or derricks, are in first class condition.
If the boom (or liaises of the boom) has been injured or bent, don't use it, but replace the broken
or bent part with new material. Don't attempt to straighten it, as the material in all probability
has been injured, and will break or collapse sooner or later.
A locomotive crane is a useful, but dangerous piece of equipment, for this reason the greatest
possible (are should be exercised in handling the same. Don't allow any man on the car or crane
cab, except the craneman, and keep workmen from under the boom. Don't attempt to shift track with
your crane standing on the same track, and don't attempt to lift a maximum load with the boom
iiori/ontal.
You must be especially careful in swinging boom sidewise or lifting loads sidewise with a
derrick car as your car will upset unless you use outriggers or guys. Don't run chances, but lift
the load straight ahead wherever possible. Sec that the boom on the derrick car is tightly guyed
at all times with wire rope running from end of boom to sides of car. Never use manila line for
this purpose, as it will stretch and your boom will get away from you, upsetting the car. Use
additional guys to end of boom when setting heavy loads.
In carrying loads with a locomotive crane or derrick car on a curve, be sure that the track is
level and the outer rail not elevated as is customary with railroad track.
Be very careful in using a wooden boom extension or outriggers, that you do not lift too
heavy loads. The increased length of the boom and the weight of extension reduce the lifting
capacity considerably. Whenever possible, avoid the attachment of guy lines to railroad tracks,
as numerous accidents have occurred by car running into the guys.
Hook onto sheets or bundles of small material so that they cannot slip out.
Don't allow men to carry glazed window sash on their shoulders when the wind is blowing.
See that gate blocks are securely fastened and that men do not stand in the "bite" of a line.
Do not use a light gate block when lifting heavy loads.
Lines should be run around two winch heads when making a heavy lift.
When you use a derrick keep the boom elevated above a horizontal line as far as possible, as gen-
erally the worst stress comes on the boom and mast as well as stiff-legs or guy lines when boom is in a
horizontal position. A maximum load for the derrick should never be lifted with the boom in a hori-
zontal position.
When you use a gin pole see that the splices are well bolted and the pole is properly guyed.
Do not lean the pole too much when lifting a load or moving the pole and see that the foot of the
pole cannot move or slip except when you desire to move it.
A number of accidents have occurred through the improper loading of push cars. See that
the load is properly placed so that it cannot roll or tumble over, especially going around a curve".
Do not allow your men to push on the side of the car with a top heavy load. They should push
or pull from the ends of the piece.
When you lift a beam or girder use scissor dogs or cast steel girder hooks wherever possible,
and if you are obliged to use either ordinary dogs or chains sec that wooden blocks are used be-
tween the chain or dog and the flange to prevent the girder from slipping.
Avoid the use of chains except for lifting light loads. Where you have heavy loads to lift
use cable slings, being careful to avoid sharp bends by using rounded wooden blocks between
cable and load. Don't put too many parts of lashing into a hook as by doing so you are liable to
open up the hook. See that exposed parts of dangerous machinery are properly covered.
4. Be Orderly, Careful. — Sec that your work is carried on in an orderly, careful manner.
See that material is unloaded and piled in an orderly, careful way so that it cannot fall, turn
or be blown over.
Unless necessary, do no hoist any material to a structure until you are ready to put it into
position and properly fasten it. In cases where you do hoist material to the structure before
putting it in its final position, see that it is piled in an orderly way so that it cannot turn or roll
over when a man steps on it.
Don't let tools or equipment such as bolts, nuts, drift pins, blocks, dolly bars, etc., lie around
so that they can be knocked off the work or so that any one can fall over them. Keep every-
thing orderly and in ship-shape and allow nothing to lie around.
5. Be Vigilant. — You must use vigilance and be on the job practically all the time to see
that your men are carrying out your instructions; that tools and equipment are in fit condition
for the work and that they are handling the work carefully and intelligently.
Be careful and insist on the men under you being careful, and do not allow any one who is
reckless and careless to work for you.
32
482 ERECTION OF STRUCTURAL STEEL. CHAP. XIV.
Whenever any question as to the safety of equipment or tools or the work which you are
erecting is brought to your attention by any of the men under you or others, investigate the
same and satisfy yourself of the safety of the same before proceeding further. If you are satisfied
the work, equipment or tools are not safe, put them in a safe condition immediately.
6. See that Proper Instruction is Given Employees. — Call attention of men to any dangerous
conditions on the job so that they can be on the lookout. Your faithful attention to this matter
is to the interest of employee and employer alike.
7. Unfit Condition. — You must see that every employe under you is in proper physical con-
dition. They should be strong, temperate, clear-headed, with good eyesight, good hearing, and
not lame or crippled.
Do not allow any man to go to work who has been drinking or drinks during working hours
or who is sick or in unfit condition. A man's mind is not clear who is at all under the influence
of liquor and thus endangers his own and fellow workmen's lives. Don't employ ignorant persons.
Don't employ any one under eighteen years of age and preferably no one under twenty-one.
Those employed between the ages of eighteen and twenty-one should be strong, sober, healthy
boys who desire to learn the business. You must secure a written permit from the parents of
all boys under twenty-one years of age, authorizing you to employ them. Forms for this purpose
will be sent you. The character of this business is such that a workman should be strong and
sound in body, temperate in habits, clear and alert in mind, to avoid accidents.
8. Use Judgment. — You must use judgment in assigning men to do certain work and see that
they are capable and experienced in the work to be done.
Signal men should be capable, experienced bridgemen, and should stand in a position where
they can be seen by the men at the hoisting engine and those connecting the work. Signals
should be clearly understood. Use none but good, careful, experienced locomotive cranemen,
derrick car men, and men on winch heads.
Don't resort to expediency by allowing an inexperienced man to do'the work where experience
counts. Educate the men up to their work. Don't throw too much on inexperienced men all
at once. You should see that the pusher and men use proper tools to do the work and handle
same properly. Don't allow your men to work on crane runway when cranes are in motion.
Don't allow men to work on scaffold that you would not work on yourself. Where there are
heavy pieces to be lifted see if the weight is marked on the piece; if not, get the weight from
the invoice and mark it on, calling pusher's attention to it.
9. Do Not Allow Men to Work in Perilous Places. — You must see that your men are not
exposed to extremely hazardous conditions and that they are not allowed to work in extremely
dangerous places.
Do not allow your men to work under loads and in places where there is imminent danger.
Be careful not to allow men to work on the roofs of buildings when there is frost, ice or snow
on the same, without taking extreme precautions. The same applies to other steel structures.
10. See That Workmen Obey Following Rules.
a. Don't Be Reckless. — More accidents occur through recklessness than any other cause.
Don't walk on rods. Don't ride a load. Don't ride on a locomotive crane.
b. Don't Be Careless. — Look where you step and be sure that on what you step is safe and
secure. Don't step on ends of loose plank. Don't start to slide down a line unless you are sure
the ends are fastened.
c. Be Orderly. — Do whatever you do in an orderly, careful manner. Pile material so that
it cannot roll, fall, tumble, or be blown over. Don't let tools or equipment such as bolts, nuts,
drift pins, blocks, dolly bars, etc., lie around so that they can be knocked off the work or so that
any one can fall over them.
d. Unfit Condition. — Don't go to work if you have been drinking or do not feel well. If you
are lame or have any defect in hearing or eyesight you should not work at this business as by so
doing you endanger your own and fellow workmen's lives. If you are inexperienced in, or un-
suited for the work to be done, don't undertake it.
e. Be Vigilant. — Watch what you are doing. Don't stand or work under a load. Don't
go in the "bite" of a line nor stand in front of a snatch block. Don't work on or about a crane
runway when the crane is in use unless there is a stop between you and the crane.
/. Don't Use Unfit Tools. — Be sure the tools and equipment you use are in good working
order. If they are not, don't use them. Don't work with men who don't observe these rules.
SPECIFICATIONS FOR THE ERECTION OF RAILWAY BRIDGES.*
AMERICAN RAILWAY ENGINEERING ASSOCIATION.
1. Work to be Done.— The Contractor shall erect, rivet and adjust all metal work in place
plrtf, ami [>erform all other work hrn-iuat'irr sj>ecified.
2. Plant. — The Contractor shall provide all tools, machinery and appliances necessary for
tin- t-x|x-ilitious handling of the work, including drift pins and fitting up bolts.
3. Falsework. — The method of erection and plans for falsework and erection equipment
shall be subject to approval by the Engineer, but such approval shall not relieve the Contractor
from any responsibility. Falsework will be built by t Falsework
matt-rial of every character will be provided by the t
The temporary structure for use during erection and for maintaining the traffic shall be
propi-rly designed and substantially constructed for the loads which will come upon it. All bents
shall be thoroughly secured against movement, both transversely and longitudinally. The bents
shall l>e well secured against settling, and piles used wherever firm bottom cannot be obtained.
Upon completion of the erection, the temporary structure, if the property of the Railway Company,
shall be removed without unnecessary damage and neatly piled near the site or loaded on cars,
as may be directed. If the property of the Contractor, it shall be removed in a manner subject
to the approval of the Engineer.
Falsework placed by the Railway Company under an old structure or for carrying traffic,
may be used as far as practicable by the Contractor during erection, but it shall not be unneces-
sarily cut or wasted.
4. Conduct of Work. — The work shall be prosecuted with sufficient force, plant and equip-
ment to expedite its completion to the utmost extent and in such a manner as to be at all times
subordinate to the use of the tracks by the Railway Company, and so as not to interfere with the
work of other contractors, or to close or obstruct any thoroughfare by land or water, except
under proper authority.
Reasonable reduction of speed will be allowed upon request of the Contractor.
Tracks shall not be cut nor shall trains be subjected to any stoppage except when specifically
authorized by the Engineer.
The Contractor shall protect traffic and his work by flagman furnished by and at the expense
of the Railway Company. The Contractor shall provide competent watchmen to guard the work
and material against injury.
5. Engine Service. — If under the contract, work train or engine service is furnished the
Contractor free of charge, such service shall consist only in unloading materials and in trans-
ferring the same from a convenient siding to the bridge site. Other engine service shall be paid
for by the Contractor at the rate of $ per day per engine, the time to include the time
necessary for the engine to come from and return to its terminal. When engine service is desired
the Contractor shall give the proper railway officials at least 24 hours' advance notice and the
Railway Company will furnish the service as promptly as possible, consistent with railroad
operations.
When derrick cars are used on main tracks, their movements shall be in charge of a train
crew, and the expense of the crew and any engine service other than as noted above shall be
charged to the Contractor.
. 6. Transportation. — When transportation of equipment, materials and men is furnished
free over the Railway Company's line, it shall be subject to such conditions as may be stated
in the contract.
7. Masonry. — The Railway Company will furnish all masonry to correct lines and elevations,
and unless otherwise stated in the contract, will make all changes in old masonry without un-
necessarily impeding the operations of the Contractor. The Railway Company's engineers will
establish lines and elevations and assume responsibility therefor, but the Contractor shall com-
pare the elevations, distances, etc., shown on plans, with the masonry as actually constructed as
far as practicable, before he assembles the steel. In case of discrepancy, he shall immediately
notify the Engineer.
8. Handling and Storing of Materials. — Cars containing materials or plant shall be promptly
unloaded upon delivery therefor, and in case of failure to do so the Contractor shall be liable for
demurrage charges. Material shall be placed on skids above the ground, laid so as not to hold
water, and stored and handled in such a manner as not to be injured or to interfere with railroad
operations. The expense of repairing or replacing material damaged by rough handling shall be
charged to the Contractor. The Contractor, while unloading and storing material, shall compare
each piece with the shipping list and promptly report any shortage or injury discovered.
* Adopted, Am. Ry. Eng. Assoc., Vol. 13, 1912, pp. 83-87, 935-945.
t Insert "Railway Company" or "Contractor," as the case may be.
483
484 ERECTION OF STRUCTURAL STEEL.
9. Maintenance of Traffic. — When traffic is to be maintained it will be carried on in such a
manner as to interfere as little as practicable with the work of the Contractor.
Changes in the supporting structure or tracks required during erection shall be at all times
under the direct control and supervision of the Railway Company.
10. Removal of Old Structure. — Unless otherwise specified, metal work in the old structure
shall be dismantled without unnecessary damage and loaded on cars or neatly piled at a site
immediately adjacent to the tracks, and at a convenient grade for future handling, as may be
directed. When the structure is to be used elsewhere all parts will be matchmarked by the
Railway Company; when the old bridge is composed of several spans the parts of each shall be kept
separate.
n. Metal Work. — Material shall be handled without damage. Threads of all pins shall be
protected by pilot and driving nuts while being driven in place.
Light drifting will be permitted in order to draw the parts together, but drifting for the
purpose of matching unfair holes will not be permitted. Unfair holes shall be reamed or drilled.
Nuts on pins and on bolts remaining in the structure shall be effectively locked by checking
the threads.
All splices and field connections shall be securely bolted prior to riveting. When the parts
are required to carry traffic, important connections, such as attachments of stringers and floor-
beams, shall have at least fifty (50) per cent of the holes filled with bolts and twenty-five (25) per
cent with drift pins. All tension splices shall be riveted up complete before blocking is removed.
When not carrying traffic, at least thirty-three and one-third (333) per cent of the holes shall have
bolts.
Rivets in splices of compression members shall not be driven until the members shall have
been subjected to full dead load stresses. Rivets shall be driven tight. No recupping or caulking
•will be permitted. The heads shall be full and uniform in size and free from fins, concentric
and in full contact with the metal. Heads shall be painted immediately after acceptance.
Rivets shall be uniformly and thoroughly heated and no burnt rivets shall be driven. All
defective rivets shall be promptly cut out and redriven. In removing rivets the surrounding
metal shall not be injured; if necessary, the rivets shall be drilled out.
12. Misfits. — Correction of minor misfits and a reasonable amount of reaming shall be con-
sidered as a legitimate part of the erection.
Any error in shop work which prevents the proper assembling and fitting up of parts by the
moderate use of drift pins, and a moderate amount of reaming and slight chipping or cutting,
shall be immediately reported to the Engineer and the work of correction done in the presence of
the Engineer, who shall check the time expended. The Contractor shall render an itemized bill
for such work of correction for the approval of the Engineer.
13. Anchor Bolts. — Holes for all anchor bolts, except where bolts are built up with the
masonry, shall be drilled by the Contractor after the metal is in place and the bolts shall be set
in Portland cement grout.
14. Bed Plates. — Bed plates resting on masonry shall be set level and have a full even bearing
over their entire surface; this shall be attained by either the use of Portland cement grout or
mortar, or by tightly ramming in rust cement under the bed plates after blocking them accurately
in position.
15. Decks. — The * will frame and place the permanent timber deck.
16. Painting. — The paint will be furnished by * and shall be of
such color, quality and manufacture as may be specified.
Surfaces inaccessible after erection, such as bottoms of base plates, tops of stringers, etc.,
shall receive two coats of paint, allowing enough time between coats for the first coat to dry before
applying the second. No paint shall be applied in wet or freezing weather, nor when the surface
of the metal is damp. Painting shall be done in good and workmanlike manner, subject to strict
inspection during progress and after completion, and in accordance with special instructions
which shall be given by the Engineer. All metal shall be thoroughly cleaned of dirt, rust, loose
scale, etc., before the paint is applied.
17. Clearing the Site. — :The Contractor, after completion of the work of erection, shall
remove all old material and debris resulting from his operations and place the premises in a neat
condition.
1 8. Superintendence and Workmen. — During the entire progress of the work the Contractor
shall have a competent superintendent in personal charge and shall employ only skilled and
competent workmen. Instructions given by the Engineer to the Superintendent shall be carried
out the same as if given to the Contractor. If any of the Contractor's employes by unseemly
or boisterous conduct, or by incompetency or dishonesty, show unfitness for employment on the
work, they shall, upon instructions from the Engineer, be discharged from the work, nor there-
after be employed upon it without the Engineer's consent.
* Insert "Railway Company" or "Contractor," as the case may be.
SPECIFICATIONS FOR THE ERECTION OF RAILWAY BRIDGES.
19. Inspection. — The work of erection shall at all times be subject to the inspection and
:it.iili C <H I In- Kiininrrr.
20. Engineer. — The term "Engineer," as used herein, shall be understood to mean the
Cliu-l Kn^im-iT of the Railway Company, or his accredited representative.
INSTRUCTIONS FOR THE INSPECTION OF BRIDGE ERECTION.*
(1) Study and observe the plans and specifications for steel construction. Study the masonry
.s ami i tu ( k i he m.isonry as built with the steel plans.
(2) F.imili.iri/i1 yourself with the local conditions affecting erection.
Make the acquaintance of the principal men engaged upon the work and of local residents
M- interests may be affected thereby.
(3) Obtain and study carefully the time table and be well posted concerning the time when
regular and extra trains are due and their relative importance. Acquaint yourself with all special
traffic arrangements, made because of the work in hand.
(4) Secure full information concerning the conditions of the work in the bridge shop and the
probable dates of shipment.
(5) Obtain reports of any uncompleted or erroneous work that must be attended to after
arrival of the material in the field.
(6) Study the erection program in order to avoid delays and be able to recommend some
other procedure in an emergency.
(7) Endeavor to have full preparations made before disturbing the track so that the erection
may proceed rapidly and the period of such disturbance be made a minimum.
(8) Keep a record of the arrival of all materials. The contractor's record should be sufficient
if available. Strive to anticipate any shortage of material and use all available facilities to hasten
delivery of the needed parts.
(9) Study the progress of the work and determine whether it is likely to be completed in the
time allotted. If not, endeavor to secure such additions to the force and equipment as will insure
such completion.
(10) Make a daily record of the force employed and the distribution of labor, in a way that
will assist in following clauses 9 and 23.
(n) Exercise a constant supervision of any temporary structure or falsework and make
soundings if necessary with the purpose of discovering any evidence of failure or lack of safety
and having it corrected before damage is done. Examine erection equipment with a view to its
safety and adequacy.
(12) Be constantly on hand when work is in progress and note any damage to the metal,
failure to conform to the specification or any especial difficulty in assembling.
(13) Make sure that each member of the structure is placed in its proper position. If match
marks are used, examine them with care.
Endeavor to have the several members assembled in such order that no unsatisfactory make-
shifts need be resorted to in getting some minor member in place.
(14) Prevent any abuse or rough usage of the material. Bending, straining and heavy pound-
ing with sledges are included in such abuse.
(15) Watch carefully the use of fillers, washers and threaded members to see that they are
neither omitted nor misused.
(16) Make certain that all parts of the structure are properly aligned and that the required
camber exists before riveting. It is possible for a structure to be badly distorted although the
rivet holes are well filled with the bolts.
(17) Watch the heating of rivets to insure against overheating and to make sure that scale
is removed.
Examine and test carefully all field-driven rivets and have any that are loose or imperfect
replaced.
Have cut out and replaced all rivets, whether shop-driven or field-driven, that may be loosened
during erection and riveting.
Prevent injury to metal while removing rivets.
(18) Present to the contractor at once for his attention any violation of the specifications
or contract, and secure a correction or refer the matter to the proper authorities as soon as possible.
(19) _Keep informed concerning the use of Company material and work trains and assist
in procuring such material and trains when needed, and preserve a record thereof.
(20) Secure a match-marking diagram of any old structure to be removed and see that each
part of such structure is properly marked in accordance therewith. Make a record of the manner
of cutting the old structure apart and report any damage to the members of the old structure.
* Am. Ry. Eng. Assoc., Vol. 14, p. 90.
486 ERECTION OF STRUCTURAL STEEL. CHAP. XIV.
Indicate by sketches or otherwise such repairs or replacement as will be found necessary in re-
erection.
(21) Secure photographic records of progress and the important features of the work where-
ever practicable.
(22) Make a record of flagging of trains, whether performed for the benefit of the Contractor
or otherwise, delays to trains, personal injuries, and accidents of every kind.
(23) Make reports as directed, showing the progress of the work, the size of the force and
the equipment in use.
Make a final report showing the cost of labor of erection per ton of material erected, the
cost of labor per rivet in riveting, the cost of correcting errors in design and fabrication and com-
menting on the design and details; and give such other information as may be useful in planning
similar work.
CHAPTER XV.
ENGINEERING MATERIALS.
IRON AND STEEL. — The following definitions were adopted by the Committee on the
Uniform Nomenclature of Iron and Steel of the International Association for Testing Materials,
September, 1906.
Cast Iron. — Iron containing .so much carbon or its equivalent that it is not malleable at any
temperature. The committee recommends drawing the line between cast iron and steel at 2.20
IK.T cent carbon.
Pig Iron. — Cast iron which has been cast into pigs direct from the blast furnace.
Bessemer Pig Iron. — Iron which contains so little phosphorus and sulphur that it can be used
for conversion into steel by the original or acid Bessemer process (restricted to pig iron containing
not more than o.io per cent of phosphorus).
Basic Pig Iron. — Pig iron containing so little silicon and sulphur that it is suited for easy
conversion into steel by the basic open-hearth process (restricted to pig iron containing not more
than i.oo per cent of silicon).
Gray Pig Iron and Gray Cast Iron. — Pig iron and cast iron in the fracture of which the iron
itself is nearly or quite concealed by graphite, so that the fracture has the gray color of graphite.
White Pig Iron and White Cast Iron. — Pig iron and cast iron in the fracture of which little
or no graphite is visible, so that the fracture is silvery and white.
Malleable Castings. — Castings made from iron which when first made is in the condition of
cast iron, and is made malleable by subsequent treatment without fusion.
Malleable Pig Iron. — An American trade name for the pig iron suitable for converting into
malleable castings through the process of melting, treating when molten, casting in a brittle state,
and then making malleable without remelting.
Wrought Iron. — Slag-bearing, malleable iron, which does not harden materially when suddenly
cooled.
Steel. — Iron which is malleable at least in some one range of temperature and in addition is
either (a) cast into an initially malleable mass; or, (b) is capable of hardening greatly by sudden
cooling; or, (c) is both so cast and so capable of hardening.
Open-hearth Steel. — Steel made by the open-hearth process, irrespective of carbon content.
Bessemer Steel. — Steel made by the Bessemer process, irrespective of carbon content.
' Blister Steel. — Steel made by carburizing wrought iron by heating it in contact with car-
bonaceous matter.
Crucible Steel. — Steel made by the crucible process, irrespective of carbon content.
Steel Castings. — Unforged and unrolled castings made of Bessemer, open-hearth, crucible
or any other steel.
Alloy Steels. — Steels which owe their properties chiefly to the presence of an element other
than carbon.
Classification of Iron and Steel. — The limits of carbon, the specific gravity and properties
of iron and steel are as follows:
Per cent of Carbon. Specific Gravity. Properties.
Cast Iron 5 to 1.50 7.2 Not malleable, not temperable
Steel 1. 50 to o.io 7.8 Malleable and temperable
Wrought Iron 0.30 to 0.05 7.7 Malleable, not temperable
It will be seen that the percentage of carbon alone is not sufficient to distinguish between steel
and wrought iron. The softer grades of steel resemble wrought iron. Very mild open-hearth
steel is often sold under the trade name of " Ingot Iron," and is reputed to have many advantages
over structural steel, most of which properties it does not possess among which is the ability to resist
corrosion.
487
488 ENGINEERING MATERIALS. . CHAP. XV.
CAST IRON. — The product of the blast furnace, where the iron ore is reduced in the presence
of a flux, is called pig iron. The term cast iron 'is commonly applied to pig iron after it has been
again melted and cast into finished form. Cast iron contains carbon, silicon, sulphur, phosphorus,
and manganese in addition to pure iron, and occasionally very small quantities of other elements.
The amount of carbon depends largely upon the presence of other elements.
Carbon. — The percentage of carbon ordinarily varies between if and 4 per cent, but in the
presence of manganese the carbon may be much higher. Carbon may occur in the form of com-
bined carbon, giving a white brittle cast iron, or in the form of graphite, giving a gray cast iron,
which is the form used in structural castings. The proper amount of carbon in cast iron depends
upon the amount of other impurities and upon the use that is to be made of the finished product.
Silicon. — The carbon is controlled by varying the amount of silicon and sulphur. Silicon
acts as a precipitant of carbon, changing it from the combined form to the graphite form. The
silicon in gray cast iron is usually between f and 3 per cent.
Sulphur. — Sulphur has the opposite effect of silicon and its presence is considered objection-
able. Sulphur produces " red-shortness " (brittleness when the iron is heated). The amount of
sulphur in gray-iron castings should not exceed 0.12 per cent.
Manganese. — Manganese and sulphur both tend to increase the amount of combined carbon,
but they tend to neutralize each other. Manganese gives closeness of grain and prevents the
absorption of sulphur on remelting. The amount of manganese in gray-iron castings is usually
less than ^ per cent; more than 2 per cent makes cast iron brittle.
Phosphorus. — Phosphorus increases the fusibility and fluidity of cast iron but at the same
time makes it brittle. A high phosphorus content is necessary in cast iron for light ornamental
castings where strength is not required. The phosphorus in gray-iron castings varies from 5. to
1 5 per cent.
Malleable Castings. — Small thin castings made of white cast iron may be decarbonized by
heating the castings in annealing pots containing hematite ore or forge iron scale. The castings
are kept at a cherry red heat for three to four days, and are then allowed to cool slowly. The metal
in malleable castings should not exceed J in. in thickness in small castings, nor | in. in large
castings, and should be of uniform thickness.
Strength of Cast Iron. — The strengths of gray-iron castings are given in Table I and in the
Specifications for Gray-iron Castings of the American Society for Testing Materials.
STANDARD SPECIFICATIONS FOR GRAY-IRON CASTINGS
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED SEPTEMBER i, 1905.
1. Process of Manufacture. Unless furnace iron is specified, all gray castings are understood
to be made by the cupola process.
2. Chemical Properties. The sulphur contents to be as follows:
Light castings not over 0.08 per cent
Medium castings o.io
Heavy castings 0.12
3. Classification. In dividing castings into light, medium and heavy classes, the following
standards have been adopted:
Castings having any section less than J in. thick shall be known as light castings.
Castings in which no section is less than 2 in. thick shall be known as heavy castings.
Medium castings are those not included in the above classification.
4. Physical Properties. Transverse Test. The minimum breaking strength of the " Arbi-
tration Bar " under transverse load shall be not under:
Light castings 2,500 Ib.
Medium castings 2,900
Heavy castings ; 3,3°°
In no case shall the deflection be under o.io in.
Sl'KCIKK ATIONS FOR (1KAY-IKO.N CASTINGS.
489
Tensile Test. Where specified, this shall not run lesa than:
Light castings 18,000 Ib. per sq. in.
Medium castings 21,000 "
Heavy castings 24,000 "
5. Arbitration Bar. The quality of the iron going into castings under specification shall be
determined l>y nic.ins of the " Arbitration Bar." This is a bar ij in. in diameter and 15 in. long.
It sli.ill he prepared as stated further on and tested transversely. The tensile test is not recom-
mended, l)iii iii i MM' it is called for, the bar as shown in Fig. i, and turned up from any of the broken
pieces ot ill transverse test shall be used. The expense of the tensile test shall fall on the pur-
chaser.
6. Number of Test Bars. Two sets of two bars shall be cast from each heat, one set from the
first and the other set from the last iron going into the castings. Where the heat exceeds twenty
tons an adtlit ional set of two bars shall be cast for each twenty tons or fraction thereof above this
amount. In case of a change of mixture during the heat, one set of two bars shall also be cast
for every mixture other than the regular one. Each set of two bars is to go into a single mold.
The bars shall not be rumbled or othetwise treated, being simply brushed off before testing.
MM\
YMyi__
'Standard Thread"
/ Y V Y
MVMflST
h
..I §
i
5 S
5
C-L ^
— (
1 11111] i
— ,"... ...^
h- 3'// i>\
FIG. i. — ARBITRATION TEST BAR. TENSILE TEST PIECE.
7. Method of Testing. The transverse test shall be made on all the bars cast, with supports
12 in. apart, load applied at the middle, and the deflection at rupture noted. One bar of every
two of e ich set made must fulfil the requirements to permit acceptance of the castings represented.
8. Mold for Test Bar. The mold for the bars is shown in Fig. 2. The bottom of the bar is
^g in. smaller in diameter than the top, to allow for draft and for the strain of pouring. The
pattern shall not be rapped before withdrawing. The flask is to be rammed up with green molding
sand, a little damper than usual, well mixed and put through a No. 8 sieve, with a mixture of one
to'twelve bituminous facing. The mold shall be rammed evenly and fairly hard, thoroughly dried
and not cast until it is cold. The test bar shall not be removed from the mold until cold enough
to be handled.
9. Speed of Testing. The rate of application of the load shall be from 20 to 40 seconds for a
deflection of o.io in.
10. Samples for Analysis. Borings from the broken pieces of the " Arbitration Bar " shall
be used for the sulphur determinations. One determination for each mold made shall be
required. In case of dispute, the standards of the American Foundrymen's Association shall be
used for comparison.
11. Finish. Castings shall be true to pattern, free from cracks, flaws and excessive shrinkage.
In other respects they shall conform to whatever points may be specially agreed upon.
12. Inspection. The inspector shall have reasonable facilities afforded him by the manu-
facturer to satisfy him that the finished material is furnished in accordance with these specifications.
All tests and inspections shall, as far as possible, be made at the place of manufacture prior to
shipment.
WROUGHT IRON. — Wrought iron is made in a reverberatory furnace from pig iron or from
molten metal taken directly from the blast furnace. The hearth of the reverberatory furnace is
fettled with high grade iron ore or mill scale, which acts as an oxidizing agent for reducing the
impurities. The puddling process may be divided into four stages: First or melting down stage,
occupying about 30 minutes, during which the silicon and manganese are oxidized and a consider-
490
ENGINEERING MATERIALS.
CHAP. XV.
able part of the phosphorus is oxidized; all oxidized products unite with the slag. Second or
clearing stage, occupying about IO minutes, during which the remainder of the silicon and manga-
nese, and more of the phosphorus are oxidized and removed from the pig iron. Third or boiling
stage, occupying about 30 minutes, in which nearly all the carbon is removed and most of the
remaining phosphorus is removed. Last or balling stage, occupying about 20 minutes, in which
the metal is gathered by the puddler into balls weighing about 75 to 100 Ib.
T
*
FIG. 2. — MOLD FOR ARBITRATION TEST BAR.
The puddled balls of iron and slag are hammered or are run through rolls to squeeze the slag
from the balls, and the resulting bars are called muck bars. The muck bar is again reheated and
rerolled and the resulting product is commercial merchant bar.
Wrought iron when broken in tension shows a fractured section irregular and fibrous. The
strength of wrought iron varies with the chemical composition, the mechanical work and heat
treatment it has received. The strength of wrought iron is given in Table I, and the specifications
for wrought-iron bars and plates as adopted by the American Society for Testing Materials are
as follows:
STANDARD SPECIFICATIONS FOR REFINED WROUGHT-IRON BARS
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
I. MANUFACTURE.
1. Process. Refined wrought-iron bars shall be made wholly from puddled iron, and may
consist either of new muck-bar iron or a mixture of muck-bar iron and scrap, but shall be free
from any admixture of steel.
II. PHYSICAL PROPERTIES AND TESTS.
2. Tension Tests, (a) The iron shall conform to the following minimum requirements as
to tensile properties:
Tensile strength, Ib. per sq. in 48,000
(See Sections 3 and 4.)
Yield point, Ib. per sq. in 25,000
Elongation in 8 in., per cent 22
(See Section 5.)
(b) The yield point shall be determined by the drop of the beam of the testing machine.
The speed of the cross-head of the machine shall not exceed ij in. per minute.
3. Permissible Variations in Tensile Strength. Twenty per cent of the test specimens re-
presenting one size may show tensile strengths 1000 Ib. per sq. in. under or 5000 Ib. per sq. in. over
that specified in Section 2; but no specimen shall show a tensile strength under 45,000 Ib. per sq. in.
4. Modifications in Tensile Strength. For flat bars which have to be reduced in width, a
deduction of 1000 Ib. per sq. in. from the tensile strength specified in Sections 2 and 3 shall be
made.
5. Permissible Variations in Elongation. Twenty per cent of the test specimens representing
one size may show the following percentages of elongation in 8 in. :
ROUND BARS.
\ in. or over, tested as rolled 20 per cent
Under i in., " " " 16
Reduced by machining 18
FLAT BARS.
f in. or over, tested as rolled 18 per cent
Under f in., " " " 16
Reduced by machining 16
6. Bend Tests, (a) Cold-bend Tests. — Cold-bend tests will be made only on bars having a
nominal area of 4 sq. in. or under, in which case the test specimen shall bend cold through 180 deg.
without fracture on the outside of the bent portion, around a pin the diameter of which is equal
to twice the diameter or thickness of the specimen.
(b) Hot-bend Tests. — The test specimen, when heated to a temperature between 1700° and
1800° F., shall bend through 180 deg. without fracture on the outside of the bent portion, as follows:
For round bars under 2 sq. in. in section, flat on itself; for round bars 2 sq. in. or over in section
and for all flat bars, around a pin the diameter of which is equal to the diameter or thickness of
the specimen.
(c) Nick-bend Tests. — The test specimen, when nicked 25 per cent around for round bars,
and along one side for flat bars, with a tool having a 6o-deg. cutting edge, to a depth of not less
than 8 nor more than 16 per cent of the diameter or thickness of the specimen, and broken, shall
not show more than 10 per cent of the fractured surface to be crystalline.
(d) Bend tests may be made by pressure or by blows.
7. Etch Tests.* The cross-section of the test specimen shall be ground or polished, and etched
for a sufficient period to develop the structure. This test shall show the material to be free from
steel.
*A solution of two parts water, one part concentrated hydrochloric acid, and one part con-
centrated sulphuric acid is recommended for the etch test.
491
492 ENGINEERING MATERIALS. CHAP. XV.
8. Test Specimens, (a) Tension and bend test specimens shall be of the full section of
material as rolled, if possible. Otherwise, the specimens shall be machined from the material
as rotted; the axis of the specimen shall be located at any point one-half the distance from the
center to the surface of round bars, or from the center to the edge of flat bars, and shall be parallel
to the axis of the bar.
(b) Etch test specimens shall be of the full section of material as rolled.
9. Number of Tests, (a) All bars of one size shall be piled separately. One bar from each
100 or fraction thereof will be selected at random and tested as specified.
(b) If any test specimen from the bar originally selected to represent a lot of material, contains
surface defects not visible before testing but visible after testing, or if a tension test specimen
breaks outside the middle third of the gage length, one retest from a different bar will be allowed.
III. PERMISSIBLE VARIATIONS IN GAGE.
10. Permissible Variations, (a) Round bars shall conform to the standard limit gages adopted
by the Master Car Builders' Association in 1883.
(b) The width or thickness of flat bars shall not vary more than 2 per cent from that specified.
IV. FINISH.
11. Finish. The bars shall be smoothly rolled and free from slivers, depressions, seams,
crop ends, and evidences of being burnt.
V. INSPECTION AND REJECTION.
12. Inspection, (a) The inspector representing the purchaser shall have free entry, at all
times while work on the contract of the purchaser is being performed, to all parts of the manu-
facturer's works which concern the manufacture of the material ordered. The manufacturer
shall afford the inspector, free of cost, all reasonable facilities to satisfy him that the material is
being furnished in accordance with these specifications. Tests and inspection at the place of
manufacture shall be made prior to shipment.
(6) The purchaser may make the tests to govern the acceptance or rejection of material in
his own laboratory or elsewhere. Such tests, however, shall be made at the expense of the purchaser.
13. Rejection. All bars of one size will be rejected if the test specimens representing that
size do not conform to the requirements specified.
STANDARD SPECIFICATIONS FOR WROUGHT-IRON PLATES
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
1. Classes. These specifications cover two classes of wrought-iron plates, namely:
Class A , as defined in Section 2 (b) ;
Class B, as defined in Section 2 (c).
I. MANUFACTURE.
2. Process, (a) All plates shall be rolled from piles entirely free from any admixture of steel.
(b) Piles for Class A plates shall be made from puddle bars made wholly from pig iron and
such scrap as emanates from rolling the plates.
(c) Piles for Class B plates shall be made from puddle bars made wholly from pig iron or
from a mixture of pig iron and cast-iron scrap, together with wrought-iron scrap.
II. PHYSICAL PROPERTIES AND TESTS.
,ile
5. Tension Tests. The plates shall conform to the following minimum requirements as to
tensile properties:
SPECIFICATIONS FOR WROUGHT-IRON PLATES.
Propertiet Considered.
CLASS A.
CLAM B.
6 In. to 24 In.,
lad.,
in Width.
Over 24 In.
to 90 In., Intl.,
in Width.
6 In. to 24 In.,
Inrl..
in Width.
Over 24 In.
to oo In., In. 1..
in Width.
ilc strength Ib. per sq. in
49.000
26,000
•16
48,000
26,000
12
48,000
26,000
H
47,000
26,000
IO
Plastic limit Ib per SQ. in
I1 It >n".iti' >n in S in., per cent
4. Modifications in Elongation. For plates under ^ in. in thickness, a deduction of i from
tin- prtvfiu. r.;r-; ul i-lon^.uioa specified in Section 3 shall be made for each decrease of -fa in. in
thickness In-low iV in.
5. Bend Tests, (a) Cold-bend Tests. — The test specimen shall bend cold through 90 deg.
without fracture on the outside of the bent portion, as follows: For Class A plates, around a pin
tin- ili.inu-ti-r of which is i-qual to ij times the thickness of the specimen; and for Class B plates,
around a pin the diameter of which is equal to 3 times the thickness of the specimen.
(b) Nick-bend Tests. — The test specimen, when nicked on one side and broken, shall show ,
for ( 'lass A plates a wholly fibrous fracture, and for Class B plates, not more than 10 per cent of
tlu- fractured surface to be crystalline.
6. Test Specimens. Tension and bend test specimens shall be taken from the finished plates
and shall be of the full thickness of plates as rolled. The longitudinal axis of the specimen shall
be parallel to the direction in which the plates are rolled.
7. Number of Tests, (a) One tension, one cold-bend and one nick-bend test shall be made
for each variation in thickness of J in. and not less than one test for every ten plates as rolled.
(b) If any test specimen fails to conform to the requirements specified through an apparent
local defect, -a retest shall be taken; and should the retest fail, the plates represented by such test
shall be rejected.
III. FINISH.
8. Finish. The plates shall be straight, smooth and free from cinder spots and holes, and
free from injurious flaws, buckles, blisters, scams and laminations.
IV. INSPECTION AND REJECTION.
9. Inspection, (a) The inspector representing the purchaser shall have free entry at all
times while work on the contract of the purchaser is being performed, to all parts of the manu-
facturer's works which concern the manufacture of the plates ordered The manufacturer shall
afford the inspector, free of cost, all reasonable facilities to satisfy him that the plates are being
furnished in accordance with these specifications. Tests and inspection at the place of manu-
facture shall be made prior to shipment.
(ft) The purchaser may make the tests to govern the acceptance or rejection of plates at his
own laboratory or elsewhere. Such tests, however, shall be made at the expense of the purchaser.
STEEL. — The three principal methods for the manufacture of steel are (i) the crucible
process, (2) the Bessemer process, and (3) the open-hearth process. The crucible process is used
for making tool steel. The Bessemer process is used for making structural steel, but on account
of its requiring a high grade ore for a satisfactory steel, and the difficulty of control, it is now
practically replaced by the open-hearth process. The following description of the methods of
manufacture of steel is taken from Kent's " Mechanical Engineer's Pocket-Book," page 451, 8th
Edition, 1910.
The Manufacture of Steel. — Cast steel is a malleable alloy of iron, cast from a fluid mass.
It is distinguished from cast iron, which is not malleable, by being much lower in carbon, and from
wrought iron, which is welded from a pasty mass, by being free from intermingled slag. Blister
steel is a highly carbonized wrought iron, made by the " cementation " process, which consists
in keeping wrought-iron bars at a red heat for some days in contact with charcoal. Not over 2
per cent of C is usually absorbed. The surface of the iron is covered with small blisters, supposedly
due to the action of carbon on slag. Other wrought steels were formerly made by direct processes
from iron ore, and by the puddling process from wrought iron, but these steels are now replaced
by cast steels. Blister steel is, however, still used as a raw material in the manufacture of crucible
steel. Case-hardening is a process of surface cementation.
494 ENGINEERING MATERIALS. CHAP. XV.
Crucible Steel is commonly made in pots or crucibles holding about 80 pounds of metal.
The raw material may be steel scrap; blister steel bars; wrought iron with charcoal; cast iron with
wrought iron or with iron ore; or any mixture that will produce a metal having the desired chemical
constitution. Manganese in some form is usually added to prevent oxidation of the iron. Some
silicon is usually absorbed from the crucible, and carbon also if the crucible is made of graphite
and clay. The crucible being covered, the steel is not affected by the oxygen or sulphur in the
flame. The quality of crucible steel depends on the freedom from objectionable elements, such as
phosphorus, in the mixture, on the complete removal of oxide, slag and blowholes by " dead-
melting " or " killing " before pouring, and on tHe kind and quantity of different elements which
are added in the mixture, or after melting, to give particular qualities to the steel, such as carbon,
manganese, chromium, tungsten and vanadium.
Bessemer Steel is made by blowing air through a bath of melted pig iron. The oxygen of
the air first burns away the silicon, then the carbon, and before the carbon is entirely burned away,
begins to burn the iron. Spiegeleisen or ferro-manganese is then added to deoxidize the metal
and to give it the amount of carbon desired in the finished steel. In the ordinary or " acid "
Bessemer process the lining of the converter is a silicious material, which has no effect on phos-
phorus, and all the phosphorus in the pig iron remains in the steel. In the " basic " or Thomas
and Gilchrist process the lining is of magnesian limestone, and limestone additions are made to the
bath, so as to keep the slag basic; and the phosphorus enters the slag. By this process ores that
were formerly unsuited to the manufacture of steel have been made available.
Open-hearth Steel. — Any mixture that may be used for making steel in a crucible may also
be melted on the open hearth of a Siemens regenerative furnace, and may be desiliconized and
decarbonized by the action of the flame and by additions of iron ore, deoxidized by the addition
of spiegeleisen or ferro-manganese, and recarbonized by the same additions or by pig iron. In the
most common form of the process pig iron and scrap steel are melted together on the hearth, and
after the manganese has been added to the bath it is tapped into the ladle. In the Talbot process
a large bath of melted material is kept in the furnace, melted pig iron, taken from a blast furnace,
is added to it, and iron ore is added which contributes its iron to the melted metal while its oxygen
decarbonizes the pig iron. When the decarbonization has proceeded far enough, ferro-manganese
is added to destroy iron oxide, and a portion of the metal is tapped out, leaving the remainder to
receive another charge of pig iron, and thus the process is continued indefinitely. In the Duplex
process melted cast iron is desiliconized in a Bessemer converter, and then run into an open
hearth, where the steel-making operation is finished.
The open-hearth process, like the Bessemer, may be either acid or basic, according to the
character of the lining. The basic process is a dephosphorizing one, and is the one most generally
available, as it can use pig irons that are either low or high in phosphorus.
Strength of Steel. — The properties most desired in steel are strength and ductility. Pure
iron has a tensile strength of about 40,000 Ib. per sq. in. and is very ductile. This strength is
usually increased by the impurities found in steel.
Carbon is the important impurity as it gives strength with the least decrease in ductility.
Campbell states that each o.oi per cent of carbon will increase the strength of acid open-hearth
steel by 1000 Ib. per sq. in., and of basic open-hearth steel by 770 Ib. per sq. in. The maximum
tensile strength of steel is reached with 0.9 to i.o per cent of carbon.
Silicon has little effect on the strength of rolled steel, but in castings 0.3 to 0.4 per cent of
silicon increases the tensile strength of steel castings and produces soundness.
Sulphur has little effect on the strength of open-hearth steel, but it produces " red-shortness,"
and produces checks and cracks during the rolling or during the cooling of castings.
Phosphorus increases the static strength of steel about 1000 Ib. for each o.oi per cent of
phosphorus. The increase in strength is obtained at a great loss in ductility and produces a steel
that is brittle and unreliable.
Manganese when above 0.3 to 0.4 per cent increases the tensile strength of steel. The
increase in strength above 0.4 per cent is about 300 Ib. per sq. in. for acid open-hearth and 130 Ib.
per sq. in. for basic open-hearth steel for each additional o.oi per cent of manganese.
From the above discussion it will be seen that if certain physical characteristics are required
in a steel the manufacturer must be left free to vary part of the impurities. For example if a
high grade structural steel with an ultimate tensile strength of 60,000 Ib. per sq. in. is desired, the
phosphorus and sulphur may be limited in addition to the prescribed physical limits if the carbon
is left open.
ALLOWABLE STRESSES IN STEEL AND IRON. 4W,
Formulas for Tensile Strength. — Campbell gives the following formulas for the strength of
.li i.| .111.1 IMM. nprll 111 .irth Steels:
, i.l >t« . I, Ultimate strength = 40,000 + 1000 C + 1000 P + X.Mn -f R.
1 ,>r l.a.Mt- steel, Ultimate strength = 41,500 + 770 C + 1000 P + X.Mn + R.
In these formulas, C = o.oi per cent carbon, P =» o.oi phosphorus, Mn = o.oi per cent
manganese above 0.4 per .cent for acid and above 0.3 per cent for basic steel, and R is a variable
<lr|H'iuling upon the heat treatment of the steel. The coefficient of Mn, X, varies as follows:
For arid steel, for o.io per cent carbon, X = 80, and for 0.60 per cent carbon, X — 480 and pro-
portiimal for intermediate values; while for basic steel, for 0.05 per cent carbon, X = no, and for
0.40 per cent carbon, X = 250 and proportional for intermediate values.
Special Steels. — The following special steels have been used. Nickel is used as an alloy for
structural and other kinds of steel, the specifications for structural nickel steel of the American
Society for Testing Materials require that there be not less than 3$ per cent of nickel. Chrome
steel — carbon steel with about 0.5 per cent chromium — was used in the Eads bridge in 1871. Chro-
mium is now used in combination with nickel, making Chromium-nickel steel; with vanadium,
making Chromium-vanadium steel, and with both nickel and vanadium, making Chromium-
nickel-vanadium steel. Copper steels are those having from I to 4 per cent of copper, carbon being
less than I per cent. Manganese steel with from 6 to 12 per cent manganese is very tough and
malleable.
Specifications for Structural Steel. — The allowable stresses for structural steel are given in
Table I and in the specifications of the American Society for Testing Materials which follow.
Allowable Stresses in Steel and Iron. — The allowable stresses Tor steel frame mill buildings are
given in the "Specifications for Steel Frame Buildings," in Chapter I. The allowable stresses
for steel office buildings are given in the "Specifications for Steel Office Buildings," in Chapter II.
The allowable stresses for steel highway bridges are given in the "Specifications for Steel Highway
Bridges," in Chapter III. The allowable stresses for steel railway bridges are given in the "Speci-
fications for Steel Railway Bridges," in Chapter IV. The allowable stresses in steel bins are
given in Chapter VIII, p. 313. The allowable stresses for steel grain bins are given in Chapter
IX, p. 326. The allowable stresses in steel head frames and coal tipples are given in the "Speci-
fications for Steel Head Frames and Coal Tipples, Washers and Breakers," in Chapter X. The
allowable stresses in steel stand-pipes and elevated tanks are given in the "Specifications for
Elevated Steel Tanks on Towers and for Stand-Pipes," in Chapter XI. The allowable stresses
for the steel and cast iron details in timber bridges are the same as for steel railway bridges given
in Chapter IV. The allowable stresses in steel reinforcement are given on page 521.
Nickel Steel. — In a paper entitled "Nickel Steel for Bridges" by Mr. J. A. L. Waddell, in
Trans. Am. Soc. C. E., Vol. 63, June 1909, the allowable unit stress in Ib. per sq. in. for carbon
steel is given as P = 18,000 — 70 l/r, and for nickel steel as P = 30,000 — 120 l/r, where / is the
length and r is the corresponding radius of gyration, both in inches. The impact coefficient
adopted by Mr. Waddell is given on page 161.
496
ENGINEERING MATERIALS.
CHAP. XV.
TABLE I.
STRENGTH PROPERTIES OF STRUCTURAL STEEL AND IRON — AMERICAN SOCIETY FOR TESTING
MATERIALS, YEAR BOOK, 1913.
Metal.
Tensile Strength, Lb. Sq. In.
Minimum Elongation,
Per Cent.
Reduction
of Area,
Per Cent.
Ultimate.
Elastic Limit.
In 8 In.
In 2 In.
BRIDGES
Structural Steel .
55,000-65,000
48,000-58,000
55,000-65,006
48,000-58,000
58,OOO-68,OOO
55,000-65,000
55,000-65,000
52,000-62,000
45,000-55,000
85,000-100,000
95,OOO-IIO,OOO
90,000-105,000
70,000-80,000
:NT BARS
55,000-70,000
80,000 min.
55,000-70,000
80,000 min.
recorded only
r BARS
80,000
80,000
48,000
47,000-49,000
80,000
70,000
60,000
18,000
21,000
24,000
40,000
\ ultimate
5 ultimate
\ ultimate
\ ultimate
| ultimate
3 ultimate
\ ultimate
\ ultimate
\ ultimate
50,000
55,00°
52,000
45,000
33,000
50,000
33,000
50,000
55,ooo
50,000
50,000
25,000
26,000
36,000
31,500
27,000
/ 1,500,000
22
22
ian 30)
16
20
15
18
22
2|
25
25
35
40
20
25
30
Rivet Steel
I ultimate
( 1,5000,00
BUILDINGS
Structural Steel
I ultimate
/ 1,400,000
Rivet Steel
I ultimate
/ 1,400,000
SHIPS
Structural Steel
I ultimate
/ 1,500,000
Rivet Steel
I ultimate
f 1,500,000
\ ultimate
/ 1,500,000
BOILER AND RIVET STEEL
Flange Steel
Firebox Steel
I ultimate
f 1,500,000
Boiler Rivet Steel *. . .
I ultimate
f 1,500,000
\ ultimate
(not greater t
( 1,500,000
\ ultimate
( 1,500,000
\ ultimate
20
( 1,500,000
STRUCTURAL NICKEL STEEL
Plates, Shapes and Bars
Eye-bars and rollers (unannealed)
Eye-bars and Pins (annealed) ....
Rivet Steel
BILLET-STEEL REINFORCEMI
f Structural
\ ultimate
f 1,400,000
\ ultimate
( 1,200,000
Plain \
[Hard
( Structural
\ ultimate
( 1,250,000
\ ultimate
f 1,000,000
Deformed \
[Hard
Cold Twisted . ....
\ ultimate
5
f 1,200,000
RAIL-STEEL REINFORCEMEN
Plain .
Deformed and Hot-twisted
I ultimate
f 1,000,000
WROUGHT IRON
Refined Bars
\ ultimate
22
10 to 16
Plates
STEEL CASTINGS
Hard
Medium
Soft
GRAY IRON CASTINGS
Light Castings
Medium Castings
Heavy Castings.. .
MALLEABLE CASTINGS
STANDARD SPECIFICATIONS FOR STRUCTURAL STEEL FOR BUILDINGS
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
I. MANUFACTURE.
I. Process, (a) Structural steel, except as noted in Paragraph (6), may be made by the
IIKT or the open-hearth procv
(b) Rivet steel, and steel for plates or angles over J in. in thickness which are to be punched,
shall be made by the open-hearth process.
II. CHEMICAL PROPERTIES AND TESTS.
2. Chemical Composition.
chemical composition:
The steel shall conform to the following requirements as to
PhosPhorus(
Sulphur
STRUCTURAL STEEL.
not over o.io per cent
" " 0.06
RIVET STEEL.
not over 0.06 per cent
0.045
3. Ladle Analyses. An analysis to determine the percentages of carbon, manganese, phos-
phorus and sulphur shall be made by the manufacturer from a test ingot taken during the pouring
of each melt, a copy of which shall be given to the purchaser or his representative. This analysis
shall conform to the requirements specified in Section 2.
4. Check Analyses. Analyses may be made by the purchaser from finished material re-
presenting each melt, in which case an excess of 25 per cent above the requirements specified in
Section 2 shall be allowed.
5. Tension Tests,
properties:
III. PHYSICAL PROPERTIES AND TESTS,
(a) The material shall conform to the following requirements as to tensile
Properties Considered.
Structural Steel.
Rivet Steel.
Tensile strength, Ib. per sq. in
55,000-65,000
48,000-58,000
Yield point, min., " "
0.5 tens. str.
0.5 tens. str.
Elongation in 8 in min per cent
I^OO.OOO1
1,400,000
Elongation in 2 in. " "
Tens. str.
22
Tens. str.
(b) The yield point shall be determined by the drop of the beam of the testing machine.
6. Modifications in Elongation, (o) For structural steel over J in. in thickness, a deduction
of I from the percentage of elongation in 8 in. specified in Section 5(0) shall be made for each
increase of J in. in thickness above $ in.
(ft) For structural steel under ^ in. in thickness, a deduction of 2.5 from the percentage of
elongation in 8 in. specified in Section 5(0) shall be made for each decrease of & in. in thickness
below ^ in.
7. Bend Tests, (a) The test specimen for plates, shapes and bars shall bend cold through
1 80 deg. without cracking on the outside of the bent portion, as follows: For material J in. or under
in thickness, flat on itself; for material over J in. to and including 1} in. in thickness, around a pin
the diameter of which is equal to the thickness of the specimen; and for material over ij in. in
thickness, around a pin the diaipeter of which is equal to twice the thickness of the specimen.
(6) The test specimen for pins and rollers shall bend cold through 1 80 deg. around a i-in.
pin without cracking on the outside of the bent portion.
(c) The test specimen for rivet steel shall bend cold through 180 deg. flat on itself without
cracking on the outside of the bent portion.
1 See Section 6.
33
497
498
ENGINEERING MATERIALS.
CHAP. XV.
8. Test Specimens, (a) Tension and bend test specimens shall be taken from the finished
rolled or forged material, and shall not be annealed or otherwise treated, except as specified in
Paragraph (&).
(b) Tension and bend test specimens for material which is to be annealed or otherwise treated
before use, shall be cut from properly annealed or similarly treated short lengths of the full section
of the piece.
(c) Tension and bend test specimens for plates, shapes and bars, except as specified in Para-
graph (d), shall be of the full thickness of material as rolled; and may be machined to the form and
dimensions shown in Fig. i, or with both edges parallel.
1
^ Parallel section not less than 9 "^ <About-$^V>
i%w ! ' •
i •
About 18"
FlG. I.
(d) Tension and bend test specimens for plates and bars over r£ in. in thickness or diameter
may be machined to a thickness or diameter of at least j in. for a length of at least 9 in.
(e) The axis of tension and bend test specimens for pins and rollers shall be I in. from the
surface and parallel to the axis of the bar. Tension test specimens shall be of the form and di-
mensions shown in Fig. 2. Bend test specimens shall be I by 5 in. in section.
(/) Tension and bend test specimens for rivet steel shall be of the full-size section of bars as
rolled.
9. Number of Tests, (a) One tension and one bend test shall be made from each melt;
except that if material from one melt differs f in. or more in thickness, one tension and one bend
test shall be made from both the thickest and the thinnest material rolled.
(b) If any test specimen shows defective machining or develops flaws, or if an 8-in. tension
test specimen breaks outside the middle third of the gage length, or if a 2-in. tension test specimen
breaks outside the gage length, it may be discarded and another specimen substituted.
IV. PERMISSIBLE VARIATIONS IN WEIGHT AND GAGE.
10. Permissible Variations. The cross-section or weight of each piece of steel shall not vary
more than 2.5 per cent from that specified; except in the case of sheared plates, which shall be
covered by the following permissible variations to apply to single plates:
(a) When Ordered to Weight. — For plates \2\ Ib. per sq. ft. or over:
Under 100 in. in width, 2.5 per cent above or below the specified weight;
loo in. in width or over, 5 per cent above or below the specified weight.
For plates under \2\ Ib. per sq. ft.:
Under 75 in. in width, 2.5 per cent above or below the specified weight;
75 to 100 in., exclusive, in width, 5 per cent above or 3 per cent below the specified weight ;
100 in. in width or over, 10 per cent above or 3 per cent below the specified weight.
(b) When Ordered to Gage. — The thickness of each plate shall not vary more than o.oi in.
under that ordered.
An excess over the nominal weight corresponding to the dimensions on the order shall be
allowed for each plate, if not more than that shown in the following table, one cubic inch of rolled
steel being assumed to weigh 0.2833 Ib.:
SPECIFICATIONS FOR STRUCTURAL STEEL FOR BRIDGES.
ALLOWABLE EXCESS (EXPRESSED AS PERCENTAGE or NOMINAL WEIGHT).
ThickneM
Nominal
For Width of Plate a* follow:
Ordered.
In.
Per Sq. Ft
Under 50
In.
50 to 70
In.. Excl.
70 In. or
Over.
Under 75
In.
75 to 100
In.. Etcl.
ioo to us
In.. Exd.
US In. or
Over.
i to A
5. 10 to 6.37
10
IS
20
. .
. .
A " A
6-37 " 7.65
8.5
12.5
17
7.65 " 10.20
7
10
15
IO.2O
. .
10
14
If
12-75
. .
8
12
16
Jt
15-30
17.85
I
10
8
10
17
13
A
20.4O
22.95
5
4-5
7
6-5
1,
12
II
f
25.50
. .
4
6
8
10
Over f
3-5
5
6-5
9
ir. Finish,
manlike finish.
V. FINISH.
The finished material shall be free from injurious defects and shall have a work-
VI. MARKING.
12. Marking. The name or brand of the manufacturer and the melt number shall be legibly
stamped or rolled on all finished material, except that rivet and lattice bars and other small sections
shall, when loaded for shipment, be properly separated and marked for identification. The
identification marks shall be legibly stamped on the end of each pin and roller. The melt number
shall be legibly marked, by stamping if practicable, on each test specimen.
VII. INSPECTION AND REJECTION.
13. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the material ordered. The manufacturer shall afford
the inspector, free of cost, all reasonable facilities to satisfy him that the material is being furnished
in accordance with these specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
14. Rejection, (a) Unless otherwise specified, any rejection based on tests made in ac-
cordance with Section 4 shall be reported within five working days from the receipt of samples.
(&) Material which shows injurious defects subsequent to its acceptance at the manufacturer's
works will be rejected, and the manufacturer shall be notified.
15. Rehearing. Samples tested in accordance with Section 4, which represent rejected
material, shall be preserved for two weeks from the date of the test report. In case of dissatis-
faction with the results of the tests, the manufacturer may make claim for a rehearing within that
time.
STANDARD SPECIFICATIONS FOR STRUCTURAL STEEL FOR BRIDGES
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
I. MANUFACTURE.
1. Steel Castings. The Standard Specifications for Steel Castings adopted by the American
Society for Testing Materials, are hereby made a part of these specifications, and shall govern the
purchase of steel castings for bridges.*
2. Process. The steel shall be made by the open-hearth process.
* In using the Standard Specifications for Steel Castings for the purchase of castings for bridges,
it is necessary to specify both the class and grade of casting desired.
500
ENGINEERING MATERIALS.
CHAP. XV.
II. CHEMICAL PROPERTIES AND TESTS.
3. Chemical Composition. The steel shall conform to the following requirements as to
chemical composition:
STRUCTURAL STEEL. RIVET STEEL.
per cent.
r>. t, ( Acid ............ not over 0.06 not over
Phosphorusj Basic ............ « „ 004 „ „
Sulphur .................... . " ' 0.05 0.04 "
4. Ladle Analyses. An analysis to determine the percentages of carbon, manganese, phos-
phorus and sulphur shall be made by the manufacturer from a test ingot taken during the pouring
of each melt, a copy of which shall be given to the purchaser or his representative. This analysis
shall conform to the requirements specified in Section 3.
5. Check Analyses. Analyses may be made by the purchaser from finished material repre-
senting each melt, in which case an excess of 25 per cent above the requirements specified in
Section 3 shall be allowed.
III. PHYSICAL PROPERTIES AND TESTS.
6. Tension Tests, (a) The material shall conform to the following requirements as to tensile
properties:
Properties Considered.
Structural Steel.
Rivet Steel.
Tensile strength Ib. per sq. in
55,000-65,000
0.5 tens. str.
i,5OO,ooo1
48,000-58,000
0.5 tens. str.
1,500,000
Yield point min Ib per sq. in
Elongation in 2 in., min., per cent
Tens. str.
22
Tens. str.
(6) The yield point shall be determined by the drop of the beam of the testing machine.
7. Modifications in Elongation, (a) For structural steel over f in. in thickness, a deduction
of I from the percentage of elongation in 8 in. specified in Section 6 (a), shall be made for each
increase of | in. in thickness above f in.
(b) For structural steel under -fa in. in thickness, a deduction of 2.5 from the percentage of
elongation in 8 in. specified in Section 6 (a), shall be. made for each decrease of YS in. in thickness
below rs m-
8. Bend Tests, (a) The test specimen for plates, shapes, and bars shall bend cold through
1 80 deg. without cracking on the outside of the bent portion, as follows: For material f in. or under
in thickness, flat on itself; for material over f in. to and including i £ in. in thickness, around a pin
the diameter of which is equal to the thickness of the specimen; and for material over if in. in
thickness, around a pin the diameter of which is equal to twice the thickness of the specimen.
(6) The test specimen for pins and rollers shall bend cold through 180 deg. around a i-in.
pin without cracking on the outside of the bent portion.
(c) The test specimen for rivet steel shall bend cold through 180 deg. flat on itself without
cracking on the outside of the bent portion.
9. Tests of Angles. Angles f in. or under in thickness shall open flat, and angles 5 in. or
under in thickness shall bend shut, cold, under blows of a hammer without cracking. This test
shall be made only when required by the inspector.
10. Test Specimens, (a) Tension and bend test specimens shall be taken from the finished
rolled or forged material, and shall not be annealed or otherwise treated, except as specified in
Paragraph (&).
(b) Tension and bend test specimens for material which is to be annealed or otherwise treated
before use, shall be cut from properly annealed or similarly treated short lengths of the full section
of the piece.
(c) Tension and bend test specimens for plates, shapes and bars, except as specified in Para-
graph (d), shall be of the full thickness of material as rolled. They may be machined to the form
and dimensions shown in Fig. I, or with both edges parallel; except that bend test specimens for
eye-bar flats may have three rolled sides.
(d) Tension and bend test specimens for plates and bars (except eye-bar flats) over if in. in
thickness or diameter may be machined to a thickness or diameter of at least f in. for a length of at
least 9 in.
1 See section 7.
SPECIFICATIONS FOR STRUCTURAL STEEL FOR BRIDGES.
601
(e) Tin- axi-, <>f IC-IIMUM and Ix-ml test specimens for pins and rollers shall be I in. from the
.Ki- .iii.l p.ti.illd in tin- ,i\i- M I the bar. Tension test specimens shall be of the form and di-
• ii?, shown in Fig. 2. Bend test specimens shall be I by J in. in section.
«<- — -- About 18"
J
rolle
Tension and bend test specimens for rivet steel shall be of the full-size section of bars as
11. Number of Tests, (a) One tension and one bend test shall be made from each melt;
except that if material from one melt differs f in. or more in thickness, one tension and one bend
test shall be made from both the thickest and the thinnest material rolled.
(6) If any test specimen shows defective machining or develops flaws, or if an 8-in. tension
test specimen breaks outside the middle third of the gage length, or if a 2-in. tension test specimen
breaks outside the gage length, it may be discarded and another specimen substituted.
IV. PERMISSIBLE VARIATIONS IN WEIGHT AND GAGE.
12. Permissible Variations. The cross-section or weight of each piece of steel shall not vary
more than 2.5 per cent from that specified; except in the case of sheared plates, which shall be
covered by the following permissible variations to apply to single plates:
(a) When Ordered to Weight. — For plates 123 Ib. per sq ft. or over:
Under 100 in. in width, 2.5 per cent above or below the specified weight;
loo in. in width or over, 5 per cent above or below the specified weight.
For plates under 12^ Ib. per sq. ft.:
Under 75 in. in width, 2.5 per cent above or below the specified weight;
75 to 100 in., exclusive, in width, 5 per cent above or 3 per cent below the specified weight;
100 in. in width or over, 10 per cent above or 3 per cent below the specified weight.
(b) When Ordered to Gage. — The thickness of each plate shall not vary more than o.oi in.
under that ordered.
An excess over the nominal weight corresponding to the dimensions on the order shall be
allowed for each plate, if not more than that shown in the following table, one cubic inch of rolled
teel being assumed to weigh 0.2833 Ib.:
13. Finish,
inlike finish.
V. FINISH.
The finished material shall be free from injurious defects and shall have a work-
VI. MARKING.
14. Marking. The name or brand of the manufacturer and the melt number shall be legibly
stamped or rolled on all finished material, except that rivet and lattice bars and other small
sections shall, when loaded for shipment, be properly separated and marked for identification.
The identification marks shall be legibly stamped on the end of each pin and roller. The melt
number shall be legibly marked, by stamping if practicable, on each test specimen.
502
ENGINEERING MATERIALS.
CHAP. XV.
ALLOWABLE EXCESS (EXPRESSED AS PERCENTAGE OF NOMINAL WEIGHT).
Thickness
Ordered
Nominal
Weight Lb.
For Width of Plate as follows:
In.
Per Sq. Ft.
Under 50
In.
50 to 70
In., Excl.
70 In. or
Over.
Under 75
In.
75 to 100
In.. Excl.
100 to 115
In., Excl.
US In- or
Over.
ito &
5. 10 to 6.37
IO
IS
2O
A "A
6.37 " 7.65
8-5
12-5
17
. .
. .
A "i
7.65 " 10.20
7
IO
15
1
10.20
10
14
1*8
. .
A
12-75
8
12
16
I
iS-30
7
10
13
17
A
17-85
6
8
IO
13
i
20.40
5
7
9
12
A
22.95
4-5
6-5
8-5
II
I
25-50
4
6
8
IO
Overf
3-5
5
6-5
9
VII. INSPECTION AND REJECTION.
15. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the material ordered. The manufacturer shall afford
the inspector, free of cost, all reasonable facilities to satisfy him that the material is being furnished
in accordance with these specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
1 6. Rejection, (a) Unless otherwise specified, any rejection based on tests made in accord-
ance with Section 5 shall be reported within five working days from the receipt of samples.
(b) Material which shows injurious defects subsequent to its acceptance at the manufacturer's
works will be rejected, and the manufacturer shall be notified.
17. Rehearing. Samples tested in accordance with Section 5, which represent rejected
material, shall be preserved for two weeks from the date of the test report. In case of dissatis-
faction with the results of the tests, the manufacturer may make claim for a rehearing within that
time.
STANDARD SPECIFICATIONS FOR STRUCTURAL NICKEL STEEL
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
I. MANUFACTURE.
1. Process. The steel shall be made by the open-hearth process.
2. Discard. A sufficient discard shall be made from each ingot intended for eye-bars to
secure freedom from injurious piping and undue segregation.
II. CHEMICAL PROPERTIES AND TESTS.
3. Chemical Composition. The steel shall conform to the following requirements as to
chemical composition:
STRUCTURAL STEEL.
Carbon ............................ not over 0.45
Manganese ................ ; ........ " " 0.70
Sulphur ............................ " "
Nickel ........................... not under
0.04
3.25
RIVET STEEL.
not over 0.30 per cent
0.60
"" '•'• o°ol
" " 0.04
not under 3.25
4. Ladle Analyses. An analysis shall be made by the manufacturer from a test ingot taken
during the pouring of each melt. A copy of this analysis shall be given to the purchaser or his
representative. This analysis shall conform to the requirements specified in Section 3.
SPECIFICATIONS FOR STRUCTURAL NICKEL STEEL.
508
5. Check Analyses. A check analysis may be made by the purchaser from finished material
mini; c.irli mi-It, and this analysis shall conform to the requirements specified in Section 3.
III. PHYSICAL PROPERTIES AND TESTS.
6. Tension Tests, (a) Th'e steel shall conform to the following requirements as to tensile
pnpertie*:
TENSILE PPOPERTIES FROM SPECIMEN TESTS.
Properties Considered.
Rivets.
Plates, Shapes
and Bars.
Eye- Bars and Rol-
lers,' Unannealed.
Eye- Bars" and
Pin*.* Annealed.
Tensile strength, Ib. per sq. in.. .
Yield point, min., Ib. per sq. in. .
Elongation in 8 in., min., per cent.
Elongation in 2 in., min., per cent.
70,000-80,000
45,000
1,500,000
85,000-100,000
50,000
1,500,000*
95,OOO-IIO,OOO
55,000
1,500,000*
90,000-105,000
52,OOO
20
20
35
Tens. Str.
Tens. Str.
Tens. Str.
16
-5
Reduction of area min., per cent..
40
25
0 Tests of annealed specimens of eye-bars shall be made for information only.
6 See Section 7.
* Elongation shall be measured in 2 in.
(6) The yield point shall be determined by the drop of the beam of the testing machine.
7. Modifications in Elongation. For plates, shapes and unannealed bars over I in. in thick-
ness, a deduction of I from the percentage of elongation specified in Section 6 shall be made for
each increase of J in. in thickness above I in., to a minimum of 14 per cent.
8. Character of Fracture. All broken tension test specimens shall show either a silky or a
very fine granular fracture, of uniform color, and free from coarse crystals.
9. Bend Tests, (a) The test specimen for plates, shapes and bars shall bend cold through
1 80 deg. without fracture on the outside of the bent portion, as follows: For material J in. or under
in thickness, around a pin the diameter of which is equal to the thickness of the specimen; and for
material over J in. in thickness, around a pin the diameter of which is equal to twice the thickness
of the specimen.
(&) The test specimen for pins and rollers shall bend cold through 1 80 deg. around a I in.
pin, without fracture on the outside of the bent portion.
(c) The test specimen for rivet steel shall bend cold through 180 deg. flat on itself without
cracking on the outside of the bent portion.
10. Tests of Angles, (a) Angles with 4 in. legs or under, and ^ in. or under in thickness,
shall open flat or bend shut, cold, under the blows of a hammer without cracking.
(b) Angles with legs over 4 in., or over J in. in thickness, shall open to an angle of 150 deg.,
or close to an angle of 30 deg., cold, under the blows of a hammer without cracking.
11. Drift Tests. Punched rivet holes pitched two diameters from a planed edge shall stand
drifting until the diameter is enlarged 50 per cent without cracking the metal.
12. Test Specimens, (a) Tension and bend test specimens shall be taken from the finished
rolled or forged material. Specimens for pins shall be taken after annealing.
(b) Tension and bend test specimens for plates, shapes and bars, except as specified in Para-
iph (c), shall be of the full thickness of material as rolled. They may be machined to the form
and dimensions shown in Fig. I, or with both edges parallel; except that bend test specimens shall
not be less than 2 in. in width, and that bend test specimens for eye-bar flats may have three
rolled sides.
< About 3">, $
< Parallel section not less than 9
-'> <About S">,
V
v
i ' '
About 18" - ->
FIG. i.
(c) Tension and bend test specimens for plates and bars (except eye-bar flats) over ij in. in
thickness or diameter may be machined to a thickness or diameter of at least J in. for a length of
at least 9 in.
504
ENGINEERING MATERIALS.
CHAP. XV.
(d) The axis of tension and bend test specimens for pins and rollers shall be I in. from the
surface and parallel to the axis of the bar. Tension test specimens shall be of the form and dimen-
sions shown in Fig. 2. Bend test specimens shall be I by f in. in section.
(e) Tension and bend test specimens for rivet steel shall be of the full-size section of bars as
rolled. •
13. Number of Tests, (a) One tension and one bend test shall be made from each melt;
except that if material from one melt differs f in. or more in thickness, one tension and one bend
test shall be made from both the thickest and the thinnest material rolled.
(b) If any test specimen shows defective machining or develops flaws, or if an 8-in. tension
test specimen breaks outside the middle third of the gage length, or if a 2-in. tension test specimen
breaks outside the gage length, it may be discarded and another specimen substituted.
94 *i*44V 2V4-' ~V+ — 94- —
IV. PERMISSIBLE VARIATIONS IN WEJGHT AND GAGE.
14. Permissible Variations. The cross section or weight of each piece of steel shall not vary
more than 2.5 per cent from that specified; except in the case of sheared plates, which shall be
covered by the following permissible variations to apply to single plates:
(a) When Ordered to Weight. — For plates 125 Ib. per sq. ft. or over:
Under 100 in. in width, 2.5 per cent above or below the specified weight;
loo in. in width and over, 5 per cent above or below the specified weight.
For plates under 12 £ Ib. per sq. ft.:
Under 75 in. in width, 2.5 per cent above or below the specified weight;
75 to 100 in. in width, 5 per cent above or 3 per cent below the specified weight;
100 in. in width and over, 10 per cent above or 3 per cent below the specified weight.
(b) When Ordered to Gage. — The thickness of each plate shall not vary more than o.oi in.
below that ordered.
An excess over the nominal weight corresponding to the dimensions on the order shall be
allowed for each plate, if not more than that shown in the following table, one cubic inch of rolled
steel being assumed to weigh 0.2833 Ib.:
ALLOWABLE EXCESS (EXPRESSED AS PERCENTAGE OF NOMINAL WEIGHT).
Thickness
Nominal
For Width of Plate as follows:
In.
Per Sq. Ft.
Under 50
In.
50 to 70
In., Excl.
70 In. or
Over.
Under 75
In.
75 to 100
In., Excl.
100 to 115
In., Excl.
115 In- or
Over.
ttoA
5. 10 to 6.37
IO
IS
2O
, .
, ,
A " A
6-37 " 7-65
8-S
12-5
17
A "1
7.65 " IO.2O
7
10
IS
A
IO.2O
12.75
••
10
8
H
12
18
16
I
I5-30
. .
7
10
13
17
A
17.85
. .
. .
6
8
IO
13
A
20.40
22.95
5
4-S
6^
9
8-5
12
II
1
2S-SO
4
6
8
IO
Overf
3-5
5
6-5
9
V. FINISH.
15. Finish. The finished material shall be free from injurious seams, slivers, flaws and other
defects, and shall have a workmanlike finish.
SPECIFICATIONS FOR BOILER RIVET STEEL. 505
VI. MARKING.
16. Marking. The name or brand of the manufacturer and the melt number shall be legibly
st.iui|)«-il in rullrd on all finished material, except that rivet and lattice bars and other small sections
sh.ill, \\hen loaded fur shipment, I"- properly separated and marked for identification. The
idem ilicati MI marks shall l>c legibly stamped on the end of each pin and roller. The melt number
shall IK- legibly marked, by stamping if practicable, on each test specimen.
VII. INSPECTION.
17. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work uii the contract of the purchaser is being performed, to all parts of the manufacturer's
works which run era the manufacture of the material ordered. The manufacturer shall afford
t he inspector, free of cost, all reasonable facilities to satisfy him that the material is being furnished
in accordance with these specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
18. Rejection, (a) Unless otherwise specified, any rejection based on tests made in accord-
ance with Section 5 shall be reported within five working days from the receipt of samples.
(6) Material which shows injurious defects subsequent to its acceptance at the manufacturer's
works will be rejected and the manufacturer shall be notified.
19. Rehearing. Samples tested in accordance with Section 5, which represent rejected
material, shall be preserved for two weeks from the date of the test report. In case of dissatis-
faction with the results of the tests, the manufacturer may make claim for a rehearing within that
time.
VIII. FULL SIZE TESTS.
20. Tests of Eye-Bars, (a) Full size tests of annealed eye-bars shall conform to the following
requirements as to tensile properties:
Tensile strength, Ib. per. sq. in 85,000-100,000
Yield point, min., Ib. per sq. in 48,000
Elongation in 18 ft., min., per cent 10
Reduction of area, min., per cent 30
(b) The yield point shall be determined by the halt of the gage of the testing machine.
STANDARD SPECIFICATIONS FOR BOILER RIVET STEEL
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
. A. Requirements for Rolled Bars.
I. MANUFACTURE.
1 . Process. The steel shall be made by the open-hearth process.
II. CHEMICAL PROPERTIES AND TESTS.
2. Chemical Composition. The steel shall conform to the following requirements as to
chemical composition:
Manganese 0.30-0.50 per cent
Phosphorus not over 0.04
Sulphur " ' 0.045
3. Ladle Analyses. An analysis to determine the percentages of carbon, manganese, phos-
phorus and sulphur shall be made by the manufacturer from a test ingot taken during the pouring
of each melt, a copy of which shall be given to the purchaser or his representative. This analysis
shall conform to the requirements specified in Section 2.
4. Check Analyses. A check analysis may be made by the purchaser from finished material
representing each melt, and this analysis shall conform to the requirements specified in Section 2.
III. PHYSICAL PROPERTIES AND TESTS.
5. Tension Tests, (a) The bars shall conform to the following requirements as to tensile
properties:
506 ENGINEERING MATERIALS. CHAP. XV.
Tensile strength, Ib. per sq. in 45,000-55,000
Yield point, min., Ib. per sq. in 0.5 tens. str.
_, . . . 1,500,000
Elongation in 8 in., mm., per cent , =*
Tens. str.
(But need not exceed 30 per cent)
(5) The yield point shall be determined by the drop of the beam of the testing machine.
6. Bend Tests, (a) Cold-bend Tests. — The test specimen shall bend cold through 180 deg.
flat on itself without cracking on the outside of the bent portion.
(b) Quench-bend Tests. — The test specimen, when heated to a light cherry red as seen in the
dark (not less than 1200° F.), and quenched at once in water the temperature of which is between
80° and 90° F., shall bend through 180° flat on itself without cracking on the outside of the bent
portion.
7. Test Specimens. Tension and bend test specimens shall be of the full-size section of
material as rolled.
8. Number of Tests, (a) Two tension, two cold-bend, and two quench-bend tests shall be
made from each melt, each of which shall conform to the requirements specified.
(b) If any test specimen develops flaws, or if a tension test specimen breaks outside the middle
third of the gage length, it may be discarded and another specimen substituted.
IV. PERMISSIBLE VARIATIONS IN GAGE.
9. Permissible Variations. The gage of each bar shall not vary more than o.oi in. from that
specified.
V. WORKMANSHIP AND FINISH.
10. Workmanship. The finished bars shall be circular within o.oi in.
11. Finish. The finished bars shall be free from injurious defects, and shall have a workman-
like finish.
VI. MARKING.
12. Marking. Rivet bars shall, when loaded for shipment, be properly separated and marked
with the name or brand of the manufacturer and the melt number for identification. The melt
number shall be legibly marked, by stamping if practicable, on each test specimen.
VII. INSPECTION AND REJECTION.
13. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the bars ordered. The manufacturer shall afford the
inspector, free of cost, all reasonable facilities to satisfy him that the bars are being furnished in
accordance with these specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
14. Rejection, (a) Unless otherwise specified, any rejection based on tests made in accord-
ance with Section 4 shall be reported within five working days from the receipt of samples.
(b) Bars which show injurious defects subsequent to their acceptance at the manufacturer'?
works will be rejected, and the manufacturer shall be notified.
15. Rehearing. Samples tested in accordance with Section 4, which represent rejected bars,
shall be preserved for two weeks from the date of the test report. In case of dissatisfaction with
the results of the tests, the manufacturer may make claim for a rehearing within that time.
B. Requirements for Rivets.
I. PHYSICAL PROPERTIES AND TESTS.
16. Tension Tests. The rivets, when tested, shall conform to the requirements as to tensile
properties specified in Section 5, except that the elongation shall be measured on a gage length not
less than four times the diameter of the rivet.
17. Bend Tests. The rivet shank shall bend cold through 180 degrees flat on itself without
cracking on the outside of the bent portion.
1 8. Flattening Tests. The rivet heads shall flatten, while hot, to a diameter 2§ times the
diameter of the shank without cracking at the edges.
19. (a) When specified, one tension test shall be made from each size in each lot of rivets
offered for inspection.
SPECIFICATIONS FOR BILLET-STEEL REINFORCEMENT BARS. 507
(b) Three bend and three flattening tests shall be made from each size in each lot of rivets
for inspection, each of which shall conform to the requirements specified:
II. WORKMANSHIP AND FINISH.
20. Workmanship. Rivets shall be true to form, concentric, and shall be made in a work-
manlike m.umri.
ji. Finish. The finished rivets shall be free from injurious defects.
III. INSPECTION AND REJECTION.
22. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the rivets ordered. The manufacturer shall afford the
in-ipivtor, five of cost, all reasonable facilities to satisfy him that the rivets are being furnished in
lance with these specifications. All tests and inspection shall be made at the place of manu-
facture prior to shipment, unless otherwise specified, and shall be so conducted as not to interfere
unnecessarily with the operation of the works.
23. Rejection. Rivets which show injurious defects subsequent to their acceptance at the
manufacturer's works will be rejected, and the manufacturer shall be notified.
STANDARD SPECIFICATIONS FOR BILLET-STEEL REINFORCEMENT BARS*
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
1. Classes, (a) These specifications cover three classes of billet-steel concrete reinforcement
bars, namely: plain, deformed, and cold-twisted.
(b) Plain and deformed bars are of two grades, namely: structural steel and hard.
2. Basis of Purchase, (o) The hard grade will be used only when specified.
(b) If desired, cold-twisted bars may be purchased on the basis of tests of the hot-rolled bars
before twisting, in which case such tests shall govern and shall conform to the requirements speci-
fied for plain bars of structural steel grade.
I. MANUFACTURE.
3. Process, (a) The steel may be made by the Bessemer or the open-hearth process.
(b) The bars shall be rolled from new billets. No rerolled material will be accepted.
4. Cold-twisted Bars. Cold-twisted bars shall be twisted cold With one complete twist in a
length not over 12 times the thickness of the bar.
II. CHEMICAL PROPERTIES AND TESTS.
5. Chemical Composition. The steel shall conform to the following requirements as to
chemical composition:
t>u~o t,^. ,«,/ Bessemer not over o.io per cent
Phosphorus i open-hearth " " 0.05 "
6. Ladle Analyses. An analysis to determine the percentage of carbon, manganese, phos-
phorus and sulphur, shall be made by the manufacturer from a test ingot taken during the pouring
of each melt, a copy of which shall be given to the purchaser or his representative. This analysis
shall conform to the requirements specified in Section 5.
7. Check Analyses. Analyses may be made by the purchaser from finished bars representing
each melt of open-hearth steel, and each melt, or lot of ten tons, of Bessemer steel, in which case an
excess of 25 per cent above the requirements specified in Section 5 shall be allowed.
III. PHYSICAL PROPERTIES AND TESTS.
8. Tension Tests, (a) The bars shall conform to the following requirements as to tensile
properties:
* For the American Railway Engineering Association specifications for steel reinforcement,
see Chapter VI, p. 272.
508
ENGINEERING MATERIALS.
CHAP. XV.
TENSILE PROPERTIES.
Properties Considered.
Plain Bars.
Deformed Bars.
Cold-twisted
Bars.
Structural Steel
Grade.
Hard Grade.
Structural Steel
Grade.
Hard Grade.
Tensile strength, Ib.
per sq. in
55,0x20-70,000
33:000
I^OO.OOO1
Tens. str.
80,000 min.
50,000
I^OO.OOO1
55,OOO-7O,OOO
33,OOO
1,250,000*
Tens. str.
80,000 min.
50,000
I,OOO,OOO1
Recorded
only.
55>°oo
5
Yield point, min., Ib.
per sq. in
Elongation in 8 in.,
min., per cent
Tens. str.
Tens. str.
(b) The yield point shall be determined by the drop of the beam of the testing machine.
9. Modifications in Elongation, (a) For plain and deformed bars over f in. in thickness
or diameter, a deduction of I from the percentages of elongation specified in Section 8 (a) shall be
made for each increase of f in. in thickness or diameter above f in.
(b) For plain and deformed bars under ^ in. in thickness or diameter, a deduction of i from
the percentages of elongation specified in Section 8 (a) shall be made for each decrease of -£§ in. in
thickness or diameter below y^ in.
10. Bend Tests. The test specimen shall bend cold around a pin without cracking on the
outside of the bent portion, as follows:
BEND TEST REQUIREMENTS.
Thickness or Diameter of Bar.
Plain Bars.
Deformed Bars.
Cold-twisted
Bars.
Structural
Steel Grade.
Hard Grade.
Structural
Steel Grade.
Hard Grade.
Under f in
I 80 deg.
d-t
I 80 deg.
d = t
I 80 deg.
d-jt
90 deg.
d = 3t
I 80 deg.
d = t
90 deg.
d = 2t
I 80 deg.
d = 4t
90 deg.
d = 4t
I 80 deg.
d = 2t
I 80 deg.
d = 3t
f in. or over
EXPLANATORY NOTE: d = the diameter of pin about which the specimen is bent;
t = the thickness or diameter of the specimen.
11. Test Specimens, (a) Tension and bend test specimens for plain and deformed bars
shall be taken from the finished bars, and shall be of the full thickness or diameter of material as
rolled; except that the specimens for deformed bars may be machined for a length of at least 9 in.,
if deemed necessary by the manufacturer to obtain uniform cross-section.
(b) Tension and bend test specimens for cold-twisted bars shall be taken from the finished
bars, without further treatment; except as specified in Section 2 (b).
12. Number of Tests, (a) One tension and one bend test shall be made from each melt of
open-hearth steel, and from each melt, or lot of ten tons, of Bessemer steel; except that if material
from one melt differs f in. or more in thickness or diameter, one tension and one bend test shall be
made from both the thickest and the thinnest material rolled.
(b) If any test specimen shows defective machining or develops flaws, or if a tension test
specimen breaks outside the middle third of the gage length, it may be discarded and another
specimen substituted.
IV. PERMISSIBLE VARIATIONS IN WEIGHT.
13. Permissible Variations. The weight of any lot of bars shall not vary more than 5 per
cent from the theoretical weight of that lot.
1 See Section 9.
SPECIFICATIONS FOR RAIL-STEEL REINFORCEMENT BARS.
609
V. FINISH.
14. Finish. The finished bars shall be free from injurious defects and shall have a workman-
like ImNi.
VI. INSPECTION AND REJECTION.
15. Inspection. The inspector representing the purchaser shall have free entry, at all times
wliiK- work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the bars ordered. The manufacturer shall afford the
in-pn tor, free of cost, all reasonable facilities to satisfy him that the bars are being furnished in
accord, UK i- with tlu.se specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
16. Rejection, (a) Unless otherwise specified, any rejection based on tests made in accord-
aim- with Section 7 shall be reported within five working days from the receipt of samples.
(6) Bars which show injurious defects subsequent to their acceptance at the manufacturer's
works will be rejected, and the manufacturer shall be notified.
17. Rehearing. Samples tested in accordance with Section 7, which represent rejected bars,
shall be preserved for two weeks from the date of the test report. In case of dissatisfaction with
the results of the tests, the manufacturer may make claim for a rehearing within that time.
STANDARD SPECIFICATIONS FOR RAIL-STEEL REINFORCEMENT BARS
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 25, 1913.
1 . Classes. These specifications cover three classes of rail-steel concrete reinforcement bars,
namely: plain, deformed, and hot-twisted.
I. MANUFACTURE.
2. Process. The bars shall be rolled from standard section Tee rails.
3. Hot-twisted Bars. Hot-twisted bars shall have one complete twist in a length not over
12 times the thickness of the bar.
II. PHYSICAL PROPERTIES AND TESTS.
4. Tension Tests, (a) The bars shall conform to the following minimum requirements as to
tensile properties:
Properties Considered.
Plain Bars.
Deformed and Hot-twisted Bars.
Tensile strength, Ib. per sq. in
80,000
50,000
1,200.000
80.000
50,000
1,000,000
Yield point, Ib. per sq. in
Tens. str.
Tens. str.
(6) The yield point shall be determined by the drop of the beam of the testing machine.
5. Modifications in Elongation, (a) For bars over f in. in thickness or diameter, a deduction
of i from the percentages of elongation specified in Section 4 (c) shall be made for each increase
of J in. in thickness or diameter above f in.
(ft) For bars under ^ in. in thickness or diameter, a deduction of I from the percentages of
elongation specified in Section 4 (a) shall be made for each decrease of fa in. in thickness or di-
ameter below -fg in.
6. Bend Tests. The test specimen shall bend cold around a pin without cracking on the
outside of the bent portion, as follows:
1 See Section 5.
510
ENGINEERING MATERIALS.
CHAP. XV.
Thickness or Diameter of Bar.
Plain Bars.
Deformed and Hot-twisted Bars.
Under f in
I 80 deg.
I 80 deg.
f in. or over
d = 3 t
90 deg.
d = 4 t
90 deg.
d = 3 t
d = 4 t
EXPLANATORY NOTE: d = the diameter of pin about which the specimen is bent;
t = the thickness or diameter of the specimen.
7. Test Specimens, (a) Tension and bend test specimens for plain and deformed bars shall
be taken from the finished bars, and shall be of the full thickness or diameter of bars as rolled;
except that the specimens for deformed bars may be machined for a length of at least 9 in., if
deemed necessary by the manufacturer to obtain uniform cross-section.
(b) Tension and bend test specimens for hot-twisted bars shall be taken from the finished
bars, without further treatment.
8. Number of Tests, (a) One tension and one bend test shall be made from each lot of ten
tons or less of each size of bar rolled from rails varying not more than 10 Ib. per yd. in nominal
weight.
(b) If any test specimen shows defective machining or develops flaws, or if a tension test
specimen breaks outside the middle third of the gage length, it may be discarded and another
specimen substituted.
III. PERMISSIBLE VARIATIONS IN WEIGHT.
9. Permissible Variations. The weight of any lot of bars shall not vary more than 5 per cent
from the theoretical weight of that lot.
IV. FINISH.
10. Finish. The finished bars shall be free from injurious defects and shall have a workman-
like finish.
V. INSPECTION AND REJECTION.
11. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the bars ordered. The manufacturer shall afford the
inspector, free of cost, all reasonable facilities to satisfy him that the bars are being furnished in
accordance with these specifications. All tests and inspection shall be made at the place of manu-
facture prior to shipment, unless otherwise specified, and shall be so conducted as not to interfere
unnecessarily with the operation of the works.
12. Rejection. Bars which show injurious defects subsequent to their acceptance at the
manufacturer's works will be rejected, and the manufacturer shall be notified.
STANDARD SPECIFICATIONS FOR STEEL CASTINGS
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS
ADOPTED AUGUST 25, 1913.
1. Classes. These specifications cover two classes of castings, namely:
Class A, ordinary castings for which no physical requirements are specified;
Class B, castings for which physical requirements are specified. These are of three grades:
hard, medium, and soft.
2. Patterns, (a) Patterns shall be made so that sufficient finish is allowed to provide for all
variations in shrinkage.
(6) Patterns shall be painted three colors to represent metal, cores, and finished surfaces.
It is recommended that core prints shall be painted black and finished surfaces red.
3. Basis of Purchase. The purchaser shall indicate his intention to substitute the test to
destruction specified in Section 1 1 for the tension and bend tests, and shall designate the patterns
from which castings for this test shall be made.
SPECIFICATIONS FOR STEEL CASTINGS.
611
I. MANUFACTURE.
4. Process. The steel may be made by the open-hearth, crucible, or any other process
approved \>y the pun h.i
5. Heat Treatment, (a) Class A castings need not be annealed miles-, otherwise specified.
(b) ( l.i^ I! i aMiiiijs shall IK- allowed to become cold. They shall then l>e uniformly reheated
to the proper teiii|HT.iture to refine the grain (a group thus reheated l.< in^ known ass an " annealing
chaise "), and allowed to cool uniformly and slowly. If, in the opinion of the purchaser or his
•itati\e, a casting is not properly annealed, he may at his option require the casting to Ix.-
re*aniiealed.
II. CHEMICAL PROPERTIES AND TESTS.
6. Chemical Composition. The castings shall conform to the following requirements as to
chemical composition:
CLASS A. CLASS B.
Carbon not over 0.30 per cent ....
Phosphorus " ' 0.06 not over 0.05 per cent
Sulphur ' 0.05
7. Ladle Analyses. An analysis to determine the percentages of carbon, manganese, phos-
phorus and sulphur shall be made by the manufacturer from a test ingot taken during the pouring
of each melt, a copy of which shall be given to the purchaser or his representative. This analysis
shall conform to the requirements specified in Section 6. Drillings for analysis shall be taken not
less than J in. beneath the surface of the test ingot.
8. Check Analyses, (a) Analyses of Class A castings may be made by the purchaser, in
which case an excess of 20 per cent above the requirement as to phosphorus specified in Section 6
shall be allowed. Drillings for analysis shall be taken not less than j in. beneath the surface.
(b) Analyses of Class B castings may be made by the purchaser from a broken tension or
bend test specimen, in which case an excess of 20 per cent above the fequirements as to phos-
phorus and sulphur specified in Section 6 shall be allowed.. Drillings for analysis shall be taken
not less than } in. beneath the surface.
III. PHYSICAL PROPERTIES AND TESTS.
(FOR CLASS B CASTINGS ONLY.)
9. Tension Tests, (a) The castings shall conform to the following minimum requirements
as to tensile properties:
HARD.
Tensile strength, Ib. per sq. in 80 ooo
Yield point, Ib. per sq. in 36 ooo
Elongation in 2 in., per cent 15
Reduction of area, " 20
MEDIUM.
70 ooo
31 500
18
25
SOFT.
60 OOO
27 ooo
22
30
1 (b) The yield point shall be determined by the drop of the beam of the testing machine.
10. Bend Tests, (a) The test specimen for soft castings shall bend cold through 120 deg.,
and for medium castings through 90 deg., around a I -in. pin, without cracking on the outside of
the bent portion.
(6) Hard castings shall not be subject to bend test requirements.
11. Alternative Tests to Destruction. In the case of small or unimportant castings, a test to
destruction on three castings from a lot may be substituted for the tension and bend tests. This
test shall show the material to be ductile, free from injurious defects, and suitable for the purpose
intended. A lot shall consist of all castings from one melt, in the same annealing charge.
12. Test Specimens, (a) Sufficient test bars, from which the test specimens required in
Section 13 (a) may be selected, shall be attached to castings weighing 500 Ib. or over, when the
512 ENGINEERING MATERIALS. CHAP. XV
design of the castings will permit. If the castings weigh less than 500 lb., or are of such a design
that test bars cannot be attached, two test bars shall be cast to represent each melt; or the quality
of the castings shall be determined by tests to destruction as specified in Section II. All test
bars shall be annealed with the castings they represent.
(b) The manufacturer and purchaser shall agree whether test bars can be attached to castings,
on the location of the bars on the castings, on the castings to which bars are to be attached, and
on the method of casting unattached bars.
(c) Tension test specimens shall be of the form and dimensions shown in Fig. i. Bend test
specimens shall be machined to I by 5 in. in section with corners rounded to a radius not over re in.
13. Number of Tests, (a) One tension and one bend test shall be made from each annealing
charge. If more than one melt is represented in an annealing charge, one tension and one bend
test shall be made from each melt.
(6) If any test specimen shows defective machining or develops flaws, or if a tension test
specimen breaks outside the gage length, it may be discarded; in which case the manufacturer and
the purchaser or his representative shall agree upon the selection of another specimen in its stead.
IV. WORKMANSHIP AND FINISH.
14. Workmanship. The castings shall substantially conform to the sizes and shapes of the
patterns, and shall be made in a workmanlike manner.
15. Finish, (a) The castings shall be free from injurious defects.
(b) Minor defects which do not impair the strength of the castings may, with the approval
of the purchaser or his representative, be welded by an approved process. The defects shall first
be cleaned out to solid metal; and after welding, the castings shall be annealed, if specified by the
purchaser or his representative.
(c) The castings offered for inspection shall not be painted or covered with any substance
that will hide defects, nor rusted to such an extent as to hide defects.
•
V. INSPECTION AND REJECTION.
1 6. Inspection. The inspector representing the purchaser shall have free entry, at all times
while work on the contract of the purchaser is being performed, to all parts of the manufacturer's
works which concern the manufacture of the castings ordered. The manufacturer shall afford the
inspector, free of cost, all reasonable facilities to satisfy him that the castings are being furnished
in accordance with these specifications. All tests (except check analyses) and inspection shall be
made at the place of manufacture prior to shipment, unless otherwise specified, and shall be so
conducted as not to interfere unnecessarily with the operation of the works.
17. Rejection, (a) Unless otherwise specified, any rejection based on tests made in accord-
ance with Section 8 shall be reported within five working days from the receipt of samples.
(b) Castings which show injurious defects subsequent to their acceptance at the manu-
facturer's works will be rejected, and the manufacturer shall be notified.
18. Rehearing. Samples tested in accordance with Section 8, which represent rejected
castings, shall be preserved for two weeks from the date of the test report. In case of dissatis-
faction with the results of the tests, the manufacturer may make claim for a rehearing within that
time.
VI. SPECIAL REQUIREMENTS FOR CASTINGS FOR SHIPS.
19. Castings for Ships. In addition to the preceding requirements, castings for ships, when
so specified, shall conform to the following requirements:
20. Heat Treatment. All castings shall be annealed.
21. Number of Tests, (a) One tension and one bend test shall be made from each of the
following castings: stern frames, stern posts, twin screw spectacle frames, propeller shaft brackets,
rudders, steering quadrants, tillers, stems, anchors, and other castings when specified.
(b) When a casting is made from more than one melt, four tension and four bend tests shall
be made from each casting.
22. Percussion Tests, (a) A percussion test shall be made on each of the following castings:
stern frames, stern posts, twin screw spectacle frames, propeller shaft brackets, rudders, steering
quadrants, tillers, stems, anchors, and other castings when specified.
(b) For this test, the casting shall be suspended by chains and hammered all over with a
hammer of a weight approved by the purchaser or his representative. If cracks, flaws, defects,
or weakness appear after such treatment, the casting will be rejected.
VII. SPECIAL REQUIREMENTS FOR CASTINGS FOR RAILWAY ROLLING STOCK.
23. Castings for Railway Rolling Stock. Castings for railway rolling stock, when so specified,
shall conform to the requirements for Class B castings, Sections I to 18, inclusive, except that
CORROSION OF IRON AND STEEL. 513
chirk analyses made in accordance with Section 8 (b) shall conform to the requirements as to
phosphorus and sulphur specified in Section 6.
CORROSION OF IRON AND STEEL.— If iron or steel is left exposed to the atmosphere
it unites \sitli oxygen and water to form rust. Where the metal is further exposed to the action
of corrosive gases the rate of rusting is accelerated but the action is similar to that of ordinary
rust inij. Nrit her dry air nor water free from oxygen has any corrosive effect. While not essential
to corrosion acids greatly hasten its action. It seems evident that some weak electrolysis is
c».-ntial for corrosive action. Where iron or steel are in contact with water electrolytic action
will always take place, although the amount is very small under ordinary conditions. Where a
considerable electrolytic force exists the corrosion is greatly hastened. The increase in the use
of electricity has doubtless had a tendency to increase the corrosion of iron and steel and to make
the problem of the preservation of iron and steel from corrosion of great importance.
In an article on "The Corrosion of Iron " in Proceedings of American Society for Testing
Materials, vol. VII, 1907, pages 211 to 228, Mr. Allerson S. Cushman shows that the two factors
wfthout which the corrosion of iron is impossible are electrolysis and the presence of hydrogen
in the electrolyzed or " ionic " condition. The electrolytic action can only take place in the
presence of oxygen or some other oxidizing agent. Rust is a hydroxide of iron — ferric hydroxide,
FeOsHi. The corrosion of iron or steel may be prevented or retarded by covering it with a coating
that will protect it from the water or the air.
It is commonly believed, with good reason, that cast iron corrodes less rapidly than either
wrought iron or steel. The graphite in the cast iron and the silicious coating that the cast iron
receives in molding doubtless assist in protecting the cast iron from corrosion.
It is also commonly believed that steel corrodes more rapidly than wrought iron. The tests
that have been made to determine the relative corrosion of wrought iron and steel are very con-
flicting, but it appears certain that the difference in the corrosion of well made steel and well made
wrought iron is very slight. The acid test as a measure of natural corrosion has been used, es-
pecially by firms manufacturing and selling " ingot iron " (very low carbon Bessemer or open-
hearth steel). Committee A- 5 on the Corrosion of Iron and Steel of the American Society for
Testing Materials in the Proceedings of the Society, vol. XI, 1911, page 100, states tliat it considers
the acid test as unreliable as a measure of natural corrosion and does not recommend its use.
In the paper on " The Corrosion of Iron " above referred to, Mr. Cushman states: — " A
very widespread impression prevails that charcoal iron or a puddled wrought iron are more re-
sistant to corrosion than steel manufactured by the Bessemer and open-hearth processes. It is
by no means certain that this is the case, but it would follow from the electrolytic theory that in
order to have the highest resistance to corrosion a metal should either be as free as possible from
certain impurities, such as manganese, or should be so homogeneous as not to retain localized
positive and negative nodes for a long time without change. Under the first condition iron would
appear to have the advantage, but under the second much would depend upon the care exercised
in manufacture, whatever process was used."
From the preceding discussion it would appear that neither " ingot iron " nor wrought iron
any advantage in resisting corrosion over a well made structural steel.
PAINT.* — The paints in use for protecting structural steel may be divided into oil paints,
tar paints, asphalt paints, varnishes, lacquers, and enamel paints. The last two mentioned are
too expensive for use on a large scale and will not be considered.
OIL PAINTS. — An oil paint consists of a drying oil or varnish and a pigment, thoroughly
mixed together to form a workable mixture. " A good paint is one that is readily applied, has
good covering powers, adheres well to the metal, and is durable." The pigment should be inert
to the metal to which it is applied and also to the oil with which it is mixed. Linseed oil is com-
monly used as the varnish or vehicle in oil paints, and is unsurpassed in durability by any other
drying oil. Pure linseed oil will, when applied to a metal surface, form a transparent coating that
offers considerable protection for a time, but is soon destroyed by abrasion and the action of the
elements. To make the coating thicker, harder and more dense, a pigment is added to the oil.
An oil paint is analogous to concrete, the linseed oil and pigment in the paint corresponding to the
* This discussion on paints is taken from the author's " The Design of Steel Mill Buildings."
34
614 ENGINEERING MATERIALS. CHAP. XV.
cement and the aggregate in the concrete. The pigments used in making oil paints for protecting
metal may be divided into four groups as follows: (i) lead; (2) zinc; (3) iron; (4) carbon.
Linseed Oil. — Linseed oil is made by crushing and pressing flaxseed. The oil contains some
vegetable impurities when made, and should be allowed to stand for two or three months to purify
and settle before being used. In this form the oil is known as raw linseed oil, and is ready for use.
Raw linseed oil dries (oxidizes) very slowly and for that reason is not often used in a pure state for
structural iron paint. The rate of drying of raw linseed oil increases with age ; an old oil being
very much better for paint than that which has been but recently extracted. Raw linseed oil
can be made to dry more rapidly by the addition of a drier or by boiling. Linseed oil dries by
oxidation and not by evaporation, and therefore any material that will make it take up oxygen
more rapidly is a drier. A common method of making a drier for linseed oil is to put the linseed
oil in a kettle, heat it to a temperature of 400 to 500 degrees F., and stir in about four pounds of
red lead or litharge, or a mixture of the two, to each gallon of oil. This mixture is then thinned
down by adding enough linseed oil to make four gallons for each gallon of raw oil first put in the
kettle. The addition of four gallons of this drier to forty gallons of raw oil will reduce the time of
drying from about five days to twenty-four hours. A drier made in this way costs more than the
pure linseed oil, so that driers are very often made by mixing lead or manganese oxide with rosin
and turpentine, benzine, or rosin oil. These driers can be made for very much less than the price
of good linseed oil, and are used as adulterants; the more of the drier that is put into the paint, the
quicker it will dry and the poorer it becomes. Japan drier is often used with raw oil, and when this
or any other drier is added to raw oil in barrels, the oil is said to be " boiled through the bung hole."
Boiled linseed oil is made by heating raw oil, to which a quantity of red lead, litharge, sugar of
lead, etc., has been added, to a temperature of 400 to 500 degrees F., or by passing a current of
heated air through the oil. Heating linseed oil to a temperature at which merely a few bubbles
rise to the surface makes it dry more rapidly than the unheated oil; however, if the boiling is con-
tinued for more than a few hours the rate of drying is decreased by the boiling. Boiled linseed
oil is darker in color than raw oil, and is much used for outside paints, It should dry in from 12 to
24 hours when spread out in a thin film on glass. Raw oil makes a stronger and better film than
boiled oil, but it dries so slowly that it is seldom used for outside work without the addition of a
drier.
Lead. — White Lead (hydrated carbonate of lead — specific gravity 6.4) is used for interior and
exterior wood work. White lead forms an excellent pigment on account of its high adhesion and
covering power, but it is easily darkened by exposure to corrosive gases and rapidly disintegrates
under these conditions, requiring frequent renewal. It does not make a good bottom coat for
other paints, and if it is to be used at all for metal work it should be used over another paint.
Red Lead (minium; lead tetroxide — specific gravity 8.3) is a heavy, red powder approxi-
mating in shade to orange; is affected by acids, but when used as a paint is very stable in light and
under exposure to the weather. Red lead is seldom adulterated, about the only substance used
for the purpose being red oxide. Red lead is prepared by changing metallic lead into monoxide
litharge, and converting this product into minium in calcining ovens. Red lead intended for
paints must be free from metallic lead. One ounce of lampblack added to one pound of red lead
changes the color to a deep chocolate and increases the time of drying. This compound when
mixed in a thick paste will keep 30 days without hardening.
Zinc. — Zinc white (zinc oxide — specific gravity 5.3) is a white loose powder, devoid of smell
or taste and has a good covering power. Zinc paint has a tendency to peel, and when exposed
there is a tendency to form a zinc soap with the oil which is easily washed off, and it therefore does
not make a good paint. However, when mixed with red oxide of lead in the proportions of i lead
to 3 zinc, or 2 lead to i zinc, and ground with linseed oil, it makes a very durable paint for metal
surfaces. This paint dries very slowly, the zinc acting to delay hardening about the same as
lampblack.
Iron Oxide. — Iron oxide (specific gravity 5) is composed of anhydrous sesquioxide (hematite)
and hydrated sesquioxide of iron (iron rust). The anhydrous oxide is the characteristic
ingredient of this pigment and very little of the hydrated oxide should be present. Hydrated
sesquioxide of iron is simply iron rust, and it probably acts as a carrier of oxygen and accele-
rates corrosion when it is present in considerable quantities. Mixed with the iron ore are
various other ingredients, such as clay, ocher and earthy materials, which often form 50 to 75
per cent of the mass. Brown and dark red colors indicate the anhydrous oxide and are considered
the best. Bright red, bright purple and maroon tints are characteristic of hydrated oxide and
make less durable paints than the darker tints. Care should be used in buying iron oxide to
see that it is finely ground and is free from clay and ocher.
Carbon. — The most common forms of carbon in use for paints are lampblack and graphite.
Lampblack (specific gravity 2.6) is a great absorbent of linseed oil and makes an excellent pigment,
Graphite (black lead or plumbago — specific gravity 2.4) is a more or less impure form of carbon,
and when pure is not affected by acids. Graphite does not absorb nor act chemically on linseed
PAINTS AND PAINTING.
oil, so that the varnish simpiy holds the particles of pigment together in the same manner as the
rem in in a com red-. Tin-re an- two kinds of graphite in common use for paints — the granular
ami ttu- llaki- graphite. 'I IK- Dixon Graphite Co., of Jersey City, uses a flake graphite combined
with silira, while tin- Detroit Graphite Manufacturing Co. uses a mineral on- with a Urge i* r-
(viu.tge of graphitic rarl><ui in granulated form. On account of the small specific gravity of the
pigment, carbon and graphite paints have a very large covering capacity. The thickness of the
out is, however, corn ->p mdingly reduced. Boiled linseed oil should always be used with carbon
pigments.
Mixing the Paint. — The pigment should be finely ground and should preferably be ground with
the oil. The materials should be bought from reliable dealers, and should be mixed as wanted.
If it is not possible to grind the paint, better results will usually be obtained from hand mixed
paints made of first class materials than from the ordinary run of prepared paints that are supposed
to have been ground. Many ready mixed paints are sold for less than the price of linseed oil,
which makes it evident that little if any oil has been used in the paint. The paint should be
thinned with oil, or if necessary a small amount of turpentine may be added; however turpentine
is an adulterant and should be used sparingly. Benzine, gasoline, etc., should never be used in paints,
as the paint dries without oxidizing and then rubs off like chalk.
Proportions. — The proper proportions of pigment and oil required to make a good paint
vary with the different pigments; and the methods of preparing the paint; the heavier and the
more finely ground pigments require less oil than the lighter or coarsely ground while ground
paints require less oil than ordinary mixed paints. A common rule for mixing paints ground in
oil is to mix with each gallon of linseed oil, dry pigment equal to three to four times the specific
gravity of the pigment, the weight of the pigment being given in pounds. This rule gives the
following weights of pigment per gallon of linseed oil: white lead, 19 to 26 lb.; red lead, 25 to 33 lb.;
zinc, 15 to 21 lb.; iron oxide, 15 to 20 lb.; lampblack, 8 to IO lb.; graphite, 8 to 10 lb. The weights
of pigment used per gallon of oil varies about as follows: red lead, 20 to 33 lb.; iron oxide, 8 to
25 lb.; graphite, 3 to 12 lb.
Covering Capacity. — The covering capacity of a paint depends upon the uniformity and
thickness of the coating; the thinner the coating the larger the surface covered per unit of paint.
To obtain any given thickness of paint therefore requires practically the same amount of paint
whatever its pigment may be. The claims often urged in favor of a particular paint that it has a
large covering capacity may mean nothing but that an excess of oil has been used in its fabrication.
An idea of the relative amounts of oil and pigment required, and the covering capacity of different
paints may be obtained from Table VIII, Chapter XIII.
Light structural work will average about 250 square feet, and heavy structural work about
150 square feet of surface per net ton of metal.
It is the common practice to estimate J gallon of paint for the first coat and f gallon for the
second coat per ton of structural steel, for average conditions.
Applying the Paint. — The paint should be thoroughly brushed out with a round brush to
remove all the air. The paint should be mixed only as wanted, and should be kept well stirred.
When it is necessary to apply paint in cold weather, it should be heated to a temperature of 130
to 150 degrees F.; paint should not be put on in freezing weather. Paint should not be applied
when the surface is damp, or during foggy weather. The first coat should be allowed to stand for
three or four days, or until thoroughly dry, before applying the second coat. If the second coat
is applied before the first coat has dried, the drying of the first coat will be very much retarded.
Cleaning the Surface. — Before applying the paint all scale, rust, dirt, grease and dead paint
should be removed. The metal may be cleaned by pickling in an acid bath, by scraping and brushing
with wire brushes, or by means of the sand blast. In the process of pickling the metal is dipped
in an acid bath, which is followed by a bath of milk of lime, and afterwards the metal is washed
clean in hot water. The method is expensive and not satisfactory unless extreme care is used in
removing all traces of the acid. Another objection to the process is that it leaves the metal wet and
allows rusting to begin before the paint can be applied. The most common method of cleaning
is by scraping with wire brushes and chisels. This method is slow and laborious. The method of
cleaning by means of a sand blast has been used to a limited extent and promises much for the
future. The average cost of cleaning five bridges in Columbus, Ohio, in 1902, was 3 cts. per sq.
ft. of surface cleaned.* The bridges were old and some were badly rusted. The painters followed
the sand blast and covered the newly cleaned surface with paint before the rust had time to form.
Mr. Lilly estimates the cost of cleaning light bridge work at the shop with the sand blast at
$1.75 per ton, and the cost of heavy bridge work at $1.00 per ton. In order to remove the mill
scale it has been recommended that rusting be allowed to start before the sand blast is used. One
of the advantages of the sand blast is that it leaves the surface perfectly dry, so that the paint can
be applied before any rust has formed.
* Sand Blast Cleaning of Structural Steel, by G. W. Lilly, Trans. Am. Soc. C. E., Feb., 1903.
516 ENGINEERING MATERIALS. CHAP. XV.
Priming or Shop Coat. — Engineers are very much divided as to what makes the best priming
coat; some specify a first coat of pure linseed oil and others a priming coat of paint. Linseed oil
makes a transparent coating that allows imperfections in the workmanship and rusted spots
to be easily seen; it is not permanent however, and if the metal is exposed for a long time the oil
will often be entirely removed before the second coat is applied. It is also claimed that the paint
will not adhere as well to linseed oil that has weathered as to a good paint. Linseed oil gives better
results if applied hot to the metal. • Another advantage of using oil as a priming coat is that the
erection marks can be painted over with the oil without fear of covering them up. Red lead paint
toned down with lampblack is probably used more for a priming coat than any other paint; the
B. & O. R. R. uses 10 oz. of lampblack to every 12 Ib. of red lead. Linseed oil mixed with a small
amount of lampblack makes a very satisfactory priming or shop coat.
Without going further into the controversy it would seem that there is very little choice between
linseed oil and a good red lead paint for a priming coat. For data on the standard shop paints
specified by different railroads, see digest of specifications in Chapter IV.
Finishing Coat. — From a careful study of the question of paints, it would seem that for ordi-
nary conditions, the quality of the materials and workmanship is of more importance in painting
metal structures than the particular pigment used. If the priming coat has been properly
applied there is no reason why any good grade of paint composed of pure linseed oil and a very
finely ground, stable and chemically non-injurious pigment will not make a very satisfactory finish-
ing coat. Where the paint is to be subjected to the action of corrosive gases or blasts, however,
there is certainly quite a difference in the results obtained with the different pigments. The
graphite and asphalt paints appear to withstand the corroding action of smelter and engine gases
better than red lead or iron oxide paints; while red lead is probably better under these conditions
than iron oxide. Portland cement paint or coal tar paint are the only paints that will withstand
the action of engine blasts.
To obtain the best results in painting metal structures therefore, proceed as follows: (i) pre-
pare the surface of the metal by carefully removing all dirt, grease, mill scale, rust, etc., and give
it a priming coat of pure linseed oil or a good paint — red lead seems to be the most used for this
purpose; (2) after the metal is in place carefully remove all dirt, grease, etc., and apply the finishing
coats — preferably not less than two coats — giving ample time for each coat to dry before applying
the next. The separate coats of paint should be of different colors. Painting should not be done
in rainy weather, or when the metal is damp, nor in cold weather unless special precautions are
taken to warm the paint. The best results will usually be obtained if the materials are purchased
in bulk from a responsible dealer and the paint ground as wanted. Good results are obtained with
many of the patent or ready mixed paints, but it is not possible in this place to go into a discussion
of their respective merits.
ASPHALT PAINT. — Many prepared paints are sold under the name of asphalt that are mix-
tures of coal tar, or mineral asphalt alone, or combined with a metallic base, or oils. The exact
compositions of the patent asphalt paints are hard to determine. Black bridge paint made by
Edward Smith & Co., New York City, contains asphaltum, linseed oil, turpentine and Kauri gum.
The paint has a varnish-like finish and makes a very satisfactory paint. The black shades of
asphalt paint are the only ones that should be used.
COAL TAR PAINT. — Coal tar paint is occasionally used for painting gas tanks, smelters, and
similar structures that receive rough usage. Coal tar paint mixed as described below has been
used by the U. S. Navy Department for painting the hulls of ships. It should give satisfactory
service where the metal is subject to corrosion. The coal tar paint is mixed as follows: The pro-
portions of the mixture are slightly variable according to the original consistency of the tar, the
use for which it is intended and the climate in which it is used. The proportions will vary
between the following proportions in volume.
Coal Tar. Portland Cement. Kerosene Oil.
New Orleans Mixture 8 I I
Annapolis Mixture 16 4 3
The Portland cement should first be stirred into the Tcerosene, forming a creamy mixture,
the mixture is then stirred into the coal tar. The paint should be freshly mixed and kept well
stirred. This paint sticks well, does not run when exposed to the sun's rays and is a very satis-
factory paint for rough work. The cost of the paint will vary from 10 to 20 cts. per gallon. The
kerosene oil acts as a drier, while the Portland cement neutralizes the coal tar.
If it is desired to paint with oil paint a structure which has been painted with coal tar paint,
the surface must be scraped and all the coal tar removed.
CEMENT AND CEMENT PAINT.— Experiments have shown that a thin coating of Portland
cement is effective in preventing rust; that a concrete to be effective in preventing rust must be
dense and made very wet. The steel must be clean when imbedded in the concrete. There is
quite a difference of opinion as to whether the metal should be painted before being imbedded or
MILL INSPECTION OF STRUCTURAL STEEL. 517
not. It is probably best to paint the metal if it is not to be imbedded at once, or is not to be used
inconcrvti'-Mrrl confirm -limi where the adhesion of tin- ci-nu-nt to the metal is an essential element.
When tin- mrt.il i-- to l>r imbedded immediately it is better not to paint it.
Portland Cement Paint. — A Portland cement paint has been used on the High St. viaduct in
Columbus, Ohio, with K""(' results. The viaduct was exposed to the fumes and blasts from
locomotives, so that an ordinary paint did not last more than six months even on the least exposed
portion^. I'lu- method of mixing and applying the paint is described in Engineering News,
April ->4tlt aii.1 J inn- 51 h, 1902, as follows: " The surface of the metal was thoroughly cleaned with
win- 1 IRISH'S and files — the bridge had been cleaned with a sand blast the previous year. A thick
coat of Japan drier was then applied and before it had time to dry a coating was applied as fol-
lo\\s: Apply with a trowel to the minimum thickness of A in. and a maximum thickness of
i in. (in extreme cases i in.) a mixture of 32 Ib. Portland cement, 12 Ib. dry finely ground lead, 4
to 6 Ib. boiled linseed oil, 2 to 3 Ib. Japan drier." After a period of about two years the coating
was in almost perfect condition and the metal under the coating was as clean as when painted.
The cost of the coating including the hand cleaning, materials and labor was 8 cts. per sq. ft.
INSTRUCTIONS FOR THE MILL INSPECTION OF STRUCTURAL STEEL.*
(1) Study the contract and specifications and secure such information concerning the pro-
posed structure as will permit a full understanding of the use to be made of the various items of the
order.
(2) Secure copies of the mill orders, shipping directions and other information concerning the
material to be inspected.
(3) Attend promptly when notified of the rolling of material and so conduct the inspection
and tests as not to interfere unnecessarily with the operations of the mill.
(4) Have the test specimens prepared and properly stamped with the melt numbers by the
manufacturer. Observe the selection and stamping of specimens and verify the melt numbers
when practicable.
(5) Attend and supervise the making of tensile, bending and drifting tests. Make sure that
the testing machines are properly handled and that the specified speed of pulling is not exceeded.
Note the behavior of the metal and check and record the results of the tests.
(6) Select the bars or other members for full-size tests as specified. Supervise such tests
and check and record their results.
(7) Secure from the manufacturer records of the chemical analyses of the melts and accept
only those in which the specified contents of impurities are not exceeded.
(8) Secure pieces of the test ingots and test specimens and have check analyses made outside
of the manufacturers' laboratory when the analyses furnished by the manufacturer are erratic or
for any other reason appear to be incorrect.
(9) Examine each piece of finished material for surface defects before shipment, requiring
the material to be handled in a manner that will permit the examination to be thorough and
complete. This inspection should detect evidence of excessive gagging or other injury due to
cold straightening.
. (10) Report promptly the shipment of any material from the mill, whose surface inspection
has been waived. Such material should be examined by the shop inspector,
(n) Verify the section of all material by measurement and by weight.
(12) Study the operations of the plant and become familiar with the various processes of
manufacture.
Cultivate the acquaintance of the mill employees and become familiar with their work so as
to have direct knowledge of the mill practice and determine as well as the circumstances permit
the correctness of the mill practice in so far as it is covered by the specifications.
(13) Record all tests and analyses on the forms provided.
(14) Keep informed as to the progress of the work in the shop and endeavor to secure the
shipment of material at such times and in such order as to avoid delay in the fabrication.
(15) Secure copies of the shipping lists and compare them with the orders and make regular
statements of the material that has been rolled and shipped.
(16) Make reports weekly or as may be directed, submitting complete records of tests,
analyses and shipments and such other information as may be required.
* American Railway Engineering Association, Adopted, Vol. 14, 1913.
518 ENGINEERING MATERIALS. CHAP. XV.
INSTRUCTIONS FOR THE INSPECTION OF THE FABRICATION OF
STEEL BRIDGES.*
(1) Acquire a full knowledge of the conditions of the contract, such as the time of delivery,
the railway company's actual need of the work, the desired order of shipment, and any special
features in connection with delivery such as the position of the girders or truss members on cars
at the bridge site.
(2) Study in advance the plans and specifications and see that all provisions thereof are
complied with. These instructions are not be construed as altering the specifications in any way.
Check every finished member against the drawings for its general dimensions and for the
section of each piece of material forming a component part of the member.
(3) Endeavor to maintain pleasant relations with foremen and the workmen and by fairness,
decisiveness and good sense interest them in the successful completion of the work.
(4) Attend constantly to the work, making inspection during the progress of the work in the
shop, striving to keep up with the output in order that errors may be corrected before the work
leaves the shop.
Attend the weighing of material whenever practicable, especially that purchased on weight
basis. Check the accuracy of the scales with test weights or by other sufficient means.
Conduct the inspection so as not to interfere unnecessarily with the routine operations of the
shop.
(5) When unusual circumstances require an explanation of the plans or some variation from
the specified procedure, take the necessary action promptly.
(6) Study the field connections, paying particular attention to clearances and making nota-
tions on the drawings so that they may be checked rapidly.
(7) Check all bevels and field rivet holes.
(8) Give careful attention to the quality of the workmanship, the condition of the plain
material, accuracy of punching, care in assembling, alignment of rivets, tightness of rivets, ac-
curacy of finishing of machined joints, painting and general finish.
(9) Make sure that reamed holes are truly cylindrical and that drillings are not allowed to
remain between assembled parts.
(10) Watch for bends, kinks, and twists in the finished members and make certain that when
leaving the shop they are in proper condition for erection.
(n) Make sure that the webs of girders do not project beyond the flange angles and that the
depth of web below the flange angles complies with the specification.
(12) Allow only the material rolled and accepted for the work to be used therein.
(13) Have the fabricated material shipped in the correct order for erection and in accordance
with instructions, as far as practicable.
(14) Measure the width of each column and the lengths of all girders between columns when
they are to be placed consecutively in a long row so as to insure that the columns and girders will
not " build out " in erection, so as to exceed the calculated length.
(15) Check " rights " and " lefts " and make sure that the proper number of each is shipped.
(16) Check base plates of girders before riveting and make sure that the camber is not
reversed.
(17) Check the space provided for driving field rivets, allowing sufficient space for the
penumatic riveter.
(18) Examine field connections after riveting to insure proper fitting and ease of erection.
(19) Make sure that shop splices are properly fitted and that matched and milled surfaces
to transmit bearing are in close contact during riveting as specified.
(20) Examine and measure bored pinholes carefully to insure proper dimensions and spacing
and smoothness of finish.
(21) Measure the spacing center to center of the end connections for sections of I-beam
floors or any similar construction in which the calculated spacing is liable to be exceeded because
of the tendency of such work to " grow " as it is assembled.
(22) Make sure that stringers connecting to floor'oeams beneath the flange have sufficient
clearance to care for their possible over-run in depth.
(23) Have the assembling of trusses and girder spans required by the specifications carefully
done and in any case insure the accuracy of field connections. If a large number of duplicate
parts are to be made, the number of parts to be assembled should be governed by the workmanship.
If errors are found, a sufficient number of parts should be assembled to make it reasonably certain
that such errors have been eliminated.
Have through girder spans with I-beam floors partially assembled and at least one bracket
bolted in its final position.
* American Railway Engineering Association, Adopted, Vol. 14, 1913, and Vol. 15, 1914.
MISCELLANEOUS METALS. 619
Have at least one upper and lower shoe of each kind assembled and make sure that there is
no interference.
(24) Make sure that iron templets used for reaming are properly set and held to line.
(25) Secure match-marking diagrams for work which has been assembled and reamed and
m. ike sure that tin- match marks are plainly visible.
(26) Have proper camber blocking used in assembling trusses and secure the desired camber
lu-furr tin- reaming is done.
(27) Require that all treads and supports for the drums of draw spans be carefully leveled
with an instrument.
(28) Study carefully the machine details and discriminate between those dimensions which
must be exact and those in which slight variations are permissible.
1 >et ermine in advance the desired accuracy of driving fits for bolts or keys and similar parts
and make sure that such accuracy is attained.
(29) Examine castings carefully for blowholes and other imperfections and discriminate
between such defects as are unimportant and those which render the castings unfit for use.
(30) Make sure that bushings, collars and similar parts are held securely in place.
(31) Make sure that all drum wheels, expansion rollers, turntable rollers and similar parts
are exact in size, so as to carry equally the loads which may be placed upon them.
(32) Ascertain in advance 'that the paint provided complies with specifications. Watch
carefully the painting directions and make sure that paint is properly applied and only where
intended.
(33) Verify all shop marks and make sure that they are legible as well as correct.
(34) Have important members so loaded as to be headed in the right direction upon arrival
at the site of the work.
(35) Try a few countersunk head bolts in the holes where they are to be used to insure a
proper fit.
(36) Make sure that small pieces are bolted in place for shipment as shown on the plans and
that other small parts are properly boxed or otherwise secured against loss.
(37) Make sure that rivets, tie rods, anchor bolts and miscellaneous parts are shipped so as
to avoid delay in erection.
(38) Examine the field rivets to insure that they are free from fins or other defects.
(39) Exercise special care in the examination of all movable structures and particularly their
moving parts.
(40) Make reports weekly or as directed, exhibiting carefully and concisely the actual con-
ditions.
(41) Observe carefully and report such unusual difficulties as may be encountered and the
means adopted in overcoming them, and endeavor by a study of the details or other means to
make recommendations which will prevent their recurrence in future work.
MISCELLANEOUS METALS. — The physical properties of the following metals depend
upon whether they are cast, rolled, or drawn, and upon the details of manufacture, and the values
given are therefore approximate.
Aluminum has a specific gravity of 2.58 to 2.7. The ultimate tensile strength per sq. in. is
about 15,000 Ib. for cast, 24,000 Ib. for sheet, and 30,000 to 65,000 Ib. for aluminum wire. The
elastic limit is about i the ultimate strength. The modulus of elasticity is about 11,000,000 Ib.
per sq. in. Aluminum is used in engineering construction principally in the form of an alloy.
Copper has a specific gravity of 8.6 to 8.9. The ultimate tensile strength varies from 36,000
to 40,000 Ib. per sq. in. for soft copper wire with an elongation in 10 in. of 35 to 20 per cent; to
49,000 to 67,000 Ib. per sq. in. for hard-drawn copper wire with an elongation varying from 3.75
per cent in 10 in., to an elongation of 0.85 per cent in 60 in. Copper is also used in an alloy with
other metals.
Zinc, or spelter, has a specific gravity of about 7.00. The ultimate tensile strength per sq. in.
varies from 3000 to 8000 Ib. It is used for galvanizing and for making alloys.
Nickel has a specific gravity of about 8.8. Nickel is used principally in alloys.
Tin has a specific gravity of about 7.35. Tin is used as a covering for iron and steel sheets and
in alloys.
Lead has a specific gravity of about 11.4. Lead is very plastic and flows easily under stress.
ALLOYS. — An alloy is a combination of two or more metals made by mixing them when in a
molten condition. Alloys are commonly mechanical mixtures; although some have a slight chem-
ical union. The properties of alloys depend not only upon the ingredients, but upon the method and
620 ENGINEERING MATERIALS. CHAP. XV.
details of manufacture. It is impossible to predict the properties of an alloy from the properties
of the metals forming it. Many alloys are sold under trade names in which the properties depend
both on the proportions of the ingredients and upon the details of manufacture. The most im-
portant alloys used by the structural engineer are as folbws:
Brass is an alloy of copper and zinc in which the copper varies from 60 to 89 per cent, and
the zinc from 40 to 1 1 per cent. A small amount of tin is sometimes added to make the brass more
easily worked. The tensile strength of brass is greatest (about 50,000 Ib. per sq. in.) when the
composition is about 62 per cent copper and 38 per cent zinc; and the ductility and malleability
are greatest when the composition is about 70 per cent copper and 30 per cent zinc. A widely used
brass has f copper and i zinc.
Delta metal is brass with I to 2 per cent iron. The tensile strength of delta metal is about
45,000 Ib. per sq. in.
Tobin bronze is brass with I to 2 per cent iron, and small amounts of lead and tin.
Bronzes are alloys of copper and tin or of copper, zinc and tin, and usually have small quan-
tities of other metals. Bronzes having more than 24 per cent tin are too weak to be used. The
tensile strength is greatest (23,000 Ib. per sq. in.) when the composition is about 80 per cent copper
and 20 per cent tin.
Phosphor bronze is an alloy of copper and tin containing i to i per cent phosphorus. It makes
excellent castings and is very hard. The ultimate tensile strength varies from 50,000 to 100,000
Ib. per sq. in.
Aluminum bronze is an alloy having 5 to 10 per cent aluminum and 95 to 80 per cent copper.
The tensile strength varies from 75,000 to 100,000 Ib. per sq. in.
Manganese-bronze as specified by the American Society for Testing Materials contains,
copper 55 to 65 per cent, zinc 39 to 45 per cent, iron not over 2 per cent, tin not over 2 per cent,
aluminum not over 0.5 per cent, manganese not over 0.5 per cent. The ultimate tensile strength
of standard test pieces cut from manganese-bronze ingots shall not be less than 70,000 Ib. per sq. in.,
with an elongation in 2 in. of not less than 20 per cent.
TIMBER. — For definitions of terms, standard def cts, specifications and allowable stresses
in timber, see Chapter VII.
STONE MASONRY. — For definitions of terms used in masonry construction and for speci-
fications for different classes of stone masonry, see Chapter VI.
For the allowable pressure on masonry, see Table IV, Chapter V, and for the weight, specific
gravity and crushing strength of masonry, see Table V, Chapter V; also see Table VIII, Chapter
II. For an exhaustive treatise on brick and stone masonry see Baker's " Masonry Construction."
CONCRETE. — The average strengths of different mixtures of Portland cement concrete as
given in Report of the Committee on Reinforced Concrete of the American Society of Civil
Engineers, 1913, are given in Table II.
TABLE II.
STRENGTH OF PORTLAND CEMENT CONCRETE.
Aggregate 1:1:2 i:ij:3 1:2:4 1:2^:5 1:3:6
Granite, trap rock 3300 2800 2200 1800 1400
Gravel, hard limestone and hard sandstone 3000 2500 2000 1600 1300
Soft limestone and sandstone 2200 1800 1500 1200 1000
Cinders 800 700 600 5°° 4°°
Specifications for concrete are given in Chapter V, and specifications for reinforced concrete
are given in Chapter VI.
Working Stresses. — The following working stresses have been recommended by the American
Railway Engineering Association for concrete that will develop an average compressive strength
of at least 2000 Ib. per sq. in. when tested in cylinders 8 in. in diameter and 16 in. long and 28 days
ALLOWABLE STRESSES IN REINFORCED CONCRETE. 521
old, under laboratory conditions of manufacture and storage, the mixture being of the same con-
as is used in the field.
Lb. per
K\. In.
Structural steel in tension 14,000
High carbon steel in tension 17,000
Steel in compression, 15 times the compressive stress in the surrounding concrete.
Concrete in bearing where the surface is at least twice the loaded area 700
I'oiirri-u- in direct compression, without reinforcement on lengths not exceeding 6 times
the K-ast width 450
Concrete in direct compression with not less than i per cent nor over 4 per cent longitudinal
reinforcement on lengths not exceeding 12 times the least width 450
Concrete in compression, on extreme fiber in cross bending 750
Concrete in shear, uncombined with tension or compression in the concrete 120
Concrete in shear, where the shearing stress is used as a measure of the web stress 40
Note. — The limit of shearing stresses in the concrete, even when thoroughly reinforced
for shear and diagonal tension, should not exceed 120
Bond for plain bars 80
Bond for drawn wire 40
Bond for deformed bars, depending on the form 100-150
The following working stresses have been recommended by the Committee on Concrete and
Reinforced Concrete of the American Society of Civil Engineers, Proceedings, vol. XXXIX,
February, 1913.
Per cent of com- Lb. per
press! ve strength sq. in.
Structural steel in tension 16,000
Concrete in compression where the surface is at least twice the loaded area 32.5
Concrete for concentric compression on a plain concrete column or pier, the
length of which does not exceed 12 diameters 22.5
Compression on columns with longitudinal reinforcement only, to the
extent of not less than I per cent and not more than 4 per cent; the
length of the column shall not exceed 12 diameters 22.5
Compression on columns with reinforcement of bands, hoops or spirals
having not less than I per cent of the volume of the column, the clear
spacing of the hooping to be not greater than one-sixth of the diameter
of the encased column and preferably not greater than one-tenth, and
in no case more than 2\ in., the ratio of the unsupported length of
column to diameter of hooped core to be not more than 8 27
Compression on columns reinforced with not less than I per cent and not
more than 4 per cent of longitudinal bars and with bands, hoops or
• spirals as above specified, where the ratio of unsupported length of
column to diameter of hooped core is not more than 8 32.625
Compression on extreme fiber of a beam, calculated for constant modulus
of elasticity (stresses adjacent of the supports of continuous beams
may be 15 per cent higher) 32.5
Shear in beams with horizontal reinforcement or without reinforcement ... 2
Shear in beams thoroughly reinforced with web reinforcement (the web
reinforcement exclusive of bent-up bars to be designed to resist two-
thirds the external shear) 6
Shear in beams reinforced with bent-up bars, only 3
Punching shear, only 6
Bond stress between concrete and plain reinforcing bars 4
Bond stress between concrete and drawn wire 2
The modulus of elasticity to be taken for the design as follows:
(a) One-fifteenth that of steel where the strength of the concrete is taken as 2200 Ib. per sq. in.,
or less.
(b) One-twelfth that of steel where the strength of the concrete is taken greater than 2200 Ib.
per sq. in. or less than 2900 Ib. per sq. in.
(c) One-tenth that of steel where the strength of concrete is taken as greater than 2900 Ib.
per sq. in.
In calculating deflection take one-eighth of the modulus of elasticity of steel.
622 ENGINEERING MATERIALS. CHAP. XV.
STANDARD SPECIFICATIONS FOR CEMENT
OF THE
AMERICAN SOCIETY FOR TESTING MATERIALS.
ADOPTED AUGUST 16, 1909.
1. General Observations. These remarks have been prepared with a view of pointing out
the pertinent features of the various requirements and the precautions to be observed in the inter-
pretation of the results of the tests.
2. The Committee would suggest that the acceptance or rejection under these specifications
be based on tests made by an experienced person having the proper means for making the tests.
3. Specific Gravity. Specific gravity is useful in detecting adulteration. The results of
tests of specific gravity are not necessarily conclusive as an indication of the quality of a cement,
but when in combination with the results of other tests may afford valuable indications.
4. Fineness. The sieves should be kept thoroughly dry.
5. Time of Setting. Great care should be exercised to maintain the test pieces under as
uniform conditions as possible. A sudden change or wide range of temperature in the room in
which the tests are made, a very dry or humid atmosphere, and other irregularities vitally affect
the rate of setting.
6. Constancy of Volume. The tests for constancy of volume are divided into two classes,
the first normal, the second accelerated. The latter should be regarded as a precautionary test
only, and not infallible. So many conditions enter into the making and interpreting of it that
it should be used with extreme care.
7. In making the pats the greatest care should be exercised to avoid initial strains due to
molding or to too rapid drying-out during the first twenty-four hours. The pats should be pre-
served under the most uniform conditions possible, and rapid changes of temperature should be
avoided.
8. The failure to meet the requirements of the accelerated tests need not be sufficient cause
for rejection. The cement may, however, be held for twenty-eight days, and a retest made at the
end of that period, using a new sample. Failure to meet the requirements at this time should be
considered sufficient cause for rejection, although in the present state of our knowledge it cannot
be said that such failure necessarily indicates unsoundness, nor can the cement be considered
entirely satisfactory simply because it passes the tests.
SPECIFICATIONS.
1. General Conditions. All cement shall be inspected.
2. Cement may be inspected either at the place of manufacture or on the work.
3. In order to allow ample time for inspecting and testing, the cement should be stored in a
suitable weather-tight building having the floor properly blocked or raised from the ground.
4. The cement shall be stored in such a manner as to permit easy access for proper inspection
and identification of each shipment.
5. Every facility shall be provided by the Contractor and a period of at least twelve days
allowed f.or the inspection and necessary tests.
6. Cement shall be delivered in suitable packages with the brand and name of manufacturer
plainly marked thereon.
7. A bag of cement shall contain 94 pounds of cement net. Each barrel of Portland cement
shall contain 4 bags, and each barrel of natural cement shall contain 3 bags of the above net weight.
8. Cement failing to meet the seven-day requirements may be held awaiting the results of
the twenty-eight-day tests before rejection.
9. All tests shall be made in accordance with the methods proposed by the Committee on
Uniform Tests of Cement of the American Society of Civil Engineers, presented to the Society
January 21, 1903, and amended January 20, 1904, and January 15, 1908, with all subsequent amend-
ments thereto. (See addendum to these specifications.)
10. The acceptance or rejection shall be based on the following requirements:
NATURAL CEMENT.
11. Definition. This term shall be applied to the finely pulverized product resulting from
the calcination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic
acid gas.
12. Fineness. It shall leave by weight a residue of not more than 10 per cent on the No. 100,
and 30 per cent on the No. 200 sieve.
SPECIFICATIONS FOR PORTLAND CEMENT.
13. Time of Setting. It shall not develop initial set in less than ten minutes; and shall not
develop hard set in less than thirty minutes, or in more than three hours.
i j. Tensile Strength. The minimum requirements for tensile strength for briquettes one
s(|ti.tre inch in cross section shall be as follows, and the cement shall show no retrogression in
strength within the periods • specified :
Age. Neat Cement. Strength.
24 hours in moist air 75 lb.
7 days (l day in moist air, 6 days in water) 150 "
28 days ( I " ' 27 ) 250"
One Part Cement, Three Parts Standard Ottawa Sand.
7 days (i day in moist air, 6 days in water) 50 lb.
28 days (i ' 27 ) 125"
15. Constancy of Volume. Pats of neat cement about three inches in diameter, one- half
inch thick at center, tapering to a thin edge, shall be kept in moist air for a period of twenty-four
hours.
(a) A pat is then kept in air at normal temperature.
(b) Another is kept in water maintained as near 70° F. as practicable.
16. These pats are observed at intervals for at least 28 days, and, to satisfactorily pass the
tests, shall remain firm and hard and show no signs of distortion, checking, cracking, or disinte-
grating.
PORTLAND CEMENT.
17. Definition. This term is applied to the finely pulverized product resulting from the
calcination to incipient fusion of an intimate mixture of properly proportioned argillaceous and
calcareous materials, and to which no addition greater than 3 per cent has been made subsequent
to calcination.
18. Specific Gravity. The specific gravity of cement shall not be less than 3.10. Should the
test of cement as received fall betow this requirement, a second test may be made upon a sample
ignited at a low red heat. The loss in weight of the ignited cement shall not exceed 4 per cent.
19. Fineness. It shall leave by weight a residue of not more than 8 per cent on the No. 100,
and not more than 25 per cent on the No. 200 sieve.
20. Time of Setting. It shall not develop initial set in less than thirty minutes; and must
develop hard set in not less than one hour, nor more than ten hours.
21. Tensile Strength. The minimum requirements for tensile strength for briquettes one
square inch in cross section shall be as follows, and the cement shall show no retrogression in
strength within the periods specified:
Age. Neat Cement. Strength.
24 hours in moist air 175 lb.
7 days ( I day in moist air, 6 days in water) 500 "
•28 days (i 27 ) 600"
One Part Cement, Three Parts Standard Ottawa Sand.
7 days (i day in moist air, 6 days in water) 200 lb.
28 days ( I 27 '" ) 275"
22. Constancy of Volume. Pats of neat cement about three inches in diameter, one-half
inch thick at the center, and tapering to a thin edge, shall be kept in moist air for a period of twenty-
four hours.
(a) A pat is then kept in air at normal temperature and observed at intervals for at least 28
days.
(b) Another pat is kept in water maintained as near 70° F. as practicable, and observed at
intervals for at least 28 days.
(c)^ A third pat is exposed in any convenient way in an atmosphere of steam, above boiling
water, in a loosely closed vessel for five hours.
23. These pats, to satisfactorily pass the requirements, shall remain firm and hard, and show
no signs of distortion, checking, cracking, or disintegrating.
24. Sulphuric Acid and Magnesia. The cement shall not contain more than 1.75 per cent
of anhydrous sulphuric acid (SOj), nor more than 4 per cent of magnesia (MgO).
CHAPTER XVI.
STRUCTURAL MECHANICS.
GENERAL NOMENCLATURE. — The following nomenclature will be used for all materials
except reinforced concrete, for which a special notation is given.
A = area of cross section.
/ = length or span.
L = length or span.
b — breadth of rectangular section.
d — depth of section; diameter of rivet.
/ = thickness of plates, etc.
R = radius of circle.
D = diameter of circle.
h = height of wall.
c = distance from neutral axis to extreme fiber.
A = total deformation in length /, or maximum deflection of beams.
5 = unit deformation.
* = horizontal coordinate of elastic curve; variable.
y = vertical coordinate or deflection of elastic curve; variable.
e = eccentricity; efficiency.
I = moment of inertia.
/c = polar moment of inertia.
/ = product of inertia.
S = section modulus.
r = radius of gyration.
P = pitch of rivets.
P = concentrated load or total stress in a member.
/ = unit fiber stress.
fe = unit compressive fiber stress.
ft = unit tensile fiber stress.
/„ = unit shearing fiber stress.
W = total uniformly distributed load; weight of a body.
w = uniformly distributed load per unit of length; load per unit of lengch at a distance
unity from left end for a uniformly varying load; unit internal pressure.
R = reactions at supports.
Mx = moment at any section.
M = maximum moment.
Vx = total shear on any section.
V = maximum total shear.
E = modulus of elasticity.
G = shearing modulus of elasticity.
X = Poisson's ratio.
+ = compressive stress.
— = tensile stress.
525
526 STRUCTURAL MECHANICS. CHAP. XVI.
REINFORCED CONCRETE NOMENCLATURE. Rectangular Beams, Reinforced for
Tension Only.
/, = tensile unit stress in steel, in pounds per square inch.
fe = compressive unit stress in concrete, in pounds per square inch.
E, = modulus of elasticity of steel, in pounds per square inch.
Ee — modulus of elasticity of concrete, in pounds per square inch.
n = elasticity ratio, E, -5- Ec.
M = bending moment, in inch-pounds.
M, = moment of resistance of steel, in inch-pounds.
Me = moment of resistance of concrete, in inch-pounds.
A = area of steel section, in square inches.
b = width of beam, in inches.
d — depth of beam to center of steel reinforcement, in inches.
k = ratio of depth of neutral axis to effective depth, d.
j = ratio of arm of resisting couple to depth, d.
p = steel ratio (not percentage), A -£• bd.
C = total compressive stress in concrete, in pounds.
T = total tensile stress in steel, in pounds.
Tee Beams.
b — width of flange, in inches.
b' = width of stem, in inches.
/ = thickness of flange, in inches.
p = steel ratio (not percentage), A -5- bd.
See also " Rectangular Beams Reinforced for Tension Only."
Rectangular Beams, Reinforced for Compression.
A' = area, of compressive steel, in square inches.
p' = steel ratio for compressive steel, A ' -f- bd.
fs' = unit compressive stress in steel, in pounds per square inch.
C — total compressive stress in concrete, in pounds.
C' = total compressive stress in steel, in pounds.
T = total tensile stress in steel, in pounds.
d' = depth to center of compressive steel, in inches.
2 = depth to resultant of compressive stresses, in inches.
See also " Rectangular Beams Reinforced for Tension Only."
Shear and Bond.
V = total shear in pounds.
/„ = unit shearing stress in concrete, in pounds per square inch.
/„ = unit bonding stress in concrete, in pounds per square inch.
2o = sum of the perimeters of the tension bars, in inches.
s = horizontal spacing of stirrups.
P = total stress carried by one stirrup.
Columns.
A = total net area, in square inches.
A, = area of longitudinal steel, in square inches.
Ae = area of concrete, in square inches.
p — steel ratio, As -f- A.
P = total axial load, in pounds.
DEFINITIONS. :»L'7
DEFINITIONS. — The following definitions will be of service in a study of structural me-
chanics.
Forces. — Forces are concurrent when tin ir lines of action meet in a point; non-concurrent
when tin it lines of action do not meet in a point. Forces are coplanar when they lie in the same
plain-; or non-coplanar when they lie in different planes. Coplanar forces only will be here con-
sidered. A force is fully defined when its amount, its direction, and position are known.
Moment of Forces. — The moment of a force about a point is its tendency to produce rotation
al>out that point, and is the product of the force and the perpendicular distance of the point from
the line of action of the force.
Couple. — A couple is a pair of equal and opposite forces having different lines of action.
The moment of a couple is equal to the product of one of the forces by the distance between the
lines of action of the forces, or the arm of the couple.
Stress. — If a body be conceived to be divided into two parts by a plane traversing it in
any direction, the force exerted between these two parts at the plane of division is an internal
stress. Stress is force distributed over an area in such a way as to be in equilibrium. Stresses
are measured in pounds, tons, etc.
Unit Stress is the measure of intensity of stress. The unit stress at any point is the number
of units of stress acting on a unit of area at that point. Unit stresses are expressed in pounds
per square inch, tons per square foot, etc.
Ultimate Stress. — Ultimate stress is the greatest stress which can be produced in a body
before rupture occurs.
Tension is the name for the stress which tends to prevent the two adjoining parts of a body
from being pulled apart when the body is acted upon by two forces acting away from each other.
Compression is the name of the stress which tends to keep two adjoining parts of a body from
being pushed together under the influence of two forces acting toward each other.
Shear is the name of the stress which tends to keep two adjoining planes of a body from
sliding on each other under the influence of two equal and parallel forces acting in opposite direc-
tions.
Axial Stresses. — When the external forces producing tension or compression act through
the center of a gravity of the body the stresses are uniformly distributed over the area, and the
stresses are axial stresses.
Simple Stress. — If P = the force producing tension, compression, or shear and A = the
area over which the stress is distributed, then
f< = P/A; fe = P/A; f, = P/A,
where /« is tensile stress, fe is compressive stress, and /„ is shearing stress.
Working Stress. — The working stress for any material is the unit stress that has been found
by experiment to be safe to allow for that particular material to give a properly designed struc-
ture. The working stress for any particular structure depends upon the material of which the
structure is built, the loads that the structure is to carry, the accuracy with which the loads and
stresses have been calculated, the possible defects in the material, etc.
Factor of Safety. — The factor of safety is the number by which the ultimate stress must be
divided to give the working stress.
Deformation or Strain is the change in the shape of a body caused by the action of an ex-
ternal force. Deformation or strain is measured in linear units. Deformation may be due to
tension, elongation; due to compression, shortening; or due to shear, detrusion or slipping of one
plane past another.
Elasticity. — Up to a certain stress in an elastic body it has been found by experiment that
stress is proportional to strain. This principle is known as " Hooke's Law." The ability of a
body to return to its original form after deformation is termed elasticity. If the stress in a body
is carried beyond a certain limit the body does not return to its original form, but a permanent
set occurs.
528 STRUCTURAL MECHANICS. CHAP. XVI.
Elastic Limit. — The elastic limit of a material is the highest unit stress to which that material
may be subjected and still return to its original shape when the stress is removed, and is the
limit within which the stresses are directly proportional to the deformations.
Yield Point. — In testing materials a point is reached beyond the elastic limit where unit
elongations increase very rapidly without any or with a very slight increase in unit stress. This
point is indicated by the drop of the scale beam of the testing machine. In steel the yield point
is from three to six thousand pounds per square inch above the elastic limit.
Modulus of Elasticity. — The modulus of elasticity of a material is the constant, which within
the elastic limit expresses the ratio between the unit stress and unit strain or deformation. If
E = modulus of elasticity, P = an axial force; A = cross sectional area of the bar, / = unit
stress = Pf A; A = deformation produced by P in a length /, and 5 = A//; then
E = (PM)/(A//) or E = f/8.
The modulus of elasticity may be defined as that force, were Hooke's law applicable without
limit, which would produce in a bar with a cross section of one square inch a deformation equal
to its original length.
The modulus of elasticity of steel is very closely E = 30,000,000 Ib. per sq. in.; the modulus
of elasticity of timber is approximately E = 1,500,000 Ib. per sq. in.; while the modulus of elas-
ticity of concrete varies from E = 1,500,000 Ib. per sq. in. to E = 3,000,000 Ib. per sq. in. with
an average value of E = 2,000,000 Ib. per sq. in.
Shearing Modulus of Elasticity. — The shearing modulus of elasticity, also called the modulus
of rigidity, is the modulus expressing the ratio between unit shearing stress and unit shearing
strain. The value of shearing modulus of elasticity for steel is about f of the value of E, or
G = 12,000,000 Ib. per sq. in.
Poisson's Ratio. — Direct stress produces a strain in its own direction and an opposite kind
of strain in every direction perpendicular to its own. For example a bar under tensile stress
extends longitudinally and contracts laterally. Poisson's ratio is the ratio of lateral strain to
longitudinal strain, and is a constant below the elastic limit. For steel Poisson's ratio is ^ to £,
while for concrete it is from | to xV
Rupture Strength. — In testing steel the cross sectional area rapidly decreases beyond the
ultimate stress and if the rupture stress be divided by the original cross sectional area the unit
stress at rupture will be less than the ultimate stress.
Ultimate Deformation. — The ultimate deformation is the total deformation in a prescribed
length, commonly 8 inches, or 2 inches. It is usually expressed in per cent for a length of 8 inches,
or of 2 inches.
Work or Resilience in a Bar. — The amount of work that can be stored up in a body under
stress within the elastic limit is called resilience or " internal work." When the external force
has been gradually applied all the work may be recovered when the force is removed.
From the law of conservation of energy the external work due to the force is equal to the
resilience or internal work. If a load P is supported at the lower end of a bar without weight, hav-
ing a length / and a cross sectional area A ; then the external work will be |P-A, where A = the
total deformation, and the internal work or resilience will be
when/ = elastic limit of the material then I/V-E is termed the Modulus of Resilience.
Stresses due to Sudden Loads. — In a bar acted on by a static load, P, gradually applied,
the total resilience will be K = fA.P. If the load P is suddenly applied we will have K = A.P,
from which it is seen that the stress produced by a sudden load is twice that produced by a load
gradually applied.
STRESSES IN BEAMS.
Impact. — The stresses due to moving loads arc greater than the stresses due to loads at rest.
Tin- in. ir. iso in stress of the moving load over tin lo.nl at rest is called impact. For a discussion
of impact stresses in railway bridges see page 161, Chapter IV.
STRESSES IN BEAMS. — When a straight lieam or bar is supported near the ends and
c.i i rics loads or forces applied transverse to the length of the axis of the beam or bar, the axis
of the member assumes a curve. The transverse loads or forces are carried by flexure, which is a
comliiii.it ion of the three simple stresses of tension, compression and shear. For example, a simple
l>e.mi renting horizontally on supports carries a concentrated load. The fibers on the lower or
convex side of the beam will be elongated and are therefore in tension, while the fibers on the
upper or concave side are shortened and arc therefore in compression. Shear is taking place
between each vertical plane of the beam and the plane adjoining between the load and each
support. Since the longitudinal stresses in a simple beam vary from a maximum rump re onion
on the concave side to a maximum tension on the convex side, the stresses will pass through
zero on some plane, called the neutral plane or axis. Also since the fibers on each side of the
neutral axis carry different amounts of stress, they will lengthen or shorten different amounts,
and there will therefore be horizontal shearing stresses as well as vertical shearing stresses.
Neutral Surface and Neutral Axis. — Under flexure a beam' is curved, and the fibers on the
concave side are in compression while the fibers on the convex side are in tension. The neutral
surface is a surface on which the fibers have zero stress, and the neutral axis is the trace of this
plane on any longitudinal section of the beam. In a simple horizontal beam carrying vertical
loads the neutral axis passes through the center of gravity of the cross section of the beam, for a
rectangular beam the neutral axis is at half the height of the beam. Where a beam carries loads
that are not at right angles to the neutral axis of the beam, the beam is in equilibrium under
flexure and direct stress, and the neutral axis or line of zero stress will not pass through the center
of gravity of the cross section of the beam, and may fall entirely outside the beam. A bar carrying
simple tension or compression may be considered as a beam in which the neutral axis is at an
infinite distance from the center of gravity of the cross section of the beam.
Reactions. — For any structure to be in equilibrium, (i) the sum of the horizontal components
of all forces acting on the beam must equal zero, (2) the sum of the vertical components of all
forces acting on the beam must equal zero, and (3) the sum of the moments about any point of
all forces acting on the beam must be equal to zero. Having the loads given the reactions can
be calculated by applying the three conditions of equilibrium.
Vertical Shear. — The vertical shear in a beam is equal to the algebraic sum of the forces
(reaction minus the loads) on the left of the section considered.
. Bending Moment. — The bending moment at any section of a beam is equal to the algebraic
sum of the moments of the reaction and the loads on the left of the section.
Relations between Shear and Bending Moment. — In a simple beam carrying vertical loads
the shear is a maximum at the supports and passes through zero at some intermediate point in
the beam. The bending moment is zero at the supports and is a maximum at some intermediate
point in the beam. The shear is the algebraic sum of all the forces on the left of a section, while
the bending moment may be defined as the algebraic sum of all the shearing stresses on the left
of the section. The definite integral of the loads to the left of the section equals the shear at the
section, and the definite integral of the shear to the left of the section is equal to the bending
, moment at the section. From the above it will be seen that maximum bending moment will
come at the point of zero shear.
Formulas for Flexure. — Applying the conditions for static equilibrium to any cross section
of a beam we have, (i) Sum of Tensile Stresses = Sum of Compressive Stresses; (2) Resisting
Shear = Vertical Shear; (3) Resisting Moment = Bending Moment.
Resisting Shear. — If the shearing stresses are uniformly distributed the shearing stress
will be
/. = VIA. d)
35
530 STRUCTURAL MECHANICS. CHAP. XVI.
The shearing stresses are not uniformly distributed and for a rectangular beam /„ = %V/A,
while in a circular beam/,, = $V/A.
Resisting Moment. — The bending moment at any section is resisted by the moment of the
tensile and compressive stresses which act as a couple with an arm equal to the distance between
the centroids of the tensile and compressive stresses. The moment of this internal couple is
called the resisting moment. If / = the unit stress at any extreme fiber on the surface of the
beam due to bending moment, c = distance from that fiber to the neutral axis, and M = the
bending moment, or the resisting moment, then
,, /•/ , M-c
M = J—, or f = ~Y~ '
where 7 = the moment of inertia of the cross section of the beam.
Moment of Inertia. — The moment of inertia of any area about any axis is equal to the sum
of the products obtained by multiplying each differential area, dA, by z2, the square of the distance
of each elementary area from the axis, 7 = ~Lz2-dA. The moment of inertia of any section is a
minimum when the axis passes through the center of gravity of the cross section.
Section Modulus. — In designing beams it is convenient to use the ratio S = I/c, so that
M = f'S, or f = M/S. The ratio 5 is known as the section modulus.
Tables of Moments of Inertia and Section Modulus. — Values of moment of inertia, 7, and
section modulus, S, for different sections are given on pages 548 to 551, inclusive. Values of
moment of inertia and section modulus of structural shapes are given in Part II.
Deflection of Beams. — In a simple beam carrying vertical loads the upper fibers are shortened
and the lower fibers are lengthened, while the fibers on the neutral axis are not changed in length
but the neutral axis assumed the form of a curve. The differential equation of the elastic curve
of a horizontal beam carrying vertical loads will be
*y - JL i«\
dy? E-I'
Substituting proper values of E, I and M, integrating twice and giving proper values to the
constants of integration, the values y, or the deflection may be calculated for any point in the
beam. The equation of the elastic curve of beams of various types are given on pages 531 to
547, inclusive.
The maximum bending moments and shears in beams due to moving concentrated loads are
given on page 542.
The moments and shears in continuous beams are given on page 543, page 544 and page 545.
Formulas for stresses in reinforced concrete beams are given on page 546, and stresses in
columns, safe working stresses, and safe loads on slabs are given on page 547.
SIMPLE AND COMBINED STRESSES.
r,3i
Tension.
p
m
JL..JSL
P
Unit tension on m-m,
Total tension on m-m,
Area For q/'yen stress,
p
A = -f- j (c)
4
where A : area section m-m
(b)
2. AXIAL COMPRESSION.
I p Unit compression onm-m,
M
HL.
m Total compression on m-m,
P--fcA (b)
Ared for given stress,
A=f
fc
(0
where A -area of section m-m.
3. SIMPLE SHEAR.
Unit shear on m-m,
(*)
P ^
m
Tola f shear onm-m,
m__ P=fyA, (b)
' P Area for given stress,
p
fy
where A=area section m-m
4. DIAGONAL frXBXX'faWUMKr.
Unit shear on n-n,
f=££sin?6^ft
Unit tensionon n-n.
i--.
I
.M~. . JD Max. unit shear on n-n,
(a)
(t>)
(c)
*fa; 0=45°;
flax, unit tension on n-n,
where %=£, A* area ofsectionm-m.
5.D/A60NAL
P
V
\
m
4
Unit she dr on n-n,
f:2j5ir??d-f£5in?0; (a)
Unit compression on n-n,
f^sin'0=£sin*0 (b)
7? /lax. unit shear on n-n,
Max. unitcompressiononnn.
S/7 f*£; 0=90°; (dj
wfierefc--£t A = area section m-m .
flax, unit shear on n-n;
4L
"777'
rlax.unft tensionon n-n,
m
Tr * '
Sk
y5' Jldx.unit compression on o-O;
n f'/(#f7f**»^*)
L I t J Lly
where Ft*j,fr=jj ,A*arc3sec.m-m
!DlA60t1AL5TR[5$tt:
rlax.unit shear on n-n;
X
* ^ tlax.unit compression on n-n,
P***i
_
flax unit tension on n-n,
^(fifl*"**H&
0 CL 4J ft
where fc=j;fy-j;A-3re3sec.m-m.
^ fa qu/red Unit stress on CE.
f\ lay off AO and SO- unit
stresses on (D ID f. fa*
a>F*nd n'f parallel to M
anJM Thenrtwnitetr-
/ w/t 'shear. E///psc/$
/ocvs off for at/wi-
ve s of0.
532
STRUCTURAL MECHANICS.
CHAP. XVI.
r
i
JL
P
T
Modulus of Elasticity,
PI
-
(3)
(c)
where A =ared sect/on m-m
\ Tbta/ deformation ,
rrj \ ^E2*AE
(/nit deformat/b/j,
P
>m
'/77
Modulus of Elasticity,
,t Q.-f-f/A.n.
A ~S ~d/l A A
"% Total deformation,
A=Gl=AO
(JmtdeFormatiop,
(b)
(c)
where A=areasectionm-m.
Percent e/ongahbr>,
^Y'/OO (a)
Percent reduction of are a,
/OO (b)
m_
r^A?
±A'
A
/= Original length.
2'= length at failure.
A= Original section area.
A '=Area ruptured sect/on.
12. THinPjpesAfiD CYu/iDER5://imN/v. PRESSURE.
Longitudinal rupture, sec.m-fn,
psvsi.f,*0 (3)
Transverse rupture, sec. n-n.
w= unit internal pressure.
8oth iongitudinaland trans-
verse s tresses are independ
ant of the form oF the ends.
D-
13. $r/?E55C5iH dfiGLE RIVETED UP JOINTS.
Unit tension onp/ate,
ft=P+(p-dH (a)
Unit compressionon rivet,
fc=P+td (b)
Unit shear on rivet,
(C)
14. STRESSES in DOUBLE R/veTFoLApJoms.
p-\ ---- \\zr
for longitudinal Joints in
pipes or cylinders P=£:
D=diam.pipe or cylinder.
Unit tension on plate,
-±-p Unit compression on rivet,
fc=P+^td (b)
unit shear on r/Vet,
For lonqil'i/d/nal/oinbin pipe
or cylinder s P^jwfip, (d)
J)-c/jdm. ofp/pe or cylinder.
15. DESIGN or SJMGLE RIVETED LAP JO/NTS.
5ee figure above. For Butt Joints see ChaptXYII
Most efficient joint for cy finders andpipe,
j 4£/. „ /i.fcl
; Cl -- ftf/y/'ry/ff
16. DESIGH OF DOUBLE RIVETED LAP JO/NTS.
See Figure above.
tfoste FFic tent joint For cylinders and pipe,
(3) 0J (C) (d)
Most eFficient joint For given thickness p/ate;
(e) (fj (g)
For/ointsw'tti more than two rows of meb see Cndpt.XYII.
(a) (bj (c) (d)
MosteFFicientjoint forgiven th/cknessplate ,
(e) (F) (q)
Forjoints with more thsntwo rows of riwts See ChaptXY//
1-LKXl KAL STKKSSKS.
Fiber stress due toa given moment in
flomenttocwseagivenfiberstressihagivenbeam,
ff'^f (b)
Section modulus for given moment and fiber stress,
liomentofinerta forgiven moment, fiberstress
and distance to extreme fiber,
I= £JT (d)
Id.
Differentialeqvdtfort from *hich equation of elastic
******* &%,-#* <*)
Jbdetermbeelasticcwve^AenTa/K/ fare const-
ant, integrate twice determining constants of
integration by substituting known ra/ues of slope
anddef/ection and corresponding values ofa .
Theequation of curve change sdt every concen-
trated had but is same throughout/or uniform
load or for uniform// varying had.
20.
Average unitshearing stress,
c V
rv=— » (a)
A
*T'j ,„ '. f l/nithorizonfalshearing stress,
rteutralAx,s- (/0fJgitudinahLr)
Fy ==r "fa, t fb)
Oi\ centroidof ,
shaded area fastac/cmomentofarea,
at>OYesecti'onconsidered,aboot
neucrafaxis. fbrhorizonta/sfyearatm-m, 9n =•
area of shaded portionmv/tip/iecfbyz, the
distance toits centroi'cf. Themax. un)6 horiz-
ontal shear w iff occur st the neutral axis.
The max. unithorizonfat 'shear for a rectang-
ular beam -^ average unit shear, for circv/ar
section^dndforanl-beammaybeasmuch
as E ^ times average unit shear.
For rolled or bvi/t I-beams tne max. unit
horizontal shear very nearly eguals Me fotaf
vertica I shear divided bf area of web.
Straight Line Formula,
'£**-0Z
A r
For constants oc and 13 see Tab/elXpaqeSO.
f?<3nt<ine's(Gordons)Formu/a,
£. «' ' &
A
For constants CCandftseeTabteJXpageSO.
Euler's Formula,
(c)
A «r*
According to Merriman cc "has the
following values;
Both ends hinged, tz"=rrz
On e end fixed and one hinged, cc "- ?jff *
Both ends fixed, oc tt=4rr?
In Eu/er 's Formula P= ultimate strength.
El. TORSIOH OF 5HAFTS.
Solid round shafts,
H
P
= horse power.
: rev. per minute.
(a)
(b)
(0
5 olid sguare shafts,
Pe=£d3f (approx.) (d)
(f)
IfiFl
22: STRESSES Itt HOOKS: Approximate Solution.
E: | | Maximum tension,
**A*I <3)
where A = area of sect ion
m-m, e - distance from line
of action ofloadtfto cent-
roidofmm, c* distance
from centroid to extreme
fiber on tension sicfe>r=
moment of inertia of sec-
tion m-m about axis thr-
ough cenlroiof. M
For exact solution see 'SlocumandHancoc^pldl.
^ /
534
STRUCTURAL MECHANICS.
CHAP. XVI.
/2 ///f OiRDERS: See also Chapter XVII
f I) flomenl all carried by Flanges,
M=A'FFh (<a)
(ZjOne-eiqhtharea oFweb a variable as Mange
ares. M-(A',*&A»)Fh (t>)
(3) Moment ofi'nertia oFnet sect/on,
M*g' (0
(4)t1omenkoFinerl/a oF gross section.
= netareaofonefJange anc/gross area
of web, I and I = moment ofinerlia oFqross
and ofnet section, h -disf. $tci oF Flanges.
24UrtSrnmTI?IC4LLOAD50ri6fAH5Jpproxim<}te5olution.
Fl-max moment For vertical loads.
I*- moment oFinertid,axis2-2
. .flax compressive Fiber stress,
25. ECCEfiTRICLOAD50flPRI5r15:5eealsoChapt. V.
'• +e\.P
kiily
Z6.FL EXURE/MD DIRECT 5TRE5S.
Flexure and compression, F--J-
A
Flexure and tension, , .^ ^ frfp^fef
k- /OForbothendshinged, 24 For one end hinged
and one Fixed, 5? For both ends Fixed>
Approximate Formula, F-jJ: -~; (c,
For direct stress either tension orcompression.
M may be due to weight oFmemberorto external load.
27. TRUE 5TRE55.
Stressatm, p.P.Mc .Stressatm')F.P Me .
f' '
In = moment 'oF inertia oFsectionm-maboutdxisn-n.
A =area oF section m-m'.
Line oF action oFre suit ant, x=firP ;
IF there is tension at m'and section tvillnotMeitJht
stress at m '=0 anal 3tm=^P(j-/) For rectanq. sect.
-*•
Fn Fz,& Fj- apparent unit stresses
ttStt ^true unit stresses.
(b)
/f any stress is tension chan-
ge its sign in above Formulas.
/y=j For steel and wrought iron.
A --jForcdstiron.
\ =Poiss on's Ratio. A ^r0 For concrete .
28. CYLINDRICAL ROLLERS.
Unit Stress Forgiven load ^JSIV^l} (3)
and roller, ~L63LzDu ,
Length Forgiven load,diam. 3W f£7f
and.unit stress, L=ZFDLlFJJ f>
Total load For given roller ... 2/nffZfJz/r
i i i rr — 5"' ft I -=• I • (t-j
and unit stress. 5 L CJ't
L oad per unit length For w=-DFf—l^ IH)
given roller and unit stress. 5 LEJ
D=diam. oF roller. L= length oF roller,
E= modulus oF elasticity.
29. THICK PIPES AttD CYllHDERS-.lntemal Pressure.
Maximum unit tension,
Maximum unit compression,
fc*w (b)
Thickness For given pressure,
unit tension and internal radius.
w= unit internal pressure.
WORK OF RESILIENCE.
585
30. 5TRC5Sf5lfirLATPLATf5 -(JfilFORflLOAD.
Gircu/ar Plate;
Circumference fixed,
' 64 tz '
Circumference supported,
c. IJ7wr'
'
Rectangular Plate,
Circumference fixed,
c.
"
Circumference supported,
Unit stress is about j
that for circumference fixed.
Square Plates,
Circumference fixed,
f- wa*.
~ > 1-9 >
Circumference supported,
(/nit stress is about j that
for circumference fixed.
See Chapter VIII, p. W and fable 115.
BARS.
Work done in stressing a bar below elastic
limit. From Otoftor Otof,
From P,toPzor fjto £,
K-iPA-l/Wi-ltFA-WAl; It,)
BEAMS.
Deflection under one loaof
Deflection at any point,
y,ft
(d)
where M* = moment at any point due to
given loadincj and M = momentat any
point due to a unit load placed at the
point at which the deflection is rey-
uired.
Y
r
V r
y y
i *
CEHTROID (CEVTER OF GRAVITY).
General formulas;
»%•*?< »
SA UJL I ).&£.£&, <b>
35. flOMEnTOFlriERTIA AfID PRODUCT OF IflERTIA.
'i
.A^; ' /6A A
*.j..+ Fig I. Structural sections canbe
Y divided into finite elements
? . . . .• -chepropert/es of which are
known. The n(a) and ft>) become
A
Static moment about given axis
Y
V
d,ory
1
8A General Formulas,
AreaA -Jf
— Trans formation Formulas,
centroid- X
beordinates of their centroids.
O by symmetry.
y-
entroidoftrapesoid
f * /• / *//» »
rig 4. Centro/dofjnytwarejs.
Axes are designated by subscripts .
536
STRUCTURAL MECHANICS.
CHAP. XVI.
34 • CAtfTJL£V£J? feAM WJTH LOAD}PjAT FREE END-
End Reaction, J?? ~ P-
Shear at any po/nf; Yx~P-
Moment at any point,
Maximum Moment", //- /*/•
Equation oFE/asfic Curve,
Beam
Shear
Diagram
Moment
Diagram
Elastic
y'f Curve •
55 -CANTILEVER BEAM WITH UNIFORM LOAD, W PER UHIT OF LENGTH-
w per unit of lengfh^
Beam
Moment
Diagram
„ Elastic
"/• Curve
?2 = wl •
Shear at any point Px- wx-
Max- Shearj I/= wl'
Moment at any point, Mx~ ^jjr
Max - Moment, at Right Support, M-
Equation of Elastic Curve
•CANTILEVEK BEAM W/TH COHCSHTKATED LOAD,P, AT ANY POIHT^
End Reaction, R? = P •
Shear hetween P and Support - P'
Moment between PandSupport=P(x-kl)
Max- Moment, at Right Support* P( l~kl)
Equation of Elastic Curve between P£/?z
Shear
^ ' A'
X! _^J__
Diagram
•£»
^ Moment
^7 Diagram
Elastic
Curve
Deflection under Load, A'=
Max- Deflection, A = (2-3k +k 3)
Diagram
A
Moment
Diagram
Elastic
% Curve
BEAM W/TH VAKJABL? LOAD
End Reaction, P? — ^^
Shear at any point, ^
Max- Shear, Y= ^L-. .
Moment at any point, Mx - —g- •
Max- Moment, M= 2^.
Equation of Elastic Curve
Max- De flee ffrn, ^=
STRESSES IN BEAMS.
537
38.5JMPLE Be AH- CONCENTRATED LOAD AT THC
End Reactions; tfj~R?*
Shear at any point:
.*,( ! J
~~j&~;~~
*
ri£
4*
Diagram
Moment
Diagram
Curve
Max- Shear, V-%.
Moment at any point *
Between />/ &P;MX °R,x - -§*•
Befwetn P& &; Mx ~X#-P(Xr&ȣ(l-xJ
Max- Moment,- M=^Pl, occurs atx-£.
f/ash'c Curve and Deflections •
Sefween R, £P>y*&f (4x3-3l*x) -
Set ween P & Rf; symmetrical abouf center.
Max- Deflection; A=4 £** % = i .
48 ET' 2
39 -SJMPLE BEAM - CONCENTRATED LOAD AT ANY Poittr-
Beam
£,
\ I
"I
End Reactions: R/ -
Shear at any po/'nf:
Between R,&P, K
Between P£R2, Yx *Rk
Max- 5fiear; fora^,^, V=
Moment at any point •
Between R, £ P; Mx=R,x =
Between P£R2; Mx =R,x-P(xra)=
MdxMcment,~M=R,a= ^^a; occurs at X" a-
Elastic Curve and Deflections:
BehveenP,&P;y='.
Between P£$;y, =
*'
t
^
-A-
t*
40-5JMPLC BEAM -Two £OUAL CoMCEMTRATeo LCA£>S,SYMMETK/CALLY PLACED-
End Reactions ; R, =RZ =P-
Shear at any point:
Between R, andleftP; VX=P-
Between L oads; yx = 0-
Between right P and Rf, l/x~P'
Max- Shear, Y^P-
Momenf at anypo/nf:
Between R, andleftP; Mx *Px •
Between Loads; Mx=R,x-P(x-a) "Pa-
Max- Momenf; M= Pa •
Elastic Curve £ 0e flections :
Diagram
Moment
8efweenJ?,&/eft P; y- & (3Za-3af-x*)-
pfj
Between Loads ;yf **-£•. (3lx-3xf-a*) •
vCl
Between right P& Re ; symmetrical with kftlodd&R, •
Max- Deflection; A "zjpr (3
538
STRUCTURAL MECHANICS.
CHAP. XVI.
yper unit length-.
4f. SIMPLE BEAM- UNIFORM LOAD-
Beam
Shear
Diagram
Moment
Diagram
Elastic
Curve
End Reactions • RI =RZ - *^r •
Shear at any point: V* - ^5- - wx •
Max- Shear ; V- *~ ; occurs <3tesch support
Moment at any point • M* = ^TX - j wx f
Max- Moment; M=£-wl2, occurs at center-
Elastic Curve and Deflections :
Max- De Fleet ion; A *j rf; T=
42. SIMPLE BEAM- TRIAN&ULAR LOAD WITH MAX/MUM AT THE CEHTFR •
R,
M-
Beam
Shear
wl Diagram
Moment
Diagram
Elastic
Curve
Total Load =
End Reactions: R, *R? = -^
5hear at any point:
between R,£ Center; Vx = *{$•-
Between Center £ ft; l/x = tvfj-l*-
Max Shear; /- ^ wl^ occurs af • supports-
Moment at any point :
Between $ and Center; MX "meff- *-
Between Center £f??; Mx =
Max- Moment; M=jJ4 wl3; occurs 3t center-
Elastic Curve and Deflections:
Between/?, & 'Center: y= ^rf&- &- £i
' ?4EIL 2 £ J6J
Between Center & R?', Symmetrical-
Max-DeFtecffon; A
Beam
43- SIMPLE BEAM- TRIANGULAR LOAD WITH MAXIMUM AT RIGHT EMD-
Total Load = ^ •
End Reactions :£j =(-wl2; Rz ~jwlz-
Shear at any point: P* ~ %jff-jf ~x*J
Max- Shear •/ V=jwZ?ocarrs af righf svpporf-
Moment at any point: Mx = -g'fZ^-x*}-
Max-Moment; M=0-064tvl3, occurs at 2=0-5774 1-
Elastic Curve and Deflections :
'1=0-5774 1 \
> «
5hear
Diagram
, Moment
~M Dfagram
Efo'sticCurve
Max- Deflection; A =
44-S/MPLe
y-^>
Beam
Shear
Diagram
Moment
Diagram
Elastic Curve-
LOAD W/TH MAXIMUM AT KfffHT END -
Total Load = w,l -i- ^- •
End React ions =8,=jfa +
Shear at any point: Vx ~ w,
Max- Shear -f V" jrfa/ +JWZ l)> occurs atrighf support-
Moment at any porn f; Mx ** ^(ix-X^+^Clx -xz)
Max- Momenf; M=(wfll-™ l*)£- (Approx-)
Elastic Curve and DefJecf/osis : t
~" J0~30
STRESSES IN BEAMS.
45.BfAM
w per unit /« not ft
Shear
Diagram*
Moment
Diagram
Elastic
Curve
SUPPORT - UffiFORM LOAD-
Reactions • RI -jwZ-jiwmffijjRi
Shear at any point f
Between R, £ Rf ; Vx - R, - \
Between Rt and End; Vx "
Mo men t dt any point:
Between P./ &Pf;Mx -fix, - i
Between Rf £Fnd;Mx s ^(^ .. .v
Max- Positive Moment; M* /%; occurs when x*
Elasftc Curvff and Def/ecfions :
Between fy&fay
4 6- BE AM OvER-HAHG/ftff Offf 5UPPORT -C0ffCeHTRATf£> L0AD AT Affy_
Reactions; R/* —
Beam
Shear
Diagram
Moment
Diagram
Elastic Curve
Shear at any point:
Be f ween f, &P, : yx =k
Between R? &%; Yx •
Moment at any point :
Between P.,£P,; Mx
Between P,£P.?; Mx •
Between Rt»
i J
? -f} (3 +xz-l)
47 -BEAM OVER-
tv per unit length
-^
U£A£4*-Mi
IA|;^| >to-
xrT^+TTv '
-w
BOTH SUPPORTS - UM/FORM LOAD •
Reactions: Ri-fflfm+l) -nyj R? =2iUn
Beam Shear at any point :
Between /eft end & P,i / Px = wfm -xj
Between RI& fa ;Vx s P./ -wfrn+Xt)
Shear Between Rz £ right end; f* = w(n-Xs.
Diagram Max -Shear; P" wm, or £/-wrri'
Moment at any point:
Moment *J™en K,£*fsMx-t
Diagram Between Rz& right end, •
Max- Positive Moment; M*R, f~, -m), occurs af*t
Elastic Max- Negative Moments;M=j wm'atRi; ff's?
Curve Points oFConfraf/exufVfXo =f£i.-nr)2:1/f&)*+ Zfr
* * Iff * ft tt/J ' -m-
= j:
„
~
48- BE AM
P,]L_Rr,
BOTH SUPPORTS -Two EXTERIOR CowCftfTKATte LOADS •
Beam ^actions. R,=
Shear at any point:
Shear
Diagram
Moment
Diagram
Elastic
Curve
Moment at any point:
Between fiKR,; Mx **P,fm-xJ
Between R, & Kt ; Mx = P,m +fa-
Between Rf£Pf; M* = Pz(/7-x3
Moment at Ri;M=P,m; at Rf>
STRUCTURAL MECHANICS.
CHAP. XVI.
FIXED AT ONE END AND SUPPORTED AT &TJIER- CONCENTRATED LOAD_AT ANY POINT-
End Reactions :£ -j
Pa
R
Beam
5hear
Shear at any pofnt:BetHeenRj& %¥,(=?.,; between P£ &, i
,
Max- Positive Moment :M=f?, a, occurs under had-
Max- Negative Moment: M=fi l-P(l-a), occurs at fixed end-
Point if Contra flexure: Xf-
Elastic Curve & Deflections :
.. .
z
Between PXR^y^
„ D/aaram i*nwr«&;y-&/LKVi-*i*m~*n<f~*V
RZ fora=HJ4l;Max-Deff- A*M09fffcfcwn under bad-
JF P Js A MOVING LOAD:
Absolute End Reactions:
RrP, occurs when a- 0;&=P, occurs when 3-1-
Absolute Maximum Shears:
Moment"
Elastic
Curve
Absolute Maximum Moments:
Max- Moment !s Negative and is M= 0-1925 PI; occurs
gf fixed end when 3= 0-5774- 1-
Absolute Maximum DeFlecfiffn :
A =0-009#£L3,occurs underload when
50 -BEAM FIXED AT ONE END AND SUPPORTED AT OTHER - UNIFORM LOAD
w per unif Jengfh
Beam
M>
tfi-t^m %far
Jimifei^SsH Di3*ram
-M \
Moment
Diagram
Elasficforve
End Reactions : P, =-gwl; fo~-g\
Shear at any point : V*=w (f-2 ~ x) •
Max- Shear; y=jrtvl, occurs #f Tight support.
Moment at any point: Mx=wxfg'l~£x)
Max- Positive Momenf;M=}2g wlf occurs sfx=§-Z •
Max-NegafiveMemenf; M~ # 'wl; incurs ai '"right 'support-
Point of 'Contra 'flexure •; X0 =jj: I •
Elastic Curve and Deflections:
= 0-0054 -, X=
S/'BEAM FIXED AT ONE END SUPPORTED
-CwcENrxATED LOAD AT CENTER-
-J
I
\^-M
y-i
Seam
Shear
Diagram
Moment
Diagram
Elastic
Curve
End Reactions: Rj=^P;
Shear at any point:
Between fij&P; ¥**£?;
Max- Shear; V=%P, occurs at £2 •
Moment at any point :
Between P., £P;Mx=%P;£etwffnP£J?z ;MX ^Pl-fePx
Max- Positive Moment: M=jj> PZ, occurs under Joad-
Max-Hegafivf Moment: M'-fcPZ, occurs at fixed end-
Elastic Curve £ Pffffect/'ens '
Between P.,£P; y=£jjj (5x?-3Z*)-
Between PSX
STRESSES IN BEAMS.
Ml
52. BEAM FIXED AT &OTH FNDS - UNJFOKM LOAD-
End Reactions: Ria#e"£wl •
Shear at any point: Y* ** j>wl- tvx •
Max- Shear; Y°£wl, occurs at supports •
Moment at any point: M* " ^fal'+lx-x*) •
Max- Positive Moment; Mafiwl* occurs ar center-
Max- Negative Moment; M'^fe wl* occurs at supports-
Points of Contra flexure; x,-0-?!15 1; xi= 0-7887 1-
Elastic Curve and Deflections :
53 -BEAM F/x£0 AT BOTH EMDS - COMC£NTKAT£D LOAD AT
Seam
Shear
Diagram
Moment
Diagram
Elastic
Curve
End Reactions: RI=RZ'=-^P-
Shear at any point: Y* =jP- Max- 5hear, Y= jP'
Moment at any point:
Between R, & P; Mx=i
Between P&R^', Mx =£P(%Z-x)-
Max- Positive Moment; M= £Pl, occurs at center-
Max-Hegafive Moment ;M -jrPl ; occurs at supports •
Points of Contra f/exure; x0=^-j Xg^^Z'
Elastic Curve and De flections :
Between Rj £P; y- JfJ^x-f-g'l)'
Between P&R?; Symmetrical-
/ D7& 7
Js^7v''-Z'a'F'
54'B£AM FIXED AT BOTH ENDS- ConcenTRATeo LOAD. AT ANY POJHT^-,
End Reactions :Rj=t
z»
Shear at any point: Between Rj <&P; Vjc*
Max- Shear; V=Rj rora<b; ?=& for <=?> b •
Moment df any point: 3^ jtf,
Negative Moments at Supports; M,--P "py Mg="P ~J*'
Between R,&P; Mx =R,x+M,' T Hote that M, carries
Between P£t*;Mx=RtXi+M,-P(xj-d) / a minus s/ffn-
MaxPosifiveMomenf:M=Rla+M,; occurs under load-
Max-ffegafive Moments occur at supports: See^bove-
Points of Contra f/exirre;Xff - J^TA > Xo^Z*
Elastic Curve and Pef/ecfions :
Between R,&P;
r^ji"-p,f » nsfx-a^~* i 7
Between P and R*; y,~~^tl±Jrr^f-'l'^dt~^dXroxJ-
Beam
Shear
Diagram
Moment
Diagram
Hsx-Def/ ;when a(b', A--
•Xj
IF P Is A Moviffs LOAD:
Absolute Max- 5hf3rs;5*P, occurs atRi tvhena°0;afRi when a* I •
Elastic Mto/ufe rfax-f/egative Moment; ft, =zjPl; occurs when a*j Z- •
Curve AksoIofvM3xt/«g9fivsMomenfjMz='jjPl} occurs when a "f- 1 •
Abso/uff Max- Positive Mfment;Ms ^-Pl;gccurs whsn
occurs at Z
Absolute Max- Def fection; Asj5rPJi } occurs when 3" —
542
STRUCTURAL MECHANICS.
CHAP. XVI.
55. MAXIMUM SHEARS AMD MOMEHTS in SIMPLE. BEAMS FOR MOVIHG COHCEMTRATE.D LOADS.
Criterion For Maximum Shear.
The maximum shear due to moving concentrated loads will occur at one support when one
oFthe loads isat that supportand will equal the total reaction. The load qivinq the maximum
must be determined by trial.
Criterion For Maximum Moment.
The maximum moment due to moving concentrated loads will occur under one of the
loads when that load is as far From one end as the center of gravity of all the loads on the
beam is from the other enc/. The load giving the greatest maximum must be Found by trial.
For beams Fixed at one orbothends and carry ing one load, see 49and54, In this chapter.
a.OftELOAD.
X
Max.Shear, X=0; V=P; at/?,.
Max.Moment, X=^i M=+PL; at P.
b. Two EQUAL L OADS.
®
2
Max.%ear,X=0; V=P+P1-^- ; atR,
7 t» £i'*
/Fa is greater than 0.5862tone load gives max. /lasiha.
c. THREE EQUAL LOADS, EQUALLY SPACED.
a 3
d. FOUR EQUAL LOADS}EQUALLY SPACED.
0
; atR,
Max.Shear, X--a;
Max-Moment, /^l;
IFais greater than O.MOljtwo loads givemax.tlaslnb.
Max.5hear.
y=4P±
Max.Momenk,X*l(l-L);
atR.
$S*tZ>
I Fa is greater than 0.26B2, three loads give max. Mas in c,
e. Two UHEQUAL LOADS.
a I
F. Two EQUAL Lo ADS AfioOriE SMALLER LOAD.
a b ,
.
©
\2 3
, X=0;
rlaxthear, X=a; V*
Max.moment may occur For one load as in a.
Sia*. moment may occur For two egual loads asinb.
STKKSSKS IN (OMINTors UKAMS.
56. ComittUOUS BEAMS, UniFORrlLMDS, COfiSTAHTMOWNTOFlHfRJIA AflDflODULuSOFf LAST/CITY.
Shear, \V'
'sfeksi HI
unitlengtfy
Span, ^ i^span
Length, ^ I,
Support, I 2
Reaction, R, RI
/1oment,f1, A
flLj
3
A
*----*! i
.~fff£3R9GL.. i*?^! sJ?a.n.
in I inn
fin., /%
ml
Relation between momentsat supports for the n^ and (ntlj — spans,
Shear to right ofn&supportj
5/jear to left offnu)^ support.
r-
Shear to right of (ntlj- support,
I/' Si . ,
' - - + wml ( ml
?
inn I
Shear at any point i
a j ynn
/
Reaction at (m/J^ support,
(O
fe)
Moment at any point in n&span
»-*
Point of max. positive momentinn^1 span, Maximum positive moment in n^span,
Vf V'2
/*— j (h) n=nnf-Q ; (i)
EXPLAtiATiOfiOF FORMULAS; n* number of- 'first span considered or its left support.
Given a continuous beam of several spans uniformly ' loaded '(for spans withno/oddw-0).
Apply formula (a) to /-and?— spans at the left end making n=l. Three unknown moments
appear,M/,r12,andMj. Ifbeamissimp/ysupportedatleftendfl^O. Next apply formu/a(a) to?—
and 3 —spans making n*2. Again there will be three unknowns fiz, M3 andty. Continue unfit
last two spans have been considered (never consider last span alone). If beam is simp/y supported
at right end, thef1Forthatsupport=0. There are now as many equations as there are unknowns
sobysolving, the momentsat all of the supports maybe Found. IF the beam is symmetrical
as to loading and dimensions, the calculations may be shortened by eguating moments which
are known, by inspection,^ be equal. Knowing the moments at the supports; the shear atanypoint,
the reactions,and the moment at any point may be calculated. (R,= fond R For last support
eguaby" for last span). For Fixed ends imagine the beam toextend one span beyond the Fixed
end and apply the for mulas,as above, equating the length and load of the imaginary span to
zero and the moment at the extreme end of the imaginary span to zero.Care should be taken
that shears and moments are us edwith their proper sign.
SPECIAL CASES;
For a beam of equal spans with equal uniform loads, Formula (a) reduces to-
Mn / 4Mm/ +Mn+2 = -£ wt*j (See also 57, of this chapter.) (j)
Fora beam of two unequal spans with unequal uniform loads and simpfy supported
at the ends, M, = 0,Mj=0 and from formula (a)
544
STRUCTURAL MECHANICS.
CHAP. XVI.
57. MOMENTS AT SUPPORTS.- CONTINUOUS 6eAMStEQML5nw5ANDEQUAL UNIFORM LOADS.
s^ v» s v>i r\i
I /lumber of Spans.
A A
0 -1
"A
0
fium her of 'Spans.
2.
3.
5.
6.
I
A A
0 --
A "A
10 °
A A A
0 -1 ^
28 28
A A
A" A A
o -4 _J
A A A
-}, -1 '
A A A A
0 • -IL -L .A
104 104 104
A A
8 II
~I04 ~I04
A
0
A
7. 0
A A A
IS II 12
~I42 ~I42 ~I42
A A A
// // //
142 ~I42 ~/42
A
0,
COEFFICIENTS OF w22, where w=/oac/perunit length and 2- length oFonespan. Eandl constant.
Maximum positive moment in any span can be calculated Prom Formula 56 j.
58. 5HEARSAT5UPPORTS:COHTIttUOUS BEAMS, EQUAL SPANS AND EQUALUtllFORM LOADS.
I.
A
A
A
5 ,5
~IO' 10 ~IO' 10
^
-p
*
4.
A A zs
+Ii !1 JI J1J1
' ?8 28' ?8 ?d'?8
a
A
A 2 Z\
n+£ H+W I JI
'58 ~18' 38 ~18' 58
Zi
A A A A 2S A A
0+4L & +5J> 42 +$l 51.55 _5i .49 55 ,63 4J_ 0
'104 ' 104' 104 "104 '104 ~/04'/04 104' 104 ~I04' 104 104'
5.
^.
A A ^A: z\ zs zs A^ A
7 n+tt MJl MM 71 JL 1LJZ lH J-l & 86 B6 n 7
J 142 ~I42' 142 ~I4ZJ 14? ~ 142' 142 ~I42' J42 ~ 142' 142 ~ 142' 142 142' ' '
COEFFICIENTS OF w?, where w= load per unit length andl:lenqth of span. £ and I constant.
Reactions at supports equal algebraic diFFerence oF shears to right and /eFt.
STRESSES IN CONTINUOUS BEAMS.
S9.Comif1UOU5 B£4M5,COfiCff17KAT£DLOAD5tCOfl5JAmriOf1[fiT Of /flfffriAAfiO MODULUS Off LA5TICITY.
if. .rjj*
Load, | 4 l||!
«' , v' \yg
l ! i __ i 4' 4
I 1
Span, ^ I
length, ^_ I,
Support, /
Reaction, R,
tlomenk, Mt
n-span
(fltljSfspan
*;
n \
p
Kn
Mn \M,
ntl
ml
Relation between moments at supports for n ^andfnti) % spans,
Ml 4-?M ,/7 *7 )iM ,7 .=—ffPllfl(-Jf})l--4rPjt/?Je -Mr* Air* l7
i '17 1 (j ril >f}f/( if) rlntljri ifH? (-/it/ '///7V>l/r/7 "n'J Zlrnt/intl(t "fitt •'"ntt + "nt/sj i
Shear to the right of n^> support, Shear to left offntlj^ support,
t /•
Shear to riqhtof(ntl)— support, Reaction at (n+i)— support,
,CI
(C)
ft+
Shear at any point in n&span,
KttfS& where ff>n equals (f)
the sum oF the loads between
n& support and point considered.
Point of max. positive moment in n^spar),
The max. positive moment occurs
where shear,as calculated From(F)
passes through zero. This point is
afwaysatoneoF the loads. (h)
Ex PL AflAT/Ofl OF FORMULAS: (See under 56.)
Moment at any point in n^span,
£lPn(x-kn ?„) equals the sum of the
moments of the loads, between
the n*-$ support and the point con-
s/dered, about the point
Maximum positive moment in the n t!?$pan,
After the point of man positive
moment has be/ocatedas de scribed
infh} the value oFx thus de6er mined
is substituted in(q) and Mxdetermined.
SPECIAL CASE,
fora beam of two unequal spans with unequal concentrated toads and with ends
simply supported, fi, =0, Ms =C
A/ -
V>
60. CONTINUOUS BEAMS OFTNO AND THREE EQmSPAHS: Uniform load, w, per unit length or load f?in center oFone span
i p
foment, 0, -1/16, 0, 0, -1/15. +1/60, 0, 0, -1/10, +1/40, 0.
faction, +7/16, +5/8, -I//6, +11/30, +/fiO, -1/10, +1/60, +4/10, +29/40, -1/ZO, +1/40,
Moment, 0, -3/H, 0, 0, -IfiO, -1/20, 0, 0, -3/40, -3/40, 0,
Reaction, +U/3Z, +///I6, -3/32, -1/20, +II/ZO, +l//?0, -1/20, -3/40, +21/40, +13/40, -3/40,
CoeFFicients of w2*dndPl', for moments at supports, andofwt and f? for reactions at supports.
By add/tionofprope r cases any beam maybe solved. For shears and moments between supports se(56&59.
36
546
STRUCTURAL MECHANICS.
CHAP. XVI.
DIAGRAMS.
OEMERAL FORMULAS.
Fs--l6tOOO,fc=650,n--l5.
61. RECTANGULAR B[AHS:Reinforced
For tension only:
7 C
• J f -/ Is
\ : M W^T
f-M . fl .
5~Ajd'pjbd*'
k= 0.579;
j=0.8757;
\F^n\ \ b
K •*• K- X
Steel rat hand depth, balanced reioForcemtnt,
„ / .
'
Fc =650;
Steel ratio and depth,
balanced reinforcement,
P =
6L SLABS: yalues Forlf'strip.
Reinforced For tension only.
kd
71 <?
Ms=%djd=.
F-£L-JL -
* Ajcl'Kpjd*'
Steel ratio and depth, balanced reinforcement,
'
TcnFc
j =0.8737 ;
M5 = 1290 d2;
M -M •
/ /c -HS >
F5? 16000;
Fc=650;
5 tee I ratio, depthand steel
area, balanced reinforcement
p =0.0077 ;
d=0.028]/W ;
_ T/. J*
5. T~E>EAM5:Neqlect!nq compression
in Web. Fort"qreiterthan"kd"u$e6l.
:/S. • b
\ CJ3 r ;•* — -— -fH
r~i — i 1 — 7 i* i T — i
w^r.4.
3d 2kd-t '
F=J± = JL .p=J<_F .
Ajd pjbd (l-k)n
Steel ratio, balanced reinforcement,
._/ t U37d-?t
J 3d0.758d-t
M5= 160 00 pjbd2
F5=I6000;FC=650S
Steel rat io, balancedreinF.
V-)t;
djd'
64. RECrAH6ULARBEAM5:ReinForced
For tens ion and compression.
rd-d'-, : g .
'.+ •*--»•
J*
(Fklpn
•j=fspjbdzj /%r4
. /V_ M _ . c'.ff-r e . r_ k
~ .00478+(.}19-r)pf
M5 use general Formula
Steel ratio, balanced reinFor cement,
X >1
Steel ratio, balanced
reinforcement,
STKKSSKS AND SAFK LOADS IN KKINFORCTll) (O.NC KKTK.
547
65 SttfAff, BOflD AND WEB REIHFORCeMCHT.
In the Following formulas 'Jd 'refers
to arm of resist ina coup/eat sect ion in
question, and fo, to tension tors at section.
Shear m Concrete & Bond Stress inTemile Steel,
Rectangular Beams, f-^C- >f=J^- •
(single or double reinforced) " &*' °~tojd'
7 -Beams, £~*v > fc^j
" Dja " zojd
Stirrups, All rectangular beams and T- beams.
Vertical stirrups, P=¥?; 5--^
jd v
Stirrups inclined 45f (not bent up bars}
P=Total stress ir?or?estirrvp.V=aff?0Mtof
shear not carried byconcrete.
For approximate results j=j in formulas.
66. COLt.
Axi
Urn
lMN$:fotiooFleno.th to/east width</?
d/ load forgiven unit stress,
t stress for given axial toad,
F - p . f - ~f
67. WORKIM STRESSES FOR STATIC LoA05(A5.C.£.)
Ultimate Strengths For Various Mixtures,
in Pounds per square inch
Aqqreqate !•' 2. 4 /•//// /-'3:6
Granite 2200 1800 1400
OraYelJardlimestonforsanJstone 2000 1600 1300
Soft Limestoneor Sandstone 1500 1200 1000
Working Stress ,/oercent of Ultimate Strength;
Shear: longitudinal b'rson/y,?.0;Partofb'rsbentup 3.0;
Sheer: thorough web re/nf. 6.0; Bond, brs4.0, wiret.O.
68. SAFE LOADS 0/iRFittFORCEDCoHCRETE SLABS: Fs=/6000,fc=650Jn=/5, M=^w2?
Total Thickness
of5/ab.
Ji
n
^\
||
Span in Feet for Safe Live Ldad
in Pounds per Square Foot of 5 lab.
M=JQ wl* (For M=£ w? * mult /ply span lengths by 0.8 94)
40
Lb.
50
Lb.
75
Lb.
100
Lb.
125
Lb.
150
Lb.
200
Lb.
250
Lb.
300
Lb.
350
Lb.
400
Lb.
In.
In.
Sq.ln.
Lb.
Ijf
4
4i
it
6
3/4
1
1
1
1
.1
/j
0.208
0.254
0.277
0.323
0.369
0.416
0459
38
44
50
56
63
69
75
8.4
9.6
104
11.7
12.9
14.1
14.5
7.9
9.5
9.0
11.2
12.5
13.5
13.9
7.0
10.0
11.2
12.7
63
7.5
8.0
9.2
il.8
5.8
6.9
7.4
8.5
9.6
10.6
11.0
5.4
6.5
7.0
8.0
9.0
10.0
10.4
4.8
5.8
6.2
7.2
8.1
9.0
9.4
43
5.3
5.7
6.6
7.4
8.5
8.6
4.0
4.9
53
6.1
6.9
7.7
8.0
3.7
4.5
4.9
5.7
6.5
7.2
7.5
3.6
4.3
4.7
5.4
6.1
6.8
7.1
69. 5AFELOAD50fiREIMFORCED CONCRETE SLABS: Fs= 16000, fc =650, n=l5, M*% *2*
Total Thick ness
of Slab.
\\
IS
1
it
Spar? in Feet for5afe Live load
in Pounds per Square Foot of Slab.
//=xj tv2 $ (For M=gw?* multiply span lengths by 0. 817)
40
Lb.
50
Lb.
75
Lb.
100
Lb.
125
Lb.
150
Lb.
^00
Id.
250
Lb.
300
Lb.
350
Lb.
400
Lb.
In
In.
Sq.ln.
Lb.
3
/
/
*
e
I
1
1
1
0.208
0.254
0.277
0.323
0.369
0.416
0.439
38
44
50
56
69
75
9.2
ii.4
12.8
142
15.5
15.9
8.6
10.1
IO.S
12.2
13.5
14.8
15.3
. 7.6
9.1
9.6
11.0
12.2
13.5
13.9
6.9
8.2
8.8
107
11.3
12.4
12.9
6.4
7.6
8.1
9.3
/0.5
11.6
S.9
7.1
7.6
8.8
9.9
109
11.4
*6.3
6.8
7.9
8.9
9.9
103
4.8
5.8
6.2
7.2
8.1
9.1
9.5
4.4
53
5.8
6.7
7.5
#.4
8.B
4.1
5.0
5.4
6.Z
7.1
7.9
83
3.9
4.7
5.1
5.9
6.7
7.5
7.8
648
STRUCTURAL MECHANICS.
CHAP. XVI.
Section
Area
A
Distance from Axis
to Extreme fibers
y and y,
Moment of
Inertia
I
Section Modulus
5=y
Radius of Gyration
a2
Y--
y I
a4
12
a5
6
|=O.E83a
a
.-;. a — -.
*
•r-
Y
T
a2
y=a
a4
3
a5
3
r°-577a
1
a
•r
Y
t
r
•---a----,
!
Y a
a4- a,4
a'- a?
6a
y^ir1
H 3,-w
"I-
Y
ji
a
i.
12
—<\
V -^
a*
y=^=0.70Ta
a4
12
6?! =
ii?110'28
—
y
.1.
»-
v=f
b-d5
12
b-d2
6
4=0.289 d
V12
4
••b-
y
b-d
y=d
b-d3
3
b-d2
3
4—
*
d
Jr
Y
.1.
b-d-b.-d,
y-d
b-d3-b,-d,3
b-d3-b,d?
• FFI*
Jb-d5-bfd?
j$
*..,
•b,»
12
6-d
Vl^b-d-bidJ
/•"^x
5
b-d
Y-b-d
b3-dj
W
b-d
' ^*v.
6[bVd?1
6«dz
VelF^i
$
k^
bd
, d-cosatb'Sino;
bd r jz z LZ • z i
bd dWaib^l
Jd-cosatb-sino:
Y- 2
6 d-cosa+b-sincc]
! R
PROPERTIES OF SECTIONS.
540
Section
Area
A
Distance from Axis
to Extreme. Filers
y and y,
Moment of
Inertia
I
Section Modulus
Radius of (kation
b-d
2
bd?
36
24
b-d
I
y=d
b-d5
12
b-d2
12
k- ..... b "--H
Ye
\i '-'J T L v 14
Y""bJb'T
y.=
36[btb,]
•d'
bib, 3
.
4
=.
64
TA
Y 2
TTld'-dfl
64
32 d
y=
< ........ d
BKn
.007d4
i92[3n-4]
--d
^=.785b<i
4
Tfj
64
irb-d
,«
JL...N — T...X
.
4
64
550 STRUCTURAL MECHANICS. CHAP. XVI.
Section
Area
A
Distances to
ExtremeFibera
yandy,
Moment of
Inertia
I
Section Modulus
Radius of Gyration
j®
T. t 0
vf
Afdz(l+2.co5J30°)l
A[d(Wcos'30°)l
d Jl+2cosz30°
=.866d?
12 [ 4-co5230° J
=.06da
6[ 4cosz30° J
=.12 d5
4V 3 cos2 30°
-f£i
32 o
d
A d2(l+2-co5E30°)
A[d(l+2cos^0°)"
dJl-t-2co5230°
2
= .577d
12 4-cos230° J
=.06d4
6[ 4cos30° J
ill 3co5z30°
:=.Lv4d
ii
tKU'
y=i
A d^ltZcw'ZZni
A[df!^co52^)l
dl|l ~t~ LC05 L L J
=.055d*
=To"d3
4 1 3cos<rZi
-IT
H-
y-d
b-dH^b-t)
b-d3-h3(b-t)
1/b'd — h I b — c)
fet?
12
6d
II I(.-[b -d ~ h (b ~ c Jj
qOf
b-d-h(b-t)
y b
25-bVh-t3
Es-b^h-t3
/ ^s-b^h-t3
?Z3*
1
12
6b
V12lb-d-h(b-t)l
ifj*
b-d-hfh-H
v-d
b-d-h3(b-t)
b-d-h3(b-t)
i/b-d-h'(b-t)
jh f~
y 2
12
6d
Vll[b-d-h(b-t)]
C*"B
b-d-h(b-t)
ii^-WWf]
2b35 + h-P A 2
I
F
y~b-d-h(b-t)
y,= b-y
— E_ 1 Y
3
y
VA
k-d-*-H*
«,„,„
d
bdV(b-t)
t-dVs3(b-t)
M^h
1 T -7
S3*
2
iz
bd
VlZ[tdt5tbrt)j
PROPERTIES OF SECTIONS.
Section
Area
A
Distances from Axis
to Extreme Fibers
yandy,
Moment of Inertia
I
Sec-IWuk
Radius of
Gyration
r
iffi
d h
.LfcuT
:ij
bsiht
d'Us'(b-t)
tvW-(b-t)(Yl-5)>
I
y
f
«
y
— i
-T
3
*
i ^^^* r i*^_^J Yi
h
.. Sbs^Wdtd+hltrlW
4b5Vh5(3t,t,)
I
ff
? M I ["
i._.i.LJ i
'' 6A
y-d-y,
st^
\l
Y
TJ
* b x
bsthtib.s,
, .idiMs?^ Ws
_ 5 5
I
y
«
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552 STRUCTURAL MECHANICS. CHAP. XVI.
STRESSES IN FRAMED STRUCTURES.
Loads. — The stresses in roof trusses are due to (i) the dead load, (2) the snow load, (3) the
wind load, and (4) concentrated and moving loads. Data for dead loads, snow loads, wind
loads, crane loads and other loads to be carried on trusses are given in Chapter I to Chapter IV,
inclusive. The loads on roof trusses are commonly given as a certain number of Ib. per sq. ft.
of horizontal projection of the roof. The loads are assumed to be transferred to the truss by
means of purlins acting as simple beams, the joint loads being equal to the purlin reactions.
Methods of Calculation. — The determination of the reactions of simple framed structures
usually requires the use of the three fundamental equations of equilibrium
2 horizontal components of forces = o (a)
'Z vertical components of forces = o (b)
S moments of forces about any point = o (c)
Having completely determined the external forces, the internal stresses may be obtained
by either equations (a) and (b) (resolution), or equation (c) (moments). These equations may
be solved] by graphics or by algebra. There are, therefore, four methods of calculating stresses:
„ , , . , T-, f Graphic Method
Resolution of Forces •< .. . ,, .
l_ Algebraic Method
,, , ~ J" Graphic Method
Moments of Forces -s . . . , , .
L Algebraic Method
The stresses in any simple framed structure can be calculated by using any one of the four
methods. The method of calculating the stresses in roof trusses by means of graphic resolution
will be explained in detail. For the calculation of the stresses in roof trusses and other framed
structures by algebraic resolution and by algebraic and graphic moments the reader is referred
to the author's " The Design of Steel Mill Buildings."
Graphic Resolution. — In Fig. i the reactions RI and RZ are found by means of the force and
equilibrium polygons as shown in (6) and (c). The principle of the force polygon is then applied
to each joint of the structure in turn. Beginning at the joint LQ, the forces are shown in (c),
and the force triangle in (d). The reaction RI is known and acts up, the upper chord stress i-x
acts downward to the left, and the lower chord stress i-y acts to the right, closing the polygon.
Stress i-x is compression and stress l-y is tension, as can be seen by applying the arrows to the
members in (c). The force polygon at joint U\ is then constructed as in (f). Stress l-x acting
toward joint U\ and load PI acting downward are known, and stresses 1-2 and 2-x are found by
completing the polygon. Stresses 2-x and 1-2 are compression. The force polygons at joints
Li and Uz are constructed, in the order given, in the same manner. The known forces at any
joint are indicated in direction in the force polygon by double arrows, and the unknown forces
are indicated in direction by single arrows.
The stresses in the members of the right segment of the truss are the same as in the left, and
the force polygons are, therefore, not constructed for the right segment. The force polygons for
all the joints of the truss are grouped into the stress diagram shown in (&). Compression in the
stress diagram and truss is indicated by arrows acting toward the ends of the stress lines and toward
the joints, respectively, and tension is indicated by arrows acting away from the ends of the
stress lines and away from the joints, respectively The first time a stress is used a single arrow,
and the second time the stress is used a double arrow is used to indicate direction. The stress
diagram in (&) Fig. I is called a Maxwell diagram or a reciprocal polygon diagram, *. e., areas'
in the truss diagram become points in the stress diagram. The notation used is known as Bow's
notation. The method of graphic resolution is the method most commonly used for calculating
stresses in roof trusses and in simple framed structures with inclined chords.
STRESSES IN ROOF TRUSSES. — The methods of calculating dead load, snow load, and
wind load stresses in roof trusses by graphic resolution will be briefly described.
STRESSES IN ROOF TRUSSES.
Dead Load Stresses. — -The dead load is made up of the weight of the truss and the roof
i iivn inu.. and is usually considered a* ,i|i|.li< •<! at the pam-1 points of the upper chords in computing
stresses in roof trusses. If the purlins do not come at the panel points, the upper chord will have
to be designed for direct stress and stress due to flexure.
The stress in a Fink truss due to dead loads is calculated by graphic resolution in (a) Fig. 2.
The loads are laid off, the reactions found, and the stresses calculated beginning at joint L<,
as explained in Fig. I. The stress diagram for the right half of the truss need not be drawn
wli-.-iv tlu- truss and loads are symmetrical as in (a) Fig. 2; however, it gives a check on the accuracy
»>f the work and is well worth the extra time required. The loads PI on the abutments have no
effect on the stresses in the truss, and may be omitted in this solution.
In calculating the stresses at joint PI, the stresses in the members 3-4, 4-5 and x-$ are
unknown, and the solution appears to be indeterminate. The solution is easily made by cutting
out members 4-5 and 5-6, and replacing them with the dotted member shown. The stresses in
the members in the modified truss are now obtained up to and including stresses 6-x and 6-7.
Sinn- the stresses 6-x and 6-7 are independent of the form of the framework to the left, as can
easily be seen by cutting a section through the members 6-x, 6-7 and j-y, the solution can be
carried back and the apparent ambiguity removed. The ambiguity can also be removed by cal-
culating the stress in f-y by algebraic moments and substituting it in the stress diagram. It will
be noted that all top chord members are in compression and all bottom chord members are in
tension.
Snow Load Stresses. — Large snow storms nearly always occur in still weather, and the
maximum snow load will therefore be a uniformly distributed load. A heavy wind may follow a
sleet storm and a snow load equal to the minimum given in § 19, " Specifications for Steel Frame
Buildings," Chapter I, should be considered as acting at the same time as the wind load. The
stresses due to snow load are found in the same manner as the dead load stresses.
Wind Load Stresses. — The stresses in trusses due to wind load will depend upon the direction
and intensity of the wind, and the condition of the end supports. The wind is commonly con-
sidered as acting horizontally, and the normal component, as determined by one of the formulas
in § 20, " Specifications for Steel Frame Buildings," Chapter I, is taken.
The ends of the truss may (i) be rigidly fixed to the abutment walls, (2) be equally free to
move, or (3) may have one end fixed and the other end on rollers. When both ends of the truss
are rigidly fixed to the abutment walls (i) the reactions are parallel to each other and to the
resultant of the external loads; where both ends of the truss are equally free to move (2) the
horizontal components of the reactions are equal; and where one end is fixed and the other end
is on frictionless rollers (3) the reaction at the roller end will always be vertical. Either case (i)
or case (3) is commonly assumed in calculating wind load stresses in trusses. Case (2) is the con-
dition in a portal or a framed bent. The vertical components of the reactions are independent of
the condition of the ends.
Wind Load Stresses: No Rollers. — The stresses due to a normal wind load, in a Fink truss
with both ends fixed to rigid walls, are calculated by graphic resolution in (b) Fig. 2. The reac-
tions are parallel and their sum equals the sum of the external loads; they are found by means of
force and equilibrium polygons. To calculate the reactions, lay off the loads PI, Pi, PI, Pt, PI,
as shown, and select the pole O at any convenient point. Then at a point on line of action of P\
in the truss diagram, draw strings parallel to the rays drawn through the ends of Pi in the force
polygon. The string drawn parallel to the ray common to forces PI and PI in the force polygon
will cut the force Pj in the tr^ss diagram. Through this point draw a string parallel to the ray
common to forces Pj and P8 in the force polygon, and so on until the strings drawn parallel to
the outside rays meet on the resultant of all the loads. The closing line of the force polygon
connects the two points on the reactions. Through point 0 in the force polygon draw line O-Y
parallel to the closing line in the equilibrium polygon, R\ and Rt are the reactions, as shown.
The stress diagram is constructed in the same manner as that for dead loads. Heavy lines
in truss and stress diagram indicate compression, and light lines indicate tension.
554
STRUCTURAL MECHANICS.
CHAP. XVI.
The ambiguity at joint P3 is removed by means of the dotted member, as in the case of the
dead load stress diagram, ft will be seen that there are no stresses in the dotted web members
in the right segment of the truss. It is necessary to carry the solution entirely through the
truss, beginning at the left reaction and checking up at the right reaction. It will be seen that
the load PI lias no effect on the stresses in the truss in this case, the left reaction being simply
reduced if PI is omitted.
ao' so'
tdj
Joint Lo
FIG. i.
Wind Load Stresses : Rollers. — Trusses longer than 70 ft. are usually fixed at one end, and
are supported on rollers at the other end. The reaction at the roller end is then vertical — the hori-
zontal component of the external wind force being all taken by the fixed end. The wind may
come on either side of the truss, giving rise to two conditions: (i) rollers leeward and (2) rollers
windward, each requiring a separate solution.
Rollers Leeward. — The wind load stresses in a triangular Pratt truss with rollers under the
leeward side are calculated by graphic resolution in (c) Fig. 2.
The reactions in (c) Fig. 2 were first determined by means of force and equilibrium polygons,
on the assumption that they were parallel to each other and to the resultant of the external loads.
Then since the reaction at the roller end is vertical and the horizontal component at the fixed end
is equal to the horizontal component of the external wind forces, the true reactions were obtained
by closing the force polygon.
In order that the truss be in equilibrium under the action of the three external forces, RI, R2
and the resultant of the wind loads, the three external forces must meet in a point if produced.
This furnishes a method for determining the reactions, where the direction and line of action of
one and a point in the line of action of the other are known, providing the point of intersection
of the three forces comes within the limits of the drawing board.
The stress diagram is constructed in the same way as the stress diagram for dead loads.
It will be seen that the load Pi has no effect on the stresses in the truss in this case. Heavy lines
in truss and stress diagram indicate compression, and light lines indicate tension.
Rollers Windward. — The wind load stresses in the same triangular Pratt truss as shown in
(c) Fig. 2, with rollers under the windward side of the truss are calculated by graphic resolution
in (d) Fig. 2.
The true reactions were determined directly by means of force and equilibrium polygons.
The direction of the reaction RI is known to be vertical, but the direction of the reaction R? is
unknown, the only known point in its line of action being the right abutment. The equilibrium
polygon is drawn to pass through the right abutment and the direction of the right reaction is
determined by connecting the point of intersection of the vertical reaction RI and the line drawn
through O parallel to the closing line of the equilibrium polygon, with the lower end of the load line.
STKKSSKS IN KOOI TRUSSES,
d a1 tf is1
iRj . i i i
(b)WiHt> LOAD, NoXouexs
(C)W/ND LOAD, Rouexs LEEWARD M WJMD LOAD, J?OLL£KS
FIG. 2.
556 STRUCTURAL MECHANICS. CHAP. XVI.
Since the vertical components of the reactions are independent of the conditions of the ends
of the truss, the vertical components of the reactions in (c) and (d) Fig. 2 are the same. It will
be seen that the load PI produces stress in the members of the truss with rollers windward. If
the line of action of RZ drops below the joint P$, the lower chord of the truss will be in compression,
as will be seen by taking moments about PS.
STRESSES IN A TRANSVERSE BENT.— A transverse bent in a steel mill building
consists of a roof truss supported at the ends on columns and braced against longitudinal move-
ment by means of knee braces, Fig. 3. The ends of the columns may be fixed at the base or
may be free to turn (pin-connected). The stresses in a transverse bent are statically indeterminate
and cannot be calculated without taking in account the deformations of the members themselves.
The following approximate method, proposed by the author in the first edition of " The De-
sign of Steel Mill Buildings," 1903, gives results that are approximately correct, are on the safe
side, and is the method now used in practice.
Dead and Snow Load Stresses. — The stresses due to dead and snow loads in trusses of a
transverse bent are calculated the same as though the trusses were supported on solid walls.
Wind Load Stresses. — The external wind loads may be taken (i) as horizontal or (2) as normal
to the surface. The columns will be assumed to be pin-connected at the tops and to be either pin-
connected or fixed at the base. It will be assumed that the horizontal reactions at the foot of
the columns are equal to each other, and equal to one-half of the horizontal component of the
external wind load. It is also assumed that the truss does not change its length, and that the
deflection of the columns at the top of the columns and at the foot of the knee brace are equal.
It is shown in " The Design of Steel Mill Buildings " that when the columns are fixed at
the base the point of contra-flexure comes at a distance of from 5 to f of the distance from the
foot of the column to the foot of the knee brace. It is usually assumed that the point of contra-
flexure is located at a point in the column one-half the distance from the foot of the column to
the foot of the knee brace. If h = height of the column, d = height from the base of the column
to the foot of the knee brace, then the distance from the base of the column to the point of contra-
flexure will be
d (d + 2ft) .
yo = ~2-(2JTJry (4)
•
The calculation of the wind stresses in a transverse bent with a monitor ventilator is shown in
Fig. 3. The bents are spaced 32 ft. centers and are designed for a horizontal wind load of 20 Ib. per
sq. ft., the normal wind load being calculated by Hutton's formula, Fig. 3, Chapter I. The point
of contra-flexure is found by substituting in equation (4) to be
42.5
The external forces are calculated for the bent above the point of contra-flexure by multiplying
the area supported at the point by the intensity of the wind pressure. For example, the load at
B is 32' X 6.75' X 20 Ib. = 4320 Ib.
The line of application and the amount of the external wind load, 1.W, is found by means
of a force and an equilibrium polygon. 1>W acts through the intersection of the strings parallel
to the rays 0-B and 0-C, and is equal to C-B (line C-B is not drawn in force polygon) in amount.
The reactions R and R' may be calculated graphically as follows: — Lay off the total wind load
2W so that it will be bisected by point A in Fig. 3. Perpendiculars dropped from the ends of
load line ~S,W to the dotted lines A B and A C will give V = 12,800 Ib., and V = 700 Ib., respec-
tively. Then R and R' are calculated as shown.
The calculation of stresses is begun at point B in the windward column, and in the stress
diagram the stresses at B are found by drawing the force polygon a-B-A-b-a. The remaining
stresses are calculated as for a simple truss. In calculating the stresses in the ventilator it was
assumed that diagonals 9-10 and 10-12 are tension members, so that 9-10 will not be in action
STRESSES IN A TRANSVERSE BENT.
when the wind is acting as shown. Before solving the stresses at the joint 6-7-9 >t was necessary
to calc-iil. itc tin- stresses in members »-li, 10-11 and 9~A. The remainder of the solution offers
no difficulty to one familiar with the principles of graphic statics.
J..I
Trusses 32-0 'c. fo c.
Dead Load '20 Ib. sq.ft.hcr.
MndLoad'20lb. - ' vert.
0 £000 10000 20000
8 A
WIND LOAD STRESS DIAGRAM
COLUMNS FIXED
(0)
FIG. 3.
The stress in post b-a is equal to V, while the stress in l-c is found by extending i-c to c'
in the stress diagram, c' being a point on the load line. The stress in post n-A is equal to V't
while the stress in ig-m is found by extending ig-m to m' in the stress diagram, m' being a point
on the horizontal line drawn through C. The kind of stress in the different members is shown
by the weight of lines in the bent and stress diagrams.
For a detailed discussion of the calculations of the stresses in a transverse bent, see " The
Design of Steel Mill Buildings."
STRESSES IN BRIDGE TRUSSES. — The stresses in bridge trusses may be calculated
by applying the condition equations for equilibrium for translation, resolution; or by applying
the condition equation for equilibrium for rotation, moments. Both resolution and moments may
be calculated algebraically or graphically, giving four methods for calculation the same as for
roof trusses.
Maximum Stresses. — The criteria for loading a truss or beam for maximum and minimum
stresses are given on page 160, Chapter IV.
Problems. — The methods of calculating the stresses in bridge trusses are shown by several
problems taken from the author's " The Design of Highway Bridges."
558 STRUCTURAL MECHANICS. CHAP. XVI.
PROBLEM *-, DEAD LOAD STRESSES IN A CAMEL-BACK TRUSS BY GRAPHIC RESOLUTION.
(a} Problem. — Given a Camel-back (inclined Pratt) truss, span 160' o", panel length 20' o",
deotri at the hip 25' o", depth at the center 32' o", dead load 400 Ib. per lineal foot per truss.
Calculate the dead load stresses by graphic resolution. Scale of truss, i" = 25' o". Scale of
loads, i" = 10,000 Ib.
(b) Methods. — The loads beginning with the first load on the left are laid off from the bottom
upwards. Calculate the stresses by graphic resolution, beginning at RI and checking up at R^.
Follow the order given in the stress diagram.
(c) Results. — The top chord is in compression and the bottom chord is in tension. All
inclined web members are in tension; while part of the posts are in compression and part are in
tension. Member 1-2 is simply a hanger and is always in tension.
PROBLEM 2. DEAD LOAD STRESSES IN A PETIT TRUSS BY GRAPHIC RESOLUTION.
(a) Problem. — Given a Petit truss, span 350' o", panel length 25' o," depth at hip 50' o",
depth at center 58' o", dead load 0.9 tons per lineal foot per truss. Calculate the dead load
stresses by graphic resolution. Scale of truss, i" = 50' o". Scale of loads, i" = 45 tons.
(b) Methods. — The loads beginning with the first load on the left are laid off from the top
downwards. Calculate RI and R.2. Calculate the stresses in the members at the left reaction
by constructing force triangle i-Y—X. Then calculate the stress in 1-2 by constructing polygon
F-I-2-F. Draw 3-2, which is the stress in member 3-2. Then pass to joint Wi where there
appears to be an ambiguity, stress 4-5 being unknown. To remove the ambiguity proceed as
follows: At JF3 on the left side of the stress diagram assume that Ws is the stress in 5-6 (the
member 5-6 is simply a hanger and the stress is as assumed). Calculate the stress in 4-5 by
completing the triangle of stresses in the auxiliary members. The stresses are now all known
at W% except 3-4 and 5~F, but the stress in 4-5 is between the two unknown stresses. First
complete the force polygon 2-3-4-5 '-Y-Y-2. Then by changing the order the true polygon
2-3-4-5- Y— Y-2 may be drawn. This solution is sometimes called the method of sliding in a
member. The apparent ambiguity at joint W^ may be removed in the same manner. The stress
diagram is carried through as shown and finally checked up at RZ. It will be seen that there is
no apparent ambiguity on the right side of the truss.
(c) Results. — It will be seen that the Petit truss is an inclined Pratt or Camel-back truss
with subdivided panels. The auxiliary members are commonly tension members in all except
the end primary panels as in the Baltimore truss in Problem 6. It will be seen that the stresses
in the first four panels of the lower chord are the same. The loads in this type of Petit truss are
carried directly to the abutments. The Petit truss is quite generally used for long span highway
and railway bridges.
PROBLEM 3. MAXIMUM AND MINIMUM STRESSES IN A WARREN TRUSS BY ALGEBRAIC
RESOLUTION.
(a) Problem. — Given a Warren truss, span 160' o", panel length 20' o", depth 20' o", dead
load 800 Ib. per lineal foot per truss, live load 1 ,600 Ib. per lineal foot per truss. Calculate the
maximum and minimum stresses in the members due to dead and live loads by algebraic reso-
lution. Scale of truss as shown.
(6) Methods. — Dead Load Stresses. — Beginning at the left end the left reaction is RI = 3-^ \W.
The shear in the first panel is 3%W, in the second panel is 2JJF, in the third panel is f TF, and
in the fourth panel is \W. Now resolving at RI the stress in i-F = — ^W- tan 0, stress i-X
= + 3 J IF- sec 0. Cut members i-F, 1-2 and 2-X and the truss to the right by a plane and
equate the horizontal components of the stresses in the members. The unknown stress 2-X
will equal the sum of the horizontal components of the stresses in i-F and 1-2 with sign changed,
= - (- 35 - 3l)JF-tan 6 = + jW tan 0. The stress in 3-F = -(7 + 2|)TF tan 0 = -
9iPF-tan 0. Stress in 4~X = - (- 9? - *f)JP'tan 0 = + i2W-tan 0; stress in 5~F = -
( + 12 + i£)TF-tan0 = + i&W-tant] and the stress in 6-X = - (- 13! - 1 1) IF- tan 0 =
+ !5lF-tan0; etc. The coefficients of the chord stresses when multiplied by IF tan 0 give
the stresses, while the coefficients for the webs when multiplied by IF- sec 0 give the web
stresses.
Live Load Stresses. — Chord Stresses — The maximum chord stresses occur when the joints
are all loaded, and the chord coefficients are found as for dead loads. The minimum live load
stresses in the chords occur when none of the joints are loaded, and are zero for each member.
Web Stresses. — The maximum web stresses in any panel occur when the longer segment into
which the panel divides the truss is loaded, while the shorter segment has no loads on it. The
minimum live load web stresses occur when the shorter segment is loaded and the longer segment
has no loads on it. The maximum stresses in members i-X and 1-2 occur when the truss is fully
STRESSES IN BRIDGE TRUSSES.
loaded. The shear in the panel is $\P, or V P> and the stress in i-X — sl-P-sec 9 — -f 125,400
Ih., while the stress in 1-2 — — ^P-accO •» — 125,400 Ib. The minimum stresses in i-X and
1-2 are zero. The maximum stresses in 2-3 and 3-4 occur when 6 loads are on the right of the
1 1. m. 1 .uxl i IHTC an- no loads on the left of the panel. The shear in the panel will then be equal
to th.- li-ft reaction, - RI - (6 X 3$ X P)/8 - >j P. The stress in 2-3 - ^-P-eec $ -
+ 94,080 Ib., while the stress in 3-4 — — V-P-sccd =• — 94,080 Ib. The minimum stresses
in 2-3 ami 3 4 will occur when there is one load on the shorter segment. In the corresponding
panel on the right of the truss, if the shorter segment is loaded, the left reaction •» \P — the
slu-.ir in the panel. The minimum stress in 2-3 =» — \P-sec0 =» —4,480 Ib., while the
minimum stress in 3-4 = + 4,480 Ib. The stresses in the remaining panels are calculated in the
^iiiu- m.imier. The maximum chord stresses are equal to the sum of the dead and live load chord
The minimum chord stresses are the dead load chord stresses. The maximum web
M roses are equal to the sum of the dead and the maximum live load web stresses. The minimum
web stresses are equal to the algebraic sum of the dead load stresses and the minimum live load
stresses.
(c) Results. — The web members 7-6 and 7-8 have a reversal of stress from tension to com-
pression, or the reverse. These members must be counterbraced to take both kinds of stress.
PROBLEM 4. MAXIMUM AND MINIMUM STRESSES IN A PRATT TRUSS BY ALGEBRAIC
RESOLUTION.
(a) Problem. — Given a Pratt truss, span 140' o", panel length 20' o", depth 24' o", dead
load 800 Ib. per lineal foot per truss, live load 1, 600 Ib. per lineal foot per truss. Calculate the
maximum and minimum stresses due to dead and live loads by algebraic resolution. Scale of
truss, i" = 20' o".
(6) Methods. — Construct three truss diagrams as shown. On the first place the dead load
coefficients and the dead load stresses. On the second place the live load coefficients and the
live load stresses. On the third place the maximum and minimum stresses due to dead and live
loads. The maximum chord stresses are the sums of the dead and live load chord stresses, while
the minimum chord stresses are those due to dead load alone. The hip vertical is simply a hanger
and has a minimum stress of one dead load and a maximum stress of one live and one dead load.
The conditions for maximum and minimum stresses in the webs are the same as for the Warren
truss, the vertical posts having stresses equal to the vertical components of the stresses in the
inclined web members meeting them on the unloaded (top) chord.
(c) Results. — There is no dead load shear in the middle panel, but it is seen that there are
stresses in the counters for live loads. Only one of the counters will be in action at one time
Whenever the center of gravity of the loads is not in the center line of the truss, that counter
will be acting that extends downward toward the center of gravity. The numerators of the
maximum and minimum live load web coefficients are o, I, 3, 6, 10, 15, 21, as for the Warren
truss. This shows that the maximum and minimum web stresses are proportional to the ordinates
to a parabola.
PROBLEM 5. MAXIMUM AND MINIMUM STRESSES IN A DECK BALTIMORE TRUSS BY ALGEBRAIC
RESOLUTION.
(a) Problem. — Given a deck Baltimore truss, span 280' o", panel length 20' o", depth
40' o", dead load 0.375 tons per lineal foot per truss, live load 0.625 tons per lineal foot per truss.
Calculate the maximum and minimum stresses due to dead and live loads by algebraic resolution.
(b) Methods. — Construct three truss diagrams and use them as shown.
Dead Load Stresses. — The auxiliary struts 1-2, 5-6, 9-10, etc., carry a full dead load com-
pression, while the auxiliary web members 2-3, 6-7, 10-11, etc., have a tensile stress of $W-sec 0.
The stress in l-F equals the shear in the panel multiplied by sec 0 = — 6|W-sec 0. The stress
in 3-F equals the shear in the panel multiplied by sec 0, plus the inclined component of the one-
half load that is carried toward the center by the auxiliary member 2-3, = — (si + i)W-sec 6
= — 6W-sec0. The stress in 3-4 is the vertical component of the stress in 3~F = + 6W.
The stress in $-Y is the horizontal component of the stress in J,-Y = — 6W-ta.n 6. The stress
in l-X and 2-X = + 6%W-tan 6. The stress in 4-5 is the inclined component of the shear in
the panel = - $\W- sec 0. The stress in 5-^" = - (- 6 - tf)W-tan 0 = + loJW-tan 9.
The remaining dead load stresses are calculated in a similar manner.
Live Load Web Stresses. — The maximum shears in the different panels occur when the longer
segment of the truss is loaded, while the minimum shears occur when the shorter segment of the
truss is loaded. The maximum stresses in the webs in the first and second panels occur for a
full live load on the bridge. The maximum shear in the third panel occurs with all loads to the
right of the panel and no loads to the left. The shear in the panel will then be equal to the left
reaction = n X J(" + 1)^/14 = fJP. The maximum live load stress in 4-5 will be =
560 STRUCTURAL MECHANICS. CHAP. XVI.
— f l-P-sec 0. With a maximum stress in 4-5 the stress in 4-7 will be = (— 66/14 + 7/i4)-P'
sec 0 = — ^fP-sec 0. This is the maximum stress, for the stress in 4-7 when there is a
maximum shear in the panel is = 10 X 11/2 X T\P-sec 0 = — f|P-sec0. In a similar
manner it will be found that maximum stresses in members 8-9 and 8-1 1 occur with a maximum
shear in 8-9. On the right side it will be seen that minimum stresses in the diagonals occur for a
minimum shear in the odd-numbered panels from the right.
(c) Results. — The dead and live loads were assumed as applied on the upper chord. The
upper chords are in compression, while the lower chords are in tension the same as for a through
truss. The live and dead load stresses are given separately on the left side of the lower truss.
PROBLEM 6. MAXIMUM AND MINIMUM STRESSES IN A THROUGH BALTIMORE TRUSS BY ALGEBRAIC
RESOLUTION.
(a) Problem. — Given a through Baltimore truss, span 320' o", panel length 20' o", depth
40' o", dead load 800 Ib. per lineal foot per truss, live load i ,800 Ib. per lineal foot per truss.
Calculate the maximum and minimum stresses due to dead and live loads by algebraic resolution.
Scale of truss, i" = 40' o".
(6) Methods. — Construct three truss diagrams as shown.
Dead Load Stresses. — The shear in each of the hangers is W, while the stress in each of the
diagonal auxiliary members is — %W-secO. The stress in the upper part of the end-post is
(+ 6^ + 5) W^-sec 0 = + 7W'sec0, where + 6JW-sec0 is the stress due to the shear and
+ \ W- sec 0 is the stress due to the half load carried toward the center by the auxiliary diagonal
member. The stress in the main diagonal in the third panel is — $%W-sec 0, where 5%W is the
shear in the panel; while the stress in the diagonal in the fourth panel is (— 4! — |) TV- sec 0 =
— sW-sec 0, where 4^W-sec 0 is the stress due to the shear in the panel and ^PF-sec 0 is the
stress carried toward the center of the truss by the auxiliary member. The chord coefficients
are calculated as in Problem 5.
Live Load Stresses. — The maximum shear in the third panel occurs with 13 loads to the
right of the panel and with no loads to the left of the panel. The shear in the panel is then equal
to the left reaction, equals 13 X KJ3 + i) X -P/i6 = H-P- The stress in the main diagonal
in the third panel is then equal to. — ^P-sec 0. The stress in the main diagonal in the fourth
panel is (— *\P -f- ^P) sec 0 = — ffP sec 0, = a maximum, the maximum shear in the panel
being 12 X 5(12 + i) X P/l6 = ff-P. In like manner the maximum stresses are found in
5th and 6th panels when there is a maximum shear in the 5th panel, and in the 7th and 8th panels
when there is a maximum shear in the 7th panel. Minimum stresses in the 3d and 4th panels
from the right abutment occur when there is a minimum shear in the 3d panel; and in the 5th
and 6th panels when there is a minimum shear in the 5th panel.
(c) Results. — The double panels next to the center require counters. It should be noticed
that in calculating the stresses in these counters the diagonal auxiliary ties will have the dead
load stress of + 5.66 tons as a minimum.
PROBLEM 7. MAXIMUM AND MINIMUM STRESSES IN A CAMEL-BACK TRUSS BY ALGE-
BRAIC MOMENTS.
(a) Problem. — Given a Camel-back truss, span 100' o", panel length 20' o", depth at hip
20' o", depth at center 25' o", dead load 300 Ib. per lineal foot per truss, live load 800 Ib. per
lineal foot per truss. Calculate the maximum and minimum stresses due to dead and live loads
by algebraic moments. Scale of truss, i" = 20' o".
(b) Methods. — Calculate the arms of the forces as shown and check the values by scaling
from the drawing.
Dead Load Stresses. — To calculate the stress in the end-post L0Ui, take center of moments
at Li, and pass a section cutting L0Ui, U\L\ and L\L^ and cutting away the truss to the right.
Then assume stress LoUi as an external force acting from the outside toward the cut section,
and stress L0Ui X 14.14 — Ri X 20 = o. Now Jf?i = 6 tons and stress L0Ui = + 8.48 tons.
To calculate the stresses in L0Li and L\Li take the center of moments at U\, and pass a section
cutting members UiU%, U\Li and LiL2, and cutting away the truss to the right. Then assume
the stress in LI L% as an external force acting from the outside toward the cut section, and LiLzX 20
— RI X 20 = o. Now RI = 6 tons and the stress in L0Li = LiL2 = — 6 tons. To calculate
the stress in U\ U2 take the center of moments at Li, and pass a section cutting members Ui Uz,
UzLz and LzLz', and cutting away the truss to the right. Then assume the stress in L\Ui as an
external force acting from the outside toward the cut section, and Ui Uz X 24.25 — RI X 40 + W
X 20 = o. Now Ri = 6, W = 3 tons, and the stress in Ui U2 = + 7.42 tons. To calculate
the stress in UiLz take the center of moments at A, and pass a section cutting members UiUz,
UiLz, and LiZ-2, and cutting away the truss to the right. Then assume the stress in U\LZ as an
STRESSES IN BRIDGE TRUSSES. 501
f.xti-rnal force acting from the outside toward the cut section, and UiLt X 70.7 + RI X 60
- W X 80 =• o. Now Ri - 6 tons and W - 3 tons, and U\Lt X 70.7 — — 120 ft. -tons, and
> U\Li = — 1.70 tons. The other dead load stresses are calculated as shown.
Live Load Stresses. — The live load chord stresses are equal to the dead load chord stresses
multiplied by 8/3. The maximum stress in U\L\ will occur with loads at Li, Lt, and L\', while
the maximum stress in counter U*L\ will occur with a load at L\ only. The maximum tension
in /'•_•/.- will occur with all the live loads on the bridge, while the maximum compression will
occur when there is a maximum stress in the counter UtLt, loads at Lt and L/. The details
of the solution are shown in the problem.
(c) Results. — The stress in the counter UtLt and the chords UtUt and LtLt may be
calculated by the method of coefficients, and will be the same as for a truss with parallel chords
having a depth of 25' o". The maximum stress in UtLt will occur with loads Lt and L/ on the
bridge, when the left reaction equals 2 X 3-P/5 = f-P. The stress in UtLt = — $P-sec0
= — 6.15 tons.
PROBLEM 8. MAXIMUM AND MINIMUM STRESSES IN A THROUGH WARREN TRUSS BY
GRAPHIC MOMENTS.
(o) Problem. — Given a through Warren truss, span 140' o", panel length 20' o", depth
20' o", dead load 800 Ib. per lineal foot per truss, live load 1,200 Ib. per lineal foot per truss.
Calculate the maximum and minimum stresses by graphic moments. Scale of truss, i" = 20' o".
Scale of loads, i" = 50,000 Ib.
(6) Methods. Chord Stresses. — Calculate the center ordinate of the parabola = w- L*/8d
= 98,000 Ib., and lay it off at 5 to the prescribed scale. Now lay off the vertical line 1-5 at the
left and right abutments. Make 1-2 = 2-3 = 3-4 = 2 (4-5). Draw the inclined lines 1-5,
2-5, 3-5, 4-5, 5-5. The intersections of these lines with verticals let drop from the lower chord
points are points in the stress parabola for the upper chord stresses. The stresses in the lower
chords are the arithmetical means of the stresses in the upper chords on each side. By changing
the scale the live load stresses may be scaled directly from the diagram.
Web Stresses. — At the distance of a panel to the left of the left abutment lay off the vertical
line 1-8 equal to one-half the total live load on the truss, to the prescribed scale, equal 1,200 X 70
= 84,000 Ibs. Now divide the line 1-8 into as many equal parts as there are panels in the truss,
and mark the points of division 2, 3, 4, etc. Connect these points of division with the panel
point 7, the first panel point to the left of the right abutment. Drop verticals from the panel
points of the lower chord of the truss to the line 1-8, and the intersections of like numbered lines
will give points on the curve of maximum live load shears.
To construct the dead load shear diagram, lay off $W, downward to the prescribed scale
under the left abutment, and reduce the shear under each load to the right by W, until the dead
load shear is — i>W at the right abutment. The dead load shear diagram is then constructed as
shown.
Maximum and Minimum Web Stresses. — The maximum shear in any panel is then the ordinate
to the right of the panel point on the left end of the panel, and the stresses in the web members
are calculated by drawing lines parallel to the corresponding member as shown. Positive stresses
are measured downwards from the live load shear curve, and negative stresses are measured
upwards from the live load shear curve.
(c) Results. — This method is an excellent one for illustrating the effect of the different
systems of loads, but consumes too much time to be of practical use. It should be noted that
the maximum ordinate to the chord parabola is not a chord stress in a Warren truss with an
odd number of panels.
PROBLEM 9. MAXIMUM AND MINIMUM STRESSES IN A PETIT TRUSS BY ALGEBRAIC
MOMENTS.
(o) Problem. — Given a Petit truss, span 350' o", panel length 25' o", depth at the hip
50' o", depth at center 58' o", dead load 0.9 tons per lineal foot per truss, live load 1.4 tons per
lineal foot per truss. Calculate the maximum and minimum stresses due to dead and live loads
by algebraic moments. Scale of truss, i" = 40' o". Scale of lever arms, any convenient scale.
(b) Methods. — Construct a truss diagram carefully to scale as shown. Construct one-
half the truss to scale on a large piece of paper and calculate the lever arms as shown, and check
by scaling from the diagram. The methods of calculation will be shown by two examples:
i. Stresses in Tie 6-7. Dead Load Stress. — Pass a section cutting members 7~X, 6-7, and
6-F, and cutting away the truss to the right. The center of moments will be at A, the inter-
section of chords 7~X and 6-F. Now assume the stress in 6-7 as an external force acting from
the outside toward the cut section. Then for equilibrium 6-7 X 477-O -f- RI X 575 — $W
37
562 STRUCTURAL MECHANICS. CHAP. XVI.
X 625 = o. Now Ri = 146.25 tons and W = 22.5 tons, and solving the equation gives stress
6-7 = — 87.8 tons.
Live Load Stresses. — The maximum live load stres's in 6-7 will occur with the longer segment
of the truss loaded. Taking moments about point A as for the dead loads the maximum live
load stress 6-7 X 477.0 + RI X 575 = o. Now RI = 55/14 X 35 tons = 137.5 tons, and the
stress in 6-7 = — 165.8 tons.
The minimum live load stress in 6-7 will occur with the shorter segment of the truss loaded.
Taking moments about the point A, 6-7 X 477-° + RI X 575 — 5? X 625 = o. Now RI = 90
tons, P = 35 tons, and stress in 6-7 = +29.1 tons.
2. Stresses in Tie 4-7. Dead Load Stress. — -Pass a section cutting members J-X, 4-7, 4-5
and 5-F, and cutting away the truss to the right. Now assume the stress in 4-7 as an external
force acting from the outside toward the cut section. Then for equilibrium about the point A,
stress 4-7 X 477-O + RI X 575 — stress 4-5 X 442.0 — 2 W X 612.5 = o. Now the member
4-5 will carry one-half the load carried by 5-6, and the stress equals 1/2 X 22.5 X 1.414 =
+ 15-9 tons. RI = 146.25 tons, and 2W = 45 tons. Then stress 4-7 = — 103.6 tons.
Live Load Stresses. — The maximum live load stress in 4-7 will occur with the longer segment
loaded. Taking moments about A as for dead loads, stress 4-7 X 477-O + R\ X 575 — stress
4-5 X 442.0 = o. Now stress 4-5 = + 24.8 tons, and RI = 66/14 X 35 = 165 tons. Then
stress 4-7 = — 175.7 tons.
The minimum live load stress in 4-7 will occur with two loads to the left of the panel. Taking
moments about the point A, the stress 4-7 X477.o-f-.Ri X575 — 2^X612.5 =o Now
.Ri = 62.5 tons and 2P = 70 tons. Then stress 4-7 = -+- 14-5 tons.
The stresses in the members in the first and second panels and in the two middle panels
may be calculated by coefficients. Check up the dead load chord stresses by comparing with
the stresses obtained by graphic resolution in Problem 2.
(c) Results. — The auxiliary members carry the stresses directly toward the abutments and
there is no ambiguity of loading as in the case of a truss subdivided as in Problem 6. However,
the method of subdividing shown in Problem 6 is used in preference to that shown in this problem.
The Petit truss is quite generally used for long span pin-connected highway and railway bridges.
PROBLEM 10. LIVE LOAD STRESSES IN A THROUGH PRATT TRUSS FOR COOPER'S E 60
LOADING.
(a) Problem. — Given a Pratt truss, span 165' o", panel length 23' 6|", depth 30' o", live
load Cooper's E 60 loading. Calculate the position of the loads and the maximum and minimum
stresses due to the prescribed loading by algebraic moments. Scale of truss, i" = 25' o".
(6) Methods. Chord Stresses. — Calculate the position of the wheels for a maximum bending
moment at the different joints in the lower chord. The criterion for maximum bending moment
at any joint in a Pratt truss is, " the average load on the left of the section must be the same
as the average load on the entire bridge." Having determined the wheel that is at the joint for
a maximum moment, calculate the maximum bending moment as shown Having calculated
the maximum bending moments, the chord stresses are found by dividing the bending moment
by the depth of the truss. The moment diagram is given in Table V6, Chapter IV.
Web Stresses. — Calculate the position of the wheels for maximum shears in the different
panels. The criterion for maximum shear in a panel is, " the load on the panel must equal the
load on the bridge divided by the number of panels." The criterion for maximum bending
moment at LI is the same as the criterion for maximum shear in panel L$L\. Having deter-
mined the position of the wheels for maximum shears in the different panels, calculate the maxi-
nVam shears as shown. The stress in a web is equal to the shear in the panel multiplied by sec 9.
Floorbeam Reaction. — The stress in the hip vertical U\Li is equal to the maximum floorbeam
reaction. This is calculated as follows: Take a simple beam with a span equal to the sum of two
panel lengths and calculate the maximum bending moment at the point in the beam corresponding
to the panel point; in this case it will be the center of the span. This bending moment multiplied
by the sum of the panel lengths divided by the product of the panel lengths will be the maximum
floorbeam reaction; in this case the maximum bending moment at the center will be multiplied
by 2 divided by the panel length.
(c) Results. — When the maximum stresses occur in chords UzUs, UzUs and L3L3', counter
U3'Ls is in action. It occasionally happens that there is more than one position of the loading
that will satisfy the criterion for maximum bending moment. In this case the moments for each
loading must be calculated.
PROBLEM n. STRESSES IN THE PORTAL OF A BRIDGE BY ALGEBRAIC MOMENTS AND
GRAPHIC RESOLUTION.
(a) Problem. — Given the portal of a bridge of the type shown, inclined height 30' o", center
to center width 15' o", load R = 2,000 lb., end-posts pin-connected at the base. Calculate the
stresses by algebraic moments and check by graphic resolution. Scales as shown.
STRESSES IN BRIDGE TRUSSES. 503
(b) Methods.— Now II - H' - 1 ,000 Ib. V - — V, and by taking moments about B,
V — 30 X 2,000/15 — 4,000 Ib. — — V'.
Algebraic Moments. — In passing sections care should be used to avoid cutting the end-posts
for the reason that these members are subject to bending stresses in addition to the direct stresses.
^Irulate the stress in member 3~F take the center of moments at joint (i) and pass a section
rutting members 4-6, 3-4 and 3~F, and cutting the portal away to the left of the section. Then
assume stress 3~F as an external force acting from the outside toward the cut section, and 3~F
X 10 X 0.447 + II X 30' — o. The stress in 3~F = — 6,710 Ib. The remaining stresses are
cMii-ul.itt-il as shown.
Graphic Resolution. — Lay off a-A = A-b = H = 1,000 Ib., and A-Y — V •» 4,000 Ib.
Then beginning at point B in the portal the force polygon for equilibrium is a-A-Y-l'-a, in
which I'-o is the stress in the auxiliary member i-a, and Y-l' is the stress in the post i-Y when
the auxiliary member is acting. The true stress in i-F is equal to the algebraic sum of the vertical
components of the stress I'-a and Y-l', and equals V = — 4,000 Ib. Next complete the force
triangle at the intersection of the auxiliary members. Stress x'-o is known and the force triangle
is a-l'-2'-a, the forces acting as shown. The stress diagram is carried through in the order shown,
checking up at the point A. The correct stresses are shown by the full lines in the stress diagram.
The true stress in 3-2 will produce equilibrium for vertical stresses at joint (l) as shown. The
maximum shear in the posts is H = l ,000 Ib. The maximum bending moment in the posts will
occur at the foot of the member 3~F, joint (3), and is M = 1,000 X 20 X 12 = 240,000 in.-lb.
(c) Results. — The method of graphic resolution requires less work and is more simple than
the method of algebraic moments.
Note: The portal is not pin-connected at joints (3) and the corresponding joint on the oppo-
site side, as might be inferred from the figure.
PROBLEM 12. WIND LOAD STRESSES IN A TRESTLE BENT.
(a) Problem. — Given a trestle bent, height 45' o", width at the base 30' o", width at the top
9' o", wind loads Po, PI, Pz, PS, Pi, as shown. Calculate the stresses in the members of the
bent due to wind loads by algebraic moments, and check by calculating the stresses by graphic
resolution. Assume that the diagonal members are tension members, and that the dotted members
are not acting for the wind blowing as shown. Scale of truss, l" = 10' o". Scale of loads,
i" = 2,000 Ib.
(b) Methods. — Algebraic Moments. — To calculate the stresses in the diagonal members take
centers of moments about the point A, the point of intersection of the inclined posts. Then to
calculate the stress in 3-4, pass a section cutting members 3-.X", 3-4 and 4~F; assume that the
stress in 3-4 is an external force acting from the outside toward the cut section, and 3-4 X 15.9'
+ 3,000 X 19.3' + 3,000 X 11.3' = o. The stress 3-4 = — 5,800 Ib. Stresses in 4-5, 5-6,
6-7, 7-8 and 8-Z are calculated in a similar manner. To obtain reaction RI take moments about
RI, and RI X 30' — 2,000 X 15' — 2,000 X 30* — 3,000 X 45' — 3,ooo X 53' = o. Then RI
.= 12,800 Ib. = — R2.
To calculate the stress in 4~F, take center of moments at joint Pi, and pass a section cutting
members $-X, 4-5 and 4~F, and assume the stress in 4~F as an external force acting from the
outside toward the cut section. Then 4~F X 15.6' — 3,000 X 15' — 3,000 X 23' = o. Then
4-Y = + 7,300 Ib.
Graphic Resolution. — The load PO is assumed as transferred to the bent by means of the
auxiliary members. The loads P0, PI, Pj, P3, P4 are laid off as shown, and with the load PO the
stress triangle F-.Y-2 is drawn. The remainder of the solution is easily followed.
(c) Results. — The stress in the auxiliary member 2- F acts as a load at the top of post 4- F.
Load Po is the wind load on the train and is transferred to the rails by the car. For the reason
that the wind may blow from the opposite direction, both sets of stresses must be considered in
combination with the dead and live load stresses in designing the columns.
564
STRUCTURAL. MECHANICS.
CHAP. XVI.
!\J
STRESSES IN BRIDGE TRUSSES.
566
STRUCTURAL MECHANICS.
CHAP. XVI.
Bridge Analysis. DecK Baltimore Truss. Problem 5 .
Max. and Min.«5tresses. Algebraic Resolution
- - r
-6 -io -ie
. * Coef. for Dead Load, and Live Load for Chords.
Maximum Web Coefficients. Minimum Web Coefficients.
0.+4a75 D.+ 48.75 CU78.75 D.+78.75 D.493.75 D.+ 9J.75 D.+95.75 -VE5O.OO4e5O.OO +35O.OO +EIO.OO 4ZIO.OO +ftO.OO -V \V3.OO
..+ 156.25 L
Live and Dead Load Stresses.
>5pan,L,-Eeo'-o'.1 =
Panel, \,= 2o'-o"
Depth, d.-^-o'-o1.'
^ox-ond Nirv.>Stresse».
-90.00 Dead Load =.375 Tons per Im.ft p.tr.
tanO=.v.oo. LiveLoad'.ezsTper lin.flper truss.
Stresses in Tons.
Bridge Analysis. Baltimore Truss. Problem 6
Wtand Algebrafc Resolution^. 5pan 320'
+izi +154 +16? +132.00 "
h-A n ^ *°*"
l/j«r«
Rl
wwwwwwv/'wwwwwwwu
Wtanff
Dead Load Coefficients . Dead Load Stresses In Tons.
\P \P \P \P
\P \P \P \P \P \P \P >•
Maximum — Live LoadV/eb Coefficients - Minimum
•H25.0 +405.0 +429.0 +152.0 +124.0 +10010
, r/W.O -/W.O -/5?.i» -I82M -H2.0 -312.0 -390-0 -590.0 -120.0 -120.0 -96.0 -96.0 -56.0 -56.0 -60.0 -60.0 > •
Maximum Stresses in Tons. Minimum Stresses in Tons
STRESSES IN BRIDGE TRUSSES.
567
568
STRUCTURAL MECHANICS.
CHAP. XVI.
Bridge Analysis. PetitTruss. Problem 9.
.Stresses by Algebraic Moments.
D-l'46.3
L-227.5
D- 146.3
i- 227.5
D-218.8
L-34O.3
D-242.O
L- 374.5
„ -616.5
-2/8.8
-559.1
/\ •
-146.3
-373.8
-146.3
-373.8
T " "
< " ! 1 «
Y
**. .'' \
.• y/iax/'mur
n and fi/'ni
•num Stres
Dead and Live Load Stresses
Dead Load * 0,6 tons per foot per truss.
Live >'--/. 4 " " .,
Span =550~0. Panel-?5-0'. A
Depth-50'-0"anol 5QL0"
Lever Arms
tti&if
tell
}S»»
S-?Ng$iir?>
H?
*^ c» o
S^kl'I^ ^
fc . 'L^X N^ -c;
S o> "^J . ^ K K
Sf^^^^u, • ffi
*>* o . •? G »1^-
g^;s v^*,^^
ISiHs
IK Slpfi^
tiff
09
•feib
V***
*$*£
^^^S}
x •« X V
l^S^va
J^^^
*J,,
111^
M&&
STRESSES IN BRIDGE TRUSSES.
CHAPTER XVII.
THE DESIGN OF STEEL DETAILS.
Introduction. — The design of any structure involves the design of the different members
and the connections. In this chapter the design of the various steel details will be considered as
fully and completely as the limited space permits. The design of the members and details of a
steel structure are governed by the specifications for the particular structure. Reference will
be made by section and page to the various specifications in this book.
MEMBERS IN TENSION. — Several different methods for making end connections of bars are
shown in Fig. I. Loop Bars, (a) Fig. I, are used for lateral bracing on highway bridges, buildings
and towers, with turnbuckles or sleeve nuts, to make them adjustable as shown in Tables 92 and
94. (All tables numbered with Arabic numerals are in Part II.) Clevises, (b) Fig. i, are used
to secure the ends of bars used as lateral bracing on highway bridges and on buildings. The pin
may be either a cotter pin as shown in Table 96, or a bridge pin as shown in Table 95. Ordinary
eye-bars, (c) Fig. I, are used principally for lower chords and main ties on bridges. Data for eye-
bars are given in Table 91. Counters are made of adjustable eye-bars as shown in Table 91.
Bottom lateral plates or skew-backs, (d) Fig. i , are used to secure the ends of bottom lateral rods
(a) Loop.
(b) Clevis.
(c)Eye
:•
O
o
0
o
(e) TopLateralor U-PJate.
(g)Anqfe
V>
(d) Bottom Lateral Plate
or Skew back. (F) Cooper Hitch. (h) Beveled Washer, Cast Iron.
FIG. i. DETAILS OF TENSION MEMBERS.
of highway bridges and are shown in Table 121. Top lateral plates or U-plates, (e) Fig. i, are
used for top lateral connections on highway bridges and for lateral bracing on buildings, highway
bridges and towers, see Table 122. The Cooper hitch has the same uses as the top lateral plate.
The angle as shown in (g) Fig. i is used for end connections for light bars in buildings and towers,
see Table 120. Cast iron beveled washers, (K) Fig. i, are used for end connections of diagonal
bracing, see Table 120. The ends of bars should be upset as shown in Tables 89 and 90, so that
the strength in the threads will be greater than the strength of the main body of the bar. The
dimensions of tie rods for beams are shown in Table 105.
571
572 THE DESIGN OF STEEL DETAILS.
In selecting bars in tension the area is determined by the formula:
CHAP. XVII.
where A is the required area, P the total tension in the bar and ft the allowable unit tensile stress.
The following problems are given to illustrate the use of the tables in selecting the details for
bars, etc.
Loop Bar. — Select a loop bar to carry a tensile stress of 48,000 lb., one end passing around a
3 in. pin and the other end around a 3^ in. pin, the center to center distance between pins being
30' o".
References. — Specification § 8, p. 55; § 33, p. 57; § 84, p. 60; § 91, p. 61; § 104, p. 61; § 108,
p. 62; § 116, p. 62; § 37, p. 141; § 49, p. 142; § 61, p. 142; § 14, p. 206; § 36, p. 206; § 15, p. 209;
§ 36, p. 210; § 230, p. 363; § 8, p. 379; § 42, p. 381; § 28, p. 385.
Solution. — Using an allowable unit stress of ft = 16,000 lb. per sq. in., the area required is,
P 48,000
A = -r = -^ - = 3-OO sq. in.
/t 16,000
A bar i% in. square has an area of 3.06 sq. in. (Table 6), and a 2 in. round bar has an area of 3.14
sq. in. (Table 6). Either bar could be used. Using the i% in. square bar the additional length
required to pass around a 3 in. pin is i' n" (Table 92), and for a 3^ in. pin is 2' i", making it
necessary to add 4' o" to the center to center distance of pins to obtain the total length of bar.
If a turnbuckle is used the upset required on a i % in. square bar is 2^ in. in diameter and 5^
in. long (Table 89), requiring 4^ in. extra material to make each upset, or 9 in. for the two up-
sets. The weight of a turnbuckle for a 2^ in. screw is 25 lb. (Table 94). The clearance between
the ends of the screws for all turnbuckles is 5 in. (Diagram at top of Table 92).
The total length and weight of the i% in. square bar is therefore:
c. to c. of pins, less 5 in., = 29' 7
Material for 2 loops = 4' o
Material for 2 upsets = o' 9
One Turnbuckle
Total Length
of i% in. square bar, @ 10.41 lb. per ft. (Table 6) = 308.0 lb.
of i% in. square bar, @ 10.41 lb. per ft. (Table 6) = 41.6 lb.
of i% in. square bar, @ 10.41 lb. per ft. (Table 6) = 7.8 lb.
@ 25 lb. (Table 94) = 25.0 lb.
Total Weight = 382.4 lb.
= 34' 4"
If a sleeve nut is used, instead of a turnbuckle, its weight for a 2 J^ in. screw, is 19 lb. (Table
94). The clearance between the ends of the screws is 3 in. for all sleeve nuts (Diagram at the top
of Table 92).
in. square bar when a sleeve nut is used is therefore:
The total length and weight of I ^
c. to c. of pins, less 3 in., = 29' 9" of I
Material for 2 loops = 4' o" of I
Material for 2 upsets = o' 9" of I
One sleeve nut
Total Length
= 34' 6"
in. square bar, @ 10.41 lb. per ft. (Table 6) = 309.8 lb.
in. square bar, @ 10.41 lb. per ft. (Table 6) = 41.6 lb.
in. square bar, @ 10.41 lb. per ft. (Table 6) = 7.8 lb.
@ 19 lb. (Table 94) = 19.0 lb.
Total Weight = 378.2 lb.
Bar with Clevises. — Select a bar to carry a tensile stress of 48,000 lb., the ends to be held
by clevises, the distance center of pins being 12' o".
References. — Same as for loop bar, also § 41, p. 58; § 39, and § 41, p. 141; § 17, § 18, and § 19,
p. 209.
Solution. — Using an allowable unit stress of ft = 16,000 lb. per sq. in., the area required is,
_ P _ 48,000 _
ft ~ 16,000
A bar i% in. square has an area of 3.06 sq. in. (Table 6), and a 2 in. round bar has an area of 3.14
sq. in. (Table 6). Either bar could be used. Using the i% in. square bar a No. 6 clevis is
required (Table 93).
MEMBERS IN TENSION. 573
The size of pin required by shear and moment can be obtained from the lower part of Table
93, and is a 2 in. pin if the forks are closed, or a 3 in. pin if the forks are used straight. The
thickness of connection plate required by bearing when a 2 in. pin is used, is 48,000 •*• (2.00 X 24,-
ooo) «• i.oo in., if a 3 in. pin is used the plate must be 48,000 -5- (3.00 X 24,000) — 0.66 in.
The weight of the bar and two clevises is estimated as follows:
The length of the rod, allowing for clearance, etc., must be reduced by A — % in. •• 8 — %
•• 7/4 in. (Table 93) at each end, or a total of 2 X 7H = i' 3"- The diameter of upset for a
l% in. square bar is 2}^ in., which requires 4^ in. material to make each upset (Table 89), or 9
in. for both upsets.
The total length and weight of 1% in. square bar is:
c. to c. of pins, less i' 3", = 10' 9" of i% in. square bar, @ 10.41 Ib. per ft. (Table 6) = 111.9 Ib.
Material for 2 upsets = o' 9" of i% in. square bar, @ 10.41 Ib. per ft. (Table 6) = 7.8 Ib.
Two No. 6 clevises @ 26 Ib. (Table 93) = 52.0 Ib.
Total Length = u' 6" Total Weight = 171.7 Ib.
Eye-Bar. — Select an eye-bar to carry a tensile stress of 190,000 Ib., with an 8 in. pin at one
end and a 6^ in. pin at the other end, the length center to center of pins being 25' o".
References.— § 33, p. 57; § 106, p. 62; § 162, p. 66; § 37, p. 141; §92, p. 144; § 141, p. 145;
§ 171, p. 147; § 14, p. 206; §36, p. 206; "Minimum Bar," p. 207; §83, p. 207; § 15, p. 209;
§ 36, p. 210; § 83, p. 213; § 136, p. 216; § 162, p. 218.
Solution. — Using an allowable unit stress of /< = 16,000 Ib. per sq. in., the area required is,
P 190,000
A = -r = -^ = 11.87 sq. in-
ft 16,000
A bar 8 in. X i% in. has an area of 12.00 sq. in. (Table i). From Table 91, the maximum thick-
ness allowed for an 8 in. bar on a 6% in. pin is 2 in., and the minimum is I in. (The value 6^
in. does not appear in the table but it is less than 7 in., which is the maximum pin which can be
used if the die referred to is used.) For an 8 in. pin the maximum thickness is 2 in. and the
minimum I % in. The bar selected satisfies these requirements as to thickness.
The extra length of bar required to form a head for a 6)^ in. pin (die for 7 in. pin) is 2' 8" for
ordering the bar, and 2' 3" for estimating the weight, and for an 8 in. pin 3' o" and 2' 6", respec-
tively (Table 91).
. The total length and weight of eye-bar is therefore:
c. to c. of pins = 25' o" of 8 in. X 1 1A in. bar. @ 40.8 Ib. per ft. (Table 2) = 1020.0 Ib.
Eye for 6H in. pin = 2' 3" of 8 in. X I >£ in. bar, @ 40.8 Ib. per ft. = gi.Slb.
Eye for 8 in. pin = 2' 6" of 8 in. X l^ in. bar, @ 40.8 Ib. per ft. = 102.0 Ib.
Total Length = 29' 9" Total Gross Weight = 1213.8 Ib.
The weight which must be deducted for pin holes (Table 6) is,
Pin hole for 61A in. pin is 1.5 -4- 12 X 112.8 = 14.1 Ib.
Pin hole for 8 in. pin is 1.5 -5- 12 X 171.0 = 21.4 Ib.
Total weight to be deducted =35-5 Ib.
The net weight of the eye-bar is then 1213.8 — 35.5 = 1178.3 Ib.
For the design of an eye-bar subject to flexure due to its own weight, see "Combined Flexure
and Direct Stress" in this chapter.
Angle in Tension. — Select an angle to carry a tensile stress of 40,000 Ib., using % in. rivets.
References— § 33, p. 57; § 39, p. 57; § 40, p. 58; § 79, p. 60; § 83, p. 60; § 84, p. 60; § 85,
p. 60; §89, p. 61; § 104, p. 61; §22, p. 105; §37, p. 141; §43, p. 141; §60, p. 142; §79, p. 144;
§80, p. 144; § 14, p. 206; § 26, p. 206; §45, p. 206; "Fastening Angles," p. 207; § 15, p. 209;
§ 26, p. 210; § 38, p. 210; § 57, p. 210; § 74, p. 212; p. 219; p. 223; § 232, p. 363; § 8, p. 379.
574
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
Solution. — If fastened by both legs as in Fig. 2 the load may be considered as axial and the
required net area, using an allowable unit stress of /» = 16,000 Ib. per sq. in., is
_ P _ 40,000 _
ft 16,000
2.50 sq. m.
Try one angle 4" X 4" X W- Gross area = 2.86 sq. in. (Table 23 or Table 25). Net
area, deducting one % in. hole for a % in. rivet = 2.86 — .33 = 2.53 sq. in. (Table 116). This
angle will satisfy the conditions. This result can be obtained directly from Table 29.
If the angle is fastened by one leg as in Fig. 3, the load will be eccentric and the problem
more difficult. An approximate solution is to consider only the area of the attached leg as effect-
ive. The solution would then be, as before
P 40,000
A — -r = -4 = 2.50 sq. in.
ft 16,000
1
o o o o
o o o o
1 —
j
1
FIG. 2. ANGLE CONNECTED BY BOTH LEGS.
FIG. 3. ANGLE CONNECTED BY ONE LEG.
Try one angle 6" X 4" X /^" with 6 in. leg attached. Gross area of 6 in. leg = 6 X J^
= 3.00 sq. in., net area = 3.00 — .44 = 2.56 sq. in., which will satisfy the conditions.
Built-up Tension Member. — Design a built-up member to carry a tensile stress of 390,000
Ib., using % in. rivets.
References— •§ 33, p. 57; § 83, p. 60; § 84, p. 60; § 89, p. 61; § 90, p. 61; § 101, p. 61; § 37,
p. 141; §44, p. 141; §61, p. 142; §75, p. 143; § 14 and §26, p. 206; §28, p. 210; §38, p. 210;
§52, p. 211; §82, p. 213; p. 219; § ii, p. 382.
Solution. — Using an allowable unit stress of ft = 16,000 Ib. per sq. in., the net area required is,
A — — — 39°>229 _
/( 16,000
24.4 sq. in.
Try 4 angles 3^" X 3^" X W and 2 plates 18 in. X K in., as shown in Fig. 4. Gross area
= 18.00 + I3-OO = 31.00 sq. in. Referring to Fig. 4, it will be seen that the section n-n is the
least section in the body of the member and that four rivet holes should be deducted from each
side to obtain the net section, giving a net area of 31.00 — 4.00 — 2.00 = 25.00 sq. in., 4.00 sq.
in. being the area of holes in the plates and 2.00 sq. in. being the area of holes in the angles, de-
ducting I in. holes for ^ in. rivets. This section has sufficient area, 24.4 sq. in. being required.
If the ends of the members are to be riveted they should be designed as outlined under
"Riveted Connections and Joints" in this chapter.
If the ends are to be pin-connected they may be designed as follows. Assume that 5^ in.
pins are to be used at each end. The bearing area required allowing a unit stress of 24,000 Ib.
per sq. in., is 390,000 -f- 24,000 = 16.2 sq. in. This requires a total thickness of plates of 16.2 -5-
5.5 = 2.95 in., or 1.48 in. on each side. The web plates are J^ in., the fill plates must be at least
Yi in., the thickness of the angles being K in., and using % in. outside plates the total thickness of
plates is 1.50 in., which satisfies the conditions, 1.48 in. being required.
MEMBERS IN COMPRESSION.
The net area through the pin hole (section m-m) must be 25 per cent in excess of the net
area of the body of the member according to a common specification. It will probably be neces-
sary to deduct the area of the pin hole and two rivet holes on each side, the rivet holes being so
n< -.ir the section m-m, see Fig. 4. The gross area through the pin hole is, web plates 2 X 18 X H
= 18.00 sq. in., angles 4 X 3.25 = 13.00 sq. in., fill plate 2X11 X *A — Il.oo sq. in., outside
plate 2 X 17 X H ~ 17.00 sq. in. making a total gross area of 59.00 sq. in. The net area is
59.00 — 2X5. 5X1. 5 — 4X1 X iH =" 36.5 sq. in. The required net area through the pin
h.)K is 1.25 X 25.00 = 31.3 sq. in.
Secthnm-m
<L
'
ID \n
o o o o
OO O
-o-o-oj-2
°°°;
o o o'o
'o o o o
booo
OO 0
OO 0
o o o o
O 0 O O O O O
3
o""ct o o o o o
J*$
0? n
L
Section n-n
FIG. 4. RIVETED TENSION MEMBER.
The net area back of the pin hole parallel with the axis of the member (section o-o) must not
be less than the net area in the body of the member (section n-n) = 25.0 sq. in. The total
thickness of the metal at this section is 1.50 in. for each side. Therefore the net length back of the
pin must be 25.00 -5- 2 X 1.50 = 8.33 in. Assuming that not over three rivets will come in this
section, the total length back of the pin hole must be at least 8.33 + 3.00 = 11.33 »n.
The number of rivets required and the size of pin plates is considered under " Riveted Connec-
tions and Joints."
Unriveted Pipe. — Design an unriveted iron pipe 12 in. in diameter to carry an internal
pressure of 400 Ib. per sq. in.
From Structural Mechanics, Chap. XVI (Formula I2a), / = wD •£• 2t; and / = w • D 4- 2/,
where / is the thickness of metal, w = unit internal pressure, D = diameter and / the allowable
tensile stress which will be taken as 12,000 Ib. per sq. in.
_ w-D _ 400 X 12
* — T™ — ~~ "- ~ — 0.20 in.
2/ 2 X I2.OOO
MEMBERS IN COMPRESSION.— The design of compression members will be shown by
several examples.
Single Angle Strut. — Select an angle to carry a compressive stress of 21,500 Ib. The length
center to center of connections is 6' o", and both legs are to be fastened at the ends, Fig. 2.
References. — Specifications §34, p. 57; §39, p. 57; §84, p. 60; §85, p. 60; §93, p. 61;
§38, p. 141; §43, p. 141; §60, p. 142; §100, p. 61; § 45, p. 206; p. 207; § 16, p. 209; §20, p. 209;
p. 223; § 231, p. 363; § 10, p. 379.
Solution. — Using /c = 16,000 — 70 l/r Ib. per sq. in., as the allowable unit stress and 125 as
the maximum value for the ratio l/r, the minimum value for r is as follows:
l/r = 125, or r = -— = $J*_!? = 0.58 in.
125 125
Any 3" X 3" angle will satisfy the requirement for l/r (Table 23). The allowable unit stress
72
will then be 16,000 — 70 X -^ = 7,300 Ib. per sq. in. The area required will be
•5°
2.95 sq. in.
A — — — 2I'5°°
~ 7« ~ 7.300
The area of one angle 3" X 3" X 9/l6" is 3.06 sq. in., which is sufficient.
576 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
Many other angles might be chosen but in no case could an angle smaller than 3" X 3" be
used, for the requirement for l/r would not be satisfied. Larger angles will give lighter sections
and be more rigid. Any angle 3%" X 3^" has a radius of gyration, r, of about 0.69 (Table 23),
giving an l/r of about 104, and an allowable unit stress of about 8,700 Ib. per sq. in. and requiring
an area of 2.47 sq. in., which would be provided by one angle 3^" X 3^" X %". The minimum
angle satisfying the l/r requirement is found as a guide in the selection of sections but is rarely a
satisfactory section, except for long members with low stresses such as lateral bracing. Table 41,
Part II, gives the safe loads for single angle struts fastened by both legs.
See also § 26, p. 203; § 45, p. 203; "Fastening Angles," p. 207; § 20, p. 209.
If the angle is fastened by one leg only as in Fig. 3, the load is eccentric and the problem is
more difficult. An approximate solution is to consider only the area of the attached leg as effect-
ive. As before the least radius of gyration must be not less than 0.58 in., which corresponds to an
allowable unit stress of 7,300 Ib. per sq. in., requiring the area of the attached leg to be at least 2.95
sq. in. The requirement for radius of gyration would be satisfied by any 3%" X 3" angle, but
to provide 2.95 sq. in. of area if attached by the 3,V£ in. leg the thickness would have to be 2.95
-r- 3.50 = 0.85 in. requiring a 3^" X 3" X %" angle, which is a very poor section and would
be much heavier than a section with longer legs to satisfy the same conditions, and much less
rigid. The least radius of gyrations of any 5" X 3/^" angle is about 0.76 in. (Table 24), and the
allowable unit stress will be
72
fe = 16,000 — 70 l/r = 16,000 — 70 X -J—? = 9,370 Ib. per sq. in.,
requiring an area of the attached leg of
P 21,500
A = -r = — -- — = 2.30 sq. m.
/« 9,370
2.-IQ
which would be provided by a 5" X 3/^" angle of thickness equal to— — - = .46 in. An angle
5" X 3^2" X 1A" could be used with the 5 in. leg attached.
Double Angle Strut. — The member a-b Fig. 5 is to consist of two angles back to back sepa-
rated by % in. connection plates at the ends and washers % in. thick in the body of the member.
Design for a compressive stress of 50,000 Ib.
References. — § 34, p. 57; § 84, p. 60; § 93, p. 61 ; § 100, p. 61 ; § 38, p. 141 ; § 60, p. 142; § 45,
p. 206; § 16, p. 209; § 20, p. 209; § 231, p. 363; § 10, p. 379.
Solution. — Using fe = 16,000 — 70 l/r Ib. per sq. in. as the allowable unit stress, and 125 as
the maximum value for the ratio l/r, the minimum value for r is found as follows
/ 8 X 12
Ir = 125, or r = = = 0.77 in.
125 125
The lengths about axes X-X and Y—Y are equal, so that for a well designed member the radii
of gyration about the two axes should be as nearly equal as practicable. This condition is satis-
fied by using angles with unequal legs, short legs turned out.
A member composed of two 2^" X 2" angles, % in- back to back, with short legs turned
out will have a least radius of gyration of about 0.78 in. (Table 40), the value for axis X-X being
about 0.78 in. and Y-Y about 0.95 in. The allowable unit stress is then /„ = 16,000 — 70 l/r
8 X 12
= 16,000 — 70 X — - = 7,39O Ib. per sq. in., requiring an area of
0.7"
P 50,000
A = -j- = ~ — = 6.76 sq. in.
/« 7,390
This area cannot be supplied by two 2^" X 2" angles, but even though it could, larger
angles would be more economical as well as more rigid. The minimum angle satisfying the l/r
DOUBLE ANGLE STRUT. 577
requirement is found so as to guide in the selection of angles but is rarely a satisfactory section,
c\< cpt for a long member with low stresses, such as lateral bracing.
Try two angles 4" X 3" with the short legs turned out, Y% in. back to back. From Table
40 it is seen that for any thickness the least radius of gyration will be about the axis X-X, and
8 X 12
will be about 1.26 in., giving an allowable unit stress of /« = 16,000 — 70 X — — z~ •• 10,670
Ib. per sq. in., which requires an area of 50,000 + 10,670 — 4.68 sq. in. The area of 2 angles
4" X 3" X £i" — 4.96 sq. in., which will satisfy the conditions. If the estimated radius of gyra-
tion does not agree closely enough with the actual radius of gyration, another calculation should
be made, but this is not often necessary.
The spacing of the washers should be such that the //r of one angle between the washers is not
8 X 12
greater than the l/r for the whole member, or l/r — - -r- = 76.2, / = 76.2 X .64 = 48.7 in.,
0.64 being the least radius of gyration of one angle 4" X 3" X W (Table 24). One washer in
the center will be sufficient.
\Y
bd
, . _ *i
d V a
FIG. 5. DOUBLE ANGLE STRUT.
If lengths about the two axes are different, as is often the case in roof trusses and portals, the
greatest value for l/r should be used, the corresponding length and radius of gyration being taken;
for example in designing the member b-d, Fig. 5, as a strut the length corresponding to the axis
Y-Y is 12' o", and to the axis X-X is 6' o". To make an efficient member the long legs should
be turned out and rv should be equal to 2 X r,.
The minimum allowable values of rx and rv are found as follows,
/r 6 X 12
l/r = 125, rx=— -__=o.58in.;
125 125
in
From Table 39 it is seen that any 2%" X 2" angle with long legs turned out and % in. back
to back is the smallest angle which will satisfy the requirements for l/r, rx = 0.58 in. and ry = 1.26
in. (approx.). The values for l/r are 124 and 114, respectively, 124 being the greater. The
allowable unit stress is then
fc = 16,000 — 70 X 124 = 7,320 Ib. per sq. in.
If the stress in b-c is the same as that in c-d, 19,000 Ib. compression, the required area is,
P 19,000
A = -f — — — = 2.60 sq. in.
/« 7.320
which will be taken by 2 angles 2%" X 2" X 5/16", having rx = 0.58 in., and ry = 1.26 in.
(Table 39). If the stresses in b-c and c-d are not equal proceed as above and design for the
maximum. The spacing of the washers should not be greater than, / = 124 X 0.42 = 52.1 in.,
0.42 in. being the least radius of gyration of one angle 2^" X 2" X 5/l6".
38
578 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
If the controlling stress were 38,000 lb.' compression, the required area for 2%" X 2" angles
would be
P 38,000
A = 7- = = 5.20 sq. in.
fc 7.320
which could not be supplied by two 2^" X 2" angles, so that two 3^" X 3" angles will be used
for which, rx = 0.90 and ry = 1.66 for % in. back to back, the values of l/r are — - = 80 and
0.90
12 X 12
-^-— = 86.8, respectively, and the allowable unit stress is, /,. = 16,000 — 70 X 86.8 = 9,930
lb. per sq. in., requiring an area of A = 30,000 -T- 9,930 = 3.83 sq. in., which will be furnished
by two angles 3^" X 3" X 5/i6". The spacing of the washers should not be greater than,
/ = 86.8 X 0.63 = 54.6 in., 0.63 in. being the least radius of gyration of one angle 3^" X 3"
X 5/i6". These results may be obtained by the use of Tables 43, 44 and 45, from which it is seen
that the allowable stress in a member composed of two angles 3^" X 3" X 5/16" about axis
i-i ( Y-Y), the length being 12' o", is 38,000 lb., and about axis 2-2 (X-X), the length being 6' o",
is 40,000 lb., and the allowable load will be 38,000 lb.
Two Angles Starred. — Design a member consisting of two angles starred, as in Fig. 6, to
carry a compressive stress of 30,000 lb., the length to be 15' o". center to center of connections.
References. — § 34, p. 57; § 84, p. 60; § 100, p. 61.
Solution. — Using 125 as the maximum value of l/r, and fe = 16,000 — 70 l/r lb. per sq. in.
as the allowable unit stress, the minimum allowable value of r is found to be
,/r,125, r = jL. 15.X" in.
125 125
Section m-m.
FIG. 6. Two ANGLES STARRED.
From Table 67 it is seen that 4" X 4" angles are the smallest equal leg angles that can be
used, and that r will be about 1.56 in., and the allowable unit stress is
fc = 16,000 — 70 X — — ^ = 7,920 lb. per sq. in.,
which requires an area of
P 30,000
A = -J- = -- — = 3.79 sq. m.
f> 7.920
The area of two angles 4" X 4" X W is 3.88 sq. in., and r = 1.57 in., which will satisfy the condi-
tions. The batten plates must have a spacing of not more than
= 75 in. = 6' 3";
f O OOl ilOOl OOO!
err.--.-.--) ~ h--|-rr-t- i">"T r-Jr"i-i =
|°9°! ~'~ i LQj.Qj "]" |ooo|
3-'9" ^ 3'-9" "J^ 3-9" J^ 3-9"
the value of 0.79 in. being the least radius of gyration for one angle 4" X 4" X 1A" (Table 23).
Convenience in detailing may make it advisable to make / much less than 6' 3". A spacing of
3' 9" was used as shown in Fig. 6.
PLATE AND ANGLE COLUMN. 579
Plate and Angle Column. — Design a plate and angle column, Fig. 7, to carry an axial load of
340,000 lb., the unsupported length being 1 6' o".
References— § 34, p. 57; § 38, p. 57; § 79, p. 60; § 94, p. 61; § 96, p. 61; § 100, p. 61; § 114,
p. 62; § 9, p. 104; § 12, p. 104; § 17, p. 104.
Solution. — A section with a 12 in. web plate and two 14 in. flange plates will be assumed. The
angles will be spaced 12% in. back to back to allow for an over-run in the web plate without inter-
fi-riiiv; with tin- cover plates.
The radius of gyration about the axis A -A, Fig. 7, is approximately 0.45 X 12.5 — 5.62 in.
(Table 136), and about the axis B-B is 0.23 X 14 = 3.22" (Table 136). The axis B-B will
control the design. The allowable unit stress is
/„ = 16,000 - 70 l/r lb. per sq. in. - 16,000 - 70 X = 11,800 lb. per sq. in.
which requires an area of
P 340,000
A = r = - - = 28.8 sq. in.
/„ I i, 800
Try a section consisting of four angles 6" X 4" X %" with long legs turned out, and 12%
in. back to back, one web plate 12 in. X % in. and two flange plates 14 in. X % in. The prop-
erties of various sections are given in Table 70. The properties of sections are calculated as
shown at the bottom of the table. The radius of gyration about the axis A-A is found to be
*A. — 3 5** in., about the axis B-B is rB = 3.14 in., and the area 29.44 sq- in.
FIG. 7. PLATE AND ANGLE COLUMN.
For this section the ratio l/r = 16 X 12/3.14 = 61.2 which satisfies the specification that
the maximum value of l/r is 125. The allowable unit stress is,
fe = 16,000 — 70 'X 61.2 = 11,700 lb. per sq. in.,
and the required area is,
P 340,000
A = 7- = - - — • = 29.1 sq. in.
fe 11,700
The area provided by the above section is 29.44 sQ- in.
Expansion Rollers. — Design the rollers for the expansion end of a single track railway bridge
of 175 ft. span, the dead load stress being 110,000 lb., the live load stress being 282,000 lb., and
the impact 178,000 lb. Total stress = 570,000 lb.
References. — § 19, p. 209; § 60, p. 212; § 62, p. 206; § 62, p. 212.
Solution. — The span being short a 6 in. roller will be used.. The allowable stress per linear
inch of rollers is 600 X d, when impact is considered, giving 600 X 6 = 3,600 lb. for 6 in. rollers.
The number of linear inches required is, 570,000/3,600 = 158 in.
Five rollers 32 in. long provide 5 X 32 = 1 60 linear inches and occupy a space about 32 inches
square.
For highway bridge expansion rollers, see § 41, p. 141; § 82, § 83, § 84, p 144.
For roof truss expansion rollers, see § 7, p. 55; § 33, p. 57; § 117, p. 62; § 15, p. 104.
MEMBERS IN FLEXURE. — The design of structural members stressed in flexure will be shown
by several examples.
I-Beam. — Select an I-Beam to carry a uniform load of 1000 lb. per linear foot, the span being
16' o" and the ends simply supported.
580 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
References— § 33, p. 57; § 42» P- 58; § 45. P- 58; § 14. P-'^H; § 39, p. 141; § 50, p. 142; § 55,
p. 142; § 17, p. 209; § 29, § 30, p. 210. Properties of Carnegie I-Beams are given in Tables 7 to
13 inclusive. Properties of Bethlehem Girder and I-Beams are given in Tables 151 to 160,
inclusive.
Solution. — The bending moment is
M = y%w-P = y% X looo X I62 = 32,000 ft.-lb. = 32,000 X 12 in.-lb. = 384,000 in.-lb.
From applied mechanics,
c
The section modulus required is then,
'' I M 384,000 . ,
S =- =— =?-2 - = 24.0 in.8
c f 16,000
The section modulus of a 9 in. I @ 35 lb. is 24.8 in.3, and of a 10 in. / @ 25 lb. is 24.4 in.3 (Taole
7), either of which will carry the load, but the IO in. I @ 25 lb. being lighter is the more economical,
and being the minimum section is more easily obtained.
The allowable bending moments in ft.-lb. for I-Beams, using a fiber stress of 16,000 lb. per
sq. in., are given in Table 7. The I-Beam could have been selected directly from the moment
making use of these values. The allowable bending moments for other unit stresses are propor-
tional.
The safe uniform load, in tons, for I-Beams are given in Table 12, using a fiber stress of
16,000 lb. per sq. in. The I-Beam could have been selected directly from the load by using
this table. Safe loads for other unit stresses are proportional.
If the I-Beam is not supported to prevent lateral deflection the allowable fiber stress must be
reduced by the compression formula as shown in Table 120.
Design an I-Beam 14' o" long to carry a concentrated load of P = 20,000 lb. at the center
of the beam. The maximum moment is at the center, and is, M = %P-l = M X 20,000 X 14
= 70,000 ft.-lb. = 840,000 in.-lb.
The required section modulus is, S = M/f = 840,000 -j- 16,000 = 52.5. In Table 7, the
lightest beam that will carry the load is a 15 in. I @ 42 lb., which has a value of 5 = 58.9 in.3,
and a bending moment of 79,000 ft.-lb. A 12 in. / @ 55 lb. will also carry the load, but is not an
economical section. A concentrated load, P, at the center will give the same maximum stresses
as a uniformly distributed load of 2P. From Table 12, a 15 in. / @ 42 lb. will carry a uniformly
distributed load of 22 tons, which is sufficient.
Two I-Beams with Separators. — Design a girder consisting of two I-Beams fastened together
by means of separators, the girder having a span of 16' o" and carrying a uniform load of 2,000
lb. per linear ft.
References— § 33, p. 57; .§ 19, p. 105; § 39, p. 141; § 17, p. 209; § 30, p. 210.
Solution. — The bending moment is
M = | w.l2 = | X 2000 X i62 = 64,000 ft.-lb. = 798,000 in.-lb.
From mechanics,
The section modulus required is,
I M 798,000 . .
S = - = -r = ~ - - 48.0 in.3
c f 16,000
Each I-Beam must have a section modulus of f X 48.0 = 24.0 in.3 The section modulus
of one 9 in. I @ 36 lb., is 24.8 in.3 and of one 10 in. / @ 25 lb., is 24.4 in.3, either of which will
carry one-half the load, but the 10 in. / @ 25 lb. being lighter is the more economical, and being
the minimum section is more easily obtained.
The allowable bending moments, in ft.-lb. for I-Beams, using a fiber stress of 16,000 lb. per
PLATE GIRDERS. 581
tq. in. are given in Table 7. The I-Beams could have been selected directly from the moment
making use of these valu<
The safe uniform load, in tons, for I-Beams is given in Table 12, using a fiber stress of 16,000
Ib. per sq. in. The I-Beams could have been selected directly from the load using this table.
If the girder is not supported to prevent lateral deflection the allowable fiber stress must be
reduced by the compression formula as shown in Table 120.
The separators for Carnegie I-Beams are given in Fig. 4, page 83, Chap. II. The separators
for lU-thlfhrm beams are given in Table 158.
Plate Girders. — The full discussion of the design of plate girders would require more space
tli.in is available. The following notes will be of value.
References. — The following references should be consulted.
Weights.— P. 115; p. 150; p. 151; p. 152; p. 153; p. 155; p. 156; p. 158.
Bending Moments and Shears. — Pages 159, 163, 164, 165, 166, 167, 173, 174.
Unit Stresses— §33, §35, §36, p. 57; §42, §43, p. 58; §36, §37, §39, §40, §41, §44, p.
Hi; § 50, § 51. § 52, § 53. § 54. P- 142; § 14. § 29. P- 206; § 14, § 15, § 17, § 18, § 19, p. 209; § 29,
§30, p. 210.
Proportion of Parts— § 3, p. 55; § 43, p. 58; § 3, p. 137; p. 202; p. 203; § 26, § 29, § 30, § 77,
p. 206; § 79, p. 207; § 26, § 27, § 29, § 31, § 32, § 38, p. 210; § 57, p. 21 1 ; § 77, § 78, § 79, p. 212;
§ 80, p. 213; pages 220, 221, 222.
Details. — Pages 54, 123, 124, 189, 190.
The gross and net areas of angles are given in Table 29; Area of Plates, Table I ; Areas to be
Deducted for Rivet Holes, Table 116; Moments of Inertia of Angles, Tables 32, 33 and 34;
Moments of Inertia of Web Plates, Table 3; Moments of Inertia of Cover Plates, Table 5; Prop-
erties of Plate Girders, Table 87; Centers of Gravity of Plate Girder Flanges, Table 88.
Nomenclature. — The following nomenclature will be used.
M = resisting moment of section.
V = vertical shear at section.
/ = allowable unit fiber stress.
/ = moment of inertia of gross section.
/' = moment of inertia of net section.
/» = moment of inertia of gross section of web plate.
/»' = moment of inertia of net section of web plate.
AF = gross area of one flange.
Af = net area of tension flange.
Aw = gross area of web.
h = distance between centers of gravity of flanges.
V = distance between gage lines of rivets in tension and compression flanges.
d = distance back to back of angles in flanges.
c = distance from neutral axis to extreme fiber.
p = pitch of rivets in flanges.
r = allowable resistance of one rivet.
w = concentrated load per unit length of rail = P/l where P = concentrated load and
/ = distance over which the load, P, is considered as distributed (see § 5, p. 202).
2« = number of rivets on one side of web splice.
Resisting Moment. — There are four methods now in use for determining the resisting moment
ot a plate girder section.
(1) Assuming that all the bending moment is carried by the flanges (see § 29, p. 206),
M = AF'-}-h (i)
(2) Assuming that one-eighth the gross area of the web is available as flange area (see § 42,
P- 58; § 50, p. 142; § 29, p. 206),
lAJ-f-h (l')
582 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
(3) By moment of inertia of net section (see § 42, p. 58; § 50, p. 142; § 29, p. 206),
M = — (i")
c
(4) By moment of inertia of gross section (used by American Bridge Co. for plate girders
for buildings),
M =*-- (i";)
c
Rivets in Flanges Which do not Carry Concentrated Loads.
(i) Assuming that all bending moment is carried by flanges,
Tr3
O O 0 0
o o
°
0
o o o o
°0
0
•e
o
0
! |v>
o
0
o
o
r *^ 1
o
J.J.^.
°0
o
0
-TH
"^"^.^.Lb—
1 >?•$-?.-
0
-o-
o
*~Nei/tral Axii
>£ ""f
o
0
[
0
0
i
o
-O1
o
O
\oooo
0 0
o
o
0 0 0 0 I
mm
Jjlllll
lljlili
HeutralAxh
FIG. 8. WEB SPLICE FOR PLATE GIRDER. FIG. 9. WEB SPLICE FOR PLATE GIRDER.
P-'-£ (2)
(2) Assuming that one-eighth the gross area of web is available as flange area,
Ai> + \AW * r-h'
P =
(3) By moment of inertia of net section,
AF' X V
p=l
(4) By moment of inertia of gross section,
2r-I'
V-AF-h
Rivets in Flanges Carrying Concentrated Loads.
(i) Assuming that all the bending moment is carried by the flanges,
P =
(2) Assuming that one-eighth the gross area of the web is available as flange area,
r
P = —
(3) By moment of inertia of net section,
P =
(3)
(4)
(5)
(6)
(7)
(8)
PLATE GIRDERS. 583
(4) By moment of inertia of gross section,
Rivets Connecting Cover Plates to Flange A ngles.
(i) and (2). Assuming that all the bending moment is carried by the flanges, or that one-
eighth the gross area of the web is available as flange area,
n-r-d-.\F
p- ~v^T
where n = number of rivets on one transverse line.
r = value of one rivet in single shear or bearing.
d = distance back to back of angles.
At = total net area of cpver plates in one flange.
(3) By moment of inertia of net section,
^n•T•r
p-vtt
where A «/ = total net area of cover plates in one flange.
he = distance between centroids of all cover plates in tension flange and all cover plates
in compression flange.
(4) By moment of inertia of gross section,
zn-I-r
P = V^h.
where A e = total gross area of cover plates in one flange.
he = distance between centroids of all cover plates in tension flange and all cover plates
in compression flange.
Web Splice. — An ordinary web splice is shown in Fig. 8. Where splice plates are designed
to carry part of the moment as well as the shear the splice shown in Fig. 9 is sometimes used.
Plates AB and A'B' are assumed to transfer that part of the moment carried by the web, and
plate CD to transfer the shear. Two lines of rivets should be used in each section of the web
spliced. The number and spacing of rivets in a web splice can be determined only by trial,
except when the first method for proportioning the section is used. The rivet most remote from
the neutral axis is the most severely stressed.
(1) Assuming that all the bending moment is carried by the flanges,
V V
r = — , and 2n = — (13)
2n r
(2) Assuming that one-eighth the area of web is available as flange area. The stress in the
outermost rivet is given by the formula, where M' is moment carried by web,
.
(3) By moment of inertia of net section. The stress in the outermost rivet is given by the
formula;
(4) By moment of inertia of gross section. The stress in tho outermost rivet is given by the
formula
For the details of a web splice, see Fig. 16.
584 THE DESIGN OF STEEL DETAILS. CHAP. XVIL
Flange Splice. — Flanges should never be spliced unless it is impossible to get material of
the required length. Flange splices should always be located at points where there is an excess
of flange section, no two parts of the flange should be spliced within two feet of each other. Rivets
in splice plates and angles should be located as close together as possible in order that the transfer
may take place in a short distance. No allowance should be made for abutting edges of spliced
members of the compression flange.
Flange angles should be spliced with a splice angle of equal section riveted to both legs of
the angle spliced. Where this is impossible the largest possible splice angle should be used and the
difference made up by a plate riveted to the vertical leg of the opposite angle. The number of
rivets required in the splice angle on each side of the joint in the angle is given by the formula,
»=/Jr (17)
where / = the allowable unit stress in the flange, A = area of spliced angle, and r = the allow-
able stress on one rivet. Rivets which are already considered as transferring the shear may be
considered as splice rivets if they are included in the splice angle.
Cover plates should be spliced with a splice plate of equal section. The number of rivets
required in the splice plate on each side of the joint is determined by the above formula if the plates
are in direct contact in the same way as for splice angles. Where one or more plates intervene
between the splice plate and cover plate which it splices, rivets should be used on each side of the
joint in excess of the number required in case of direct contact, to an extent of one-third that
number for each intervening plate (see § 79, p. 144, and § 57, p. 211).
The above methods for flange splicing apply only when methods (i) and (2) of proportioning
sections are used, but may be used with sufficient accuracy when methods (3) and (4) are used.
Strictly speaking for methods (3) and (4) splice angles and plates should have moments of inertia
about the neutral axis, equal to the moments of inertia of the members they splice, about the
neutral axis. An exact analysis for the number of rivets required in splices would give a less
number than obtained from above formula.
Stiff eners. — For method of designing stiff eners see §43, p. 58; §52, p. 142; §79, p. 207;
§79, p. 212; p. 221.
Pins and Pin Packing. — A pin under ordinary conditions is a short beam and must be designed
(i) for bending, (2) for shear, and (3) for bearing. If a pin becomes bent the distribution of the
loads and the calculation of the stresses are very uncertain.
The cross-bending stress, /, is found by means of the fundamental formula for flexure,
f = M-c/I, where the maximum bending moment, M, is found as explained later; / is the moment
of inertia; and c is one- half the radius of a solid or hollow pin.
The safe shearing stresses given in standard specifications are for a uniform distribution of
the shear over the entire cross-section, and the actual unit shearing stress to be used in designing
will be equal to the maximum shear divided by the area of the cross-section of the pin.
The bearing stress is found by dividing the stress in the member by the bearing area of the
pin, found by multiplying the thickness of the bearing plates by the diameter of the pin.
References. — §41, p. 58; §90, p. 61; §99, p. 61; § 107, p. 62; §39, p. 141; § 40 and §41,
p. 141; § 74, p. 143; § 75, p. 143; § 76, p. 143; §92, p. 144; § 141, p. 145; § 142, p. 145; § 144,
p. 146; § 17, p. 209; § 18, p. 209; § 19, p. 209; §28, p. 210; § 52, p. 21 1 ; § 54, p. 21 1 ; § 136, p.
216; p. 219; p. 220; p. 402.
Details of Pins. — Details of bridge pins are given in Table 95, Part II.
Stresses in Pins. — The method of calculation will be illustrated by calculating the stresses in
the pin at U\ in (a) Fig. 10. In the complete investigation of the pin U\, it would be necessary
to calculate the stresses when the stress in UiUz was a maximum, and when the stress in U\Lz
was a maximum. Only the case where the stress in U\ Uz is a maximum will be considered. How-
ever, maximum stresses in pins sometimes occur when the stress in UiLz is a maximum, and this
case should be considered in practice.
PINS AND PIN PACKING.
Bending Moment. — The stresses in the members are shown in (c) Fig. 10, which gives the
force polygon for the forces. The make-up of the members is shown in (a), and the pin packing
on one side is shown in (b). The stresses shown in (c) are applied one-half on each side of the
iiicinlMT. the pin acting like a simple beam. The stresses are assumed as applied at the centers
of the plates which make the members.
!>< '$ J r**fey5
j Him,tPl.< r^t I'*** • * '•
^1
_£ -^ ^^ ^r
(d)
>&*>
I /^c"'
j 1-165400*0.55- 07660
i Vertical Components,
\ Moments at
1 5=0*"
•<w**m> | - i'^;^r"
force Di'aqram-^tre55e5 U . ' 5-0*"
, v Total Moment at 4Z-8 7=I26300<I.S}=23IIOO*"
- ^08600 * +285000 2 8-176500*3.06
-15 1600*" -dJ/MxIll-ZdWOO*''
3. CALCULATION OF STRESSES IN A PIN.
FIG. 10.
Calculation of Stresses in a Pin. — The amounts of the forces and the distances between their
points of application as calculated from (6) are shown in (d) Fig. 10. The horizontal and vertical
components of the forces are considered separately, the maximum horizontal bending moment
and the maximum vertical bending moment are calculated for«the same point, and the resultant
moment is then found by means of the force triangle.
In (d) the horizontal bending moments are calculated about the points I, 2, 3, 4; the maximum
horizontal moment is to the right of 3, and is 208,600 in.-lb. The vertical bending moments are
calculated about points 5, 6, 7, 8; the maximum bending moment is to the right of 8, and is
283,000 in.-lb. The maximum bending moment is at, and to the right of 4 and 8, and is, M =
+ 283,000* = 351,600 in.-lb. Substituting in the formula,/ = M-c/I, the maximum
bending stress is / = 16,600 Ib. per sq. in. The allowable bending stress in pins for which this
bridge was designed was i8,oop Ib. per square inch. The allowable bending moments on pin
are given in Table 98.
Shear.— The shear is found for both the horizontal and vertical components as in a simple
beam, and is equal to the summation of all the forces to the left of the section. The maximum
horizontal shear is between I and 2, and is 165,400 Ib. The shear between 2 and 3 is 165,400
— 99,300 = 66,100 Ib. The maximum vertical shear is between 6 and 7, and is 126,300 Ib. The
resultant shear between 2 and 3, and 6 and 7, is, V = ^i 26,300* + 66,100* = 145,000 Ib., which
is less than the horizontal shear between I and 2. The maximum shear, therefore, comes
586
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
between I and 2, and is 165,400 Ib. The maximum shearing unit stress is 165,400 -5- 28.27 =
5,850 Ib. per sq. in. The allowable shearing stress was 9,000 Ib. per sq. in.
Bearing. — The bearing stress in L$U\ is 160,650 -5- (6 X 1.94) = 13,800 Ib. Bearing stress
in UiUz is 165,400 -j- (6 X 1.88) = 14,600 Ib. Bearing stress in UiLj. is 42,200 -j- (6 X 0.89)
= 7,900 Ib. Bearing stress in t/iLg is 107,000 4- (6 X IT'S) = 12,400 Ib. per sq. in. The
allowable bearing stress was 15,000 Ib. per sq. in. Allowable bearing stresses on pins are given
in Table 97.
For the calculation of the stresses in the pins of a 160 ft. steel highway bridge, see the author's
"The Design of Highway Bridges," Chap. XXII, Part III.
Pin Packing. — For details of pin packing see pages 219, 220 and page 402. Details of pins
are given in Table 95, Part II.
Corrugated Steel Roofing. — For the calculation of the strength of corrugated steel and for
a diagram for the safe loads for corrugated steel, see Fig. 18, Chap. I, page 22.
Bearing Plates. — The bearing plates required for beams and columns, Fig. II, may be deter-
mined by the following formulas.
Let R = reaction of beam or load on column.
A = area of bearing plate.
w = allowable unit pressure in masonry.
/ = allowable fiber stress in plate.
P = projection of bearing plate beyond any edge of beam or column.
Area of bearing plate,
Y/////7/77,
FIG. ii. BEARING PLATES.
A-*
w
Thickness of bearing plate required by a given projection,
n$R jyv
t=HATf = Hj
Safe projection for a given thickness of plate,
*-*Viif"<Vw
(18)
(19)
(20)
The allowable pressures of bearing plates on masonry (value of w) are given in Table VIII,
page ^75. Standard bearing plates for I-beams are given in Table 8; for channels in Table 15.
The length of I-beams which should bear on plates in order that the full shearing strength be
developed is given in Table 11; and of channels in Table 16.
For a full discussion of bearing plates, see Bulletin No. 35, University of Illinois Engineering
Experiment Station, entitled "A Study of Base and Bearing Plates for Columns and Beams,"
by Professor N. Clifford Ricker.
COMBINED FLEXURE AND DIRECT STRESS.— The formulas for combined flexure and
direct stress are given in section 26, Chapter XVI. The design of members stressed in com-
bined flexure and direct stress will be shown by several examples.
Eye-Bar. — An eye-bar in a structure carries a direct stress due to the dead and live loads,
and in addition is stressed in flexure due to its own weight.
COMBINED FLEXURE AND DIRECT STRESS. 587
If P = direct stress in eye-bar; M\ - bending moment due to weight in in.-lb.; c — distance
from neutral axis to extreme fiber - h/2, where h - depth of eye-bar; / - length of bar, c. to c.
of pins, / - thickness of eye-bar in inches; / — moment of inertia of eye-bar «• -fa t-tf; k ia a
coefficient depending upon the condition of the ends being approximately 10 for eye-bars with pin
rmls, 24 for one pin end and one fixed end, and 32 for two fixed ends; E — modulus of elasticity
p
of sti>el — 28,000,000 Ib. per sq. in.; and ft — -—? — unit stress due to direct loads. Then
* • n
the stress due to combined flexure and direct stress will be
k-E
Now, Mi = Iw-P, where w = 0.28 t-h = the weight of the bar per lineal inch; P = ft- t-h;
A/z; / = iV'A5; k = 10; and E = 28,000,000 Ib. per sq. in.; and substituting
Jw-/*-JA 4,900,000%
b-h* , h'b-h-P t . /AV
ft + 23,000,000 r )
10 X 28,000,000 •" \/ /
(22)
12 10 X 28,000,000
then /i is the extreme fiber stress in the bar due to weight, and is tension in the lower fiber and
compression in the upper fiber.
If the bar is inclined, the stress obtained by formula (22) must be multiplied by the sine
of the angle that the bar makes with a vertical line.
Diagram for Stress in Bars Due to Weight. — Taking the reciprocal of equation (22)
, 23,000,000 I 7
1 = h + \LL_ = y. +
fi 4,9OO,oooA 4,9oo,oooA
and
A diagram for solving equation (23) is given in Table 134, Part II, which see. The intersections
of the inclined lines in Table 134 correspond to depths of eye-bar that give maximum stresses
due to weight.
End-Post. — Design the end-post, Fig. 12, for a 160 ft. span through highway bridge. Panel
length, 20' o"; depth of truss c. to c. of pins, 24' o"; length of end-post, 31' 3". The direct
stresses are as follows: dead load stress = 30,000 Ib.; live load stress = 60,000 Ib.; impact =
loo/(i6o -f- 300) X 60,000 = 13,000 Ib.; total direct stress due to dead load, live load and
impact = 103,000 Ib. The bridge is to be a class C bridge designed according to the "General
Specifications for Highway Bridges," in Chapter III. From § 38 of the specifications the allow-
able unit stress is/e = 16,000 — 70 l/r. The section will be made of two channels and one cover
plate. Try a section made of two 10 in. channels @ 15 Ib., and one 14 in. by 5/16 in. plate, (6),
Fig. 12. From Table 82, Part II, the radius of gyration about the horizontal axis A -A, is rA = 3.99
in., and about the vertical axis B-B is, rB = 4.67 in., and the eccentricity is, e = 1.70 in. The
allowable stress is then fe = 16,000 — — • = 9,400 Ib. per sq. in. The required area will
o^yy
be = 103,000 -f- 9,400 = 10.96 sq. in. The actual area is 13.30 sq. in. While the section ap-
pears to be excessive, it will be investigated for stress due to weight, eccentric loading and wind
before rejecting it.
The area, radii of gyration and the eccentricity may be calculated as follows.
To calculate the area
area of two 10 in. channels (Table 14) = 8.92 sq. in.
area of one 14 in. by 5/16 in. plate (Table 2) = 4.38 sq. in.
Total area = 13.30 sq. in.
588
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
To locate the neutral axis A-A , take moments about the lower edge of the channels
8.92 X 5 +4-38 X 10.156
13-30
= 6.70 in.
The eccentricity is e = 6.70 — 5.00 = 1.70 in. The moment of inertia IA> about axis A-A
may be calculated as follows:
Let Ic = I of channels about center of channels (Table 14).
IP = I of plate about center of plate (Table 4).
AC = area of channels (Table 14).
Ap = area of plate (Table i).
1
1
tVj ^
§f
s?
1
J
KH
V--7400
a =3.87
= 12.50'
FIG. 12. END-POST OF A HIGHWAY BRIDGE.
Then IA = Ie + Ip + Ac X i-7o2 + APX 34562.
= 2 X 66.9 + 0.04 + 8.92 X I-702 + 4.38 X 34562
= 133-8 + 0.04 + 25.76 + 52.20
= 211.80 in.4
Then rA = ^IA + A = ^2 11.80 -r- 13.3 = 3.99 in.
The moment of inertia IB, about axis B-B may be calculated as follows.
Let Ic' = I of channels about neutral axis parallel to the web (Table 14).
IP' = I of plate about vertical axis (Table 3).
Ac = area of channels (Table 14).
From Table 82 the distance back to back of channels is 8% in. From Table 14 the distance
from neutral axis to back of channel is 0.639 in. The ^'stance from neutral axis of channels to
axis B-B is 4.25 + 0.639 = 4-889 in. (4.89 in. will be used).
Then IB = // + •/„' + Ac X 4-«92
= 4.60 + 71.46 + 9.82 X 4.8g2
= 4.60 + 71.46 + 213.28
= 289.34 in.4 __ _
Then rB = ^IB •*- A -. "^289.34 -*- 13.3 = 4.67 in.
DESIGN OF END-POST. 589
Stress Due to Weight of Member. — The total weight of the member will be
Two 10 in. channels @ 15 lb., 31' 6" long - 945 Ib.
One 14 in. X 5/16 in. plate @ 14.88 lb., 30' o" long - 447 Ib.
Details and lacing about 25 per cent «• 308 lb.
Total Weight, W - 1700 lb.
The bending moment due to weight of member is M = \W'l-t>\n B.
Stress due to weight
M-c IW-l-smO.*
Jw P-P P-t*
A loE A loE
The stress due to weight in the upper fiber will be
- = j X 1.700 X 375 X 0.645 X 3-6125
2II8 103.000 X375*
10 X 30,000,000
= 940 lb. per sq. in.
The stress due to weight in the lower fiber is
/'«. = - 6.70 X 94° -*• 3-6i25
= — 1745 lb. per sq. in.
Stress Due to Eccentric Loading. — The pins were placed i inch above the center of the channels,
and the stress due to eccentric loading will be
_ M,-c _ P X (1.70 - Q-5) X c ,
T - ?-* ~ P'*
~ loE ~ loE
The eccentric stress in the upper fiber will be
, _ 103,000 X 1.20 X 3.6125
~ 211 8 - l0^000 X 375>
10 X 30,000,000
= — 2,280 lb. per sq. in.
The eccentric stress in the lower fiber is
fe = + 6.70 X 2,280 -r- 3.6125
= + 4,230 lb. per sq. in.
The resultant stress due to weight and eccentric loading is/z =/«•+/«= + 940 — 2,280 =
— 1,340 lb. in the upper fiber, and — 1,745 + 4i23° = 2485 lb. per sq. in. in the lower fiber.
The allowable stress due to weight and eccentric loading is greater than 10 per cent of the
allowable stress and must be considered, with the allowable unit stress increased by 10 per cent
(§ 48, p. 142).
The total unit stress in the member will be, / = 103,000 -f- 13.30 + 2,485 = 7,752 + 2,485
= 10,237 lb. per sq. in. The allowable unit stress when weight and eccentric loading are con-
sidered is 9,400 X i.io = 10,340 lb. per sq. in., which is sufficient.
Stress Due to Wind Moment. — The stresses in the portal and the direct wind stresses in the
end-post when the end-post is assumed as pin-connected at the base are shown in (d) and (e) Fig.
12. The end-posts may both be assumed as fixed if the windward end-post is fixed. To fix the
windward end-post the bending moment must not be greater than the resisting moment which
will be
M, = H-y0 = (90,000 - V - D')a/2
where V = 5,060 lb. and D' = 7,000 lb. the direct stress due to wind, and a = distance center
to center of metal in the sides of the end-post = 8.87 in., (/), Fig. 12. (The impact stress is
omitted.) If y«is taken equal to \d = 10' o" = 120 in., we will have
2,000 X 120 < (90,000 — 5,060 — 7,000) 8.87/2
which makes 240,000 < 345,600, and the end-post may be assumed as fixed at the base.
590 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
The stress due to bending moment due to wind loads in the leeward end-post will be,
M-c
/. = p^ (27)
I ?;
_ 240,000 X 7
= ^8 (90,000 + 5.060 + 7,000)2582 = 6'73° lb> *** Sq' m'
10 X 30,000,000
The total stress due to direct wind load will be fw = (5060 + 7ooo)/i3.3O = + 910 Ib. per
sq. in. The total maximum wind load stress will come on the windward fiber of the leeward
end-post, and will befw" = + 6,370 + 910 = + 7,280 Ib. per sq in.
The maximum stress due to direct dead and live loads (not including impact) and wind load
stresses will be
/ = 90,000 -5- 13.30 + 7,280
= 6,770 + 7,280 = 14,050 Ib. per sq. in.
From § 46 in the specifications the allowable stress may be increased 50 per cent when direct
and flexural wind stresses are considered.
The allowable stress when both direct and flexural wind stress are considered is then
fe = 9,400 X 1.50 = 14,000 Ib. per sq. in.
The stresses in the windward post will be less than in the leeward end-post calculated above.
While the section assumed appeared to be excessive, the additional area and the width of
plate .are required to take the flexure due to wind loads.
For the method used by the C. M. & St. P. Ry. for the design of an end-post, see p. 222.
Column of a Transverse Bent. — Design a column similar to that of the transverse bent shown
in Fig. 3, Chapter XVI, but having column length of 25' 6" and being hinged at the base. Direct
stress = + 12,800 Ib., bending moment at foot of knee brace = 181,250 ft.-lb. Shear = H
= 13,500 Ib.
References. — § 34 and § 38, p. 57; § 79, § 80 and § 84, p. 60; § 94, § 97, § 98 and § 100, p. 61.
Solution. — A section composed of four angles and a plate will be used. The column will be
supported laterally by the girts so the length in that direction will be taken as % X 25' 6" = 12.75
ft.
Try 4 angles 5" X Z1A" X 1A", long legs out, 18^ in. back to back and one web plate 18 in.
X % in. Distance between rivet lines = i8J^ —2X2 = 14^2 in. Maximum allowable
distance for % in. plate = 40 X % = 15 in.
Using method at bottom of Table 69, A = 22.75 in-2; I A — I.3H m-4; IB = 94-6 in.4;
rA ~ 7-59 in-; ?B = 2-°4 in. The greatest value of / -r- r — 12.75 X 12 -j- 2.04 = 75.0. The
maximum allowable value of I -r- r = 125. The allowable unit stress is:
1.50(16,000 — 70 Ijr) = 1.50(16,000 — 70 X 75.0) = 16,100 Ib. per sq. in.
The actual unit stress is:
S
I2JOO __ 181,250 X 13X9.25 = I6>ooolb.
__
A T - P'P 22-75 _ I2'8o° x 25-5 x
10 X 30,000,000
Floorbeam. — Floorbeams are designed in the same way as other plate girders. The section
cut away for clearance at the joint must be strengthened by means of plates as shown in Fig. 13.
To determine the strength at the weakest section, A-A, the following method is used.
The floorbeam is drawn to scale in Fig. 13, so that distances can be scaled and the maximum
floorbeam reaction 189,980 Ib. be resolved graphically, in the center line of the post, into 80,000
Ib. normal to A-A, which produces direct tension on the section A-A, and 173,000 Ib. parallel
to A-A, which produces shear and flexural stress.
DESIGN OF A FLOORBEAM.
.V.M
Rivt t holes arc considered as spaced 3 in. along the section A-A, for when the beam is detailed
ii i-, not probable that they will be spaced closer than 3 in. Holes are deducted from the tension
side only. I in. holes being deducted for % in. rivets.
The plates may not be exactly as indicated on Fig. 13 for it may be necessary to alter them
slightly in detailing, but small changes will not change the results materially. It is quite an
a<l\. mtage to have the investigation made before the beam is completely detailed as alterations
are more easily made at that time if the beam proves weak in any particular.
The curved angle at the bottom will not be considered as adding to the strength.
Values for the area, eccentricity and moment of inertia are found as follows.
First the moments and moments of inertia of the separate parts are found about an axis
through the geometric center of the section, the eccentricity is then calculated. The moment
of inertia about an axis through the center of gravity is found by subtracting the product of the
FIG. 13. DETAIL OF FLOORBEAM CONNECTION.
area and the eccentricity squared from the moment of inertia about the axis through the geometric
center or
J — J - A .iA
*C — •*»» 1 r
Note. — For sake of simplicity the total section was divided up as follows:
A, includes three 1A in. and two % in. plates, the 6" X %" legs of the flange angles and %
in. -\-% in. of the 4" X Y*" leg. The spaces allowed for clearance were considered as solid with
no appreciable error.
B, includes the remainder of the 4" X %" legs of flange angles.
C, includes the % in. outside plates considered as solid.
D, includes the rivet holes, i in. in diameter and 3.5 in. long, spaced 3 in. center to center.
592
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
TABLES OF AREAS, MOMENTS AND MOMENTS OF INERTIA.
Section.
Size,
In.
Area,
Sq. In.
In!
Moment,
In.-Lb.
Yo,
In.
In*'.
A
35-5 X 2.75
+97.6
O
O
O
O
Moment of Inertia about own axis
+ 10,250
B
5.75 X 0.625
+ 3-6
Me
+ 17-4
>ment of Inert
+ 62.6
a about own c
+ 17-4
LX1S
+ 1,088
o
c
18.0 X 0.75
+ I3'5 M
Me
- 8.8 -118.6
>ment of Inertia about own £
- 8.8
ixis
+ 1,044
+ 365
12,747
D
5XIX3-S
— 17.5
- 9-3
+ 162.6
- 9-3
Moment of Inertia about own axis
- 315
+97.2
+ 106.6
IO.QIQ
e = 106.6 -5- 97.2 = i.io A-e"1- = 97 2 X i.io2 = 117
Total moment of inertia about centroidal axis = 10,802
The bending moment of this section, from Fig. 14 is
M = 189,980 X 27 = 5,130,000 in.-lb.
or
M = 173,000 X 29.5 = 5,130,000 in.-lb
The direct tension is 80,000 Ib.
The shear on the section -is 173,000 Ib.
Compression in extreme fiber due to moment
Si = M-c' -f- I = (5,130,000 X 16.65) -*• 10,802 = + 7,850 Ib. per sq. in.
Tension in extreme fiber due to moment is
Si = M-c" '/I = 5,130,000 X 18.85 -*• 10,802 = — 8,950 Ib. per sq. in.
Tension on whole section due to direct stress
S2 = P/a = 80,000 -f- 97.2 = — 820 Ib. per sq. in.
Total compression in extreme fiber
S = Si + Sz = 7,850 — 820 = + 7,030 Ib. per sq. in.
Total tension in extreme fiber
S = Si + Sz = — 8,950 - 820 = — 9,770 Ib. per sq. in.
Unit shear is approximately
S = 173,000 -r 97.2 = 1,780 Ib. per sq. in.
The allowable unit stress in compression = 16,000 Ib. per sq. in. (Spec. § 16).
The allowable unit stress in tension = 16,000 Ib. per sq. in. (Spec. § 15).
The allowable unit stress in shear = 10,000 Ib. per sq. in. (Spec. § 19).
END CONNECTIONS FOR TENSION AND COMPRESSION MEMBERS.— For simple
connections with concentric stresses the number of rivets in riveted end connections may be taken
as equal to the total stress in the member divided by the allowable stress on one rivet for bear-
ing or for shear, Table 114, whichever gives the larger number of rivets. Specifications uni-
formly require that the connections of members be designed to develop the full strength of the
member. The minimum number of rivets in shop connections should be two rivets, except for
lacing bars; while the minimum number of rivets in field connections should be three rivets,
except for lacing bars. In lateral bracing or stiff bracing or struts the actual number of rivets
required to develop the full strength of the member should be increased by two rivets, for the
reason that two rivet holes are almost certain to be badly distorted by the drift pins in draw-
ing the member up. Rivets should be grouped symmetrically about the neutral axis of the
member or the eccentric stresses should be calculated and provided for. The strength of a struc-
ture depends very much upon the strength of the connections, and the details of the joints and
connections should be worked out with great care.
DESIGN OF END CONNECTIONS.
References.— § 49, p. 58; § 78, § 79, § 80, § 81, § 85, p. 60; § 40, § 41, p. 141; § 60, J 62, p. 142;
5 63, § 64, § 65, § 66, § 74, p. 143; § 18, § 19, p. 209; § 37, § 39, § 40, p. 210; $ 41, 5 42, J 52, p. 211;
§ 71, p. 212, p. 219, p. 223; Tables 106 to 119 inclusive.
Strut or Tie. — Design the end connection for a 4" x 4" x %" angle, carrying a stress (either
triiMkr or compressive) of 40,000 lb., the angle being fastened by both legs to a % in. plate as shown
in Fig. 2, using % in. rivets.
Solution. — The allowable stress on one % in. rivet in single shear is 5,300 lb. and in bearing
s in. plate is 6,750 lb., using 12,000 lb. per sq. in. and 24,000 lb. per sq. in. as the allowable
stresses in shear and bearing, respectively. Table 114. The shear evidently controls, and the
number of rivets is
40,000
5-300
7.6 or 8 rivets.
Four of these will be placed in the main angle and four in the lug angle. In order to transfer
the proper portion of the stress to the lug angle, the number of rivets between the main angle
and lug angle must be equal to the number of rivets in the lug angle, or four in this case.
If the angle is connected by one leg only the eight rivets will be put in one leg as shown in
Fig- 3-
Pin-connected Top Chord. — Design the end connection for the top chord of a pin-connected
bridge as shown in Fig. 14. Length center to center of pins = 25' o". Rivets Y$ in.
Solution. — The connections should be designed to carry the full strength of the member and
not the stress that it carries. The allowable unit stress is/c = 16,000 — 70 l/r = 16,000 — 70 X
- = 13,420 lb. per sq. in. Total stress = 13,420 X 51.84 = 695,700 lb.
O.I2
The entire stress of 695,000 lb. must be transferred from the member to the pin through the
pin plates and web plates. In the body of the member the stress is distributed among the dif-
ferent parts in proportion to the gross area, or as follows:
F-
", O O O O O
o;ooooooooo
0
o o o o
JTX° ooo
O|O O O O O
c
Y/fy OOO
Oj O O O O O
0
^*^o ooo
O]O O O O O
o
:
\6 b 6 6
"djo b" 6 6 6" o b 6 b
0
o o o o
Zm.Pb.ZOxi
2 Top £4x4 XK"
Are a of Sectional. 84/n.*
Leastfec/ius
of Gyration =8J2/n.
FIG. 14. END CONNECTION OF TOP CHORD.
Item.
Material.
Area X Unit Stress = Total Stress.
Stress on One Side.
I Cover Plate
2 Top Angles
2 Web Plates
2 Bottom Angles
24 in. X -fg in.
4/TX4"XA"
20 in. X i in.
6" X 4" X f'/
13.50 X 13,420 = 181,000 lb.
6.62 <T = 88,900 "
20.00 " = 268,500 "
11.72 " = 157,300 "
90,500 lb.
44,450 ;;
134,250
78,650 "
51.84 X 13,420 = 695,700 lb.
347,850 lb
39
594 THE DESIGN OF STEEL DETAILS. CHAP. XVII.
The total bearing area required on one side of the member is,
A = 347,850 = in
24,000
The total thickness of bearing required on one side, using a 6% in. pin, is,
14.49
/ = -7— = 2.32 in.
6.25
This thickness will be provided by the plates A, B, C, D and E as shown in Fig. 14. The
plate B in the web and has a thickness of % in. Plate C must act as a fill plate so must be of the
same thickness as the bottom angles or ^ in. The outside plate E and the inside plate A should
be thinner than D so they will be made % in., and D will be made J^> in. The actual thickness of
bearing is then 2.375 in., and the required thickness is 2.32 in. In arranging the plates a clear-
ance of y% in. should be allowed between the plates which pass around the pin, and the nearest
plate as shown in Fig. 14. It is necessary to put a 3/16 in. fill plate, F, opposite the top angle
to make up for the difference in thickness in the % in. bottom angle and the 7/16 in. top angle.
The stress transmitted to a plate by the pin is equal to the ratio of its thickness to the total
thickness, multiplied by the total stress. The stresses in the various plates are as follows.
Stress in A = ~~ X 347. 850 = 54.92O lb.
B = x 347>8s° = 73'24° lb-
*5/D
C = 2^375 X 347'85° = 9Il53°lb'
X 347,850 = 73,240 lb.
E = rf^ x 347,850 = 54.920 ib.
2-375
Total = 347,850 lb.
An exact solution for the number and location of rivets is not practicable. A common solu-
tion is to consider that all the pin plates transmit their stress to the web and that the web, in turn,
distributes this stress over the section. This solution overstresses the web in the vicinity of the pin.
A better solution is to consider that the stress in the cover plate and top angles is transmitted
in double shear or bearing on the vertical leg of the top angles from the web plates and pin plates
through the rivets in the vertical leg of the angles. The stress in the bottom angles is transmitted
in double shear or bearing on the vertical leg of the bottom angles from the web plates and pin
plates through the rivets in the vertical leg of the angles. The stress on the rivets between the
web plate and plate C is equal to the sum of the stresses in C, D and E, minus one-half the sum of
the stresses in the cover plate, top angles and bottom angles on one side.
The number of rivets in the plate A is determined by the stress in A only, and is controlled
by single shear and is,
L.M^.srrveto,
7,220
The number of rivets in the plate E is determined by the stress in E only, and is controlled
by single shear and is,
7,220
The number of rivets between D and the top angle and between B and the top angle is de-
termined by bearing on the 7/16 in. angle and is,
90,500 + 44,450
» = v '3 ^^- = 15 rivets.
9,190
The number of rivets between D and the bottom angle and between B and the bottom angle is,
KCCKNTKIC KIYKTKI) (ONNKC TIO.N.
595
78,650
n - - - - 9 nvets.
9,190
The number of rivets between C and web, B, is determined by single shear, and is
m 73.340 + 54.920 + 91.530 - 1(90.500 + 44.450 + 78.650)
7,220
End Connections for I-Beams. — The end connections for Carnegie I-Bcams are given in
Tulili-s 117 and 118, and for Bethlehem I and Girder Beams in Tables 156 and 157, respectively.
Tin- i-nd connections for short beams, and for beams carrying heavy loads should be carefully
i 1 1\ i->tigatcd for direct and bending stresses. Rivets should never be used in direct tension,
Connections where rivets would be in direct tension should be provided with turned bolts.
Eccentric Riveted Connections. — The actual shearing stresses in riveted connections are
ofu-n very much in excess of the direct shearing stresses. This will be illustrated by the calcula-
tion of the shearing stresses in the rivets in the standard connection shown in Fig. 15, which is
assumed as loosely bolted to a column.
The eccentric force, P, may be replaced by a direct force, P, acting through the center of
gravity of the rivets and parallel to its original direction, and a couple with a moment M = P X 3
in. = 60,000 in.-lb. Each rivet in the connection will then take a direct shear equal to P divided
by n, where n is the total number of rivets in the connection, and a shear due to bending moment M.
The shear in any rivet due to moment will vary as the distance, and the resisting moment
exerted by each rivet will vary as the square of the distance of the rivet from the center of gravity
of all the rivets.
Now, if a is taken as the resultant shear due to bending moment in a rivet at a unit's distance
from the center of gravity, we will have the relation,
M = a(df + df + <# + ^4* + dfi2)
and
c =
M
The remainder of the calculations are shown in Table I. The resultant shears on the rivets
are given in the last column of the table and are much larger than would be expected.
The force and equilibrium polygons for the resultant shears and load P, drawn in Fig. 15,
close, which shows that the connection is in equilibrium.
TABLE I.
Direct Shear, S = 2O.OOO -5- 5 = 4,000 Ib?
Moment = 20,000 X 3 = 60,000 in.-lb. = a(d\* + df + d3* + d? -f- df)
Where a — Moment shear on rivet 3, = 2,630 Ib.
Rivet.
d,
In.
<p.
In.«
Moment,
In.-Lb.
M,
Lb.
s.
Lb.
R,
Lb.
I
2
3
4
5
2.70
1.90
I.OO
1.90
2.70
£•
I.OO
3.61
7.29
19,185
9,500
2,630
9,500
I9,l8S
7,100
5,000
2,630
5,000
7,100
4,000
4,000
4,000
4,000
4,000
9,300
3,200
6,630
3,200
9,300
aZd* = 22.80 a = 60,000 in.-lb.
20,000
a = 2,630 Ib. = moment shear on rivet 3.
M — shear due to Moment.
S = Shear due to Direct Load, P.
R = Resultant Shear.
596
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
Note. — In the analysis above it was assumed that the beam connections were bolted and
that the bolts would not transmit tension in the direction of their length. If the connection is
bolted or riveted rigidly so that the bolts or rivets may transmit tension (rivets should never
transmit tension) in the direction of their length, the resisting moment thus developed will de-
crease the shearing stresses on the rivets in the connection due to bending moment.
o -woo 8000 leooo
Equilibrium Polygon
FIG. 15. STRESSES IN AN ECCENTRIC RIVETED CONNECTION.
Web Splice. — The plate girder shown in Fig. 1 6 is to be spliced at a section where the bending
moment is 1,667,000 in.-lb. and the shear is 165,000 Ib.
Solution. — The method which assumes that one-eighth the area of the web is available as
flange area will be used. The formula for stress in the outermost rivet is
(H)
1 \ 4U / \ <2*JU~ /
V = total shear at the section.
M' = moment carried by web.
2« = number of rivets on one side of the splice.
22d2 = the sum of the squares of the distances of the rivets, on one side of the splice, from the
neutral axis.
The joint must first be designed and then investigated. The number of rivets required is
several rivets in excess of the number required to carry the direct shear. The number of % in.
rivets required for shear alone is determined by bearing on the Yi in. web plate, and is
V 164,000
2n = — = — - = 15.6, (Table 114).
r 10,500
I
A joint with 17 rivets spaced as shown in Fig. 16 will be assumed. An odd number of rivets
simplifies the calculation.
V = 165,000 ib.
M' = 1, 667.000.X 3.00 -r- 12.50 = 400,000 in.-lb.
2n = 17.
dn = 16 in.
= 2(22 -f 42 + 62 + 82 + I02 + I22 + I42 + i62) = 1632 in.2
DESIGN OF RIVETED JOINTS.
Then the maximum stress on the outside rivet will be,
M7
Thr .ill.iwable value of r for a % in. rivet is 14,400 Ib. in double shear and 10,500 Ib. in
Inuring on }<j in. web plate (Table 1 14), so the joint is satisfactory.
Net area of flange angles = 9.50 in.*
One-eighth of area of web plate = 3.00 "
Total flange area « 12.50 "
:B
°SiS.
r°K~
0°°0
o±o
"T ?
*!* *J
,00000000 o o o o !
OOOOOO|OOOOOO|
FIG. 16. DETAILS OF A WEB SPLICE.
Riveted Joints in Cylinder, Pipe or Tank. — A cylinder 46 in. in diameter is to be designed to
carry an internal pressure of 100 Ib. per sq. in* Compute the required thickness of plate and
design a longitudinal double riveted lap joint of equal efficiency for all parts. Reduce to com-
mercial dimensions and investigate.
Solution. — The unit stresses allowed by specifications for tanks are/t = 12,000 Ib. per sq. in.,
ft = 12,000 Ib. per sq. in.,/e = 24,000 Ib. per sq. in., for shop joints.
From "Structural Mechanics," Chapter XVI.
e = 2/« _ _ 2 X 24,000
ft + 2/e 12,000 + 2 X 24,000
= 0.80
w-D
loo X 46
2ft-e 2 X 12,000 X 0.80
d = 4f° -t = 4 X 24,000
*••/» 3.1416 X 12,000
= 0.24 in.
X .24 = 0.61 in.
(I6a)
(166)
(I6c)
This joint would have the efficiencies for tension, compression and shear all equal, but the
sizes could not be obtained from stock so that the joint must be altered to suit commercial sizes.
Make t = % in., d = % in., p = 3 in., and investigate. the joint.
2
p
6,900
(p - d)t ~ 2.375 X 0.25
P 6,900
2t-d 2X0.25X0.625
P 6,900
. — - ^ — — ^ T T ^rw\ 1
1 1, 600 Ib. per sq. in.
= 22,100 Ib. per sq. in.
(140)
(146)
598
THE DESIGN OF STEEL DETAILS.
CHAP. XVII.
Other considerations such as water-tightness enter into the design of joints; see Table 113.
Table I la, page 370 gives the properties of water tight joints. By efficiency is meant the ratio
of the strength of the joint to the strength of a plate of equal thickness. Under effective section
of plates in Table I la, page 370, is given the thickness of an unriveted plate which would have
the same strength as the joint.
The most efficient joint for a given thickness of plate is found as follows: For single riveted
lap joint in a ^ in. plate,
k£ .j = 4 X 24,000
•fa 3.14 X 12,000
: I-9U in- (IS/)
d =
X 0.25 = 0.637 i
p-d
r * *_ - 0.67.
Use % in. rivets with 2 in. pitch.
Formulas for Riveted Joints. — The general formulas for the investigation of lap joints with
any number of rows of rivets are (For Nomenclature, see Chapter XVI.),
P P P
For design of a joint of maximum efficiency,
*'/« -^i£. d
~ 2ft-e'
= _i/L.,. fi = [
~ Vfa *' P
(29)
ft + k-fc'
where k = number of rows of rivets.
For a butt joint with a single strap plate and a single row of riyets the joint becomes two
single riveted lap joints and the formulas for riveted lap joints may be used (Structural Mechanics
13 and 15). For a butt joint with double strap plates and a single row of rivets on each side,
p _ p _ p
*\ = (P-d)t ' fe=zTd] fv = j^n '
For a butt joint with double strap plates and double riveting on each side,
P P P
When a single strap plate is used it should never be thinner than the main plate, and when double
strap plates are used they should never be thinner than J^ the thickness of the main plate.
For data on riveted joints for tanks and stand-pipes, see Table Ila, page 370.
DESIGN OF LACING BARS FOR COLUMNS.— It is difficult to calculate the bending
stresses in a built-up column, and since the shearing stresses depend on the bending stresses the
design of lacing bars must be largely a matter of judgment until sufficient tests are made to
establish empirical formulas. The following method gives results that agree with tests and with
good practice.
For a column with a concentric loading, experiments show that the allowable unit stress may
be represented by the straight line formula, p = 16,000 — 70 llr Ib. per sq. in., where p = allow-
able unit stress in the member; / = length of the member, c. to c. of end connections, and r =
radius of gyration of the column, both in inches. Now the allowable unit stress on a short block
is 16,000 Ib. per sq. in., and the 70 llr represents the increase in the fiber stress in the column.
\Y -I
Now if we assume that this fiber stress is caused by a uniform horizontal load, W, then -—
701-1
— , where I = moment of inertia of the cross-section of the column = A -rz, where A = the
DESIGN OF LACING BARS. .V.»'.»
.ur.i <>f the cross-section of the column, and c = the distance from the neutral axis of column
W • I 70./I • t* • I
to the extreme fiber in the plane parallel to the plane of the lacing bars. Then — — —
O T'C
and W — 560 Now the shear in the column will be S — W/2, and the shear is 5 —
c
280 , and the stress in a lacing bar will be « 280 X esc 0, where 6 = the angle made by
c c
tlu- 1 tar with the axis of the column. In a laced channel column the shearing stress above will be
t.ikfii by two lacing bars. This shows that the stresses in the lacing bars in the column with a
concentric loading depend upon the make-up of the column, and are independent of the length
of the column.
Mr. C. C. Schneider by a somewhat different method has deduced the same formula on page
195 of the Report of the Royal Commission on Collapse of Quebec Bridge, 1908.
If the column carries a direct shear in addition to the shear due to the concentric load, or if
the column has an eccentric load the additional shearing stresses must be considered in designing
the lacing. The total stress in the lacing bar will be the total shear at the section multiplied by
the cosec of the angle made by the lacing bar with the axis of the column.
STRUCTURAL ENGINEERS' HANDBOOK
PART II.
STRUCTURAL TABLES.
Introduction. — The tables, in Part II include the properties of simple rolled sections; the
properties of compound sections; the properties of built-up sections for columns, struts and
chords; safe loads for angles, beams and channels, and of angle struts; properties of rivets and
riveted joints, and miscellaneous data for structural design. It has been the aim to give tables
and data that will be of use to the designing engineer and to the student in the designing room
rather than to give safe loads, stresses and other predigested data that may be used by the novice.
To this end properties of sections are given while safe loads for columns and chords have been
omitted. Tables of trigonometric functions and logarithms and other tables that are readily
available have not been included. The tables are arranged so that each page is self-contained
and self-explanatory. In the tables the properties of rolled sections are grouped together for ease
in reference, and are followed by properties of built-up sections. The tables in Part II are num-
bered in Arabic numerals.
Original Tables.— Tables 3, 4, 5, 13, 19, 20, 21, 22, 32, 33, 34, 35, 36, 37, 38, 39, 40, 56, 57,
58, 59, 6<\ 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 78, 79, 80, 81, 82, 83, 84, 85, 86,
87, 134, 135 and 136, covering 136 pages, were calculated especially for this book. The tables
have been calculated and checked with great care and are believed to be accurate. These tables
are fully protected by copyright and are not to be copied without permission from the author.
The properties of compound sections consisting of two or four angles or of two channels,
placed in different relative positions, may be used in designing struts, columns or chords where
the sections are held together by means of lacing and tie plates; or the properties of built-up
sections may be obtained by combining the moments of inertia of the compound sections and the
moments of inertia of one or two plates in the proper relative positions. The built-up sections
are all designed to comply with standard specifications and with the standards of the American
Bridge Co. for rivet spacing and structural details. To illustrate the use of the tables of compound
sections in building up struts, columns and chords, a one page table is given for each built-up
section in common use, in which the properties for the usual proportions are given and the methods
for calculating additional values by using the key tables of compound sections are given. The
method of calculating the properties of built-up sections by using the moments of inertia of com-
pound sections is shown in Table I.
STANDARD TABLES.— The other tables in Part II have been taken from Carnegie Steel
Company's "Pocket Companion," Cambria "Steel," American Bridge Company's "Book of
Standards," and other sources to which credit has been given. Many of the copied tables have been
rearranged and extended. The properties of I-Beams in Table 7, properties of channels in Table
14, and properties of angles in Table 23 and Table 24 were taken from American Bridge Com-
pany's " Book of Standards," but have been checked with the recent edition of Carntgie's " Pocket
Companion."
STRUCTURAL TABLES.
TABLE I.
i+u+m
/
I
M
B
, \B
A
B
A
B
^
A
A A
A A
U
4=
5
AoF4l* Table tt.
AoFPI.
IAoFPL=.
B
Tablet.
T,Jab/e5.
Iz,Table4.
\B
Required A
Required IA
Required IB
\B
AoFZPI. Tablet.
IA =r1omentoF Inertia, A xisA-A. I^= Moment oF Inertia, Axis X-X .
IgMomentoFlnertidtAxisB-B. IY=riomentoFlnertia, Axis Y-Y .
% =Radiu5oF6yratior)jAxisA-A. I,=MomentoF Inertia, Axis /-/ .
rs= Radius oFOyration, Axis B-B. Iz=rJomentoF Inertia, AxisZZ.
A = Area.
r^Jotallj-TotalA.
r* — \IT/)f
ilIfTotalA.
TOP CHORD SECTIONS.— The top chord sections given in Tables 82 to 86 were calculated
to comply with the standard specifications which follow, unless otherwise noted in the tables.
Specifications. — All top chord sections shall comply with the following requirements.
Thickness of Metal. — The minimum thickness of metal shall be % in. for highway bridges
and % in. for railway bridges.
Cover Plates. — The cover plate shall have a thickness not less than one-fortieth (tg) the dis-
tance between gage lines of rivets in the flange angles on each side of the section. The cover
plate shall always have the minimum thickness that will comply with the above requirements.
Web Plates. — The web plates shall have a thickness not less than one-thirtieth (sV) the
distance between gage lines of rivets in the flange angles in the line of stress. As much of the
metal as practicable shall be concentrated in the web plates and flange angles.
Proportions of Chord Section. — There shall be a top cover plate which shall have a minimum
thickness permitted by the specifications. As much of the metal as possible shall be concentrated
in the web plates and flange angles. The top and bottom angles shall be so selected as to bring
the neutral axis of the section as near the center of the web plates as practicable. The moments
of inertia of the section about the two rectangular axes shall be approximately equal.
STRUCTURAL TABLES.
BARS AND PLATES.
PAGE
Table i . Areas of Bars and Plates 9
Table 2. Weights of Steel Bars and Plates 12
Table 3. Moments of Inertia of Plates about Axis l-l 15
Table 4. Moments of Inertia of Plates about Axis 2-2 17
Table 5. Moments of Inertia of Two Plates i inch Wide about Axis X-X 18
Table 6. Weights and Areas of Round and Square Bars 21
I-BEAMS.
Table 7. Properties of Carnegie I-Beams 23
Table 8. Elements of Carnegie I-Beams 25
Table 9. Dimensions and Elements of Standard Carnegie I-Beams 27
Table 10. Dimensions and Elements of Supplementary Carnegie I-Beams 27
Table 1 1. Web Resistance of I-Beams 28
Table 12. Safe Loads and Deflections for Carnegie I-Beams 29
Table I2a. Per cent Reductions for Lateral Deflection in Beams and Channels 30
Table 13. Safe Loads and Deflections of Supplementary Carnegie I-Beams 31
CHANNELS.
Table 14. Properties of Carnegie Channels 32
Table 15. Elements of Carnegie Channels 33
Table 16. Web Resistance of Channels 34
Table 17. Safe Loads and Deflections of Carnegie Channels 35
Table 18. Safe Loads and Deflections of Carnegie Channels Laid Flat 37
Table i8a. Coefficients of Deflection 37
Table 19. Moments of Inertia of Two Channels, Flanges Turned Out, Distances Back to
Back 38
Table 20. Moments of Inertia of Two Channels, Flanges Turned In, Distances Back to Back 40
Table 21. Moments of Inertia of Two Channels, Flanges Turned In, Distances Inside to
Inside of Web 42
Table 22. Properties of Two Channels, Flanges Turned Out, Small Distances 44
ANGLES.
Table 23. Properties of Equal Leg Angles 45
Table 24. Properties of Unequal Leg Angles 48
Table 25. Areas of Angles 53
Table 26. Weights of Angles 54
Table 27. Overrun of Pencoyd Angles 55
Table 28. Overrun of Pennsylvania Steel Co. Angles 56
Table 29. Net Areas and Allowable Tension Values for Angles 57
Table 30. Safe Loads for Angles with Equal Legs 60
Table 31. Safe Loads for Angles with Unequal Legs 61
Table 32. Moments of Inertia of Four Angles with Equal Legs, Axis X-X 65
3
STRUCTURAL TABLES.
Table 33.
Table 34.
Table 35.
Table 36.
Table 37.
Table 38.
Table 39.
Table 40.
Table 41.
Table 42.
Table 43.
PAGE
Moments of Inertia of Four Angles, Unequal Legs, Axis X-X, Long Legs Out. . 73
Moments of Inertia of Four Angles, Unequal Legs, Axis X-X, Short Legs Out. . 81
Moments of Inertia of Four Angles, Equal Legs, Axis Y-Y 88
Moments of Inertia of Four Angles, Unequal Legs, Axis Y-Y, Long Legs Out. . 89
Moments of Inertia of Four Angles, Unequal Legs, Axis Y-Y, Short Legs Out. . 90
Radii of Gyration of Two Angles with Equal Legs, Both Axes 91
Radii of Gyration of Two Angles, Unequal Legs, Both Axes, Long Legs Out ... 92
Radii of Gyration of Two Angles, Unequal Legs, Both Axes, Short Legs Out. . . 93
Safe Loads of Single Angle Struts, Equal Leg Angles 94
Safe Loads of Single Angle Struts, Unequal Leg Angles 95
Safe Loads of Two Angle Struts, Axis i-i ; Equal Legs and Unequal Legs with
Long Legs Turned Out 96
Safe Loads of Two Angle Struts, Axis 2-2; Equal Legs and Unequal Legs with
Long Legs Turned Out 98
Safe Loads of Two Angle Struts; Equal Legs and Unequal Legs with Short Legs
Turned Out . 101
MISCELLANEOUS SECTIONS.
Table 46. Properties and Elements of Z-Bars 103
Table 47. Elements of Carnegie Equal Tees 104
Table 48. Elements of Carnegie Unequal Tees 105
Table 49. Elements of A. S. C. E. and Light Rails 106
Table 50. Elements of Carnegie Bulb Beams 107
Table 51. Elements of Carnegie Bulb Angles 107
Table 52. Elements of Carnegie H-Beams 108
Table 53. Carnegie Trough Plates 109
Table 54. Carnegie Corrugated Plates .- no
Table 55. Buckle Plates in
COLUMNS AND STRUTS.
Table 56. Properties of Three I-Beams 112
Table 57. Properties of Two Channels Laced, Flanges Turned Out 113
Table 58. Properties of Two Channels Laced, Flanges Turned In 114
Table 59. Properties of Two Channels and Two Plates 115
Table 60. Properties of Two Channels and One I-Beam, Flanges Turned Out 116
Table 61. Properties of Two Channels and One I-Beam, Flanges Turned In 117
Table 62. Properties of Two Channels and One Built I-Beam, Flanges Turned Out 118
Table 63. Properties of Two Channels and One Built I-Beam, Flanges Turned In 119
Table 64. Properties of One Channel and One I-Beam 120
Table 65. Properties of One Channel and One Built I-Beam 121
Table 66. Properties of One Channel and One Angle 122
Table 67. Properties of Two Angles and Four Angles Starred 123
Table 68. Properties of Four Angles Laced 124
Table 69. Properties of Four Angles and One Plate (Built H) 125
Table 70. Properties of Four Angles and Three Plates (Built H with Covers) 126
Table 71. Properties of Four Angles and Two Plates Laced (Two Built Channels Laced). 127
Table 72. Properties of Four Angles and Four Plates (Two Built Channels and Two Plates) 132
4
STRUCTURAL TABLES.
PAGE
Table 73. Properties of Four Angles Laced and Eight Angles Battened 134
Table 74. Properties of Eight Angles and Three Plates (Two Built Channels and One Built
I-Beam) 135
Table 75. Properties of 4 Z-Bars and Three Plates 136
TOP CHORD SECTIONS.
ilile 77. Top Chord Sections of Two Angles and One Web Plate 137
T.iltk- 78. Top Chord Sections of Two Angles and One Cover Plate, Legs Turned Out. . . 139
Table 79. Top Chord Sections of Two Angles and One Cover Plate, Legs Turned In. . . . 140
Table 80. Top Chord Sections of Two Angles, One Web Plate and One Cover Plate 141
Table 81. Top Chord Sections of Two Angles, Two Web Plates and One Cover Plate 142
Table 82. Top Chord Section of Two Channels and One Plate 143
Table 83. Top Chord Sections of Four Angles-and Three Plates; Highway Bridges 146
Table 84. Top Chord Sections of Four Angles and Three Plates 156
Table 85. Top Chord Sections of Six Angles and Three Plates 184
Table 86. Top Chord Sections of Eight Angles and Five Plates 203
PLATE GIRDERS.
Table 87. Properties of Plate Girders 204
Table 88. Centers of Gravity of Plate Girder Flanges 205
DETAILS FOR BARS.
Table 89. Upset Screw Ends for Square Bars 206
Table 90. Upset Screw Ends for Round Bars 207
Table 91. Ordinary and Adjustable Eye-Bars 208
Table 92. Loop Bars ** 209
Table 93. Clevises 210
Table 94. Turnbuckles and Sleeve Nuts 211
95-
96.
97-
' Table
Table
Table
Table 98.
Table 99.
Table 100.
Table 101.
Table 102.
Table 103.
Table 104.
Table 105.
PINS, BOLTS AND NUTS.
Bridge Pins and Nuts 212
Cotter Pins 213
Bearing Values of Pins 214
Bending Moments on Pins 215
Long Pilot Nuts 216
Short Pilot Nuts 217
Standard Screw Threads and General Dimensions of Bolt Heads and Nuts. ... 218
Dimensions of Bolt Heads and Nuts 219
Weights of Bolts with Hexagon Heads and Nuts 220
Weights of Bolts with Square Heads and Nuts 221
Lengths of Bolts and Tie Rods 222
RIVETS AND RIVETING.
Table 106. Weights of Rivets 223
Table 107. Lengths of Rivets and Bolts for Beam Framing 224
Table 108. Lengths of Field Rivets for Various Grips 225
5
STRUCTURAL TABLES.
PAGE
Table 109. Standards for Rivets and Riveting 226
Table 1 10. Standards for Riveting 227
Table in. Standards for Riveting 228
Table 112. Standards for Riveting 229
Table 1 13. Standards for Riveting 230
Table 1 14. Shearing and Bearing Value of Rivets 231
Table 115. Multiplication Table for Rivet Spacing 232
Table 116. Areas to be Deducted for Rivet Holes 234
BEAM AND LATERAL CONNECTIONS.
Table 117. Old Standard Connections for Beams and Channels 235
Table 1 1 8. Standard Connections for Beams and Channels 236
Table 1 19. Beveled Beam Connections 237
Table 120. Sway Rod and Lateral Connections 238
Table 121. Lateral Connections for Highway Bridges 239
Table 122. Lateral Connections and Stub Ends 240
MISCELLANEOUS.
Table 123. Lag Screws, Hook Bolts and Washers 241
Table 124. Weights of Lag Screws, Wrought Washers, Track Bolts 242
Table 125. Weights of Steel Wire Nails and Spikes 243
Table 126. Weights of Nails and Spikes 244
Table 127. Weights and Dimensions of Pipe and Pipe Coupling 245
Table 128. Standard Gages, Comparative Table 247
Table 129. Standard Gages and Weights of Sheet Steel 248
Table 130. Clearance Dimensions and Wheel Loads for Electric Cranes 249
Table 131. Clearance Dimensions and Wheel Loads for Electric Cranes 250
Table 132. Crane Girder Specifications 251
Table 133. Typical Hand Cranes 252
Table 134. Stress in Eye-Bars Due to Weight 253
Table 135. Safe Uniform Load on Square Flat Plates 254
Table 136. Approximate Radii of Gyration for Compression Members 255
Table 137. Details of a Steel Stair 256
BETHLEHEM SECTIONS.
Table 151. Properties of Bethlehem I-Beams 257
Table 152. Properties of Bethlehem Girder Beams 258
Table 153. Properties of Bethlehem H-Columns 259
Table 154. Properties of Bethlehem Compound Columns 261
Table 155. Elements of Bethlehem I-Beams and Girder Beams 262
Table 156. Standard Connection Angles for Bethlehem I-Beams. 263
Table 157. Standard Connection Angles for Bethlehem Girder Beams 264
Table 158. Cast Iron Separators for Bethlehem Girder and I-Beams 265
Table 159. Safe Loads on Bethlehem I-Beams 266
Table 160. Safe Loads on Bethlehem Girder Beams 267
6
STRUCTURAL TABLES.
MATHEMATICAL AND MISCELLANEOUS. FACE
Table 161. Decimal Parts of a Foot and Inch 268
T.il.le 162. Table of Bevels 269
Table 163. Ordinates for 16' o" Chords 270
Talilc- 164. Natural Tangents 271
Table 165. Squares, Cubes, Square Roots and Cube Roots of Numbers 272
TABLE 1.
AREAS OF BARS AND PLATES.
i ~~~1
SQUARE INCHES.
Width,
Inches.
•.
A
i
A
i
A
I
A
i
A
i
tt
i
H
i
u
i
.Ol6
.031
.047
.063
.078
.094
.109
.125
.141
.156
.172
.188
.203
.22
.23
•25
.Ojl
.063
•094
•"5
.156
.188
.219
.250
.281
.313
•344
•375
.406
-44
•47
•50
.047
.094
.141
.188
•234
.281
.328
•375
.422
•469
•Sl6
•563
.609
.66
•70
•75
I
.063
.125
.188
.250
•313
•375
.438
.500
-563
.625
.688
.750
.813
.88
•94
1. 00
ij
.078
.156
•234
•313
•391
469
•547
.625
•703
.781
.859
.938
I. Old
1.09
1.17
1.25
It
.094
.188
.2SI
•375
.469
•563
•656
•750
.844
•938
1.031
1.125
I.2I9
1.31
1.41
1.50
If
.109
.219
.328
438
•547
.656
.766
•875
.984
1.094
1.203 1.313
1.422
i-53
1.64
i-75
2
.125
.250
•375
.500
•625
-750
•875
I.OOO
1.125
1.250
1.375 1.500
1.625
i-75
1.88
2.00
2\
.141
.281
.422
.563
•703
.844
•984
.125
1.266
1.406
1.547 1-688
1.828
i-97
2. II
2.25
2\
.156
.313
.469
.625
.781
-938
1.094
.250
1.406
1-563
1.7191.875
2.O3I
2.19
2.34
2.50
2\
.172
•344
.516
.688
.859
1.031
1.203
•375
1-547
1.719
1.891 2.063
2.234
2.41
2.58
2-75
3
.188
•375
•563
•750
.938
1.125
1-313
.500
1.688
I.87S
2.063
2.250
2.438
2.63
2.81
3.OO
Si
.203
.406
.609
.813
1.016
1.219
1.422
.625
1.828
2.031
2.234
2438
2.641
2.84
3.05
3-25
3*
.219
•438
.656
.875
1.094
1-313
I-53I
.750
1.969
2.188
2.406 2.625
2.844
3.06
3.28
3-50
3i
.234
.469
•703
•938
1.172
1.406
1.641
.875
2.109
2-344
2.5782.813
3-047
3-28
3-52
3-75
4
.250
.500
•75°
I.OOO
1.250
1.500
1.750
2.OOO
2.250
2.500
2.750
3.000
3.250
3-50
3-75
4.00
4l
.266
•531
•797
1.063
1.328
1.594
1.859
2.125
2.391
2.656
2.922
3-188
3-453
3-72
3.98
4-25
4*
.281
•563
•844
1.125
1.406
1.688
1.969
2.25O
2-531
2.813
3-094'3-375
3-656
3-94
4.22
4.50
4i
.297
•594
.891
1.188
1.484
1.781
2.078
2-375
2.672
2.969
3.266 3.563
3-859
4.16
4-45
4-75
5
•313
.625
•938
1.250
1-563
1.875
2.188
2.500
2.813
3-125
3438
3-750
4.063
4-38
4.69
5.00
si
.328
.656
.984
1.313
1.641
1.969
2.297
2.625
2-953
3.281
3.609
3-938
4.266
4-59
4.92
5-25
si
•344
.688
1.031
1-375
1.719
2.063
2.406
2.750
3-094
3438
3.78i
4.125
4.469
4.81
5.16
5-50
si
•359
.719
1.078
1.438
1.797
2.156
2.516
2-875
3-234
3-594
3-953
4-3I3
4.672
5-03
5-39
5-75
6
•375
•75°
1.125
1.500
1.875
2.250
2.625
3.000
3-375
3-750
4.125
4.500
4-875
5-25
5.63
6.00
6}
391
.781
1.172
1-563
1-953
2-344
2-734
3-125
3-516
3.906
4.297
4.688
5.078
5-47
5-86
6.25
6J
.406
.813
1.219
1.625
2.031
2.438
2.844
3.250
3.656
4.063
4.469
4-875
5.281
5.69
6.09
6.50
6J
.422
.844
1.266
1.688
2.109
2.S3I
2-953
3-375
3-797
4.219
4.641
5-063
5484
5.91
6.31
6-75
7
•438
•875
1-313
1.750
2.188
2.625
3-063
3-500
3-938
4-375
4.813
5-250
5.688
6.13
6.56
7.00
7*
•453
.906
1-359
1.813
2.266
2.719
3.172
3.625
4.078
4-531
4.984
5438
5-891
6-34
6.80
7-25
7*
.469
.938
1.406
1-875
2-344
2.813
3.281
3-750
4.219
4.688
5-I56
5.625
6.094
6.56
7.01
7-50
7f
.484
.969
1-453
1.938
2.422
2.906
3-391
3.875
4-359
4.844
5-3285-813
6.297
6.78
7.27
7-75
8
.500
1. 000
1.500
2.000
2.500
3.000
3-500
4.000
4.500
5.000
5.500
6.000
6.500
7.00
7-50
8.00
Bf
.516
1.031
1-547
2.063
2.578
3.094
3.609
4.125
4.641
5.156
5.672
6.188
6.703
7.22
7-73
8.25
H
•531
1.063
1-594
2.125
2.656
3.188
3.719
4.250
4.781
5-3I3
S-844|6.375
6.906
7-44
7-97
8.50
8i
•547
1.094
1.641
2.188
2-734
3-281
3.828
4-375
4.922
5-469
6.0166.563
7.109
7.66
8.20
8-75
9
•563
1.125
1.688
2.250
2.813
3-375
3.938
4.500
5.063
5.625
6.188
6.750
7.3I3
7.88
8.44
9.00
9l
•578
1.156
1-734
2.3I3
2.891
3.469
4.047
4.625
5-203
5-78i
6-359
6.938
7.516
8.09
8.67
9-25
3
•594
1.188
1.781
2-375
2.969
3-563
4.156
4-750
5-344
5-938
6.53i|7.i25
7719
8.31
8.91
9.50
9*
.609
1.219
1.828
2.438
3-047
3-656
4.266
4-875
5.484
6.094
6.703,7-313
7.922
8-53
9.14
9-75
10
•625
1.250
1-875
2.500
3.125
3-750
4-375
5.000
5-625
6.250
6.875 7-500
8.125
8-75
9-38
10.00
IOJ
.641
1.281
1.922
2.563
3.203
3-844
4.484
5.125
5-766
6.406
7.047 7-688
8.328
8.97
9.61
10.25
10*
.656
1.313
1.969
2.625
3.281
3-938
4-594
5-250
5.906
6.563
7.2197.875
8-531
9.19
9.84
10.50
I0|
.672
1-344
2.016
2.688
3-359
4.031
4703
5-375
6.047
6.719
7.391 8.063
8-734
9.41
10.08
10.75
II
.688
1-375
2.063
2.750
3438
4.125
4.813
5.500
6.188
6-875
7.563 8.250
8.938
9-63
10.31
II.OO
111
.703
1.406
2.109
2.813
3-5i6
4.219
4.922
5.625
6.328
7-031
7-734 8-438
9.141
9.84
10.55
11.25
III
.719
1.438
2.156
2.875
3-594
4-313
5-031
5-750
6.4,69
7.188
7.906 8.625
9-344
1 0.06
10.78
11.50
II j
•7.U
1.469
2.203
2.938
3.672
4.406
5.141
5-875
6.609
7-344
8.0788.813
9-547
10.28
11.02
11.75
12
•750
1.500
2.250
3.000
3-750
4-Soo
5-250
6.000
6.750
7.500
8.2509.000
9-750
10.50
11.25
12. OO
40
TABLE 1.— Continued.
AREAS OF BARS AND PLATES.
SQUARE INCHES.
Width,
Inches.
Thickness, Inches.
A
i
A
i
A
i
A
i
A
f
it
J
ti
i
«
i
ja|
.781
1-563
2-344
3-13
3-9i
4-69
5-47
6.25
7-03
7.81
8-59
9-38
10.16
10.94
11.72
12.50
13
.813
1.625
2.438
3-25
4.06
4.88
5-69
6.50
7-3i
8.13
8-94
9-75
10.56
11.38
12.19
13.00
isi
.844
1.688
2-531
3-38
4.22
5.06
5.91
6-75
7-59
8.44
9.28
10.13
10.97
11.81
12.66
I3-50
14
.87S
1-75°
2.625
3-50
4-38
5-25
6.13
7.00
7.88
8-75
9-63
10.50
11.38
12.25
I3-I3
14.00
142
.906
1.813
2.719
3-63
4-53
5-44
6-34
7-25
8.16
9.06
9-97
10.88
11.78
12.69
13-59
14.50
1$,
•938
1.875
2.813
3-75
4.69
5-63
6.56
7-50
8-44
9-38
10.31
11.25
12.19
I3-I3
14.06
15.00
IS*
.969
1-938
2.906
3-88
4.84
5-8i
6.78
7-75
8.72
9.69
10.66
11.63
12.59
13-56
14-53
I5-50
16
I.OOO
2.OOO
3.000
4.00
S-oo
6.00
7.00
8.00
9.00
IO.OO
II.OO
I2.OO
13.00
14.00
15.00
16.00
i6J
1.031
2.063
3-094
4-13
5-i6
6.19
7.22
8.25
9.28
10.31
"•34
12.38
I3-4I
14.44
15-47
16.50
I7i
1.063
2.125
3.188
4-25
5-31
6.38
7-44
8.50
9.56
10.63
11.69
12.75
13.81
14.88
15-94
17.00
fa
1.094
2.188
3.281
4-38
5-47
6.56
7.66
8-75
9-84
10.94
12.03
I3.I3
14.22
15-31
16.41
17-5°
18
1.125
2.25O
3-375
4-50
5-63
6-75
7.88
9.00
10.13
11.25
12.38
I3-50
14.61
15-75
16.88
1 8. co
I8|
1.156
2.313
3-469
4-63
5-78
6-94
8.09
9-25
10.41
11.56
12.72
13.88
15.03
16.19
17-34
18.50
19
1.188
2-375
3-563
4-75
5-94
7-13
8.31
9-50
10.69
11.88
13.06
14.25
15-44
16.63
17.81
19.00
19!
1.219
2.438
3-656
4.88
6.09
7-3i
8-53
9-75
10.97
12.19
I3-4I
14.63
15.84
17.06
18.28
19.50
20
1.250
2.500
3-750
S-oo
6.25
7-50
8-75
IO.OO
11.25
12.50
13-75
15.00
16.25
I7-50
18.75
20.00
203
1.281
2-563
3.844
5-13
6.41
7.69
8-97
10.25
n-53
12.81
14.09
I5-38
16.66
17.94
19.22
20.5O
21
1-313
2.625
3-938
5-25
6.56
7.88
9.19
10.50
11.81
13-13
14.44
15-75
17.06
18.38
19.69
2I.OO
«|
1-344
2.688
4.031
5-38
6.72
8.06
9.41
10-75
12.09
13-44
14.78
16.13
17-47
18.81
20.16
21.50
22
1-375
2.750
4.125
5-50
6.88
8.25
9-63
II.OO
12.38
13-75
I5-I3
16.50
17.88
19.25
20.63
22.OO
22^
1.406
2.813
4.219
5-63
7-03
8-44
9.84
11.25
12.66
14.06
15-47
16.88
18.28
19.69
21.09
22.5O
23
1.438
2-875
4-3I3
5-75
7.19
8.63
10.06
11.50
12.94
14.38
15.81
17-25
18.69
20.13
21.56
23.OO
232
1.469
2.938
4.406
5-88
7-34
8.81
10.28
11.75
13.22
14.69
16.16
17.63
19.09
20.56
22.03
23.50
24
1.500
3.000
4.500
6.00
7-50
9.00
10.50
I2.OO
I3-50
15.00
16.50
18.00
19.50
2I.OO
22.50
24.00
25
1-563
3-125
4.688
6.25
7.81
9-38
10.94
I2.5O
14.06
15-63
17.19
18-75
20.31
21.88
23-44
25.OO
26
1.625
3.250
4.875
6.50
8.13
9-75
11.38
I3.OO
14.63
16.25
17.88
19.50
21.13
22.75
24-38
26.OO
27
1.688
3-375
5.063
6-75
8.44
10.13
11.81
I3-50
I5-I9
16.88
18.56
20.25
21.94
23.63
25-31
27.00
28
1.750
3.500
5-250
7.00
8-75
10.50
12.25
I4.OO
15-75
17-50
19.25
2I.OO
22.75
24.50
26.25
28.00
29
1.813
3-625
5-438
7-25
9.06
10.88
12.69
14.50
16.31
18.13
19.94
21-75
23-56
25.38
27.19
29.OO
3°
1.875
3-75°
5.625
7-50
9-38
11.25
I3-I3
15.00
16.88
18-75
20.63
22.50
24.38
26.25
28.13
30.OO
3i
1-938
3-875
5-813
7-75
9.69
11.63
I3-56
I5-50
17.44
19.38
21.31
23-25
25.19
27.13
29.06
3I.OO
32
2.OOO
4.000
6.000
8.00
IO.OO
I2.OO
14.00
16.00
18.00
20.00
22.00
24.00
26.00
28.00
30.00
32.OO
33
2.063
4.125
6.188
8.25
10.31
12.38
14.44
16.50
18.56
20.63
22.69
24-75
26.81
28.88
30.94
33-oo
34
2.125
4.250
6-375
8.50
10.63
12-75
14.88
17.00
I9-I3
21.25
23-38
25-50
27.63
29-75
31.88
34-oo
35
2.188
4-375
6.563
8-75
10.94
I3-I3
I5-3I
17-50
19.69
21.88
24.06
26.25
28.44
30.63
32.81
35-oo
36
2.25O
4.500
6-750
9.00
11.25
I3-50
15-75
18.00
20.25
22.50
24-75
27.00
29.25
31.50
33-75
36.00
37
2.313
4.625
6.938
9.25
11.56
13.88
16.19
18.50
20.81
23-13
25-44
27-75
30.06
32.38
34-69
37-oo
38
2-375
4-7.^
7-125
9-50
11.88
14.25
16.63
19.00
21.38
23-75
26.13
28.50
30.88
33-25
35-63
38.00
39
2.438
4-875
7.313
9-75
12.19
14.63
17.06
19.50
21.94
24.38
26.81
29.25
31.69
34-13
36-56
39.00
40
2.500
5.000
7-Soo
IO.OO
12.50
I5.OO
I7-50
20.00
22.50
25.00
27.50
30.00
32.50
35-00
37-50
40.00
4i
2-563
5-125
7.688
10.25
12.81
15.38
17.94
20.50
23.06
25.63
28.19
30.75
33-31
35-88
38-44
41.00
42
2.625
5.250
7-875
10.50
13-13
15-75
18.38
21.00
23-63
26.25
28.88
31-50
34-13
36.75
39-38
42.00
43
2.688
5-375
8.063
10.75
13-44
16.13
18.81
21.50
24.19
26.88
29-56
32.25
34-94
37.63
40.31
43-oo
44
2.750
5.500
8.250
II.OO
13-75
16.50
19.25
22.OO
24.75
27.50
30.25
33-oo
35-75
38.50
41.25
44.00
45
2.813
5-625
8.438
11.25
14.06
16.88
19.69
22.5O
25-31
28.13
30-94
33-75
36.56
39.38
42.19
45-oo
46
2.875
5-750
8.625
11.50
14.38
17-25
20.13
23.00
25.88
28.75
31-63
34-50
37.38
40.25
43-13
46.00
47
2.938
5-875
8.813
u-75
14.69
17.63
20.56
23.50
26.44
29-38
32.31
35-25
38.19
4i-i3
44.06
47-oo
48
3.000
6.000
9.000
I2.OO
15.00
18.00
21.00
24.00
27.00
30.00
33-00
36.00
39-oo
42.00
45.00
48.00
10
TABLE 1.— Continued.
AREAS OF BARS AND PLATES.
SQUARE INCHES.
Width.
liulu-s.
Thickness. Inches.
A
I
A
i
A
1
A
*
A
1
H
!
H
i
H
i
49
3-06
6.13
<;.iv
12.25
15.31
18.38
21.44
24.50
27.56
30.63
33-69
36.75
39.81
42.88
45-94
49.00
50
3-13
6.25
<>.3s
12.50
15-63
18.75
21.88
25.00
28.13
31-25
34-38
37-50
40.63
43-75
46.88:50.00
Si
3-19
6.38
9.56
12.75
15.94
I9.I3
22.31
25.50
28.69
31.88
35.06
38.25
41.44
44.63
47.81
51.00
52
3.25
6.50
9-75
13.00
16.25
19.50
22-75
26.00
29.25
32.50
35-75
39.00
42-25
45.50
48.75
52.00
S3
3-3'
6.63
9-94
13.25
16.56
19.88
23.19
26.50
29.81
33-13
36.44
39-75
43.06
46-38
49.69
53-oo
54
3-38
6-75
10.13
13-5°
16.88
20.25
23.63
27.00
30.38
33-75
37-13
40.50
43-88
47-25
50.63
54.00
55
3-44
6.88
10.31
13-75
17.19
20.63
24.06
27.50
30.94
34-38
37-8i
41.25
44-69
48.13
51-56
55-00
56
3-50
7.00
10.50
14.00
17.50
21.00
24.50
28.00
31-5°
35-oo
38.50
42.00
45-50
49-00
52-50
56.00
57
3.56
7-13
10.69
14-25
17.81
21.38
24.94
28.50
32.06
35-63
39-19
42.75
46.31
49.88
53-44
57.00
58
3-63
7-25
10.88
14-50
18.13
21-75
2S-38
29.00
32.63
36-25
39-88
43-50
47-13
50-75
54-38
58.00
59
3-69
7.38
1 1. 06
14-75
18.44
22.13
25.81
29.50
33-19
36.88
40.56
44-25
47-94
51-63
55-31
59-00
60
3-75
7.50
11.25
15.00
18.75
22.50
26.25
30.00
33-75
37-50
41.25
45-00
48.75
52.50
56.25
60.00
61
3-8i
7.63
11.44
I5-25
19.06
22.88
26.69
30-50
34-31
38.13
41.94
45-75
49.56
53.38
57-19
61.00
62
3.88
7-75
11.63
I5-50
19.38
23-25
27.13
31.00
34-88
38.75
42.63
46.50
50.38
54-25
58-13
62.00
63
3-94
7.88
11.81
15-75
19.69
23.63
27.56
31-50
35-44
39.38
43-31
47-25
51.19
55-13
59.06
63.00
64
4.00
8.00
I2.OO
16.00
20.00
24.00
28.00
32.00
36.00
40.00
44.00
48.00
52.00
56.00
60.00
64.00
65
4.06
8.13
12.19
16.25
20.31
24.38
28.44
32.50
36-56
40.63
44.69
48-75
52.81
56.88
60.94
65.00
66
4-13
8.25
12.38
16.50
20.63
24-75
28.88
33-00
37-13
41-25
45-38
49-50
53.63
57-75
61.88
66.00
67
4.19
8.38
12.56
16.75
20.94
25-13
29.31
33-50
37.69
41.88
46.06
50.25
54-44
58.63
62.81
67.00
68
4-25
8.50
12.75
17.00
21.25
25.50
29-75
34-oo
38-25
42.50
46.75
51.00
55-25
59-50
6375
68.00
69
4-31
8.63
12.94
17-25
21.56
25.88
30.19
34-50
38.81
43-13
47-44
51-75
56.06
60.38
64.69
69.00
70
4.38
8-75
I3.I3
17-50
21.88
26.25
30.63
35.00
39.38
43-75
48.13
52.50
56.88
61.25
65-63
70.00
7i
4-44
8.88
I3.3I
17-75
22.19
26.63
31.06
35-50
39-94
44-38
48.81
53-25
57-69
62.13
66.56
71.00
72
4.50
9.00
I3.50
18.00
22.50
27.00
31.50
36.00
40.50
45-oo
49-50
54.00
58.50
63.00
67-50
72.00
73
4-56
9-13
13.69
18.25
22.81
27.38
31-94
36-50
41.06
45-63
50.19
54-75
59-31
63.88
68.44
73-oo
74
4-63
9-25
13.88
18.50
23-13
27.75
32.38
37-00
41.63
46-25
50.88
55-50
60.13
64.75
69.38
74.00
75
4.69
9-38
14.06
18.75
23.44
28.13
32.81
37-50
42.19
46.88
51.56
56.25
60.94
65-63
70.31
75-oo
76
4-75
9.50
14.25
19.00
23-75
28.50
33-25
38.00
42.75
47-50
52.25
57-oo
6i.75
66.50
71-25
76.00
77
4.81
9-63
14.44
19.25
24.06
28.88
33-69
38.50
43-31
48.13
52-94
57-75
62.56
67-38
72.19
77-oo
78
4.88
9-75
14.63
19.50
24-38
29.25
34-13
39.00
43.88
48.75
53-63
58.50
63-38
68.25
73-13
78.00
79
4-94
9.88
14.81
19-75
24.69
29.63
34.56
39-50
44-44
49.38
54-31
59-25
64.19
69.13
74.06
79-oo
80
5.00
IO.OO
15.00
20.00
25.00
30.00
35-oo
40.00
45.00
50.00
55-oo
60.00
65.00
70.00
75-00
80.00
81
5.06
10.13
I5-I9
20.25
25-3I
30.38
35-44
40.50
45-56
50.63
55-69
60.75
65.81
70.88
75-94
81.00
82
5-»3
10.25
I5-38
20.50
25.63
30.75
35-88
41.00
46.13
51.25
56.38
61.50
66.63
71-75
76.88
82.00
83
5-19
10.38
15.56
20.75
25-94
31-13
36.31
41.50
46.69
51.88
57.06
62.25
67.44
72-63
77.81
83.00
84
5-25
10.50
15-75
2I.OO
26.25
31-50
36.75
42.00
47-25
52-50
57-75
63.00
68.25
73-50
78-75
84.00
85
5-31
10.63
15-94
21.25
26.56
31.88
37-19
42.50
47.81
53-13
58.44
6375
69.06
74-38
79-69
85.00
86
5-38
10.75
16.13
21.50
26.88
32.25
37.63
43.00
48-38
53-75
59-13
64.50
69.88
75-25
80.63
86.00
87
5-44
10.88
16.31
21-75
27.19
32.63
38.06
43-50
48.94
54-38
59.81
65-25
70.69
76-13
81.56
87.00
88
5-50
11.00
16.50
22.OO
27.50
33-00
38.50
44.00
49.50
55-00
60.50
66.00
7I-50
77-00
82.50
88.00
89
5.56
11.13
16.69
22.25
27.81
33-38
38.94
44-50
50.06
55-63
61.19
66.75
72.31
77-88
83.44
89.00
90
5.63
11.25
16.88
22.5O
28.13
33-75
39-38
45-00
50.63
56-25
61.88
67.50
73-13
78-75
84.38
90.00
91
5-69
11.38
17.06
22.75
28.44
34-13
39.81
45.50
51.19
56.88
62.56
68.25
73-94
79-63
85-31
91.00
92
5-75
11.50
17.25
23.00
28.75
34-50
40.25
46.00
51-75
57-50
63.25
69.00
74-75
80.50
86.25192.00
93
5.81
11.63
17.44
23.25
29.06
34-88
40.69
46.50
52.31
58-13
63-94
69.75
75-56
81.38
87.19
93.00
94
5.88
11.75
17-63
23.50
29.38
35-25
4I-I3
47.00
52.88
58.75
64.63
70.50
76.38
82.25
88.13
94.00
95
5-94
11.88
17.81
23-75
29.69
35-63
41.56
47-50
53-44
S9.38
65-31
71.25
77-19
83-13
89.06
95.00
96
6.00
12.00
18.00
24.00
30.00
36.00
42.00
48.00
54-oo
60.00
66.00
72.00
78.00
84.00
90.00
96.00
97
6.06
12.13
18.19
24.25
30.31
36.38
42.44
48.50
54.56
60.63
66.69
72-75
78.81
84.88
90.94
97.00
98
6.13
12.25
18.38
24.50
30.63
36.75
42.88
49.00
55-13
61.25
67-38
73-50
79-63
85-75
91.88
98.00
99
6.19
12.38
18.56
24.75
30.94
37-13
43-31
49.50
•55-69
61.88
68.06
74-25
80.44
86.63
92.81
99.00
IOO
6.25
12.50
18.75
25.00
31.25
37-50
43-75
50.00
56.25
62.50
68.75
75-00
81.25
87.50
93-75
IOO.O
11
TABLE 2.
WEIGHTS OF STEEL BARS AND PLATES.
POUNDS PER LINEAL FOOT.
Width,
Inches.
Thickness, Inches.
A
i
A
1
A
i
A
1
A
i
ft
f
H
i
«
i
|
•°S3
.106
•159
.213
•27
•32
•37
•43
.48
•53
•58
.64
.69
•74
.80
•85
1
.106
.213
•319
•425
•53
.64
•74
•85
.96
i. 06
1.17
1.28
1-38
1-49
i-59
1.70
3
•159
•319
.478
•638
.80
.96
1. 12
1.28
i-43
i-59
1-75
I.9I
2.07
2.23
2-39
2-55
I
.213
•425
•638
.850
i. 06
1.28
1-49
1.70
1.91
2.13
2-34
2-55
2.76
2.98
3-19
3-40
If
.266
•531
•797
1.063
i-33
i-59
1.86
2.13
2-39
2.66
2.92
3-19
3-45
3-72
3-98
4-25
ij
•319
.638
•956
1-275
i-59
1.91
2.23
2-55
2.87
3-19
3-Si
3.83
4.14
4.46
4.78
5.10
If
•372
•744
I.ItO
1.488
1.86
2.23
2.60
2.98
3-35
3-72
4.09
4.46
4-83
5-21
5-58
5-95
2
•425
.850
1-275
1.700
2.13
2-55
2.98
3-40
3-83
4-25
4.68
5.10
5-53
5-95
6.38
6.80
*\
.478
•956
1-434
I-9I3
2-39
2.87
3-35
3-83
4-30
4.78
5.26
5-74
6.22
6.69
7.17
7.65
^
•S3I
1.063
1-594
2.125
2.66
3-19
3-72
4-25
4.78
5-31
5-84
6.38
6.91
7-44
7-97
8.50
2f
•584
1.169
1-753
2.338
2.92
3-Si
4.09
4.68
5.26
5-84
6-43
7.01
7.60
8.18
8.77
9-35
3
.638
1-275
I-9I3
2-550
3-19
3-83
4.46
5.10
5-74
6.38
7.01
7-65
8.29
8-93
9-56
IO.20
si
.691
1.381
2.072
2.763
3-45
4.14
4-83
5-53
6.22
6.91
7.60
8.29
8.98
9.67
10.36
II.O5
34
•744
1.488
2.231
2.975
3-72
4.46
5.21
5-95
6.69
7-44
8.18
8-93
9-67
10.41
ii. 16
II.9O
3f
•797
1-594
2.391
3.188
3-98
4.78
5-58
6.38
7.17
7-97
8-77
9-56
10.36
ii. 16
11-95
12-75
4
.850
1.700
2.550
3.400
4-25
5-io
5-95
6.80
7.65
8.50
9-35
IO.20
II.O5
11.90
12.75
I3.6O
4i
•9°3
i. 806
2.709
3-613
4-52
5.42
6.32
7-23
8.13
9-03
9-93
IO.84
11.74
12.64
13-55
14-45
4J
•956
I-9I3
2.869
3-825
4.78
5-74
6.69
7-65
8.61
9-S6
10.52
11.48
12.43
13-39
14-34
I5.30
x«a
4*
1.009
2.019
3.028
4.038
5-05
6.06
7.07
8.08
9.08
10.09
II. IO
12. II
13.12
H-I3
IS-H
l6.I5
s
1.063
2.125
3.188
4-250
5-31
6.38
7-44
8.50
9-56
10.63
11.69
12.75
13.81
14.88
iS-94
I7.OO
si
1.116
2.231
3-347
4-463
5-58
6.69
7.81
8-93
10.04
ii. 16
12.27
13-39
14.50
15.62
16.73
17.85
55
1.169
2.338
3-5o6
4.675
5-84
7.01
8.18
9-35
10.52
11.69
12.86
14.03
I5-I9
16.36
17-53
18.70
si
1.222
2-444
3.666
4.888
6.ii
7-33
8-55
9-78
II.OO
12.22
r3-44
14.66
15.88
17.11
18-33
19-55
6
1-275
2.550
3-825
5.100
6.38
7.65
8-93
IO.20
11.48
12-75
14.03
I5-30
16.58
17-85
19-13
2O.4O
6*
1.328
2.656
3-984
5-3I3
6.64
7-97
9-30
10.63
11-95
13.28
14.61
15-94
17-27
18.59
19.92
21.25
6}
I.38I
2.763
4.144
5-525
6.91
8.29
9.67
II.O5
12-43
I3.8l
15-19
16.58
17.96
19-34
20.72
22. IO
61
1-434
2.869
4-303
5-738
7.17
8.61
10.04
11.48
12.91
14-34
15.78
17.21
18.65
20.08
21.52
22-95
7
1.488
2-975
4-463
5-950
7-44
8-93
10.41
II.9O
13-39
14.88
16.36
I7.85
19-34
20.83
22.31
23.80
7i
I-54I
3.081
4.622
6.163
7.70
9.24
10.78
12-33
13-87
I5-4I
i6.95
18.49
2O.O3
21-57
23.11
24.65
7i
1-594
3.188
4.78 s
6-375
7-97
9-56
n. 16
12-75
14-34
15-94
17-53
I9-I3
2O.72
22.31
23.91
25.50
71
1.647
3-294
4.941
6.588
8.23
9.88
ii-53
I3.I8
14.82
16.47
18.12
19.76
21.41
23.06,24.70
26.35
8
1.700
3.400
5 100
6.800
8.50
IO.20
11.90
13.60
15-30
I7.OO
18.70
20.40
22. IO
23.80
25-50
27.2O
8J
1-753
3.506
5-259
7.013
8.77
IO.52
12.27
14.03
1578
17-53
19.28
2I.O4
22.79
24-54
26.30
28.05
8*
i. 806
3-6/3
5-4I9
7.225
9-03
10.84
12.64
14-45
16.26
1 8. 06
19.87
21.68
23.48
25.29 27.09
28.90
8f
1.859
3-719
5-578
7438
9-30
II. ID
13.02
14.88
i6.73
18.59
20.45
22.31
24.17
26.03 27.89
29-75
9
i-9i3
3-825
5-738
7.650
9-56
11.48
13-39
I5.30
17.21
I9.I3
21.04
22.95
24.86
26.78
28.69
3O.6O
9i
1.966
3-931
5-897
7.863
9-83
II-79
13.76
15-73
17.69
19.66
21.62
23-59
25-55
27-52
29.48
31-45
9l
2.019
4.038
6.056
8.075
10.09
12. II
I4-I3
l6.I5
18.17
20.19
22.21
24.23
26.24
28.2630.28
32.30
9f
2.072
4.144
6.216
8.288
10.36
12.43
14.50
16.58
18.65
20.72
22.79
24.86
26.93
29.01 31.08
33-15
10
2.125
4-250
6-375
8.500
10.63
12-75
14.88
I7.OO
19-13
21.25
23.38
25-50
27.63
29.7531.88
34-00
ioj
2.178
4-356
6-534
8.713
10.89
13.07
15-25
17-43
19.60
21.78
23.96
26.14
28.32
30.49
32.67
34-85
10?
2.231
4-463
6.694
8.925
II. 10
13-39
15.62
17.85
20.08
22.31
24-54
26.78
29.OI
31.24
33-47
35-70
iol
2.284
4-569
6-853
9.138
11.42
I3-7I
iS-99
18.28
20.56
22.84
25.I3
27.41
29.70
31.98
34-27
36.55
II
2-338
4-675
7.013
9-350
11.69
14.03
16.36
18.70
21.04
23-38
25.71
28.05
30.39
32.73
35.06
37-40
II*
2.391
4.781
7.172
9-563
n-95
14-34
16.73
I9.I3
21.52
23.91
26.30
28.69
31.08
33-47
35-86
38.25
II*
2-444
4.888
7-331
9-775
12.22
14.66
17.11
19-55
21.99
24.44
26.88
29-33
31-77
34-21
36.66
39-io
III
2.497
4-994
7.491
9.988
12.48
14.98
17.48
19.98
22.47
24.97
2747
29.96
3246
34-96
37-45
39-95
12
2-55°
5.100
7.650
IO.20
12-75
I5-30
17-85
2O.4O
22.95
25-50
28.05
30.60
33-15
35-70
38.25
40.80
12
TABLE 2.— Continued.
WEIGHTS OF STEEL BARS AND PLATES.
POUNDS PER LINEAL FOOT.
Width,
beta.
Thickness, Inches.
A
i
A
i
A
1
A
i
A
1
H
i
U
i
H
I
12*
2.66
S-3I
7-97
10.63
13.28
15-94
18.59
21.25
23.91
26.56
29.2
319
34-5
37-2
39-8
42-5
13
2.76
5-53
8.29
11.05
13.81
16.58
'9-34
22. IO
24.86
27-63
30-4
33-2
35-9
38.7
41.4
44-2
13*
2.87
5-74
8.61
11.48
H-34
17.21
20.08
22.95
25.82
28.69
31.6
34-4
37-3
40.2
43-o
459
H
2.98
5-95
8-93
11.90
14.88
17-85
20.83
23.80
26.78
29.75
32.7
35-7
38.7
41.7
44-6
47-6
H*
3-08
6.16
9.24
12.33
15-41
18.49
21-57
24.65
27-73
30.81
33-9
37-0
40.1
43-i
46.2
49-3
'5
3.19
6.38
9.56
12.75
15-94
19-13
22.31
25.50
28.69
31.88
35-1
38.3
41.4
44-6
47-8
51.0
IS*
3-29
6.59
9.88
13.18
16.47
19.76
23.06
26.35
29.64
32.94
36.2
39-5
42.8
46.1
49-4
52.7
|6
3-40
6.80
IO.2O
13.60
17.00
20.40
23.80
27.2O
30.60
34.00
37-4
40.8
44-2
47-6
510
54-4
16*
35i
7.01
IO.52
14.03
17-53
21.04
24-54
28.05
31-56
35.06
38.6
42.1
45-6
49.1
52.6
56.1
17
3-61
7-23
10.84
14-45
18.06
21.68
25.29
28.90
32.51
36.13
39-7
43-4
47.0
50.6
54.2
57.8
irt
3-72
7-44
II.IO
l.f.SS
18.59
22.31
26.03
29-75
33-47
37-19
40.9
44-6
48.3
52.1
55-8
59-5
1.8
3.83
7-65
11.48
I5-30
19-13
22.95
26.78
3O.6O
34-43
38.25
42.1
45-9
49-7
53-6
57-4
61.2
18*
3-93
7.86
11.79
15-73
19 66
23-59
27.52
31-45
35-38
39-31
43-2
47.2
51.1
55-0
59-0
62.9
19
4.04
8.08
12. II
I6.I5
20.19
24.23
28.26
32.30
36.34
40-38
44-4
48.5
52.5
56-5
60.6
64.6
19*
4.14
8.29
12.43
16.58
20.72
24.86
29.01
33-15
37-29
41.44
45-6
49-7
53-9
58.0
62.2
66.3
20
4.25
8.50
12-75
17.00
21.25
25-50
29-75
34-00
38.25
42.50
46.8
51.0
55-3
59-5
63.8
68.0
-2Oj
4.36
8.71
13.07
17-43
21.78
26.14
30.49
34-85
39-21
43.56
47-9
52.3
56.6
61.0
65.3
69.7
21
4.46
8.93
13-39
17.85
22.31
26.78
31.24
35-70
40.16
44-63
49-1
53-6
58.0
62.5
669
71.4
21*
4-57
9.14
13-71
18.28
22.84
27.41
31.98
36.55
41.12
45-69
50.3
54-8
59-4
64.0
68.5
73-i
22
4.68
9-35
14.03
18.70
23-38
28.05
32.73
37-40
42.08
46.75
51-4
56.1
60.8
65.5
70.1
74-8
22*
4.78
9-S6
14-34
I9.I3
23.91
28.69
3347
38.25
43-03
47-81
52.6
57-4
62.2
66.9
71.7
76-5
23
4.89
9.78
14.66
1955
24.44
29-33
34.21
39.10
43-99
48.88
53-8
58.7
63-5
68.4
73-3
78.2
23*
4-99
9-99
14.98
19.98
24.97
29.96
34-96
39-95
44-94
49-94
54-9
59-9
64.9
69.9
74-9
79-9
24
5.10
10.20
I5-30
20.40
25-50
30.60
35-70
40.80
45.90
51.00
56.1
61.2
66.3
71.4
76.5
81.6
2|
S-3I
10.63
15-94
21.25
2656
31.88
37-19
42.50
47-8i
53-13
58.4
63.8
69.1
74-4
79-7
85.0
26
5-53
1 1. or
16.58
22. IO
27.63
33-15
38.68
44.20
49-73
55-25
60.8
66.3
71.8
77-4
82.9
88.4
27
5-74
11.48
17.21
22.95
28.69
34-43
40.16
45.90
51.64
57.38
63.1
68.9
74.6
80.3
86.1
91.8
28
5-95
11.90
17.85
23.80
29-75
35-70
41.65
47.60
53-55
59.50
65-5
71.4
77-4
83-3
89-3
95-2
29
6.16
12.33
18.49
24.65
30.81
36.98
43-14
49-30
5546
61.63
67.8
74-o
80. i
86.3
92-4
98.6
30
6.38
12.75
I9-I3
25.50
31.88
38.25
44-63
51.00
57.38
63-75
70.1
76-5
82.9
89-3
95-6
IO2.O
31
6.59
13.18
1976
26.35
3294
39-53
46.11
52.70
59-29
65.88
72.5
79.1
85.6
92.2
98.8
105.4
32
6.80
13.60
20.40
27.2O
34-00
40.80
47.60
54.40
61.20
68.00
74-8
81.6
88.4
95-2
IO2.O
108.8
33
7.01
14.03
21.04
28.05
35.06
42.08
49.09
56.10
63.11
70.13
77.1
84.2
91.2
98.2
IO5.2
II2.2
34
7-23
14-45
21.68
28.90
36-13
43-35
50.58
57.80
65-03
72.25
79-5
86.7
93-9
IOI.2
108.4
II5.6
3§
7-44
14.88
22.31
29-75
37-19
44-63
52.06
59-50
66.94
74.38
81.8
89-3
96.7
104.1
in. 6
II9.0
36
7-65
IS-30
22.95
3O.6O
38.25
45.90
53-55
61.20
68.85
76.50
84.2
91.8
99-5
IO7.I
114.8
122.4
37
7.86
15-73
23-59
31-45
39-31
47.18
55-04
62.90
70.76
78.63
86.5
94-4
IO2.2
IIO.I
117.9
125.8
38
8.08
16.15
24.23
32.3O
40.38
48.45
56.53
64.60
72.68
80.75
88.8
96.9
105.0
II3.I
121. 1
129.2
39
8.29
16.58
24.86
33-15
41.44
49-73
58.01
66.30
74-59
82.88
91.2
99-5
107.7
1160
124-3
132.6
40
8.50
17.00
25-50
34-00
4250
51.00
59-50
68.00
76.50
85.00
93-5
102.0
IIO-5
119.0
127.5
I36.O
4i
8.71
17-43
26.14
34-85
43.56
52.28
60.99
69.70
78.41
87.13
95-8
104.6
"3-3
122.0
130.7
139-4
42
8.93
17.85
26.78
35-70
44-63
53-55
62.48
71.40
80.33
89.25
98.2
107.1
116.0
I25.C
133-9
142.8
43
9.14
18.28
27.41
36.55
45-69
54-83
63-96
73-io
82.24
91.38
100.5
109.7
118.8
127.9
I37.I
146.2
44
9-35
18.70
28.05
37-40
46.75
56.10
6545
74-80
84.15
93-50
102.9
II2.2
I2I.6
1309
140.3
149.6
4I
9.56
I9.I3
28.69
38.25
47-81
57.38
66.94
76.50
86.06
95.63
105.2
II4.8
124.3
133-9
143-4
153-0
46
9-78
19-55
29-33
39.10
48.88
58.65
68.43
78.20
87.98
97-75
107.5
II7.3
127.1
136.9
146.6
156.4
47
9-99
19.98
29.96
39-95
49-94
59-93
69.91
7990
89.89
99.88
109.9
II9.9
129.8
139.8
149.8
159.8
48
10.20
20.40
30.60
40.80
51.00
61.20
714°
81.60
91 80
IO2.O
112. 2
122.4
132.6
142 8
153-0
163.2
13
TABLE 2.— Continued.
WEIGHTS OF STEEL BARS AND PLATES.
POUNDS PER LINEAL FOOT.
Width.
Inches.
Thickness, Inches.
A
t
A
i
A
i
A
i
A
f
«
1
«
i
ti
I
49
10.4
20.8
31.2
41.7
52.1
62.5
72.9
83.3
93-7
104.1
H4.5
125.0
135-4
I45.8
1562
166.6
SO
10.6
21.3
3i'9
42-5
53-i
63.8
74-4
85.0
95-6
106.3
116.9
127.5
138.1
148.8
159-4
170.0
SI
10.8
21.7
32.5
43-4
54-2
65.0
75-9
86.7
97-5
108.4
119.2
130.1
140.9
I5I-7
162.6
173-4
52
ii. i
22.1
33-2
44-2
55-3
66.3
77-4
88.4
99-5
110.5
121,6
132.6
H3-7
154-7
165.8
176.8
53
n-3
22-S
33-8
45.1
56.3
67.6
78.8
9O.I
101.4
1 1 2.6
123.9
135-2
146.4
157.7
168.9
180.2
54
»-5
23.0
34-4
45-9
57-4
68.9
80.3
91.8
103-3
114.8
126.2
137-7
1492
160.7
I72.I
183.6
55
11.7
23-4
35-i
46.8
58.4
70.1
81.8
93-5
105.2
116.9
128.6
140.3
151.9
163.6
175-3
1870
56
119
23-8
35-7
47.6
59-5
71.4
83-3
95-2
107.1
119.0
130.9
142.8
154-7
166.6
178.5
190.4
57
I2.I
24.2
36.3
48.5
60.6
72.7
84.8
96.9
109.0
121. 1
133-2
145-4
157-5
169.6
I8I.7
193-8
58
12-3
24.7
370
49-3
61.6
74.0
86.3
98.6
110.9
123-3
135-6
147-9
160.2
172.6
184.9
197.2
59
12.5
2S.I
37-6
50.2
62.7
75-2
87.8
100.3
1128
125.4
137-9
150-5
163.0
175-5
I88.I
2OO.6
60
12.8
25-5
38.3
51.0
63.8
76.5
89-3
102.0
114.8
127.5
140.3
i53-o
165.8
178.5
I9I.3
204 o
61
13.0
25-9
389
Si-9
64.8
77-8
90.7
103.7
116.7
129.6
142.6
155-6
168.5
181.5
194.4
207.4
62
13.2
26.4
39-5
52.7
65-9
79.1
92.2
105.4
118.6
I3I.8
144.9
158.1
171-3
1845
197.6
210.8
63
13-4
26.8
40.2
53-6
66.9
80.3
93-7
107.1
120.5
133.9
147-3
160.7
174.0
187.4
200.8
214.2
64
13.6
27.2
40.8
54-4
68.0
81.6
95-2
108.8
122.4
136.0
149.6
163.2
176.8
1904
204.0
217.6
65
13-8
27.6
41.4
55-3
69.1
82.9
96.7
110.5
124.3
I38.I
iSi-9
165.8
179.6
193-4
2O7i2
22 1. 0
66
14.0
28.1
42.1
56.1
70.1
84.2
98.2
112. 2
126.2
140.3
154-3
168.3
182.3
196.4
2IO-4
224.4
67
14.2
28-S
42.7
57-o
7L.2
85-4
99-7
II3-9
128.1
142.4
156.6
170.9
185.1
199-3
213.6
227.8.
68
H-5
28.9
43-4
57-8
72-3
86.7
IOI.2
II5.6
130.1
i?4-5
159.0
1734
187.9
202.3
216.8
231.2
69
14.7
29-3
44.0
58.7
73-3
88.0
102.6
II7-3
132.0
146.6
161.3
176.0
190.6
205-3
219.9
234.6
70
14.9
29.8
44.6
59-5
744
89-3
IO4.I
II9.O
133-9
148.8
163.6
178-5
193-4
208.3
223.1
238.0
7i
I5.I
3O.2
45-3
60.4
75-4
90-5
IO5.6
I2O.7
135-8
150.9
166.0
181.1
196.1
211. 2
226.3
241.4
72
15-3
3O.6
45-9
61.2
76-5
91 8
I07.I
122-4
137-7
153-0
168.3
183.6
198.9
214.2
229.5
244.8
73
15-5
3I.O
46.5
62.1
77.6
93-i
108.6
I24.I
139.6
iSS-i
170.6
1862
201.7
217.2
232.7
248.2
74
15-7
31-5
47-2
62.9
78.6
944
IIO.I
I2S.8
141.5
157-3
173.0
188.7
204.4
22O.2
235-9
251.6
75
15-9
3J-9
47.8
63.8
79-7
95-6
iii.6
127-5
H34
159-4
175-3
191-3
207.2
223.1
239.1
255-0
76
16.2
32.3
48.5
64.6
80.8
96.9
113.1
129.2
145.4
161.5
177.7
193.8
2IO.O
226.1
242.3
258.4
77
16.4
32.7
49.1
65.5
81.8
98.2
"4-5
130.9
147-3
163.6
180.0
196.4
212.7
229.1
245-4
261.8
78
16.6
33-2
49-7
66.3
82.9
99-5
116.0
132.6
149.2
165.8
182.3
198.9
215-5
232.1
248.6
265.2
79
16.8
33-6
5° 4
67.2
83-9
100.7
II7-5
134-3
151.1
167.9
184.7
201.5
218.2
235.0
251.8
268.6
80
17.0
34-0
51.0
68.0
85.0
IO2.0
119.0
136.0
153-0
170.0
187.0
204.0
221.0
238.0
255.0
272.O
81
17.2
34-4
51.6
68.9
86.1
103.3
120 5
137-7
154-9
172.1
189.3
206.6
223.8
24I.O
258.2
275-4
82
17.4
34-9
52.3
69.7
87.1
104.6
I22.O
139-4
156.8
174-3
191.7
209.1
226.5
244.0
261.4
278.8
83
17.6
35-3
529
70.6
88.2
105.8
123.5
I4I.I
158-7
176.4
194.0
211.7
229.3
246.9
264.6
282.2
84
17.9
35-7
53-6
71.4
89.3
I07.I
125.0
142.8
160.7
178.5
1964
214.2
232.1
249-9
267.8
285.6
85
18.1
36.1
54.2
72.3
9°-3
108.4
126.4
144.5
162.6
180.6
198.7
216.8
234.8
252.9
2709
289.0
86
18.3
36.6
54-8
73-i
91.4
1097
127.9
146.2
164.5
182.8
201.0
219.3
237.6
255-9
274.1
292.4
87
18.5
37-0
55-5
74.0
92.4
IIO.9
129.4
147.9
166.4
184.9
2034
221.9
240.3
258.8
277-3
295-8
88
18.7
37-4
56.1
748
93-5
II2.2
130.9
149.6
168.3
187.0
205.7
224.4
243.1
261.8
280.5
299.2
89
18.9
37-8
56.7
75-7
94.6
II3-5
132.4
ISI.3
170.2
189.1
208.0
227.0
245-9
264.8
283.7
3O2.6
90
19.1
38.3
57-4
76.5
95-6
II4.8
133-9
153-0
172.1
191-3
2IO.4
229.5
248.6
267.8
286.9
306.0
91
19-3
38.7
58.0
77-4
96.7
116.0
135-4
154-7
174.0
1934
212-7
232.1
251.4
270.7
290.1
309-4
92
19.6
39-1
58.7
78.2
97.8
117.3
136.9
156.4
176.0
195-5
2I5.I
234.6
254.2
273-7
293-3
312.8
93
19.8
39-5
59-3
79.1
98.8
118.6
138.3
I^S.I
177.9
197.6
2174
237.2
256.9
276.7
296.4
3l6.2
94
2O.O
40.0
59-9
79-9
99.9
119.9
139.8
159.8
179.8
199.8
219.7
239-7
259-7
279.7
299.6
319.6
95
2O.2
40.4
60.6
80.8
100.9
121. 1
I4L3
l6l.5
181.7
201.9
222.1
242.3
262.4
282.6
302.8
323.0
96
2O.4
40.8
61.2
81.6
IO2.O
122-4
142.8
163.2
183.6
204.0
224.4
244.8
265.2
285.6
306.0
326.4
97
2O.6
41.2
61.8
82.5
103.1
123.7
144-3
164.9
185.5
206.1
226.7
2474
268.0
288.6
309.2
329.8
98
20.8
41.7
62 5
83.3
104.1
I25.O
145.8
1 66.6
1874
208.3
229.1
249.9
270.7
291.6
312.4
333-2
99
2I.O
42.1
631
84.2
105.2
126.2
147-3
168.3
189.3
210.4
231.4
252.5
273-5
294-5
315-6
336.6
100
21-3
42.5
63.8
85.0
106.3
127-5
148.8
170.0
191 3
212.5
233.8
255.0 276.3
297-5
318.8
340.0
' 14
TABLE 3.
MOMENTS OF INERTIA OF PLATES, Axis i-i.
Moments of Inertia 1
About
L
of One Plate.
Axis i-i.
.3 •
Thickness of Plate in Inches.
Ii
£~
I
A
I
A
*
A
1
tt
i
ii
t
M
i
B
2.6
3-3
3-9
4.6
5-2
5-9
6.S
7-2
7-8
8-5
9-i
9-8
10.4
6
4-5
5.6
6.8
7-9
9.0
10. 1
"•3
12.4
13-5
14.6
15.8
16.9
18.0
7
7-1
8.9
10.7
12.5
14.3
16.1
17.9
19.6
21.4
23.2
25.0
26.8
28.6
8
10.7
13-3
1 6.0
18.7
21.3
24.0
26.7
29.3
32.0
34-7
37-3
40.0
42.7
9
15.2
19.0
22.8
26.6
30-4
34-2
38.0
41.8
45-6
49-4
53-2
57-0
60.7
10
20.8
26.0
31-3
36.S
41.7
46.9
52.1
57-3
62.5
67-7
72-9
78.1
83-3
ii
27.7
34-7
41.6
48-5
55-5
62.4
69-3
76.3
83-2
90.1
97-o
104.0
110.9
12
36.0
45-0
54-0
63.0
72.0
81.0
90.0
99-0
108.0
117.0
126.0
135.0
144.0
13
45.8
57-2
68.7
80. i
91-5
103.0
114.4
125.9
137-3
148.8
160.2
171.6
183.1
H
57.2
71-5
85.8
1 00.0
"4-3
128.6
142.9
157.2
I7L5
185.8
200.1
214.4
228.7
IS
70.3
87.9
105.5
123.0
140.6
158.2
175-8
193-4
210.9
228.5
246.1
263.7
281.2
16
85.3
106.7
128.0
149.3
170.7
192.0
213-3
234-7
256.0
277-3
298.7
320.0
341-3
17
102.4
127.9
153-5
179.1
204.7
230.3
255-9
281.5
307-1
332-7
358.2
383.8
409-4
18
121.5
I5I-9
182.3
212.6
243.0
273-4
303.8
334-1
364-5
394-9
425.3
455-6
486.0
19
142.9
178.6
2*4-3
25O.I
285.8
32I.S
357-2
393-o
428.7
464.4
500.1
535-9
571.6
20
166.7
208.3
250.0
291.7
333-3
375-0
416.7
458.3
500.0
'541-7
583.3
625.0
666.7
21
192.9
241.2
289.4
337-6
385-9
434-1
4823
530.6
578.8
627.0
675-3
723.5
771.7
22
221.8
277.3
332-7
388.2
443-7
499.1
554-6
610.0
665-5
721.0
776.4
831-9
887.3
23
2S3-5
316.9
380.2
443-6
507.0
570-3
6337
697.1
760.4
823.8
887.2
950.6
1013.9
*4
288.0
360.0
432.0
504.0
576.0
648.0
720.0
792.0
864.0
936.0
1008.0
1080.0
1152.0
1$
325-S
406.9
488.3
569.7
651.0
732-4
813.8
895-2
976.6
1057.9
1139-3
1220.7
1302.1
26
366.2
457-7
549-3
640.8
732-3
823.9
9I5-4
1007.0
1098.5
1190.0
1281.6
I373-I
1464.7
27
4IO.I
512.6
615.1
717.6
820.1
922.6
1025.2
1127.7
1230.2
1332.7
1435-2
1537-7
1640.3
28
457-3
571-7
686.0
800.3
9H-7
1029.0
"43-3
1257-7
1372.0
1486.3
1600.7
1715.0
1829.3
29
508.1
635-I
762.2
889.2
1016.2
1143.2
1270.3
1397-3
1524-3
1651.3
1778.4
I90S-4
2032.4
30
562.5
703.1
843-8
984-4
1125.0
1265.6
1406.3
1546.9
1687.5
1828.1
1968.8
2109.4
2250.0
31
620.6
775-8
931.0
1086.1
1241.3
1396.5
1551.6
1706.8
1861.9
2017.1
2172.3
2327.4
2482.6
32
682.7
853-3
1024.0
1194.7
1365-3
1536-0
1706.7
1877-3
2048.0
2218.7
2389-3
2560.0
2730.7
33
748.7
935-9
1123.0
1310.2
1497-4
1684.5
1871.7
2058.9
2246. i
2433-2
2620.4
2807.6
2994.8
34
818.8
1023.5
1228.2
1433-0
1637-7
1842.4
2047.1
2251.8
2456.5
2661.2
2865.9
3070.6
3275.3
35
893.2
1116.5
1339-8
1563.2
1786.5
2009.8
2233.1
24564
2679.7
2903.0
3126.3
3349-6
3572.9
36
972.0
1215.0
1458.0
1701.0
1944.0
2187.0
2430.0
2673.0
2916.0
3I59-0
3402.0
3645.0 3888.0
37
1055-3
1319.1
1582.9
1846.7
2110.5
2374-4
2638.2
2902.0
3165-8
3429.6
3693-4
3957-3 4221.1
38
1143.2
1429.0
1714.7
2000.5
2286.3
2572.1
2857.9
3H3-7
3429.5
37I5-3
4001.1
4286.9 4572.7
39
1235.8
1544.8
1853.7
2162.7
2471.6
2780.6
3089-5
3398.5
3707-4
4016.4
4325-3
4634-3
4943-2
40
1333-3
1666.7
2000.0
2333-3
2666.7
3000.0
3333-3
3666.7
4000.0
4333-3
4666.7
5000.0
5333-3
4*
H35-9
1794.8
2153.8
2512.7
2871.7
3230.7
3589.6
3948.6
4307.6
4666.5
5025.5
5384-5 5743-4
42
1543-5
1929.4
23I5.3
2701.1
3087.0
3472-9
3858.8
4244.6
4630.5 5016.4
5402.3
5788.2 6174.0
43
1656.4
2070.5
2484.6
2898.7
3312.8
3726.9
4141.0
4555-0
4969-2 5383-3
5797.4 6211.5
6625.6
44
1774-7
2218.3
2662.0
3105.7
3549-3
3993.0
4436.7
4880.3
5324.0 5767.7
6211.3
6655.0
7098.7
15
TABLE 3.— Continued.
MOMENTS OF INERTIA OF PLATES, Axis i-i.
1
u
\
Moments of Inertia 1
1 About
of One Plate.
' I
I
a .
'*%
P
Thickness of Plate in Inches.
i
&
$
&
*
&
i
H
«
if
{
H
i
45
1898
2373
2848
3322
3797
4271
4746
5221
5695
6170
6645
7119
7594
46
2O28
2535
3042
3549
4056
4563
5070
5577
6083
6590
7097
7604
8111
47
2163
2704
3244
3785
4326
4867
5407
5948
6489
7030
7570
8m
8652
48
2304
.2880
3456
4032
4608
5184
5760
6336
6912
7488
8064
8640
9216
49
2451
3064
3677
4289
4902
5515
6l28
6740
7353
7966
8579
9191
9804
SO
2604
3255
3906
4557
5208
5859
6510
7161
7812
8464
9H5
9766
10417
52
2929
3662
4394
5126
5859
6591
7323
8056
8788
9520
10253
10985
11717
54
3280
4IOI
4921
574i
6561
738i
8201
9021
9841
10662
11482
12302
13122
56
3659
4573
5488
6403
7317
8232
9H7
10061
10976
11891
12805
13720
H63S
58
4065
5081
6097
7U3
8130
9146
IOl62
11178
12194
13211
14227
15243
16259
60
4500
5625
6750
7875
9000
10125
II25O
12375
13500
14625
15750
16875
18000
62
4965
6206
7448
8689
9930
11172
12413
13654
H895
16137
17378
18619
19861
64
546l
6827
8192
9557
10923
12288
13653
15019
16384
17749
I9"5
20480
21845
66
5989
7487
8984
10482
11979
13476
H974
16471
17968
19466
20963
22461
23958
68
6551
8188
9826
11464
13101
H739
16377
18014
19652
21290
22927
24565
26203
70
7H5
8932
10719
12505
14292
16078
17865
19651
21437
23224
25010
26797
28583
72
7776
9720
11664
13608
15552
17496
19440
21384
23328
25272
27216
29160
31104
74
8442
10553
12663
H774
16884
18995
2II05
23216
25326
27437
29548
31658
33769
76
9H5
11432
I37I8
16004
18291
20577
22863
25150
27436
29722
32009
34295
36581
78
9886
12358
14830
17301
19773
22245
24716
27188
29659
32131
34603
37074
39546
80
10667
13333
16000
18667
21333
24000
26667
29333
32000
34667
37333
40000
42667
82
11487
H359
17230
20102
22974
25845
28717
31589
3446o
37332
40204
43076
45947
84
12348
IS435
18522
2I6O9
24696
27783
30870
33957
37044
40131
43218
46305
49392
86
I325I
16564
19877
23190
26502
29815
33128
36441
39753
43066
46379
49692
53005
88
I4I97
17747
21296
24845
28395
31944
35493
39043
42592
46141
49691
53240
56789
90
I5I87
18984
22781
26578
30375
34172
37969
41766
45562
49359
53156
56953
60750
92
16223
20278
24334
28390
32445
36501
40557
44612
48668
52724
56779
60835
64891
94
17304
21630
25956
3O282
34608
38934
43260
47586
5I9H
56237
60563
64889
69215
96
18432
23040
27648
32256
36864
41472
46080
50688
55296
59904
64512
69120
73728
98
19608
24510
29412
343H
39216
44118
49020
53922
58824
63727
68629
73531
78433
IOO
20833
26042
31250
36458
41667
46875
52083
57292
62500
67708
72917
78125
83333
1 02
22108
27636
33163
38690
44217
49744
55271
60798
66325
71853
77380
82907
88434
^04
23435
29293
35152
4IOII
46869
52728
58587
64445
70304
76163
82021
87880
93739
106
24813
31016
37219
43422
49626
55829
62032
68235
74438
80642
86845
93048
99251
108
26244
32805
39366
45927
52488
59049
65610
72171
78732
85293
91854
98415
104976
no
27729
34661
41594
48526
55458
62391
69323
76255
83187
90120
97052
103984
110917
112
29269
36587
43904
5I22I
58539
65856
73173
80491
87808
95125
102443
109760
117077
114
30865
38582
46298
54015
61731
69447
77164
84880
92596
100313
108029
"5746
123462
116
32519
40648
48778
56908
65037
73167
81297
89426
97556
105686
113815
121945
130075
118
34230
42787
51345
59902
68460
77017
85575
94132
102689
111247
i 19804
128362
136919
1 20
36000
45000
54000
63000
72000
81000
90000
99000
108000
117000
126000
135000
144000
16
TABLE 4.
MOMENTS OF INERTIA OF PLATES, Axis 2-2.
Momenta of Inertia 9
2 About
of One Plate. - Wl
— *- Axi« a-3.
Width
THICKNESS OF PLATE IN INCHES.
in
i
A
I
A
i
A
1
H
i
H
i
•«
i
5
.01
.01
.02
•03
•05
.07
.10
.14
.18
.22
.28
•34
42
6
.01
.02
•03
.04
.06
•09
.12
.16
.21
•27
•33
41
•So
7
.01
.02
.03
•05
•07
.10
.14
.19
•25
•31
•39
48
.58
8
.01
.02
.04
.06
.08
.12
.16
.22
.28
•36
45
•55
.67
9
.01
.02
.04
.06
.09
•13
.18
.24
•32
.40
•50
.62
•75
10
.01
•03
.04
.07
.10
•IS
.20
.27
•35
45
•56
.69
.83
ii
.01
.03
•OS
.08
.11
.16
.22
•30
•39
49
.61
.76
.92
12
.02
•03
•05
.08
•13
.18
•24
•33
42
•54
.67
.82
.00
13
.02
.06
•09
.14
•19
.26
•35
.46
•58
•73
.89
.08
M
.02
.04
.06
.10
•is
.21
.28
•38
49
•63
•78
.96
•17
15
.02
.04
•07
. -10
.16
.22
•31
41
•S3
•67
.84
1.03
•25
16
.02
.04
•07
* .11
•17
.24
•33
43
•56
.72
.89
1. 10
•33
i?
.02
.04
.07
.12
.18
•25
•35
.46
.60
.76
•95
1.17
.42
18
.02
•05
.08
•13
.19
.27
•37
49
.63
.80
1. 00
1.24
•SO
19
.02
•05
.08
.20
.28
•39
•Si
.67
•85
i. 06
1.30
.58
20
.03
•05
.09
•14
.21
•30
4i
•54
.70
.89
.12
1-37
.67
21
•03
•05
•09
.IS
.22
•31
43
•57
•74
•94
•17
1-44
•75
22
•03
.06
.10
•15
.23
•33
45
.60
•77
.98
•23
1.51
.83
33
•03
.06
.10
.16
.24
•34
47
.62
.81
1.03
.28
1.58
.92
24
.03
.06
.11
•17
•25
.36
49
•65
.84
1.07
•34
1.65
2.OO
25
•03
.06
.11
•17
.26
•37
•Si
.68
.88
1. 12
.40
1.72
2.08
26
.03
.07
.11
.18
•27
•39
•53
.70
.91
1.16
45
1-79
2.17
37
.04
.07
.12
•19
.28
.40
•55
•73
•95
1. 21
•Si
1.85
2.25
28
.04
•07
.12
.20
.29
.42
•57
.76
•98
I.2S
.56
1.92
2.33
29
.04
.07
•13
.20
•30
43
•59
•79
1.02
1.30
.62
1.99
2.42
30
.04
.08
•13
.21
•31
•44
.61
.81
1.05
i-34
.67
2.06
2.50
32
.04
.08
•14
.22
•33
47
•6S
.87
1. 12
i-43
•79
2. 2O
2.67
34
.04
•09
•IS
.24
•35
•50
.69
.92
1. 2O
1.52
.90
2-33
2.83
36
.05
.09
.16
•25
•38
•53
•73
.98
1.27
1.61
2.OI
247
3.00
38
•OS
.10
•17
.27
.40
•56
•77
1.03
i-34
1.70
2.12
2.61
3-17
40
•OS
.10
.18
.28
.42
•59
.81
i. 08
1.41
1.79
2.23
2.75
3-33
42
.05
.11
.18
.29
•44
.62
•85
1.14
1.48
1.88
2-34
2.88
3-50
44
.06
.11
.19
•31
.46
•65
.90
1.19
i-55
i-97
2.46
3.02
3-67
46
.06
.12
.20
•32
.48
.68
•94
1.25
1.62
2.06
2-57
3.16
3-83
48
.06
.12
.21
•33
.50
•7i
.98
1.30
1.69
2.15
2.68
3.30
4.00
50
.07
•13
.22
•35
•52
•74
.02
i-35
1.76
2.23
2-79
343
4-17
52
•07
•13
.23
•36
•54
•77
.05
1.41
1.82
2.32
2.90
3-57
4-33
54
.07
•14
.24
•38
•56
.80
.10
1.46
1.90
2.41
3-01
3-71
4.50
56
.08
.14
•25
•39
•58
•83
•H
1.52
1.96
2.50
3-13
3-85
4.67
58
.08
•IS
•25
.60
.86
.18
1-57
2.04
2-59
3-24
3.98
4.83
60
.08
.26
.42
•63
.89
.22
1.63
2.II
2.68
3-35
4.12
5.00
17
TABLE 5.
MOMENTS OF INERTIA OF Two PLATES ONE INCH WIDE, Axis X-X.
1
f
Moments of Inertia X X '< For Distances
of Two Plates <? Measured
One Inch Wide, ! from
Axis X-X. | Inside to Inside
JL
<i" ^
j, ?
Thickness of Plate in Inches.
d
•
Ins.
i
A
i
ft
i
ft
i
ii
1
H
i
H
i
i
5
3-4
4-4
S-4
6-5
7.6
8-7
9-9
II. 2
12.5
13-8
15-2
16.6
18.2
1.6
5*
3-8
4.8
5-9
7-i
8-3
9-5
10.8
12.2
13.6
15.0
16.5
18.1
19.7
1.8
5f
4.1
5-3
6-5
7-7
9.0
10.4
n.8
13.2
14.7
16.3
17.9
19.6
21-3
2.0
51
4-5
5-7
7.0
8.4
9.8
11.2
12.7
H-3
15-9
17.6
19-3
21. 1
22.9
2.2
6
4-9
6.2
7-6
9-1
10.6
12. 1
13-8
154
17.2
18.9
20.7
22-7
24.7
2-3
6i
5-3
6-7
8.2
9.8
11.4
I3-I
14.8
16.6
18.5
20.4
22.3
24.4
26.5
2-5
61
5-7
7-3
8.9
10.5
12.3
I4.I
15-9
17.8
19.8
21.8
23-9
26.1
28.3
2-7
6!
6.1
7.8
9-5
"•3
13.2
IS-I
17.0
19.1
21.2
23.3
25-5
27.8
SOI
0-°
7
6.6
8.4
10.2
12. 1
14.1
16.1
18.2
20.4
22.6
24.9
27.2
29-7
32.2
3-2
7i
7.0
8-9
10.9
12.9
15.0
17.2
19.4
21.7
24.1
26.5
29.0
31.6
34-2
3-4
1\
7-5
9-5
n.6
13-8
16.0
18.3
20.7
23.1
25.6
28.2
30.8
33-5
36.3
3-6
71
8.0
IO.2
12.4
147
17.0
19.5
22.O
24-5
27.2
29-9.
32.7
35-5
38-4
3-9
8
8-S
10.8
13.2
IS.6
18.1
2O.6
23-3
26.0
28.8
31.6
34-6
37-6
40.7
4.1
81
9.0
"•5
14.0
l6.5
19.2
21.9
24.7
27-5
30.5
33-5
36.5
39-7
43-o
4-4
8^
9.6
12. 1
14.8
I7-S
20.3
23.1
26.1
29.1
32.2
35-3
38.6
41.9
45-3
4.6
B|
10. 1
12.8
iS-6
I8.S
21.4
24.4
27.5
30-7
33-9
37-2
40.6
44.1
47-7
4-9
9
10.7
13.6
16.5
I9-S
22.6
25.7
29.0
32.3
35-7
39-2
42.8
46-4
50.2
5-2
9l
"•3
14-3
17.4
2O.5
23-8
27.1
30.5
34-Q
37-6
41.2
45-0
48.8
52.7
5-5
9*
11.9
IS.O
18.3
21.6
25.0
28.5
32.1
35-7
39-5
43-3
47.2
51-2
55-3
5-8
9!
12.5
IS-8
19.2
22.7
26.3
29-9
33-7
37-5
41.4
45-4
49-5
53-7
57-9
6.1
10
I3-I
16.6
20. 2
23.8
27.6
31.4
35-3
39-3
43-4
47.6
Si-9
56.2
60.7
6.4
ioi
13-8
17.4
21.2
25.0
28.9
32.9
37-0
41.2
45-5
49.8
54-3
58.8
63-5
6-7
10*
14.5
18.3
22.2
26.2
30.3
34-5
38.7
43-1
47-5
52.1
56.7
61.5
66.3
7.i
I0|
iS-i
19.1
23.2
27.4
31-7
36.0
40-5
45-0
49-7
54-4
59-2
64.2
69.2
7-4
n
IS-8
2O.O
24-3
28.6
33-1
37-6
42.3
47.0
Si-9
56.8
61.8
66.9
72.2
7-7
"J
16.5
20-9
25-4
29.9
34-5
39-3
44.1
49.0
54-i
59-2
64.4
69.8
75-2
8.1
ill
17-3
21.8
26.C
31.2
36.0
40.9
46.0
5i-i
56-4
61.7
67.!
72.7
78-3
8.4
iif
18.0
22-7
276
32.5
37-5
42.7
47-9
53-2
58.7
64.2
69.8
75-6
81.4
8.8
12
18.8
23-7
28.7
33-9
39-i
44.2
49-8
55-4
61.0
66.8
72.6
76.8
84.7
9-2
I*|
19-5
24.7
29.9
35-2
40.7
46.2
51.8
57-6
63-5
69.4
75-5
81.7
88.0
9.6
ia{
20.3
25-7
3I-I
36.6
42-3
48.0
53-9
59-8
65-9
72.1
78.4
84.8
91-3
IO.O
I2|
21. 1
26.7
32.3
38.1
43-9
49-9
55-9
62.1
68.4
74.8
81.3
88.0
94-7
10.4
13
21-9
27-7
33-6
39-5
45-6
$1.8
58.1
64-5
71.0
77-6
84-3
91.2
98.2
10.8
13*
22.8
28.8
34-8
41.0
47-3
53-7
60.2
66.8
73-6
80.4
87.4
94-5
101.7
II. 2
I3J
23.6
29.8
36.1
42.5
49-0
55-6
62.4
69-3
76.2
83-3
90-5
97.8
105-3
11.6
i3i
24-5
3°-9
37-4
44.0
50.8
57-6
64.6
71.7
78.9
86.2
93-7
101.3
108.9
I2.O
H
25.4
32.0
38.8
45-6
52.6
59-7
66.9
74-2
81.7
89.2
96.9
104.7
112.7
12-5
Hi
26.3
33-1
40.1
47-2
54-4
61.7
69.2
76.8
84-5
92-3
IOO.2
108.3
116.5
12-9
Hi
27.2
34-3
4i-S
48.8
56.3
63.8
71-5
79-4
873
95-3
103-5
111.9
120.3
13-4
T ,3
X4*
28.1
35-5
42.9
50.S
58.2
66.0
73-9
82.0
90.2
98.4
106.9
II5-5
124.2
13-8
IS,
29.1
36-7
44-3
52.1
60. i
68.1
76.3
84.7
93-1
101.7
IIO-4
119.2
128.2
H-3
I5f
3O.O
37-9
45-8
53-9
62'O
70.4
78.8
87.4
96.1
104.9
H3-9
123.0
132.2
14.8
IS1
3I.O
39-1
47-3
55-6
64.0
72.6
81.3
90.1
99.1
108.2
1174
126.8
136.3
15-3
IS|
32.O
40-3
48.7
57-3
66.0
749
83.8
92.9
102.2
111.5
I2I.O
130.7
140.4
15-7
For Moment vf Inertia, deducting for rivet holes, multiply tabular value by net width.
18
TABLE 5.— Continued.
MOMENTS OF INERTIA OF Two PLATES ONE INCH WIDE, Axis X-X.
Momenta of Inertia XX For Distance*
of Two Plates • <f Measured
One Inch Wide, from
Axis X-X.
Inside to Inside.
«•
H
1 >
d
Thickness of Plate in Inches.
Ins.
i
A
1
A
i
A
1
u
1
11
i
H
z
i
16
33-o
41.6
50.2
59-i
68.1
77.2
86.4
95-8
105-3
114.9
124.7
134.6
144-7
16.2
i6J
34-0
42.9
51.8
60.9
70.2
79-5
89.0
98.7
108.5
118.4
128.4
138.6
149.0
16.8
16
35.1
44-2
53-4
62.8
72-3
81.9
91.7
101.6
111.7
121.9
132.2
142.7
153-3
17-3
16;
36.1
45-5
SS-o
64.6
74-4
84-3
94-4
104.6
114.9
125-4
136.0
146.8
157-7
17.8
18:
42.8
53-9
65-1
76.4
87-9
99-6
111.4
123.3
135-5
147-7
160.1
172.7
185-5
21. 1
18;
43-9
55-3
66.8
78-5
90-3
IO2.2
"4-3
126.6
139.0
151.6
164.3
177.2
190.3
21.7
20
52.5
66.1
79-8
93-6
107.7
I2I-9
136.2
150.8
165-5
180.3
195-4
2IO.6
226.0
26.0
2O
53-8
67.7
81.7
95-9
110.3
124.8
139-5
154.4
169.4
184.6
200.0
215.6
231.3
26.6
22;
63.3
79-6
96.0
II2.6
129.4
146.4
163.6
180.9
198.5
216.2
234-1
252.2
270.5
31-3
22i
64.7
81.3
98.1
115.1
132-3
149.6
167.2
184.9
202.8
220.9
239.2
257.6
276.3
32.0
24;
7S-o
94-3
"3-7
133-3
153-2
173.2
193-4
213.8
234-5
255-3
276.3
297.5
319.0
37-i
24-
76.6
96.2
1 1 6.0
136.0
156-3
176.7
197-3
218.1
239-2
260.4
281.8
303.5
325.3
37-9
261
87.8
110.3
132.9
155.8
178.9
2O2.2
225.8
249-5
273-5
297.6
322.0
346.6
371.5
43-5
26
894
112.3
135-4
158.7
182.3
2O6.O
230.0
254-1
278.5
303-1
328.0
353-0
378.3
44-3
28
101.5
127-5
153-7
180.0
206.7
233-5
260.6
287.9
3I5.5
343-2
371.2
399-5
428.0
50.3
28.
103.3
129.7
156.3
183.2
210.3
237.6
265.1
292.9
320.9
349-2
377-6
406.3
435-3
51-2
30:
116.3
146.0
175-9
206.0
236.4
267.1
297.9
329.1
360.5
392.1
424.0
456.1
488.5
57-7
30
118.2
148.4
178.7
209.4
240.3
271 4
302.8
334-4
366.3
398.4
430.8
463-4
496.3
58.6
32
132.0
165-7
199.6
233.8
268.2
302.8
337-8
373-o
408.5
444-2
480.2
516.4
553-0
65-5
32
I34-1
168.2
202.7
237-3
272.3
307-5
342.9
378.7
414.7
450-9
487.4
524.2
561-3
66.5
34:
148.8
186.7
224.0
263.2
301.9
340.9
380.1
419.6
459-5
499-5
539-9
580.5
621.5
73-9
34J
150.9
189.4
228.1
267.0
306.3
345-8
385.6
425-7
466.0
506.7
547-6
588.8
630.3
74-9
36;
166.5
208.9
251-5
294-5
337-7
381.2
425.0
469.1
5I3-5
558.1
603.1
648.3
694.0
82.7
36*
168.8
211.7
255.0
298.5
342-3
386.4
430.7
475-4
520.4
5657
611.2
657.1
703.3
83.8
38}
185.3
2324
279.7
3274
375-4
423-7
472-3
521.2
570-5
620.0
669.8
720.0
770.5
92.0
38;
187.7
235-4
283.4
331-7
380.3
429.2
478.4
527-9
577-8
627.9
678.4
729.2
780.3
93-2
40;
205.0
257-1
309-5
362.2
415.2
468.5
522.2
576.1
630.5
685.1
740.1
795-3
851.0
101.9
40;
207.6
260.3
3I3.3
366.6
420.3
474-3
528.6
583-2
638.2
6934
749-1
805.0
861.3
103.1
42!
225.8
283.1
340-7
398.6
456.9
515.5
574-5
633-8
693-5
753-4
813.8
874.4
935-5
112. 2
42:
228.4
286.4
344-7
403-3
462.3
521.6
581.2
641.2
701.5
762.2
823.2
884.6
946.3
II3.6
44:
247-5
310.3
373-4
436.9
500.7
564.8
629.4
694.2
759-5
825.0
891.0
957-3
1024.0
123-1
44
250.3
3I3.8
377.6
441.7
506.3
571.1
636.4
702.0
767.9
834.2
900.9
967-9
1035-3
124.6
46
270.3
338.8
407.6
476.8
546.4
616.4
686.7
757-4
828.5
899-9
971.7
1043.9
1116.5
134-4
46
273.2
342-4
412.0
481.9
552.3
623.0
694.0
765-5
837.3
909.5
982.0
1055.0
1128.3
135-9
48:
294.0
368.5
443-4
518.6
594.2
670.2
746.5
823-3
900.5
978.0
1055.9
U34-3
1213.0
146.3
48;
297.1
372.3
447-9
523.9
600.3
677.0
754-2
831-7
909.7
988.0
1066.7
1145.8
1225.3
147.8
50;
318.8
399-5
480.6
562.0
643.9
726.2
808.9
892.0
975-5
1059-4
1143.6
1228.4
1313.5
158.6
5°
321.9
403.4
485-3
567.6
650.3
733-4
816.8
900.7
985.0
1069.7
1154.8
1240.4
1326.3
l6o.2
52:
344-5
431-7
5I9-3
607.3
695.7
784.5
873-7
1053-5
1144.0
1234-9
1326.2
1418.0
17L5
52;
347-8
435-8
524.2
613.0
702.3
791.9
882.0
972.5
1063.4
1154.7
1246.5
1338.7
I43I-3
I73-I
5*
371-3
465.2
559-5
654-3
749-4
845.0
941.1
1037-5
"34-5
1231.8
1329.6
1427.8
1526.5
184.8
54:
374-7
469.4
564.6
660.2
756.3
852-7
949-7
1047.0
1144.8
1243.0
1341.7
1440.8
1540.3
186.5
56;
399-0
499-9
601.2
703.0
805.2
907-8
1010.9
1114.5
1218.5
1322.9
1427.8
1533-2
1639.0
198.6
56;
402.6
504-3
606.5
709.2
812.3
915.8
1019.8 1124.3
1229.2
1334-5
1440.3
1546.6
1653-3
200.4
For Moment of Inertia, deducting for rivet holes, multiply tabular value by net width.
19
TABLE 5.— Continued.
MOMENTS OF INERTIA OF Two PLATES ONE INCH WIDE, Axis X-X.
Moments of Inertia
of Two Plates
One Inch Wide,
Axis X-X.
d
£_-
J— ______
X
f
For Distances
Measured
from
Inside to Inside,
t.
~ (
<-•
d
Ins.
Thickness of Plate in Inches.
i
A
i
A
i
ft
§
u
1
il
i
tt
i
J
581
6oj
427.8
431-4
427.5
461.3
535-9
540-5
573-1
577-8
644.4
649-9
689.2
694.8
753-5
759-9
805.7
812.3
862.9
870-3
922.7
930.3
972-9
981.1
1040.1
1048.7
1083.3
1092.5
1158.1
1 167.6
1194.1
1204.3
1276.5
1287.0
I305.5
1316.5
1395-5
1406.9
1417-3
1429.3
1514.9
1527-3
I529-5
IS42.5
1634-7
1648.1
1642.3
1656.1
I755-I
1769-5
1755-5
1770.3
1876.0
1891.3
213.0
214.8
227.8
229.7
62i
62!
64*
488.3
492.2
52O.O
524.1
611.6
616.5
6SI-3
656.4
735-4
741.2
783-1
789.1
859.7
866.5
915.4
922.4
984.4
992-3
1048.2
1056.3
1109.7
1118.5
1181.5
1190.6
1235-4
1245.3
I3I5-3
I325-4
1361.7
1372.5
1449.6
1460.8
1488.5
1500.3
I584-5
1596.7
1615.7
1628.5
1719.8
1733-0
1743-5
1757-3
1855-7
1869.9
1871.7
1886.5
1992.1
2007.4
2OOO..5
2016.3
2129.0
2145-3
243.2
245.1
259.0
261.0
66J
552.8
556.9
586.5
590.8
692.3
697.5
734-5
739-9
832.3
838.6
883.0
889.5
972-9
980.1
1032.1
1039.6
1113.9
1122.3
1181.7
1190-3
1255-5
1264.9
I33I-8
I34I-5
1397.6
1408.1
1482.5
1493.2
1540.3
1551-8
1633-7
I 45.6
1683.5
1696.0
1785.5
1798.4
1827.2
1840.8
1937-8
1951.8
1971.4
1986.1
2090.6
2105.7
2Il6.2
2131.9
2244.0
226O.2
2261.5
2278.3
2398.0
2415-3
275-4
277.4
292.2
294-3
7ol
705
725
621.3
625.7
657.0
661.6
778.0
783.5
822.8
828.4
935-3
941.9
989.0
995-8
1093.1
1100.8
1155.8
1163.7
1251.4
1260.3
1323.2
1332-3
1410.3
1420.3
1491.1
1501.4
1569.8
1580.9
1659-7
1671.1
1729.9
1742.1
1828.8
1841.3
1890.5
1903.8
1998.5
2OI2.2
2051.6
2066.1
2168.7
2183.6
2213.3
2228.9
2339.6
2355-5
2375-6
2392.3
25II.O
2528.1
2538.5
2556.3
2683.0
2701.3
309.6
3274
329.6
74f
698.4
736.3
775-2
815.1
874.5
921.9
970-5
1020.4
1051.2
1 108.1
1166.5
1226.4
1228.4
1294.9
1363-1
H33-0
1406.3
1482.3
1560.3
1640.3
1584.7
1670.3
1758.1
1848.2
1763.7
1858.9
I956.S
2056.7
1943-3
2048.1
2155-6
2265.9
2123.5
2237.9
2355-3
2475-7
2304-3
2428.3
2555-6
2686.1
2485.7
2619.4
2756.5
2897.2
2667.7
28II.O
2958.1
3108.9
2850.3
3003.3
3160.3
3321.3
348.0
367.0
386.4
406.3
00 00 00 00
00 ON-f>- to
MHM|HW^*MH
855-9
897-8
940.7
984.6
1071.6
1123.9
1177.6
1232.5
1287.8
I3S0.7
1415.1
1481.0
1578.1
1653-3
1730.3
1722.3
1806.3
1892.3
1980.3
1940.5
2035.0
2131.9
2230.9
2159-3
2264.5
2372.1
2482.3
2378.9
2494.6
2613.1
2734-4
2599.0
2725.4
2854.8
2987.2
2819.9
2956-9
3097.1
3240.6
304I-3
3189.0
3340-1
3494-8
3263.5
3421-8
3749-7
3486.3
3655-3
3828.3
4005.3
426.7
447-6
469.0
490.9
925
945
1029.4
1075-3
II22.2
II70.I
1288.6
1346.0
1404.6
1464.5
1548.4
1617.4
1687.7
1759-6
1809.0
1889.4
1971.6
2055.6
2070.3
2162.3
2256.3
2352-3
2332.3
2435.8
2541.6
2649.7
2595.0
2710.1
2827.8
2947.9
2858.4
2985.2
3114.7
3246.9
3122.5
3260.9
3402.3
3546.7
3387-4
3537-4
3690.7
3847.2
3653-0
3814.6
3979-8
4148.4
3919-3
4092.6
4269.7
4450-5
4186.3
4371-3
4560.3
4753.3
5I3-3
536.2
559-6
583-5
985
1005
1025
1045
I2I8.9
1268.8
I3I9-7
I37I.6
1525-6
1588.0
1651.6
1716.5
1833-0
1908.0
1984.4
2062.3
2141.3
2228.7
2317.9
2408.8
2450.3
2550-3
2652.3
2756.3
2760.0
2872.6
2987.4
3104.5
3070.6
3I95-7
33234
3453-6
3381.9
3519.7
3660.2
3803.5
3694.0
3844.4
3997-8
4154.2
4006.9
4169.9
4336.2
4505.7
4320.6
4496.2
4675-4
4858.0
4635-0
4823-4
5015-4
5211.3
4950.3
5151-3
5356.3
5565.3
607.9
632.8
658.2
684.1
io6j
1424.4
1478.3
1533-2
1589.1
1782.7
1850.0
1918.7
1988.6
2141.7
2222.6
2305.0
2388.9
2501.5
2596.0
2692.2
2790.1
2862.3
2970.3
3080.3
3192-3
3223.8
3345-4
3469.2
3595-3
3586.2
3721-4
3859-0
3999-2
3949-5
4098.2
4249.7
4404.0
43I3-5
4475-9
4641.3
4809.7
4678.5
4854-5
50337
5216.2
5044.2
5233-9
5427.0
5623.7
5410.8
5614.1
5821.2
6032.0
5778.3
5995-3
6216.3
6441.3
710.5
737-5
764-9
792.8
1145
116*
1X84
1205
1645.9
1703.8
1762.7
1822.6
2059-7
2132.1
2205.7
2280.6
2474-3
2561.2
2649.6
2739-5
2889.8
2991.3
3094-5
3199-4
3306.3
3422.3
3540-3
3660.3
3723.6
3854-2
3987.0
4I22..I
4141.8
4287.0
4434-6
4584.8
4561.0
4720.8
4883-3
5048.5
4981.0
5I55-4
5332.8
5513.2
5402.0
5591.0
5783.3
5978.8
5823.8
6027.5
6234.6
6445-3
6246.6
6464.9
6687.0
6912.8
6670.3
6903.3
7H0.3
7381.3
821.2
850.1
879-5
909.4
For Moment of Inertia, deducting for rivets, multiply tabular value by net width.
20
TABLE 6.
WEIGHTS AND AREAS OF SQUARE AND ROUND BARS AND CIRCUMFERENCES or ROUND BARS.
ONE CUBIC FOOT OF STEEL WEIGHING 489.6 LB.
\Vrinht
Wright
Air. l
Air.!
Circum-
Weight
Weight
Area
Am
Circum-
of
of
Ol
Iftrni r
•9*1-1 -1
of
of
of
1. 1, .,,. ,
or Diam-
eter in
1 11> llr -t.
I5.ii
15. ir
15., i
15,1
Q
1 nicicnett
or Diam-
eter in
Inches.
i
Bar
llT.r
Q
Q
One Ft.
One Ft.
in Si.
in S<i.
in
One Ft
One Ft.
inSq.
in Sq.
in
Long.
Long.
Inches.
Inches.
lilt hr,.
Long.
Long.
Inches.
Ill' hr-,.
beta
Q
•l
•?O.6o
24..O1
9.OOOO
7.0686
'/ i ' i^
f
.013
.053
.010
.042
.0039
.0156
.0031
.0123
.1963
•3927
V
JW.WW
31.89
33-20
*T J
25.04
26.08
9-3789
9.7656
7.3662
7.6699
/•-»- i
9.6211
9.8175
A
.119
.094
.0352
.0276
.5890
A
34-55
27.I3
10.160
7.9798
10.014
i
.212
.167
.0625
.0491
.7854
j
35-92
28.20
10.563
8.2958
IO.2IO
A
•333
.261
•0977
.0767
.9817
A
37-31
29.30
10.973
8.6179
10.407
i
.478
•375
.1406
.1104
1.1781
1
38.73
30.42
11.391
8.9462
IO.6O3
A
.651
.511
.1914
•1503
1-3744
A
40.18
3L56
II. SI',
9.2806
10.799
1
.850
.667
.2500
.1963
1.5708
i
41.65
32.71
12.250
9.62II
10.996
V
1.076
.845
.3164
.2485
1.7671
6
43-14
33-90
12.691
9.9678
11.192
1.328
1.043
.3906
.3068
I.9635
44.68
35-09
13.141
10.321
11.388
•
i
i. 608
1.262
4727
•3712
2.1598
i
46.24
36.31
13-598
IO.68O
11.585
I.9I3
1.502
•5625
.4418
2.3562
-
47.82
37-56
14.063
11.045
II.78I
•
i
2.245
1.763
.6602
.5185
2-5525
1
49.42
38.81
14-535
II.4l6
11.977
2.603
2.044
.7656
.6013
2.7489
51-05
4O.IO
15.016
11.793
12.174
•
1
2.989
2-347
.8789
.6903
2.9452
i
52-71
41.40
15-504
12.177
12.370
i
3.400
2.670
I.OOOO
.7854
3.1416
4,
54-40
42-73
16.000
12.566
12.566
A
3.838
3.014
1.1289
.8866
3-3379
A
56.11
44.07
16.504
12.962
12.763
i
4-303
3379
1.2656
.9940
3-5343
i
57.85
45-44
17.016
I3-364
12.959
A
4-795
3.766
1.4102
1.1075
3.7306
A
59-62
46-83
17-535
13772
I3.I55
1
5-312
4-173
1.5625
1.2272
3.9270
j
61.41
48.24
18.063
I4.I86
I3-352
A
5-857
4.600
1.7227
1-3530
4-1233
A
63.23
49.66
18.598
14.607
I3-548
1
6.428
5.049
1.8906
1.4849
4-3I97
1
65.08
51.11
19.141
I5-033
13-744
A
7.026
5-518
2.0664
1.6230
4.5160
A
66.95
52.58
19.691
15466
I3-94I
i
7.650
6.008
2.2500
1.7671
4.7124
£
68.85
54-07
20.250
15.904
I4.I37
V
8.301
6.520
2.4414
I.9I75
4.9087
F
70.78
55-59
20.816
16.349
14-334
8.978
7-05I
2.6406
2.0739
5.1051
I
7273
57-12
21.391
16.800
I4.530
i
9.682
7.604
2.8477
2.2365
S-30I4
H
74.70
58-67
21-973
I7.257
14.726
10.41
8.178
3.0625
2.4053
5-4978
a
76.71
60.25
22.563
I772I
14.923
•
1
11.17
8-773
3.2852
2.5802
5.6941
H
78.74
61.84
23.160
18.190
15.119
11.95
9.388
3-5156
2.7612
5-8905
j
80.8 1
63.46
23.766
18.665
I5.3I5
12.76
IO.O2
3-7539
2.9483
6.0868
H
82.89
65.10
24-379
19.147
15.512
2
13.60
10.68
4.0000
3.1416
6.2832
5
85.00
66.76
25.000
I9.635
15.708
A
14.46
11.36
4-2539
3-3410
6-4795
A
87.14
68.44
25.629
2O.I29
15.904
i
15-35
12.06
4-SI56
3.5466
6.6759
i
89.30
70.14
26.266
20.629
IO.IOI
A
16.27
12.78
4-7852
37S83
6.8722
A
91.49
71.86
26.910
21.135
16.297
I
17.22
13-52
5.0625
3.976i
7.0686
*
93-72
73.60
27.563
21.648
16.493
A
18.19
14.28
5-3477
4.2000
7-2649
A
75-37
28.223
22.l66
16.690
1
19.18
15.07
5.6406
4.4301
7.4613
I
98.23
77-15
28.891
22.691
16.886
A
20.20
15.86
5.94H
4.6664
7.6576
A
100.5
78.95
29.566
23.221
17.082
*
21.25
16.69
6.2500
4.9087
7.8540
l
102.8
80.77
30.250
23758
17.279
"«
22.33
17-53
6.5664
5.I572
8.0503
A
IO5 2
82.62
30.941
24.301
17.475
23-43
18.40
6.8906
5.4119
8.2467
1
IO7.6
84.49
31.641
24.850
17.671
i
24.56
19.29
7.2227
5.6727
8.4430
H
IIO.O
86.38
32.348
254O6
17.868
2571
20.20
7-5625
5-9396
8.6394
f
II2.4
88.29
33-o63
25.967
18.064
*
26.90
21.12
7.9102
6.2126
8.8357
H
II4.9
90.22
33-785
26-535
18.261
28.10
22.07
8.2656
6.4918
9.0321
i
II74
92.17
34.516
27109
18.457
1
29-34
23.04
8.6289
6.7771
9.2284
1*
II9.9
94.14
35.254 27.688
18.653
21
TABLE 6.— Continued.
WEIGHTS AND AREAS OF SQUARE AND ROUND BARS AND CIRCUMFERENCES OF ROUND BARS-
ONE CUBIC FOOT OF STEEL WEIGHING 489.6 LB.
Thickness
or Diam-
eter in
Inches.
Weight
of
. Bar
One Ft.
Long.
Weighti
of
Bar
One Ft.
Long.
Area
of
Bar
in Sq.
Inches.
Area
of
Bar
in Sq.
Inches.
Circum-
ference
Bar
in
Inches.
Thickness
or Diam-
eter in
Inches.
Weight
of
Bar
One Ft.
Long.
Weight
of
Bar
One Ft.
Long.
Area
of
Bar
in Sq.
Inches.
Area
of
Bar
in Sq.
Inches.
Circum-
ference
Bar
in
Inches.
6
122.4
96.14
36.000
28.274
18.850
9
275-4
216.3
Sl.OOO
63.617
28.274
TV
125.0
98.14
36.754
28.866
19.046
i
16
279-3
219.3
82.129
64.505
28.471
i
8
127.6
IO0.2
37-5I6
29.465
19.242
1
283.2
222.4
83.266
65-397
28.667
A
I3O.2
IO2.2
38.285
30.069
19-439
iV
287.0
225.4
84.410
66.296
28.863
i
132.8
104.3
39.063
30.680
I9.635
1
290.9
228.5
85-563
67.201
29.060
ft
135-5
106.4
39.848
31.296
19.831
5
16
294-9
23I-5
86.723
68.112
29.256
f
138.2
108.5
40.641
3I-9I9
2O.O28
f
298.9
234-7
87.891
69.029
29.452
ft
140.9
IIO-7
41.441
32-548
20.224
TV
3O2.8
237-9
89.066
69-953
29.649
i.
143-6
II2.8
42.250
33-I83
20.420
2
306.8
241.0
90.250
70.882
29.845
TV
146.5
114.9
43.066
33-824
20.617
TV
310.9
244.2
91.441
71.818
30.041
f
149.2
117.2
43.891
34-472
20.813
f
3I5-0
247.4
92.641
72.760
30.238
JJL
16
I52.I
119.4
44-723
35-125
21.009
tt
3I9-I
250.6
93.848
73-708
30.434
f
154-9
121.7
4S-563
35.785
2I.2O6
L
323.2
253-9
95-063
74.662
30.631
H
157-8
123.9
46.410
36.450
21.402
H
3274
257-1
96.285
75.622
30.827
1
160.8
126.2
47.266
37.122
21.598
i
331-6
260.4
97-5I6
76.589
31.023
if
163.6
128.5
48.129
37.800
21-795
it
335-8
263.7
98.754
77-56i
3I.O22
7
166.6
130.9
49.000
38.485
21.991
10
340-0
267.0
IOO.OO
78.540
31.416
ft
169.6
133-2
49.879
39-175
22.187
p
344-3
2704
101.25
79-525
31.612
i
172.6
135-6
50.766
39-87I
22.384
i
348.5
273-8
102.52
80.516
31.809
ft
175-6
137.9
51.660
40-574
22.580
tV
352.9
277.1
103.79
81-513
32.005
i
4
178.7
140.4
52.563
41.282
22.777
i
357-2
280.6
105.06
82.516
32.2OI
5
Iff
181.8
142.8
53-473
41-997
22.973
TV
361.6
284.0
106.35
83-525
32.398
f
184.9
145-3
54-391
42.718
23.169
!
366.0
287.4
107.64
84.541
32-594
TV
188.1
147-7
5S-3i6
43-445
23.366
TV
370-4
290.9
108.94
85-562
32.790
1
191.3
150.2
56.250
44.179
23.562
I
374-9
294.4
110.25
86.590
32.987
9
Tff
194.4
152.7
57-I9I
44.918
23-758
TV
379-4
297.9
in-57
87.624
33-I83
f
197.7
155.2
58.141
45.664
23-955
5
8
383.8
301.4
112.89
88.664
33-379
tt
200.9
157.8
59.098
46.415
24.151
U
388.3
305.0
114.22
89.710
33-576
f
204.2
160.3
60063
47-173
24-347
f
392-9
308.6
115-56
90.763
33-772
H
207.6
163.0
61.035
47-937
24.544
Tf
397-5
312.2
116.91
91.821
33-968
8
210.8
165.6
62.016
48.707
24.740
1
402.1
3I5-8
118.27
92.886
34-165
i4
Tt
214.2
168.2
63.004
49.483
24.936
Tf
406.8
3I9-5
119.63
93-956
34-36i
8
217.6
171.0
64.000
50.265
25-I33
II
411.4
323.1
I2I.OO
95-033
34-558
TV
22I.O
1736
65.004
5I-054
25-329
TV
416.1
326.8
122.38
96.116
34-754
i
224.5
176.3
66.016
5I-849
2S-525
i
g
420.9
330.5
123.77
97.205
34-950
ft
228.O
179.0
67.035
52.649
25.722
tV
425-S
334-3
I25.I6
98.301
35 H7
1
231.4
181.8
68.063
53-4S6
25.918
i
430-3
337-9
126.56
99.402
35-343
A
234-9
184.5
69.098
54.269
26.114
5
T6
435-1
341-7
127.97
100.51
35-539
f
238.5
187-3
70.141
55.088
26.311
t
439-9
345-5
129.39
101.62
35-736
TV
242.0
190.1
71.191
55-9H
26.507
TV
444-8
349-4
130.82
102.74
35-932
2
245.6
193.0
72.250
56.745
26.704
\
449-6
353-1
132.25
103.87
36.128
ft
249-3
195-7
73-3i6
57.583
26.900
fV
454-5
357-o
I33-69
105.00
36.325
5
8
252.9
198.7
74391
58.426
27.096
f
459-5
360.9
135 H
106.14
36.521
H
256.6
20 1. 6
75-473
59-276
27.293
11
16
464.4
364-8
136.60
107.28
36.717
3
260.3
204.4
76-563
60.132
27.489
3
469.4
368.6
138.06
108.43
36.914
«
264.1
207.4
77.660
60.994
27.685
if
474-4
372.6
13954
109.59
37.110
|
267.9
210.3
78.766
61.862
27.882
1
479-5
376.6
I4I.O2
110.75
37306
1 5
16
271.6
213-3
79-879
62.737
28.078
15
16
484-5
380.6
142.50
111.92
37.503
22
TABLE 7
PROPERTIES OF CARNEGIE I BEAMS
r\ I1
r
Distance
\ . 1 I
Maximum
Center to
1
i
V
r
i
Section
M. ,, lu-
Bending Mo-
ment <& 16,000
Center
Required
toMak*
£
"3
w
* a
lus
Lb. per
Sq. In.
Radii of
ja
g
0
JO
I-
Moment of
r = Radius of
***t *"
Gyration
tqpd
if
i
a
i
E
Inertia
Gyration
p
F
Axis i-i
Axis 2-2
Axis i-i
Axis 2-2
Axis i-i
Axis i-i
ft
II
I*
rl
r»
Si
Mi
Inches
Pounds
Inches*
Inches
Inches
Inches4
Inches4
Inches
Inches
Inches*
Foot- Pounds
Inches
24
"5
34-oo
0.750
8.000
2 955-5
83.23
9-33
•57
246.4
328 ooo
18.39
no
32.48
0.688
7-938
2 883.5
81.0
9.42
.58
240.3
321 ooo
18.58
105
30.98
0.625
7.875
2 811.5
78.9
9-53
.60
234.3
312 ooo
18.78
100
29.41
0-754
7.254
2 380.3
48.56
9.00
.28
198.4
264 ooo
17.82
95
27.94
0.692
7.192
2 309.6
47.10
9.09
•30
192.5
257 ooo
17-99
90
26.47
0.631
7-I3I
2 239.1
45.70
9.20
•31
186.6
249 ooo
18.21
85
25.00
0.570
7.070
2 168.6
44-35
9-3i
•33
180.7
241 ooo
18.43
80
23.32
0.500
7.OOO
2 087.9
42.86
9.46
•36
174-0
232 ooo
18.72
2O
100
29.41
0.884
7.284
655.8
52-65
7-50
•34
165.6
221 OOO
14.76
95
27.94
0.810
7-210
606.8
50.78
7-58
•35
160.7
214 ooo
14.92
90
26.47
0-737
7-137
557.8
48.98
7-67
-36
155.8
208 ooo
I5.IO
85
25.OO
0.663
7.063
508.7
47-25
7-77
•37
150.9
2OI OOO
I5-30
80
23-73
0.600
7.OOO
466.5
45.81
7.86
•39
146.7
196 ooo
15-47
75
22.O6
0.649
6-399
268.9
30-25
7-58
•17
126.9
169 ooo
14.98
70
20.59
0-575
6-325
219.9
29.04
7.70
.19
I22.O
163 ooo
15.21
65
19.08
0.500
6.250
169.6
27.86
7-83
.21
II7.0
156 ooo
15-47
18
90
26.47
0.807
7-245
I 260.3
52.00
6.90
40
I4O.O
187 ooo
I3-5I
85
25.OO
0.725
7.163
I 22O.6
49.99
6-99
.42
135-6
181 ooo
13.69
80
23-53
0.644
7.082
I I8O.9
48.08
7.09
•43
I3I.2
175 ooo
13.89
75
22.05
0.562
7.000
I 141.3
46.23
7.19
•45
126.8
169 ooo
14.08
70
20.59
0.719
6.259
921.3
24.62
6.69
.09
IO2-4
136 ooo
13.20
65
19.12
0.637
6.177
881.5
23-47
6-79
.11
97-9
131 ooo
13.40
60
I7-65
0-555
6.095
841.8
22.38
6.91
•13
93-5
125 ooo
13.63
55
15-93
0.460
6.000
795-6
21.19
7.07
•IS
88.4
118 ooo
13-95
IS
100
29.41
1.184
6-774
900.5
50.98
5-53
.31
1 20. 1
160 ooo
10.75
95
27.94
1.085
6-675
872-9
48.37
5-59
•32
116.4
155 ooo
10.86
90
26.47
0.987
6.577
8454
45-91
5-65
•32
II2.7
150 ooo
10.99
85
25.00
0.889
6.479
817.8
43-57
5-72
.32
IO9.O
145 ooo
11.13
80
23.81
0.810
6.400
795-5
41.76
5-78
.32
106.1
141 ooo
11.25
75
22.06
0.882
6.292
691.2
30.68
S-6o
.18
92.2
123 ooo
10-95
70
20-59
0.784
6.194
663.6
29.00
5-68
•19
88.5
118 ooo
n. ii
65
19.12
0.686
6.096
636.0
27.42
S-77
.20
84.8
113 ooo
11.29
60
17.67
0.590
6.000
609.0
25.96
5.87
.21
81.2
108 ooo
11.49
55
16.18
0.656
5746
511.0
17.06
S-62
.02
68.1
91 ooo
11.05
50
14.71
0.558
5.648
4834
16.04
5-73
.04
64.5
86 ooo
11.27
4S
I3-24
0.460
5-550
455-8
15.00
5-87
.07
60.8
81 ooo
11.54
42
12.48
0.410
5-500
441-7
14.62
5-95
.08
58-9
79 ooo
11.70
12
55
16.18
0.822
5.612
321.0
I7-46
4-45
.04
53-5
71 ooo
8.65
SO
14.71
0.699
S-489
303-3
16.12
4-54
•05
50.6
67 ooo
8.83
45
13.24
0.576
5-366
285.7
14.89
4-65
.06
47-6
63 ooo
9.06
40
11.84
0.460
5-250
268.9
13.81
4-77
.08
44-8
60 ooo
9.29
35
10.29
0.436
5.086
228.3
10.07
4.71
•99
38.0
51 ooo
9.21
3I-S
9.26
0.350
5.000
215.8
9.50
4.83
I.OI
36.0
48 ooo
9-45
23
TABLE 7.— Continued
PROPERTIES OF CARNEGIE I BEAMS
1 ' 1
r
Maximum
Distance
Center to
0
1
t
K
a
r i
Section
Modu-
Bending Mo-
ment @ 16,000
Required
to Make
1
In
Pi
a
V
"o
%
E
.1
lus
Lb. per
Sq. In.
Radii of
R
M
i
<
j
o
M
I =
Moment of
r= Radius of
(jy ration
Equal
'C
™
5
1
Inertia
Gyration
T
H
^
r^ ^!
Axis i— i
Axis 2-2
Axis i-i Axis 2-2
Axis i-i
Axis i-i
TT
I,
la
r»
r*
Si
Mi
Inches
Pounds
Inches*
Inches
Inches
Inches*
Inches*
Inches
Inches
Inches 3
Foot-Pounds
Inches
JO
40
11.76
0.749
5.099
IS8.7
9-50
3-67
.90
31-7
42 ooo
7-12
35
IO.29
O.6O2
4-952
146.4
8.52
3-77
.91
29-3
39 ooo
7-32
30
8.82
0-455
4.805
134.2
7-65
3-90
•93
26.8
36 ooo
7-57
25
7-37
0.310
4.660
122. 1
6.89
4.07
•97
24.4
33 ooo
7.91
9
35
10.29
0.732
4.772
IH.8
7-31
3-29
.84
24.8
33 ooo
6.36
30
8.82
0.569
4.609
101.9
6.42
340
.85
22.6
30 ooo
6.58
25
7-35
0.406
4.446
91.9
5-65
3-54
.88
20.4
27 ooo
6.86
21
6.31
0.290
4-330
84-9
5-16
3-67
.90
18.9
25 ooo
7.12
8
25-5
7-SO
0.541
4.271
68.4
4-75
3-02
.80
I7.I
23 ooo
5-82
23
6.76
0-449
4.179
64-5
4-39
3-09
.81
16.1
21 OOO
5.96
2O-5
6.03
0-357
4.087
60.6
4.07
3-17
.82
15.1
20 ooo
6.12
18
5-33
0.270
4.000
56.9
3-78
3-27
.84
14.2
19 ooo
6.32
7
20
5.88
0.458
3.868
42.2
3-24
2.68
•74
12. 1
16 ooo
5-15
I7-S
S-iS
0-353
3.763
39-2
2-94
2.76
•76
II. 2
15 ooo
5-31
IS
4.42
0.250
3.660
36.2
2.67
2.86
.78
IO-4
14 ooo
5-50
6
17.25
5.07
0-475
3-575
26.2
2.36
2.27
.68
8-7
II 600
4-33
14-75
4-34
0.352
3-452
24.0
2.09
2-35
.69
8.0
10 700
449
12.25
3.61
0.230
3-330
21.8
1-85
2.46
.72
7-3
9 700
4.70
5
14-75
4-34
0.504
3-294
15.2
1.70
1.87
-63
6.1
8 loo
12.25
3.60
0-357
3-147
13.6
1 45
i-94
•63
54
7 300
9-75
2.87
O.2IO
3.000
12. 1
1.23
2.05
•65
4.8
6 400
4
10.5
3-09
O.4IO
2.880
7 I
I.OI
1.52
•57
3-6
4 800
9-5
2.79
0-337
2.807
6-7
•93
•55
•58
34
4 500
8.5
2.50
0.263
2-733
6.4
-85
•59
.58
3-2
4 200
7-5
2.21
O.I9O
2.660
6.0
•77
.64
•59
3-0
4 ooo
7-5
2.21
0.361
2.521
2.9
.60
•IS
.52
1.9
2 600
3
6-5
I.9I
0.263
2.423
2.7
•53
•19
•52
1.8
2 400
5-5
1.63
O.I7O
2.330
2-5
.46
1.23
•53
i-7
2 20O
SUPPLEMENTARY BEAMS
27
83
24.41
0.424
7.500
2888.6
53-i
10.88
1.47
214.0
285 300
21.56
24
69-5
20.44
0.390
7.000
I928.O
39-3
9.71
1-39
160.7
214 220
19.22
21
57-5
16.85
0-357
6.500
1227.5
28.4
8-54
1.30
116.9
155 880
16.87
IS
46.0
13-53
O.322
6.000
733-2
19.9
7.36
I.2I
81.5
i 08 620
14-52
IS
36.0
10.63
0.289
5-Soo
405.1
13-5
6.17
I-I3
54-0
72 020
12.14
12
27-5
8.04
0.255
5.000
199.6
8-7
4.98
1.04
33-3
44 350
9-74
10
22.O
6.52
O.232
4.670
II3-9
6-4
4.18
0.99
22.8
30 370
8.12
8
17-5
5-15
0.210
4-330
58.3
4-5
3-37
0-93
14.6
19 450
6.48
24
TABLE 8
ELEMENTS OF CARNEGIE I BEAMS
J)
ft «*4>|
Aft #
Jig- "S Jt~J
iJlv^-.-f .
-•**• JU
^w* ---I*
1
if
Flange
Web
JWeb
t
k
Maximum
Bending
Moment
Gage
Grip
Dis-
tance
111
P
•Sg
i
f
b
c
Inches
Pounds
Inches
Inches
Inches
Inches
Inches
Ft.-Lb.
Inches
Inches
Inches
Inches
Inches
1
24
"5
8
a
20;
328 ooo
4
ii
A
100
7
|
2O
264 ooo
4
I
A
95
7
tt
2Oi
257 ooo
4
A
{
16
90
7
|
20
249 ooo
4
;
f
5 *
85
7i
A
A
2O
.441 ooo
4
f
80
7
i
i
2Oi
232 ooo
4
;
;•„
.
2O
100
7
|
A
1 6.
221 OOO
4
I
i
^
95
7;
f$
A
l6*
214 ooo
4
I
i
K
90
7
f
f
208 ooo
4
I
A
«j
85
80
^
i
i6j
'•
!
2OI OOO
196 ooo
4
4
I
I
f
J
16
p
75
6|
H
17
i
169 ooo
4
\
}
i*"
70
6|
A
A
17
i
163 ooo
4
|
1
"«
65
6J
i
17
i
156 ooo
4
*
A
X
18
90
7i
H
A
I4i
f
187 ooo
4
I
*
X
85
7i
i
f
14:
181 ooo
4
I
A
VO
80
75
7
A
i
14\
14'
.
.
175 ooo
169 ooo
4
4
I
I
T^
70
65
60
6J
6J
i
jrJ
is
136 ooo
131 ooo
125 ooo
31
3i
35
1
t
1Q
55
6
i
15;
I
118 ooo
32
5
A
15
100
6J
iA
II
2
160 ooo
3|
X
f
95
6i
ij
II
2
155 000
I
I
£
£"
90
6i
i
*
II
2
150 ooo
34
I
A
i
12
85
6|
i
J
A
II
2
145 ooo
3l
I
$
5-
S
80
6j
1
H
A
II
2
141 ooo
3f
I
i
Be
15
75
6|
1
A
ll\
123 ooo
3*
H
|
70
6i
H
1
II;
'
118 ooo
3i
i
A
]*"
6i
n
t
II;
113 ooo
|
A
"-
w
<•«
60
6
f
A
II
108 ooo
3i
|
I
.T
X
M
55
e^
tt
A
12!
91 ooo
S
S
1
•
12
«*
3
5°
r
A
A
12'
86 ooo
Si
1
X
45
42
9
i
A
12:
12;
1
81 ooo
79 ooo
3
J
A
M
12
oc
90 ooo
3Jr
^ .
i
oo
86 ooo
3^
?
^"
55
5°
45
5
S
S
S
A
A
9
9
9
71 ooo
67 ooo
63 ooo
si
3
'
|
i
12
jg j
40
S
i
9
60 ooo
3
.
A
35
3i-5
S
5
t
A
91
9'
51 ooo
48 ooo
3
3
t
A
\J
41
25
TABLE 8.— Continued
ELEMENTS OF CARNEGIE I BEAMS
ti i
In
jj
•"Q
g.sS
Gage
Grip
Dis-
tance
M>
n
rt
•gh
Flange
Web
iWeb
t
k
'1'c |
'3 > rt
a*
OH
Q
£R
gal
f
b
c
S5^
Ǥ
Inches
Pounds
Inches
Inches
Inches
Inches
Inches
Ft.-Lb.
Inches
Inches
Inches
Inches
Inches
PC
10
4°
Sl
f
3
8
8
I
42 ooo
2f
i
A
^
35
S
A
8
I
39 ooo
2f
i
I
3
g
o .
30
4*
£
i
8
I
36 ooo
2f
5
A
*•„ jH
25
4J
16
A
8
I
33 ooo
2f
i
vx
9
35 •
4f
3.
1
7
I
33 ooo
25
2
A
»l« .
30
41
A
A
7
I
30 ooo
2i
2
1
3
8
X ^
25
4*
A
A
7
I
27 ooo
4
J
4
00
21
4l
A
i
7
I
25 ooo
2§
5
A
8
25-5
23
4l
4i
A
A
4
6|
1
1
23 ooo
21 OOO
aj
A
16
5
16
3
8
20.5
4*
A
6i
i
20 ooo
24
A
X —
18
4
4-
8
6i
i
19 ooo
2?
A
A
m|oo ^H
7
20
3i
2
1
si
I
16 ooo
2i
f
A
X +:
17-5
3f
i
A
5!
8
15 ooo
2j
8
i
1
8
io*
15
3l
4
1
Si
8
14 ooo
2i
J
A
6
I7-25
3l
£
4
4^
3
4
II 600
2
3
8
Te
14-75
1
A
4?
10 700
2
f
i
8
6
12.25
3!
4"
i
4^
f
9 700
2
f
A
_g
5
14-75
12.25
3f
3s
!
i
3!
35
|
8 100
7 300
If
If
I
A
1
6
"•
9-75
3
T
i
y
3
6 400
If
|
A
S
4
10.5
al
A
*
2f
|
4 800
l£
A
4"
vb
9-5
2*
3
8
A
a!
f
4 5°o
li
A
1
1
,
X
8.5
2f
i
a!
8
4 200
l£
T6
A
2
7-5
3
A
8
2f
1
4 ooo
1^
A
A
X
3
7-5
25
f
A
if
|
2 600
ii
A
i
vb
6-5
2*
4-
|
if
|
2 400
ii
A
A
3
8
6
3
A
i
Jf
8
2 2OO
i|
PF
i
SUPPLEMENTARY BEAMS
16" X i "
27
83.0
7i
A
i
2l|
2f
285 3OO
4
1
A
1
X i' - 4"
16" X i"
24
69.5
7
3
8
A
19
2|
214 22O
4
H
i
1
X i' - 4"
i 6" X i"
21
57-5
61
f
A
i6J
*J
155 880
4
H
i
1
Xi'- 4"
16" X i"
18
46.0
6
A
A
14
2
I O8 62O
3f
f
i
1
XI'- 4"
12" X i"
15
36.0
si
A
A
«i
If
72 O2O
3i
A
i
3
X i'-4"
12" X f"
12
27.5
5
1
1
8f
If
44 350
3
1
A
3
4
Xi'- o"
8" X i"
IO
22.O
4l
i
1
7*
If
30 370
2f
A
A
f
Xi'- o"
8" X f "
8
17-5
4l
i
4
1
5l
Ij
19 450
2|
A
A
a
X o' - 8"
26
TABLE 9
DIMENSIONS AND ELEMENTS OF STANDARD CARNEGIE I BEAMS
j, „-«-— 4j^
ir'* ' \i'i
• LOPE Of FLANOUl:*
J
Weight
Area
_/
Width
of
Thick-
Ill'SS Ol
Root.
Toe.
Radius.
Axil i-i
Axis 3-2
IN
Foot
OI
Section
Flange,
b
Web,
t
m
n
r
Ii-i
Si-i
ri-i
IM
S*-t
r*-i
In.
Pounds
Sq. In.
Inches
Inches
Inches
Inches
Inches
Inches*
Inches'
Inches
Inches'
Inches*
In.
24
105
30.98
7-875
0.625
.404
0.800
O.6o
2 811.5
234-3
9-53
78-9
2O.O
.60
24
90
26.47
7-I3I
0.631
.142
0.600
O.6o
2 238.4
186.5
9.20
45-7
12.8
•31
24
80
23.32
7.OOO
0.500
.142
O.6oo
O.6o
2 087.2
173-9
9.46
42.9
12.2
•36
2O
80
23-73
7.000
0.600
.183
0.650
0.70
I 466.3
146.6
7.86
45-8
I3.I
•39
20
65
19.08
6.250
0.500
.029
0.550
0.60
I 169.5
117.0
7.83
27.9
8.9
.21
18
75
22.O5
7.000
0.562
•195
0.659
0.66
I 141.3
126.8
7.19
46.2
13.2
•45
18
60
17.65
6.095
0-555
0.922
0.460
0.56
841.8
93-5
6.91
22.4
7-3
•13
18
55
15-93
6.000
0.460
0.922
0.460
0.56
795-5
88.4
7.07
21.2
7.1
•IS
IS
60
17.67
6.000
0.590
1.041
0.590
0.69
609.0
81.2
5.87
26.O
8-7
.21
IS
50
14.71
5.648
0.558
0.834
0.410
O.5I
4834
64-5
5-73
16.0
5-7
.04
IS
42
12.48
5.500
0.410
0.834
0.410
0.51
441.8
58.9
5-95
I4.6
5-3
.08
12
40
11.84
5-250
0.460
0.859
0.460
0.56
268.9
44.8
4-77
13-8
5-3
.08
12
9.26
5.000
0.350
0.738
0-350
0-45
215.8
36.0
4-83
9-5
3-8
.01
10
30
8.82
4.805
0-455
0.673
0.310
0.4!
134-2
26.8
3-90
7.6
3-2
0.93
IO
25
7-37
4.660
0.310
0.673
0.310
0.41
122. 1
24.4
4.07
6.9
3-o
0.97
9
21
6.31
4-330
0.290
0.627
0.290
0-39
84.9
18.9
3.67
5-2
2.4
0.90
8
18
5-33
4.000
0.270
0.581
0.270
0-37
56.9
14.2
3-27
3-8
1-9
0.84
6
12.25
3.61
3-330
0.230
0.488
0.230
0-33
21.8
7-3
2.46
1.8
i.i
0.72
TABLE 10
DIMENSIONS AND ELEMENTS OF SUPPLEMENTARY CARNEGIE I BEAMS
1
P
'
1
? a. Jl'f
i
_£ M
in-
71.
p '-. \ri
SLOPE OF FLANGES 1 :•
•a
i
11
2&
^
11
•Stf.
J3 M
iJr
£E
H.O
II-
E*
E
a
i
Dimensions for Double
Curve
Axis i-i
Axis 2-a
0
P
R
r
Ii-i
Si-i
ri-i
I»-l
St-s
rt-t
In.
Lb.
Sq.In.
In.
In.
In.
In.
In.
In.
In.
In.
In.«
In.'
In.
In.<
In.'
In.
27
24
21
18
15
12
10
8
83.0
69.5
57-5
46.0
36.0
27-5
22.0
17-5
24.41
20.44
16.85
13-53
10.63
8.04
6.52
5-15
7-50
7.00
6.50
6.00
5-50
5.00
4-67
4-33
0.424
0.390
0-357
0.322
0.289
0.255
0.232
O.2IO
1.185
1.091
0.996
0.900
0.805
0.710
0.647
0.583
0.596
0.540
0.484
0.427
0.371
0.315
0.277
0.240
I.52I
1.392
1.263
I-I34
1.005
0.876
0.790
0.704
0.208
0.195
0.172
0.159
0.146
0.123
0.114
0.105
6-45
5.88
5-31
4-75
4.18
3-6i
3-24
2.86
0.65
0.60
0.55
0.50
0-45
0.40
0-37
o-33
2888.6
1928.0
1227.5
733-2
405.1
199.6
113.9
58.3
214.0
160.7
116.9
8l.S
54-0
33-3
22.8
14.6
10.88
9-71
8.54
7-36
6.17
4.98
4.18
3-37
S3-i
39-3
28.4
19.9
I3-S
8-7
6.4
4-5
I4.I
II. 2
8.8
6.6
4-9
3-5
2-7
2.1
1-47
•39
.30
.21
•13
.04
0-99
0-93
27
TABLE 11.
WEB RESISTANCES FOR I-BEAMS.
r
CARNEGIE I-BEAMS, FROM CARNEGIE'S POCKET COMPANION.
Depth
of
Beam.
Weight
per
Foot.
Allowable
Web
Shear.
Allowable
Buckling
Resistance.
Min.
End
Bear-
ing.
End
Reac-
tion
Depth
of
Beam.
Weight
Foot.
Allowable
Web
Shear.
Allowable
Buckling
Resistance.
Min.
End
Bear-
ing.
End
Reac-
tion
a=3i".
Inches.
Pounds.
Pounds.
Pounds
per Sq. In.
Inches.
Pounds
Inches.
Pounds.
Pounds.
Pounds
per Sq. In.
Inches.
Pounds.
27
83.0
114480
7970
27.1
34650
55-0
98520
16470
4-3
87890
50
0
8
3880
16030
4-S
'
2830
115.0
180000
13460
11.8
95880
45-0
69120
15390
4.8
57620
IIO.O
165120
12960
12.5
84690
12
40.0
55200
14480
5-3
43300
10
5-0
150000
12350
13-4
73320
35
0
S
232O
14230
5-4
i
10330
IOO.O
180960
13490
11.8
96620
31-5
42000
13060
6.2
29710
24
95-0
166320
13000
12.5
85610
27-5
30600
10850
8.1
17990
90.0
85.0
80.0
69-5
151440
136800
I2OOOO
93600
12410
11710
10690
8340
13-3
14-5
16.5
22.8
744io
63410
50780
30910
10
40.0
35-0
30.0
25.0
74900
60200
45500
31000
16690
16120
15190
13410
3-S
3-7
5-0
75010
58220
41470
24940
21
57-5
74970
8820
18.6
27540
22.O
23200
11540
6.2
16060
IOO.O
176800
15080
8-3
113320
35-0
3O.O
65880
51210
16870
16260
3-1
3-3
71010
53200
95-0
162000
14720
8.6
101370
9
25.O
36540
15160
3-7
35390
20
90.0
85.0
80.0
147400
132600
I200OO
14300
13780
13230
9.0
9-5
IO.I
89590
77630
67460
2I.O
25-5
26100
43280
13620
16440
4-4
2.9
22710
48920
75.0
70.0
65.0
1 298OO
II5OOO
IOOOOO
13660
12980
12080
9.6
10.4
11.6
7S38o
63420
51320
8
23.O
20.5
18.0
17-5
35920
28560
21600
16800
15910
15120
13870
12400
3-0
3-3
3-8
4-5
39290
29690
20600
14320
90.0
145260
15140
7-4
97730
20 .0
32060
16350
2.5
39310
18
85.0
80.0
75.0
70.0
65.0
60.0
130500
115920
101160
129420
114660
99900
14700
14160
13450
14670
14110
13380
7-7
8.2
8.9
7-8
8.3
9.0
85260
72940
60480
84350
71890
59420
7
6
17-5
15-0
17-25
14-75
12.25
24710
I7SOO
28500
2II2O
I380O
15570
14150
16810
16050
14480
2.7
3-2
2.1
2.2
2.6
28850
18580
39930
28250
16650
55-0
82800
I222O
IO.2
44980
17.0
I9OOO
16726
1.7
30180
46.0
57960
9320
14.8
24020
14-75
2520O
17280
1.6
41370
IS
75-0
70.0
65.0
60.0
55.0
50.0
132300
117600
102900
88500
98400
83700
I6O5O
15690
I52IO
I460O
I5O4O
14340
5-6
5.8
6.1
6.5
6.2
6.7
102660
89160
756SO
62440
71530
58020
5
4
12.25
9-75
10.5
9-5
8.5
7-5
17850
IO5OO
I64OO
13480
IO52O
76OO
16580
14870
17310
16940
16360
I536o
1.8
2.1
1-3
1-4
1-4
1.6
28120
14830
31940
25690
19360
I3I30
45.0
69000
13350
7-5
44520
7-5
IO83O
17560
I.O
26940
42.0
61500
I267O
8.1
37660
3
6.5
7890
17020
I.O
19020
36.0
43350
IOOIO
II. 2
20970
5
.5
5100
15950
i.i
II530
For explanation of above table see footnote Table 16.
CAMBRIA I-BEAMS UNIFORMLY LOADED, FROM CAMBRIA'S HANDBOOK.
•5
££
X <U "^
c c
J3
"M^
*'.£"H
da
j* £ *j
x v-6
a o
.a
%£ «<U-0
. ^
o.
V
C
!&
nj
§1
ft
B
Q
'Z £
M
S3
ft .- fc)
•135
§1
o,
Q
!& ^
S$
In.
Lb.
Lb.
Ft.
In.
Lb.
Lb.
Ft.
In. Lb.
Lb.
Ft.
In.
Lb. Lb.
Ft.
3
5-5
10900
1-7
8
18
36310
4.2
12 50 •
176250
3-2
18
55 109040
8.8
6.5
17790
i.i
20.25
5356o
3.1
55
213760
2.8
60 155580
6.6
7-5
25230
•9
22.75
72760
2.4
65 194040
5-5
4
7-5
15330
2.1
2S.2S
91590
2.1
IS 42
45
86530
106100
7-3
6.2
70 232870
4-9
8.5
22670
1.6
9
21
42450
4.8
SO
146260
4.8
20
65 129150
9.6
9-5
30820
1.2
25
71530
3-1
55
186740
4.0
70 169980
7-3
10.5
37820
I.I
30
109620
2.3
60
222970
3-6
75 206910
6.7
5
9-75
12.25
14-75
20050
39730
57400
2.6
1-5
1.2
IO
35
25
30
146670
48960
86630
1-9
5-4
3-4
IS 60
65
70
160940
201330
237380
5-5
4.6
4-1
20
80 182710
85 214600
90 257610
8.7
7-7
6.6
6
12.25
25130
3-1
35
126460
2.6
75
276990
3-7
95 295400
6.0
14.75
44320
2.O
40
165320
2.2
80
316160
3-4
IOO 333150
5-5
17.25
62890
1.6
12
31-5
62890
6.2
IS 80
247900
4-6
24
80 127540
14-7
7
IS
30510
3-7
35
91730
4-5
85
287290
4-2
85 166820
n.8
17.5
49320
2.5
40
130540
3-5
90
322350
3-9
90 202450
IO.I
20
69540
1-9
12
40
99380
4-9
95
361780
3-6
95 239330
8.8
45
138110
3-8
IOO
399220
3-4
100 277070
7-9
28
TABLE 12
SAFE LOADS, IN TONS, AND DEFLECTIONS, CARNEGIE I BEAMS
AMERICAN BRIDGE COMPANY STANDARDS
Size
\VViKht
per Foot.
Pound*
LENGTH or SPAN IN FEET
10
ii
13
U
14
is
16
n
18
20
22
24
26
28
30
33
24"
IIJ.
100.
95.
90.
85.
80.
1 10
88
86
83
80
77
101
81
79
77
74
7i
94
76
73
71
69
66
88
71
68
66
64
62
82
66
A4
62
60
58
77
62
60
59
57
55
73
59
57
55
54
52
66
53
5»
5°
48
46
60
48
47
45
44
42
55
44
43
41
40
39
5»
41
39
38
37
36
47
38
37
36
34
33
44
35
34
33
32
3i
41
33
32
3i
30
29
Def.
.10
.12
.14
.16
.18
.20
.22
.28
•33
.40
JJ_
34
33
32
31
32
26
25
24
•54
.62
•7'
28
27
26
25
24
21
20
19
20"
100.
95-
90.
85.
80.
75-
7°-
65.
74
71
69
67
65
56
54
52
68
66
<4
62
60
52
50
48
*3
61
59
57
*6
4*
46
45
59
57
55
54
52
45
43
42
55
54
52
50
49
42
41
39
52
50
49
47
46
40
38
37
49
48
46
45
43
38
36
35
44
43
42
40
39
34
33
3i
40
39
38
37
36
3i
30
28
37
36
35
34
33
28
27
26
32
31
3°
29
28
24
23
22
29
29
28
27
26
23
22
21
/>,/.
.12
.14
.16
.19
.21
.24
•27
4i
40
38
37
30
29
28
26
•33
.40
.48
.56
•65
•74
45
18"
90.
85-
80.
75-
70.
&
60.
55-
62
60
58
56
45
44
42
39
57
55
53
52
42
40
38
36
53
Si
5°
48
39
11
34
49
48
46
45
36
35
33
3i
46
45
43
42
34
33
3i
29
43
42
4i
39
32
3i
29
28
37
36
35
33
27
26
25
24
33
32
3i
30
25
24
23
21
3i
30
29
28
23
21
21
2O
28
27
26
26
21
20
19
18
26
25
25
24
19
19
18
17
24
24
23
22
18
17
17
16
23
22
2J
21
17
16
16
15
Def.
•13
.16
.18
.21
.24
•27
•30
•37
•45
•53
.62
•72
£5
•94
15"
IOO.
95-
90.
85-
80.
75-
70.
&
60.
55-
50-
45-
42.
53
52
5°
48
47
4i
39
3l
36
30
29
27
26
49
4*
46
45
44
3|
36
35
33
28
26
25
24
46
44
43
4i
40
35
34
32
3i
26
25
23
22
43
4i
40
39
38
33
3i
30
29
24
23
22
21
40
39
37
36
35
3i
29
28
27
23
21
2O
2O
38
37
35
34
33
29
28
27
25
21
20
19
IS
36
34
33
32
3i
27
26
25
24
20
19
18
17
32
31
3°
29
28
25
24
23
22
18
17
16
16
29
28
27
26
26
22
21
21
20
17
16
IS
H
27
26
25
24
24
20
2O
19
18
IS
14
H
13
25
24
23
22
22
19
18
17
17
H
13
12
12
23
22
21
21
20
18
17
16
IS
13
12
12
II
21
21
20
19
»9
16
16
IS
H
12
II
II
10
20
19
19
57
49
47
45
43
36
34
32
31
Si
45
43
41
39
33
3i
29
29
Def.
.//
•13
.16
.19
.22
•*5
.28
•32
•36
•44
•53
.64
•75
.87
•99
12"
55-
50.
45-
40.
35-
3i-5
29
27
25
24
20
19
26
25
23
22
18
17
24
22
21
20
17
16
22
21
2O
18
16
y
20
•19
18
17
H
H
19
18
17
16
H
13
18
17
16
IS
13
12
17
16
IS
H
12
II
16
IS
H
13
ii
ii
H
13
13
12
10
IO
»3
12
12
II
9.2
8.7
12
II
II
10
8.5
8.0
ii
10
9.8
9.2
7.8
7-4
IO
9.6
9.1
8-5
7.2
6.9
9-5
9.0
8.4
8.0
6.8
6-4
Def. -
.14
•'7
.20
•23
•2?
•31
-35
.40
-45
•55
.67
•79
•93
/./
1.2
The figures give the safe uniform load in tons, based on extreme fiber stress of 16,000 lb., or
the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one-half of figures given for allowable load and four-fifths
values given for deflection.
Figures for deflections are given in inches.
For figures at right of heavy zigzag lines, deflections are considered excessive for plastered
ceilings.
29
TABLE 12.— Continued.
SAFE LOADS, IN TONS, AND DEFLECTIONS, CARNEGIE I BEAMS.
AMERICAN BRIDGE COMPANY STANDARDS.
Size.
Weight
per
Foot,
Pounds.
LENGTH OF SPAN IN FEET.
4
s
6
7
8
9
10
ii
12
13
M
IS
16
17
18
20
22
7-7
7-i
6-5
5-9
24
10"
40.
35-
30.
25-
34
3i
29
26
28
26
24
22
24
22
2O
19
21
2O
18
16
19
17
16
H
17
16
H
13
-'7
IS
14
13
12
H
13
12
II
13
12
II
IO
12
II
IO
9-3
II
IO
9-5
8.7_
•37
II
9-8
8.9
8.1
.42
10
9.2
8.4
7-7
.48
94
8-7
8.0
7-2
•54
8-5
7-8
7-2
6.5
7-i
«S
6.0
54
Def.
.04
.06
.08
.77
•13
.20
.24
.28
-.?2
.66
.<?o
•05
9"
35-
30.
25-
21.
27
24
22
2O
22
2O
18
17
19
17
16
H
17
IS
H
13
IS
13
12
II
13
12
II
IO
12
II
9-9
9.2
II
IO
9-1
8.4
IO
9-3
8.4
7-7
9-5
8.6
7-8
7-2
8.8
8.1
£3
_6_7
.47
8-3
7-5
6.8
6j_
•47
7.8
7-1
6.4
5-9
•5?
74
6-7
6.1
5-6
6.6
6.0
54
5-o
6.0
S-5
s-°
4.6
5-5
S-o
4-5
4.2
Def.
•05
.07
.09
.12
•*s
.18
.22
..27
•3i
,36
.60
S-i
4.8
4-5
4.2
.67
•74
4.6
4-3
4.0
3-8
.89_
4.2
3-9
3-7
34
7.7
3^8"
3-6
34
3-2
1.2
27"
2-5
2.3
1-4
8"
25-5
23-
20.5
18.
18
17
16
IS
IS
H
13
13
13
12
12
II
II
II
IO
9-5
IO
9.6
9.0
8.4
9-1
8.6
8.1
7-6
8-3
7-8
7-3
6.9
7-6
7.2
6-7
6-3
7-o
6.6
6.2
5-8
6-5
6.1
5-8
54
o.i
5-7
54
5-i
•47
S-7
54
5-i
4-7
•53
4.0
3-7
3-5
.61
2.9
2.6
24
•7'
54
S-i
4.8
4-5
.60
3-8
3-5
3-3
.68
Def.
•05
.07
.10
•13
•i?
.21
•25
•30
•35
.41
£L
3-2
3-o
2.8
7.0
2.9
2-7
2-5
7.7
7"
20.
17-5
IS-
13
12
II
ii
IO
9-2
9-2
8-5
7-9
8.0
7-5
6-9
7-i
6.6
6.1
6.4
6.0
5-5
S-8
54
S-o
54
S-o
4.6
4-9
4.6
4-3
4.6
4-3
3-9
4-3
4.0
3-7
•5.?
3-6
3-3
3-i
Def.
.06
.00
.12
•15
•19
.24
.20
•34
.40
^
3-3
3-o
2.8
•77
•95
6"
17.25
14-75
12.25
12
IO
9-7
9-3
8-5
7-8
7.8
7-1
6-S
6.6
6.1
5-5
5-8
5-3
4.8
5-2
4-7
4-3
4-7
4-3
3-9
4.2
3-9
3-5
3-9
3-6
3-2
3-6
3-3
3-0
3-i
2.8
2.6
2-7
2-5
2-3
.80
Def.
.04
.07
.10
.14
.18
.22
.28
-.?.?
.40
•47
•54
.62
2.2
1.9
i-7
5"
14-75
12.25
9-75
8.1.
7-3
6.5
6.5
5-8
5.2
54
4.8
4-3
4.6
4.2
3-7
4.0
3-6
3-2
3-6
3-2
2.9
3-2
2.9
2.6
2-9
2.6
2.3
2.7
2.4
2.2
2-5
2.2
2.O
2-3
2.1
1.8
2.0
1.8
1.6
1.9
i-7
i-S
Def.
•05
.08
.12
^
3-o
2.8
2.7
.16
.27
•27
-.?.?
.40
.48
•56
•(>5
•74
Js_
.06
^,
4"
10.5
9-5
8-5
7-5
4.8
4-5
4.2
4.0
3-8
3-6
34
3-2
2.7
2.6
2.4
2.3
2.4
2-3
2.1
2.O
2.1
2.O
1-9
1.8
1.9
1.8
i-7
1.6
i-7
1.6
i-S
i-4
1.6
i-S
1.4
i-3
Def.
.07
.TO
•11
.20
.26
• 33
.41
•50
.60
3"
7-5
6-5
5-5
2.6
2.4
2.2
2.1
1.9
1.8
i-7
1.6
i-5
.20
i-S
1.4
i-3
i-3
1.2
I.I
1.2
I.I
.98
I.O
.96
.88
•94
.87
.80
.86
.80
•73
Def.
.op
.14
•27
•35
•45
•55
.67
.<?o
The figures give the safe uniform load in tons, based on extreme fibre stress of 16,000 lb., or
the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one-half of figures given for safe loads and four-fifths of
the values given for deflections. Figures for deflections are given in inches.
For figures at right of heavy zigzag lines, deflections are excessive for plastered ceilings.
TABLE 12 A.
PERCENT OF TABULAR SAFE LOADS FOR BEAMS AND CHANNELS WITHOUT LATERAL SUPPORT.
Authority.
Ratio of Span, or Distance Between Lateral Supports,
to Flang
e Width.
10
IS
20
25
30
35
40
45
50
55
~56~
ove
60
Si
not
*.
47
alb
70
43
wed
75
39
byJ
80
~&
\.me
8s
90
95
IOO
Cambria
Am. B. Co.
IOO
IOO
IOO
91
99
81
93
72
87
63
80
S3
73
44
67
Rati<
61
)s ab
33
ricai
3°
iBr
28
dge
26
Co.
The tabular safe loads should be reduced in accordance with the ratios given in the above table
in order to insure that the stresses in the compression flanges should not exceed the allowed unit stress.
30
TABLE 13.
SAFE LOADS, IN TONS, AND DEFLECTIONS, SUPPLEMENTARY I-BEAMS.
Sixe.
Weight.
Span in Feet, Safe Uniform Load in Tons, and Deflection in Incbe*.
27"
83.0
Span
10
II
12
13
14
'5
16
»7
18
20
22
24
26
28
30
Load
"4
104
95
88
81
76
7i
67
63
57
52
47
44
40
38
Dtf,
.06
.08
.00
.70
.12
.74
.16
.7<?
.20
•25
•30
•35
•**
.*?
•55
24
69.S
Span
10
ii
12
»3
14
IS
16
17
IS
20
22
24
26
28
30
Load
86
78
71
66
61
•'4
57
53
50
47
43
39
35
33
3°
28
Dtf.
.07
.08
,IO
.12
.7<5
.7*
.20
.22
.28
•J4
.40
•47
•54
.62
21
57-5
Span
9
10
II
12
13
H
IS
16
17
IS
20
22
24
26
28
Load
69
62
56
52
48
44
4i
39
36
34
31
28
26
•45
24
22
ft/.
.06
.0?
.IO
.72
•JJ
•IS
.18
.20
•-2J
•25
•J2
•38
•55
.62
18
46.0
Span
8
9
IO
II
12
13
H
15
16
17
18
20
22
24
26
Load
54
48
43
39
36
33
3i
29
27
25
24
22
20
IS
16
ft/.
.06
.08
.09
.77
•A?
.16
.761
.27
.24
•27
•30
•57
•45
•53
.62
IS
36.0
Span
7
8
9
10
II
12
13
H
IS
16
17
18
20
22
24
Load
4i
36
32
29
26
24
22
20
19
18
17
16
14
13
12
Dtf.
.06
.07
.00
.77
•'3
.7<5
.79
.22
•25
.2<?
•52
•36
•44
•54
.64
12
27-5
Span
6
7
8
9
10
II
12
13
H
15
16
17
18
20
22
Load
29
25
22
2O
18
16
15
13
12
12
ii
IO
10
8.8
8.0
Dtf.
•OS
•07
.00
.77
•'4
•i?
.20
•23
•27
•31
•35
.40
•45
•55
•67
10
22.O
Span
6
7
8
9
IO
ii
12
13
H
IS
16
17
18
20
22
Load
20
17
IS
13
12
ii
IO
9-3
8-7
8.1
7.6
7-i
6-7
6.1
5-5
Dtf.
.06
.08
.77
•13
•17
.20
.2^
.28
•32
•37
.42
.*?
•54
.66
.80
8
I7-S
Span
' 5
6
7
8
9
IO
II
12
13
H
IS
16
17
18
20
Load
IS
13
ii
9-7
8.6
7.8
7-i
6.4
6.0
;.;
s.-2
4.8
4.6
4-3
3-9
Dtf.
.os
.07
.10
•13
•'7
J7
•25
•30
•55
.40
.<<5
•53
.60
.07
•*J
The figures give the safe uniform load in tons, based on extreme fiber-stress of 16,000 lb.;
or the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one half of figures given for allowable load and four-
fifths values given for deflection.
Figures for deflection are in inches.
For figures to right of heavy zigzag lines, deflections are considered excessive for plastered
ceilings.
31
TABLE 14
PROPERTIES OF CARNEGIE CHANNELS
I
ti
1
•g
f-r.
-1
\__L_,
1-4?
Section
Modu-
Dis-
tance
from
Center
Maximum
Bending
Moment
@ 16,000
Distance
Back to
Back Re-
quired
to Make
Ii
&
1
§
I
FM
o
I = Moment
r = Radius of
lus
Gravity
Lb. per
Sq. In.
Radii of
Gyration
g
B
B
|
.a
of Inertia
Gyration
to Out-
side of
Equal
I
P
12
Axisi-i
Axis 2-2
Axis i -i
Axis 2-2
Axis i- 1
Web
Axis i-i
iHr
Ii
II
ri
ri
Si
X
Mi
J [
Inches
Pounds
Inches1
Inches
Inches
Inches4
Inches4
Inches
Inches
Inches3
Inches
Ft.-Lb.
Inches
IS
55
16.18
0.8l8
3.818
430.2
12.19
5-16
.868
57-4
.823
76 ooo
8-53
50
14.71
0.720
3.720
402.7
11.22
5-23
•873
53-7
.803
72 ooo
8.71
45
13.24
O.622
3.622
375-1
10.29
5-32
.882
5O.O
.788
67 ooo
8.92
40
11.76
0.524
3.524
347-5
9-39
5-43
•893
46.3
.783
62 ooo
9-15
35
10.29
0.426
3.426
320.0
8.48
5-58
.908
42.7
.789
57 ooo
9-43
33
9.90
0.400
3.400
312.6
8.23
5.62
.912
41.7
•794
56 ooo
9-50
12
40
11.76
0.758
3.418
197.0
6.63
4.09
•751
32.8
.722
44 ooo
6.60
35
10.29
0.636
3.296
179-3
5-90
4.17
•757
29-9
.694
40 ooo
6.8 1
30
8.82
0.513
3-173
161.7
5-21
4.28
.768
26.9
.677
36 ooo
7.07
25
7-35
0.390
3.050
144.0
4-53
4-43
•785
24.0
.678
32 ooo
7-36
20.5
6.03
O.28O
2.940
128.1
3-9i
4.61
.805
21.4
.704
28 ooo
7.67
10
35
10.29
0.823
3-I83
II5-5
4.66
3-35
.672
23-1
•695
31 ooo
5-17
30
8.82
0.676
3-036
103.2
3-90
3-42
.672
2O.6
.651
28 ooo
5-40
25
7-35
0.529
2.889
91.0
3-40
3-52
.680
18.2
.620
24 ooo
5-67
20
5-88
0.382
2.742
78.7
2.85
3-66
.696
15-7
.609
21 OOO
5-97
15
4.46
0.240
2.6OO
66.9
2.30
3-87
.718
13-4
•639
18 ooo
6-33
9
25
7-35
0.615
2.815
70-7
2.98
3.10
•637
15-7
.615
21 OOO
4.84
20
5.88
0.452
2.652
60.8
2-45
3-21
.646
13-5
•585
18 ooo
5-12
15
4.41
0.288
2.488
50.9
1.95
3-40
.665
•590
15 ooo
5-49
13-25
3-89
0.230
2.430
47-3
1.77
3-49
•674
10.5
.607
14 ooo
5-63
8
21.25
6.25
0.582
2.622
47-8
2.25
2-77
.600
11.9
.587
16 ooo
4-23
18.75
5-Si
0.490
2.530
43-8
2.01
2.82
.603
II.O
-567
15 ooo
4-38
16.25
4.78
0-399
2-439
39-9
I.78
2.89
.610
IO.O
•SS6
13 ooo
4-54
13-75
4.04
0.307
2-347
36.0
i-SS
2.98
.619
9.0
•557
12 OOO
4.72
11.25
3-35
O.22O
2.260
32-3
i-33
3-"
.630
8.1
•576
II OOO
4-94
7
19-75
5-8i
0.633
2.513
33-2
1.85
2-39
•565
9-5
-583
12 6OO
3-48
17.25
5-07
0.528
2.408
30.2
1.62
2-44
•564
8.6
•555
II 500
3-64
14-75
4-34
0.423
2.303
27.2
1.40
2.50
.568
7-8
•535
10 300
3.80
12.25
3.60
0.318
2.198
24.2
1.19
2-59
•575
6.9
.528
9 200
3-99
9-75
2.85
O.2IO
2.090
21. 1
.98
2.72
.586
6.0
•546
8 ooo
4.22
6
15-5
4.56
0.563
2.283
19-5
1.28
2.07
•529
6-5
•546
8 700
2.91
13.0
3.82
0.440
2.l6o
17-3
1.07
2 13
•529
5-8
•517
7 700
3-09
10.5
3-09
0.318
2.038
I5.I
.88
2.21
•534
5-o
•503
6 700
3-28
8
2.38
O.2OO
1.920
13.0
•70
2-34
•542
4-3
•517
5 800
3-52
5
11.5
3.38
0.477
2.037
10.4
.82
i-75
•493
4.2
.508
5 500
2-34
9
2.65
0.330
1.890
8.9
.64
1.83
•493
3-5
.481
4 700
2.56
6-5
1-95
1-750
7-4
.48
i-95
.498
3-o
.489
3 900
2-79
4
7.25
2.13
0.325
1.725
4.6
•44
1.46
•455
2-3
•463
3 ooo
1.85
6.25
1.84
O.252
1.652
4-2
•38
1.51
•454
2.1
•458
2 8OO
1.96
5-25
i-SS
O.I8O
1.580
3-8
•32
1.56
•453
1.9
•464
2 5OO
2.06
3
6
1.76
0.362
1. 602
2.1
•3i
i. 08
.421
1.4
•459
I 800
1.07
5
1.47
0.264
1.504
1.8
•25
1. 12
•415
1.2
•443
I 600
I.I9
4
1.19
O.I7O
1.410
1.6
.20
I.I7
.409
I.I
•443
I 400
I-3I
32
TABLE 15
ELEMENTS OF CARNEGIE CHANNELS
vlj 1
f^> J|
4-
i
t
r
pi_
-••i-c
!
jl
i
I
1
Hn
t
k
h
Maximum
Bending
Moment
USX
1
6
|
if g,
|S =
i§
1
d
f
b
c
In.
Pounds
In.
In.
In.
In.
In.
In.
Ft.-Lb.
In.
In.
In.
In.|
In.
In.
IS
SS
50
45
40
35
33
B
§
V,
A
I
1
12;
i :
I*
11
12;
Ij
li
I
I
1
ij
2*
2A
76 ooo
72 ooo
67 ooo
62 ooo
57 ooo
56 ooo
f
2
2
2
2
1
!
s
1
*
J
12
Be
12
40
35
30
25
20.5
Ij
33
J
3i
i!
6
i
IO
IO
10
IO
10
2*
2
44 ooo
40 ooo
36 ooo
32 ooo
28 ooo
j
j
2
2
If
If
3
;
i
1
12
5^5 ".0
^X:
10
35
30
25
20
15
J
2
2:
2
!
.
i
8;
8
8
8
8i
i
^
]
]
If
Ij
31 ooo
28 ooo
24 ooo
21 OOO
18 ooo
j|
i;
l\
I!
1
*
A
A
i
f
8
x>
00
9
25
20
IS
13-25
2f
I
i
7i
7i
7i
zs
I
}
I
I ~ffi
21 000
18 ooo
15 ooo
14 ooo
1
If
if
if
i
A
H
A
f
8
8
21.25
18.75
16.25
13-75
11.25
2i
2.
2;
~ *
2;
•
\
f
i
6|
6i
6i
6;
6{
i
I
If
16 ooo
15 ooo
13 ooo
12 OOO
II OOO
ij
i
n
li
t\
f
f
f
8
xS
7
19-75
17.25
14-75
12.25
9-75
a
2*
1
i
i
Si
55
5<
•
;
1}
12 6OO
II 500
10 300
9 200
8 o-?o
i
I;
I
I
I
•
1
I
I
6
6
1
i
A
f
8
6
15-5
13
10.5
8
2}
2
{
I
i
4
4j
4]
4'
8 700
7 7°°
6 700
q 800
^ !
I;
I]
I
1
;
T8
I
f
1
f
6
X
?
5
ii-5
9
6-5
2
j
A
i
3
3
5 5°°
4 7oo
3 900
I
ij
ij
t
A
i
i
6
4
7.25
6.25
5-25
i
t
2
2
2
3 ooo
2 800
2 qoo
I
I
I
S
i
i
6
3
6
5
4
1
j
i
t
I
I
I
I
I
I
800
600
4OO
;
-
•
i
i
«
6
33
TABLE 16.
WEB RESISTANCES FOR CHANNELS.
CARNEGIE CHANNELS, FROM CARNEGIE'S POCKET COMPANION.
Depth
of
Chan-
nel.
Weight
per
Foot.
Allowable
Web
Shear.
Allowable
Buckling
Resistance.
Min.
End
Bear-
ing.
End
Reac-
tion
a=3i".
Depth
of
Chan-
nel.
Weight
per
Foot.
Allowable
Web
Shear.
Allowable
Buckling
Resistance.
Min.
End
Bear-
ing.
End
Reac-
tion
1=3*"-
Inches.
Pounds.
Pounds.
Pounds
per Sq. In.
Inches.
Pounds.
Inches.
Pounds.
Pounds.
Pounds
per Sq. In.
Inches.
Pounds.
55-0
122700
15820
5-7
93830
21.25
46560
16620
2.8
53200
50.0
108000
15390
6.0
80350
18.75
39200
16170
2.9
43580
45-0
93300
14820
6.4
66840
8
16.25
31920
15530
3-2
34070
•
40.0
78600
14040
6.9
53350
13-75
24560
14490
3-5
24460
35.0
63900
12900
7-9
39850
11.25
17600
12700
4-3
15370
33-0
60000
12510
8.2
36270
19
75
4
4310
17090
2.3
56780
50.0
102830
16150
4.8
86250
17-25
36960
16700
2.4
46300
45.0
88140
15680
5-0
71760
7
14-75
29610
16130
2.6
35830
4
3.O
73450
15020
5-4
57260
12
25
2
226O
15190
2.9
25360
J
37.0
64610
14470
5-7
48540
9-75
I47OO
13230
3-5
14580
3
5-0
58760
14020
6.0
42770
32.O
48750
13000
6.8
32900
IS-5
33780
17150
2.O
48280
13
O
2
64OO
16640
2.1
36610
40.0
90960
16260
4-4
80090
10.5
I9O8O
15730
2.3
25010
35-0
76320
15730
4.6
65040
8.0
I2OOO
13810
2.8
13810
12
3
3.O
61560
14950
S-o
49850
25.0
46800
13670
5-8
34660
ii
5
23850
17180
1.7
38920
20.5
33600
H570
7-4
21060
5
9-0
16500
16380
1.8
25670
6
5
9500
I44SO
2.2
13040
3
5.0
82300
16900
3-4
83430
30.0
67600
16440
3-6
66670
7-25
I3OOO
16870
1.4
24670
IO
25.0
52900
15730
3-9
49910
4
6.25
IOO8O
16250
1-5
18430
2O.O
38200
14470
4-4
33160
5-25
7200
15150
1.6
12270
I
5-0
24000
11780
6.0
16970
6.0
IO86O
17560
I.O
27020
25.O
55350
16470
3-2
58220
3
S-o
7920
17030
I.O
19110
20. o
40680
15550
3-5
40420
4.0
5100
15940
i.i
11520
I
25920
13590
4-4
22500
13.25
20700
I222O
16170
Safe end reaction R — fi, X t(a + d/4). Safe interior load P = 2/4 X l(al + rf/4).
In these formulas R is the end reaction, P the concentrated load, I the web thickness, d the depth of the beam,
o1 half the distance over which the concentrated load is applied and a the whole distance over which the end reaction
is applied.
while /» is the safe resistance of the web to buckling in pounds per
square inch by the formula 19000
— IO
od/2r
(d/2 = / in column formula).
'
fhe ta
bles give for beams with unsupported webs:
i. The allowable shear V, on the gross area of beam or channel webs at 10,000 pounds per square inch.
2. Allowable buckling resistance /j, in pounds per square inch computed from this compression formula.
3. The distance a, or the distance over which the end reaction must be distributed when the shearing stress,
V, in the web is the maximum allowable of 10,000 pounds per square inch.
4. The allowable end reaction (R) when a is taken at 3$" which is the usual length of beam actually resting
on the 4" angles ordinarily used in building construction for beam seats.
CAMBRIA CHANNELS, UNIFORMLY LOADED, FROM
CAMBRIA HAND BOOK.
.g
Jc *'
. j
cd
4
££
.-,
. ^
J3
u
l£
' <UT3
. •
.a
-!_» .
M 0>T
c o
a
E
a
it
333
SI
a
p
Q
h
Ifl
lj
I
!&
si|
1$
a
1
'C ti
^
ss
In.
Lb.
Lb.
Ft.
In.
Lb.
Lb.
Ft.
In.
Lb.
Lb.
Ft.
In.
Lb.
Lb.
Ft.
3
4
10970
i.i
6
8
20280
2.3
8
18.75
83150
i.S
12
20.5
41390
5-5
S
17830
0.8
10.5
3958o
1.4
21.25
101800
1-3
25
7S44C
3-5
6
25260
.6
13
58300
i.i
30
i 14230
2.6
15-5
76540
I.O
9
13.25
28120
4.0
35
i 56000
2.1
4
S.2S
14300
1.4
IS
42250
2.9
40
I9392C
1.9
6.25
21660
i.i
7
9-75
22950
2.8
20
80980
1.8
7-25
29830
•9
12.25
43660
1.7
25
118810
1.4
IS
33
8343C
5.4
14-75
62200
1.4
35
9S07C
4-9
5
6.5
17390
1.6
17-25 •
82110
1.2
IO
IS
30570
4-7
40
130940
4-3
9
35900
i.i
19-75
99880
I.I
20
67420
2.6
45
171400
3-2
ll.S
54920
•9
25
107670
1.9
50
211750
2.8
8
11.25
25560
3-4
30
147010
1.6
55
251710
2-5
13-75
44800
2.2
35
182940
1.4
16.25
64140
1.7
34
TABLE 17
SAFE LOADS, IN TONS, AND DEFLECTIONS, CARNEGIE CHANNELS
AMERICAN BRIDGE COMPANY STANDARDS
Weight
LENGTH OF SPAN IN FKET
Size
per
Foot.
Pounds
8
9
10
ii
12
13
U
IS
16
18
20
32
24
26
38
30
55-
38
34
3;
28
2S
24
22
20
19
17
IS
H
13
12
II
10
5°-
36
32
29
26
24
22
20
19
18
16
H
13
12
II
IO
9-S
45-
33
30
27
24
22
21
19
18
17
IS
13
12
II
10
Q-S
8.9
IS
40.
3i
27
2.S
22
21
19
18
16
15
14
12
II
IO
9-S
8.8
8.2
35-
28
25
23
21
19
18
16
IS
H
13
II
IO
9-S
8.8
8.1
7.6
33-
28
25
22
2O
19
17
16
is
14
12
II
10
9-3
8.6
7-9
7-4
Def.
•07
.09
.//
•1.3
.16
.10
.22
•25
.28
•36
•44
•5.?
.64
•75
.87
•99
40.
22
19
18
16
is
13
13
12
ii
9-7
8.8
8.0
7-3
6-7
6-3
S-8
35-
2O
18
16
H
n
12
II
10
10
8.9
8.0
7-2
6.6
6.1
S-7
S-3
,,"
3°-
18
16
H
13
12
II
IO
9.6
9.0
8.0
7-2
6.5
6.0
5-5
S-i
4.8
25.
16
H
13
12
II
9-9
9-1
8.5
8.0
7-1
6.4
5-8
5-3
4-9
4.6
4-3
20.5
H
13
ii
IO
9-5
8.8
8.1
7.6
7-i
6-3
5-7
5-2
4-7
4-4
4-1
3-8
Def.
.00
.11
.14
•17
.20
••*.?
•27
•3i
•35
•45
•55
.67
•79
•P.?
/./
1.2
35-
IS
H
12
II
10
9-s
8.8
8.2
7-7
6.8
6.2
S-6
S-i
4-7
4-4
4.1
30.
H
12
II
10
9.2
8-5
7-9
7-3
6.9
6.1
5-5
5-o
4.6
4-2
3-9
3-7
10"
25-
12
II
9-7
8.8
8.1
7-5
6.9
6.S
6.1
5 -4
4-9
44
4.0
3-7
3-5
3-2
20.
II
9-1
8.4
7-6
7-0
6.5
6.0
q.6
5.3
4-7
4-2
3-«
3-S
3-2
3-o
2.8
15-
8.9
7-9
7-i
6-S
S-9
5J
s-i
4.8
4-5
4.0
3-6
3-2
3-o
2-7
2.6
2-4
Def.
.//
• '?
•17
.20
.24
£*
• ?•?
• ?7
.42
-.«
.66
.«y0
•95
/./
f-3
i-5
25-
IO
9-3
8.4
7.6
7.0
6.4
6.0
1-6
<?.2
4-7
4.2
3-8
3-.S
3-2
3-0
2.S
o"
20.
9.0
8.0
7-2
6.6
6.0
5-5
S-i
4.8
4-5
4.0
3-6
3-3
3-o
2.8
2.6
2.4
y
IS-
7-5
6.7
6.0
5-5
5-0
4.6
4-3
4.0
3-8
3-3
3-o
2.7
2-5
2-3
2.2
2.0
I3-2S
7.0
6.2
5-6
5-i
4-7
4-3
4.0
3-7
3-5
3-i
2.8
2.6
2-3
2.2
2.O
1-9
a/.
.12
-IS
.18
.22
•27
•3*
-J6
.41
•47
.60
•74
.89
/./
1.2
1.4
i-7
The figures give the safe uniform load in tons, based on extreme fiber stress of 16,000 lb., or
the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one-half of figures given for safe loads and four-fifths of
the values given for deflections.
Figures for deflections are given in inches.
For figures at right of heavy zigzag lines, deflections are considered excessive for plastered
ceilings.
35
TABLE 17.— Continued
SAFE LOADS, IN TONS, AND DEFLECTIONS, CARNEGIE CHANNELS
AMERICAN BRIDGE COMPANY STANDARDS
Size
Weight
per
Foot,
Pounds
LENGTH OF SPAN IN FEET
5
6
7
8
9
10
ii
12
13
14
IS
16
18
20
22
24
8"
21.25
18.75
16.25
13-75
11.25
13
12
II
9.6
8.6
II
9-7
8.9
8.0
7-2
9.1
8.4
7.6
6.9
6.2
7-9
7-3
6-7
6.0
5-4
7-i
6-5
5-9
5-3
4.8
6.4
5-8
5-3
4.8
4-3
5-8
5-3
4.8
4-4
3-9
5-3
4-9
4-4
4.0
3-6
4-9
4-5
4.1
3-7
3-3
4.6
4-2
3-8
3-4
3-i
4.2
3-9
3-5
3-2
2.9
4.0
3-7
3-3
3-o
2-7
Def.
•05
.07
.10
•13
•17
,21
•25
•30
•35
.41
•47
•5.?
7"
19-75
I7-25
14-75
12.25
9-75
10
9-2
8-3
7-4
6-7
8.4
7-7
6.9
6.1
5-6
7-2
6.6
5-9
5-3
4-8
6-3
5-8
5-2
4.6
4.2
5-6
5-i
4.6
4.1
3-7
5-i
4.6
4.1
3-7
3-3
4.6
4.2
3-8
3-4
3-o
4.2
3-8
3-5
3-1
2.8
3-9
3-5
3-2
2.8
2.6
3-6
3-3
3-o
2.6
2.4
3-4
3-i
2.8
2-5
2.2
~3T'
3-2
2.9
2.6
2-3
2.1
Def.
.06
.09
.12
•15
.10
.24
.20
•34
.40
.46
.6l
6"
15-5
13-
10.5
8.
7.0
6.2
51
4.6
5-8
5-i
4-5
3-9
S-o
4-4
3-8
3-3
4-3
3-9
3-4
2-9
3-9
3-4
3-o
2.6
3-5
3-i
2-7
2-3
3-2
2.8
2.4
2.1
2.9
2.6
2.2
1-9
2-7
2-4
2.1
1.8
•47
2-5
2.2
1-9
i-7
2-3
2.1
1.8
i-S
2.2
1.9
i-7
1.4
Def.
•o?
.10
.14
.18
.22
.28
•33
.40
•54
.62
•7i
5"
«-S
9-
6-5
4-4
3-8
3-2
3-7
»•»
2.6
3-2
2-7
2-3
2.8
2-4
2.O
2-5
2.1
1.8
2.2
1.9
1.6
2.0
i-7
1.4
I.9
1.6
i-3
1-7
i-5
1.2
1.6
1.4
i.i
i-S
i-3
I.O
1.4
1.2
•99
Def.
.08
.12
.16
.21
•27
•33
.40
.48
-.0
•65
•74
&
4"
7-25
6.25
5-25
2.4
2.2
2.0
2.O
1-9
i-7
i-7
1.6
1.4
1-5
1.4
i-3
1.4
1.2
I.I
1.2
I.I
I.O
i.i
I.O
.92
I.O
•93
.84
•94
.86
.78
.87
.80
.72
.81
.81
•74
.67
.76
.70
•63
Def.
.TO
•15
.20
.26
•34
.41
•50
.60
.70
•03
/./
3"
6.
5-
4-
1-5
1-3
1.2
1.2
I.I
•97
i.i
•94
.83
.92
.82
•73
.82
•73
.64
•74
.66
.58
.67
.60
-53
.61
•55
.48
•57
•5°
•4^
•53
•47
.41
•49
•44
•39
.46
4^
•36
Def.
.14
.20
•27
•35
•45
•55
•67
.80
•93
/./
1.2
7.4
The figures give the safe uniform load in tons, based on extreme fiber stress of 16,000 lb., or
the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one-half of figures given for safe loads and four-fifths of
the values given for deflections.
Figures for deflections are given in inches.
For figures at right of heavy zigzag lines, deflections are considered excessive for plastered
ceilings.
36
TABLE 18.
SAFE LOADS, IN TONS, AND DEFLECTIONS, CARNEGIE CHANNELS LAID FLAT.
AMERICAN BRIDGK COMPANY STANDARDS.
Sise
Weight
JP**
Foot.
Pounds.
LENGTH or SPAN IN FEET.
Size.
Wright
JR*1"
foot.
r.iuii'U
LENGTH or SPAN "in FEET.
3
4
$
6
7
8
9
3
4
5
6
7
8
•'
IS"
55-
50.
45-
40.
35-
33-
u
6.4
5-9
y
5-4
S-i
4.8
4-5
4-3
4-2
4-3
4.1
3-9
3-6
3-4
3-4
3-6
3-4
3-2
3-o
2.8
2.8
3-1
2-9
2.8
2.5
2.4
2-4
2-7
2.6
2.4
2.2
2.1
2.1
2-4
2-3
2.1
2.0
1-9
1-9
8"
21.25
18.75
16.25
13-75
11.25
•9
.8
•7
•5
•4
•5
•3
.2
.1
.O
1.2
I.I
I.O
.92
.84
.98
.91
.84
•77
.70
.84
.78
•72
.66
.60
•74
.68
.63
.58
•53
%
.1,1
.56
•Si
•47
Dff.
•of
.08
•13
.18
.24
•32
.40
D,t.
•0.3
•OS
.08
.12
.10
.21
.26
7"
19-75
17-25
14-75
12.25
9-75
•7
•5
•4
.2
.1
i-3
i.i
I.O
•95
•8.5
I.O
•93
.84
.76
.67
.85
•77
.70
-63
.56
•73
.66
.60
•54
.48
.64
.58
•53
•47
.42
•57
•52
•47
.42
•37
12"
40.
35-
30.
25-
20.5
4-4
4.0
3-7
3-4
3-1
3-3
3-o
2.8
2-5
2-3
2.6
2.4
2.2
2.0
1.9
2.2
2.O
.8
•7
•5
•9
.6
•4
•3
.6
•5
•4
•3
.2
1-5
1-3
1.2
I.I
I.O
Dff.
.0<?
.OQ
.14
.20
.26
• ?f
•44
Dtj.
•°3
.ob
.00
H
18
24
•30
6"
15-5
13-
10.5
8.
•3
.1
.0
.88
.98
.87
•76
.66
.78
.69
.61
•53
•6S
•58
•51
•44
.56
.50
•43
.38
•49
•43
.38
•33
•43
•39
•34
.29
10"
35-
30.
25-
20.
15-
3-3
2.9
2-7
2-4
2.1
2-5
2.2
2.O
.8
•5
2.O
•7
.6
•4
.2
.6
•4
•3
.2
.O
•4
.2
.1
.O
.89
.2
.1
.O
.89
.78
I.I
I.O
.89
•79
.69
Dff.
•OS
.10
•15
.22
.20
.38
.48
5"
11.5
9-
6-5
•95
.81
.67
•7i
.60
•SO
•57
.48
.40
•47
.40
•34
.41
•35
.29
•36
•3°
.25
•32
•27
.22
Dff.
.04
07
//
•15
.21
•27
•34
9"
25.
20.
IS-
13.25
2.4
2.1
1.8
i-7
.8
.6
•3
•3
•4
•3
.1
.0
1.2
I.O
.91
.86
I.O
.90
.78
•74
.90
•79
.68
•65
.80
.70
.61
•57
Def.
.06
.//
•17
.24
•32
.42
•54
Def.
.04
.08
.12
•n
.22
•29
•37
The figures give the safe uniform load in tons, based on extreme fiber stress of 16,000 lb., or
the end reactions from safe uniform load in thousands of pounds.
For load concentrated at center, use one-half of figures given for safe loads and four-fifths of
the values given for deflections. Figures for deflections are given in inches.
For figures at right of heavy zigzag lines, deflections arc excessive for plastered ceilings.
TABLE ISA.
COEFFICIENTS OF DEFLECTION, UNIFORMLY DISTRIBUTED LOADS.
For Concentrated Load at center use four-fifths the tabular coefficient.
Fiber Stress, Pounds
Fiber Stress, Pounds
Fiber Stress, Pounds per
• Span,
per Square Inch.
Span,
K.-.-r
per Square Inch.
Span,
Ki-i-r
Square Inch.
Feet.
16000
14000
12500
pcct.
16000
14000
12500
JTCCL.
16000
14000
12500
I
0.017
0.014
0.013
16
4-237
3.708
3-3io
31
15.906
13.918
12.427
2
O.o66
0.058
0.052
17
4.783
4.186
3-737
32
16.949
14.830
13.241
3
0.149
0.130
0.116
18
5-363
4.692
4.190
33
18.025
I5-772
14.082
4
0.265
0.232
0.207
19
5-975
5.228
4.668
34
I9-134
16.742
14.948
5
0.414
0.362
0.323
20
6.621
5-793
5-172
35
20.276
17.741
I5-84I
6
0.506
0.521
0.466
21
7.299
6.387
5-703
36
21.451
18.770
16.759
7
0.8II
0.710
0.634
22
8.01 1
7.010
6.259
37
22.659
19.827
17.703
8
1-059
0.927
0.828
23
8.756
7.661
6.841
38
23.901
20.913
18.672
9
I-34I
I- 173
1.047
24
9-534
8.342
7.448
39
25-175
22.O28
19.668
10
1.655
1.448
1.293
25
10-345
9.052
8.082
40
26.483
23.172
2O.6oo
ii
2.003
1.752
1.565
26
11.189
9.790
8.741
4i
27.824
24.346
21-737
12
2.383
2.086
1.862
27
12.066
10.558
9-427
42
29-197
25-548
22.810
13
2-797
2.448
2.185
28
12-977
n-354
10.138
43
30.603
26.779
23.909
14
3-244
2.839
2-534
29
13.920
12.180
10.875
44
31-954
28.039
25-034
IS
3-724
3-259
2.909
30
14.897
13-034
11.638
45
33-517
29.328
26.185
To find the deflection in inches of a section symmetrical about the neutral axis, such as beams,
channels, zees, etc., divide the coefficient in the table corresponding to given span and fiber stress
by the depth of the section in inches. For unsymmetrical sections, such as angles and channels
laid flat, divide the coefficient by twice the distance from neutral axis to most extreme fiber.
37
TABLE 19.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED OUT, DISTANCES FROM BACK TO BACK.
:
Properties
For Distances
of Two Channels, g~-
Flanges Turned Out.
-Y Measured from
Back to Back.
Y
™
Depth.
5"
6"
7"
8"
9"
Weight.
6.50
9.00
8.00
10.50
9-75
12.25
11.25
13-75
16.25
'3-25
15.00
20.00
Area 2[s
3-9°
5-3°
4.76
6.18
5-7°
7
.20
6.70
8.08
9-56
7-78
8.82
11.76
Ix-2 [s
14.8
I7.8
26.0
30.2
422
48-4
64.6
72.0
79.8
94.6
101.8
121 .6
Flange 2 [s
si
si
4
4i
4l
4i
4i
4J
5
5
5 Si
b
Moments of Inertia of 2 Channels About Axis Y-Y for Various Distances Back to Back. InA
3 "
16.4
22.1
20.8
26.5
25-8
32.O
31-5
37-3
44-o
38.1
42.4
56.0
3l
18.4
24.8
23.2
29.7
28.8
35-8
35.1
41.6
49-o
42-3
47-2
62.3
20-5
27.7
25.9
33-i
32.O
39-7
38.9
46.1
54-4
46.8
52.2
69.0
3l
22.8
30.7
28.6
36.6
35-4
44-o
42-9
50.9
60. i
51-5
57-5
76.1
4
25.1
33-9
31.6
40.4
38.9
4
8.4
47.1
55-9
66.0
56.4
63.1
83-5
4l
27.6
37-3
34-6
44-4
42.6
5
3.1
51-6
61.2
72-3
6l.6
68.9
91-3
4*
3O.2
40.8
37-8
48.6
46-5
58.0
56.2
66.8
78-9
67.I
75-o
99-4
4f
33-o
44-5
41.2
52-9
50.6
63.1
61.0
72.6
85-7
72.8
81.4
107.9
S
35-8
48.4
44-7
57-5
54-8
68.4
66.1
78.6
92-9
78.7
88.1
116.8
si
38.8
52-4
48.4
62.2
59-2
74-o
7i-3
84.9
100.3
84.9
95-i
126.1
5*
41.9
56.6
52.2
67.2
63.8
79.8
76.8
9i-5
108.1
91-3
102.3
135-7
5l
61.0
56.2
72-3
68.6
85.8
82.5
98.2
116.1
97-9
109.8
HS-7
6
48.4
65-5
60.3
77-6
73-6
92.0
88.4
105.3
124.5
104.8
117.6
156.0
6i
Si-9
70.2
64.6
83-1
78-7
9
8-5
94-5
112. 6
133-2
II2.O
125.6
166.8
55-5
75-i
69.0
88.8
84.0
105.2
100.8
120.2
142.1
II9-3
133-9
177.8
6$
59-2
80. i
73-5
94-8
89.5
112. 1
107.3
128.0
I5I-4
I27.O
142.5
189-3
7
63.0
85-1
78.2
100.8
95-2
II9.2
114.0
I36.I
160.9
134.8
I5I-4
2OI.I
7|
67.0
90.5
83-1
107.1
10 1. 0
126.6
120.9
144.4
170.8
143.0
160.6
213-3
7*
71.1
96.0
88.1
113.6
107.1
134.2
128.1
153-0
180.9
I5I-3
170.0
225.9
7t
75-3
101.7
93-3
120.3
113-3
142.0
135-4
161.8
i9i-3
160.0
179.7
238.8
8
79-6
107-5
98.6
127.2
119.6
I5O.I
143.0
170.9
2O2.O
168.8
189.7
252.1
8i
84.0
"3-5
104.0
134-2
126.2
158.3
150.8
180.2
2I3.O
177.8
200.O
265.8
8j
88.6
119.7
109.6
Hi-5
132.9
1 66. 8
158.7
189.8
224.4
187.2
2IO-5
279.8
8|
93-3
126.1
iiS-4
148.9
139-9
175-5
166.9
200.O
236.0
196.7
221-3
294.2
9
98.1
132.6
121.3
156.6
146.9
184.4
175-3
209.7
247-9
206.5
232.4
3O9.O
9l
103.0
139-3
127.3
164.4
154.2
193.6
183.9
22O.I
260.2
216.6
243-7
324.1
9}
108.0
146.1
133-5
172-5
161.7
203.0
192.8
230.7
272.7
227.0
255-3
339-6
9*
113.2
I53-I
140.0
180.7
169.3
212.6
201.8
24I-5
285.6
235-7
267.2
355-5
10
118.5
160.3
146.4
189.1
177.1
222-4
2II.O
252.6
298.7
248.2
279.4
371-7
IOj
123.9
167.7
197.7
185.1
232.5
22O-5
264.0
3I2.I
259-3
291.9
388.3
105
129.5
175-2
159.8
206.5
193-3
242.8
230.1
275.6
325-8
270.5
304.6
405-3
lOf
I35-I
182.8
166.7
215-5
2OI.6
253-3
240.0
287.4
339-9
282.1
317.6
422.6
II
140.9
190.7
173-8
224.7
2IO.I
264.1
250.1
3OO.O
354-2
293.8
330.9
440-3
Hi
146.8
198.7
181.1
234.1
218.8
275.0
260.3
3II-9
368.8
305-1
344-5
458.4
II?
152.8
206.8
188.4
243.6
2277
286.2
270.8
324-5
383-8
3I7-9
358.3
476.9
Ill
159.0
215.2
196.0
253-4
236.7
297.6
281.5
337-4
399-o
330.3
372.4
495-7
12
165-3
223.7
203.7
263.4
246.0
309-3
292.4
350.5
4I4-5
343-0
386.8
514.8
38
TABLE 19.— Continued.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED OUT, DISTANCES FROM BACK TO BACK.
r
i if
; --riles For Distance*
of Two Channels, .3F"~ \"~X Measured from
Flanges Turned Out. Back to Back.
Jr *i iL
t
Depth.
xo"
13"
.5"
Weight.
15.00
.30.00
35.00
20.50
35.00
30.00
35-00
33-°o
35.00
40.00
45-00
50.00
55-0°
Area 3 [s
8.93
11.76
14.70
13.06
14.70
17.64
30.58
19.80
30.58
2J-52
36.48
39.43
33-36
Ix-3[s
133-8
157-4
182.0
356.3
388.0
3*3.4
358.6
635.3
640.0
695.0
750.3
805.4
§60.4
Flange 3 [s
si
si
si
6
6i
61
61
61
7
7
7i
7i
7l
b
Moments of Inertia of a Channels About Axis Y -Y for Various Distances Back to Back. In.4.
5 "
92-5
119.4
149.9
I3I.6
157-5
188.5
221.8
231.3
439.6
272.3
306.9
343.4 381.7
si
99-6
128.7
161.6
HI'S
169.4
202.8
238.5
247.9
256.8
292.0
329-0
368.2
409.1
SJ
107.0
138.4
173-8
I5I.7
181.8
217.6
255-9
265.1
274.7
312.4
352.0
393-8
437-5
si
114.7
148.5
186.4
162.3
194.6
233-0
273.9
283.0
293.2
333-5
375-9
420.4
466.9
6
122.7
158.9
199.4
173-3
207.9
248.9
292.6
301-5
312.4
355-4
400.5
447-9
497-3
6}
131.0
169.7
213.0
184.6
221.7
2654
3 "-9
32O.6
332.2
378.0
426.0
476.4
528.8
6)
139-5
180.9
227.0
196.4
235-9
282.5
331-9
340-3
352.7
401.3
452.3
505-7
561.2
6i
148.3
192.4
241.4
208.5
250.5
300.0
352-5
360.6
373-8
425.0
479-5
536.0
594-7
7
157-4
204.3
256.3
22 1. 0
265.7
318.2
373-8
381.5
395-5
450.2
507-5
567-2
629.1
7i
166.8
216.6
271.7
233-8
281.2
336.9
395-7
403.1
417.9
475.8
536.2
599-3
664.6
7*
176.4
229.2
287-5
247.1
297-3
3S6.I
418.2
42S-3
440.9
502.1
565-9
632.3
701.1
71
186.3
242.2
303-8
260.7
313.8
375-9
441.4
448.1
464.6
529-1
596.3
666.2
738.6
8
196.6
255-5
320.6
274.7
330-8
396.3
465.3
471-5
489.0
556.9
627.6
701.1
777.1
8i
207.0
269.2
337-8
289.1
348-2
417.2
489-7
495-5
5I3-9
585-3
6597
736.9
8 1 6.6
ft
217.8
283.3
355-5
303.8
366.1
438-6
514.8
520.2
539-5
614.6
692.6
77-6
857-2
81
228.8
297.8
33-6
3l8.9
3844
460.6
540.6
545-5
565.8
644.5
726.4
811.2
898.7
9
240.2
312.7
392.2
334-4
403-2
483-2
567-0
571-4
592-7
675.2
761.0
849.8
941.3
9i
251.7
327.9
411.2
350-3
422-5
506.3
594-0
597-9
620.3
706.7
796.4
889.2
984.9
&
263.6
343-4
430.7
366.6
442.2
530.0
621.7
625.0
648.5
738-8
832.7
929.6
1029.4
9l
275.8
359-4
450-7
383-2
462.4
554-2
650.0
652.8
677-3
771.7
869.8
970.9
1075.0
10
288.2
375-7
471.1
400.2
483.0
578-9
679.0
681.2
76.7
805.4
9077
1013.2
II2I.6
10}
300.9
392-3
492.0
417.6
504.1
604.2
708.6
710.1
736.9
839-7
946.4
1056.4
1169.2
loj
3I3-9
409.4
513.
435-!-
525.6
630.1
738-8
739-7
767.6
874.8
958.9
1100.4
1217.9
lof
327.2
426.8
535-2
453-5
547-7
656-5
769.8
770.0
799.0
910.7
1026.3
1145.4
1267.5
II
340-7
444-6
557-4
472-0
570.1
683-5
801.4
800.8
830.9
947-3
1067.6
1191.2
1318.1
, "i
354-6
462.7
580.1
490.9
593-1
711.0
833-6
832.3
863.6
984.6
1109.6
1238.1
1369-8
"1
368.7
481.2
603.3
510.2
616.5
739-1
866.4
864.4
896.9
IO22.6
1152.5
1285.8
1422.5
"i
383-1
500.1
627.0
539-9
640.3
767-7
899.9
897.1
930-9
1061.4
1196.2
1334-4
1476.2
12
397-7
5I9-4
651.0
549-8
664.6
796-8
934-0
930.4
965.5
IIOO-9
1240.7
1384.0
1530.9
12}
412.7
539-0
675-5
570.2
689.4
826.6
968.7
964-3
1000.7
II4I.2
1286.0
H34-5
1586.6
12^
427.9
558-9
700.6
591.0
714.6
856.8
1004.1
998.9
1036.6
II82.2
1332.2
H85-9
1643.3
I21
443-4
579-3
726.0
612. i
740-3
887.7
1040.2
1034.1
1073.2
1223.9
1379.2
1538.2
1701.0
13
459-2
600.0
752.0
6337
766.5
919.0
1076.9
1069.9
1110.4
1266.3
1427.1
I59I-5
1759-7
13}
475-2
621.1
778-4
655-6
793-1
951.0
1114.2
1106.3
1148.2
I309-5
1475-7
1645-7
1819.5
!3i
491.6
642.5
805.2
677-9
820.2
9834
1152.2
"43-3
1186.6
1353-5
1525.2
1700.8
1880.2
*3i
508.2
664.4
832.6
700.6
8477
1016.5
1190.8
1181.0
1225.7
I398.I
1575-5
1756.8
1942.0
14
525.1
686.6
860.3
723.6
875-7
1050.1
1230.1
1219.2
1265.5
1443-5
1626.7
1813.7
2004.8
Hi
542-3
709.1
888.6
747-0
904.1
1084.2
1270.0
1258.1
1305-9
1489.7
1678.6
1871.6
2068.6
14*
559-7
732.0
9I7.3
770.8
933-1
1118.9
1310.5
1297.6
1347-0
1536.5
I73I-4
1930-4
2133.4
Hi
577-4
755-3
946.4
795-0
962.4
1154.1
I35I-7
1337-8
1388.6
I584.I
1785.0
1990.0
2199.2
15
595-5
789.0
976.0
819.5
992-3
1189.9
1393-6
1378.5
1431.0
1632.4
1839-5
2050.7
2266.0
J5i
613.7
803.0
1006. i
844.5
1022.5
1226.2
1436.0
1419.9
H73-9
1681.5
1894.8
2II2.2
2333.9
I5i'
632-3
827.4
1036.7
869.8
1053-3
1263.1
1479.2
1461.9
I5I7-5
I73L3
1950.9
2174.6
2402.7
ISi
651.21852.1
1067.6
895-5
1084.5
1300.5
1522.9
1504-5
1561.8
I78I.9
2007.8
2238.0
2472.6
16
670.4 877.1
1099.1
921.5
1116.1
1338.5
1567.-?
1547.7
i6o6.2
18^.1
2065.6
2302.3
-543-5
39
TABLE 20.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED IN, DISTANCES FROM BACK TO BACK.
1
Properties „
r
For Distances
of Two Channels, ^L •** Measured from
Flanges Turned in. _, J <_ Back to Back.
i
Y
Depth.
7"
8"
9"
10"
Weight.
9-75
12.25
11.25
13-75
16.25
13-25
15.00
20.00
15.00
20.00
25.00
Area 2 [s
5-7°
7.20
6.70
8.08
9-56
7.78
8.82
11.76
8.92
11.76
14.70
Jx_2[s
42.2
48.4
64.6
72.0
79.8
94.6
101.8
121. 6
133.8
157-4
182.0
Web z[s
A
I
ft
I
ii
ft
A
i
i
J
«A
b
Moments of Inertia of 2 Channe s about Axis Y-Y for Various Distances Back to Back. In.4.
7 "
5I.7
66.0
59-9
73-i
86.4
68.6
78.6
IO4.8
77-6
104.0
128.7
7*
56.0
71.4
64-9
79-2
93-6
74-4
85.1
II3.6
84.1
112.7
139-5
7i
60.5
77-i
70.2
85-5
IOI.I
80.4
92.0
122-7
90.9
121.7
150.8
-3
7*
83.0
75-6
92.1
108.9
86.6
99-i
132.2
98.0
131-1
162.5
8
70.0
89.2
81.2
98.9
117.0
93-i
106.5
I42.I
105.4
140.9
174-7
75-o
95-5
87.0
106.0
125-3
99.8
114.1
152.3
113.0
151.1
187.4
85
80.2
IO2.I
93-i
II3-3
134.0
106.8
I22.O
l62.9
120.9
161.6
200.5
8|
85-5
IO8.9
99-4
120.9
143.0
114.0
130.3
173-8
129.1
172-5
214.1
Q
91.1
116.0
105.8
128.7
152-3
121.4
138.7
185.2
137.6
183.7
228.1
9i
96.8
123.2
112.5
136.8
161.8
129.1
147-5
196.8
146.3
195-4
242.6
92
102.7
130.7
119.4
145-2
171.7
I37-I
156.5
2O8.9
155-3
207.4
257-5
9l
108.8
138.4
126.5
153-8
181.9
145-3
165.8
221-3
164.7
219-7
272.9
10
115.0
146.4
133-8
162.6
192.4
153-7
175-4
234-1
174.2
232.4
288.8
121.5
154.5
I4I-3
171.7
203.1
162.3
185.3
247-3
184.1
245-5
305-1
io|
128.1
162.9
149.0
181.1
214.2
171.2
195-4
260.8
194.2
259.0
321.9
10*
134-9
171-5
157-0
190.7
225.6
180.4
205.8
2747
204-7
272.8
339-2
II
141.9
180.4
165.1
200.5
237.2
189.8
2l6.5
289.O
215-4
287.0
356.9
ll\
149.0
189.4
173-5
2IO.6
249.2
199.4
227.5
303-6
326.3
301.6
375-0
198.7
182.0
22 1. 0
261.5
209.3
238.7
318.6
237.6
316.5
393-7
III
163^8
208.2
190.8
231.6
274.1
219.4
250.2
334-0
249-1
331-8
412.7
12
I7I-5
218.0
199.8
242.5
286.9
229.8
262.O
349-7
261.0
347-5
432.3
III
179-4
227.9
209.0
253-6
300.1
240.4
274.1
365-8
273.1
363-5
452.3
I2|
187.4
238.1
218.4
265.0
3I3-6
25I-3
286.4
382.3
285.4
379-9
472.8
195.6
248.5
228.0
276.6
327-3
262.4
299-1
399-2
298.1
396.7
493-7
13
204.0
259.2
237.8
288.5
341-3
273-7
312.0
416.4
311.0
413.8
5I5-I
13*
212.6
270.0
247.8
300.6
355-7
285.3
325-I
433-9
324.2
431-3
536.9
ill
221-4
281.1
258.1
3I3.0
370.3
297.1
338.6
451-9
337-7
449.2
559-2
I3f
230.3
292.4
268.5
385-3
309.2
352.3
470.2
351-5
4674
582.0
14
239-4
304.0
279.1
338.5
400.5
321-5
366.3
488.9
365-5
486.0
605.2
14*
248.7
315.7
289.9
351-7
416.1
334-0
380.6
507-9
379-8
505.0
628.9
258.1
327.7
301.0
365.I
432.0
346.8
395-1
527-3
390-5
5244
653-0
14!
267.8
339-9
312.3
378.7
448.1
359-9
409.9
547-o
409-3
544-1
677.6
15
277.6
352.4
323.8
392.6
464-5
373-2
425.0
567.2
424-5
564.1
702.6
IS*
287.6
365-0
335-5
406.8
481.3
386.7
440.4
587-7
439-9
584.6
728.1
ill
. 297.8
377-9
347-4
421.2
498.3
400.5
456.0
608.6
455-7
605.4
754-1
is!
308.1
391.0
359-5
435-8
5IS-7
4I4-S
472.0
629.9
471-7
626.6
780.5
16
318.7
404-4
371-9
450.7
533-3
428.8
488.2
651-5
487.9
648.1
807.4
16}
3294
417.9
3844
465.9
SSi-3
443-3
5047
673-5
504-S
670.0
834.8
340-3
431-7
397-2
481.3
569-5
458.0
5214
695.8
521.3
692.3
862.6
i6f
351-3
445-7
410.1
497-0
588.1
473-0
538.4
718.6
538.4
7i5-0
890.9
17
362.6
460.0
423-3
512.9
606.9
488.2
555-8
741.6
555-8
738.0
919.6
374-0
474-4
436.6
529.1
626.0
503-7
573-3
765-1
573-5
761.3
948.8
I7i
385-6
489.1
450.2
545-5
645-5
5I9-4
591.2
788.9
591-4
785-1
978.4
I7f
397-4
504.0
464.0
562.2
665.2
535-3
609.3
813.1
609.7
809.2
1008.5
18
409-3
519.2
478.0
579-1
685.2
551.6
627.7
837-6
628.2
833-7
1039.1
40
TABLE 20.— Continued.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED IN, DISTANCES FROM BACK TO BACK.
r
Properties -j.
i -r For Distance*
of Two Channels. Jr' f— -* Measured from
Flanges Turned In. J , 1. Back to li&ck.
•
^
I'rplh.
«"
15"
Weight.
"0-5
»S
3°
35
4°
33
35
4°
45
50
55
Area 2 [s
12.06
14.70
17.64
20.58
»3-5»
19.80
20.58
23.52
26.48
29.42
32.36
Ix-»[»
256.2
288.0
323-4
358.6
394-0
625.2
640.0
695.0
750.2
,
Weba[s
A
!
'1
I
i
•S
*A
'I
b
Moments of Inertia of 2 Channc
s About Axis Y-Y for Various Distances Back to Back. In.*.
9"
181.6
223.8
268.2
309.9
349-0
288.T
300.4
343-7
385.5
424.6
461.9
9i
193.2
238.1
285.4
329.8
371.6
307.1
319.8
366.0
410.4
452.2
492.1
91
205.2
252.8
303.0
350.4
394-9
326.3
339-9
388.9
436.3
480.8
5234
9l
217.6
268.0
321.3
371-6
418.9
346-2
360.6
412.6
462.9
510-3
555-7
10
230.4
283.7
340.1
393-4
443-7
366.7
381.9
437-0
490.4
540.7
589.0
IOJ
243-5
299.8
359-4
415.9
469.2
387.9
403.9
462.2
518.7
572-0
623.3
ioj
257.1
316-3
379-3
439-0
495-5
409.6
426.5
488.1
547-8
604 2
658.6
io|
270.9
333-3
399-7
462.7
522.5
432-0
449-8
514-7
577-8
637.4
694.9
ii
285.2
350.9
420.7
487.2
550.2
455-0
473-7
542.1
608.5
671.5
732.2
"i
299.9
368.8
442.3
512.2
578.7
478.6
498-3
570.2
640.2
706.5
770.6
III
314-9
387-2
464-4
537-9
607.9
502.8
523.5
599-0
672.6
742.4
809.9
u|
330.3
406.0
487.0
564.2
637-9
527-7
549-3
628.6
705.9
7793
850-3
12
346.1
425.4
510.2
591-2
668.5
553-1
575-8
658.9
739-9
817.0
891.7
12\
362.2
445-1
534-0
618.8
699.9
579-2
602.9
690.0
774-9
8557
934-1
i at
378.8
4654
558.3
647.1
732.0
605.9
630.7
721.7
810.6
895-3
977-5
12!
395-7
486.1
583-1
676.0
764-9
633.2
659.1
754-3
847.2
935-8
1021.9
13
413.0
5073
608.5
705.6
798.5
661.1
688.2
787-5
884.6
977-3
1° 7-3
13*
430.6
528.9
634-5
735-8
832.8
689.7
7I7.9
821.5
922.8
1019.6
1113.8
13*
448.7
SSi.o
661.0
766.6
867.9
718.9
748.2
856.2
961.9
1062.9
1161.2
!3J
467-1
573-6
688.0
798.1
903.7
748.7
779-2
891-7
1001.8
1107.1
1209.7
14
485.9
596.6
715-7
830.2
940.3
779-1
810.8
927.9
1042.5
1152-3
1259.1
14*
505.0
620.1
743-8
863.0
977-6
810.1
843.1
964.8
1084.0
1198.3
1309-6.
14*
524.6
644.0
772.5
896.4
1015.6
841.7
876.0
1002.4
1126.4
1245.2
1361.1
Hi
544-5
666.4
801.8
930.4
1054-3
874.0
909.6
1040.8
1169.6
1293.1
1413-6
IS
564-8
693.2
831.6
965-1
1093.8
906.9
943-8
1080.0
1213.6
I34L9
1467.1
iSl
585.5
7i8.5
862.0
1000.5
1134.0
940-4
978-7
1119.8
1258.4
I39I-7
1521.7
IS*
606.6
7443
892.9
1036.5
1175.0
974-5
1014.2
1160.4
1304-1
H42.3
1577.2
!5l
628.0
770-5
924.4
1073.1
1216.7
1009.3
1050.3
1201.7
1350.6
1493-9
I633-7
16
649.8
797-2
956.4
1110.3
1259-1
1044.6
1087.1
1243.8
1397-9
1546-3
1691.3
16}
16}
672.0
694.5
824-3
851-9
989.0
IO22.I
1148.2
1186.8
1302.3
1346.2
1080.6
1117.2
1124.5
1162.6
1286.6
1330.2
1446.1
1495.1
1599-7
1654.0
1749-9
1809.4
i6\
717-5
879.9
1055.8
1226.0
1390-8
1154.4
1201.3
1374-4
1544.9
1709-3
1870.0
17
740-8
908.5
1090.0
1265.8
1436.2
1192.2
1240.6
1419.4
1595-5
1765.4
I931-7
i7t
764-5
937-4
II24.8
1306.3
1482.3
1230.7
1280.6
1465.2
1647.0
1822.5
1994-3
17*
788.6
966.9
1160.1
1347-4
1529.1
1269.8
1321.3
1699.3
1880.5
2057.9
171
813.0
996.8
1196.0
1389-2
1576.7
I309-5
1362.5
1558.9
1752.5
19394
2122.5
18
837-8
1027.1
1232.4
1431.6
1625.0
1349.8
I404-5
1606.8
1806.4
1999.2
2188.2
I8J
863.0
1057-9
1269.4
1474-7
1674.0
1390.7
1447.0
1655.5
1861.2
2060.0
2254.8
i8j
888.6
1089.2
1306.9
1518.4
1723.8
1432-3
1490.2
1704.9
1916.8
2I2I.6
2322.5
i8f
914.6
1120.9
1345-0
1562.8
1774-3
1474.4
1534-1
I755-I
1973-3
2184.2
2391.2
19
940.9
1153.1
1383-6
1607.7
1825.6
1517.2
1578.6
1 806.0
2030.5
2247.7
2460.8
!9i
967-6
1185.8
1422.8
1653-3
1877-5
1560.6
1623.7
1857.6
2088.6
2312.2
2531.6
!9i
994-7
1218.9
1462.5
1699.6
1930.3
1604.6
1669.5
1910.0
2147.5
2377-5
2603.3
191
1022.2
1252.4
1502.8
1746.5
1983-7
I649-3
1715.9
1963.1
2207.3
2443.8
2676.0
20
IO50O
1286.5
1543.6
1794.1
2037.9
1694.5
1763-0
2016.9
2267.8
2510.9
2749.8
42
41
TABLE 21.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED IN, DISTANCES INSIDE TO INSIDE OF WEB.
f
Properties ,_
For Distances
of Two Channels, ^ — *dC Measured from
Flanges Turned In. Inside to Inside of Web.
I
Depth.
7
8
9
IO
Weight.
9-75
12.25
11.25
13-75
16.25
13-25
15.00
20.00
15.00
20.00
25.00
Area 2 [s
5-7°
7.20
6.70
8.08
9-56
7.78
8.82
11.76
8.92
11.76
14.70
Ix-2[s
42.2
48.4
64.6
72.0
79.8
94.6
ioi .8
121. 6
133.8
!57-4
182.0
Web2[s
I
i7*
i
Jl
A
1%
I
1
I
tjs
b
Moments of Inertia of 2 Channels About Axis Y-Y for Various Distances Inside to Inside of Web. In.4.
7 "
59-i
80.4
68.9
88.6
110.5
79-4
94.2
138.1
90.4
I3I-5
177.7
7*
63-7
86.4
74-3
95-3
118.6
85.6
IOI-4
148.1
97-4
I4I-3
190.5
7f
68.4
92.7
79-8
IO2.2
127.0
92.1
108.9
158.6
104.8
I5I-5
203.7
7*
73-4
99-2
85-7
109-5
135-8
98.7
116.6
169.4
112.4
I62.O
217.4
8
78.5
105.9
91.6
Il6.9
144.8
105-7
124.6
180.6
120.3
172.9
23I-5
8*
83.8
II2.8
97-8
124.6
154.2
II2.8
132.9
192.1
128.4
184.2
246.1
85
89-3
I20.O
104.3
132.6
163.8
I2O.2
204.0
136.9
195.8
261.2
03
°4
127.4
110.9
140.8
173-7
127.9
150-3
216.3
145.6
207.8
276.7
9
100.8
135.0
117.7
149.2
184.0
135-8
159-5
229.0
154.6
22O.2
292.7
9t
106.9
142.8
124.8
158.0
194-5
143-9
168.9
242.0
163.9
233.O
309.1
113.1
150.9
132.0
166.9
205.3
152.3
178.5
255-4
173-5
24<5.I
326.0
9*
119.4
159.2
139-5
176.2
216.5
160.9
188.5
269.1
183-3
259-5
343-4
10
126.0
167.7
147.2
185.6
227.9
169.8
198.7
283.2
193-4
273-4
361.2
ioi
132-7
176.4
I55-I
195-4
239-6
178.9
209.2
297.7
203.8
287.6
379-5
IOJ
139.6
185.4
163.1
205.3
251.6
188.3
220.0
312.6
214.5
302.2
398.2
iof
146-7
194.6
I7L5
215.8
264.0
197.9
23I.I
327.8
225-5
3I7.I
417.4
II
154.0
204.0
180.0
226.1
276.6
207.7
242.4
343-4
236.7
3324
437-0
lit
161.5
213.6
188.7
236.8
289.5
217.8
254-0
359-4
248.2
348.1
457-2
III
169.1
223.5
197.6
247.8
302.7
228.1
265.9
375-7
260.0
364.2
477-7
Ilf
176.9
233.6
206.8
259.0
3i6.3
238.7
278.0
392.4
272.1
380.6
498.7
12
184.9
243.9
216.1
270.5
330.1
249-5
290.4
409.4
284.4
397-4
520.2
I21
193.0
254.5
225.7
282.3
344-2
260.6
303.2
426.9
297.1
4I4-S
542.2
12]
201.4
265.2
235-4
294-3
358.6
271.9
3l6.2
4447
310.0
432.0
564-6
I2|
209.9
276.2
245.4
306.5
373-3
283.4
3294
462.8
323-2
449-9
587.5
13
218.6
287.4
255-6
319.0
388.3
295.2
342-9
481.3
336.6
468.2
610.8
13*
227.4
298.9
266.0
331-8
403-6
307-3
356.7
500.2
350.4
486.8
634.6
I3f
236.5
310.5
276.6
344-8
419.2
3I9-5
370.8
5I9.S
364-4
505.8
658.8
13*
245-7
322.4
287.4
358.1
435-1
332.O
385.2
539-1
378-7
525-I
683-5
14
255.1
334-5
298.4
371.6
451.4
344-8
399-8
559-1
393-3
544-8
708.7
14*
264.7
346.9
309-7
385.3
467.9
357-8
414.7
579-5
408.1
564-9
73.4-3
14^
274.5
359-4
321.1
399-4
484.7
429.9
600.2
423-3
5854
760.4
14*
284.4
372.2
332-8
413.6
501.8
384-5
445-4
621.3
438.7
606.2
786.9
15
294-5
385-2
344-6
428.2
519.2
398.3
461.1
642.8
454-4
627.4
813.9
IS*
304.8
398.5
356.7
442.9
536.9
412.3
477-1
664.6
470.4
649.0
841.4
15*
3I5-3
411.9
369.0
458.0
554-9
426.5
493-4
686.9
486.6
670.9
869.3
i5f
326.0
425.6
38i.S
473-2
573-2
440.9
510.0
709.4
503-I
693.2
897.7
16
336.8
439-5
394-2
488.8
591.8
455-6
526.8
7324
519-9
7I5-9
926.5
i6j
347-8
453-7
407.1
504.6
610.7
470.6
543-9
755-7
537-0
738.9
955-8
16^
359-0
468.0
420.2
520.6
629.9
485.8
561-3
779-3
554-4
762.3
985.6
i6|
370-4
482.6
433-5
536.9
649.4
501.2
579-0
803.4
572.0
786.1
1015.8
17
381.9
497-4
447-1
553-4
669.1
516.9
596.9
827.8
590.0
810.2
1046.5
17*
393-6
512-5
460.8
570.2
689.3
532.8
615.2
852.6
608.2
834-7
1077.6
I7f
405-5
5277
474-8
587.3
709.6
549-0
633-6
877.7
626.7
859.6
1109.2
17!
417.6
543-2
488.9
604.6
730.3
5654
652.4
903.2
64S-4
884.8
1141.3
18
429.9
558.9
503-3
622.1
751-3
582.0
671.5
929.1
664.5
910.4
1173.8
42
TABLE 21.— Continued.
MOMENTS OF INERTIA OF Two CHANNELS, BOTH AXES.
FLANGES TURNED IN, DISTANCES INSIDE TO INSIDE OF WEB.
Properties
=|
For Distances
of Two Channels, X'~~ l"~~" 1 —
Flanges Turned in.
"~X Measured from
Inside to Inside of Web.
^ -Jj
Depth.
,2"
15"
Weight.
20.5
»5
30
35
40
33 35
4°
45
5°
55
Area a [s
1 2. 06
14.70
17.64
20.58
33.52
19.80 20.58
23.52
26.48
29.42
3*-3°
fet[*i
356.2
2880
3»3-4
358.6
394-0
625.2 640.0
695.0
750.3
860.4
Web2[s
A
i
i
M
11 1
»A
*i
XA
«t
b
Moments of Inertia of a Channels about Axis Y-Y for Various Distances Inside to Inside of Webs. In.4.
9"
208.2
269.9
342.1
417.9
497-2
350-3
369.2
441.8
518.0
596.4
678.2
9*
22O-7
285.6
361-5
441.1
524.2
370-9
390.8
467.1
547-1
629.4
7I5.I
9*
233-5
301-7
381.4
464.9
552.0
392-2
413.0
493.2
577-0
663.2
753-0
9*
246.7
318.4
401.9
489.3
580.5
414.0
435-9
5I9.9
607.8
698.0
791.9
10
260.4
335-4
423.0
514-4
609.7
436.5
459-5
547-4
6394
733-7
831.8
10}
274-3
353-o
444-6
540.2
639.7
459.6
483-7
575-7
671.8
770.3
872.7
IOJ
288.7
371.0
466.7
566.6
670.4
4834
508-5
604.7
705.0
807.9
914.6
io|
3034
389-5
498.4
593-6
701.9
507.7
533-9
634-4
739-1
846.4
957-6
II
318.6
408.4
512.7
621.3
734-1
532.7
560.0
664.8
774-0
885.7
1001.5
III
334-0
427.8
536.5
649.6
767.0
558.3
586.8
696.0
809.7
926.0
1046.5
III
350-0
447-6
560.9
678.6
800.6
584.5
614.2
727.9
846.3
967-3
1092.4
III
366.1
467.9
585.8
708.2
835.0
611.3
642.2
760.6
883.6
1009.4
II39-4
12
382.8
488.7
611.2
738.4
870.2
638.7
670.9
794-0
921.8
1052.5
1187.4
I2j
399-8
510.0
637.2
769-3
906.0
666.8
700.2
828.1
960.9
1096.4
1236.4
Ml
417.2
531-6
663.8
800.9
942.6
695-5
730.2
862.9
1000.7
1141.3
1286.4
iaf
434-9
553-7
690.9
833.0
979-9
724.8
760.8
898-5
1041.4
1187.2
1337-5
13
453-0
576.3
718.6
865.9
1018.0
754-7
792.0
934-9
1082.9
1233-9
1389-5
13}
471.6
599-4
746.8
899-3
1056.8
785-2
824.0
971.9
1125-3
1281.5
1442-5
131
490.4
622.9
775-6
933-4
1096.3
816.4
856-5
1009.7
1168.5
1330.1
1496.6
13!
5097
646.9
804.9
968.2
1136.6
848.2
889.7
1048.2
1212.5
1379.6
I55I-7
14
529.3
671.3
834-8
1003.6
1177.6
880.5
923-5
1087.6
1257-3
1430.0
1607.8
14}
549-4
696.2
865.2
1039.6
1219.4
9I3-5
958.0
1127.6
1302.9
1481.4
1664.9
. Hi
569.7
721.6
896.2
1076.3
1261.8
947-2
993-1
1168.3
1349-4
1533-6
1723.0
5!
590-5
747-4
927.6
1113.6
1305-0
981.4
1028.9
1209.8
1396.7
1586.8
1782.1
15,
611.7
773-6
959.8
1151.6
1349.0
1016.3
1065.2
1252.0
1444.9
1640.9
1842.2
IS}
633.2
800.4
9924
1190.2
1393-7
1051.8
1102.3
1294.9
1493-8
1695.9
1903.4
15*
655.1
827.6
1025.6
1229.5
H39-I
1087.9
1 140.0
1338.6
1543-6
i75!-9
1965.5
is:
677.4
855.2
1059-3
1269.3
1485-2
1124.6
1178.3
1383-0
1594-3
1808.7
2028.7
16
700.0
883-3
1093-6
1309.9
1532.1
1161.9
1217.3
1428.2
1645.7
1866.5
2092.8
16*
723.0
911.9
1128.4
I35I-I
1579-7
1199.9
1256.9
1474.1
1698.0
1925.1
2158.0
i6J
746.5
940.9
1163.8
1392.9
1628.0
1238.5
1297.1
1520.7
1751-1
1984.8
2224.2
i6J
770.2
970.4
1199.7
1435-4
1677.1
1277.7
1338-0
1568.0
1805.0
2045-3
2291.4
17
794-4
1000.4
1236.2
1478.5
1727.0
I3I7.5
1379.6
1616.1
1859.8
2106.7
2359.6
I7l
818.9
1030.8
1273.2
1522.2
1777.6
1357-9
1421.8
1664.9
I9I5-3
2169.1
2428.9
17*
843-9
1061.7
1310.8
1566.6
1828.9
1399.0
1464.6
1714.5
1971.8
2232.4
2499.1
I7l
869.1
1093.0
1349.0
1611.7
1880.9
1440.6
1508.1
1764.8
2029.0
2296.6
2570.4
18
894.8
1124.8
13877
1657.4
1933-6
1482.9
1552.2
1815.8
2087.1
2361.7
2642.6
18}
920.9
1157.0
1426.9
1703.7
1987.1
1525-8
1596.9
1867.6
2146.0
2427.8
2715.9
is',
947-3
1189.7
1466.7
1750.7
2041.4
1569-4
1642.3
1920.1
2205.7
2494-7
2790.2
18}
974-1
1222.9
1507.0
1798.3
2096.3
1613.5
1688.4
1973-3
2266.2
2562.6
2865.5
19
1001.3
1256.5
1547-9
1846.5
2152.1
1658.3
I735-I
2027.3
2327.6
2631.4
2941.8
19}
1028.8
1290.6
1589.4
I895-4
2208.5
I703-7
1782.4
2082.0
2389.8
2701.1
3019-1
19*
1056.8
1325.1
1631.4
1945.0
2265.7
1749-7
1830.4
2137-4
2452-8
2771.8
3097-5
19}
1085.1
1360.1
I673-9
1995.2
2323.6
1796.3
1 880.0
2193-6
2516.7
2843-3
3176.8
20
1113.7
1395-6
1717.0
2046.0
2382.2
1843-5
1928.3
2250.5
2581.4
2915.8
3257-1
43
TABLE 22.
PROPERTIES OF Two CHANNELS, SPACED SMALL DISTANCES.
T
Properties
For Distances
of Two Channels. 3P--- i
Flanges Turned Out.
-X Measured from
Back to Back.
< — o — *
Y
-
Chan-
Axis Y-Y.
nels.
A iria V— V
4
4
Total
Area.
^ \ A 1 o J\. — uV •
b = o.
b = l».
b = i".
b=|".
b = 2".
Q
Q
i>
*
Ix
Iy
Iy
Iy
Iy
Iv
rv
y
y
In.
Lb.
In.*
In.1'
In.
In.1
In.
In.1
In.
In.1
In.
In.4
In.
In.1
In.
4
2.38
3-2
I.I7
5-4
1.50
3
5
2-94
3-6
1. 12
.1
O.6o
1.4
0.70
6.6
1.50
6
. 3-52
4.2
1. 08
•4
O.62
1.8
0.71
2.4
0.82
3-1
o-93
8.1
1.52
S|
3.10
7-6
I.56
-3
0.65
i-7
0.74
2.2
0.84
2.8
o-95
7-3
i-53
4
6|
3-78
8.4
.6
0.64
2.O
o-73
2.6
0.84
3-4
0-95
8-5
1.52
7l
4.26
9.2
1.46
.8
0.65
2.4
0.74
3-0
0.84
3-9
o-95
IO.O
1-53
6|
3-90
14.8
1-95
1.9
0.69
2.4
0.78
3-1
0.89
3-9
0.99
9.6
T S7
9
5-30
17.8
1.83
2-5
0.68
3-2
0.78
4.1
0.88
5-2
0.98
12.9
1.56
8
4.76
26.0
2-34
2-7
0.74
3-4
0.84
4.2
o-93
5-2
1.03
12.4
1.61
6
10^
6.18
30.2
2.21
3-3
0-73
4-2
0.82
5-3
0.92
6-5
i. 02
iS-7
i. 60
13
7.64
34-6
2.13
4.2
0.74
5-3
0.83
6.6
o-93
8.2
1.03
19.7
1.61
9f
5-70
42.2
2.72
3-7
0.80
4-5
0.89
5-6
0.99
6.8
1.09
iS-6
1.65
7
7.20
48.4
2-59
4-4
0.78
5-5
0.87
6-7
0.97
8-3
.07
19.2
1.63
Hi
8.68
54-4
2.50
5-3
0.78
6.6
0.87
8.1
0.97
.07
23-3
1.64
n|
6.70
64.6
3. H
4-9
0.85
6.0
0.94
7-2
1.03
8-7
.14
19-3
1.70
8
I3f
8.08
72.0
2.98
5-6
0.83
6.8
0.92
8-3
I.OI
IO.I
.12
22.7
1.68
9-56
79.8
2.89
6-5
0.83
8.0
0.91
9.8
I.OI
n.8
.11
26.7
1.67
13*
7-78
94-6
3-49
6.4
0.90
7-7
0.99
9-3
1.09
II.O
.19
23.6
1.74
9
15
8.82
101.8
3-40
7.0
0.89
8.4
0.97
IO.I
1.07
12. 1
.12
26.2
1.72
20
11.76
I2I.6
3-21
8-9
0.87
IO.O
0.96
13-1
1.05
IS-7
•15
34-5
1.71
IS
8.92
133.8
3-87
8.2
0.96
9.8
1.05
11.6
1.14
13-7
1.24
28.6
1.79
20
11.76
157-4
3-66
IO.O
0.92
I2.O
I.OI
H-3
1. 10
17.0
1. 2O
36.2
i-75
10
25
14.70
182.0
3-52
12.4
0.92
14.9
I.OO
17.9
I.IO
21-3
1.20
45-4
1.76
30
17.64
206.4
3-42
15.2
0.93
18.4
1. 02
22.1
1. 12
26.3
1.22
55-9
1.78
35
20.58
231.0
3-35
19.2
0.96
23.1
1. 06
27.6
1.16
32-8
1.26
68.5
1.82
20^
12.06
256.2
4.61
13-4
1.05
16.1
1-15
18.8
1.24
21-9
1-34
42.8
1.89
25
14.70
288.0
4-43
15.8
1.03
18.5
1. 12
21.7
1. 21
25-3
I-3I
50-5
1.85
12
30
17.64
323-4
4.28
18.5
i. 02
21.7
I. II
25-5
1. 2O
29.9
1.30
60.0
1.85
35
20.58
358.6
4.17
21.7
i. 02
25-5
I. II
30.1
1. 21
35-3
I-3I
70.9
1.86
40
23.52
394-0
4.09
25-5
1.04
30.1
I-I3
35-4
1.22
4I-5
1.32
83.0
1.88
33
19.80
623.2
5-62
28.8
i. 20
33-i
1.29
38.0
1.38
43-5
1.48
80.2
2.OI
35
20.58
640.0
5.58
29.8
i. 20
1.28
39-1
I.38
44-8
1.47
82.8
2.OI
40
23.52
695.0
5-43
33-i
1.18
38^1
1.27
43-8
1.36
5°-3
1.46
93-5
1.99
15
45
26.48
750.2
5-32
37-i
1.18
42.6
1.26
49.1
1.36
56.3
1.45
105.2
1.99
5°
29.42
805.4
5-23
41.2
1.18
47-7
1.27
55-o
1.36
63.2
1.46
118.1
2.OO
55
32-36
860.4
5.16
46.1
1.19
53-2
1.28
61.4
i-37
70-5
1.47
I3I-9
2.O2
44
TABLE 23
PROPERTIES OF EQUAL LEG ANGLES
3
Maximum
.
Ji( ::> ! ; !i .'
41
I
Distance
from
j
1-
-
i
Least
Radius of
Moment
('i i ' i ' >' >' >
1
1
M
Center
Gyration
*
•
1
of Gravity
to Back
t
».
Sq'.?iK
1
'
j
Moment
of Inertia
Section
Modulus
Radius of
Gyration
Axis 3-3
Axis i-i
X
I.
Si
n
n
Mi
Inches
Inches
Pounds
Inches'
Inches
Inches4
Inches9
Inches
Inches
Foot-
Pounds
8X8
ji
62.7
18.44
2.45
106.56
19,21
2.40
1-55
25 600
59-8
17-59
2.43
102.31
18.38
2.41
1-55
24 500
If
56.9
16.73
2.41
97-97
17-53
2.42
1-55
23 400
JA
54-o
I5-87
2-39
93-53
16.67
2-43
1.56
22 200
i
51-0
15.00
2.37
88.98
15.80
2.44
1.56
21 100
U
48.1
14.12
2-34
84-33
14.92
2-44
i.S6
19 900
45-o
13.23
2.32
79.58
14.02
2-45
i-57
18 700
I
42.0
12-34
2.30
74.72
I3-"
2.46
i-57
17 500
38.9
11.44
2.28
69.74
12.19
2-47
16 200
• $
35-8
10-53
2.25
64.64
11.25
2.48
i!58
15 ooo
•
32-7
9.61
2.23
59-43
10.30
2-49
1.58
13 700
t
29.6
26.4
8.68
7-75
2.21
2.19
54-09
48-63
9-34
8-37
2.50
2.50
1.58
1.58
12 5OO
II 20O
6X6
i
37-4
11.00
1.86
3546
8-57
i. 80
.16
II 40O
I
35-3
10.37
1.84
33-72
i. 80
.16
10 800
33-1
9-73
1.82
31.92
7-63
1.81
•17
IO 20O
1
31-0
9.09
i. 80
30.06
7-iS
1.82
-17
9 550
28.7
8-44
1.78
28.15
6.66
1.83
8 900
i
26.5
7.78
26.19
6.17
1.83
• 17
8 250
•
24.2
7.11
1-73
24.16
5-66
1.84
.18
7 550
A
21.9
6-43
1.71
22.07
5-H
1.85
.18
6 850
19.6
5-75
1.68
19.91
4.61
1.86
.18
6 150
A
17.2
5-o6
1.66
17.68
4.07
1.87
1.19
5 450
1
14.9
4-36
1.64
15-39
3-53
1.88
1.19
4 700
.5X5
i
30.6
9.00
1.61
19.64
5.80
1.48
.96
7 73°
i*
28.9
8.50
i-59
18.71
5-49
1.48
.96
7 320
i
27.2
7.98
i-57
17-75
5-17
1.49
.96
6 890
i
25.4
7-47
1-55
16.76
4.85
1.50
•97
' 6 470
j-
23.6
6-94
1.52
15-74
4-53
i-Si
•97
6 040
i
21.8
6.40
1.50
14.68
4.20
•97
5 600
2O.O
5-86
1.48
I3-58
3-86
1.52
•97
5 150
f
18.1
16.2
5-31
4-75
1.46
1-43
12.44
11.25
3-Si
3-15
i-53
1.54
.98
.98
4 680
4 200
A
14.3
4.18
1.41
IO.O2
2-79
1-55
.98
3 720
1
12.3
3-6i
1.39
8.74
2.42
1.56
•99
3 230
4X4
H
19.9
5.84
1.29
8.14
3-oi
1.18
•77
4 oio
i
18.5
5-44
1.27
7-67
2.8l
1.19
•77
3 750
H
17.1
5-03
1.25
7.17
2.61
1.19
•77
3 480
I
15-7
4.61
1.23
6.66
2.40
1.20
•77
3 200
A
14-3
4.18
1. 21
6.12
2.19
1. 21
•78
2 92O
*
12.8
3-75
1.18
5-56
•97
1.22
.78
2 630
A
11.3
1.16
4-97
•75
1.23
.78
2 330
1
9.8
2!86
1.14
4-36
.52
1-23
•79
2 030
A
8.2
2.40
1. 12
3.72
•29
1.24
•79
I 720
i
6.6
1.94
1.09
3-04
•05
1-25
•79
I 4OO
45
TABLE 23.— Continued
PROPERTIES OF EQUAL LEG ANGLES
n 3
Maximum
1
Distance
i
I If I-'' '
Least
Moment
"So
1
*o
!
1
R
1
from
Center
of Gravity
to Back
i-
3
/ 1 i
'i
Radius of
Gyration
@ 16,000
Lb. per
Sq. In.
1
H
1
Moment of
Inertia
Section
Modulus
Radius of
Gyration
Axis 3-3
Axis i-i
X
Ii
Si
ri
r?
Mi
Inches
1 nches
Pounds
Inches'
Inches
Inches4
Inches'
Inches
Inches
Foot-
Pounds
32X31
H
I7.I
S-°3
• 1.17
5-25
2.25
I. O2
0.67
3 000
f
16.0
4.69
MS
4.96
2. II
1.03
0.67
2 8lO
14.8
4-34
1. 12
1.96
1.04
0.67
2 6lO
8
13.6
3-98
I.IO
4-33
1.81
1.04
0.67
2 410
A
12.4
3.62
1. 08
3-99
1.65
•05
0.68
2 2OO
A
n. i
9.8
3-25
2.87
1. 06
I.O4
3.26
1.49
1.32
.06
.07
0.68
0.68
I 990
I 760
t
8-5
2.48
I.OI
2.87
.07
0.69
I 530
TS
7.2
2.09
•99
245
:9s
.08
0.69
I 310
*
5-8
1.69
•97
2.OI
•79
.09
0.69
I 050
A
44
1.28
•94
i-SS
.60
I.IO
0.69
800
•h
1.07
•93
•5i
I.IO
0.69
680
3X3
8
"•5
3.36
.98
2.62
1.30
.88
•57
I 730
A
10.4
3.06
•95
243
1.19
.89
•58
I 585
A
94
8-3
2-75
243
•93
.91
2.22
2.00
1.07
•95
.90
.91
•58
•58
I 430
I 27O
7-2
2.II
.89
I.76
•83
.91
•58
i no
A
6.1
1.78
.87
.92
•59
950
1
4-9
1.44
.84
1.24
'58
•93
•59
770
^
3-7i
1.09
.82
.96
44
•94
.60
590
1
2.50
0.74
.80
.66
•3°
•95
.60
400
2fX2f
i
8-5
2.5O
•87
1.67
.89
.82
•53
i 190
A
7-6
2.22
•85
1.51
•79
.82
•53
i 050
f
6.6
1.92
.82
1.33
.69
•83
•55
920
5-6
1.62
.80
1.15
•59
.84
•54
790
^
4-5
I-3I
.78
•95
.48
•85
•54
640
A
3-39
1. 00
.76
•73
•37
.86
•54
490
2.29
0.68
•73
•Si
•25
.87
•55
33°
2|X2|
i
7-7
2.25
.81
1.23
•73
•74
47
970
A
6.8
2.00
.78
i. n
.65
•74
.48
870
3
5-9
1-73
.76
.98
•57
•75
.48
760
S-o
1.47
•74
•85
.48
.76
.48
640
1
4.1
1.19
•72
.70
•39
•77
49
530
TS
3-07
.90
.69
•55
•30
.78
49
400
i
2.08
.61
.67
•38
.20
•79
•SO
270
2iX2|
A
6.8
6.1
2.OO
1.78
•74
.72
.87
•79
•58
•52
.66
.67
43
43
770
690
f
5-3
i-55
.70
.70
45
.67
43
600
A
4-5
.68
.61
•39
.68
44
520
i
3.62
1.07
.66
•Si
•32
.69
44
430
A
2-75
.81
•63
•39
.24
.70
44
320
1
1.86
•55
.61
•27
.16
•7i
45
220
46
TABLE 23.— Continued
PROPERTIES OF EQUAL LEG ANGLES
1 /
Maximum
J
1
Distance
from
Center
^H]"
Least
Radius of
Gyration
Bending
Moment
(•/ .", oo •
Lb. oer
V
1
\
1
of Gravity
to Back
"1
Sq'. hi.
3
'
1
of Angle
Moment
of Inertia
Section
Modulus
Radius of
Gyration
Axis 3-3
Axis i-i
X
Ii
Si
ri
n
Mi
Inches
Inches
Pounds
Inches*
Inches
Inches*
Inches'
Inches
Inches
Foot-
Pounds
2X2
A
5-3
1.56
.66
•54
.40
•59
•39
530
f
4-7
1.3.6
.64
.48
•35
•59
•39
470
A
3-92
1. 15
.61
.42
•30
.60
•39
400
A
3-19
2.44
•94
•59
•57
•35
.28
•25
•19
.61
.62
•39
.40
330
250
i
I.6S
48
•55
•19
•13
.63
.40
170
I $ \f I i
* 4 ^^ ^ J
^
4.6
1.34
•59
•35
.30
•Si
•33
400
}
3-99
1.18
•57
.26
•Si
•34
350
A
3-39
I.OO
•55
.27
23
•52
•34
310
A
2.77
2.12
.82
.63
•53
•Si
•23
.18
.19
•14
•53
•54
•34
•35
250
190
*
1-44
•43
.48
•13
.IO
•55
•35
130
lixij
3-35
•99
•Si
•19
•19
•44
.29
250
2.86
.84
•49
.16
.16
•44
.29
22O
2-34
.69
•47
•14
•134
•45
.29
1 80
n
i. 80
•53
•44
.11
.10
.46
•29
I4O
i
1.23
•36
.42
.078
.072
.46
.30
90
1 1 *^ T i
j^
2-33
.68
.42
.091
.109
•36
•23
ISO
A
1.92
1.48
.56
•43
.40
•38
.077
.061
.091
.071
•37
•38
•24
.24
1 2O
90
i
I.OI
•30
•35
.044
.049
•38
•25
70
T 1- ^^ T 1-
A
1.32
•39
•35
.044
.057
•34
.22
75
i
•9i
.27
•33
.032
.040
•34
.22
50
1X1
A
1.49
1.16
•44
•34
•34
•32
.037
.030
.056
.044
.29
•3°
•19
•19
75
60
i
.8
•23
•30
.022
.031
.31
.20
40
.109
•7i
.21
.29
.020
.028
•3i
.20
40
1XJ
A
I.OO
.30
.29
.019
•033
.26
.18
40
i
.70
.21
.26
.014
.023
.26
•19
3°
A
•S3
.16
.25
.Oil
.018
•27
.20
20
IX}
A
.84
•25
.26
.012
.024
.22
•IS
32
A
•59
•45
.18
.14
.23
.22
.0088
.0069
.017
.013
•23
•23
•IS
•15
23
17
fxf
A
.48
•37
•15
.11
.20
•19
.0048
.0038
.0113
.0088
.18
•19
.12
.12
IS
ii
JXi
A
•38
.29
.11
.085
!i6
.0023
.0019
.007
.0055
•IS
•15
.IO
.IO
9
7
47
TABLE 24
PROPERTIES OF UNEQUAL LEG ANGLES
bj
IH
{*cf ^
W.SM
j? M
g CS M
g S M
i^jJri-'-l . _'— i
•3 ° 60
^"o"4
1
m
w
0
1
g3fe
|{5
£•?!
12
e
l]ll
8§-Jh
2
M
a
1
«|j
u*£Ja
Moment of
Section
Radius of
•§
E<JI~!>
l®1>s>
o
s
"M
<
c 2^j
Gj O O
e 2 ^*
Inertia
Modulus
Gyration
"o
'* £w
'*fc/j
«
i
(5°
<3°
Axis
Axis
Axis
Axis
Axis
Axis
Axis
g
M
s|i
£& <~
ft O ^
i-i
2-2
i-i
2-2
i-i
2-2
3-3
9
T,
Tn
Si
M:
M.
11
12
1
In.
In.
Lb.
in.'
In.
In.
In.«
In.-
In.'
In.3
In.
In.
In.
Ft.-Lb.
Ft.-Lb.
8X6
I
44.2
I3.OO
1.65
2.65
38.78
80.78
8.92
15.11
1-73
2.49
.28
•543
20 150
II 900
T6
41.7
12.25
1.63
2.63
36.85
76.59
8-43
14.27
1-73
2.50
.28
•545
19 030
II 250
7
8
39-1
11.48
1.61
2.6l
34.86
72.31
7-94
1341
1.74
2.51
.28
•546
17 900
10 600
it
36.5
10.72
1-59
2-59
32.82
67.92
744
12-55
i-75
2.52
.29
•549
16 730
9 900
f
33-8
9-94
1-56
2.56
30.72
63.42
6-93
11.67
1.76
2-53
.29
•553
is 560
9 250
H
31.2
9-iS
1.54
2-54
28.56
58.82
6.41
10.77
1.77
2-54
•29
•556
14 400
8 550
5
8
28.5
8.36
1.52
2.52
26.33
54.10
5.88
9.87
1.77
2-54
•30
•554
13 160
7 850
9
T6
25-7
7.56
1.50
2.50
24.04
49.26
5-34
8-95
1.78
2-55
•30
•556
ii 930
7 100
\
23.0
6-75
1.47
2-47
21.68
44-31
4-79
8.02
1.79
2.56
•30
•558
10 700
6 400
T6-
2O.2
5-93
i-45
2-45
19.25
39-23
4-23
7.07
i. 80
2-57
•30
.560
9 420
5 640
8X3^
I
35-7
10.50
.92
3-17
7-8
66.2
3-0
13-7
.86
2.51
•73
1 8 400
4 ooo
if
33-7
9.90
.89
3-H
74
62.9
2.9
12.9
.87
2.52
•73
17 200
3 870
31-7
9-3°
.87
3.12
594
2.7
12.2
.87
2-53
•73
1 6 200
3 600
16
29.6
8.68
•85
3.10
6.7
55-9
2-5
II.4
.88
2-54
•73
15 200
3 330
3
4
27-5
8.06
.82
3-07
6-3
52.3
2-3
10.6
.88
2-55
•73
14 100
3 060
A
25-3
743
.80
3-05
5-9
48-5
2.2
9-8
.89
2.56
•73
13 ooo
2 930
i
23.2
6.80
.78
3-03
54
44-7
2.O
9.0
.90
2-57
•74
12 OOO
2 660
9
2I.O
6.15
•75
3.00
5-0
40.8
1.8
8.2
.90
2-57
•74
10 900
2 400
|
I8.7
5-50
•73
2.98
4-5
36.7
1.6
7-3
.91
2-58
•74
9 700
2 I9O
T6
I6.S
4.84
.70
2-95
4.1
32.5
I.J
6.4
.92
2-59
•74
8 600
2 OOO
7X3J
I
32.3
9-50
.96
2.70
7-53
45-37
2.96
10.58
.89
2.19
•74
.241
14 100
3 950
i|
30.5
8-97
•94
2.69
7.18
43-13
2.80
IO.OO
.89
2.19
•74
.244
13 350
3 740
1
28.7
8.42
.91
2.66
6.83
40.82
2.64
9.42
.90
2.20
•74
•247
12 550
3 520
13
16
26.8
7-87
.89
2.64
6.46
38.44
2.48
8.82
.91
2.21
•74
.250
II 750
3 310
3
4
24.9
7.31
•87
2.62
6.08
35-99
2.31
8.22
.91
2.22
•74
•253
10 950
3 080
H
23.O
6-75
•85
2.60
5-69
3347
2.14
7.60
.92
2.23
•74
•257
10 150
2 850
I
21.0
6.17
.82
2.57
5-28
30.87
1.97
6-97
•93
2.24
•75
•259
9 300
2 630
¥
I9.I
5-59
.80
2-55
4-85
28.19
1. 80
6-33
•93
2.25
•75
.262
8 450
2 4OO
^
17.0
S-oo
.78
2-53
4.41
25.42
1.62
5-68
•94
2.25
•75
.264
7 570
2 160
A
15.0
4.40
•75
2.50
3-95
22.56
1.44
S-oi
•95
2.26
•76
.267
6 680
I 92O
t
I3.O
3-8o
•73
2.48
348
19.60
1.26
4-33
.96
2.27
.76
.270
5 770
I 680
6X4
!
30.6
9.00
1.17
2.17
10.75
30.75
3-79
8.02
1.09
I.8S
•85
.414
10 700
5 050
H
28.9
8.50
.14
2.14
10.26
29.26
3-59
7-59
.10
.86
•85
.418
IO 1 2O
4 790
1
27.2
7.98
.12
2.12
9-75
27-73
3-39
7-iS
.11
.86
.86
.421
9 550
4 520
T¥
25.4
7-47
.IO
2.IO
9-23
26.15
3.18
6.70
.11
.87
.86
425
8 950
4 240
a
23.6
6-94
.08
2.08
8.68
24-5I
2-97
6.25
.12
.88
.86
.428
8 350
3 960
ii
21.8
6.40
.06
2.O6
8.II
22.82
2.76
5-78
•13
.89
.86
431
7 700
3 680
5
8
20.O
5-86
.03
2.03
7.52
21.07
2-54
•13
.90
.86
434
7 080
3 390
9
T6
18.1
5-3i
.OI
2.01
6.91
19.26
2.31
4-83
.14
.90
.87
438
6 450
3 080
16.2
4-75
•99
1-99
6.27
17-39
2.08
4-33
•IS
.91
.87
440
5 770
2 770
A
14-3
4.18
.96
1.96
5-6o
15.46
1.85
3-83
.16
.92
.87
•443
5 100
2 470
1
12.3
3.61
•94
1.94
4.90
1347
i. 60
3-32
•17
•93
.88
446
4 430
2 140
48
TABLE 24.— Continued
PROPERTIES OF UNEQUAL LEG ANGLES
S*
|
l^jH ^|
M|
J"
I
1
a
g
i2*!
j|J
^j^-
|
iflj
:: .. - r
•3
1
J
B
a
1
c
io>°
^ Z. ~J
Moment of
Inertia
Section
Modulus
Radius of
Gyration
•«
IF
- — — .-
F
5 °
•^ °
Axis
Axis
Axis
Axis
Axis
Axis
Axis
§
•* o Ji
'^l
i-i
2-2
i-i
2-3
i-i
2-2
3-3
H
'
XI
XI
Ii
It
Si
Si
rt
n
n
Mi
Mi
In.
In.
Lb.
In.*
In.
In.
In.*
In.<
In.«
In.»
In.
In.
In.
Ft.-Lb.
Ft.-Lb.
6X3*
I
28.9
8.50
I.OI
2.26
7.21
29.24
2.90
7-83
•92
1.85
•74
•317
10 450
3 870
tt
27.3
8.03
•99
2.24
6.88
27.84
2-74
7.41
•93
1.86
•74
-320
9 880
3 650
1
25-7
7-55
•97
2'. 2 2
6-55
26.39
2-59
6.98
•93
1.87
•75
.323
9 300
3 45°
H
24.0
7.06
•95
2. 2O
6. 20
24.S.,
2-43
6-SS
•94
1.88
•75
•327
8 750
3 240
f
22.4
6.56
•93
2.18
5-84
23-34
2.27
6.10
•94
1.89
•75
•331
8 150
3 030
H
2O.6
6.06
.90
2.15
5-47
21.74
2. II
5-65
•95
1.89
•75
•334
7 550
2 8lO
f
18.9
5-55
.88
2.13
5.08
20.08
•94
5-19
.96
1.90
•75
-338
6 920
2 59°
n
17.1
5-03
.86
2. II
4.67
18.37
•77
4.72
.96
1.91
•75
•341
6 300
2 360
*
15-3
4.50
.83
2.08
4-25
16.60
•59
4.24
•97
1.92
.76
•344
5 650
2 I2O
A
13-5
3-97
.81
2.06
3-8i
H-77
.41
3-75
.98
1-93
.76
•347
5 ooo
I 880
i
11.7
3.42
.78
2.04
3-34
12.86
•23
3-25
•99
1.94
•77
•35°
4 33°
I 640
A
9-8
2.87
•75
2.O2
2.85
10.88
1.04
2.74
1. 00
1.95
•77
•353
3 650
I 380
5X4
I
24.2
7.11
1. 21
I.7I
9-23
16.45
3-31
4-99
•H
i-S2
.84
6 650
4 410
H
22.7
6.65
1.18
1.68
8-74
15-54
3-"
4.69
•IS
1.53
.84
6 250
4 150
I
21. 1
6.19
1.16
1.66
8.23
14.60
2.90
4-37
•IS
1-54
.84
S 830
3 870
H
19-5
5.72
1.14
1.64
7.70
13.62
2.69
4.05
.16
1.54
.84
'.617
s 400
3 590
1
I7.8
5-23
1. 12
1.62
7.14
12.61
2.48
3-73
.17
i-SS
.84
.620
4 970
3 310
A
16.2
4-75
I.IO
i. 60
6.56
11.56
2.26
3-39
.18
1-56
•85
•623
4 520
3 oio
14.5
4-25
.07
1.57
5.96
10.46
2.04
3-05
.18
•85
.626
4 070
2 720
A
12.8
3-75
•OS
i-SS
5-33
9-32
1.81
2.70
.19
iis8
•85
.629
3 600
2 420
f
II.O
3-23
•03
4.66
8.14
i-S7
2-34
.20
.86
.631
3 120
2 090
5X3*
i
22.7
6.67
.04
1.79
6.21
15-67
2.52
4.88
.96
i-53
•75
•455
6 510
3 360
H
21.3
6.25
.02
1.77
5-89
14.81
2-37
4-58
•97
i-54
•75
.460
6 no
3 160
*
19.8
5.81
.OO
5-55
13.92
2.22
4.28
.98
i-SS
•75
•464
5 71°
2 960
ft
18.3
5-37
•97
1.72
5.20
12.99
2.O6
3-97
.98
1.56
•75
.468
5 290
2 750
1
16.8
4-92
•95
1.70
4-83
12.03
1.90
3.65
•99
1.56
•75
.472
4 870
2 530
A
15.2
4-47
•93
1.68
4-45
11.03
3-32
1. 00
i-57
•75
•476
4 430
2 310
^
13-6
4.00
.91
1.66
4-os
9-99
Iisi
2-99
I.OI
1.58
•75
•479
3 990
2 O8O
A
I2.O
3-53
.88
1-63
3-63
8.91
i-39
2.64
I.OI
i-59
•76
.482
3 520
I 850
f
10.4
3-05
.86
1.61
3-i8
7.78
1. 21
2.29
1. 02
i. 60
•76
•485
3 060
i 610
A
8-7
2.56
.84
I-S9
2.72
6.60
I. O2
1.94
1.03
1.61
•76
•489
2 590
I 360
5X3
H
19.9
5.84
.86
.86
3-71
13.98
•74
4-45
.80
i-SS
.64
•336
5 930
2 320
f
18.5
5-44
.84
.84
3-Si
.63
4.16
.80
i-SS
.64
•34°
5 550
2 170
H
17.1
5-°3
.82
.82
3-29
12. 2?
3-86
.81
1.56
.64
•345
5 150
2 OIO
1
iS-7
4.61
.80
.80
3.06
"•37
•39
3-55
.82
.64
•349
4 740
I 850
A
14-3
4.18
•77
•77
2.83
10.43
•27
3-23
.82
1^58
•65
•353
4 3IQ
I 690
1
12.8
3-75
•75
•75
2.58
9-45
2.91
.83
•65
•357
3 880
I 530
A
"•3
3-31
•73
•73
2.32
8-43
1.02
2.58
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3 440
I 360
1
9-8
2.86
.70
.70
2.04
7-37
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2.24
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1.61
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2 990
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8.2
2.40
.68
.68
1-75
6.26
•75
1.89
.85
1.61
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.368
2 52O
I OOO
49
TABLE 24— Continued
PROPERTIES OF UNEQUAL LEG ANGLES
L|
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°
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Modulus
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1.27
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1.94
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3-°9
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4.76
1-35
1.72
1.24
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2 290
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1. 21
2.99
4.17
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1.26
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1.26
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4X3
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2.87
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4.69
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1.42
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2.68
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1.22
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2.42
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1.30
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1.68
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1.25
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2 240
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8-5
2.48
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1.28
1.92
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1.46
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1.26
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i 160
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7-2
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1.65
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1.23
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1.27
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1.28
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12.5
3.67
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2 35°
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A
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1.45
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1.07
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1.44
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550
50
TABLE 24.— Continued
PROPERTIES OF UNEQUAL LEG ANGLES
h
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90
51
TABLE 24.— Continued
PROPERTIES OF UNEQUAL LEG ANGLES
He-!2 3
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ifXi
i
1.81
•54
•3°
•49
.041
•°93
•059
.106
.28
.42
.21
140
80
A
1.40
.41
.28
•47
•033
•075
.046
.082
.28
•43
.21
IIO
60
1
.96
.29
.26
•44
.024
•053
.032
•057
.29
•44
.22
75
40
ifXf
A
1.32
•39
.24
•49
.022
.071
•035
.081
.24
•43
.19
IIO
45
.91
.27
.22
•47
.017
•051
.026
.056
•25
•44
.20
75
35
ijXl
1
•85
•25
•23
.41
.Ol6
•039
.024
.047
•25
.40
.19
60
30
iTeXH
A
i. 08
•32
.24
•37
.015
•°33
.027
.048
.22
•32
.16
64
35
iXf
A
I.OO
•30
•23
•35
.OI3
.027
.025
.042
.21
•3°
.16
55
3°
i
.70
.21
.21
•33
.0094
.020
.017
.030
.22
•3i
.16
40
20
iXf
A
.92
•27
.19
•38
.0074
.025
.017
.041
•17
•31
•13
55
20
1
.64
.19
•17
•35
.0055
.019
.OI2
.029
•17
•3i
•13
40
16
txj
•095
.42
•13
•13
•3i
.O022
.0093
.OO54
.017
•13
.28
.12
20
7
Hxi
A
.62
•19
•15
•3i
.OO32
.on
.0091
.022
•13
•25
.11
3°
12
52
TABLE 25
AREAS OF ANCLES
AREAS IN SQUARE INCHES
DIMENSIONS IN INCHES
ANGLES WITH EQUAL LEGS
SIZE
i
A
1
A
i
A
*
A
i
tt
i
«
J
«
i
iA
it
SUE
8'X8'
7.7?
S f,K
0.61
IO.C1
11.44
12.14.
11.2"?
14.. 1 2
K.OO
15.87
16.71
8"X8r
6 X6
4-36
5.06
5-75
''•45
7.11
7.78
8.44
9.09
9-73
10.37
11.00
6 X6
s xs
—
—
3.61
4.18
4-75
S-3I
5.86
6.40
6.94
7-47
7.98
8.50
9-00
5 X5
4 X4
—
2.40
2.86
3-31
3-75
4.18
4.61
5-03
5-44
S-84
4 X4
liXli
2.OQ
1 Is
7 87
1.2C
1.62
1 08
A. -1J.
1 60
c.ctt
liXli
3 X3
1.44
1.78
2. II
2-43
2.7S
3.06
3-36
3 X3
2fX2f
1.31
1.62
1.92
2.22
2.50
2}X2}
2JX2J
0.90
1.19
1.47
i-73
2.OO
2.2S
2iX2|
2jX2}
081
T06
MI
lo^
I 78
2.OO
21X2}
2 X2
0.71
0.94
I.IS
1.36
I.S6
2 X2
liXl}
—
0.62
0.8 1
1 .00
1.17
1-34
ilXii
liXiJ
0.36
O.C1
0.60
084
008
liXii
i}Xii
O.1O
0.4.1
o.?6
068
iJXi}
i Xi
O.21
CM 4.
0.44
i Xi
ANGLES WITH UNEQUAL LEGS
SIZE
i
A
i
A
1
A
i
A
t
ft
1
H
I
H
I
iA
Ij
SIZE
7'X3i'
....
4.40
S-00
5-59
6.17
6.75
7.31
7.87
8.42
8.97
9.SO
7'X3l'
6 X4
. . . .
—
3.61
4.18
4-75
S-3I
s.86
6.40
6.94
7-47
7.98
8.50
9-OO
6 X4
6\3i
3-42
3-97
4.50
S-03
5-55
6.06
6.56
7.06
7-55
8.03
8.50
6 X3i
S X4
—
3-23
3-75
4.25
4-75
5-23
S-72
6.19
6.65
7.11
S X4
S X3i
2.56
3-05
3-53
4.00
4-47
4.92
5-37
S.8i
6.25
6.67
5 X3i
5 X3
2.40
2.86
3-3i
3-75
4.18
4.61
5-03
5-44
5.84
S X3
4 X3i
2.25
2.67
3.09
3-SO
3-90
4-30
4.68
5.06
5-43
4 X3i
4 X3
2.09
2.48
2.87
3-25
3.62
3.98
4-34
4.69
5-°3
4 X3
3iX3
I.Q1
2. 1O
•?f>r.
i.oo
1.14.
1 f>7
4.00
4.31
4..6z
liXl
3iX2i
1.44
1.78
2. II
2-43
2.75
3.06
3-36
3.6S
3iX2|
3 X2j
1.31
1.62
1.92
2.22
2.50
2.78
3 X2}
3 X2
1.19
1.47
i-73
2.00
2.25
3 X2
2JX2
0.8 1
i. 06
i-3»
i-SS
I.78
2.OO
2JX2
SIZE
i
A
i
A
I
A
i
A
f
H
!
H
i
H
I
iA
I*
SIZE
53
TABLE 26
WEIGHTS OF ANGLES
ANGLES WITH EQUAL LEGS
WEIGHTS IN POUNDS PER FOOT
DIMENSIONS IN INCHES
Size
1
ft
i
s
16
3
8
rV
J
ft
5
8
H
I
if
1
H
I
/A
/I
Size
8*X8*
26.4
29.6
32.7
35 8
38 o
42.0
45-O
48.1
5I.O
C4..O
560
8*X8*
6 X6
14.9
17.2
19.6
21.9
24.2
26.5
28.7
31.0
3S-3
37-4
6 X6
S XS
12-3
H-3
16.2
18.1
2O.O
21.8
23.6
25-4
27.2
28.9
30.6
S XS
4 X4
8.2
9.8
"•3
12.8
14-3
IS-7
17.1
18.5
19.9
4 X4
35X35
7.2
8-5
9.8
II I
12.4
13.6
14.8
16.0
17.1
35X3!
3 X3
4-9
6.1
7-2
8-3
9-4
10.4
"-S
3 ?\3
3 V 2-
4- 5
r £
6 6
76
8 <?
22V2a
21X2i
•3.1
4.1
en
Q
68
7-7
2z X 2-J-
1 i
^ 8
36
4- 5
5-3
6.T
6.8
21X"1
2 X2
3-9
1 7
5 3
2 X2
ifXif
2.1
2.8
3-4
4.0
4.6
ifXif
T ^ N/ T ^
I 2
T 8
•I .3
2.0
3>A
15X15
T ^ ^^ T ^
I O
T r
I.Q
2.3
T Vl
o 8
1.2
I.c
i X i
ANGLES WITH UNEQUAL LEGS
Size
1
iV
1
1
A
i
ft
1
A
5
I
H
3
13.
16
1
15
it
/
/A
/I
Size
7'X3i'
15.0
17.0
19.1
2I.O
23.0
24.9
26.8
28.7
3°-5
32.3
7"x3r
6 X4
12.3
H-3
16.2
18.1
20.O
21.8
23.6
25-4
27.2
28.9
30.6
6 X4
6 X35
11.7
13-5
iS-3
17.1
18.9
2O.6
22.4
24.O
25-7
27-3
28.9
6 X35
S X4
I I.O
12.8
H-5
16.2
I7.8
19.5
21. 1
22-7
24.2
S X4
S X35
8-7
10.4
I2.O
13.6
15.2
16.8
18.3
19.8
21-3
22.7
S X3l
S X3
8.2
9-8
"•3
12.8
H-3
iS-7
17.1
I8.S
19.9
5 X3
4 X3l
7-7
9.1
10.6
11.9
13-3
14.7
16.0
17-3
18.5
4 X3l
4 X3
7.2
8.3
9.8
II. I
12.4
13-6
14.8
16.0
I7.I
4 X3
31X3
6.6
7-9
9.1
IO.2
11.4
12.5
13-6
14.7
15-8
3lX3
32X2*
4-9
6.1
7-2
8-3
9-4
10.4
"•S
12.5
32X2!
3S/ *y —
A *2
4-5
5-6
6.6
7-6
8-S
9-5
3 X2*
3 X2
4.1
S-o
5-9
6.8
7-7
3 X2
21 X2
i 8
•3.7
4..C
6T
68
2|X2
Size
1
iV
i
tV
3
8
ft
}
9
T6
5
I
tt
a
if
7
8
if
i
/A
Ji
Size
54
TABLE 27
OVERRUN OF PENCOYD ANGLES
Overrun of Angles in Inches
Size of
Angle
Thickness in Inches
Inches
I*
iA
i
«
I
H
3
tt
i
A
i
A
i
A
i
A
i
8 X8
6 X6
4 X4
3 xl
2jX2.}
2 X2
ifXif
8 X6
7 X3i
6 X4
6 X3J
S X4
S X3J
5 X3
4 X3l
4 X3
3 2 xx 3
i i NX* ^ '
j 2 XX * J
3 X2
2^X2
2 Xlf
!
A
t
S
i
0
£
0
0
i
A
0
A
i
A
i
A
o
A
A
0
o
0
o
t
i
0
A
A
o
0
0
A
i
i
1
1
o
o
o
A
o
A
i
A
A
i
j
o
i
i
s
!
i
i
t
0
o
0
A
A
0
A
i
o
o
0
o
o
1
1
i
0
0
o
0
0
0
o
A
A
I
A
o
i
0
A
A
0
o
0
A
0
55
TABLE 28
OVERRUN OF PENNSYLVANIA STEEL Co. ANGLES
Overrun of Angles in Inches
Size of
Angle
Thickness in Inches
Maximum Length of Angles
Inches
l|
IA
i
15
16
8
It
i
H
!
9
T6
i
2
A
3
8
A
i
A
1
Feet
8 X8
6 X6
s xs
45X4!
4 X4
3*Xji
3 X3,
2|X2|
2^X2i
2 X2
i|Xi|
8 X6
6 X4
6 X3i
S X4
5 X3i
5X3
4^X3
4 X3£
4 X3
3*X3i
3*Xaf
3 X2i
3 X2
f
§
A
A
A
i
A
A
f
A
A
f
A
A
f
A
A
A
A
56 for if to 105 for \"
88 for i" to 105 for A"
70
70
70
70
70
35 for \" to 50 for A"
SO
50
50
63 for if to 105 for |"
70
70
70
70
70
70
70
70
70
70
. 70
65
\
A
A
i
A
A
i
A
1
1
<5
|
1
A
S
|
A
A
Te
A
A
i
A
1
i
A
\
A
A
I
A
A
o
1
i
i
f
A
A
1
A
i
A
A
3
8
A
A
A
A
i
A
f
£
A
i
A
1
I
A
|
A
i
1
A
i
A
A
A
A
I
A
i
A
4
A
A
A
3
f
11
32
f
f
A
i
¥
A
1
A
A
A
H
A
A
f
2
A
f
A
A
A
1
A
t
A
A
!
1
A
1
A
f
A
i
A
A
A
A
A
A
i
56
TABLE 29.
CARNEGIE ANGLES.
NET AREAS AND ALLOWABLE TENSION VALUES IN THOUSANDS OF POUNDS.
Maximum Fiber Stress, 16,000 Pounds per Square Inch.
Size.
Inches
Thiclc-
neM.
Inches.
Weight
per Foot,
Pounds.
Area,
Inches'.
Net Areas and Stresses — Two Holes Deducted.
i Inch Rivets.
i Inch RlveU.
| Inch Rivets.
Area.
Inches*.
Stress.
Area,
Inches*.
Stress.
Area,
[ndMt*.
Stress.
8X8
8X8
8X8
8X8
8X8
8X8
8X8
8X8
8X8
8X6
8X6
8X6
8X6
8X6
8X6
8X6
8X6
8X6
8X6
6X6
6X6
6X6
6X6
6X6
6X6
6X6
6X6
6X6
6X4
6X4
6X4
6X4
6X4
6X4
6X4
6X4
6X4
SX3if
5X3i
5 X3i
5X3}
5 X3i
5 X3it
5X3
5 X3
5X3
5X3
I
i
I
:
!
'
i
!
i
;
;
i
j
;
i
i
i
i
f
i
1
i
[
fr
1
*
V
*
1
i
V
t
\-
f
k
i
51.0
48.1
45.0
42.0
38.9
35-8
32.7
29.6
26.4
44.2
41.7
39-1
36.5
33-8
31-2
28.5
25-7
23.0
20. 2
33-i
31-0
28.7
26.5
24.2
21.9
19.6
17.2
14.9
27.2
25-4
23.6
21.8
2O.O
18.1
16.2
14-3
12.3
16.8
15.2
13.6
I2.O
10-4
8.7
12.8
"•3
9-8
8.2
15.00
14.12
13.23
12.34
11.44
10-53
9.61
8.68
7-75
13.00
12.25
11.48
10.72
9-94
9-15
8.36
7.56
6.75
5-93
9-73
9.09
8-44
7.78
7.11
6-43
5-75
5.06
4-36
7.98
7-47
6-94
640
5.86
5-31
4-75
4.18
3.61
4.92
4-47
4.00
3-53
3-05
2.56
3-75
3-3i
2.86
2.40
13.00
12.24
11.48
10.72
9-94
9.16
8.36
755
6-75
11.00
10.37
973
9.10
8-44
7.78
7.11
6-43
5-75
5-05
7.98
747
6-94
6.41
5.86
5-30
4-75
4.18
3 61
6.23
5.85
5-44
5-03
4.61
4.18
3-75
3-30
2.86
3-67
3-34
3.00
2.65
2.30
i-93
2-75
2.43
2. II
1.77
208.0
195.8
1837
171.5
159.0
146.6
133-8
120.8
108.0
176.0
165.9
155-7
145.6
135-0
124.5
113.8
102.9
92.0
80.8
127.7
119.5
III.O
1 02. 6
93-8
84.8
76.0
66.9
57-8
99-7
93-6
87.0
80.5
73-8
66.9
60.0
52.8
45-8
58.7
53-4
48.0
42.4
36.8
30.9
44.0
38.9
33-8
28.3
13-25
12.48
11.70
10.92
10.13
9-33
8.52
7.70
6.87
11.25
10.61
9-95
9-30
8.63
7-95
7.27
6.58
5.87
5.16
8.20
7.67
7-13
6.58
6.02
5-45
4.87
4.29
3-70
6-45
6.05
5-63
5.20
4-77
4-33
3-87
3-41
2-95
3-83
3-49
3.12
2.76
2-39
2.OI
2.87
2-54
2. 2O
I8S
212.0
199-7
187.2
174-7
I62.I
149-3
136.3
123.2
109.9
l8o.O
169.8
159-2
148.8
138.1
127.2
116.3
105.3
93-9
82.6
131.2
122.7
114.1
105-3
96-3
87.2
77-9
68.6
59-2
103.2
96.8
90.1
83-2
76.3
69-3
61.9
54-6
47-2
61.3
55-8
49.9
44-2
38.2
32.2
45-9
40.6
35-2
29.6
8.67
7.84
7.00
138.7
125.4
II2.O
7.42
6.72
6.00
5-27
II8.7
107.5
96.0
84.3
6.17
5-59
5.00
4.40
3.80
98.7
89.4
80.0
70.4
60.8
4-92
4-47
4.00
3-52
3-05
3-98
3-63
3-25
287
2.49
2.09
3.00
2.65
2.30
1.93
78.7
71-5
64.0
56.3
48.8
63.7
58.1
52.O
45-9
39-8
33-4
48.0
42.4
36.8
30.9
43
57
TABLE 29 — Continued.
CARNEGIE ANGLES.
NET AREAS AND ALLOWABLE TENSION VALUES IN THOUSANDS OF POUNDS.
Maximum Fiber Stress, 16,000 Pounds per Square Inch.
Size,
Inches.
Thick-
ness,
Inches.
Weight
per Foot,
Pounds.
Area,
Inches2.
Net Areas and Stresses — One Hole Deducted.
i Inch Rivets.
j Inch Rivets.
I Inch Rivets.
Area,
Inches2.
Stress.
Area,
Inches2.
Stress.
Area,
Inches2.
Stress.
6X6
1
•?•?.!
9-73
8.85
141.6
8.96
14.-? .4.
\J /\ w
6X6
8
«
J J
3I.O
9.09
8.28
132.5
8.38
TJ T
134.1
6X6
1 o
I
28.7
8.44
7.69
123.0
7.78
I24.C
\J /\ *J
6X6
4
H
w /
26. c
7.78
7.09
in -4
7.18
T J
II4-.Q
\J s\ \J
6X6
18
5
8
w»3
24.2
/ * / v
7.11
6.48
J T
103.7
6.56
T y
105.0
6.64
106.2
6X6
&
21-9
6-43
S-87
93-9
5-94
9S-o
6.01
96.2
6X6
1
19.6
S-7S
S-2S
84.0
5-31
85.0
5-37
85-9
6X6
A
17.2
5.06
4.62
73-9
4.68
74-9
4-73
75-7
6X6
I
14.9
4-36
3-98
63-7
4-°3
64.5
4.08
65-3
6 X A.
|
27.2
7.98
7.IO
nl.6
7.21
1 1C. A
*-> /\ 4-
6 X A
8
41
m/mm
2C.4.
/ *y^
7.4.7
/
6.66
* * j •^
106.6
/ •"
6.76
x J T
108.2
W /\ *^
6 V A.
16
|
•*O>T.
21.6
/ T/
6.04.
6.10
QQ.O
/
6.28
IOO.C
V s\ *|-
6 y a.
4
H
"j'^
21.8
v* J7T
6.AO
#»»«P
"?.7I
7:7
QI.4.
c.8o
^W.J
02. 8
W /'N *f-
6X4
16
I
2O.O
V*T
5.86
j t
S-23
-7 p ^.
837
J •*-"•
5-31
7
85.0
5-39
86.2
6X4
&
18.1
5-31
4-75
76.0
4.82
77.1
4.89
78.2
6X4
I
16.2
4-75
4-25
68.0
4-31
69.0
4-37
69.9
6X4
A
14-3
4.18
3-74
59-8
3.80
60.8
3-85
61.6
6X4
1
12.3
3-6l
3-23
Si-7
3.28
52.5
3-33
53-3
5X3!
1
16.8
4.92
4.29
68.6
4-37
69.9
4-45
71.2
5X3*
*
15.2
4-47
3-9i
62.6
3-98
63-7
4-05
64.8
5X3!
2
13.6
4.00
3-50
560
3.56
57-0
3.62
57-9
5X3!
A
I2.O
3-53
3-09
49.4
3-iS
S0.4
3.20
51.2
5X3*
I
IO.4
3-°5
2.67
42.7
2.72
43 -S
2.77
44-3
5X3*
A
8.7
2.56
2.25
36.0
2.29
36.6
233
37-3
5X3
I
IS-7
4.61
3-98
63-7
4.06
65.0
4.14
66.2
5X3
&
14-3
4.18
3.62
57-9
3-69
S9-o
3-76
60.2
SX3
1
12.8
3-75
3-25
52.0
3-3i
53-0
3-37
53-9
5X3
A
"•3
3-3i
2.87
45-9
2-93
46-9
2.98
47-7
5X3
f
9.8
2.86
2.48
39-7
2-53
40.S
2.58
4i-3
5X3
A
8.2
2.40
2.09
33-4
2.13
34-i
2.17
34-7
4X4
§
iS-7
4.61
3-98
637
4.06
65.0
4.14
66.2
4X4 .
&
14-3
4.18
3.62
57-9
3-69
S9-o
3-76
60.2
4X4
1
12.8
3-75
3-25
52.0
3-3i
S3-o
3-37
53-9
4X4
A
"•3
3-3i
2.87
45-9
2-93
46.9
2.98
47-7
4X4
t
9.8
2.86
2.48
39-7
2-53
4°-S
2.58
4i-3
4X4
A
8.2
2.40
2.09
33-4
2.13
34-i
2.17
34-7
4X4
i
6.6
1.94
1.69
27.0
1.72
27.5
i -75
28.0
4X3
i
ii. i
325
2-75
44.0
2.81
4S-o
2.87
45-9
4X3
A
9.8
2.87
2-43
38.9
2-49
39-8
2-54
40.6
4X3
1
8.5
2.48
2.IO
33-6
215
34-4
2.2O
35-2
4X3
A
7.2
2.09
1.78
28.5
1.82
29.1
1.86
29.8
4X3
1
5-8
1.69
1.44
23.0
1.47
23-5
1.50
24.0
58
TABLE 29.— Continued.
CARNEGIE ANGLES.
NET AREAS AND ALLOWABLE TENSION VALUES IN THOUSANDS OF POUNDS.
Maximum Fiber Stress, 16,000 Pounds per Square Inch.
Size.
liu lies.
Thfck-
ni-ss.
beta.
Weight
per Foot,
Pounds.
Area,
Inches'.
Net Areas and Stresses— One Hole Deducted.
i Inch Rivet*.
} Inch Rivets.
I Inch Rivets.
Area,
Inches*.
Stress.
Area,
Inches*.
Stress.
Area,
Inches*.
Stress.
3iX3J
3iX3i
3iX3i
3ix3i
3iX3i
3iX3J
3iX3l
3iX3
3iX3
3iX3
3iX3
3iX3
3iX2|
3iX2*
3iX2j
3*X2j
3iX2j
3 X3
3 X3
3 X3
3 X3
3 X3
3 X2j
3 X2*
3 X2*
2iX2|
2jX2i
2* X2|
2iX2j
2j X 2
2j X 2
2* X 2
2* X 2
2X2
2X2
2X2
2X2
2 X ij
2 X ij
2 X \\
I
A
i
A
i
A
i
i
A
1
A
1
i
A
1
A
i
*
A
I
A
\
i
A
1
1
A
i
A
1
A
i
A
I
A
i
A
A
1
A
I3.6
12.4
II. I
9.8
8-S
7.2
5-8
10.2
9-1
7-9
6.6
5-4
9-4
8-3
7.2
6.1
4-9
9-4
8-3
7.2
6.1
4-9
6.6
5-6
4-5
5-9
S-o
4.1
3-07
5-3
4-5
3-62
2-75
4-7
3.92
3.19
2.44
3-39
2-77
2.12
3-98
3.62
325
2.87
2.48
2 log
1.69
3.00
2.65
2.30
1-93
1.56
2-75
2-43
2.II
I.78
1.44
2-75
2-43
2. II
I.78
1.44
.92
.62
•31
•73
•47
1.19
0.90
i-SS
I.J1
106
0.8 1
1.36
I4S
0.94
0.71
I.OO
0.8 1
0.62
3-35
3.06
2-75
2-43
2.10
I.78
1.44
2.50
2.21
1.92
1.62
I-3I
2.25
1-99
i-73
1.47
1.19
2.25
1.99
1-73
1.47
1.19
i-S4
i-3i
i. 06
53-6
49.0
44.0
38.9
33-6
28.5
23-0
40.0
35-4
3°-7
25-9
21 O
36.0
31.8
27.7
23-5
19.0
36.0
31.8
27.7
23-5
19.0
24.6
2I.O
17.0
3-43
3-'3
2.81
2.49
2.15
1.82
1.47
2.56
2.27
1.97
1.66
i-34
2.31
2.05
1.78
i-5«
1.22
2-31
2.05
I.78
I.5I
1.22
i-59
i-35
1.09
1.40
i. 20
0.97
0.74
1.22
1.04
0.84
0.65
54-9
SO.I
4S-o
39-8
34-4
29.1
23-5
41.0
36.3
3I-S
26.6
21.4
37-o
32.8
28.5
24.2
I9-S
37-o
32.8
28.5
24.2
I9-S
25.4
21.6
17.4
22.4
19.2
15-5
ii. 8
I9-S
16.6
13-4
10.4
3-SI
3.20
2.87
2.54
2.20
1.86
1.50
2.62
2.32
2. 02
I.7O
1.37
2-37
2.IO
1.83
i-SS
1.25
2-37
2.IO
1.83
i-SS
1.25
1.64
i-39
1. 12
1.45
1.24
I.OO
0.76
1.27
1. 08
0.87
0.67
1. 08
0.92
0.75
0.57
0.77
0.62
0.48
S6.2
SI.2
45-9
40.6
35-2
29.8
24.0
41.9
37-i
32.3
27.2
21.9
37-9
33-6
29.3
24.8
20.0
37-9
33-6
29-3
24.8
20.0
26.2
22.2
17.9
23.2
19.8
16.0
12.2
2O-3
17.3
13-9
10.7
173
147
I2.O
9.1
12.3
9-9
7-7
TABLE 30
SAFE LOADS, IN TONS, FOR EQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
SIZE OF ANGLE
LENGTH OF SPAN IN FEET
i
2
3
4
5
6
7
I3-356
6-377
8
9
IO
II
12
1
8
_3
1
8
8"X8"
li"
I
93493
44.640
46.747
22.32O
31.164
14.880
23-373
11.160
18.699
8.928
I5-S82
7.440
11.687
5.580
10.388
4.960
9-349
4.464
8-499
4.058
7.791
3.720
6"X6"
I
I
45-707
18.827
22.854
9-4I3
15.236
6.276
11.427
4.707
9.141
3-765
7.618
3.138
6.529
2.689
5713
2-353
5.078
2.092
4-571
1.883
4-155
1.712
3.809
1.569
s"xs"
I
1
30.933
12.907
I5-467
6-453
10.311
4.302
7-733
3.227
6.187
2.581
5-I56
2.151
4.419
1.844
3.867
1.613
3-437
1-434
3-093
1.291
2.812
I-I73
2.578
1-075
4"X4"
ft
i
16.053
5.600
8.027
2.800
5-351
1.867
4.013
1.400
3-2II
I.I2O
2.676
•933
2.293
.800
2.007
.700
1.784
.622
1.605
.560
1-459
.510
1.338
467
3f"X3r
H
A
12.000
2.72O
6.000
1.360
4.0OO
.907
3.000
.680
2.4OO
•544
2.000
•453
1.714
.388
1.500
•340
1-333
.302
i. 200
.272
1.091
•247
I.OOO
.227
3"X3"
I
I
6-933
i. 600
3-467
.800
2.311
•533
1-733
.400
I.387
.320
1.156
.267
.990
.229
.867
.200
.770
.178
•693
.160
•630
•H5
•578
•133
2f'X2f"
*
i
4-747
1-333
2-373
.667
1.582
•444
1.187
•333
•949
.267
.791
.222
.679
.190
•593
.167
•527
.148
•475
•133
•431
.121
•396
.III
2|"X2|"
£
i
3-893
1.067
1.947
•533
1.298
•356
•973
.267
•779
•213
•649
.I78
•SS6
.152
.487
•133
•433
.118
•389
.107
•354
.097
•324
.089
2l"X2$"
*
i
3-093
-853
1.546
.427
1.031
.284
•773
.213
.619
.171
•515
.142
.442
.122
•387
.107
•344
•095
•309
.085
.281
.078
.258
.071
2"X2"
&
1
2-133
•693
1.067
•347
.711
-231
•533
•173
.427
•139
•356
.116
•305
.099
.267
.087
•237
.077
•213
.069
.194
.063
.178
.058
if'Xif"
A
i
i. 600
•533
.800
.267
•533
.178
.400
•133
.320
.107
.267
.089
.229
.076
.200
.067
.178
•059
.160
•053
.101
.038
•145
.048
•133
.044
i|"Xi|"
I
i
1.013
-384
•507
.192
•338
.128
•253
.096
.203
•077
.169
.064
•145
•055
.127
.048
•113
•043
.092
•035
.084
.032
ii"XiJ"
£
.587
.261
•293
•131
.196
.087
.147
.065
.117
.052
.098
.044
.084
•037
•073
•033
.065
.029
•059
.026
•053
.024
.049
.022
ii"Xii"
£
•304
.213
.152
.107
.101
.071
.076
•053
.061
•043
.051
.036
•043
.030
.038
.027
•034
.024
.030
.021
.028
.019
.025
.018
i"Xi"
i
.109
.299
.149
.149
•075
.099
.050
•075
•037
.060
.030
.050
.025
•043
.O2I
•037
.OI9
•033
.017
.029
•015
.027
.013
.025
.012
1»\/ 111
8 Xs
*
A
.176
.096
.088
.048
•059
.032
.044
.024
•035
.019
.029
.Ol6
.O2I
.012
.OIO
.008
.025
.OI4
.022
.OI2
.020
.Oil
.018
.OIO
.016
.009
.015
.008
s//va"
4 Al
A
A
.128
.069
.064
-Q35
.030
•023
•043
.023
.032
.017
.026
.014
.018
.OIO
.Ol6
.009
.014
.008
.013
.007
.012
.006
.on
.006
.005
.004
5'/v 5"
8 Ag
i
A
.060
.047
.020
.016
.015
.012
.012
.009
.OO9
.O07
.007
.OO6
.007
.005
.006
.005
.005
.004
rxi"
I
3
3~2
•037
.029
.019
.015
.012
.OIO
.009
.007
.007
.OO6
.OO6
.005
.OO5
.O04
.005
.004
.004
.003
.004
.003
.003
.003
.003
.002
Safe Load in tons of 2000 pounds uniformly distributed, for maximum fiber stress of 16,000
pounds per square inch. The Safe Load includes weight of Angle. The Safe Load for Angles of
intermediate thickness can be assumed as approximately proportional to their area or weight.
60
TABLE 31
SAFE LOADS, IN TONS, FOR UNEQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
SIZE OF ANGLE
*
LENGTH OF SPAN IN FEET
i
a
3
4
5
6
7
8
9
10
ii
13
UNEQUAL LEG ANGLES
8"X6"
i"
A
8
6
80.586
47-573
40.293
23-786
26.862
15.857
20.147
11.893
16.117
9-515
I3-43I
7.928
11.512
6.796
10.073
5-946
8-954
5-286
8.058
4-757
7.326
4-325
6.7IS
v'/'.f
8
6
37.706
22.^0
18.853
11.280
12.568
7.520
9.426
5.640
7-541
4-512
6.284
3760
5-387
3.222
4-7I3
2.820
4.189
2.567
3-77'
2.256
3.428
2.051
j.ua
1.880
8"X3i"
i
A
8
3*
73.488
I 'i.OJg
36.744
8.039
24.496
5-359
18.372
4.020
14.696
3.216
12.500
2.679
10.498
2297
9.186
2.OIO
8.165
1.786
7-349
i. 608
6.681
1.461
6.250
I-34C
8
3*
34-.3I2
7.801
17.156
3.900
"•437
2.600
8-578
1.950
6.862
1.560
5-718
1.300
4.901
1.114
4.289
0-975
3.812
0.867
3-431
0.780
3-"9
0.709
2-859
o.6^c
7"X3i"
i
1
i
i
I*
56.427
15.787
28.213
7.893
18.819
5.262
14.107
3-947
11.285
3-157
9.404
2.631
8.061
2.255
7-053
1-973
6.270
1-754
5-643
1-579
5-I30
1-435
4-702
1.316
3?i
23.093
6.720
"•547
3-360
7.698
2.240
5-773
i. 680
4.619
1-344
3.845
1.120
3-299
.960
2.887
.840
2.566
•747
2.309
.672
2.099
.611
1.924
-560
6"X4"
6
4
42-773
20.213
21.387
10.107
H-257
6.738
10.693
5-053
8-555
4-043
7.129
3.369
6.110
2.888
5347
2.527
4-753
2.246
4.277
2021
3.888
1.838
3-5'M
i/-S4
6
4
17.707
8-533
8-853
4.267
5.902
2.844
4.427
2-133
3-541
1.707
2-951
1.422
2.529
1.219
2.213
1.067
1.967
.948
I-77I
-853
1.609
.776
1.476
.711
6"X3*"
i
A
6
3*
41.760
15-467
20.880
7-733
13-920
5-I56
10.440
3-867
8.352
3-093
6.960
2.578
5.966
2.209
5.220
1-933
4.640
1.719
4.176
1.546
3-796
1.407
3.480
i.:*<
6
Jj
14-613
5-547
7-307
2-773
4.871
1.848
3.653
1.386
2.923
1.109
2-435
.924
2.087
•792
1.827
•693
1.624
.616
1.461
•555
1.328
.504
i. 218
.462
5"X4"
i
f
i
A
H
A
5
4
26.613
I7-653
13-306
8.826
8.871
5.884
6-653
4413
5-323
3-531
4-435
_2.942
2.080
1-395
3.802
2.522
^783
1.196
3-327
2.207
1.560
1.046
2-957
1.961
2.661
1.765
2.418
1.605
2.217
1.471
5
4
12.480
8-373
6.240
4.186
4.160
2.791
3.120
2.093
2.496
1-675
1-387
•930
1.248
-837
1.134
.761
1.040
•697
5"X3l"
A
26.026
13.440
13-013
6.720
8.675
4.480
6.506
3-360
5-205
2.688
4-338
2.240
3-718
1.920
3-253
1. 680
2.892
1-493
2.603
J-344
2.366
1.222
2.i6c
I.I2C
h
10.346
5-44°
5-173
2.720
3-449
1.813
2.587
1.360
2.069
1.088
1.724
.907
1.478
•777
1.293
.680
1.149
.604
1-035
•544
.941
•494
•844
•459
S"X3"
5
3
23-733
9.280
11.867
4.640
7.911
3-093
5-933
2.320
4-747
1.856
3-955
1.546
3-390
1.326
2.967
1.160
2.637
1.031
2-373
.928
2.157
•843
1.977
•773
5
3
10.080
4.000
5.040
2.000
3-360
1-333
2.520
I.OOO
2.016
.800
1.680
.666
1.440
•571
1.260
.500
I.I2O
•444
1.008
.400
.931
•363
.840
•333
4i"X3"
H
A
4*
3
19-306
9.120
9-653
4-560
6-433
3.040
4.827
2.280
2.053
I.OCO
3.861
1.824
3.217
1.520
2758
1.303
2-413
1.140
2.145
1.013
1.931
.912
1-755
.829
l.6Sc,
.760
4*
3
8.213
4.000
4.106
2.OOO
2.738
1-333
1.643
.800
1.369
.666
I-I73
•571
1.027
.500
•913
•444
.821
.400
•747
-363
.684
•333
Safe Load in Tons of 2000 pounds uniformly distributed, for maximum fiber stress of 16,000
pounds per square inch. The Safe Load includes weight of Angle. The Safe Load for Angles of
intermediate thickness can be assumed as proportional to their area or weight.
61
TABLE 31.— Continued
SAFE LOADS, IN TONS, FOR UNEQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
SIZE OF ANGLE
"Sw
|a
LENGTH OF SPAN IN FEET
i
a
3
4
5
6
7
8
9
10
ii
12
UNEQUAL LEG ANGLES
4"X3i"
H"
4
sj
15-573
12.267
7.787
6.133
5-I9I
4.089
3-893
3.067
3-II5
2-453
2-595
2.044
2.225
1-752
1.947
1-533
1.730
I-363
1-558
1.227
1.416
i. in;
1.298
1.022
A
4
3h
6.720
5-333
3-36o
2.667
2.240
1.778
1.680
1-333
1-344
1.067
I.I2O
.889
.960
.768
.840
.667
•747
•592
.672
•533
.619
485
.560
•444
4"X3"
if
4
3
I5-307
8.960
7-653
4.480
5-102
2.987
3.827
2.240
3.061
1.792
2-551
1-493
2.187
1.280
I-9I3
I.I2O
1.701
•99?
I-53I
.896
i-39i
.814
1-275
•747
i
4
3
5-333
3.200
2.667
i. 600
1.778
1.067
1-333
.800
1.067
.640
.889
•533
.762
•457
.667
400
•593
•355
•533
.320
485
•297
•444
.267
4"X2i"
I
4
2i
11.627
4-053
5-813
2.026
3-875
I-35I
2.907
1.013
2.325
.811
1.938
-675
i. 66 1
•599
1-453
•507
1.291
•451
1.163
.405
1-057
.368
.969
•338
t
£
7-4I3
2.613
3-707
1.307
2.471
.871
1-853
•653
1.483
•523
1-235
•435
1.059
•373
.927
•327
.824
.290
.741
_.26l
•725
.203
•674
.237
.618
.218
.604
.169
4"X2"
3
8
4
2
7-2.53
2.027
3-627
1.013
2.418
•675
1.813
•507
1.451
•405
1.209
•338
1.036
.289
.907
•253
.806
.225
•659
.184
1
4
2
5-oi3
1.440
2.507
.720
1.671
.480
1.253
.360
1.003
.288
•835
.240
.716
.206
.627
.180
•557
.160
.501
.144
•456
•131
.418
.120
3l"X3"
if
3*
3
"•733
8.800
5.867
4.400
3-9II
2-933
2-933
2. 2OO
2-347
1.760
1-955
1-578
1.676
1-257
1.467
I.IOO
1.304
.978
I-I73
.880
1.067
.800
.978
•733
1
3*
3
4.160
3-093
2.080
1-547
I-387
1.031
I.O4O
•773
.832
.619
•693
•W
•594
.442
.520
•387
.462
•344
.416
•309
-378
.281
•344
.258
3l"X2j"
11
16
si
a*
9.867
5.280
4-933
2.640
3-289
1.760
1-333
.729
2.467
1.320
1-973
1.056
1.644
.880
1.409
•754
1-233
^660
.500
•273
1.096
.587
.987
.528
.897
.480
.822
_440
•333
.182
1
4
3*
aj
4.000
2.187
2.OOO
1.093
I.OOO
•547
.800
•437
.666
•364
•571
.312
•444
•243
.400
.219
•364
.199
3*"X2"
f
3*
2
5.600
2.027
2.800
I.OI3
1.867
.675
1.400
•507
I.I2O
•405
•933
•338
.800
.289
.700
•253
.622
.225
.560
.203
•509
.184
•467
.169
1
I*
2
3.840
1-387
I.92O
•693
1.280
.462
.960
•347
.768
.277
.640
•231
•548
.198
.480
•173
.427
•154
•384
.149
•349
.126
.320
•US
3i"X2"
A
31
2
6-933
2.827
3466
I-4I3
2.311
•942
1-733
.707
1.386
-?6S
I-I55
.471
.990
.404
.867
•353
.770
•3H
•693
.283
.630
•257
-578
•235
i
3i
2
3.360
1-387
1.680
•693
I.I2O
.462
.840
•346
.672
.277
.560
.231
.480
.198
.420
^173
•313
.087
•373
.154
•336
.148
•305
.126
.280
•US
3i"Xif"
A
3i
if
2.507
•693
1.253
•347
•835
.231
.627
•173
.501
•139
.418
•115
-358
.099
.278
.077
.251
.069
.228
.063
.209
•057
3"X2M"
A
,1*
6.240
5-547
3.120
2-773
2.O8O
1.849
1.560
1-387
1.248
I.IO9
1.040
_X)24
1.040
.844
.891
•792
.780
_^93
.780
•633
•693
.616
.624
•555
.567
•504
.567
.461
.520
.462
3"X2H"
5
3
2H
6.240
5.067
3.120
2-533
2.O8O
1.689
1.560
1.267
1.248
I.OI3
.891
•724
•693
•563
.624
^507
.613
•437
.520
.422
3"X2i"
A
£
6-133
4-373
3.067
2.187
2.044
1.458
1-533
1.093
1.227
•875
1.022
.729
.876
•625
.767
••547
.681
.486
•557
•397
•5"
•364
A
h
2.293
1-653
1.147
.827
.764
•SSI
•573
•413
•459
•331
.382
•275
.328
.236
.287
.207
•255
.184
.229
.165
.208
.150
.191
• 138
Safe Load in tons of 2000 pounds uniformly distributed, for maximum fiber stress of 16,000
pounds per square inch. The Safe Load includes weight of Angle. The Safe Load for Angles of
intermediate thickness can be assumed as approximately proportional to their area or weight.
62
TABLE 31.— Continued
SAFE LOADS, IN TONS, FOR UNEQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
SUE OF ANGLES
iv
F
LENGTH OF SPAN IN FEET
i
2
3
4
5
6
7
8
9
10
ii
13
UNEQUAL LEG ANGLES
3"X2"
i"
3
2
5-333
2.507
2.667
1-253
1.778
•835
1-333
.627
1.067
.501
.889
.418
.762
-358
.667
•313
.592
.278
•533
•251
•485
.228
•444
.209
A
3
2
2.187
1.067
1.093
•533
•729
•355
•547
.267
437
.213
•365
.178
.312
.152
•273
•133
•243
.118
.219
.107
.199
.097
.182
.089
2*"X2"
i
2i
2
3-733
2-453
1.867
1.227
1.244
.818
•933
.613
•747
.491
.622
.409
•533
•35°
.467
•307
.415
.272
•373
•245
•339
.223
.311
.204
A
2*
2
'•Sf
1.067
-773
•533
•515
•355
•387
.267
•309
.213
.258
.178
.221
•152
•193
•133
.172
.118
•155
.107
.141
.097
.129
.089
2j"XlJ"
A
2*
If
2-453
1.280
1.223
.640
.818
.427
•613
.320
.491
.256
.409
.213
•35°
• 183
.307
.160
.272
.142
•245
.128
.223
.116
.204
.107
A
*f
If
1-547
.800
•773
.400
•5i5
.267
•387
.200
•309
.160
.258
•133
.221
.114
.193
.100
.172
.089
•155
.080
.141
•073
.129
.067
2i"Xli"
A
2:
I
2-347
.907
I-J73
•453
.782
.302
•587
.227
.469
.181
•391
•151
•335
.129
.293
•113
.261
.IOI
•235
.091
.213
.082
.195
-075
A
at
3
1-493
.587
•747
•293
•497
•195
•373
.147
.299
.117
•249
.098
.213
.084
.187
.073
.166
.065
.149
•059
.136
•053
.124
•049
.102
.029
2i"Xli"
A
2;
I;
1.227
-352
.613
.176
.409
.117
•307
.088
•245
.070
.204
•059
•175
.050
•153
.044
.136
-039
.123
•035
.in
.032
2i"Xli"
*
2:
i-
2.880
1-387
1.440
•693
.960
.462
.720
•347
•576
•277
.480
.231
.411
.198
.360
•173
-320
-154
.288
•139
.262
.126
.240
.115
A
2}
ij
1.227
-587
.613
•293
.409
.195
•307
•147
•245
.117
.204
.098
•175
.084
•153
.078
.136
-065
.123
•059
.in
•053
.102
.049
2"XI*"
I
2
Ii
1.813
1.067
.907
•533
.604
•355
•453
.267
•363
.213
•302
.178
•259
.152
.227
•133
.2OI
.118
.181
.107
-165
.097
.151
.089
i
2
ii
.693
.400
•347
.200
.231
•133
•173
.100
•139
.oSo
.115
.067
..099
.057
.087
.050
.077
.044
.069
.040
.063
.036
.058
•033
2"Xl|"
f
2
If
1.760
.907
.880
•453
•587
.302
.440
.227
•352
.181
•293
•151
.251
.129
.220
.113
.195
.101
.176
.091
.160
.082
.147
.075
A
2
If
.960
•5°i
.480
.251
.320
.167
.240
.125
.192
.100
.160
.083
•137
.072
.I2O
.063
.107
.056
.096
.050
.087
•045
.080
.042
2"Xli"
1
2
IT
1.227
.517
•613
.259
.409
.172
•307
.129
•245
.103
.204
.086
•175
.074
•153
.065
.136
.057
• 123
.052
.in
.047
.IO2
.043
A
2
Ii
.960
.400
.480
.200
.320
•133
.240
.100
.192
.080
.160
.067
•137
.057
.I2O
.050
.107
.044
.096
.040
.087
.036
.080
•033
Safe Load in Tons of 2,000 pounds uniformly distributed, for maximum fiber stress of 16,000
pounds per square inch. The Safe Load includes weight of Angle. The Safe Load for Angles
of intermediate thickness can be assumed as proportional to their area or weight.
63
TABLE 31. — Continued
SAFE LOADS, IN TONS, FOR UNEQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
SIZE OF ANGLE
3U
tJJS
r
LENGTH OF SPAN IN FEET
i
2
3
4
5
6
7
8
9
10
II
12
UNEQUAL LEG ANGLES
ii"xii"
i"
if
a
.960
•SO?
.480
•253
.320
.169
.240
.127
.192
.IOI
.160
.084
•137
.072
.I2O
.063
.107
.056
.096
•051
.087
.046
.080
.042
i
if
i|
.501
.277
.251
•139
.167
.092
.125
.069
.IOO
•055
.083
.046
.072
.040
.063
•035
.056
.031
.050
.028
.045
.02 1,
.042
.023
i?"Xii"
i
it
i|
.907
.411
•453
.205
.302
•137
.227
.103
.l8l
.082
•151
.068
.129
.059
•113
.051
.101
.046
.091
.041
.082
•037
•°75
.034
i
if
a
.496
.229
.248
•"5
•I6S
.076
.124
•057
.099
.046
.083
.038
.071
•033
.062
.029
•055
.025
.050
.023
•°45
.021
.O4I
.019
if'xii"
A
i*
ii
.853
.603
.426
.301
.284
.2OI
.213
•151
•171
.I2O
.142
.IOO
.122
.086
.107
•075
.095
.067
.085
.060
.077
•055
.071
.O5O
A
if
it
•533
.389
.267
•195
.178
.129
•133
.097
.107
.078
.089
.065
.076
.056
.067
.049
•059
•043
•053
•039
.048
•°35
.044
.032
if'Xi"
i
it
i
•565
•3iS
.283
•157
.188
.105
.141
.079
•113
.063
.094
.052
.O8l
•045
.071
•°39
.063
•035
.056
.031
.051
.029
.047
.026
i
a
i
•304
.171
• 152
.085
.101
•057
.076
•°43
.061
•034
.051
.028
.044
.024
.038
.O2I
•034
.019
.030
.017
.028
•015
.025
.OI4
i2"XZ"
A
i
•432
.187
.216
•093
•144
.062
.108
.047
.086
•037
.072
.031
.062
.027
•054
.023
.048
.021
•043
.019
•039
.017
.036
•015
.025
.on
i
i
.299
•139
.149
.069
.099
.046
•°75
•035
.060
.028
.050
.023
•043
.020
•037
.017
•033
.015
.030
.014
.027
.013
if'Xf"
i
?
.251
.128
.125
.064
.083
•043
•063
.032
.050
.026
.042
.021
.036
.018'
.031
.Ol6
.028
.014
.025
.013
.023
.012
.021
.Oil
I&"XH"
A
iA
»
.256
.144
.128
.072
.085
.048
.064
.036
•051
.029
•043
.024
.036
.020
.032
.018
.028
.016
.026
.014
.023
.013
.021
.OI2
T//v/3//
1 A4
A
i
3
.224
•133
.112
.067
•075
.044
.056
033
•045
.027
•037
.022
.032
.OI9
.028
.017
.025
.015
.022
.OI3
.O2O
.OI2
.OI9
.Oil
1
I
|
.160
.091
.080
•045
•°53
.030
.040
.023
.032
.018
.027
.tfl5
.023
.013
.O2O
.Oil
.018
.OIO
.Ol6
.009
.OI4
.008
.OI3
.007
i"Xf"
A
I
5
8
.219
.091
.IO9
•045
•073
.030
•055
.023
.044
.018
.036
.015
.031
.013
.027
.on
.024
.OIO
.022
.009
.020
.008
.018
.007
1
I
5
8
•iSS
.064
.077
.032
.051
.021
•039
.Ol6
.031
.013
.026
.on
.022
.OO9
.019
.008
.017
.007
.OIO
.003
.015
.OO6
.014
.O06
.013
.005
i"Xi"
•095
I
V
.091
.029
•045
.OI4
.030
.OIO
.023
.007
.018
.OO6
.015
.005
.013
.OO4
.Oil
.004
.OO9
.OO3
.008
.003
.007
.OO2
M"xf"
A
¥
2
•ii7
.048
•059
.024
•°39
.Ol6
.029
.OI2
.023
.OIO
.019
.008
.017
.OO7
.015
.006
013
.005
.012
.005
.Oil
.004
.010
.004
Safe Load in tons of 2,000 pounds uniformly distributed, for maximum fiber stress of 16,000
pounds per square inch. The Safe Load includes weight of Angle. The Safe Load for Angles of
intermediate thickness can be assumed as approximately proportional to their area or weight.
64
TABLE 32.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
TT
Moments of Inertia „ For Distances
of Four Angles, •» . . . X , Measured
Axis X-X, from
Equal Legs. Back to Back.
a," X a,"
3"X3"
Thick.
A"
J"
A"
1"
A"
J"
Thick.
t"
A"
1"
A"
1"
A"
1"
Ar*a4Li
3*°
4.76
5.88
6.92
8.00
9.00
Area 4 [s
5.76
7.12
8-44
9.73
11.00
13.34
'3-44
d"
Moments of Inertia About Axis X-X, In.4.
d"
Moments of Inertia About Axis X-X, In.4.
si
17
22
27
31
35
39
6i
38
46
54
61
68
75
80
si
19
25
30
35
39
43
6|
42
5°
58
67
75
83
88
6
21
28
33
39
44
48
7
46
55
65
73
82
89
96
61
24
30
37
43
48
53
71
5°
60
70
80
89
97
104
6fj
26
33
40
47
53
58
7i
54
65
76
86
96
106
114
61
28
36
44
58
64
n
58
70
82
93
104
114
123
7
31
40
48
56
64
70
8
62
76
89
IOI
"3
124
133
7t
33
43
52
61
69
76
81
67
81
95
108
121
133
H3
7i
36
46
57
66
75
83
8i
72
87
102
116
130
H3
154
7i
39
50
6l
7i
81
89
8|
77
94
110
125
153
165
8
42
54
66
77
87
96
9
82
100
117
133
H9
164
177
81
45
58
7i
82
94
104
9l
87
106
125
142
159
175
189
H
48
62
76
88
IOI
in
9i
93
H3
134
169
1 86
20 1
81
66
81
94
108
119
9*
99
1 20
161
1 80
198
214
9
54
71
87
IOI
"5
127
10
105
127
150
171
191
211
228
9l
58
75
92
107
123
136
iol
in
135
158
r-i
202
223
241
9i
62
80
98
iH
H5
105
117
H3
I67
191
214
236
256
9*
65
85
104
121
139
154
io|
123
177
202
226
249
270
10
69
90
no
128
H7
163
II
130
159
1 86
213
239
263
285
iol
73
95
116
136
155
172
III
137
167
196
224
251
277
300
io|
77
100
123
H3
164
182
ni
144
176
206
237
264
292
316
io|
81
106
130
173
192
iif
184
217
248
278
307
333
II
85
112
137
159
183
203
12
158
193
227
260
292
322
349
Ilj
90
H7
144
168
192
214
I2j
166
203
238
272
306
338
366
"i
94
123
176
202
225
III
174
212
250
285
320
354
384
III
99
129
Js8
185
212
236
I2|
181
222
261
298
335
370
402
12
104
135
166
194
222
247
13
189
232
273
312
35°
387
420
I2l
109
142
174
203
233
259
198
242
285
325
366
404
439
I2i
H3
148
182
216
244
271
I3i
206
252
297
339
382
422
458
I2|
119
155
190
222
255
283
13!
215
263
309
354
398
439
478
13
124
162
198
232
266
296
H
224
274
322
368
414
458
498
I3l
129
169
207
242
278
309
14!
233
28S
335
383
43i
476
Si8
X3i
134
I76
216
252
20X)
322
Hi
242
296
348
399
448
496
539
13!
140
I83
225
263
302
336
14!
251
3°7
362
414
466
SIS
560
H
146
191
234
273
3H
35°
IS
261
319
376
430
484
535
582
Hi
198
243
284
327
364
isi
270
331
390
446
502
555
604
Hi
157
2O6
253
295
339
378
280
343
404
463
521
576
626
Hi
163
2I4
262
307
352
393
11!
290
355
419
480
539
597
649
15
169
222
272
318
366
408
16
300
368
434
496
559
618
673
15!
175
230
282
33°
379
423
16!
311
381
449
5H
578
640
697
IS*
182
238
292
342
393
438
16*
321
394
464
532
598
662
721
15*
188
246
303
354
407
454
i6|
332
407
480
550
619
685
745
Moment of Inertia of Net Area = Tabular Value X Net Area -s- Gross Area (approx.).
65
TABLE 32. — Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
T
Moments of Inertia For Distances
of Four Angles, X X , Measured
Axis X-X, ~ a from
Equal Legs. Back to Back.
3^"X3^"
Thick.
A"
1"
A"
1"
A"
f"
11"
Thick.
1"
A"
J"
A"
1"
tt"
\"
Area 4 [s
8.36
9.92
IMS
13.00
14.48
is-92
17.36
Area 4 [S
9.92
11.48
13.00
14.48
15-92
'7-36
18.76
d"
Moments of Inertia about Axis X-X, In.*.
d"
Moments of Inertia about Axis X-X, In.*.
7\
73
86
97
109
119
129
139
20|
836
961
1083
I2OI
I3H
1426
I53i
7\
79
93
105
118
129
140
150
2O|
858
987
III2
1234
1350
1466
1573
8
86
IOO
114
127
139
151
163
22j
1026
1181
1332
1477
1617
1756
1886
8f
92
108
122
137
150
163
175
22^
1052
I2IO
1364
1514
1657
1800
1934
85
99
116
131
H7
161
175
189
24*
1237
1424
l6o6
1782
1952
2121.
2279
84
106
124
157
173
188
203
245
1265
1456
1642
1823
1997
2169
2331
9
H3
132
150
1 68
185
20 1
217
26j
1467
1690
1907
2117
2319
2521
2710
9|
1 20
141
161
1 80
198
215
232
26|
1498
1725
1946
2161
2367
2573
2766
91
128
150
171
192
211
229
247
28|
1718
1979
2234
2480
2718
2955
3178
9!
136
160
182
204
224
244
263
28^
1750
2016
2276
2528
2770
3OII
3239
10
144
169
193
216
238
259
280
30|
1988
2291
2586
2872
3H9
3424
3684
i°!
153
179
2O5
229
253
275
297
2O23
2331
2632
2923
3205
3485
3750
IO?
162
190
217
243
267
291
315
32!
2278
2625
2965
3294
3611
3927
4227
io|
171
200
229
257
283
308
333
32I
2315
2669
3014
3348
3671
3993
4297
ii
1 80
211
241
271
299
325
352
34!
2588
2983
337°
3744
4106
4466
4807
Ml
189
223
254
285
315
343
371
341
2628
3030
3422
3802
4170
4535
4883
Ilj
199
234
268
301
332
362
391
36!
2917
3364
3800
4223
4632
5039
5426
Il|
209
246
28l
316
349
380
411
J6|
2960
3413
3856
4285
4700
5H3
5505
12
220
2S8
295
332
366
400
432
38!
3267
3768
4257
4731
5190
5646
6081
I2j
230
271
3IO
348
385
419
453
38^
3312
3820
43 1 6
4797
5262
5725
6166
ui
241
284
325
365
403
440
475
4°i
3636
4194
4740
5268
578o
6289
6774
u!
252
297
34°
382
422
460
498
402
3684
4249
4802
5337
5856
6372
6864
*. 13
264
310
355
399
441
482
521
42!
4025
4644
5248
5834
6401
6966
7505
135
275
324
37i
417
461
503
545
42?
4075
4702
53H
5907
6481
7053
7599
13!
287
338
387
^35
481
525
'569
444
4434
5117
5783
6429
7055
7678
8273
13!
299
353
404
454
502
548
594
44?
4487
5177
5852
6505
7139
7769
8372
14
312
368
421
473
523
571
619
46!
4863
5612
6344
7053
7740
8425
9079
14*
324
383
438
493
545
595
645
46*
4918
5776
6416
7133
7828
8520
9182
145
337
398
456
513
567
619
671
5312
6131
6930
7706
8457
9206
9922
14!
4H
474
533
590
644
698
48}
5369
6197
7006
7790
8549
9306
10030
15
364
430
492
554
613
669
725
5°!
578o
6672
7543
8388
9206
IO022
10803
J5i
378
446
511
575
636
695
753
505
5840
6742
7622
8475
9302
IOI27
10916
IS?
392
462
530
596
660
721
782
52!
6269
7237
8182
9099
9987
10873
11721
is!
406
479
549
618
685
748
811
6331
7309
8264
9189
10087
10982
11839
16
421
496
569
641
709
775
840
54*
6777
7824
8847
9838
10800
II758
12677
i6J
435
5H
589
663
735
803
870
54|
6842
7899
8931
9933
10904
II872
12799
165
450
532
609
687
760
831
901
7305
8435
9537
10607
11644
12679
13671
i6|
466
55°
631
710
787
860
932
56j
7372
8513
9625
10705
11752
12796
13798
18
546
645
740
834
924
ion
1097
58!
7853
9068
10254
11405
12521
13634
14701
i8j
563
665
763
860
953
1043
1131
§8}
7923
9149
i°345
11507
12633
13756
H833
i8f
580
685
787
887
982
1075
1166
60^
8421
9724
10997
12232
13429
14623
15770
i8f
598
706
811
913
1012
1107
1 202
6oi
8494
9808
11091
12338
13546
H75I
15906
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
66
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANCLES WITH EQUAL LEGS, Axis X-X.
ir 7
Moments of Inertia
For Distances
of Four Angles, X
X Measured
Axis X-X,
d from
Equal Leg*.
J
Back to Back.
— > v
Size.
4" X 4"
Thuk.
A"
1"
A"
•"
A"
1"
Thick.
1"
A"
*"
A" 1"
14"
1"
Area 4 [s
9.60
11.44
13.24
15.00
16.72
18.44
Area 4 1»
11.44
13-24
15.00
16.72
'8.44
30.12
21.76
d"
Moments of Inertia About Axis X-X, In.4.
d"
Moments of Inertia About Axis X-X, In.4.
si
109
128
146
164
179
195
24i
1398
1612
1819
2016
2215
2408
2595
81
117
137
157
I76
192
209
24<
1430
1648
1860
2062
2267
2463
2656
9
125
146
168
188
205
224
261
1661
1915
2162
2398
2636
2866
3089
9l
133
156
179
200
219
239
261
1695
1955
2208
2448
2692
2926
3155
9*
141
166
191
213
234
255
28J
1946
2245
2536
2813
3093
3364
3627
9l
ISO
177
203
227
249
272
28^
1984
2289
2585
2868
3154
3429
3697
10
159
1 88
215
241
265
289
30]
2255
2602
2939
3262
3587
3902
4208
IOJ
169
199
228 256
281
306
3°i
22-95
2648
2992
3320
3652
3972
4283
10*
179
211
241
271
297
325
2586
2985
3373
3744
4118
4481
4832
IOJ
189
223
255
286
3IS
343
32!
2629
3035
3429
3807
4188
4556
4914
II
199
235
269
302
332
363
341
2941
3395
3836
4259
4686
5099
5501
III
210
248
284
319
350
383
34*
2986
3448
3896
4326
4760
5179
5587
II*
221
26l
299
336
369
403
36*
3318
3831
4329
4808
5290
5758
6212
III
232
274
314
353
388
424
36*
3367
3887
4393
4879
5369
5843
6304
12
243
288
330
371
408
446
38J
37i8
4293
4853
5391
5932
6457
6968
1*1
255
3O2
346
389
428
468
38*
3769
4353
4920
5466
6016
6548
7065
iai
267
316
363
408
449
491
40*
4141
4782
5406
6007
6610
7197
7767
I2f
280
331
380
427
471
SIS
40*
4195
4845
5477
6086
6699
7292
7869
13
293
346
397
447
492
539
42!
4587
5297
5989
6656
7325
7976
8609
306
362
467
515
563
42*
4644
5364 6064
6739
7418
8077
8717
13*
319
377
434
488
538
588
44i
5°55
5839 6603
7338
8078
8796
9495
13!
333
394
452
509
561
614
44*
5909 6681
7426
8175
8902
9609
14
347
410
47i
530
585
641
46*
5547
6408
7246
8055
8867
9656
10424
' Hi
361
427
491
552
609
667
46*
5610
6481
7329
8146
8969
9767
10543
14*
376
444
Sii
575
634
695
481
6061
7003 7919
8804
9693
10557
H397
14}
390
462
598
660
723
48*
6127
7079 8006
8900
9799
IO672
11522
IS
406
480
552
621
686
752
Sol
6599
7624 8623
9587
10555
II497
12413
421
499
573
645
713
781
50
6667
7703 8713
9687 10667
Il6l8
12544
I
437
517
595
670
740
8 10
52l
7159
8272 9356
10404 11455
12478
13473
If!
453
536
617
695
767
841
52*
7231
8355 9450
10508
11571
I26O4
13609
16
469
556
639
720
795
872
54i
7742
8946 10119
11253
12392
13499
14577
ifl
486
576
662
746
824
903
54*
7816
9032 10217
11362
12512
I363O
14718
16*
503
596
685
772
853
935
8348
9647 10913
12137
13365
I456I
15724
16*
520
616
709
799
883
968
56
1
8425
9736 11014
12250
13490
15870
18
611
724
834
939
1039
1141
58
8977
10374' 11736
13054
14375
15662
16914
I8J
630
747
969
1072
1176
58
9057
10467 11841
13170
14505
15803
17066
lfl$
649
770
886
999
1105
1213
60
i
9629
11128 12589
14004
15423
16804
18148
I8J
669
793
913
1030
1138
1250
60
9712
11224 12698
14125
15557
I695O
18306
20}
793
941
1084
1222
1353
1486
62j
10303 11908 13473
14987
16507
17986
19426
20i
825
967
1114
1256
1527
62}
10389 12007 13585
15113
16646
I8I37
19589
22j
976
1158
1335
1506
1668
1832
64!
uooi 12715 14386
16004
17628
19208
20747
22*
IOIO
1187
1369
IS43
1710
1879
64*
11089 12817
14502
16134
I777I
19364
20915
Moment of Inertia of Net Area = Tabular Value X Net Area 4- Gross Area (appro*.).
67
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
Iff
T
1^3
Moments of Inertia For Distances
of Four Angles X X Measured
Axis X-X, a from
Equal Legs. Back to Back.
Size.
5" X 5"
Thick.
1"
ft"
V
ft"
1"
Thick.
t"
ft"
J"
ft"
t"
tt"
!"
Area 4 [s
14.44
16.72
19.00
21.24
23-44
Area 4 [s
14.44
16.72
19.00
21.24
23-44
25.60
27.76
d"
Moments of Inertia About Axis X-X, In.4.
d"
Moments of Inertia About Axis X-X, In.4.
28}
2377
2743
3107
3457
3802
4139
4474
282
2423
2797
3168
3524
3877
4220
4562
IOJ
250
287
322
355
387
30}
2759
3185
3608
4016
4419
4811
5201
iof
264
303
34i
375
4IO
303
2809
3243
3674
4089
4499
4899
5296
II
279
320
360
396
433
32}
3170
3660
4H8
4618
5082
5434
5984
11}
294
337
379
418
457
322
3224
3722
4218
4696
5168
5628
6086
III
309
355
400
44i
482
34l
3610
4169
4725
5262
5792
6309
6823
III
325
373
420
464
507
345
3667
4235
4800
5345
5884
6409
6932
12
342
392
442
488
533
36}
4079
4712
5341
5949
6549
7134
7717
12}
359
412
464
512
560
362
4140
4782
5420
6037
6646
7241
7833
III
376
432
486
537
588
38}
4577
5287
5994
6678
7352
8011
8667
I2f
394
452
Sio
563
616
385
4641
536i
6078
6772
7456
8124
8789
I31
412
473
533
589
645
40}
5103
5896
6686
7449
8203
8939
9672
431
495
558
616
675
405
5975
6775
7549
8313
9059
9802
Isl
450
517
583
644
70S
42}
5659
6539
7415
8264
9100
9918
10733
13!
469
540
608
673
737
423
5730
6622
7509
8368
9216
10044
10869
14
489
563
634
702
769
44i
6243
7215
8182
9120
10045
10949
11849
14}
51°
586
661
73i
80 1
445
6318
7302
8281
9230
10166
11081
11992
142
531
610
689
762
835
46}
6857
7924
8988
10019
11036
12030
13021
14!
552
635
717
793
869
462-
6935
8015
9091
10135
11163
12169
13171
IS
574
660
745
825
904
48}
7499
8667
9831
10961
12074
13163
14248
15}
596
686
774
857
939
481
8762
9939
11081
12207
13308
14405
I53
619
712
804
890
976
50}
8170
9443
10712
"945
I3I59
H347
I553I
15!
642
739
834
924
1013
503
8256
9543
10825
12071
13298
14499
15695
16
666
766
865
958
1051
52}
8870
10253
11632
12971
14291
15582
16869
16}
690
794
897
993
1089
S*{
8959
10357
11750
13103
14436
15740
17040
i6|
715
822
929
1029
1129
9598
11096
12589
14040
15470
16869
18263
i6|
739
851
961
1065
1169
543
9692
11204
12712
14177
15621
17033
18441
18
871
1003
"34
1257
1380
S6}
10356
"973
I358S
I5I52
16696
18206
19712
18}
899
1035
1170
1298
1424
565
10453
12085
13712
15294
16852
18377
19897
I8J
927
1068
1207
1339
1469
58}
i"43
12883
14618
16306
17968
19595
21217
i8|
956
IIOI
1244
1380
ISIS
583
11243
12999
14750
16453
18131
19772
21409
20}
"37
1310
1481
1645
1806
OO^
"958
13827
15690
17502
19288
21035
22777
2O|
1169
1347
1523
1691
1857
OO 2
12062
13947
15826
I765S
19456
21219
22976
22}
1403
1618
1831
2034
2235
O2x
12802
14804
16799
18741
20654
22526
24393
22^
H39
1659
1877
2085
2292
622
12910
14928
16940
18899
20828
22716
24599
24}
1699
1960
2218
2466
2710
64}
13676
15814
17946
20023
22067
24069
26065
245
1738
2005
2269
2523
2773
64i
13787
15943
18093
20186
22247
24265
26278
26}
2023
2335
2644
2940
3233
66}
H578
16858
19132
21347
23527
25662
27792
26|
2066
2384
2700
3002
3302
66J
14693
16991
19283
21515
23713
25865
28012
Moment of Inertia of Net Area = Tabular Value X Net Area -f- Gross Area (approx.).
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
T
Moments of Inertia For Distances
,.t lour Angles. -X X , Measured
Axis X-X. ~ « from
Equal Legs. Back to Back.
Siie.
6"X6"
Thick.
1"
A"
i"
ft"
1"
H"
1"
il"
1"
\V
i"
Area 4 [s
17-44
20.24
23.00
25.72
28.44
31.12
33-7°
36.36
P-..--
41-48
44-00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
III
432
497
560
618
678
735
787
840
891
942
990
I4t
586
675
762
842
924
1004
1077
"Si
1223
1293
1362
610
703
793
878
963
1046
"23
1200
1275
1349
1421
i6|
795
917
1035
"47
1260
1370
1472
1575
1675
1773
1869
i6J
824
950
1072
1788
1306
1420
1526
1633
1737
1839
1938
18;
1039
"99
1354
1502
1652
1797
^934
2071
2205
2336
2464
i8j
1072
1237
1398
1551
1705
1855
1996
2138
2276
2412
2545
20;
1317
1521
1720
1910
2IOI
2288
2464
2640
2812
2982
3H7
2OJ
1354
1564
1769
1964
2161
2353
2535
2716
2894
3069
3239
22J
1631
1884
2131
2368
2607
2840
3061
3282
3497
37"
3919
22i
•
1672
1932
2186
2429
2674
2913
3I4O
3367
3589
3808
4O2I
24:
1979
2287
2589
2878
3170
3455
. 3726
3996
4261
4523
4778
24!
2025
2341
2649
2946
3244
3536
3813
4091
4362
4630
4892
26;
2362
2731
3092
3440
3789
4131
4458
4784
5102
5417
5725
26i
2412
2790
3159
3513
3871
4220
4554
4887
5212
5535
5850
28i
2780
3216
3642
4053
4466
4871
5258
5644
6021
6395
6761
281
2835
3279
37H
4133
4555
4967
5362
5756
6141
6523
6896
30:
3233
3740
4237
4717
5200
5672
6125
6576
7017
7456
7884
3292
3809
4315
4804
5295
5776
6238
6698
7H7
7594
8031
32:
3721
4306
4879
5433
5990
6535
7060
7581
8092
8599
9095
32J
3784
4379
4962
5526
6093
6648
7181
7712
8232
8748
9253
34}
4243
49"
5566
6200
6837
7461
8062
8660
9244
9826
I039S
34*
43"
4990
5655
6299
6947
8192
8799
9394
9985
10563
•361
4801
5558
6300
7019
7741
8449
9132
98lO
I047S
i"35
II782
36J-
4873
5641
6395
7125
7858
8577
9270
9959
10634
"305
11962
381
5393
6244
7079
7889
8702
9500
10269
11034
11783
12528
13257
38*
5470
6333
7180
8001
8826
9635
10416
11192
11952
12708
13448
4oi
6021
6972
7905
8810
9720
10612
"474
12330
13169
14003
14821
40*
6102
7065
8011
8929
9851
10756
11629
12497
13347
14194
I5O22
42 i
6683
7739
8776
9783
10795
11787
12747
13699
14632
15562
16472
42*
6768
7838
8888
9909
10933
11938
12910
13875
14821
15762
16685
44i
7380
8548
9694
10808
11926
13024
14087
15141
16174
17203
I82II
44i
7470
8651
9112
10939
12072
13183
14259
15326
16372
17414
18435
46
(
8112
9396
10657
11884
I3"5
14323
15494
16655
17794
18927
2OO39
46.
8206
9505
10781
1 2O2 2
13268
14490
15675
16850
18001
19149
20273
48
8879
10285
11667
I30II
14360
15685
16969
18242
19491
20735
2I9S4
48
_
8977
10399
11796
I3I55
14520
15859
17158
18446
19709
20966
22200
5°i
9681
11215
12722
I4IOO
15663
17108
18511
19902
21266
22625
23957
Sof
9783
"334
12857
15829
17291
18709
20115
21493
22867
24214
52i
10517
12185
13823
15420
17022
18594
2OI2I
21635
23119
24598
20049
52*
10624
12309
13964
15577
17196
18785
20327
21856
23356
24850
26316
Moment of Inertia of Net Area = Tabular Value X Net Area -f- Gross Area (approx.).
69
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
Tf
Moments of Inertia
of Four Angles, X
Axis X-X,
Equal Legs.
__, .
— £,
— > N
r
For Distances
Measured
' from
Back to Back.
f
Size.
6" x 6"
Thick.
i"
A"
i"
A"
i"
H"
\"
\l"
i"
if"
i"
Area 4 [s
17.44
20.24
23.00
25.72
28.44
31.12
33-76
36.36
38.92
41.48
44.00
d"
Moments of Inertia about Axis X-X, for Various Distances Back to Back of Angles, In.4.
54?
COz
5^12
11389
II500
12295
12411
13196
13325
14247
14381
14971
15118
16164
16317
16701
16865
18034
18205
18438
18619
19911
20099
20143
20341
21753
21959
21799
22OI3
23544
23767
23440
23671
25318
25558
25050
25297
27058
27315
26654
26917
28793
29066
28228
28507
30495
30785
ssf
6oJ
6o|
13236
I33S6
I42I2
14337
15338
15478
16470
16615
17404
17562
18689
18853
19419
19596
20855
21038
21440
21636
23027
23230
23426
23639
25161
25382
25357
25588
27237
27476
27269
27518
29292
29550
29H5
29411
31309
31585
31015
31299
33321
32851
33I51
35294
35605
6aj
64!
15223
15352
16269
16402
17643
17792
18856
19010
20021
2OI9I
21398
21574
22342
22532
23881
24077
24671
24880
26371
26588
26958
27187
28817
29054
29184
29432
3"99
3H56
31388
31655
33557
33833
33S5I
33837
35872
36167
35709
36013
38179
38494
37825
38148
40445
40778
68J
17350
17488
18466
18608
20109
20269
21403
21568
22822
23003
24291
24478
25471
25673
27113
27322
28128
28352
29943
30173
30739
30984
32723
32975
33282
33547
35432
35706
35799
36084
38113
38407
38269
38575
40745
41060
40733
41058
43370
43706
43152
43496
45947
46303
7o£
?°|
72*
19616
19762
208OI
20952
22738
22907
24113
24287
25807
25999
27368
27567
28806
29022
30551
30773
31814
32052
33742
33987
34769
35029
36877
37H5
37650
37932
39935
40225
40500
40803
42960
43272
43299
43623
45930
46264
46090
46436
48893
49249
48830
49197
51802
52179
74f
m
8oJ
22177
23436
24731
26060
25708
27169
28670
30212
29180
30839
32544
34295
32575
34429
36334
38291
35979
38027
40133
42296
39324
41564
43867
46232
42587
45015
47SI2
50075
45814
48428
53875
48983
51780
54655
57607
52145
55124
58186
61331
55250
58408
61654
64989
oo oo oo oo
00 Cs4» »
MlMNIh-MiMUlH
27424
28823
30257
31726
31794
33417
35080
36784
36093
37936
39825
41760
40299
42359
44470
46633
44515
46792
49125
5I5IS
48660
5H49
53701
56315
52707
55405
58172
61005
56707
59612
62590
65641
60638
63746
66932
70196
64559
67870
71264
74741
68411
71921
75520
79206
92?
942
96*
33230
34768
36342
37950
38528
40313
42138
44004
43742
45769
47842
49961
48847
51112
53429
55797
53962
56466
59026
61644
58992
61730
64531
67394
63907
66876
69912
730i6
68764
71960
75229
78571
73537
76957
80454
84029
78301
8i943
85669
89478
82980
86843
90793
94831
98*
ioo|
102^
1045
39593
41271
42984
44732
47857
49844
51872
52126
54338
56595
58898
58217
60689
63211
65785
64319
67050
69838
72683
70319
73307
76357
79469
76187
79426
82733
86107
81985
85472
89031
92664
87682
9HI3
95222
99109
93369
97344
101401
105542
98958
103172
107474
111865
io8|
46515
48332
50185
52072
53940
56049
58198
60387
61247
63643
66084
68571
68411
71088
738i7
76597
75585
78544
81560
84633
82643
85879
89178
92539
89548
93057
96634
100278
96369
100147
103997
107920
103074
107116
111236
"5434
109765
i 14072
118461
122934
116343
120909
125563
130306
Moment of Inertia of Net Area = Tabular Value X Net Area -j- Gross Area (approx.).
70
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
T
Moment* of Inertia For Pittance*
.•i 1 our Angle*. -A X M Measured
Axis X-X. ~ « from
Equal Leg*. Back to Back.
JL .,
SiM.
8"X8"
Thick.
»"
A"
i"
H"
I"
»"
i"
11"
i"
'A"
1 1"
Air. i 4:-
31.00
34-7*
3844
42.13
45-76
49-36
52.93
5<M8
60.00
63.48
66.93
d"
Moment* of Inertia About Axis X-X for Variou* Distances Back to Back of 'Angles. In.*.
i6j
1333
H83
1631
1775
1910
2046
2179
2310
2430
2554
2674
18;
1686
1877
2065
2249
2423
2598
2769
2937
3094
3254
3409
I8«
1
1740
1937
2132
2322
2502
2683
2860
3034
3196
336i
3523
20;
2146
2391
2634
2871
3095
3321
3542
376o
3964
4172
4375
20;
2208
2461
2710
2954
3186
3419
3646
3871
4082
4296
4505
22;
i
2669
2976
3279
3576
3859
4H3
4421
4696
4955
5218
5475
22;
1
2739
3°S4
3365
3670
3961
4253
4538
4821
5087
5357
5621
24
3254
3630
4001
4366
47H
5064
5406
5745
6066
6390
6708
24l
3332
3716
4097
447i
4828
5186
5536
5884
6213
6546
6871
26]
3901
4353
4801
5240
5661
6083
6*497
6907
7296
7690
8075
26.
3987
4448
4906
5355
5786
6217
6640
7060
7458
7861
8255
28
4610
5 H5
5677
6198
6699
7201
7693
8182
8647
9116
9576
28-
4703
5249
5792
6324
6835
7348
7850
8349
8824
9303
9773
30;
S38i
6008
6630
7241
7829
8418
8996
9569
10117
10669
II2II
30:
5482
6120
6754
7377
7977
8577
9166
9751
10310
10872
II425
32;
6214
6939
7659
8367
9050
9733
10404
11070
11708
12350
12980
3*i
6323
7060
7794
8SH
9209
9904
10587
11266
11915
12569
I32IO
34}
7109
7940
8766
9578
10363
1 1 147
11918
12684
13419
I4I57
14882
34*
7225
8070
8910
9736
IOS34
11331
12114
12893
13641
14392
I5I29
361
8066
9010
9950
10873
11768
12660
13538
14410
15249
16091
16919
36*
8190
9149
10103
11041
11950
12856
13748
H634
15486
16342
17183
381
9085
10150
II2IO
12253
13264
14272
15263
16250
17200
18152
19089
38*
9217
10298
"373
12431
13457
14480
15487
16488
I74S2
18419
19369
4°;
10166
11360
12547
H7I7
14851
15982
17095
18202
19270
20340
21393
•40*
10306
11516
12720
13905
15056
16203
I733I
18454
19538
20623
21690
42i
11309
12638
13962
15264
16530
I779I
19032
20268
21461
22656
23831
42;
11456
12803
14144
15464
16746
18024
19282
20534
21743
22954
24H5
44;
12514
13987
I54S3
16897
18300
19699
21076
22446
23772
25098
26402
44l
12669
14160
15645
17107
18528
19944
21338
22726
24069
25412
26733
46]
13781
15404
17021
18613
20162
21705
23225
24738
26202
27667
29IO8
46'
13944
15586
17222
18833
20401
21963
23501
25032
26514
27997
29456
48:
15110
16891
18666
20414
22116
23811
25480
27142
28753
30363
31947
48i
15280
17082
18877
20645
22366
24081
25769
27450
29080
30709
32312
Soi
16501
18448
20387
22299
24161
26014
27840
29659
3H23
33186
34921
50
16679
18647
20608
22540
24423
26291
28143
29982
31766
33548
35302
52i
17954
20074
22186
24268
26297
28317
30307
32290
34214
36136
38028
S2J
18140
20282
22416
24520
26571
28612
30623
32626
34571
36513
38426
S4i
19469
21769
24061
26321
28525
30718
32879
35033
37125
39212
41269
54i
19663
21986
24301
26584
28810
31026
33208
35384
37497
39606
41684
S6A
21046
23534
26014
28459
30845
33219
35578
17889
40155
42416
44644
56i
21247
23759
26263
28732
31141
33538
35900
38254
40542
42826
45075
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
71
TABLE 32.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis X-X.
T
Moments of Inertia For Distances
of Four Angles, X X Measured
Axis X-X, ~ d from
Equal Legs. Back to Back.
JL,.
Size.
8" X 8"
Thick.
i"
A"
1"
tt"
J"
il"
I"
li"
i"
'iV
it"
Area 4 [s
31.00
34-72
38-44
42.12
45-76
49-36
52.92
56.48
60.00
63.48
66.92
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
S8i
22685
25368
28043
30680
33256
35817
38342
40858
43306
45747
48152
S8|
22894
25602
28302
30964
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132248
141029
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166623
106^
81015
90665
100299
109813
119161
128432
I37S87
146723
155682
164581
173361
io8J
84212
94244
104260
114151
123871
I335I2
143029
152531
161848
171101
180232
iioj
87471
97892
108297
118574
128673
138689
148578
158451
168134
177749
187237
112^
90792
101610
112412
123081
133567
143966
154233
164484
174539
184523
194376
iui
94174
105397
116603
127672
138552
H934I
159994
170630
181065
191425
201649
n6|
97619
109254
120872
J32347
143628
154815
165861
176890
187710
198454
209056
Il8|
101126
113180
125217
137107
148796
160388
171833
183262
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205609
216596
120^
104694
117176
129639
141950
154056
166060
177912
189747
201362
212891
224270
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
72
TABLE 33.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
1 — ill) — ' *
Moments of Inertia For Distances
nr Angles. X X Measured
Axis X-X. " <* from
Long Legs Turned Out. Back to Back.
3" X a«". Long Leg* Out.
3K"X»«". Long L«gs Out.
TUck
J"
U"
A"
1"
A"
i"
A"
ft"
A
A"
I'
V' .1 ( [i
5-»4
6.48
7.68
8.88
10.00
II. 13
5-76
7.13
8.44
9.73
ii. oo
13.34
^3-44
14.60
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles. In.4.
si
26
3i
36
41
45
49
30
35
41
47
52
56
60
64
Si
29
35
41
46
Si
55
34
40
46
53
59
62
67
72
6
32
39
45
52
57
61
37
44
52
59
65
69
74
79
6}
35
43
50
57
63
67
41
49
57
65
72
76
82
88
6}
38
47
55
62
69
74
44
53
62
70
79
84
9°
97
61
51
59
68
75
81
48
58
68
76
85
92
99
106
7
45
55
64
73
81
89
Si
62
73
82
92
IOO
108
116
7i
49
60
69
79
87
96
55
67
79
89
99
109
118
126
A
53
65
75
86
95
104
60
73
85
97
108
118
127
137
71
57
70
81
93
103
"3
64
78
92
104
116
127
138
148
8
6l
75
87
IOO
in
122
69
84
99
112
125
137
148
159
8}
66
81
94
107
119
131
74
90
106
120
134
147
159
171
si
71
86
IOO
"5
128
I4O
79
97
"3
129
144
158
171
184
81
75
92
107
123
137
ISO
85
103
121
138
154
169
183
197
9
80
98
114
131
146
160
90
no
129
147
164
1 80
195
2IO
9}
85
104
122
139
155
171
96
117
137
156
175
192
208
224
in
129
148
165
182
IO2
124
146
166
1 86
204
221
238
9l
96
118
137
157
175
193
1 08
I3l
154
176
197
216
235
253
10
IO2
125
145
167
1 86
205
114
139
I63
1 86
209
229
249
268
10}
107
132
154
176
197
217
121
H7
173
197
221
242
264
284
"3
139
162
1 86
208
229
127
155
182.
208
233
256
279
3OO
I0l
120
146
171
196
219
241
134
163
192
219
246
270
294
316
II
126
154
180
207
231
254
141
172
2O2
231
259
285
310
334
11}
132
162
190
218
243
268
148
181
212
243
272
299
326
iij
139
170
199
229
255
281
155
190
223
256
286
315
342
369
146
178
209
240
268
295
I63
199
234
267
300
330
359
387
12
IS2
187
219
251
281
310
170
208
245
280
3H
346
377
406
12}
159
196
229
263
294
325
I78
218
256
293
329
362
395
426
I2|
I67
205
240
275
308
340
1 86
228
268
306
344
379
413
445
174
214
250
288
322
355
195
238
280
320
360
396
432
465
13
182
223
261
301
336
371
203
248
292
334
375
414
451
486
I89
233
273
3H
350
387
212
259
305
349
392
431
470
507
!3i
197
242
284
327
365
403
2 2O
270
317
363
408
450
490
529
i3l
2OS
252
296
340
380
420
229
281
330
378
425
468
5"
*4
214
262
308
354
396.
437
238
292
344
393
442
487
531
574
I4.J
222 273
320
368
412
455
248
303
357
409
460
507
553
597
Hi
231 283
333
382
428
473
257
315
371
424
477
526
574
620
Hi
239 294
345
397
444
491
267
327
385
441
495
547
596
644
15
248 305
358
412
461
509
277
339
399
457
5H
560
619
668
15}
257 3l6
371
427
478
528
287
351
414
474
533
588
642
693
isi
266 327
385
443
495
547
297
364
429
491
552
609
665
718
i$!
276 339
398
458
5<-7
307
376
444
508
572
631
689
744
Moment of Inertia of Net Area = Tabular Value X Net Area -S- Gross Area (approx.).
44
73
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
Moments of Inertia J For Distances
of Four Angles, 3£ X JL Measured
Axis X-X, from
Long Legs Turned Out. Back to Back.
Size.
4" X 3". Long Legs Turned Out.
Thick.
i"
A"
I"
ft"
i"
ft"
1"
Thick.
1"
ft"
i"
ft"
i"
H"
1"
Area 4 [s
6.76
8.36
9.92
11.48
13.00
14.48
15.92
Area 4 [s
9.92
11.48
13.00
14.48
15-9*
1736
18.76
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
61
48
58
68
78
86
94
IO2
16
525
604
678
75i
821
890
954
6!
52
63
84
85
94
103
III
i6J
543
625
702
777
849
921
987
7
57
69
81
92
IO2
112
122
i65
646
725
804
879
953
1023
7*
62
75
88
IOO
III
122
132
16}
580
667
750
831
908
983
1055
75
67
81
95
109
121
132
144
184
699
804
904
1 002
1096
1190
1276
71
72
88
103
117
I3O
143
155
183
719
828
93i
1032
1129
1226
1315
8
77
94
in
126
I4O
154
I67
20j
874
1007
H33
1256
1375
1493
1603
8^
83
101
"9
136
IJI
166
1 80
20^
897
1034
1163
1290
1412
1533
1646
85
89
1 08
127
145
l62
178
193
22^
1069
1233
1388
1539
1686
1831
1967
81
95
116
136
iSS
173
191
2O7
222
1095
1262
1421
1577
1727
1876
2015
9,
IOI
124
I4S
166
185
204
221
24l
1284
1481
1668
1851
2028
2204
2368
9l
107
131
154
177
197
217
236
24s
1313
1514
1705
1892
2073
2253
2421
921
H4
140
164
1 88
2O9
231
251
26*
ISI9
1753
1975
2192
2402
2611
2808
9f
121
148
174
199
222
245
267
263
1550
1788
2015
2237
2451
2664
2865
10
128
157
184
211
236
260
283
28J
1774
2047
2308
2562
2809
3053
3284
IOj
135
166
195
223
249
275
3OO
281
1808
2085
2351
2611
2862
3111
3347
104
143
175
206
236
264
291
317
30*
2049
2364
2666
2961
3247
3530
3799
io|
185
217
249
278
307
335
305
2085
2406
2713
3013
33°3
3592
3865
II
159
194
229
262
293
324
353
32?
2344
2705
3051
3389
3716
4042
4350
"1
I67
204
241
276
309
32!
2382
2749
3101
3445
3777
4108
4422
III
175
215
253
290
324
358
39i
34i
2658
3068
3462
3846
4218
4588
4940
II*
184
225
265
304
341
376
410
342
2699
3H5
3515
39°5
4283
4659
5016
12
192
236
278
319
357
395
430
36*
2992
3455
3898
4332
4751
5169
5566
I2j
2O I
247
291
334
374
4H
451
tf|
3035
3504
3955
4395
4820
5244
5647
III
211
259
305
350
392
433
472
385
3346
3864
4847
5317
5785
6231
I2|
22O
270
366
409
453
494
385
3392
3917
4421
4913
5390
5864
6316
13
23O
282
332
382
428
473
Si6
4O 4
3720
4296
4850
539°
59H
6435
6932
i3i
240
294
347
398
446
494
539
4^2"
3768
4352
49"
5460
5991
6519
7023
132
25O
307
361
415
465
515
562
42j
4"4
5364
5963
6543
7120
7672
131
260
319
376
432
485
536
585
425
4164
4810
5430
6037
6624
7209
7767
14
270
332
391
450
505
558
610
44|
4527
5229
5905
6565
7204
7840
8449
J4i
28l
345
407
468
525
634
458o
5291
5974
6642
7289
7933
8548
14!
292
359
423
486
546
&l
659
465
4961
5730
6472
7195
7896
8595
9263
I4l
303
372
439
SOS
567
627
685
46!
5016
5795
6544
7276
7986
8692
9367
15,
3H
386
456
524
588
651
711
48*
54H
6254
7064
7855
8621
9384
10115
i5i-
326
401
472
543
610
675
738
4^2
5472
6322
7140
7939
8714
9486
10224
15!
338
415
490
563
632
700
765
5^4
5887
6801
7683
8543
9377
10208
11004
is!
35°
430
507
583
655
725
792
505"
5948
6871
7762
8631
9475
10314
11118
Moment of Inertia of Net Area = Tabular Value X Net Area -r- Gross Area (approx.).
74
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
me—"
T
Moments of Inertia
j
For Distances
of Four Angle*,
Axis X-X.
X X
•
Measured
from
Long Leg* Turned Out.
1
Back to Back.
Size.
5" X 3". Long Legs Turned Out.
Thick.
A"
1"
ft"
»"
ft"
1"
H"
Thick.
1"
ft"
r
ft"
1"
IV
. \H-.l .4, s
9.60
n.44
*3-»4
15.00
16.72
'8.44
20.12
Area 4 [s
11.44
13-24
15.00
16.72
18.44
20.12
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
64
73
83
93
104
114
123
132
6J
78
90
IO2
114
125
135
H5
7
83
98
III
124
136
H7
158
Ifi
820
942
1062
1179
1290
1401
71
90
106
1 2O
134
148
159
171
18
845
970
1094
1214
1329
1443
7*
97
"5
130
145
160
173
1 86
20
1024
1178
1329
1475
1616
1755
7i
105
124
I4O
157
172
187
201
20;
1052
1209
1364
1514
1659
1802
8
"3
133
151
169
1 86
20 1
217
22;
1251
1440
1625
1804
1978
2I5O
81
121
142
l62
181
200
216
233
22
1282
1475
1664
1848
2026
2202
B{
129
152
173
194
214
232
250
24i
1501
1728
1951
2167
2377
2585
8|
I38
163
185
207
229
248
267
24*
1534
1766
1994
2215
2430
2642
9
147
173
197
221
244
265
286
26}
1774
2043
2307
2564
2813
3060
9t
IS6
184
2IO
236
260
282
304
26*
1810
2085
2354
2615
2871
3122
9i
166
196
223
250
276
300
334
281
2070
2385
2694
2994
3286
3575
9i
176
208
237
265
293
3i8
344
28i
2109
2429
2744
3049
3348
3642
10
1 86
220
251
28l
310
337
365
3°1
2389
2753
3110
3457
3796
4130
iol
197
232
265
297
328
357
386
30*
2430
2801
3164
3517
3863
4203
rol
207
245
280
3H
346
377
408
32
2730
3H7
3556
3954
4343
4726
10!
219
258
295
331
366
398
431
32i
2774
3198
3614
4018
4414
4803
ii
230
272
3"
349
385
420
454
34i
3094
3568
4032
4484
4927
5362
nl
242
286
327
367
405
442
478
34
3H2
3623
4094
4552
5002
5444
n|
254
300
342
385
426
464
502
36:
3482
4016
4539
5047
5547
6038
ii|
266
315
360
404
447
487
527
36.
3532
4073
4604
5120
5627
6126
'12
277
330
377
424
469
5"
553
381
3892
4489
5°7S
5645
6205
6755
12}
292
345
395
444
491
535
579
38*
3945
4551
5144
5721
6289
6847
I2j
305
361
413
464
513
560
606
4°
4325
4990
5641
6275
6899
7512
I2j
3i8
377
432
485
537
585
634
4°i
4381
5054
57H
6356
6988
7609
13
332
393
451
506
560
611
662
42i
4781
5517
6237
6939
7630
8309
I3t
346
410
470
528
585
638
691
42:
•
4839
5584
63H
7024
7724
8411
13*
361
427
490
550
609
665
721
44:
5259
6070
6864
7636
8398
9146
I3l
375
444
Sio
573
634
693
75i
44i
5321
6141
6944
7726
8497
9253
H
390
462
530
596
660
721
782
46]
5761
6650
7520
8367
9203
10023
Hi
406
480
55i
620
687
750
813
46]
•
5825
6724
7604
8461
9306
10136
Hi
421
499
573
644
713
779
845
48j
6286
7256
8206
9132
10045
10941
Hi
437
518
595
668
74i
809
878
48*
6353
7334
8294
9229
10153
11058
IS
453
537
617
694
769
840
911
Sol
6833
7889
8922
9929
10923
11899
i5i
470
557
639
719
797
871
945
Soi
6903
7970
9014
10031
11036
1 202 1
is*
487
577
662
745
826
903
979
52;
74°3
8548
9668
10760
11839
12897
isi
504
597
686
772
855
935
1015
52!
7476
8632
9764
10866
11956
13024
16
521
618
710
799
885
968
1050
54i
7996
9234
10445
11625
12791
13935
16!
539
639
734
826
916
1002
1087
54!
8072
932i
10544
"735
12913
14067
i6i
557
660
759
854
947
1036
1124
56;
8612
9946
11251
12523
13781
15014
i6|
575
682
784
882
978
1070
1162
SV
8691
10037
"354
12637
13907
15152
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
75
TABLE 33. — Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
' — jy — '"— ;r
Moments of Inertia For Distances
of Four Angles, X X , Measured
Axis X-X, a from
Long Legs Turned Out. Back to Back.
Size.
5" x 3%"> Long Legs Turned Out.
Thick.
iV
t"
iV
\"
ft"
I"
ii"
I"
Thick.
!"
ft"
i"
iV
1"
\\"
!"
Area 4 [s
10.24
12. 2O
14.12
16.00
17.88
19.68
21.48
23.24
Area4Ls
12. 2O
14.12
16.00
17.88
19.68
21.48
23.24
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, InA
-1
98
us
131
H5
160
171
187
198
7!
105
124
141
157
173
1 88
202
2I4
8
133
152
169
1 86
202
218
231
20J
1060
1221
1375
1530
1676
1821
1957
81
121
143
163
182
200
217
235
249
20^
1088
1254
1412
1571
1721
1871
2OII
130
153
175
195
215
233
252
268
22j
1298
1497
1686
1876
2057
2236
2405
si
139
163
I87
208
230
249
270
287
225
133°
1533
1727
1922
2107
2291
2464
9
148
174
2OO
222
246
267
288
307
Hi
I56l
I800
2029
2259
2477
2694
2899
9i
158
1 86
213
237
262
284
308
328
242
1595
1840
2074
2309
2532
2754
2964
9l
I67
197
226
252
279
303
328
349
265
1848
2132
2404
2677
2937
3194
3439
9*
I78
209
240
268
296
322
348
265
1886
2175
2453
2732
2997
3260
3510
10
188
222
254
284
3H
341
37°
394
281
2159
2492
2810
3131
3435
3738
4026
I0j
199
235
269
3OO
332
362
392
418
2o;j
22OO
2539
2864
3190
3501
3809
4102
io|
2IO
248
284
318
382
4H
442
3^4
2495
2880
3249
3621
3974
4325
4659
io|
221
26l
3OO
335
371
404
438
467
3°2
2539
2930
3306
3684
4044
4401
474i
II
233
275
316
353
391
426
462
493
3 24
2856
3296
3720
4H6
4551
4954
5339
III
245
290
332
372
412
449
486
519
32^
29O2
335°
3781
4214
4626
5036
5427
III
258
3°4
349
391
433
472
512
547
341
3240
3741
4223
4707
5168
5627
6065
III
27O
32O
367
4ii
455
496
538
574
34s
3290
3798
4288
4780
5248
57H
6159
12
284
335
385
431
477
520
564
603
361
3649
4214
4758
5304
5825
6342
6838
12\
297
35i
403
451
500
546
592
633
362
3702
4275
4827
538i
5909
6435
6938
12^
367
422
472
524
571
620
663
38?
4083
4715
5325
5937
6520
7101
7657
I2|
325
384
441
494
548
598
648
694
382
4139
4779
5398
6019
6610
7199
7763
i3i
339
401
460
516
573
625
678
725
1
4541
5244
5924
6606
7255
7902
8523
354
418
481
539
598
652
708
758
4°i
4600
5312
66oi
6692
7350
8005
8634
13!
369
436
501
562
623
68 1
738
791
42!
5023
5802
6555
7310
8030
8747
9435
13!
384
454
522
586
650
709
770
824
425
5085
5873
6636
7400
8129
8855
9552
14
399
473
543
610
677
739
802
859
44?
5530
6388
7217
8050
8843
9634
10393
Hi
492
565
634
704
769
835
894
44?
5595
6463
73°3
8i45
8948
9748
10517
Hi
432
5"
587
659
732
800
868
93°
6061
7002
7912
8826
9697
10564
H399
. Hi
448
531
610
685
761
831
902
967
46?
6129
7080
8001
8925
9806
10683
11527
i5t
465
551
633
711
790
863
938
1004
484
6616
7644
8639
9637
10589
"537
12450
482
657
738
819
895
972
1042
48^
6687
7726
8732
974i
10703
11662
12585
15^
500
592
68 1
765
849
929
1008
1081
5°i
7196
8315
9398
10485
11521 12554
13548
isf
518
613
70S
792
880
962
1045
II2I
5°2
7270
8400
9495
10593
11640
12684
13688
16
536
635
730
820
912
997
1082
1161
521
7800
9013
10189
11368
12492
13613
14693
i6j
554
657
756
849
943
1032
II2O
1 202
S2|
7878
9103
12090
11481
12616
13748
14839
t6f
573
679
878
976
1067
IIS9
1244
8429
9740
IIOI2
12287
13503:14715
15884
i6|
592
702
808
908
1009
1104
1199
1286
542
8509
9833
IIII7
12404
13632
14856
16035
18
693
821
945
1063
1182
1294
1406
1510
56?
9082
10496
II867
13241
14553
15860
17121
i8j
714
846
974
1096
1219
1334
1449
1556
562-
9165
10592
II976
13363
14687
16006
17279
i8|
735
872
1004
1129
1256
1374
1493
1604
581
9759
11279
12754
14232
15642
17048
18405
i8f
757
897
1033
1163
1293
1415
1538
1652
58^
9846
H379
12867
14358 15781
17199
18569
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
76
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
'==n[r==' T
j
Moments of Inertia
For Distance*
of Four Angle*, X X i
Axi* X-X, " «
Measured •
from
Long Legs Turned Out.
1
Back to Bade.
Size.
6" X 4"» koQg L«gs Turned Out.
Thick.
i"
A"
1"
A"
1"
W
I"
11"
i"
II"
i"
Area 4 1*
14-44
16 72
19.00
21.24
33-44
25.60
27.76
29.88
31.92
34-o°
36.00
d"
Moments of Inertia About Axis X-X for Various Distance* Back to Back of Angles, In.*.
8
I78
203
227
251
273
293
3H
333
352
370
385
10
273
312
350
387
423
455
489
521
551
581
606
10
288
330
370
409
448
482
5i7
552
583
6T5
642
It
408
468
526
583
639
689
791
839
886
927
12
427
490
551
6X1
669
722
777
829
879
929
972
M
572
658
740
822
901
974
1049
1122
1190
1259
1320
14
595
684
770
855
937
1013
1092
1167
1238
1310
1374
16
765
88 1
992
1103
I2IO
1310
1413
1512
1605
1700
1784
16
791
911
1027
1141
1252
1356
1462
1564
1662
1760
1848
18
987
H37
1282
1426
1566
1698
1831
1961
2084
2209
2321
18
1017
1171
1321
1470
1614
1750
1888
2O22
2149
2277
2393
20
1238
1427
1611
1792
1969
2136
2306
2471
2627
2786
2930
20
1271
H65
1654
1841
2O23
2195
2369
2539
2700
2863
3011
22
1518
1750
1977
2201
2419
2626
2836
3040
3234
3431
3611
22
1555
1793
2025
2255
2478
2691
2906
3315
3701
24
1826
2107
2381
2652
2916
3167
3421
3669
3905
4144
4363
24^
1867
2154
2434
2711
2981
3238
3498
3752
3993
4238
4463
26;
2164
2497
2823
3H5
3459
3759
4062
4358
4639
4925
5188
26
2208
2548
2881
32IO
3530
3837
4146
4448
4736
5027
5296
28
2530
2920
3303
3681
4050
4402
4759
5IO6
5438
5775
6085
28
2578
2976
3366
3751
4127
4486
4850
5204
5542
5885
6202
.30;
2925
3377
3821
4259
4687
5097
55"
59H
6300
6692
7054
30
2977
3437
3889
4335
4770
5187
5609
6020
6412
6810
7180
32
3349
3868
4377
4880
537i
5842
6318
6782
7226
7677
8094
32|
3404
3931
4450
4961
5460
5939
6423
6895
7346
7804
8230
34
3802
4391
4971
5544
6102
6639
7181
7710
8216
8730
9207
34
3861
4459
5048
5629
6197
6743
7293
7830
8344
8865
9351
36
4284
4949
5604
6249
6880
7488
8100
8698
9269
9851
10392
36;
4346
5021
5685
6341
6981
7597
8219
8825
9406
9995
10545
38
4795
5539
6274
6998
7705
8387
9074
9745
10387
11040
11649
38
4861
5616
6360
7094
7811
8503
9200
9880
10531
11192
11811
40
5334
6164
6982
7788
8577
9337
10104
10852
11568
12297
12978
40
5404
6244
7073
7890
8689
9460
10236
10995
11720
12458
I3H9
42
5903
6821
7728
8622
9495
10339
11189
12019
12813
13622
14378
42
•
5976
6906
7824
8729
9613
10468
11328
12169
12974
I379I
H558
44
6500
7512
8512
9497
10461
11392
12329
13245
14122
15015
15851
44
6577
7601
8613
9610
10585
11527
12476
13403
14291
I5I93
16040
46
7127
8237
9334
10416
"473
12496
13526
H532
15495
16476
17396
46
7207
8330
9440
10533
11603
12638
13679
14697
15671
16662
17594
48
7787
8995
10194
11376
12533
13651
H777
15878
16932
18005
19013
48
•
7866
9092
10305
11499
12668
13800
H938
16050
17116
18199
19220
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
77
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
c=ll[f==' — ^
Moments of Inertia
of Four Angles,
Axis X-X,
Long Legs Turned Out.
f
X
For Distances
Measured
* from
Back to Back.
1 *
Size.
6" X 4", Long Legs Turned Out.
Thick.
1"
A"
i"
ft"
i"
tt"
1"
11"
V
IS"
i"
Area 4 [s
14.44
16.72
19.00
21.24
23-44
25.60
27.76
29.88
31.92
34.00
36.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
SOS
53|
8466
8553
9179
9270
9786
9887
10611
10716
11093
11207
12029
12148
12379
12508
13425
13559
13639
13780
14792
14939
14858
15012
16116
16277
16085
16252
17447
17622
17284
17464
18749
18937
18433
18625
19997
20197
19602
19805
21267
21478
20701
20917
22462
22687
541
545
56*
5«*
9921
IOOI5
10691
10789
11469
H579
12361
I247S
13003
13127
14015
14144
I45I3
14652
15644
15788
15992
16145
17238
17397
I742S
I7S92
18785
18958
18866
19047
20339
20527
2O275
20470
2l86o
22O62
21626
21833
23318
23533
23000
23220
24801
25029
24295
24529
26200
26443
0
II49I
H593
12319
12425
13286
13404
14244
H367
15065
15199
16153
16292
16817
16967
18032
18187
18532
18697
19873
20043
20196
20376
21659
21845
21869
22064
23453
23655
23505
23715
25209
25427
25074
25297
26894
27125
26669
26907
28606
28852
28176
28429
30225
30486
62!
64*
64!
13176
13286
14063
HI75
15236
15363
16262
16392
17279
17423
18443
18592
19291
I945I
20591
20757
21260
21437
22694
22877
23172
23365
24737
24937
25094
25303
26790
27006
26974
27199
28798
29030
28778
29017
30725
30972
30611
30866
32684
32947
32346
32616
34539
34818
66\
6s|
68^
14978
15094
15922
16042
17321
17455
18413
18552
19646
19799
20886
21043
21934
22105
23320
23496
24175
24364
25703
25898
26353
26559
28021
28233
28541
28764
30348
30578
30682
30922
32625
32873
32736
32991
34811
35074
34825
35097
37034
37314
36803
37092
39HO
39437
701
705
72!
16894
I70I8
17896
18023
19539
19682
20698
20845
22164
22326
23480
23647
24747
24929
26218
26405
27278
27478
28900
29106
29739
29958
31509
31734
322IO
32447
34128
34372
34629
34885
36692
36955
36950
37221
39153
39432
39311
39600
41656
41953
4IS49
41855
44030
44345
78f
19057
2OI2I
2I2I2
22333
22042
23272
24536
25833
25006
26403
27838
29311
27923
29484
31087
32733
30781
32502
34270
36086
3356i
35440
37370
39350
36352
38388
40480
42627
39086
41276
43526
45836
41707
44045
46447
48914
44375
46864
49422
52047
46907
49540
52246
55024
CO CO CO CO
CO O-v-f- to
MlHMlMWlMMl-1
23483
24662
25869
27105
27164
28528
29925
31356
30822
32370
33957
35582
34421
36151
37925
39740
37948
39857
41812
438i5
41383
43466
45600
47786
44829
47087
49401
51770
48205
50634
53123
55672
51444
54037
56695
59417
54741
57502
60332
63229
57874
60795
63789
66855
<s
945
96*
28371
29665
30988
32340
32821
34318
35850
374H
37245
38946
40685
42462
41598
43499
45442
47427
45865
47961
50105
52295
50023
523"
54651
57041
54194
56674
59210
6l8oi
58281
60949
63677
66465
62202
65051
67964
70941
66195
69228
72330
75499
69993
73202
76484
79838
100^
1025
1045
33720
35130
36569
38036
39012
40644
43309
44007
44277
46129
48020
49949
49455
51526
53639
55794
54532
56816
59H7
61524
59483
61976
64520
67115
64448
67150
69908
72721
69312
7222O
75187
78214
73982
77086
80254
83487
78736
82402
85415
88857
83264
87761
90331
93973
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
78
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
=^r7= r
I
Moments of Inertia For Distance*
of Kour Angles. Jf X i Measured
Axis X-X. - 0 from
Long Legs Turned Out. Back to Back.
Size.
8" X 6". Long Legs Turned Out.
Thick.
A"
\"
A"
I"
\V
i"
H"
I"
Jl"
z"
Area 4 Is
37.00
30-34
33-44
36.60
39-76
43.88
45-9*
49.00
53.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.*.
12
624
704
778
853
926
997
IO62
1128
"93
1255
H
84I
950
1053
1156
1256
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1536
1627
1714
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1096
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1410
1505
1600
1695
1786
16
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1283
1423
1564
1701
1837
1963
2089
2214
2335
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2033
2164
2295
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2398
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2733
2900
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2474
2647
2820
2993
3159
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2109
2346
2581
2812
3040
3255
3469
3683
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2168
2411
2654
2891
3125
3347
3568
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4030
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3833
4271
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6869
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9237
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7238
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8558
9190
9814
10443
11050
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5273
5985
6675
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5905
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12664
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401
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10727
11836
12927
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15062
16094
17136
18145
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16495
17627
18770
19877
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11892
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15538
16705
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19010
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10216
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15623
16937
18213
19466
20730
21955
44!
10339
11746
13116
14476
15812
I7H3
18434
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20981
22222
461
11221
12748
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17167
18612
20017
21396
22787
24136
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12895
14402
15895
17365
18828
20249
21643
23051
24416
12273
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18783
20367
21907
23417
24943
26422
48!
12408
14098
IS747
17382
18990
20593
22149
23677
25219
26715
50;
13372
I5I9S
16974
18738
20473
222OI
23882
25531
27196
288II
50;
I35I3
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I7I53
18936
20689
22437
24135
25082
27485
29II7
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I4SI9
16499
18433
20350
22236
24II5
25944
27737
29548
31304
14666
16666
18620
20556
22462
24360
26207
28019
29848
31623
Moment of Inertia of Net Area = Tabular Value X Net Area -i- Gross Area (approx.).
79
TABLE 33.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
LONG LEGS TURNED OUT.
' — [l|r~"""T
Moments of Inertia
of Four Angles, X
Axis X-X, *
Long Legs Turned Out.
X
For Distances
Measured
from
Back to Back.
led Out.
i . i
£ Legs Tur
Size.
8" X 6", Lon
Thick.
iV
1"
ft"
i"
ii"
i"
1?"
i"
ir
i"
Area 4|s
23.72
27.00
30.24
33-44
36.60
39-76
42.88
4S-92
49.00
52.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.1*.
54i
542
56*
561
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Moment of Inertia of Net Area = Tabular Value X Net Area -J- Gross Area (approx.).
80
TABLE 34.
MOMENTS OF INERTIA OF FOUR ANCLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
T
Moments of Inertia For Distance*
of Four Analcs, X A Measured
Axis X-X, from
Short Legs Turned • hit. Back to Back.
JL,
Size.
3" X atf". Short Legt Out.
3," X aj". Short Legs Out.
4" X 3", Short Legs Out.
Thick.
i"
A"
1"
A"
i"
I"
A"
1"
A"
i"
A"
1"
A"
1'
A"
Area4|s
3-»4
6.48
7-68
8.88
IO.OO
5.76
7.12
8-44
9.72
11.00
8.36
992
".48
13.00
•4.48
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
6}
33
41
47
53
59
Ox
37
44
58
65
7
40
48
56
64
7*
43
53
61
70
77
7\
47
57
66
76
84
47
57
67
76
84
7\
62
72
82
91
51
62
72
82
92
8
55
67
78
89
98
55
67
78
89
99
8*
59
72
84
95
106
60
72
84
96
107
8}
63
77
90
IO2
114
64
78
91
103
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88
103
118
131
144
82
68
83
96
no
122
69
83
97
in
124
95
ill
127
155
9
72
88
103
118
131
73
89
104
119
133
IOI
119
136
151
166
9i
77
94
no
125
140
78
95
112
127
142
108
127
H5
161
178
82
100
117
134
149
84
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119
136
152
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135
155
172
190
92
87
107
124
142
158
89
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127
144
162
123
144
165
184
202
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92
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132
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168
94
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153
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130
153
175
195
215
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98
120
140
160
178
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122
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163
182
138
162
1 86
207
229
lOJ
104
127
148
169
189
106
129
173
193
H7
172
197
220
242
10}
109
134
156
179
200
112
136
160
183
205
155
182
209
233
257
II
"5
141
165
189
211
118
144
169
193
216
164
192
221
246
272
III
121
149
174
199
222
125
152
179
204
228
173
203
233
260
287
Hi
127
I56
183
2IO
234
160
188
215
241
182
214
245
274
303
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164
192
220
246
138
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198
226
253
192
225
2S8
289
319
12
140
172
202
231
2S8
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177
208
237
266
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237
272
304
335
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181
211
243
271
152
1 86
218
249
280
211
249
285
319
352
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189
222
254
284
159
195
229
261
293
222
261
299
335
370
12i
161
198
232
266
297
167
204
240
274
308
232
273
314
388
13
168
207
242
278
3"
175
213
251
287
322
243
286
329
368
406
13*
176
216
253
290
325
182
223
262
300
337
254
299
344
385
425
13^
184
225
264
303
339
190
233
274
313
352
265
313
359
402
444
13!
191
235
275
316
353
199
243
286
327
367
277
326
375
420
464
14
199
244
287
329
368
207
253
298
341
383
289
340
391
438
484
Hi
207
254
299
343
383
216
264
3"
355
400
301
355
407
457
505
Hi
215
266
310
357
399
224
275
323
370
415
313
369
424
476
526
Hi
223
275
323
37i
415
233
286
336
385
432
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442
495
548
IS
232
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431
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SIS
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296
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366
431
495
556
615
is)
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318
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430
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271
332
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503
379
447
5H
577
639
16
268
33°
387
445
498
281
344
405
464
522
393
464
533
599
663
16*
277
341
401
461
516
291
3 Co
420
480
540
408
481
553
620
687
loj
287
353
415
477
534
301
369
434
497
560
422
498
573
643
712
EO1
297
365
429
493
552
3ii
3^^
450
515
579
437
515
593
665
737
18
348
428
503
579
648
366
449
529
606
682
5H
607
699
785
870
184
358
441
519
596
669
377
463
546
625
704
53i
626
721
810
898
1 84
369
454
534
689
389
477
363
645
726
547
646
744
836
926
I8J
380
468
550
633
710
401
492
580
664
748
564
666
767
862
955
Moment of Inertia of Net Area = Tabular Value X Net Area -j- Gross Area (approx.).
81
TABLE 34. — Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
18
f
_,
Moments of Inertia For Distances
of Four Angles, X X d Measured
Axis X-X, from
Short Legs Turned Out. Back to Back.
JL ,.
Size.
S" X 3". Short Legs Turned Out.
Thick.
ft"
i"
&"
i"
_S_"
TS
I"
W
Thick.
i"
T78"
i"
TV
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11"
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15.00
16.72
18.44
20. 12
Area [45
11.44
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15.00
16.72
18.44
20. 12
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
I0|"
147
i74
198
222
244
265
286
22*
1046
I2O2
1356
1505
1649
1791
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210
235
259
281
303
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274
298
322
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1835
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2186
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174
206
235
263
29O
315
340
24*
1303
1499
1692
1878
2059
2238
II*
184
217
248
278
307
333
30O
26J
1523
1753
1979
2198
2410
262O
III
194
229
26l
293
323
352
380
26*
1556
1791
2O22
2245
2463
2678
12
2O4
241
275
309
341
371
4OI
281
1796
2068
2335
2594
2847
3950
12*
215
253
289
325
359
39°
422
28*
1831
2IO9
2382
2646
2904
3158
iaf
226
266
304
342
377
411
444
3°i
2091
2409
2721
3024
3320
36ll
i*l
237
282
319
359
396
43i
467
30*
2130
2454
2772
3080
3381
3678
13
248
293
335
376
416
453
490
32i
2410
2777
3137
3487
3829
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ijf
20O
307
35i
394
436
475
5H
32*
2451
2825
3192
3547
3896
4239
13*
272
321
367
413
456
497
538
34*
2751
3172
3584
3984
4376
4762
i3f
284
336
384
432
477
520
563
34*
2796
3223
3642
4048
4447
4839
14
297
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401
45i
499
544
589
36*
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5398
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52i
568
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Hi
323
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593
642
38*
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6074
Hi
336
398
456
512
567
619
670
38*
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698
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40*
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IS*
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4346
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665
726
787
42*
4402
5079
5742
6386
7021
7645
16
408
484
554
624
691
754
818
44i
4802
5541
6265
6969
7663
8344
16}
424
502
575
647
717
783
849
44*
4861
5609
6342
7055
7757
8447
i6|
439
520
597
672
744
813
881
46*
5281
6094
6891
7667
8431
9182
i6|
455
539
618
696
771
843
914
46*
5342
6165
6972
7756
8530
9289
17
472
558
641
721
799
873
947
48i
5782
6674
7547
8398
9236
10059
17*
488
578
663
747
827
904
981
48*
5847
6748
7632
8491
9339
10172
17*
505
598
686
773
856
936
1015
501
6307
7280
8234
9162
10078
10977
I7f
522
618
710
799
886
969
1051
5°5
6374
7358
8322
92 o
10186
11094
18
539
639
733
826
916
IOOI
1086
52*
6854
7913
8950
9960
10956
H935
181
557
660
758
854
946
i°35
1123
52*
6924
7994
9042
10062
11069
12057
l8f
575
682
782
882
977
1069
1160
54i
7425
8572
9696
10791
11872
12933
i8f
593
703
808
910
1009
1104
1198
54*
7497
8657
9792
10897
11989
13060
20
690
818
939
1059
1174
1285
1395
56i
8018
9258
10472
"655
12824
I397I
2Oj
710
841
967
1090
1209
1323
H37
56*
8094
9346
10572
11766
12946
14104
20*
730
866
995
1122
1244
1362
1479
58*
8634
9970
11279
12553
13814
15050
20j
751
890
1023
"54
1280
1401
1522
58*
8712
10061
11382
12668
13940
15187
21
772
915
1052
1186
1316
i44i
1565
6oJ
9273
10709
12115
13485
14840
16169
21*
793
94i
1081
1219
1353
1482
1609
60*
9354
10803
12222
13603
14971
16311
*lj
815
966
IIII
1253
1390
1523
1654
6z\
9935
11474
I298I
I44SO
15903
17328
Ml
837
992
1141
1287
1428
1564
1699
62*
10019
H57I
13092
I4S73
16038
17475
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
82
TABLE 34.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
T'
Moments of Inertia For Distance*
of Kour Ang es. JK. X i Measured
Axis X-X, from
Short Legs Turned Out. Back to Back.
A......
Size.
5"X 3i". Short Legs Turned Out.
Thick.
1"
ii"
*"
ft"
1"
»r
\"
Thick.
I"
A"
*"
ft"
1"
W
I"
Area 4 [s
12.20
14.13
16.00
17.88
19.68
21.48
"3-24
Area 4 [s
13.20
14.13
16.00
17.88
19.68
21.48
23.24
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
10
\
193
221
246
272
296
320
340
32:;
2001
3002
3388
3775
4H3
4509
4859
10
[
204
234
26l
288
3H
339
361
32;!
2646
3054
3446
3840
4214
4587
4942
II
216
247
276
305
332
359
382
34;;
2967
3426
3867
4309
473i
5H9
5550
II
t
228
26l
292
322
351
380
405
3015
348i
3929
4379
4807
5233
5639
II
..
240
275
308
340
371
401
428
36}
3358
3877
4378
4880
5357
5833
6288
Ilj
253
200
324
359
391
423
451
36*
3409
3936
/j.4,4/1
4953
5439
5921
6383
12
266
305
341
378
412
445
475
38*
3773
4357
4920
5485
6024
6559
7072
I 2
i
280
321
359
398
433
469
Soi
38|
3827
4419
4990
5564
6no
6653
7173
12
294
337
377
418
456
493
526
4213
4866
5495
6127
6729
7328
7903
f "2.
1
308
354
396
439
478
517
553
402
4270
493i
5569
6210
6820
7427
8010
13
323
370
415
460
502
543
580
42}
4677
5402
6102
6805
7474
8140
8780
13*
338
388
434
482
525
569
608
42*
4737
5471
6180
6892
7570
8245
8893
13*
353
406
454
504
550
595
637
44i
5165
5967
6741
7518
8258
8995
9704
13!
369
424
475
527
575
623
666
443
5228
6039
6823
7610
8359
9105
9822
14
386
443
496
551
601
651
6;6
46!
5678
6560
7412
8267
9082
9894 10674
Hi
402
462
518
575
627
679
727
46*
5744
6636
7498
8363
9188
10009 10798
14*
419
482
540
599
654
709
759
48*
6215
7181
8115
9052
9945 Io83S
11691
141
437
502
563
625
682
739
791
48*
6285
7260
8205
9152
10055 10955
11821
IS
454
522
586
650
710
770
824
5of
6777
7830
8850
9872
10847
11819
12754
is;
472
543
609
677
739
80 1
858
6849
7913
8944
9977
10963 11945
12890
IS
491
564
633
704
768
833
892
5°!
7363
8508
9617
10728
11789 12846
13864
15;
510
586
658
731
798
866
928
52*
7438
8594
9715 10838
11909
12977
14005
16
529
609
683
759
829
899
964
S4i
7973
9214
10415 11620
12770
I39I5
15020
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549
631
709
788
860
933
IOOO
54*
8052
9304
10518 11734
12895 HOS2
15167
16*
569
654
735
817
892
968
1038
561
8608
9948
11246
12548
13790 15028
16223
i6J
589
678
761
846
925
1^03
1076
56*
8689
10041
"352
12667
13921 15170
16376
18
697
803
902
1003
1097
1190
1277
58i
9267
10710
12109 I35i2
14850 16184 17472
18]
720
829
932
1036
"33
1230
1320
58*
9352
10807
12219113635
14985 i6332'i763i
18,
743
856
962
1070
1170
1270
1363
60}
9950
11501
13004
14511
I5949I7383
18768
i8j
767
883
992
1104
1207
1311
1407
60*
10038
11601
i3"8
14639
16089! 17536
18932
20
915
1055
1186
1319
1445
1569
1686
62!
10658
12319
I393I
15546
17088 18625
2OIIO
20
942
1085
1221
1357
1487
1615
1735
62*
10749
12424
14049
15678 17233(18783
2O28O
22
"35
1309
1473
1639
1796
1952
2099
64*
11391
13166
14890
16617 18266 19909
21498
22
"65
1342
ISII
1682
1843
2003
2153
64*
11485
13274
15012
16753
18416
20073
21675
24
1379
1591
1792
1995
2187
2377
2558
66J
12148
14042
15881
17724
19483
21237
22934
24
1412
1628
1834
2042
2239
2434
2618
661
12245
I4I53
16007
17864 19638 21406
23116
26
1648
1901
2H3
2386
2617
2846
3063
68]
12929
H945
16904
18866 20739 22608
24415
26
1684
1942
2189
2438
2674
2908
3129
68*
13029
15060
17034
19011
20899
22782
24603
28j
1941
2240
2526
2813
3086
3357
3615
7ol
13734
15^77 17958^0044
22035
24021
25943
28
1980
2284
2576
2869
3148
3424
3687
70*
13837
1599618093 20194
22200
24201
26137
30
2259
2607
2941
3276
3595
3912
4214
72i
14564
16837
19045
21258
23371
25478
27518
3oJ
2301
2655
2995
3337
3661
3984
4291
72*
14670
16959
19183
21412
23540
25663
27717
Moment of Inertia of Net Area = Tabular Value X Net Area -j- Gross Area (approx.).
83
TABLE 34. — Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
ir "r
Moments of Inertia For Distances
of Four Angles, J£ X fl. Measured
Axis X-X, from
Short Legs Turned Out. Back to Back.
JL,
Size.
6" X 4". Short Legs Turned Out.
Thick.
1"
&"
_i"
ft"
I"
W'
r
H"
V
18"
i"
Area 4 [s
'4-44 .
16:72
19.00
21.24
23-44
25.60
27.76
29.88
31.92
34.00
3* .00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
I2|"
322
370
414
459
502
541
581
619
655
691
722
i*i
442
508
57i
633
693
748
805
858
911
962
1007
Hi
461
530
595
660
723
78i
840
897
95i
1005
IO52
i6i
606
697
785
871
955
1033
III2
1188
1262
1335
I4OO
16*
629
723
814
904
991
1072
"55
1235
1311
1386
H54
i8i
799
920
1037
1152
1264
1369
1476
1578
1677
1776
1864
I8|
825
950
1071
1190
1306
HIS
1525
1632
1734
1836
1928
2Oj
1021
"77
1327
1476
1620
1756
1895
2028
2156
2285
2401
2O^
1051
I2II
1366
151
1668
1808
i95i
2089
2221
2353
2473
22\
12/2
1466
1655
1842
2023
2195
2369
2537
2699
2862
3010
22j
I30S
ISOS
1699
1890
2077
2253
2432
2606
2772
2939
3091
24*
ISS2
1790
202 1
2250
2473
2685
2899
3107
3306
3507
3691
242
1589
1832
2070
2304
2533
2749
2969
3183
3387
3592
3781
26J
1860
2146
2425
2701
2970
3226
3485
3736
3977
4220
4443
26£
1901
2193
2479
2760
3035
3297
3562
3819
4066
43H
4543
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2198
2536
2868
3195
3513
3818
4126
4424
4711
5001
5268
28£
2242
2587
2925
3259
3585
3895
4210
45i6
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5103
5376
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2564
2960
3348
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4104
4461
4822
5173
SSio
5850
6165
3oi
2612
3015
34io
3800
4181
4545
4913
5272
5614
596i
6282
32i
2959
3417
3866
4309
474i
5156
5574
598i
6372
6767
7134
34
3011
3476
3933
4384
4824
5246
5672
6087
6484
6886
7260
34*
3383
3907
4422
4930
5425
5901
6382
6849
7298
7752
8174
34^
3439
3971
4494
5010
55H
5998
6486
6963
7418
7880
8310
36|
3836
4431
5016
5593
6156
6698
7245
7777
8288
8805
9287
36|
3895
4499
5°93
5679
6251
6801
7356
7898
8416
8941
9431
38i -
4318
4988
5648
6299
6934
7546
8163
8764
934i
9926
10472
38i
438i
5060
5730
6390
7035
7656
8282
8893
9478
10071
10625
40^
4829
5579
6318
7047
7759
8446
9137
9812
10459
11115
11729
405
4895
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6405
7H3
7866
8562
9263
9948
10603
11268
11891
4*J
5369
6203
7026
7838
8631
9396
10167
10919
11640
12372
13058
425
5438
6283
7118
7940
8743
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10300
11062
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12534
13229
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5937
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8671
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10398
11252
12085
12885
13697
14458
442
6010
6945
7868
8778
9668
10527
11392
12237
13046
13867
14638
46i
6535
7552
8557
9547
10515
U45I
12393
13312
14194
15090
I593I
46^
6611
7640
8657
9659
10639
11586
12539
I347I
14363
15269
16120
*8|
7161
8276
9379
10465
11527
12555
13589
H598
15567
16551
17476
48£
7241
8369
9484
10583
11657
12697
13742
14764
15744
16738
17674
5oi
7816
9034
10239
11426
12587
13710
14841
15944
17004
18080
19093
5o£
7900
9i3i
10349
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12722
13858
15001
16118
17189
18275
19300
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9826
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12429
13693
14917
16148
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18505
19677
20781
52|
8588
9927
11252
12557
13834
15071
16315
I753I
18697
19881
20997
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (approx.).
84
IAMLE 34.— Continued.
in INERTIA OK FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
MI OUT LEGS TURNED OUT.
T
Moment* of Inertia
For Distances
i >ur Angles, JL A (
Measured
Axi. X-X.
I....I.
Short Legs Turned Out. Back to Back.
JL...1
Si«.
6" X 4". Short Legs Turned Out.
Thick.
1"
A"
»"
A"
t"
ii"
I"
ir
t"
11"
i"
Area 4 [a
14-44
16.73
19.00
21.24
23-44
25.60
27.76
29.88
31.92
34-<»
36.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.4.
54
//
9213
10650
12073
13475
14846
16175
175"
18816
20069 1 21342
22542
54
9304
10756
12193
13608
H993
16335
17685
19004
20269
21554
22767
56
9955
11509
13047
H563
16046
17484
18929
20341
21697
23075
24375
56
10049
11618
13172
14701
16199
17651
19110
20537
21906
23296
24609
58;
10725
12400
14059
15693
17292
18844
20403
21926
23389
24876
26280
58
10824
12514
14189
15837
17452
19016
20591
22130
23606
25105
26523
60
US2S
13325
15110
16866
18586
20255
21932
23571
25H5
26744
28256
60
11627
13443
15244
17016
18751
20434
22127
23782
25370
26983
28509
62
12353
14284
16198
18082
19927
21718
23517
25276
26965
28681
30305
62
12459
14406
16336
18237
20097
21903
23719
25494
27197
28928
30566
64
13211
15276
17324
19340
21314
23231
25157
27040
28849
30686
32426
64
13320
15402
17467
19500
21491
23423
25366
27266
29089
30942
32696
66
14097
16301
18488
20641
22748
24796
26853
28C6<;
30796
32759
34619
66
14210
16432
18636
20806
22931
24994
27069
29098
31045
33023
34898
68
15012
17360
19690
21984
24229
26412
28604
30748
32807
34900
36883
68
15128
17495
19843
22154
24418
26617
28827
30989
33064
35173
37172
70
15956
18453
20930
23369
25758
28080
30411
32692
34882
37109
39220
70
16076
18591
21088
23545
25952
28291
30641
32940
35H7
37390
39517
72
16929
19578
22208
24797
27332
29798
32274
34696
37021
39386
41629
72
17052
19721
22371
24978
27533
30016
32510
34951
37294
39676
41935
74
18058
20885
23692
26454
29160
31792
34435
37022
39505
42O29
44425
.76:
19092
22082
25051
27972
30835
33619
36416
39152
41780
44451
46987
78
20155
23312
26447
29533
32556
35498
38452
41343
44118
46940
49620
80
21247
24576
27882
31136
34325
37427
40543
43593
46520
49498
52326
82
22368
25873
29355
32782
36140
39408
42690
45902
48986
52123
55104
84
23517
27203
30866
34470
38002
41440
44892
48272
51516
54817
57954
86
24696
28567
32415
36201
399"
43524
47150
50701
54110
57578
60875
88
25903
29965
34002
37974
41867
45658
49464
53190
56768
60408
63869
90
27140
31396
35627
39789
43869
47844
51833
55739
59489
63305
66935
92
28405
32860
37290
41647
45919
50081
54258
58347
62275
66271
70073
94
29699
34358
38990
43548
48015
52369
56738
61016
65124
69304
73282
96
31022
35889
40729
45491
50IS9
54708
59273
63744
68037
72406
76564
98
32374
37454
42506
47476
52349
57099
61864
66531
71014
75575
79918
IOO
33755
39052
44321
49504
54586
59541
64511
69379
74054
78812
83344
IO2
35164
40683
46i74
51575
56870
62034
67213
72286
77159
82118
86841
IO4
36603
42348
48065
53688
59201
64578
69971
75253
80327
85491
90411
io6J
38070
44047
49994
55843
6i579
67173
72784
78280
83560
88933
94053
io8i
39566
45779
51961
58<HI
64003
69820
75653
81367
86856
92442
97767
noj
41092
47544
53966
60282
66475
72SI7
78577
84513
90216
96020
101553
iia|
42646
49343
56008
62564
68993
75267
8I5S7
87719
93639
99665
105410
Moment of Inertia of Net Area = Tabular Value X Net Area •*• Gross Area (approx.).
85
TABLE 34.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
HIT ""
Moments of Inertia For Distances
of Four Angles, J[ X d Measured
Axis X-X, from
Short Legs Turned Out. Back to Back.
JL *
Size.
8" X 6", Short Legs Turned Out.
Thick.
A"
i"
A"
1"
W
1"
H"
i"
11"
i"
Area 4 [s
23.72
27.00
30.24
33-44
36.60
39 -76
42.88
45-92
49.00
52.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.*.
i6J"
955
1079
1197
I3H
1429
1541
1645
1750
1854
1954
ijjf
1214
1373
1524
1675
1822
1967
2103
2238
2373
2503
I8J
1254
1418
1575
1731
.1883
2033
2174
23H
2454
2588
20j
1554
1759
1955
2150
2341
2520
2706
2883
3059
3229
20j
1600
1812
2013
2215
2411
2605
2788
2970
3152
3327
22*
1942
22OO
2447
2692
2933
3170
3395
3619
3842
4058
22^
1994
2259
2512
2765
3012
3256
3488
3717
3947
4169
24i
2377
2694
2999
3301
3508
3891
4170
4447
4724
499i
24^
2435
2760
3072
3382
3686
3987
4273
4557
4841
5H5
26J
2860
3243
3611
3977
4336
4692
5031
5366
5703
6029
26^
2924
3315
3692
4066
4433
4797
5H4
5488
5833
6166
28i
3390
3845
4284
4720
5H7
5572
5977
6378
6781
7170
28^
3460
3924
4372
4818
5254
5687
6101
6511
6923
7320
3oi
3968
4501
5017
5530
6032
653i
7009
7482
7956
8416
30*
4043
4587
5"3
5635
6148
6636
7144
7626
8110
8579
32i
4593
5212
5811
6406
6990
7570
8127
8677
9230
9765
32*
4674
53°4
59H
6520
7"5
7705
8273
8833
9396
9941
34*
5265
5976
6665
7349
8021
8688
933i
9964
10602
11218
34*
5353
6075
6776
7472
8i5S
8834
9487
10131
10780
11407
36*
5985
6794
758o
8360
9125
9886
10620
H343
12071
12776
36*
6078
6900
7698
8491
9268
10042
10787
11522
12262
12978
38*
6752
7667
8555
9437
10303
11164
ii995
12814
13639
H437
3 81
6852
7780
8681
9576
10455
11329
12173
13004
13841
14652
40?
7567
8593
959i
10581
H553
12521
13456
14376
15304
16203
4°2
7672
8713
9725
10728
11715
12696
13645
14578
I55I9
16431
42^
8429
9573
10687
11791
12877
13957
15003
16031
17068
18072
42?
8540
9700
10828
11948
13048
I4H3
15202
16244
17295
18313
44t
9339
10608
11844
13069
14274
15473
16635
17777
18929
20045
44i-
9456
10741
U993
13234
H454
15668
16845
18002
19169
20299
46£
10296
11696
13061
14414
15744
17069
18354
19615
20889
22123
46*
10419
11836
13217
I4S87
15933
17274
18574
19852
21140
22390
48i
11301
12839
14339
15825
17288
18744
20158
21545
22946
24304
48*
11430
12985
14502
16007
17486
18959
20389
21793
23210
24584
5ol
12353
H03S
15677
17304
18904
20499
22047
23567
25102
26590
50*
12487
14188
15848
17493
19111
20734
22290
23827
25378
26883
s4
13452
15285
17075
18849
20504
22333
24023
25681
27355
28979
52*
13593
15445
17254
19047
20810
22568
24277
25952
27644
29285
54*
14599
16590
18534
20461
22357
24246
26084
27887
29707
3H72
54?
14746
16757
18721
20667
22583
24491
26349
28169
30007
3i79i
56*
15793
17948
20054
22140
24193
26240
28231
30184
32156
34070
56*
IS946
18122
20248
22355
24428
26494
28506
30478
32469
34402
Moment of Inertia of Net Area = Tabular Value X Net Area -f- Gross Area (approx.).
86
TABLE 34.— Continued.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis X-X.
SHORT LEGS TURNED OUT.
T" f
Moments of Inertia J J For Distances
of Four Ang es.
Axis X-X. *
v
\
K ,1 Measured
T from
Short Legt Turned Out. Back to Back.
JL....I
Size.
8" X 6". Short Legt Out.
Thick.
A"
J"
A"
1"
H"
i"
jg"
i"
tt"
i"
Area4l§
33.73
27.00
30.24
33.44
36.60
;t>7"
43.88
45-9»
49.00
52.00
d"
Moments of Inertia About Axis X-X for Various Distances Back to Back of Angles, In.*.
58]
"
I703S
19360
21634
23886
26103
28312
30464
32573
34704
36771
58=
I7I94
I954I
21836
24109
26347
28577
30750
32878
35029
37"6
60
18324
20827
23274
25699
28085
30465
32782
35054
37349
39577
60
18489
21014
23484
25930
28338
30739
33079
35371
37687
39935
62:
Io66l
22347
24975
27578
30141
32696
35187
37627
40093
42486
62*
19831
22541
25192
27818
30403
32981
35494
37955
40442
42857
64;
2I04S
23922
26737
29525
32270
35007
37677
40292
42934
45499
64i
2I22I
24122
26961
29773
32541
35302
37995
40631
43296
45883
66J
22476
25550
28559
31538
34472
37398
40252
43048
45874
48617
66J
22659
25757
28791
31795
34753
37703
40581
43400
46248
49014
68]
23955
27232
30441
33619
36748
39869
42914
45897
48911
51838
68]
24H3
27446
30681
33884
37037
40183
43254
46259
49298
52248
70}
25482
28969
32384
35766
39096
42418
45661
48837
52047
55l64
70*
25676
29190
32631
36039
39395
42743
46012
49211
52446
55587
72i
27056
30759
34388
37980
41518
45048
48494
51869
55280
58593
72*
27256
30987
34642
38261
41826
45382
48856
52255
55691
59029
74*
28883
32838
36714
40551
44330
48101
51785
55390
59035
62575
76*
30557
34743
38846
42907
46908
50899
54800
58617
62477
66226
78J
32279
36702
41038
45330
49558
53777
57901
61937
66017
69980
8oJ
34049
387IS
43291
47820
52282
56734
61088
65347
69654
73839
82J
35866
40782
45604
50377
55079
59771
64361
68850
73390
77801
.841
37730
42903
47978
53000
57949
62887
67719
72445
77224
81867
86J
39642
45078
50412
55691
60893
66083
71163
76131
81156
86038
88*
4l6oi
47308
52907
58449
63909
69359
74693
79910
85185
90312
90|
43608
49591
55463
61273
66909
72714
78309
83780
89313
94691
92i
45662.
51928
58078
64164
70162
76148
82010
87742
93539
99173
94"
.
47764
54319
60755
67122
73398
79662
85797
91796
97863
103759
96]
49913
56764
63491
70147
76707
83256
89670
95941
102284
108450
98,
-
52109
59263
66288
73239
80090
86929
93629
100179
106804
113244
IOO
54353
61816
69146
76398
83546
90681
97674
104508
114422
118143
IO2-
-
56645
64423
72064
79623
87075
94513
101804
108929
116138
123145
104)
l
58983
67085
75043
82916
90677
98425
106020
113442
120951
128251
106]
61370
69800
78082
86275
94352
102416
110321
118047
125863
133462
108
63803
72569
81182
89702
98101
106487
114709
122744
130873
138776
no
66284
75392
84342
93195
101923
110637
119182
"7532
I3598I
144195
II2J
68813
78269
87562
96755
105818
114867
123741
132413
141186
H97I7
114
71389
81200
90843
100382
109786
119176
128386
U7385
146490
155343
n6J
74012
84185
94185
104075
113827
123564
133116
142449
151892
161074
118
76683
87224
97587
107836
117942
128033
137993
147605
157392
166908
120
79402
90318
101049
111664
122129
132580
142835
152853
162990
172847
Moment of Inertia of Net Area = Tabular Value X Net Area -5- Gross Area (appro*.).
87
TABLE 35.
MOMENTS OF INERTIA OF FOUR ANGLES WITH EQUAL LEGS, Axis Y-Y.
Moments of Inertia
of Four Angles,
Axis Y-Y,
Equal Legs.
L
r
For Distances
Measured
from
Back to Back.
Distance Back to Back in Inches.
89
.2 B
ox;
all
•<
Distance Back to Back in Inches.
In.
i
A
t
ft
1
In.
1
3X3X1
; A
5-44
5-76
7.12
8-44
9.72
n.oo
12.24
13-44
2.1
2.7
3-4
4.2
9.0
11.4
13-7
16.0
18.4
20.8
23-3
2-5
3-3
4-2
5-i
10.3
I3-I
iS-7
18.4
26.5
2.6
3-5
4-4
5-3
10.7
I3-S
16.3
19.0
21.9
24.7
27-5
2.8
3-7
4.6
5-5
n.o
14.0
16.8
19.7
22.6
25.6
28.5
6.2
15.0
1 8.0
21.0
24.2
27.4
30.5
3-4
41
5-6
6.7
12.6
16.0
19.2
22.5
25-9
29.2
32-S
3-7
4.9
6.1
7-3
13-5
17.1
2O.6
24.0
27.6
31.2
35-1
4.76
5-88
6.92
8.00
6.76
8.36
9.92
11.48
13.00
14.48
5-3
6.6
7-9
9-3
14.2
18.0
21.8
2S-4
29.2
32.8
36-5
6.2
7.8
9-3
n.o
16.1
20. 2
24-3
28.6
32.8
37-o
41.2
6-5
8.1
9-7
"•5
16.6
25.0
29-5
33-7
38.1
42-5
6-7
8-5
IO.I
11.9
17.1
21.4
25-7
30-3
34-7
39-2
43-7
7-3
9.2
n.o
12.9
18.1
22.7
27.2
32.1
36.8
41.6
46.3
7-9
9-9
11.9
14.0
19.2
24.0
28.8
34-o
39-o
44.1
49.1
10.7
20.3
25-4
30.5
36.0
4i-3
46.7
52.0
g
oHe
'*<
Distance Back to Back of Angles in Inches.
In.
In.*
i
A 1 A
2 i
i» il
4x4x1
6x6x1
7.76
9.60
11.44
13.24
15.00
16.72
18.44
14.44
16.72
19.00
21.24
23-44
25.60
27.76
17.44
20.24
23.00
25.72
28.44
31.12
33-76
38.92
44.00
31.00
34-72
38.44
42.12
45-76
52.92
60.00
66.92
21.5
26.9
32.3
37-7
43-i
49.0
54-5
62.7
73-2
84.0
94-8
105.6
116.4
126.8
108.5
126.5
144.6
163-5
181.8
200.1
219.6
256.6
294.0
343-2
385-9
428.8
471.8
516.8
603.2
692.9
780.8
23-6
29.7
35-8
41.7
47-8
54-3
60.5
68.1
79-5
90.9
103.1
24-3
30-5
36-7
42.8
49-o
55-7
62.1
69.5
81.1
92.8
105.2
11^. /
126.3
138.1
ll/.l
129.0
141.0
25.0
31-3
37-6
43-9
50-3
57-i
63-7
70.9
82.7
94-7
107.4
II9-5
131.6
143-9
119.8
139.8
159.8
180.9
2OI.2
221.6
243-3
284.6
326.3
369.8
4I5-9
462.4
508.8
557-6
651.1
748.4
8434
25.6
32.1
38.6
45-i
51.6
58.6
65-3
72-3
84.4
96.7
109.6
I22.O
134-4
146.9
I2I.8
142.2
162.5
184.0
2O4.6
2254
247-5
289.5
332-0
374-4
421.2
468.2
5I5-3
S64-7
659-4
758.0
854-3
26.3
32-9
39-5
46.2
52-9
60. i
67.0
73-8
86.1
98.6
111.9
124-5
I37-I
150.0
123.9
144.6
165-3
187.1
208.1
229.2
25I-7
294-4
337-7
379-1
426.5
474.1
521.8
571-9
667.9
767-8
865.4
26.9
33-7
40.5
47-4
54-3
61.6
68.7
75-3
87-9
100.6
114.2
127.0
140.0
i53-o
125.9
147.0
168.1
190.3
211.7
233.2
256.0
299-5
343-5
383-8
431.8
480.1
528.4
579-2
676.4
777-7
876.6
27.4
34-5
41.6
48.6
55-7
63-2
70-5
76.8
89.7
102.7
116.5
129.6
142.8
156.2
128.1
149-5
171.0
193-5
215-3
237.1
260.4
304.8
349-5
388.7
437-3
486.2
535-1
586.5
685.1
787.7
887.9
28.9
36-3
43-7
Si-i
58-5
66.5
74.1
79-9
93-3
106.9
121.3
135-0
148.7
162.6
132.4
154-5
176.8
200. i
222.7
245-3
269.4
3I5-2
361.6
398.5
448.4
498.5
702.7
808.0
910.9
136.8
159.8
182.8
206.9
230.3
253-7
278.6
326.1
374-1
408.5
459-7
511.2
562.7
616.9
720.8
828.8
934-5
141.4
165.2
188.9
213-9'
238.1
262.3
288.1
337-2
386.9
418.9
471-3
524.2
577-o
632.6
739-2
850.1
958-5
146.2
170.7
195-3
221. 1
246.1
266.7
297.9
348.7
40O.O
429.4
483.2
537-4
591-7
648.7
758-1
871.8
983.1
151.0
176-5
201.8
228.5
254-4
275-7
307-9
360.3
413-5
440.2
495-4
55i-o
606.6
665.1
777-3
894.1
1008.3
Radii of Gyration about Axis Y-Y, same as given in table of Radii of Gyration of Two Angles.
TABLE 36.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis Y-Y.
LONG LEGS OUT.
Moment* of Inertia
.•: I -I'li: Yngles,
Axil
Long Legs Turned Out.
I J
r i
lances
Meaturcil
ln.m
Ha. k t , 1;.. k.
In
\\2\t\
n
II!
In.*
3-24
4.24
S.24
6.2O
7.12
5.76
7.12
8.44 21.4
9.72
11.0028.6
6.76
Distance Back to Back in Inches.
3-9
1:1
7-9
9-3
H-3
18.1
25.1
21-3
8.36 26.8
9.92 32.1
11.4837.5
13.0043.2
14.48 48.6
15.92 54.0
4.6
6.2
7-7
9-3
10.9
16.0
20.2
24.2
28.2
32.3
23-7
29.6
35-4
41.4
47-7
53-7
59-9
6.4
8.1
1-9.7
"•3
16.4
20.7
24.9
29.0
33-2
24-3
3°-3
36-3
42.4
48.9
55-i
6.7
8.4
10. 1
1 1. 8
16.9
21.3
25.6
29.8
34-i
24.8
31.0
37-2
43-5
50.1
56.4
61.3 62.7
*
5-4
7.2
9.1
10.9
7-8
9.8
6.2
8.4
10.5
11.712.6
9-93!
12.7,13.7 14-7
17.9 18.9! I
22.523
27.028.5 30.1
31-5
36.1
26.1
39-1
59-3
33-3135-1
38.140.2
27.428.8
32.634.235.9
41-043-0
4S-747-9SO-3
52-7 55-3 58-0
62.2
65.3
65.969.072.6
US
In.
"t
5*3 *ft
" tt
u
<-
Distance Back to Back in Inches.
5.24
6.48
7.68
8.88
10.00
6.24
7.72
9.20
10.60
12.00
9.60
11.44
13.24
15.00
16.72
18.44
20. 1 2
9-o
II. 2
13.8
16.0
18.3
14.4
18.0
21.6
25.2
29.2
52.3
62.7
73-2
84.0
94-o
i
10.3
12.9
15-7
18.4
21.0
16.1
20. 2
24-3
28.3
32-7
56.3
67.6
79-3
90-5
101.8
105.3-113.8
115-9,125.2
10.6
'3-3
16.2
19.0
21.7
16.6
20.7
25.0
29.1
33-7
57-4
68.9
80.8
92-3
103.8
no. i
127.7
I
II. O
13.8
16.8
19.6
22.4
17.0
21.3
25.7
30.0
34-6
58.5
70.2
82.4
94.1
105.8
118.3
130.2
i
11.7
14.7
17.9
2I.O
24.0
1 8.0
22.6
27.2
31-7
36.7
60.8
73.0
85.6
97.8
IIO.O
123.0
135-3
12.5
15.7
19.1
22.4
25.6
19.0
23.9
28.8
33-5
38.8
63.2
75-8
89.0
101.6
114.2
127.8
140.6
i
13-3
16.7
20.3
23-8
27.2
20.1
25-2
30-4
35-4
41.0
65.6
78.7
92-4
105-5
118.7
132.7
146.1
•08
u bo
In.
f
10.24
12. 2O
14.12
16.00
17. ss
19.68
21.48
23.24
14.44
16.72
19.00
21.24
23.44
25.60
27.76
31.92
36.00
23.72
27.00
30.24
33-44
36.60
39-76
45-92
52.00
Distance Back to Back of Angles in Inches.
52-3
62.7
73-i
84.0
94.6
105.0
115.6
126.8
108.2
126.1
144.8
162.9
i
56-5
67.8
79.1
90.9
102.4
II3-7
125.1
137-4
"5-5
134-5
154.6
173-9
233-0
271.8
180.9193.1
200.1 213.7
2I8.I
254-2 .
292.8 312.6
299.2
342.0
386.2
428.8
471.2
514.0
6O2.O
688.0
57-6
69.2
80.7
92-7
104.4
"5-9
127.6
140.1
II7-3
136.7
157-1
176.7
196.3
217.2
236.9
276.3
317.8
I
58.8
70.5
82.2
94.6
106.5
118.2
130.1
142.9
119.2
139.0
159-7
179.6
199-5
22O.8
240.8
280.9
59-9
71.9
83-9
96.4
108.6
I2O.6
132.7
145.8
121. 2
I4I.2
162.3
182.6
202.8
224.4
244.7
285.5
323.1 328.4
321.9 325.8
61.1
73-3
85-5
98-3
110.7
123.0
135-3
148.7
123.1
143-5
164.9
185.5
206.1
228.1
248.8
290.2
f
63-5
76.2
88.9
IO2.2
II5.I
127.8
140.7
154.6
I27.I
148.2
170.3
I9I.6
212.9
235.6
252.8 1256.9
62.3
74-7
87.2
IOO.2
II2.9
1254
138.0
I5I.6
I25.I
145.8
167.6
188.5
209.5
295-0
333-8,339-3
299.8
344-9
367-9
4I5.5
461.5
507-S
553-8
648.6
372-4
420.6
467.2
5I3.8
560.7
656.7
741.8 751.1
329-8
377-0
4257
473-0
520.2
567.6
664.91673.1 681.5
760.5 1769.9 779.5
333-9 337-9
381.6 386.2
431.0 436.3
478.8 1484.7
526.6 533.1
I
65.9
79-2
92.4
106.2
119.6
132.9
146.2
160.6
I3I-3
153-0
175-9
197.9
219.9
243-3
265-4
309-6
356.2
346.2
395-7
447.0
496.7
546.3
596.2
698.5
799-0
354-7
40S-4
458-0
508.9
559-8
611.0
715-8
818.8
363-3
4I5-3
469,3
5214
573-5
626.0
733-5
839.1
381.2
435-8
497-4
547-2
601.9
657.1
769.9
880.9
Radii of Gyration about Axis Y-Y, same as given in table of Radii of Gyration of Two Angles.
45
89
TABLE 37.
MOMENTS OF INERTIA OF FOUR ANGLES WITH UNEQUAL LEGS, Axis Y-Y.
SHORT LEGS OUT.
Moments of Inertia
of Four Angles,
Axis Y-Y,
Short Legs Turned Out.
For Distances
Measured
from
Back to Back.
_
v'Sn
N g
55 •<
Distance Back to Back in Inches.
fi
Distance Back to Back in Inches
In.
In.2
A
3-24
4.24
5-24
6. 20
7.12
5-76
7.12
8.44
9.72
11.00
6.76
8.36
9.92
11.48
13.00
14.48
I5-92
2.0
2.7
3-4
4.1
4.8
5-2
6.6
8.0
9-4
10.8
9.1
11.4
13-7
16.1
18.6
21. 1
23.6
2.5
3-4
4-3
il
6.2
7-9
9.6
II. 2
12-9
IO.S
18.5
21.5
24.4
27.2
2.6
3-5
4-5
5-4
6.4
6-5
8-3
10.0
11.7
13-5
10.9
13.6
16.4
19.2
22.3
25-3
28.2
I
2.7
3-7
4-7
6.8
8.6
10.4
12.2
I4.I
"•3
14.1
17.0
19.9
23.1
26.2
29-3
3-o
4.1
s-2
6-3
7-5
7-4
9-4
"•3
13-3
15.4
18.2
21.4
24.8
28.2
31-5
3-3
4.6
5-8
7.0
8.2
8.0
IO.2
12-3
H-S
16.7
12.9
16.2
19-5
22.9
26.7
30.2
33-7
In.
In.*
3-7
5-°
6.4
7-7
9.1
8.7
n.o
13-4
15-7
18.2
13.8
17.4
20.9
24.6
28.6
32.4
36.2
A
5.24
6.48
7.68
8.88
6.24
7.72
9.20
10.60
9.60
11.44
13-24
15.00
16.72
18.44
20.12
5-2
6.6
8.0
9-5
10.8
9.0
11.4
13-8
16.0
18.6
"•3
13.6
16.1
18.5
6.2
7-8
9-5
II. 2
12-9
IO.4
6-5
8.1
9-9
11.7
13-4
10.7
13-5
16.3
18.4 19.1
21-4 22.2
7-3
9.2
II. 2
13.2
15.2
II.9
15.0
18.1
21.2
24.6
15-3
I8.S
22.0
25-3
28.7
23.8 28.0 ,29.1 !3O.2 32.6
26.4 31.1 32.3 33.6 136.2
13.2
l6.0
13-7
16.6
19.7
6.7
8-5
10.3
12.2
I4.O
II. I
I4.O
16.9
19.8
23.O
14.2
17.2
20-4
22.6 23.5
21.0 24.7 J25-7 26.7
1
I
7-9
10.0
12.2
14.4
l6.S
12.7
16.0
19.4
22.7
26.4
16.5
19.9
23-7
27-3
30.9
35-i
39-o
I
8.6
10.8
13-2
15-6
17.9
13.6
17.2
20.8
24-3
28.2
17.7
21.4
25.4
29-3
33-2
37-7
41.8
55 <!
Distance Back to Back of Angles in Inches.
In.
In.2
6x4*1
8x6x^5
" 4
10.24
12.20
14.12
16.00
17.88
19.68
21.48
23.24
14.44
16.72
19.00
21.24
23-44
25.60
27.76
31.92
36.00
23.72
27.00
30.24
33-44
36.60
39-76
45-92
52.00
18.1
21.7
25-5
29.4
33-3
37-i
41.0
45-4
32.4
37-8
43-7
49-3
54-9
61.2
67.1
78.9
92.1
126.9
145.1
164.2
182.6
20 1. o
219.6
258.5
296.7
1
20.4
24.6
28.8
33-3
37-7
42.1
46.6
51-6
36.0
42.1
48.7
SS-o
61.3
68.4
75-o
88.5
103.4
21.0
25-3
29.7
34-4
38-9
43-4
48.0
53-3
37-o
43-2
50.0
56.5
63-1
70-3
77.1
91.0
106.3
I
21.7
26.1
30.6
35-5
40.1
44-8
49-6
SS-o
38.0
44-4
Si-4
58.1
64.8
72-3
79-3
93-6
109.3
140.6
160.9
182.3
202. 8
223.5
244-3
287.8
330-7
22.4
26.9
31.6
36.6
41.4
46.2
51-2
S6.7
39-o
45-6
52-8
59-7
66.6
74-3
81.5
96.2
112.4
143.0
163.7
185-5
206.4
227.4
248.7
293.0
336.7
23-7
28.6
33-6
38.9
44.0
49-2
54-4
60.4
41.1
48.2
55-8
63-1
70.4
78-5
86.2
101.7
118.8
148.1
169.5
192.1
213.8
235-6
257.7
3037
349-0
24-5
29-5
34-6
40.1
45-4
50.7
56.1
62.2
42.2
49-5
57-3
64.8
72-3
80.7
88.5
104.5
122. 1
150.7
172.5
195-5
217.6
239.8
262.3
309.1
355-4
I
26.0
31-3
36.8
42.6
48-3
53-9
59-7
66.1
44-6
52.2
60.5
68.4
76.4
85-2
93-5
110.3
128.9
156.0
178.6
202.5
225.4
248.5
271.8
320.4
368.3
161.5
184.9
209.7
233-5
257-4
281.6
331-9
381-7
167.2
I9I-S
217.2
241.8
266.5
291.7
343-9
395-5
173.0
198.3
224.8
250.4
276.0
302.1
356.1
409.6
179.1
205.2
232.7
259.2
285.8
312.7
368.8
424-3
Radii of Gyration about Axis Y-Y, same as given in Table of Radii of Gyration of Two Angles.
90
TABLE 38.
RADII OF GYRATION OF Two ANGLES WITH EQUAL LEGS, BOTH AXES.
Radii of Gyration
of Two Angles,
Equal Leg*.
For Distance*
Measured from
l:.u k t., ({a. k.
oj
£•<
In.
2X2X&
g'S-E
«HI
In.*
1.42
1.88
2.30
2.7*
2.88
3.56
4.22
4.86
5-50
6.12
6.72
.61
.60
•59
•93
f&
•91
•91
•90
.89
.88
Axis Y-Y.
Distance Back to Back in Inches.
.84
-8SJ
.86!
.88 j
-25 'i
.26,1
.271
.28,1
.29!:
.3211.
•95
.98
.98
•99
34I-36
1.38
371-39
38 1.40
391.41
401.42
i-43
J_
-99
•99
i .00
I.OIJI
1.381
1.4011
1.41 1
1.42 I
i-43
1.45
1.46
i
i
1.09 i
1.091.14
i.ioi.is
i. ii 1.16
1.48
1.50
14 ai
1-52
i-53
1.54
i-SS
1.56
i-57
1.58
i. 60
1.62
•88
In.
2.38
2.94
346
4.00
3-38
4.18
4.96
5-74
6.50
7.24
7.96
Axis Y-Y.
Distance Back to Back in Inches.
•77
•7<>
•75
•75
•09
.OK
.07
.07
06
i
47
.48
•49
•50
I
.05 1.51
•041-52
.14 1.17 i
.15 1.17 i
,16 1. 1* i
.171.201
.541.571
.561.581
•57 1-59 i
.58 1.60 i
.591.61 1 1
.60 1.62 i
191.241
201.25,1
I
«9
3°
1.261.31
1.27 1.32
59 1-63
60 1.65
1.67
1.69
1.661.70
1.6711.72
1.671.73
1.69
1-75
661.701.76
1
i-34
i-35
1-36
i-73
i-74
i-75
1-77
1.78
i. 80
i .81
In.
' <
In.t
Axis Y-Y.
Distance Back to Back of Angles in Inches.
i
1
I
I
I
•i
6i6il
3.88
4.80
5.72
6.62
7.50
8.36
9.22
7.22
8.36
9-50
10.62
11.72
12.80
13-88
8.72
10.12
11.50
12.86
14.22
I5-56
16.88
19.46
22.00
I5-50
I7-36
19.22
21.06
22.88
26.46
30.00
33-46
1.25
1.24
1.23
1.23
1.22
1. 21
1. 2O
I.S6
i-SS
i-54
i-53
1-52
i-Si
1.50
1.88
1.87
1.86
1.85
1.84
1.83
1-83
1.81
i. 80
2-Si
2.50
2-49
2.48
2-47
2-45
2.44
2.42
1.66
1.68
1.68
1.69
1.70
1.71
1.72
2.08
2.09
2.IO
2.13
2.14
2-49
2.50
2-51
2.52
2-53
2-53
2-55
2-57
2-59
3-32
3-33
3-34
3-35
3-36
3-38
3.40
3.42
•75
.76
•77
.78
•79
.80
.81
2.17
2.18
2.19
2. 2O
2.21
2.22
2.23
1.77
I.78
1.79
1. 80
1.81
1.82
1.83
2.19
2.2O
2.21
2.22
2.23
2.24
2.25
1.79
1. 80
1.81
1.82
1-83
1-85
1.86
2.22
2.22
2.23
2.25
2.26
2.27
2.28
2.62
2.63
2.64
2.65
2.66
2.67
2.68
2.70
2.72
3-44
3-46
3-47
348
3-49
3-Si
3-53
3-55
1.82
1-83
1.84
1.85
1.86
1.87
1.88
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.64
2.65
2.66
2.67
2.68
2.69
2.71
2-73
2-75
3-47
3-48
3-49
3-50
3-5i
3-53
3-55
3-57
1.84
1.85
.86
.87
.88
.90
.91
2.26
2.27
2.28
2.29
2.30
2.32
2-33
2.66
2.67
2.68
2.70
2.71
2.71
2-73
2-75
2-77
3-49
3-50
3-Si
3-52
3-53
3-55
31Z
3-6o
1.86
1.87
1.88
1.89
1.90
1.92
1-93
2.28
2.29
2.30
2.32
2-33
2-34
2-35
2.69
2.69
2.71
2.72
2-73
2-74
2.76
2-77
2-79
3-52
3-53
3-53
3-54
3-56
3-57
3.60
3.62
1.88
1.89
1.90
1.92
i-93
1.94
1-95
2.31
2.32
2-33
2-34
2.35
2.36
2-37
2.71
2.72
2-73
2.74
2.75
2.76
2.78
2.80
2.82
3-54
3-55
3-56
3-57
3-58
3.60
3.62
3-64
1.93
1.94
1.95
1.96
1.97
i-99
2.OO
2-35
2-37
2-.38
2-39
2.40
2.41
2.42
2-75
2.76
2-77
2-79
2.80
2.81
2.83
2.85
2.87
3-58
3-59
3.60
3-6i
3.62
3-64
3.67
3-69
2.80
2.81
2.82
2.84
2.85
2.85
2.88
2.90
2.92
3-63
3-64
3-64
3.65
3.71
3-74
2.85
2.86
2.87
2.88
2.89
2.90
2.92
2-94
2.97
3-67
3-68
3-69
3-70
3.72
3-74
3.76
3-79
2.90
2.91
2.91
2-93
2-94
2-95
2.97
2-99
3-01
3-72
3-73
3-74
3-75
3-76
3.78
3.81
3-83
2-94
2-95
2.96
2.98
2-99
3-00
3.02
3-04
3.06
3-77
3-78
3-78
3-79
3.81
3.83
3-86
3.88
Moments of Inertia about Axis Y-Y equal one-half of values given in Table of Moments of
Inertia of Four Angles, Table 35.
91
TABLE 39.
RADII OF GYRATION OF Two ANGLES WITH UNEQUAL LEGS, BOTH AXES.
LONG LEGS OUT.
Radii of Gyration
of Two Angles,
Long Legs Turned Out.
For Distances
Measured from
Back to Back.
"88
""Si
In.
25X2X3%
' 1
•f
4*3*1
1.62
2.12
2.62
3-IO
3-56
2.88
3-S6
4-22
4.86
5-5°
3-38
4.18
4.96
5-74
6.50
7.24
7.96
Axis Y-Y.
Distance Back to Back in Inches.
.101
.11 i
I
i
i.f-
19 1.22 1.24 1.29
20 1.23 1.25 I.3O
1.24
,67
69
70
•71
1.87
1.24 1.261.31
1.251.281.32
1.26
-29, i -3 3
1.691.71 1.76
1.70
1.72
1-73,
1.741.76
i-73
1.74
1.89:1.92
1.901.93
I.9II-94
901.921.95
92,1.941.96
I
I
I
I
1.93 i. 95 'i
1.94 1.96 i
1.77
1.79
i. 80
1.81
1.96
i
1.341.38
1.36:140
I-37I42
i.38|i.44
1.46
1.81
1.82
1.85
1.86
2.OI
1 .97J2.O2
I.98!2.03
I.9O
I.9I
1.9912.04 2.09
2.01 2JOO2.I1
97;2.O22.O7 2.12
14
In.
2.06 5x3x1%
2.07
2.08
" H
2.62
3-24
3'
4.44
5.00
3.12
3-
4.60
5-30
6.00
4.80
5-72
6.62
7-5°
8.36
9.22
IO.OO
•85
Axis Y-Y.
Distance Back to Back in Inches.
•r-
•33
•34
•35
1.52
i
1.40 1.42
141x43
i-43 MS
1.44 1.46
1-45,147
1.61 1.63
1.5211.6111.64
.66 1.71
i.53'i.62!i.6s 1.67 1.72 1.77 1.82
1.54 1.63 1.66 1.68 1.73 1.78 1.83
1.55 1.65! 1.68! i. 70 1.75 i .80 1.85
^•33 2.42 2.4^ 2.47]2«52 2.57 2.02
2.34 2.43:2.4612.48 2.53 2.58 2.63
2.35 2.45'2.47;2.49 2.54 2.59 2.64
2.36 2.46 2.48 2.50 2.55 2.60 2.65
2.37 2.47 2.49 2.52 2.57 2.61 2.66
2.392.48^.51 2.53 2.582.63 2.68
2.4o|2.49'2.52 2.54 2.59 2.64 2.69
JL_L
451 i.SO i-SS i-59
.46 1.51 1.5611.60
.48:1.53 1.581.62
.49! i. 54 1.59 1-64
.50! 1.55 i.oo 1.65
.651.701.75 1-79
- - / j -is
1.76 1.81
8"**
35 .<
In.
In.2
AxisY-Y.
Distance Back to Back of Angles in Inches.
I
I
I
>1
8x6x,
5.12
6.10
7.06
8.00
8.94
9.84
10.74
11.62
7.22
8.36
9-5°
10.62
11.72
12.80
13.88
15.96
18.00
I3-50
15.12
16.72
18.30
19.88
22.96
26.00
1.03
i .02
i .01
i .01
i.oo
•99
.98
.98
1.17
1.16
i-i5
1.14
1-13
1-13
1. 12
I. II
I.O9
1.80
1.79
1.78
1.77
1.77
1.76
1.74
1-73
2.26
2.27
2.28
2.29
2.30
2.31
2'. 3 2
2-33
2.74
2-75
2.76
2-77
2.78
2-79
2.80
2.82
2.8S
3-55
3-56
3-57
3-58
3-59
3.60
3.62
3-64
2-35
2.36
2:37
2.38
2-39
2.40
2.41
2-43
2.83
2.84
2.85
2.86
2.87
2.89
2.90
2.92
2-95
2-37
2.38
2-39
2.41
2.42
2-43
2-44
2.46
2.85
2.86
2.88
2.88
2.89
2.91
2.92
2.94
2-97
2-39
2.40
2.41
2-43
2.44
2.45
2.46
2.48
2.87
i QQ
2. So
2.9O
2.91
2.92
2.94
2-95
2-97
2-99
3.68
3-69
3-7i
3-71
3-72
3-73
3-76
3-78
2.42
2-43
2.44
2.45
2.46
2.48
2.49
2.51
2.90
2.91
2.92
2-93
2-94
2.96
2.97
2.99
3.02
3-71
3-71
3-73
3-74
3-75
3-76
3-78
3.80
2.44
2-45
2.46
2.48
2.49
2.50
2.51
2-53
2.92
2-93
2-95
2.96
2-97
2.98
2.99
3.01
3-04
3-73
3-74
3-75
3-76
3-77
3-78
3-8i
3.82
2.47
2.48
2.49
2.50
2.51
2.52
2-53
2-55
2.94
2-95
2-97
2.98
2-99
3.01
3.02
3-04
3-°7
3-75
3-76
3-77
3-78
3-79
3.80
3-83
3-85
2-49
2.50
2.52
2-53
2-54
2-55
2.56
2.58
2.97
2.98
2-99
3.00
3-Qi
3-03
3-°4
3.06
3-09
3-77
3-78
3.80
3.81
3-82
3-82
3-85
3-87
2-54
2-55
2.56
2.58
2-59
2.60
2.61
2.63
3.01
3.02
3-04
3-05
3.06
3.08
3-09
3-i.i
3-14
3.82
3-83
3-84
3-85
3-86
3-87
3-9°
3-92
3-87
3.88
3-89
3-90
3-9i
3-92
3-95
3-97
3-91
3-92
3-94
3-95
3-96
3-97
3-99
4.02
3-97
3-99
4.00
4.01
4.02
4.04
4.07
4.01
4.02
4-03
4.04
4-05
4.06
4.09
4.12
Moments of Inertia about Axis Y-Y equal one-half of values given in Table of Moments of
Inertia of Four Angles, Table 36.
92
TABLE 40.
RADII OF GYRATION OF Two ANGLES WITH UNEQUAL LEGS, BOTH AXES.
SHORT LEGS OUT.
Radii of Gyration
of Two Angle*,
Short Leg* Turned Out.
For Distance*
Measured from
l;.i. k
In.
;; i
" A
"r?
• ?
4x3 x}
:: f
:?
1.62
2.12
2.62
3-10
3-56
2.88
Axis Y-Y.
Distance Back to Back in Inches.
•70
•78
.78
•77
.76
1. 12
4-22
4.86
5-50
1. 10
1.09
1.09
.88
.89
.91
.92
•93
1.04
•96,1-05
•97 1-07
•98)1.07
.99 i. 08
.16
1.24
3.381.281
4.18 1.27 1.17 1.25
4.96 1.26 1.17 1.26
5.74 1.25 1. 18 1.27
6.50 1.25 1.20 I.2S
7.24 1.24 1.21.1.30
7.961.23 I.22JI.3I|I.
.90
.91
•93
•94
•95
i. 06
i. 08
.09
.10
.11
•-7
.28
.28
1.29
1.32
I
.96 1
.98 1
04
i. oo 1.05
1.01 1.06
1.02 1.07
I.I3I.I8
10 1.15 i.
11 1.16 i.
.31 1.36,1
.321-361
•33 1.3.8 1
.35,
.361
In.
I
1.073x2^
1.09
i. ii
1.23
1.27
1.29
1-44
1.18 1.23
i-34 i-38
39
401.45
41146
,431.48
1.40.1.45 1.50
1.4111.4611.51
-f
"tt
2.62
3-24
3-84
4.44
5-00
3-12
3-86
4.60
5-30
6.00
4.80
5-72
6.62
7-50
8.36
9.22
10.06
•95
•94
•93
.92
.91
i. ii
1.09
i. 08
1.07
1.61
1.61
1.60
i-59
1.58
i-S7
1.56
Axi* Y-Y.
Distance Back to Back in Inches.
i
09
.10
I
.21
.22
.23 * 1. 26
•2411.27
* I I
.13 1.18
.14.1.19
.16 1. 21
.I7I.221
•33!i-38'
•35 i-39
.36 1.40
•39,1.43
22 1.26
.23 1.27
.24 1.29
.26,1.31
.28,1.33
29JI-34
I
1.23 1.28
1.24 1.29
1.26; 1.3 1
I-27I-33
1.281.34
i-43|i.48
1.44,149
1.45 1.50
1.46,1.51
1.481.53
1.3111.36
1-32,1-37
1-341 1-39
1-35 '* '"
1.41
1.43
1-36
1-38
In.
Axis Y-Y.
Distance Back to Back of Angles in Inches.
J
A I I
I
I
I
I
•i
6x4x1
5.12
6.10
7.06
8.00
8-94
9.84
10.74
11.62
^
7.22
8.36
9-50
10.62
11.72
12.80
13.88
IS-96
18.00
11.86
13-50
"„ l-i.12.
l6.72
^18.30
19.88
' 22.96
I J26.00
1.61
1.60
1.59
1.58
'•57
1.56
1.56
1-55
1-93
1.92
1.91
1.90
1.90
1.89
1.88
1.86
1.85
2-57
2.56
2-55
2-54
2-54
2-53
2.51
2-49
1.33
i-34
i-35
1.36
1-37
1.38
1.38
1.40
1.50
1.50
i-5i
1.52
i-53
I<5!
1.56
1-58
1.60
2.31
2.32
2-33
2-34
2-34
2-35
2.37
2-39
1.41
1.42
i-43
144
1-45
1.46
1.47
1.49
1.58
ri9
i. 60
1.61
1.62
1.63
1.64
1.66
1.69
1-43
1.44
1.45
1-47
1.48
1.49
i 50
1.51
1.60
1.61
1.62
1.63
1.64
1.66
1.67
1.69
1.72
1.46
1.46
1-47
1.49
1.50
1.51
1.52
1-54
1.62
1.63
1.65
1.66
1.67
1.68
1.69
1.71
1.74
2-43
2-44
2.46
2.46
2-47
2.48
2.51
2.52
1.48
1.49
1.50
1.51
1.52
i-53
1.54
1.56
1.64
1.66
1.67
1.68
1.69
1.71
1.72
1-74
1.77
2-45
2.46
2.48
2-49
2-49
2.50
2-53
2-54
•54
•55
•S<5
•57
•59
.66
.68
.6$
.70
•7i
•73
•74
•7*
•79
2.47
2.48
2.50
2-51
2.52
2.52
2-55
2-57
1.52
i-53
1.54
1.56
i-57
1.58
i-59
1.61
1.69
1.70
1.71
1.72
i-73
i-75
1.76
1.79
1.82
2.49
2.51
2.52
2-53
2-54
2-55
2-57
2.59
i-SS
1.56
i-57
•58
•59
.60
.62
.63
•71
>7*
•74
77
•79
.*i
.84
2.52
2-53
2-54
2>5I
2.56
2-57
2.59
2.62
1-59
i. 60
1.62
1.63
1.64
1.66
1.67
1.69
1.76
1.77
1.78
1.79
1.81
1.82
1.84
1.86
1.89
2.56
2-57
2-59
2.60
2.61
2.62
2.64
2.66
2.61
2.62
2.63
2.64
2.65
2.66
2.69
2.71
2.66
2.66
2.68
2.69
2.70
2.71
2-74
2.76
2.70
2.71
2-73
2-74
2-75
2-77
2-79
2.81
2.75
2.76
2.77
2-79
2.80
2.81
2.83
2.86
Moments of Inertia about Axis Y-Y equal one-half of values given in Table of Moments of
Inerlia of Four Angles, Table 37.
93
TABLE 41
SAFE LOADS OF SINGLE ANGLE STRUTS
EQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
»v n
Safe loads in thousands of pounds for least 'jl T° left of heavy line values of 1/r do not
radius of Crayon _ T ««* "S^ ^ ^^ of ^ ^ ^
1 — v* exceed 150
X3
Size
Thickness
Length in Feet
Inches
Inches
3
4
s
6
7
8
9
10
ii
12
13
14
IS
ijxii
ifXif
2 X2
»|Xa|
3 X3
35X3!
4 X4
*5 X5
6 X6
A
f
A
A
A
ft
f
A
A
3
8
A
A
1
f
A
2
9
T6
3
8
TV
i
f
8
4
5
7
7
9
ii
10
13
16
17
21
25
28
26
31
35
3i
37
42
48
49
56
64
7i
60
70
80
89
98
4
5
4
5
7
8
5
7
8
8
ii
13
IS
18
22
25
23
28
32
28
34
39
44
46
53
60
67
g
76
85
93
7
9
ii
13
16
18
21
21
25
28
26
31
35
40
42
49
£
62
I4
63
72
80
89
9
ii
12
H
ii
13
15
18
18
22
25
23
27
32
36
39
45
52
58
Si
59
67
75
83
13
16
18
16
19
2J
21
24
28
32
36
42
47
53
^
56
63
7i
78
15
18
21
24
18
21
24
28
33
38
43
48
45
52
59
66
73
24
27
3i
35
21
24
27
30
3°
35
39
44
42
49
£
68
27
31
35
39
39
45
Si
57
63
30
34
39
43
48
27
31
35
39
43
36
42
47
53
58
33
38
43
48
53
Note: The values in this table have been calculated on the assumption that the angle is fas-
tened by both legs. — M. S. K.
94
TABLE 42
SAFE LOADS OF SINGLE ANGLE STRUTS
UNEQUAL LEG ANGLES
AMERICAN BRIDGE COMPANY STANDARDS
Safe loads in thousa
radius of gyration
P " i6,(
nds of p
ounds for least 3^
1/r
U-.
To left of heavy line values of 1/r do not
exceed 125
To right of heavy line values of 1/r do not
exceed 150
^4
Size
Thickness
Length in Feet
Inches
Inches
3 4
5
6
7
8
9
10
ii
12
13
2 xi|
2JX2
3 X2
3 X2i
3lX2j
3*X3
4 X3
5 X3*
6 X4
A
!
A
i
A
!
t
t
1
A
I
1
5
8
ii
13
12
IS
IS
18
21
16
20
24
23
27
32
36
25
30
35
39
32
39
45
50
47
55
62
70
77
7
8
10
10
12
13
16
18
H
17
21
21
24
28
32
23
27
31
35
3°
35
4i
46
44
51
58
65
71
6
8
7
9
ii
13
IS
12
IS
17
18
21
24
28
20
23
27
31
27
32
37
42
4i
47
S3
59
65
8
II
12
IO
12
H
•
13
IS
17
20
IS
17
20
22
IS
18
21
24
17
2O
23
26
12
!1
16
18
18
22
25
28
IS
18
21
24
24
29
33
37
37
43
49
54
59
21
25
29
33
2l
26
30
34
36
20
34
39
44
49
54
30
35
39
44
4» |
27
31
35
39
.42
Note: The values in this table have been calculated on the assumption that the angle is fas-
tened by both legs. — M. S. K.
95
TABLE 43 .
SAFE LOADS OF Two ANGLE STRUTS, Axis i-i
EQUAL LEG, AND UNEQUAL LEG WITH LONG LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
1
Safe loads in thousands of pounds with 2 SErSBTpEL, T°eSd° [£*** ^ Va'UeS °f 1/r d° nOt
respect »«*«_ ^ ^ Wlt To^^ of heavy line values of 1/r do not
1
Size
of
Angles
I
_o
H
°§
11
•§*
f*O
11
°R
•Sj§
14
HS
°t
g<
Length in Feet
In.
In.
In.
Lb.
In.z
6
7
8
9
10
ii
12
13
14
IS
16
17
18
19
20
21
22
23
24
2 X2
2|X2
2^X2|
3 X2
3 X2j
3 X3
jixai
31X3
3?X3i
4 X3
¥
? '
A
i
A
i
A
i
A
3
8
1
5
16
I
A
i
A
*
i
5
?
A
a
A
3
8
A
3
f
A
1
A
I
A
i
A
i
•98
•99
1.24
1.25
1.26
1.19
i. 20
1.52
i-53
i-55
i-45
1.46
1.48
i-39
1.40
1.41
1.42
1.44
1.71
i-73
1.74
1.76
1.77
1.66
1.67
1.69
1.70
i. 60
1.61
1.63
1.64
1-93
1.94
1-95
1.96
1.97
1.99
S-o
6.4
5-6
7-4
9.0
8.2
IO.O
8.2
IO.O
11.8
9.0
II. 2
13.2
9.8
12.2
14.4
16.6
18.8
9.8
12.2
144
16.6
18.8
13.2
15-8
18.2
20.4
14.4
17.0
19.6
22.2
14.4
17.0
19.6
22.2
24.8
27.2
1.44
1.88
1.62
2.12
2.62
2.38
2-94
2.38
2-94
346
2.62
3-24
3-84
2.88
3-56
4.22
4.86
5-50
2.88
3.56
4.22
4.86
5-50
3-86
4.60
5-30
6.00
4.18
4.96
5-74
6.50
4.18
4-96
5-74
6.50
7.24
7.96
16
21
19
25
32
28
35
30
37
44
33
4i
48
36
44
52
61
69
38
47
55
64
72
5°
60
69
78
54
64
74
84
56
66
77
87
97
107
H
19
18
24
30
26
33
29
36
42
3i
39
46
34
42
50
58
66
3"6
45
53
62
70
48
57
66
75
52
61
7i
81
54
64
75
85
94
104
13
17
17
23
28
25
31
27
34
40
30
37
44
32
40
47
55
62
35
43
Si
59
67
46
u
72
49
59
68
77
52
62
72
82
9i
100
12
16
16
21
26
23
29
26
33
38
28
35
42
30
38
45
52
59
33
4i
49
57
65
44
53
61
69
47
i6
65
74
Si
60
70
79
88
97
II
H
IS
20
25
21
26
25
31
37
27
33
40
29
36
42
49
56
32
40
47
55
62
42
So
58
66
45
53
62
7i
49
58
67
76
85
94
9
13
8
ii
J2_
15
19
16
20
ii
H
18
IS
18
9
13
16
H
18
23
20
24
24
29
35
25
3i
37
27
33
40
46
53
3i
38
45
52
59
40
48
I6
63
43
Si
59
67
47
56
65
73
82
90
•3l
17
21
18
22
22
28
33
24
29
35
25
3i
37
43
49
29
36
43
50
57
38
46
53
60
4i
48
56
64
45
54
62
7i
79
87
16
17
21
i!
18
22
27
18
23
27
32
37
16
20
23
16
20
24
17
21
25
29
33
H
18
22
IS
18
.22
21
26
31
22
28
33
23
29
35
40
46
28
34
4i
48
54
36
44
50
58
38
46
53
61
43
Si
60
68
76
84
20
25
29
21
26
31
22
27
32
38
43
26
33
39
45
Si
34
4i
48
54
36
43
5°
57
4i
49
57
65
73
80
18
23
27
19
24
29
20
25
30
40
25
3i
37
43
49
32
39
45
52
34
4i
47
54
40
47
55
62
70
77
17
2O
30
2L.
26
31
36
41
19
24
29
34
38
25
3°
34
40
25
30
36
40
18
22
27
31
36
23
27
32
37
23
28
33
37
16
21
25
29
33
23
29
35
4i
46
3°
37
42
49
32
38
45
Si
38
45
52
59
67
74
22
28
33
38
44
28
34
40
_46_
30
35
\t
27
31
27
32
37
43
27
33
39
44
29
34
47
36
43
So
56
64
70
29
34
40
45
Si
57
27
32
37
43
48
53
25
30
35
40
45
5°
23
28
32
37
42
47
34
4i
47
54
61
67
32
39
45
5i
57
64
30
36
42
48
54
60
96
TABLE 43.— Continued
SAFE LOADS OF Two ANGLE STRUTS, Axis i-i
EQUAL LEG, AND UNEQUAL LEG WITH LONG LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
Safe load* in thousands of pounds with j.
respect to axis i-i
p ™ 16,000 — 70 1/r
L
To left of heavy line values of 1/r do not
* exceed 125
To right of heavy line value* of 1/r do not
exceed 150
"Tr
4.-H"
1
Size of Angles
1
H
"58
II
(So
II
H
•58
f]
4
•<(
<i
H
Length in Feet
In.
In.
In.
Lb.
In.*
6
7
8
9
10
II
12
13
14
16
18
20
22
24
26
28
30
3»
M
*
4X4
5X3
5X3}
5X5
6X3*
6X4
6X6
f
iV
A
1
iso
!
i
f
;.
i
i
?
1
H
l.So
I.8i
1.83
1.84
2.47
-•4s
2.49
2.50
2.40
2.40
2.41
2.43
2-44
2.45
2.46
2.48
2.22
2.23
2,24
2-95
2.96
2.98
3-oo
2.87
2.88
2.90
2.91
2.92
2-93
2.94
2.62
2.63
2.64
2.6t
2.66
2.67
2.68
16.4
19.6
M.6
25.6
16.4
19.6
22.6
25.6
174
20.8
24.0
27.2
30.4
33-6
36.6
39-6
24.6
28.6
32.4
23-4
27.0
30.6
37-8
24.6
28.6
32.4
36.2
40.0
43-6
47-2
29.8
34-4
39-2
43-8
48.4
53-o
57-4
4.80
5-72
6.62
7.50
4.80
5.72
6.62
7-5°
5-12
6.10
7.06
8.00
8-94
9.84
10.74
11.62
7.22
8-36
9-50
6.84
7-94
9.00
II. 10
7.22
8.36
9-50
10.62
11.72
12.82
13.88
8.72
IO.I2
11.50
12.86
14.22
15.56
16.88
63
76
88
99
67
80
93
104
7i
85
98
112
125
137
ISO
162
99
"5
131
98
114
129
159
103
119
136
152
167
183
198
123
l$
162
181
20 1
220
239
61
73
85
96
65
78
90
102
69
83
96
109
122
134
146
I58
97
112
127
96
III
126
I56
101
117
133
149
164
179
I9S
120
139
159
177
196
215
233
59
70
81
93
6i
76
88
IOO
68
81
93
106
119
131
H3
155
94
109
124
94
109
124
153
99
114
130
145
161
176
191
117
136
155
173
192
2IO
228
s
78
89
62
74
86
97
66
79
9i
103
"5
127
139
151
9i
105
120
92
107
121
ISO
97
112
127
142
157
172
I87
114
133
151
169
I87
205
221
I4
65
75
86
61
72
84
95
"4
76
89
IOO
112
I24
135
H7
88
1 02
116
90
105
119
146
94
109
124
139
154
169
183
112
130
I4S
|6S
183
200
218
52
62
72
82
59
70
81
92
62
74
86
98
109
120
132
H3
86
99
112
88
102
116
143
92
107
122
136
151
I65
179
109
126
144
161
178
195
212
1°
60
69
79
II
79
90
60
72
84
95
105
117
128
139
83
96
109
86
IOO
114
140
90
105
119
133
H7
161
175
106
123
140
157
'74
190
207
48
&
75
56
66
77
87
59
70
81
92
103
114
124
135
80
93
106
84
98
in
137
88
102
116
130
144
158
171
103
1 20
136
'I3
169
1 86
202
45
54
63
72
&
64
75
85
57
68
79
89
IOO
I 10
121
131
77
90
1 02
82
96
1 08
134
86
IOO
"3
127
140
154
167
IOO
117
133
149
165
181
196
•41
49
57
65
Si
61
7i
80
53
64
74
84
94
104
114
123
72
83
95
78
9i
103
128
82
95
108
121
134
147
159
95
no
126
141
156
171
1 86
36
44
Si
58
32
38
45
52
28
33
39
45
34
4i
48
31
37
44
5°
32
38
44
51
57
63
70
76
28
33
39
45
28
34
40
45
F
62
68
47
8,
75
50
59
69
78
88
97
roC
"5
66
77
88
74
87
98
122
78
90
I O2
115
i-7
139
IS'
89
1CX]
118
132
H7
161
175
44
53
61
70
46
55
64
73
81
90
99
107
61
7i
81
71
82
93
"5
73
85
97
109
1 20
131
H3
84
97
in
124
138
T
"'4
41
49
57
65
42
Si
59
67
75
83
9i
99
55
64
74
67
78
88
109
69
80
91
IO2
"3
124
135
78
91
103
116
129
141
154
38
45
52
60
39
46
54
62
69
76
84
92
50
58
66
55
35
42
49
I6
63
70
77
84
44
52
59
•
52
47
IS
78
48
56
64
72
80
87
95
43
50
57
7-
44
5'
;s
5
n
So
*7
11
!«
t:b
4<>
- ^
I
?"
63
73
83
103
65
75
86
96
107
lit
127
72
84
96
108
1 20
1 3-
143
59
68
78
97
61
70
80
90
IOO
109
119
67
78
89
IOO
in
122
133
55
64
73
9i
56
65
75
84
93
IO2
III
51
60
68
84
-2.
61
69
78
86
95
103
61
72
82
92
1 02
112
122
g
74
84
93
102
III
5°
59
67
75
84
92
101
97
TABLE 44
SAFE LOADS OF Two ANGLE STRUTS, Axis 2-2
EQUAL LEG, AND UNEQUAL LEG WITH LONG LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
1
Safe loads in thousands of pounds with tSS55C=HI T°e^d i^T* "^ Va'UeS °f '" d° "^
respect to^axis 2-2 _ ^ ^ M ^,, To right of hea vy line values of 1/r do no±
1
Section
Modulus
Radius of
Gyration
Weight of
Two Angles
per Foot
^8
g^
«J
•
en
E
1
u
B
Length in Feet
Sj
it
ri
In.»
In.
In.
Lb.
In.*
In.
3
4
s
6
7
8
9
10
ii
12
13
14
a"X2" Angles
.38
.50
.62
.61
.98
•99
5'°
6.4
1.44
1.88
t
17
22
15
20
13
17
II
IS
9
12
2j"X2" Angles
.40
•5°
.62
.60
•59
•58
1.24
1.25
1.26
5-6
7-4
9.0
1.62
2.12
2.62
J
A
19
25
31
17
22
27
IS
19
23
12
16
19
10
13
15
2i"X2j" Angles
.80
.96
•77
.76
1.19
1. 20
8.2
IO.O
2.38
2.94
*
ffc
30
37
28
34
25
3i
22
28
2O
24
17
IS
18
21
3" X2" Angles
.50
.64
•74
•57
•57
•16
1.52
1-53
i.">S
8.2
IO.O
n.8
2.38
2.94
3.46
A
28
34
40
24
30
35
21
25
29
17
21
24
14
17
19
3" X2j" Angles
.80
•98
1.16
•75
•74
•74
1.45
1.46
1.48
9.0
II. 2
13.2
2.62
3-24
3-84
A
i
33
4i
48
30
37
44
27
33
40
24
30
35
21
26
31
18
22
27
16
19
22
3" X3" Angles
1.16
1.42
1.66
1.90
2.14
•93
.92
.91
.91
.90
i-39
1.40
1.41
1.42
1.44
9.8
12.2
14.4
16.6
18.8
2.88
3.56
4.22
4.86
5-5°
i
*
38
47
I6
64
73
36
44
I!
60
67
33
4i
48
55
62
30
37
44
50
57
28
34
40
46
52
25
3A
36
42
47
22
28
32
37
42
20
24
29
33
37
17
21
25
28
32
3i"X2|" Angles
.82
I.OO
1.18
1.36
1.52
•74
•73
.72
•7i
.70
1.71
i-73
1.74
1.76
1.77
9.8
12.2
14.4
16.6
18.8
2.88
3-56
4.22
4.86
5- "Jo
t
A
1
36
45
I3
61
68
33
4i
48
55
62
3°
36
43
49
55
26
32
38
43
48
23
28
33
38
42
20
24
28
32
35
17
20
23
3i"X3" Angles
1.44
1.70
1.96
2.2O
.90
.90
.89
.88
1.66
1.67
1.69
1.70
13.2
15-8
18.2
20.4
3-86
4.60
5-3°
6.00
A
3
8
f
Si
61
70
79
47
56
65
73
44
52
60
67
40
48
&
37
44
S2
56
33
39
45
SO
29
35
40
44
26
3i
35
39
22
26
30
33
TABLE 44.— Continued
SAFE LOADS OF Two ANGLE STRUTS, Axis 2-2
EQUAL LEG, AND UNEQUAL LEG WITH LONG LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
Safe loads in thousands of pounds with re- j.
spect to axis 2-2
p - 16,000 — 70 1/r
I—
To left of heavy line values of 1/r do not
exceed 125
To right of heavy line values of 1/r do not
exceed 150
=•=*=-•
4-X"
1
Section
Modulus
Radius of
Gyration
1?
*&
8
°1?
If
H
1
Length hi Feet
Si
n
ri
In.»
In.
In.
Lb.
In.'
In.
3
4
5
6
7
8
9
10
II
13
13
14
15
16
17
18
19
3i"X3i"Anglea
1.96
2.30
2.64
2.98
1. 08
1.07
1.07
1. 06
l.6o
i.'-i
1.63
1.64
14.4
17.0
19.6
22.2
4.18
4.96
5-74
6.50
t
57
68
78
89
I4
64
74
83
&
69
78
47
I6
65
73
44
f
60
68
41
48
I6
63
3&
44
Si
58
35
40
47
53
31
37
42
47
28
33
38
42
25
29
33
37
4" Xj" Angles
1.48
1.74
I.98
2.24
2.46
2.70
•89
.88
.87
.86
.86
•85
1.93
1.94
'•95
1.96
i-97
1.99
14.4
17.0
19.6
22.2
24.8
27.2
4.18
4.96
5-74
6.50
7.24
7.96
1
55
65
75
85
95
104
Si
60
70
79
88
96
47
56
64
72
81
88
43
Si
59
66
73
80
39
46
53
60
66
72
35
4i
48
53
59
64
3i
37
JE
47
52
57
27
32
36
40
45
49
23
27
4" X4" Angles
2.S8
3-04
3.50
3-94
1.24
1.23
1.23
1.22
i. 80
1.81
1.83
1.84
16.4
19.6
22.6
25-6
4.80
5-72
6.62
7-5°
A
f
A
i
67
80
92
i°5
64
76
88
99
61
72
83
94
57
68
79
89
54
64
74
84
Si
60
70
79
48
56
65
74
44
53
61
68
41
49
56
63
38
45
52
58
35
4i
47
53
3i
37
43
48
28
33
38
43
S"X3" Andes
1.50
I.78
2.04
2.30
-85
.84
.84
.83
2.47
2.48
2.49
2.150
16.4
19.6
22.6
25.6
4.80
5-72
6.62
7-50
A
I
A
63
74
86
97
58
69
79
QO
53
63
73
82
48
&
74
44
to
67
39
46
53
59
34
40
46
52
29
34
40
44
S"X3j" Angles
2.04
2.42
2.78
3.12
3.46
3. so
4.12
4-44
•03
.02
.OI
.01
.OO
•99
.98
.98
2.40
2.40
2.41
2-43
2.44
2.45
2.46
2.48
174
20.8
24.0
27.2
30.4
33-6
366
39.6
5-12
6.10
7.06
8.00
8.94
9.84
10.74
11.62
A
f
rV
A
t
¥
69
83
95
108
121
132
144
156
65
78
89
IOI
113
124
I3I
146
61
73
84
95
105
116
126
136
57
68
78
88
98
107
"7
126
53
62
72
81
90
99
107
116
48
&
75
83
9i
98
106
44
I!
60
68
75
82
89
96
40
47
54
61
68
74
80
86
36
42
48
55
60
66
7i
76
32
37
43
48
53
11
66
S"XS" Angles
4.84
5-58
6.30
1.56
155
1-54
2.22
223
2 24
24.6
28.6
324
7.22
8.36
9-50
A
*
IO4
120
I36
IOO
116
131
96
ill
126
92
107
121
88
IO2
116
84
98
in
81
93
i°5
77
88
TOO
73
84
95
69
79
90
65
75
*s
61
70
79
57
66
74
S3
61
69
49
57
64
46
52
59
42
48
54
99
TABLE 44.— Continued
SAFE LOADS OF Two ANGLE STRUTS, Axis 2-2
EQUAL LEG, AND UNEQUAL LEG WITH LONG LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
„..,,., , ijr==> . To left of heavy line values of 1/r do not
Safe loads in thousands of pounds with T tl'tf^ — exceed 125
respect to axis 2-2 JjP T • ht f heavy line values of 1/r d n t
p = 16,000 - 70 1/r JJB^ ISO
1
Section
Modulus
Radius
of
Gyration
O •»->
£1
O <u
+» p.
JS a>
68 A
'C M
*<
8
•s|
8<
<i
H
%
D
|
JS
H
Length in Feet
82
rj
ri
In.'
In.
In.
Lb.
In.»
In.
3 1 4
S
6 | 7
8
9
10
II
12
13
14
16
18
19
20
22
33
6"X3i" Angles
2.46
2.82
3-18
3.88
•99
.98
•97
.96
2-95
2.96
2.98
^.00
23-4
27.0
30.6
37-8
6.84
7-94
9.00
II. IO
3
8
&
I
1
92
107
121
148
86
IOO
H3
139
80
93
105
129
75
86
97
119
69
79
89
no
63
73
82
IOO
57
66
74
90
51
59
66
80
46
52
58
71
40
45
Si
61
6" X4" Angles
3.20
3-70
4.16
4.62
5.08
5-52
5-94
•17
.16
•IS
.14
•13
•13
.12
2.87
2.88
2.90
2.91
2.92
2-93
2-94
24.6
28.6
32-4
36.2
40.0
43-6
47-2
7.22
8.36
9-5°
10.62
11.72
12.82
13.88
1
A
I
A
f
u,
16
3
4
IOO
116
131
H7
161
177
191
95
no
124
139
153
167
1 80
90
104
117
131
144
157
170
84
97
no
123
135
148
160
79
9i
103
H5
127
138
149
74
85
96
107
118
129
139
69
79
90
IOO
109
119
128
64
73
83
92
IOO
IIO
118
59
67
76
84
92
IOO
108
53
61
62
76
83
9i
97
48
55
62
68
74
81
87
43
49
55
60
66
72
76
6"X6" Angles
7.06
8.14
9.22
10.28
11.32
12.34
I3-32
1.88
1.87
1.86
1-85
1.84
1.83
1.83
2.62
2.63
2.64
2.65
2.66
2.67
2.68
29.8
34-4
39-2
43-8
48-4
S3-o
57-4
8.72
IO.I2
II.5O
12.86
14.22
I5-56
16.88
A
5
9
¥
8
H
a
128
148
168
188
208
228
247
124
144
163
182
202
220
239
1 20
139
158
177
195
213
231
116
135
153
171
189
206
224
112
130
148
I65
182
199
216
1 08
126
142
159
176
192
208
i°5
121
137
153
169
185
2OO
IOI
117
132
147
163
178
193
97
112
127
I42
156
170
185
93
107
122
136
ISO
I63
177
89
103
117
130
H3
156
169
85
98
in
124
137
149
162
77
89
101
112
124
135
146
69
80
91
IOI
III
1 2O
131
66
75
85
95
104
H3
123
62
7i
80
89
98
1 06
"5
54
62
70
77
85
92
IOO
50
57
65
7i
78
TABLE 45
SAFE LOADS OF Two ANGLE STRUTS
EQUAL LEG, AND UNEQUAL LEG WITH SHORT LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
Safe loads in thousands of pounds for least
radius of gyration
p - 16,000 — 70 1/r
i
t To left of heavy line values of I/r do not
exceed 125
To right of heavy line values of 1/r do not
exceed 150
Section
Modulus
Radius of
Gyration
Weight of
Two Angles
per Foot
°f
fl«
k
1
Length in Feet
s>
ri
h
In.»
In.
In.
Lb.
In.»
In.
3
4
s
6
7
8
9
10
ii
12
13
i ;
ii"Xi|"Angles
.21
.27
•78
•79
.46
•41
3-6
4-8
1. 06
M8
A
II
H
9
12
7
9
2" X i {"Angles
.36
.46
•67
.68
•63
•63
4.2
5-4
1.20
i.«;6
A
14
19
13
17
II
15
IO
12
8
IO
I i"X if" Angles
.28
•38
.88
.89
•54
•53
4.4
5-6
1.24
1.62
t
H
18
12
16
10
H
8
ii
2" X 2" Angles
•38
.50
.98
•99
.62
.61
S-o
6.4
1.44
1.88
t
17
22
15
20
13
17
ii
IS
9
12
2 J"X2" Angles
•%
.76
•94
.92
•94
•95
•79
.78
.78
5-6
7-4
9.0
1.62
2.12
2.62
A
A
21
27
33
19
25
31
17
23
28
16
20
tt
14
18
22
12
16
19
IO
13
17
2 J"X2j" Angles
.80
.96
1.14
1.19
i. 20
1. 21
•77
.76
•75
8.2
IO.O
u.8
2.38
2.94
3-46
I
f
30
37
44
28
34
40
25
31
36
22
28
32
20
24
28
17
IS
18
21
21
24
....
3" X2" Angles
1. 08
1. 32
I.S6
.89
.90
•91
•95
•95
•94
8.2
IO.O
11.8
2.38
2.94
3-46
1
3i
39
46
29
36
43
27
33
39
25
31
36
22
28
33
20
25
3°
18
22.
27
16
20
23
13
17
20
3" X2|" Angles
1. 12
1.38
1.62
•13
.14
.16
•95
•94
•93
9.0
II. 2
13.2
2.62
3-24
3-84
1
35
43
Si
33
40
48
30
37
44
28
34
4i
26
32
37
23
29
34
21
26
3°
19
23
27
16
20
23
3" X3" Angles
1.16
1.42
1.66
1.90
2.14
•39
.40
.41
.42
1.44
•93
.92
.91
.91
.90
9.8
12.2
144
16.6
18.8
2.88
3-56
4.22
4.86
5-50
J
{
38
f
64
73
36
44
£
60
67
33
4i
48
55
62
3°
37
44
Si
57
28
34
4°.
46
52
25
3i
36
42
47
23
28
32
37
42
20
24
29
33
37
17
21
25
28
32
101
TABLE 45. — Continued
SAFE LOADS OF Two ANGLE STRUTS
SHORT LEG TURNED OUT
AMERICAN BRIDGE COMPANY STANDARDS
To left of heavy line values of I/r do not
Safe loads in thousands of pounds for least f! — exceed 125
radius of gyration To right of heavy line values of 1/r do not
p = 16,000 - 70 1/r -1J«-H" exceed 150
i
Section
Modulus
Radius
of
Gyration
i§
Hta
3&
•§j3
"55 M
£ c
£<
°|
^H
•
en
0)
J
o
'£
H
Length in Feet
S,
n
rj
In.«
In.
In.
Lb.
In.«
In.
3
4
5
6
7
8
9
10
ii
12
13
14
IS
16
17
18
19
20
21
4" X3" Angles
2.46
2.92
3-36
3-78
4.18
4.60
1.30
I-3I
1.32
i-33
i-34
136
1.27
1.26
1.25
1.25
1.24
1.23
14.4
17.0
19.6
22.2
24.8
27.2
4.18
4.96
5-74
6.50
7-24
7.96
A
t
f
A
f
59
69
80
9i
1OI
in
56
66
76
87
96
106
8
73
82
9i
IOO
50
I9
69
78
86
95
48
I6
65
73
82
89
45
8
69
77
84
42
5°
57
65
72
78
39
46
53
60
67
73
37
43
49
I6
62
68
34
40
46
52
57
62
31
36
42
47
28
33
38
43
47
5i
25
3°
34
38
4*
46
52
57
S"X3" Angles
3-78
4.48
S-I6
5-82
6.46
7.10
1.22
1.23
1.24
1.25
1.26
1.28
1.61
1.61
i. 60
i-59
1.58
i-57
16.4
19.6
22.6
25-6
28.6
31-4
4.80
5-72
6.62
7.50
8.36
9.22
A
1
t
¥
67
80
92
105
117
129
64
76
88
IOO
in
123
60
72
83
95
106
117
57
68
79
90
IOO
in
54
64
75
85
95
105
5°
60
70
80
89
99
47
56
66
75
84
93
44
52
61
70
78
87
40
49
57
65
72
81
37
45
I2
60
67
75
34
4i
48
54
61
69
3i
37
43
49
56
63
27
33
39
44
50
57
51
5" X3i" Angles
3.88
4-58
5-28
5-98
6.64
7-30
7-94
8.56
1-45
1.46
1.47
1.49
1.50
i-Si
I-S2
i-S3
1.61
i. 60
i-S9
1.58
1-57
1.56
1.56
i-SS
174
20.8
24.0
27.2
30-4
33-6
36.6
39-6
I'12
6.10
7.06
8.00
8.94
9.84
10.74
11.62
-A
1
8
f
73
87
IOI
114
128
141
iS4
167
70
84
97
no
123
136
148
160
67
80
93
105
118
130
142
154
64
77
89
IOI
"3
125
136
148
61
73
85
96
108
119
130
141
58
70
HI
92
103
114
124
135
55
66
77
87
98
108
118
128
£
73
83
93
103
H3
122
49
59
69
78
88
97
107
116
46
55
65
74
83
92
IOI
109
43
52
61
69
78
86
95
103
40
48
57
65
73
81
89
97
37
45
53
60
68
75
83
90
34
4i
48
56
63
70
77
84
31
38
44
Si
f
64
7i
77
28
34
40
47
S3
I9
65
7i
59
65
;;
6" Xai" Angles
6.50
7-5°
8.48
9-44
10.38
11.30
12 2O
i-39
1.40
1.41
1.42
1-43
1.45
1.46
1.94
i-93
1.92
1.91
i 90
1.89
1.89
234
27.0
30.6
34-2
37-8
41.2
44.8
6.84
7-94
9.00
10.06
II. IO
12.12
13.12
A
A
f
f
97
"3
128
H3
158
173
187
93
108
123
137
152
166
1 80
89
103
117
131
H5
159
172
85
98
112
125
138
T
165
81
94
106
119
132
145
157
76
89
IOI
"3
125
138
15°
72
84
96
107
119
131
142
68
79
90
IO2
112
124
135
64
74
85
96
106
117
127
60
70
80
90
99
no
119
56
65
74
84
93
103
112
F
60
69
78
86
96
104
47
55
64
72
80
43
5i
58
66
73
82
89
39
46
53
60
67
75
82
89
97
68
74
6" X4" Angles
6.64
7.66
8.66
9.66
10.62
11.56
12.50
1.62
1.63
1.65
i 66
1.67
1.68
1.70
i-93
1.92
1.91
1.90
1.90
1.89
1.88
24.6
28.6
324
36.2
40.0
43-6
47.2
7-22
8.36
9-50
10.62
11.72
12.82
13.88
f
A
2
9
TS
f
tt
f
104
121
138
154
170
1 86
202
IOI
117
133
148
164
179
195
97
112
128
143
158
173
188
93
108
123
138
152
167
181
89
104
118
132
146
1 60
174
86
99
H3
127
140
154
167
82
95
109
122
134
147
160
78
91
IO4
116
129
141
153
74
86
99
in
123
135
H7
7i
82
94
105
117
128
140
67
78
89
IOO
III
122
133
63
74
84
95
105
"5
126
59
69
79
89
99
109
119
56
65
75
84
93
103
112
52
61
70
79
87
96
105
48
56
65
73
81
90
99
45
52
60
68
76
83
92
41
48
55
62
70
77
85
71
78
102
TABLE 46
PROPERTIES AND ELEMENTS OF Z BARS
1
1
I
Actual Size
I
Moments of
Inertia. I
Radii of Gyration, r
•
1
Inches*
Inches
Nominal
1
H
1
Si
1
1
1
eutral Axis
ugh Center of
vity Perpen-
ular to Web
eutral Axis
ough Center
rravity Coin-
nt with Web
eutral Axis
ugh Center of
vity Perpen-
ular to Vveb
1? •£ •- '5
i M > *
3 3 0 w
S o,1: =
ast Radius,
?utral Axis
Diagonal
1
1
1
E ft B a
'Z.jz
'/ ^ 2 —
Vj£
I
In.
In.
In.
In.
Lb.
Sq.In.
.a0T>
H-3-1
£W°
H-sl
In.
In
In.
1
6
1
IS-6
I8.3
21.0
4-59
5-39
6.19
25.32
29.80
9-II
10.95
12.87
2-35
2-35
2-36
1.41
1.43
1-44
0.83
0.83
0.84
2}
•
•9«
6
3i.
22.7
6.68
34-64
12-59
2.28
i-37
0.8 1
6
fi
6*
?f
25-4
28.0
7.46
8.25
38.86
43.18
14.42
16.34
2.28
2.29
i-39
1.41
0.82
0.84
2}
1
6
i
6
1*
29-3
8.63
42.12
15-44
2.21
i-34
0.8 1
ft
6A
6*
if
31-9
34-6
9.40
10.17
46.13
50.22
17.27
19.18
2.22
2.22
1.36
1.37
0.82
0.83
2}
i
A
5,
3i
n.6
3-40
I3-36
6.18
1.98
1.35
0-75
A
it
If
13-9
16.4
4.10
4.81
16.18
19.07
7-65
9.20
1.99
1-99
i-37
138
0.76
0.77
2*
i
i
5,
3i
17.9
5-25
19.19
9.05
I.9I
1.31
o-74
5
TS
It
If
20. 2
22.6
5-94
6.64
21.83
24-53
10.51
12.06
I.9I
1.92
1-33
0.75
0.76
^
i
5
H
5
3}
23-7
6.96
23.68
ii-37
1.84
1.28
0-73
1
sA
3A
26.O
7.64
26.16
12.83
I.8.;
1.30
0.74
a|
i
i*
it
3*
28.3
8-33
28.70
14.36
1.86
0.76
A
i*
3A
8.2
10.3
2.41
3-03
6.28
7-94
4-23
5-46
1.62
1.62
1-33
1-34
0.67
0.68
2
1
*
41
3A
12.4
3-66
9-63
6-77
1.62
1.36
0.69
4
i
:c
It
3A
13.8
15.8
17.9
4.05
4.66
5-27
9.66
11.18
12.74
6-73
7.96
9.26
1-55
1.29
1.31
1.33
0.66
0.67
0.68
2
f
4
f
4
3A
18.9
5-55
12. II
8-73
1.48
1.25
0.66
H
4A
3i
20.9
6.14
I3-52
9-95
1.48
1.27
0.67
2
}
i
4]
i iV
23.0
6-71
14.97
11.24
1.49
1.29
0.68
A
!*
,11
zi«
6.7
8.4
1-97
2.48
2.87
2.81
3-64
1. 21
1. 21
1.19
1. 21
0.55
0.56
If
i
3
f
ft
!*
2ii
9-7
11.4
2.86
3.85
4-57
3.92
4-75
1.16
I.I7
I.I7
I.I9
0-54
0.55
If
1
3
i
3,
2tt
12.5
3-69
4-59
4.85
1. 12
1.15
0-53
i
A
3A
si
14.2
4.18
5.26
5.70
1. 12
I.I7
o-54
i
103
TABLE 47.
ELEMENTS OF CARNEGIE EQUAL TEES.
J
2
^fe
2
Size.
Weight
per Foot.
Area
of
Sec-
tion.
Axis i-r.
Axis 2-2.
Flange.
Stem.
Min. Thickness.
I
r
S
X
I
r
S
Flange.
Stem.
In.
In.
In.
In.
Lb.
In.2
In.<
In.
In.«
In.
In.4
In.
In.3
4
4
i
\
13-5
3-97
5-7
1.20
2.O
1.18
2.8
0.84
1-4
4
4
i
3
8
10.5
3-09
4-5
1. 21
1.6
1-13
2.1
0.83
I.I
3l
3*
§
1
II.7
3-44
3-7
1.04
i-S
1.05
i-9
0.74
I.I
3i
si
I
3
8
9.2
2.68
3-o
1.05
1.2
I.OI
i-4
o-73
0.81
3
3
1
\
9-9
2.91
2-3
0.88
I.I
0-93
1.2
0.64
0.80
3
3
A
A
8.9
2-59
2.1
0.89
0.98
0.91
I.O
0.63
0.70
3
3
I
i
8
7.8
2.27
1.8
0.90
0.86
0.88
0.90
0.63
0.60
3
3
s
T^
A
6-7
i-9S
1.6
0.90
0.74
0.86
o-7S
0.62
0.50
*\
2l
t
f
6.4
1.87
I.O
0.74
o-59
0.76
0.52
0.53
0.42
2|
2j
A
A
5-S
i. 60
0.88
0.74
0.50
0.74
0.44
0.52
0-35
2l
2j
A
A
4-9
i-43
0.65
0.67
0.41
0.68
o-33
0.48
0.29
2l
2*
i
i
4.1
1.19
0.52
0.66
0.32
0.65
0.25
0.46
O.22
2
2
A
A
4-3
1.26
0.44
o-S9
0.31
0.61
0.23
0.43
0.23
2
2
i
i
3-S6
1.05
0-37
0-59
0.26
o-59
0.18
0.42
0.18
If
If
i
i
3-°9
0.91
0.23
0.51
0.19
o-S4
0.12
0.37
0.14
If
li
i
i
2.47
o-73
0.15
o-45
0.14
0.47
0.08
0.32
O.IO
I*
I*
A
A
1-94
0-57
O.II
0-45
O.II
0.44
0.06
0.32
0.08
II
ii
i
i
2.O2
0-59
0.08
0-37
O.IO
0.40
0.05
0.28
0.07
II
ij
A
A
i-S9
0.47
0.06
o-37
0.07
0.38
0.03
0.27
0.05
I
i
A
A
1-25
0-37
0.03
0.29
0.05
0.32
O.O2
O.22
0.04
I
i
i
8
8
0.89
0.26
O.O2
0.30
0.03
0.29
O.OI
O.2I
0.02
104
TABLE 48.
ELEMENTS OF CARNEGIE UNEQUAL TEES.
f
i 1 ^ 1 „ I
'l
T
Section
Index.
Size.
Weight
per
Foot.
Area
of
Section.
Axis i-i.
Axis 2-2.
Flanee.
Stem.
Minimum
Thickness.
I
• r
s
X
I
r
s
Flange.
Stem.
In.
In.
In.
In.
Lb.
In.«
In.*
In.
In..
In.
!„.•
In.
In.'
T 50
S
3
\
i
|
13-4
3-93
2.4
0.78
I.I
0-73
5-4
•17
2.2
T 51
T 52
«
•
*f
3i
<
6
i
i
10.9
15-7
3.l8
4-.OO
i-5
5-i
0.68
1.05
0.78
2.1
0.63
I. II
4.1
3-7
.14
0.90
1.6
1-7
T 54
4:
3
i
i
9-8
2.88
2.1
0.84
O.gi
0.74
3-o
.02
1-3
T 53
4:
•
3
/
I
i
8.4
2.46
1.8
0.85
0.78
0.71
2-5
.01
i.i
T 56
4'
•
^\
-
9.2
2.68
1.2
0.67
0.63
0-59
3-o
.05
i-3
T 55
4i
•
3
i
*
i
7.8
2.29
I.O
0.68
0.54
o-57
2-5
.05
i.i
T|57
4
5
1
'.
i
15-3
4.50
10.8
1.55
3-i
1-56
2.8
0.79
1-4
T 58
4
5
1
*
i
11.9
3-49
8.5
!.S6
2.4
1.51
2.1
0.78
i.i
T 59
4
4f
i
•
14.4
4-23
7-9
2-5
i-37
2.8
0.81
1.4
T 60
4
4*
II. 2
3-29
6-3
1.39
2.0
i-3i
2.1
0.80
i.i
T 61
4
3
>
9-2
2.68
2.O
0.86
0.90
0.78
2.1
0.89
i.i
T 44
4
3
i
f
A
7-8
2.29
i-7
0.87
0.77
0.75
1.8
0.88
0.88
T 62
4
-
i
\
8.S
2.48
1.2
0.69
O.62
0.62
2.1
0.92
I.O
T 63
4
2}
A
l"
fc
7-2
2.12
I.O
0.69
0-53
0.60
1.8
0.91
0.88
T 64
4
2
1
\
1
7.8
2.27
O.6o
0.52
0.40
0.48
2.1
0.96
i.i
T.6S
4
2
A
A
6-7
1-95
o-53
0.52
o-34
0.46
.8
0.95
0.88
T 66
si
4
i
•
12.6
3-70
5-5
1. 21
2.O
1.24
•9
0.72
i.i
T 67
3
4
i
•
9.8
2.88
4-3
1.23
•5
1.19
•4
0.70
0.8 1
T 69
3
3
:
•
10.8
3-17
2.4
0.87
.1
0.88
•9
0.77
i.i
T 70
3
3
8-5
2.48
i-9
0.88
0.89
0.83
•4
0.75
0.8 1
T 71
31
3
i
f
i
7-5
2. 2O
1.8
0.91
0.85
0.85
.2
0.74
0.68
T 72
3
4
r
.
•
11.7
3-44
5-2
•23
•9
•32
.2
0.59
0.8 1
T 73
3
4
i
*
A
10.5
3.06
4-7
•23
•7
•29
.1
0-59
0.70
T 74
3
4
i
\
i
f
9-2
2.68
4.1
•24
•5
•27
0.90
0.58
0.60
T 75
T 76
3
3
' 3f
3i
1
"
ii
A
10.8
9-7
3-17
2.83
3-5
3-2
.06
.06
•5
•3
.12
.IO
.2
.O
0.62
0.60
0.80
0.69
T 77
3
3*
i
i
8-5
2.48
2.8
.07
.2
.07
0.93
0.61
0.62
T 78
3
2*
-
i
2.07
i.i
0.72
O.6O
0.71
0.89
0.66
0.59
T 79
3
Sjl
i
i
T<
fc
6ii
1.77
0.94
0.73
0.52
0.68
0-75
0.65
0.50
T 31
3,
A
\
;
S-o
1.47
0.78
0-73
0-43
0.66
0.61
0.64
0.40
T 82
2*
3
i
2.07
i-7
0.91
0.84
0-95
0-53
0.51
0.42
T 83
2;
i
3
i
r
J
,
6.1
1-77
i-5
0.92
O.72
0.92
0.44
0.50
o-35
T 86
2;
f
ij
A
2.87
0.84
0.08
0.31
0.09
0.32
0.29
0.58
0.23
T 87
2
If
2
j
j
i
3-09
2-45
0.91
0.72
0.16
0.27
0.42
0.61
0.15
O.I9
0.42
0.63
0.18
0.06
0-45
0.92
0.18
0.08
T6os
i*
It
i
-
1-25
0.37
0.05
0-37
O.O5
0-33
0.04
0.32
0.05
T6o3
it
t
No. 9
I
0.88
0.26
O.OI
0.16
O.OI
0.16
O.O2
0.31
0.04
46
105
TABLE 49.
ELEMENTS OF A. S. C. E. AND LIGHT RAILS.
|* 0—
_La"
— *l
1
^-^ f
*• 18 4
-- f -
12'Rad.
" ?
.Li
4^
'"•
-6- J
'
Section
Index.
Weight
per
Yard.
Area
of
Section.
Dimensions.
Axis i-i.
a
b
c
d
e
f
g
h
I
r
S
X
Pounds.
In..
In.
In.
In.
In.
In.
In.
I
In.
In.
In.«
In.
In.«
In.
noA
no
10.80
61
6J
»i
Iff
3ti
2*f
55-2
2.26
17.2
2.92
looA
IOO
9.84
Sf
Sf
2f
itt
3A
tt
A
2t^r
44.0
2.11
14.6
2-73
95A
95
9.28
sA
sA
2H
lit
2ff
tt
A
2^ft
38.8
2.O5
13-3
2.65
goA
90
8.83
sf
sf
2f
itt
2tt
tt
A
2tW
34-4
1-97
12.2
2-55
8SA
85
8-33
SA
sA
2A
Iff
2f
It
9
T6
2H
30.1
1.90
II. I
2.47
8oA
80
7.86
S
5
*i
If
2f
1
fi
*A
26.4
1.83
IO.I
2.38
75A
75
7-33
4tt
4tt
2M
Itt
2ff
tt
&
2l"A
22.9
i-77
9.1
2.30
7oA
70
6.8 1
4f
4l
2yV
itt
2M
T6
ff
2&
19-7
1.70
8.2
2.22
65 A
65
6-33
*A
4A
2M
iA
2f
fi
*
If*
16.9
1.63
7-4
2.14
6oA
60
5-93
4t
4t
2f
i A
2H
ff
ft
ittf
14.6
i-S7
6.6
2.05
5SA
55
5-38
4rV
4rV
2t
iii
2ii
f*
H
lift
I2.O
1.50
5-7
i-97
SoA
SO
4.87
3i
3l
2|
it
2fV
H
A
if*
9-9
i-43
S-o
1.88
4SA
45
4.40
3tt
3ri
2
iA
Itt
tt
ft
itt
8.1
1.36
4-3
1.78
4oA
40
3-94
3i
3i
If
iA
Iff
5
8
25
64
IT7?'?
6.6
1.29
3-6
1.68
3SA
35
3-44
3A
3A
If
ft
If*
A7
ft
ff
Itt
5-2
1.23
3-o
i. 60
3oA
30
3.00
3i
3i
lit
1
Iff
17
32
ft
Iff
4.1
1.16 '
2-5
1.52
25A
25
2-39
2f
2f
If
ff
Itt
li
64
if
IT%
2-5
1.02
1.8
i-33
2OA
20
2.OO
2f
2f
Itt
ft
Itt
A
i
lit
1.9
0.99
1.4
1.27
i6A
16
i-SS
2|
2f
iii
It
Iff
3
8
A
irk
1.2
0.89
I.O
i-iS
I4A
H
i-34
2fV
2A
iA
f
>A
tt
4
«i
0.76
0-75
0-73
1.02
I2A
12
1.18
2
2
i
TS
iA
11
3"2
fV
H
0.66
0-75
0.63
0.96
loA
10
0.96
If
If
15
-If
H
19
64
Tl?
tt
0.40
0.65
0.46
0.87
8A
8
0.77
iA
iA
15
if
9
&
it
0.26
0.58
0.32
0-7S
106
TABLE 50.
ELEMENTS OF CARNEGIE BULB BEAMS.
j
)
k
kV-
Depth
Wt.
Area
of
Width
nf
Thick-
ness
Axis
I-I.
Axi«
»-3.
Beam.
p*r
Foot.
Sec-
tion.
Flange.
of
Web.
I
r
s
X
I
r
S
r
In.
Lb.
In.*
In.
In.
In.«
In.
In.«
In.
In.«
In.
In.»
In.
IO
36.6
IO.62
5.500
0.625
140.4
3.64
25-3
4-45
7.6
0.84
2.8
2-75
IO
28.1
8.12
5-2SO
0-375
118.6
3.82
20.7
4.28
6-3
0.88
2-4
2.63
9
30.1
8.83
5-125
0.563
95.8
3-29
19.4
4.06
5-4
0.78
2.1
2.56
9
24-3
7-iS
4.938
0-375
84.0
3-43
16.6
3-95
4.6
0.80
•9
2.47
8
24.2
7.11
5-I56
0.469
62.8
2-97
14.1
3-54
4-5
0.79
-7
2.58
8
2O.O
5.86
5.000
0.313
55-6
3.08
12.2
3-43
3-9
0.82
.6
2.50
7
23-3
6.85
5.094
0-531
45-5
2.57
II.7
3-H
4-3
0.79
•7
2-55
7
18.1
5-32
4.875
0-313
38.8
2.70
9-7
2.98
3-6
0.82
•5
2-44
6
17.2
5.00
4-524
0.430
24.4
2.20
7-2
2.61
2-7
°-73
.2
2.26
6
14.0
4.11
4J2S
0.281
21.6
2.28
6.1
2.46
2.2
0.72
.0
2.19
TABLE 51.
ELEMENTS OF CARNEGIE BULB ANGLES.
t-r
t
T *
/a
Depth
of
Beam.
Wt.
per
Foot.
Area
of
Sec-
tion.
Width
of
Flange.
Thick-
ness
of
Web.
Axis i-i.
Axis 2-2.
I
r
S
z
I
r
S
y
In.
Lb.
In.'
In.
In.
In.«
In.
In.»
In.
In.«
In.
In.'
In.
IO
32.0
9.41
3.500
0.625
116.0
3-51
21.6
4.62
6.2
0.82
2-3
o-77
10
26.6
7.80
3.500
0.484
104.2
3-66
19.9
4-75
S-o
0.8o
1.8
0.72
9
21.8
6.41
3.500
0.438
69-3
3-33
14.5
4.21
4-3
0.82
I-5
0.72
8
19-3
5-66
3.500
0.406
48.8
2.95
II.7
3-83
3-7
0.8 1
!-3
0.71
7
7
20.0
18.3
5-81
5-37
3-000
3.OOO
0.500
0.438
36.6
34-9
2.51
2.56
10.0
9.6
3-34
3.36
2.9
2.6
0.71
0.69
i.i
0.70
0.68
7
16.1
4.71
3-000
0-344
32.2
2.61
8.7
3-30
2.7
0.76
1.2
0.72
6
17-3
<;.o6
3.000
0.500
23.9
2.16
7.6
2.84
2-5
0.70
I.I
0.71
6
6
15.0
13.8
4-38
4.04
3.000
3-000
0.406
0-375
21. 1
20.1
2.19
2.21
6-7
6.6
2$
2.3
0.72
0.69
1.0
0.82
0.69
0.65
6
12.4
3.62
3.000
0.313
18.6
2.28
5-7
2.71
1.8
0.70
0.75
0.64
5
10.0
2-94
2.500
0.313
IO.2
1.86
4.1
2.49
0.95
0.57
o-49
0-57
4
14.3
4.21
3.500
0.500
8.7
1.44
3-7
1.65
3-9
0.96
1-5
o-99
4
1 1. 9
1-48
3.1; oo
0.371;
7-9
I.qo
JJ
1-77
SJ
0.94
1.2
0.94
107
TABLE 52.
ELEMENTS OF CARNEGIE H BEAMS.
'
!
^
E
Depth
of
Beam.
Wt.
per
Foot.
Area
of
Sec-
tion.
Width
of
Flange.
Thick-
ness
of
Web.
Axis i-i.
Axis 2-2.
I
r
s
I
r
S
In.
Lb.
In.*
In.
In.
In.<
In.
In. 3
In.«
In.
In.'
8
6
5
4
34-0
23.8
I8.7
13.6
IO.OO
7.00
5-5°
4.00
8.0
6.0
5-o
4.0
•375
•313
•313
.313
IIS4
45-i
23.8
10.7
3-40
2-54
2.08
1.63
28.9
IS.O
9-5
£J
3S-i
14.7
7-9
3-6
1.87
i-45
i. 20
0-95
8.8
4-9
3-i
1.8
TABLE 53.
CARNEGIE TROUGH PLATES.
_f
»- Or >j*---° *
— "*— 4*— Or— *
ELEMENTS OF TROUGH PLATES.
Single Section.
Riveted Section.
Section
Index.
Size.
Inches.
Weight
per Foot,
Pounds.
a,
Inches.
d.
Inches.
Weight per Section
Square Foot, I£od]jl,lif.1J9?e
Pounds. Fo*)t w'dth.
M i.»
9iX3|
23.2
8
6J
34.8 15.58
M 13
9l X 3f
21.4
8
6f
32.1 14.28
Mia
9i X 3J
197
8
6i
29.6 13.00
M ii
9i X 3i
1 8.0
8
6i
27.0 11.79
M 10
9iX3J
16.3
8
6
24.5 10.69
ALLOWABLE
UNIFORM LOAD IN POUNDS PER SQUARE FOOT.
Span
Fiber Stress, 16,000 Lbs. per Sq. In.
Fiber Stress, 12,000 Lbs. per Sq. In.
Feet.
M 14
M 13
M 12
M ii
M
IO
M 14
M 13
M 12
M ii
M 10
5
6647
6093
5547
5030
4561
4986
457°
4160
3773
3421
6
4616
4231
3852
3493
3167
3462
3173
2889
2620
2376
7
3392
3109
2830
2567
2327
2543
2331
2124
1925
1745
8
2597
2380
2167
1965
1782
1948
1785
1625
H74
1336
9
2052
1880
1712
1553
1408
1539
1410
1284
1164
1058
. IO
1662
1523
1387
1258
1140
1246
1142
1040
943
855
ii
1373
1259
1146
1039
942
1030
944
860
780
707
12
"54
1058
963
873
792
866
1
722
655
594
13
983
901
821
744
675
738
676
615
558
506
14
!
U8
777
707
642
582
636
5S3
531
481
436
IS
739
677
616
559
507
554
509
462
419
38i
16
649
595
542
491
445
487
446
406
368
334
17
575
527
480
435
395
431
395
360
328
296
18
513
470
428
388
352
385
353
321
291
264
19
460
422
384
349
316
345
316
288
261
237
20
415
38i
347
3H
285
312
286
260
236
214
The values given in above tables are the safe loads per square
foot of floor surface and are
based upon the average resistance of the riveted portion within distance a.
The weight of the plates are included in the safe loads and must be deducted to obtain the
net superimposed safe load.
Safe loads for other fiber stresses than those
given in table may
be obtained from the values
given by direct proportion of the fiber stresses.
The weight per square foot does not include the weight of rivet heads or other details.
109
TABLE 54.
CARNEGIE CORRUGATED PLATES.
vM
'\y
f
TV
^
/
ss:%w
. _«_ .
^
^
4
¥"
ELEMENTS OF CORRUGATED PLATES.
Single Section.
Riveted Section.
Section
Index.
Size,
Inches.
Weight per
Foot,
Pounds.
a,
Inches.
d.
Inches.
Weight per
Square Foot,
Pounds.
Section
Modulus,
One Foot
Width,
Inches'.
M3S
I2& X 2}
23-7
»*
a|
23-3
4-39
M34
I
ITS X 2
M
20.8
I2iV
2TS
20.4
3-84
M 33
I2& X 2f
17.8
I2lV
2|
17-5
3.28
M 32
1
3f X if
I2.O
8f
If
I6.S
1-95
M3i
!
31 Xi
TS
10. 1
O 3
IT*
13-8
i-55
M 30
!
if Xii
8.1
81
ii
II-5
1. 10
ALLOWABLE UNIFORM LOAD IN POUNDS
PER SQUARE FOOT.
Span
in
Feet.
Fiber Stress, 16,000 Ib. per sq.
in.
Fiber Stress, 12,000 Ib. per sq. in.
M3S
M34
M33
M32
M3i
M30
M3S
M34
M 33
M32
M3I
M30
5
1873
1638
1400
832
661
469
1405
1229
1050
624
496
352
6
1301
1138
972
578
459
326
976
853
729
433
344
244
7
956
836
7H
425
337
240
717
627
536
3i8
253
1 80
8
732
640
547
325
258
183
549
480
4IO
244
194
138
9
578
506
432
257
204
145
434
379
324
193
153
109
10
468
4IO
35°
208
165
H7
3
51
307
262
156
124
88
ii
387
339
28
9
172
137
97
290
255
217
129
103
73
12
325
284
243
H4
ii
5
82
244
213
182
108
86
61
13
277
242
207
123
9
3
69
208
182
155
92
73
52
14
239
209
179
106
8
1
60
179
157
134
80
63
45
IS
208
182
156
92
74
52
156
137
117
69
Si
39
The values given in above tables are the safe loads per square foot of floor surface and are
based upon the average resistance of the riveted portion within distance a.
The weight of the plates are included in the safe loads and must be deducted to obtain the
net superimposed safe load.
Safe loads for other fiber stresses than those given in table may be obtained from the values
given by direct proportion of the fiber stresses.
The weight per square foot does not include the weight of splice bars, rivet heads or other details.
110
TABLE 55.
BUCKLE PLATES.
AMERICAN BRIDGE COMPANY STANDARD.
ii,
-^^**™B^
L
^.
,i
f
gr
tf* 1 -»i- * <n- • n*- •
;\ 7
\ ;
/
\
7
\ :
/
:
'•/ N
\
/ \
/
\
L^
JJ.
J.*!-
j
Size of Buckle.
Radii of Buckle.
Number
Widths of Flanges and Fillets.
1
Rised,
of
Buckles
I
Sidel.
Ft.-In.
Side b.
Ft.-In.
In.
Sidel.
Ft.-In.
Side b,
Ft.-In.
in One
Plate.
End Flanges
h. U.
Fillets
It.
Side Flanges
bi, bt.
I
3-11
4_
6
3*
6- 8j
\
8-9J
I to 8
2
4-6
3-
ii
si
8-9*
6- 8j
[ to 7
•5 ^ i
3
3-u
3-
6
3
7-9i
\
6-3
I to 8
5
L
^
v
•o c •—
'C1 « 3
4
3-6
3-n
3
6-3
7- 9!
. I to 9
^O ^H
vo
^«?
5
3- 9
3-
9
3
7- i;
7- ii
i to 8
pi
« *J
r
I
« o -
3 k O
6
3- i
3-
9
3
4-ioi
7- ii
i to 10
1
1
e
' cr~ <-•
7
3- 9
3-
i
3
7- ii
4-io|
i to 8
£
: '
I
3
™ ^ ~4 fL
8
3-8
3~
8
2
10- 2
IO- 2
i to 8
2 "3
'H
1
:^ 2 S
9
2- 8
3-
8
2
5- 5
10- 2
[ to U
•p W
1
i^
";
! ° -fi
10
3-8
2-
8
2
10- 2
5- 5
i to 8
i
%^
1
1
^
^
! « ^ f
ii
2- 2
3-
8
2
3-7*
10- 2
i to 14
i c
^M -^
Xl GO o
12
3- 8
2-
2
2
IO- 2
3-71
i to 8
iS
T3
t>
8
^m
*o o a*
13
3- o
3~
0
2
6-10
6-10
I to 10
ctf
0)
a
> CO
fc
0
"c3
U
B if M
ct ** C
H
2- 9
2-
9
3
3-10;
3~ioj
I tO II
1*
w
T3
•
19
2- 6
2-
9
^
3-10;
4-7i
I to 12
1
co C
cu u
0.
x-otc
20
2- 9
2-
6
4- 7i
3-10-
1
I to ii
>»
iw
CO
CO
>,
So st
21
2- 6
2-
6
3
3-10;
3-10;
L
I to 12
2
g~*
JJ
IS
e jj g
22
3- 5
3-
6
3
5-"i
\
6-3
[ to 9
E
u
O
«*i
^-S «
23
3-6
3-
5
3
6-3
5-113
96
i to 9
B
3
5
O La C
T3 O «.
24
3-6
3-
9
3
6-3
7- if
[ to 9
PH
vo
£
.—
25
3- 9
3-
6
3
7- i]
6-3
[ to 8
^
T
.,
^
<u -~ .
26
3- 4
3-
i
3
5- n
\
4-10]
[ to 9
«;
« '
t
4
t
. 4_» "^ -^* r"
^ *^ --i 4-* C
c 3 -a —
27
3- i
3-
2
3
4-10
5- ii
i
I tO 10
1
jg
1
i
28
^ — o
3-
I
3
4- 7=
4-10;
[ to 10
E
: "5
• .
g
L
:> » u 2
29
3- i
3-
0
3
4-10
4-7i
i to 10
||
3
gTi2^
3°
2- 6
2-
0
2'
3-10]
2— 6-
^
I tO 12
*e 'L
r
j
: . v H
31
2- 0
2-
6
2'
2- 6-
V
3~IO;
I to 15
.— *^
i
G
^
H
i
ti
3 ^ \
32
5-6
3-
6
3'
13- i
\
5- 4:
i to 5
^
;i-
H
<
1
H
i*
5^ 6^^
33
3-6
5-
6
3i
5- 4-
13- I-
i
i to 9
o ^ *T3
34
4- o
4-
0
3
8- IJ
8- i.
i to 7
w O ^
Plates are steel \", A", i
" or A" thick.
Plates of greater length than given in table may be made by splicing with bars, angles, or tees.
All plates are made with buckles up, unless otherwise ordered. When buckles are turned down,
a drain hole should be punched in the center of each buckle and should be shown on sketch.
Buckles of different sizes should not be used as it increases the cost of the plate.
Connection
holes are generally for
I", f" or J" rivets or bolts.
Different sized holes in same
plate will increase the cost of the plate.
Spacing for holes lengthwise of plate should be in multiples of 3
and should not exceed 12".
Odd spaces to be at end of plate and in even }".
Minimum spacing crosswise
4J", usually 6".
Die number must be shown on drawings.
Sketches for Buckle Plates should indicate allowable overrun in length and width.
111
TABLE 56.
PROPERTIES OF COLUMN SECTIONS.
«=r:=
Properties of ,
Three I-Beam A~- \
Section. /
csfj;
B
' ^
- \ -
h
zr=y
r Minimum
[ ---.4 I-Beam
\ for Web.
__i
SERIES I
AND II.
SERIES I.
SERIES II.
Flange
Beams.
Web
Beam.
Total
Area.
Moments of Inertia and
Radii of Gyration.
Web
Beam.
Total
Area.
Moments of Inertia and
Radii of Gyration.
f
I
1
I
i
Q
1
1
Axis A- A.
Axis B-B.
jj
fi
8
|
M
1
Axis A-A.
Axis B-B.
IA
TA
IB
re
IA
TA
IB
TB
In.
Lb.
In.
Lb.
In."
In.4
In.
In.«
In.
In.
Lb.
In.2
In.<
In.
In.<
In.
IO
«
«
«
«
25
25
30
3°
35
35
8
IO
8
10
8
IO
18
25
18
25
18
25
20.07
22.11
22.97
25.01
25.91
27.95
'248
251
272
275
297
300
3-51
3-37
3-44
3-32
3-38
3-27
325
528
387
619
455
717
4.02
4.89
4.11
4-97
4.19
5.06
9
12
9
12
9
12
21
3I-S
21
31-5
21
31-5
2I.O5
24.00
23-95
26.90
26.89
29.84
249
254
274
278
298
3O2
3-44
3-25
3-38
3-21
3-33
3.18
418
788
494
915
576
1050
4-45
5-73
4-54
5-83
4-63
5-93
12
fl
«
(«
«
"l5"
<
<
<
<
3i-5
3i-S
35
35
40
40
IO
15
10
15
IO
15
25
42
25
42
25
42
25-89
3I.OO
27-95
33-06
3'-°S
36.16
439
446
464
471
545
552
4.12
3-79
4.07
3-78
4-19
3-91
635
1552
703
1688
797
1884
4-95
7.07
S-oi
7.14
5.06
7.22
12
18
12
18
12
18
31-5
55
3I-S
55
3I-S
55
27.78
34-45
29.84
36.51
32-94
39.61
441
453
466
478
547
559
3-98
3-63
3-95
3-62
4.08
3-76
94i
2373
1032
2565
1162
2841
5.82
8.30
5-88
8.38
5-94
8.47
42
42
45
45
5°
50
60
60
IO
15
10
15
IO
IS
IO
is
25
42
25
42
25
42
25
42
32-33
37-44
33-85
38.96
36.79
41.90
42.71
47.82
890
898
919
926
974
981
1225
1233
5-24
4.89
5.21
4.87
5-i4
4.84
5-42
5-07
828
1953
876
2054
974
2254
1165
2641
5.06
7.22
5-09
7.26
5-14
7-33
5-22
7-43
12
18
12
18
12
18
12
18
3i-5
55
3i-5
55
3i-5
55
3i-5
55
34.22
40.89
35-74
42.41
38.68
45-35
44.60
51-27
893
90S
921
933
976
988
1228
1239
5-ii
4-70
5-07
4-69
5-02
4.67
5-24
4.91
1206
2939
1274
3082
1408
3360
1668
3901
5-94
8.48
5-97
8-53
6.04
8.61
6.ii
8.72
18
it
n
t
<
<
55
II
60
65
65
70
70
12
18
12
18
12
18
12
18
31-5
55
3I-S
SS
3I-S
55
3i-5
55
41.12
47-79
44.56
51-23
47.50
54-17
50.44
57-11
1601
1612
1693
1705
1773
1784
1852
1864
6.24
S-8i
6.16
S-77
6.09
5-74
6.06
5-71
1496
3552
1652
3879
1789
4163
1930
4452
6.03
8.62
6.09
8.70
6.12
8-77
6.19
8.84
IS
20
IS
20
IS
20
IS
20
42
65
42
65
42
65
42
6S
44-34
50-94
47.78
54-38
50.72
57-32
53-66
60.26
1606
1619
1698
1712
1778
1791
1857
1871
6.O2
5-64
5-96
5.61
5-92
5-59
5-88
S-57
2388
4546
2622
4943
2827
5288
3035
5639
7-35
9-44
7.41
9-53
7-47
9.60
7-52
9.66
20
i
<
A5
65
70
70
75
75
IS
20
IS
20
IS
20
42
65
42
65
42
65
50.64
57-24
53-66
60.26
56.60
63.20
2354
2367
2454
2468
2552
2566
6.82
6-43
6.76
6.40
6.71
6-37
2790
5234
2997
5586
3203
5933
7.42
9-S6
7.48
9-63
7-52
9-69
18
24
18
24
18
24
55
80
55
80
55
80
54-09
61.48
SMI
64.50
60.05
67.44
2360
2382
2461
2483
2SS9
2581
6.60
6.23
6.56
6.21
6.53
6.19
4116
7870
4406
8363
4692
8851
8.72
11.31
8.78
n-39
8.84
11.46
24
«
«
<(
K
<f
M
80
80
85
85
90
90
IOO
IOO
15
20
15
20
15
20
15
20
42
65
42
65
f
65
42
65
59.12
65.72
62.48
69.08
65.42
72.02
71.28
77.88
4190
4204
4352
4365
4493
4506
4775
4789
8.42
8.00
8-35
7-95
8.29
7.91
8.18
7.84
3329
6i5S
3S6i
6548
3767
6893
4187
7597
7-50
9.68
7-55
9-73
7.60
9.78
7.66
9.88
18
24
18
24
18
24
18
24
55
80
55
80
55
80
55
80
62.57
69.96
6S-93
73-32
68.87
76.26
74-73
82.12
4197
4219
4358
4380
4499
4521
4782
4804
8.18
7.76
8.13
7-73
8.08
7.70
8.00
7-65
4872
9173
5194
9723
548i
10207
6060
1 1 193
8.82
ii-45
8.87
11.51
8.92
11.56
9.01
11.66
Heavier web beams, of same depth as those given in table, may be substituted by subtracting
area and moments of inertia of given beam, respectively, from values given in table, and adding
the corresponding properties of new beam. The radii of gyration must then be recalculated from
the formula r = V/ -4- A.
112
TABLE 57.
PROPERTIES OF COLUMN SECTIONS.
''it
4
Properties of * ~i
Two Channels Laced. •** •
1
•-0J---
"V~
- 1 "
M
t
-A
1|
Flange*
Turned Out.
J
T
B
Channels.
Total
Area.
Moments of Inertia and Radii of Gyration.
Web
of
Chan-
nel.
Gages.
Max.
Rivet.
Axis A-A. .
Axis B-B.
Depth.
Weight.
Distance Inside to Inside of Webs in
Inches = b'.
4i
Si
61
IA
TA.
IB
IB
IB
IB
IB
r«
t
d
h
In.
Lb.
In.'
In.«
In.
In.«
In.
In.«
In.
In.'
In.
In.
In.
In.
In.
it
9-75
5-70
7.2O
42
48
2.72
2-59
43
51
2-73
2.65
59
71
3.22
3-14
79
95
3-72
3.64
j{
I
u
!ft
H
4j
5j
6*
8
11.25
13-75
16.25
6.70
8.08
65
72
80
3.10
2.98
2.89
47
53
57
2.65
2-57
2-45
66
76
82
3.06
2-94
88
IO2
112
3.63
3-55
3-43
1
I
H
;|
f
6*
7f
8J
9
I3.2S
15.00
20.00
7.78
8.82
11.76
95
IO2
122
3-49
3-40
3-21
|
3-55
3-47
3-34
127
138
172
4.04
3-95
3-83
1 60
175
220
4-54
4-45
4-32
i
';;
|
f
M
6
7
8
10
I5.0O
2O.OO
25.00
8.92
11.76
14.70
134
157
182
3-87
3.66
3-52
107
129
150
3-4°
3-3i
3-19
140
170
199
3-95
3.80
3-68
176
217
256
4-44
4.29
4.17
j
j
it
If
if
1
.
8
9
10
12
M
20.50
25.00
35.00
12.06
14.70
20.58
2S6
288
359
4.61
4-43
4.17
240
281
353
4-47
4-37
4.14
296
348
441
4.96
4.87
4-63
358
423
5-45
5-13
1
f
;;
I
I;
1
;;
9f
10]
III
!
33.00
45.00
55.00
19.80
26.48
32.36
625
750
860
5.62
5-32
5.16
54°
660
758
5.22
4.99
4.84
646
796
920
5.68
548
5-33
763
946
1098
6.18
5.98
5-83
ti
if
x
j
The table given above is intended to serve only as a guide in the choice of sections, and not as
a complete table. The pioperties of sections not given in table may be found as follows:
Example. — Required the properties of a section consisting of 2 [s 10 in. at 15 lb., laced, with flanges
turned out, 8J in. back to back. Distance inside to inside of web = 8 J + J = 8f ".
From Table 14, Area = 8.92 in.1.
/4 = Ix in Table 19 = 133.8 in.4; rA = \
IB = IY in Table 19 = 207.0 in.4; rB = VJ
A = Vi33.8-i-8.92
A = -^207.0 -s- 8.92 =
3.87 in.
4.81 in.
113
TABLE 58.
PROPERTIES OF COLUMN SECTIONS.
J?
hf
n
Flanges
—A Turned In.
i
I.A— 1— a
rTi
Properties of
Two Channels Laced. -4—
L ^A
pn..|....Y
Channels.
Total
Area.
Moments of Inertia and Radii of Gyration.
Axis .
\. A
Axis B-B.
Distance Back to Back of Channels in Ir
,
b.
Depth.
wt.
c es
7l
8i
9i
I0j
nl
IA
TA
IB
rB
IB
rB
IB
rB
IB
rB
IB
rB
In.
Lb.
In.'
In."
In.
In.'
In.
In.*
In.
In.*
In.
In.*
In.
In.'
In.
7
9-75
12.25
5.70
7-2O
42.2
48.4
2.72
2.59
60.5
77-i
3.26
3-27
80.2
IO2.I
3-75
3-77
IO2-7
130.7
4.24
4.26
I28.I
162.9
4-74
4.76
156.3
198.7
5-24
5-27
7*
8*
9*
10*
II*
8
11.25
13-75
6.70
8.08
64.6
72.0
3-IO
2.98
70.2
85-5
3-24
3-25
93-1
II3-3
3-73
3-74
119.4
145-2
4.22
4-23
149.0
181.1
4-72
4-73
182.0
22 1. 0
5-21
5-23
8*
9*
10*
II*
12*
9
13-25
15.00
20.00
7-78
8.82
11.76
94-6
101.8
I2I.6
3-49
3-40
3-21
106.8
I22.O
162.9
3-70
3-72
3.72
I37-I
156.5
208.9
4.20
4.21
4.22
171.2
195-4
260.8
4.69
471
4-71
209.3
238.7
318.6
5.18
5.20
5.20
25L3
286.4
382.3
5-68
5-70
S-70
9*
10*
n*
12*
13*
10
15.00
20.00
25.00
8.92
11.76
14.70
133-8
157-4
182.0
3-87
3-66
3-52
iSS-3
207.4
257-5
4.17
4.20
4.18
194.2
259.0
321.9
4.68
4.69
4.68
237.6
316-5
393-7
5-16
5-19
5-18
285.4
379-9
472.8
5-66
5.68
5-67
337-7
449-2
559-2
6.15
6.18
6.17
10*
u*
12*
13*
14*
12
20.50
25.00
30.00
35-00
1 2.06
14.70
17.64
20.58
256.2
288.0
3234
358.6
4.61
4-43
4.28
4.17
257-1
316-3
379-3
439-0
4.62
4.64
£&
3I4.9
387-2
464-4
537-9
5-13
5-13
5-12
378.8
558.3
647.1
5-59
5.62
l'.6i
448.7
551.0
66 1. o
766.6
6.10
6.12
6.12
6.10
524.6
644.0
772-S
896.4
6-S9
6.62
6.62
6.60
I2|
13*
H*
IS*
16*
IS
u
d
33-oo
35-oo
40.00
45.00
19.80
20.58
26.48
625.2
640.0
695.0
750.2
5.62
5-57
5-44
5-32
605.9
630.7
721.7
810.6
5-53
5-54
5-54
5-53
718.9
748.2
856.2
961.9
6.O2
6.03
6.03
6.O2
841.7
876.0
1002.4
1126.4
6.52
6.52
6.51
6.52
974-5
1014 2
1160.4
I304.I
7.02
7.02
7-03
7.02
1117.2
1162.6
1330.2
1495.1
7-Si
7-52
7-52
7-52
The table given above is intended to serve only as a guide in the choice of sections, and not as a
complete table. The properties of sections not given in table may be found as follows:
Example i: Required the properties of a section consisting of 2 [s 10 in. at 15 lb., laced, with
flanges turned in, 10* in. back to back.
From Table 14, Area = 8.92 in.2. _ _
I ^ = Ix from Table 20 = 133.8 in.4; rA = V/A -T- A = Vi33-8 •*- 8.92 = 3.87 in.
IB = Iy from Table 20 = 194 2 in.4; rB = V/B -i- A = Vi94-2 -r- 8.92 = 4.68 in.
Example 2: Required the proper-ties of a section consisting of 2 [s 10 in. at 15 lb., laced, with
flanges turned in, 12 in. inside to inside of web.
From Table No. 14, Area = 8.92 in.2.
I = I
_
A = x om Table 21 = 133.8 in.4; TA = V/A -f- A = Vi33-8 -i- 8.92 = 3.87 in.
IB = IY from Table 21 = 284.4 in.4; rB = V/B -5- A =• "^284.4 -5- 8.92 = 5.65 in.
114
TABLE 59.
PROPERTIES OF COLUMN SECTIONS.
Properties of
Two Channels and A-
Two Plates. fl
I!
,
Turned
Out.
* T
-4* ....
L
t:
It!-
T.; .1
B
Channels.
Cover
Plates.
Total
Area.
Inside
to
Inside
of Web.
Back
to
Back.
Moments of Inertia and Radii
of Gyration.
Gages.
Web
of
Chan-
nel.
Max
Rivet.
I
}
Axis A-A.
Axifl H H.
Plate.
Chan-
nels.
b'
b
IA
rA
IB
TB
8
h
t
In.
Lb.
In.
In.'
In.
In.
In.«
In.
In.«
In.
In.
In.
In.
In.
Z
H
12.25
IOX:
CI
10.70
13.20
12.20
1470
i*
I
108
144
114
150
3-18
3-31
3.06
3.20
101
122
113
134
3-07
3-04
3-04
3.02
::
It
\t
4
1
8
N
u
II;25
13-75
12 X
I2.7O
I5-70
14.08
17.08
7l
M
H
M
I
167
223
174
230
3.62
3-76
3-52
1 86
222
204
240
3-83
3^81
3-74
;:
4
A
H
J
2
u
20.00
I2X
16.78
19.78
20.76
23.76
7t
6f
6f
366
320
393
4.17
4-30
3-92
4.06
235
271
280
316
3-74
3-70
3-67
3-64
*
If
M
T>
J
IO
I5.OO
25.OO
I4X
1942
26.42
25.20
32.2O
%
u
?,*
8
417
628
465
676
4^8
4.29
4-58
389
504
492
606
4-47
4-37
4.42
4-34
iii
M
If
|
1C
I
12
2O.5O
25.00
35;po
i6X
" I
24.06
32.06
26.70
34-70
36.58
44.58
10
M
it
9l
9l
8i
M
715
1053
747
1085
984
1335
5-45
5-73
5-29
5-59
5-19
5-47
614
785
679
849
882
1053
5.05
4-95
5-04
4-94
4.91
4.86
H
M
If
A
f,
H
«
1C
33;oo
45.00
55;po
i8X
«
33-30
42.30
39-98
48.98
50.36
59.36
II*
M
M
M
M
9f
1423
1999
1548
2124
1942
2536
6-54
6.87
6.22
6.59
6.21
6.54
III9
1362
I3II
1554
1584
1827
5-79
5.68
5-72
5-63
5-6i
5-55
«
H
«
*
1
»
«
The table given above is intended to serve only as a guide in the choice of sections, and not as a
complete table. The properties of sections not given in table may be found as follows:
Example: Required the properties of a section consisting of 2 [s 12 in. at 20^ lb., flanges turned out,
9J in. back to back, and 2 Pis. l6"Xi".
Item.
A
IA
IB
TA
'B
Number.
Section.
Size.
Table.
In.*
Table.
In.«
Table.
In.«
In.
In.
2
2
[s
Pis
12 in. at 20 J
i6"Xi"
H
I
1 2.O6
16.00
19
5
256
626'
19
3
350
341
/"88T
xf^~
V 28.06
\28.o6
Total
28.06
882
691
5.61
4-96
115
TABLE 60.
PROPERTIES OF COLUMN SECTIONS.
Properties of
Channel and I- Beam A.
HH
IT
. Channel Flanges Out.
Minimum I- Beam
Section.
for Web.
SERIES I
AND II.
SERIES I.
SERIES II.
Flange
Channels.
Web Beam.
Moments of Inertia and
Radii of Gyration.
Web Beam.
Moments of Inertia and
Radii of Gyration.
£
4
43
43
Total
Area.
Axis A- A.
Axis B-B.
J
jj
Total
Area.
Axis A- A.
Axis B-B.
Q
JOQ
O.
m
'a
.Sf
"25
'§.
V
'S
Q
£
IA
rA
IB
TB
Q
£
IA
l-A
IB
rB
In.
Lb.
In.
Lb.
In.*
In.*
In.
In.*
In.
In.
Lb.
In.2
In.*
In.
In.*
In.
6
8.00
6
12.25
8-37
28
1.82
82
3-13
7
15.00
9.18
29
1.77
114
3-53
"
10.50
M
9-79
32
I.8i
99
3-19
"
"
10.60
33
I.76
137
3-59
7
9-75
6
I2.2S
44
2.18
95
3.20
7
15.00
IO.I2
45
2.II
3.60
12.25
"
10.81
50
2.16
114
3-24
u
11
1 1 .62
Si
2.IO
155
3-66
8
11.25
6
12.25
10.31
66
2.54
no
3-27
7
15.00
II. 12
67
2.46
ISO
3-67
M
13-75
«
M
11.69
74
2.51
127
3-30
H
ii
I2.5O
75
2.44
172
3-71
9
I3-25
7
I5.OO
12. 2O
97
2.82
171
3-74
8
18.00
13.11
98
2.74
226
4-iS
15.00
M
13.24
104
2.81
188
3-76
"
"
I4-I5
106
2-73
247
4.17
"
20.00
"
"
16.18
124
2.77
237
3-83
M
u
17.09
125
2.71
309
4-25
IO
15.00
8
I8.OO
14.25
138
253
4.22
9
2I.OO
IS-23
139
3.O2
325
4.62
"
20.00
u
"
17.09
161
3-07
312
4.28
"
"
18.07
163
3.0O
398
4.69
"
25.00
"
"
20.03
1 86
3-05
377
4-34
"
U
2I.OI
187
2.98
477
4-77
12
20.50
9
2I.OO
18-37
261
3-77
419
4.78
IO
25.OO
19-43
263
3-68
522
5.18
"
25.00
M
21.01
293
3-74
48*
*
4.82
M
"
22.07
295
3.66
605
5-24
"
30.00
"
"
23-95
329
3-70
568
4.87
«
"
25.01
330
3-63
701
5-29
"
35-00
"
M
26.89
364
3.68
652
4.92
"
II
27-95
366
3.62
801
5-35
II
40.00
M
"
29-83
399
3-66
740
4.98
M
H
30.89
401
3-6o
90S
5-41
15
33-00
IO
25.OO
27.17
632
4.82
803
5-44
12
3I-50
29.06
635
4.67
1146
6.28
"
35-00
M
M
27-95
647
4.81
829
5-45
"
M
29.84
650
4.67
1181
6.29
II
40.00
ii
M
30.89
702
4-77
927
5-48
M
"
32.78
70S
4.64
1317
6-34
II
45.00
ii
"
33.85
757
4-73
1030
5-52
"
"
35-74
760
4.61
1457
6.38
II
50.00
ii
"
36.79
812
4.70
"35
5-55
"
M
38.68
815
4-59
1600
6-43
II
55-oo
II
39-73
867
4.67
1244
5.60
H
41.62
870
4-57
1747
6.48
The table given above is intended to serve only as a guide in the choice of sections, and not as a
complete table. The properties of sections not given in the table may be found as follows:
Example: Required the properties of a section consisting of 2 [s 10 in. at 20 lb., flanges turned out,
and one 1 9 in. at 21 lb.
Item.
A
IA
IB
rA
TB
Num-
ber.
Sec-
tion.
Size.
Table.
In,
Table.
In,
Table.
In.*
In.
In.
2
I
[s
I
10 in. at 20 lb.
9 in. at 21 lb.
14
7
11.76
6-31
19
7
1574
5-2
19
7
312.7
84.9
/I62.6
/397-6
\ 18.07
\ 18.07
Total
18.07
162.6
397-6
3.OO
4-69
116
TABLE 61.
PROPERTIES OF COLUMN SECTIONS.
Properties of .
Channel and I -Beam A"
U =J
.._A Channel Flanges In.
Minimum I -Beam
Section.
for Web.
SERIES I
AND 11.
SERIES I.
SERIES II.
Flange
Channels.
Web Beam.
Moments of Inertia and
Rauii of Gyration.
Web Beam.
Moments of Inertia and
Radii of Gyration.
4
a
j
4
j
Total
Area.
Axis A-A.
Axis B-B.
t
i
Total
Area.
Axis A-A.
Axis B-B.
&
i
1
1
IA
rA
IB
TB
j-
IA
rA
IB
TB
In.
Lb.
In.
Lb.
In.'
In.«
In.
In«
In.
In
Lb.
In.'
In.«
In.
In.1
In.
6
8.00
7
15.00
9.18
29
1.77
86
3.06
8
18.00
10.09
30
I 72
123
3-49
M
10.50
ii
(i
10.60
33
I.76
106
3 16
"
14
11.51
34
1.72
149
3.60
7
9-75
7
15.00
10.12
45
2. 1 1
95
3-07
8
18.00
11.03
46
2.04
135
3-50
ii
12.25
ii
"
11.62
51
2.IO
117
3-17
"
"
12-53
52
2.04
I63
3-6i
8
11.25
8
18.00
12.03
68
2.38
149
3-52
9
21.00
13.01
70
2.32
203
3-95
13-75
H
<i
13.41
76
2.38
174
3-6o
II
14-39
77
2.32
234
4-03
9
I3-2S
9
2I.OO
14.09
IOO
2.66
221
3-96
10
25.00
IS-IS
101
2.5&
292
4-39
'*
15.00
H
M
I5-I3
107
2.66
244
4.02
u
"
16.19
109
2-59
321
4-45
20.00
"
18.07
127
2.65
3M
4.17
16
"
I9-I3
129
2.60
405
4.60
10
15.00
9
21.00
I5-23
139
3-02
240
3-97
IO
25.OO
16.29
141
2-94
316
4.40
ii
20.00
**
ii
18.07
163
3-oo
305
4.11
u
"
I9-I3
164
2-93
396
4-55
25.00
ii
ii
21.01
187
2.98
378
4.24
M
22.07
189
2-93
483
4.68
12
20.50
IO
25.OO
19-43
263
3.68
383
4.44
12
3i;5o
21.32
266
3-53
599
5-30
"
25.00
ii
ii
22.O7
295
3.66
458
4-55
"
23.96
298
3-52
70S
5-42
(i
30.00
**
ii
25.01
330
3.63
545
4.67
"
«
26.90
333
3-52
827
5-54
i«
35-00
ii
ii
27.95
366
3-62
637
4-77
M
M
29.84
368
3-Si
954
5-66
ii
40.00
ii
ii
30.89
401
3-6o
732
4.87
H
"
32.78
404
3-Si
1086
5-76
15
33-00
12
31.50
29.06
635
4.67
855
5.42
IS
42.OO
32.28
640
4-45
1458
6.72
ii
35-oo
ii
"
29.84
650
4.67
887
5-45
<
"
33-06
655
4-45
1507
6.75
**
40.00
ii
ii
32.78
705
4.64
1010
5-55
'
"
36.00
710
4-44
1694
6.86
ii
45.00
ii
ii
35-74
760
4.61
1138
5.64
1
"
38.96
765
4-43
1887
6.96
u
50.00
it
ii
38.68
815
4-59
1268
5-73
1
H
41.90
820
4.42
2083
7-05
ii
55-oo
ii
41.62
870
4-57
1403
5.81
U
44.84
875
4.41 2284
7-15
The table given above is intended to serve only as a guide in the choice of sections, and not as a
complete table. The properties of sections not given in the table may be found as follows:
Example: Required the properties of a section consisting of 2 [s 10 in. at 20 lb., flanges turned in
and one 19 in. at 21 lb.
Item.
A
IA
IB
TA
TB
Num-
ber.
Section.
Size.
Table.
In.'
Table.
In.«
Table.
In.«
In.
In.
2
I
[s
I
10 in. at 20 lb.
9 in. at 21 lb.
14
7
11.76
63I
21
7
157-4
5-2
21
7
2 20. 2
84-9
[1626
/305-I
\ 18.07
\ 18.07
Total
18.07
162.6
305.1
3.00
4.11
117
TABLE 62.
PROPERTIES OF Two CHANNELS AND A BUILT I-BEAM.
FLANGES TURNED OUT.
Properties of
Two Channels
and
a Built I -Beam.
A— -
B
Channel Flanges Out.
Distance Back to Back
of Channels Equals
Width of Web Plate Plus J".
Series I and 2.
Series i.
Series 2.
Channel.
Axis A-A. Axis B-B.
,
II
II
§1
~
o c
o
3 '5
Axis A-A.
S'S
C aj
go
Axis B-B.
In.
12
12
12
12
12
12
IS
IS
is
15
IS
15
Lh.
25
30
2Oj
25
30
33
35
40
33
35
40
In.
In.
In.*
In.
In.
In.
In.2
In.*
In.
In.*
8x1
8x|
32*35*i
21. 18
23.82
26.76
24.98
27.62
30.56
32.72
33-50
36.44
34-99
35-77
38-71
269
301
337
282
3H
349
651
666
721
663
677
733
3-57
3-S6
3-55
3-36
3-37
3-37
4.46
4.46
4-45
4-35
4-35
4-35
4O2
464
536
436
498
571
652
672
747
982
1010
1117
4-35
441
4.48
4.18
4-25
4-33
4.46
4.48
4-53
S-30
5-32
5-37
ioxf
loxf
ioxf
I2X§
22.93
25-57
28.51
25-73
28.37
31-31
33-47
34-25
37-19
35-74
36-52
39-46
270
302
337
282
349
651
666
721
663
677
733
3-44
3-44
3-44
3-31
3-32
3-33
4.41
4.41
4.41
4-3i
4-3i
4-3i
610
700
804
657
747
851
961
989
1096
mo
1138
1245
In.
5-23
5-3i
S-OS
S-I3
5-21
S-36
5-38
5-43
S-57
5.58
5.62
The above table is intended to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of sections not given in table may be obtained as follows:
Example: Determine the properties of a section composed of 2 channels 15" X 55 lb., I plate
12" X 3" and 4 angles 4" X 4" X J" ', I2|" back to back.
Solution:
Item.
Area.
Moment of Inertia.
Radius of Gyration.
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B.
Table
No.
A
Table
No.
IA
Table
No.
IB
r\
fB
=V/IA-A
-I/IB+A
In.»
In.<
In.<
In.
In.
2 [sis"x55 lb.
T pi T_//i//
19
I
32
32.36
6.00
15.00
19
4
35
860
o
S3
19
3
32
1587
72
389
J9I3
^2048
^53-36
4^4"*4"*i"
^53.36
Total
A =
5336
IA =
913
IB =
2048
rA = .414
TB = 6.2O
118
TABLE 63.
PROPERTIES OF Two CHANNELS AND A BUILT I-BEAM.
FLANGES TURNED IN.
1
Properties of
1
\ Channel Flanges In.
Two Channels
A"
r~
a ----A Distance Inside to Inside
and
r^
OfCha
in«-U Email
a Built I I tea in.
i
c.
\
Width of Web Plate Plus J".
Series i
and a.
Series i.
Series 2.
Channels.
1
H
V
1
i
Azis A-A.
Axis B-B.
V
R
3
Axis A-A.
Axis B-B.
c
„
.
«.
J ,
i
—
.
„
,
S
J
)
1
i
1
S •
I
i .S
a Z .
.a
«
«
$ S .
1
rt
9 2
A
£
<
V
1 .
^0.1
PS
1«O.2
$
1
5 ^o".l
£
*o 5
^c"!
0.
Q
•s
V
"o
H
S
«
«*-
— J8
o
•o
H
s •
5
0<g
05 's"
1/3
(7i
A
IA
rA
IB
rB
£
A
IA
••A
IB
•B
In.
Lb.
In.
In.
In.*
In <
In
In «
In.
In.
In.*
In *
In
In*
In
12
20}
\
3*3*&
loxj
21.68
269
3
-52
453
4-57
I2X*
23.68
270
3-38
683
5-38
12
12
25
30
«
«
24-32
27.26
3OI
336
3
3
•52
•52
535
631
4.70
4.81
M
26.32
29.26
3O2
337
3-38
3-39
798
930
5-53
5-64
12
20*
3i*3i*t
14*1
27.23
282
3
.22
1054
6.22
i6xi
29.98
283
3.08
1449
6-93
12
25
29.87
3H
3
.24
I2O5
6-35
32.62
'315
3-ii
1644
7.10
12
3°
32.81
349
3
•25
1380
6-49
35-56
350
3-H
1867
7-25
IS
33
3Jx3Jxi
I2X|
34-22
651
4.36
I°34
5-50
14*1
34-97
651
4-3i
It
t3i
6.40
IS
35
35.00
666
4
1068
5-52
"
35-75
666
4-32
1477
6-43
IS
40
37-94
721
4
1 201
5-63
38.69
721
4.32
1652
6-54
IS
33
4*4*!
16
4
37-24
663
4.22
1963
7.26
i8x*
40.24
667
4.07
2582
8.01
is
35
'
38.02
677
4.22
2O2I
7.29
"
41.02
679
4.07
2655
8.05
IS
40
40.96
733
4
.23
2245
7.41
43-96
735
4.09
2933
8.18
The above table is intended
to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of sections not given in table may be obtained as follows:
.Example: Determine the properties of a section composed of 2 channels 15" X 55 lb., i plate
18" X f" and 4 angles 4" X 4" X i", i8J" back to back.
Solution:
Moment of Inertia.
Radius of Gyration.
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B.
Item.
IA
Table
No
A
Table
No
Table
No
IB
"A
«I
•
A+A
•I/IB+A
In.«
In.4
In.4
In.
In.
2[si5"x55 lb.
21
32.36
21
860
21
2716
/.— 0_
I PI— iS'^'xt"
I
32
11-25
15.00
4
35
0
56
3
32
304
969
\58.6i
\58.6i
Total
A =
58.61
IA=
916
IB =
3989
rA = 3-96
TB = 8.25
119
TABLE 64.
PROPERTIES OF ONE CHANNEL AND ONE I-BEAM.
B
l/t "if \l
Properties of A u i | " 4 Properties of
One Channel '" e " One Channel
and One I-Beam. d! ~" and One I-Beam.
cL
j '-f
-3—t i 'T
B
Ser. i & 2
Series i.
Series 2.
Beam.
Channel.
Axis A-A.
Axis B-B.
Channel
Axis A-A.
Axis B-B.
at
4
J
M
3
o
oment
Inertia.
dius of
ration.
t3 *n
11
"o d
CO .2
o.
i
1
oment
Inertia.
dius of
ration.
1|
||
|d
"3 d
o
11
0
2
I
•>
H
Ȥ<*-
Q§C5
oSr*?
X
S
H
S«M
fg<5
W^j
*;"
Q
£
H
£
°
(ZiVj
"o
«(->
Q
£
°
"o
K(J
A
IA
rA
e
IB
rB
A
IA
rA
e
IB
rB
In.
Lb.
In.
Lb.
In.'
In.«
In.
In.
In.<
In.
In.
Lb.
In.'
In.<
In.
In.
In.«
In.
8
18
5
6*
7.28
77
3-25
0.99
II. 2
1.24
6
8
7-71
80
3-22
I-I3
16.8
1.48
H
205
n
"
7.91
81
3-2O
0.91
II-4
1. 2O
it
H
8.41
84
3.16
1.04
17.0
1.42
9
21
6
8
8.69
116
3-6S
I.I5
18.2
i-45
8
Hi
9.66
124
3-58
i-44
37-5
1-97
II
25
II
II
9-73
124
3-57
I. O2
18.6
1.38
"
10.70
133
3-52
1.30
37-9
1.88
IO
25
6
8
9-75
162
4.08
1.14
19-9
i-43
8
Hi
10.72
173
4.O2
i -45
39-2
1.91
"
30
**
"
1 1. 20
176
3-97
0.99
2O.6
1.36
M
*
12.17
188
3-92
1.28
39-9
1.81
12
3J5
8
ill
12.61
295
4.84
1.50
41.8
1.82
10
IS
13.72
313
4-77
1.82
76.4
2.36
40
U
«
I5-I9
353
4.82
1.25
46.1
i-74
<(
16.30
373
4.78
i-53
80.7
2.22
is
42
8
Hi
iS-83
578
6.04
I.5I
46.9
1.72
IO
is
16.94
610
6.00
1.87
81.5
2.19
II
N
12
20^
18.51
649
5-92
2.31
142.7
2.78
15
33
22.38
729
5-7i
3-iS
327.2
3-82
So
8
III
18.06
624
5-88
1.32
48.3
1.63
IO
15
19.17
658
5-86
1-65
82.9
2.08
"
M
12
20^
20.74
702
5-8i
2.06
144.1
2.64
IS
33
24.61
79i
5-67
2.86
328.6
3.6S
"
60
8
Hi
2I.OO
754
5-99
I.I4
58.3
1.67
10
IS
22.13
791
5-98
1-43
92.9
2.O5
II
12
20^
23.68
838
5-95
1. 80
154-1
2-55
15
33
27-57
938
S-83
2-55
338.6
3 -SO
18
55
8
III
19.28
1004
7.21
1.50
53-5
1.67
IO
IS
20.39
1056
7.19
1.88
88.1
2.08
"
12
20^
21.96
1122
7-14
2-35
149-3
2.61
15
33
2S-83
1257
6-97
3-30
333-8
3-59
cc
65
8
"I
22-47
IO96
6.98
1.28
55-8
1.58
IO
15
23.58
"Si
6.98
1.63
90.4
1.96
"
"
12
20^
25-IS
1223
6.97
2.06
151.6
2.46
15
33
29.02
1373
6.88
2-94
336.1
3-40
75
8
III
2540
1360
7-32
1.14
78.7
1.76
IO
IS
26.51
1418
7-3i
i -45
113.1
2.06
(1
C|
12
20^
28.08
1494
7-29
1.84
174-3
2-49
IS
33
31-95
1656
7-24
2.67
358.8
3-37
20
65
9
I3l
22.97
1470
8.00
1-63
75-2
1.81
IO
IS
23-54
1507
8.00
1.82
94.8
2.OI
"
"
12
20^
25.11
1594
7-97
2.30
156.0
2-49
IS
33
28.98
1779
7.84
3-29
340-5
3-43
II
70
9
I3l
24.48
1524
7.89
1-53
.76.3
i-77
IO
IS
25-05
1562
7-89
1.71
95-9
1.96
CC
l|
12
20^
26.62
1652
7.88
2.17
I57-I
2-43
15
33
30-49
1846
7-79 3-12
341.6
3-34
80
9
I3l
27.62
1777
8.02
1.36
1.84
IO
15
28.19
1816
8.03
1.52
112.7
2.OO
M
12
2O5
29.76
1912
8.02
1.94
173-9
2.42
15
33
33.63
2I2O
7-94
2.83
358.4
3.26
24
80
9
I3i
27.21
2539
9.66
1.66
90.2
1.82
IO
IS
27-78
2594
9.66
1.86
109.8
1.99
*
12
20^
29-35
2734
9.66
2.38
171.0
2.41
IS
33
33-22
3033
9-55
346
355-5
3-27
"
90
9
i3j
30.36
2700
9-43
1.49
93-o
1-75
IO
IS
30.93
2755
9-43
1.67
II2.6
I.9I
"
"
12
20|
32.50
29O2
9-45
2-15
173-8
2.31
IS
33
36.37
3219
9.40
3.16
358-3
3-14
100
IO
IS
33-87
2904
9.26
i-53
115.5
1.85
15
40
41.17
3548
9.28
3-35
396.1
3-io
II
12
205
35-44
3055
9.29
i-97
176.7
2.23
15
33
39.31
3387
9.28
2.92
361.2
3-03
"
IO5
IO
15
35-44
3338
9.69
1.46
145-8
2.03
IS
40
42.74
3997
9-67 ': 3-23
426.4
3.16
12
205
37-oi
3492
9.71
1.89
207.0
2.36
15
33
40.88
3831
9.67 2.81
391-5
3-09
120
TABLE 65.
PROPERTIES OF ONE CHANNEL AND A BUILT I-BEAM.
U
/t -i
r1 \\
Properties of A
One Channel
and
One Built I- Beam.
/:
IU A Ba
* A \l
ck to Back of Angles Equals
rtdth of Web Plate Plus j"
Fop Angles, Short Legs Out.
torn Angles, Long Legs Out.
I-
f
e *
T"
[
\
T
..t. '1
i
:=a.i.
/»•
Plate.
Channel.
Angles.
AxisA-A.
Axis B-B.
Web.
Depth.
\\viuht.
Bottom.
Top.
Total
Area.
Moment
of Inertia.
Radius
of Gy-
ration.
Eccen-
tricity.
Moment
of
Inertia.
Radius
of Gy-
ration.
A
IA
rA
e
IB
rB
In.
In.
Lb.
In.
In.
In.J
In.«
In.
In.
In.«
In.
i6xl
"
IO
9
Sx3*xi
«<
x[
.
21.52
24.96
979
1166
6-75
6.83
1. 2O
0.92
"5
132
2.31
2.30
«
«
•
" i
(i
28.26
1340
6.89
0.71
148
2.29
"
12
20.5
6x4x
4x4x5
24.97
H44
6.77
207
2.87
-
M
u
" -
29-03
1367
6.86
1. 08
233
2.84
"
"
H
" '.
i
M
I
32.97
1572
6.91
0.83
260
2.81
l8xj
IO
IS
5x3 $x;
3JX31
x;
24.52
1338
7-39
I.I9
117
2.19
"
H
"
1
ii
.
27.96
1577
7-Si
0.92
134
2.19
"
M
"
]
"
i
31 26
1802
7-59
0.72
152
2. 2O
-
12
2O-S
6x4xj
4X4xf
27.97
1555
7-46
1.42
209
2-73
"
"
"
"
.
"
32.03
1838
7-58
1. 10
237
2.72
"
"
"
" ;
M
1
35-97
2103
7.64
0.86
265
2.71
20XJ
12
20-5
6x4x;
x;
28.97
1971
8.24
1.52
209
2.69
«
H
"
«
M
,
33-03
2329
8-39
1.19
237
2.68
"
"
"
f
"
;
36.97
2662
8.49
0-93
265
2.68
H
IS
33
6x6x:
*6x^
t]
35.84
2317
8.04
2.30
395
3-32
•
«t
«
« _
•
:
40.90
2725
8.16
1.90
423
3.22
*
«
"
" \
«<
;
45.84
3104
8.24
1-59
45i
3.14
24x|
12
20.5
6x4x|
4x4x|
33-97
3133
9.62
1.56
212
2.50
M
M
"
« i
" '
i
38-03
3656
9.81
1.24
241
2.52
C(
H
"
"
41.97
4150
9-95
0-99
270
2.54
"
IS
33
6x6xi
*6x4xf
40.84
3686
9-50
2.42
398
3-12
M
(C
« _
"
45-90
4290
9-67
2.03
427
3-05
M
M
M
" \
«
1
50.84
4858
9.78
1.72
457
3.00
3Ox£
12
20.5
6x4x1
4x4
x;
41.47
5546
11.56
1.61
217
2.29
"
"
« j
.
45-53
6381
11.84
1.30
246
2.32
M
"
"
" ;
i
«
;
49-47
7174
12.05
1.05
276
2.36
"
15
33
6x6x
!
*6x4
d
53-40
7490
11.84
2.19
432
2.85
M
It
" :
"
,
58-34
8413
I2.OI
1.88
463
2.82
M
"
« :
«
i
63.16
9293
12.13
1.63
495
2.80
36x}
12
20.5
6x6xj
\
*6x4
54-03
10485
13-93
1.32
248
2.14
"
"
"
«
"
58.97
11825
14.16
i. 06
278
2.17
"
M
H
<( .
'
"
63-79
13104
I4.3I
0.85
311
2.2O
"
IS
33
6x6xJ
*6x4
X
57-90
11483
14.08
2-43
433
2.74
"
(«
a
"
"
62.84
12859
14.31
2.IO
463
2.72
"
'
L
"
67.66
14170
14.47
1.82
495
2.70
47
121
TABLE 66.
PROPERTIES OF BUILT STRUTS.
igp
Long Leg of Angle Turned Out.
Back of Angle Flush with
Properties of A \
One Channel *= L—
t~
and One Angle. — i - -
eZZ
Flange of Channel.
Depth
of
Chan-
Weight
of
Chan-
Size of Angle.
Total
Area.
Axis A-A.
Axis B-B.
Mo-
ment
of
Radius
of
Gyra-
Section
Modu-
Eccen-
tricity.
Mo-
ment
of
Radius
of
Gyra-
Section
Modu-
Eccen-
tricity.
nel.
nel.
Inertia.
tion.
lus.
Inertia.
tion.
lus.
A
IA
rA
SA
e
IB
TB
SB
e'
In.
Lb.
In.
In.*
In.*
In.
In.'
In.
In.*
In.
In.'
In.
4
si
25X2IX1
2.74
5-7
1.44
2.23
-56
1-97
•85
0.8l
+.05
3 X2jXj
2.86 _
5-8
1-43
2.22
.62
2.82
•99
I.OO
+ •17
s
63
2~ X2— X^
3-14
10.3
1.81
3-24
.68
2.27
.85
.90
-.03
3 X2^Xi
3.26
10.8
1.82
3-34
-n
3-19
•99
.09
+.07
35X25X4
3-39
II. i
1.81
3-36
.So
4.41
1.14
•33
+.19
4 X3 XA
4.04
12. 1
i-73
3-56
.90
6.96
•94
+.41
6
8
25X25X1
3-57
I7.8
2.23
4-74
.76
2.62
.86
.01
— .11
3 X25X1
3-69
I8.3
2.23
4.78
•83
3-59
•99
.19
— .01
35X25X1
3.82
18.9
2.23
4-85
.90
4.89
I-I3
•44
+.09
4 X 3XA
4-47
20. 2
2.13
4-99
1.05
7.61
1.30
2.06
+.31
7
9f
3\/ /ji \/ i
/\ ^2 /> 4
4.16
29.1
2.64
6.62
.89
4.06
•99
I-3I
-.09
3 5 -^ 2^ '^ 4~
4.29
30.O
2.64
6.71
•97
5-42
1. 12
i-SS
+ .01
4 X3 XA
4-94
31-8
2.54
6.83
1.16
8-31
1.30
2. 2O
+ .22
S X3 XA
S-2S
33-2
2.51
6-94
1.29
13-73
1.62
3-°3
+ 47
8
Hi
4 X3 XA
5-44
47-5
2-95
9.06
1.24
9.07
1.29
2-34
+•13
5 X3 XA
5-75
49-6
2-93
9.21
i-39
14.74
1. 60
3.I8
+.36
S X3IXA
5-91
49-5
2.89
9.22
i-37
14.76
1-58
3-18
+.36
6 X35Xf
6.77
53-3
2.81
9.48
1.62
25.82
i-95
4.91
+•74
6 X4 X|
6.96
53-4
2-77
9-S6
1-59
25.87
i-93
4.91
+•73
9
i3i
4 X3 XA
5-98
68.0
3-37
11.70
1.31
9.91
1.29
2.5O
+.04
5 X3 XA
6.29
70.7
3-35
11.86
1.46
15.82
i-59
3-34
+.26
5 X3iXA
6-45
70.7
3-3i
11.88
i -45
15.84
i-57
3-34
+.26
6 X35Xf
7-3i
76.0
3.22
12.20
i-74
27.42
i-94
5-H
+.63
6 X4 X|
7-50
76.0
3-i8
12.23
1.71
27.46
1.91
5.10
+.62
10
IS
4 X3 XA
6-55
94-i
3-79
I4.8I
i-3S
10.82
1.28
2.68
-•03
5 X3 XA
6.86
97-7
3-77
15.00
i-Si
16.97
i-S7
3-Si
+•17
5 X3^XA
7.02
97-7
3-73
15.00
1-52
16.99
i-SS
3-52
+ •17
6 X3iXf
7.88
104.8
3-65
I5-36
1.83
29.05
1.92
5-31
+ .52
6 X4 X|
8.07
io)..6
3.60
15-35
1.82
29.10
1.90
S-3i
+•52
12
203
4 X3 XA
8.12
172.3
4.61
23-45
1-35
13-25
1.28
3.16
— .20
S X3 XA
8-43
177.9
4-59
23.68
1-52
19.90
1-54
3-97
— .02
S X3JXA
8-59
178.8
4.56
23-73
i-54
19-93
1.52
3-97
— .02
6 X3sX|
9-45
190.7
4-49
24.19
1.89
33-i6
1.87
5.81
+ •29
6 X4 X|
9.64
190.8
4-45
24.19
1.90
33-iS
1.85
S-8i
+ .29
IS
33
4 X3 XA
11.99
392.6
5-72
45-25
1.18
18.86
1.25
4.26
-•43
5 X3 XA
12.30
404.0
5-72
45-75
i-33
26.82
1.48
5-i3
-•23
S X3sXA
12.46
405.4
5-7°
45-71
i-37
26.87
1-47
5.15
— .22
6 X35Xf
13.32
430.9
5-69
46.70
1.72
41.47
1.76
6.84
-.06
6 X4 X|
I3-5I
43L3
5.66
46.65
i-75
41.47
i-75
6.84
-.06
122
TABLE 67.
PROPERTIES OF STARRED ANGLES.
Two Angles Starred.
Two Angles Starred.
Four Angles Starred,
Four Angles Starred.
Equal Legs.
Unequal Legs.
Equal Legs.
Unequal Legs.
c (1
*
M
A
|
3
\
\B
A_^=J
A
A j— -*F A
A
f £-J
—j _A
* — • -1
if— "
F*
SO
1 \°
i
A
IB
A
3
Values for Axes A-A &
Values for Axis A-A same
B-B same as in Tables
as in Table 38.
39 & 40 respectively.
Radius of
Size of
Angles.
Total
Area.
Least
Radius
of Gy-
ration.
Size of
Angles.
Total
Area.
Least
Radius
of Gy-
ration.
Size of
Angles.
Total
Area.
Radius
of Gy-
ration.
Size of
Angles.
Total
Area.
Gyration.
Axis
A-A.
Axis
B-B.
A
re
A
re
A
rA
A
rA
rB
In.
In.*
In.
In.
In.*
In.
In.
In.*
In.
In.
In.*
In.
In.
2X2X;
1.88
•77
2*X2X}
2.12
•73
2X2XJ
3-76
-85
2*X2xi
4.24
.11
.80
«
2.72
•74
" *
3.10
.78
u
5-44
.88
" 1
6.20
•13
•81
2jx2ix;
2.38
•97
3x2^
2.62
1 .00
Z\X2\\\
4.76
1.05
3x2jxJ
5-24
•31
.00
" •
3-46
•95
" i
3-84
I.OO
\
. 6.92
1.07
" i
7.68
33
.02
3X3X;
2.88
1.17
3ix3xj;
3.12
1.22
3X3XJ;
5-76
1.25
3$x3xJ
6.24
•52
.20
4.22
1.16
1
4.60
1. 2O
1
8-44
1.27
« r
1
9.20
•53
•23
" (
5-50
1-13
" J;
6.00
1.18
" i:
11.00
1.29
" J:
12.00
•55
.24
"
6.72
1. 10
" 1
7-34
1.16
« i
i
13-44
1.32
" i
14.68
•57
.26
3$x3$x
3.38
i-37
4x3x^
3.38
1.23
3ix3^xJ
6.76
1-45
4x3xi
6.76
•77
.16
"
4.96
i-35
" i'
4.96
1. 21
" I
9.92
1.48
" i
9.92
.80
•17
" i
6.50
1.33
" |
6.50
I.I9
" i
13.00
1.50
' |
13.00
1.82
.20
"
7.96
1.31
« j.
7.96
I.I7
' I
15.92
1-52
" i
15.92
1.84
.22
4X4X
3.88
1-58
5x3x1
5-72
1.16
4x4x^1
7.76
1.66
5x3xf
11.44
2-34
.09
5-72
1-56
« '
7.50
1.16
i
11.44
1.68
1
I5.OO
2.36
.11
. " :
7.50
i p
9.22
•IS
" i
15.00
1.70
" i
18.44
2-39
.14
" •
9.22
1.51
<;
10.88
•IS
t
18.44
1.72
" i
21.76
2.41
.16
5X5x
7.22
1.98
5*3ix|
6.10
•37
5x5x|
14.44
2.08
5x3$xf
12. 2O
2.27
•34
9-50
1.95
" *
8.00
•35
« 1
19.00
2.IO
1
1 6.00
2.29
•36
"
11.72
1.92
" 1
9.84
•34
" i
23-44
2.12
" i
19.68
2.31
•38
" ;
13-88
1.89
" '
11.62
•33
" i
27.76
2.14
" I
23-24
2-33
.40
6x6x
8.72
2.37
6x4x5
7.22
S6
6x6x|
17.44
2.49
6x4x1
14.44
2-74
•50
" .
11.50
2-35
9.50
•56
« i
23.00
2.51
(t J
19.00
2.76
•Si
"
I
4.22
2-33
« 1
11.72
•55
" 1
28.44
2-53
" i
23-44
2.78
•53
"
I
6.88
2.30
13.88
•55
« 3
33-76
2-55
" 4
27.76
2.80
•56
"
19.46
2.28
i '
15.96
•54
" I
38.92
2-57
" i
31.92
2.82
•58
" i
22.OO
2.26
" i
18.00
•54
" I
44.00
2-59
i
36.00
2.85
.60
8x8xi
15.50
3-17
8x6x3
I3-50
2-39
8x8x|
31.00
3-32
8x6x$
27.00
3-56
2.32
19.22
3-H
« i
i
16.72
2.38
«<
38.44
3-34
" 1
33-44
3-S8
2-33
22.88
3-12
« j
19.88
2.36
" i
45.76
3.36
« i
39.76
3.60
2-35
26.46
3.09
i '
22.96
2-35
i
52.92
3-38
« T
45.92
3.62
2-37
" i
30.00
3.07
" i
26.00
2-34
" i
60.00
3-40
" I
52.00
3-64
2.39
For unequal leg angles, the angle between
When angles are not in contact, use tables 38,
B-B & C-C varies between 10° & 34°.
39, & 40-
Tie plates for unequal le« angles = J''.
123
TABLE 68.
PROPERTIES OF FOUR ANGLES LACED.
f
B
Properties For Equal Legs and
of A >i[ A ! Unequal Legs with
Four Angles Laced. * d Long Legs Turned Out.
Four
Angles.
Total
Area.
Moments of Inertia and Radii of Gyration.
Axis B-B.
Axis A-A.
Thickness of 2 Lacing
Bars = /.
Distance Back to Back of Angles in Inches = d.
2 Bars
2 Bars
*"-•".
81
ioi
ui
141
I6J
IB
rB
IB
ru
IA
rA
IA
rA
IA
rA
IA
rA
IA
rA
In.
In1
In4
In.
In4
In
In 4
In.
In4
In.
In 4
In.
In 4
In.
In 4
In.
" 3
8
" i
" 1
" I
5-24
7.68
IO.OO
9.92
13.00
15.92
12
18
24
39
S3
66
1.50
1-53
i-SS
1.98
2.OI
2.04
13
'9
26
I-SS
I-S8
1. 60
2.03
2.06
2.08
71
100
128
127
162
•193
3.68
3.61
3-57
3-58
3-53
348
"3
162
208
206
264
317
4.64
4-59
4.56
4-Si
4.46
167
240
308
305
392
472
S-64
5-59
5-55
5-55
549
5-44
231
333
428
423
546
659
6.64
6.58
6-54
6-53
6.48
6-43
3°S
440
567
725
879
7's8
7-54
7-52
7.48
7.42
2 Bars
i" — i"
1 — 2
2 Bars
S If Sit
IS '— 8
10}
12}
M
16}
,.»
" !
4x4x8
" §
9.92
13.00
15.92
1144
15.00
18.44
27
37
46
39
S3
67
.66
.69
.70
.86
.88
.91
29
39
49
42
56
•71
•73
.76
.91
•93
.96
190
243
291
211
271
325
4-38
4-32
4.27
4.29
4-25
4.20
284
365
440
316
408
491
5-34
5-30
5.26
S-2S
5.22
S-i6
398
513
619
444
575
695
6-34
6.28
6.23
6.22
6.19
6.14
532
687
831
596
772
935
7-32
7-27
7.18
7.22
7.17
7.12
685
887
I07S
770
999
1213
8.31
8.26
8.21
8.20
8.16
2 Bars
& II 5»
re ~ s
2 Bars
til 311
~ 4
«*
12}
14*
16}
182
5X32-XJ
« !
8
6x4X5
" f
« 3
'i
12. 2O
16.00
19.68
19.00
2344
27.76
76
1 02
128
170
213
257
2.50
2-53
2-55
2.99
3.01
3-04
79
1 06
133
176
220
265
2-55
2.58
2.60
3-04
3.06
3-09
248
318
382
370
448
517
4-Si
4.46
440
4.41
4-37
4-32
367
472
571
SSi
669
777
5-48
S-43
S-39
S-39
5-34
5-29
659
800
770
937
1092
647
641
6-37
6.36
6.32
6.27
679
878
1067
1027
1252
1462
7.46
7.41
7.36
7-35
7-32
7.26
872
1129
1374
1321
1614
1888
845
840
8.36
8.34
8.30
8.24
The above table is intended to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of other sections may be found as follows:
The areas and moments of inertia of four angles about the axis A- A are given in Table 32, for
equal leg angles; Table 33, for unequal leg angles, long legs out, and Table 34, unequal leg angles,
short legs out; the axis A- A corresponding to axis X-X in Tables. The radius of gyration about
axis A- A may be calculated from the formula rA = V/A -5- A.
The moments of inertia of four angles about the axis B-B are given in Tables 35, 36 and 37,
the axis B-B corresponding to Y-Y in Tables. The radii of gyration of four angles about the axis
B-B may be calculated from the formula rB = V/B -f- A, or may be found from Tables 38, 39 and
40, the radius of gyration of four angles being equal to that of two angles.
124
TABLE 69.
PROPERTIES OF FOUR ANGLES AND ONE PLATE.
Properties of
Plate and Angle
Column Sections.
B
=jjjf=
*-
J—
•— r
Without
A ; Flange Plates
Long Legs Out.
d - Width of Web Plate Plus i In.
1
Series I
and II.
Series I.
Series II.
Web
Plate.
Four
AiiKlcs.
Total
Area.
Moments of Inertia and
Radii of Gyration.
Four
Angles.
Total
Area.
Moments of Inertia and
Radii of Gyration.
Axis A-A. Axis B-B.
Axis A-A.
Axis B-B
IA
TA
IB
rB
IA
TA
IB
TB
In.
In.
In.«
In.«
In
In.4
In.
In.
In.»
In.4
In.
In.«
In
8xt
B*A
M
8x|
u
3x2jx}
A
3Jx2jxft
4f3xf
A
7.24
8.48
9.62
10.94
12.92
14.48
8l
97
1 10
127
143
161
3-36
3-38
3-38
3.40
3-33
3-34
10
13
21
25
37
43
1.19
1.23
1.47
•"•SI
1.70
i-73
3J*2jxl
" 4
4*3*A
4X3x^
7.76
9.12
10.86
12.42
16.00
17.48
00
1 08
122
141
I78
194
3.41
3-43
3-35
3-36
3-33
3-33
16
20
3°
36
S°
56
•44
•49
.67
•71
•77
•79
ioxiV
iox|
<{
"?*
l<
$*»***
4*3*1
T«
5X3bf
<wK
« f
10.25
11.57
13.67
I5-23
15-95
17.87
21.00
22.88
24.68
181
208
237
267
279
31S
360
393
424
4.20
4.24
4.16
4.18
4.18
4.20
4.14
4.14
4.15
21
25
37
44
7i
82
98
in
123
1.42
1.47
1.65
1.69
2.IO
2.15
2.16
2. 2O
2.22
«9^j
6K«zi
::1
"•f
6x4xi
TS
" i
11.49
13-05
18.19
20.47
22.75
24.99
24.00
26.24
28.44
2O I
232
319
361
4OI
440
4I2
451
489
4.18
4.22
4.19
4.20
4.20
4.19
4.14
4.15
4.15
3°
36
119
139
160
180
165
187
206
.62
.67
2.56
2.61
2.65
2.69
2.62
2.66
2.69
I2X&
M
12x1
.::
«
I2xJ
«
M
M
4?3*A
4,3x1
?!
s^K
" F
:: f
12. II
I3-67
1442
15.98
16.70
18.62
20.50
22.OO
23.88
25.68
27.48
29.24
3°4
350
359
404
421
476
526
544
596
643
692
735
5'^1
5.06
4-99
5-02
5-O2
5-04
5.06
4-97
5.00
5.00
5.02
5.01
32
36
37
44
70
82
95
98
in
123
I3S
149
1-57
1.62
1. 60
1.66
2.05
2.10
2.15
2. II
2.l6
2.19
2.21
2.26
5x3i*A
6Hx(
"1
= J
6x4xJ
:; •%
= 1
13-99
15-95
18.94
21.22
23.50
25-74
27.94
25.OO
27.24
29.44
3I.6O
33-76
355
412
481
544
605
665
723
623
683
74i
794
849
5.02
5-04
5.04
5-o6
5-07
5-08
5-09
4-99
5.01
5.02
5-oi
5.01
58
69
119
139
160
180
200
165
1 86
206
228
249
2.04
2.08
2.51
2.56
2.61
2.65
2.67
2.57
2.61
2.65
2.69
2.72
The above table is intended to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of other sections may be found as follows:
Example: Required the properties of a section composed of 4 A 5" X 3J" X A"> l°n§ legs
out, I2j" back to back, and one plate 12" X A".
Item.
Area.
Moment of Inertia.
Radius of Gyration.
Axis A-A. Axis B-B.
Axis A-A.
Axis B-B.
Tal
,!«•
>.
A Table JA Table !B
TA-I
rB-K
/IA+A
'IB + A
In.
No. No. . .
In.1 In.4 In.4
In.
In.
4^5*3i*& 33
I PI— I2X& I
14.12 33 403 36 84
5-25 3 63 4 o
/ 466
Vlo^
vi **
V 19.37
Totals A =
19-17 I* = 466 IB = 84
TA - 4.90
r= = 2.08
125
TABLE 70.
PROPERTIES OF FOUR ANGLES AND THREE PLATES.
9
Properties of with
Plate and Angle A IJ ^a Fiance Plates
Column Sections. 11 d = width of Web Plate Plus i In.
b
Series I and II.
Series I.
Series II.
Web
Plate.
Four
Angles.
Two
Cover
Plates.
Total
Area.
Moments of Inertia and
Radii of Gyration.
Two
Cover
Plates.
Total
Area.
Moments of Inertia and
Radii of Gyration.
Axis A- A.
Axis B-B.
Axis A-A.
Axis B-B.
IA
rA
IB
TB
IA
TA
IB
TB
In.
In.
In.
In.*
In.«
In.
In.<
In.
In.
In."
In.<
In.
In.<
In.
iox|
d
I ox|
4*3*1
5
5X3^x1
2
ioxf
"*
I2X|
\
21.17
26.75
26.20
33-00
459
598
556
723
4.62
4-73
4.60
4.68
IOO
134
I8l
242
2.17
2.24
2.63
2.71
10x5
"I
12x5
" f
23.67
29.25
29.20
36.00
540
682
653
824
4.78
5-16
4-73
4.78
121
154
217
278
2.26
2.46
2-73
2.78
I2X§
M
I2x|
(I
I2X|
«
12X2
d
5x3sxl
" i
5^3 M
" I
6x4xf
2
6x4X5
" J>
I2X|
"J
"1
« 5.
I4xf
"*
"I
« 5
8
25.70
32.50
34-oo
40.68
29.44
37-50
39-oo
46.94
794
1034
1052
1290
916
1197
1215
1496
5-31
5.66
5-59
5-63
5-58
5-65
5.58
5.64
179
239
242
303
291
388
394
492
2.64
2.71
2.67
2-73
3-H
3-22
3-18
3-24
12x5
« 5
f
« 3
14X5
(( 5.
8
« 5.
28.70
35-50
37-oo
43-68
32.94
41.00
42.50
50.44
929
H73
1191
1387
1073
1360
1378
1664
5-69
5-75
5-68
5-64
5-71
5-76
5-69
5-75
215
275
278
339
348
446
45i
549
2.74
2.78
2.74
2.78
3-25
3-29
3.26
3-30
.I4ff
I4x|
I4x|
6x4X5
" 1
2
6x4X5
" !
6x4x1
«
«<
M
II
<c
«<
M
I4x|
"*
"1
« 5
8
" !
"1
" il
" if
" if
" ii
" -V1-
28
" 2f
30.19
38.25
40.00
47-94
49.69
56.69
63.69
70.69
77.69
84.69
91.69
98.69
1261
1644
1672
2052
2081
2529
3006
3512
4048
4615
5214
5846
6.46
6.55
6.46
6-54
6.47
6.68
6.87
7-os
7.22
7-38
7-54
7.69
291
388
394
492
499
613
728
842
956
1071
1185
1299
3.10
3-19
3-H
3.20
3-17
3-29
3-38
3-45
3'51
3-S6
3.60
3-63
14X2
"f
"f
"f
<< 3
" I
" II
" I*
" If
" 2
"2i
"22
33-69
41-75
43-50
Si-44
53-19
60.19
67.19
74.19
81.19
88.19
95.19
102.19
1469
1857
1885
2263
2292
2764
3255
3776
4327
4910
5525
6l75
6.60
6.67
6.58
6.63
*57
6-74
6.96
7-13
7-30
7.46
7.62
7-77
348
446
45i
549
556
671
785
899
1014
1128
1242
1356
3-21
3-27
3-22
3.26
3-23
3-34
3-42
3-48
3-53
3-58
3.62
3-64
The above table is intended to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of other sections may be found as follows:
Example: Required the properties of a section composed of 4 A 5" X 3 \" X r$", long legs
out, I2j" back to back, one web plate 12" X TS" and two flange plates 12" X f".
Item.
Area.
Moment of Inertia.
Radius of Gyration.
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B.
Table
No.
A
Table
No.
IA
Table
No.
IB
rA=l/lA-A
TB= I/Is-*- A
In.
In.'
In.«
In."
In.
In.
4^5x35X^5
I PI— 1 2x^
2 PI— I2xf
33
i
I
14.12
5-25
9.00
33
3
5
403
63
359
36
4
3
84
0
108
X/82S
J I92
\28.37
V 28.37
Total
A =
28.37
/A =
825
/B =
192
'A = 5-39
rB = 2.60
126
TABLE 71.
PROPERTIES OF FOUR ANGLES AND Two PLATES, LACED.
IB
B
-*-- — ••_ b •• Width, Back to Back
Properties of ^— i
Four Angles and
IT r
of Angles, for Equal
Two Plates, A
[A A
' A Moments of Inertia
I "« d * i • II "- about Axes A A and B B
Laced.
Angles Turned Out "a"T~"
• ---^----J| with Angles Turned Out.
and
c *• Same as b, but
•— t t l - 1 ]f nrlfh Anrrli-n TiirnrH In
Angles Turned In. C." — i ^^- « ,. . ~.... ....».-_ ._...™ ....
d — Depth of Web Plates + J".
IB IB
^•ri.. •
Series i.
Series a.
Series 3.
Series 4.
ocrics
I. •». .«
and 4.
3g
«l °§
c£ Bii
*i
3s
*i
W t
c3 41
v« •
£§
§•3
*|
3d
33
cS
11
O"S
3s
«-• nj
if
"o e
<n.S
3 «-»
-8
Size of
o S
II
**
SI
fl
II
|J
^8
•n &
<2o
21
II
1J
**
11
,o<!
II
ij
**
if
&0
~ 2
24
Angles.
A
I
r
b
c
A
I
r
b
c
A
i
r
b
c
A
I
T
b
c
In.
In.«
In.«
In.
In.
In.
In.»
In.«
In.
In.
In.
In.«
In.<
In.
In.
In.
In.«
In.«
In.
In.
In.
8"xi" Web Plates.
8"x|" Web Plates.
8"*i" Web Plates.
8"x|" Web Plates.
2jx2jxl
8.76
83
3.08
5-4
6-7
10.76
94
2-95
5-3
6-3
12.76 105
2.87
5-4
5.8
14.76115
2-79
5-3
5-4
" 1
10.92
109
3-16
5-3
7.0
12.92 119
3-04
5-3
6.6
14.92
130
2-95
5-4
6.1
16.92 141
2.89
5-2
5.8
" i
13.00
132
3-19
5-2
7-3
15.00
H3
3-09
5-2
6.9
17.00
154
3-01
5-3
6.5
19.00
165
2-95
5-2
6.1
3x3x1
9.76
93
3-09
S-i
6.8
11.76
104
2-97
5.1
6.4
13.76
"5
2.89
S-i
6.0
15.76
126
2.83
5-i
5-6
" 1
12.44
123
3-15
5.0
7.1
14.44 134
3-°5
5-o
6.7
16.44
H5
2.97
5.0
6.4
18.44
156
2.91
5.0
6.0
** 4
15.00
151
3-^7
4.8
7-4
17.00
162
3-09
4.9
7.0
19.00
173
3.02
4-9
6-7
2I.OO
184
2.96
S-o
6-3
liteixl
13.92
137
3.14
4.6
7-3
15.92
148
3-05
4-7
6.9
17.92
159
2.98
4-7
6.6
19.92
170
2.92
4.8
6.2
i
17.00
1 68
3-15
4-5
7-5
19.00 179
3-07
4.6
7.2
21.00
190
3.01
6.9
23.00
2O I
2.96
4.6
6-5
" i
19.92
196
3-15
4-3
7-7
21.92 2073.08
4.4
7-4
23.92
218
3.02
4-3
25.92
229
2.97
4-4
6.8
lo"xl" Web Plates.
io"xf" Web Plates.
io"x£" Web Plates.
io"xf" Web Plates.
2l,\2\\\
9.76
142
3-82
6.4
7-5
12.26
162
3.63
6-5
7-3
14.76
183
3-52
6.6
7.0
17.26
2043.446.8
6-7
" 1
11.92
185
3-94
6.6
8.1
14.42
205
3-77
6-7
7.8
16.92
226
3.66
6.7
7-5
19.42
2473.566.8
« if
14.00
224
4.00
6.9
8.8
16.50
244
3-85
6-9
8.4
19.00
265
3-73
6.8
8.0
21.50
286
3-65
6.8
7-5
3X3X}
10.76
159
3.84
6-7
8-3
13.26
179
3-68
6-7
7-8
15.76
200
3-56
6-7
7-4
18.26
221
348
6-7
6.9
" I
13-44
209 3.94
6.7
8-7
15.94 229
3-79
6-7
8.2
18.44 250
3-67
6.6
7-8
20.94
271 3.606.6
7-3
." 1
16.00
256
4.00
6.6
9.0
18.50
276
3-86
6.6
8.6
21.00
297
3-76
6.6
8.1
23.50
318
3-68
6.6
7-7
3ix3hl
14.92
232
3-94
6.4
8.9
17.42
252
3.80
6-5
8-5
19.92
273
3-70
6.4
8.0
22.42
294
3-62
6.4
7-5
" i
18.00
285
3-98
6.2
9.1
20.50 305
3-86
6-3
8.7
23.00
326
3.76
6-3
8-3
25.50
3473.696.3
7.8
" t
20.92
333
3-99
6.0
9-3
2342353
3-88
6.1
8.9
25.92
374
3-78
6.2
8-5
28.42
395 3-72 6.2
8.1
I2"xi" Web Plates.
I2"xf" Web Plates.
I2"xj" Web Plates.
I2"xf" Web Plates.
2jx2ixl
10.762204.52 8.4
9-4
13.76
256
4.32
8-3
9.0
16.76
292
4.17
8.2
8-5
19.76
328 4.08 8.2
8.0
8
12.92 2884.72 8.5
9-9
15.92
324
4-Si
8.4
9-4
18.92
360
4-36
8.3
8.9
21.92
396 4-25
8-3
8.4
" i
15.00 343 4.78
8.6
10.3
18.00
379
4-59
8.5
9.8
2I.OO
4iS
4-45
84
9-3
24.00
45i
4-34
8-3
8.8
3x3x1
11.762464.57
8-3
9-7
14.76
282
4-37
8.2
9-3
17.76
318
4-23
8.1
8.8
20.76
354
4.13
8.0
8-3
" 1
14.443224.72
8.2
IO.2
17.44
358
4-53
8.2
9-7
20.44
394
4-39
8.1
9.2
23-44
430 4.28
S.I
8-7
" i
17.00 392 4.80
8.2
10.6
20.00
428
4-63
8.2
IO.I
23.00
464
4.49
8.2
9.6
26.00
500
4-39
&a
9.0
jteM
15.923564.73
8.0
10.4
18.92
392
4-55
7-9
9-9
21.92
428
4.42
7-9
9-4
24-92
4*4
4.31
8.0
S-9
i
19.00 437 4.80
8.0
10.7
22.00
473
4.64
7-9
IO.2
25-00 509
4-Si
7-9
9-7
28.00
545 4-41
8.0
9.2
" i
21.92
5124.83
7-9
1 1.0
24.92
548
4-69
7-9
10.6
27.92
584
4-57
7-9
IO.I
30.92
620
4.48
7-9
9.6
4x4x1
17.44
388 4.72
7-7
10.5
20.44
424
4.58
7-7
IO.O
23-44
460
4-43
7-7
9.4
26.44
496
4-33
7-7
9.0
" *
21.004804.78
7-7
10.8
24.00
5164.64
7.6
10.3
27.00 552 4.53
7.6
9.8
30.00
588443
7.6
9-3
" I
24.44 563 >8o
7-6
n. i
27.44
599 4.67
7-5
10.6
30.44 635 4.57
7-5
IO.I
33-44
671 4.51
7-5 J9-7
127
TABLE 71.— Continued.
PROPERTIES OF FOUR ANGLES AND Two PLATES, LACED.
E
B
b - Width, Back to Back
Properties of
Four Angles and I
f
p.
r"
"1
of Angles, for Equal
Moments of Inertia
Two Plates, A
1
A A
A about Axes A-A and B-B
Laced. __>
Angles Turned Out i
and f— '
Angles Turned In.
f±l
t-i~-
pi":,
LiJ
— when Angles Are Turned Out.
c = Same as b with Angles
Turned In.
d= Depth of Web Plates + J".
IB
IB
Series i.
Series 2.
Series 3.
Series 4.
Series
i, 2,3
and 4.
3*
<u ti
gn
°j
•o'S'
O"M
1J
• «-.
,o
'-4J
E
If
3s
B
I
nertia.
o a
01 0
S '•"
5 "3
2 <*
ment
nertia.
3 '£
*%
St
Size of
H^
(So
*f
H*
^ $
0
ff
1
"o
KC5
*3
**
1« >,
£><
Angles.
A
I
r
b
C
A
I r
b
c
A
I
r
b
C
A
I
r
b
c
In.
In.*
In.*
In.
In.
In.
In.*
In.< In.
In.
In.
In.*
In.«
In.
In.
In.
In.*
In.'
In.
In.
In.
14" x |" Web Plates.
14" x 1" Web Plates.
14" x f' Web Plates.
14" x|" Web Plates.
3X3x^
16.26
414
5.05
9.6
10.3
19.76
471
4.89
9.6
IO.O
23-
26
528
4-77
9-5
9-5
26.76
585
4.67
9.6
9.0
18.94
52O
5.24
9-7
10.9
22.44
577
5-07
9-7
10.4
25-94
634
4-94
9-6
9.9
29.44
691
4.84
9.6
9-5
2
21.50
620
5-37
9.8
II.4
25.00
677
5.20
9.8
10.8
28.
50
734
5-07
9-7
10.3
32.00
791
4-97
9.6
IO.O
31X31X|
20.42
570
5.28
9.6
II. I
23.92
627
5.12
9.6
10.6
27.42
684
4-99
9-5
IO.2
30.92
741
4.89
9-5
9.8
« 1
5
23.50
685
5.40
9.6
1 1.6
27.00
742
5.25
9.6
n. i
30.50
799
5-
12
9-5
10.6
34.00
856
5.02
9-5
IO.I
26.42
791
5-47
9.6
I2.I
29.92
848
5-32
9.6
1 1.6
33-42
905
5-
20
9-5
II.O
36.92
962
5-io
9-5
10.5
4X4X|
21.94
616
5.30
9-3
II.4
25.44
673
5-15
9-3
10.9
28.94
730
5.02
9.4
10.5
32.44
787
4-93
9.4
IO.O
2
25.50
747
5.41
9-3
11.8
29.00
804
5.26
9-3
11.3
32.50
861
5-
IS
9-3
10.8
36.00
918
5-05
9-4
10.4
« 5
g
28.94
867
5-47
9.2
12. 1
32.44
924
5-34
9.2
11.7
35-
94
9
81
5-
23
9-3
11.2
39-44
1038
5-13
9-3
10.8
i6"xf" Web Plates.
l6"xf" Web Plates.
l6"xf" Web Plates.
l6"xl" Web Plates.
31X31X|
25.92
873
5.80
II.O I2.O
29.92
9595-66
II.O
1 1 -5
33.92 1044
5.53 10.9 n.o
37.92 1129 5.46 10.9 10.5 |
" 5
29.00
1028
5.96
II. I 12-4
33.00 1114 5.81
II.O
11.9
37.0011995.
69 ii.o 11.5
41.00 1284 5.60 10.9
1 1 .0 J
" f
31.92
1172
6.06
II. I
12.8
35-92
12585.92
n. i
12.3
39-92
1343
5.80
II.O
n-9
43-92
1428 5.70
II.O
ii-5
4X4X|
27.44
937
5.84
IO-9
12. 1
31-44
1023
e.
71
10.9
1 1.7
35-44
1108
5.60
10.9
39-44
1 193
5.50
10.8
n. i
2
31.00
1113
5-99
10.9
12-5
35.00
II995-85
10.9
12.2
39.00 1284
5-74
10.9
n.8
43.0013695.64
10.8
11.4
34-44
1276
6.09
IO.9
1362
5-96
10.9
12.6
42.44
H47
5-
84
10.8
12. 1
46.44
1532
5-74
10.8
11.7
6x6xf
33-44
1165
5.90
9.8
12.8
17-44
12515-78
9.8
12.4
41.
44
1336
5.68
9.9
I2.I
45-44
1421
5.60
IO.2
11.6
2
39.00
1413
6.02
9-7
13.2
43.00
1499 5.91
9-7
12.8
47.00
1584
5.81
9-8
12.6
51.00 1669
5.72
IO.I
12. 1
a 5
1
44-44
1647
6.09
9.6
13.6
48.44
17335-
98
9.6
13.2
52.44
1818
5-
89
9-7
13-0
5644 1903
5.81
IO.O
12.5
'( 3
4
49.76
1867
6.12
9-5 i4-o
53-76
19536.03
9-5
13-6
57.76
2038
5-94
9.6
13-4
61.762123 5.87
9-9
12-9
i8"x|" Web Plates.
i8"xf" Web Plates.
i8"xf" Web Plates.
i8"xj" Web Plates. |
3ix3|xf
27.92 1171
6.49 12.4 13.2
32.42 1293
6.32 12.4
12.8
36.92 1414
6.19 12.5
12.5
41.42
15366.09
12.4
12. 1
2
31.001373
6.66 12.6 13.7
35.50 1495 6.49
12.5
13-3
40.00 1616
6.36 12.5
12.9
44.50
17386.25
12.4
12.4
« 5
8
33-92
1561
6.78
12.7
14.2
38.42 1683 6.62
12.6
13-7
42.92
1804
6.48
12.5
13.2
47.42
1926
6.38
12.4
12.7
4X4X|
29.44
1256
6-53
12.4
13.5
33-94
1378
6.38
12.2
12.9
38.44
H99
6.25
12.2
12.6
42.94
1621
6.14
I2.I
12. 1
" 2
33.00 1485
6.71
12.5 14.0
37.50 1607 6.55
12.3
13.4
42.00
1728
6.42
12-3
13.0
46.50
1850
6.31
12.2
12-5
" 1
36.44 1699
6.82
12.6 14.5
40.94 1821
6.67
12.4
13-9
45-44
1942
6-54
12.4
13-4
49-94
2064
6-43
12-3
12-9
6x6xf
41.00
1884
6.78
11.5
14.8
45.50 2006
6.64
II- 5
14.3
50.00
2127
6.53
II. 5
13.8
54.50
2249
6-43
II.4
13-3
(1 5
8
46.44 2191 6.87
11.3 15.2
50-94' 23 1 3 6.7411-3! 14-7
55-44
2434
6.63
11.3
14.2
59-94
2556
6.53
II.4
13-7
11 3
4
5 1. 70 2482 6.92
II. 2
15.5
56.26 2604
6.80 II. 2 15.1
60.76
2725
6.69
11.3
14.6
65.26
2847
6-59
II-3
I4.I
« 7
8
56.92 2762 6.96
II. I
15.2
61.4228846.85 n. i 15.5
65.92
3005
6.74
II. 2
15.0
70.42
3127
6.66 1 1. 2
14-5
128
TABLE 71.— Continued.
PROPERTIES OF FOUR ANGLES AND Two PLATES, LACED.
IB
B
h
— Width, Back to Back
Properties of far— -y-v
Four Angles and J
r "T
:r^L
of Angles for Equal
Moments of Inertia
TW
trws, A..
A i Ajj
1 A al
x>ut Axes A-A and B— B
Lacea.
Angles Turned Out
f iR-r *
ith Angles Turned Out.
c = Same as b. but
**.&*!. ,.,fc~~i «M,JI d.su^j"Ki."4.r.
IB IB
t^-.ri' .J
Series x.
Series a.
Series 3.
Series 4.
ESSraM
I. 2. 3
** -i
"oa
•y d
"3 S3
.
« a
"3 e
II
"SB
and 4.
ii
Momen
f Inerti
"•S
=32
a|
II
j|
_ o
S'S
=32
i!
11
ll
il
I*
•24
II
11
(So
;°!
•O<,
Size of
o
o
**
hM W
Angles.
A
I
r
b
c
A
I
r
b
c
A
I
r
b
c
A
r
b
c
In.
In.»
In.«
In.
In.
In.
In.«
In.«
In.
In.
In.
In.*
In.«
In.
In.
In.
In.*
In.
In.
In.
2o"xi" Web Plates.
2o"xf" Web Plates.
2o"xJ" Web Plates.
2o"xf " Web Plates.
3i*3i*f
29.92
15257.1413.814.5
34.92 1691 6.96 13.7 14.0
39.92 1858 6.83
13.6
13-5
44.92
6.72 13.5
13.0
\
33-oo
1779 7-34 H-OJ 15-0
38.0019457.15 13.914.5
43.OO 2112 7.O2 13.8
14.0
48.00 6.90 13.6 13.5
" 1
35.92
2017
7-50
14.2
15.6
40.92
21837.31
14.0
15.0
45-9223507.I5
13-9
14.5
50.92 7.03
13.7
14.0
4x4x1
3J-44
35.00
1634
1923
7.21
7.41
13-7
13-9
14.8
15.4
36.44
40.00
1800
2089
7-03 13-6
7-23 13-8
14.2
14.8
41.44
45.00
1967
2256
6.89
7.08
13-6
13-7
13.8
14-3
46.44
50.00
6.78
6.96
13-5
13.6
13-3
I3.8
<«
*
38.44
2194
7-58
14.1
1 6.0
43-44
2360
7-37
13-9
15-3
48.44
2527
7-23
13-9
14.8
53-44
7.10
13.7
I4.2
6x6xJ
43-00
2436
7-53
I3-I
16.2
48.00
2602
7-36
13.2
15-6
53-oo
2769
7-23
13-3
15-2
58.00
7.12
13.4
14.2
" f
48.44 2828 7.64
I3-I
16.6
53-44
2994
7-49
I3-I
16.1
58.44
3161
13.2
15.6
63-44
7-24
13-3
14.7
it
53.76 3202
58.92 3561
7.72
7-79
13.0
12.9
17.0
17.4
58.76
63.92
33687.57
3727 7.64
13.0
12.9
16.5
16.9
63763535
68.92 3894
7-45
7.52
I3-I
12.9
16.0
16.4
68.76 7.34 13.1
73.92 7.42112.9
15.2
15-7
22"x|" Web Plates.
22"xf " Web Plates.
22" xl" Web Plates.
22"xi" Web Plates.
3.'xV'x*
37.42 2161
7.60
15.0 15.2
42.92 2383 7.45
14.9 14.8
48.42
2605
7-34 14-9
H-3
53.92 7.24 14.8
13-9
" i
40.50 2473
7.82
15-3
iS-7
46.00 2695 7.68 15.2 15.3
5I-50
2917
7-53 i5-i
14.8
57.007.43 15.0
14.4
" f
43-42
2766
7.98
15-5
16.2
48.92 2988 7.82
15-4
15-8
54-42
32IO
7-67
15-3
15-3
59-92 7.57
15-2
14.9
4x4x1
38.94
2296
7.68
15-5
44.44 2518 7.54
15.0
15.2
49-94
27407.41 15.1
14.8
55-44
7.30 15.1
14.2
42.50 2652 7.90 15.3116.1
48.0028747.74 15.2
157
53.5030967.61 15.2
15-3
59.007.51 15.1
H-7
"' I
45-94
2988
8.07
15.6
16.7
51.4432107.90
15.4
16.2
56.94 3432
776 iS-3
'5-7
62.44 7-65 I5-I
IS-3
" Xf
50.50
55-94
3295 8.08 14.6
3783 8.22 I4.6
17.0
17.4
56.0035177.93
61.444005 8.08
14.6
14.6
16.5
16.9
61.503739
66.94 4227
7.80 14.6
7-93 H-6
16.1
16.5
67.00
72-44
7.69 14.6
7-83 H-6
15-6
16.0
« i
61.26 4249 8.33 14.6
17.9
66.7644718:1914.6117.4
72.26 4693 8.05 14.6 16.9
77.76
7.96,14.6
16.5
H
66.42 4698
8.42 14.6
18.3
71.92 4920 8.27 14.6117.8
77.42 5142
8.15 14.617.4
82.92
8.04114.5
16.9
24"x|" Web Plates.
24"*!" Web Plates.
24"xJ" Web Plates.
24"«" Web Plates.
4X4x|
41.44 2870 8.32
45.00' 3300 8.56
16.4
16.6
16.7
17-3
47-443i58j8.i6
51.0035888.47
16.3 16.3
16.5 16.9
53.44 3446] 8.03 |i6. i
57.00 3876 8.25 16.4
16.0
59-44
63.00
7-93
8.14
16.0
'I'6
16.0
" i
48.44
3707
8.75
16.8
17.9
54-44 3995
8.57
16.7
17.4
60.44 4283
8.42
16.6
66.44 8.30
16.5
16.4
6x6xJ
53-oo
4089 8.79 16.2
18.4
59.004377
8.62
16.1
17.9
65.00 4665 8.47
16.0 17.4
71.008.36
1 6.0
16.9
" f
58.44 4684 8.96 16.2
18.9
64-44^972
8-79
16.1 18.4
70.44 5260 8.64 16.0 17.9
76.44 8.53
1 6.0
17.4
« 3
t
63-76,5253 9-o8
16.2
19.3
69.765541
8.92
16.2 18.9
75.7658298.7716.1
18.3
81.768.66 16.1
17."
" J
68.92
58029.18
16.2
19.8
74.92 6090
9.02
16.2 19.3
80.92 6378 8.88 16.1
18.8
86.92
8.76
16.1
18.3
8x8xJ
61.00
4772 8.85
iS-3
19.0
67.00 5060
8.69
15.3 18.5
73.0053488.5615.3
1 8.0
79-oo
8-45
15.3
17-5
" 1
68.44'5537;8.98
15.2
19.6
74.4458258.85 15.2 19.1
80.446113 8.72 15.2
1 8.6
86.44 8.60
i
1 8.0
|
75.7662689.11
15.1
20.1
81.7665568.96 15.1 19.6
87.7668448.84 15.1
19.1
93.76 8.72
15-3
18.5
" 1
82.92 69769.16
15.0
20.5
88.92 7264 9.04 15.0 19.9
94.92 7552 8.93 15.0 19.4
100.92 8.82
15.2
19.0
I
90.00 7653 9.22
14.9
20.8
96.00 7941 9.IO 14.9 2O.2
I02.0O 8229 8.99 14.9
19.7
108.00 8.89 15.2
19.5
129
TABLE n— Continued.
PROPERTIES OF FOUR ANGLES AND Two PLATES, LACEa
Properties of
Four Angles and
Two Plates, /
Laced.
Angles Turned Out
and
Angles Turned In.
IB
B
, b = Width, Back to Back
of Angles, for Equal
^ Moments of Inertia
A about Axes A-A and B-B
JI for Angles Turned Out.
n c = Same as b, but
]Jf with Angles Turned In.
d = Depth of Web Plates + i".
L—
J
f-
£::•
Ir
i
"-4
^_L_ 1
ST"
*
tj^m
IB
Series
1,2,3
and 4
Series i.
Series 2.
Series 3.
Series 4.
3s
o *-*
S'-S
°>5
§'l
=32
o|
*$
£<
IJj
•3d
O
If
II
O !H
"o a
rt >>
II
3 g
=3 B
r\5 "h
•°|
Size of
Angles.
A
i
r
b
C
A
I
r
b
C
A
r
b
c
A
r
b
c
In.
In.*
In.<
In.
In.
In.
In.*
In.'
In.
In.
In.
In.*
In.
In.
In.
In."
In.
In.
In.
26"xf" Web Plates.
26" x|'
' Web Plates.
26" x 1" Web Plates.
26" xi" Web Plates.
" \
1
6x6x^
" i
<< s
4
« 1
1
8x8x|
<« s
s
43-94
47.50
50-94
55-50
60.94
66.26
71.42
63-50
70.94
78.26
85.42
92.50
3526
4039
4523
4990
5702
6385
7043
5818
6737
7617
8471
9289
8.96 17.7
9.23 18.0
9.42 18.2
9.48' 17.7
9.68 17.8
9.82 17.8
9-94 17-9
9.58 16.8
9-75 16.8
9.88 16.8
9.96 16.7
10.02 1 6.6
1 8.0
18.6
19.2
19.7
2O.2
20.8
21-3
20-5
2I.O
21.6
22.O
22.3
50-44
54-00
57-44
62.00
67.44
72.76
77.92
70.00
77-44
84.76
91.92
99.00
3892
4405
4889
5356
6068
6751
7409
6184
7103
7983
8837
9655
8.79
9-05
9-23
9.29
9-49
9-64
9.76
9.40
9-58
9.71
9.81
9.88
I7.6
I7.8
18.1
17.7
17.7
17.8
17.9
16.8
16.8
16.7
16.6
1 6.6
I7.6
18.1
18.7
19.2
19.7
20. 2
20.8
2O.O
2O.4
2O.9
21.4
21-9
56.94
60.50
63-94
68.50
73-94
79.26
84.42
76.50
83-94
91.26
98.42
105.50
8.63
8.88
9.07
9-15
9-34
9-47
9.60
9.26
9-44
9-56
9.67
9.76
17-5
17.7
18.0
17.6
17.6
17.7
17.8
16.8
16.8
16.7
16.6
16.6
I7.I
I7.6
18.2
18.7
19.2
19.7
2O.2
194
19.9
204
2O-9
21.4
63-44
67.00
70.44
75-00
80.44
85.76
90.92
83.00
90.44
97.76
104.92
II2.OO
8-54
8.76
8.94
9-O2
9.2O
9-34
946
9-13
9-32
9-45
9.64
17.4
I7.6
17.9
17-5
<7'5
17.6
17.7
16.8
16.8
16.7
16.6
16.6
16.6
17.1
17.7
18.1
18.6
19.1
19.6
18.8
19-3
19.8
20.3
20.8
28" xf" Web Plates.
28" x I" Web Plates.
28
" xi" Web Plates.
28"x 1 1" Web Plates.
4x4x1
6x6x2
It 5
8
" 3
" !
" 3
" f
" I
53-44
57-oo
60.44
65.00
70.44
7576
80.92
73-oo
80.44
87.76
94.92
IO2.OO
4728
5329
5898
6458
7299
8106
8885
7447
8536
9579
10594
11568
9.41
9.67
9.88
9-97
10.17
10.35
10.47
10.10
10.30
10.45
10.56
10.65
18.8
19.1
19.4
19.0
19.1
19.2
19-3
18.3
18.3
18.3
18.3
18.3
18.6
19-3
19.9
20.4
20.9
21.5
22.O
21.2
21.8
22.4
22.8
23-3
60.44
64.00
67.44
72.00
77-44
82.76
87.92
80.00
87.44
94-76
101.92
109.00
5185
5786
6355
6915
7756
8563
9342
7904
8993
10036
IIO5I
I2O25
9.27
9-51
9.71
9.81
IO.OI
IO.2I
IO.3I
9-94
10.14
10.30
10.42
10.50
18.8
19.0
19-3
18.9
19.0
19.1
19.2
18.3
18.3
18.3
18.3
18.4
18.4
18.9
19-5
19.9
20-4
2I.O
21-5
2O.7
21.2
21.7
22.2
22.8
67-44
71.00
74-44
79.00
84-44
89.76
94-92
87.00
94-44
101.76
108.92
116.00
9.15
9-38
9-57
9.66
9.87
10.03
10.16
9.81
10.00
10.15
10.27
10.37
18.7
19.0
19.2
18.9
19.0
19.1
19.2
18.4
18.4
18.4
18.4
184
I7.8
I8.3
18.9
19-5
2O.O
20.5
2I.O
20. 2
20.7
21.2
21.7
22-3
74-44
78.00
81.44
86.00
91.44
96.76
101.92
94.00
101.44
108.76
115.92
123.00
9-05
9.27
9-45
9-55
9-74
9.90
10.03
9.69
9.90
10.03
10.06
10.25
18.6
18.9
18.8
18.9
19.0
19.1
18.4
18.4
18.4
18.4
18.4
17-4
18.0
18.5
19.0
19-5
20. o
20.5
19.7
20.3
20.9
21.3
21.8
3o"xf" Web Plates.
30" x 1" Web Plates.
30" xi" Web Plates.
3o"x 1 |" Web Plates.
4X4X|
" f
6x6x5
U 3
4
1
8X8X5
« 5
8
« 1
« 7
8
" I
56.44
60.00
6344
68.00
73-44
78.76
83.92
76.00
83-44
90.76
97.92
105.00
5670
6367
7027
7690
8670
9613
10522
8857
10129
"352
12541
13685
IO.02
I0.3O
10.51
10.64
10.86
11.05
1 1. 20
10.78
1 1. 02
11.20
11.32
11.42
20. i
20.5
20.8
20.5
20.7
20.9
2I.O
19.9
19.9
19.9
20.0
2O.O
19.9
2O.6
21.2
21-7
22.2
22.8
23-4
22-5
23.0
23.6
24.1
24-7
63-94
67.50
70.94
75-50
'80.94
86.26
91.42
83.50
90.94
98.26
105.42
112.50
6233
693O
7590
8253
9233
IOI76
11085
9420
10692
H9I5
I3I04
14248
9.88
IC.I2
10-35
10.46
10.68
10.86
1 1. 02
10.62
10.85
11.02
11.15
11.25
2O.O
2O.4
2O.7
2O.4
2O.6
20.7
2O-9
20.O
2O. I
2O.2
2O.2
20.2
19-5
2O.O
2O.5
21.2
21.8
22-3
22-9
22.0
22-5
23.1
23-6
24.2
71.44
75-00
78.44
83.00
88.44
93-76
98.92
91.00
98.44
105.76
112.92
120.00
9.76
IO.OO
IO.2O
10.30
IO.5I
10.70
10.85
10.46
10.70
10.85
II.OO
II. II
2O.O
2O-3
2O-5
2O.3
20-5
20.6
20.8
19.8
19.8
19.8
19.9
19.9
ig.O
19.6
2O.2
20.8
21.4
21-9
22-5
21-5
22.0
22.6
23.1
23-7
78.94
82.50
85-94
90.50
95-94
101.26
106.42
98-50
105.94
113.26
120.42
127.50
9-56
9.89
1 0.06
10.18
10.40
10.56
10.71
10.35
10.56
10.73
10.90
10.98
19.9
2O.2
20.4
2O.2
20.4
20.5
20.7
19.9
2O.O
2O. I
2O. I
2O. I
18.6
19.2
19.7
20.3
20.8
21.4
21.9
21. 1
21.8
22.4
22.9
23.4
130
TABLE 71.— Continued.
PROPERTIES OF FOUR ANGLES AND Two PLATES, LACED.
IB
B
b - Width. Back to Back
Properties of
\r nn
' — ]i) of Angles, for Equal
Four Angles and A
FA ! . F
Moments of Inertia
Two Plates, Laced. ° H — \
L..A <» AJ|— -i
II A about Axes A-A and B-B
Angles Turned Out ~~fll"~k~~
and
k- |L...l....jr~ with Angles Turned Out.
1 c - Same as b. for
Angles Turned In **- — KWK
it^. t_._ IJL^ i
Anolo* Tnrn*«J In
d - Depth of Web Plates + J"-
IB
IB
Series
Series i.
Series a.
Series 3-
Series 4.
and 4.
H^
Moment
of Inertia.
Radius of
Gyration.
5!
H*
Moment
of Inertia.
Radius of
Gyration.
jf
II
Radius of
Gyration.
a|
II
Radius of
Gyration.
si
21
oj
||
A
I
r
b
c
A
I
r
b
C
A
r
b
C
A
r
b
C
In.
In.»
In.«
In.
In.
In.
In.'
In.«
In.
In.
In.
In.'
In.,
In.
In.
In.« In.
In.
In.
32"xJ" Web Plates.
32"xJ" Web Plates.
32"xi" Web Plates.
32"xiJ" Web Plates.
4*4*1
59.44 f-725
10.65
21.4
21. 1
67.44
7408 10.47
21-3
20.7
75.44 IO-35 2I-2 2O.2
83-44
10.25 2I-I
19.8
" i
63.00 7525
10.94
21.8
21.8
71.00
8208
10.75
21.7
21.3
79.00 10.60 21.6
20.8
87.00
IO.5O 21.4
20.4
" t
66.44 8284
II.IO
22.1
22.4
74-44
8967
10.97
22.0
21.9
82.44 IO.82
21.8
21.4
90.44
10.70 21-7
20.9
6x6xi
71.00 9058
11.30
21.8
23.0
79.00
9741
II. II
21.7
22.5
87.00
10.95
21.6
21.9
95.00
10.80
21.5
21.4
" i
76.44 10189
"•55
22.O
23.6
84.44
10872
"•35
21-9
23.1
92-44
11.18
21.8
22.5
100.44
11.04
21.7
22.O
(i j
^
81.76 11277
"•75
22.2
24.2
89.76
11960
"•55
22.1
23.6
97.76
"•37
21.9
23.1
105.76
11.23
21.8
22.5
a '
86.92 12328 11.90
22.4
24.8
94.92
I30II
11.72
22-3
24.2
IO2.92
"•54
22.1
23-7
110.92
11.38
22.O
23.1
8x8xJ
79.00 10419
11.50
21.3
23-9
87.00 1 1 102
11.30
21.3
23-3
95-oo
11.14
21.2
22.8
103.00
II.OO
21.2
22.2
" t
86.44 11890 11.74
21.4
24.6
94-44
12573
"•55
21.4
24.0
102.00
11.40
21-3
23-3
110.44
11.25
21-3
22.9
" i
93.76 13305
11.92
21.6
25-3
101.76
13988
11.71
21-5
24.7
109.76
"•55
21.4
24.1
117.76
11.42
21-3
23-5
" 1
100.92 14683
12.06
21.6
25.8
108.92
15366
11.89
21-5
25.2
116.92
11.72
21.4
24.6
124.92
11.57
21-3
24.0
' i
108.00 16011
I.l. IS
21.6
26.2
116.00
16694
12.00
2I.5I25.6
124.00
11.85
21.4
25.1
132.00
11.70
21-3
-4-5
34"xi" Web Plates.
34"x£" Web Plates.
34"xi" Web Plates.
34"xiJ" Web Plates.
4x4x1
62.44! 7899 "-25 22.622.2
70.94
8718
11.08
22.5
21.8
79-44
10.95
22-4 21.4
87.94
10.85
22.3
2I.O
" i
66.00 8809 11.55 23-° 22-9
74.50
9628
"•37
22.9
22.5
83.00
II. 21
22.8 22.0
91.50
II.IO
22.7
21.6
i
69.44
9673
II.80
234 23-7
77.94 10492
11.60
23-3
23.2
86.44
"45
23.1
22.6
94-94
11.30
23.0
22.1
6x6xi
74.00 10568] 1 1. 95
23-2 24.3
82.50 11387
11.75
23.0
23.8
91.00
11.58
22-9
23-3
99-50
"45
22.7
22.8
" f
79.44 11860
12.23
23.424.9
87.94 12679
I2.O2
23.2
24-3
96.44
11.84
23.1
23.8
104.94
11.70
22.9
23-3
« 3
•4
84.76 13105
12.45
23-7
25.6
93.26 13924
12.23
23-5
25.0
101.76
12.03
234
24-5
110.26
11.89
23.2
23-9
" J
89.92
H307
12.63
23-9
26.2
98.42 15126
12.37
23-7
25.7
106.92
1 2. 2O
23.6
25.2
"542
12.05
234
24.4
8x8xJ
82.00
12138
12. l6
22.8
25-2
90.50 12957
11-97
22.7
24.6
99.00
II.8O 22.6
24.1
107.50
11.65 22.5
23-5
" 1
89.44
13823
12.44
22-9
25-9
97.94' 14642
12.24
22.9
254
106.44
1 2.O6
22.8
24.8
114.94
11.90 22.7
24.2
** i
96.76
15447
12.65
23-1
26.7
105.26 16266
12-44
23.0
26.1
113.76
12.25
22.9
25-5
122.26
12. IO 22.8
24-9
" I
103.92
17027
12.81
23.1
27.2
112.42 17846
12.60
23.O
26.6
120.92
12-44
23.O
26.0
129.42
12.2822.9
254
' i
I I 1. 00
I8S54
12.97
23.2
27-7
119.50 19373
12-75
23.1
27.1
128.00
12-55
23-1
26.5
136.50
I2.4O 23.O 25.9
36"xJ" Web Plates.
36"xj" Web Plates.
36"xl" Web Plates.
36"xi J" Web Plates.
4*4*1
65.44
9199
11.85
23.923.4
74-44
10171
11.70
23-9
23.0
83-44
"•55
23-9
22.7
92.44
"45
23-5
22.3
i
69.00
10225
12.18
24.3 24.1
78.00
III97
11.97
24.2
23.7
87.00
11.8424.2
23-3
96.00
11.70
23-8
22.8
" 1
72.44
II2OI
12.45
24.7 24.9
81.44
12173
12.7-3
24.5
24.4
90.44
12.06 24.4
23.8
99-44
11.91
24.2
23-3
6x6xi
77-oo
12227
1 2.60
24.6 25.5
86.00
I3I99
12.40
24.4
25.0
95.00
12.22
24-3
24.4
104.00
12.06
24.1
23-9
" f
82.44
13690
12.85
24.8 26.2
91.44
14662
12.66
24.8
25.8
100.44
12.48 24.7
25-3
109.44
12.30
24-7
24.9
, 3
87.76
I5I02
13-12
25.1 26.8
96.76
16074
12.90
25.1
26.5
105.76
12.7024.8
25-7
114.76
12-54
25-2
25-9
i
92.92
16466
13-32
25-3 27-5
101.92
17438
13.08
25.5
26.9
110.92
12.90 25.O
26.3
119.92
12.71
25.8
26.9
8x8x|
85.00
14022 12.85
24.3 26.5
94.00
14994
12.64
24.2
25-9
103.00
12.45 24.0
25-3
II2.OO
12.30
23-9
24-7
•
92.44 15935 13.14
24-5 27.3
101.44
16907
12.92
24.4
26.6
110.44
12.7424.2
26.1
119.44
12-57
24.1
25.4
'
99.76 17782 13.36
24.7 28.1
108.76
18754
I3-I4
24.6
27.4
117.76
12.95 244
26.8
126.76
12.78
24.3
26.1
i
106.92 19580 13.55
24.7 28.6
115.92
20552
I3-32
24.6
28.0
124.92
13.09 24.5
27.3
133.92
12.96
24.4
26.7
' i
114.00 21318113.69
24.8 29.1
123.00
22290
1345
24.7
28.5
132.00 13.25 24.6 27.8
I4I.OO
13-12
24.5
27.2
131
TABLE 72.
PROPERTIES OF FOUR ANGLES AND FOUR PLATES.
3
e
1
P"T
Properties of A
A ! Edges of Angles Flush with
Four Angles and
- 1 \ — d Edges of Cover Plates.
Four Plates.
. d = Depth of Web Plates Plus J".
^
J L...1
1
3
Series i, 2 and 3.
Series i.
Series 2.
Series 3,
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B
1
1
"o .
*° a
"8 .
"o a
E
o
0 C
o d
4
"o
*0 «
*o .
"3 c
Size of
Angles.
Cover P
|
a-s
I"
Is
« >>
5-5
v C
3
Is
3
o
H
Momen
Inerti
11
rt >>
fXO
S -a
3 tj
-3 ^
j >>
Is
o
H
C '2
& a
O k-H
C'3
V tl
ij
IS
a >.
A
IA
rA
IB
rB
A
IA
rA
IB
rB
A
IA
rA
IB
rB
In
In.
In.2
In 4
•In
In 4
In.
In 2
In 4
In.
In 4
In
In 2
In*
In.
In 4
In.
12" X f" Web Plates.
12" X 4" Web Plates.
12" X f" Web Plates.
3x3xi
I4xf
25.26
717
5-32
442
4.19
28.26
753
5.16
481
4.13
31.26
789
5.O2
516
4.06
16
2
28.76
874
5-51
499
4.17
31.76
910
5-35
538
4.12
34.76
946
5-22
57.3
4.06
" f
32.26
1037
5-67
557
4.15
35.26
1073
5-52
595
4.II
38.26
IIO9
5-39
630
4.06
3X3xf
Hxf
27.94
793
5-33
5"
4.28
30-94
829
5.18
550
4-22
33-94
865
5-05
585
4-15
2
31.44
950
5.50
568
4.26
34-44
986
5-35
607
4-19
37-44
IO22
5-23
642
4.14
I
34-94
1113
5-65
626
4-23
37-94
1149
5-53
664
4.18
40-94
1185
5-38
699
4-13
3 2^3 2^5
i6xf
30.92
890
5.36
737
4.88
33.92
926
5.22
786
4.81
36.92
962
5.10
833
4-75
11 4
34-92
1069
5-53
822
4-85
37.92
1105
5-40
871
4-79
40.92
II4I
5-28
918
4-73
8
38.92
1254
5.68
907
4-83
41.92
1290
5-55
956
4-78
44.92
1326
543
1003
4.72
3 2^3 ^^^
i6xf
34-oo
971
5-34
840
4-97
37.00
1007
5-22
890
4.91
40.00
1043
5.11
936
4.84
**
" 4
38.00
1150
5-52
926
4.94
41.00
1186
5-38
975
4.88
44.00
1222
5-27
1022
4.82
42.00
1335
5-64
IOII
4.92
45.00
1371
5-52
1060
4.86
48.00
1407
541
IIO7
4.81
14" X f " Web Plates.
14" X 4" Web Plates.
14" X f" Web Plates.
34x34x|
i8xf
33-92
1317
6.24
1093
5.68
37.42
1374
6.06
1183
5.62
40.92
H3I 15-91
1268
5-57
2
38.42
1583
6.42
1215
5-63
41.92
1640
6.26
1304
5-58
4542
1697 6.12
1390
5-54
8
42.92
1857
6.58
1336
5-58
46.42
1914
6.42
1426
5-54
49.92
1971
6.38
I5II
5-Si
34x34*4
i8xf
37.00
1432
6.22
1235
578
40.50
1489
6.07
1325
5-72
44.00
1546
5-93
1410
5-66
" 4
41.50
1698
6.40
1357
5-72
45-0°
1755
6.3O
1446
5-67
48.50
1812 6.12
1532
5.62
8
46.00
1972
6-55
1478
5.67
49-50
2029
6.41
1568
5-63
53-00
2086 6.28
1653
5-60
4x4x1
i8xf
3544
1363
6. 20
1057
547
38.94
1415
6.O3
1130
5-39
42.44
1473 5.89
1198
5-33
u
" 4
39-94
1629
6-39
1178
5-44
4344
1686
6.23
1251
5-37
46.94
1743 6.10
I32O
5-30
8
44-44
1903
6-55
1300
5.41
47-94
1960
6.42
1373
5-35
51.44
2017 6.26
1441
5-29
4x4x5
i8xf
39-00
1494
6.19
1203
5.56
42.50
1551
6.04
1276
548
46.00
1608 5.91
1345
541
"
5
43-50
1760
6.36
1325
5-52
47.00
1817
6.22
1397
545
50.50
1874 6.09
1466
5-39
"
8
48.00
2034
6.51
1446
549
51-50
2091
6.38
1519
543
55.00
2148 6.25
1588
5-38
16" X f" Web Plates.
16" X 4" Web Plates.
16" X f " Web Plates.
32X32X1
20x4
41.92
2234
7.30
1716
6.40
45-92
2319
7.II
1863
6.37
49.92
2405
6-94
2OO4
6-34
" 5
8
46.92
2622
748
1883
6.34
50.92
2707
7.29
2030
6.32
54-92
2793
7-13
2171
6.29
" f
51.92
3022
7-63
2049
6.28
55-92
3107
7.46
2196
6.27
59-92
3193
7-30
2337
6.25
34x34*4
20x4
45-oo
2389
7.29
1903
6.50
49.00
2474
7.II
2050
647
53-00
2560
6-95
2191
643
"
8
50.00
2777
745
2069
6.43
54.00
2862
7.28
2217
6.41
58.00
2948
7.14
2357
6.38
4
55-°°
3177
7.56
2236
6.45
59-00
3262
7-44
2383
6-35
63.00
334«
7-30
2524
6-33
4x4x1
20x4
43-44
2298
7.28
1674
6.21
4744
2383
7.09
1797
6.16
51-44
2469
6-93
1915
6.10
"
8
48.44
2686
744
1840
6.16
5244
2771 7.27
1964
6.12
56-44
2857
7.12
2082
6.07
" i
5344
3086
7.60
2007
6.13
57-44
3i7i 743
2130
6.09
61.44
3257
7.28
2249
6.05
4x4x4
20x4
47.00
2474
7.26
1869
6.31
51.00
2559 7-09
1992
6.25
55-oo
2645
6-94
2IIO
6.2O
" *
52.00
2862
7.42
2035
6.26
56.00
2947 ,7-26
2158
6.21
60.00
3033
7.11
2277
6.16
57-oo
3262
7-55
22O2
6.22
61.00
3347 741
2325
6.19
65.00
3433
7.27
2444
6.13
132
TABLE 72.— Continued.
PROPERTIES OF FOUR ANGLES AND FOUR PLATES.
Properties of •
Four Angles and
Four Plate*. .
J
I
3
r . Edges of Angles Flush with
4— — d Edges of Cover Plates.
1 d - Depth of Web Plates Plus J".
JW—.t,
Series i. jand 3.
Series i.
Series a.
Series 3.
Size of
Angles.
I
2
1
1
H
Axis A-A.
Axis B-B.
1
o
H
Axis A-A.
Axis B-B.
1
|
rS
Axis A-A.
Axis li-l:.
^ .
H
ij
i
IJ
II
gO
i!
- c
ij
«*.
•Sri
N
**i
go
•s
||
c C
ij
si
'oa
o
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11
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ii
ij
m
1*
I!
go
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H
ij
M
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M O
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a >>
go
}i
II
91
Is
3 '—
'•5 t
a x
go
A
U
r\
IB
rB
A
IA
«A
IB
ru
A
IA
"A
IB
rB
In.
In
In.*
In.<
In.
In.«
In.
In.2
In.<
In.
In.<
In.
In.«
In.<
In.
In.«
In.
18" X i" Web Plates.
1 8" X i" Web Plates.
18" X i" Web Plate*.
3i*3i*i
((
3i*3i*J
«
4*4*1
«
4*4*1
«
22X
« .
22\
" :
«
22xJ
" 1
« j
22XJ
" i-
« ;
49.92
5542
60.92
53-00
S8-50
64.00
Si-44
56.94
62.44
55-00
60.50
66.00
3158
3686
4229
3360
3888
4431
3243
3771
43H
3472
400O
4543
7-97
8.15
8-34
7.96
8.16
8.32
7-94
8.14
8.32
7-95
8.13
8.30
2564
2786
3008
28O2
3023
3245
2484
2705
2927
2734
2956
3178
7-17
7.10
7-03
7.27
7.20
7-13
6.95
6.89
6.85
7-06
7.00
6-94
54.42
59-92
65-42
57-50
63.00
68.50
55-94
^•44
66.94
59-50
65.00
70.50
3279
3807
4351
3481
4009
4553
3364
3892
4436
3593
4121
4665
7.76
7.98
8.16
7-79
7.98
8.15
7.76
7.96
8.14
7-77
7-96
8.14
2780
3002
3224
3018
3239
346l
2669
2891
3"3
2919
3HI
3363
7-l6
7.II
7.02
7.25
7.17
7.II
6.91
6.86
6.8 1
7.01
6-95
6.91
58.92
64.42
69.92
62.00
67.50
73-00
60.44
65-94
71.44
64.00
69.50
75-oo
3401
3929
4472
3603
4131
4674
3486
4014
4557
3715
4243
4786
7.60
7.8l
8.00
7.63
7.82
8.00
7-59
7.80
8.00
7.62
7.80
8.00
2989 7.13
3211 7.06
3432 7-oi
32267.22
34487-I5
3670 7.09
2849 6.87
307^6.82
3293 '6-79
30996.96
3321 6.92
3543 6.88
20" X i" Web Plates.
20" X |" Web Plates.
20" X I" Web Plates.
jkjW
«
jfcaixl
H
•«
4x4xJ
M
4X4*1
H
24*
«
« ;
24 \!
« j
24*i
« 5
« j
24X<
" j.
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57-oo
63.00
69.00
59.92
65.92
71.92
59.00
65.00
71.00
62.44
68.44
74-44
4426
5127
5844
4664
5365
6082
4571
5271
5988
4841
5542
6259
8.83
9.02
9.22
8.82
9.02
9.22
8.80
9.01
9.18
8.80
9.00
9.17
3717
4005
4293
3999
4287
4575
3640
3928
4216
3952
4240
4528
8.08
7.98
7.88
8.18
8.06
7.98
7.86
7-77
7-71
7-96
7.87
7.80
62.00
68.00
74.00
64.92
70.92
76.92
64.00
70.00
76.00
67.44
73-44
79-44
4593
5293
6011
4831
5531
6249
4737
5437
6155
5008
5708
("1426
8.61
8.83
9.01
8.62
8.84
9.02
8.60
8.82
9.01
8.62
8.82
9.00
4031
4319
4607
43U
4601
4889
3916
4204
4492
4228
4516
4804
8.07
7.98
7.89
8.15
8.06
7*-97
7.84
7-78
7-70
7.92
7-84
7.78
67.00
73-oo
79.00
69.92
75-92
81.92
69.00
75.00
81.00
72.44
7*44
84-44
4759
546o
6178
4997
5698
6416
4903
5604
6322
5174
5875
<'5W
8-45
8.65
8.85
8.46
8.67
8.86
8.44
8.65
8.84
8-45
8.66
8.85
4337
4625
4913
4619
4907
5195
4184
4472
4760
4496
4784
5072
8.04
7.96
7-89
8.12
8.04
7.96
7-79
7-73
7.67
7.88
7.80
7-76
22" X i" Web Plates.
22" X i" Web Plates.
22" X f" Web Plates.
3i*3i*i
M
3i*3i*t
u
«
4x41*
«
4*4*!
M
28x|
« ;
28x;
" j
28x
«
28x
« :
« ;
70.00
77.00
84.00
72.92
79.92
86.92
72.00
79.00
86.00
75-44
82.44
89.44
6933
7930
8949
7226
8223
9242
7112
8109
9128
7448
8445
9464
9.96
10.15
10.32
9-96
10.15
10.31
9-95
10.13
10.30
9-94
10.12
10.28
6351
6808
7265
6758
7216
7673
6276
6733
7191
6731
7188
7646
9-53
9.40
9-31
9.63
9.51
9.40
9-34
9.24
9-15
9-45
9-34
9.26
75-50
82.50
89-50
78.42
8542
92.42
77.50
84-50
91.50
80.94
87.94
94-94
7155
8152
9171
7448
8445
9464
7334
8331
9350
7670
8667
9686
9-74
9-94
10.13
9-75
9-95
10.13
9-74
9.94
IO.II
9-74
9-94
IO.II
6894
7351
7809
7302
7759
8217
6764
7222
7679
7219
7677
8i34
9-56
9-44
9-35
9.65
9-54
9-43
9-35
9-25
9.16
9-45
9-35
9.26
81.00
88.00
95.00
83.92
90.92
97.92
83.00
90.00
97-00
86.44
93-44
100.44
7377
8373
9393
7670
8666
9686
7556
8552
9572
7893
ssss
9908
9-55
9.76
9-95
9-56
9.76
9-95
9-55
9-75
10.04
9-56
9-76
9.96
7422 9-58
7879 9.47
83379-37
78309.66
8287 9.56
8745 9-45
7242 9.35
7699 9.25
81579.17
7697 9.45
8I549-35
8612 9.26
133
TABLE 73.
PROPERTIES OF FOUR ANGLES LACED AND EIGHT ANGLES BATTENED.
4;
Four Angles.
\A
k— o ->«
Eight Angles.
A
+&
A
Battened (Gray Column).
-y— f T i
r< d — *•;
M
Laced (Box Column).
Size
of Angles.
Area
of Four
Angles.
Axis A-A.
Size
of Angles.
Area
of Eight
lAngles.
Axis A-A.
i!
11
•3
ll
a >.
KO
C-OJ
^"o
li
rt >,
w_rt
!jj
g^
ll
rt >,
II
II
"8
!§
11
(3 >,
MO
!'£
|«
••32
5 >>
KO
c-2
11
.§1
=52
IA
rA
IA
'A
IA
rA
IA
rA
IA
rA
IA
rA
In.
In."
In.
In.«
In.
In.<
In.
In.
In.*
In.*
In.
In.«
In.
In.«
In.
Value of d in Inches.
Value of d in Inches.
8}
10}
12}
ui
145
i6j
" I
5-76
8.44
II.OO
72
IO2
130
3-53
3-48
3-44
117
i67
214
4-50
4-45
4.41
174
249
320
5-49
5-44
5-39
3x3x1
" 1
" 1
2
11.52
16.88
22.OO
183
263
338
3-97
3-95
3-92
251
362
466
4.67
4.60
330
478
616
5-35
5-32
5-29
i of
12}
14!
ia|
Mi
i6j
2
" f
9.92
13.00
15.92
190
243
291
4-38
4-32
4.28
284
365
440
5-35
5-30
5.26
398
513
620
6-33
6.28
6.24
32X3^X5
« 1
2
" f
19.84
26.OO
31.84
306
394
476
3-93
3-89
3-87
419
542
656
4-59
4-57
4-54
553
716
868
5-28
5-25
5-22
12}
14!
16}
Hi
i6|
i8|
Tl
11.44
15.00
18.44
3l6
408
491
5.26
5-22
444
575
695
6.23
6.19
6.14
596
772
935
7.22
7.17
7.12
4*4*1
" f
22.88
30.00
36.88
477
618
750
4-54
628
815
990
5-24
5-21
802
1042
1267
5-92
5.89
5-86
16}
i8f
20}
I8|
20^
22}
6x6xf
" 1
" f
" f
17.44
23.00
28.44
33-76
824
1072
1306
1526
6.87
6.82
6-77
6.72
1072
1398
1705
1996
7.84
7-79
7-74
7.68
1354
1769
2161
2535
8.81
8.76
8.72
8.66
6x6xf
« i
" i
« 3
34.88
46.00
56.88
67.52
1180
1542
1887
2216
5-82
5-79
5-76
5-73
H63
1914
2343
2755
6.48
6-45
6.42
6-39
1781
2331
2856
3360
7.14
7.12
7.08
7-°5
The table given above is intended to serve
only as a guide in the choice of sections and not
as a complete table. The properties of other
sections may be found as follows:
Example: Required the properties of a
square box column consisting of 4 A 4"x4"x3",
laced, I3j in. back to back.
Solution: Table 32 evidently applies to
angles with legs turned in, as well as angles
with legs turned out.
Area, from Table 32 = 15.00 in.2
/A = /x, from Table 32 = 467 in.4
The
only as a
as a com
sections n
Exau
column c
15! in. ba
Solul
moment <
+ 43 = ^
= 30.00 s
Thei
r =-\
table given above is intended to serve
guide in the choice of sections and not
plete table. The properties of other
lay be found as follows:
iple: Required the properties of a
onsisting of 8 A 4"x4"x5", battened,
ck to back.
ion: From Tables 32 and 35 the
jf inertia about axis A-A equals 645
88 in.4 and the area equals 2 X 15.00
q. in.
•adius of gyration equals
rA =
A/7A -j- A = -^467 -j- 15.00 = 5.58 in.
// -T- A = A/688 -f- 30.00 = 4.79 in.
134
TABLE 74.
PROPERTIES OF EIGHT ANGLES AND THREE PLATES.
!B
fr^-iif^r T d - Width of Web Plate
Properties u uy u
Plus One-half Inch.
Eight Angles A_ - ---^ d)
b - Width of Flange Plate*
Plus One-half Inch.
and
Three Plates.
«• H-Q — •*
1 fl I
Large Sections may be
_J— Laced on Open Sides.
IB
Size of
Inside Angles.
Axis A-A.
Axis B-B.
Web
Plate.
Flange
Plates.
Size of
Outside Angles.
Total
Area
Moment of
Inertia.
Radius of
Gyration.
Moment of
Inertia.
Radius of
Gyration.
A
IA
rA
IB
rB
In.
In.
In.
In.
In.t
In.*
In.
In.«
In.
I8x
i8x
3l*3i-
tl
3ix3$xf
46.84
3238
8.31
1198
•5-06
"
1
\
' i
59-75
4135
8-32
1534
5.07
" 1
\
72.34
5016
832
1856
5-06
2OX;
20X;
4x4x1
4X4XJ
60.00
5051
9.17
1976
5-74
"
74-38
6261
9.17
2431
5-7i
.
<
88.52
7459
9.18
2875
5-70
22X;
22X
4X4XJ
•
4x4x1
71-
24
7319
IO.I3
2708
6.16
a
86.37
8885
10.14
3285
6.16
I
i
i
101.26
10434
IO.I5
3845
6.16
24xi
24x1
4x4x1
4X4x$
75.00
9175
II.O5
3356
6.69
j
" I
90.88
11139
11.06
4070
6.69
" I
!
|
'
" i
106.52
13083
11.08
4767
6.68
26xJ
26xi
6x6x;
6x6xf
126.02
17447
11.77
7021
7.46
" i
1
'
" i
146.09
20234
11.77
8102
7-44
" i
" I
" i
166.00
23001
11.77
9168
7-43
28xJ
28xj
6x6x;
-
6x6xf
130.52
21081
12.71
8376
8.01
" I
" 1
" j
!
" i
151-34
24456
12.71
9672
7-99
" i
" I
" i
172.00
27809
12.71
10943
7.98
3<xcf
3oxl
6x6xJ
6x6xJ
146.27
27369
13.67
10456
8-45
" i
" i
" ;
\
" i
167.84
3H33
13.68
11988
8-45
i
" I
" i
189.25
35477
13.69
13496
8-45
• The above table is intended to serve only as a guide in the choice of sections and not as a com-
plete table. The properties of other sections may be found as follows:
Example: Required the properties of a section
composed
of a 20" X f " web plate, two 24"
X i" flange plates, four 4" X 4" X i" inside angles and, four 6"
by 4" legs, /= 2oi", b = 24J7'.
X 4" X f " outside angles fastened
Solution:
Moment of Inertia
Radius of Gyration.
Item.
Axis A-A.
Axis B-B. Axis A-A.
Axis B-B.
Table A
No
Table IA
No
Table
No
IE
rA
rB
-vu+x
-V/IB+A
In.
In
4
In.« In.
In
I-Wb. PI.
2OX§
I 12 50
3 4*7
4.
O
2-F1. Pis.
4-! ns. A
4-Outs. A
24xf
4x4x1
I 36.00
32 15.00
34 27.76
5 3972
32 1222
34 1895
3
35
33
17:
5
342
8 /75o6
. '5205
\9i.26
6 \9i.26
,l
Total . .
A = 91.26
IA = 7506
IB =
5205 rA = 9.07
fB - 7-55
135
TABLE 75
ELEMENTS OF Z-BAR COLUMNS
AMERICAN BRIDGE COMPANY STANDARDS
Dimensions in Inches 2 EJdl 2 RIVETS f" DIAM.
Size of 1
Column 1
'oS
N^
Size of Z-Bars
is
1
O
"ao
§
H
STANDARD DIMENSIONS
Axis i-i
Axis 2-2
' 4-1
II
v M
8
<
il
Size of Flanges
"o
w rt
il
if
,3$
"o
jj rt
§1
11
a
il
w
I
In.
6
In.
Ins.
In.
In.
In.
Lbs.
Sq. In.
a
m
N
**
H
01
i
0)
C/J
A
2f X3 X2f
2HX3^fX2|i
6"T7l
it
5A
S|
i
i
t^
84-7
IO5.I
I25.I
134.6
I53-I
3-o
3-o
2.9
2.9
2.9
31-7
41.8
53-4
55-2
67.1
1.8
I .Q
I .Q
1.8
1-9
31-5
39-6
47.6
53-5
61.2
9.26
11.64
14.01
I5.63
18.00
2J-6-X38 X2|i
ST
6|6
If'
• r - — ^3
1
t "
S3sl
•O" t
2
ipq£
^r^ Vi^
U*1 l**|
k— — 8Ji-"-~ *j
8
i
M
N
H
1
A
t
9
2| X4 X2f
316X4l X316
3J6X4|6X3l
3tVX4 X3tV
3s X4T&X38
3rVX4t X3rV
8L
85
Jfi
i 3
7l
7A
6fs
6f6
is" ^
134-7
166.9
1994
22O.6
250.8
280.4
296.3
351-5
3-4
3-4
3-4
3-4
34
3-3
3-3
3-3
3-3
65.7
85.8
107.8
115.6
138.6
163.0
167.3
192.8
220.5
2.4
2.4
2-5
2-4
2.5
2.5
2.5
2-5
2.6
37-5
47-0
56.5
64-3
73-9
83.6
90.1
99.9
109.7
11.03
I3.83
16.71
18.90
21-74
24.58
26.58
29-37
32.25
1
(* — 3X--—r
1
8f3
8t!
9
2
u
-f^l
i^J .4.
m"
•j
16
5
8
ft
3
v f
"^
1 !•
J
10
if
M
N
**
H
1
3
8
I
f
11
16
3
4
3AX5 X3p
3Axs|6X3A
3i X5 i X3i
3§6X5i X3f6
3l X5 X3i
3AX5TVX3&
!oT
Itt
XL
a6
itt
2
9TV
9s
9A
8|3
8C
K__-7X-"— >J
193-8
23I.O
267.6
287.6
32I.I
354-3
364-8
395-5
3-5
3-5
3-4
3-4
3-4
3-3
3-3
3-3
3-9
3-9
3-9
3-8
3-8
3-8
3-7
3-7
3-7
147.4
183.4
222.0
234-4
273-7
3I5-6
32O.O
363.0
3-o
3-2
53-1
64.0
75-0
83.0
93-7
104.7
III.O
121.7
K.63
1883
22.06
24.42
27.58
30.78
32.65
35-8i
f*
^fi
*-
<
^ ^
*!
? P
V
2
. i
-JO*-'
H
ii
12
03
cq
N
^8
H
V
1
f
3i X6 X3i
3^X6^X3^
1^
"f!
If
rp
Jfl
2
il
Ii|i
!o}i
I0j
337-0
391-4
444-6
469.1
518.0
566.5
579-7
622.5
666.6
287.8
346.9
409.2
426.3
489.2
555-8
562.4
628.2
699.1
3-6
3-7
3-7
3-6
3-7
•1.8
3-7
3-7
3-8
72.6
85.2
97-7
1 06. i
118.4
130.9
137-9
149.6
162.0
21.36
25.06
28.76
31.22
38.50
40.56
44.02
47.64
|* 8J^'—
H
/"•v j
9
T6
f
H
13.
16
7
3l X61 X3J
»i X6 X"?~
3^X6^X3^
3f X6J X3l
/> 1 \s £. \x/»l
^
Sf^^
\2/ f
1
IL
32 Xo X32
3^X6^X3^
3f X6| X3f
I24
,j
-
H-,,,-
V
3
136
TABLE 77.
PROPERTIES OF CHORD SECTIONS.
McCuNTIC-MARSHAL CONSTRUCTION Co. STANDARDS.
Properties of
Two Angles and
One Web Plate.
A-
Long Legs Turned Out.
Top of Plate J" Below
Back* of Angles.
s3
K
"o
•1
Size of Angles.
H
AxisA-A.
Axis MR
Size of Web Plate.
Size of Angles.
Total Area.
AxisA-A.
Axis B-B.
Moment
of Inertia.
Radius of
Gyration.
Section.
Modulus.
Centroid.
Moment
of Inertia.
"S B
Moment
of Inertia.
Radius of
Gyration.
Section
Modulus.
Centroid.
i!
1 Radius of
Gyration.
A
IA
rA
SA
e
I,,
r,
A
IA
TA
SA
e
IB
TB
In.
In.
In.*
ln.«
In.
In.»
In.
In.«
In.
In.
In.
In.*
In.«
In.
In.*
In.
In.'
In.
6X1
2 X2 XI
3-38
II. I
I.8l
6-3
1.77
1-7
.70
ioxi
2*X2jXl
4.88
47.2
3-10
15-5
3-04
3-'
.80
2iX2 XI
3.62
II.7
1. 80
1.66
•93
2|X2JXA
544
50.1
3-°3
17-8
2.82
3-9
•85
3 X2 XI
4.88
49-3
3.19
16.8
2-93
5.1
1.03
7X1 2 X2 X'
3.63
17.1
2.17
9.1
1.87
1.7
.68
3 X2^Xl
5-12
49-3
3-09
17.0
2.90
5-2
1. 00
2iX2 XJ
3-87
I7.8
2.14
8.9
1.99
3.1
.90
3 X2^XA
5-74
52.2
3-02
19.6
2.67
6-5
1. 06
3 X2 X
4-13
I8.7
2.13
IO.O
1.87
5.1
1. 12
3^X25X1
5-38
5i-3
3.09 18.5
2.77
8.0
1.22
3 X2jX
4-37
18.7
2.07
9-9
1.90
5-2
1.09
3§X2^X -fa
6.06
54-o
2.99
21.2
2-55
IO.I
1.29
4 X3 XA
6.68
55-7
2.89
22.8
2.44
14.8
1.49
8X1
2 X2 XI
3-88
24.4
2.51
9.8
2.48
1.7
.66
2JX2 XI
4.12
25.6
2.49
10.9
2-34
3.1
.87
ioXA
2f X2^Xf5
6.07
•58.6
3-io
I9.I
3-0?
4.1
.82
2jX2§X;
4.38
25.6
2.42
II.O
2-33
3.1
.84
3 X2$Xl
5-75
57-6
3.16
18.2
3-i6
5-3
.96
2*X2iXl
s.
4-94
27.1
2-34
I2-5
2.16
3-9
.89
3 X25XA
6-37
61.2
3.10
2I.O
2.91
6-7
I. O2
3 X2 XI
4.38
26.8
2.47
I2.I
2.21
1.09
3$X2jXl
6.01
60.0
3.16
19.8
3-03
8.2
I.I7
3 X2|Xi
4.62
26.8
2.41
I2.I
2.22
5-2
i. 06
3|X2jXA
6.69
634
3.08
22.7
2.80
10.3
1.25
3 X2iX
1
5.24
28,7
2.30
13-6
2.04
6.5
i. ii
4 X3 X&
7.31
65-5
2.99
24-3
2.69
IS i
1.44
4.88
27.9
2.39
13.3
2.IO
8.0
1.28
4 X3 X|
8.09
68.3
2.91
27.2
2.51
18.2
1.50
3iX2jx!
'.
5-56
29.2
2.29
I5-I
1.94
IO.I
i-35
5 X3 XA
7-93
69.2
2.96
27.8
2.49
28.7
I-9I
•
5 X3 XI
8.85
72.1
2.85
3I.I
2.32
344
1.97
8X&
2iX2|Xi
V
544
31-7
2.41
13-5
2-35
4.1
.87
5 X3^XA
8.25
69.3 2.89
27.6
2.51
2S>
1.87
3 X2iXJ
,
5.12
31-3
2.47
12.9
2.42
5-3
i. 02
5 X3^X|
9.23
724
2.81
30.8
MS
J4-6
1.94
3 X2JX&
5-74
33-2 2.40
14.8
2.24
6-7
i. 08
5-38
32.6 2.46
14.2
2.3O
8.2
1.24
loXf
3 X2JXA
6.99
69-5
3-15
22.2
3.13
6-9
•99
3*X2*X-
56
6.06
34-3
2.38
16.1
2.13
10.4
1-31
3iX2jXA
7.31
72.1
3-14
23-9
3.01
10.6
1. 21
4 X3 XA
7-93
74-5
3.07
25-9
2.88
15-5
I.4O
8X|
3iX2jXT
5*
6.56
39-i
2-44
17.1
2.29
10.6
1.28
4 X3 XI
8.71
77.8
2.99
28.7
2.71
18.6
I.46
4 X3 X&
7.18
40.6
2.38
18.1
2.22
15.2
1.47
5 X3 X&
8-55
78.9
3.03
29-3
2.69
29-7
1.85
4 X3 X|
7.96
42-5
2.31
20.3
2.09
l8.<>
5 X3 XI
947
82.4
2.94
32.8
2-51
35-i
1-93
9X1
2jX2jXi
463
354
2.76
13.2
2.68
3-i
.82
12X1
3 X2JX1
5.62
81.2
3.80
22.2
3-65
5-2
.96
3 X2 X;
4-63
37-3
2.84
13-5
2.77
5.1
1.05
3 X2^XA
6.24
86.2
3-73
25.6
3-37
6-5
i. 02
3 X2JX;
4.87
37-0
2-75
14.5
2-55
5-2
1.03
3iX2jXl
5.88
84-3
3.7824.2
349
S.o 1.17
3iX2jX;
5-13
384
2-73
15-8
2-43
8.0
i. 25
3iX2^X A
6.56
89.1
3. 67(27.8
3.20
10.1 1.24
4 X3 X&
7.18
92.0
3.5830.2
3-os
14.8 1.44
9X&
3 X2JXT
s*
t
6.05
6-37
45-8
47-5
2-75
17-5
19.0
2.62
2.50
6.7
10.3
1.05
1.28
S X3 XA
5 X3 XI
7.80 96.8 3.52 34.3 2.82 28.1 1.90
8.72 100.8 3.41 38.6 2.61 33.8 1.97
3iX2jX|
7-03
49-5
2.65 21. 1
2.3412.4 1-33
5 X 3 i X A
8.12 96.8 3.45 34.0 2.85 28.3 1.87
4 X3 X&
6.99
49.1
2.65 20.2 2.41 15.1 1.48
5 X3*X|
9.10 100.6 3.33 38.1 2.64 33.9 1.94
48
137
TABLE 77 .—Continued.
PROPERTIES OF CHORD SECTIONS.
McCLINTIC-MARSHALL CONSTRUCTION Co. STANDARDS.
f
B
F
3* Long Legs Turned Out.
Properties of "*"" '{.
P
Two Angles and
Top of Plate \" Below
One Web Plate.
Backs of Angles.
feb Plate.
i
tal Area.
Axis A-A.
Axis B-B.
S
£
4
1
3
Axis A-A.
Axis B-B.
•u a
C'5
D C
s y
0 C
S3-2
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12
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v tl
eg
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W'B
4J_g
u £
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In.
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In.
In.
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In *
In.
In.3
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i2XA
3 X2|Xis
6-37
94-8
3~^4
24.0
3-95
5-3
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4 X3 X|
12.50
168.6
3-67
49.1
3-43
26.4
7^46
3 /N 2 2" PN 15
6-99
100.7
3-79
27.5
3.67
6-7
.98
5 X3 Xf
11.72
166.4
3-76
46.8
3-55 36.5
1.77
3— ^^ *? — "V —
2 /\ ^2 /^ 4
6.63
98.5
3-86
25-9
3.81
8.2
I. II
S X3 X|
I3-50
I78.2j3.63
55-9
3. 1948.9! i. 90
j»i V i i N^ 5
J 2 /^ ^ 2 ^^ 1 6
7.31
104.5
3-78
29.6
3-53
10.3
I.I9
S X3lX|
14.00
178.213.56
55-7
3.2049.7
1.88
4 X3 XA
7-93 107.9
3-70
32.O
3-37
15.1
1.38
6 X3|Xf
12.84
174.1
3-69
52.0
3.35 61.6
2.19
4 X3 XI
8.71 112.8
3.60
35-8
3-iS
18.2
1.44
6 X3|X|
15.00
186.3
3-52
62.1
3.00 82.0
2-34
S X3 XA
8.55 II3-8
3-64
36.3
3-13
28.7
.82
6 X4 XI
I5-50
186.3
3-52
61.5
3-03 82.5
2.31
5 X3 Xf
9.47 119.0
3-55
40.9
2.91
34-4
.92
5 X3IXA
8.87 113.9
3-58
36.4
3.13
28.8
.80
I4Xf
4 X3 Xf
IO.2I
196.5
4-39
47.8
4.n'i8.6
i-35
5 X3lXf
9.85 119.0
3-47
40.9
2.92
34-6
.88
5 X3 Xf
10.97
207.4
4-34
54-i
3-83
35-i
i-79
5 X3lXf
11.35 207.5
4.28
54-4
3.81
35-3
1.76
I2Xf
3 X2|XA
7-74
II4-3
3-84
29-3
3-9i
6.9
•95
6 X3lXf
12.09 216.6
4-23
60.5
3-59
59-6
2.22
3lX2|XA
8.06
118.5
3-83
3-77
10.6
•IS
6 X4 Xf
12.47
216.7
4.16
60.5
3-59
59-6
2.19
4 X3 XA
8.68
122.7
3-76
34-o
3-6i
iS-5
•34
4 X3 Xf
9.46
128.4
3-68
38.0
3-38
18.6
.40
I4X|
4 X3 XI
I3-50
258.2
4-37
62.2
4.16
26.4
I.40
5 X3 XA
9-30
129.9
3-74
38.4
3-38
29.2
•77
5 X3 XI
14.50273.3
4-34
70.1
3-89
48.9
1.84
5 X3 Xf
IO.22
135-8
3-64
43-2
3-H
35-i
1-85
5 X3lX|
15.00273.5
4.27
70.8
3-87
49-2
1.81
S X3IXA
9.62
129.5
3-8o
38.4
3-37
29.4
i-75
6 X3lXf
13.84265.7
4-38
65-3
4.07
61.6
2. II
5 X3lXf
10.60
135-8
3.58
43-i
35-3
1.82
6 X3lX|
16.00 285.3
4.22
78-3
3-64
82.0
2.26
6 X3lXf
n-34
141.8
3-54
47-9
2.96
59-6 2.30
6 X4 X|
16.50
285.0
4.16
78.1
3-65
82.5
2.24
6 X4 Xf
11.72
145.0
3-52
48.7
2.98
59-6
2.26
i6Xf
5 X3lXf
I2.IO
299.6
4.98
66.4
4-52
35-3
1.70
i2XA
4 X3 XA
10.99
149.1
3-68
45-i
3-3i
22.3
1.42
6 X3lXf
12.84 312 6
4.94
73-3
4.27
59-7
2.l6
5 X3 Xf
10.97
150.0
3-69
44-8
3-35
35-8
1.81
6 X3lX|
15.00
334-7
472
88.1
3.80
80.0
2.30
5 X3lXf
n-35
I5I-5
3-6S
45-2
3-35
35-9
1.78
5 X3IXA
12.31
i57-i 3-57
49-6
42.0
1.85
i6X|
6 X3lXf
14.84
382.5
5-09
79-5
4.81
61.6
2.O;
6 X3lXf
12.09
158.4 3.62
50.2
3^6
60.6
2.24
6 X3|XA
i5-94|399-o
5-03
87-5
4-55
71.9
2.1'
6 X3IXA
13.19
164.3 3-52
SS-o
2-99
70.6 2.31
6 X3lX|
17.00 412.4
4.92
95-5
4-32
82.0
2.18
6 X4 XA'i3-6i
164.43.48
54-8
3-oo
70.6 2.28
6 X4 XI
17.50412.1
4.85
95-6
4-3i
82.5
2.17
138
TABLE 78.
PROPERTIES OF TOP CHORD SECTIONS.
IB
Properties of
Two Angles
and
One Cover Plate.
Angles Turned Out.
. I
Short Legs Against
Plate, and Turned Out.
Edges of Angles Flush
with Edges of Plate.
'•lift-
IB
S-rics
Series X.
Series 2.
and 2.
•
AxisA-A.
AxisB-B.
_;
AxisA-A.
AxisB-B.
1
K
"o
.§
Size of Angles
1
Moment
of Inertia.
Radius of
Gyration.
Section
' Modulus.
Upper Fiber.
Centroid.
Moment
of Inertia.
Radius of
Gyration.
"3
1
1
Moment
of Inertia.
Radius of
Gyration.
Section
Modulus.
Upper Fiber.
Centroid. |
Moment
of Inertia.
Radius of
Gyration.
in
A
IA
rA
SA
e
IB
rB
A
IA
rA
SA
e
IB
r.
In.
In.
In.*
In.«
In.
In.'
In.
In.«
In.
In.
In.*
In.«
In.
In.'
In.
In.«
In
ioxi
3"Jxi
5-12
3-7
.86
5-8
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48.5
3.08
3x2ixf
6-34
S-l
.90
6.6
•53
62.5
3-14
« xi
5.88
8.2
1.18
9.0
.66
49.0
2.89
1x3 xf
7.46
II. 2
1.23
10.6
.81
63.0
2.91
iox&
3«ixi
5-74
4.0
.84
6-3
•33
53-7
3-05
3X2|xf
6.96
5-6
•90
7-3
.46
67-7
3 12
w xi
6.50
8-7
1.16
IO.O
•57
54-2
2.89
W xf
8.08
11.9
1.22
11.5
•73
68.2
2.90
I2xi
3*2ixi
5.62
3-9
-83
6.4
•36
82.8
3-84
3x2ixf
6.84
5-3
.89
7-4
.48
106.2
3-94
W xi
6.38
8-5
1.16
IO.2
.60
86.1
3-67
W xf
7.96
11.6
I.2I
11.7
•75
110.7
3-73
8.12
18.8
1-52
15-5
.96
98.6
3-48
10.06
24-3
1.56
17.9
i. ii
124.0
3-Si
I2X&
3*2ixi
6-37
4.1
.80
6.9
.28
91.8
3-79
3X2ixf
7-59
5-7
.87
8.0
.41
115.2
3-89
Pt3 xi
7-13
9-1
1.13
II. I
•Si
95.1
3-65
«* I
8.71
12.4
I.I9
12.7
.66
119.7
8.87
19.8
1.49
I7.I
•85
107.6
3-48
10.81
25.6
1.54
19.4
1. 01
133.0
3-Si
I2xf
3x2ixi
7.12
4-4
•79
7-5
.22
100.8
3.76
3x2ixf
8-34
6.1
.86
8.6
•34
124.2
3.86
4x3 xi
7.88
9-5
1. 10
11.9
•43
104.1
3-64
4x3 xf
9.46
13.0
1.18
13-8
•58
128.7
3.69
9.62
20.8
1.47
18.4
•76
116.6
348
11.56
26.9
i-53
20.7
.92
142.0
3-50
I4xi
3x2ixi
6.12
4.0
.81
7-o
•32
128.4
4-58
3X2ixf
7-34
5-5
•87
8.1
•44
163.5
4-72
4X3X i
6.88
8.8
1.13
II.O
•55
135-9
4-45
4X3 xf
8.46
12.0
1.19
12.7
.70
174-3
4-54
5x3ix^
8.62
19-3
1.50
17.0
.89
I59-I
4-30
5X35X&
10.56
25-0
i-54
19.2
1-05
199.8
4-35
6x4 xf
10.72
3M
1.86
24.4
1.27
179.1
4.09
6x4 xi
13.00
46.2
1.88
27.7
1.42
220.9
4.12
I4x&
3x2ixi
6-99
4.2
•78
7-7
.24
142.7
4-52
3x2ixf
8.21
5-9
•85
8.7
•37
177.7
4.65
4x3 xi
7-75
9-3
i. ii
12.3
•45
150.2
4.40
4X3 xf
9-33
12.8
1.17
13-9
.61
188.6
4-49
5x3ixj^
9-49
20.4
1.47
18.7
.78
173-4
4.27
5x3ix^
"•43
26.4
1.52
20.9
•95
214.1
4-33
6x4 xf
11.59
39-o
1.83
26.7
193-4
4.08
6x4 x|
I3-87
48.6
1.87
30.0
235-1
4.11
14*N
3X2ixi
7-87
4-5
.76
8.2
.18
157.0
4-47
3x2ixf
9.09
6-3
-83
9-4
•3°
192.0
4-59
4x3 xi
8.63
IO.2
1.07
I3-I
•37
164.5
4-37
4x3 xf
IO.2I
13-5
14.8
•53
202.9
4-46
Sx3*x&
10.37
21.4
1.44
20. 2
.69
187.7
4-25
5x3ixrt
12.31
27.6
1.50
22.4
.86
228.4
4.31
6x4 xf
12.47
40.8
1.81
28.7
1.04
207.7
4.08
6x4 xi
14-75
50.8
1.85
32.0
1.22
249-5
4.11
i6xi
4X3 xi
7-38
9.0
1. 10
I2.O
•50
199.5
5.20
4x3 xf
8.96
12.3
1.18
13-8
.65
254-8
5-33
5X3ix}%
9.12
19.8
i-47
18.2
.84
236.8 5.09
5*3 **&
11.06
25.7
1.52
2O.6
1 .00
296.9
5.18
6x4 xf
11.22
38.0
1.84
26.2
1.20
27I-3
4.91
6x4 xi
I3-50
47-4
1.87
27.4
1.36
334-4
4.98
i6x&
4x3 xi
8.38
9-5
1.07
13-2
41
220.9
5-13
4X3 xf
9-96
13.1
1.15
15.1
•56
276.2
5.27
5x3 ix A
10.12
20.9
1-44
2O. I
•73
258.1 5.05
5x3ix^
12.06
27.1
1.50
22.6
.89
318.2
5-«4
6x4 xf
12.22
42.0
1.81
28.8
1.08
292.7
4-90
6x4 xi
14.50
49-9
1.85
32.0
1.25
355-7
4-95
i6xf
5x3ix&
II. 12
21.9
1.40
21.8
•63
279.4
5.02
5x3ix&
13.06
28.5
1.48
24.4
.80
339-6
5.10
6x4 xf
13.22
41.9
1.78
31.0
.98
314.0
4.87
6x4 xi
15.50
52.2
1-83
34-3
I-I5
377-0
4-93
8x6 x^
17.86
106.0
2-44
54-7
1.56
307.84.15
8x6 xA
21.12
129.6
2.48
61.4
1.74
361.3
4.13
139
TABLE 79.
PROPERTIES OF TOP CHORD SECTIONS.
Properties of
Two Angles A
i
• •*• . Short Legs Against
Jf..A Plate, and Turned In.
...ci.iJn
and
One Cover Plate.
Angles Turned In.
Backs of Angles Flush
with Edges of Plate.
IB
Series
Series i.
Series 2.
i and 2.
Axis A-A.
Axis B-B.
Axis A-A.
Axis B-B.
w
§5
.•
S
s
&
•jj
^3
-B.2
"o d
C •§ .S
•d
'e-S
"eg
*M
4(j
*j d
•d
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o d
i
4j
"rt
C 4_»
0) ,_,
e o
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.2-35;
8
8 <S
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13
81
p 8
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v ti
c a;
3 "3
PH
a
o£
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a
o£
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41
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3
rt >.
09
A
IA
TA
SA
e
IB
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A
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In.
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In.'
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8x1
3X25xl
4.62
3-6
0.88
5-1
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41.4
2-99
3X25xf
5-84
4-9
•91
5-8
•59
54-3
3-05
"
4X3 xl
5-38
7-9
I.2I
8.1
•73
494
3-03
4X3 xf
6.96
10.8
1.25
9.6
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66.0
3.08
8xA
3x2|xl
5-12
3-9
0.87
5-6
•39
44-o
2-93
3X2|xf
6-34
5-3
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6.4
•52
S7-o
3.00
"
4X3 xl
5-88
8.4
1. 2O
8-7
•65
52.1
2.98
4X3 xf
7.46
11.4
1.24
10.3
.80
68.6
3-03
iox|
3X2|xl
5-12
3-8
0.86
5-8
.41
71.7
3-74
3X2jxf
6-34
5-2
.90
6.6
•53
93-6
3-84
u
4X3 xl
5.88
8.4
1.19
9.2
.66
85.0
3.80
4x3 xf
7.46
1.23
10.6
.81
113.0
3-89
•"
5x3?xA
7.62
18.1
i-S4
14.1
1.03
114.9
3-88
5x35xA
9.56
23-5
1.57
16.5
1.17
147.9
3-93
"
6x4 xf
9.72
34-9
1.89
2I.O
1.41
149.6
3-92
6x4 x£
I2.OO
43-7
1.91
24-3
i-5S
186.1
3-94
ioxA
3x2bl
5-74
4.1
0.83
6.2
•33
76.9
3-66
3X2§xf
6.96
5-6
.90
7-3
.46
98.8
3-76
"
4x3 xl
6.50
8.8
1.16
IO.O
•57
90.2
3.72
4x3 xf
8.08
I2.O
1.22
11.5
•73
118.2
3.82
"
5x3 ixA
8.24
19.2
i-53
15-5
•93
I2O.I
3-82
5x3§xA
IO.I8
24.7
I.S6
17-8
i. 08
153-2
3-88
II
6x4 xf
10.34
36.7
1.88
22.6
i-3i
3-87
6x4 x|
12.62
45-6
I.9O
25.8
1.46
191-3
3-89
icxf
3x25x1
6-37
4.2
0.81
6.6
.26
82.1
3-59
3X2jXf
7-59
5-9
.88
7-7
•39
104.0
3-70
u
4x3^1
7-13
9-3
1.14
10.6
•49
954
3.66
4x3 xf
8.71
12.6
i. 20
12.2
.66
123.4
3.76
"
5X32XT6
8.87
22.O
1.50
16.5
.84
125.4
3-76
5x3lxA
10.81
25-9
•54
18.8
I.OO
158.4
3-83
T*
6x4 xf
10.97
38.2
1.87
24.0
1. 21
1 60.0
3-82
6x4 x|
13-25
47-5
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27-3
i-37
196.5
3-85
12x1
4X3 xl
6.38
8.6
1.16
10.2
.60
132.3
4-55
4x3 ^f7
7.96
11.7
.21
11.7
•75
175-0
4.69
"
5x3 *xA
8.12
18.8
1.52
IS-5
.96
177.8
4.68
1 0.06
24.3
.56
17.9
i. ii
228.4
4.76
"
6x4 xf
IO.22
36.0
1.88
22.8
i-33
230.6
4.76
6x4 Xz
12.50
45-o
.90
26.0
1.48
287.0
4-79
I2XA
4X3 xl
7-13
9.1
I-I3
II. I
•Si
I4I-3
445
4x3 xf
8.71
12.4
.19
12.7
.66
184.0
4.60
II
(4
5x3lxA
6x4 xf
8.87
10.97
19.8
37-9
1-49
1.86
I7.I
24.8
•85
1.22
186.8
239.6
4-59
4.67
5X3 5X A
6x4 xf
10.81
I3-25
25.6
47-2
•54
.89
19.4
27-9
I.OI
1.38
237.6
296.0
4.69
4-73
I2xf
4X3^1
7-88
9-5
I.IO
II.9
43
150.3
4-37
4X3 xf
9.46
I3-I
.18
13.8
•58
193.0
4-52
"
9.62
20.8
1.47
18.4
.76
195.8
4-51
5X35XA
11.56
26.9
•53
20.7
•92
246.6
4.62
Cl
6x4 xf
11.72
39-6
1.84
26.4
1. 12
248.6
4.61
6x4 x|
14.00
49-2
.87
29.6
1.29
305-0
4.67
14x1
4X3 xl
6.88
8.8
1-13
II.O
•55
192.4
5-29
4x3 xf
8.46
12.0
.19
12.7
.70
252.9
547
"
5x3ixA
8.62
19-3
1.50
I7.O
.89
257.0
5.46
5x3 «xA
10.56
25.O
•54
19.2
1.05
328.9
5-58
u
6x4 xf
10.72
37-i
1.86
24.4
1.27
332-2
5.56
6x4 X5
13.00
46.2
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27-7
1.42
412.9
5-63
HxA
4X3^1
7-75
9-3
i. ii
12-3
45
206.7
5.16
4x3 xf
9-33
12.8
•17
13-9
.61
267.2
5-34
"
9-49
20.4
1.47
I8.7
.78
271.3
5-34
5x3 £xA
"43
26.4
•52
20.9
•95
343-1
548
u
6x4 xf
n-59
39-o
1.83
26.7
346.4
546
6x4 Xl
I3-87
48.6
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30.0
!-3!
427.2
5-54
I4xf
4X3 xl
8.63
9-9
1.07
13.!
•37
22 1. 0
5.06
4x3txf7
IO.2I
13-5
•IS
14.8
•53
281.5
5-25
"
5x3|xA
10.37
21.4
1.44
20. 2
.69
285.5
5-24
12.31
27.6
•50
22.4
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3574
5«39
"
6x4 xf
12.47
40.8
1.81
28.9
1.04
360.6
5-38
6x4 xj
H-75
508
1.85
32.0
1.22
441.4
547
(i
8x6 xA
17.11
103.7
2.46
51-6
1.64
489.7
5-35
8x6 xA
20-37
126.7
2.49
581
1.81
591.2
5-40
140
TABLE 80.
PROPERTIES OF TOP CHORD SECTIONS.
,e
! I
Tror\nMo«f A_.. f__A. Long Legs Turned Out.
On^Web Plate * l^'wVV'V'VV'
JB
Series i and a.
Series i.
Series's.
AxisA-A.
Axis B-B.
AxlsA-A.
Axis B-B.
of Web Plate
J
1
of Top Plate.
Total Area.
of Top Plate.
Total Area.
Moment
of Inertia
Radius of
Gyration.
Section
Modulus,
Ipper Fiber.
Centroid.
Moment
of Inertia.
Radius of
Gyration.
u
Moment
of Inertia
Radius of
Gyration
Section
Modulus,
fpper Fibe
Centroid.
Moment
of Inertia
Radius of
Gyration.
1
1
1
_>
1
;_>
99
A
IA
FA
SA
e
IB
TB
A
IA
FA
SA
e
IB
re
In.
In.
In.
In.'
In.«
In.
In.«
In.
to.*
In.
In.
In.'
In.«
In.
In..
In.
In.'
In.
6x1
2 X2 xl
6x1
4.88
I4.8
1.74
10.3
I.I9
6.1
1. 12
6x|
5.63
16.2
1.70
II.8
•99
8.4
1.22
8x1
2 X2 xl
6x1
5-38
31-6
2.42
15-8
•75
6.1
1.07
6x|
6.13
34-5
2-37
18.4
•50
8.4
•17
21,x2t,x11
6x}
5-88
32-3
2-34
16.5
7-6
I.I4
6x|
6.63
35-o
2.30
18.9
.48
9-9
.22
" A
6x1
6-44
32.9
2.26
17-5
•63
8.4
1.14
6x|
7.19
35-5
2.22
19,7
•43
10.7
.22
3 x2.',x]
8x1
6.62
34-4
2.28
19.5
•Si
15-8
i-55
8x|
7.62
37-i
2 21
22.5
.27
21.2
.67
" A
8x1
7.24
35-3
2.21
20.8
•45
17.1
1.54
8x|
8.24
37-7
2.14
23-5
•23
22-5
65
SX/'0
2jx2jxl
6xj
6.38
38.0
2-44
17.6
.91
7-6
I.IO
6x|
7-13
4i-3
2.41
20.2
.67
IO.O
.18
" s,
6x;
6-94
38.9
2-37
18.8
.82
8.4
J.IO
6xj
7.69
41.9
2-33
21. 1
.61
10.8
.18
3 X2jxl
8xi
7.12
40-5
2.38
20.8
.70
16.0
1.49
8.12
44.0
2-33
24.1
•45
21.3
.62
A
8X;
7-74
41.4
2.31
22. 0
-63
17-3
1.49
8xi
8.74
44-7
2.26
25.2
.40
22.7
.61
8x|
3 *2*xl
8x1
7.62
46-3
2.46
21.8
1.87
16.2
1.46
8xg
8.62
48.5
2-37
23.O
•73
21-5
.58
" A
8xj
8.24
47-3
2-39
23-3
1.78
17.6
I 46
8x|
9.24
49-4
2.31
24.1
.67
22.9
•57
4 X3 x^
iox;
10.93
54-9
2.24
3I-I
1.40
46.8
2.07
10x5
12.18
58.6
2.19
34-3
.21
57-2
2.17
" i
loxj
11.71
55-5
2.18
32.1
1.36
49.9
2.06
10x5
12.96
59-2
2.14
•19
60.3
2.16
loxi
2jx2|xl
6x1
6.38
58.1
3.06
23.0
2.30
7-6
1.09
6x|
7-13
63-4
2.96
26.1
2. 02
9.9
1.18
" A
6x];
6-94
60.0
2.94
24.7
2.18
8.4
I.IO
6x|
7.69
64.4
2.89
27.9
•93
10.7
1.18
3 X3fX]
8xj
7.12
62.4
2.96
27.1
2.05
15-8
1.49
8x1
8.12
67.2
2.88
3'-5
.76
21.2
1.62
" A
8x]
7-74
64.3
2.88
29.0
1.94
17.1
1.49
8x|
8.74
68.3
2.81
33-0
.70
22-5
i. 60
4 *3 *A
IOXJ
10.43
72.4
2.63
38.6
1.50
46.1
2.10
iox|
u.68
76.5
2.56
42.7
•29
56.5
2. 2O
loxj
II. 21
73-o
2-55
41.1
49-9
2.O9
ioxi
12.46
77.0
2-49
43-7
.26
59-4
2.18
iox&
3 *2ixi
8x}
7-75
73-5
3.08
28.7
2.31
1 6.0
i-43
8x|
8-75
79-6
2-99
32-9
.01
21.3
1.56
" A
8x1
837
75-3
3.00
30.8
2.20
17.4
143
9-37
80.9
2-95
35-3
.94 22.7
I.S6
4 xl x^f
ioxj
11.06
85.8
2-79
41.1
I.7I
46.4
2.06
iox'
12.31
91.0
2-75
46.7
•49 56.9
2.15
' 1
ioxj
11.84
87.0
2.71
42.8
1.66
49-4
2.05
ioxj
13.09
91.8
2.69
48.5
•45
59-9
2.14
5 X3IXA
I2XJ
12.75
90.5
2.66
46.8
1.56
82.8
2.56
I2X\
14.25
95-8
2-59
51.8
•35
100.8
2.66
" i
I2X,
13-73
91.9
2-59
49-o
1.50
88.6
2-55
I2\'.
15-23
96.9
2.52
53-o
•33
106.6
2.64
loxf
3 «Jxl
8x1
8-37
83-7
3-i6
30.1
2-53
16.2
1.38
8x|
9-37
90.8
3.11
34-9
2.23
21.5
1.51
" A
8x1
8-99
85.8
3.10
32.4
2.42
17.6
1.40
8x|
9-99
92-5
3-05
36-9
2.15
22.9
4 *3 XA
loxj
u.68
98.4
2.92
43-2
1.90
46.8
2.OO
ion
12.93
104.6
2.81
47-3
1.67
57-2
2.IO
i
ioxf
12.46
99-7
2.83
45-2
1.84
49-9
2.00
I0\l
I3-7I
105.42.77
49-5
1.63
60.3
2.10
5 *3i*A
I2X?
13.37103.72.78
49-4
i-73
83-4
2.50
I2XJ
14.87
uo.o 2.72
54-7
1.51
101.4
2.6l
" f
I2XJ
14.35 105.3 2.71
1.68
89.3
2.50
I2XJ
I5-85
I I 1-5 2.<>$
56.4
107.3
2.60
141
TABLE 81.
PROPERTIES OF TOP CHORD SECTIONS.
;B
. | - i
Properties of
Two Angles, A Hi
f-J Q Angle Legs Turned Out.
A Edges of Angles Flush
Two Web Plates
with Edges of Top Plate.
and
Web Plates i" Below
One Cover Plate.
Backs of Angles.
IB
Series i and 2.
Series i.
Series 2.
8
d
Axis A-A.
Axis B-B.
oj
Axis A-A.
Axis B-B.
a
.3
8
5
§
Li
Is
s
_ ii
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Hi
<;
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"o a
a m".o
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1= **
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a 5J
w
3
B
a
o
g
P V
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1
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o
H
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1
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In.
In.'
In.'
In.
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In.
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Bxl
25X2£xJ
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8.88
58
2.56
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69.5
2.80
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10.13
64
2.52
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I.78
79-9
2.81
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10.88
76
2.64
27.9
2.47
79-9
2.71
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12.13
86
2.66
33-3
2.19
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2-73
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25x25X5
If
9.96
60
2-45
27.4
1.94
82.2
2.87
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II. 21
66
2-43
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1.69
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M
a
11.96
80
2.58
30.8
2-33
91.6
2-77
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13.21
88
2-57
35-6
2.08
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2.78
8xi
22X25XJ
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9-38
60
2-53
27-5
1-95
125.4
3-66
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10.88
67
2.48
33-3
1.64
143-4
3-63
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11.38
80
2.65
30.7
2.36
145-7
3-57
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12.88
89
2.63
36.8
2.05
163.7
3-56
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25X25xf
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10.46
62
2.44
29.7
1.84
146.4
3-74
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11.96
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2-39
35-0
i-57
164.4
3-71
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12.46
83
2.58
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2.23
166.7
3-65
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13.96
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2.56
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184.7
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25X25X£
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10.38
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3-24
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2.66
136.8
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11.88
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2.28
154.8
3.6l
k. 3
8
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12.88
143
3-33
41.9
3.16
162.2
3-55
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14.38
159
3-33
50.1
2.80
180.2
3-54
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25X25X5
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11.46
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3-H
41.2
2-49
157-8
3-71
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12.96
123
3.08
48.4
2.17
175-8
3.68
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a
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13.96
149
3-27
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2.98
183.2
3-62
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15.46
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3-25
53-9
2.66
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141$
10.88
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3-22
40-5
2-53
219.1
4-47
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12.63
125
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49.6
2.14
247-8
4-43
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13-38
149
3-34
45-3
3-04
262.9
4-43
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15-13
166
3-31
54-8
2.65
291.6
4-39
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25X25X5
u
11.96
116
3.12
43-9
2.38
250.6
4.58
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I3-7I
127
3-04
52.7
2.04
279.2
4-51
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14.46
154
3-26
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2.88
294.4
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16.21
170
3-23
58.3
2-53
323.0
4.46
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3X3X1
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I5-38
244
3-98
60.4
3-79
258.1
4.10
14X5
17-13
270
3-97
72.2
3-37
286.7
4.09
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18.38
295
4.01
66.5
4.19
296.1
4.01
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20.13
328
4-03
78-5
3.80
324.8
4.02
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3X3X5
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16.72
254
3-90
66.7
3-56
292.6
4.18
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18.47
279
3.88
77-9
3.20
321.2
4.17
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19.72
309
3.96
73-2
3-97
330-7
4.09
21.47
339
3-97
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3.62
359-3
4.09
I2X§
3X3X1
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17.88
280
3.96
77-7
3-22
437-3
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19.88
304
3-9i
90.6
2.85
480.0
4.91
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20.88
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4-03
84-3
3-65
499-9
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22.88
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4.02
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3X3xf
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19.22
286
3.86
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3.06
486.3
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21.22
309
3-82
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529.0
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22.22
348
3-96
90.1
3-50
548.9
4-97
24.22
377
3-95
102.8
3-17
591.6
4-94
i4x-i
3X3xf
i6xf
2O.72
43 i
456
103.2
3.80
521.1
5.01
16X5
22.72
464
4-52
118.1
3-43
563-8
4-98
" 4
"
"
24.22
524
4-65
II2.I
4-30
594-0
4-95
"
26.22
565
4-64
127.3 3-94
636.7
4-93
« f
3x3x5
ft
22.OO
441
4.48
109.9
3-64
569.0
5.08
"
24.OO
472
4-44
124.1 3.31
621.7
5-09
" 4
25.50
537
4-59
II9.I
641.9
5.02
"
27.50
577
4-58
I33-83-8I
684.6
4-99
14x1
3x3xf
i8xf
21.47
443
4-54
1097
3-66
740.9
5-87
184
2372
477
4.49
126.5 3.28
801.6
5.81
" 4
"
14
24.97
539
4.64
II8.6
4.17
849.1
5-83
"
27.22
582
136.0 3.79
909.8
5-78
" f
3x3x5
"
22.75
452
4.46
116.1
3-52
805.6
5-95
"
25.OO
484
4.40
132.2 3.16
866.3
5-89
" 4
M
26.25
S5i
4.58
125.6
4.02
913.8
5-90
28.50
593
4.56
142.4 3.66
974-5
5-85
142
TABLE 82.
PROPERTIES OF TOP CHORD^SECTIONS.
Propertie*
of
Top Chord Section*.
B
i Two Channel*
and
One Plate.
1, <
*J~
•
_j_
fr
iAj*-
Sec-
tion
Num-
ber.
Channels.
Cover
Plate.
Bto B
Chan-
nels.
Total
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Gage*.
Web
of
Chan-
nels.
Max.
Rivet.
I
I
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Plate.
Chan-
nels.
b
e
IA
IB
'A
rB
g
h
In.
Lb.
In.
In.
In.'
In.
In.«
In.«
In.
In.
In.
In.
In.
In.
I
2
3
4
6
8
9
10
ii
12 .
13
IS
16
17
18
19.
20
21
22
23
24
2
27
28
29
30
32
33
34
3I
36
5
5
6
6
7
7
6.50
9.00
8.00
10.50
9-75
12.25
8X}
8XA
ioxi
IOXA
12x1
i2XA
8X}
8XA
ioxi
12X1
i2XA
ioXi
IOXA
12x1
i2XA
HXA
14x1
ioxi
12x1
14x1
ioXi
12X1
"XA
ioXi
IOXA
12X1
HXA
14x1
tf
tf
3j
si
7l
«i
si
9i
7i
9i
M
5,1
71
7i
9*
ii
5-90
6.40
6.40
7-03
6.90
7.65
7-30
7.80
7.80
8-43
8.30
9.05
7.26
7.89
7.76
8.51
9-14
IO.OI
8.68
9.31
9.18
9-93
10.56
"•43
8.20
8.83
8.70
9-45
10.08
10.95
9.70
10.33
IO.2O
10.95
11.58
12.45
0.89
.04
.03
.18
•H
•30
0.72
0.84
0.84
0.99
0.95
1. 10
i. 08
1*5
1. 21
1-39
i-Si
1.67
0.90
i. 06
i. 02
1.19
•3i
•47
.11
•30
.25
•45
•59
•77
0-93
.11
.07
.25
.38
•55
23-9
25-6
25-3
27.1
26.5
28.3
27.8
29.7
29-5
31-7
31.0
33-3
42.0
44-8
44.0
46.9
48.7
Si-3
47-6
50-9
50.0
53-5
SS-8
58.9
65.1
69.2
68.0
72.5
75-3
79-3
72.8
77-5
76.2
81.4
84.8
89.8
34-7
37-3
67.6
72.8
II3-5
122.5
39-9
42.5
79-7
84-9
I35-I
144.1
73-i
78-3
124.0
133.0
204.9
219.2
83.1
88.3
143.0
152.0
235-7
250.3
80. i
85-3
I37-I
146.1
225.8
240.1
92.1
97-3
i68!i
260.7
275.0
2.01
2.OO
1.99
1.96
1.96
1.92
1.95
1-95
1.95
1.94
1-93
1.92
2.41
2.38
2.38
2-35
2.31
2.26
2-34
2-34
2-33
2.32
2.30
2.27
2.82
2.80
2.80
2-77
2-73
2.69
2-74
2.74
2-73
2-73
2.71
2.69
2.42
2.41
3-25
3-22
4-05
4.00
2-34
2-33
3.20
3-17
4.04
3-99
3-17
3-15
4.00
3-95
4-74
4.67
3-09
3.08
3-95
3-9i
4-73
4.68
3-13
3-u
3-97
3-93
4-73
4.68
3-08
3-07
3-95
3-92
4-74
4.70
6
8
10
u
6
8
.ft
-19
•33
H
i
H
II
10
"
"
ll
7f
$
7i
M
M
M
1}
.20 "
•32
«
II
I
9i
M
M
«
"I
«
'<
«
7l
Ij
.21
f
ill
"
ii
u
H
III
it
«
M
II
'I2
f
II
143
TABLE 82.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
B
L. _/4 J
Properties ^
of
Top Chord Sections.
» A
^
Two Channels
* and
One Plate.
H
-^
£
--->
Li
Sec-
tion
Num-
ber.
Channels.
Cover
Plate.
B to B
Chan-
nels.
Gross
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Gages.
Web
of
Chan-
nel.
Max.
Rivet.
1
a
i
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Plate.
Chan-
nel.
b
e
I
A
IB
rA
rB
g
h
In.
Lb.
In.
In.
In.2
In.
In."
In."
In.
In.
In.]
In.
In.
In.
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Si
52
53
54
M
57
58
I9
60
61
62
63
64
65
66
67
68
69
70
72
73
74
75
76
77
78
8
8
9
9
10
10
10
11.25
13-75
I3.25
15.00
15.00
2O.OO
25.00
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7
9
tt
ii
u
6|
8|
I0f
8|
iof
6|
8|
lof
(i
i of
tt
It
7l
9l
ill
9.70
10.45
II.08
n-95
12.70
13.70
11.08
11.83
12.46
13-33
14.08
15.08
10.78
ii-53
12. 16
13-03
13.78
14.78
11.82
12-57
13.20
14.07
14.82
15.82
I3-30
14.17
14.92
15.92
16.80
17.92
16.14
17.01
17.76
18.76
19.64
20.76
19.08
19-95
20.70
21.70
22.58
23.70
1.28
1-49
1.64
1.84
1.98
2.16
1. 12
1.32
1.46
I.6S
I.78
1.96
1.29
I-5I
1.68
1.89
2.04
2.23
1.17
i-39
1.54
i-75
1.90
2.09
1.70
1.92
2.09
2.30
'2-45
2.64
1.40
i. 60
1-75
i-95
2.09
2.28
1.18
1*7
1.50
1.62
1-73
i-99
99-9
106.2
110.4
116.3
I2O.2
1254
IO9.2
Il6.3
I2I.O
127.8
132.5
138.7
140.9
149-5
155-3
163.5
169.1
176.8
1497
IS8.8
165.2
174.2
180.3
188.6
2II-7
222.8
230.4
240.6
247.7
257.1
242.1
255-2
264.4
276.9
286.9
297.8
271.8
286.2
296.8
3I3-6
325.2
336.0
150.2
159-3
247.2
261.4
378.5
4OO.O
168.3
177-3
276.6
290.9
421.9
443-2
162.9
171.9
268.2
282.4
409.9
431-3
I74-I
183.1
287.4
301.7
439-4
460.7
289.4
303-6
441.9
641.2
671.6
341.2
355-o
520.4
542-0
752-3
782.7
383-9
398.2
588.8
610.1
851-4
881.8
3.21
3-19
3.16
3-12
3.08
3-03
3-14
3-13
3-12
3.10
3-07
3-03
3.62
3.60
3-57
3-54
3-50
3-46
3.56
3-55
3-54
3-52
3-49
3-45
3-99
3-97
3-93
3-89
3-84
3-79
3-88
3-87
3.86
3-84
3-82
3-79
3-77
3-79
3-79
3.80
3-79
3-77
3-93
3-90
4-72
5-46
5-40
3-90
3-87
4.71
4.67
5-48
5-42
3-89
3-86
4.70
4.66
5-45
5-40
3-84
3-82
4.67
4-63
5-44
5-40
4.67
4-63
5-44
5-39
6.18
6.12
4.60
4-57
5-41
5-37
6.19
6.14
4.48
4-47
5-33
5-30
6.14
6.10
9l
it
9\
tt
tt
I*
.22
tt
•31
3
4
tt
3
'.',*
tt
it
tt
it
tt
9l
tt
if
H
tt
•23
3
n|
it
•29
tt
3
4"
n|
132
iil
tt
It
.24
tt
3
4
tt
tt
iil
If
•38
3
4
isl
iil
n
It
it
M
•53
tt
a
it
3
144
TABLE 82.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
B
u _y4 •
Propertie*
of
Top Chord Section*.
, !
—i
, Two Channel*
and
One Plate.
"H
_.
1
t
h«-
Sec-
tion
Num-
ber.
Channels.
Cover
Plate.
Bto B
Chan-
nels.
Total
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Gage*.
Web
of
Chan-
nels.
Max.
Rivet.
I
•5
1
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Plate.
ftian-
nels.
b
e
IA
IB
rA
«B
g
h
In.
Lb.
In.
In.
In.'
In.
In.<
In>
In.
In.
In.
In.
In.
In.
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
IOI
IO2'
103
IO4
105
106
107
1 08
109
no
III
112
"3
114
"1
no
117
1x8
119
1 20
12
12
12
IS
IS
IS
20.50
25.00
30.00
33.00
35-00
40.00
45.00
i6Xi
l8Xf
20X&
i8Xf
20X&
i6Xf
i8Xf
20XJ
i8X|
22X&
i8Xf
i8X&
22XA
i8X|
20XA
22X&
i8X|
20X&
22Xi
22XA
Ill
9,1
ill
9
n
io|
M
I2f
«
IO|
M
'*«
10}
I2f
X2t
1 8.06
19.06
18.91
19.94
20.8 1
22.06
20.70
21.70
21.45
22.58
23.45
2470
23.64
24.64
24.39
25.52
26.39
27.64
26.55
27.68
28.55
29.80
30.80
32.18
27.33
28.46
29.33
30.58
31.58
32.96
30.27
31.40
32.27
33.52
34.52
35.90
33-23
34.36
35.23
36.48
37.48
38.86
2.06
2.28
2.21
2.46
2.62
2.83
1-79
2.01
i-95
2.17
2.32
2-53
i-57
1.77
1.71
1.92
2.06
2-34
1.96
2. 2O
2.36
2.6O
2-77
3-oo
1.90
2.14
2.30
2-53
2.70
2.92
1.71
1.94
2.09
2.31
2.47
2.68
1.56
i-77
1.92
2.12
2.28
2.48
409.8
427.6
422.4
440.6
452.5
469.8
451.4
471-5
465.1
486.5
500.3
520.5
494-9
5I7-3
510.1
534-1
549-8
567.6
922.8
961.0
986.7
1024.5
1050.2
1085.5
940-5
979-7
1005.6
1044.4
1070.8
1107.9
1005.1
1047.0
1074.8
1116.7
"45-4
1186.2
1068.2
III2.O
1141,9
1186.4
1217.2
1260.6
485-8
507-I
682.1
712.4
957-5
999.1
550.0
571-3
774-9
805.2
1084.7
1126.3
611.4
632.7
865.7
896.0
I2II.I
1252.7
936.7
967.0
I307.I
1348.7
I8l6.5
965.7
996.0
1346.7
1388.3
l8ll.7
1867.1
1039-3
1069.6
1453-5
I495-I
1956.5
2OII.9
II27.9
II58.2
1577-3
l6l8.9
2I2O.7
2I76.I
476
4-74
4-73
4.70
4.66
4.61
4.67
4.66
4.66
4.64
4.62
4-59
4-58
4-58
4-57
4.58
4-S6
4-53
5-90
5-89
5.88
5.86
5.84
5-8i
5-87
5.87
5.86
5.84
5-82
5-79
5-76
5-77
5-77
5-77
5-76
5-75
5-67
5.69
5-70
5.70
5-70
5-19
S.l6
6.00
5-98
6.78
6-73
5-13
6.01
5-98
6.80
6-75
5.08
5.06
5-96
5-93
6.78
6-73
5-94
676
6.72
7-56
7.50
5-95
5.92
6.78
6-74
7-58
7-52
5-86
5-84
6.71
6.68
7-52
7-48
5-82
5-8i
6.69
6.66
7.52
7.48
•?
A
.28
1
17
«
<
«
13
If
•39
I
«
«
«
17
«
«
«
13
17
2
M
I
tt
«
17
19
?
1°
H
M
M
17
»A
•t;
J
19
<«
«
IS
2&
•52
|
17
«
«
«
19
«
«
«
17
19
2|
M
K
.62
it
M
145
TABLE 83.
PROPERTIES OF TOP CHORD SECTIONS.
f
r^
r
Properties of -4j i
Highway Bridge ! 4
Top Chord Sections. 4
],A Four Angles
1 .._!".« and
Three Plates.
a,
i
. 2
J.J
.lux
i
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
f~, .
Eccen-
Liross Area.
tricity.
Axis
Axis
Axis
Axis
Section
A-A..
B-B
A-A.
B-B.
Number.
Web.
Cover.
Top.
Bottom.
A
e
IA
IB
TA
TB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
12" X 14" Section. A Series.
*I
I2"xt"
I4"*A"
25x25X1^
2|x2|xiV
16.26
1.66
359
351
4.70
4-65
2
" A
u
u
M
17.76
1-52
381
378
4-63
4.61
3
" I
u
(I
It
19.26
1.40
402
404
4-57
4.58
4
" TV
(I
M
ii
20.76
1.30
423
429
4-52
4-55
5
" *
ii
"
11
22.26
1. 21
443
453
4.46
4-52
6
" A
11
M
ti
23.76
I.I4
463
476
4.41
4.48
7
" I
"
M
IS
25.26
1.07
483
498
4-37
4-44
*8
I2x|
I4*A
2^X2|Xj^
,1-13
^2A^2A8
16.80
1.45
384
367
4.78
4.67
9 '
" A
"
"
18.30
i-33
405
394
4.70
4-63
10
" 1
"
M
«<
19.80
1.23
425
420
4-63
4.60
ii
" A
u
a
M
21.30
1.14
445
445
4-57
4-57
12
" i
u
«
a
22.80
1.07
465
469
4-52
4-54
13
;; A
"
M
«
24.30
I.OO
485
492
4-47
4.50
H
a
<s
a
«
25.80
0.94
504
5H
4.42
4-47
*iS
12x1
H^A
2^X2^X^
2|x2^XiV
17.32
1.25
4°5
383
4-83
4.70
16
" P
"
"
18.82
1.16
425
410
4-75
4.66
i?
<(
u
U
20.32
i. 06
445
436
4.68
4-63
18
' A
«
((
It
21.82
o-99
465
461
4.61
4-59
19
)l
«
It
ii
23.32
0-93
484
485
4-55
4-56
20
' A
«
«
"
24.82
0.87
503
508
4-50
4-52
21
' I
«
M
U
26.32
0.82
522
53°
4.46
4-49
*22
I2X^
H^A
2|x2|xrV
2|X2|^J
1782
1.07
425
398
4.88
4-73
23
" A
u
•
"
19.32
0.99
444
425
479
469
24
" I
te
"
ii
20.82
0.92
463
45i
4.71
4-65
25
"A
"
M
it
22.32
0.86
483
476
4-65
4.62
26
••<. i
?
«
«<
11
23.82
0.80
502
500
4-59
4.58
2?
It 9
T¥
«
M
it
25-32
0.75
521
523
4-54
4-55
28
" I
K
((
((
26.82
0.71
54°
545
4-49
4-Si
*29
I2Xj
!4xA
2§X2|xfV
2§X2^X^
18.32
0.91
442
414
4.91
4-75
3°
<< 5
T6
tt
It
19.82
0.84
461
441
4.82
4.71
31
" I
«
a
n
21.32
0.78
480
467
4-74
468
32
" A
«
it
n
22.82
o-73
499
492
4.67
4.64
33
" i
a
"
it
24.32
0.68
5i8
5i6
4.61
4.60
34
"A
"
"
"
25.82
0.64
536
539
4-56
4-56
35
(<
M
" •
27.32
0.61
555
56i
4-Si
4-53
* Spacing of rivet lines of web greater than 30 X thickness of plate.
146
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f?
f
1
r
Properties of A\ .
. __.._1^ Four Angles
Highway Bridge • "..- '. — 11
Top Chord Sections. q
. .*_ and
Three Plates.
U
Li
i
Plates.
Angles.
Moments of
Inertia
Radii of Gyra-
tion.
(~* A
Eccen-
Lfioss Area.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
'B
Inches.
Inches.
Inches.
Inches.
Inches*.
Inches.
Inches*.
Inches4.
Inches.
Inches.
i a" X 14" Section. B Series.
37
38
ftttft
"•t
^A
2tsfA
M
16.58
1 8.08
19.58
1.52
1-39
1.28
377
398
419
368
395
421
4-77
4.69
4.62
4.71
4.67
4.64
39
40
e
«
H
H
21.08
22.58
I.I9
I. II
439
459
446
470
4.56
4.51
4.60
4-56
41
« >
"
H
M
24.08
1.04
479
493
4.46
4-52
42
« 5
' «
"
M
25.58
0.98
498
SIS
4.41
4-49
*43
12x1
MX A
2jx2^xA
3X2|xf
17.18
1.29
403
387
4-84
4-74
44
'A
M
H
~
18.68
1.18
423
414
4.76
4.70
45
" i
II
"
H
20. 1 8
1.09
443
440
4.69
4.67
46
"A
II
"
«
21.68
1. 02
463
465
4.62
4.63
47
" *.
M
H
"
23.18
0-95
482
489
4.56
4-59
48
49
"t
M
M
M
M
24.68
26.18
0.90
0.85
501
520
512
534
4-Si
4.46
4-55
4-51
*5°
I2XJ
J4xA
2ix2jx^
3x2jx^V
17.76
1.07
427
406
4.90
4.78
Si
"A
'
"
"
19.26
0.99
446
433
4.81
4-74
52
" i
1
"
M
20.76
0.92
465
459
4-73
4.70
.53
54
!
•
M
I
22.26
23.76
0.86
0.80
485
5°4
484
508
4.67
4.60
4.66
4.62
M
*t
1
II
M
25.26
26.76
0.75
0.71
523
541
553
4-55
4-5°
4-58
4-54
*57
12X1
*4*A
2jx2jxA
3X2$X$
18.32
0.88
447
424
4-94
4.81
58
'A
U
"
M
19.82
0.82
466
4-85
4-77
59
"I
H
M
"
21.32
0.76
485
477
4-77
4-73
60
" A
M
II
M
22.82
0.71
504
502
4.70
4.69
61
" 1
M
M
"
24.32
0.67
522
526
4.63
4.65
62
" A
"
M
"
25.82
0.63
541
549
4-57
4.61
63
" I
H
"
27.32
0.59
560
571
4-52
4-57
*64
12x1
I4^A
2jx2ixA
3X2jx^
18.88
0.71
466
443
4-97
4-84
65
A
"
"
*
20.38
0.66
485
470
4.88
4.80
66
• " I
'
"
M
21.88
0.6 1
504
496
4.80
4.76
67
A
1
"
"
23-38
0-57
522
521
4-71
4-72
68
« i
1
"
"
24.88
0-54
541
545
4.66
4.68
69
70
"P
'
H
(t
26.38
27.88
0.51
0.48
559
578
568
590
4.60
4-55
4.64
4.60
* Spacing of rivet lines of web greater than 30 X thickness of plate.
147
TABLE S3.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
, n
r
Properties of 4j i
Highway Bridge j -I
Top Chord Sections. 4
[A Four Angles
1 .._L".T«I and
fc Three Plates.
U
Li
i
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
"• r-r\<2Q A rpa
Eccen-
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
14" X 16" Section. A Series.
*7i
HXI
i6xf
3*3xA
3X3Xy\
20. 1 2
2.14
606
546
5-49
5-21
*72
" A
"
"
«
21.87
1-97
641
585
5-41
5-17
73
« 3
8
u
"
"
23.62
1.82
677
623
5-35
5-13
74
" A
"
"
"
25-37
I.7O
711
660
5-29
5.10
75
"i
14
14
14
27.12
1-59
744
696
5-24
5.06
76
" A
"
"
M
28.87
1.49
777
731
5-19
5.02
77
" I
"
"
"
30.62
1.41
808
765
5-14
4-99
*78
14x1
i6x|
3*3*A
3X3xf
20.78
1.88
648
570
5-58
5-24
*79
" A
U
«
"
22.53
i-73
683
609
5-50
5.20
80
" I
"
1
"
24.28
1.61
716
647
5-43
5-16
81
" TS
M
'
(4
26.03
1.50
749
684
5.12
82
" 2
Ifl
i
M
27.78
1.41
781
72O
5-30
5-09
83
« 9
TS
M
'
14
29-53
1.32
813
755
5-25
5.06
84
" !
"
i
"
31.28
1-25
845
789
5.20
5-04
*85
14x1
i6x|
3*3xA
3X3xA
21.44
1.64
688
594
5-66
5.26
*86
" A
"
14
M
23.19
1.52
722
633
5-58
5-22
87
" t
"
M
"
24.94
1.41
754
671
5-5°
5.18
88
" A
M
M
"
26.69
1.32
786
708
5-42
5-15
89
" \
U
II
(4
28.44
1.24
816
744
S-36
90
" TS
M
"
M
30.19
1.17
848
779
5-30
5.08
9i
8
ff
14
(4
31-94
I.IO
879
813
5-24
5-04
*92
I4x|
i6xf
3X3X3^
3x3x£
22.O6
•43
721
618
5-72
5-29
*93
" A
"
"
!
23.81
•32
755
657
5-25
94
<« 3
8
"
"
• '
25.56
•23
786
695
5-54
5.21
95
" A
u
14
1
27.31
•15
818
732
5-47
96
" *
"
"
'
29.06
.08
848
768
5-40
5-14
97
" A
M
"
'
30.81
.02
879
803
5-34
C IO
98
" I
"
"
<
32.56
o-97
909
837
5-28
5-07
*99
14x1
i6xf
3x3xA
3x3xA
22.68
•23
756
641
5-77
5-31
*IOO
" A
M
"
"
24-43
.14
787
680
>68
5-27
IOI
" I
II
"
"
26.18
.07
817
718
5-24
IO2
" A
"
"
u
27-93
I.OO
848
755
5-50
5-2O
103
" 5
"
"
"
29.68
0.94
878
791
5-43
5.16
IO4
;; A
l(
"
M
31-43
0.89
908
826
5-37
5.12
!°5
" i
"
ii
14
33.18
084
938
860
5-32
5-09
* Spacing of rivet lines of web greater than 30 X thickness of plate.
148
TABLE S3.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
r
J
r1
Properties of A'.
Highway Bridge
Top Chord Sections. A
1.4 Four Angles
1"~CT and
Three Plates.
•
iJJ
L.1
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
n .
Eccen-
»rosd .'\IV;L.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
n
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches
*io6
14x1
i6x|
3X3*A
3*3*1
23.28
1.05
784
665
5-80
5-34
*io7
" TV
"
H
it
25.03
0.98
814
704
5-70
5-30
108
"1
"
M
H
26.78
0.92
844
742
S.6l
5.26
109
" TV
"
"
"
28.53
0.86
875
779
5-53
5.22
no
" *
"
"
"
30.28
0.81
904
815
5.46
5-19
in
" A
"
M
"
32.03
0.76
934
850
5-39
5-iS
112
" I
M
"
"
33-78
Q-73
963
884
5-34
5-12
14" X 16" Section. B Series.
•113
14x1
i6xj
3*3xfV
4x3xfV
20.74
1.87
654
590
5-62
5-33
*u4
" TV
"
"
"
22.49
1.72
689
629
5-53
5.29
US
" I
H
"
u
24.24
1. 60
722
667
5-46
5.24
116
tt T
It
M
tt
25.99
i-49
755
704
5-39
5.20
"7
" i
"
"
"
27.74
1.40
788
740
5-33
5.16
118
" TV
"
"
ft
29.49
1.32
819
775
527
5 12
119
" I
"
" .
tl
31.24
1.24
851
809
5.22
5.08
*I20
I4x}
i6x|
3*3xrV
4x3x1
21.52
i-57
704
624
5-72
5.38
*I2I
" fV
"
'
23-27
1.46
736
663
5-62
5-34
122
tt 3
tt
'
"
25.02
136
768
701
5-54
5.29
•123
" A
tt
1
«
26.77
127
800
738
5-25
124
« i
"
t
If
28.52
1.19
831
774
5-40
5-21
125
; >6-
"
'
tl
30.27
I 12
862
809
534
5-17
126
" 1
"
tt
32.02
1. 06
892
843
5.28
5-13
*I27
14x1
i6x|
3x3*rV
4x3 x A
22.30
I-3I
748
658
5-79
5-43
*I28
" Hi
'
"
M
24.05
1. 21
780
697
5-38
129
" I
1
"
"
25.80
I-I3
810
735
5-6o
5-33
130
" A
1
H
M
27-55
1. 06
841
772
5-52
529
131
« i
1
M
ft
29.30
1. 00
872
808
5-45
5-25
132
" X-
1
"
ft
3I-05
0.94
902
843
538
5-21
133
" I
'
"
tt
32.80
089
932
877
5-33
5-17
*I34
*I35
'""A
l6x|
3x3fA
4*2*4
23.06
24.81
1. 08
I.OO
787
817
690
729
5.84
5-73
5-47
5.42
136
'• r
'
"
"
26.56
0.93
848
767
5-65
5-37
137
" A
1
"
"
28 31
0.88
877
804
556
5-32
138
" *
1
H
H
30.06
0.83
907
840
5-49
5-28
139
" A
'
"
"
3I.8I
0.78
938
875
5.42
5-24
140
" 1
'
"
<<
33 56
0.74
967
909
5-37
5.20
* Spacing of rivet lines of web greater than 30 X thickness of plate.
149
TABLE 83. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
'T"(
i
1
1
r
Properties of ill-
Highway Bridge • "..-. ----4
Top Chord Sections <|
L4 Four Angles
e~ and
Three Plates
1
LJ
Ll
j
i
Plates.
Angles.
Moments
of Inertia.
Radii of Gyra-
tion.
r* rr»QQ A t¥*a
Eccen-
'
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*I4I
HXJ
i6x|
3*3*A
4*3*A
23.80
0.85
824
724
5-88
5-SI
*I42
" A
tt
"
M
25-55
0.79
853
763
5-77
5-47
143
" f
n
u
M
27.30
0-74
883
80 1
5-68
5-42
144
"A
66
66
"
29.05
0.69
913
838
5-6o
5-37
H5
" i
"
"
"
30.80
0.65
942
874
5-52
5-32
146
It 9
"
66
tl
32.55
O.62
971
909
546
5-28
147
" 7
"
66
H
34-3°
o-59
IOOO
943
5-40
5-24
*I48
I4XI
i6xf
3x3xA
4X3X
I
24-52
0.65
856
756
5-91
5-55
*I49
" A
M
"
tt
26.27
0.61
884
795
5.80
5-50
15°
tt 3
"
"
66
28.02
o-57
914
833
5-71
5-45
It 7
"
"
66
29.77
o-54
942
870
5-62
5-41
152
it 1
M
14
«
3I-S2
0.51
972
906
5-55
5-36
153
" A
II
"
"
33-27
0.48
IOOI
941
5-48
5-32
154
" f
II
"
**
35-02
0.46
1030
975
5-42
5-28
14" X 17
" Section.
"155
Hxi
I7x|
3*3xA
k
21.12
1.96
665
704
5-6i
5-77
""156
" A
"
M
tl
22.87
1.82
699
751
5-52
5-73
157
" f
"
"
66
24.62
1.69
734
797
5-45
5.68
158
tt i
"
M
61
26.37
i-57
767
842
5-39
5-65
159
tt i
66
tt
66
28.12
1.47
800
886
5-33
5.61
160
tt 9
66
16
66
29.87
1-39
833
929
5-28
5-57
161
" 1
"
66
"
31.62
864
971
5.22
5-54
*l62
HXJ
ITXf
3x3xA
4X3X-
f
2I.9O
1.67
715
743
5-71
5-82
"163
" A
66
tt
66
23.65
i-55
748
790
5.62
5-77
164
" f
"
"
"
25.40
1.44
780
836
5-54
5-73
165
" A
66
tt
"
27-I5
i-35
813
88 1
5-47
5-69
1 66
« i
"
66
66
28.90
1.27
845
925
5-65
167
u 9
"
66
*«
30.65
1.19
875
968
5-35
5-62
1 68
tt 5
8
"
**
**
32.40
l-IJ
907
IOIO
5-29
5-58
"169
I4x£
17X1
3*3xA
4x3 x A
22.68
1.40
761
781
5-79
5-86
"170
(( 5
M
tt
it
24-43
1.30
792
828
5-69
5.82
171
" r
"
"
66
26.18
1.22
824
874
S-6o
5-77
172
" A
"
"
"
27-93
I.I4
855
919
5-53
5-73
173
" i
"
tt
"
29.68
1.07
886
963
5-69
174
" A
66
"
M
31-43
I.OI
917
1006
5-40
5-65
175
" f
66
(i
"
33-18
0.96
946
1048
5-34
* Spacing of rivet lines of web greater than 30 X thickness of plate.
150
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
T ^
r
Properties of ^J
llinhw.iy Bridge
Top Chord Sections. <(
i
. lA. Four Angles
.t and
^ Three Plates.
i=L
LI
i
Plates.
Angles.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Bottom.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches*.
Inches*.
Inches.
Inches.
'176
14x1
17*1
3x3xA
4x3x1
23-44
I.I7
801
819
5-84
5.90
*I77
" A
«
"
25.19
1.09
832
866
5-75
5.86
178
"1
"
H
"
26.94
I. O2
862
912
5-66
5.82
179
" A
"
"
"
28.69
0.96
893
957
5-58
5-78
1 80
" i
"
"
"
30-44
0.90
923
1001
5-Si
5-74
181
" A
"
"
M
32.19
0.85
953
1044
5-44
5-70
182
" t
M
H
33-94
0.8 1
983
1086
5-38
5.66
*i83
14x1
17*1
3*3xA
pc3x,
V
24.18
0.94
839
858
5-89
5-95
'184
" A
M
"
25-93
0.88
869
905
5-79
5-90
185
" 1
"
M
H
27.68
0.82
898
951
5-69
5-86
1 86
" A
«
"
"
29-43
0.77
928
996
5-61
5-8i
187
« i
"
"
M
31.18
0-73
958
1040
5-54
5-77
1 88
" A
"
"
M
32.93
0.69
987
1083
5-47
5-73
189
" I
"
"
H
34-68
0.66
1017
1125
5-41
5.69
190
" H
u
H
"
36.43
0.63
1046
1166
5-35
5-65
•191
14x1
I7xf
3x3xA
4X3 x
I
24.90
o.75
871
895
591
5-99
*I92
" A
M
"
«
26.65
0.70
901
942
5.81
5-94
193
" }
H
"
"
28.40
0.66
930
988
5.72
5-89
194
" A
"
"
"
30.15
0.62
959
1033
5.64
5-85
195
<( i
i(
"
«
31.90
0-59
988
1077
5.56
5-8i
196
" A
u
"
(C
33-65
0.56
1018
II2O
5-50
5-77
197
" I
«
"
«
35-40
0-53
1047
Il62
5-44
5-73
I98
!i t*
«
"
"
37-iS
0.50
1076
I2O3
5.38
5-69
199
« i
M
"
38.90
0.48
1105
1243
5-33
S-65
*2OO
I4x}
I7x|
3*3*A
t
Wxj
1
25.62
0.57
903
931
5-94
6.03
*20I
" A
M
i<
«
27-37
0-53
978
5-84
5.98
2O2
;; t
H
"
H
29.12
0.50
96!
1024
5-75
5-93
203
" A
M
"
"
30.87
0.47
990
1069
5.66
5-88
2O4
" i
H
M
«
32.62
0-45
1018
III3
5-59
5-84
2O5
M
"
M
34-37
0.42
1048
1156
5-53
5.80
206
M
"
"
36.12
0.40
1076
1198
5.46
5-76
2O7
M
M
M
37-87
0.38
1105
1239
5.40
5.72
208
"
"
39-62
0-37
"35
1279
5-35
5.68
* Spacing of rivet lines of web greater than 30 X thickness of plate.
151
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
rn
P
Properties of A' . J^A Four Angles
Highway Bridge ". j ".. _ '[ ..—T^~ and
Top Chord Sections. q £ Three Plates.
LJ
LJ
1
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra^
tion.
r* A
Eccen-
Bottom.
Lrross Area.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches*.
Inches4.
Inches.
Inches.
IS" X 17" Section.
*2O9
isxA
I7X|
3x3xtV
4X3 x A
23.50
.89
821
766
5-91
5-71
*2IO
« 3
8
"
"
M
25.38
•75
862
816
5.83
5-67
211
" TV
u
"
It
27.25
•63
OO2
865
5-75
5-63
212
" 4
"
"
"
29.13
•52
942
912
5.68
5-59
213
tL $
cc
M
M
31.00
•43
983
958
5.62
5-56
214
"< L
tc
U
"
32.88
•35
IO2I
1003
5-57
5-52
215
16
M
"
u
34-75
1.28
1059
1047
5-52
5-49
216
« 3
4
M
"
"
36.63
1. 21
1097
1090
5-47
5-46
*2I7
I5xf\
I7x|
3x3xf\
4X3X|
24.28
1.61
877
807
6.01
5-76
*2l8
" f
u
"
u
26.16
1.49
917
857
5-92
5-72
219
' iV
"
u
H
28.03
i-39
956
906
5-84
5.68
22O
2
Cl
u
M
29.91
994
953
5.76
5-64
221
' 9
"
"
"
31-78
1.23
1033
999
5-70
5.60
222
' r
tt
"
M
33-66
1.16
1071
1044
5-64
5-57
223
' H
"
"
"
35-53
I.IO
1108
1088
5-58
5-54
224
c 3
4
H
37-41
1.05
1145
1131
5-53
5-50
*225
i5xrV
I7x|
3x3xA
4X3 xiV
25.06
1.36
929
845
6.08
S-8i
*226
" f
"
M
H
26.94
1.26
967
895
5-98
576
226
" TV
U
u
"
28.81
1.18
1005
944
5-90
5-72
227
" 4
tt
"
H
30.69
I. ii
1042
991
5-82
5-68
228
U 9
"
"
tt
32-56
1.04
1080
1037
576
5-64
229
" r
(t
U
"
34-44
0.99
1117
1082
5.69
5-6i
23O
" li
U
M
tt
36.31
0-94
H54
1126
5-63
5-57
231
" i
4
tt
H
38.19
0.89
1191
1169
5-58
5-53
*233
I8*f
I7xf
M
tt
4X3X4
25.82
27.70
I-I3
1.05
973
IOIO
883
933
6.14
6.04
5-84
5.80
234
. . 7
"
ie
1
29-57
0.99
1047
982
5-95
576
235
" r
"
"
c
31-45
0-93
1084
1029
5-87
5-72
236
" A
"
"
1
33-32
0.88
II2I
1075
5-79
5.68
237
" §
"
H
1
35-20
0.83
1158
1 120
5-73
5-64
238
" H
"
"
f
37-07
0.79
1194
1164
5-68
5-6i
239
(( 3.
4
"
*
38-95
0-75
I23O
1207
5-62
5-57
* Spacing of rivet lines of web greater than 30 X thickness of plate.
152
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
-H
t
~l
r
Properties of A] i
Highway Bridge i I~._ 1
Top Chord Sections. q
,. 1/1 Four Angles
L. «I and
^ Three Plates.
LJ
LI
j,
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
f\ 4
Eccen-
VjrOSS ArCil.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A- A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches*.
Inches.
Inches4.
Inches4.
Inches.
Inches.
•440
isxA
I7*f
3x3x15
4x34xA
26.56
0.91
1016
920
6.18
5-88
*24I
' 1
"
u
28.44
0.85
1052
970
6.08
5-84
242
' A
"
"
"
30.31
0.80
1089
IOI9
5-99
5.80
243
' i
«
M
H
32.19
0-75
1125
1066
5-91
5-76
244
' A
"
"
"
34.06
0.71
Il6l
iii-
5-84
5-72
245
' I
"
"
«
35-94
0.68
"97
"57
5-77
5-68
246
' ii
"
«
"
37-81
0.64
1233
I2OI
5-71
5.64
247
' i
"
M
0.61
1269
1244
5.6S
5-60
*248
I5*A
1 7*1
3X3X&
4X3X|
27.28
0.72
1055
959
6.22
5-92
*249
" i
"
"
"
29.16
0.67
1091
1009
6.12
5.88
250
' A
"
M
"
3I-03
0.63
1127
1058
6.03
5-84
251
c i
"
"
1
32.91
0.60
1162
"05
5-94
5.80
252
' A
ii
"
1
34-78
o-57
"99
1151
5-87
5-75
253
' t
"
M
1
36.66
0-54
1234
1196
5-8o
5.71
254
255
•f
M
M
'
38.53
40.41
0.51
0.49
1270
1305
1240
1283
5-74
5-68
5.67
'256
isxA
17*1
3X3X&
4X3X&
28.00
0.54
1089
995
6.24
5.96
'257
" 1
"
"
"
29.88
0.51
1124
1045
6.14
5.91
258
' A
"
M
"
31-75
0.48
1160
1094
6.04
5.87
259
c i
M
"
"
o-45
"95
1141
5-96
5-82
260
' A
«
M
"
35-50
0-43
1231
1187
5-89
5-78
261
' 1
"
"
"
37-38
0.41
1267
1232
5-82
5-74
262
' H
M
a
"
39-25
0-39
1302
1276
5-76
5-70
263
' 1
'
<{
H
4I-I3
0-37
1337
1319
5-70
5.66
IS" X 18" Section.
*264
!5xA
i8x&
3X3X&
4X3X&
25.00
2.25
872
93i
5-90
6.10
•265
i
M
26.88
2.09
915
991
5-83
6.07
266
A
H
28.75
i-95
958
1050
5-77
6.04
267
$
M
30.63
1.83
IOOO
1108
6.01
268
A
"
32.50
1.73
1042
1164
5^66
5.98
269
!
"
34-38
1.64
1082
1219
5.61
5-95
270
ti
"
36.25
i-SS
1122
1272
5-56
5-92
271
1
"
38.13
1.47
1161
1324
5-52
5-89
* Spacing of rivet lines of web greater than 30 X thickness of plate.
49
153
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
T>
T ^
jr
Properties of ,4j '_ 1
Highway Bridge !
Top Chord Sections. t?
. •fc^* Four Angles
fi and
^ Three Plates.
U
LJL
1
Plates.
Angles.
Moments of
Radii of Gyra-
Inertia.
tion.
Eccen-
VjiOSS /iiCcl .
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2?2
i5xA
I8x&
3X3X&
4X3X|
2578
1.97
933
976
6.OI
6.15
" 1
"
M
"
27.66
1.84
974
1036
5-93
6.12
274
" A
"
M
u
29-53
1.72
1015
1095
5-86
6.09
275
<< i
2
ft
"
u
3I.4I
1.62
1055
H53
5-79
6.06
276
" A
tt
M
"
33-28
1.53
1096
1209
5-73
6.O2
277
a 5
"
u
M
35-16
i-45
ii35
1264
5-68
5-99
278
" 1*
H
M
M
37.03
J-37
1174
1317
5-63
5-96
279
" f
H
"
38.91
1212
1369
5-58
5-93
*28o
isxA
iSxiV
3X3X&
4x3 x A
26.56
1.72
988
IO2O
6.10
6.2O
*28l
" f
M
"
u
28.44
1.61
1028
IO8O
6.01
6.16
282
"A
«
M
"
30.31
1.51
1068
H39
5-93
6.13
283
"1
{(
M
"
32.19
1.42
1107
1197
5.86
6.09
284
"A
"
M
u
34-06
1146
1253
5-79
6.06
285
" f
"
"
It
35-94
1.28
1184
1308
5-74
6.03
286
" H
M
H
"
37-Si
1. 21
1222
1361
5.68
6.00
287
" f
U
M
U
MS
I26O
1413
5-63
5-97
*288
isxA
I oX"jg"
3X3XTS
4X3X5
27-32
1.50
1038
1063
6.16
6.24
*28g
" 3
8
M
H
"
29.20
1.40
1077
1123
6.07
6.2O
290
" A
"
M
M
31.07
1.32
II82
5-99
6.17
291
" i
"
"
"
32.95
1.24
H53
1240
5-92
6.14
292
" A
"
"
"
34.82
1.18
1192
1296
5-85
6.10
293
" f
"
H
"
36.70
1. 12
1229
1351
5-79
6.07
294
"H
"
H
H
38.57
1. 06
1266
1404
5-73
6.04
295
" 3
"
"
M
40.45
I.OI
1303
1456
5-68
6.00
*296
isxA
IoX]^
3x3xA
4x3xA
28.06
1.28
1085
1107
6.21
6.28
*297
" 3
8
"
"
«
29.94
1. 2O
1123
1167
6.12
6.24
298
" A
U
M
M
31.81
I-I3
1160
1226
6.04
6. 20
299
" i
"
M
"
33.69
1.07
1197
1284
5-96
6.17
300
" A
"
(l
"
35.56
I.OI
1235
1340
5-89
6.14
301
" f
M
"
u
37-44
0.96
1272
1395
5.83
6.10
302
" H
"
"
"
39-31
0.92
1309
1448
5-77
6.06
303
" 3.
41.19
0.88
1345
1500
5-7i
6.03
* Spacing of rivet lines of web greater than 30 X thickness of plate.
154
TABLE 83.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f"
Properties of -<iL_ j
Highway Bridge
Top Chord Sections. q
. __.._1^ Four Angles
.€_' and
t Three Platen
JLJ
L.1
i
Plates.
Angles.
Moments of
Radii of Gyra-
Inertia.
tion.
«"»_.__ A wv
Eccen-
tricity
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*304
iSxft
i8XrV
3X3XxV
4x-3xf
28.78
1.09
1127
1149
6.26
6.31
*3°5
" 1
1
30.66
1.03
1164
1209
6.16
6.27
306
307
1
32-53
34-41
0.97
0.92
I2OI
1237
1268
1326
6.07
5-99
6.24
6.2O
308
" TV
'
36.28
0.87
1275
1382
5-92
6.17
3°9
" 1
'
38.16
0.83
I3II
1437
5-86
6.14
310
3"
"r
<
40.03
41.91
0.79
0.75
1347
1383
1490
1542
5-8o
5-74
6.10
6.06
i 5* fV
iSxA
3*3*fV
4*3 xH
29.50
0.92
1165
1191
6.28
6.36
*3J3
" 1
<
3I-38
0.86
I2O2
1251
6.19
6.32
314
" A
1
33-25
0.81
1238
1310
6.10
6.28
315
"i
1
35-13
0.78
1274
1368
6.O2
6.24
316
"A
'
37.00
0-73
1311
1424
5-95
6.2O
317
" !
38.88
0.69
1347
1479
5-88
6.16
319
"P
'
40.75
42.63
0.66
0.63
1383
1419
1532
1584
5-82
5-76
6.13
6.09
I
* Spacing of rivet lines of web greater than 30 X thickness of plate.
155
TABLE 84.
PROPERTIES OF TOP CHORD SECTIONS.
T"'
J3
^ P
Properties -4j i _.._i^. Four Angles
of ! 3- and
Top Chord Sections. q £ Three Plates.
If > "2
f . 1
ji.i 'II II' »..*4
B
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
y-» _ A
Eccen-
VjTOSS /\rCt\.
tricity.
Axis
Axis
Axis
Axis
Section
A-A.
B-B.
A-A.
B-B.
Number.
Web.
Cover.
Top.
Bottom.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.] Inches.
Inches.
15" X 18" Section. A series.
*IOOI
ISxf
iSxrV
3X3X|
4x3x1
28.31
1.96
988
1067
5-91
6.14
IO02
" TV
"
"
"
30.19
1.84
IO29
1126
5-84
6. 1 1
1003
« ^
"
M
i
32.06
i-73
IO7O
1184
5-78
6.08
1004
"A
U
(i
i
33-94
1.63
III2
1240
5-72
6.05
1005
« 5
8
M
U
i
i-SS
II5I
1295
5-67
6.01
1006
" H
M
"
'
37-69
1.47
II9I
1348
5.62
5-98
1007
" f
H
II
'
1.40
1229
1400
5-58
5-95
*ioo8
isxf
iSxrV
3x3x1
4x3 x A
29.09
i-73
1043
IIII
5-99
6.18
1009
" A
"
ft
"
30.97
1.62
1084
1170
5-92
6.15
IOIO
" %
t4
U
M
32.84
i-53
1123
1228
5-85
6. 1 1
IOII
" A
It
"
"
34-72
i-45
1163
1284
5-79
6.08
IOI2
« 5
8
M
U
M
36.59
i-37
I2O2
1339
5-73
6.05
IOI3
" H
"
11
"
38.47
1.30
1241
1392
5-68
6.01
IOI4
" f
II
II
M
40.34
1.24
1279
1444
5-63
5-98
*ioi5
iSxf
iSxrV
3x3x1
4X3 x£
29.85
1-52
1093
1156
6.05
6.22
1016
" j^
"
"
U
31-73
i-43
1132
1215
5-97
6.19
1017
" i
M
"
11
33-6o
i-35
II7I
1273
5-90
6.IS
1018
" A
ft
M
n
35-48
1.28
I2IO
1329
5-84
6.12
1019
" f
H
"
it
37-35
1. 21
1248
1384
5-78
6.09
1020
"H
"
H
It
39-23
I-I5
1286
H37
5-73
6.05
IO2I
C< 3
"
H
M
41.10
I.IO
1323
1489
5-67
6.O2
*IO22
J 8
iSxfV
3X3xf
4x3 xjV
30-59
1.32
II4O
1199
6.10
6.26
IO23
" A
H
"
M
32-47
1.25
1178
1258
6.O2
6.22
1024
« i
2
M
"
M
34-34
1.18
1216
1316
5-95
6.19
IO25
it 9
U
M
a
36.22
1. 12
1255
1372
5-89
6.16
IO26
" f
"
H
"
38.09
1. 06
1292
1427
5-83
6.12
IO27
« 1 1
U
"
M
39-97
I.OI
1329
1480
5-77
6.08
1028
« 3
1
M
"
M
41.84
0.97
1366
1532
5-71
6.05
*IO29
ISxf
iSxjV
3X3X1
4x3x1
3I-3I
I.I5
1183
1241
6.15
6.30
1030
A
U
"
i
33-19
1. 08
I22O
1300
6.06
6.26
1031
' 1
It
U
'
3S-o6
1.02
1257
1358
5-99
6.22
1032
< 9
16
"
U
i
36.94
0.97
1295
1414
5-92
6.19
1033
' f
*'
H
'
38.81
0-93
1332
1469
5-86
6.15
1034
( 1 1
cc
a
1
40.69
0.88
1368
IS22
5.80
6.12
1035
' r
"
II
1
42-56
0.84
1405
1574
5-75
6.08
* Spacing of rivet lines of web greater than 30 X thickness of plate.
156
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
.=
f"
Properties A±_
of • "... L-._ll
Top Chord Sections. 4
___Li Four Angles
L .._l"jt and
T Three Plates.
LJ
L.t
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
/"* A
Eccen-
* iross An •
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches
Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches.
'1036
I5xf
iSxrV
3X3X1
4x3xfi
32.03
0.98
1223
1284
6.18
6-33
1038
f
M
M
1!
33-91
35-78
092
6.87
1260
1297
1343
1401
6.10
6.O2
6.29
6.25
1039
A
"
"
"
37-66
0.83
1334
H57
5-95
6.22
1040
1
"
"
"
39-53
0.79
1370
1512
5-89
6.19
1041
ii
"
"
M
41.41
0.76
1406
1565
5-83
6.J5
1042
1
"
"
"
43-28
0.72
1442
1617
5-77
'1043
iSxf
iSxrV
3X3xf
4X3X1
32.73
0.82
1259
1327
6.2O
6-37
1044
A
"
"
34.61
0.78
1295
1386
6.12
6-33
1045
i
"
"
"
36.48
0-74
1331
1444
6.04
6.29
1046
A
"
"
"
38.36
0.70
1368
1500
5-97
6.25
1047
I
"
"
"
40.23
0.67
1404
ISS5
5.90
6.22
1048
H
H
"
"
42.11
0.64
1440
1608
5-85
6.18
1049
t
"
"
"
43-98
0.61
1475
1660
5-79
6.14
15" X 18" Section. B Series.
1050
iSxf
l8xf
3$x3$xf
5x3ix|
29.06
1.50
1035
1042
5-96
5-98
1051
' A
"
"
M
30.94
.41
1074
1090
5.89
5-93
•1052
'*
"
"
"
32.81
•33
i"3
"37
5-82
5.88
1053
' A
"
H
"
34.69
.26
1151
1183
5-76
5-84
1054
' f
H
"
M
36.56
.20
1190
1228
5-70
5-79
1055
: t*
u
M
"
38.44
.14
1227
1272
5-65
5-75
1056
' i
M
M
"
40.31
.08
1265
1315
5.6o
5-71
1057
ijxf
iSxf
3^x3ixf
5x35x^1^
30.02
•25
1095
1095
6.04
6.04
1058
' A
U
"
"
31.90
.18
"33
"43
5-96
5-99
1059
* I
If
M
M
33-77
.11
1170
1190
5-89
5-94
1060
1061
:t
«
"
M
35-65
37-52
•05
.00
1207
1245
1236
1281
5.82
5-76
5-89
5.84
1062
' H
"
H
"
39-40
0.95
1282
1325
5-70
5.80
1063
' 1
'
"
"
41.27
0.91
1319
1368
5-65
5-75
1064
icxf
i8x|
35X3ixf
5x3ixi
30.96
i. 02
"49
1148
6.09
6.09
1065
P
•'
*
"
32.84
0.96
1186
1196
6.00
6.03
1066
" *
"
H
M
34-71
0.91
1222
1243
5-93
5-98
1067
" A
"
H
"
36.59
0.86
1259
1289
5-86
5-93
1068
" f
"
"
"
38.46
0.82
1296
1334
5.80
5.88
1069
1070
•ij
M
M
''
«
40.34
42.21
0.78
0-75
1332
1368
1378
1421
5-74
5-69
5-84
5-80
1 * Spacing ot rivet lines of web greater than 30 X thickness of plate.
157
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
B
Properties -A\
of !
Top Chord Sections. a,
=
ir
tl Four Angles
and
Three Plates.
JLJ
Li
B
Plates.
Angles.
3ross Area.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
IO7I
I5*t
l8xf
31X31X|
5x31x^6-
31.90
0.80
1200
I2OI
6.13
6.13
1072
' TS
"
"
M
33-78
0-75
1236
1249
6.05
6.08
1073
« i
2
"
u
H
35-6S
0.71
1272
1296
5-97
6.03
1074
' TS
u
M
(C
37-53
0.68
1308
1342
5.90
5-98
1075
8
u
H
M
39-40
0.65
1344
1387
5-84
5-93
1076
' H
"
M
"
41.28
0.62
1380
H3I
5-78
5-89
1077
' f
Cl
"
43-iS
0-59
1416
H74
5-72
5-84
1078
I5xf
l8x|
3 2^x35X3^
5X35S
f
32.80
O.6o
1246
1253
6.16
6.18
1079
" _L
"
u
"
34-68
0-57
1282
1301
6.08
6.12
1080
<< 1
2
u
"
H
36.55
0-54
1317
1348
6.00
6.07
1081
"ft
u
"
H
38.43
0.51
1353
1394
5-93
6.O2
1082
" f
"
"
M
40.30
0.49
1389
H39
5-87
5-97
1083
" H
H
M
U
42.18
0.47
H2S
1483
5.81
5-92
1084
«( 3
M
**
M
44-05
o-45
1460
1526
5-76
5.88
1085
ISxf
i8xf
3?x3|xf
5x3|x
16
33-70
0.41
1289
1305
6.18
6.22
1086
" TS
H
"
M
0-39
1325
1353
6.10
6.16
1087
"1
li
M
H
37-45
0-37
1360
1400
6.O2
6. 1 1
1088
;ft
H
"
M
39-33
o-35
1395
1446
5-95
6.06
1089
<' 5
8
U
"
"
41.20
o-34
H3I
1491
5-89
6.01
1090
" H
H
"
"
43.08
0.32
1467
1535
5-83
5-96
1091
" f
«
M
ii
44-95
0.31
I5O2
1578
5-78
5-92
1092
isxf
l8xf
31X31X|
5X3^
|
34-58
0.25
1326
1358
6.19
6.26
1093
" TS
M
((
36.46
0.23
1361
1406
6. 1 1
6.2O
1094
5
M
U
"
38.33
O.22
1396
1453
6.03
6.15
1095
I 9
"
M
"
40.21
O.2I
1431
1499
5-96
6.10
1096
' f
M
"
H
42.08
O.2O
1467
1544
5-90
6.05
1097
< 11
16
"
"
M
43.96
O.I9
I5O2
1588
5-84
6.00
1098
< 3
4
"
"
H
4S.83
0.18
1537
1631
5-79
5-96
IS" X 19" Section. A Series.
*IO99
I5xf
I9XT6
3X3X|
28.75
2.04
IOO2
1240
5-91
6-57
IIOO
ft
u
30-63
1.92
1044
1310
5-84
6-54
HOI
1
"
32.50
1.81
1086
1378
5-78
6.51
IIO2
&
tt
34.38
1.71
1128
H45
5-73
6.48
1103
i
14
36.25
1.62
1168
1510
5.68
6-45
1104
11
16
"
38.13
i-54
1207
1574
5-63
6-43
1105
3.
"
40.00
1.47
1247
1637
5-59
6.40
* Spacing of rivet lines of web greater than 30 X thickness of plate.
158
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
r
P
Properties A\
of ; L'.~ LTZXTT:
Top Chord Sections. 4
LA. Four Angles
1 .._!_" ~£ and
Three Plates.
a.
J.JI
Li
i
Plates.
Angles.
Momenta of
Inertia.
Radii of Gyra-
tion.
f~" fa A «u
Eccen-
1. 1 1 (>**3 iAiv.i.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-d.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*uo6
I5xf
I9*A
3X3x|
4X3xA
29-53
1.81
1059
1291
5-99
6.61
1107
1108
It
\
"t
3I.4I
33-28
1.71
IIOO
1140
1361
1429
5-92
5-85
6.58
6-55
1109
"A
1
"
M
35.l6
1.52
1180
1496
5-79
6.52
1 1 10
" 1
'
"
14
37-03
1.45
1219
1561
5-74
6-49
mi
' tt
4
14
"
38.91
1.38
1258
1625
5-69
6.46
1112
" i
*
"
"
40.78
I-3I
1297
1688
5-64
6.43
*ui3
iSxi
i9xA
3X3xf
4x3xJ
30.29
1.61
1 1 10
1341
6.05
6.65
1114
" A
"
<t
32.17
1.51
"49
1411
5-98
6.62
IMS
" i
"
"
tt
34-04
1-43
1 1 88
H79
5-91
6-59
1116
i< »
"
14
tt
35-92
1.36
1228
1546
5-85
6.56
1117
" f
"
"
ft
37-79
1.29
1266
IOI1
5-79
6-53
1118
1119
"f1
"
«
ft
tt
41.54
1.23
1.17
1304
1342
1675
1738
5-73
5.68
6.50
6-47
*II20
ISX|
1 9* A
3X3X|
4x3fA
31-03
1.41
1158
1390
6.1 1
6.69
1 121
1122
">
44
"
14
32.91
34-78
1-33
1.26
1196
1235
1460
1528
6.03
5-96
6.66
6.63
•1123
" A
44
u
"
36.66
i. 20
1273
1595
5-89
6.60
1124
" f
M
"
44
38.53
1.14
1660
5.83
6.57
1125
1126
"1*
"
<<
14
14
40.41
42.28
1.09
1.04
1348
1385
1724
1787
5-77
5.72
6-53
6.50
*II27
I5xf
i9xA
3x3x1
4X3X|
31-75
1.24
I2OI
H37
6.15
6-73
1128
" A
44
"
"
33.63
1.17
1239
1507
6.07
6.70
1129
.. i
"
tt
44
35-50
i. II
1277
1575
6.00
6.66
1130
tt >
"
"
tt
37.38
1.05
1315
1642
5-93
6.63
II3I
" 1
"
"
tt
39-25
1. 00
1352
1707
5-87
6.60
1132
" tt
"
tt
tt
41.13
0.96
1388
1771
5-8i
6.56
1133
" i
"
tt
tt
43-00
0.91
H25
1834
576
6-53
*"34
iSx|
!9xA
3x3x1
4x3xtt
3247
1.07
1243
1486
6.19
6.76
"35
" A
"
ft
"
34-35
I.OI
1280
1556
6.10
6-73
1136
" 1
44
"
c
36.22
0.96
1317
1624
6.03
6.70
"37
" A
"
"
1
38.10
0.91
1354
1691
5.96
6.66
1138
" 1
"
"
1
39-97
0.87
1391
1756
5.90
6.63
"39
1140
«r
«
It
ft
;
41.85
43-72
0.83
0.79
1427
1463
1820
1883
5-84
5-79
6.60
6.56
* Spacing of rivet lines of web greater than 30 X thickness of plate.
159
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
rH
J
1
r
Properties A\
[A Four Angles
of • -..- LTT^L...
1 "~e_ and
Top Chord Sections. 4
^ Three Plates.
LJ
Li.
B
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
y~s „ \ —-,
Eccen-
Lrioss /vrca..
tricity.
Axis
Axis
Axis
Axis
Section
A-A.
B-B.
A-A.
B-B.
Number.
Web.
Cover.
Top.
Bottom.
A
e
IA
IB
TA
TB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*ii4i
iSxf
i9XiV
3X3X5
4x3xf
33-17
0.92
1279
1535
6.21
6.80
1142
" A
M
35-05
0.87
1316
1605
6.13
6.77
"43
" £
M
36.92
0.82
1352
1673
6.05
6-73
"44
" F
"
38.80
0.78
1388
1740
5-98
6.70
"45
H
40.67
0-75
1425
1805
5-92
6.66
1146
" It
u
42-55
0.71
1461
1869
5-86
6.63
"47
« 3
4
"
44.42
0.68
1497
1932
5.81
6-59
IS" X 19" Section. B Series.
1148
15x5
!9xA
32X3§xf
5X3!xf
30.62
1.83
1094
1250
5-98
6-39
"49
1150
|f
H
t
H
32-50
34-37
.72
-63
1136
1176
1308
1365
5-91
5-85
6-34
6.30
1151
" A
H
1
M
36.25
•55
I2IJ
1421
5-79
6.26
1152
" f
M
1
"
38.12
•47
1255
1476
5-73
6.22
"S3
"H
(I
1
M
40.00
.40
1294
1530
5-68
6.18
"54
« 3
4
U
t
"
41.87
•34
1333
1583
5-64
6.14
"55
ISxf
igxrV
35x3 Jxf
SX^XTS
3I-S8
•58
1160
1310
6.06
6.44
1156
" A
«
"
"
3346
•49
1 200
1368
5-98
6-39
"57
" 1
H
(C
H
35-33
.41
1239
H25
5-92
6-35
1158
" A
M
H
"
37-21
•34
1277
1481
5-86
6.31
"59
" f
u
"
"
39.08
.27
1317
1536
5.80
6.27
1160
" it
H
M
H
40.96
.21
I3SS
IS90
5-75
6.23
1161
" f
"
H
"
42-83
.16
1392
1643
5-70
6.19
1162
iSxf
i9xA
31X31X|
5X3 |x§
32.52
•35
1218
1371
6.12
6-49
"63
'" A
"
<«
u
34-40
.27
1256
1429
6.04
6-44
1164
" ^
a
"
"
36.27
.21
1294
1486
5-97
6.40
"65
" A
"
"
H
38-15
•IS
1332
1542
5-9i
6.36
1166
" 5
8
M
cc
"
40.02
.09
1370
1597
5-85
6.32
1167
"H
M
"
M
41.90
.04
1407
1651
5-79
6.28
1168
« 3_
M
M
"
43-77
.00
14 H
1704
5-74
6.24
1169
ISxf
1 9X3^
31X31X|
Sx3ix_^
3346
•13
1274
1431
6.17
6-54
1170
" A
«
"
"
35-34
.07
13"
1489
6.09
6-49
1171
" 1
"
(C
"
37-"
.02
1348
1546
6.O2
6-45
1172
'' Yg
H
H
M
38.99
o-97
1385
1602
5-96
6.41
"73
" f
"
II
"
40.86
0.92
1423
1657
5-90
6-37
"74
" ^j
M
M
u
42-74
0.88
1460
I7II
5-84
6-33
"75
" 1
"
"
"
44.61
0.85
1496
1764
5-79
6.29
* Spacing of rivet lines of web greater than 30 X thickness of plate.
160
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
I
nr*
-
T
Properties A\
of • _"._ L..-4
Top Chord Sections. 4
Li Four Angles
"."€1 and
Three Plates.
4
LJ
Li
j
,
Moments of
Radii of Gyra-
Plates.
Angles.
Inertia.
tion.
f* * ^^
Eccen-
1 1 < >ss /\ii M.
tricity.
Axis
Axis
Axis
Axis
Section
A-A.
B-B.
A-A.
B-B.
Number
Web.
Cover.
Top.
Motto
m.
A
e
IA
IB
rA
tm
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
1176
ISX|
J9XA
3ix3ix|
5x3^
:f
34-36
0-93
1325
1490
6.21
6-59
"77
" A
"
41
1
36-24
0.88
1362
1548
6.13
6-53
1178
« i
"
"
1
38.11
0.84
1398
1605
6.06
6.48
"79
"A
"
"
1
39-99
0.80
1434
1661
5-99
6.44
1180
" 1
H
"
1
41.86
0.76
1472
1716
5-93
6.40
1181
1182
:p
«
«
<
43-74
45.61
o-73
0.70
1508
1544
1770
1823
5-87
5-82
6.36
6.32
1183
icrl
*9xA
3ix3|x|
5x3|x
|>
35.26
0.74
1372
1549
6.24
6.63
1184
" A
"
"
"
37-H
0.70
1408
1607
6.16
6.58
1185
" \
"
"
"
39-01
0.67
1444
1664
6.08
6-53
1186
" A
H
M
"
40.89
0,64
1479
1720
6.01
6.48
1187
" I
"
M
"
42.76
0.6 1
1516
1775
5-95
6-44
1188
" fi
"
"
H
44.64
o-59
1552
1829
5-89
6.40
1189
« a
M
"
"
46.51
0.56
1587
1882
5-84
6.36
1190
I5xf
*9xA
3ix3Jxf
5X3J3
3
36.14
0.58
1413
1609
6.25
6.67
1191
"A
c
"
"
38 02
055
1448
1667
6.16
6.62
1192
"*
'
"
M
39.89
0.52
1484
1724
6.09
6-57
"93
"A
1
"
"
41-77
0.50
1520
1780
6.03
6.52
"94
" ;
1
M
"
43-64
0.48
1556
1835
5-97
6.48
JI95
' fi
1
"
"
45-52
0.46
1591
1889
6.44
1196
" i
'
II
M
47.39
0.44
1627
1942
5^86
6.40
J 16" X 19" Section. A Series.
*"97
i6x|
*9xA
3X3X|
4X3X1
29.49
2.12
"65
1270
6.28
6.56
1198
" A
"
H
H
31-49
1.99
1216
1344
6.21
6-53
"99
" i
"
M
"
33-49
1.87
1265
1417
6.15
6.51
1200
« >
"
"
"
35-49
I.76
1315
1488
609
6.48
1 201
" i-
1
"
"
M
3749
1.67
1364
1558
6.04
6.45
1202
" H
"
M
"
39-49
1-58
1412
1626
5-98
6.42
1203
" 4
'*
"
M
41.49
1459
1693
5-93
6-39
'1204
i6x|
!9xA
3X3X1
4x3xA
30.27
1.88
1229
1321
6.37
6-60
1205
" A
"
H
32.27
1.77
1278
1395
6 29
6-57
I2O6
" i
" .
"
"
34-27
1.66
1326
1468
6.22
6-54
1207
" A
"
M
"
36.27
1-57
1374
1539
6.15
6.51
1208
" f
M
"
M
1.49
1422
1609
6.09
6.48
I2O9
" !i
"
"
"
40.27
1.42
1469
1677
6.04
6.45
1210
" i
"
"
"
42.27
1515
1744
5-99
6.42
* Spacing of rivet lines of web greater than 30 X thickness of plate.
161
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
*H
J
1
r
Properties A\ .
of I
Top Chord Sections. ^
-4-
[A Four Angles
1 -."*' and
Three Plates.
L_l
B
Plates.
Angles.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
'
tricity.
Axis
Axis
Axis
Axis.
Section
A-A.
B-B.
A- A.
B-B.
Number.
Web.
. Cover.
Top.
Bottom.
A
e
U
IB
r\
rB
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches.
16" X 19" Section. A Series.
*I2II
i6xf
I9*A
3x3xf
4x3x1
3L03
.67
1287
1371
6-45
6.65
1212
" A
i
i
u
33-03
•57
1335
1445
6.36
6.62
1213
cc 1
1
'
M
35-03
.48
1382
1518
6.28
6.58
1214
"A
'
'
"
37-03
.40
1429
1589
6.21
6-55
1215
" I
'
'
M
39-03
•32
1476
1659
6.IS
6.52
1216
" tt
i
i
"
41.03
.26
1522
1727
6.09
6-49
1217
" 4
i
'
"
43-03
.20
1567
1794
6.04
6.46
*I2l8
i6xf
i9xyV
3x3x1
4
^3xA
31-77
.46
1342
1420
6.50
6.69
1219
" A
"
"
M
33-77
•38
1389
1494
6.41
6.65
I22O
" i
"
H
"
35-77
•30
H3S
1567
6-33
6.62
1221
it 9
"
u
"
37-77
•23
1481
1638
6.26
6.58
1222
" I
it
H
"
39-77
•17
1527
1708
6.19
6-55
1223
" ii
"
"
H
41-77
.11
1572
1776
6.13
6.52
1224
" S.
**
"
"
•43-77
.06
1617
1843
6.08
6-49
*I225
i6xf
I9XTT
3X3xf
4X3X|
32.49
1.28
1392
1467
6-55
6.72
1226
" A
it
"
u
34-49
1.20
H38
1541
6.46
6.68
1227
u i
"
H
ft
36.49
I.I4
1483
1614
6-37
6.65
1228
(( 9
T?
H
It
ft
38.49
1. 08
1528
1685
6.30
6.62
1229
" I
"
H
H
40.49
1.03
1573
1755
6.23
6.58
I23O
"H
"
"
u
42-49
0.98
1618
1823
6.17
6-55
1231
« 3
4
M
"
"
44.49
0-93
1662
1890
611
6.52
*I232
i6x|
!9XrV
3X3xf
4x3xH
33-21
I.IO
H39
1516
6.58
6.76
1233
(( 7
«
H
"
35-21
I.O4
1484
1590
6-49
6.72
1234
" i
2
«
H
u
37-21
098
1528
1663
6.41
6.68
1235
" A
t(
u
"
39.21
0.93
1573
1734
6-33
6.65
1236
" 1
H
u
H
41.21
0.89
1617
1804
6.26
6.62
1237
<* 11
M
U
"
43-21
0.85
1662
1872
6. 20
6.58
1238
" 1
"
M
"
45-21
0.81
1705
1939
6.14
6-55
*i239
i6xf
I9X^
3X3xf
4X3xf
33-91
0.94
1481
1565
6.61
6-79
1240
" A
"
"
"
35-91
0.89
1526
1639
6.52
6.76
1241
" 1
"
M
"
37-91
0.84
1569
1712
6-43
6.72
1242
" A
M
"
"
39-91
0.80
1614
1783
6.36
6.68
1243
« 5
8
M
l(
"
41.91
0.76
1658
1853
6.29
6-65
1244
" ri
M
"
"
43-91
0-73
1702
1921
6.23
6.61
1245
" f
"
"
"
45-91
0.70
1745
1988
6.17
6.58
* Spacing of rivet lines of web greater than 30 X thickness of plate. J
162
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
rTT
F
Properties 4i_ .
of ! X —
Top Chord Sections. <f
. "~y^ Four Angles
. .€L and
5 Three Plates.
i
*
J.J
LI
i
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Eccen-
i MOSS * \rv*i.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
Ifc
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches*.
Inches*.
Inches.
Inches.
16" X 19" Section. B Series.
*I246
l6xf
1 9* A
3ix3Jx|
5*3Jxf
31-37
1.90
1271
1275
6.36
6-37
1247
it i
"
'
(i
33-37
1.79
1320
1337
6.29
6-33
1248
" i
"
1
ii
35-37
1.69
1368
1398
6.22
6.28
1249
"A
M
<
M
37-37
1. 60
1417
I4S8
6.15
6.24
1250
" 1
«
1
"
39-37
1.52
1464
1516
6.10
6.2O
1251
"H
"
1
ii
41-37
1.44
1573
6.05
6.16
1252
"}
"
'
ii
43-37
i-37
1558
1629
6.00
6.13
'1253
i6xf
igxA
3i*3ixf
5x3 i*A
32-33
1.64
1345
1335
6-45
6.42
1254
"A
"
<
"
34-33
1.54
1393
6.37
6.38
1255
" i
H
1
"
36.33
1.46
1440
I4S8
6.30
6-33
1256
"A
"
'
"
38.33
1.38
1487
1518
6.23
6.29
1257
" f
u
'
"
40.33
1534
1576
6.17
6.25
1258
;; H
"
1
"
42.33
1.25
1579
1633
6. 1 1
6.21
1259
(i
1
"
44-33
1.19
1625
1689
6.05
6.17
'1260
i6xf
1 9x A
3$x3Jxf
5x3 £x£
33-27
1.40
1412
1396
6.51
6.48
1261
1262
:?
«
M
1
I!
35-27
37-27
1.32
1.25
1459
1504
1458
1519
6.42
6-35
6.42
6.38
.1263
" .*.
"
1
M
39-27
1.18
1550
1579
6.28
6-34
1264
« 5
"
'
"
41.27
I-I3
1595
1637
6.21
6.30
1265
" H
M
t
(C
43-27
1. 08
1640
1694
6.15
6.26
1266
(« 3
"
1
45-27
1-03
1685
I7SO
6.10
6.22
•"1267
i6xf
I9*A
3ix3|x|
5x3*xflf
34-21
1.17
1475
1456
6-57
6.52
1268
"A
«
'
"
36.21
1. 10
1521
1518
6.48
6.47
1269
M
"
1
(C
38.21
1.05
1565
1579
6-39
6.42
1270
"
1
H
40.21
I. CO
1610
1639
6.32
6.38
1271
" i
"
1
"
42.21
o-95
1655
1697
6.26
6-34
1272
" H
M
1
"
44-21
0.91
1699
1754
6. 20
6.30
1273
" 1
"
'
"
46.21
0.87
1743
1810
6.14
6.26
"1274
i6xf
I9XA
3Jx3Jx|
5*3jxf
35-»
0.96
1534
1514
6.61
6-57
1275
"A
"
"
H
37-n
0.91
1578
1576
6.52
6.51
1276
« I
"
1
"
0.85
1622
1637
6.44
6.46
1277
" A
"
1
M
41.11
0.82
1666
1697
6.36
6.42
1278
" f
"
1
"
43-"
0.78
1711
1755
6.29
6.38
1279
" H
"
1
"
45-"
0-75
1754
1812
6.23
6.34
1280
"i
"
1
"
47.11
0.72
1798
1868
6.17
6.30
* Spacing of rivet lines of web greater than 30 X thickness of plate.
163
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
7 ^
r
Properties 4j_ .
|^4 Four Angles
of i if.—
I_ .6 and
Top Chord Sections. q
i Three Plates.
iJJ
LI
B
Plates.
Angles.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
ross rea.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*I28l
i6xf
J9XA
31X31X|
5X3 xH
36.01
0.77
1586
1573
6.64
6.60
1282
A
'
38.01
0-73
1630
1635
6-55
6.56
1283
5
'
4O.OI
0.69
1673
1696
6-47
6.5I
1284
A
1
42.01
0.66
1717
1756
6-39
6.46
1285
I
'
44.01
0.63
1761
1814
6.32
6.42
1286
T6
1
46.01
0.60
1803
1871
6.26
6-37
1287
f
t
48.01
0-57
1847
1927
6.2O
6-33
*I288
i6xf
*9XA
31X31X|
5x3|xf
36.89
0-59
1632
1634
6.65
6.65
1289
A
it
38.89
0.56
1678
1694
6.56
6-59
1290
i
It
40.89
o-53
I72O
1755
6.48
6-55
1291
A
"
42.89
0.51
1764
1815
6.41
6.50
1292
5
8
"
44.89
0.48
1807
1873
6.34
6.46
1293
H
It
46.89
0.46
1850
1930
6.28
6.42
1294
3
"
48.89
0.44
1893
1986
6.22
6-37
16" X 20" Section. A Series.
"1295
i6xf
20xA
3x3x1
4x3x|
29-93
2.21
1180
1463
6.28
6.99
1296
" A
"
"
31-93
2.O7
1232
1550
6.21
6-97
1297
" i
H
"
u
33-93
i-95
1282
1635
6.15
6-94
1298
" A
U
n
"
35-93
1.84
1332
1719
6.09
6.92
1299
tt 5
8
It
tt
"
37-93
1.74
1382
1801
6.04
689
1300
" tt
"
tt
"
39-93
1-65
1431
1881
5-99
6.86
1301
" 1
H
"
it
41-93
1-58
1478
1959
5-94
6.84
*I3O2
i6x|
20xA
3x3x1
4x3xA
30.71
i-97
1246
1519
6-37
7.04
1303
"A
"
tt
"
32.71
1-85
1297
1606
6.30
7.01
1304
« 1
2
"
"
it
34-71
i-75
1346
1691
6.23
6.98
1305
« 9
«
it
tt
36.71
1-65
1394
1775
6.16
6.95
1306
" I
M
ti
it
38.71
i-57
1442
1857
6.10
6-93
1307
" tt
"
it
"
40.71
1.49
1490
1937
6.05
6.90
1308
It 3.
U
"
M
42.71
1.42
1536
2015
6.00
6.87
*i3°9
i6xf
20xA
3x3x1
4X3X5
31-47
1.76
1306
1576
6.44
7.08
1310
" A
It
«
33-47
1355
1663
6.36
7-05
1311
" i
tt
M
"
35-47
^$6
1402
1748
6.29
7.02
1312
" A
"
a
It
37-47
1.48
1449
1832
6.22
6.99
1313
« 5
8
"
"
it
39-47
1.40
1496
1914
6.16
6.96
1314
"H
"
"
tt
41.47
i-33
1543
1994
6.10
6-93
1315
" f
"
"
It
43-47
1.27
1589
2072
6.05
6.90
* Spacing of rivet lines of web greater than 30 X thickness of plate.
164
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
!
T1!
r
Properties A\
Of ! 11
Top Chord Sections. cf
[A Four Angles
. .~C and
r Three Plates.
JLJ
Li
li
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
r* F « A *-rtx
Eccen-
Web.
»I ( t"^S ^\ n°;i .
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*I3l6
l6xf
20X&
3x3x|
4x3frV
32.21
i-SS
1361
1631
6.50
7.12
1317
1
V
"
"
34-21
1.46
1409
1718
6.42
7.09
1318
" *
"
"
"
36.21
-38
H55
1803
6-34
7.06
1319
" I
V
"
M
"
38.21
1501
1887
6.27
7-03
1320
" i
"
"
"
40.21
•25
1548
1969
6. 20
7-00
1321
" i
i
"
H
"
42.21
.19
2049
6.15
6-97
1322
"i
"
"
it
44-21
•13
1638
2127
6.09
6-94
*I323
i6xf
20X&
3X3X|
4x3x
I
32.93
•37
1412
1685
6-55
7.16
1324
1
v
M
"
"
34-93
.29
H59
1772
646
7.12
132?
"]
M
1
"
36.93
.22
1504
1857
6.38
7.09
11326
" ^
"v
"
1
M
38.93
.16
1550
1941
6.31
7.06
1327
"i
"
1
"
40.93
.IO
1595
2023
6.24
7.03
1328
« •
"
1
1
42-93
•05
1641
2103
6.18
7.00
1329
"\
"
1
'
44-93
.00
1685
2181
6.13
6-97
'1330
i6x|
20XxV
3X3X|
4x3x1*
33-65
.19
1461
1739
6.59
7.19
i33i
1332
:l
v
H
H
H
35-65
37-65
.12
.06
1507
1551
1826
I9II
6.50
6.42
7.16
7.12
1333
^
"
M
1
39-65
.01
1596
1995
6-35
7.09
1.334
" i
•
"
M
1
41.65
0.96
1641
2077
6.28
7.06
1335
" H
i
It
"
1
43-65
0.92
1686
2157
6.22
7-03
1336
|
H
"
1
45-65
0.88
1730
2235
6.16
7.00
*i337
1338
i6x|
***
3X3X|
4x3*i
34-35
36.35
1.03
0.98
1504
1549
1794
1881
6.62
6-53
7-23
7.19
'339
it
i
It
it
"
38.35
0-93
1593
1966
6.45
7.16
134°
>
"
"
"
40.35
0.88
1638
2050
6-37
7-13
1341
«
;
M
"
"
42-35
0.84
1682
2132
6.3O
7.10
1342
" tt
H
"
"
44-35
0.80
1727
2212
6.24
7.06
1343
*< .
t
14
"
M
46.35
o-77
1770
220X}
6.18
7.03
16" X 20" Section. B Series.
*I344
i6x|
20XA
3ix3|x|
«
31.81
1.99
1288
1473
6.36
6.80 :
1345
1346
"
r
M
•
33-81
35-8i
1.87
1.76
1339
1388
1547
l62O
6.28
6.22
6.76
6.72
1347
•
fir
"
1
37-8i
1.67
H37
1691
6.16
6.68
1348
" j
;
It
1
39-81
i-59
1485
1761
6.10
6.64
1349
1350
" j
** ,
S*
«
•
41.81
43.81
1.51
1.44
1532
1579
1829
1896
6.05
6.00
6.6 1
6.58
* Spacing of rivet lines of web greater than 30 X thickness of plate.
165
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
I
Properties A±_. .1 _.._4^ Four Angles
of ! 4 -V- and
Top Chord Sections. tf <i Three Plates.
! . . "21
i«J ILJL
Plates.
Angles.
OTOSS Arcs,.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
tricity
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB-
rA
rs
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*i35i
l6xf
20X&
31X31X|
5X3 ^Xj^
32.77
1.72
1364
1541
6.45
6.85
1352
"A
"
«
"
34-77
1.62
1412
1615
6-37
6.81
1353
« *.
a
"
"
36.77
1-54
H59
1688
6.30
6-77
1354
u
M
M
38-77
1.46
1506
1759
6.23
6.74
1355
" r
H
"
N
40.77
1.39
1553
1829
6.17
6.70
1356
"H
11
"
"
42.77
1.32
1599
1897
6.66
1357
« 3
If
H
u
44-77
1.26
1646
1964
6^06
6.62
*i358
i6x|
20X;rV
3sx3|xf
5x3 |x$
33-71
1.49
1431
1609
6-51
6.91
1359
" A
H
"
"
35-71
i 40
H79
1683
6-43
6.86
1360
"i
"
"
"
37-71
1-33
1525
1756
635
6.82
1361
"A
"
"
"
39-71
1.26
1571
1827
6.29
6.78
1362
" I
"
"
M
41.71
i. 20
1617
1897
6.22
6-74
1363
" H
"
M
"
43-71
1.15
1661
1965
6.16
6.70
1364
« 3
4
"
H
M
45-71
1. 10
1707
2032
6.ii
6.66
"1365
i6xf
20X&
31X31X|
5x3ix^
34-65
1.26
1497
1677
6-57
6.96
1366
"A
M
«
a
36.65
1.19
1543
1751
6.48
6.91
1367
" i
'
"
"
38.65
1-13
1588
1824
6.41
6.87
1368
" TS
'
M
"
40.65
1.07
1633
1895
6-34
6.83
1369
« 5
8
1
M
"
42-65
i. 02
1678
1965
6.27
6-79
1370
" i~6
'
"
a
44-65
0.98
1722
2O33
6.21
6-75
i37i
« 3
*
"
"
46.65
0.94
1767
2IOO
6.15
6.71
*i372
i6x|
20Xj^
31X31X|
5x3|xf
35-55
1.05
1556
1742
6.61
7.00
1373
"A
M
"
<
3755
0-99
1600
1816
6-53
6-95
1374
« 1
u
H
1
39-55
0-94
1644
1889
6-45
6.91
1375
" Jk
"
(C
'
41-55
0.90
1698
1960
6-37
6.87
1376
1
"
H
1
43-55
0.86
1733
2030
6.31
6.83
1377
" tt
"
"
1
45-55
0.82
1777
2098
6.24
6.78
1378
» a
H
1
47-55
0.78
1822
2165
6.19
6.74
*I379
i6xf
20Xj^
31X31X|
5X35XT6
36.45
0.86
1610
1808
6.64
7.04
1380
"A
"
U
M
38-45
0.81
1655
1882
6.56
6-99
1381
" i
"
1
"
40.45
0.77
1698
1955
6.48
6-95
1382
" A
M
'
H
4245
0-73
1742
2026
6.41
6.91
1383
" I
"
i
H
44-45
0.70
1786
2096
6-34
6.87
1384
"H
"
'
"
46.45
0.67
1829
2164
6.28
6.83
1385
" a
"
1
"
0.64
1873
2232
6.22
6.79
* Spacing of rivet lines of web greater than 30 X thickness of plate.
166
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
r"
1
|
~\
r
Properties >tL .
,,i i
Top Chord Section*. </
JU
~~
-
. ..-4^ Four Angles
.C and
F Three Plates.
LI
i
Plates.
Angles.
Moments of
Radii of Gyra-
r A
Eccen-
Inertia.
tion.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches*.
Inches
Inches*.
Inches*.
Inches.
Inches.
'1386
i6xf
2oxrV
3ix3ix|
5x3 ix|
37-33
0.68
1660
1875
6.67
7.09
1387
M
H
"
39-33
0.64
1704
1949
6.58
7.03
1388
"
"
M
41-33
0.61
1747
2O22
6.50
6-99
1389
' A
"
"
"
43-33
0.58
1790
2093
6.42
6.94
1390
' 1
"
"
"
45-33
0.56
1834
2163
6.36
6.90
1391
' H
"
"
"
47-33
o-53
1876
2231
6.30
6.86
1392
' 1
M
"
"
49-33
0.51
1920
2298
6.24
6.83
18" X 21
" Section. A Series.
*I393
i8xA
2IXJ
3X3X1
4X3X
f
35-43
2.56
1712
1912
6-95
7-35
1394
"
"
"
37-68
2.40
1787
2O23
689
7-33
1395
«)
"
"
<c
39-93
2.27
1860
2132
6.82
1396
" 1
n
"
"
42.18
2.15
1931
2239
6-77
7.29
11397
" tt
H
M
H
44-43
2.04
2002
2345
6.72
7.27
1398
" i
M
"
46.68
1.94
2O72
2449
6.66
7.24
*I399
i8xA
2IXJ
3X3xf
4x3 x A
36.21
2-33
1799
1975
7-05
7-39
1400
" i
M
"
38.46
2.19
1871
2086
6-97
7-37
1401
" A
"
'I
II
40.71
2.07
1942
2195
6.91
7-35
1402
" 1
M
M
M
42.96
1.96
2OI2
23O2
6.85
7-32
1403
" H
"
"
"
45.21
1.86
2081
2408
6.79
7-3°
1404
" 1
"
"
47.46
1.78
2149
2512
6-73
7.28
*I4°5
iSxrV
:.i\\
3x3xf
4x3*1
36.97
2.12
1878
2O39
7.13
7-43
1406
" 1
"
"
M
39.22
2.OO
I948
2I5O
7-05
7-4i
1407
" A
"
"
«
41.47
1.89
2018
2259
6.98
7-38
1408
" f
"
"
"
43-72
1.79
2086
2366
6.91
7-36
1409
' H
"
"
"
45-97
1.70
2154
2472
6.85
7-33
1410
" i
"
"
48.22
1.62
2221
2576
6-79
7.31
"1411
1412
'"x*
21 \\
M
3X3X|
4
jc3xf
6
37-71
39-96
1.92
1.81
1952
2O2I
2IOO
2211
7.20
7.11
7-46
7-44
1413
" A
"
"
"
42 21
172
2089
232O
7-03
7-42
1414
" f
"
M
"
4446
1-63
2155
2427
6.96
7-39
1415
1416
"t
M
M
M
"
46.71
48.96
i-55
1.48
2222
2288
2533
2637
6.90
6.84
7-36
7-34
* Spacing of rivet lines of web greater than 30 X thickness of plate.
167
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
F*^
r
Properties -^J--.
of
Top Chord Sections. q
. 44 Four Angles
•?- and
£ Three Plates.
i
. If
LJI
j
}
LJL
Plates.
Angles.
Gross Area.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Bottom.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches'.
Inches.
Inches.
*I4I7
I8X&
21x5
3*3*1
4X3X
t
38-43
1.74
2O2I
2l6o
7-25
7-5°
1418
" 5
M
u
H
40.68
1.64
2088
2271
7.17
7-47
1419
" 9
H
U
It
42.93
i-SS
2154
2380
7.09
7-45
1420
" I'
«
H
"
45.18
1.48
222O
2487
7.01
7.42
1421
" H
(C
M
(C
47-43
1.41
2286
2593
6-94
7.40
1422
« 3
4
"
H
49.68
i-34
2351
2697
6.88
7-37
*H23
i8x^
2IX§
3X3X|
4X3X1
i
39-15
1-56
2087
2221
7-30
7-53
1424
" 5
M
((
M
41.40
1.47
2153
2332
7.21
7-51
1425
«< 9
TF
"
It
H
43-65
1.40
2219
2441
7-13
7.48
1426
" 8
H
ii
(C
45-90
1-33
2283
2548
7-05
7-45
1427
« 11
16
"
ft
"
48.15
1.27
2348
2654
6.98
7-43
1428
« 3.
"
11
"
50.40
I.2I
2412
2758
6.92
7.40
*I429
I8X;&
2IXJ
3X3xf
4X3 X
1
39-85
I.4O
2146
2282
7-34
7-57
H30
" 1
"
'
"
42.10
1.32
2212
2393
7-25
7-54
1431
« 9
TS
"
c
M
44-35
1.25
2276
25O2
7.16
7-Si
H32
It 5
H
'
(C
46.60
I.I9
2340
2609
7.09
7.48
1433
« 11
16
"
1
"
48-85
I.I4
2404
2715
7.02
746
H34
" 1
"
M
51.10
1.09
2467
2819
6-95
7-43
18" X 21" Section. B Series.
*H35
i8x|
2IX1
31X31X|
5X32X
3
35.06
2-49
1779
1805
7.12
7.18
" A
II
<«
H
37-31
2-34
1853
I9OI
7-°5
7.14
H37
" i
M
ft
H
2.21
1925
1996
6.98
7.10
u 9
"
It
"
41.81
2.09
1995
2O9O
6.91
7.07
H39
" 5
8
II
It
"
44.06
1.98
2065
2183
6.84
7.04
1440
" H
"
U
M
46.31
1.89
2135
2275
6.79
7.01
1441
" f
"
It
(C
48.56
1. 80
22O4
2366
6-74
6.98
*I442
I8xf
21X5
3ix3|xf
5X3 5X-
&
36.02
2.21
1883
1880
7-23
7-23
*H43
" 1^6
II
"
"
38.27
2.08
1954
1977
7.14
7.19
1444
"*
"
(C
"
40.52
1.97
2O24
2O72
7.06
7-iS
H45
" A
H
M
tt
42-77
1.86
2O93
2l66
6-99
7.12
1446
« 5
8
M
M
"
45.02
1.77
2161
2259
6-93
7.09
H47
" H
M
It
ft
47.27
1.69
2229
2351
6.87
7.06
1448
« 3
"
"
"
49-52
1.61
2296
2443
6.81
7-03
* Spacing of rivet lines of web greater than 30 X thickness of plate.
168
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
Properties -A'.
of ! _.._ l.._±.._
Top Chord Sections. (f
T
_mm lA Four Angles
_ .«! and
> Three Plates.
*
J.JI
LL
i
Plates.
Angles.
Moments of
Radii of Gyra-
»r<)->s A i ' '. i .
Eccen-
Inertia.
tion.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches'.
laches.
Inches*.
Inches4.
Inches.
Inches.
*I449
itei
21 Cj
3i*3*xf
5X3^xJ
36.96
1.96
1975
1957
7-31
7-28
"A
M
"
"
39-21
1.84
2045
2053
7.22
7.24
1451
" i
"
"
"
41.46
1.74
2112
2147
7.14
7.20
1452
H53
f
"
M
M
43-71
45.96
I.6S
1-57
2180
2247
2242
2335
7.06
6-99
7.16
7-13
1454
1 ft
"
"
1C
48.21
1.50
2313
2427
6-93
7.10
H5S
" I
"
H
"
50.46
i-43
2379
2518
6.87
7.07
*i456
I8xl
2lxj
3J*3$xf
5*3JUA
37-90
1.71
2066
2033
7.38
7-32
*i457
uP
"
"
40.15
.61
2134
2129
7.29
7.28
1458
" *
"
"
M
42.40
•53
22OO
2224
7.19
7.24
1459
" A
H
"
M
44.65
•45
2265
2318
7.12
7.21
1460
« t
M
M
"
46.90
•38
2331
2411
7.05
7-17
1461
" H
"
"
"
49.15
•32
2395
2503
6.98
7.14
1462
"i
(C
"
"
51.40
.26
2460
2594
6.92
7.10
'1463
l8xf
2IXJ
3Jx3j.\2
S^3ix|
38.80
.48
2145
2106
7-44
7-37
*i464
" A
"
"
"
41.05
.40
2211
2203
7-34
7-33
1465
" it
"
M
H
43-30
•33
2276
2298
7.25
7.29
1466
" A
"
M
"
45-55
.26
2340
2392
7.17
7-25
1467
" 1
"
ff
"
47.80
.20
2405
2485
7.09
7.21
1468
"ft
"
M
"
' 50-05
•IS
2439
2577
7.02
7.18
1469
" i
"
"
"
52.30
.10
2532
2668
6.96
7.14
*i470
i8x|
2IxJ
j.lxv'.xi;
5x35xi«
39-70
.27
2224
2l8o
7-47
7.41
*H7i
u¥
"
"
"
41.95
.20
2288
2276
7.38
7-37
1472
*
"
"
44.20
.14
2351
2371
7.29
7-33
1473
" A
"
"
"
46.45
.09
2415
2465
7.21
7.29
1474
" t
M
(C
"
48.70
.04
2478
2558
7-13
7.25
H75
" H
"
M
"
50.95
0.99
2542
2650
7.06
7.21
1476
"i
"
"
M
53-20
0.95
2604
2741
7.00
7.18
;i477
i8x|
2IXJ
3i*3$xf
5X3^XJ
40.58
i. 08
2293
2255
7-Si
7-45
"A
M
!<
"
42.83
i. 02
2356
2351
7.42
7.41
H79
" *
"
"
"
45.08
0.97
2419
2446
7-32
7-37
1480
« 9
"
"
M
47-33
o-93
2481
2540
7.24
7-33
1481
" 1
"
(C
"
49.58
0.89
2546
2633
7.16
7.29
1482
» 11
H
M
"
5I-83
o.8c
2607
2725
7.09
7.25
H83
"i
M
"
54.08
0.8 i
2670
2816
7.03
7.21
* Spacing of rivet lines of web greater than 30 X thickness of plate.
50
169
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
T"t=
Properties A\
of ! —
Top Chord Sections. a,
= =4=3
Trp=>
)
.__[A Four Angles
.. .C and
i Three Plates.
•
1
fl
Li
i
Plates.
Angles.
Moments of
Radii of Gyra-
Inertia.
tion.
"* »-rtoq A TPa
Eccen-
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B .
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
18" X 22" Section. A Series.
*I484
i8x&
22x|
3X3X|
4x3x1
35-93
2.65
1735
2170
6-95
7-77
" 5
M
"
H
38.18
2-49
1811
2297
6.89
7.76
1486
"A
II
II
U
40.43
2.35
1885
2422
6.83
7-74
1487
" f
II
II
II
42.68
2.23
1957
2545
6-77
7-72
1488
"H
M
M
"
44-93
2.12
2028
2667
6.72
7.70
1489
<< 3.
M
M
47.18
2.02
2099
2787
6.67
7-68
*I490
I 8X;&
22x|
3x3xf
4X3 x A
36.71
2.42
1823
2240
7-°5
7.81
1491
" 5
"
ft
"
38.96
2.28
1896
2367
6.98
7.80
1492
" TS
"
"
H
41.21
2.l6
1968
2492
6.91
7-78
H93
« 5
a
M
"
4346
2.OS
2038
2615
6.85
7-76
1494
"ft
M
Cl
"
45-71
1.94
2108
2737
6-79
7-74
1495
"f
M
U
47.96
1.85
2177
2857
6.74
7.72
*I496
I8X;&
22X|
3x3xf
4X3X|
37-47
2.21
1904
23IO
7-13
7.85
H97
" i
"
M
tt
39-72
2.O9
1975
2437
7-05
7-83
1498
"A
II
"
u
41.97
1.97
2045
2562
6.98
7-8i
1499
" f
a
"
"
44.22
1.87
2114
2685
6.92
7-79
1500
"ft
II
M
II
46.47
I.78
2182
2807
6.85
7-77
1501
» 3.
M
II
II
48.72
1.70
2250
2927
6.80
7-75
*I5°2
i8xA
22XJ
3X3X|
4x3 x rs
38.21
2.O2
1979
2379
7.20
7.89
1503
"1
M
U
H
40.46
I.9O
2048
2506
7.12
7-87
" A
II
II
U
42.71
1. 80
2117
2631
7.04
7-85
1505
" 1
U
"
U
44.96
I.7I
2184
2754
6-97
7-83
1506
"H
H
II
"
47-21
1.63
2251
2876
6.90
7-8o
1507
(C 3
I
U
II
49.46
1-56
2318
2996
6.85
7-78
*i5o8
l8Xj5_
22x£
3x3x1
4X3X|
38.93
1.83
2049
2445
7.26
7-93
I5°9
it 1
"
"
"
41.18
i-73
2118
2572
7.17
7.90
1510
" _»-
16
"
"
"
43-43
1.64
2185
2697
7.09
7.88
1511
« 5
8
«
(I
"
45.68
1.56
2251
2820
7.02
7-86
1512
" ii
"
"
M
47-93
1.49
2317
2942
6-95
7.84
1513
« 3
4
M
50.18
1.42
2383
3062
6.89
7.81
* Spacing of rivet lines of web greater than 30 X thickness of plate.
170
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
]
T ^
r
Properties Ai
of i -I
Top Chord Sections. <f
._lfl Four Angles
. .€. and
it Three Plates.
_j
LI
i
I'Uitos.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
i I ( )^S A I « ' I
Eccen-
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inchea*.
Inches4.
Inches.
Inches.
*I5I4
iSxrV
22xJ
3X3x1
4x3xft
39-6S
.65
2116
2513
7-30
7.96
ISIS
" *
"
H
"
41.90
•57
2183
2640
7-22
7-94
1516
" A
"
M
it
44.15
•49
2249
2765
7.14
7-92
1517
" s
H
"
u
46.40
.41
2888
7.06
7.89
1518
" \6
"
"
M
48-65
•34
2379
3010
6.99
7.87
1519
" 1
"
"
"
50.90
.29
2444
3130
6-93
7.84
1521
•nA
22XJ
3x3x1
4x3x1
40-35
42.60
•49
2177
2243
2581
2708
7-35
7.26
8.00
7-97
1522
* ^
"
It
"
44.85
•34
2308
2833
7.17
7-95
1523
1 7
"
"
"
47.10
.28
2372
2956
7.09
7.92
1524
1 ri
"
"
M
49-35
.22
2437
3078
7-03
7.90
1525
' i
«
"
M
51.60
•17
2501
3198
6.96
7.87
1
18" X 22" Section. B Series.
^1526
i8x|
22XJ
35X33xf
5x3|xf
35-56
2-59
1801
2052
7.II
7.60
" A
"
"
M
2-43
1877
2l66
7-05
7-57
Is28
a i
M
"
"
40.06
2.3O
1950
2277
6.98
7-54
1529
"rV
"
H
"
42-31
2.17
202 1
2386
6.92
7-51
1530
" f
"
"
M
44.56
2.O6
2093
2493
6.86
.7-48
1531
1532
"-?
M
'
M
46.81
49.06
1.96
1.87
2163
2232
2599
2702
6.80
6-75
7-45
7.42
*IS33
i8xf
22Xj
33X33Xf
5X33XT5
36.52
2.31
1906
2137
7-23
7-65
*I534
" TV
"
1
M
38.77
2.18
1978
2250
7.14
7.62
1535
« i
M
1
M
41.02
2.O6
2049
2361
7.07
7-59
1536
"A
"
'
It
43-27
1-95
2118
2470
7.00
7.56
1537
" f
"
'
It
45-52
1.85
2188
2577
6-93
7-53
1538
1539
'f
«
'
M
47-77
50.02
1.76
1.68
2257
2324
2683
2787
6.87
6.82
7-50
7-47
*iS4o
l8x|
22xJ
33X33xf
5x3ixj
3746
2.05
2OO2
2222
7.31
7.70
*iS4i
" TV
(i
"
"
39-71
i-93
2O72
2335
7.22
7.67
1542
« i
"
"
M
41.96 .
1.83
214!
2446
7.14
7.64
1543
" A
M
"
"
44.21
1.74
2208
2555
7.06
7.60
1544
" f
"
It
"
46.46
1.65
2276
2662
7.00
7-57
1545
" tt
"
«
"
48.71
1.58
2343
2768
6-94
7-54
1546
" i
"
"
50.96
1. 15
2409
2872
6.88
7-Si
* Spacing of rivet lines of web greater than 30 X thickness of plate.
171
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
Properties -4j -
of : 4— -
Top Chord Sections. £f
f"
. .---i^ Four Angles
£- and
^ Three Plates.
1J1
LJL
Plates.
Angles.
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
JTOSS Area..
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches. 1
*i547
i8xf
22x|
3IX3IX|
5x32X^6
38.40
I.8I
2093
2306
7-38
7-75
"1548
" A
"
"
K
40.65
I.7I
2161
2419
7.29
7-71
1549
« i
"
"
"
42.90
.62
2229
2530
7.21
7.68
1550
"A
u
H
M
45-15
•54
2294
2639
7-13
7.64
i55i
" 1
• "
14
H
47.40
•47
2360
2746
7.06
7-61
1552
" it
(4
"
M
49.65
.40
2426
2852
6-99
7-58
1553
n 3
4
M
M
M
51.90
•34
2491
2956
6-93
7-54
*i554
i8xf
22x|
35X3^x|
Sx3ix|
39-30
•58
2177
2388
7-44
7.80
*i555
" A
"
"
"
41-55
•50
2243
2502
7-35
7.76
1556
" i
"
M
"
43.80
.42
2309
2613
7.26
7-73
1557
u 9
II
"
(I
46.05
•35
2373
2722
7.18
7.69
1558
« 5
8
"
"
"
48.30
.29
2438
2829
7.11
7-66
1559
" H
"
"
"
50.55
•23
2502
2935
7.04
7.62
1560
" i
H
"
U
52.80
1.18
2566
3039
6.97
7-59
"1561
i8xf
1
3|X31X|
5x3ixii
40.20
i-37
2255
2470
7-49
7.84
*i562
" A
"
"
"
42.45
1.30
2320
2584
7-39
7.80
1563
" a
"
U
"
44.70
1.24
2385
2695
7-30
7-77
1564
" A
M
M
u
46.95
1.18
2448
2804
7.22
7-73
1565
" I
n
"
"
49.20
1. 12
2512
2911
7-iS
7.69
1^66
" H
"
"
M
51-45
1.07
2576
3017
7.08
7.66
1567
« 3
4
M
*'
M
53-70
I.O3
2639
3121
7.01
7-63
*I568
i8x|
22x£
stoixi
5X3 ?Xf
41.08
1.18
2326
2553
7-53
7-89
'1569
" 7
"
"
"
43-33
1. 12
2390
2667
7-43
7-85
1570
" 1
"
"
U
45.58
I. O6
2454
2778
7-34
7.81
1571
" A
M
"
14
47.83
I.OI
2516
2887
7-25
7-77
1572
- " 1
U
"
"
50.08
0.97
2579
2994
7.17
7-73
1573
" it
II
«
"
52.33
0-93
2642
3IOO
7.11
7.70
1574
« 3.
"
"
54.58
0.89
2705
3204
7.04
7.66
20" X 23" Section. A Series.
*I575
20X|
23 x£
3ix3ix|
5x3lx|
42.56
2.51
2530
2697
7.71
7-97
1576
A
"
"
"
45.06
2-37
2628
2836
7.64
7-94
1577
" I
"
"
"
47.56
2.25
2724
2973
7-57
7.91
1578
66 1 1
"
"
H
50.06
2.13
2820
3107
7.51
7.88
1579
" 1
**
M
"
52-56
2.03
2914
3239
7-45
7-85
* Spacing of rivet lines of web greater than 30 X thickness of plate.
172
TABLE St.— Continued.
PROPERTIES OF Top CHORD SECTIONS.
\
— j i
fl
r
Properties A±_
of 1
Top Chord Sections. d
4=
L4 Four Anglo
1 .._L".~«I and
Three Plato.
JLJ
j
i
Q
Plates.
Angles.
Cross An -a.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
.tion.
Web.
Bottom.
Axis.
Axis
Axis
Axis
Section
Number.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
IB
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
inches4.
Inches.
Inches.
*I580
20XJ
23 xj
3ix3ixf
5
x3ix
A
43-52
2.25
2655
2790
7.8l
8.01
1581
V
M
"
"
46.02
2.13
2750
2929
7-73
7.98
1582
-
"
"
"
48.52
2.O2
2844
3066
7.66
7-95
1583
1584
"i
i
««
it
"
51.02
53-52
1.92
1.83
2938
3029
3200
3332
7-59
7.52
7.92
7.89
•1585
20XJ
23xJ
3ix3Jx|
•X3$x
j
44.46
2.O2
2769
2884
7.89
8.06
1586
1587
"i
V
«
H
«<
H
46.96
49.46
I.9I
.82
2862
2954
3023
3160
7.81
7-73
8.03
8.00
I588
1589
?!
1
it
it
U
M
«
51.96
5446
•73
•65
3046
3136
3294
3426
7.66
7-59
7.96
7-93
*I590
20XJ
23xi
3*x3Jxf
5
*3ix
A
45.40
•79
2880
2978
7-97
8.10
1591
" :
V
M
"
"
47.90
•70
2971
3"7
7.89
8.07
1592
" \
"
"
"
50.40
.62
3061
3254
7.80
8.04
1593
;;-
i
"
"
"
52.90
•54
3ISI
3388
7.72
8.00
1594
«' :
1
«(
M
**
55-40
•47
3239
3520
7.64
7-97
*I59S
20x3
I
23xJ
3*x3*xf
5X3 ixf
46.30
i-59
2980
3068
8.03
8.14
1596
'* •
%
M
"
M
48.80
1.50
3069
3207
7-93
8. u
1597
M
"
H
5I-30
1-43
3158
3344
7-85
8.07
1598
"
*
U
"
"
53-80
1.36
3247
3478
7-77
8.04
1599
H
H
M
56-30
1.30
3334
3610
7.70
8.01
*i6oo
20X|
23xi
3i*3ix!
5
*3*x
H
47-20
•39
3077
3159
8.08
8.18
1601
"
*
<«
"
"
49.70
.32
3164
3298
7.98
8.14
1602
«
M
"
"
52.20
.26
3251
3435
7.90
8.11
1603
" t*
"
u
"
54-70
.20
3339
3569
7.82
8.08
1604
**
t
H
H
"
57-20
•15
3426
3701
7-74
8.05
*'£l
20X<
23xi
3*x3ix|
5x3iJ
1
48.08
.21
3164
3251
8.ii
8.23
1606
1607
((
"
[
(i
M
«
50.58
53.08
•IS
.09
3250
3336
3390
3527
8.02
7-93
8.19
8.15
1608
«
£
M
"
M
55-58
.04
3423
3661
7-85
8.12
1609
I
M
58.08
1 .00
3509
3793
7-77
8.08
* Spacing
of rivet lines of web greater than 30 X thickness of plate.
173
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
r
1
3
1
r
Properties <A.\
of { "..- L..JI
Top Chord Sections. c{
\A. Four Angles
1 — ."?* and
JT Three Plates.
i .
. T
1=41
IU.I
1
Plates.
Angles.
Moments of
Radii of Gyra-
Eccen-
Inertia.
tion.
Bottom.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
20" X 23" Section. B Series.
*i6io
20X&
23x5
4x4xA
6x4x3^
43-98
2.29
2782
2721
7-95
7.86
1611
2
tt
tt
"
46.48
2.17
2877
2845
7.87
7.82
1612
"
n
"
48.98
2.06
2973
2966
7-79
7-78
1613
"
ft
{*
51.48
1.96
3066
3085
7.72
7-74
1614
" it
tt
tt
it
53.98
1.87
3158
3202
7-65
7.70
1615
ft 3.
tt
ti
tt
56.48
I.78
3250
3317
7-58
7.66
*i6i6
20XrV
23XJ
- 4x4x3^
6x4x5
45.12
2.OI
2919
2832
8.04
7.92
1617
" 2
'
u
"
47.62
I.9I
3012
2956
7-95
7.88
1618
" A
'
tt
"
5O.I2
1.81
3104
3077
7.87
7.84
1619
" I
t
If
it
52.62
1-73
3195
3196
7-79
7-79
1620
"it
I
If
tt
55-12
1-65
3285
3313
7.72
7-75
1621
tt 3
'
tt
n
57.62
1.58
3376
3428
7-6S
7.71
*l622
20XA
23*2
4x4x1^
6x4xr
k
46.24
i-75
3050
2941
8.12
7-97
1623
2
U
"
it
48.74
1.66
3065
8.03
7-93
1624
"p
tt
"
it
51.24
1.58
3230
3186
7-94
7.88
1625
ii 5
8
tt
"
tt
53-74
3319
3305
7.86
7-84
1626
" tt
tt
tt
ft
56.24
1.44
3408
3422
7-78
7.80
1627
" f
It
n
58.74
1.38
3497
3537
7.72
7.76
*i628
20X&
23x5
4x4xA
6x4x
\
47-34
i-Si
3170
3048
8.18
8.02
1629
" 5
tt
"
"
49.84
1-43
3258
3172
8.08
7.98
1630
ft 9
tt
tt
tt
52-34
1.36
3347
3293
8.00
7-93
1631
" r
"
"
"
54-84
1.30
3434
3412
7.92
7.89
1632
" tt
a
"
tt
57-34
1.24
3529
7-84
7.84
1633
« 3
4
it
tt
59-84
1.19
3609
3644
7-77
7.80
"1634
20X3*5
23*£
4x4xA
6x4xf
\
48.42
1.28
3279
3157
8.23
8.08
1635
« 1
M
"
"
50.92
1.22
3366
3281
8.13
8.03
1636
"*
tt
"
"
53-42
1.16
3453
3402
8.04
7.98
1637
" I
tt
"
n
55-92
I. II
3539
3521
7.96
7-94
1638
" tt
"
"
tt
58.42
1. 06
3625
3638
7.88
7.89
1639
" f
60.92
1. 02
3712
3753
7.81
7-85
* Spacing of rivet lines of web greater than 30 X thickness of plate.
174
TABLE M.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
p
1
r
Properties •&
of I ---
Top Chord Sections.
J-=
= =f=
J
--J^' Four Anglo
,» Three Plates.
L.1
Plates.
Angles.
Gross Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
TA
rB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches*.
Inches4.
Inches.
Inches.
*l64O
20X&
23*i
4x4x5^
6x4xf
49-5°
1. 06
3384
3265
8.27
8.12
1641
" i
"
u
"
52.00
1. 01
3470
3389
8.17
8.07
1642
" A
H
"
"
54-50
0.96
3556
3510
8.08
8.02
1643
" t
H
H
M
57-00
0.92
3641
3629
7-99
7.98
1644
" H
"
"
"
59-50
0.88
3726
370
7.91
7-93
1645
" 1
"
"
M
62.00
0.85
3861
7.84
7.89
20" X 24" Section. A Series.
*l646
20xJ
24X&
stab!
5x3Jx|
44.56
2.87
2651
3104
7.71
8-35
1647
" .*.
tt
"
"
47.06
2.71
2754
3262
7-65
8-33
1648
" 1
"
u
"
49-56
2-57
2855
3418
7-59
8.31
1649
" M
"
"
M
52.06
2-45
2954
3572
7-54
8.29
1650
" f
"
"
M
54-56
2-34
3051
3724
748
8.27
*i6si
20xi
24x&
3ix3^xf
5x3lxA
45-52
2.61
2784
3207
7.82
8-39
1652
" A
"
«
"
48.02
2.48
2883
3365
7-75
8.37
1653
" f
"
"
M
50.52
2.36
2980
3521
7.68
8-34
1654
" H
"
"
"
53-02
2.25
3077
3675
7.62
8.32
1.655
" i
M
"
55-52
2.14
3173
3827
7.56
8.30
*i6s6
20X1
24X&
3ix3|xf
5x3jxJ
46.46
2.38
2907
3310
7.91
8-44
1657
" A
"
u
48.96
2.26
3003
3468
7.83
8.41
1658
" I
it
"
"
51.46
2.15
3098
3624
7.76
8-39
1659
1660
::»
a
M
«
SI'^
56.46
2.05
1.96
3193
3286
3778
3930
7.69
8-37
8.34
*i66i
20x|
24X&
3|X3JX|
5x3jxA
47.40
2.16
3024
3413
7.98
8-49
1662
" *
"
«
49.90
2.05
3118
3571
7-90
8.46
1663
" 4
M
"
"
52.40
i-95
3211
3727
7.83
8.44
1664
« 11
"
"
"
54-90
1.86
3305
3881
7.76
8.41
1665
" I
"
"
"
57-40
1.78
3396
4033
7-69
8.38
*i666
20X*
24xA
3h3Jxf
5x3Jx|
48.30
1.95
3132
3513
8.05
8-53
1667
" A
u
"
"
50.80
1.86
3224
3671
7-97
8.50
1668
« 5
"
"
a
53.30
1.77
3315
3827
7.89
847
1669
" ii
"
"
"
55.80
1.69
3407
3981
7.81
845
1670
" i
H
"
«
58-30
1.62
M97
4133
7-74
842
| * Spacing of rivet lines of web greater than 30 X thickness of plate.
175
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
T" ^
r
Properties -4o ..
of ! 1L...
Top Chord Sections. ,«
l^ Four Angles
*. and
^ Three Plates.
JLJ
L.1
£
Plates.
Angles.
Moments of
Radii of Gyra-
Inertia.
tion.
r* fyyn a A ff»Q
Eccen-
Bottom.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*i67i
20x|
24*11?
3^x35xf
SX31X.
ti
49.20
1.76
3234
3613
8.II
8-57
1672
a g
u
"
M
5I-70
1.67
3325
3771
8.02
8-54
1673
ti ¥
It
it
11
54-20
1. 60
34H
3927
7-94
8.51
1674
« u,
16
tt
"
"
56.70
i-53
3504
4081
7.86
8.48
1675
"*
"
u
"
59-20
1.46
3593
4233
7-79
8-45
*i676
20x|
24X&
3|x3-|xf
5x3^x
i
50.08
i-57
3329
37H
8.15
8.61
1677
"A
it
tt
"
52.58
1.50
3872
8.06
8.58
1678
" I
"
K
"
55-08
i-43
35o6
4028
7.98
8-55
1679
"H
tt
"
"
57.58
1-37
3595
4182
7-90
8.52
1680
" f
H
"
"
60.08
3683
4334
7-83
8-49
20" X 24" Section. B Series.
*i68i
20X^
24X&
4x4xrV
6x4x1
6
45.98
2.65
2910
3134
7-95
8.26
1682
" 5
1
tt
"
48.48
2.51
3009
3276
7.88
8.22
1683
rV
'
"
"
50.98
2-39
3108
3415
7.81
8.18
1684
" 1
t
11
"
5348
2.28
3205
3552
7-74
8.15
1685
« 11
I
"
it
55.98
2.17
3300
3687
7.68
8.H
1686
« 3
4
1
it
tt
58.48
2.08
3396
3820
7.62
8.08
*i687
20Xi^
24X5^
4x4x1^
6x4xi
\
47.12
2-37
3056
3257
8.05
8.31
1688
" \
'
tt
<
49.62
2.25
3152
3399
7-97
8.28
1689
" T$
c
"
i
52.12
2.14
3248
3538
7.90
8.24
1690
8
t
"
'
54.62
2.05
3343
3675
7.82
8.20
1691
" ii
t
H
1
57-12
1.96
3435
3810
7-76
8.17
1692
" a.
'
U
1
59.62
1.87
3528
3943
7.69
8-13
"1693
20X175-
24XTS
4X4Xj^
6x4x5^
48.24
2. II
3194
3375
8.14
8-37
1694
" 5
"
it
"
50-74
2.OI
3288
3517
8.05
8-33
1695
« 9
"
It
tt
53-24
I.9I
338i
3656
7-97
8.29
1696
" ¥
u
"
"
55-74
1-83
3473
3793
7.89
8-25
1697
n 1^
"
It
tt
58.24
i-75
3564
3928
7.82
8.21
1698
" 1
"
"
tt
60.74
1.68
3655
4061
7.76
8-17
"1699
20Xj^
24*11?
4X4XTV
6X4X;
\
49-34
1.87
3323
3495
8.21
8.41
1700
.- i.
"
H
"
51.84
1.78
34H
3637
8.12
8.38
1701
" T6
tt
"
tt
54-34
1.70
3506
3776
8.03
8-34
1702
" I
"
tt
tt
56.84
1.62
3595
3913
7-95
8.30
1703
"H
it
"
tl
59-34
1-55
3685
4048
7.88
8.26
1704
" i
i(
'*
"
61.84
1.49
3775
4181
7.81
8.22
* Spacing of rivet lines of web greater than 30 X thickness of plate.
176
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
. I '
T h
F
Properties 4J_
of f -~-~ -T^4-~
Top Chord Sections. ((
1 J j
\A Four Angles
CP and
Three 1'lates.
Li
i
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
f - . \
Eccen-
Uross AM
tricity.
Axis
Axis
Axis
Axis
S.-i-tion
N umber.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
TA
rB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches*.
Inches.
Inches.
*I70S
20X&
24*1*
4x4x3^
6x4X1^
50.42
.64
3441
3615
8.26
8-47
1706
i
"
52.92
•57
3530
3757
8.17
8-43
1707
16
"
5542
.50
3620
3896
8.08
8-39
1708
|
"
57.92
43
3708
4033
8.00
8-35
1709
ii
"
60.42
•37
3796
4168
7-93
8.31
1710
i
62.92
•32
3885
4301
7.86
8.27
•1711
20X&
24X&
4x4x3^
6x4X4
5I-50
1-43
3554
3733
8.31
8.51
1712
i
"
54.00
1.36
3642
3875
8.21
8.47
1713
rs
"
56.50
1.30
3730
4014
8.12
8.43
1714
1
"
59-00
1.25
3817
4l5l
8.04
8-39
1715
ii
"
61.50
i. 20
3904
4286
7-97
8-35
1716
" i
"
64.00
I-I5
3992
4419
7.90
8.31
22" X 25" Section. A Series.
\7\l
2?f
25X&
Sixtfxft
5*3*4
52.55
55-30
2-57
2-44
3839
3967
4129
4323
8-55
8.47
8.87
8.84
1719
1720
-r
H
«
«
58-05
60.80
2-33
2.22
4093
4219
45H
4703
8.40
8-33
8.82
8.80
•1721
22X&
25X&
3ix3|x&
5x3 i* A
5349
2-35
3983
4242
8.63
8.90
1722
" f
H
"
a
56.24
2.24
4108
4436
8-54
8.88
1723
1724
•r
«
«
«
58.99
61.74
2.14
2.O4
4232
4355
4627
4816
8-47
8.40
8.86
8.83
*I725
22X&
25X&
3ix3ixt»-
Sx3ixf
54-39
2.15
4116
4350
8.70
8.94
1726
" ^
"
"
"
57-H
2.O5
4238
4544
8.61
8.92
1727
" H
14
"
"
59.89
i-95
436i
4735
8-53
8.89
1728
" t
II
"
"
62.64
1.86
4483
4924
8.46
8.87
*I729
22X-&
25X&
3ix3Jx&
5x33x^5
55-29
1.96
4242
4460
8.76
8.98
1730
" i
u
"
«<
58.04
1.86
4363
4654
8.67
8.96
I73i
" tt
"
«
"
60.79
1.78
4483
4845
8-59
8-93
1732
" i
1.70
4603
5034
8.51
8.90
* Spacing of rivet lines of web greater than 30 X thickness of plate.
177
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
T"<
t
1
r
Properties A\
[A Four Angles
of I "..- l.._Il
1 L".T<|_ and
Top Chord Sections. d
^ Three Pktes.
L
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
(~* A
Eccen-
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottcm.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*i733
22X^
2SX9
3ix3ix^
5x3Jxf
56.17
1.77
4361
4570
8.8l
9.O2
1734
" I
u
"
58.92
1.69
4480
4764
8.72
8.99
1735
" H
"
"
tt
61.67
1.62
4598
4955
8.63
8.96
1736
" t
"
u
"
64.42
i-SS
4716
5H4
8-55
8-93
22" X 25" Section. B Series.
*i737
22X1
25xA
4x4XiV
6x4x3
52.18
2-47
3974
3939
8-73
8.69
*I738
" rV
"
"
a
54-93
2-34
4102
4"3
8.64
8.65
1739
" I
u
"
"
57-68
2.23
4227
4284
8.56
8.62
1740
"H
"
"
it
60.43
2.13
4351
4453
8.49
8.58
1741
" i
H
M
"
63.18
2.04
4473
4620
8.41
8-55
*i742
22x£
25XiV
4x4xrV
6x4Xj^j-
53.30
2.21
4141
4070
8.81
8.74
*i743
"A
«
«
"
56-05
2.IO
4265
4244
8.72
8.70
1744
" I
u
M
"
58.80
2.OO
4388
4415
8.64
8.67
1745
" ii
"
"
"
6i-55
I.9I
4509
4584
8.56
8.63
1746
" 3
"
"
"
64.30
1.83
4630
4751
8-49
8.60
*i747
22XJ
25X&
4x4fTV
6x4xf
54-40
1.96
4299
4200
8.89
8.79
*I748
tt 9
rs
"
u
57-iS
1.87
4419
4374
8.79
8-75
1749
" I
"
it
"
59-90
I.78
4539
4545
8.70
8.71
1750
" H
n
it
"
62.65
1.70
4659
47H
8.62
8.67
1751
" 3.
"
ft
"
65.40
1.63
4778
4881
8-54
8.64
*i752
22X|
25xA
4X4X&
6x4xii
5548
1.74
4441
4331
8-95
8.84
*I753
" A
"
M
58-23
1.66
456o
4505
8.85
8.80
1754
(( 5
8
"
"
a
60.98
1-58
4678
4676
8.76
8.76
1755
" 11
16
"
H
"
6373
1.51
4796
4845
8.68
8.72
1756
« 3
4
"
tt
M
66.48
i-45
4913
5012
8.60
8.68
*I757
22x|
25X;&
4X4X&
6x4x|
56.56
1-52
4580
4461
9.00
8.88 1
*i7S8
" rs
M
"
"
59-31
1-45
4697
4635
8.90
8.84
1759
« 5
8
"
•*
tt
62.06
i-39
4814
4806
8.81
8.80
1760
" H
"
u
u
64.81
1-33
4930
4975
8.72
8.76
1761
" a
"
M
"
67.56
1.27
5046
SH2
8.64
8-73
* Spacing of rivet lines of web greater than 30 X thickness of plate.
178
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
T"t
J
r
Properties -il_ j
of ! 4
Top Chord Sections. 4
. ..-y^- Four Angles
*L and
5 Three Plates.
JLJ
Li
*J. ^_^«AJ
i
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
f* t-naa A rt*r\
Eccen-
JIOSS /ViCcl.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
22" X 26" Section. A Series.
'1762
"2X&
26xf'
3sx3^xA
5X3 i*i
54-74
2-93
4006
4681
8.56
9-25
1763
" 1
"
«
ii
57-49
2.80
4138
4901
8.48
9-23
1764
" H
u
"
M
60.24
2.67
4270
5116
8.41
9-21
1765
M J
"
"
"
62.99
2-54
4402
5326
8.36
9.19
*I766
22X&
26xf
3jX3JxA
5*3j*&
55-68
2.71
4160
4804
8.64
9.29
1767
" I
t<
«
58-43
2-59
4289
5024
8-57
9.27
1768
"tt
M
u
H
61.18
2-47
4418
5239
8.50
9-25
1769
" 1
"
M
"
63-93
2.36
4546
5449
8-43
9-23
*i77o
22X&
26xf
3 23 2 16
5X35X|
56.58
2.51
4300
4923
8.72
9-33
1771
" I
"
"
"
59-33
2.40
4427
5H3
8.64
9.31
1772
" li
"
"
"
62.08
2.29
4554
5358
8-57
9.29
1773
" J
"
"
"
64-83
2.19
4679
5568
8.50
9.27
*I774
22X&
26x|
3 53 2 X"jo
5X3 hit
5748
2.32
4436
5042
8.78
9-37
1775
" f
"
"
ft
60.23
2.21
4562
5262
8.70
9-35
1776
" -H
"
"
"
62.98
2. II
4686
5477
8.63
9-33
1777
« 3
M
"
M
65-73
2. 02
4809
5687
8.56
9.31
*i778
22X&
•zG\l
35X3 2X~Jg
5*3*xJ
58-36
2.14
456o
5163
8.84
9.41
1779
" I
"
"
"
61.11
2.04
4684
5383
8.76
9-39
1780
" H
"
M
"
63.86
i-95
4806
5598
8.68
936
1781
" i
"
M
M
66.61
1.87
4927
5808
8.60
9-34
22" X 26" Section. B Series.
"1782
22xi
26xf
4X4xtV
6x4 x'.
54-37
2.83
4148
4475
8-73
9.07
*I783
" TS
"
"
"
57-12
2.69
4280
4672
8.65
9.04
1784
" f
M
"
M
59-87
2-57
4410
4866
8-57
9.01
1785
" 4
"
"
U
62.62
2.46
4538
5058
8.51
8.99
1786
" I
"
"
(l
65-37
2.36
4664
5247
8-45
8.96
*I787
22xJ
26xf
4*4xrV
6x4x&
55-49
2-57
4325
4619
8.82
9.12
*I788
1789
'
M
"<
'«
58.24
60.99
2-45
2-34
4453
458o
4816
5010
8.74
8.66
9.09
9.06
1790
" H
H
"
M
6374
2.24
4705
5202
8-59
9-03
1791
" ^
66.49
2.15
4829
5391
8.52
9.00
* Spacing of rivet lines of web greater than 30 X thickness of plate.
179
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
r
j 1
-\
r
Properties Hj j
of I
Top Chord Sections.
. {A Four Angles
. .*_ and
^ Three Plates.
JLJI
JLxI
B
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
-» r^QQ A *-Qo
Eccen-
tricity.
Axis
Axis
Axis
Axis
Section
A-A.
B-B.
A-A.
B-B.
Number.
Web.
Cover.
Top.
Bottom.
A
e
IA
IB
TA.
rB
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*I792
22x5
26xf
4x4x1^
6x4x|
56.59
2-33
,449°
4761
8.91
9.17
*I793
« 9
16
"
ii
"
59-34
2.23 *
'4614
4958
8.82
9.14
1794
« 5
8
"
M
M
62.09
2.13
4738
5152
8.74
9.II
1795
" H
M
"
H
64.84
2.04
4861
5344
8.66
9.08
1796
" f
(1
"
"
67-59
i-95
4984
5533
859
9-05
*I797
22X|
26xf
4x4x ^ g
6x4X^6
57-67
2. II
4642
4904
8.97
9-22
"A
"
'
60.42
2. 02
4764
5101
8.88
9.19
1799
" f
"
1
63.17
i-93
4886
5295
8.80
9.16
1800
" H
"
1
65.92
1.85
5007
5487
8.72
9-13
1801
" f
"
1
68.67
1.77
5128
5676
8.64
9.09
*l802
22x|
26x|
4x4x^~^
6x4x5
58.75
.90
4790
5046
9-03
9.27
*i8o3
« 9
"
'
61.50
.81
4911
5243
8.94
9.24
1804
" I'
"
i
64.25
•73
5031
5437
8.85
9.20
1805
" 11
u
1
67.00
.66
5150
5629
8.77
9.17
1806
"I"
M
69.75
.60
5268
5818
8.69
9-13
22" X 28" Section.
*I807
22X-^
28xf
4x4x1
6x4x5
57-47
2-77
4326
5601
8.67
9.87
1808
" f
"
"
"
60.22
2.65
4457
5844
8.60
9-85
1809
" 11
"
"
"
62.97
2-53
4586
6083
8-53
9-83
1810
" a
H
«
M
65.72
2.42
47H
6320
8.47
9.81
*i8il
22Xj^
28xf
4x4x|
6X4X^
58.59
2-53
4502
5771
8.76
9-92
1812
" f
H
H
M
6i.34
2.42
4630
6014
8.68
9.90
1813
" tt
"
H
"
64.09
2.31
4756
6253
8.61
9.88
1814
" 1
"
"
•"
66.84
2.22
4881
6490
8-55
9.86
*i8i5
22X&
28xf
4X4X1
6x4xf
59-69
2.3O
4666
5939
8.84
9-97
1816
" f
"
u
"
62.44
2. 2O
479i
6182
8.76
9-95
1817
ii 11
"
"
"
65.19
2.IO
4916
6421
8.68
9-93
1818
4
u
"
M
67.94
2. 02
5038
6658
8.61
9.90
*i8i9
22X^
28x|
4X4X5
6X4X^
60.77
2.O9
4818
6108
8.90
10.03
1820
" f
K
u
"
63-52
2.OO
4940
6351
8.82
IO.OO
1821
" tt
M
it
"
66.27
1.92
5062
6590
8.74
9-97
1822
" SL.
"
"
M
69.02
1.84
5182
6827
8.67
9-95
* Spacing of rivet lines of web greater than 30 X thickness of plate.
180
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
Properties
ot
Top Chord Sections.
r
f
i "
Four Angles
and
Three Plate*
..-^
il+"
|
- "-T
Li
Section
Number.
Plates.
Angles.
I'.ross ARM.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Web.
Cover.
Top
Bottom.
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches*.
Inches*.
Inches.
Inches.
1824
1825
1826
" 4i
<«
it
u
it
fegxj
61.85
64.60
67-35
7O.IO
1.89
I.8I
173
1.67
4966
5086
5206
5325
6275
6518
6757
6904
8.96
8.87
8.79
8.72
10.07
10.04
IO.OI
9-99
24" X 27" Section. A Series.
1828
1829
*i83o
1831
1832
'1833
1834
1835
*i836
1837
•1838
'1839
1840
1841
" J
« ,
24X
«
«
24X
u
«
i
i
i
i
i
u
«
H
3* j 2 To
3*3 2 x i Q
3*3 * Ts
M
M
5x3lxi6"
5*3**!
60.62
63.62
66.62
61.56
64-36
67-36
62.46
65.46
68.46
63-36
66.36
69.36
64.24
67.24
70.24
3-00
2.86
2-73
2.79
2.66
2.54
2.60
2.48
2-37
2.41
2.30
2. 2O
2.23
2.13
2.O4
5138
5308
5476
5318
5484
5648
5483
5647
5809
5644
5804
5964
5792
595°
6107
5655
5919
6174
5789
6051
6308
5918
6179
6437
6048
6309
6567
6179
6440
6698
9-21
9-13
9.07
9-29
9.22
9-15
9-37
9.29
9.21
9-44
936
9.28
9-49
9.40
9-32
9.66
9.64
9.62
970
9.68
9.66
9-74
9.72
9.70
9-77
9-75
9-73
9.81
9-79
9-77
| 24" X 27" Section. B Series.
^1842
1844
1845
'1846
*I847
1848
1849
;i8So
1852
1853
" i
" H
" i
2"Xf
;/
TL
27*f
27*f
a
27^1
M
u
H
It
«
u
M
6x4xf
«
6o.OO
63.00
66.OO
69.00
6l.I2
64.12
67.12
70.12
62.22
65.22
68.22
71.22
2.92
2.78
2.65
2-54
2.66
2-54
2-43
2.32
2.43
2.32
2.22
2.12
5296
5464
5631
5797
5506
5670
5832
5994
5702
5863
6022
6181
5372
5610
5844
6075
5529
5767
6ooi
6232
5684
5922
6156
6387
9-39
9.24
9.17
9-49
9.40
9.32
9-25
9-57
9.48
9.40
9.32
9.46
9-43
9.41
9-39
9-Si
9.49
9.46
9-43
9.56
9-53
9-50
9-47
* Spacing of rivet lines of web greater than 30 X thickness of plate.
181
TABLE 84. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
I— 1
T
1 P
Properties ,/Jj
of' [ —
14
Four Angles
and
e
Top Chord Sections. tj 5 Three Plates.
LJ I L.I
1
Plates.
Angles.
Moments of
Radii of Gyra-
Inertia.
tion.
/-* A rf.3
Eccen-
vjrosa x\rLd.
tricity.
Axis
Axis
Axis
Axis
Section
Number.
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches*.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*i854
24X&
27xf
4x4x3^
6x4xH
63-30
2.21
5883
5840
9.64
9.61
*i8S5
« 5
8
"
"
"
66.30
2. II
6040
6078
9-55
9-58
1856
" H
"
u
H
69.30
2.O2
6197
6312
9.46
9-55
1857
« a
"
u
"
72.3O
1-93
6353
6543
9-38
9-Si
"1858
24X&
27xf
4x4x^V
6x4xf
64-38
1.99
6061
5994
9.71
9.66
*i8S9
" 1
M
M
"
67.38
1.90
6217
6232
9.61
9.62
1860
" H
"
"
M
70.38
1.82
6371
6466
9-52
9-59
1861
" 3.
tt
*'
(t
73-38
i-75
6524
6697
9-43
9-56
24" X 28" Section. A Series.
*i862
24xf
28xf
3|x3|xtV
5X3 M
61.24
3.10
5190
6232
9.21
10.09
1863
" H
"
u
"
64.24
2.96
6521
9.14
10.07
1864
" 3.
M
"
67.24
2.82
5531
6808
9.07
10.06
*i865
24x|
28xf
3|x3|x^f
5x3|x^
62.18
2.89
5372
6377
9.29
10.13
1866
" H
u
*•
"
65.18
2.76
5539
6666
9.22
IO.II
1867
« 3
4
"
"
M
68.18
2.63
5707
6953
9-15
10.10
*i868
24X§
28xf
35x3^X16
5x35xf
63.08
2.70
5540
6518
9-37
10.17
1869
" H
"
"
M
66.08
2-57
5706
6807
9.29
10.15
1870
" 3.
M
"
M
69.08
2.46
5869
7094
9.22
10.13
•1871
24xf
28x|
3^x3^X16
SX31X1^
63.98
2.50
5705
6659
9-44
IO.20
1872
" H
"
"
"
66.98
2-39
5866
6948
10.18
1873
" t
H
"
M
69.98
2.29
6027
7235
9.28
10.17
*i874
24xf
28xf
35x3^x3^
5x3ixf
64.86
2.32
5855
6791
9-50
10.23
1875
"H
H
H
"
67.86
2.22
6014
7080
9.42
IO.2I
1876
" 3.
((
"
70.86
2.13
6172
7367
9-34
IO.I9
24" X 28" Section. B Series.
*i877
24X&
28xf
4x4x3^
6x4x|
60.62
3-01
5352
5930
9-39
9.89
*i878
8
M
H
ii
63.62
2.87
5522
6i9S
9.31
9.87
1879
" H
"
"
"
66.62
2-74
5690
6457
9.24
9.84
1880
" f
M
69.62
2.62
5855
6715
9.17
9.82
* Spacing of rivet lines of web greater than 30 X thickness of plate.
182
TABLE 84.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
T~e
j
i !
r
Propcrtiea Al j
of ! 4
Top Chord Sections. q
\A Four Angle*
. .€. and
i Three Plates.
LJ
LI
1
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
f * \ r
Eccen-
. ii USS -Alt M .
tricity.
Axis
Axis
Axis
Axis
Section
A-A.
B-B.
A-A.
B-B.
Number.
Web.
Cover.
Top.
Bottom.
A
e
IA
IB
rA
IB
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*i88i
24*^
a i
28xf
4*4*&
6x4x3^
61.74
2.76
5563
6lOO
9-49
9-94
*i882
it
M
"
64.74
2.63
5729
6365
9.41
9.92
1883
1884
-1*
ii
II
«
67.74
70.74
2.52
2.41
5892
6055
6627
6885
9-33
9-25
9.89
9.86
"1885
24xA
28xf
4*4*lV
6x4X1
62.84
2-53
5762
6268
9.58
9-99
*i886
" t
ii
"
"
65.84
2.41
5925
6533
9-49
9.96
1887
" t*
"
"
"
68.84
2.30
6086
6795
9.40
9-93
1888
"I
"
"
"
71.84
2.21
6244
7°53
9-32
9.91
*i88g
24*rV
28xf
4*4*lV
6x4xJ£
63.92
2.3O
5947
6437
9-65
10.03
*i89O
" f
"
"
"
66.92
2. 2O
6106
6702
9-55
IO.OO
1891
" H
"
it
"
69.92
2.11
6263
6964
9-47
9.98
1892
"I
"
ii
1C
72,92
2.02
6420
7222
9-39
9-95
*i893
24xA
28xf
4*4*&
6x4xf
65.00
2.O9
6126
6604
9.71
10.08
"1894
;; i
"
<t
"
68.00
2.00
6283
6869
9.61
10.05
1895
"
"
"
71.00
I.9I
6439
7131
9.52
10.03
1896
«. }
it
"
"
74.00
1.83
6591
7389
9-44
IO.OO
24" X 30" Section.
*l897
24xf
30xH
4*4*1
6x4xJ
65-85
3-22
5747
7465
9-35
10.65
1898
" <
i
"
ii
68.85
3.08
5921
7785
9.28
10.63
1899
(i \
"
"
"
71.85
2-95
6093
8103
9.21
10.62
*I900
24*
3°xH
4*4*1
6x4x^6"
66.97
2.99
5966
7663
9-44
10.70
1901
" •
i
ii
ii
"
69.97
2.86
6136
7983
10.68
1902
" i
ii
"
"
72.97
2-74
6304
8301
9.29
10.66
*I903
241
3°XH
4*4*1
6x4x3
68.07
2.76
6i73
7859
9-52
10.74
1904
ii
i
"
ii
•
71.07
2.65
6339
8179
9-44
10.72
1905
« ;
"
"
M
74.07
2-54
6504
8497
9-37
10.71
'1906
24*
3°XH
4*4*1
6x4x-£J
69.15
2.56
6363
8056
9-59
10.79
1907
ii _
i
!{
"
72.15
2.45
6526
8376
9.51
10.77
1908
ii :
II
u
«
75-iS
2-35
6687
8694
9-43
10.75
'1909
24X
3oxH
4*4*1
6x4 \,
70-23
2-35
6552
8250
9.67
10.84
1910
ii
*
II
"
73-23
2.25
6712
8570
9.58
10.82
1911
Ii
"
ii
"
76.23
2.17
6871
8888
9-49
10.80
* Spacing of rivet lines of web greater than 30 X thickness of plate.
183
TABLE 85.
PROPERTIES OF TOP CHORD SECTIONS.
1
TT
f
sat
Properties -4j
j.
44 Six Angles
& and
OI J, -• —
Top Chord Sections.
1
£ Three Plates.
i. — 0
^ JS
T
J5
Plates.
Angles.
Gross
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Section
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Bottom.
A-A.
B-B.
A-A.
B-B.
Web.
Cover.
Top.
ber.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
16" X 20" Section. A Series.
*2OOI
l6xf
20X^
3fx3ix|
31X31X|
3lx3i-x|
35-63
I.O4
1553
1480
6.60
6-44
2OO2
;; A
it
"
i
"
37.63
0.98
1597
1551
6.5I
6.41
2003
'
"
'
tt
39-63
o-93
1642
1621
6-44
6.38
2004
" 9
'
"
i
tt
41.63
0.89
1686
1689
6.36
6.36
2005
" I
1
H
1
it
43-63
0.85
1730
1756
6.30
6-34
2006
« li
16
t
"
i
it
0.81
1774
1821
6.24
6.31
20O7
" 3
4
'
M
'
it
47-63
0.78
1818
1887
6.18
6.29
*2008
i6xf
2OXi$
3 Jx3^xf
3§x3^xA
32X3:2X16
37-19
0.72
1633
1547
6.63
6-44
2009
" A
tt
"
it
u
39-19
0.69
1677
1617
6-54
6.42
2OIO
It 1
2
tt
"
tt
It
41.19
0.66
1720
1686
6.46
6.40
201 1
" A
tt
"
"
"
43-19
0.63
1763
1754
6-39
6-37
2OI2
« 5
8
tt
"
it
(C
45-19
0.60
1807
1821
6.12
6-34
2OI3
" 11
16
tt
"
It
It
47.19
o-57
1850
1886
6.26
6.32
2OI4
" i
tt
M
tt
tt
49.19
o-55
1894
1951
6.2O
6.30
*2OI5
2Ol6
i6x|
20XTS
3 2x32X8
tt
J 2^2X2
38.71
40.71
0.42
0.41
1729
1772-
1612
1682
6.68
6.60
6-44
6.42
2OI7
" ¥
"
tt
it
"
42.71
o-39
1815
1751
6.52
6-39
2Ol8
" A-
u
"
tt
"
44.71
0.38
1858
1819
6-44
6-37
2OI9
" I
it
it
it
"
46.71
0.36
1901
1885
6.38
6-34
202O
" H
"
11
It
"
48.71
0-34
1944
1949
6.32
6.32
2O2I
tt a
(f
tt
tt
M
50.71
o-33
1987
2014
6.26
6.29
*2022
i6x|
20Xtk
3lx3^x|
33X3|xj^
3|x3|x^
40.19
0.16
1803
1675
6.70
6-45
2O23
" A
u
"
n
u
42.19
0.16
1845
1745
6.6 1
6.42
2O24
" *
(C
"
"
tt
44.19
0.15
1888
1813
6-53
6-39
2O25
It 9
16
M
tt
"
It
46.19
0.14
1931
1880
6.46
6-37
2O26
« 5
g
"
tt
tt
tl
48.19
0.13
1973
1946
6.40
6-35
2O27
" tt
"
it
it
tt
50.19
O.I2
2016
2OIO
6-34
6.32
2O28
" 1
"
tt
tt
"
52.19
O.I2
2059
2074
6.28
6.29
*2O29
i6xf
20Xj^
3ix3ix|
3ix3ix|
31X31X5
41.63
-.08
1870
1738
6.70
6.46
2030
" A
"
"
«
"
43-63
-.08
1913
1807
6.62
6-44
2031
" i
"
"
u
It
45-63
-.07
1956
1874
6-54
6.41
2O32
" i%
it
tt
It
"
47-63
-.07
1998
1941
6-47
6.38
2033
!! fi
"
"
It
"
49-63
-.07
2041
2OO7
6.41
6.36
2034
T6
it
"
"
u
5I-63
-.07
2084
2O70
6-35
6-34
2035
tt 3
4
"
tt
ft
it
53-63
-.06
2126
2134
6.30
6.32
* Spacing of rivet lines of web greater than 30 X thickness of plate.
184
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
Properties
of
Top Chord Sections.
ji
3
.44 Six Angles
*£- and
*l Three Plates. .
A\
4
4=
_LJ
L J
=1
i
Plates.
Angles.
Gross
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Section
Web.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
ber.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches*.
Inches.
Inches4.
Inches*.
Inches.
Inches.
16" X 20" Section. B Series.
•2036
l6*t
20X&
3*x3ix|
5*3ixf
3i*3ixf
36.77
0.77
1640
1606
6.67
6.61
2037
T.
V
"
'
M
"
38.77
0-73
1684
1677
6-59
6.58
2038
"j
"
'
"
M
40.77
0.70
1727
1747
6.51
6-55
2039
M
i
b
M
'
"
M
42.77
0.67
1771
1815
6-43
6.52
2040
" 1
M
1
H
H
44-77
0.64
1814
1882
6.36
6.48
2041
' H
(1
i
"
"
46.77
0.61
1858
1947
6.30
6-45
2042
" \
M
"
M
"
48.77
0.58
1902
2013
6.24
6.42
*2043
i6xf
zoxrV
3ix3Jx|
5X3 b A
35X3i*lV
38.51
o-43
1725
1695
6.69
6.63
2044
it
76
"
"
"
H
40.51
0.42
1768
1765
6.60
6.60
2045
" 1
"
"
"
"
42.51
0.40
1810
1834
6.52
6-57
2046
M
• :
6
M
"
H
"
44-51
0.38
1854
1902
6.45
6-54
2047
" i
M
"
M
"
46.51
0.36
1897
1970
6-39
6.51
2048
" -
J
"
*
M
"
48.51
o-34
1940
2034
6.32
6.48
2049
1
"
"
H
"
50.51
o-33
1982
2099
6.26
6-45
*2050
i6x|
20XA
3Jx3ixf
5x3^xJ
3$x3|x|
40.21
O.I2
1826
1781
6-74
6.65
2051
M
h
"
"
"
"
42.21
O.I 2
1868
1852
6.65
6.62
2052
I
"
"
"
"
44.21
O.I I
1911
1920
6-57
6.58
1053
" *
"
"
M
"
46.21
O.I I
1954
1988
6.50
6-55
2054
" \
M
H
"
"
48.21
O.I I
1996
2054
6-43
6.52
2055
" H
"
"
"
H
50.21
O.IO
2039
2119
6-37
6-49
2056
" s
4
[
"
"
M
"
52.21
O.IO
2082
2183
6.31
6.46
'2057
i6xf
20XtV
3Jfx3ix|
5x3Jxx"»~
3Jx3Jx&
41.89
-•15
1903
1866
6-75
6.67
2058
2059
l\
V
«.
«
It
M
«
45.89
-.14
-.14
1946
1988
1936
2004
6.66
6.58
6.64
6.61
2060
2061
u
>
H
M
M
M
«
47.89
49.89
-•13
-•13
2031
2074
2071
2137
*5'
6-45
6.58
6-55
2062
" ft
H
"
"
"
51.89
— .12
2115
22OI
6.39
6.52
2063
**
[
"
"
"
53.89
— .12
2158
2265
6.32
6.48
'2064
Ifel
2QxA
3ix3Jxf
5x3$xf
3zX3ix|
43-51
-.41
1978
1951
6.74
6.70
2065
M
r.
u
"
"
"
45-51
-•39
202 1
2O2O
6.65
6.66
2066
"
"
"
"
"
47-51
-•37
2063
2087
6.58
6.63
2067
*
F
tt
"
M
"
49-51
-•36
2107
2154
6.52
6.60
2068
«
"
«
1<
<«
SI-SI
-•34
2150
222O
6.46
6-57
2069
"
I1
M
"
"
M
53-51
-•33
2192
2283
6.40
6-53
2070
(i
1
"
"
"
55-51
-.32
2235
2347
6-34
6.50
* Spacing of rivet lines of web greater than 30 X thickness of plate.
51
185
TABLE 85. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
T'T
/
=*
Properties ^
of ,7 -—
Top Chord Sections.
=f=
4^- Six Angles
^— and
^ Three Plates.
.1=1
L Jk
I
=».*_
1
Plates.
Angles.
Moments of
Radii of Gyra-
Gross
Eccen-
Inertia.
tion.
Section
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
16" X 22" Section.
*2O7I
i6xf
22xJ
3ix3ixf
Sx3|xf
31X31X|
39.02
1. 21
1761
2163
6.72
745
2072
" A
44
14
(1
il
41.02
I-I5
1807
2259
6.64
7.42
2073
" i
44
44
M
44
43.02
1. 10
1851
2354
6.56
7.40
2074
« 9
T6
44
44
M
44
45-02
1.05
I897
2448
649
7-37
2075
" f
"
44
"
44
47.02
I.OO
1942
2540
6-43
7-35
2076
" H
"
44
u
44
49.02
0.96
1988
2630
6-37
7-33
2077
" 3.
"
"
A
44
51.02
0.92
2031
2718
6.31
7-30
*2078
i6xf
22X^
3|x3|xf
5x35XiV
3 2"X3 ^x i ^
40.76
0.86
1873
2276
6.78
747
2079
" rV
44
"
"
"
42.76
0.82
1917
2372
6.70
745
2080
<« i
2
"
"
"
44
44.76
0.78
1960
2467
6.62
743
2081
(( 9
"
"
44
14
46.76
o-7S
2OO5
2560
6-55
7.40
2082
" P
44
44
44
ft
48.76
0.72
2049
2652
6.48
7-38
2083
" H
**
"
"
"
50.76
0.69
2093
2741
6.42
7-35
2084
« 3
"
44
N
44
52.76
0.67
2136
2828
6.36
7-32
*2o85
i6xf
22X|
3|x3|x|
Sx3?x|
3?x32"X^
42.46
0.56
1970
2388
6.81
7-50
2086
" A
"
"
"
"
44.46
0-53
2OI3
2483
6-73
7-47
2087
" ^
44
"
"
44
46.46
0.51
2056
2577
6.65
745
2088
« 9
"
"
44
44
48.46
0.49
2099
2670
6-59
7.42
2089
. " I'
"
44
44
44
50.46
0.47
2142
2761
6.52
7.40
2090
" TF
"
44
44
44
52.46
o-45
2186
2850
6-45
7-37
2091
" f
44
44
44
44
5446
°43
2229
2937
6.40
7-35
*2O92
i6xf
22x|
,ix«ixa
5X31X3%
3 2~x3^Xig
44.14
0.27
2060
2498
6.83
7-52
2093
" T*5
"
"
"
44
46.14
0.26
2IO3
2593
6-75
7-5°
2094
« i
2
"
"
(4
44
48.14
0.25
2145
2687
6.68
7-47
2095
« 9
44
44
"
(C
50.14
0.24
2188
2779
6.61
7-44
2096
" F
44
44
44
44
52.14
0.23
2231
2869
6-54
7-42
2097
" H
"
"
(4
44
54-H
0.22
2274
2957
6.48
7-39
2098
" i
*'
44
44
It
56.14
O.22
2316
3043
6.42
"2099
i6xf
22x£
3|x3|xf
P'V^i'V —
5X32X8
31X31X|
45-76
0.02
2139
2605
6.84
7-55
2IOO
" A
44
|4
44
44
47.76
O.O2
2182
2699
6.76
7-52
2101
" \
"
44
"
44
49-76
O.O2
2224
2792
6.69
7-49
2IO2
t-i 9^
«
44
"
u
5I-76
O.O2
2267
2883
6.62
7.46
2IO3
" f6
tt
"
u
44
53-76
O.O2
2310
2973
6.56
7-44
2IO4
«< 11
16
"
44
44
"
O.O2
2353
3061
6.50
7.41
2IO5
<( 3
4
"
"
"
((
57.76
O.02
2395
3H7
6-44
7-38
* Spacing of rivet lines of web greater than 30 X thickness of plate.
186
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
i ...
3
Properties I " • • —
f
JL^i Six Angles
Top Chord Sections. $
Three Plates.
JLJ
= Ji
I
=>.i.
i
Plates.
Angles.
Gross
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Section
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
Bottom.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches*.
Inches*.
Inches.
Inches.
*2I06
2IO7
l6x|
22XJ
33X33XJ
5«3j*«
33X3JX.U
47.38
49.38
— .21
— .20
2212
2255
2712
2806
6.83
6.76
7.56
7-54
2108
" A
"
M
"
M
51.38
-.19
2297
2899
6.69
2109
.. 9
"
"
"
"
53-38
-.18
2340
2989
6.62
7.48
11 IO
"
M
"
M
-.18
2383
3078
6.56
7-45
2III
" H
"
"
"
(C
57-38
-•17
2426
3165
6.50
7-43
2112
"1
"
"
**
"
59-38
-.16
2468
3251
6-45
7.40
*2H3
i6x|
22XJ
33X33X|
5x33xf
35X3sxf
48.96
-.41
2275
2817
6.83
7-59
2114
" A
"
M
"
"
50.96
-.40
2318
29IO
6.74
7.56
2115
" 3
1
"
H
"
52.96
-.38
2360
3OO2
6.67
7-53
2116
" rs
'
"
M
{<
54.96
-•37
2404
3092
6.61
7-50
2117
" f
'
"
H
"
56.96
-•35
2447
3181
6-55
7-47
2118
" H
1
"
"
"
58.06
-•34
2492
3268
6.50
7-44
2119
" f
'
"
"
M
60.96
-•33
2532
3353
6-44
7.41
18" X 22" Section. A Series.
L
*2I20
l8x|
22xJ
33X35xf
33X35X|
35x35x1
39.38
.58
2177
2086
743
7.28
1*2121
»F
"
«
|]
•
41.63
•49
2243
2196
7-34
7.26
2122
3
43-88
.41
2309
2304
7-25
7.24
2123
"A
M
1
"
'
46.13
•34
2374
2410
7.17
7-23
2124
" f
«
'
"
1
48-38
.28
2439
25H
7.10
7.21
2I2|
2126
:>
«
«
«
!
50.63
52.88
•23
•17
2503
2566
2616
2716
7-03
6.96
7.19
7.16
*2I27
l8x|
22.\!
3ix35xf
33X35X&
Six^xA
40.94
1.22
2310
2176
7-51
7.29
*2I28
"rV
"
"
"
43-19
1.16
2374
2285
7.41
7.28
2129
" 3
"
M
'
«
45-44
1. 10
2437
2393
7-32
7.26
2130
"A
"
M
1
M
47.69
1.05
2500
2500
7.24
7.24
2131
" f
"
it
'
"
49-94
1. 00
2564
2604
7.17
7.22
2132
2133
:>
«
M
«
M
52.19
54-44
0.96
0.92
2627
2689
2703
2802
7.10
7-03
7.20
7.18
*2i34
l8x|
22xJ
33X35X|
33x35X5
32X32XJ
42.46
0.90
2428
2259
7.56
7.29
*2i35
2136
[f
!
1!
M
u
44.71
46.96
0.85
0.8 1
2491
2553
2368
2475
746
7-37
7.28
7.26
2137
<« 9
1
"
(C
(i
49.21
0.77
2616
2581
7-29
7.24
2138
" i
•
"
"
"
51.46
0.74
2678
2683
7.21
7.22
2139
« 11
1
M
"
"
53-71
0.71
2740
2784
7.14
7.20
2140
" 1
*
M
H
"
55-96
0.68
2801
2883
7.08
7.18
| * Spacing of rivet lines of web greater than 30 X thickness of plate.
187
TABLE 85. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
1
f ^
ss
Properties -4j_
of '
Top Chord Sections.
=4=j
i Jk
4J. Six Angles
.e_ and
t Three Plates.
iJ
L
J
=.i.
1
3
Plates.
Angles.
Gross
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
A-A.
B-B.
A-A.
B-B.
IN um-
Web.
Cover.
Top.
ber.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2I4I
I»X^7
22xl
35X3*x|
3ix3lx_9,
3§x
3ix^
43-94
O.6o
2538
2345
7.60
7-30
*2I42
'"
"
"
"
46.19
0-57
2600
2454
7.51
7.29
2143
tt i
"
M
M
M
48.44
0-55
2660
2559
7-42
7-27
2144
it 9
TS
"
" j
it
M
50.69
0.52
2722
2665
7-34
7-25
2145
tt 5.
"
ft
it
M
52-94
0.50
2785
2765
7.26
7-23
2146
" tt
it
"
n
"
55-19
0.48
2845
2866
7.18
7.21
2147
tt 3
ti
"
ft
tt
57-44
0.46
2906
2966
7.II
7.19
*2i48
i8xf
22x|
3 iX3ixf
3lx3ix|
3i:
c3ix|
45-38
o-34
2636
2426
7.62
7-31
*2I49
" A
"
"
tt
ti
0.32
2697
2535
7-53
7-29
2150
" 1
tt
"
it
it
49.88
0.31
2757
2640
7-44
7.27
2151
" A
it
"
tt
it
52.13
0.30
2818
2744
7-35
7-25
2152
" I
"
M
tt
ft
54-38
0.29
2879
2846
7.27
7-23
2153
"tt
"
"
tt
n
56-63
o-37
2940
2947
7.20
7.21
2154
" 1
U
It
tt
it
58.88
0.36
3001
3044
7.14
7.19
*2i55
i8xf
22x|
31X3IX|
3|X31X1£
3ix
3ix^i
46.82
0.12
2722
2506
7-63
7-32
*2is6
" A
"
"
"
•'
49.07
O.I I
2783
2613
7-53
7-30
2157
tt i
2
"
"
it
M
5I-32
O.I I
2843
2719
7-44
7.28
2158
"F
M
"
tt
"
53-57
O.IO
2904
2824
7.36
7.26
2159
"
"
it
"
55.82
O.IO
2965
2924
7.29
7.24
2160
"I*
"
"
it
M
58-07
O.O9
3025
3024
7.22
7-22
2161
ft 3
4
"
"
"
tt
60.32
O.O9
3086
3122
7-iS
7.2O
*2l62
i8x|
22X|
31X31X|
3ix3lx|
35-
j3Ix|
48.22
— .11
2802
2585
7.62
7-32
*2i63
"A
u
"
" '
"
5°-47
— .11
2863
2693
7-53
7-30
2164
it i
"
"
tt
tt
52-72
— .10
2923
2797
7-44
7.28
2165
ft 9
"
M
tt
"
54-97
— .10
2984
2902
7-36
7.26
2166
ft 5
8
H
H
"
ti
57-22
— .10
3045
3OOI
7.29
7.24
2167
" H
It
"
tt
ft
59-47
-.09
3105
3IOI
7.22
7.22
2168
ft 3
"
"
"
it
61.72
-.09
3166
3198
7.16
7.20
18" X 22" Section. B Series.
*2l69
i8xf .
22X|
31X31X|
SX3IX|
31}
C3ixi
40.52
.29
2297
2241
7-53
7-44
*2I70
A
"
42.77
.22
2361
2351
7-43
7-42
2171
|
"
45.02
.16
2426
2459
7-34
7-39
2172
9
F
"
47.27
.IO
2489
2566
7.26
7-37
2173
5
8
M
49-52
.05
2552
2669
7.18
7-34
2174
tt
M
Si-77
1. 01
2615
2772
7.11
7-32
2175
3.
"
54.02 0.97
2678
2872
7.04
7.29
* Spacing of rivet lines of web greater than 30 X thickness of plate.
188
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
~H
=*
Properties Aj
.._}
A4 Six Angles
Top Chord Sections. *f
!
1 • *r-~ &nd
,j Three Plates.
U
= J
f
1
Plates.
Angles.
Moments of
Radii of Gyra-
Graii
Eccen-
Inertia.
tion.
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
•Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches.
'2176
i8x|
22xi
3Jx3**f
5*3ixA
3i*3ixi6-
42.26
O.OO
2437
2357
7.60
7-47
*2i77
" A
'
<
M
«
44-51
0.86
2500
2467
7.50
7-44
2178
" i
1
''
"
"
46.76
0.82
2563
2574
7.41
7.42
2179
" A
'
1
«
"
49.01
0.78
2624
2681
7-33
7-39
2180
- i
'
'
"
H
51.26
0.75
2684
2783
7-25
7-37
2181
" H
1
1
M
"
53-51
0.72
2746
2885
7.17
7-34
2182
uj
'
1
"
"
55.76
0.69
28lO
2985
7.10
'2183
i8xf
22xJ
3ix3Jx|
5*3$xi
3Jx3Jxi
43 .96
0.57
2563
2466
7-64
7-49
*2I84
" A
«i
"
"
"
46.21
0.55
2623
2575
7-54
7-47
2185
" i
"
"
"
"
48.46
0.52
2685
2682
7-45
7-44
2186
" A
"
"
«
"
50.71
0.50
2745
2788
7.36
7.41
2187
" f
u
H
"
"
52.96
0.48
2807
2890
7.28
7-39
2188
" rt
"
"
"
"
55-21
0.46
2868
2991
7.21
7-36
2189
" i
M
"
u
"
57-46
0-44
2930
3090
7.14
7-34
*2I90
i8xf
22XJ
3J*3$xf
5x3 |x A
3y^-32^if
45.64
0.26
2680
2578
7.66
7.52
*2I9I
"A
"
«
"
"
47.89
0.25
2741
2687
7-56
7-49
2192
" i
«
M
"
"
50.14
0.24
2801
2792
7-47
7-46
2193
" A
"
"
H
"
52.39
0.23
2862
2898
7-39
7-44
2194
" 1
"
"
"
M
54-64
O.22
2923
2998
7.31
7.41
2195
" tt
"
M
"
H
56.89
O.2I
2984
31OI
724
7.38
2196
" i
"
«
"
«
59-14
O.2O
3045
3199
7.18
7-36
*2i97
itel
22xJ
3i*3$xf
5x3|x|
3jx3^xf
47.26
— .02
2782
2685
7.67
7-54
2199
f?
«
«
M
H
M
49-51
5I-76
— .02
— .02
2843
2904
2794
2899
7-57
7.48
7-Si
7.48
2200
"A
*
«
"
"
54-oi
— .OI
2964
3003
7.40
7.46
1 22OI
" f
"
M
H
H
56.26
— .OI
3025
3105
7-33
7-43
1 2202
" H
"
"
"
H
58.51
— .01
3086
3206
7.26
7.40
1 22O3
" i
"
"
M
"
60.76
— .OI
3H6
3303
7.20
7-37
*2204
i8x|
22XJ
3i*3Jxf
SX3^X^
3lxj|x^
48.88
-.27
2875
2791
767
7.56
1*2205
1 22O6
••t
M
M
H
U
M
<•
53.38
-.26
-•25
2937
2998
2898
3004
7-57
7.48
7-53
7.50
1 2207
" A
"
M
"
M
-.24
3059
3109
7.41
7.48
2208
" 1
"
"
"
"
57-88
-.23
3"9
3209
7-34
7-45
2209
" H
"
"
"
"
60.13
— .22
3180
3309
7-27
7.42
1 2210
" 1
M
M
"
62.38
— .21
3241
3407
7.20
7-39
* Spacing of rivet lines of web greater than 30 X thickness of plate.
189
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
Properties -~j
of I
Top Chord Sections.
L 1 l^L Six Angles
1- \ ^— and
^ Three Plates.
J
3
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
KAV
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Der.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*22II
i8xf
22x1
3lx3lxf
Sx3ix£
i
50.46
-•50
2958
2896
7-65
7-57
*22I2
"A
tt
'
tt
52.71
-.48
3O2O
3003
7-55
7-54
2213
" i
'
'
tt
54.96
-.46
3081
3108
7-47
7-52
2214
" -$r
TS
'
'
"
57-21
-44
3142
3212
7.40
7-49
2215
ft j>
t
'
"
59-46
-.42
3203
3312
7-33
7-47
22l6
" It
'
'
it
61.71
-.41
3265
3412
7.26
7-44
2217
« 3
4
t
63.96
-•39
3326
3508
7.20
7.41
18" X 24" Section.
2218
1 8x1
24XTS
3lx3ixf
Sx3ixf
3l
,3ix|
47-52
i-S9
2584
3215
7-37
8.23
2219
It 9
Tff
"
"
u
it
49-77
1.52
2650
3354
7-29
8.21
222O
" I
"
tt
tt
it
52.02
1-45
2716
349i
7.22
8.19
2221
" it
tt
"
tt
54.27
i-39
2781
3625
7.16
8.17
2222
it 3
tt
tt
56-52
1-34
2846
3757
7.10
8.15
2223
1 8x1
24X3^
-ix«ixa
5X3 xrV
3lx
3lxA
49.26
1.26
2736
3354
7-45
8.25
2224
" A
"
"
it
i. 20
2801
3492
7-37
8.23
2225
« 5
g
tt
"
"
53-76
1.15
2865
3628
7-30
8.21
2226
" it
it
"
M
56.01
I.IO
2928
3761
7-23
8.19
2227
« a
it
"
"
58.26
i. 06
2991
3893
7.17
8.17
2228
1 8x1
g
3lx3lxf
5x3 1x1
,1
S,1XI
50.96
0-95
2874
3494
7.51
8.28
2229
"A
((
it
"
a
53-21
0.91
2937
3632
7-43
8.26
2230
ft 5
I
It
tt
"
M
5546
0.88
2999
3767
7-36
8.24
2231
" H
tt
it
M
"
57-71
0.84
3061
3900
7.28
8.22
2232
" f
"
tt
tt
"
59-96
0.81
3124
4031
7.22
8.20
2233
1 8x1
24XTS
3lx3lxf
Sx3ix^
3^
3lxA
52.64
0.67
3OOI
3631
7-55
8.31
2234
mt
"
"
"
"
54-89
0.64
3063
3768
747
8.28
2235
tt 5
g
"
tt
"
(C
57-H
0.62
3125
3903
7-39
8.26
2236
" it
"
it
H
(C
59-39
0.60
3186
4035
7-32
8.24
2237
" 3.
4
tt
"
«
tt
61.64
0-57
3248
4165
7.26
8.22
2238
1 8x1
24X&
3lx3lx|
5x3lxf
33
x3lx§
54.26
0.42
3H4
3766
7-58
8-33
2239
" ¥
tt
"*
"
If
56.51
0.40
3176
3902
7-50
8.3I
224O
" 1
"
tt
"
It
58.76
o-39
3237
4036
7.42
8.29
2241
" It
tt
U
"
tt
61.01
0-37
3297
4168
7-35
8.26
2242
" 3.
tt
"
"
63.26
0.36
3359
4298
7.29
8.24
* Spacing of rivet lines of web greater than 30 X thickness of plate.
190
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
/
1
? ^
1
=/
Properties -4:
.tf4 Six Angles
Top Chord Sections. *»
"
Three Plato.
LJ
=
f
B
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
hor
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
ucr.
Outside.
Inside.
A
e
IA
IB
rA
r«
Inches.
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches*.
Inches4.
Inches.
Inches.
2243
I8xj
24X&
3ix3ixf
5x35X1$
3*x
3*xft
55-88
0.18
3221
3895
7-59
8-35
2244
2245
•f
u
a
M
H
u
58.13
60.38
0.18
0.17
3282
3343
4031
4165
7-Si
7-44
8-33
8.31
2246
2247
-I*
««
M
M
H
62.63
64.88
0.16
0.16
3403
3464
4296
4425
7-37
7.31
8.28
8.26
2248
i8xj
24x&
steW
5x3ixi
3*
M*x|
5746
-•03
33H
4026
7.60
8.37
2249
" A
"
M
M
H
59-71
-•03
3375
4161
7.52
8-35
225O
" f
"
"
"
H
61.96
-•03
3436
4294
7-45
8.33
2251
" tt
"
«
"
"
64.21
-.03
3496
4424
7-38
8.30
2252
.„ j
M
M
H
66.46
-.03
3557
4553
7-32
8.28
20" X 24" Section. A Series.
*22S3
20X*
24X&
35-x3ixf
3ix3^xf
3*
X31X|
48.38
1.94
3136
3i7i
8.04
8.09
2254
M
"
"
"
50.88
1.85
3227
3324
7.96
8.08
2255
"
u
"
(C
5338
1.76
3319
3477
7.88
8.06
2256
II
"
H
H
55-88
1.68
3627
7.81
8.05
2257
H
"
"
"
58.38
1.61
3500
3777
7-74
8.04
'2258
20XJ
24X&
3ix3ix|
3ix3§xA
3*3
3ix^
49-94
1.61
3310
3282
8.14
8.10
2259
<c f
"
«
"
"
52.44
1-53
3400
3435
8.05
8.09
1 2260
" 1
M
"
M
M
54-94
1.46
3489
3587
7-96
8.08
2261
•" tt
"
"
"
"
57-44
1.40
3577
3736
7.88
806
1 2262
" 1
"
59-94
i-34
3665
3886
7.82
8.05
•2263
20.\.\
24X&
3ix3ix|
3ix3|xJ
3*
X3jxj
51.46
I.3I
3466
3387
8.21
8.12
2264
(( §>
C(
"
"
«
1.25
3553
354°
8.12
8.10
2265
" 1
"
"
"
"
56.46
1.19
3640
3691
8.03
8.09
2266
H 11
"
M
H
M
58.96
1.14
3728
3839
7-95
8.07
2267
(i 3
M
M
"
"
61.46
1.09
3815
3988
7-89
8.05
*2268
20xJ
24x&
3Jx3i*f
3ix3ix&
3l>
'3h&
52.94
i. 02
3617
3497
8.26
8.13
2269
N
ft
M
"
55-44
0.97
3703
3649
8.17
8.II
2270
"
<«
"
"
57-94
0-93
3788
3799
8.08
8.09
2271
M
"
"
"
60.44
0.89
3874
3947
8.00
8.08
2272
H
M
"
62.94
0.86
3959
4°95
7-93
8.06
* Spacing of rivet lines of web greater than 30 X thickness of plate.
191
TABLE 85. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
? 1
I
=i
Properties \ • •
j
\A Six Angles
of I
L
— •-&£- and
Top Chord Sections.
j
^ Three Plates.
I f
i f i
f
JLc=!i
L= j cJJL
=.x.
B
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
ber.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2273
20xl
24xA
35*35x1
,1X,IX5
3ix3ix|
54.38
0.76
3752
3599
8.30
8.13
2274
" A
"
"
«
"
56.88
0-73
3836
3751
8.21
2275
;; ti
"
M
H
M
59.38
0.70
3921
3900
8.12
8.10
2276
Te
"
"
"
K
61.88
0.67
4005
4047
8.04
8.08
2277
« 3
"
"
tt
64-38
0.64
4090
4195
7-97
8.07
*2278
20x|
24X&
35x35x1
3lx3lxli
3ix3lxli
55.82.
0-53
3873'
3700
8.33
8.14
2279
<< 9
16
"
"
"
u
58.32
0.50
3957
3851
8.23
8.12
2280
" 5
8
"
"
"
"
60.82
0.48
4041
4000
8.14
8.10
2281
" tl
"
" '
"
M
63-32
0.46
4"5
4H7
8.06
8.08
2282
" 1
M
u
M
M
65.82
0.45
4209
4294
7-99
8.07
*2283
20X|
24x^6-
3ix3lxa
35X35xf
32-x3|xf
57.22
0.30
3985
3800
8-35
8.15
2284
«( 9
"
"
**
59-72
0.29
4068
3951
8.25
8.13
2285
8
"
(C
"
"
62.22
0.28
4151
4099
8.16
2286
" H
"
"
(C
M
64.72
0.27
4235
8.08
8.09
2287
" 1
"
"
M
67.22
O.26
4319
4392
8.01
8.08
20" X 24" Section. B Series.
*2288
20X^
24XJ^
31X31XI
Sx3|xf
3|x3|xf
49.52
1.67
3285
3354
8.14
8.22
2289
" A
"
"
"
"
52.02
1.59
3375
3507
8.05
8.20
2290
" f
"
"
"
"
54-52
1.52
3465
3660
7-97
8.19
2291
« 11
16
"
"
M
(C
57.02
1.45
3554
3810
7-89
8.17
2292
" f
II
u
H
14
59-52
i-39
3642
3960
7.82
8.15
*2293
20X|
24X1%
31X31X|
5X35XTV
35X35XT6
51.26
1-33
3473
3495
8.23
8.25
2294
• • 9
T6
"
"
"
5376
1.27
3560
3648
8.14
8.23
2295
« 5
8
"
"
M
"
56.26
1. 21
3648
3800
8.05
8.22
2296
" ii
"
M
M
M
58.76
1.16
3734
3949
7-97
8.20
2297
« a
u
"
(1
"
61.26
i. ii
3820
4099
7.90
8.18
*2298
20X|
m
32X35X|
5X3 M
31X31X1
52.96
0.98
3644
3631
8.30
8.28
2299
" 1^
"
"
(I
"
5546
0-93
3732
3784
8.20
8.26
2300
" f
"
"
M
H
0.90
3817
3935
8.II
8.23
2301
" H
"
II
u
M
60.46
0.86
3902
4083
8.03
8.21
2302
« 3
4
"
"
ll
62.96
0.83
3988
4232
7.96
8.19
* Spacing of rivet lines of web greater than 30 X thickness of plate.
192
TABLE 85.— Continued.
PROPERTIES OP TOP CHORD SECTIONS.
f
r '
n
'
^
Properties ^
-i^ Six Angles
of ,i ~
T~ and
Top Chord Sections.
^ Three Plates.
U
L
J
1
j
,
Plates.
Angles.
Gross
Eccen-
Moments of
Inertia.
Radii of Gyra-
tion.
Bnction
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
Inches*.
Inches.
Inches.
'2303
MB}
24X&
3ix3Jx|
5*3ixrV
3i*
3ix&
54.64
0.69
3807
3771
8-34
8.30
2304
2305
[f
«
«
H
M
57-14
59.64
0.66
0.63
3891
3975
3923
4073
8.25
8.16
8.28
8.26
2306
2307
:f»
M
«
-
It
62.14
64.64
0.61
0-59
4059
4H3
4221
4369
8.07
8.00
8.24
8.22
'2308
20XJ
24X&
3*x3ixf
5x3ixf
3a:
<3M
56.26
0.42
3949
3904
8.38
8-33
2309
2310
:J
«
M
H
58.76
61.26
0.40
0.38
4033
4117
4056
4205
8.29
8.20
8.3I
8.28
2311
M
"
H
"
63-76
0.36
4208
4352
8.12
8.26
2312
" i
"
"
66.26
0-34
4284
4500
8.04
8.24
'2313
20XJ
24X&
3Jx3ix|
SX3UH
3*x
3 Mi
57.88
0.16
4081
4036
8.40
8-35
2314
2315
•f
«
N
H
H
60.38
62.88
0.15
0.15
4164
4247
4186
4336
8.30
8.22
8-33
8.31
2316
" tt
"
M
"
M
65.38
0.14
4331
4483
8.14
8.28
2317
" 1
H
M
"
67.88
0.14
4414
4630
8.06
8.26
*23I8
20XJ
24X&
3ix3^x|
5x3|xf
3|
*35*1
59-46
-.07
4200
4166
8.40
8-37
2319
" A
M
"
"
"
61.96
-.07
4283
4317
8-31
8-35
2320
" t
M
"
M
M
64.46
-.06
4366
4465
8.23
8.32
2321
"H
"
"
M
M
66.96
-.06
4450
4611
8.15
8.30
1 2322
" a
14
"
M
"
69.46
-.05
4533
4758
8.08
8.28
| 20" X 26" Section.
*2323
20XJ
26xf
3ix3ix|
5x3ixf
3*
«3ixf
52.27
2.14
3485
4272
8.16
9.04
2324
" A
"
"
"
tt
54-77
2.04
3579
4468
8.08
9.03
2325
" I
M
"
M
"
57-27
1.95
3673
4661
8.01
9.02
2326
" H
"
"
"
"
59-77
1.87
3765
4851
7-94
9.01
2327
" 1
H
H
"
"
62.27
1.79
3856
5039
7-87
8-99
•2328
2OxJ
a6x|
3Jx3Jx|
SxsJxxV
3a-*
l]*?s
54.01
1.78
3694
4443
8.27
9.07
2329
T«
"
"
"
"
56.51
1.71
3783
4638
8.18
9.06
2330
" t
"
M
"
"
59.01
1.63
3874
4831
8.10
9.05
2331
" H
"
H
"
M
61.51
3963
5020
8.03
9.04
2332
" i
M
M
"
64.01
I.5«
4052
5207
7.96
9.02
* Spacing of rivet lines of web greater than 30 X thickness of plate.
193
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
Tl
f
B9
Properties ^\
of j
Top Chord Sections.
=H
44 Six Angles
£- and
^ Three Plates.
1. fl
L
J
I
.
3
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
A-A.
B-B.
A-A.
B-B.
Web.
Cover .
Top.
ber.
Outside.
Inside.
A
e
IA
IB
rA
TB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inc hes.
*2333
20x5
26xf
32-x35xf
5X35X5
35X35X2
55-71
1.46
3879
4614
8-35
9.IO
2334
" 9
M
ti
*•
"
58.21
1.40
3967
4809
8.26
9.09
2335
" I'
(I
ii
«
H
60.71
1-34
4056
50OO
8.17
9.08
2336
" H
u
u
H
(C
63.21
1.29
4H3
5189
8.10
9.06
2337
tl 3
I
11
"
"
65-7I
1.24
4230
5375
8.02
9.04
*2338
20X2
26xf
35X35x|
SX31XJ^
35X35X&
57-39
1.16
4°S3
4782
8.40
9-13
2339
"A
M
a
"
"
59-89
i. ii
4139
4976
8.31
9.II
2340
" f
M
it
H
"
62.39
i. 06
4226
5167
8.23
9-10
2341
" tt
"
tt
"
"
64.89
i. 02
4312
5355
8.15
9.08
2342
" 1
le
M
"
67-39
0.99
4397
5541
8.08
9.07
*2343
20x5
26x|
35X35x|
5x3|xf
35
S35X|
59.01
0.89
4211
4945
8-45
9-15
2344
" A
"
M
M
H
61.51
0.85
4296
5138
8.36
9.14
2345
(( 5
8
"
U
"
H
6^.01
0.82
438i
5328
8.27
9.12
2346
" ii
"
M
"
M
66.51
0.79
4466
5516
8.19
9.II
2347
" f
M
69.01
0.76
455°
5701
8.12
9.09
*2348
2ox|
26xf
35X35X5
5x35X16
35*
3lxli
60.63
0.63
4358
5107
8.48
9.18
2349
" T6
"
M
"
«
63-13
0.60
4442
5299
8-39
9.17
2350
« 5
M
«
"
"
65.63
0.58
4527
5489
8.31
9-15
2351
" H
u
a
"
M
68.13
0.56
4611
5675
8.23
9-13
2352
" 3.
M
"
M
70.63
0-54
4694
5860
8.15
9.II
*2353
20X2
26x|
3lx3|xf
5x35x5
35
S31X|
62.21
0.40
4489
5267
8.50
9.2O
2354
T6
"
"
"
"
64.71
0.38
4573
5459
8.41
9.19
2355
« 5
8
"
(C
"
"
67.21
o-37
4657
56,8
8.32
9.17
2356
"H
"
"
u
"
69.71
0-35
4740
5834
8.25
9.15
2357
" f
"
1C
"
"
72.21
o-34
4824
6017
8.17
9-13
22" X 26" Section. A Series.
*23S8
22x2
26x^
4x4x5
4x4x2-
4x4x1
59-13
i-55
4811
4499
9.02
8-73
*2359
" -fg
«
"
"
u
61.88
1.48
4928
4691
8.92
8.71
2360
" f
"
"
"
M
64.63
1.41
5045
4879
8.83
8.69
2361
'' 11
u
"
M
"
67.38
i-35
5163
5066
8-75
8.67
2362
« 3
4
"
"
u
70.13
1.30
5282
5246
8.68
8.65
* Spacing of rivet lines of web greater than 30 X thickness of plate.
194
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
p
Properties A\
of j
Top Chord Sections.
=f=
L4 Six Angles
5- and
, j Three Plates.
U
L J
JL
j,
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
Gross
Eccen-
Section
Bottom. •
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
K»r
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
ucr.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4
Inches4
Inches.
Inches.
•2363
22xJ
26x&
4X4xi
4*4*16-
4*4*1*
60.85
1.23
5023
4640
9.09
8-73
*2364
" A
"
M
M
"
63.60
I.I8
5137
4832
8.99
8.7I
2365
" 4
"
M
M
"
66.^5
I.I3
5252
5019
8.90
8.69
2366
« 11
M
"
H
H
69.10
1. 08
5367
5204
8.8l
8.67
2367
" ^
"
M
"
"
71.85
1.04
5483
5385
8-73
8.65
*2368
taxi
26XTV
4X4XJ
4*4*f
4*4*1
62.57
0-93
5219
4777
9.13
8.74
•2369
fV
"
"
"
"
65.32
0.89
5332
4967
9-°3
8.72
2370
" 1
"
it
ii
H
68.07
0.85
5445
5154
8.94
8.70
2371
2372
:f»
II
M
"
H
«
70.82
73-57
0.81
0.79
5558
5671
5339
5519
8.86
8.78
8.68
8.66
*2373
22XJ
26xA
4x41!
4*4*t*
4*4*H
64-25
0.67
5397
4916
9.16
8-75
*2374
" rV
II
"
"
"
67.00
0.64
5509
5106
9.06
8-73
2375
" 1
M
U
"
"
69-75
0.61
5620
5291
8.97
8.71
2376
" M-
M
"
"
" .
72.50
0-59
5732
5475
8.89
8.69
2377
" 4
U
"
M
75-25
o-57
5844
5655
8.81
8.67
\*2378
22xJ
26x^
4*4*i
4*4*1
4*4*1
65.89
0.41
5563
5047
9.19
8-75
*2379
" A
M
"
"
68.64
0.40
5675
5235
9.09
8.73
2380
" I
"
"
"
H
71-39
0.38
5786
5420
9.00
8.71
2381
" tt
M
"
"
"
74.14
0-37
5888
5604
8.91
8.69
| 2382
i. 3
M
H
H
76.89
0-35
6009
5783
8.84
8.67
1 22" X 26" Section. B Series.
*2383
22X*
26xA
4*4*i
6.\4x J
4*4*i
61.13
1.14
5104
4891
9.14
8-95
•2384
" iV
**
H
1
"
63.88
1.09
5219
5083
9.04
8.93
2385
« 5
M
"
1
"
66.63
1.05
5333
5271
8.95
8.90
2386
« 11
M
M
'
"
69-38
I.OI
5446
5458
8.86
8.87
2387
« j
M
H
"
72.13
0.97
556o
5638
8.78
8.84
*2388
22XJ
26xA
4*4*i
6.\4\19^
4*4*A
63.11
0.80
5333
5082
9.20
8.98
*2389
" A
II
"
'
"
65.86
0.77
5445
5274
9.10
8.95
2390
« 5
"
"
1
"
68.61
0.74
5557
546i
9.00
8.92
2391
" •H'
II
"
1
"
71.36
0.71
5670
5646
8.91
8.89
2392
" $
M
74.11
0.68
5782
5827
8.83
8.87
* Spacing of rivet lines of web greater than 30 X thickness of plate.
195
TABLE 85. — Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
"I ^
)
-^3
Properties ^p-i
of I
=td
^..^4 Six Angles
*£— and
Top Chord Sections.
^ Three Plates.
'U
L
J
JL
J
$
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2393
22X1
26x3^-
4x4x£
6x4x|
43
4xf
65.07
0.48
5544
5267
9.24
9.00
*2394
" A
"
"
"
"
67.82
0.46
5656
5457
9.14
8.97
2395
" f
"
"
•"
"
70-57
0-44
5767
5644
9.04
8.94
2396
" ii
"
M
"
"
73-32
0.42
5879
5829
8-95
8.92
2397
"f
"
H
"
H
76.07
0.41
5991
6009
8.87
8.89
*2398
22x£
26xj^f
4x4^
6x4xH
4x
4xii
66.99
0.19
5735
5456
9-25
9.O2
*2399
" TS
(1
"
"
"
69.74
0.19
5846
5646
9.15
8-99
2400
" f
It
"
"
"
72-49
0.18
5957
5831
9.06
8.97
2401
" ii
"
"
"
"
75-24
0.18
6068
6015
8.98
8.94
2402
<( 3
M
M
"
"
77-99
0.17
6179
6i95
8.90
8.91
'2403
22X|
26x^
4X4X|
6x4xf
4>
4xf
68.89
-.07
5913
5636
9.26
9-04
*2404
" A
"
"
"
"
71.64
-.07
6024
5824
9.16
9.01
2405
" f
"
"
"
"
74-39
-.07
6i35
6009
9.08
8.98
2406
" ii
"
"
"
"
77-14
-.06
6246
6193
8.99
8.96
2407
" f
M
M
«
H
79.89
-.06
6357
6372
8.92
8-93
33" X 26" Section. C Series.
*2408
22X|
26x&
4X4X|
6x4x|
6x4x5
63-13
0.77
5378
4915
9-23
8.82
*2409
« 9
"
"
"
"
65.88
o-73
5491
5106
9-13
8.80
2410
« 5
8
(6
"
"
"
68.63
0.70
5604
5293
9.04
8.78
2411
" ii
"
M
"
(t
71-38
0.67
5479
8-95
8.76
2412
" 1
"
"
"
"
74-13
0.65
5828
5659
8.86
8-73
*24i3
22x|
26xJ»r
4X4X|
6x4x&
6x4x-&
65-37
0.40
5621
5110
9.28
8.84
*24H
« 9
T6
«
a
«
68.12
0.38
5732
5301
9-1.7
8.82
2415
" f
H
"
M
"
70.87
0-37
5844
5487
9.08
8.80
2416
" ii
"
"
"
"
73-62
0.36
5955
5671
8-99
8.78
2417
ll 3
"
u
"
<c
76.37
0-35
6066
5851
8.92
8.76
'2418
22x£
26x&
4X4X|
6x4xf
63
4xf
67.57
0.07
5845
5298
9-31
8.86
*24I9
« 9
"
"
"
"
70.32
0.07
5956
5487
9.21
8.84
2420
" r
H
"
"
"
73-07
0.07
6067
5673
9.12
8.82
2421
" ii
M
"
"
"
75.82
0.06
6178
5857
9-03
8.80
2422
" 3.
M
78.57
0.06
6289
6035
8.95
8-77
* Spacing of rivet lines of web greater than 30 X thickness of plate.
196
TABLE 85.— Continued.
PROPKKIII s m. 'I'm- ( HORD SECTIONS.
f
1 1
•
•P
Properties
of
Top Chord Sections.
*T~"~
— j. —
< z*
Six Angles
and
Three Plates.
1
j...
i _J
<
!=» ail
1
Plates.
Angles.
Moments of
Radii of Gyra-
1 1 1 ' • r 1 1 .1 .
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
A-A.
B-B.
A-A.
B-B.
ber.
Web.
Cover.
Top.
Outside.
Inside.
A
e
IA
IB
TA
TB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches'.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2423
22x1
26x&
4x4x1
6x4xH
6x4xH
69.73
-•23
6047
5480
9-32
8.87
*2424
M
*
M
M
7248
— .22
6158
5679
9-21
8.85
2425
M
"
"
"
75-23
— .21
6269
5863
9-12
8.83
2426
«
M
"
M
77.98
— .20
6380
6046
9.04
8.80
2427
u
M
H
M
80.73
-.19
6491
6224
8.96
8.78
*2428
22x1
26x&
4X4X1
6x4x1
6x4xi
71.89
-•51
6233
5773
9-32
8.87
•2429
" A
M
"
"
•
74.64
-•49
6344
5860
9.22
8.85
2430
" 1
"
M
M
"
77-39
-.48
6455
6044
9.14
8.83
2431
" tt
"
"
"
"
80.14
-•47
6567
6227
9.06
8.81
2432
" i
"
"
M
82.89
-.46
6678
6404
8.98
8.79
22" X 38" Section.
2433
2434
2435
2436
2437
22X|
" ft
" i
22x|
; H
28x|
28xf
4X4X1
M
u
6x4x1
«
6x4x3^
M
«
H
66.94
69.69
72.44
69.22
71.97
1.89
1.81
1.74
1.50
1.44
5326
5447
5566
5636
5753
6156
6389
6620
6391
6623
8.92
8.84
8.77
9.02
8-94
9-59
9.58
9.56
9.61
9-59
2438
** 3.
M
M
M
M
74.72
1-39
5870
6853
8.87
9.58
2439
22xf
28x|
4X4X1
6x4x1
6x4x1
71.50
1.14
5920
6627
9.10
9.62
2440
2441
n»
U
M
«
«
<«
M
74-25
77-oo
1. 10
1. 06
6035
6149
6858
7087
9.01
8-94
9.61
9.60
2442
22X§
28xf
4x41!
6x4x&
6x41 ^r
73-74
0.8 1
6184
6858
9.16
9.64
2443
" H
H
"
"
"
76.49
0.78
6297
7088
9.07
9.63
2444
" i
H
(I
"
M
79.24
0.75
6409
7315
8.99
9.61
2445
22X§
28xf
4X4X1
6x4xf
6x4xf
75-94
0.50
6422
7086
9.20
9.66
2446
1*
"
M
"
"
78.69
0.48
6534
73'5
9.11
9.64
2447
" i
M
H
H
"
81.44
0.47
6645
7542
9.04
9.63
2448
22X|
28x|
4x4x1
6x4xH
r>.\4\ ] ,',
78.10
O.22
6642
73"
9.22
9.68
2449
: H
M
H
H
"
80.85
O.2I
6753
7539
9.14
9.66
2450
" i
M
M
83.60
O.2I
6864
7765
9.06
9.64
'Spacing of rivet lines greater than 30 X thickness of plate.
197
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
f ^
=»
Properties -4. —
^4 Six Angles
of ,
ft- and
Top Chord Sections.
£ Three Plates.
•• J
L
f
J
1
Plates.
Angles.
Moments of
Radii of Gyra-
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
U
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches*.
Inches*.
Inches.
Inches.
2451
22X|
28xf
4x4x2
6x4x5
6x4x5
80.26
-.05
6851
7536
9.24
9.69
2452
" H
83.01
-•05
6962
7763
9.16
9.67
2453
" *
85.76
-.04
7073
7988
9.08
9-65
24" X 28" Section. A Series.
*2454
24XTTT
28xf
4x4x1
4x4x|
4x4x3
67.00
2.OO
6348
6117
9-73
9-S6
*2455
" f
"
"
"
7O.OO
1.92
6502
6376
9.64
9-54
2456
" H
u
"
"
73-00
1.84
6656
6631
9-55
9-53
2457
" *
76.00
I.76
6810
6882
9.46
9-5i
*24S8
24xA
28xf
4x4x2
4x4x^
43
'4XTW
68.72
1.69
6617
6287
9.81
9-57
*2459
" t
M
u
M
u
71.72
1.62
6770
6545
9.72
9-55
2460
" U
74.72
1.56
6920
6799
9-63
9-54
2461
" 'i
"
77.72
1.50
7071
7050
9-54
9-52
*2462
24*&
28xf
4x4x5
4X4xf
4>
^xf
70.44
1.38
6873
6456
9.88
9-58
*2463
" 5.
a
73-44
i-33
7O2I
6712
9.78
9-56
2464
"*!
76.44
1.28
7170
6966
9.69
9-55
2465
"
"
"
79-44
1.23
7319
7215
9.61
9-53
*2466
24X&
28x|
4x4x5
4x4xU
4x4x1!
72.12
i. ii
7103
6625
9.92
9-58
*2467
" 1
75-12
1.07
7250
6880
9.82
9-56
2468
16
78.12
1.03
7397
7133
9.72
9-55
2469
4
81.12
1. 00
7543
7382
9-53
*2470
24XTir
28xf
4x4x1
4x4x1
4x4x1
73-76
0.86
7318
6785
9.96
9-59
*247i
" f
"
"
76.76
0.82
7465
7040
9.86
9-58
2472
" i!
"
"
79.76
o-79
7611
7292
9-77
9-56
2473
" I
"
u
u
"
82.76
0.76
7767
7540
9.69
9-55
24" X 28" Section. B Series.
*2474
24X^
28xf
4x4x5
6x4X5
4J
4X2
69.00
1.61
6713
6.567
, 9-87
9.76
*247S
" f
ft
"
72.00
i-54
6865
6826
9-77
9-74
2476
" H
"
u
75-00
1.48
7015
7081
9.67
9.72
2477
" 31
£{
"
78.00
i-43
7164
7332
9-58
9.69
* Spacing of rivet lines of web greater than 30 X thickness of plate.
198
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
1 T
r
Properties Aj
of ,1
Top Chord Sections.
=tzj
A4 Six Angles
*j- and
j Three Plates.
1, f|
L
J
UL
j
I
Plates.
Angles.
Moments of
Inertia.
Radii of Gyra-
tion.
Gross
Eccen-
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
ber.
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches1.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2478
28x|
4x4xi
6x4x^5
41.
n&
70.98
1.26
7010
6794
9-94
9.78
•2479
u
H
H
"
73-98
1. 21
7158
7052
9.84
9.76
2480
M
(C
"
"
76.98
I.I7
7305
7306
9-74
9-74
2481
M
flfl
"
"
79.98
I-I3
7452
7557
9.65
9.72
*2482
2 -J. \ j g
a8x{
4*4*3-
6x4x1
4x4x1
72-94
0.94
7285
7019
9-99
9.81
*2483
" I
"
"
"
75-94
0.90
7431
7275
9.89
9-79
2484
I'P
M
M
M
78.94
0.87
7577
7529
9.80
9-77
2485
" i
(C
"
H
M
81.94
0.84
7723
7778
9.71
9-75
'2486
24x&
28x|
4*4X3-
6x4xH
4^
Utt
74.86
0.64
7535
7244
10.03
9.84
•2487
" t
M
"
"
«
77-86
O.62
7680
7499
9-93
9.82
2488
" tt
"
"
"
H
80.86
O.6O
7825
7752
9.84
9.80
2489
" I
14
M
H
83.86
0.58
7970
8001
9-75
9-77
'2490
24X&
28xf
4X4X|
6x4x1
4x4x1
76.76
0.36
7770
7460
10.05
9.86
*249I
" I
"
"
"
79.76
o-35
7913
7715
9.96
9.83
2492
" 4
"
"
H
H
82.76
o-34
8057
7967
9.87
9.81
2493
" 1
"
"
H
85.76
0-33
8202
8215
9.78
9-79
24" X 28" Section. C Series.
*2494
24X&
28x|
4x4xJ
6x4xJ
6x
7I.OO
1.23
7061
6606
9.98
9.65
249?
j 1
14
"
«
74.00
1.19
7208
6864
9.87
9.63
2496
Hi*
ft
M
"
"
77.00
1.14
7356
7119
9.78
9.62
2497
5.
"
"
"
8O.OO
I.IO
7503
7368
9.69
9.60
*2498
"4 ^ 1 ti
28x|
4X4xJ
6x4x^
6x<
p<&
73-24
0.85
7379
6838
10.04
9.66
2499
" 1
(C
a
"
1
76.24
0.82
7525
7095
9-93
9.64
2500
H
M
"
"
H
79.24
0.79
7671
7348
9.84
9-63
2501
" 1
M
"
M
(f
82.24
0.76
7598
9-7S
9.61
*2502
2-|.\ j ^
28x|
4x4x1
6x4xf
61
4*t
75-44
0.53
7670
7068
10.08
9.68
'2503
" 1
"
M
<
78.44
0.51
7815
7322
9.98
9.67
2504
" H
M
"
"
<
81.44
0.49
7960
7575
9.89
9.65
2505
" i
"
1
84.44
0.47
8104
7823
9.80
* Spacing of rivet lines of web greater than 30 x thickness of plate.
199
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
f
"i"^-\
r
Properties
of .i
Top Chord Sections.
.LJ
=4=
LM
-^ Six Angles
f- and
j, Three Plates.
ul
j
i
Section
Num-
ber.
Plates.
Angles.
Gross
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Web.
Cover.
Top.
Bottom.
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Outside.
Inside.
A
e
U
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2507
2508
2509
24XT5
" f
" H
« 3
28xf
M
H
ti
6x4x^5
it
6x,
t?H
77.60
80.60
83.60
86.60
O.2O
O.2O
O.I9
0.19
7937
8081
8225
8369
7298
7551
7803
8051
IO.IO
IO.OO
9.92
9-83
9.70
9.68
9.66
9.64
*25II
2512
2513
24Xj.
" H
" a
28xf
H
«
u
6x4x5
u
It
6x4x5
H
M
7976
82.76
85.76
88.76
-.08
-.08
-.07
-.07
8185
8329
8473
8617
7519
7772
8022
8269
IO.I2
10.02
9-93
9.85
9.71
9.67
24" X 30" Section.
2515
2516
MXL
« 3
3°f
u
6T!
6x4x1
72.57
75-57
78-57
2-43
2-33
2.24
6831
6993
7152
7875
8187
8498
9.70
9.62
9-53
10.42
10.41
10.40
2518
2519
2"XH
" f
3Oxj^
it
6x4x3^
6x4x1^
u
74-85
77-85
80.85
2. 02
1.94
1.87
7228
7384
7539
8157
8468
8778
9-83
9-74
9.66
10.44
10.43
10.42
2521
2522
" 3
3Oxxi
4x4x5
II
6x4x5
M
6x
«
77-13
80.13
83-13
1.64
i-59
1.52
7593
7745
7896
8439
8749
9057
9.92
9.84
9-75
10.46
10.45
10.44
2524
2525
2"X||
" I
3°;f
4x4x5
M
6x.
l-Xiif
H
79-37
82.37
85.37
1.29
1.24
i. 20
7934
8083
8231
8716
9025
9332
IO.OO
9.91
9.82
10.47
10.46
10.45
2527
2528
2"X|i
" 1
«
4x4x5
M
6x4X5
H
6x
ll
M
81-57
84-57
87-57
0.96
o-93
0.90
8248
8395
8541
8989
9297
9603
10.05
9-97
9.88
10.50
10.48
10.46
2530
2531
rj>
3oxH
4Xf*
M
6xi
::H
83-73
86.73
8973
0.66
0.64
0.62
8531
8677
8822
9258
9565
9870
10.09
IO.OO
9.91
10.52
10.50
10.49
* Spacing of rivet lines of web greater than 30 X thickness of plate.
200
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
'
••
T'TT
•H
3
A !
£f ' T"-"-
Top Chord Sections.
JLa
-
L
J
A4 Six Angles
r~ and
,i Three Plates.
JL
J,
Section
NHMI-
ber.
Plates.
Angles.
Gross
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Web.
Cover.
Top.
Bottom.
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Outside.
Inside.
A
e
IA
IB
rA
r.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches*.
Inches4.
Inches.
Inches.
2533
2534
24x|
3°XH
4X4x1
6x4x1
6x4xf
«
85.89
88.89
91.89
0.38
0-37
0.36
8806
8950
9094
9526
9832
10135
10.13
10.04
9-95
10.53
10.52
10.50
26" X 30" Section. A Series.
*2535
*2S36
2537
26x;
i
M
4x4x1
M
4
K4xl
75-63
78.88
82.13
2-47
2-37
2.27
8220
8421
8623
8157
8499
8834
10.38
10.32
10.26
10.38
10.37
10.36
•2538
*2539
2540
26x;
i
3°XH
IXiXl
<(
«
43
4,x&
77-35
80.60
83.85
2.06
1.98
8559
8757
8953
8363
8704
9038
10.52
10.43
10.34
10.40
10.39
10.38
*2542
2543
26x;
J,
3OXH
Tl
T*
4
*4xf
«
M
79.07
82.32
85-57
-85
.78
8878
9062
9265
8563
8904
9237
10.59
10.49
10.40
10.41
10.40
10.39
*2344
2546
26*
i
<«
4x4x1
M
4*
4*H
80.75
84.00
87.25
•57
•45
9169
9360
9551
8764
9103
9425
10.65
10.55
10.45
10.42
10.41
10.39
*2547
•2548
| 2549
26x;
I
3oxtt
4x4x1
M
4X44
4x4xf
82.39
85.64
88.89
•32
•27
.22
9441
9629
9817
8962
9301
9632
10.70
10.60
10.50
10.43
10.42
10.41
1
26" X 30" Section. B Series.
*255o
2552
26X
i
«
4x4x1
«
4x4x1
77-63
80.88
84.13
2.08
2.OO
1.92
8669
8865
9061
8669
9011
9346
10.56
10.46
10.37
10.57
10.55
10.53
*25S3
*2554
2555
26x
I
M
4x4x1
6x4^
M
4X4X&
M
79.61
82.86
86.ii
1-73
1.65
i-57
9042
9238
9434
8939
9280
9614
10.65
10.55
10.46
1 0.60
10.58
10.56
*2557
2558
26x
1C
1C
I
M
4x41!
M
4x4x1
81-57
84.82
88.07
1.41
1.36
1.31
9389
9577
9766
9203
9544
9877
10.72
10.62
10.53
10.62
10.60
10.58
* Spacing of rivet lines of web greater than 30 X thickness of plate.
52
201
TABLE 85.— Continued.
PROPERTIES OF TOP CHORD SECTIONS.
' T
• T
I
sar
Properties -4^
l^ Six Angles
of i
£— and
Top Chord Sections.
^ Three Plates.
0=4
L
Jl
T
=».*_
J
t
Plates.
Angles.
Moments of
Radii of Gyra-
Gross
Eccen-
Inertia.
tion.
Section
Bottom.
Area.
tricity.
Axis
Axis
Axis
Axis
Num-
Kor
Web.
Cover.
Top.
A-A.
B-B.
A-A.
B-B.
ucr.
Outside.
Inside.
A
e
IA
IB
rA
rB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches2.
Inches.
Inches4.
Inches4.
Inches.
Inches.
*2559
26xf
3oxxi
4x4x5
6x4xH
4x
4xH
83-49
I. II
9707
9468
10.78
10.64
" IS
M
"
M
"
86.74
1.07
9894
9807
10.68
10.62
2561
" I
"
M
H
89.99
1.03
lOOSl
10139
10.58
10.61
*2562
26x|
30xH
4x4x5
6x4X4
4x4x1
85-39
0.82
IOOII
9730
10.83
10.67
*2563
" tt
u
"
u
M
88.64
0.80
10195
10069
10.72
10.65
2564
<< 3
4
"
"
"
"
91.89
0.78
10379
10400
IO.62
10.63
26" X 30" Section. C Series.
'2565
26xf
30X11
4x4x5
6x4X5
6:
C4x|
79.63
1.70
9100
8727
10.69
10.46
*2566
" H
"
"
"
H
82.88
1-63
9292
9067
10.59
10.45
2567
" i
u
M
M
fl
86.13
i-57
9481
9403
10.49
10.44
'2568
26xf
30XT!
4X4X5
6x4x^
6x
4XT*
81.87
1.33
9500
9004
10.76
10.48
*2$6g
" 11
"
d
M
"
85.12
1.28
9688
9343
10.66
10.47
2570
" t
M
M
"
"
88.37
1.24
9875
9676
10.56
10.46
*257i
26xf
3°xii
4x4x5
6x4xf
6:
C4xf
84.07
0.99
9870
9275
10.83
10.50
*2572
" tt
"
ft
"
a
87.32
o-95
10056
9614
10.73
10.49
2573
" 1
It
M
"
90.57
0.91
10243
9946
10.63
10.47
*2574
26xf
3°xii
4x4x1
6x4xH
6x
4x!i
86.23
0.66
IO2I2
9548
10.88
10.51
*2S7S
" ii
M
a
«
N
89.48
0.63
10397
9885
10.77-
10.50
2576
" I
it
u
"
"
92-73
0.61
10582
10215
10.67
10.49
*2577
26xf
3ox^
4x4x5
6x4xf
6:
qjcf
88.39
o-37
I053O
9817
10.92
10.53
*2S78
"ft
"
"
«
H
91.64
0.36
IO723
10154
10.82
10.52
2579
" 3
"
<«
"
it
94.89
o-35
10897
10483
10.72
10.51
26" X 32" Section.
2580
26xf
32X|
4x4x5
6x4xf
6:
C4xf
84.94
2.77
9017
10718
10.30
11.23
2581
f" 7
ft
87.22
2-39
9498
11048
10.44
11.25
2582
2
89.50
2.03
9948
H379
10.54
11.27
2583
« 9
T6
9
T6
91.74
1.69
10369
11703
10.63
11.29
2584
" I
1
93-94
i-37
10761
12023
10.70
11.31
2585
" H
H
96.10
i. 06
III24
12338
10.76
"•33
2586
« 3
4
i
98.26
0.80
11466
12652
10.80
n-35
* Spacing of rivet lines of web greater than 30 X thickness of plate.
202
TABLE 86.
PROPERTIES OF TOP CHORD SECTIONS.
f
Eight Angles with
Short Legs Turned Out
and Five Plates.
rirn
Properties of .-«4-
Extra Heavy
Top Chord Sections. <l
.1. JL J
j.
Lg
Ll
Sec-
tion
Num-
ber.
Plates.
Angles.
Gross
Area.
Eccen-
tricity.
Moments of
Inertia.
Radii of Gyra-
tion.
Web.
Cover.
Top.
Bottom.
Axis
A-A.
Axis
B-B.
Axis
A-A.
Axis
B-B.
Outside.
Inside.
Outside.
Inside.
A
e
U
IB
r\
TB
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.
Inches.*
Inches.
Inches.*
Inches.4
Inches.
Inches
22" X 28" Section.
2901
2902
2903
2904
2905
2906
22X&
" i
" A
" 1
" «
" i
28Xi
«
M
H
«
H
6X4Xi
«
«
«
«
a
6X4X2-
«
«<
H
6X6Xf
«
«
«
«<
«
6X6X1
H
H
M
M
M
99.94
105.44
110.94
1 16.44
121.94
127.44
0.65
O.62
0-59
0.56
0-53
0.51
7436
7660
7884
8107
8330
8554
9070
9478
9871
10255
10627
10987
8.62
8.52
8.42
8.34
8.26
8.19
9-53
9.48
9-43
9-38
9-33
9.28
24" X 30" Section.
2907
2908
2909
2910
2911
24X*
" A
" I
" H
" i
30Xf
H
«
<«
«
6X4Xi
M
H
M
«
6X4Xi
«
M
M
6X6X1
<«
«
M
M
6X6Xf
«
«
«<
«
119.51
I25-5I
I3I-5I
137.51
I43-5I
0.64
0.61
0.58
0-55
0-53
IO7IO
IIOOO
11290
11580
11870
12874
I34I3
13934
14441
14937
9-47
9-36
9.27
9.18
9.10
10.38
10.34
10.29
10.25
10.20
26" X 32" Section.
2912
2913
2914
29IS
26X&
" f
" H
" i
32Xf
«
M
1C
6X4Xi
H
«
H
6X4Xi
M
«
«<
6X6X!
M
«
6X6X1
n
H
«<
131.26
137.76
144.26
150.76
0.74
0.70
0.67
0.64
13505
13874
14243
14613
16638
17335
18015
18682
10.14
10.03
9-94
9.85
11.26
11.22
11.17
11.13
28" X 34" Section.
2916
2917
2918
28x1
" H
" 1
34Xf
«
«
6X4Xi
«
«
6X4Xi
«
M
6X6X1
«
M
6X6X2
«
144.01
151.01
158.01
0.83
0.79
0.76
16791
17253
17715
21238
22126
22997
10.80
10.69
10-59
12.14
12.10
12.06
30" X 36" Section.
2919
2920
3QXH
" 1
36Xf
6X4Xi
«<
6X4XJ
«
6X6XJ
«
6X6Xi
«
157.76
165.26
0.92
0.88
20627
21196
26810
27920
11.44
"•33
I3-03
I3.OO
203
TABLE 87.
PROPERTIES OF PLATE GIRDERS.
Some specifications require that plate girders be proportioned by the moment of inertia of
their gross section and some by the moment of inertia of their net section. The moment of inertia
of the gross section can be obtained by direct addition from Tables 3, 5 and 33. The moment of
inertia of the net section is obtained by subtracting the moment of inertia of the holes from that
of the gross section. The moment of inertia of the holes can be calculated by the formula / = AJP,
the moment of inertia of the holes about their own axis being negligible, AQ being the diametral
area of the hole and h the distance from the neutral axis to the center of the hole.
The method of calculating the moments of inertia of plate girders will be illustrated by a typical
example.
Example: Determine the moment of inertia and section modulus of a section consisting of
4 angles s"x3^"x^", long legs out, 24!" back to back, i web plate 24"x|", 2 cov. plates I2"xf".
Moment of Inertia and Section Modulus of Gross Section.
Item.
b. to b. Angles.
Extreme Fiber.
Moment of Inertia, Axis A-A.
Section Modulus.
d
c
Table.
I
S = lie.
Inches.
Inches.
Inches.
Inches4.
Inches*.
4 A 5x3^
I Wb. PI. 24xf
2 COV. PI. I2xf
24.5
«
12.25 + 0.625
33
3
5
2074
432
2366
4872
12.875'
12.875
Total / =
4872
S = 378.4
Moment of Inertia of Rivet Holes (£" Rivets, i" holes).
Location.
Number.
Size.
Area.
Dist. to 0 of
Hole,
Dist.2
Aoh*
t Xd
Ao = t X d
h
h'
Inches.
Inches.*
Inches.
Inches5.
Inches4.
Web
Flange
2
4
ifxl
l|xl
2-75
4.50
10.3
12.3
106.1
I5I-3
292
68 1
Total =
973
The Moment of inertia of the net section is 4872 — 973 = 3899 in.4, and the section modulus
is 3-899 -h 12.875 = 302.8 in.3.
Approximate Methods.
The use of the moment of inertia of the net section in proportioning plate girders, requires
that holes in the compression flange be deducted as well as those in the tension flange. This only
approximates the true condition so that great accuracy in calculating the moment of inertia of the
net section does not seem warranted. The following approximate solutions give results which are
sufficiently accurate for use in design.
ist Approximate Method:
Net / of Angles = Gross I X ^ '_ A^_ = 2074 X —^ = 1556 Table 33.
Gross Area
Net 7 of Web PL = Gross 7 of Net Depth = 7 of 22" X f " PL = 333
Net 7 of Cov. Pis. = Gross 7 of Net Width = 7 of 2 - 10" X f " Pis. = 1972
Total Moment of Inertia of Net Section = 3861 in.4
2d Approximate Method:
^N^fet Arcs ^2 *7C
Net 7 = Gross 7 X „ . = 4872 X ^^ = 3989 in.4
Gross Area 40.00
This method gives more accurate results for sections without cover plates.
204
TABLE 88.
CENTERS OF GRAVITY OF PLATE GIRDER FLANGES.
CHICAGO, MILWAUKEE & ST. PAUL RY.
c
(.
::j
— i .
1
— — ? — '
^~! — |
N ' '
Tf— -— --I f
cgr.-^
r"§i c&-' *~~ r
L=L J
ffl
4 IJ
Type
/ &
0?
* i-f
Type 5
TYPE i.
TYPE 2.
Two 6" x 4" Bottom Angles.
Four 6" x 4" Bottom Angles.
Two Top
Thickness in Inches.
Two Top
Thickness in Inches.
Angles.
Angles.
1
\
i
i
{
i
i
A f
1
i
Inches.
In.
In.
In.
In.
In.
Inches.
In.
In.
In. In.
In.
In.
8X8XJ
3.81
4.12
4-35
4-55
4.70
O \/ O V./ 1
O ^v O y"\ 2
5-12
5-53
5.69 5.85
6.07
6.27
i
3.62
3.90
4.12
4-30
4-45
i
4.81
5.22
5.40 5.54
5-79
5-98
3-49
3-75
3.96
4-13
4.27
a
4-59
4.99
5.16 5.30
5-SS
5-75
I
3-39
3-70
3-83
3-99
4-1.3
j
4.42
4.80
4.96 5.11
5-25
5-57
I
3-33
3-55
3-73
3-89
4-03
i
4.28
4-6S
4.81 4.96
5.19
5.41
\\
3-28
3.48
3-67
3-81
3-94
li
4-38
4-53
4.66 4.82
5-o6
5-26
TYPE 3.
Width
Size
of
Thickness of Plate,
Inches.
of Angles.
Plate.
In.
In.
o
1
i
t
i
i
i
Ii
ii
t|
ii
II
il
ii
3
2}
3
6X6XJ
13
1.68
1. 12
. .98
.86
•73
•63
•52
43
•33
•»4
•IS
.07
— .02
— .10
— _
18
I.OC
> -95
.82
.70
• 59
.48
39
.29
.20
.11
.03
-.06
-.14
— .
22
IS
1.0;
' .92
•79
.66
•55
•45
35
•25
.16
.07
— .01
— .IO
-.18
— .
20
16
1.0.
[ -89
•75
•63
•52
.41
31
.21
.12
.04
-.os
-•13
— .21
— .
29
6X6X1
13
1.73
1.24
^i.n
•99
•87
•77
.67
S7
•47
• 3S
.30
.21
•13
.04
-.04
.
14
1.21
1.08
•95
.8.3
•73
•63
^"3
•43
•34
•25
•17
.08
.OO
-.08
IS
I.iq
l 1.05
.92
.80
.69
•59
•49
•39
• 30
.21
•13
.04
-.04
— .
12
16
l.lt
1 1. 02
.89
•77
•65
•55
45
•35
.26
•17
.09
.OO
-.08
— .
10
6X6XJ
13
1.78
1-34
\. I.2I
1. 10
•99
.89
•79
69
.60
•51
.42
•34
•25
.16
.
Of)
14
1-31
1.18
1.07
•95
.8s
•75
65
•55
.46
.38
.29
.20
.12
•05
IS
I.2C
11.15
1.03
.92
.81
•71
6 1
.42
•33
.25
.16
.06
.00
16
I.2<
> 1.13
I.OO
.88
.78
.67
59
•47
•38
.29
.21
.12
.03
-.04
6X6X1
13
1.82
1.42
, 1.30
1.19
1.09
•99
.89
So
.62
•54
•45
•37
•29
21
i-3c
M.27
1.16
i. os
•95
.8s
76
.66
.57
•49
.40
•32
•24
16
IS
i-35
' 1.24
I-I3
I.OI
.91
.81
72
.62
•S3
•44
•36
•27
.19
.
11
16
i-3f
1.22
1. 10
.98
•87
•78
OS
•58
•49
.40
•32
.22
•14
.07
8X8Xi
17
2.19
i.-p
Jl.32
1.17
1.03
•90
.78
•56
•36
•17
— .
CI
-•33
-.64
18
i.4<
) 1.29
1.14
I.OO
.86
•74
•52
•32
•13
-.04
-•37
-.68
8X8X1
17
2.23
1.6-
I i-47
1.32
1.19
.07
•95
•73
•53
•34
17
-.16
-.48
18
i.6(
>i-44
1.29
I. IS
.02
•91
.69
•49
.30
.
12
— .21
-.52
8X8X!
17
2.28
1-7
; i .00
1.46
1.33
.22
.10
.88
.68
•46
•31
— .02
-.36
18
1.7-
1 1.57
1.43
1.29
•17
.06
.84
.64
•42
27
-.06
-.40
8X8X1
17
2.32
1.8
; 1.71
1-57
i-45
•33
.22
I.OO
.81
.62
•45
.11
— .20
18
1.8
i 1.67
1-53
1.41
.29
.18
•96
•77
•57
40
.07
-•25
8X8X1
17
2.37
1.9-
[ 1.80
1.68
i-55
•45
•35
1-13
•94
•75
58
•25
-.08
18
l-9<
> 1.76
1.64
LSI
.40
•30
1.09
.89
.71
53
.20
— .12
8X8XH
17
2.41
2.O
: 1.89
1.77
1.66
•55
•45
1-25
I.O
5
.87
.70
•36
.06
18
1-9
3 1.85
1-73
1.62 .50
.40
i. 20
I.OO
.83
•65
•32
.OI
205
TABLE 89.
UPSET SCREW ENDS FOR SQUARE BARS.
AMERICAN BRIDGE COMPANY STANDARD.
m
•-^tlTlftitMt^
HSU
\
.i
•I
Pitch and Shape of Thread A. B. Co. Standard.
BAR.
UPSET.
Side of
Square
d,
Inches.
Area,
Sq.
Inches.
Weight
per
Foot,
Lbs.
Diameter
b,
Inches.
Length
a,
Inches.
Additional
Length
for
Upset
+ 10%,
Inches.
Diameter
at
Root of
Thread
c,
Inches.
Area.
At Root
of
Thread,
Sq. Inches.
Excess
Over
Area of
Bar, %.
* i
O-S^S
1.91
ii
4
4
0-939
0.693
23.2
* i
0.766
2.6o
ii
4
3*
1.064
0.890
16.2
i
I.OOO
3-40
i*
4
4
1.283
1.294
29.4
il
1.266
4-30
if
4
3i
1.389
I-SIS
19.7
ij
1-563
5-31
if
4i
\\
1.615
2.049
31-1
if
1.891
6-43
2
4l
4
I.7II
2.300
21.7
ij
2.250
7-65
*i
5
5
1.961
3-O2I
34-3
if
2.641
8.98
2|
5
4l
2.086
3-4I9
29-5
il
3-063
10.41
»i
5i
4l
2-175
3-7I6
21.3
if
3-516
. n-95
2f
si
5
2.425
4.619
3i-4
2
4.000
13.60
2f
6
5
2-550
5.108
27.7
*i
4-516
15-35
3
6
4*
2.629
5.428
20. 2
*l
5-063
17.21
3i
6§
5^
2.879
6.509
28.6
2|
5.641
19.18
3i
7
6i
3.IOO
7-549
33-8
a*
6.250
21.25
3f
7
7
3-3I7
8.641
38-3
i^
2g
6.891
23-43
3f
7
si
3-3I7
8.641
25.4
2|
7-563
25.71
4
71
6i
3-567
9-993
32.1
»i
8.266
28.10
4l
8
7i
3-798
11-330
37-1
3
9.000
30.60
4l
8
6
3-798
11-330
25-9
3l
9.766
33-20
4i
8|
7
4.028
12.741
30.5
3l
10.563
35-91
4f
8J
71
4-255
14.221
34-6
Upsets marked * are special.
206
TABLE 90.
UPSET SCREW ENDS FOR ROUND BARS.
AMERICAN BRIDGE COMPANY STANDARD.
ymm
t.ft
Pitch and Shape of Thread A. B. Co. Standard.
BAR.
UPSET.
Diameter
d.
Inches.
Area,
Sq.
Inches.
Weight
per Foot,
Lb.
Diameter
b.
Inches.
Length
a,
Inches.
Additional
Length
for Upset
+10 %.
Inches.
Diameter
at Root
of Thread
c.
Inches.
Area.
At Root
of Thread,
Sq. Inches.
Excess
Over Area
of Bar. %.
*i
0.442
1.50
I
4
4
0.838
0-5SI
24-7
* I
0.601
2.04
ii
4
S
1.064
0.890
48.0
i
0.785
2.67
if
4
4
1.158
1.054
34-2
ii
0.994
3-38
ii
4
4
1.283
1.294
30.2
ii
1.227
4.17
it
4
4
1.389
I-5I5
23-5
if
1.485
5-05
if
4
4
1.490
1.744
17-5
ii
1.767
6.01
2
4i
4i
I.7I1
2.300
30.2
if
2.074
7-oS
2|
4i
4
1.836
2.649
27.7
if
2.405
8.18
2i
5
4
1.961
3-O2I
25.6
if
2.761
9-39
2f
5
4
2.086
3419
23.8
2
3.142
10.68
2i
si
4
2.175
3.716
18.3
2j
3-547
12.06
2|
Si
Si
2.300
4.156
17.2
.2i
3.976
I3-52
2l
6
4i
2.550
5.108
28.4
*2f
4.430
15.06
3
6
4i
2.629
5428
22.5
2i
4.909
16.69
Si
6i
Si
2.879
6.509
32.6
2|
5.412
18.40
Si
6i
4i
2.879
6.509
20.3
2f
5-940
20.19
si
7
si
3-IOO
7-549
27.1
2j
6.492
22.07
Si
7
6
3.3I7
8.641
33-i
3
7.069
24.03
Si
7
5
3-3I7
8.641
22.2
Si
7.670
26.08
4
7i
6
3 '5^7
9-993
30.3
3i
8.296
28.21
4
7i
5
3 *5^7
9-993
20.5
3l
8.946
30.42
4i
8
si
3-798
11-330
26.6
si
9.621
32.71
4i
8
s
3-798
11.330
I7.8
Si
10.321
35-09
4i
8i
si
4.028
12.741
23-4
si
11.045
37-55
4f
8i
6
4-255
14.221
28.8
3i
n-793
40.10
4l
81
si
4.255
14.221
2O.6
Upsets marked * are special.
207
TABLE 91
STANDARD EYE BARS
AMERICAN BRIDGE COMPANY STANDARDS
ORDINARY EYE BARS
'
C
j
ADJUSTABLE EYE BARS
1 ,
.Xi
sr~T
9-1 ?
H3
t
71
Jl "-V^fx"
\<C MIIHIIHII t)I !
11 — ^q
i |
;
N-.A-- ^
BAR
HEAD
BAR
SCREW END
d
1
2
3
Thick-
ness
d
.<$
p
Max. Pin
Add. Material A
d
Min. Thickness,
In.
d
11
Wo
d
a
Add. Material B
For Order-
ing Bar,
In.
For Figur-
ing Weight,
In.
d
3
•o
Is
If
For Order-
ing Bar,
Ft. & In.
Fo' Figuring
Weight of
Bar, Ft. &
In.
d
t
ti
3
1
f
* of
If
If
I- 0
I- 4
I- 9
o- 7
O-II
i- 4
2
*f
1
If
II
2
39-6
36.6
3i-4
4
4l
3
12
12
II
8
71
71
37-S
6
7
* 8
3l
I- 3
i- 7
2- 0
o-io
I- 2
i- 7
4
1
1
I
3
41.2
38.1
36.7
s
5
12
12
12
8
8
7l
40.0
H
f
71
81
* 9l
Sf
4l
3
i- 6
i-n
2- 4
I- I
i- 5
I-IO
3
*l
I
2|
34-3
41.6
23-9
ij
si
12
13
13
7l
9l
81
41.7
4
If
f
1
i
10
ii
*I2
si
I-II
2- 3
2- 8
i- 6
I-IO
2- 2
4
*j
1
I
2|
2f
23-9
32.0
35-7
44.6
si
I1
61
13
II
13
14
8|
71
81
9l
37-S
S
6
7
8
2
f
i
i
12
*'3*
I
2- I
2- 8
3- 3
I- 8
2- 2
2- 9
35-o
S
!
i
ij
li
3f
36.2
24.1
30.2
34-2
38.3
6
6
6|
7
7
12
II
12
13
H
8
7
8
9
2
2
2
2
2
2
f
i
i
I4f
5f
6* ,
•81
2- 6
3- 2
I-IO
2- I
2- 8
37-S
i
If
ii
i6|
7
8
9
2- 7
2-1 1
3~ 4
2- 2
2- 6
2-1 1
6
*i
if
[i
i
ts
25-8
28.0
33-2
37-3
7
7
7l
8
12
12
13
H
71
8
9l
35-7
Ii
~T
Ii
Ji
II
il
18
19
*20
7
8
9
2- 8
3— ^
3- 4
2- 3
2- 6
2-1 1
.37-5
7
11
if
4!
26.9
29.5
32.4
35-4
7l
8
81
8|
12
13
14
14
8
9
10
20
*22
71
9*
38.9
2-1 1
3~ 7
2- 6
3- i
24
9
3- 5
3 -9
4- i
2-10
3- 3
3- 7
8
If
ij
if
i!
25-9
27.4
29-3
3i-4
35-2
8
8|
8|
9
9i
12
13
13
IS
8
01
°2
81
2
9
10
3S-o
12
282
10
n|
13
37-S
3-8
4- 2
4-8
3- 3
3-8
4- i
Bars marked * should only be used when un-
avoidable.
Minimum length of short end from center of pin
to end of screw 6'-6", preferably i'-o".
Thread on short end to be left hand.
Deduct Pin Holes when figuring weights.
H
2
2
if
if
31
33
*34
12
4- 3
4-10
s- s
3- 9
4- 4
4- 8
35-7
16
if
if
36
*37l
14
16
37-S
344
4-1 1
s- s
4- S
4-10
Bars marked * should only be used when ab-
solutely unavoidable.
Deduct Pin Holes when figuring weights.
208
TABLE 92.
LOOP RODS.
AMERICAN BRIDGE COMPANY STANDARD.
• l*? ' I'f r*"^****
Thl^d ~^*> "Tti* Left Thread ., ^—— -~"t *k.
i
»*V For Turnbuckle
•H& For Slew* Nut
— f- -«s^^==aBr~
[inhnura Length=4' 7"-' 4" A •*
1
pe of Thread A. E. Co. Standard.
" IN FEET AND INCHES FOR ONE LOOP.
^ - 4-I7P + S-8oR.
Pitch and Sha
ADDITIONAL LENGTH "A
j
Oi.un.
of 1'in,
P.
Diameter or Side "R" of Rod in Inches.
J
t
I
Ii
It
H
ii
it
ii
ii
2
2
at
2l
3
3i
*4i
4i
f
*si
*s
6
*6t
7
o- 9*
o-io
o-n
I- 0
i- i
I- 2
i- 3
x~ 4
i- S
i- 6
i-7i
O-IO
o-ioi
o-nj
i-oi
I- Ii
i- 3
1-4
i- S
i- 6
i- 7
i- 8
i- 9
I-IO
i-ii
2- O
2- I
2- 2i
o-n
o-ni
i-oi
i- ii
1:1
j-7i
I-IO
i-ii
2- O
2- I
2- 2
2- 3
2- 4
2- S
2- 6
2- 7
o-ui
I- 0
I- I
I- 2
i- 3
5- si
i-6i
!:9i
i-ioi
I-IIi
2-oi
2- Ii
2- 2i
2-3i
2- 6
2- 7
2- 8
2- 9
2-IO
2-1 1
3- o
I- I
I- 2
i- 3
i- 4
i- 6
i- 7
i- 8
i- 9
I-IO
i-n
2- Oi
2- Ii
2- 2i
2-3i
2-4i
2- si
2- 6i
2- 7i
2- 8i
2- 9i
2-ioi
3- o
3- i
i- si
i- 7
i- 8
i- 9
I-IO
i-n
2- O
2- I
2- 2
2- 3
2- 4
2- S
2- 6
2-7*
- - ^i
2-9i
2-ioi
2-1 1 i
3-oi
3-ii
i- si
i- 6i
1-7}
i- 8i
i-ioi
i-n>f
2- o|
2- 2
2- 3
2- 4
2- S
2- 6
2- 7
2- 8
2-9
2LIO
2-1 1
3- o
3- i
3- 2i
i- S
i- 6
i- 7
i- 8
2— O§
2- Ij
2-3i
2- 4i
2- si
2- 6i
2-7i
2- 9
2-10
2-1 1
3- o
3- i
3- 2
3- 3
i- 6
i- 7
i- 8
i- 9
I-IO
i-n
2- 0
2- I
2- 2
2- 3
2-4i
2- Si
2- 6i
2- 7i
2- 8i
2- 9i
2-ioi
2-1 1 i
3- oi
3- ii
3~ 2i
l- H
i-8i
i-n
2- 0
2- I
2- 2
2- 3
2- 4
tk
2- 7
2- 8
2- 9
2-IO
2-1 1 i
3- oi
3-ii
3— 2i
3- 3i
3-4i
i— 9i
i— ioi
i-ui
2 — Oj
2- Ii
2- 2i
2- 3i
2-4i
2- 6
2- 7
2- 8
2- 9
2-IO
2-1 1
3- o
3- i
3- 2
3- 3
3- 4
3- S
Pins marked * are special. Maximum shipping length of "L" = 35 feet.
209
TABLE 93.
CLEVISES.
AMERICAN BRIDGE COMPANY STANDARD.
All dimensions in inches.
ffffl>%\
\4iffldt
)
i
— »j
i Clearance I
i^-
-ine
EH
±X3:^ .
"HPr nl
1 Pi
->J
fs
---~j=r
f-
^^
]F — ^
t ^^_^-—
i
— —
~T
K
i4"
^L^
P
M>
IT lj
T^-1
ft||p<=
^>_f|Z,
*=rT
k/
T
.4 -
Grip = thickness of plate + i".
Number of
Clevis.
Head.
Diameter
of Pin,
P.
d • 1 4 " ' 1
3 a o 5
W E F A
Diameter
of Upset.
Nut.
Weight,
Pounds.
*O
l-i CO
11
ej
3
D
.i •
£3
T
Max. Min.
Max. Min.
N
B
3
4
5
6
7
3
4
5
6
7
i
3
i
ii i
2 \\
3 2
3* 2i
is 3A il S
2 3f if 6
2| 4! 2i 7
3 Si 2| 8
3'i 6A 3i 9
tO tO tO M M
OB|-4 MjM OD|M Oc _' OD|M
|0 tO l-l l-l l-l
».|W MH »|M
If
1 3
3f
4f
S
4
8
16
26
36
3
4
S
6
7
CLEVIS NUMBERS FOR VARIOUS RODS AND PINS.
Rods.
Pins.
Round.
Square.
Upset.
i
H
Ii
il
2
2l 2j
al
3
3i
3*
3
i
I
If
If
if
3
3
3
3
3
4
4
0»M W"
4
4
4
4
4
4
4
4
4
4
4
4
4
I
l|
Ij
If
l|
if
if
if
2
2|
2i
2|
I
4
4
S
S
s
5
5 5
5 5
5 S
5 S
q 5
5
S
S
S
If
If
2
2f
2f
j
5
5
5
6
6
6
6
6
6
6
6
6
6
6
6
5 1 q
6 "T~
6 6
If
If
2
7
7
7
7
7
7
7
7
7
7
6 6
7
6
7
7
7
7
7
Clevises to be used with the Rods and Pins given above.
Clevises above and to right of zigzag line may be used with forks straight, those below and to
left of this line should have forks closed so as not to overstress pin.
210
TABLE 94.
TURNBUCKLES AND SLEEVE NUTS.
AMERICAN BRIDGE COMPANY STANDARD.
All Dimensions in Inches.
TURNBUCKLES.
SLEEVE NUTS.
l/i; j _UL^i£l__
<* i . T
i i*\i
(S)i frc — *C^ ^riT^c^?
tO^^^-^^CJ [3HZI3
1-^5 U.....t.r._.J
PS!
A - 6"; A - 9"o for turnbuckles marked *.
Pitch and shape of thread, A. B. Co. Standard.
Pitch and shape of thread. A. B. Co. Standard.
Dbun.
Standard Dimensions.
5"O
Diatn.
Standard Dimensions .
•c-S
of
Si
of
Sis
Screw.
II
Screw.
:>§
U
D
L
C
t
G
B
£&«
U
D
L
A
B
C
t
>&
1
A
7t
A
A
,
iA
i
o
A
19
/ 8
7 ,'V
A O
|
16
j
I
if
i
16
}
4
/ 16
7}
0
|
4
i
8
I
* 5
if
i
•
A
•
H
/ 3
H
4
A
o
f
16
j
• *
44
7i
1 O
H
16
A
4
f
iA
ii
8
i
1 O
1}
/ 8
81
x o
16
•i
4
|
J. O
2
2
•
i
iA
V4
M
ii
B J
1
8
i
3
i
ii
7
If
ii
It
i
3
i
ii
9
iA
A
ii
2A
4
I
l|
7
If
1}
It
i
3
i|
iH
9l
iA
}
ii
2A
S
It
If
7i
2
2A
If
A
4
ii
ii
9f
iA
}
1}
si
6
ll
If
7i
2
2A
If
A
4
if
2A
10}
lit
}
if
3A
7
If
2
8
si
si
Ii
f
5
ii
si
10}
if
1
if
3A
8
ii
2
8
si
si
Ii
1
6
11
2A
10}
2
1
1}
Si
10
if
si
8}
si
3A
Ii
A
8
if
si
"i
2}
1
2
Si
ii
if
si
8i
2f
3A
Ii
A
9
11
2H
n|
*A
H
si
3i
12
ii
si
9
Si
Si
si
}
10
»
3
12
M
H
si
4i
14
2
M
9
Si
si
si
}
ii
si
3A
12}
2}
II
si
4i
17
2}
• 2f
9i
Si
4A
si
A
14
si
si
I2f
2H
H
si
4f
2O
si
2f
9i
3i
4A
si
A
IS
si
3A
13}
2f
U
si
4}
22
si
3
10
Si
4}
si
1
18
2}
Si
13}
3A
H
3
Sf
25
si
3
10
Si
4i
si
1
19
si
4i
Hi
Si
ft
si
Sf
33
si
Si
10}
4i
4H
2i
H
23
2i
4A
I4l
3A
I aJ
si
6A
36
2}
Si
ii
4l
si
Si
1
27
3
4i
IS
Si
I 35"
3}
6|
40
3
Si
ii
fl
sf
Si
i
28
Si
4i
isf
3}
iA
4
6f
So
Si
Si
Hi
S
sH
si
ff
35
si
si
16}
4i
i&
4
71
65
Si
4
12
si
6}
si
i
40
si
Si
17}
4A
1 16
S
81
95
Si
4i
12}
Sf
6tt
si
tt
47
4
6
18
4l
iA
S
8f
1 08
4
4i
13
6}
7A
4i
i
55
*4i
6i
21}
4i
if
sA
9l
140
4l
4f
13}
6}
7}
4i
iA
65
*4}
6}
22}
5}
ii
6}
lOf
I9S
4i
5
14
6}
7«
4f
iA
75
*4f
7i
23}
sl
2
6}
nl
20 ?
•s
7i
J m
24
J 9
6
si
v*
6}
* * 4
*V3
250
211
TABLE 95.
BRIDGE PINS AND NUTS.
AMERICAN BRIDGE COMPANY STANDARD.
All Dimensions in Inches.
I Distance between Shoulders -J*" i •
! i Distance between Nuts = Grip ^. | j* *"•• *i
("
a -f-fef?
^ i ^~-^\ i t"
;
4 i
O^ i
.
i !
,'/ !
•
j *^api ^
:s: !
"~^J T
PH
To obtain grip, add &" for each bar. Nuts threaded 6 threads per inch.
To obtain distance between shoulders, add amount given in table to grip.
Pin.
Nut. .
Diameter of Pin,
d.
Thread.
Add
Thick-
Diameter.
Depth
Diam-
eter
S-S
Pattern
a
b
Grip.
t
n
m
c
s
Rough
Hole.
|
No.
2, 2}
If
i
1
i
2i|
3f
2f
1
iA
i.i
PN 21
2
ii
4
I
•7 9
3l6
4i
3f
1
1.7
PN 22
3, *3i, 35
4
ij
i
l|
S
3^
|
2A
2-S
PN23
*3f, 4
3
if
5
ii
4*
4^
3
g
2H
3-7
PN 24
*4i, 44, *4i
3s
12
5
if
8
6|
A
3w
4.6
PN2S
5, *5i
4
If
^
i^
7&
|
i
3ii
6.2
PN 26
Si *5f, 6
if
5
if
7
8f
5
8
4A
•7.8
PN27
*6i, *6J
5
l|
]
if
7l
8^
7
|
4iT
9-9
PN28
*6|, 7
S?
2
f
if
8f
91
f
5*
11.8
PN 29
*7i, *7i
si
2
f
if
8f
10
8
\
14-3
PN3o
*7f, 8, *8i
6
2i
f
*f
9J
io|
8f
3
4
5H
18.6
PN 31
*8z> 9
6
2j
f
if
III
9J
f
23.8
PN32
*92> 1°
6
4
4"
2i
ni
13
f
5x1
PN 33
Pins marked * are special.
212
TABLE 96.
COTTER PINS.
AMERICAN BRIDGE COMPANY STANDARD.
All Dimensions in Inches.
«w
f
-
* * 1
£
1 &
**?»
---
^
»i
"7
/i\ ^
1
fl
H
i
? (-* j*0J £
n
!
J i V,,LX '
;
,J *
-t-
1
</\> *
HORIZONTAL OR VERTICAL PIN FINISHED.
HORIZONTAL PIN ROUGH OR FINISHED.
Pin.
Head.
G
Cotter.
Pin.
G
Cotter.
P
H
C
D
P
C
D
!j
ll
2
J
l}
2
i
l|
ij
2^
1^
2i
l}
2
H«
•1
l|
«•
*1
i
2
2i
_j_
3
2
i
3
f
4
2]
cu
3i
2l
a
3}
i
•2i
2|
2]
3l
O
4
,
2f
C
O
4
•
3
Sj
3;
1
S
S
1
3i
V
S
5
sl
4
6
1
!
3i
6
•
si
4l
6
^
•
3f
6
]
•
213
TABLE 97
BEARING VALUES OF PINS.
Pin.
Bearing Value of Plate i" Thick for Unit Stress per Square Inch of
Diam. of Pin
in In.
Diam. in In.
Area.
12 000
15 ooo
20 000
22 OOO
24 ooo
I
.785
12 OOO
15 ooo
20 ooo
22 OOO
24 ooo
I
ii
1.227
15 ooo
18 800
25 ooo
27 500
30 ooo
ii
if
1.767
18 ooo
22 5OO
30 ooo
33 ooo
36 ooo
I*
if
2.405
21 OOO
26 300
35 ooo
38 500
42 ooo
If
2
3-I42
24 ooo
30 ooo
40 ooo
44 ooo
48 ooo
2
»f
3-976
27 ooo
33 800
45 ooo
49 500
54 ooo
2i
ai
4.909
30 ooo
37 Soo
50 ooo
55 ooo
60 ooo
2*
»i
5-94°
33 ooo
41 300
55 ooo
60 500
66 ooo
2f
3
7.069
36 ooo
45 ooo
60 ooo
66 ooo
72 ooo
3
3l
8.296
39 ooo
48 800
65 ooo
71 500
78 ooo
3f
3J
9.621
42 ooo
52 500
70 ooo
77 ooo
84 ooo
3*
3f
11.045
45 ooo
56 300
75 ooo
82 500
90 ooo
3i
4
12.566
48 ooo
60 ooo
80 ooo
88 ooo
96 ooo
4
4i
14.186
51 ooo
63 800
85 ooo
93 Soo
IO2 OOO
4i
4*
15.904
54 ooo
67 500
90 ooo
99 ooo
108 ooo
4f
4f
17.721
57 ooo
71 300
95 ooo
104 500
114 ooo
4t
5
I9-63S
60 ooo
75 ooo
100 ooo
no ooo
I2O OOO
5
5|
21.648
63 ooo
78 800
105 ooo
115 5oo
126 ooo
5f
5|
23758
66 ooo
82 500
no ooo
121 OOO
132 ooo
si
5f
25.967
69 ooo
86 300
115 ooo
126 5OO
138 ooo
si
6
28.274
72 ooo
90 ooo
I2O OOO
132 ooo
144 ooo
6
6J
30.680
75 ooo
93 800
125 ooo
137 500
150 ooo
6|
61
33-I83
78 ooo
97 500
130 ooo
143 ooo
156 ooo
6|
6|
35-785
81 ooo
101 300
135 ooo
148 500
162 ooo
6f
7
38.485
84 ooo
105 ooo
140 ooo
154 ooo
168 ooo
7
7i
41.282
87 ooo
108 800
145 ooo
159 500
174 ooo
7i
71
44-179
90 ooo
112 5OO
150 ooo
165 ooo
180 ooo
7|
7f
47-173
93 ooo
116 300
155 ooo
170 500
186 ooo
7f
8
50.265
96 ooo
I2O OOO
160 ooo
176 ooo
192 ooo
8
8J
53456
99 ooo
123 800
165 ooo
181 500
198 ooo
8J
8£
56.745
102 OOO
127 500
170 ooo
187 ooo
204 ooo
8|
8f
60.132
105 ooo
131 300
175 ooo
192 500
2IO OOO
8|
9
63.617
108 ooo
135 ooo
180 ooo
198 ooo
216 ooo
9
9i
67.201
III OOO
138 800
185 ooo
203 500
222 OOO
9*
9*
70.882
114 ooo
142 500
190 ooo
209 ooo
228 ooo
9}
9i
74.662
117 ooo
146 300
195 ooo
214 500
234 ooo
9i
10
78.540
120 OOO
150 ooo
2OO OOO
22O OOO
240 ooo
IO
ioi
82.516
123 ooo
153 800
205 ooo
225 500
246 ooo
iol
10^
86.590
126 ooo
157 500
2IO OOO
231 ooo
252 ooo
io£
I0|
90.763
129 ooo
161 300
215 ooo
236 500
258 ooo
lof
II
95-033
132 ooo
165 ooo
22O OOO
242 ooo
264 ooo
II
Hi
99.402
135 ooo
168 800
225 ooo
247 500
270 ooo
"?
III
103.869
138 ooo
172 500
230 ooo
253 ooo
276 ooo
Ill
III
108.434
141 ooo
176 300
235 ooo
258 500
282 ooo
III
12
113.097
144 ooo
180 ooo
240 ooo
264 ooo
288 ooo
12
214
TABLE 98
BENDING MOMENTS ON PINS.
I'm.
Max. Momenta in Inch-Pounds for Fiber Strew per Square Inch of
Diam.
of Pin
in In.
Di. mi.
in In.
Area.
15 ooo
18 ooo
20 ooo
22 OOO
22 5OO
24 ooo
25 ooo
I
.785
I 470
I 770
I 960
2 160
2 2IO
2 360
2 450
I
1.227
2 880
3 450
3 830
4 220
4 3'°
4 600
4 790
ii
1.767
4 970
5 960
6 630
7 290
7 460
7 950
8 280
|I
2.405
7 890
9 470
10 500
II 580
II 800
12 630
13 200
11
2
3-I42
ii 800
14 ioo
15 700
17 280
17 700
18 800
19 600
2
2}
3.976
16 800
20 IOO
22 400
24 600
25 200
26 800
28 ooo
2}
2j
4.909
23 ooo
27 6OO
30 7OO
33 700
34 Soo
36 800
38 300
2\
22
S-940
30 600
36 800
40 8OO
44 900
45 900
49 ooo
51 ooo
2*
3
7.069
39 800
47 7°°
53 ooo
58 300
59 600
63 600
66 300
3
3i
8.296
50 600
60 700
67 400
74 ioo
75 800
80 900
84 300
3t
9.621
63 ioo
75 800
84 2OO
92 600
94 700
IOI OOO
105 200
3i
SI
11-045
77 7°°
93 200
103 500
113 900
116 500
124 300
129 400
4
12.566
94 200
113 ioo
125 700
138 200
141 400
150 800
157 IOO
4
4l
14.186
113 ooo
135 700
150 700
165 8OO
169 600
180 900
i 88 400
4i
4|
15.904
134 200
161 ooo
178 900
196 8OO
201 300
214 700
223 700
4i
4*
17.721
157 800
189 400
2IO 400
231 50O
236 700
252 500
263 ooo
5
19.635
184 ioo
220 000
245 400
270 ooo
276 ioo
294 Soo
306 800
s
sl
21.648
213 ioo
255 700
284 ioo
312 5OO
319 600
340 900
355 200
si
si
23.758
245 ooo
294 ooo
326 700
359 300
367 500
392 ooo
408 300
si
Sl
25-967
280 ooo
336 ooo
373 300
410 600
419 900
447 900
466 600
Sl
6
28.274
318 ioo
381 700
424 ioo
466 500
477 ioo
508 900
530 ioo
6
6}
30.680
359 500
431 400
479 400
527 300
539 300
575 200
599 200
6}
6}
33.183
404 400
485 300
539 200
593 ioo
606 600
647 ioo
674 ooo
6i
61
35785
452 900
543 Soo
603 900
664 300
679 400
724 600
754 800
6!
7
38.485
505 ioo
606 ioo
673 Soo
740 800
757 700
808 2OO
841 800
7
7}
41.282
561 200
673 400
748 200
823 ioo
841 800
897 9OO
935 300
7}
7i
44-179
621 3OO
745 500
828 400
911 2OO
93i 900
994 ooo
i 035 400
71
7i
47-173
685 500
822 600
914 ooo
I OO5 4OO
i 028 200
i 096 800
i 142 500
7l
.8
50.265
754 ooo
904 800
I 005 300
I 105 800
i 131 ooo
i 206 400
256 600
8
8}'
53456
826 900
992 300
I IO2 5OO
I 212 8OO
240 400
i 323 ooo
378 200
8}
8i
56.745
904 400
i 085 300
I 2O5 8OO
I 326 4OO
356 600
i .447 ooo
507 300
B]
81
60.132
986 500
i 183 900
I 315 400
I 446 9OO
479 800
i 578 500
644 2OO
81
9
63.617
i 073 500
I 288 200
I 431 400
i 574 500
610 300
i 717 700
789 200
9
9}
67.201
i 165 500
I 398 6OO
i 554 ooo
i 709 400
748 300
i 864 800
942 500
9l
9i
70.882
i 262 600
i 515 ioo
i 683 500
i 851 800
893 900
2 O2O IOO
2 104 300
9i
9l
74-662
i 364 900
I 637 900
i 819 900
2 001 900
2 047 4OO
2 183 900
2 274 900
9f
10
78.540
i 472 600
i 767 ioo
i 963 500
2 159 800
2 208 900
2 356 2OO
2 454 400
10
10}
82.516
i 585 900
i 903 ooo
2 114 5OO
2 325 900
2 378 800
2 537 400
2 643 IOO
10}
10}
86.590
i 704 700
2 045 7OO
2 273 OOO
2 500 300
2 557 ioo
2 727 600
2 841 200
IOJ
iol
90-763
i 829 400
2 195 300
2 439 200
2 683 2OO
2 744 ioo
2 927 IOO
3 049 ioo
iol
II
95.033
i 960 ioo
2 352 IOO
2 613 400
2 874 800
2 940 IOO
3 136 ioo
3 266 800
II
11}
99.402
2 096 8OO
2 516 IOO
2 795 700
3 075 200
3 145 ioo
3 354 800
3 494 600
11}
"i
103.869
2 239 7OO
2 687 600
2 986 20O
3 284 900
3 359 Soo
3 583 500
3 732 800
III
III
108.434
2 388 900
2 866 700
3 185 200
3 503 800
3 583 400
3 822 300
3 981 600
"i
12
113.097
2 544 700
3 053 600
3 392 900
3 732 200
3 817 ooo
4 071 500
4 241 200
12
215
TABLE 99.
LONG PILOT NUTS.
AMERICAN BRIDGE COMPANY'S STANDARDS.
i .
Pilot Nuts are made from Special Hard Steel
and finished all over.
Screw, 6 Threads per Inch.
|
^
~Z
t TT|
t t f
Hjfp-^i^
•£ ^
i io
ij
D
°*
E v
S
H
5 -a
T
._ Length
~ over All.
•y c •
"S °TJ
E
e ^
•21
i
_g C <u
O
P
3
1
M
R
F
N
Q>g
A
tt Diam.
ro of Holes.
Weight
in
Pounds.
II
" o
D
2"
3
3l
3f
4x
1
4*
Sl
55
Sf
6
61
6|
6f
75
7f
8
81
1)
9
9l
9*
9f
IO
!o|
II
2
%
3
M
4
iA"
II
1-5-
3l6
tt
2"
II
M
H
H
II
It
(t
c
6
u
7
8
9
IO
2"
u
M
U
ai
H
II
I-S
2.
3-
4-
S-
7-
9-
ii.
12.
14.
16.
19.
24.
30.
33-
40.
45-
49-
58.
64.
70.
77-
85-
95-
IO2.
no.
92.
99.
107.
119.
130.
142.
ICo»
loo.
172.
1 86.
203.
*"
2!
3
3l
4
6
6|
r
7!
8
81
sl
o
QT
9l
10
ii
4
i
'ff
5
16
f
I
i
t
4
ii
f
1
li*
i
if
ij
iA
u
Ij
Ii
If
u
20i
M
II
II
II
27
u
Ij
Ij
2
II
M
%
f
it
7
g
I
4
u
u
u
li"
2
2f
II
40
U
T^
J8
H
II
u
Ij
I
42
4A
«
"5
«
S
4M
II
2|
13
3
M
M
M
II
M
M
«
«
«
II
Sl
sA
»
145
"
43
"
«
»
M
6
SM
M
16
«
«
«
II
«
«
H
M
II
H
«
u
u
M
Ij
M
M
2j
I7l
u
8
u
3
M
Sf
M
2f
M
«
II
II
M
(1
II
M
tt
3
u
u
U
II
5?
II
M
M
„
«
"
«
"
i
"
216
TABLE 100
SHORT PILOT NUTS AND DRIVING NUTS.
AMEKK AN HKIUGE COMPANY'S STANDARDS.
-l-.-j
9 <Jf
i -*
U-4.-J
H i
L
O
^
-
L.
H8!
ITT
"•^^_^
'."."."""I
0
s
T
t t
! LI
IS
f
i
1
|
1
j
i— p--*i
• i
— «... i
Dimensions in Inches.
Dimensions in Inches.
"3
Q
D
s
E 3"°
IJa
a
H
M Length
r over AU.
Sd
2 5
T
m
I
R
Weight in
Pounds.
"o .
S
D
S
s
•s^ .
g'ao
H
H Length of
Thread.
M Length
^ overAU.
1*1
en *
E
•a 5
R
G
P
* ^^
c o
5^
B
Weight in
Pounds.
S-
i.
i.
i-S
2.
3-
3-
4-
3-
4-
S-
6.
6.
8.
9-
u.
IO.
12.
14.
16.
19-
21.
24.
28.
33-
36.
40.
45-
48.
Si-
SS-
59-
•f
2$
3t
4|
4f
51
6i
6J
7J
g|
ii."
2
2i
3
4
4i
/J
6
i A"
^ 16
2H
3A
3H
IA
sH
«'
M
M
4"
S
Si
3
71
7J
*|
III
^i
2"
2A
2f
2i
M
2|
'j
«
32A
3i
II
f)
4i
si
<«
M
I
4
5
8
ii
22
27
67
86
1 20
150
ii
i A
ii
4i
2|
J
3!
4}
Jl
1
L
*
9i
9
IO
IO.J
II
2
2j
«
2A
it
«
M
U
0
3
2H
2i
H
It
Jj
3A
M
M
4
u
3H
"
H
H
»
3
81
s}
»
4
4*
«
U
Pilot Nuts and Driving Nuts are made from special
hard steel. Pilot nuts are finished all over.
Screws 6 threads per inch.
When short pilot nuts are needed on bottom chord
pins, long pilot nuts are to be sent for all other pins,
in addition.
S
4H
3
ii
<
Si
sA
M
M
H
M
M
M
«
6
sH
M
M
H
•
«
3i
«
7
«
M
M
M
M
«
53
217
TABLE 101.
SCREW THREADS.
AMERICAN BRIDGE COMPANY STANDARD.
BOLTS, RODS, EYE BARS, TURNBUCKLES, SLEEVE NUTS, AND CLEVISES.
l^_ _p >.!
1 1
1 1 -j'
--ik - tf '
F
Diameter.
Area.
Number
Diameter.
Area.
Number
of
of
Total
Net,
Total
Net
Threads
Total,
Net,
Total
Net
Threads
d,
In.
c.
In.
Dia., d,
Sq. In.
Dia., c,
Sq. In.
per
Inch.
d,
In.
c,
In.
Dia., d,
Sq. In.
Dia., c,
Sq. In.
per
Inch.
i
4
.185
.049
.027
2O
.2i
2.175
4.909
3-7I6
4
8
.294
.no
.068
16
2|
2.300
5.412
4.156
4
I
.400
.196
.126
13
2f
2.425
5-940
4.619
4
1
•507
•3°7
.202
ii
2J
2-550
6.492
5.108
4
4
.620
.442
.302
10
1
•731
.601
•419
9
3
2.629
7.069
5428
3f
Jl
2.879
8.296
6.509
3f
I
•83
8
.785
•551
8
3|
3.IOO
9.621
7-549
31
is
•939
•994
•693
7
3l
3.3I7
11.045
8.641
3
Ij
1.064
1.227
.890
7
If
1.158
1.485
1.054
6
4
3-5
67
12.566
9-993
3
I*
1.283
1.767
1.294
6
4i
3798
14.186
H.330
if
1.389
2.074
I.
I
S
si
4.028
I5-904
12.741
3
if
1.490
2.405
1-744
5
a
4-255
17.721
14.221
2f
If
1.615
2.761
2.049
5
5
4.480
I9-63S
15.766
2i
2
1.711
3.142
2.300
42
Si
4-73°
21.6.
tf
17-574
2j
25
1-836
3-547
2.649
4J
si
4-953
23-758
19.268
28
2?
1.961
3-976
3.021
42
sl
5-203
25.967
21.262
2|
2f
2.086
4-430
3-4I9
42
6
5423
28.274
23-095
2j
BOLT HEADS AND NUTS.
AMERICAN BRIDGE COMPANY STANDARD.
{ojf'il
fi
1
1
:3 ~":<&
|w~
Rj
\
"
j\i
j_
^
1
1
Rough Nut. Finished Nut.
Rough Head.
Finished Head.
f
g f
g
f '
h
f
h
I-5d + i"
d i.Sd + &"
d-A"
i.Sd + 1"
o.5f i-5d + jV'
o.5f-TV"
For Screw Threads, Bolt Heads and Nuts, the American
Bridge Company has
adopted the
Franklin Institute Standard, commonly known as United States Standard.
218
TABLE 102.
BOLT HEADS AND NUTS, DIMENSIONS IN INCHES.
AMERICAN BRIDGE COMPANY STANDARD.
HEAD.
NUT.
i
Hexagonal.
Hex. or
Square.
Square.
1
Hexagonal.
Hex. or
Square.
Square.
•38
Htiaeooal.
Square.
Hexa£tt»l-
Square.
II
o
Square.
y--v1
li
<^
Bex. or
Square.
fQl
I
Diameter.
IT
Dlametor.
S
Diameter.
m
Diameter.
Q
Diameter.
LJ
Diameter.
Q
Diameter.
Diameter.
Long.
Short.
Height.
Long.
Short.
Long.
Short.
Height.
Long.
Short.
i
t
J
i
tt
i
1
i
1
J
i
tt
J
1
tt
tt
1
I
tt
f
tt
tt
1
I
tt
i
I
|
A
Ii
i
[
i
i
$
i
ii
1
1
Ii
iA
A
i)
iA
f
ij
iA
1
ii
iA
J
lA
ii
1
itt
ii
f
iA
ii
i
iH
ii
i
itt
iA
f
2A
IT
fr
1
iH
iA
i
2A
iA
I
Ij
if
tt
aA
ii
[
i
ij
if
i
2A
if
Ii
2i
itt
tt
2A
itt
ii
ai
itt
ii
2rV
itt
ij
2&
2
i
2if
2
ii
2tV
2
ii
2«
2
if
2A
2A
ii
si
2
fc
if
2rV
2A
if
si
a*
ii
2f
2f
iA
si
2'
f
ii
2f
2|
ii
si
2|
If
3
2A
iA
si
2]
fc
if
3
2A
if
si
2A
Ij
3A
2f
if
3*
2f
if
3A
2f
if
Si
2|
3A
2tt
ii
4A
2
rl
i|
3To"
2H
ii
4^
' 2}f
2
3f
si
iA
4A
3i
2
3f
3i
2
4r«
Si
2*
4A
Si
if
4H
si
2i
4A
3i
2i
4«
Si
2i
4i
3i
itt
Si
si
2i
4i
3i
2j
si
Si
2f
4H
4i
ai
6
4i
2f
4tt
4i
2f
6
4i
3
Sf
4i
2A
6A
4f
3
si
4f
3
6A
4i
sft
S
ai
7A
S
3i
Sit
S
Si
7A
S
L 3i
6i
Si
2tt
7f
si
3i
6i
Sf
si
7f
Si
BOLT THREADS, LENGTH IN INCHES.
Length,
Diameter, Inches.
i 1 i
1 i
i I Ii
Ij
I to ij
f 4
i
xi
if to 2
f 1
i
ii i4
i4
2\ to 24
f f
i
ii ii
1} if
2f to 3
i 1
i
ii i4
if if 2!
3ito 4
i f
ii
ii ii
If If 2j
2i
4ito 8
I I
ii
ij if
2 2j 2i
2f
8i to 12
I I
ii
if 2
2i 24 3
3
I2j tO 2O
I I
ii
2 2
2i 2i 3
3
Bolts not listed are threaded about 3 times the diameter; in no case are standard bolts threaded
closer to the head than J inch.
219
TABLE 103.
BOLTS WITH HEXAGON HEADS AND NUTS.
AMERICAN BRIDGE COMPANY STANDARD.
WEIGHT IN POUNDS PER 100 BOLTS.
Length
Under
Head,
Inches.
Diameter of Bolt, Inches.
Length
Under
Head,
Inches.
Diameter of Bolt, Inches.
i
f
i
i
i
i
I
!
i
I
I
If
2
19
20
22
23
24
33
34
36
38
40
52
54
57
60
63
8
9
9-
10
\
k
58
60
63
66
68
92
96
IOO
105
109
137
143
149
156
162
194
202
2IO
219
227
264
274
296
307
93
132
2l
26
43
66
97
137
io|
7i
114
168
236
318
2|
27
45
69
101
143
ii
74
118
174
244
329
2f
29
47
72
105
148
ii
\
77
122
181
253
341
3
3°
49
75
109
154
12
80
127
187
26l
352
3i
31
Si
78
114
160
12
i
82
131
193
27O
363 ^
Si
33
54
82
118
165
13
85
135
199
278 '
374
si
34
56
85
122
171
I3l
8*
!
139
206
287
385
4
35
58
88
126
176
14
91
144
212
295
396
4i
37
60
90
I3O
1 80
H
f
93
148
218
304
407
4l
38
62
94
134
1 86
IS
96
152
225
312
418
4f
39
64
97
138
191
IS
r
99
157
231
321
43°
S '
4i
66
IOO
143
197
16
IO2
161
237 '
329
441
si
42
68
103
147
202
16
105
165
243
338
452
si
"44
7i
106
151
208
17
107
170
25O
346
463
sf
45
73
109
156
213
17
i
t
no
174
256
355
474
6
46
75
112
160
219
18
113
177
262
364-
485
6i
48
77
US
164
225
18
116
183
268
372
496
6|
49
79
119
1 68
23O
19
119
187
275
38
i
507
6f
51
81
122
173
236
192
121
191
28l
389
519'
7
7i
7*
. 7i
52
53
55
56
84
86
88
90
125
128
134
177
181
185
190
241
247
252
258
20
124
196
287
398
530
Per Inch
Per Inch
Additional
5-6
8-7
12.5
17.0
22
3
Additional
5-6
8.7
12-5
17.0
22-3
HEXAGON NUTS AND BOLT HEADS.
WEIGHTS IN POUNDS FOR ONE HEAD AND ONE NUT.
Diameter of Bolt, Inches.
ii
ii
i!
2
2*
3
Hexagon Head and
Weight of Shank pe
Nut
i-73
•3479
2-95
.5007
4.61
.6815
6.79
.8900
13.0
I-39I
22.O
2.003
r Inch
220
TABLE 104.
BOLTS WITH SQUARE HEADS AND NUTS.
AMERICAN BRIDGE COMPANY STANDARD.
WEIGHT IN POUNDS PER 100 BOLTS.
Length Under
Head. Inches.
Diameter of Bolt, Inches.
1
A
1
A
1
1
K
i
i
I
Ii
Ij
ii
2
*i
•i
^\
3
3*
4
4i
s
si
6
*'
•'
9
10
12
14
4
4
5
S
5
6
6
6
7
7
8
9
10
10
II
7
7
8
8
9
9
10
10
ii
12
13
H
IS
16
17
II
II
12
13
14
IS
is
16
17
18
20
21
23
25
26
28
29
31
32
34
IS
16
17
18
19
20
21
22
24
25
28
30
32
34
36
38
40
42
45
49
S3
61
22
23
24
26
27
28
30
31
33
35
38
4i
43
46
49
52
55
57
60
65
7i
82
93
37
39
41
43
45
47
49
Si
54
58
62
66
7i
75
79
84
88
92
97
105
114
131
148
56
59
62
64
67
7i
74
77
80
86
92
98
104
in
H7
123
129
136
142
154
167
192 .
217
IOI
104
109
"3
117
126
134
142
151
159
168
176
185
193
202
218
235
269
303
144
ISO
ISS
161
167
178
189
198
209
220
232
243
254
265
276
298
320
364
409
Per Inch
Additional...
1.4
2.2
3-1
4-3
5-6
8-7
12.5
17.0
22.3
SQUARE NUTS AND BOLT HEADS.
WEIGHTS IN POUNDS FOR ONE HEAD AND ONE NUT.
Diameter of Bolt, Inches. i{ ij if a 2\
3
Square Head and Nut
Weight of Shank per I
2.OC
3-Si S-48 8.08 15.5
7 .5007 .6815 .8900 1.391
26.2
2.OO3
ich . .^4.'
221
TABLE 105.
LENGTHS OF BOLTS AND TIE RODS.
|« Grip »j
|-« Grip »-j
Length »j
t» Length >i
Grip.
Diameter.
i" f
Grip.
Diameter.
Grip.
Diameter.
8|
9
9
9
It
9*
9
IO
IO
10
IO
10*
10*
ID*
10*
II
II
II
II
11}
II*
II*
II*
12
12
12
12
93
9*
9*
10
IO
10
IO
10*
10*
105
10*
II
II
II
II
11}
11}
II*
"i
12
12
12
12
9
9
9*
9*
9*
9}
10
IO
10
IO
10*
10*
10*
IO*
II
II
II
II
II*
II*
12
12
12
12
9*
9j
9i
92
10
10
10
10
IO*
10*
10*
10*
II
II
II
II
II*
II*
II*
II*
12
12
12
12
9*
9!
9*
10
10
IO
IO
10*
10*
10*
10*
II
II
II
II
II*
II*
II*
Length-
For Cut Threads
use |", i" and i" Rods
Genter-to-Genter-of-Beams
For Rolled Threads use
fi" instead of f" Rods
H" instead of J" Rods
C to C
Beams.
Lgth.
C to C
Beams.
Lgth.
C to C
Beams.
Lgth.
C to C
Beams.
Lgth.
C to C
Beams.
Lgth.
C to C
Beams.
Lgth.
I-O
I-I, 2, 3
i-4, 5, 6
i-7, 8, 9
I-IO, II
2-0
-1, 2, 3
1-6
i-9
2-O
2-3
2-3
2-6
2-4, 5, 6
2-7, 8, 9
2-IO, II
3-o
3-i, 2, 3
3-4, 5, 6
3-7, 8, 9
2-9
3-0
3-3
3-3
3-6
3-9
3-10, ii
4-0
4-i, 2, 3
4-4, 5, 6
4-7, 8, 9
4-10, ii
4-3
4-3
4-6
4-9
5-o
5-3
5-3
S-i, 2, 3
5-4, 5, 6
5-7, 8, 9
5"IO, H
6-0
6-1, 2, 3
6~4, 5, 6
5-6
5-9
6-0
6-3
6-3
6-6
6-9
6-7, 8, 9
6-10, ii
7-0
7-i, 2, 3
7-4, 5, 6
7-7, 8, 9
7-10, ii
7-0
7-3
7-?.
7-6
7-9
8-0
8-0
8-1, 2, 3
8-4, 5, 6
8-7, 8, 9
8-10, ii
8-3
8-6
8-9
9-0
9-3
222
TABLE 106.
STRUCTURAL RIVETS.
AMERICAN BRIDGE COMPANY STANDARD.
WEIGHT IN POUNDS PER 100 RIVETS WITH BUTTON HEADS.
Under
Head,
Inches.
Diameter of Rivet, Inches.
Length
Under
Head.
Inches.
Diameter of Rivet, Inches.
i
i
1
i
1
i
Ii
ii
1
i
1
i
i
i
ii
Ii
s
18
33
53
78
109
146
190
252
Ii
i
i
6
7
7
12
13
13
i
i
*
i
18
19
19
20
34
34
35
36
54
55
56
57
80
82
83
85
III
"3
"5
118
149
152
155
IS7
193
197
200
204
2S6
260
265
269
23
35
50
68
91
130
i
7
14
24
36
52
7i
95
134
f
20
36
58
86
1 20
1 60
207
273
i
8
15
25
37
54
74
98
139
i
2O
37
60
88
122
163
211
278
i
8
is
26
39
56
77
102
H3
i
21
38
61
89
124
166
2I4
282
2
9
16
27
4i
58
80
105
148
6
21
38
62
91
126
169
218
287
i
9
17
28
43
60
82
109
152
i
22
39
63
93
128
171
222
291
1
9
18
29
44
62
85
112
156
1
22
40
64
94
130
174
225
295
1
10
18
30
46
64
88
116
161
1
22
40
65
96
132
177
229
3OO
i
10
19
31
47
67
91
119
165
*
23
4
i
66
97
135
180
232
304
1
ii
20
32
49
69
93
123
169
1
23
42
67
99
137
182
236
308
1
ii
20
34
50
7i
96
126
174
f
24
43
68
IOO
139
185
239
313
i
ii
21
35
52
73
99
130
178
i
24
43
69
IO2
141
188
243
317
3
12
22
36
54
75
102
133
182
7
24
44
70
I04
143
191
246
321
i
12
22
37
55
77
I°S
137
187
i
25
45
7i
105
145
194
250
326
i
13
23
38
57
79
107
141
191
1
25
45
73
107
147
196
253
33°
i
13
24
39
58
81
HO
144
195
1
26
46
74
108
149
199
257
334
*
13
24
40
60
84
113
148
200
i
26
47
75
1 10
152
202
26O
339
f
14
25
4i
61
86
116
151
204
1
26
47
76
in
154
205
264
343
i
14
26
42
63
88
118
155
208
f
27
48
77
H3
156
207
267
347
*
IS
27
43
64
90
121
158
213
i
27
49
78
»4
158
210
271
352
4
IS
27
44
66
92
I24
162
217
8
27
So
79
116
160
213
274
356
i
IS
28
45
68
94
127
165
221
i
28
SO
80
118
162
216
278
360
i
16
29
47
69
96
130
169
226
1
28
Si
81
119
164
219
28l
365
f
16
29
48
7i
98
132
172
230
f
29
52
82
121
166
221
285
369
i
16
30
49
72
101
135
176
234
\
29
52
83
122
169
224
288
373
§
17
31
50
74
103
138
179
239
1
29
53
84
124
171
227
292
378
*
17
31
Si
75
105
HI
183
243
f
30
54
86
125
173
230
295
382
*
18
32
52
77
107
143
i86N
247
i
30
54
87
127
175
232
299
386
•
Button Heads.
Diameter of Rivets, Inches.
1
i
1
f
1
i
Ii
Ii
ioo Heads as made on rivets, Pounds . . .
2-4
S-o
9-7
1 6.0
24.0
35-o
49.0
78.0
100 Heads as driven in work, Pounds . . .
1-9
4.0
7-5
12.5
I8.S
27.0
37-5
51.0
223
TABLE 107.
LENGTHS OF FIELD RIVETS AND BOLTS FOR BEAM FRAMING.
'tkf.
A_£
1" Rivets. i n~
u
$*
J t
^L.F
ifTr
HP
BEAMS
Single.
24"
20"
1 8"
15"
12"
10"
9"
8"
7"
6"
5"
4"
3"
Dou
Riv.
In.
ble.
Bolt
In.
BEAMS
Bolt I
In.
<iv.
In.
If .
-
12.25
9-75
7-5
8-5
5-5
6-5
2*
2
25
21
25
18
20.5
IS
17-5
14-75
12.25
9-5
7-5
2|
2j
42
31-5
23
17.25
10.5
2f
2
2|
80
65
55
60
45
50
60
35
40
3°
35
35
3°
25
20
14-75
2f
«4
85
90
70
75
80
85
65
75
80
55
65
45
3
95
IOO
"5
90
95
70
85
70
75
80
So
55
60
40
3l
IOO
90
85
65
3t
2f
90
3f
95
IOO
i
Si
3
| CHANNELS
If
2
2
2j
2i
E
2?
2 is
8.00
6.50
5-25
4.00
2|
2
| CHANNELS
20.5
IS
13.25
11.25
13-75
9-75
6.25
5.00
2|
15.00
12.25
10.50
9.00
7-25
6.00
2f
2l
33
35
25
20
20
16.25
18-75
14-75
11.50
2|
2f
40
25
13
30
35
25
21.25
17-25
19-75
15.5°
2f
45
50
40
3°
3
a*
55
35
3*
2f
Top An
1-**
Jle
£
all
all
all
all
all
?J
if
BEAMS
all
all
all
2|
2
42 to
31-5
35
aj
55 to
70
40 to
65
2f
2j
^
H
Bottom i
gle = i'
EJ -
[••
^i-
80 to
IOO
65 to
75
60 to
75
2f
115
80 to
IOO
80 to
IOO
3
a*
all
2?
if
| CHANNELS
all
all
all
all
all
2f
20.5
25
30
all
all
2f
2
all
35
40
2|
24
1 8"
*5
9
8"
7
6"
5
4
3
Top &
Bott.
224
TABLE 108.
STRUCTURAL RIVETS.
AMERICAN BRIDGE COMPANY STANDARD.
LENGTHS OF FIELD RIVETS FOR VARIOUS GRIPS.
Dimensions in Inches.
j*— Crip, or" *i
CK
k-Grip, «r*
A
)
fc — Grip, &---•{ }*"Grip, ft— J.
u
i (
M
' [/
j* -Length- *j
! >*
r* — -Length *
K
• — *i }* — -Length >\
Grip a.
Diameter.
Gripb.
Diameter.
i
f
i
i
X
*
i
i
i
i
if
ii
ii
2
2i
|
,1
I
xj
i
ij
il
2
2i
2
1
2i
j
i!
I
I
I
if
if
i
i
i
if
ii
I
2
2\
2f
2i
2f
j
•I
ii
ii
!j
ij
2;
2\
M
2f
2f
;
i
1
ij
ii
2
2
2
4
4
a|
i
I:
:
2
2
2
2
2
2f
2i
4
3
•
2
2
2
2
2
I
2
3
3
;
si
.
i
2i
2
2
2
2
2
3
3i
3
.
3i
1
4
2
2
2
2
j
3
3i
si
;
3f
f
2i
2;
2
2
23
Si
sl
si
3i
31
i
2f
21
2
2
3
2
3
si
.1
3i
Sl
2
2i
2l
3
3
si
I
3
3f
3i
Si
4
i
2i
3
si
3
3i
i
3
3i
St.
4
4i
1
3
31
3i
3
31
3
3i
4
4i
a
|
3i
3§
3
31
[
35
4
4
a
4f
I
3-
3i
3
31
'
3!
4i
4
4
a
f
31
3
3i
.
4
4i
4
a
a
i
31
3
3
3
3l
'
4i
4l
4i
a
I
3f
si
3
[
Si
4
•3
4f
4i
4i
4i
5
3
3i
4
4
4
4i
a
4ji
a
5
si
4
4;
4i
4
4i
'
•
a
S
Si
si
4
a
41
41
•
4i
S
5;
Si
sf
41
4
a
41
4j
'
4i
Si
5:
Si
si
41
4:
41
4^
S
Si;
Si
51
sf
41
4
4:
41
si
51
S'
Si
si
4^
41
4i
S
si
Si
si
Si
si
4i
4i
4J
S
si
4
sf
sf
si
Si
6
4
4i
5
5
Si
SJ
|
si
si
6
6
6}
S
51
Si
Si
sl
;
si
6
6j
6
6|
*
S:
Si
5:
Si
si
6
6
6
6,
61
5'
5
S
Si
si
6i
6
6
6
6J
j
5
Si
Si
Si
$
6:
6
6
6
6J
sl
51
sl
6
6i
6
65
6
7
Si
6
6
6
6i
61
6;
6
7
7i
i
6
6i
6i
6i
6i
S
6;
6i
7
7
7i
5
6i
6i
61
6
61
7
7'
7l
6
6
61
I
/
7
/ '
7
tl
6
6
6f
/
7
*
7
_|
6
6
/
7
1 t
7
7i
61
7
/
7
/ •
7
/ B
8
7
7
f
/
7
ft
M
7i
7\
-1
I
/ b " o
8 8J 8J
/ B
7i
/ 9
71
7f
225
TABLE 109.
STANDARDS FOR RIVETS AND RIVETING.
!***!
"
GAGES
in Inches
9
flax
Rivet
Leg
6agef1ax
Rivet
PROPORTIONS Of RIVETS
in inches
2t
Diameter
of
Shank
full Head
Diameter Height
Radii
Oounfersunk
Diametet Depth
it
16
'52
If*
WmtfLtxctubf
3?
34
64
59
64
L
16
3
4
n.
32
51
64
RIVET 5PACIN6
64
43
64
/I
SheofRivel Min.DMance
inches
25
32
inches
II
16
64
19
64
76
19
32
3
16
MINIMUM 5TA66ER fOR RIVETS
Pi
1
a
c
inches
1
b
in inches
Forz'Rivet For § Rivet
, i n ,i/i
C
inches
/I
in inches
For 7 n fret
i'"
a=lg
t For § Rivet
15
76
>
K-f'-
STANDARD
',4
9
16
'1
15
16
/3
16
C
*^y
~
'16
7.
16
nKsctunaflsji/frwprJextham
&
226
TABLE 110.
STANDARDS FOR RIVETING.
D /STANCE if TO $ OF §TftG6EJ?ED PlVETS.
! 0
0 !
-iflh
VALUES OFXF02 VWYIN6 VfiLUEo OFflfiNDB.
VAWtt
OFd
'
/I
VflLUE5 OF A
/
2k
/I
li
fit
2}
/I
/I
/9
2k
&
2/
2k
tfsifc
2
o/ ?y o// o/^
*k w LTZ fa
2%
nli o/5
w w
o /
%-%r
0/5 2 I
t]8W
be/ow or to the right of upper zigzag line are large enough Forg Riv.
a . t H t a H
lower
^:
'*
227
TABLE 111.
STANDARDS FOR RIVETING.
SPflCIHO OF5TA66ERED
RIVETS in fluGLES
STAGGER OF R/I/ETJ REQUIRED
->
•c
<-
,-— —
>
>-
>
A
"f
^
C //7
inches
bin inches
ONE HOLE OUT
J\ • \
5umof
Gages
Sizeoffffvet
%'riv.
54^.
7//r/v.
3/ //f
7/s"
-<-
llf.
a=l Foi
<
•<
<
~/*'
t
<
<
<
•>
"/'
/s
15
16
3
•i
or
6
o
,3
7
8
/J
176
1
//
6
1/6
*
L_L J ^
Iz
76
//
//
?
fj
i
73
ii
//i
//I
"vx_ L j T i
Z
4
ft
'16
16
*l>k
y=c&arufriv.+£
Two HOLES OUT
/I
i
I5_
•I
Zj
§
$6
//i
J
3
7
8
Ih
3
5
?8
>
)-
>•
/
'ivt
//
^?
3
4
It
^J
z|
Ire
^1
9
76
1
4
ije
5
//
3
8
IS
16
4+
If
3/1
/^
//<5
0
/3
16
5
3/i
J|
//
|
ii, j
f.i
*
^
[ I • i ^
-?2
/^
'/6
7
T6
ft^h-Vr
6
5/
3/
//
0
6i
3f
Jj
V. \ r^ \
ir % rivets; Ij for jj rivets
"••*-H
7
¥
•*/
71
i
^
8
_
^/
With£ rivets inm ember deduct trivets iTb <" bn
H 2. " " H " / " b}b '
a 3 // // // // 2* " b/'b '
•5J
7 " ^~ (fey^y2
' " For 4 rivets take b
it
i H // / // // ^
i
4
^/
, // //
J /^55 /77(3J7 ^ For£ .
/ *]
% more than b for j".
228
TABLE 112.
STANDARDS FOR RIVETING.
J£J£
i - - • ' i
CLEARANCE FOR COVER PLATE RIVETING
1 L '___'•__' 1
Vp-""-^'!^ -c
H
k=r~=H:=r~£r=
:=rJ ^
/v ,» it" ~.n o /' ill 7/' jif it' r* r'* fit
•>?//? 22? 3 $2 4 4z 5 5z 6
PS5SS~5S5
^i^jL^
i
/ 9^ O1^ 5*^5^ ^^0^ Z 7i-^~ 2\^ Z ^ 7\f 7*^
^ t'S ^4 ^4 ^3 ^8 ^ ~*& ~*8 ~* 4 ^4 ^S
K-,
>, 0 ± 1 It. 2 2L2
1
/ 2? 2$ 2$ 2 1$ 0
i *
n
//
INJMUM STAGGER FOR RIVETS
C t^P? "Q
£* *j>' * O^^S.
>\ ,-' ''^ "* >,
UML "^ '*
J&//e £/" Z)
in Inches-
\C ,/*• ,£" ,1" fS" ,3"
fo\ '8 ' 16 '4 '16 '8
. 7 It , ill , oil
Ife 1? 1*6
,5" ,//» ,3"
'8 '76 U
' /6 '6 '16 *M *M ^16
B" IS. L a M. '
•g 16 7 76 16 ~2
% A /* // /is f
7 tL i7 ,$ ,S //
J 12 '76 If >76 '4
i ,15 ,3 iff ,B i9
1 1/6 <4 '16 If '76
f4 ?- ? i/s i'B i7
is f% * Jje 1% 18
T6 0
£39
84/6
Ire Ii I
/* !l /£
ff '/6 >8
//3 /3 iJL
'76 >4 '16
J 0
is /i A
76 7e 8
/J & H
/f /J ^
i o
i i # o
/—/—/- / — n
'8 '16 '4 ' 16 V
CLEARANCE FOR
WEB RIVETING
RIVETS IN
ANG
VI
Distance '
I-/ plus thicknt
angles, but neve,
CRIMPED
LES
1^'T
'b"shoul(/be
ss of chore/
r /ess than 2".
STANDARD RIVET DIES
•CiHP^
j f^\forj-"Rivets
*?'$ s*
ll^'i*^ 7"
'3 'if' " ii "
i 2"\Forf Rivets
'~?~1S' M ^*
L •# J 7
, ~iit, 7'
i 2jr: " /' »•
!*--->!
229
TABLE 113.
STANDARDS FOR RIVETING.
<§Tf)NOaeD 2/VETSPACIN6 fOP GQULNN6
-J.
hH
p
-"t
— + *-- -•- --+
1_
1
— r
i
1 '
THICKNESS
OFPLffTE
^'RIVETS
i'KIVETS
%'eiVETS
i>/^fr«5
g&VETS
a
E>
c
D
R
B
C
D
fi
5
g
fi
/?
B
C
D
a
b
c
D
i "
G
a
5
8
2
/
3"
10
i
A
^Z
7J.
L4
*
1$
J
nl
<4
'$
I"
-4
i
3
4
?±
t-4-
4
It
7
8
?./
f|
n
%
/
?l
/^
/<9
^
n
oA
±4
H
5 "
10
4
7
8
ol
t-2
,1
'2
2
/
4
/I
*^
^
It
ol
£&
,7
>8
3."
8
/I
/
?*-
<%
'i
2
/
^
/I
?L
<3
li
3
2
H
'4
*L
">3
#
7" '
16
g
/
oZ
f|
/J
^
£4
,1
'8
3
2
?!
H
%
%
/ "
2
g
^
^
/I
2j>
ti
&
9L
*-8
tf
ii
&
?J_
t*
5"
&
9+
*2
H
z'
5
oJ.
<9
H
i
%
9-f-
*4
3"
A
230
TABLE 114
SHEARING AND BEARING VALUE OF RIVETS
Values above or to right of upper zigzag lines are greater than double shear.
Values below or to left of lower zigzag lines are less than single shear.
Rivet
Single Shear
at 6000
Pounds
Bearing Value for Different Thicknesses of Plate at 12 ooo Lbs. Per Square Inch.
i*
J*
*$
i"
A"
1"
A"
i"
A"
t"
H"
i"
tt"
i"
tt"
I"
*
§
*
i
/
.196
.307
.442
.601
.785
I ISO
I 840
2650
3 610
4710
I 500
I KSo
1 880
2340
2 8lO
2 250
2810
3380
3 Q40
2 630
3 ooo
3 75°
3 280
3940
4590
5 260
4 220
4690
5630
2 250
2 630
3 ooo
4500
5250
6000
5 060
S9IO
6750
6 190
6750
7880
9000
3 280
6560
7500
7 220
8250
8530
9750
9190
10500
9840
II 25C
3750
4S00
12 OOO
Rivet
Single Shear
at 7 500
Pounds
Bearing Value for Different Thicknesses of Plate at 15 ooo Lbs. Per Square Inch
Ed
s°
jp!
42 j?
i"
A"
i"
A"
i"
A"
I"
tt"
1"
tt"
r
tt"
i"
i
I
i
i
/
.196
.307
.442
.601
.785
1470
2 300
3 3io
4510
5890
I 880
2J40
2810
3 280
.575°
2340
2930
3 520
2810
3520
4 220
492Q
5630
3 280
3750
4690
4 100
4920
IS740
6560
s 270
5860
7030
5630
6 560
7500
6330
7380
8 440
7730
8 440
9 840
4 100
4690
8 200
9380
9 020
10 310
10660
12 100
ii 480
13 130
12 3OO
14060
ii 250
15 ooo
Rivet
Single Shear
at 10 ooo
Pounds
Bearing Value for Different Thicknesses of Plate at 20 ooo Lbs. Per Square Inch
IS
Q
&
«x
i"
A"
i"
A"
i"
A"
I"
B"
r
tt"
r
tt"
I"
|
.196
•307
.442
.601
.785
I 960
3070
4420
6 oio
7850
2 5OO
3 no
3 130
3910
4690
5470
6250
375°
4690
5630
6560
7500
4 380
5 ooo
6 250
547°
6560
7660
8750
7030
7810
9 380
3750
4380
5 ooo
7500
8750
IOOOO
8 440
9840
ii 250
10310
12 030
ii 250
13 130
10940
12 500
14 22O
16 250
15310
17500
16410
18750
I375o|i5ooo
20 ooo
| -Rivet
Single Shear
at ii ooo
Pounds
Bearing Value for Different Thicknesses of Plate at 22 ooo Lbs. Per Square Inch
i
la
n
<%
1"
A"
r
A"
r
A"
f"
H"
*"
H"
i"
if"
I"
1
:
/
.196
.307
.442
.601
.785
2 160
3370
4860
66lO
8640
2750
•i 44.0
3440
4300
s; 160
4130
5 160
6 190
7 220
4 8lO
5500
6880
6020
7220
8420
9630
7730
8590
10 310
4130
4 810
5500
8250
9630
II OOO
9280
10 830
12 380
11340
13230
12 380
14440
6020
6880
12 O3O
I37SO
15 640
16840
19250
18050
20630
8 250
15 I3o|i6 500)17 880
22 OOO
Ri\
F
Q
ret
<&
Single Shear
at 12 ooo
Pounds
Bearing Value for Different Thicknesses of Plate at 24 ooo Lbs. Per Square Inch
1"
A"
1"
A"
*"
A"
1"
H"
i"
H"
i"
«"
I"
i
!
I
1
/
.196
.307
.442
.601
.785
2 360
3680
5300
7 22O
9420
3 ooo
3 7!>°
3750
4690
; f>iO
4500
5630
6750
7880
C 2CO
6000
7 500
6s6d
7880
9190
10 500
8 440
9380
II 250
4500
5250
6000
9000
10 500
12 OOO
10 130
ii 810
13 500
12 380
13500
IS 750
IS 000
6560
7500
13 130
15 ooo
14440
16 500
17060
19500
18380
21 000
9 ooo
22 5OO
24OOO
231
TABLE 115
MULTIPLICATION TABLE FOR RIVET SPACING
I
Pitch of Rivets in Inches
i
a
^
2i
2\
23
!
5
3
7
0.
w
I~S
7?
*t
*• 4
8
2
8
*
?
OQ
2
2
-^\
-2i
-2f
- 3
-3l
-3i
-Si
- 4
-4i
-4l
-4f
- s
-si
-si
-sf
3
-3l
-3f
- 4!
-4i
-4!
-Si
- sf
- 6
-6f
-61
-7!
- 7*
-7!
-81
- 8f
J
4
-4i
- s
-si
- 6
- 6i
- 7
- 7i
- 8
- 8i
- 9
- 9i
-10
-105
-ii
-ni
4
5
-sf
-61
-6|
-7i
- 8!
-81
- 9f
-10
-iof
-ill
-ii!
T- r>i
I— O2
i- i!
i- if
I- 2f
5
6
-6f
-7i
-81
- 9
-9f
-lof
-ill
I- 0
i-of
i- i*
i- 2i
i- 3
i-3i
i-4*
i- si
6
7
-7!
-81
-9f
-ioi
-nf
i- o-l
i- it
I- 2
i- 2!
1-3!
T- A&-
i 4s
i- si
i- 6|
i- 71
i-8|
7
8
- 9
-IO
-ii
I- O
i- i
I- 2
i- 3
i- 4
i- S
i- 6
i- 7
i- 8
i- 9
I-IO
i-ii
8
9
-10*
-ii|
i- of
i- ii
I- 2|
i- 3s
i- 4!
i- 6
i- 7!
T R1
I- HI
i- 9l
i-ioi
i-nf
2- Of
2- i!
9
10
-III
i- of
I- If
i- 3
i-4l
i- si
1-6-3
i- 8
i-9i
i- 1 of
i-iif
2- I
2-2|
2- 3i
2-4f
10
ii
i- of
i- if
I- 3!
i-4i
i-s!
i-7i
i- 8f
I-IO
I-nf
2- -Of
2-2|
2- 3i
2- 4!
2-61
2- 7f
ii
12
i- ii
i- 3
i-4i
i- 6
i-7*
i- 9
i-iof
2- 0
2- I*
2- 3
2- 4i
2- 6
2-7i
2- 9
2- 1 0*
12
13
I- 2|
i- 4i
i-s!
i- 7i
i- 9s
i-iof
2- Of
2- 2
2-3f
2- 5*
2- 61
2- si
2-IOg
2-1 if
3- if
13
14
i- 3f
i- si
i- 7i
i- 9
i-iof
2- Of
2-2l
2- 4
2- si
2-7i
2-9i
2-1 1
3- of
3- 2i
3-4*
14
15
1-4!
i-6f
i- 8|
i- 1 of
2- Of
2-2|
2- 45
2- 6
2-7!
2- 9l
2-1 1 f
3- ii
3-3!
3- Si
3-7!
15
16
i- 6
i- 8
I-IO
2- 0
2- 2
2- 4
2- 6
2- 8
2-10
3-o
3- 2
3- 4
3-6
3- 8
3-10
16
i7
i- 7s
i- 9!
i-nf
2- ii
2- 3f
2— S?
2-7!
2-IO
3- o*
3- 2!
3- 4§
3-6i
3-81
3-iof
4- °!
17
18
i- 81
I- 1 Of
2- Of
2- 3
2- si
2-7i
2-9!
3 — o
3-2*
3- 4*
3-6f
3- 9
3-i 1 1
4- ii
4-3f
18
19
i-9f
i-iif
2— •9 —
~8
2-4i
2- 61
2- 9!
2-1 if
3- 2
3- 4!
3-6!
3- 9!
3-i ii
4- i!
4- 4l
4-6|
19
20
i-iof
2- I
2-3!
2- 6
2- 8*
2-1 1
3- ii
3- 4
3- 6i
3- 9
3-ii*
4- 2
4- 4*
4- 7
4- 9*
20
21
i-iif
2- 2|
2-4l
2-7i
2-Iof
3- of
3-3!
3-6
i 8s
3" °8
3-ni
4- iff
4- 4i
4-7!
4- 9i
5- of
21
22
2- Of
2- 3i
2- 61
2- 9
2-1 if
3- 2-i
3- si
3-8
3-iof
4- ii
4- 4l
4- 7
4- 9s
5- of
5-3*
22
23
2- i!
2- 4f
2- 7f
2-Iof
3— Is
3-4l
3-7*
3-10
4- o!
4-3!
4~ 6f
4- 9i
S-of
S-3i
5-6!
23
24
2- 3
2- 6
2- 9
3 — o
3- 3
3-6
3- 9
4.— o
4- 3
4-6
4~ 9
c — o
S- 3
S-6
S- 9
24
25
2- 4s
2-7i
2-Iof
3- ii
3- 4f
3-7f
3-io!
4- 2
4-5*
4- 81
4-1 1 1
s- 2i
s-sf
5-8!
s-n!
25
26
2- Si
2- 8f
2-1 if
3- 3
3-61
3- 9i
4~ of
4- 4
4-7i
4-io*
5- if
5- S
5-81
5-i ii
6-2f
26
2?
2-6f
2-9!
3- i*
3- 4i
3-7!
3-ni
4- 2f
4-6
4- 9!
S-of
S-4!
5-7*
S-IP!
6- 2!
6-sf
27
28
2- 7i
2-1 1
3-2*
3-6
3-9i
4- i
4- 4i
4-8
4-i i*
5- 3
5-6*
S-io
6- ii
6-5
6- 8*
28
20
2— 8 g
3- oi
3-3!
3-7i
3-1 1 !
4- 2f
4-6|
4-10
5- if
s-s!
5-8!
6- oi
6- 4!
6-7!
6-nf
29
30
2-9!
3-ii
3- Si
3- 9
4- of
4- 4i
4-81
5 — o
s-3i
S-7i
5-1 1!
6-3
6- 6f
6-ioi
7- 2!
30
8
i
/*
4
4
/*
i\
/f
*l
2
4
*
2-
4
28
2\
4
m
I
1
Pitch of Rivets in Inches
a
232
TABLE 115.— Continued
MULTIPLICATION TABLE FOR RIVET SPACING
:
Pitch of Rivets in Inches
•
-
3
A
3*
3\
Ji
3l
4
4*
4\
4\
S
J*
5i
5l
6
*
i
i
a
-6
-6}
-6J
-6}
- 7
-7i
-8
-8i
- 9
-9i
-10
-ioi
-n
-"i
I-O
.-
3
-9
-9l
-9!
-loj
-ioi
-Hi
I-O
1-0}
i- ii
1-2}
i- 3
1-3!
i-4i
i-s*
1-6
•
;
1-0
I-0|
i- i
i- ii
I- 2
i- 3
1-4
i- 5
i- 6
i- 7
i- 8
i- 9
I-IO
I-II
2-0
/
S
i-3
i-3l
i-4i
i-4i
i- si
1-6}
1-8
i-9*
i-ioi
i-n}
2- I
2-2}
2-3i
2-4!
2-6
5
(>
1-6
1-6}
i-7i
1-8}
1-9
i- ioi
2-O
2- ii
2- 3
2-4i
2- 6
2-7i
2- 9
2-ioi
3-o
6
7
1-9
i-9i
1-10}
i-nf
2-0*
2-2}
2-4
2-5f
2-7i
2- 9}
2-1 1
3- 0}
3-2i
3-4*
3-6
7
8
2-0
2- I
2- 2
2- 3
2- 4
2- 6
2-8
2-IO
3- o
3- 2
3- 4
3-6
3-8
3-10
4-0
i
9
2-3
2-4i
2-5*
t- <>*
2-7i
2-9*
3-o
3-4
3-4i
3-6}
3- 9
3-"}
4-ii
4-3!
4-6
9
to
2-6
2-7*
2- 8i
2-9J
2-1 1
3-ii
3-4
3-6i
3- 9
3-1 1 i
4- 2
4-4i
4- 7
4-9i
S-o
ti-
ii
2-9
2-IO§
2-11}
3- iJ
3-2i
3-5*
3-8
3-10}
4-ii
4-4}
4- 7
4-9!
S-oi
5-3*
5-6
ii
u
3-0
3-i»
3- 3
3-4i
3-6
3-9
4-0
4- 3
4-6
4- 9
5- o
5- 3
5-6
5- 9
6-0
u
rj
3-3
3-4l
3-6}
3-73
3- 9i
4-oJ
4-4
4-7}
4-ioi
s-i?
5- 5
5-8}
S-i i i
6-2!
6-6
*3
'4
3-6
3-7*
3- 9i
3-"*
4- i
4-4i
4-8
4-1 1 i
5- 3
5-6i
5-io
6- ij
6-5
6- 8i
7-o
'4
'5
3-9
3-ioJ
4- 0}
4-2|
4-4i
4-8}
S-o
5-3f
5-7i
S-ii}
6-3
6- 6J
6-ioi
7-2}
7-6
15
16
4-0
4- 2
4~ 4
4-6
4- 8
5- o
5-4
5-8
6- o
6-4
6- 8
7- o
7- 4
7-8
8-0
16
'7
4-3
4- Si
4-7*
4-91
4-1 1 i
5-3f
5-8
6-0}
6-4i
6- 8}
7- i
7- si
7-9i
8- i!
8-6
i/
18
4-6
4-8J
4-ioi
5-of
5- 3
S-7i
6-0
6-4i
6-9
7- ii
7-6
7-ioi
8-3
8-7i
9-0
iB
\i<)
4-9
4-»i
5-1}
5-4J
S-6i
S-"}
6-4
6- 8f
7- ii
7-6}
7-1 1
8-3!
8- 8i
9- i*
9-6
K,
r
5-°
5-2*
5- 5
5-7i
5-10
6-3
6-8
7- i
7-6
7-1 1
8-4
8-9
9- 2
9- 7
IO-O
ao
n
5-3
5-5l
5-8}
5-io|
6- ii
6- 6}
7-0
7- Si
7-ioi
8-3!
8-9
9- 2}
9- 7i
io- of
10-6
_>/
»
5-6
5-8}
5-1 1 1
6-2}
6-5
6-ioi
7-4
7- 9i
8-3
8- 8i
9- 2
9-7i
10- I
10- 6i
I I-O
aa
rj
5-9
5-"i
6- 2}
6- si
6- 8i
7-2}
7-8
8- 1}
8-7i
9- i*
9- 7
io- oj
io- 6\
ii- 0}
1 1-6
»3
r*
6-0
6-3
6- 6
6-9
7- o
7-6
8-0
8- 6
9- o
9-6
io- o
io- 6
II- 0
u- 6
I2-O
-';
r
6-3
6-6|
6-9*
7- of
7-3i
7-95
8-4
8-10}
9- 4*
o-io|
io- 5
10-11}
u- Si
n-iif
12-6
»5
F
6-6
6-9*
7-oi
7-3!
7- 7
*- ij
8-8
9- zi
9- 9
io- 3i
10-10
ii- 4i
n-ii
12- si
13-0
ad
k
6-9
7- of
7- 3l
7- 7i
7-ioi
8-5*
9-0
9-6J
io- i£
io- 8}
ii- 3
u- 9!
12- 41
12-11}
13-6
*?
P
7-0
7~3i
7- 7
7-ioi
8- 2
8-9
9-4
9-1 1
io- 6
ii- i
n- 8
12- 3
12-10
13- 5
14-0
at
r;
7-3
7-6|
7-10}
8- i*
8- si
9- of
9-8
io- 3*
IO-IO}
ii- si
12- I
12- 8}
13- 3i
13-10!
14-6
->U
Uo
7-6
7- 9f
8- ij
8-5*
8-9
9-4i
10-0
io- 7i
ii- 3
n-ioi
12- 6
13- iJ
13- 9
14- 4i
15-0
30
J
3\
3*
Jf
Ji
Ji
4
4\
4\
4\
5
5*
5i
5i
6
I
x
Pitch of Rivets in Inches
T.
54
233
TABLE 116.
AREAS TO BE DEDUCTED FOR RIVET HOLES, MAXIMUM RIVETS, AND RIVET SPACING.
AREAS IN SQUARE INCHES, TO BE DEDUCTED
FROM RIVETED PLATES
OR SHAPES TO OBTAIN NET AREAS.
Thickness
Diameter of Hole in Inches (Diam. of Rivet + £")•
of Plates.
Inches.
1
A
i
A
i
ft
t
ii
f
ii
i
ii
i
iA
ii
I A
ii
i
.06
.08
.09
.11
•13
•14
.16
•17
•19
.20
.22
•23
•25
27
.28
•3°
•31
A
.08
.10
.12
.14
.16
.18
.20
.21
•23
•25
•27
.29
•31
33
•35
•37
•39
f
.09
.12
.14
.16
•19
.21
•23
.26
.28
•30
•33
•35
•38
40
.42
•45
•47
TV
.11
•14
.16
.19
.22
•25
.27
•30
•33
•36
.38
.41
•44
46
•49
•52
•55
i
•13
.16
.19
.22
•25
.28
/
I
•34
•38
.41
•44
•47
•50
S3
•56
•59
•63
TV
.14
.18
.21
•25
.28
•32
•35
•39
.42
.46
•49
•53
•56
60
•63
.67
.70
!
.16
.20
•23
•27
•31
•35
•39
•43
•47
•Si
•55
•59
•63
66
.70
•74
.78
ft
•17
.21
.26
•30
•34
•39
•43
•47
•52
•56
.60
.64
.69
73
•77
.82
.86
3
.19
•23
.28
•33
•38
.42
•47
•52
•56
.61
.66
.70
•75
80
.84
.89
•94
fi
.20
•25
•30
•36
.41
.46
I
•56
.61
.66
[
.76
.81
86
.91
.96
.02
i
.22
.27
•33
•38
•44
•49
•55
.60
.66
.71
•77
.82
*8
93
.98
1.04
.09
ft
•23
.29
•35
.41
•47
•53
•59
.64
.70
.76
.82
.8
8
•94
I
00
1.05
i. ii
•17
i
•25
•31
•38
•44
•SO
•56
•63
.69
•75
.81
.8*
!
•94
I.OO
i. 06
1-13
1.19
•25
ITV
•27
•33
.40
.46
•53
.60
.66
•73
.80
.86
•93
I.OO
i. 06
i
13
i. 20
1.26
•33
i?
.28
•35
.42
•49
•56
•63
.70
•77
.84
.91
•9*
5
1.05
1-13
i
20
1.27
•34
•4i
«A
•30
•37
•45
•52
•59
.67
•74
.82
.89
.96
1.04
i. ii
1.19
i
26
i-34
.41
.48
i\
•31
•39
•47
•55
•63
.70
•78
.86
•94
i. 02
1.09
1.17
1-25
i
33
141
.48
•56
iA
•33
.41
•49
•57
.66
•74
.82
.90
.98
.07
.1.15
1.23
51
i
39
148
-56
.64
if
•34
•43
•52
.60
.69
•77
.86
•95
1.03
.12
.20
1.29
1*8
i
46
i-55
•63
.72
iiV
•36
•45
•54
•63
.72
.81
.90
•99
i. 08
•17
.26
i-35
1.44
i
53
1.62
1.80
ii
.38
•47
•56
.66
•75
.84
•94
1.03
I-I3
.22
•31
1.41
1-5°
i
59
1.69
.78
1.88
iA
•39
•49-
•59
.68
.78
.88
.c
>8
1.07
1.17
.27
•37
1.46
1.56
1.66
1.76
.86
i-95
if
.41
•Si
.61
•7i
.81
.91
i. 02
1. 12
1.22
•32
.42
1.52
1.63
i
73
1.83
•93
2.03
IT&
.42
•53
•63
•74
.84
•95
1.05
1.16
1.27
•37
•47
1.58
1.69
i
79
1.90
2.OO
2. II
if
•44
•55
.66
•77
.88
.98
1.09
i. 20
I-3I
.42
•53
1.64
i-75
i
86
i-97
2.08
2.19
IT!
•45
•57
.68
•79
.91
i. 02
I-I3
1.25
1.36
•47
•59
1.70
1.81
i
93
2.04
2.15
2.27
if
•47
•59
.70
.82
•94
i. 05
1.17
1.29
I.4I
•52
.64
1.76
i.
^8
i
99
2. II
2.23
2-34
iH
.48
.61
•73
•85
•97
1.09
1. 21
i-33
I.4S
•57
.70
1.82
1.94
2
06
2.18
2.3O
2.42
2
•50
•63
•75
.88
I.OO
i.i3
I.2S
1.38
I.SO
•63
•75
1.8
8
2.OO 2
13
2.25
2.38
2.50
MAXIMUM RIVET IN LEG OF ANGLES OR FLANGE OF BEAMS AND CHANNELS.
Leg of Angle
f
i
ij
l\
i*
If
2
25
3
3f
4
5 6
7
8
Max. Rivet
i
|
1
I
h
f
j
1
f
1
I
1 1
i
i|
Depth of Beam
3
4
5
6
7
8
9
JO
12
15
18
20 24
Max. Rivet
f
I
!
1
f
f
f
f
f
1
i i
Depth of Channel
3
4
5
6
7
8
9
10
12
15
Max. Rivet
2
1
1
i
1
1
f
f
f
-I
*
RIVET SPACING IN INCHES.
Minimum Pitch.
Max. Pitch in Line of Stress.
Min. Edge Dist
Size of
Rolled.
Max. Edge
Rivet.
Allowed.
Preferred.
At Ends of
Comp.Mem.
Bridges.
Bld'gs.
Sheared.
Dist.
i"
I?
If
2
4
ji «
6
I
1
I
ji^
f"
If
2
2|
4l
£"0 |:2 ,;
" li
f"
2i
2*
3
5
£ g.S-2-g
'
ij
Pj
1"
2f
3
3l
6
o c5 o"S
'
If
«ca
234
TABLE 117.
OLD STANDARD CONNECTIONS FOR BEAMS AND CHANNELS.
AMERICAN BRIDGE COMPANY.
5ize
Two ANGLE CONNECTIONS
OME ANGLE CONNECTIONS
24
Weiqht36punds
4f
—i-SS
"•f
: .
M
n
IL
Weiqht 30 pounds
&'! ff
18
-
itt
••<•!
<?<>
* 7" i'?'*
M
Weiqht 25 pounds
15
f/ . // 7 « , .. //
• **. « ^» " « " 7 " i ** "
)^2L56x4xf6xlO
=* Weiqht 27pounds
t Weiqht ITpounds
IE
ir;^j
=
*1
215 6x4xjx7i
Weiqht 20 pounds
^'^7 Weiqht I3pounds
10
9
• Weight 14pounds
s
m'
IL 6x6x76x5*
Wei^ht9P°und5
Weiqht 7 pounds
2fe6x4xix£"
Weiqht 6 pounds
IM
=•/( H
4S3
Weiqht 5 pounds
IL6*x6x?6XC1'
Weiqht 4pounds
We qhts of connections include qross weiqhts of angles and weiqhts of shop rivets
235
TABLE 118.
.NEW STANDARD CONNECTIONS FOR BEAMS AND CHANNELS.
AMERICAN BRIDGE COMPANY.
5W
21"
2%"
n
-$]
*"3-
i-,«4-
-- -©-
*- — y • * f^ ^> I ==a c. ^» • — ' ^^ ^^ i — ^
2 Angles 4'Jt4x^"x 1-SMi" ZAnglea 4x4'x^!>l!6^" aAngles 4'x4"x Vzd-ZVz ZAngles 4"x4'x^gxO-ll'/2"
jjj" __ Rivets and bolts-%"diam.
rf
C———^ » « r - -^* r — ^ ^fc -a • r ^^ ^*-
2 Angles 4'x4'x'^e'xO-ll1/2' 2 Angles 4'x 4"x^gx o'-8^' 2 Angles e'U'x^'xO-S1/^' 2Anjfles6"x 4x%"xO-3"
LIMITING VALUES OF BEAM CONNECTIONS.
I Beams.
Value of Web
Connection.
Values of Outstanding Legs of Connection Angles.
Field Rivets.
Field Bolts.
Depth,
Inches.
Weight,
Lb. Per
Foot.
Shop Rivets
in Enclosed
Bearing,
Pounds.
%" Rivets or
Turned Bolts,
Single Shear,
Pounds.
Min. Allow-
able Span in
Feet,
Uniform Load.
%" Rough
Bolts, Single
Shear, Pounds.
Min. Allow-
able Span in
Feet,
Uniform Load.
27
24
24
21
20
18
18
12
12
IO
IO
9
83
80
69*
r
42
36
3if
275
25
22
21
18
17*
s*
9t
66,800
67,500
52,700
40,200
45,000
41,400
29,000
36,900
26,000
23,600
17,200
27,900
20,900
26,100
24,300
18,900
11,300
10,400
9,500
61,900
53>ooo
53,000
44,200
35.300
35,300
35,300
35,3oo
35,300
26,500
26,500
17,700
17,700
17,700
17,700
17,700
8,800
8,800
8,800
18.4
17-5
16.3
15-5
17.6
13-3
15-0
8.9
n. i
8.1
10.3
74
6.9
5-7
4-3
4.4
6.2
4.4
2.9
49,500
42,400
42,400
35,3oo
28,300
28.300
28,300
28,300
28,300
21,200
21,200
.14,100
14,100
14,100
14,100
14 loo
7,100
7,100
7,100
23.1
21.9
2O.2
I7.6
22.1
16.7
15-4
II. I
II. I
9.0
IO-3
9.2
8.6
7-i
5-4
5-5
7.8
ALLOWABLE UNIT STRESS IN POUNDS PER SQUARE INCH.
Single
Shear
Rivets Shop 12,000
Rivets and Turned Bolts. Field 10,000
Rough Bolts Field 8,000
Bearing
Rivets — enclosed Shop 30,000
Rivets — one side Shop 24,000
Rivets and Turned Bolts . . .Field 20,000
Rough Bolts Field 16,000
t = Web thickness, in bearing, to develop max. allowable reactions, when beams frame
opposite.
Connections are figured for bearing and shear (no moment considered).
The above values agree with tests made on beams under ordinary conditions of use.
Where web is enclosed between connection angles (enclosed bearing), values are greater
because of the increased efficiency due to friction and grip.
Special connections shall be used when any of the limiting conditions given above are
exceeded — such as end reaction from loaded beam being greater than value of connection;
shorter span with beam fully loaded; or a less thickness of web when maximum allowable
reactions are used.
236
TABLE 119.
STANDARD BEVELED BEAM CONNECTIONS.
AMERICAN BRIDGE COMPANY.
BEVELED BEAM CONNECTIONS - RIVET SPACIM & CLEARANCES
W=j or less, use Standard
^ „ , -f^ connection angles (bent)-
\*v<^
'eSk W°$*tolg'use Special
connection angles (bent)-
For large duplication modify these details where necessary to
per/nit machine riveting- Table covers plates uptoj> thick •
Omit cut P where
Ca-2> "in 12, 'or less
i " t
c=% or /ess-
\F=2>"orfesS'
a
b
Max-
c
Max-
w
D
E
H
Length of Bent Plates
L
P
P'
t*
P*
P*
F=upto3
"F-5"to4
/"
1?
9"
16
If
j//
£4
f"
/i"
1?
2
12
T6
/J
2s-
L. 4
See notes shore*
/i
/I
/I
3
12
%
/i
**
,
/i
2
H
4
12
%
H
5L2
,1"
3?
&
10"
tlf
10"
12"
/i
?i
2k
5
12
%
lit
4
4
3
II
ft
Mi
12
!Lz
ft
5
6
12
9
16
IL*
4i
4±
3
12
0*
II
12
fi
?L
*• 4-
3t
7
12
*
H
5
5
3^
IX
/4t
Hi
12
/I
3
X
8
12
/c
n
51
&
3}
/3
J5Lz
12'
/2
/I
#
4
9
12
£
ti
tt
12
/I
3|
4i
10
12
i
It
31
I2i
2
4
5
II
12
*
It
5i
12L2
2
4i
5k
12
12
*
16
0
3|
121*
4
4^
5k
12
II
?
i
*i
12
H
4i
Bk
12
10
i
i
3
12
fi
5
6
12
9
?
i
j
3
12
/i
f>L2
61
12
8
i
2
&
12
f3
'4
6
7k
12
7
1
i
^
IX
2
6L?
Bk
12
6
i
i
**
&
2i
7i
10
12
5
/
4
i
4
15
2Lz
9
l/t
12
4
i
/
4%
/3J
^
II
14
237
TABLE 120.
STANDARD SWAY ROD AND LATERAL CONNECTIONS.
AMERICAN BRIDGE COMPANY.
SWAY ROD CONNECTIONS-
-*V Specify hexagonal nuts on all sway rods-
f S *S *S V <? ^"N.
i ->x^7 Bolts can have hexagonal or square heads or nuts-, • ~^ ^•>,
Hole for rod punched ft" larger than rod
Rod -
5
Size of Angle
R
5
Size oF Angle
R
f?
6" to 12"
12"
fi
12"
6"tol?
6"bl2
12"
.
3
f
BEVELED WASHERS, CAST IRON
L /2"
Sketch
Round
Rod
Upset
A
B
C
D
E
F
6
H
L
R
X
K
Size of Slot
in Plate
Weight
Pounds
A
7"
8 t"
Hone
i"
tf
If
I"
9"
/f
9"
16
7"
fi
7"
8
If
3/
£"
'4
4"
f
/+'x?-i*
'8 **%
1-8
A
1 ,,
ft
/A*
8 fi
?£
*8
//
H
/3
16
/3
16
7
J
n
>i
4
2
5
ft
fi**k
2-6
B
3 /
None
?'
*-8
ft
/
9
If
9
If
A
4
n
*i
4
2
*i
ii
ti*#
2-3
B
1 a
'' ,t
?L
t-8
ft
a
/3
16
/5
/6
3
4
'i
4
6
*t
6
3
fj^i_
3-8
For rods above // dfam- use clews connections-
238
TABLE 121.
STANDARD LATERAL CONNECTIONS FOR HIGHWAY BRIDGES.
AMERICAN BRIDGE COMPANY.
SKEWBACK "A" Weight 6-8 Ibs-
Skewback A For rods up to /£ round
or /j square (upset to /j- "round) ;
For upsets fg diam- or /ess, angle,
of rod may vary From 32 °(7j "in /2 ")
to 60° (12" in 6%")-
For upsets greater than /$ diam- up
to Ij diam-j angle oF rod may vary From
41 j> °(!0t "in 12 ") to 60 °(l2 "in 6jj") -
Standard slot in beam 3? * 6 "-
:t£
0
:O
;•*;
•
•L- oFwebJ
' r if
Radius = 3 j
-
N<S
k.^
i "
H»J^->K- >k- -•--->«-- -->««;'*?i^
.' '- '.* ft / " ^ ^ \s~i
+
4-
SKEWBACK B, Weight 17 Ibs-
" » , H
Skewback B For rods 1$ round
f ft * r ft i
or/y square (upset to/j roundj;
\lj> "round (upset to/ 3 round) or
up to \ . 3 // x L o a j\
\Ig square (upset to Z round-J
For upsets f§ "diam- or less ,
angle oF rod may vary From 33^
(8"inl2")to60°(l2"m6%'):
For upsets greater than /j- "diam -
up to 2 "diam -, angle oF rod may vary From
4%JG!f.
"
Standard 'slot in beam 4$ *6z
SKEWBACK'C" Weight 23/hs-
Skewback C For rods /J round or
l~6 square (upset to 2 "round) j
. J/jf round (upset to 2ji"round)or
up to\ ,/ n / ° , H ' ,.
l/j square (upset to 2# round)
C-L- oF web
40i
For a// rods*
Standard slot in beam 4%"*6j>*
Where upse t end oF rod fs greater
than 2g diam -, hole in washer will
be drilled to Fit upset •
239
TABLE 122.
STANDARD LATERAL CONNECTIONS AND STUB ENDS.
AMERICAN BRIDGE COMPANY.
U PLATE A , Weight 3 -9 IBs - U PLATE Bf Weight 8-6 Ibs -
For rods up to ^"square or/ft round (upset to I j"J ^'square or Ij round (upset tof^'J
nr-i- c»»l"* II" t~~ '0rr0(/S\.,-f.~ /I". il" if. AA-Vi
Plate 5"*i*Il"Iong.
\up to 1% square or ground (upset to2*)
WASHER
Weight 0-5 Ibs>
WASHER
Weight lib
Max- hole I?
"
STUB END //*/
Weight 4-3 Ibs-
t !
w-*t«-*j
STUB END N?3- COOPER HITCH
Weight 3*5 Ibs-
Plate 2"*%", 7-j>"/ong. Plate 2"*%', ?£ lay*
Holes %"diam* . Holes 7% dram'
4?"
I" I"
C\j ' '
STUB END N*4-
Weight 5-2 Ibs-
Plate 4**i",3i"/aty
Weight 5- Bibs-
/" I"
7* / jy
j round, 7? long
2 Hex- Huts? $*Tap-
j round, 7J> long j round, 7^ long % round, 8"/ong-
2 Hex- Nuts- j" Tap. Z Hex- Nuts- j'Tdp- ? Hex-Huts- j"Tdp
240
TABLE 121
STANDARD LAC SCREWS, HOOK BOLTS AND WASHERS.
AEERICAN BRIDGE COMPANY.
LAG SCREWS
Length
Diameter
Diam
ft
/i
fi
Min-
Length Length
Ji
fi
II
2
2
2i
3
3|
5
6
8
Max-
6"
6
8
10
12
12
12
12
12
12
12
12
No-Thread
per inch
5
4
3
Length of Lag
5crew&Head
Length
2
2i
3
3<
4
4i
5
Si
6
7
8
9
10
11
12
Lenth
I"
'*.
fi
j}
2
2i
5
5
5
Heads dre the same as For square hedd bolts
Threaded portion is not tapered except at point
CLAMP
$ Cored Ho/e
*3&
*Tr.;>sJj
^
\ *8
c •*--
k
1?"
5/ze
Exam
Dimensions of Clamp Weight
in Ibs-
18"
15
12
9&IO/i
5&6
B
'Til
D
0-4
04
0-4
0-4
0-4
OGEE WASHERS
'r
(Recess for naif lock -
5/ze
Bolt
r
4
Dimens/ons of Washer
A B C D E R r
II"
/i
2?
31
i
Weight
in Pounds
0-4
0-7
1-0
SKEWBACK WASHERS
Used
With
<
Dimensions of Washers
M
H
D
R
3*
w
4%
4%
Weight
ir? Pounds
1-2
I'8
2-5
2-7
5-0
3 ••*
ffooK BOLTS, 4*or£ Square,
In bil/ing Hook Bolts give dimensions A,
SdrLj all other dimensions sne standard-
Unless otherwise specified, 5" will
be made "- Hex- nuts furnished-
CASTlROff
241
TABLE 124.
WEIGHTS OF WASHERS AND TRACK BOLTS.
WEIGHTS OF LAG SCREWS.
Pounds per Hundred. (Kent's Pocket-book.)
Diam.
- Length, Under Head, in Inches.
In.
it
6.88
if
2
af
2i
3
3*
4
4*
S
Si
6
7
8
9
IO
I
A
j
!
7-50
"•75
16.88
8.25
12.62
I/.lS
9-25
12.88
18.07
9.62
13.28
19.18
10.82
16.62
22.OO
34-07
II.SO
18.18
24.00
35.88
I3-3I
18.88
26.82
39-25
64.00
14.82
19.50
28.25
42.62
67.88
16.50
21.25
30-37
47-75
71-37
17-37
23.56
33-88
51.62
79.37
18.82
2S-3I
35-37
55-12
86.62
38.94
61.88
92.75
44-37
68.75
97-50
77.00
108.75
90.00
124.75
For American Bridge Company's Standard Lag Screws see Table 123.
WROUGHT IRON OR STEEL PLATE ROUND WASHERS.
Diam
In.
Hole.
In.
Thick-
ness
B.W.G
No.
Bolt.
In.
Num-
ber in
200 Lb.
Diam,
In.
Hole.
In.
Thick-
ness
B.W.G
No.
Bolt.
In.
Num-
ber in
200 Lb
Diam,
In.
Hole.
In.
Thick-
ness
B.W.G.
No.
Bolt.
In.
Num-
ber in
200 Lb
A
I
18
16
16
85200
34800
2620O
I44OO
8400
5800
if
2
2f
12
IO
IO
9
9
9
4600
2600
22OO
I6OO
I2OO
it
if
it
if
if
if
it
if
900
6OO
570
460
432
366
STANDARD CAST, O G WASHERS.
Diam.
of Bolt.
Bottom
Diam.
Top
Diam.
Hole.
Thick-
ness.
Weight.
Diam.
of Bolt.
Bottom
Diam.
Top
Diam.
Hole.
Thick-
ness.
Weight,
In.
In.
In.
In.
In.
Lb.
In.
In.
In.
In.
In.
Lb.
If
if
2t
if
2*
It
It
I*
If
2
.a
44
6
61
71
2*
it
+}
it
il
I
!'
9|
i?i
TRACK BOLTS.
With United States Standard Hexagon Nuts.
Lb.
45 to 85
In.
In.
Il
230 6.3
240 6.0
2545-7
260 5.5
266 5.4
Lb.
45 to 85
30 to 40
In.
In.
283
375
4103
435
465
Lb.
20 to 30
In.
5x3
5x2
715
760
800
820
242
TABLE 125.
WEIGHTS OF STEEL WIRE NAILS AND SPIKES.
AMERICAN STEEL AND WIRE Co.
STANDARD STEEL WIRE NAILS AND SPIKES.
Size*, Lengths and Approximate Number per Pound.
Size.
In.
**
"I
OCQ
*1
(3s
i
a
£
1*1
as
rfl
'7; -'-
in
i
&
1
Barbed
Car.
Hinge.
V
|
i
J
I1
3
B
I
In
Size.
!
33
!
!
K
J
I
714
469
411
365
251
230
176
151
103
1615
1346
906
775
700
568
400
357
41
38
30
23
17
13
10
8
6
5
4
3
2
2
2
3
3
].
5i
6
8
9
10
12
207-
1781
issi
2d Ex. Fine
2d
3d Ex. Fine
3d
'~4«T
5d
6d
7d
Id
9d
lOd
I2d
I0d
20d
30d
4od
Sod
ted
A Diam.
i
i
i
i
i
i
i
i
2
2
2
3
3
!»
si
6
8
9
IO
12
876
—
1351
1010
411
—
.—
—
710
1560
1351
IOI<
77*
47C
2d Ex. Fine
2d
3d Ex. Fine
3d
4d
5d
6d
.. 7d
8d
2!
iod
I2d
iod
2Od
30d
4O<1
sod
ted
•ft Diam.
568
-—
807
635
225
5<>S
—
—
142
124
92
82
62
SO
40
30
23
429
274
235
157
139
99
90
69
62
49
37
3i6
271
181
161
106
96
69
63
49
31
24
18
14
II
157
139
99
00
69
54
43
31
584
500
309
238
189
172
121
H3
00
62
473
406
236
2IO
145
132
94
88
71
52
46
187
142
103
-'74
235
_'<).}
I.W
125
114
83
165
118
103
76
69
54
50
42
35
26
24
18
IS
13
274
142
124
M
82
f>2
57
SO
43
31
2.S
21
17
IS
50
82
38
62
30
12
II
10
9
50
25
23
22
19
- —
35
._.:.
.:::.
-----
—
—
~
MISCELLANEOUS STEEL WIRE NAILS.
Approximate Number per Pound.
Washburn
& Moen
Gauge.
11
Ma
Q.S
Length in Inches.
1
i
i
i
Ij
II
i}_
2
21
3
12
H
16
19
22
25
30
35
41
50
57
69
83
105
137
178
236
31
4
4i
8
9
IO
13
14
17
20
24
28
33
39
46
55
70 .
5
6
6
8
IO
ii
13
IS
18
21
25
29
7
8 9
10
3}
4
4i
si
61
7i
9
ooo
oo
0
i
a
3
4
6
8
9
10
II
12
13
M
15
16
17
18
19
20
21
22
.362
.331
.307
.283
.263
•244
.225
.207
.192
.177
.162
.148
.135
.120
.105
.092
.080
.072
.063
.054
.047
.041
.035
.032
.028
,
>s
u
!«
tf
2
0
2
5
«)
0
7
5
i
i
<j
9
8
i
3
6
S
3
i)
23
27
32
38
44
SO
60
71
82
IOO
us
138
165
209
274
357
473
584
761
1038
1379
1778
20
23
27
32
37
43
Si
00
71
85
98
IlS
142
179
235
306
406
500
653
800
182
17
20
24
28
32
38
45
53
62
75
86
103
124
157
20.1
268
350
I3»
S7I
779
I4.
16
19
23
26
30
36
42
SO
00
09
82
99
125
164
214
284
350
10
12
'4
10
19
32
26
30
35
43
49
59
71
90
H7
I S3
9
IO
12
H
16
19
23
26
31
37
43
52
62
79
103
1
9
II
13
15
it
21
25
30
35
41
50
6
8
9
II ]
13 1
IS -
18 .
4i 4
5 4*
6 5
7 6
8 7
o 8
I IO
=
57
65
76
00
1 06
123
149
172
207
248
314
411
536
710
876
1143
1558
JllfKJ
2667
3750
4444
i.
i
"
1
'
12
I.J
If
n
25
Si
4-
91
70
<>i
1*4
163
»I3
.("•
100
1 20
141
164
200
22Q
276
333
418
548
714
947
1168
1523
2077
2758
3556
fOOO
5926
7618
311
247
299
345
414
496
628
822
1072
1420
1752
2280
3116
4138
5334
7500
8888
11428
169
197
239
275
331
397
502
658
857
1136
1402
1828
2495
3310
4267
0000
7111
9143
W.&M.
Gauge.
II 12
"
—
-
ooo
oo
o
I
a
3l 3
31 3t
4t 4
I JI
These approximate numbers are an average only, and the figures given may be varied either way, by changes
in the dimensions of heads or points. Brads and no-head nails will have more to the pound than table shows,
and large or thick-headed nai s will have less.
243
TABLE 126.
WEIGHTS OF NAILS AND SPIKES.
FROM CAMBRIA STEEL.
CUT STEEL NAILS AND SPIKES.
Sizes, Lengths and Approximate Number per Pound.
2d
3d
4d
5d
6d
7d
8d
9d
xod
i2d
i6d
20d
2Sd
3od
4od
Sod
6od
740
460
280
210
1 6O
1 2O
88
73
60
46
33
23
20
i6J
400
260
1 80
125
100
80
68
52
48
40
34
24
880
530
350
300
210
168
130
104
96
86
76
420
300
2IO
180
130
107
88
70
52
38
30
26
1 6
IOO
80
60
52
38
26
20
18
16
17
9
H
6
51
5
750
600
500
450
310
280
2IO
400
304
224
340
280
220
1 80
1462
1300
I IOO
800
650
960
750
To-
bacco.
130
97
85
68
58
48
Brads.
120
94
74
62
50
40
27
Shingle
90
72
60
SQUARE BOAT SPIKES.
Approximate Number in a Keg of 200 Pounds.
Length of Spike — Inches.
Size.
1"
A"
i"
3000
1660
1320
2375
1360
1140
2050
1230
940
1825
1175
800
990
650
8
880
600
525
475
Size.
A"
*"
600
450
590
375
335
260
400
300
240
II
320
260
205
175
1 6
160
RAILROAD SPIKES.
Size Under
Head.
Inches.
Average
Number
per Keg
of 200 Lb.
Spikes per Mile of
Single Track.
Ties 2 Ft. c. to c.t
4 Spikes per Tie.
Pounds.
Kegs.
Rail Used.
Weight
per Yard.
Pounds.
Size Under
Head.
Inches.
Average
Number
per Keg
of 200 Lb.
Spikes per Mile of
Single Track.
Ties 2 Ft. c. to c.,
4 Spikes per Tie.
Pounds. Kegs.
Rail Used.
Weight
per Yard.
Pounds.
5* XI
5 XA
5 XJ
4 XI
300
375
400
450
530
600
7040
5870
5170
4660
3960
3520
29i
26
75 to ~oo
45 " 75
40 " 56
35 " 40
30 " 35
25 " 35
4iXA
4 XA
3iXA
4 Xi
3iX|
3 XI
680
720
900
IOOO
1190
1240
3110
2910
2350
2090
1780
1710
I4J
8i
20 tO 3O
20 " 30
16 " 25
16 " 25
16 " 20
244
TABLE 127.
PIPE — BLACK AND GALVANIZED.
NATIONAL TUBE COMPANY STANDARD.
STANDARD PIPE.
Diameters. Inches.
Weight per Foot.
Pounds.
Couplings.
ClwA
Thick-
Threads
•MI
in.
ness,
per Inch.
External.
Internal.
Inches.
Plain
Ends.
Threads
and
Diameter,
Inches.
Length,
Inches.
Weight,
Pounds.
Couplings.
i
*
.405
.269
.068
•244
.245
27
.562
i
.029
1
.540
•364
.088
•424
425
18
.685
I
.043
s
•675
•493
.091
.567
.568
18
.848
Ii
.070
i
.840
.622
.109
.850
.852
H
1.024
If
.116
1
1.050
.824
•"3
I.I30
I-I34
H
I.28I
ii
.209
I
I-3IS
1.049
.133
1.678
1.684
iii
I-576
if
•343
Ii
1.660
1.380
.140
2.272
2.281
"i
1.950
2i
•535
Ii
1.900
1.610
.145
2.717
2.731
iii
2.218
2f
•743
2
2-375
2.067
•154
3-652
3.678
II|
2.760
2f
1.208
•1
2.875
2.469
.203
5-793
5.819
8
3.276
2j
1.720
3
3-Soo
3.068
.216
7-575
7.616
8
3-948
3i
2.498
si
4.000
3-548
.226
9.109
9-2O2
8
4-591
3f
4.241
4
4-500
4.026
•237
10.790
10.889
8
5.091
3f
4.741
4i
5.000
4.506
-247
12.538
12.642
8
5-591
3l
5-241
s
5-563
5-047
.258
14.617
14.810
8
6.296
4i
8.091
6
6.625
6.065
.280
18.974
19.185
8
7-358
4i
9-554
7
7.625
7.023
.301
23-544
23-769
8
8.358
4i
10.932
8
8.625
8.071
•277
24.696
25.000
8
9-358
4l
I3-905
8
8.625
7.981
.322
28.554
28.809
8
9-358
4!
13-905
I»
9.625
8.941
•342
33-907
34.188
8
10.358
si
17.236
,0
10.750
10.192
.279
31.201
32.000
8
11.721
6|
29-877
,0
10.750
10.136
-307
34.240
35-ooo
8
11.721
6i
29.877
,0
10.750
IO.O2O
-365
40.483
41-132
8
11.721
6i
29.877
»
11.750
11.000
•375
45-557
46.247
8
12.721
6i
32-550
12
12.750
12.090
•330
43-773
45.000
8
I3-958
6i
43.098
12
12.750
12.000
•375
49.562
50.706
8
I3.958
6i
43.098
13
14.000
13.250
•375
54.568
55-824
8
I5.2O8
6i
47.152
H
15.000
14.250
•375
58-573
60.375
8
16.446
6J
59-493
IS
16.000
I5-250
•375
62.579
64.500
8
17.446
6i
63.294
The permissible variation in weight is 5 per cent above and 5 pei cent below.
Furnished with threads and couplings and in random lengths unless otherwise ordered.
Taper of threads is J" diameter per foot length for all sizes.
The weight per foot of pipe with threads and couplings is based on a length of 20 feet including
the coupling, but shipping lengths of small sizes will usually average less than 20 feet.
All weights and dimensions are nominal. On sizes made in more than one weight, weight
desired must be specified.
245
TABLE 127.— Continued.
PIPE — BLACK AND GALVANIZED — Concluded.
NATIONAL TUBE COMPANY STANDARD.
EXTRA STRONG PIPE. DOUBLE EXTRA STRONG PIPE.
Size,
In.
2
2*
3*
9
10
ii
12
13
H
15
Diameters,
Inches.
External.
•405
•540
•675
.840
1.050
I-3I5
1. 660
1.900
2-375
2.875
3.500
4.000
4-500
5.OOO
5-563
6.625
7.625
8.625
10.750
11.750
12.750
14.000
I5.OOO
I6.OOO
Internal.
•215
.302
•423
•546
.742
•957
1.278
1.500
1-939
2.323
2.900
3-364
3.826
4.290
4.813
5-76i
6.625
7.625
8.625
9-750
10.750
11.750
13.000
14.000
15.000
Thick-
ness,
Inches.
•095
.119
.126
.147
-154
.179
.191
.2OO
.218
.276
.300
.318
•337
•355
•375
•432
.500
.500
.500
.500
.500
.500
.500
.500
.500
Weight
per Foot,
Pounds.
Plain
Ends.
•3H
•535
-738
1.087
1-473
2.171
2.996
3-631
5.022
7.661
10.252
12.505
14.983
17.611
20.778
28.573
38.048
43-388
48.728
54-735
60.075
65-415
72.091
77-431
82.771
Size,
In.
44
5
6
7
Diameters,
Inches.
External. Internal
.840
1.050
I-3I5
1.660
1.900
2-375
2.875
3.500
4.000
4.500
5.000
5-563
6.625
7.625
8.625
•252
•434
•599
1-503
1.771
2.300
2.728
3-I52
3-58o
4.063
4.897
5-875
6-875
Thick-
ness,
Inches.
.294
.308
•358
•382
.400
•436
•552
.600
.636
'674
.710
•750
.864
•875
-875
Weight
per Foot,
Pounds.
Plain
Ends.
1.714
2.440
3-659
5.214
6.408
9.029
I3-695
18.583
22.850
27-541
32.530
38-5S2
53.160
63.079
72.424
Furnished with plain ends and in random lengths
unless otherwise ordered.
Permissible variation in weight, for extra strong
pipe, 5 per cent above and 5 per cent below.
For double extra strong pipe, 10 per cent above
and 10 per cent below.
All weights and dimensions are nominal.
LARGE O. D. PIPE.
Weight per Foot, Pounds.
Thickness, Inches.
i
14
15
16
i?
18
20
21
22
28
3°
36.713
42-053
44-723
47-393
45.682
49.020
52.357
55-695
59-032
65-708
69.045
72-383
54-568
58.573
62.579
66.584
70.589
7S--599
82.604
86.609
94.619
102.629
63-37I
68.044
72.716
77-389
82.061
91.407
96.079
100.752
1 10.097
119.442
128.787
138.132
72.091
77-431
82.771
88.111
93-451
104.131
109.471
114.811
125.491
136.172
146.852
I57-532
80.726
86-734
92.742
98.749
104757
116.772
122.780
128.787
140.802
152.818
164.833
176.848
89.279
95-954
102.629
109.304
H5-979
129.330
136.005
142.680
156.030
169.380
182.730
196.081
106.134
114.144
122.154
130.164
138.174
154.194
162.204
170.215
186.235
202.255
218.275
234.296
122.654
132.000
I4L345
150.690
160.035
178.725
138.842
149.522
160.202
170.882
181.562
202.923
Furnished with plain ends and in random lengths, unless otherwise ordered.
All weights and dimensions are nominal.
246
TABLE 128.
STANDARD GAGES. COMPARATIVE TABLE.
CARNEGIE STEEL Co.
Thickness in Decimals of an Inch.
§Lai
1 *•
B |
s 1
e
"(5 i)
It
Qtm
3 gj S
j5 9
— s^
£x
8§E^
ll '
Number.
jfejl
!*!l
§5*
few
11
X rt
%
§ •
IfiftJ
$ J-
I
I -2-a
II
j|3
Tjj-S
J «3
? w~
5 1
•g |
H
^7.
•J
M
•a
1 *
i
0000000
.500
.4900
.coo
oooooo
.46875
.580000
.4615
JC
.4.64.
00000
.5OO
~ f J
•4375
.516500
•43°)
.450
T T
•432
oooo
0
•454
tj/ j
.4062?
.460000
.3938
T J
.4OO
™
000
~J r
•425
~ J
•375
.409642
.3625
.360
.372
.5000
oo
.380
•34375
.364796
.3310
•330
•348
•4452
o
.340
.3125
.324861
.3065
•305
•324
•3964
I
.300
.28125
.289297
.2830
.285
.3OO
•3532
2
.284
.265625
.257627
.2625
.265
.276
•3147
3
•259
.25
.229423
•2437
.245
.252
.2804
4
•238
•234375
•204307
.2253
.225
.232
.2500
5
.220
.21875
.181940
.2070
.205
.212
.2225
6
.203
.203125
.162023
.1920
.190
.192
.1981
7
.180
.1875
.144285
.1770
•175
.176
.1764
8
.165
.171875
.128490
.1620
.160
.100
.1570
9
.148
.15625
.114423
.1483
•145
.144
.1398
10
•134
.140625
.101897
•1350
.130
.128
.1250
ii
.120
.125
.090742
.1205
.1175
.116
.1113
12
.109
•109375
.080808
•1055
.105
.104
.0991
13
.095
•09375
.071962
.0915
.0925
.092
.0882
•083
.078125
.064084
.0800
.0806
.080
.0785
15
.072
.0703125
.057068
.0720
.070
.072
.0699
16
.065
.0625
.050821
.0625
.061
.064
.0625
17
.058
.05625
•045257
.0540
.0525
.056
.0556
18
.049
•05
•040303
.0475
.045
.048
.0495
19
.042
•04375
.035890
.0410
.040
.040
.0440
20
•035
•0375
.031961
.0348
•035
.036
•0392
21
.032
•034375
.028462
•03175
•031
.032
.0349
22
.028
.03125
.025346
.0286
.028
.028
•03125
23
.025
.028125
.022572
.0258
.025
.024
.02782
24
.022
.025
.O2OIOI
.0230
.0225
.022
.02476
25
.O2O
.021875
.OI79OO
.0204
.O2O
.O2O
.02204
26
.018
.01875
.015941
.0181
.018
.018
.01961
27
.Ol6
.0171875
.014195
.0173
.017
.0164
•01745
28
.014
.015625
.012641
.0162
.Ol6
.0148
.015625
29
.013
.0140625
.011257
.0150
.015
.0136
.0139
30
.OI2
.0125
.OIOO25
.0140
.014
.OI24
.0123
31
.010
.0109375
.008928
.0132
.013
.OIl6
.OIIO
32
.009
.01015625
.007950
.0128
.OI2
.OIO8
.0098
33
.008
.009375
.007080
.0118
.Oil
.OIOO
.0087
34
.007
.00859375
.006305
.0104
.010
.0092
.0077
35
.005
.0078125
.005615
.0095
.0095
.0084
.0069
36
.004
.00703125
.005000
.0090
.009
.0076
.0061
37
.006640625
.004.4 c 7
.0081;
.008 c
.0068
.OOC4
J f
38
.00625
00106;
r*fvj
.0080
.ww^
.008
.0060
'•—— • J*Y
.0048
J
19
*OO^ tj ^ I
.007 c
.007 c
Wf. V
J X
40
•OO^ IA A
****/ j
vw/ J
.007
.0048
'
IWW/
Unless otherwise specified, all orders in gages will be executed to Birmingham Wire Gage.
247
TABLE 129.
STANDARD GAGES AND WEIGHTS OF SHEET STEEL.
CARNEGIE STEEL Co.
UNITED STATES STANDARD GAGE
FOR
SHEET AND PLATE STEEL.
Gage
Number.
Thickness
in
Fractions
of an Inch.
Thickness ,
in
Decimals
of an Inch.
Weight per
Square
Foot, in
Pounds,
Steel.
Gage
Number.
Thickness
in
Fractions
of an Inch.
Thickness
in
Decimals
of an Inch.
Weight per
Square
Foot, in
Pounds,
Steel.
ooooooo
i
•5
20.4
17
ifjr
.05625
2.295
oooooo
H
.46875
19.125
18
.05
2.04
ooooo
A
•4375
17.85
19
ifo
•04375
1.785
20
^T
•0375
1-53
oooo
H
.40625
16.575
ooo
*
•375
15-3
21
•034375
1.4025
oo
tt
.34375
14-025
22
.03125
1.275
o
A
.3125
12.75
23
.028125
I.I475
24
A
.025
1. 02
I
.28125
11-475
2
.265625
10.8375
25
rfff
.021875
.8925
3
.25
IO.2
26
if*
.01875
•765
4
if
.234375
9.5625
27
sVs
.0171875
.70125
28
&
.015625
•6375
5
A
.21875
8.925
6
H
.203125
8.2875
29
sfs
.0140625
•57375
7
A
.1875
7-65
30
&
.0125
•Si
8
B
• I7I87S
7.0I2S
31
515
.0109375
.44625
32
rib
.01015625
.4H375
9
A
.15625
6.375
IO
A
.140625
5-7375
33
3?5
•009375
•3825
II
i
.125
5-1
34
life
.00859375
•350625
12
&
.109375
4-4625
35
B?5
.0078125
.31875
36
•t&v
.00703125
.286875
13
A
.09375
3.825
14
jC
.078125
3.1875
37
26«<f
.006640625
.2709375
IS
dh
.0703125
2.86875
38
ibv
.00625
•255
16
A
.0625
2.55
BIRMINGHAM WIRE GAGE.
EQUIVALENTS IN INCHES.
CORRESPONDING WEIGHTS OF FLAT ROLLED STEEL.
Gage
Thickness,
Pounds
Gage
Thickness,
Pounds
Number.
Inches.
per
Square Foot.
Number.
Inches.
per
Square Foot.
oooo
•4S4
18.5232
17
.058
2.3664
ooo
.425
17-34
18
.049
1.9992
19
.042
1.7136
oo
.380
15.504
2O
.035
1.428
o
.340
13.872
21
.032
1.3056
i
.300
12.24
22
.028
1.1424
2
.284
11.5872
23
.025
i. 02
3
.259
10.5672
24
.022
0.8976
4
".238"
9.7104
25
.020
0.816
26
.018
0.7344
S
.220
8.976
27
.016
0.6528
6
.203
8.2824
28
.014
0.5712
7
.180
7-344
8
.165
6.732
29
.013
0.5304
30
.012
0.4896
9
.148
6.0384
31
.010
0.408
IO
.134
5.4672
32
.009
0.3672
II
.120
4.896
12
.109
4.4472
33
.008
0.3264
34
.007
0.2856
13
.095
3.876
35
.005
0.2040
14
.083
3.3864
36
.004
0.1632
IS
.072
2.9376
16
.065
2.651
248
TAHI.K 130.
CLEARANCE DIMENSIONS AND WHEEL LOADS, ELECTRIC CRANES.
McCLINTIC-MARSHALL CONSTRUCTION Co.
<••
It
-dl
=3
-
Ijn L \
P|
L'~CjyeLff. Cayet
/o
//„__
ll
-A-f^^-^^"|>s<^ ^r\***
3
4..1
i&U-—.! =IH
Elllld 4,'! ii* T" L-''>
l\p, j 1 P, T P I
TvP7^ I Zr
U 1 ^i
-4
m
i
! —
H
\ P &
U-- __ — _»4
LW
J
SAT
This table is for hoist of about 32 ft.
a .
ll
8 £
Higher hoist may increase wheel base.
°"v
r.. ;
2 15 ci
1
Dimensions "R" and "J" can be reduced if necessary.
jji?
S?
*d
°Jf &
2
tf •
^ j"o
u
Dimensions in Feet and Inches.
da
^
|UJ
S H
A
R
J
K
L
M
N
0
P
S
Q
E
G
Tons.
Ft.
In.
Ft.-In.
Ft.-In.
Ft.-In.
Ft.-In.
Ft.-In.
Ft.-In.
Ft.-In.
Lb.
Lb.
In.
Lb.
In.
In.
3
\
to 30
Oi
4-10
3-1 1
1-9
i- 6
5-2
S-9
6- 9
9600
16700
IS
35
9
ii
3
40
9i
4-1 1
3-1 1
1-9
I- 6
5-2
5-9
6-1 1
10400
192
00
IS
3S
9
ii
3
50
10
S- 2
3-1 1
1-8
i- S
S-2
5-9
8- 4
11300
23300
18
35
9
ii
3
00
IO
S- 3
3-1 1
1-8
i- 5
S-2
5-9
10- 0
1 2600
27700
18
40
9
ii
S
to 30
9*
5- 4
4- 6
2-0
2- O
S-2
5-9
8- o
11600
19500
IS
40
5
s
S
40
IO
5- 7
4- 6
2-0
I-II
S-2
S-9
8- 6
12800
22^
LOO
18
40
5
7
S
SO
10
S- 8
4- 6
2-O
I-II
5-2
S-9
8- 8
14100
262OO
18
40
5
7
.5
00
10}
4- 6
2-0
I-II
S-2
S-6
10- 0
iSSoo
31300
21
40
5
8
5
70
I OS
6- o
4- 6
2-0
I-II
5-2
S-6
ii- 8
17100
37300
21
40
5
8
5
80
lot
6- 2
4- 6
2-O
I-II
5-2
S-6
13- 4
18900
43400
21
45
5
8
?f
to 30
10
5-1 1
S- 3
2-4
2- 4
S-2
S-6
8- 6
14900
22300
21
40
7
IO
7'
40
IO
6- o
S- 3
2-4
2- 4
S-2
S-6
8- 8
16200
24000
21
4S
7
IO
7
50
IO
6- I
5- 3
2-4
2- 4
S-2
5-6
8-10
17600
28800
21
45
7
IO
7
00
IO
6- 2
5- 3
2-4
2- 4
5-2
5-6
IO- o
19100
34100
21
45
7
IO
7'
70
II
6- 6
S- 3
2-3
2- 2
S-2
5-3
ii- 8
20800
40700
24
50
7
9
T
So
II
6- 8
5- 3
2-3
2- 2
S-2
5-3
13- 4
22700
47000
24
SO
7
9
10
to 30
IO
6- 2
5- 7
2-7
2- S
6-2
S-9
8- 8
18500
23500
21
45
6
14
1°
40
II
6- 6
5- 7
2-6
2- 4
6-2
5-6
8- 6
19800
28400
24
SO
6
14
10
50
II
6- 7
S- 7
2-6
2- 4
6-2
S-6
8- 8
2 1 2OO
32400
24
50
6
U
10
60
II
6- 8
S- 7
2-6
2- 4
6-2
S-6
IO- O
2270O
37)
oo
24
SO
6
14
10
70
II
6- 9
5- 7
2-6
2- 4
6-2
5-6
ii- 8
24500
43100
24
50
6
14
10
So
II
O-II
S- 7
2-6
2- 4
6-2
S-6
13- 4
26800
52100
24
55
6
14
IS
to 30
II
6- 7
5-1 1
2-9
2- 7
6-2
5-6
9- 6
25700
29600
24
55
4
6
IS
40
II
6- 9
S-i I
2-9
2- 7
6-2
S-6
9- 6
27IOO
339
00
24
SS
4
6
IS
50
II
6-10
2-9
2- 7
6-2
5-6
9- 8
28500
38600
24
00
4
6
IS
60
II
6-1 1
S-il
2-9
2- 7
6-2
S-6
10- C
20000
44000
24
60
4
6
IS
70
12
7- I
s-n
2-8
2- 8
6-2
s-s
II- 8
3I8OO
51200
M
60
4
8
IS
So
12
7- 4
S-i I
2-8
2- 8
6-2
5-S
13- 4
34300
59800
-;
60
4
8
20
to 30
II
7- I
6-10
3-2
3- 5
6-2
5-5
9- 6
32300
34200
24
60
7
16
20
40
12
7- 3
6-io
3-2
3- 5
6-2
s-s
9- 6
34300
38800
24
65
7
16
20
SO
12
7- 5
6-10
3-2
3- 5
6-2
5-5
9- 8
36300
4SOOO
24
65
7
16
JO
00
12
7- 6
6-10
3-2
3- 5
6-2
5-S
IO- 0
38300
507
00
24
65
7
16
20
70
12
7- 8
6-10
3-2
3- 5
6-2
5-5
ii- 8
40300
58200
24
70
7
16
20
So
12
7-10
6-10
3-2
3- S
6-2
5-5
13- 4
42800
70600
24
70
7
16
55
249
TABLE 131.
CLEARANCE DIMENSIONS AND WHEEL LOADS, ELECTRIC CRANES
McCLINTIC-MARSHALL CONSTRUCTION Co.
1
" m ~ "Hi
-
jl
-p4-
i
-iHJ .ui
L''--£aqeL.H. CageB.H.-'
£__1__^' \
jft ri_ H'
£L ^^f==^ j&
*3
P*
—
ife^crr^i #•-$$
;
.1 V — SI 1
0, ^Jl ii * . 4Ji lit ijl i"
'- >m~ ••''(•; i 1 J 'ulrofic
—
L.n.^4 5? .< L^isl •
t p ° i iAJ
[//j
This table is for hoist of about 32 ft.
JB
S
t>
ggfe
K
Higher hoist may increase wheel base.
Dimensions "R" and "J" can be reduced if necessary.
•0-3
Ii
•o .
(2"
&~Jii
o
a
ol
85
•^
&
B£
* 2 «H
iSs-S
Dimensions in Feet and Inches.
U
o3 Q
s §;.*!
A
R
J
K
L
M
N
0
p
Pi
S
£
Q
E
G
i
o
H
Ft.
In.
Ft.-In.
Ft.-In.
Ft.-
In.
Ft.-
In.
Ft.-
In.
Ft.-
In.
Ft.-In.
Ft.-
In.
Lb.
Lb.
In.
Lb.
In.
In.
2S
to 40
12*
7- 7
7- 8
5- o
2- 8
6-2
5-5
0- 0
40200
44500
24
70
ii
18
25
50
12*
7- 9
7- 8
S- o
2- 8
6-2
5-5
9- 2
42700
50700
24
70
ii
18
25
25
60
70
13}
13}
8- o
8- 2
7- 8
7- 8
5- o
5- o
2- 9
2- 9
6-2
6-2
5-3
5-3
10- 0
ii- 8
453oo
47900
59500
69100
27
27
75
7S
ii
ii
19
19
25
So
8- 5
7- 8
5- o
2- 9
6-2
5-3
13- 4
50800
79900
27
75
ii
19
30
to 40
8- o
8- 0
5- 2
2-IO
6-2
5-3
o- 8
46200
51100
27
7S
ii
17
30
00
8- 6
8- o
5- i
2-1 1
6-2
10- 4
52200
68000
80
ii
19
30
So
8-1 1
8- 0
5- i
2-1 1
6-2
5-1
13- 4
58800
90700
30
So
ii
19
40
to 40
IS*
8- 9
9- I
5- 5
3- 2
6-2
4-9
II- 8
61000
69300
36
8S
12
18
40
50
IS*
S-i I
9- I
5- 5
3- 2
6-2
4-9
II-IO
64800
77400
36
8s
12
18
40
60
IS*
9- i
9- I
5- 5
3- 2
6-2
4-9
12- 2
68600
87000
36
90
12
18
40
65
isl
9- 2
9- I
5- S
3- 2
6-2
4-9
12-2
• 70500
92200
36
90
12
18
40
70
IS*
9- 3
9- I
5- 7
3- 6
6-2
5-3
II- 4
4- 2
71000
96800
24
70
12
21
40
So
IS*
9- 6
9- I
5- 7
3-6
6-2
5-3
12- 6
4-10
75600
112900
24
70
12
21
50
to 40
IS*
9- S
9-10
S-i
3- 9
6-2
5r3
II- 2
3- 6
74000
77100
24
70
13
20
SO
50
15*
9- 7
9-10
s-i
3- 9
6-2
5-3
ii- 4
3- 8
77600
86500
24
70
13
2O
SO
00
13*
9- 7
9-10
S-i
3- 9
6-2
5-3
ii- 6
3-10
43000
98500
24
70
13
20
SO
65
13*
9- 2
9-10
5-1
3- 9
6-2
5-3
II- 6
3-io
44000
103400
24
70
13
2O
SO
70
13*
10- o
9-10
5—1
3-1 1
6-2
5-0
II-IO
4- 2
45000
112700
27
75
14
22
50
So
13*
10- 3
9-IO
s-i
3-1 1
6-2
5-0
12- 6
4- 9
47000
131700
27
75
14
22
60
60
16
8-10}
13 2
13- 2
4~
4-
15- 2
15- 2
94000
127000
IOO
I -II
I -II
60
80
16
8-10}
13- 2
4-
15- 4
103000
158000
IOO
I -II
I -II
60
to 40
14*
10- 6}
13- 2
4- o
12- 4
3- 6
44000
I IOOOO
IOO
I -II
I -II
60
60
14*
10- 6}
13- 2
4- 0
12- 4
3- 6
47000
127000
ISO
I -II
I -II
60
80
Hi
10- 6}
13- 2
4- 0
12- 4
3- 6
51500
158000
ISO
I -II
I -II
75
to 40
I4i
ii- 6
is- 2*
4- 6
16- o
S- o
55000
141000
IOO
2-2
2-2
75
60
ii- 6
IS- 2*
4- 6
16- o
5- o
60000
160000
150
2-2
2-2
75
80
ii- 6
IS" 2$
4- 6
16- o
5- o
64000
184000
150
2-2
2-2
IOO
to 40
l8j
13- 5}
is- si
4- I
16- o
5- o
83000
190000
ISO
4- 7
4- 7
IOO
60
i8J
13- 5}
is- s}
4- i
16- o
5- o
86000
217000
ISO
4- 7
4- 7
IOO
80
18}
13- 5}
IS- 5}
4- I
16- o
S- o
89000
243000
ISO
4- 7
4- 7
ISO
to 40
19
IS- 9}
18-11}
6- o
18- o
6- o
130000
310000
ISO
4- 7
4- 7
150
60
19
IS- 9l
18—11}
6- o
18- o
6- o
134000
333000
150
4- 7
4- 7
ISO
So
19
IS- 9}
18-11}
6- o
18- o
6- o
139000
364000
150
4- 7
4- 7
250
TABLE 132.
CRANE GIRDER SPECIFICATIONS.
McCLINTlC-MARSHALL CONSTRUCTION Co.
—1^
j
p v&l ~3
Weight of
Rail per
Yard.
Lb.
Weight of
Rail Splices
per Pair
with Bolts.
Lb.
Weight of
Rail
Clamp.
Lb.
Weight of
Hook
Bolts.
Lb.
Crane Stop.
Plates.
Lb.
Cast
Iron.
Lb.
Area of
Rail.
Sq. In.
Height
and Width
of Base
of Rail.
In.
Web of
Rail.
Width of
Head
of Rail.
In.
In.
16
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
5
5
5
5
5
13
13
IS
IS
«4
H
22
22
22
23
79.2
86.2
92.4
2.7
2.7
2.7
2.7
3-2
•5
•5
•5
•5
•5
•9
•9
•9
•3
•3
•3
•4
•4
•5
•5
•5
•5
•5
56
^
56
57
57
57
74
74
74
74
75
75
75
35
35
35
35
35
35
50
So
50
50
50
5°
50
1.6
. 2.0
2-5
3-4
3-9
4-4
4-9
5-4
I'9
6.4
6.9
7-4
7-8
8-3
8.8
9-3
9.8
3
3'
3H
I
4«
2
2i
2H
II*
Crane Rails: Crane Rails are attached to the girder by means of clips or hook bolts, the latter being used
chiefly for I- Beams, the flange being too narrow for a clip, and has the advantage of saving punching in the top
flange. Clips and hook bolts provide for adjusting slight inaccuracies in the alignment of the rails. Rail Splices
should consist of a flat bar fish plate or a rolled fish plate as angle splices are apt to interfere with the flange of
the crane wheels. Provide our standard crane stop at the end of the rail.
Dimensions: In preparing design indicate clearly distances A, R. J, E, G and distances of floor line to top
of rail. These dimensions should be submitted to owners with design, but before ordering or manufacturing
any material for the work the owner's approval should be obtained for same. .
251
TABLE 133.
TYPICAL HAND CRANES.
McCLINTIC-MARSHALL CONSTRUCTION Co.
n
Wt. of Rails.
.
In
Wt. of Rails. I
1
9
a
m
B
£ &
j
*u 2
1
<u 2
' 1
9
"3
^1
.§§
-*-* t-i
^§
1
sS
rt
09
|
ijiS
•>-S
«
— "S
rt
w
|
*H
u g
1/3 S
S
JS"g
U
S
s
0
u
^3
U
i
^U
u
03
^3
Tons.
Ft.
Ft.
Lb.
Ft.
In.
Lb. per Yd.
Tons.
Ft.
Ft.
Lb.
Ft.
In.
Lb. per Yd.
2
30
4
3100
4
7
30
30
IO
30
7
13000
5
IO
40
40
2
50
5
4000
4,
7
30
30
IO
50
8
14400
5,
10
40
4o
4
30
4
5400
4j
8
30
30
12
30
7
20700
5j
IO
45
45
4
CO
5
6500
8
30
30
12
50
8
22300
10
45
45
6
30
6
8000
5
9
30
35
14
30
7
26000
si
10
50
50
6
7
92OO
5
9
30
35
H
50
8
28000
sl
10
50
50
8
30
6
10500
5
IO
35
40
16
30
7
32300
6
12
50
55
8
50
.7
IlSoo
5
IO
35
40
16
50
8
35000
6
12
50
55
252
TABLE 134.
DIAGRAM FOR STRESS IN EYE-BARS DUE TO WEK.HT.
dye to weight
Indirect fibre stress
fr= depth of bor,inches
/-length of bor inches
= I2
1.5 2 3 456789
I&II. Depth of Bar in Inches
IID/V/2 in Tens of Thousandths
Problem. — Required stress due to weight of a 4 in. x i in. eye-bar, 20 ft. long, which has a
direct tension of 56,000 Ib.
Then, h = 4 in.; L = 20 ft., and /i = 14,000 Ib. per sq. in. The stress due to weight, /i,
is found from the diagram as follows: On the bottom of the diagram, find h = 4 in.; follow up the
vertical line to its intersection with inclined line marked, L = 20 ft., then follow the horizontal
line passing through the point of intersection out to the left margin and find, yt = 3-3 tens of
thousandths; then follow vertical line, h = 4 in., up to its intersection with inclined line marked,
ft = 14,000, and then follow the horizontal line passing through the point of intersection to left
margin and find, y\ = 7.2 tens of thousandths. Now y\ + yt = 7-2 + 3.3 = 10.5. Find y\
+ yt = 10.5 on lower edge of diagram, follow vertical line to its intersection with line marked
"Line of Reciprocals" and find on right margin, /i = 950 Ib. sq. in.
For a bar inclined at an angle 0 with a vertical line multiply the fiber stress calculated for a
horizontal bar as above, of the same length, and multiply the fiber stress thus obtained by sin 9.
For example if the bar above is inclined at an angle of 45 degrees with the vertical; the fiber stress
due to weight is, /i = 950 x sin 8 = 950 x 0.707 = 672 Ib.
Every imeisection of the inclined ft and L lines has for its abscissa a value of h, which will
have a maximum fiber stress, /i, for the given values of ft and L. For example for L = 30 ft.;
ft = 1 2, ooo Ib., we find h = 8.3 in., and fi = ijoolb. A deeper or shallower bar will give a smaller
value of /i.
253
TABLE 135.
DIAGRAM FOR STRESSES IN SQUARE PLATES.
2000
50
2 3 4 56789 10 15
Side of Square in Fee~t,
Safe Loads on Square Plates. — The safe loads on square plates for a fiber stress of 10,000
pounds per square inch may be obtained from the diagram. As an example, required the safe load
for a j-in. plate 3 feet square. Begin at 3 on the bottom of the diagram, follow upward to the
line marked s-in. plate, from the intersection follow to the left edge and find 280 Ib. per sq. ft-
For any other fiber stress multiply the safe load found from the diagram by the ratio of the fiber
stresses. To use the diagram for a rectangular plate take a square plate having the same area.
For formulas for strength of plates, see page 313, Chapter VIII.
254
TABLE 136.
APPROXIMATE RADII OF GYRATION OF famous STRUCTURAL SECTIONS.
.1
\B d-Mean c/iam.
-
\B
H-i
\B
*"
zi iJrs
j t.±
] ""i
•\B
r
\B
\B
\B
Ji__ ..._* rB=0.24b
\B
j L
r
\s
U
ILJ
L J *
- b
\B
B
'B
\5
J
Li
255
TABLE 137.
DETAILS OF A STEEL STAIR.
18 Treads oF 10"= IZ'O'
~r*"
256
TABLE 151
PROPERTIES OF BETHLEHEM I BEAMS
u *-*
||
Jj 1 /I
.0
a
_3
•O
1
1}
H£
Bit!
g
S
|
w
1-9
5
§
"C -
IS
'~~-2
|
1
h
£
•S
I
I I ^
g
1
fl
flfe
Ii
"5
K
H
•
IM
E
O
"
,~ ~~-
ft ***
5
1
•
1
.a
a
i
!i
Moment of Inertia
Radius of Gy-
ration
*
1
ii
£|
•o "
III
H
?
£
>
v o
3
s"
•o
rt «**
r*
Axis
Axis
Axis
Axis
Axis
fl
w **O
S rt
i-i
a-a
i-i
a-a
i-i
9
2
X-*i
11
s
II
I.
It
n
ri
Si
MI
m
In.
Lb.
In,
In.
In.
In.
in.
in.'
In.
In.
In.'
Lb.
Ft.-Lb.
Ft.-
Lb.
In.
30
1 2O
35-30
•540
10.500
.010
5 239-6
165.0
I2.I8
2.16
349-3
103 800
465 740
I 960
23.98
28
105
30.88
•500
10.000
.Oil
4 014.1
I3I-5
11.40
2.06
286.7
89 ooo
382 300
I 830
22-43
26
90
26.49
.460
9.500
.Oil
2 977.2
101.2
10.60
i-95
229.0
75 300
305 350
I 700
20.84
24
84
24.80
.460
9.250
.012
2 381.9
9I.I
9.80
1.92
198.5
75 loo
264 660
I 570
19.22
83
24.59
.520
9.130
.012
2 240.9
78.0
9-55
1.78
186.7
93 100
248 980
I 570
18.76
73
21.47
•390
9.000
.012
2 091.0
74-4
9.87
1.86
174-3
54 ooo
232 340
I 570
19.38
2O
82
24.17
•570
8.890
.015
i 559-8
79-9
8.03
1.82
156.0
i 02 400
207 980
307
15.65
72
21.37
.430
8.750
.015
i 466.5
75-9
8.28
1.88
146.7
64 900
195 540
307
16.13
69
20.26
.520
8.145
.015
i 268.9
51.2
7.91
1.59
126.9
88 200
169 190
307
I5-5I
64
18.86
.450
8.075
.015
I 222.1
49-8
8.05
.62
122.2
69 400
162 950
307
15-77
59
17.36
•375
8.000
.015
I 172.2
48-3
8.22
.66
II7.2
50 ooo
156 290
307
16.09
18
59
17.40
•495
7.675
.Ol6
883.3
39-1
7.12
•50
98.1
78 ooo
130 860
177
13-93
54
I5.87
.410
7.590
.Ol6
842.0
37-7
7.28
•54
93-6
57 500
124 740
177
14.24
52
15.24
•375
7-555
.Ol6
825.0
37-i
7.36
.56
91.7
49 200
122 22O
177
14.38
48.5
14.25
-320
7.500
.Ol6
798-3
36.2
748
•59
88.7
36 700
118 260
177
14.62
IS
7i
20.95
.520
7.500
.O2O
796.2
61.3
6.16
•7i
106.2
77 900
141 540
980
11.85
64
18.81
.605
7-195
.O2O
664.9
41.9
5-95
•49
88.6
93 900
118 200
980
11.51
54
15.88
.410
7.000
.O2O
610.0
38.3
6. 20
•55
81.3
54 800
108 450
980
I2.OO
46
13-52
.440
6.810
.020
484.8
25.2
5-99
-36
64.6
60 ooo
86 180
980
u.66
12.02
•340
6.710
.O2O
456.7
24.0
6.16
.41
60.9
39 900
81 180
980
I2.OO
38
11.27
.290
6.660
.O2O
442.6
23-4
6.27
•44
59-o
30 100
78 680
980
12.20
12
36
10.61
.310
6.300
.025
269.2
21.3
5.04
.42
44.9
32 200
59 830
785
9.67
32
9-44
•335
6.205
.025
228.5
1 6.0
4.92
.30
38.1
35 800
50 770
785
9-49
28.5
8.42
.250
6. 1 20
.025
216.2
15-3
5.07
•35
36.0
22 2OO
48 050
785
9-77
10
28.5
8.34
•390
5-990
.029
134.6
12. 1
4.02
.21
26.9
39 800
35 880
654
7.67
23-5
6.94
.250
5.850
.029
122.9
' II. 2
4.21
.27
24.6
21 OOO
32 770
654
8.03
9
24
7.04
•365
5-555
•033
92.1
8.8
3.62
.12
20.5
33 900
27 290
590
688
20
6.01
•250
5-440
•033
85.1
8.2
3-76
•17
18.9
2O IOO
25- 220
590
716
8
19-5
5-78
•325
5-325
•037
60.6
6-7
3-24
1. 08
15.1
26 900
20 200
522
6.ii
17-5
5.18
.250
5-250
•037
574
6.4
3-33
I. II
14-3
18 900
19 130
522
6.28
257
TABLE 152
PROPERTIES OF BETHLEHEM GIRDER BEAMS
S'Jf
JS ' 4
- 2
S
"3
1
&
ll
g|cm
§
I
|
'I
%a
fa-S
t , J
I
0
i
l|d
O --H
*"* o3
i- <U *-< —
M
i
_,
"8
E
B rt
a v
§
J3
E'S"'^,
rt B
W
u 8*0
a
V
•3
J
I
|
c
^ o
Moment of Inertia
Radius of Gy-
ration
i
i
|f
•2 S
T3 U
•n B
fpl
Q
*
H
1
o|
Axis i-i
Axis 2-2
Axis i- 1
Axis
Axis
B
I
o
w .*-*
<!
^j m
gjH
2-2
i- 1
|
S
IT
O u
Ii
II
ri
T2
Si
Mi
m
I
In.
Lb.
In.*
In.
In.
In.
In,
In,
In.
In.
ln.»
Lb.
Ft.-Lb.
Ft.-
Lb.
In.
30
200
58.71
•750
15.00
.OIO
9 150.6
630.2
12.48
3.28
610.0
189 300
813 390
I 960
24.09
1 80
53.00
.690
13.00
.OIO
8 194.5
433-3
12.43
2.86
546.3
165 200
728 400
I 960
24.20
28
1 80
52.86
.690
14-35
iOII
7 264.7
533-3
11.72
3.18
518.9
161 500
691 880
I 830
22.57
165
48.47
.660
12.50
.on
6 562.7
371-9
11.64
2.77
468.8
150 300
625 O2O
I 830
22.6o
26
160
46.91
•630
13.60
.on
5 620.8
435-7
10-95
3-05
4324
135 900
576 490
I 7OO
21.03
ISO
43-94
•630
I2.OO
.on
5 153-9
314.6
10.83
2.68
396.5
135 900
528 6OO
I 700
20.99
24
140
41.16
.600
I3.OO
.012
4 201.4
346.9
IO.IO
2.90
350.1
121 7OO
466 820
I 570
19-35
1 20
35-38
•530
I2.OO
.012
3 607.3
249.4
10. IO
2.66
300.6
98 5OO
40O 820
I 570
19.48
2O
140
41.19
.640
I2.5O
.015
2 934-7
348.9
8.44
2.91
293-5
124 2OO
391 28O
I 307
I5-85
112
32.81
•550
I2.OO
•015
2 342.1
239-3
8.45
2.70
234.2
98 500
312 290
I 307
16.01
18
92
27.12
.480
II.5O
.016
i 591-4
182.6
7.66
2.59
176.8
76 100
235 760
I 177
14.41
IS
I4O
41.27
.800
n-75
.020
i 592-7
331-0
6.21
2.83
212.4
134 2OO
283 ISO
980
*n.o6
IO4
30.50
.600
11.25
.020
I 220.1
213.0
6.32
2.64
162.7
94 300
216 910
980
11.49
73
21.49
•430
10.50
.020
883.4
-123.2
6.41
2-39
117.8
59 200
157 080
980
11.89
12
70
20.58
.460
10.00
.025
538.8
114.7
5.12
2.36
89.8
57 200
119 730
785
* 9.08
55
16.18
•370
9-75
.025
432.0
81.1
5-17
2.24
72.0
42 300
96 ooo
785
* 9-3i
IO
44
12-95
•310
9.00
.030
244.2
57-3
4-34
2.IO
48.8
29 800
65 130
654
* 7.60
9
38
11.22
.300
8.50
•033
170.9
44.1
3-90
1.98
38.0
26 700
50 630
590
* 672
8
32-5
9-54
.290
8.00
•037
1144
32.9
3-46
1.86
28.6
23 600
38 140
522
* 5-85
* Denotes that the distance given is less than the distance center to center of beams placed
close together with flanges in contact.
258
TABLE 153
PROPERTIES OF BETHLEHEM H COLUMNS
•
1
s
i
•=f=
|
|
i
/^
y |i
§
m
•o
"3
1
,x
i p
— -*- i
1
r— ?— .
M
1
1
jj
w3
Are.i of
1
Moment of
Inertia
Radius of
Gyration
Section
Modulus
Axis
Axis
Axis
Axis
Axis
Axis
i-i
2-3
i-i
2-2
i-i
2-2
D
T
B
W
M
N
G
L
Ii
II
n
rs
Si
Si
In.
Lb.
In. In.
In.
In.
In.
In.
In.
In.'
In.«
In.«
In.
In.
In.»
In.»
14" H COLUMNS
13
j
83-5
i
i
13.92
•43
.620
•755
19 '•
24.46
884.9
294.5
6.01
3-47
128.7
42-3
13
!
91.0
13.96
•47
•683
.817
I9l
26.76
976.8
6.04
3-49
140.8
46.6
14
99-o
.
I
14.00
•Si
•745
.880
I9tt
29.06
070.6
356.9
6.07
3-50
153-0
51.0
H
106.5
•
14.04
•55
.808
.942
I9H
3L38
166.6
387.8
6.10
3-52
165.2
55-2
H
II4-5
•
1
14.08
•59
.870
1.005
20^
33-70
264.5
420.3
6.13
3-53
177-5
59-7
14
122.5
I
14.12
•63
•933
1.067
20fV
36.04
364.6
453-4
6.16
3-55
189.9
64.2
14
130.5
I
V
14.16
.67
•995
1.130
20j
38.38
466.7
486.9
6.18
3.56
202.3
68.8
14
138.0
I
;
14.19
.70
1.058
1.192
20|
40.59
568.4
5197
6.21
3-58
214.5
73-3
H1
146.0
I
\
I4.23
•74
I.I2O
1-255
2Oj
42.95
674-7
554-4
6.24
3-59
227.1
77-9
14*
154.0
I;
14.27
•78
1.183
1.317
20|
1?
45-33
783.3
6.27
3.61
239-8
82.6
IS
162.0
IT
"6
I4.3I
.82
1.245
1.380
20j
M
47-71
r 894.0
626!?
6.30
3.62
252.5
87.5
15
170-5
ii
I
14-35
.86
1.308
1.442
20j
g
50.11
2 007.0
662.3
6-33
3.64
265.4
92-3
15
178.5
I
k
14-39
.90
1-370
i-SOS
21
S*"
52.51
2 122.3
699.0
6.36
3-65
278.3
97-2
IS
186.5
I,
14.43
•94
1-433
1.567
21*
V
54.92
2 239.8
736.3
6-39
3.66
291.4
IO2.I
15
195-0
I
"6
14.47
.98
1.495
1.630
2ii
1
57-35
2 359-7
774.2
6.41
3-67
304-5
IO7.O
15
203.5
If
1.02
1.558
1.692
2l|
G
.2
59-78
2 481.9
8126
6-44
3-69
3177
1 1 2.0
15)
2II.O
I
i
H-54
1.05
1.620
1-755
2Il^
62.07
2 603.3
849.8
6.48
3-70
330.6
Il6.9
15
219.5
\t
14.58
.09
1.683
1.817
2I&
64.52
2 73O.2
889.3
6.51
344-0
I22.O
16
227.5
I
1
14.62
•13
1-745
1.880
2lft
66.98
2 859.6
9294
6-53
3-73
357-5
I27.I
16*
236.0
I]
14.66
•17
i. 808
1.942
2lT$
69.45
2 991.5
970.0
6.56
374
371.0
132.3
i6J
244-5
I
1
14.70
.21
1.870
2.005
2lH
71.94
3 125-8
i 011.3
6-59
3-75
384-7
137.6
161
253.0
2
14-74
•25
1-933
2.067
22^
74-43
3 262.7
i 053.2
6.62
3-76
398.5
142.9
i6J
261.5
2
V
14.78
.29
1-995
2.130
22&
76.93
3 402.1
i 095.6
6.65
3-77
412.4
148.3
i6f
27O.O
2>
14.82
•33
2.058
2.192
22]^r
79-44
3 544-1
i 138.7
6.68
3-79
426.4
153-7
16;
278.5
2
V
14.86
•37
2. 1 2O
2-255
22lV
81.97
3 688.8
i 182.4
6.71
3-80
440-5
I59.I
i6J
287.5
,
I4-90
•41
2.183
2.317
22&
8.4-50
3 836.1
i 226.7
6-74
3-81
454-7
164.7
12-' H COLUMNS
"I
64.5
j
11.92
•39
.567
683
I6J
19.00
499-0
168.6
5-13
2.98
84-9
28.3
II*
71-5
i
11.96
•43
.630
-745
v
20.96
556.6
188.2
5-15
3.00
93-7
31-5
12
78.0
12.00
•47
.692
.808
17
j?
22.94
615.6
208.1
5.18
3.01
1 02. 6
34-7
12
84.5
1
I2.O4
•Si
•755
.870
1
24.92
676.1
228.5
5-21
3-03
111.5
37-9
12;
91.5
12.08
•55
.817
•933
17!
jj
26.92
738.1
249-2
5.24
3-04
120.5
12-
98:5
1
12.12
•59
.880
•995
I7s
B
28.92
801.7
270.1
5-27
3-o6
129.6
44^6
12
105.0
I
12.l6
•63
•942
1.058
*7iV
3
°
30.94
866.8
291-7
5-30
3.07
138.6
48.0
12
1 1 2.0
I]
h
12.2O
•67
1.005
1. 120
17^
3296
933-4
3I3.6
5-33
3.08
147.9
51.4
12
II8.5
I
t
12.23
.70
1.067
1.183
I7ii
.3
34.87
I OOO.O
335-0
536
3-io
156-9
54-8
12,
;
125-5
I
V
12.27
•74
1.130
1.245
i?H
36.91
I 069.8
357-7
5-38
3-H
166.2
58.3
13
132.5
1
12.31
.78
1.192
1.308
JTtt
38.97
I 141-3
380.7
5.41
3-13
175-6
61.9
259
TABLE 153.— Continued
PROPERTIES OF BETHLEHEM H COLUMNS
i
z
=j
=>
i
o
8
B
1
1
/^.
1
W I I
SQ
— l
•3
£
fe
"8
O
IT
_JL
&
is
a
*o
»>
fe*^4*S_.
. «_-t 1
1
» i »
Q
a
S
g""
*
1
1
•S- - -c -f-^ 71 •
& | V f j
^
'—&
Moment of
Radius of
Section
i
E"
H
1 - r»
1 * O >(
Inertia
Gyration
Modulus
o
Axis
Axis
Axis
Axis
Axis
Axis
i-i
2-2
i-i
2-2
i-i
2-2
D
T
B
W
M
N
G
L
Ii
12
n
n
Si
s,
In.
Lb.
In.
In.
In.
In.
In.
In.
In.
In.2
In.«
In.«
In.
In.
In.«
In.'
12" H COLUMNS
135
139-5
lA
12-35
.82
I-25S
1.370
18
« 5M
41.03
I 214.5
404.1
5-44
3-H
185.0
654
I3l
146.5
If
12.39
.86
I-3I7
1-433
181
1*
43-io
I 289.4
428.0
5-47
3-15
194.6
69.1
13!
153-5
iA
12.43
.90
1.380
1-495
is!
2 i
45-19
I 366.0
452-2
5-50
3-16
204.3
72.8
!3z
161.0
15
12.47
•94
1.442
1-558
i8f
47.28
I 444-3
477-0
5-53
3-18
214.0
76.5
10" H COLUMNS
9l
49-o
A
9-97
•36
•5H
.611
HA
14-37
263.5
89.1
4.28
2-49
53-4
17.9
10
54-o
5
8
IO.OO
•39
-577
•673
HA
15-91
296.8
1004
4-32
2.51
59-4
20. i
io|
59-5
H
10.04
•43
•639
•736
14 A
i
17-57
331-9
112. 2
4-35
2-53
65.6
22.3
10!
65-5
1
10.08
•47
.702
.798
I4f
t»
19-23
368.0
124.2
4-37
254
71.8
24.6
iof
71.0
fi
10.12
•Si
•764
.861
14}
*•
20.91
405.2
136.5
4.40
2.56
78.1
27.0
i of
77-o
|
10.16
•55
.827
•923
Hi
jj,
22.59
443-6
I49.I
4-43
2-57
84-5
29-4
iof
82.5
if
IO.2O
•59
.889
.986
14!
9
24.29
483.0
162.0
4-46
2.58
90.9
31-8
iof
88.5
i
10.24
•63
•952
.048
14!
g
25-99
523-S
I75-I
4-49
2.60
97-4
34-2
io|
94-o
iA
10.28
.67
.014
.in
15
8
27.71
565-2
188.6
4.52
2.61
103.9
36.7
II
99-5
is
10.31
.70
•077
•173
iSl
j
29.32
607.0
2OI.7
4-55
2.62
110.4
39-i
III
I05-S
iA
10.35
•74
•139
-236
ISA
31.06
651.0
215.6
4-58
2.64
117.0
41.7
III
111.5
IT
10.39
•78
.202
.298
32.80
696.2
229.9
4.61
2.65
123.8
44-3
Ilf
117.5
iA
10.43
.82
.264
-361
isA
34-55
742.7
244.4
4-64
2.66
130.6
46-9
III
123-5
if
10.47
.86
•327
1.423
isA
36.32
790.4
259-3
4.67
2.67
137-5
49-5
8" H COLUMNS
71
32.0
A
8.00
•31
•399
•476
III
9-17
105-7
35-8
3-40
1.98
26.9
8.9
8
34-5
i
8.00
•3i
.462
•538
III
10.17
121.5
41.1
346
2.OI
30-4
10.3
8|
39-o
A
8.04
•35
•524
.601
nA
11.50
139-5
472
3-48
2.O3
34-3
11.7
81
43-5
I
8.08
•39
.587
.663
iiA
12.83
158-3
53-4
3-Si
2.04
38.4
13.2
81
48.0
H
8.12
•43
•649
.726
V
14.18
177-7
59-8
3-54
2.O5
42.4
14.7
85
53-o
f
8.16
•47
.712
.788
"H
5
15-53
197.8
66.3
3-57
2.O7
46.5
16.3
8|
57-5
rl
8.20
•Si
•774
•851
12
ii
16.90
218.6
73-i
3.60
2.08
50.7
17.8
81
62.0
1
8.24
•55
•837
•913
I2A
1
18.27
240.2
80.0
3-63
2.O9
54-9
19-4
8|
67.0
if
8.28
•59
.899
.976
I2|
1
19.66
262.5
87.1
3.65
2. 1 1
59-2
21.0
9
7i-S
i
8.32
•63
.962
1.038
Ml
1
21.05
285.6
94-4
3-68
2.12
63-5
22.7
9}
76-5
iA
8.36
.67
1.024
I.IOI
I2f
.2
22.46
309-5
101.9
3-7i
2.13
67.8
24.4
%
81.0
i|
8.39
.70
1.087
1.163
23-78
333-5
109.2
375
2.14
72.1
26.O
9l
8S-S
XA
8.43
•74
1.149
1.226
IS
25.20
359-o
117.2
3-77
2.l6
76.6
27-8
9l
90-5
i|
8.47
.78
1. 212
1.288
I2f
26.64
38S-3
125.1
3.80
2.17
81.1
29.6
260
TABLE 154.
PROPERTIES OF BETHLEHEM COMPOUND COLUMNS.
U- -c-— ! 4 IB
1<1 * 1 b 1
i
r-T-r1 t <
• | '
14" x 148 1.1..
Special H H >.;?
^ 0 _A.._
; A Reenforced
with
Section.
UM_^
k...i j
Cover Plate*
I'
1* * \
T.
1
•|! S 'I
1
|
|4 g .---Vj
B
Total Section.
Dimensions.
Moment of Inertia.
Radius of Gyra-
Section Modu-
tion.
lus.
Depth.
Cover Plates.
Axis
AvU
Weight.
Area.
H
Section.
Width.
Thick-
ness.
G
A-A
B-B.
A-A.
B-B.
A-A.
Al*
B-B.
H
C
P
IA
IB
rA
rn
SA
SB
In.
Lb.
In.*
In.
In.
In.
In
IB.*
In.<
In.
In.
In.»
In.*
i6|
284.0
83.52
16
It
23lV
3737-7
I32I.9
6.69
3-98
449-6
165.2
I6|
290.8
85.52
D
16
1^
23w
3876-9
1364.6
6-73
3-99
462.9
170.6
l6}
297.6
87.52
Mi
16
if
23!
4018.2
1407.3
6.78
4.01
476.2
175-9
17
304-4
89.52
16
rT^
23!
4161.7
1449.9
6.82
4.02
489.6
181.2
17
3II.2
91.52
16
rf
23 !7f
4307.2
1492.6
6.86
4.04
503-0
186.6
17
318.0
93-52
16
*T8
23 J
4454-9
1535-3
6.90
4-05
516.5
191.9
17
324.8
95-52
T
16
4
23l
4604.8
1577-9
6-94
4.06
530.0
197.2
17
331.6
97-52
i
16
Jffc
23 T>
4756.8
1620.6
6.98
4.08
543-6
202.6
17
338.4
99.52
16
if
23 H
4911.0
1663.3
7.02
4.09
557-3
207.9
173
345-2
IOI.52
16
ill
234
5067.5
1705.9
7.07
4.10
571-0
213.2
I7I
350.3
IO3.O2
B
17
if
24*
5132.5
1901.6
7.06
4-30
582.4
223.7
17?
357-5
105.15
14.90
17
itt
24ir
5298.7
1952.8
7.10
4-31
597-0
229.7
17}
364.7
107.27
17
1}
24U
5467.2
2003.9
7.14
4-32
611.7
235-8
Fi8
372.0
109.40
17
i|£
24?
5638.1
2055.1
7.18
4-33
626.5
241.8
18!
379-2
111.52
W
17
2
5811-5
2106.3
7.22
4-35
641.3
247.8
18;
386.4
113.65
1.41
17
2-fa
24 f£
5987.2
2157-5
7.26
4-36
656.1
253.8
i8i
393-6
"5-77
17
2$
251^
6165.4
2208.7
7-30
4-37
671.1
259.8
18;
400.9
117.90
M
17
2^f
25*
6345-9
2259.8
7-34
4-38
686.0
265.9
is;
408.1
1 20.02
0.808
17
2J
25A
6529.0
2311.0
7.38
4-39
701.1
271.9
isi
4I5-3
122.15
17
2ft
2sA
67I4-S
2362.2
7.41
4.40
716.2
277.9
l8f
423.4
124.52
18
2}
25!
6832.6
2655.6
7.41
4.62
733-7
295.1
18
431.0
126.77
18
2ft
26
7029.0
2716.4
7-45
4-63
749-8
301.8
18}
438.7
129.02
N
18
2f
26^
7228.1
2777.1
7.48
4.64
765.9
308.6
19
446.3
131.27
0.942
18
2TT
26^
7429.8
2837.9
7.52
4-65
782.1
3I5-3
I9i
•
454.0
I33.52
18
26J
7634.2
2898.6
7-56
4.66
798.3
322.1
19
461.6
135-77
18
aA
26|
7841-3
2959-4
7.60
4.67
814-7
328.8
19
469-3
138.02
L
18
af
8051.1
3O2O.I
7-64
4.68
831.1
335-6
19
.
476.9
484.6
140.27
142.52
11.06
18
18
*
rfS
8263.6
8478.9
3080.9
3141.6
7.68
7-71
4-69
4.70
847.6
864.1
342-3
349-1
Columns composed of a 14" X 148 Ib. Special Column Section, reenforced with cover plates
of width and thickness given in table. The total thickness, P, may be made of two or more plates,
each of punchable thickness.
261
TABLE 155.
ELEMENTS OF BETHLEHEM I-BEAMS AND GIRDER BEAMS.
ELEMENTS OF BETHLEHEM I BEAMS.
-JP1^. Pi .
CK?
T
R- 1
" vn 7
-*-
-*--
--*-
l O O
j-
f~ ~^
I
+-
i
1 0 O
_t.
Ui jl
L_.B.^J -*ii«-Q^Wtl/s'
' ' '1
ig
Dimensions, in Inches.
QJ flj
> hf
JD
Dimensions, in Inches.
> So
•six
5 §
•3 |^
ra
0.5 o
t> u1-'
• fn
g- " C
SP«
,rfa
Q
s.
F
W
L
K
G
A
B
C
rt C
O ^
a
r \y
L :
C G
A
B
r.
rt o
s
>
S""
3°
I2O.O
io|
H
26A
Iff
If
6i
sA
A
I
IS
71
.0 7
\ ||
iif i
1 tt
4i
Si
A
1
28
105.0
10
i
24H
ifi
li
6
si
A
I
IS
IS
64.0 7
54-o 7
re <n
»
"A i
H f
.1 23
32 32
4
4
sA
t f
4
1
1
IS
46.0 6
rl A
I2| I"
A. 17
•31
J4
STTT
A
i
26
90.0
95
tt
23
it
ft
Si
sA
A
I
IS
41.0 6
23. 11
J2 32
I2| I
1 17
L6 32
3|
sA
4
i
is
38.0 6
20. i9
32 64
i^ii
3^
sA
A
1
24
84.0
9i
if
21
il
1
Si
sA
A
i
12
36.0 6
19 5
64 T6
9i i-
A A
3i
sA
A
f
24
83.0
9t
64
2lA
ill
H
si
Si
A
i
12
32.0 6
-3_ 21
16 64
i°A •
ff A
3i
sA
i
3
24
73 -°
9
6^
2lA
iM
fe
si
si
I
12
28.5 6
t i
i°A •
If A
3i
si
A
1
2O
82.0
8f|
tt
I7t
iA
f
s
"iA
f
1
IO
28.5 s
** If
8| f
I t
3i
qf
i
f
2O
72.0
8|
A
iA
1
s
sA
i 1
IO
23
•S 5
Bi
81 -
tt f
3i
si
A
f
2O
2O
2O
69.0
64.0
S9-o
8A
8
tt
29
*i
i7i
175
ij
ii
ii
I4
f *
4f
4i
4i
sA
sf
A
>
9
9
24.0 5
20.0 5
A H
Si
71 *
f
! 1
3
3
II
A'
f
f
18
59.0
7*-|
5
15!
is
A
4i
si
A
i
18
18
S4-o
52.0
7A
ill
-9
4i
4i
sA
i i
1
8
8
19-5 s-
17-5 s-
f."
6f «
6f -
- A
i A
2|
sA
si
A4
I*
18
48.5 7i
li
15!
ii
A
4l
sA
i
^
ELEMENTS OF BETHLEHEM GIRDER
BEAMS.
S , fi
&tf ,
r
i- -t
v wl r
I
—
n
t!
I*
Jj * ^
K
J i
•*{**
K
l^._ D _-! .! *. Q 1X\»/ JftyiiP
1
o * «5
J8«"
Dimensions, in Inches
> &
*S ..!
a S
Dimensions, in Inches
V «i
> b*
til
•£?[2j3
^H a
•3 rtJ
a^^"
^ §
O03"
H"
F
W
L
K
G
A
B
G
|5
1""
^^ i
' W
L I
: G
A
B
c
|.S
3°
3°
2OO.O
iSO.O
15
13
3.
It*
2S4
25 A
2it
It
II
9
Si
stt
A
A
i
i
18
92.0 ii
i fi
Hf H
35.
3 2
7i
si
A
i
28
iSO.O
Hii
tt
23!
2A
1^
ioi
-11
A
i
IS
140.0 1 1
[3 51
4 '64
10* 2j
~G ^-^2
7l
qlf
A
i
28
165.0
125
fi
23!
2TK
iA
^H
3
i
15
104.0 1 1
j; fl
7i
Ss
1
i
15
73.0 ic
4 A
12^6 Ti
i ri
61
sA
4
i
26
160.0
i^if
f
2lf
ZTS
iA
Qi
18
f
i
12
70.0 ic
> M
9 15
f
6
Sir
5
i
26
150.0
12
1
2l|
2T6
ii
8
.1
)8
1
i
12
55-° S
II
if
6
Ss
i
i
24
24
140.0
I2O.O
13
12
if
u
20
2Oj
2
If
li
If
9
8
58
)5
<L°
i
i
IO
44.0 9
A
7f ii
ii
si
sA
A
7
8
20
20
140.0
II2.O
12
41
35.
64
IS 16
i6|
23~2"
it
1
81
8
.5
>89
)T6^
!
A
i
i
9
38.0 8
iif
6| it
^t*
si
sA
A
1
L,
8
32.5 8
tt
6 i
A
s
sA
A_
LJ
262
TABLE 156.
STANDARD CONNECTION ANGLES FOR BETHLEHEM I-BEAMS.
1
30'I _
Weigh
K! 4
Vj- A **
g
&
, ' Weigh
*\/f'f $"<£
BEAM CoNtfecTioxs
'r_?,' tt'^ri* t*"1
g22 » vftr** . r^?i'
:
\
1%
141
S4/%4
' Weigh
Ih
a !
j
WeifhtSZIb-
*>46/b-
?" 2
\ '
*4/&
ti~ f5'^
f37!i>-
Weight rg Ik- ' Wtighttf lb- ^ Might ?41b> ' ^Weight 18 lb- , Weyhttf/b-
Spacing same in both Itgs of angles un/ess otherwise shown- AH holes JJ- Didm- for 4. Dfam- Rivets or Bolts-
Minimum Spans on which the Above Connection Angles may be Used for Greatest Safe Uniformly Distributed Loads.
Depth of
Beam, Inches.
Weight per
Foot, Lbs.
Least Span, in Feet, for Various Conditions.
Rivets : Shearing 10,000 Lbs., Bearing 20,000 Lbs. per Square In.
Field Connection.
Rivet Shear,
8,000 Lbs. per
Square Inch.
Con-
nection
to Web
of
Beam.
Field
Con-
nection.
When Two Beams Frame Opposite Each Other to a
Beam or Girder with a Web Thickness as Follows :
ft"
i"
ft"
1"
A"
J"
30
I2O.O
23.0
21. 1
22.1
24.8
28.4
33-1
39-7
49-7
26.3
28
105.0
22.7
19.2
20.1
22.7
25-9
30.2
36.2
45-3
24.0
26
9O.O
22.1
17-3
I8.I
20.4
23-3
27.1
32.6
40.7
21.6
24
84.0
21-9
I7.I
17.9
20. 2
23.1
26.9
32.2
40.3
21.4
IM
73-0
22.7
15.0
15-7
17.7
20.2
23.6
28.3
35-4
iS.8
20
72.0
2O.2
14.7
IS-4
17-4
19.9
23.2
27.8
34-8
18.4
20
59-0
I8.S
II.8
12-3
13-9
IS-9
18.5
22.2
27.8
14.7
,8
48.5
16.4
10.7
II. 2
12.6
14.4
16.8
20. 2
25.2
13-4
•5
71.0
12. 1
1 6.0
16.8
18.9
21.6
25-1
30.2
37-7
20.0
15
S4-o
II. 8
12.3
12.8
14.5
16.5
19-3
23.1
•28.9
15-3
IS
38.0
12. 1
8.9
9-3
10.5
12.0
14.0
16.8
21.0
II. I
12
36.0
IO-3
9.0
9-S
10.6
12.2
14.2
17.0
21-3
ii-3
12
28.5
10.3
7-2
7-6
8-S
.9-8
11.4
13-7
I7.I
9.1
10
23-S
8-7
7.4
7-8
8.7
10.0
u.6
14.0
I7-S
9-3
9
20.0
6-7
5-7
6.0
6-7
7-7
9.0
10.8
I3-S
7-1
8
17-5
S-i
4-3
4-5
S-i
5.8
6.8
8.2
IO.2
5-4
The greatest value given of the least span for any of the governing conditions is the minimum
span for which the connection may be used.
263
TABLE 157.
STANDARD CONNECTION ANGLES FOR BETHLEHEM GIRDER BEAMS.
i
i
z
'WelghfL
, „. $EAM CONNECTIONS
$ ?6"&?8"(7 %2£ t« &
'/*. ' Might 67 »j ' Migfn
'&*'
' Weight 48 lb'
I !
Xjg X/'-p '
>57/t>
18
I
17 t
^iH. "*
$
IL
Weight 3?ft>- Weigh/ft It> -n Weight 17 1 b*
• ofengles unless otherwise shown. All holes JG Dam-for'^.Diam-Rfv&fs orBoJfs-
I
Weight41Ib-
Spacing same in bofh legi
Minimum Spans on which the Above Connection Angles May be Used for Greatest Safe Uniformly Distributed Loads.
Depth of Beam,
Inches.
Weight per
Foot, Lbs.
Least Span, in Feet, for Various Conditions.
Rivet : Shearing 10,000 Lbs., Bearing 20,000 Lbs. per Sq. In.
Field Connection.
Rivet Shear,
8,000 Lbs. per
Square Inch.
Con-
nection
to Web
of
Beam.
Field
Con-
nection.
When Two Beams Frame Opposite Each Other to a
Beam or Girder with a Web Thickness as Follows :
A"
i"
A
\"
rV
1"
30
30
200.O
180.0
24-S
22.O
24-5
22.O
25.7
23.0
28.9
25-9
33-i
29.6
38.6
34-S
46.3
41.4
57-8
Si.8
3°-7
27-5
28
28
180.0
165.0
24.I
21.8
24.1
21.8
25.2
22.8
28.4
25.6
324
29-3
37-8
34-2
45 -4
41.0
56.8
Si-3
3O.I
27.2
26
26
160.0
150.0
2O. I
18.4
2O. I
18.4
21.0
19-3
23-7
21.7
27.0
24.8
3I-S
28.9
37-8
34-7
47-3
43-4
25.1
23.0
24
24
140.0
I2O.O
19.2
18-3
19.2
I6.S
20.1
17-3
22.6
194
25-9
22.2
30.2
25-9
36.2
45-3
38.9
24.0
20.6
2O
2O
140.0
II2.O
197
16.8
197
15-7
2O.6
16.4
23.2
•I8.S
26.5
21. 1
30.9
24.7
37-i
29.6
46.4
24.6
19.6
18
92.0
14.6
II.9
12.4
I4.O
16.0
18.6
22.3
27.9
14.8
IS
IS
IS
140.0
104.0
73-o
18.3
14.0
13-9
I8.3
I4.O
10.2
19.2
14.7
10.6
21.6
16.5
I2.O
24.7
18.9
13-7
28.8
22.O
16.0
34-5
26.4
19.1
43-i
33-i
23-9
22.9
17-5
12.7
12
12
70.0
SS-o
11.6
ii-S
10.8
8.7
11.4
9.1
12.8
10.2
14.6
II.7
17.0
13-7
20.4
16.4
25-5
20.5
13-5
10.9
10
44.0
9-3
5-9
6.2
6.9
7-9
9-3
n. i
13-9
7-4
9
38.0
"•3
7.6
8.0
9.0
10.3
I2.O
14.4
18.0
9-5
8
32.5
8.8
S-8
6.0
6.8
7-7
9-0
10.8
13.6
7-2
The greatest value given of the least span for any of the governing conditions is the minimum
span for which the connection may be used.
264
TABLE 158.
CAST IRON SEPARATORS FOR BETHLEHEM GIRDER BEAMS AND I-BEAMS.
BKTHLKIIKM GIKOKK
BEAM
bf
c
°>*
s.
o)
Bn
lll.l 1
2>*
c
n
c
5)i
II! M 1 IlKAMS.
I
I
|
5
5
H M
I I
I i
2>
°>
o)
I
^
<:
^
2)
\
I
C
*
II
H E
HI
1 1
<AJ U^.J <•£-»
eparahrsferlS*tt>50"tMimare£"n>tti>l.
tparatorsfor 8" hl5" beams are £ metal.
<• ! c c !
W--— *4 K----H K--->J
Separators for 18 "to 50 "beams are -g metal.
Separators for 8* to /5* beams are j"metal.
Beam.
Distances.
Bolts.
Weights.
Beam.
Distances.
Bolts.
Weights.
A
&
&
1
1
!
"o
U
o
0
U
(/5
.£
•3
i
U
g
U
•2
DO
J
Separators.
Bolts.
i
a
1
I
1
•
1
t
'o
<J
o
U
Separators.
Bolts.
;/}
.a
•3
^
S
u.
SM^
J3.2
J3
||
W3
J3
•o
£
i.
O
h
^c/j
11
d|
o S
fijl
en
j=
•3
%
U
o
CJ
.c
H
J
(/I
M
•5
P
1
*ri
-•a
ii
M
in
JO
•6
P
1
iS
3}
ll
In.
Lb.
In.
In.
In.
In.
Lb.
Lb.
Lb.
Lb.
In.
Lb.
In.
In.
In.
In.
Lb.
Lb.
Lb.
Lb.
Separators with Three Bolts.
Separators with Three Bolts.
30
30
28
28
26
26
2OO.O
I8O.O
l80.0
165.0
1 6O.O
150.0
III
Jf»
14
12
IS
13
Hi
I2f
I3f
12*
IO
IO
8
3
17*
isi
i6J
l$
16
I4i
73.0 4.50
64.5 4.50
65.0 4.15
59-1 4-iS
59.0 3.85
53-0,3-85
7-7
7.0
7-4
6.8
7-1
6.6
•375
•375
•375
•375
•375
•375
30
28
26
120.0
IO5.O
9O.O
Hi
iof
10*
10!
10*
9l
IO
?!
I2f
12
nj
50.1
43-9
39-3
4.50
4.15
3-8S
6.0
5-7
5-5
•375
•375
•375
Separators with Two Bolts.
Separators with Two Bolts.
24
24
20
20
18
IS
IS
IS
12
12
I4O.O
I2O.O
I4O.O
II2.O
92.O
I40.O
104.0
73-o
70.0
55.0
lil
&
12
I2i
U?
II
ioi
io|
I3i
12}
I2f
12
IlJ
III
II*
IOJ
IO
10
12*
12*
IO
IO
IO
7*
5!
5
5
I5i
Hi
H*
\i,
i
12*
12
III
50.0
47-0
39-o
38.0
34-0
22.O
22.0
21.0
I7-S
I7-S
3-50
3.50
2.80
2.80
2.60
I-SO
1 .60
1 .60
1.30
1.30
4.6
4-3
4-5
4-3
4-2
4-3
4.2
4.0
3-8
3-8
•25
•25
•25
•25
•25
•25
•25
•25
•25
•25
24
24
20
20
18
IS
IS
IS
12
12
84.0
73-o
72.0
S9-o
48-5
71.0
54-o
38.0
36.0
28.5
9V
9i
9i
S5
8
8
7j-
6\
6j-
9i
9i
9
8J
7l
7i
7
If
6J
12*
12*
10
IO
10
7*
?!
5
5
nl
ii
10}
10
9l
9i
li
8
7i
35-
35-
28.
26.
22.
13-
12-3
13-3
9.1
9.0
3.65
3-65
3.00
3.00
2.70
I.6S
I.6S
1. 80
1.30
1.30
3i
3-6
3-5
3-4
3-2
3-2
3-1
3.0
2.8
2.8
•25
•25
•25
•25
•25
•25
•25
•25
•25
•25
Separators with One Bolt.
Separators with One Bolt.
10
9
8
44.0
38.0
32-5
9*
9
Si
91
8}
8i
—
10}
ioi
')J
I 1.0
IO.O
8.0
1. 10
1 .00
.85
1.8
i-7
i-7
•125
•125
•i-5
10
9
8
23-5
2O.O
I7-S
6J
si
si
6
?!
7l
b
£i
5-5
1. 10
I .OO
.85
M
1-3
1-3
.125
• 125
.125
Separators for 18 to 30' inch beams are f inch metal.
Separators for 8 to 15 inch beams are * inch metal.
All bolts } inch diameter.
56
265
TABLE 159.
SAFE LOADS, IN TONS, AND DEFLECTIONS, IN INCHES, BETHLEHEM I-BEAMS.
Depth.
Weight.
Length of Span in Feet.
In.
Lb.
8
IO
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
3°
1 2O
*
103
•44
93
•39
85
•36
78
•33
72
•30
67
.28
62
.26
58
•25
55
•23
52
.22
49
.21
47
.20
44
•19
Def.
.18
.22
•27
J£
•37
•43
•50
•57
.64
•71
.80
.88
•97
28
105
*
85
.41
76
•37
70
•33
64
•3i
59
.28
55
.26
5i
.24
48
•23
45
.22
42
.20
40
.19
38
•19
36
.18
Def.
.19
.24
.29
•34
.40
.46
•53
.61
.78
•77
•85
•95
3i
• 17
1.04
26
90
*
.___.
68
•38
61
•34
56
•31
Si
.28
4£
.26
44
.24
4i
•23
38
.21
36
.20
34
.19
32
.18
29
.16
.......
......
......
Def.
.21
•25
•3i
-.?7
•43
•50
•57
•65
•74
•83
.92
7.O2
7.72
24
84
73
*
88
77
•52
76
66
•45
.14
^
56
48
47
45
•37
66
58
•39
59
52
•35
53
46
•3i
48
42
.29
44
39
.26
4i
36
.24
38
33
.22
35
3i
.21
33
29
.20
3i
27
•19
29
26
•17
28
24
•17
26
23
.16
Def.
.TO
.18
.22
.2<?
•.?.?
.40
•47
•54
.62
•71
JSo
.89
I.OO
7.7O
2O
82
72
69
64
59
*
69
65
56
54
52
•44
52
49
42
4i
39
•33
46
43
38
36
35
.29
42
39
34
33
3^
.26
38
36
3i
30
28
.24
35
33
28
27
26
.22
32
32
26
25
24
.20
30
28
24
23
22
•19
28
26
23
22
21
•17
26
24
21
2O
20
.16
24
23
20
19
18
• IS
23
22
19
18
17
•15
22
21
18
17
16
.14
21
20
17
16
16
•13
-----
......
Def.
.r.?
.16
.21
•27
•33
.40
.48
•56
•65
•74
•85
.96
7.07
7.7p
7.32
18
59
54
48-5
*
—
44
42
39
•39
37
36
34
•34
33
31
3°
.29
29
28
26
.26
26
25
24
.24
24
23
21
.21
22
21
20
.20
20
19
1 8
.18
19
18
17
•17
17
17
16
.16
16
16
15
•1$
IS
15
14
•14
IS
14
13
•13
14
13
12
.12
13
12
12
.12
Def.
•'3
.18
.24
•30
•37
•44
•53
.62
.72
•83
•94
7.06
7.7p
i-33
7.47
15
71
54
46
4i
38
47
36
29
27
26
•33
40
31
25
23
22
.28
35
27
22
2O
2O
.26
3i
24
19
18
17
.22
28
22
17
16
16
.20
26
20
16
IS
H
.18
24
18
H
H
13
.16
22
17
13
12
12
•IS
20
15
12
12
II
.14
19
H
ii
ii
10
•13
18
H
ii
IO
10
.12
17
13
IO
IO
9
.12
16
12
IO
9
9
.11
15
II
9
9
8
.10
H
II
9
8
8
.10
......
Def.
r6
.22
.28
.36
•44
•53
.64
•75
.87
•99
I-I3
7.2.?
1-43
7.60
7.76
12
36
32
28.5
24
20
19
•31
20
17
16
.26
.20
17
IS
H
.22
•2?
IO
9
.19
15
13
12
.20
13
II
II
•17
12
10
IO
.16
ii
9
9
.14
IO
8
8
•13
9
8
7
.12
9
7
7
.11
8
6
.11
7
6
6
.10
I
6
.09
Def.
•14
14
13
.26
•17
II
IO
.24
•35
•45
•55
.67
•79
•93
1.08
7.24
7.47
i-59
IO
28.5
23-5
. *
^^1
12
II
.22
9
8
.16
8
7
•IS
7
7
•13
6
.12
6
5
.11
6
5
.10
5
5
.09
5
4
.09
Def.
.24
•32
.42
•54
.66
.80
•95
7.72
7.30
i-49
9
24
20
*
14
13
.29
9
8
.20
8
7
•17
6
•IS
6
6
• 13
5
S
.12
5
S
.11
5
4
.10
4
4
.09
4
4
.09
4
3
.08
Def.
.12
.18
8
8
.21
•27
.36
•47
.60
•74
£9
i. 06
7.24
1.44
7.66
8
19-5
17-5
*
10
IO
.26
•11
7
6
•17
6
5
• 15
S-o
4.8
• 13
4-5
4.2
.12
4.0
3-8
.11
3-7
3-5
.10
3-4
3-2
.09
Def.
.21
• 30
.41
-S3
.67
•<??
7.OO
7.70
\
The figures give the safe uniform load, in tons of 2000 lb., based on an extreme fiber stress of
16000 lb. per sq. in., or end reactions for safe uniform load in thousands of lb.
Figures for deflection in inches.
For loads concentrated at center, use one -naif of figures given for allowable load, and four-
fifths of deflections.
For figures to right of heavy lines, deflections are excessive for plastered ceilings.
Figures given apply only when beams are secured against lateral deformation.
* Increase of safe load in tons for each pound increase in weight of I-Beam.
266
TABLE 160.
SAFE LOADS, IN TONS, AND DEFLECTIONS IN INCHES, BETHLEHEM GIRDER BEAMS.
Depth.
WeiKht.
Length of Span in Feet.
In.
Lb.
ID
ll
14
16
18
30
23
24
id
38
30
33
34
36
3«
86
77
.21
40
42
44
30
200
1 80
*
181
162
•44
I63
I46
•39
I48
132
•36
136
121
•33
125
112
•30
116
104
.28
1 08
9£
.26
IO2
91
.25
96
86
•23.
90
HI
.22
81
73
.20
77
69
.19
a
.is
...
Def.
.18
154
139
.41
.22
•27
•32
•J7
•43
•50
•57
.64
•71
£o
.W
•P7
l.nfi
28
ISO
165
138
I2S
•37
126
114
•33
"5
104
•3i
106
96
.28
99
89
.26
92
83
.24
86
78
•23
81
74
.22
%
.20
%
.19
?
62
.18
66
60
•17
63
57
•17
.
Def.
.10
128
H7
•38
.24
•2P
•34
40
.46
•53
.67
.78
•77
*5
•P5
7.04
1.14
26
1 60
150
11A
106
•34
105
96
•3i
96
88
.28
89
81
.26
82
76
.24
77
70
•23
72
66
.21
68
62
.20
^74
64
59
•19
61
56
.18
58
53
•17
55
5°
.16
52
48
•IS
1-23
..._.
—
--•
..._.
Def.
.21
•25
•.?/
•37
•43
•50
•57
•65
•S3
•92
7.02
7.72
24
140
120
*
..._.
IS6
134
•52
.10
133
"5
•45
.14
117
IOO
•39
.18
104
89
•35
.22
93
80
•31
85
73
.29
78
67
.26
£
.24
67
57
.22
62
53
.21
58
5°
.20
55
47
.18
52
45
•17
49
42
• 17
I.OO
47
40
.16
Def.
.28
•33
.40
•47
•54
.62
££
.80
.80
7.70
2O
140
112
* '
130
104
•44
.12
~79
^39
•'3
112
89
•37
98
78
•33
.21
87
69
.29
78
62
.26
7i
57
.24
65
52
.22
60
48
.20
56
45
•19
52
42
•17
49
32
.16
46
37
•IS
43
35
•15
41
33
•H
39
3»
•13
Def.
.16
•27
•JJ
.40
.48
•56
•65
•74
•<?5
.06
7.07
7.79
1-32
18
92
—
67
•34
59
•29
.24
52
.26
47
.24
43
.21
39
.20
36
.18
34
•17
3A
.16
29
•IS
28
•H
26
•13
25
.12
24
.12
Def.
.18
• 30
•37
•44
•53
.62
•72
•83
.p^i 7.06
7.79
1-33
1-47
IS
140
104
73
*
"3
87
63
•39
.77
94
72
52
•33
81
62
45
.28
.22
7i
54
39
.25
.28
63
48
35
.22
~J6
57
43
3i
.20
51
39
29
-.18
47
3*
26
.16
44
33
24
•IS
40
3i
22
.14
38
29
21
•13
35
27
20
.12
33
26
18
.12
Def.
.16
•44
•53
.64
•75
.87
•99
'•'3
1.28
12
70
55
48
38
•31
40
32
.26
34
27
.22
30
24
.20
27
21
.18
24
19
.16
22
17
•H
20
16
•13
18
IS
.12
17
H
.11
16
13
.10
15
12
.IO
14
ii
.09
Def.
.14
.20
•2?
•35
16
.16
•45
IS
• IS
•55
.67
•79
•93
1.08
7.24
I.4I
/•5P
IO
44
*
26
.26
•17
22
.22
.24
19
•19
•32
H
•17
**
ii
• IS
13
•13
12
.12
ii
.11
IO
.10
9
.09
9
.09
8
.08
8
.08
Def.
.42
• f4
.66
JBo
•95
7.7.2
7..JO
1.40
7.69
7.97
9
38
2O
•23
.18
IS
.21
.21
17
.20
~7
13
•17
13
•15
•47
IO
• 13
II
•13
IO
.12
9
.11
8
.10
8
.09
7
.08
7
.07
Def.
.00
-74
.80
1.06
1.24
i-44
7.66
8
32*
*
8
.12
8
.10
7
.09
6
.08
Def.
.30
.41
• f?
.67
T3
I.OO
7.79
The figures give the safe uniform load in tons, of 2000 lb., based on extreme fiber stress of
16000 lb. per sq. in., or end reactions for safe uniform load in thousands of pounds.
Figures for deflections are given in inches.
For load concentrated at center, use one-half of figures given for allowable load and four-
fiftha values given for deflection.
For figures at right of heavy zigzag lines deflections are considered excessive for plastered
ceilings.
Figures given apply only when beams are secured against lateral deformation.
* Increase of safe load in tons for each pound increase in weight of Girder Beams.
267
TABLE 161
DECIMAL PARTS OF A FOOT AND INCH
DECIMAL PARTS OF A FOOT
Decimal Parts
of an Inch
Ins.
.0 .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167
A
.0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526 .8359 .9193
A
.0313
TV
.0052 .0885 .1719 .2552 .3385 .4219 .5052 .5885 .6719 .7552 .8385 .9219
A
.O625
A
.0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 -7578 .8411 .9245
A
.0938
i
.0104 .0938 .1771 .2604 .3438 .4271 .5104 .5938 .6771 .7604 .8438 .9271
-1
.125
A
.0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297
A
•IS63
A
.0156 .0990 .1823 .2656 .3490 .4323 .5156 .5990 .6823 .7656 .8490 .9323
A
-I87S
&
.Ol82 ,IOl6 .1849 .2682 .3516 .4349 .5182 .6oi6 .6849 .7682 .8516 -9349
~h
.2188
1
.0208 .1042 .1875 .2708 .3542 .4375 .5208 .6042 .6875 .7708 .8542 .9375
i
•25
A
.0234 .1068 .1901 .2734 .3568 .4401 .5234 .6068 .6901 .7734 .8568 .9401
A
.2813
A
.O26O .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7760 .8594 .9427
A
.3125
11
32
.O286 .II2O .1953 .2786 .3620 .4453 .5286 .6l2O .6953 .7786 .862O .9453
H
•3438
t
.0313 .1146 .1979 .2813 .3646 .4479 .5313 .6146 .6979 .7813 .8646 .9479
1
•375
H
.0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 .8672 .9505
if
.4063
A
.0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531
A
•4375
H
.0391 .1224 .2057 .2891 .3724 .4557 .5391 .6224 .7057 .7891 .8724 .9557
H
.4688
1
.0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583
i
2
•5
H
.0443 .1276 .2109 4943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609
H
.5313
A
.0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7135 .7969 .8802 .9635
rV
•5625
if
.0495 .1328 .2161 .2995 .3828 .4661 .5495 .6328 .7161 .7995 .8828 .9661
If
•5938
I
.0521 .1354 .2188 .3021 .3854 .4688 .5521 .6354 .7188 .8021 .8854 .9688
1
.625
11
.0547 .1380 .2214 .3047 .3880 .4714 .5547 .6380 .7214 .8047 .8880 .9714
ii
•6563
H
.0573 .1406 .2240 .3073 .3906 .4740 .5573 .6406 .7240 .8073 .8906 .9740
H
.6875
ii
3 2
.0599 .1432 .2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099 .8932 .9766
If
.7188
1
.0625 .1458 .2292 .3125 .3958 .4792 .5625 .6458 .7292 .8125 .8958 .9792
3
4
•75
25
32
.0651 .1484 .2318 .3-151 .3984 .4818 .5651 .6484 .7318 .8151 .^984 .9818
If
•78i3
H
.0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844
H
.8125
H
.0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870
H
•8438
1
.0729 .1563 .2396 .3229 .4063 .4896 .5729 .6563 .7396 .8229 .9063 .9896
8
•875
H
•°75S -r589 -2422 -32SS 4089 -4922 -5755 -6589 -7422 .8255 .9089 .9922
29
~32
.9063
15
16
.0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948
15
16
•9375
31
T2
.0807 .1641 .2474 .3307 .4141 .4974 .5807 .6641 .7474 .8307 .9141 .9974
ft
.9688
268
TABLE 162
TABLE OF BEVELS
AMERICAN BRIDGE COMPANY STANDARDS
T
— """"""" *^"
-L.
r
-i*tf -
-.
0)
o
i
a
3
4
5
6
7
8
9
10
II
1
Angle V
Angle V
Angle V
Angle V Angle V
Angle V
Angle V
Angle V
Angle V
Angle V
Angle V
Angle V
I
I
i
a
i
i
S
I
S
.S
Si
S
S
<?
S
•s
S
3
S
.£
t
.s
3
2
S
3
5
J
S
O
O
00
4
46
9
28
14
02
18
26
22
37
26
34
30
IS
33
41
36
52
39
48
42
31
A
O
09
4
55
9
36
14
II
18
34
22
45
26
41
3°
22
33
48
36
58
39
54
42
35
A
o
18
5
04
9
45
14
19
18
42
22
52
26
48
30
29
33
54
37
04
39
59
42
40
A
0
27
S
12
9
54
14
27
18
5°
23
oo
26
55
30
35
34
00
37
09
40
04
42
45
i
o
36
5
21
10
03
14
36
18
58
23
08
27
02
30
42
34
06
37
IS
40
09
42
5°
A
o
45
S
30
IO
ii
14
44
19
06
23
IS
27
IO
30
49
34
12
37
21
40
IS
42
55
A
o
54
S
39
10
20
14
53
19
14
23
23
27
17
30
55
34
18
37
26
40
20
43
oo
A
I
03
5
48
IO
29
15
01
19
22
23
30
27
24
3
i
02
34
24
37
32
40
25
43
04
i
12
S
57
IO
37
15
09
19
30
23
38
27
31
3
i
08
34
31
37
38
40
30
43
09
A
21
6
06
IO
46
15
18
19
38
23
45
27
38
3
i
IS
34
37
37
43
40
35
43
14
A
30
6
IS
10
54
IS
26
19
46
23
53
27
45
3
i
21
34
43
37
49
40
41
43
19
H
38
6
23
II
03
is
34
19
54
24
oo
27
52
3
i
28
34
49
37
54
40
46
43
23
1
47
6
32
II
12
IS
43
20
02
24
08
27
59
3
i
34
34
55
38
oo
40
Si
43
28
H
56
6
41
II
2O
15
Si
20
IO
24
IS
28
06
3
t
41
35
01
38
05
40
56
43
33
A
2
05
6
50
II
29
15
59
20
18
24
23
28
13
3
i
47
35
07
38.
ii
41
OI
43
38
if
2
14
6
59
II
38
16
07
20
26
24
30
28
20
3
i
54
35
13
38
17
4i
06
43
42
§
2
23
7
08
II
46
16
16
20
33
24
37
28
27
32
oo
35
19
38
22
4i
ii
43
47
'H
2
32
7
16
II
55
16
24
2O
41
24
45
28
34
32
°7
35
25
38
28
4i
16
43
52
A
2
41
7
25
12
03
16
32
20
49
24
52
28
40
32
13
35
3i
38
33
41
21
43
56
H
2
50
7
34
12
12
16
40
20
57
25
oo
28
47
32
20
35
37
38
39
41
26
44
OI
i
2
59
7
43
12
2O
16
49
21
05
25
07
28
54
32
26
35
42
38
44
41
31
44
05
ft
3
08
7
52
12
29
16
57
21
12
25
14
29
OI
32
32
35
48
38
49
41
36
44
IO
H
3
17
8
oo
12
37
17
05
21
2O
25
22
29
08
32
39
35
54
38
55
41
41
44
15
If
3
26
8
09
12
46
17
13
21
28
25
29
29
15
32
45
36
oo
39
oo
4i
46
44
19
i
3
35
8
18
12
54
17
21
21
36
25
36
29
21
32
51
36
06
39
06
41
51
44
24
H
3
44
8
27
13
°3
17
29
21
43
25
43
29
28
32
58
36
12
39
ii
41
56
44
28
H
3
52
8
35
13
ii
17
38
21
Si
25
Si
29
35
33
04
36
18
39
16
42
OI
44
33
H
4
OI
8
44
13
20
17
46
21
59
25
58
29
42
33
10
36
23
39
22
42
06
44
37
I
4
10
8
53
13
28
17
54
22
07
26
05
29
49
33
17
36
29
39
27
42
II
44
42
ft
4
19
9
02
13
37
18
02
22
14
26
12
29
55
33
23
36
35
39
32
42
16
44
47
H
4
28
9
10
13
45
18
10
22
22
26
20
30
02
33
29
36
4i
39
38
42
21
44
Si
H
4
37
9
19
13
54
18
18 22
30
26
27
30
09
33
35
36
46
39
43
42
26
44
56
269
TABLE 163
ORDINATES FOR i6'-o" CHORDS
AMERICAN BRIDGE COMPANY STANDARDS
^-n"
— ""? t — 7-^
^^•i- ~r ~~*****^
On all drawings for <, — 6 'S / ^"S^.
curved work where radius /!$ "? by V
exceeds facilities of Temp- / } t t / — S
let Shop Floor, make a /
sketch as shown giving [w._2/0»>[<-2'o'4*-2/0*i<-^Of'>J
i~
// 1
J
Radius
R
Ordinates for i6'-o"
Templet in Inches
Radius
R
Ordinates for i6'-o"
Templet in Inches
Radius
R
Ordinates for i6'-o"
Templet in Inches
Ft. In.
Ft. In.
Ft. In.
a
b
C
d
a
b
c"
d
a
b
C
d
16'- 6'
Ili
l8|
23 8"
24l
24'-8"
7i
121
IS
16
Si'-6"
3f
Sl
7
7i
16- 8
"I
i8f
23i
24i
25-0
7
III
14!
isf
53-o
3f
5k
6f
7i
16-10
II
I8J
22?
241
25-4
6f
lit
Hi
54-6
3l
Sf
61
71
17- o
IQf
181
•7,5
22 g
24
25-8
6f
III
I4f
ill
56-0
3
si
6j
6|
17- 2
iof
i8|
22f
23 f
26-0
6f
"I
I4i
58-0
2|
s
6|
17- 4
iof
17!
22|
23}
26-4
6|
Hi
14
14!
60-0
2|
4l
6
6f
17-6
IOJ
i7l
2l|
26-8
6f
ni
13!
Hf
62-6
2f
4l
Sf
6|
17- 8
iof
iff
2Ig
23
27-0
65
ii
I3l
14}
65-0
2|
4f
si
Si
17-10
174
2lf
22f
27-6
6}
iof
131
67-6
2J
4}
Sf
Sf
18- o
I0|
i7i
2l|
22*
28-0
6i
io|
I3i
14
70-0
2f
4l
sl
si
18- 2
IO
i6|
21
22\
28-6
6|
iof
12!
I3f
72-6
2f
4
5
sl
18- 4
9l
i6f
20}
22
29-0
6
io|
I2g
ill
7S-o
3i
4f
Si
1 8- 6
9l
i6f
20i
2I|
29-6
5f
IO
I2j
I3i
77-6
2i
3|
4f
5
18- 8
9f
i6f
20f
III
30-0
Sf
9f
I2j
I37
80-0
2I
31
4f
.3
18-10
9f
20|
2lf
30-6
Sl
9l
12
84-0
2
8
4i
4s
19- o
9|
i6|
I9l
2li
31-0
Sf
9j
III
I2{
88-0
l|
3i
4l
4f
19- 2
9f
is!
I9i
21
31-6
9f
III
92-0
l|
3i
3l
4l
19- 4
9l
isf
I9i
20f
32-0
si
9i
III
I2j
96-0
If
3
3J
4
19- 6
9f
isl
195
20|
32-9
si
9
III
III
100-0
If
2|
Si
3l
19- 8
9l
isl
I9i
20f
33-6
si
8f
iof
H|
105-0
If
2f
3i
3l
19-10
9l
isf
19
20\
34-3
5.
8i
iof
Hf
IIO-O
l|
2f
3i
3i
20- o
9
15!
i8|
2O
3S-o
4!
8f
iof
III
115-0
ii
3l
31
20- 3
8|
IS
l8|
igf
35-9
4|
81
lOj
io|
I2O-O
if
2|
3
3i
20- 6
8f
Hf
i8f
192
36-6
4f
8
IO
io|
130-0
2$
2f
33
20- 9
8|
Hf
i8i
I9i
37-3
41
7l
9f
iof
140-0
if
2
2|
21- o
8i
Hi
17!
19
38-0
4*
71
9l
ioj
150-0
i|
1 5
2f
2i
21- 3
8f
Hi
17}
18}
38-9
4f
7?
9f
IO
160-0.
i
If
2i
2J
21- 6
81
I4T
I8J
39-6
4f
71
9!
1 80-0
I
If
2
2f
21- 9
81
i7i
184
40-3
4}
7}
9
9}
2OO-O
j
Ii
If
22- O
8|
*ll
17
I8|
41-0
4l
7t
8|
225-0
f
Ii
l|
l\
22- 3
.8
;3t
i6f
17}
42-0
4
61
8|
91
250-0
I
l|
Ii
ii
22- 6
7f
16}
43-o
4
6]
85
9
300-0
2
I
ii
22- 9
7f
131
I7f
44-0
3!
61
if
8}
350-0
1
2
I
I
i|
23- o
7l
13
i6i
i7i
45-0
3f
6i
8i
8|
400-0
f
3
4
T
8
i
23- 4
7*
I2|
16
17
46-3
3s"
6|
7l
8f
500-0
f
f
f
3
4
23- 8
7i
I2|
isf
i6f
47-6
31
6|
7f
8f
625-0
i
1
5
8
24- o
71
I2f
is}
16-2
48-9
32
6
7f
7l
750-0
1
1
i
24- 4
7l
"I
i6x
50-0
3f
Sf
7i
_3
7s
lOOO-O
1
1
3
8
1
270
TABLE 164
NATURAL TANGENTS
il
o'
g
10'
//
20'
*/
30'
35'
40'
45'
So'
551
60'
i!
0
i
2
3
4
.0000
•0175
.0349
.0524
.0699
.001 5
.0189
.0364
.0539
.0714
.0029
.0204
.0378
•0553
.0729
.0044
.0218
•0393
.0568
•0743
.0058
.0233
.0407
.0582
.0758
.0073
.0247
.0422
.0597
.0772
.0087
.0262
•0437
.0612
.0787
.0102
.0276
.0451
.0626
.0802
.0116
.0291
.0466
.0641
.0816
.0131
.0306
.0480
.0655
.0831
.0146
.0320
.0495
.0670
.0846
.0160
.0335
.0509
.0685
.0860
.0175
.0349
.0524
.0699
.0875
0
I
2
3
4
i
I
9
.0875
.1051
.1228
.1405
.1584
.0890
.1066
•1243
.1420
•1599
.0904
.1080
•1257
•.H35
.1614
.0919
.1095
.1272
.1450
.1629
.0934
.1110
.1287
.1^63
.1644
.0948
.1125
.1302
.1480
.1658
.0963
•i'39
.1317
•H95
•1673
.0978
•"54
•1331
.1509
.1688
.0992
.1169
.1346
.1524
.1703
.1007
.1184
.1361
•1539
.1718
.1022
.1198
.1376
•1554
•1733
.1036
• 1213
.1391
.1569
•I7t8
.1051
.1228
.1405
.1584
.1763
6
J
9
10
ii
12
13
14
•1763
.1944
.2126
.2309
.2493
.1778
.1959
.2I.fi
.2324
.2509
•1793
.1974
.2136
•2339
•2524
.1808
.1989
.2171
•2355
.2540
.1823
.2004
.2186
.2370
•2555
.1838
.2019
.2202
.2385
•2571
.1853
.2035
.2217
.2401
.2586
.1868
.2050
.2232
.2416
.2602
.1883
.2065
.2247
.2432
..6.7
.1899
.2080
.2263
.2447
.2633
.1914
.2095
.2278
.2462
.2648
.1929
.2110
.2293
.2478
.2664
.1944
.2126
.2309
.2493
.2679
10
ii
12
13
14
15
16
3
19
.2679
.2867
•3057
.3249
•3443
.2695
.2883
•3°73
•3265
•3460
.2711
.2899
•3089
•3281
•3476
.2726
.2915
•3105
.3298
•3492
.2742
.2931
.3121
•3314
.3508
•2758
.2946
•3137
•3330
•3525
•2773
.2962
•3153
•3346
•35*i
.2789
.2978
.3169
•3362
•3558
.2805
.2994
•3185
•3378
•3574
.2820
.3010
.3201
•3395
•3590
.2836
.3026
.3217
•34"
.3607
.2852
.3041
•3233
•3427
.3623
.2867
•3057
•3249
•3443
.3640
IS
16
17
18
19
20
21
22
23
24
•3640
•3839
.4040
.4245
.4452
.3656
•3855
.4057
.4262
.4470
•3673
.3872
.4074
•4279
•4487
•3689
.3889
.4091
.4296
•4505
.3706
.3906
.4108
•4314
•4522
.3722
.3922
.4125
•4331
.4540
•3739
•3939
.4142
•4348
•4557
•3755
•3956
.4159
•4365
•4575
•3772
•3973
.4176
•4383
•4592
•3789
•399°
.4193
.4400
.4610
•3805
.4006
.4210
.4417
.4628
.3822
.4023
.4228
•4435
.46^5
•3839
.4040
.4245
•4452
.4663
20
21
22
23
24
25
26
2?
28
29
.4663
•4877
•5°95
•5317
•5543
.4681
•4895
.5114
•5336
•5562
.4699
4913
•5132
•5354
•558i
.4716
•4931
•5150
•5373
.5600
•4734
.4950
.5169
•5392
.5619
.4752
.4968
•5187
•54"
•5639
•4770
.4986
.5206
•543°
.5658
.4788
.5004
•5224
•5448
•5677
.4806
.5022
•5243
.5467
•5696
•4823
.5040
.5261
•5486
•5715
.4841
•5059
.5280
•55°5
•5735
.4859
•5°77
•5298
•5524
•5754
.4877
•5095
•5317
•5543
•5774
25
26
27
28
29
30
31
32
33
34
•5774
.6009
.6249
.6494
.6745
•5793
.6028
.6269
•6515
.6766
•5812
.6048
.6289
.6536
.6787
•5832
.6068
.6310
.6556
.6809
.5851
.6088
.6330
•6577
.6830
•5871
.6108
.6350
.6598
.6851
.5890
.6128
.6371
.6619
.6873
.5910
.6148
•g9i
.6640
.6894
•593°
.6168
.6412
.6661
.6916
•5949
.6188
.6432
.6682
.6937
•5969
.6208
•6453
.6703
•6959
•5989
.6228
.6473
.6724
.6980
.6009
.6249
.6494
•67*5
.7002
30
31
32
33
34
%
37
38
39
.7002
.7265
•7536
•7813
.8098
.7024
.7288
7558
.7836
.8122
.7046
.7310
•7581
.7860
.8146
.7067
•7332
.7604
.7883
.8170
.7089
•7355
.7627
.7907
•8i9S
.7111
.7377
.7650
•7931
.8219
•7133
.7400
•7673
•7954
.8243
•7155
.7422
.7696
.7978
.8268
•7177
•7445
.7720
.8002
.8292
.7199
.7467
•7743
.8026
•8317
.7221
.7490
.7766
.8050
•8342
.7243
•7513
.7789
.8074
.8366
.7265
•7536
.7813
.8098
.8391
%
%
39
40
4i
42
43
44
40
4i
42
43
44
.8391
.8693
.9004
•9325
•9657
.8416
.8718
.9030
•9352
.9685
.8441
.8744
•9057
.9380
.9713
£466
.8770
.9083
.9407
•9742
.8491
.8796
.9110
•9435
.9770
.8516
.8821
•9137
.9462
.9798
.8541
.8847
.9163
.9490
.9827
.8566
.8873
.9190
•9517
.9856
.8591
.8899
.9217
•9545
.9884
.8617
.8925
.9244
•9573
•99»3
.8642
•8952
.9271
.9601
.9942
.8667
.8978
.9298
.9629
.9971
.8693
.9004
•9325
-9657
1 .0000
it
o'
f
10'
15'
20'
25'
30'
35'
40'
45'
50'
ss1
60'
t\
271
TABLE 165.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM i TO 99.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
I
I
I
I.OOOO
I.OOOO
50
250O
I25OOO
7.0711
3.6840
2
4
8
I.4H2
1.2599
51
2601
132651
7.1414
3.7084
3
9
27
I.732I
1.4422
52
2704
140608
7-2III
3-7325
4
16
64
2.OOOO
I-S874
53
2809
148877
7.2801
37563
5
25
125
2.2361
I.7IOO
54
2916
IS7464
7.348S
37798
6
36
216
2.4495
I.8I7I
55
3025
166375
7.4162
3.8030
7
49
343
2.6458
I.9I29
56
3136
175616
74833
3-8259
8
64
512
2.8284
2.OOOO
57
3249
I85I93
7.5498
3.8485
9
81
729
3.0000
2.O8OI
58
3364
I95II2
7.6158
3.8709
10
100
IOOO
3.1623
2.1544
59
3481
205379
7.68II
3-8930
ii
121
1331
3.3166
2.224O
60
3600
2I6OOO
7.7460
3-9H9
12
144
1728
3.464I
2.2894
61
3721
226981
7.8102
3.9365
13
169
2197
3.6056
2.3513
62
3844
238328
7.8740
3-9579
14
196
2744
3-7417
2.4IOI
63
3969
250047
7-9373
3-9791
15
225
3375
3-8730
2.4662
64
4096
262144
8.0000
4.0000
16
256
4096
4.0OOO
2.5198
65
4225
274625
8.0623
4.0207
17
289
4913
4.I23I
2.5713
66
4356
287496
8.1240
4.0412
18
324
5832
4.2426
2.6207
67
4489
300763
8.1854
4.0615
19
361
6859
4-3S89
2.6684
68
4624
314432
8.2462
4.0817
20
4OO
8000
44721
2.7144
69
476l
328509
8.3066
4.1016
21
441
9261
4.5826
2.7589
70
4900
343000
8.3666
4.1213
22
484
10648
4.6904
2.8O2O
7i
5041
3579U
8.4261
4.1408
23
529
12167
47958.
2.8439
72
5184
373248
8.4853 '
4.1602
24
576
13824
4.8990
2.8845
73
5329
389017
8.5440
4-1793
25
625
15625
5.000O
2.9240
74
5476
405224
8.6023
4.1983
26
676
17576
5.0990
2.9625
75
5625
421875
8.6603
4.2172
27
729
19683
5.1962
3.0000
76
5776
438976
8.7178
4-2358
28
784
21952
5-29IS
3.0366
77
5929
456533
87750
4-2543
29
841
24389
5-38S2
3.0723
78
6084
474552
8.8318
4.2727
30
900
27000
5-4772
3.1072
79
6241
493039
8.8882
4.2908
31
961
29791
5-5678
3-I4H
80
6400
5I2OOO
8.9443
4.3089
32
IO24
32768
5-6569
3-I748
81
6561
53 H4I
9.0000
4.3267
33
1089
35937
5-7446
3.2075
82
6724
551368
9-0554
4-3445
34
1156
39304
5-83IO
3.2396
83
6889
571787
9.1104
4.3621
35
1225
42875
5.9l6l
3.27II
84
7056
592704
9.1652
4-3795
36
1296
46656
6.0000
3.30I9
85
7225
614125
9.2195
' 4-3968
37
1369
50653
6.0828
3-3322
86
7396
636056
9.2736
4.4140
38
1444
54872
6.1644
3.3620
87
7569
658503
9-3274
4.4310
39
1521
59319
6.2450
3-3912
88
7744
681472
9.3808
4.4480
40
I6OO
64000
6.3246
342OO
89
7921
704969
9.4340
4.4647
4i
1681
68921
6.4031
3.4482
90
8100
729000
9.4868
4.4814
42
1764
74088
6.4807
3.4760
9i
8281
7S357I
9-5394
4-4979
43
1849
79507
6-5574
3-5034
92
8464
778688
9-59I7
4.5144
44
1936
85184
6.6332
3.5303
93
8649
804357
9.6437
4-5307
45
2025
91125
67082
3-5569
94
8836
830584
9.6954
4-5468
46
2116
97336
6.7823
3-5830
95
9025
857375
9.7468
4-5629
47
2209
103823
6-8557
3.6088
96
9216
884736
9.7980
4.5789
48
2304-
110592
6.9282
3-6342
97
9409
912673
9.8489
4-5947
49
2401
117649
7.0000
3-6593
98
9604
941192
9.8995
4.6104
99
9801
970299
9-9499
4.6261
272
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 100 TO 199.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
100
1 0000
1000000
IO.OOOO
4.6416
ISO
22500
3375000
12.2474
5.3133
IOI
I020I
1030301
10.0499
4.6570
151
228OI
3442951
12.2882
5.3251
IO2
10404
1061208
10.0995
4.6723
152
23104
3511808
12.3288
5-3368
103
I0609
1092727
10.1489
4.6875
153
23409
3581577
12.3693
5-3485
104
I08l6
1124864
10.1980
4.7027
154
23716
3652264
12.4097
5.3601
105
II025
1157625
10.2470
4-7177
155
24025
3723875
12.4499
5.37I7
106
II236
1191016
10.2956
4.7326
156
24336
3796416
12.4900
5-3832
107
II449
1225043
10.3441
4-7475
157
24649
3869893
12.5300
5-3947
108
iiM>4
1259712
10.3923
4.7622
IS8
24964
39443"
12.5698
5.4061
109
11881
1295029
10.4403
4.7769
159
25281
4019679
12.6095
54175
1 10
I2IOO
1331000
10.4881
479H
160
25600
4096000
12.6491
5.4288
III
I232I
1367631
10-5357
4.8059
161
25921
4173281
12.6886
5-4401
112
I2S44
1404928
10.5830
4.8203
162
26244
4251528
12.7279
S.45I4
113
12769
1442897
10.6301
4-8346
163
26569
4330747
12.7671
5.4626
114
12996
1481544
10.6771
4.8488
164
26896
4410944
12.8062
5-4737
"5
I322S
1520875
10.7238
4.8629
165
27225
4492125
12.8452
5.4848
116
13456
1560896
10.7703
4.8770
166
27556
4574296
12.8841
5-4959
ii7
13689
1601613
10.8167
4.8910
167
27889
4657463
12.9228
5.5069
118
13924
1643032
10.8628
4.9049
168
28224
4741632
12.9615
5.5178
119
I4l6l
1685159
10.9087
4.9187
169
28561
4826809
13.0000
5-5288
1 20
14400
1728000
10.9545
4-9324
170
28900
4913000
13-0384
5-5397
121
14641
1771561
II.OOOO
4.9461
171
29241
5000211
13-0767
5-5505
122
14884
1815848
11.0454
4-9597
172
29584
5088448
13.1149
5-56i3
123
I5I29
1860867
11.0905
4-9732
173
29929
5I777I7
13.1529
5-5721
124
IS376
1906624
11-1355
4.9866
174
30276
5268024
13.1909
5-5828
125
15625
I953I25
11.1803
5.0000
175
30625
5359375
13.2288
5-5934
126
15876
2000376
11.2250
5-0133
176
30976
5451776
13.2665
5-6041
127
l6l29
2048383
11.2694
5.0265
177
31329
5545233
13.3041
5-6I47
128
16384
2097152
11:3137
5-0397
178
31684
5639752
I3-34I7
5-6252
129
16641
2146689
"•3578
5-0528
179
32041
5735339
I3.379I
5-6357
130
16900
2197000
11.4018
5-0658
1 80
32400
5832000
13.4164
5.6462
131
I7l6l
2248091
11.4455
5.0788
181
32761
5929741
I3-4536
5-6567
132
17424
2299968
11.4891
5.0916
182
33"4
6028568
I3-4907
5.6671
133
17689
2352637
11.5326
5-1045
183
33489
6128487
13.5277
5-6774
134
17956
2406104
11.5758
5.1172
184
33856
6229504
13-5647
5.6877
13S
18225
2460375
11.6190
5.1299
185
34225
6331625
13.6015
5.6980
136
18496
2515456
11.6619
5.1426
1 86
34596
6434856
13.6382
5.7083
137
18769
2571353
11.7047
5.I55I
187
34969
6539203
13.6748
5-7I8S
138
19044
2628072
n-7473
5-1676
1 88
35344
6644672
13.7113
5-7287
139
I932I
2685619
11.7898
5.1801
189
35721
6751269
13-7477
5-7388
I4O
19600
2744000
11.8322
5.I925
190
36100
6859000
13-7840
5-7489
I4I
I988I
2803221
11.8743
5.2048
191
36481
6967871
13.8203
5-7590
142
20164
2863288
11.9164
5.2171
192
36864
7077888
13.8564
5.7690
H3
20449
2924207
11.9583
5-2293
193
37249
7189057
13.8924
5-7790
144
20736
2985984
I2.OOOO
5-2415
194
37636
7301384
13.9284
5.7890
US
2IO25
3048625
I2.O4I6
5.2536
195
38025
74H875
13.9642
5-7989
146
2I3IO
3112136
I2.O83O
5.2656
196
38416
7529536
14.0000
5.8088
H7
21609
3176523
12.1244
5-2776
197
38809
7645373
H-0357
5.8186
148
21904
3241792
I2.I6S5
5.2896
198
39204
7762392
14.0712
5-8285
149
222OI
3307949
I2.2O66
5-30I5
199
39601
7880599
14.1067
5-8383
273
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 200 TO 299.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
2OO
40000
SOOOOOO
14.1421
5.8480
250
62500
15625000
15.8114
6.2996
201
40401
8120601
14.1774
5-8578
251
63001
15813251
15.8430
6.3080
2O2
40804
8242408
14.2127
5-8675
252
63504
16003008
IS-8745
6.3164
2O3
41209
8365427
14.2478
5-877I
253
64009
16194277
15.9060
6.3247
204
41616
8489664
14.2829
5.8868
254
64516
16387064
15-9374
6.3330
205
42O25
8615125
14.3178
5.8964
255
65025
16581375
15.9687
6-34I3
206
42436
8741816
I4-3527
5-9059
2S6
65536
16777216
I6.000O
6.3496
207
42849
8869743
I4-3875
5-9I55
257
66049
16974593
16.0312
6-3579
208
43264
8998912
14.4222
5-9250
258
66564
17173512
16.0624
6.3661
2O9
43681
9129329
14.4568
5-9345
259
67081
17373979
16.0935
6-3743
2IO
44100
9261000
14.4914
5-9439
260
67600
17576000
16.1245
6.3825
211
44521
9393931
14.5258
5-9533
261
68I2I
17779581
l6-i555
6.3907
212
44944
9528128
14.5602
5.9627
262
68644
17984728
16.1864
6.3988
213
45369
9663597
14-5945
5-9721
263
69169
18191447
16.2173
6.4070
214
45796
9800344
14.6287
5.9814
264
69696
18399744
16.2481
6.4151
215
46225
9938375
14.6629
5-9907
265
70225
18609625
16.2788
6.4232
216
46656
10077696
14.6969
6.0000
266
70756
18821096
16.3095
6.4312
217
47089
10218313
14.7309
6.0092
267
71289
19034163
16.3401
6-4393
218
47524
10360232
14.7648
6.0185
268
71824
19248832
16.3707
6-4473
219
47961
10503459
14.7986
6.0277
269
72361
19465109
16.4012
6-4553
22O
48400
10648000
14.8324
6.0368
270
72900
19683000
16.4317
6-4633
221
48841
10793861
14.8661
6.0459
271
73441
19902511
16.4621
6-47I3
222
49284
10941048
14.8997
6.0550
272
73984
20123648
16.4924
6.4792
223
49729
11089567
I4-9332
6.0641
273
74529
20346417
16.5227
6.4872
224
50176
11239424
14.9666
6.0732
274
75076
20570824
16.5529
6.4951
225
50625
11390625
I5.0OOO
6.0822
275
75625
20796875
16.5831
6.5030
226
51076
HS43I76
I5-0333
6.0912
276
76176
21024576
16.6132
6.5108
227
5IS29
11697083
15.0665
6.IOO2
277
76729
21253933
16.6433
6.5187
228
51984
11852352
15.0997
6.1091
278
77284
21484952
16.6733
6.5265
229
52441
12008989
15.1327
6.1 180
279
77841
21717639
16.7033
6-5343
230
52900
12167000
15.1658
6.1269
280
78400
21952000
16.7332
6.5421
231
5336i
12326391
15.1987
6-1358
28l
78961
22188041
16.7631
6-5499
232
53824
12487168
I5-23I5
6.1446
282
79524
22425768
16.7929
6-5577
233
54289
12649337
15.2643
6-1534
283
80089
22665187
16.8226
6-5654
234
54756
12812904
15.2971
6.1622
284
80656
22906304
16.8523
6.5731
235
55225
12977875
15.3297
6.1710
285
81225
23149125
16.8819
6.5808
236
55696
13144256
I5-3623
6.1797
286
81796
23393656
16.9115
6.5885
237
56169
I33I2053
IS-3948
6.1885
287
82369
23639903
16.9411
6.5962
238
56644
13481272
15.4272
6.1972
288
82944
23887872
16.9706
6.6039
239
57121
13651919
I5-4596
6.2058
289
83521
24137569
17.0000
6.6115
240
57600
13824000
15.4919
6.2145
290
84100
24389000
17.0294
6.6191
24I
58081
13997521
15.5242
6.2231
291
84681
24642171
17.0587
6.6267
242
58564
14172488
I5-5563
6.2317
292
85264
24897088
17.0880
6-6343
243
59049
14348907
I5-5885
6.2403
293
85849
25IS3757
17.1172
6.6419
244
59536
14526784
15.6205
6.2488
294
86436
25412184
17.1464
6.6494
245
60025
14706125
I5-652S
6.2573
295
87025
25672375
17.1756
6.6569
246
60516
14886936
15.6844
6.2658
296
87616
25934336
17.2047
6.6644
247
61009
15069223
15.7162
6.2743
297
88209
26198073
I7-2337
6.6719
248
61504
15252992
15.7480
6.2828
298
88804
26463592
17.2627
6.6794
249
62001
15438249
15-7797
6.2912
299
89401
26730899
17.2916
6.6869
274
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 300 TO 399.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
( 11. Root.
300
90000
27000000
17.3205
6.6943
350
122500
42875000
18.7083
7-0473
301
90601
27270901
17-3494
6.7018
351
123201
43243551
18.7350
7.0540
302
91204
27543608
I7-378I
6.7092
352
123904
43614208
18.7617
7.0607
303
91809
27818127
17.4069
6.7166
353
124609
43986977
18.7883
7.0674
3°4
92416
28094464
I7-43S6
6.7240
354
125316
44361864
18.8149
7.0740
3°S
93025
28372625
17.4642
6.7313
355
126025
44738875
18.8414
7.0807
306
93636
28652616
17.4929
6.7387
356
126736
45118016
18.8680
7-0873
307
94249
28934443
I7-52I4
6.7460
357
127449
45499293
18.8944
7.0940
308
94804
292.18112
17-5499
6-7533
358
128164
45882712
18.9209
7.IOO6
309
95481
29503629
17.5784
6.7606
359
I2888I
46268279
18.9473
7.1072
310
96100
29791000
17.6068
6.7679
360
129600
46656000
18.9737
7.1138
3"
96721
3008023 1
17.6352
6.7752
361
130321
47045881
I9.OOOO
7.1204
312
97344
30371328
17.6635
6.7824
362
131044
47437928
19.0263
7.1269
313
97969
30664297
17.6918
6.7897
363
131769
47832147
19.0526
7-1335
3H
98596
30959144
17.7200
6.7969
364
132496
48228544
19.0788
7.1400
3iS
99225
31255875
17.7482
6.8041
365
133225
48627125
19.1050
7.1466
316
99856
31554496
17.7764
6.8113
366
133956
49027896
I9-I3"
7.I53I
317
100489
3I8S50I3
17.8045
6.8185
367
134689
49430863
19.1572
7.I596
318
101124
32IS7432
17.8326
6.8256
368
135424
49836032
I9-I833
7.1661
319
101761
32461759
17.8606
6.8328
369
136161
50243409
19.2094
7.1726
320
102400
32768000
17.8885
6.8399
370
136900
50653000
19-2354
7.I79I
321
103041
33076161
17.9165
6.8470
37i
137641
51064811
19.2614
7-I855
322
103684
33386248
17.9444
6.8541
372
138384
51478848
19.2873
7.1920
323
104329
33698267
17.9722
6.8612
373
139129
51895117
I9-3I32
7.1984
324
104976
34012224
18.0000
6.8683
374
139876
52313624
19-3391
7.2048
325
105625
34328125
18.0278
6-8753
375
140625
52734375
19.3649
7-2II2
326
106276
34645976
18.0555
6.8824
376
HI376
53157376
19.3907
7.2177
327
106929
34965783
18.0831
6.8894
377
142129
53582633
19.4165
7.2240
328
107584
35287552
I8.II08
6.8964
378
142884
54010152
19.4422
7.2304
329
108241
35611289
18.1384
6.9034
379
143641
54439939
19.4679
7.2368
330
108900
35937000
18.1659
6.9104
380
144400
54872000
19.4936
7.2432
33i
109561
36264691
18.1934
6.9174
38i
145161
55306341
19.5192
7-2495
332
110224
36594368
18.2209
6.9244
382
145924
55742968
19.5448
7.2558
333
110889
36926037
18.2483
6.9313
383
146689
56181887
I9-5704
7.2622
334
111556
37259704
18.2757
6.9382
384
H7456
56623104
19.5959
7-2685
335
112225
37595375
18.3030
6.9451
385
148225
57066625
19.6214
7.2748
336
112896
37933056
18.3303
6.9521
386
148996
57512456
19.6469
7.28II
337
II3569
38272753
18.3576
6.9589
387
149769
57960603
19.6723
7.2874
338
114244
38614472
18.3848
6.9658
388
150544
58411072
19.6977
7.2936
339
114921
38958219
18.4120
6.9727
389
I5I32I
58863869
19.7231
7.2999
340
115600
39304000
18.4391
6.97Q5
390
152100
59319000
19.7484
7.3061
341
116281
39651821
I8.I662
6.9864
39i
152881
59776471
19-7737
7.3124
342
116964
40001688
18.4932
6.9932
392
153664
60236288
19.7990
7.3186
343
117649
40353607
18.5203
7.0000
393
154449
60698457
19.8242
7.3248
344
118336
40707584
18.5472
7.0068
394
15523^
6 i 162984
19.8494
7.3310
345
119025
41063625
18.5742
7-0136
395
156025
61629875
19.8746
7-3372
346
119716
41421736
18.6011
7.0203
396
156816
62099136
19.8997
7.-3434
347
120409
41781923
18.6279
7.0271
397
157609
62570773
19.9249
7-3496
348
121104
42144192
18.6548
7-0338
398
158404
63044792
19.9499
7.3558
349
121801
42508549
18.6815
7.0406
399
159201
63521199
19.9750
7.3619
275
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 400 TO 499.
No.
Square.
Cube.
ISq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
400
160000
64000000
2O.OOOO
7.3681
450
2O25OO
91125000
21.2132
7.6631
401
160801
64481201
20.0250
7-3742
451
203401
9I73385I
21.2368
7.6688
402
161604
64964808
20.0499
7-3803
452
204304
92345408
21.2603
7.6744
4°3
162409
65450827
20.0749
7.3864
453
205209
92959677
21.2838
7.6801
404
163216
65939264
20.0998
7-3925
454
206116
93576664
21.3073
7-6857
405
164025
66430125
20.1246
7.3986
455
207025
94196375
21.3307
7.6914
406
164836
66923416
20.1494
7.4047
456
207936
94818816
21.3542
7.6970
407
165649
67419143
20.1742
7.4108
457
208849
95443993
21.3776
7.7026
408
166464
67917312
20.1990
7.4169
458
209764
96071912
21.4009
7.7082
409
167281
68417929
20.2237
7.4229
459
2Io68l
96702579
21.4243
7-7I38
410
l68lOO
68921000
20.2485
7.4290
460
2Il6oo
97336000
21.4476
7-7I94
411
168921
69426531
20.27*31
7-4350
461
212521
97972181
21.4709
7.7250
412
169744
69934528
20.2978
7.4410
462
213444
98611128
21.4942
7.7306
413
170569
70444997
20.3224
7.4470
463
214369
99252847
21.5174
7.7362
414
171396
70957944
20.3470
7-4530
464
215296
99897344
21.5407
7.7418
415
172225
7H73375
20.3715
7-4590
465
216225
100544625
21.5639
7-7473
416
173056
71991296
20.3961
7.4650
466
217156
101194696
21.5870
7-7529
417
173889
72511713
20.4206
74710
467
218089
101847563
2 1. 6lO2
7-7584
418
174724
73034632
20.4450
74770
468
219024
102503232
21.6333
7.7639
419
I7556I
73560059
20.4695
7.4829
469
219961
103161709
21.6564
7-7695
420
176400
74088000
20.4939
7.4889
470
220900
103823000
21.6795
7-7750
421
177241
74618461
20.5183
7.4948
471
221841
104487111
2I.7O25
7-7805
422
178084
75I5H48
20.5426
7-5007
472
222784
105154048
21.7256
7.7860
423
178929
75686967
20.5670
7.5067
473
223729
105823817
21.7486
7-79I5
424
179776
76225024
20.5913
7.5126
474
224676
106496424
21.7715
7.7970
425
180625
76765625
20.6155
7-5I8S
475
225625
107171875
21.7945
7.8025
426
181476
77308776
20.6398
7-5244
476
226576
107850176
2I.8I74
7.8079
427
182329
77854483
20.6640
7-5302
477
227529
I0853I333
21.8403
7-8i34
428
183184
78402752
20.6882
7-536I
478
228484
109215352
21.8632
7.8188
429
184041
78953589
20.7123
7.5420
479
229441
109902239
2I.886I
7.8243
43°
184900
79507000
20.7364
7-5478
480
230400
110592000
21.9089
7.8297
43i
185761
80062991
20.7605
7-5537
481
231361
111284641
21.9317
7-8352
432
186624
80621568
20.7846
7-5595
482
232324
111980168
21-9545
7.8406
433
187489
81182737
20.8087
7-5654
483
233289
112678587
21.9773
7.8460
434
188356
81746504
20.8327
7.5712
484
234256
113379904
22.0000
7-85I4
435
189225
82312875
20.8567
7-5770
485
235225
114084125
22.0227
7.8568
436
190096
82881856
20.8806
7.5828
486
236196
114791256
22.0454
7.8622
437
190969
83453453
20.9045
7.5886
487
237169
115501303
22.0681
7.8676
438
191844
84027672
20.9284
7-5944
488
238144
116214272
22.0907
7.8730
439
192721
846045 19
20.9523
7.6001
489
239121
116930169
22.1133
7.8784
440
193600
85184000
20.9762
7.6059
490
24OIOO
117649000
22.1359
7-8837
441
194481
85766121
2I.OOOO
7.6117
491
241081
118370771
22.1585
7.8891
442
195364
86350888
2I.O238
7.6174
492
242064
119095488
22.1811
7.8944
443
196249
86938307
21.0476
7.6232
493
243049
119823157
22.2036
7.8998
444
197136
87528384
2I.O7I3
7.6289
494
244036
120553784
22.2261
7-9051
445
198025
88121125
2I.O95O
7-6346
495
245025
121287375
22.2486
7-9105
446
198916
88716536
2I.II87
7.6403
496
246016
122023936
22.2711
7-9158
447
199809
89314623
21.1424
7.6460
497
247009
122763473
22.2935
7.9211
448
200704
89915392
21. l66o
7-6SI7
498
248004
123505992
22.3159
7.9264
449
20l6oi
90518849
21.1896
7-6574
499
249001
124251499
22.3383
7-93I7
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 500 TO 599.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
500
2SOOOO
125000000
22.3607
7-9370
550
302500
166375000
23-452I
8.1932
Sol
25IOOI
125751501
22.3830
7-9423
551
303601
167284151
23-4734
8.1982
502
252004
1 26506008
22.4054
7-9476
552
304704
168196608
23-4947
8.2031
503
253009
127263527
22.4277
7.9528
553
305809
169112377
23.5160
8.2081
504
254016
128024064
22.4499
7.9581
554
306916
170031464
23.5372
8.2130
s°5
255025
128787625
22.4722
7-9634
555
308025
170953875
23-5584
8.2180
506
256036
129554216
22.4944
7.9686
556
309136
171879616
23-5797
8.2229
507
257049
130323843
22.5167
7-9739
557
310249
172808693
23.6008
8.2278
508
258064
131096512
22.5389
7.9791
558
3"364
173741112
23.6220
8.2327
509
259081
131872229
22.5610
7-9843
559
312481
174676879
23.6432
8.2377
Sio
260100
132651000
22.5832
7-9896
560
313600
175616000
23.6643
8.2426
Si*
26II2I
133432831
22.6053
7.9948
561
314721
176558481
23-6854
8.2475
S'2
262144
134217728
22.6274
8.0000
562
315844
177504328
23-7065
8.2524
513
263169
135005697
22.6495
8.0052
563
316969
178453547
23.7276
8.2573
5'4
264196
135796744
22.6716
8.0104
564
318096
179406144
23.7487
8.2621
5»S
265225
136590875
22.6936
8.0156
565
319225
180362125
23.7697
8.2670
516
266256
137388096
22.7156
8.0208
566
320356
181321496
23.7908
8.2719
Si7
267289
138188413
22.7376
8.0260
567
321489
182284263
23.8118
8.2768
5i8
268324
138991832
22.7596
8.0311
568
322624
183250432
23.8328
8.2816
519
269361
139798359
22.7816
8.0363
569
323761
184220009
23.8537
8.2865
520
270400
140608000
22.8035
8.0415
570
324900
185193000
23.8747
8.2913
521
271441
141420761
22.8254
8.0466
571
326041
186169411
23.8956
8.2962
522
272484
142236648
22.8473
8.0517
572
327184
187149248
23.9165
8.3010
S23
273529
143055667
22.8692
8.0569
573
328329
188132517
23-9374
8-3059
524
274576
143877824
22.8910
8.0620
574
329476
189119224
23-9583
8.3107
525
275625
144703125
22.9129
8.0671
575
330625
190109375
23-9792
8.3155
526
276676
I4553I576
22.9347
8.0723
576
331776
191102976
24.0000
8.3203
527
277729
146363183
22.9565
8.0774
577
332929
192100033
24.0208
8.3251
528
278784
I47I97952
22.9783
8.0825
578
334084
193100552
24.0416
8.3300
529
279841
148035889
23.OOOO
8.0876
579
335241
194104539
24.0624
8.3348
'53°
280900
148877000
23.0217
8.0927
580
336400
195112000
24.0832
8.3396
S3i
281961
149721291
23-0434
8.0978
58i
337561
196122941
24.1039
8-3443
532
283024
150568768
23.0651
8.1028
582
338724
197137368
24.1247
8.3491
533
284089
I5HI9437
23.0868
8.1079
583
339889
198155287
24.1454
8-3539
534
285156
152273304
23.1084
8.1130
584
341056
199176704
24.1661
8.3587
535
286225
I53I30375
23.1301
8.1 180
585
342225
200201625
24.1868
8.3634
536
287296
153990656
23.1517
8.1231
586
343396
201230056
24.2074
8.3682
537
288369
I548S4I53
23-1733
8.1281
587
344569
202262003
24.2281
8.3730
538
289444
155720872
23.1948
8.1332
588
345744
203297472
24.2487
8-3777
539
290521
156590819
23.2164
8.1382
589
346921
204336469
24.2693
8.3825
54°
291600
157464000
23-2379
8.1433
590
348100
205379000
24.2899
8.3872
54i
292681
158340421
23.2594
8.1483
591
349281
206425071
24.3105
8.3919
542
293764
159220088
23.2809
8-1533
592
350464
207474688
24.3311
8.3967
543
294849
160103007
23-3024
8.1583
593
351649
208527857
24.3516
8.4014
544
295936
160989184
23.3238
8.1633
594
352836
209584584
24.3721
8.4061
545
297025
161878625
23.34?2
8.1683
595
354025
210644875
24.3926
8.4108
546
298116
162771336
23.3666
8.1733
596
355216
211708736
24.4131
8.4155
547
299209
163667323
23.3880
8.1783
597
356409
212776173
244336
8.4202
548
300304
164566592
23.4094
8.1833
598
357604
213847192
24.4540
8.4249
549
301401
165469149
234307
8.1882
599
358801
214921799
24-4745
8.4296
277
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 600 TO 699.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
6dO
360000
216000000
24.4949
8-4343
650
422500
274625000
25-495I
8.6624
60 1
361201
217081801
24-5I53
8.4390
651
423801
27S89445I
25 5H7
8.6668
602
362404
218167208
24-5357
8-4437
6S2
425104
277167808
25 5343
8.6713
603
363609
219256227
24.5561
8.4484
653
426409
278445077
25-5539
8.6757
604
364816
220348864
24.5764
8-4530
654
427716
279726264
25-5734
8.6801
605
366025
221445125
24.5967
8-4577
655
429025
281011375
25.5930
8.6845
606
367236
222545016
24.6171
8.4623
656
430336
282300416
25.6125
8.6890
607
368449
223648543
24-6374
8.4670
657
431649
283593393
25.6320
8-6934
608
369664
224755712
24.6577
8.4716
658
432964
284890312
25-65I5
8.6978
609
370881
225866529
24.6779
8-4763
659
434281
286191179
25.6710
8 7022
610
372100
226981000
24.6982
8.4809
660
435600
287496000
25 6905
8.7066
611
373321
228099131
24.7184
8.4856
661
436921
288804781
25.7099
8 7110
612
374544
229220928
24.7386
8.4902
662
438244
290117528
25.7294
8.7IS4
613
375769
230346397
24.7588
8.4948
663
439569
291434247
25.7488
8.7198
614
376996
23H75544
24.7790
8-4994
664
440896
292754944
25.7682
8.7241
615
378225
232608375
24.7992
8.5040
665
442225
294079625
25.7876
8.7285
616
379456
233744896
24.8193
8.5086
666
443556
295408296
25.8070
8.7329
617
380689
234885II3
24-8395
8.5132
667
444889
296740963
25.8263
8-7373
618
381924
236029032
24.8596
8.5178
668
446224
298077632
25-8457
8.7416
619
383161
237176659
24.8797
8.5224
669
447S6I
299418309
25.8650
8.7460
620
384400
238328000
24.8998
8.5270
670
448900
300763000
25.8844
8.7503
621
385641
239483061
24.9199
8.5316
671
450241
302111711
25.9037
87547
622
386884
240641848
24.9399
8.5362
672
451584
303464448
25.9230
8.7590
623
388129
241804367
24.9600
8.5408
673
452929
304821217
25.9422
87634
624
389376
242970624
24.9800
85453
674
454276
306182024
25.9615
8.7677
625
390625
244140625
25.0000
85499
675
455625
307546875
25.9808
8.7721
626
391876
245314376
25.0200
8-5544
676
456976
308915776
26.0000
8.7764
627
393129
246491883
25.0400
8-5590
677
458329
310288733
26.0192
8.7807
628
394384
247673152
25.0599
8-5635
678
459684
311665752
26.0384
87850
629
395641
248858189
25.0799
8.5681
679
461041
313046839
26.0576
8.7893
630
396900
250047000
25.0998
8.5726
680
462400
314432000
26.0768
8-7937
631
398161
251239591
25.1197
8-5772
68 1
463761
315821241
26.0960
8.7980
632
399424
252435968
25.1396
8.5817
682
465124
317214568
26.1151
8.8023
633
400689
2S3636I37
25-I595
8.5862
683
466489
318611987
26.1343
8.8066
634
401956
254840104
25-I794
8.5907
684
467856
320013504
26.1534
8.8109
635
403225
256047875
25.1992
85952
685
469225
321419125
26.1725
8.8152
636
404496
257259456
25.2190
8-5997
686
470596
322828856
26.1916
8.8194
637
405769
258474853
25.2389
86043
687
471969
324242703
26.2107
8.8237
638
407044
259694072
25 2587
86088
688
473344
325660672
26.2298
8.8280
639
408321
260917119
25.2784
86132
689
474721
327082769
26.2488
8.8323
640
409600
262144000
25.2982
86177
690
476100
328509000
26.2679
8.8366
641
410881
263374721
25.3180
8.6222
691
477481
329939371
26.2869
8.8408
642
412164
264609288
25-3377
8.6267
692
478864
331373888
26.3059
8.8451
643
413449
265847707
25-3574
8.6312
693
480249
332812557
26.3249
8.8493
644
4H736
267089984
25-3772
8-6357
694
481636
334255384
26.3439
8.8536
645
416025
268336125
25 3969
8.6401
695
483025
335702375
26 3629
8.8578
646
417316
269586136
25.4165
8.6446
696
484416
337153536
26.3818
88621
647
418609
270840023
25 4362
8 6490
697
485809
338608873
264008
8.8663
648
419904
272097792
254558
86535
698
487204
340068392
26.4197
8.8706
649
421201
273359449
25-4755
8.6579
699
488601
341532099
26.4386
8.8748
278
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 700 TO 799.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
700
490000
343000000
26.4575
8.8790
750
562500
421875000
27.3861
9.0856
701
491401
344472101
26.4764
8.8833
751
564001
423564751
27.4044
9.0896
702
492804
345948408
26.4953
8.8875
752
565504
425259008
27.4226
9-0937
703
494209
347428927
26.5141
8.8917
753
567009
426957777
27.4408
9-0977
704
495616
348913664
26.5330
8.8959
754
568516
428661064
27.4591
9.1017
70S
497025
350402625
26.5518
8.9001
755
570025
430368875
27-4773
9.1057
706
498436
351895816
26.5707
8.9043
756
57IS36
432081216
27-4955
9.1098
707
499849
353393243
26.5895
8.9085
757
573049
433798093
27.5136
9.1138
708
501264
354894912
26.6083
8.9127
758
574564
4355I95I2
27.5318
9.1178
709
502631
356400829
26.6271
8.9169
759
576081
437245479
27.5500
9.I2I8
710
504100
357911000
26.6458
8.9211
760
577600
438976000
27.5681
9.1258
711
505521
3S942543I
26.6646
8.9253
761
579I2I
440711081
27.5862
9.1298
712
506944
360944128
26.6833
8.9295
762
580644
442450728
27.6043
9-I338
713
508369
362467097
26.7021
8-9337
763
582169
444194947
27.6225
9.1378
7H
509796
363994344
26.7208
8.9373
764
583696
445943744
27.6405
9.1418
715
5II22S
365525875
26.7395
8.9420
765
585225
447697125
27.6586
9-I458
716
512656
367061696
26.7582
8.9462
766
586756
449455096
27.6767
9.1498
717
514089
368601813
26.7769
8.9503
767
588289
451217663
27.6948
9-1537
7l8
515524
370146232
26.7955
8-9545
768
589824
452984832
27.7128
9-1577
719
516961
371694959
26.8142
8.9587
769
591361
454756609
277308
9.1617
720
518400
373248000
26.8328
8.9628
770
592900
456533000
27.7489
9-I6S7
721
519841
374805361
26.8514
8.9670
77i
594441
458314011
27.7669
9.1696
722
521284
376367048
26.8701
8.9711
772
595984
460099648
277849
9.1736
723
522729
377933067
26.8887
8.9752
773
597529
461889917
27.8029
9-1775
724
524176
379503424
26.9072
8.9794
774
599076
463684824
27.8209
9.1815
725
525625
381078125
26.9258
8.9835
775
600625
465484375
27.8388
9.1855
726
527076
382657176
26.9444
8.9876
776
602176
467288576
27.8568
9.1894
727
528529
384240583
26.9629
8.9918
777
603729
469097433
27.8747
9-1933
728
529984
385828352
26.9815
8.9959
778
605284
470910952
27.8927
9-1973
729
53I44I
3874*20489
27.0000
9.0000
779
606841
472729139
27.9106
9-2OI2
73°
S32QOO
389017000
27.0185
9.0041
780
608400
474552000
27.9285
9.2052
73i
534361
390617891
27.0370
9.0082
781
609961
476379541
27.9464
9.2091
732
535824
392223168
27-0555
90123
782
611524
478211768
27.9643
9.2130
733
537289
393832837
27.0740
9.0164
783
613089
480048687
27.9821
9.2170
734
538756
395446904
27.0924
9.0205
784
614656
481890304
28.OOOO
9.2209
735
540225
397065375
27.1109
9.0246
785
616225
483736625
28.0179
9.2248
736
541696
398688256
27.1293
9.0287
786
617796
485587656
28.0357
9.2287
737
543169
4003I5S53
27.1477
9.0328
787
619369
487443403
28.0535
9.2326
738
544644
401947272
27.1662
9.0369
788
620944
489303872
28.0713
92365
739
546l2I
403583419
27.1846
9.0410
789
622521
491169069
28.0891
9.2404
740
547600
405224000
27.2029
9.0450
790
624100
493039000
28.1069
9.2443
74i
549081
406869021
27.2213
9.0491
791
625681
4949I367I
28 1247
9.2482
742
550564
408518488
27 2397
9-0532
792
627264
496793088
28.1425
9.2521
743
552049
410172407
27.2580
9.0572
793
628849
498677257
28.1603
9.2560
744
553536
411830784
27.2764
9-0613
794
630436
500566184
28.1780
9-2599
745
555025
413493625
27.2947
9.0654
795
632025
502459875
28.1957
9.2638
746
556516
415160936
27.3130
9.0694
796
633616
504358336
28.2135
9.2677
747
558009
416832723
27-33I3
9-0735
797
635209
506261573
28.2312
9.2716
748
559504
418508992
27.3496
9-0775
798
636804
508169592
28.2489
9-2754
749
561001
420189749
27.3679
9.0816
799
638401
510082399
28.2666
9.2793
279
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS FROM 800 TO 899.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
800
640000
512000000
28.2843
9.2832
850
722500
614125000
29.1548
9.4727
801
641601
513922401
28.3019
9.2870
851
724201
616295051
29.1719
9.4764
802
643204
515849608
28.3196
9.2909
8S2
725904
618470208
29.1890
9.4801
803
644809
517781627
28.3373
9.2948
853
727609
620650477
29.2062
9.4838
804
646416
519718464
28.3549
9.2986
854
729316
622835864
29.2233
94875
805
648025
521660125
28.3725
9.3025
855
731025
625026375
29.2404
9.4912
806
649636
523606616
28.3901
9.3063
856
732736
627222016
29.2575
9-4949
807
651249
525557943
28.4077
9.3102
857
734449
629422793
29.2746
9.4986
808
652864
527514112
28.4253 .
9.3140
858
736164
631628712
29.2916
9.5023
809
654481
529475129
28.4429
9-3I79
859
737881
633839779
29.3087
9.5060
810
656100
531441000
28.4605
9.3217
860
739600
636056000
29.3258
9-5097
811
657721
5334"73I
28.4781
9-3255
861
741321
638277381
29.3428
9-5I34
812
659344
535387328
28.4956
9.3294
862
743044
640503928
29.3598
9-5I7I
813
660969
537367797
28.5132
9-3332
863
744769
642735647
29.3769
9.5207
814
662596
539353H4
28.5307
9-3370
864
746496
644972544
29-3939
9.5244
8i5
664225
541343375
28.5482
9.3408
865
748225
647214625
29.4109
9.5281
816
665856
543338496
28 5657
9-3447
866
749956
649461896
29.4279
9-53I7
817
667489
S453385I3
28.5832
9-3485
867
751689
651714363
29.4449
9-5354
818
669124
547343432
28.6007
9-3523
868
753424
653972032
29.4618
9-5391
819
670761
549353259
28.6182
9-356I
869
755i6l
656234909
29.4788
9-5427
820
672400
551368000
28.6356
9-3599
870
756900
658503000
29.4958
9.5464
821
674041
553387661
28.6531
9-3637
871
758641
6607763 1 1
29.5127
9-5501
822
675684
555412248
28.6705
9-3675
872
760384
663054848
29.5296
9-5537
823
677329
557441767
28.6880
9-37I3
873
762129
665338617
29.5466
9-5574
824
678976
559476224
28.7054
9-3751
874
763876
667627624
29-5635
9.5610
825
680625
561515625
28 7228
9-3789
875
765625
669921875
29.5804
9-5647
826
682276
563559976
28.7402
9.3827
876
767376
672221376
29-5973
9-5683
827
683929
565609283
28.7576
9.3865
877
769129
674526133
29.6142
9-57I9
828
685584
567663552
28.7750
9.3902
878
770884
676836152
29.6311
9-5756
829
687241
569722789
28.7924
9.3940
879
772641
679151439
29.6479
9-5792
830
688900
571787000
28.8097
9-3978
880
774400
681472000
29.6648
9-5828
831
690561
573856191
28.8271
9.4016
88 1
776161
683797841
29.6816
9.5865
832
692224
575930368
28.8444
9-4053
882
777924
686128968
29.6985
9.5901
833
693889
578009537
28.8617
9.4091
88.3
779689
688465387
29-7I53
9-5937
834
69SSS6
580093704
28.8791
9.4129
884
781456
690807104
29.7321
9-5973
835
697225
582182875
28.8964
9.4166
885
783225
693I54I25
29-7489
9.6010
836
698896
584277056
28.9137
9.4204
886
784996
695506456
29.7658
9.6046
837
700569
586376253
28.9310
9.4241
887
786769
697864103
29 7825
9.6082
838
702244
588480472
28.9482
9.4279
888
788544
700227072
29.7993
9.6118
839
703921
590589719
28.9655
9.4316
889
790321
702595369
29.8161
9.6154
840
705600
592704000
28.9828
9-4354
890
792100
704969000
29.8329
9.6190
841
707281
594823321
29.0000
9-4391
891
793881
707347971
29.8496
9.6226
842
708964
596947688
29.0172
9.4429
892
795664
709732288
29.8664
9.6262
843
710649
599077107
29.0345
9.4466
893
797449
7I2I2I957
29.8831
9.6298
844
712336
601211584
29.0517
9-4503
894
799236
714516984
29.8998
9-6334
845
714025
603351125
29.0689
9.4541
895
801025
716917375
29.9166
9.6370
846
715716
605495736
29.0861
9-4578
896
802816
719323136
29-9333
9.6406
847
717409
607645423
29.1033
9.4615
897
804609
721734273
29.9500
9.6442
848
719104
609800192
29.1204
9.4652
898
806404
724150792
29.9666
9.6477
849
72O8OI
611960049
29.1376
9.4690
899
808201
726572699
29-9833
9-6513
280
TABLE 165.— Continued.
SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF NUMBERS PROM 900 TO 999.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
No.
Square.
Cube.
Sq. Root.
Cu. Root.
900
810000
729000000
3O.OOOO
9.6549
950
902500
857375000
3O.822I
9.8305
901
8II80I
731432701
30.0167
9-6585
951
904401
860085351
30.8383
9.8339
902
813604
733870808
30.0333
9.6620
952
906304
862801408
30.8545
9-8374
903
815409
736314327
30.0500
9.6656
953
908209
865523177
30.8707
9.8408
904
817216
738763264
30.0666
9.6692
954
910116
868250664
30.8869
9.8443
90S
819025
741217625
30.0832
9.6727
955
912025
870983875
30.9031
9-8477
906
820836
743677416
30.0998
9.6763
956
913936
873722816
30.9192
9.8511
907
822649
746142643
30.1164
9.6799
957
915849
876467493
30.9354
9.8546
908
824464
748613312
30.1330
9-6834
958
917764
879217912
30.95 '6
9.8580
909
826281
75 1089429
30.1496
9.6870
959
919681
881974079
30.9677
9.8614
910
828100
753571000
30.1662
9.6905
960
921600
884736000
30.9839
9.8648 '
911
829921
75605803 i
30.1828
9.6941
961
923521
887503681
31.0000
9.8683
912
831744
758550528
30.1993
9.6976
962
925444
$90277 I 28
31.0161
9.8717
9'3
833569
761048497
30.2159
9.7012
963
927369
893056347
31.0322
9.8751
914
835396
763551944
30.2324
9.7047
964
.929296
895841344
31.0483
9.8785
9IS
837225
766060875
30.2490
9.7082
965
931225
898632125
31-0644
9.8819
916
839056
768575296
30.2655
9.7118
966
933156
901428696
3 1 .0805
9.8854
917
840889
771095213
30.2820
9.7I53
967
935089
90423 1063
31.0966
9.8888
918
842724
773620632
30.2985
9.7188
968
937024
907039232
31.1127
9.8922
919
844561
776151559
30.3150
9.7224
969
938961
909853209
31.1288
9.8956
920
846400
778688000
30.3315
9.7259
970
940900
912673000
31-1448
9.8990
921
848241
781229961
30.3480
9.7294
971
942841
915498611
31.1609
9.9024
922
850084
783777448
30.3645
9.7329
972
944784
918330048
31.1769
9.9058
923
851929
786330467
30.3809
9.7364
973
946729
921167317
31-1929
9.9092
924
853776
788889024
30.3974
9.7400
974
948676
924010424
31.2090
9.9126
925
855625
791453125
30.4138
9-7435
975
950625
926859375
31.2250
9.9160
926
857476
794022776
30.4302
9-7470
976
952576
929714176
31.2410
9.9194
927
859329
796597983
30.4467
9-7503
977
954529
932574833
31.2570
9.9227
928
861184
799178752
30.4631
9-7540
978
956484
935441352
31.2730
9.9261
929
863041
801765089
30.4795
9-7575
979
958441
938313739
31.2890
9.9295
93°
864900
804357000
30.4959
9.7610
980
960400
941192000
31.3050
9.9329
93i
866761
806954491
30.5123
9-7645
981
962361
944076141
31.3209
9.9363
•932
868624
809557568
30-5287
9.7680
982
964324
946966168
31.3369
9.9396
933
870489
812166237
30.5450
9-77I5
983
966289
949862087
3I-3528
9-9430
934
872356
814780504
30.5614
9.7750
984
968256
952763904
31.3688
9.9464
935
874225
817400375
30.5778
9-7785
985
970225
955671625
3L3847
9-9497
936
876096
820025856
30.5941
9.7819
986
972196
958585256
31.4006
9-9531
937
877969
822656953
30.6105
9-7854
987
974169
961504803
31.4166
9-9565
938
879844
825293672
30.6268
9-7889
988
976144
964430272
314325
9.9598
939
881721
827936019
30.6431
9.7924
989
978121
967361669
31.4484
9.9632
940
883600
830584000
30.6594
9-7959
990
980100
970299000
3I-4643
9-9666
941
885481
833237621
30.6757
9-7993
991
982081
973242271
31.4802
9.9699
942
887364
835896888
30.6920
9.8028
992
984064
976191488
31-4960
9-9733
943
889249
838561807
30.7083
9-8063
993
986049
979146657
31.5119
9.9766
944
891136
841232384
30.7246
9.8097
994
988036
982107784
3I-5278
9.9800
945
893025
843908625
30.7409
9.8132
995
990025
985074875
3I-5436
9-9833
946
894916
846590536
30.7571
9.8167
996
992016
988047936
31-5595
9.9866
947
896809
849278123
30.7734
9.8201
997
994009
991026973
31-5753
9.9900
948
898704
851971392
30.7896
9.8236
998
996004
994011992
3I-59II
9-9933
949
900601
854670349
30.8058
9.8270
999
998001
997002999
3 1 .6070
9-9967
57
281
INDEX.
REFERENCES ARE TO PAGES IN PART I.
PAGE
"A" Derrick 468, 472
Alnitiiu-nts, Bridge, 245, 250, 252, 253, 254,
255, 256, 267
Aggregate for concrete 241, 272
Algebraic moments 561, 562, 563
Algebraic resolution 552, 558, 559, 560
Alloy steels 487, 495, 519
Alternate stresses 57, 141, 206, 209
Allowable pressures on foundations, 236, 249,
250, 386
Allowable pressures on masonry, 56, 75, 236,
249. 379
Allowable stresses, 56, 57, 80, 105, 141, 209,
362, 379- 382
in bearing plates, 56, 75,
236, 379
" cast iron 65, 104
" concrete 520, 521
" highway bridges, 117, 141
" hoisting rope, 342, 443,
444
" manila rope 443
" mill buildings 8, 57
" office buildings. . .79, 105
" " railway bridges, 173, 205,
209
" " rivets 370
" stand-pipes 387, 382
" steel 495
" steel reinforcement. . 521
" steel tanks 379
" timber, 58, 138, 204, 208,
298
" wire rope. . .342, 443, 444
" wrought-iron, 65, 104, 495
Allowance .or draw 223
Aluminum 519
Aluminum bronze 520
Anchors 62, 94, 95, 144, 212
Anchors, Wall 105
Anchor bolts 105, 147, 381, 484
Anchorage 144, 381, 484
Angle of friction, 236, 300, 301, 302, 311, 312
Angle of repose, 236, 300, 301, 302, 311, 312,
321
Angle connections, 65, 145, 404, 407, 408, 413,
430, 574
Angle connections, Cost of 430
Angle, Detail of 409
Angle strut 409, 575, 576
Angles 410, 416, 417, 418, 427
Angles fastened by both legs 141, 207
SS3
Angles, Minimum . .60, 142, 143, 206, 21 1, 223
Angles, Overrun of 221, 411
Angles, Starred 578
Angles in tension 573
Annealing 63, 146, 214, 217, 480
Anthracite coal bin 300, 301, 302, 304
Anthracite coal, Weight of 311
Anti-condensation lining, 28, 29, 31, 52, 53, 59,
439
Anti-condensation lining, Cost of 439
Arbitration bar 489, 490
Arch 266
Arch, Masonry 271
Arch, Roof 13, 14
Arris 267
Ash bin 300, 301, 302, 306
Ashes, Weight of 69, 300, 31 1
Ashlar 267
Ashlar masonry 270
Ashlar stone 269
Asbestos 28, 29, 52, 53, 59, 439
Asbestos, Cost of 439
Asbestos covered steel sheets 28
Asphalt 178, 181, 182, 516
Asphalt paint 516
Auger 461
Average cost of steal 433
Backing 267, 270, 271
Backing-out punch 452, 462
Ballasted floor 178, 194
Ballasted floor trestle 284
Ballast, Weight of 204, 208
Baltimore bridge truss 109, 560, 566
Bars. 62, 416, 426
Bars, Lacing 414, 598
Minimum 60, 142, 207
Shop cost of 431
Bases, Cast-iron column 92, 93, 94, 104
Bases, Column 104
Base plates 62
Batten plates 61 , 143, 21 1
Batter 249, 267, 277
Batter of columns 380
Batter pile 279
Bay 3
Beam bridges, 108, no, 117, 118, 119, 120, 121,
149
Beam bridges, Weight of 113
Beams 404, 407, 408, 416, 418
Deflection of 533
Details of 82, 407, 408
884
INDEX.
Beams, Flexure in 533
Reinforced concrete 546
Rolled 58, 104, 142
Separators for 83
Shop cost of 43°
Shear in 533. 542
Stresses in, 529, 536, 537, 538, 539, 540, 541,
543. 544. 545
Bearing pile 279
Bearing plate 75. 379. 586
Bearing power of piles 75, 477
Becket 448, 480
Bed 267
Bed plates 66, 144, 146, 217, 484
Bench wall 267
Bending moment 160, 529
Bending moment tables 166, 167
Bending moments in railway bridges, 163, 164,
165, 166, 167, 171, 172
Bending stresses in wire rope 344
Bent 277
Bent, Transverse 12, 556
Bessemsr pig iron 487
Bessemer steel 487, 494, 497, 507
Bethlehem H-columns 405
Bevels 41 1
Beveled washer 571
Bill of castings for Howe truss 289
malarial 389, 425
rivets 400
timber 288, 473
Billet-steel reinforcement 507
"Bite" of a line 481
Bin gates 362
Bins 299, 319, 362
Bins, Grain 319
Bins, Cost of 429, 433, 434, 436
Bins, Cost of erection of 436
Blister steel 487, 493
Blocks for Manila rope 446, 448, 450
Blocks for wire rope 447, 449
Boiler steel 431, 505
Bolsters 144, 212
Bolts, 65, 95, 143, 145, 211, 216, 287, 297, 458
Boits, Anchor, see "Anchor bolts"
Bolts, Falsework 458
Bolts, Turned 65, 145
Bond 267, 270, 521, 526, 547
Bond in concrete 521, 526, 547
Boom 468, 469, 470, 471
Brace, Shop details of 394
Bracing, 4, 9, 18, 55, 62, 97, 98, 100, 105, 137,
212, 223, 361, 381
Lateral 62, 137
Transverse 9, 18, 62, 137, 223, 361
Weight of 4
Wind 55, 62, 98, 100, 101 , 102
Bracket 97
Brass 520
Brass, Weight of 69
Break-water 249
Brick 428
Brick floor 8, 34
Brick, Weight of 69, 237
Bridge abutments, 245, 250, 252, 253, 254, 255
clearances 137, 200
erection 395, 429, 441, 485
floors, U2h, 178, 179, 180, 181, 182
piers 245, 255, 257, 258, 259, 260
Signal 157
span, Length of 137
specifications 137, 185, 208
shop cost of 434
trusses 107, 137, 149, 401
trusses, Stresses in 558, 569
Steel for 499
Timber 277, 285
Types of 137, 207
Waterway for 250
Weight of 112, 150, 151, 157
Bronze 520
Build 267
Building columns 19, 20, 21, 84, 93
Floor plan for 8l
Foundations for 94
Height of 55
materials 69
paper 28
Buildings, Specification for 55, 103, 497
Steel office 69
Waterproofing 76
Weight of tall steel 70
Buckle plates 132, 138, 315, 359, 360
Bulb angles 418
Built-up tension members 574
Bulkhead 277, 297
Bull wheel 469
Bunkers, Suspension 309, 315, 316
Burlap 178 179, 180, 181, 182, 243
Caisson 94
Cages 346, 362
Cain's formulas for retaining walls 230
Calculation of stresses in tall buildings. ... 76
Calculation of stresses in highway bridges, 117,
558.
Calculation of stresses in railway bridges. . 164
Camber 14, 144, 206, 207, 212, 213
Camel back truss 109, 558, 567
Cant hook 458
Cantilever bridge no
Cantilever beam 536
Cap 277, 279, 296
Capacity of coal tipples 355, 356
Car puller 337
Car, Push 459
Carbon 488, 494, 514
Carbon steel 149, 152, 173
Card of mill extras . .430, 431
Carrying hook 458
Cast iron 65, 104, 215, 297, 384, 487, 488
column bases 92, 93, 94
details 286, 287
separators 83
Weight of 69
Castings, Steel 63, 66, 510
Caulking 380, 386, 387
plates 380
1NDI X.
885
Caulking, tool 462
:n paint 5l(>
('cm. -lit, Speeili.aii.in-> I'or 522
( 't-iil' r .if gravity 535
(Vnt i-ring 267
( Vnt rif u^al force 140, 205, 209
( Vnt n >i< 1 535
Ch.iins 451
Annealing 480
• of 440
Channels 417, 418, 427
Channels, Separators for 83
( 'hords, Upper 6l
Chords for railway bridge 175, 176
Chords, Shop cost of 434
Chrome steel 495
Chromium-nickel steel 495
Circular ends 221
girder 367
steel bin 313, 317, 326, 333
ventilator 29, 59, 423, 427
( 'lamp 267
Classification of bars 431
material 426
Claw bar 453
Clearance diagram 200
for members 401
standards 412, 413
of riveted members 219, 412, 413
Clerestory 3
Clevis 571, 572
Clinch rivets 19, 23
Closing rivets 52
Coal bin 300, 301, 302, 303, 304, 318
breakers 361
bunkers 315, 316
Friction of 312
tar paint 516
tipples 339, 352, 361, 363, 436
tipples, Cost of 436
tipples, Shaking equipment for. 353, 357, 358
washers 361
Weight of 311
Coefficient of friction 236, 321
Coke bins 312
Coke, Weight of 311
Cold cutter 452
Co'd twisted bars 508
Columns, 15, 61, 85, 93, 104, 176, 403, 404,
405, 406, 426, 526, 547, 579, 590
Column bases 92, 93, 94, 104
Column bases, Pressure on 56
Column, Details of, 86, 87, 88, 89, 90, 91, 374
Column formulas 79, 80, 533
Column, Length of 79, 80, 8 1
Column, Loads on 74, 104
Column schedule 85, 94, 402, 404
Column splices 90, 91
Columns, Mill building 19, 20, 21, 54
Columns, Office building 84, 98, 102
Columns, Shop cost of 433
Columns, Stresses in 368, 521
Columns, Timber 58, 298
Columns, Weight of 4
PAGE
Combination highway bridge 295, 435
Combined stresses. . 57, 141, 209, 531, 534, 587
Compressivc stress 57, 527, 531
Compression members 61, 141, 143
Compression flanges 142
Compression formulas 79
Concrete 56, 266, 428
Abutment 245
Aggregage 241
Details of construction of 275
floor 8, 32, 33, 54, 132, 179, 180
in foundations 386
Ingredients in 237
Mixing 240
Proportions of 273
retaining walls 234, 238, 239, 241
Specifications for 272
Strength of 520
Weight of 69, 204, 208, 237, 381
Connection ang.es, 65, 145, 404, 407, 408, 413,
574, 595
Conductors 423, 427
Connections 60
Connections, Clearance for 412, 413
Connections, Field 216
Floorbeam 183, 184, 185
Strength of 142
Shop cost of 430
Connecting bar 453, 461
Conductors 26, 59
Contents of abutments 254, 255
Contents of piers 258, 259
Contents of retaining walls 240
Continuous beams 543, 544, 545
Continuous sash 42
Conventional signs for materials 399
Conventional signs for rivets 398
Conveyors 334, 335
Cooper's Conventional loading, 151, 159, 162,
163, 164, 165, 166, 167, 168, 172
Cooper's abutments 254
Cooper's piers 255, 261
Cooper hitch 571
Cop3.
407
Cope chisel 453
Coping 267, 270
Coulomb's theory 225, 227
Copper 519
rivets 23, 52
steel 495
Weight of 69
Corner finish 59
Cornice 26, 52, 59
Corrosion of iron or steel 513
Corrugated steel, 15, 52, 56, 59, 320, 423, 427,
456
plans 51
roofing 27, 28, 51, 586
Cost of 429, 439
Details of 22, 23, 24
door 44
fastenings 19
Minimum thickness of 8
Safe loads for 22
886
INDEX.
Corrugated steel, shear 456, 460
tools 456
Weight of 4, 25
Corrugated iron floor 34
Cost of drafting 429
erection 347. 436. 437, 43®
erection of tubular piers 437
erection of steel head frame 347
floors 439
laying corrugated steel 439
material 428, 440
mill extras 430
painting 430, 433, 438
roofing 439
riveting. 436, 437, 438
tar and gravel roofing 32, 439
tile roofing 31
steel grain elevators 337
structural steel 425, 428, 429
Counters 142, 206, 210
Counterbalanced windows 39
Counterfort retaining wall 239
Couple 527
Course 267
Coursed 267
Cover plates 220
Crab 442, 443
Cramps 267
Crane girders 54, 426, 542
Crane posts 61
Cross frame 224
Cross-eyed fuller 462
Cross-grain 278
Crow bar 453
Culvert 266, 271, 435
Culverts, Shop cost of 435
Culverts, Waterway for 250
Cuppers 453
Cutting to exact length 430
Cut-water 249
Curb 138
Cylinder piers 255, 260, 261, 265
Cylinder piers, Shop cost of 435
Dead loads, 55, 116, 139, 202, 204, 207, 208,
361
Dead loads of office buildings 70
Dead load stresses 553, 556
Dead man 470
Deck beams 418
Deck plate girders 400
Deck truss, Stresses in 566
Deep bins 311, 319, 325
Deflection of beams, 530, 533, 536, 537, 538,
539, 540, 541,. 543, 544, 545
Deformation 527, 532
Deformed bars 508, 509
Delta metal 520
Depth of bridge trusses 125
Depth of plate girders 210
Depth of trusses 210
Derrick car 470, 480, 481
Derrick crab 442
Derricks 480
Design of bearing plates 586
bins 313, 326
columns 579
end-post 587
floorbeam 590
I-beam 580
lacing bars 598
pins. . 584
plate girders 581
railway bridges 219
retaining walls 231, 232, 234
rollers 579
steel details 571
stand-pipes 381
Design drawings 421
Design for flexural stress 579
Detail notes 410
Details of angle struts 409
beams 82, 333, 407, 408
framework 85
bridges 119, 120, 175
columns, 19, 20, 21, 86, 87, 88, 89, 90, 91
Cost of 429
end-post 396
head frames 347, 348, 349, 350
office buildings 103
roof trusses, 16, 17, 18, 390, 391, 392, 393
stand-pipes 369, 371, 379
tanks 369
top chord 397
wall construction 96
wind bracing 98
Diagonal stresses '. 531
Diagonal tension 531
Diamond point 453
Dimension stone 267
Disc pile 279
Dolly 454, 455, 456, 461
Door 43, 54f 60, 329, 422, 428, 440
Door track 48
Dote 279
Dowel 268, 277
Draft 268
Drafting, Cost of 429
Drafting, Structural 389
Drainage table 251
Drainage for highway bridge floors ....... 138
Draw, Allowance for 223
Draw spans 157
Dressing stone 269
Drift bolt 277, 282, 283, 284, 297
Drift pin 386, 452, 462
Drifting 484
Duchemin's formula 5
Dumping devices 363
Dun's drainage table 251
Dry masonry 271
Earth, Weight of 69, 237
Eave strut 9, 23, 49, 50
Eave strut, Shop cost of 433
Eccentricity 222
Eccentric loads 142, 534
Eccentric riveted connections 595
INDEX.
ss7
PAGE
• inii- ilt-sii^n 135, 174
. I'l.m.-d 66, 145
•list. HUTS of rivets 6O, 143, 2IO
pl.iti-s 415, 420, 421, 422
iii-y of turklr 447, 451
Kl.ist icity 527
Kl.istir limit 496, 528
Klrrtrir railway bridges II2O, 139
Klr< trie light pole 136
(tors for grain bins 334
KK -v.itecl tanks 365, 379
Kllipsr of >t rcss 531
l-'.lon^.ition of steel 62, 63, 496
Klongation of wrought iron 491, 492, 496
Kn^ine service 483
Knuiiuvring materials 487
Hud bracing 212
End connections for I-beams 595
End connections for top chord 593
End-post, Bending in 222
Design of 587
Details of 196, 396
End shears 163, 164, 165
Kquivalcnt uniform loads 151, 159
Erection diagram 389, 395
plan for mill buildings 408
plan 400
Erection of armory 479
bridges 147, 437, 438, 441, 483
corrugated steel 439
head frames 363
plate girders 441
stand-pipes 386
steel 67, 100, 411, 441
steel frame buildings 436
tubular piers 437
Erection, Specifications for 483
Instructions for 479
Inspection of bridge 485
Erection tools 443, 448 to 467
Estimates 348, 425
Examples of abutments, 250, 252, 253, 254,
255, 256
bins 317
coal tipples 352
head frames 346
grain elevators 328
highway bridges, 127, 128, 129, 130, 131
office buildings 101
plate girders 184, 189, 190
railway bridges, 185, 191, 192, 193, 194,
196, 197, 198, 199
retaining walls 237
steel mill buildings, 48, 49, 50, 51, 52, 53, 54
Expansion, 104, 133, 144, 206, 211, 212, 423,
434
Expansion joints 243, 268, 382
Expansion rollers 579
Experiments on grain pressure 325
Extrados 268
Eye-bars, 62, 66, 144, 145, 207, 213, 216, 217,
222, 571, 573
Lye-bars, Shop cost of . . . • • 434
Stresses in 586
PAGE
Eye-bars, Tests 147, 218, 505
Weight of 573
Eye-bar hook 457
Fabrication of steel, Inspection 518
Face 268
Facing 268
Factor of safety 527
Factory ribbed glass 8, 41
Fall line ball 448
Fall lines 468, 469, 470, 471
Falsework 473, 476, 483
Cost of erection of 437
Falsework piles 281
Falsework plans 389
Falsework bolts 458
Fastening angles 141, 207
Fence 135, 136
Fence, Shop cost of 434
Felloe guard 134, 135, 136
Felt and asphalt 4
Field bolts 58, 143
Field connections 66, 67, 145, 216, 484
paint 516
rivets 58, 66, 146, 217, 400, 467
rivets, Number of 437, 438
riveting 106
Filler plates 65, 144, 145, 211, 216
Filler rings 143
Final set 268
Fink trusses 9, 10
Firebox steel 431
Fireproofing 69
Fireproof construction 69
Fish plate 277
Fixed beam 540
bearings 144
sash 41 , 42
Flange plates 60, 142
rivets 142, 210, 221
splices 220, 584
steel 43 1
Flashing, Stack 29
Flashing 52, 59, 427
Flat plates 313, 535
Flemish bond 267
Flexure 529
in beams 533
Flexure, Members in 579
Flexure and direct stress 534
Flo^s. 33, 34, 329, 439
Cost of 439
Highway bridge i
Live loads for 71,
Plank
for railway bridges 176, 194, 204, 208
Shop 8
Specifications for 32
Timber 35
Waterproofing bridge, 133, 178, 179, 180,
181, 182
Floor panels 99
Floor plans 81, 85, 99, 402, 403
Flooring, steel plate 34
888
INDEX.
PAGE
Floorbeam connection 59°
Floorbeam reactions 163, 164, 165
Floorbeam, Design of 59°
Floorbeams 82, 113, 212, 216, 222
Floorbeams for highway bridge 113, 138
Floorbeams for railway bridges . . 183, 184, 185
Floorbeams, Shop cost of . . , 434
Weight of in
Flush 268
Footing 268
Footwalks 137
Forces 527
Forked ends 211
Forms 237, 241, 243, 268, 274
Foundations, 53, 54, 56, 75, 95, 100, 104, 268,
334. 372, 386
Foundations, Pressure on, 232, 234, 236, 247,
248, 249, 250
Foundation plan 389
Frame trestle 277, 288
Framework of steel frame buildings, 9, 49, 53
Framework of office buildings 85
Freezing weather, Placing concrete in, 240, 243,
274
Freight 433
Freight rates 438
Friction, Coefficient of 236
Friction on bin walls 312
Friction of wheat 321
Frost-proofing 373, 381
Fuller . 462
Fuller's rule 240
Gallows frame . . . 472
Gantry traveler 472, 474, 475
Garners 337
Gaspipe, Cost of 440
Gates, Bin 362
Gin pole 468, 470, 480
Girders, Beam 404, 407, 408
Circular 367
Crane 54
Plate 57,58
Riveted 400, 403
Girder hook 457, 481
Girts.. 3, 9, 14, 50, 56, 62, 277, 297
Spacing of 59
Weight of 4
Glass 8, 36, 37, 38, 60
Glass roof tile 31
Glass, Weight of 69
Glazing 41
Grain elevator 319, 337, 433, 434
Grain bins 319, 325
Grain shovel 337
Goose neck 471, 480
Gordon's formula 80
Graphic moments 561
Graphic resolution 552, 558, 559
Graphite paint 67
Grillage 94
Grout 268
Guard rail 177, 277, 281, 284, 287, 297
Guard timbers 139, 277, 281
Gusset plate 219
Gutters 23, 26, 59, 423, 427
Guy derrick 468, 469, 472
Hacked bolt
Handle gouge 452,
Hammer
Hand holes
Hand gouge
Handrailing
Head frames 339, 346,
Head sheaves
Head works for mines
Heart wood
Heating shop buildings
Highway bridges
Highway bridge abutments
Highway bridges, Allowable stresses in, 115
Classes of
Combination
Examples of. . 122, 127, 128, 129, 130,
Erection of
Shop cost of
Field rivets in
Floors for '. .H2h, 132
Floorbeams for
Headroom for
Impact for i i2c
Joists and stringers for
Loads for i i2d,
Painting 146
Piers for
Plate girder
Railing for
Sidewalks for
Rollers for 133,
Spacing of trusses for
Specifications for.
Stresses in ...115,
Timber
Types of 107, 1 10,
Weight of
Header 268,
Hoist
Hoisting
Hoisting blocks 446, 447, 448, 449,
Hoisting engine 442,
Hoisting rope 341, 350, 360, 443, 444,
Hooks, Stresses in
Hopper bins 312, 316, 317,
Hot twisted bars
Howe truss 10, 109, 286, 287, 290,
Howe truss, Cost of metal in
Hub guard 134, 135,
Hutton's formula for wind pressure
Hyperbolic logarithms
95
462
279
222
452
137
436
363
339
278
8
107
256
, 141
137
295
147
435
437
,138
138
137
'138
II2g
, H7
261
122
137
137
135
137
137
557
292
137
in
270
443
339
450
443
480
533
3i8
509
291
436
136
5
322
I-Beams 427, 580
Impact 161, 204, 205, 208, 528, 529
impact on office buildings 72, 103
Impact formulas 161
Impact on highway bridges 117, 141
Impact on railway bridges. . 161, 204, 205, 208
Impact on timber 298
INDEX.
888
PACK
Imp.u t te-ts 162
Indirect splices 144, 211
Initial set 268
Inili.il stress 62, 207, 381
lns|>cetion of steel .it mill 215
brid^i' ere. tion 485
bridge material 217
1 67, 105, 146, 517, 518
I list met i< >ns for erection of structural steel, 479
estimating 426
inspection of steel 517
Intermediate sill 277
Intrados 268
Invoices 218
Iron, Corrosion of 513
Iron oxide 514
Iron details for Howe truss, 286, 287, 289, 291
ack stringers 277, 297
acks 459
anssen's solution for stresses in bins. .... 319
_ oints 66, 268
joints in concrete 275
joists for highway bridges 138
Ket chum's modified sawtooth roof, 9, n, 44, 48
Key wrench 455
Knee brace 97
Knot 278
Knots in manila rope 444, 445
Lacing bars, 61, 65, 143, 145, 211, 216, 414, 598
Lacing bars, Design of 598
Ladder 373, 374, 376, 377, 378, 381, 383
Lagging 268
Laitance 275
Lampblack 514
Landing stage 363
Laps of corrugated steel 59
Lateral bracing 62, 149, 223
connections 372, 373, 374
plate 571
pressure 321
Laterals 137
Lattice bars, see "Lacing bars"
Lead 519
Lead, Red 514
, Weight of 69
s 279
Leg bridge 108
Lxmgths of angles 417, 418
channels 418
I-Beams 418, 430, 431, 432
plates 418, 419, 420, 421, 422
of columns 79, 80
compression members, 61, 141, 209, 363,
379
span.. 55
Lettering shop drawings 398
Lewis 268
Lifting capacity of tackle 449, 450
List of drawings 389
•• erection tools 463, 464, 465, 466, 467
rivets 389
58
PAGE
Linseed oil 514
Live loads 70, 139
Live loads on columns 74, 104
floors 73
highways bridges 1 16
office-buildings 71, 72, 103
railway bridges 202, 205, 208
Live load stresses 563
Loads 55. 70, 73, 361
Minimum 7, 56, 74, 104
Snow 4, 72
Wind. 5, 72
Loads on bin walls 324
columns 74, 104
foundations 56, 75, 104, 236, 249
highway bridges H2d, H2g, 139, 140
masonry 56
office buildings 70, 103
piles , 57,477
railway bridges 151, 209
roofs 74
stand-pipes 382, 387
timber floors 35
Lock 268
Locks 270
Logarithms, Hyperbolic 322
Locomotives, Heaviest 154
Locomotives, Weight of 154, 205
Long rivets 143, 2 1 1
Longitudinal braces 296
forces 141
strut 277
X-brace 277
Loop bars 571, 572
Louvres, 3, 12, 24, 43, 44, 52, 59, 423, 427
Machinery loads 362
Manhole 378
Malleable castings 487, 488
Manila rope 440, 443, 480
Manganese 488, 494
Manganese Bronze 520
Manufacture of cast-iron 488
steel 493
wrought-iron 489
Marking diagram 395
Maul 452, 462
Masonry 56, 520
abutments, 245, 246, 250, 252, 253, 254, 255,
256
Classification of 266
Dressing of 266, 267
piers 261
plan 389
Pressure on, 56, 75, 104, 141, 209, 236, 542
retaining walls -234, 238
SpeciBcations for 269
Weight of 96
Mast 468, 469, 471
Mastic, Asphalt 181, 182
Material, Classification of 426
Conventional signs for 399
Engineering 487
Estimating 426
890
INDEX.
Material, Ordering 4*5. 4*6, 417
Weight of 69, 237
Maximum bending moments in beam, 160, 542
Maximum bending moments in bridges, 163,
164, 165
Maximum length of member, 61, 141, 209, 363,
379
diameter of rivet 143
stresses 160, 558
Merchandise, Weight of 73
Metal, Minimum thickness of 142, 210
Mill building columns 15, 19, 20, 21
Mill buildings, Cost of details of 429
Cost of 433
Design drawings for 421
Erection plans for 408
Erection of 441
Estimates for 425
Walls for. 7
Mill extras, Cost of 430, 431
Mill inspection of steel 146
Mill orders 67
Milling plates 432
Minimum angles 8, 60, 143, 206, 211, 223
bar 207
loads 56, 74, 104
thickness of corrugated steel 8
thickness of metal, 8, 105, 142, 210, 363, 380,
382, 387
sections 60
Mine buildings 8, 436
Misfits 484
Mixing concrete 240, 242, 274
Modulus of elasticity 528
Moments in continuous beams 544
Moments of forces. 527
Moments in railway bridges, 163, 164, 165,
171, 172, 174
Moment of inertia, 530, 535, 548, 549, 550, 551
Moment splices 220
Moment table 167
Monitor ventilator 3, 41, 43, 59
Mortar 268, 269
Muntin 38, 39, 40, 41, 42, 43
Nails, Cost of 440
Naperian logarithms 322
Natural bed , 268
Natural cement 522
Net sections 60, 61, 141, 206, 210, 220
Neutral axis 529
Neutral surface 529
Newel posts 135, 136
Nickel 519
Nickel steel 149, 152, 173, 495, 496, 502
Nigger head 442
Nuts, Pilot 66
Oblong steel pier 263, 265
Office buildings 69, 402
Calculation of stresses in 76
Columns for, 98, 102, 104, 402, 403, 404,
405, 406
Cost of 433, 436
Office buildings, Erection of 105, 441
Estimates for 426
Floorbeams for 99, 105, 403
Floor plans of 99, 402, 403
Foundations for 100
Loads on 70, 72, 103
Spandrel sections for 100
Specifications for 103
Oil paint 513
Oil tanks 386
Old man 456, 460
Open-hearth steel, 62, 487, 494, 497, 499, 502,
505, 507
Ordering material 415, 416, 417
Ore bins 318
pockets 313
Weight of 311
Out of wind 278
Overrun of angles 221, 222, 411
Packing block 277
pins 584
spool 277
Paint 207, 440, 513, 515
Paint, Amount of 440, 515
Cost of 435
Proportions of 515
Painting, 31, 67, 146, 147, 217, 329, 363, 386,
. 3.87, 43«, 484. 515
Painting, Cost of 438
Panel 3
Panels, Floor 99
Panel, Length of 135, 175
Parapet 268
Paving 268, 428
Pedestals, . 135, 144, 184, 186, 187, 188, 189,
190, 191, 193, 194, 197, 423, 424
Petit bridge truss 109, 558, 562, 564, 568
Phosphorus 62, 488, 494
Phosphor bronze. -. 520
Piers, Bridge 245, 248, 268
Pig iron 487
Piles 57, 279, 296, 476
Piles, Bearing power of 75
Specifications for 281
Pile driver 279, 477
foundations 94
trestles 277, 281, 284
Pipe, Design of 532, 534, 575
Pilot nuts 66, 146, 217, 467, 484
Pilot points 146, 217, 467, 484
Pins, 58, 61, 62, 66, 143, 146, 210, 211, 217, 219
Pins, Cost of 434
Design of 584
Pin holes 66, 146. 217
packing 219
plates 61, 143, 2il
Pin-connected trusses, 133, 191,
197, 402, 435
Pin maul 452
Pitch 3. 268
Pitch of roof 14, 30, 55
Pitch of rivets 60, 142, 143, 210
Pitch pockets 278
INDEX.
PACE
Pitch streaks 278
1'itclu-d 268
Pivoted windows 40
Pivoted sash 36, 37, 41
Placing concrete 240, 243, 274
Plans 55
Plans, Shop 67, 147, 218
Plans of structures 81, 85, 389
Planing 65
Planing edges 66
Planing metal 400
Plan, Floor 85
Plank, Floor II2k, 138
Plastered ceiling, Weight of 4, 69
Plaster walls 53
Plati-s 416, 419, 420, 421, 422, 426
Batten 61 , 443
Base 62, 144, 146, 586
Buckle 315
Flat 313
Floor 194
Fillers 65, 211
Minimum thickness of 380, 382
Pin 61, 143, 211
Sheared 415, 419, 420, 422
Splice 65, 145
Tie 61, 211
Universal mill 415, 420, 421, 422
Wall 105, 144, 212
Web 65, 142
Plate girders, 54, 57, 58, no, 142, 149, 206,
210, 212. 433, 435, 534, 581
Cost of 433.435
Design of 220, 534, 581
Erection of 441
Examples 184
Field rivets in 438
Flanges in 220
Plate girder highway bridges, 122
railway bridges.. . .173, 174, 175, 203, 400
weight of 150, 151, 152, 153, 155, 158
Pleisner's experiments 321
Pointing 268, 269
Poisson's ratio 528
Pole, Electric light 136
Pony trusses 213
Portals 97, 149, 193, 198, 212
Portals, Stresses in 563, 569
Portland cement 267, 522, 523
Amount of 240
paint 516
Specifications for 522
Posts 277, 296
Cost of 434
Newel 135, 136
Pratt truss. . . .10, 107, 108, 109, 121, 122, 565
Pressure on bin walls 302
Pressure on foundations 75
Pressure of grain 325
Pressure on masonry 56, 75, 104
Pressure on retaining walls 225
Product of inertia 535
Proportions of concrete 240, 273
Punching 216, 430
Purchase ring 457
Purlin, 3, 4, 9, 26, 27, 49, 50, 53, 54, 55, 56,
59.62
Push car 459
Quicksand 249
Radius of gyration 548, 549, 550, 551
Rafter 3, 18, 50
Rail jack 459
Rails, Cost of 440
Rails, Fastenings for 204, 208
Rail steel reinforcement 509
Railway bridges, Allowable stresses in, 173, 209
Clearances of 200
Design of 174, 219
Details of 175, 176
Examples of 184, 185
Field rivets in 438
Floors for 176
Impact on 161, 162
Loads on 202, 208
Painting 217
Piers for 255, 257, 258, 259, 260, 265
Piles 281
Shop cost 435
Specifications for 188, 208, 483
Steel trestle 149
Types of 201
Weight of 150 to 158
Rankine's theory f 225. 226
Ratchet 460
Rate of hoisting 350, 360
Reaming 65, 66, 145, 363, 435, 484
Ream wrench 454
Red heart 279
Red lead-paint, 67, 207, 438, 439, 514, 515, 516
Reinforced concrete 521, 526, 546
Reinforced concrete floor, 34,1 i2h, 179, 180, 266
retaining walls 239
Specifications for 272
Stresses in 521
walls 53
Resilience 528, 535
Resisting moment 530
Resisting shear 529
Retaining walls 225, 268
Reversal of stress 362
Ridge roll 24, 52, 59, 427
Rigid bracing 55, 137, 212, 361
Rigid members 207, 213, 222
Rigging 447, 449, 45<>
Ring.
279
Ring dolly 455
shake 279
stones 268
Riprap 268
Rivet buster 452, 462, 463
clamp 456
clearance 412, 413
hammer 452, 456, 462
heads 427
holes 65, 145
list 389
892
INDEX.
Rivet pitching tongs 456
snaps 452, 456, 462, 467
spacing 60, 142, 219, 410, 423
steel 62, 383, 496, 505
sticking tongs 456
Rivets 58, 65, 145, 210, 219, 379
Clinch 23, 24
Conventional signs for 398
Diameter of 60
Field 55, 66, 141, 146, 217, 363, 400
Flange . 142
Maximum diameter of 60, 143
Pitch of 60, 142, 143
Size of 144, 215
Riveting 145, 216, 467
Cost of 436, 437, 438
bins 332, 333
stand pipes 387
tanks. . 373, 375
Riveted bridges, Examples of, 119, 120, 127,
128, 151, 194, 401
Riveted bridges, Field rivets in 437, 438
Riveted connections 219, 595
joints. 370, 378, 380, 532, 597
girders 403
tension members 143
Road rollers H2d, 117, 139
Rods 6l, 62, 416
Rods, Anchor 94, 95
Minimum size of 142
Rollers, 55, 57, 63, 66, 133, 134, 141, 144, 146,
184, 186, 188, 189, 191, 193, 194, 197, 206,
209, 212, 217, 434, 534, 579
Rolling loads 542
Roof covering, 4, 7, 15, 18, 26, 56, 71, 74
Roof, Pitch, see pitch of roof
Roof trusses, 7, n, 15, 16, 17, 18, 46, 49, 53,
54. 55. 105, 354, 359, 433, 441
Roof trusses, Erection of 441
Spacing of 14, 62
Stresses in 7, 552
Types of 9, 10
Weight of 3,55
Roof for steel bin 335, 336, 337
steel tank. 372, 375, 382
steel stand-pipe 382
Roofing 23, 28, 29, 51, 423, 428, 439
Corrugated steel 28, 29, 51
Cost of 439
Slate 29
Tar and gravel 29, 32
Tile 31, 54m
Tin 31
Rooster 469
Rope, Cost of 440
Rope, Hoisting 341, 443, 444
Rot. 279
Rubbed 268
Rubble 268
Rubble concrete 266, 274
Rubble stone 271
Rules for shop drawings 391
Rupture strength 528
Rust 513
Safe bearing of soils 56, 75, 236, 249, 386
Safe loads on corrugated steel 22
floors 35
P^es 57, 75,477
slabs 547
Safety hooks 346, 362
Sag rod 54
Sand, Amount in concrete 240
Sand bin 300, 301, 302, 305
Sand blast 515
Sand, Friction of 312
Sand, Weight of 69, 237
Sandstone, Weight of 237
Sandwich door 44, 60
Sapwood 278
Sash 36, 42, 60
Sash brace 277
Saw tooth roof 8,9, 1 1 , 46
Section modulus 530
Segmental rollers 134
Segmental bottom 366
Separators 83, 277, 297, 430, 580
Set, Rivet 452, 456, 462, 467
Schneider, C. C 70, 72, 599
Scale hoppers 337
Screens 362
Screw bolt 95
pile 279
thread 66, 146, 2 1 7
Shackle 447, 457
Shackle bar 453
Shaft, Torsion in 533
Shake 279
Shaking screen. 352, 355, 356, 358
Shallow bins. 299
Shear 57, 526, 529, 531 , 542, 547
Shear in beams 536 to 545
Shear in bridges 164 to 170
Shear in concrete 521
Shear, Elastic deformation due to 532.
Shear in lacing bars 598
Shear in plate girder 173, 174
Shear in rivets 370
Shear, Corrugated steel 456, 460
Shear legs 468
Sheared plates 419, 420, 422
Sheathing ' 3. 4. 3°. 32, 53, 54- 56
Sheaves 346, 348, 350, 360, 363, 443, 444
Sheet pile 279
Shipping invoice 67, 218
Shim . 277
Shoes 133, 184, 186, 187, 188, 279, 423, 424
Shop bills 399
Shop coat of paint 516
Shop cost of bins 433, 434
bridges 434, 435
columns 433
combination bridges 435
culverts ... 435
eave struts 433
floorbeams 434
eye-bars 434
grain bins 433, 434
Howe truss metal 436
INDEX.
898
PAGE
Shi >p cost of office buildings 433
pl.n. • girders 433, 435
434
434
433
stand-pipes 433, 434
Mecl mill building! 433
Meel lu-ad frame 347
structural steel 429
M"ks 433,434
towers 434
t uluilar piers 435
Shops I >csign of 7
Shop details 55. 396, 397
Shop doors 43
Shop drawings. . . . 138, 389, 400, 401, 402, 403
Shop drawings, Cost of 429
Shop drawings, Rules for 391, 398
Shop floors 8, 32, 33, 34, 54, 67, 147
Shop plans 195, 196, 218
Shop rivets, see "Rivets"
Shutters 59
Sidewalks 113, 115, 275
Signal bridges 157
Silicon 488, 494
Sill 277,296
Skeleton construction 69
Skew bridge . . 108
Skips 346, 348, 362
Skylight 4, 8, II, 38, 54, 60, 428, 440
Slabs, Safe loads on 547
Slate, Weight of 4, 30, 69
Slate roofing 28, 29, 30, 53, 54, 56
Slate roofing, Cost of 440
Sleeve nut 572
Sliding door 43, 46, 48, 60
Sliding sash 36, 37
Slope wall 268
Snap, Rivet 452, 456, 462, 467
Snatch block 447, 448
Spacing columns 98
girts 59
plate girders 179
purlins 55, 59. 62
trusses 55, 62, 202, 203, 208
Spall 268
Spandrel sections 96, 100, 268
Span, Length of 55
Snow loads. 4, 56, 72, 553, 556
Snow, Weight of 4, 69
Soffit 268
Specifications for cast iron, 215. 297, 384, 488
coal tipples 361
concrete floor 32
erection 483
painting 67, 217
Portland cement 522
retaining walls 241
shop floors 32
stone 269
steel 62, 105, 213, 272, 363, 383
steel castings 510
head frames 361
highway bridges 137
PACE
S[* i ifirations for steel, mill buildings 55
office buildings 102
railway bridges 188, 208
reinforcement 272, 507, 509
stand-pipes 379, 386
tanks 379, 386
tar and gravel roof 32
timber bridges 292
timber piles 281
tubular piers 257
wrought-iron 215, 297, 491
Spikes 297
Splices. 61, 90, 91, 2ii, 363, 584
Splices, Indirect 144, 211
Splices in plate girder 220, 583, 596
Splice plates 145, 216
Split bolt 95
Spool 442, 443
Spouts 335
Spud 454
Stack collars 427
Stack flashing 29
Stand-pipes 365
Allowable stresses in 382
Design of 381
Erection of 442
Painting 387
Shop cost of • 433, 434
Standard angle connections 595
Stark-weather 249
Starred angles 578
Steamboat jack 460
Steamboat ratchet 460
Steel bins 299, 300, 359
castings.. . .63, 66, 146, 213, 217, 487, 510
coal tipples 361
column bases 94
columns 104
Corrosion of 513
cylinder piers 262
details 571
door 44, 46, 47, 60
erection 67, 328, 329, 441
estimates 425
grain elevators 319, 329, 337
head frames. . . . .339, 348, 352, 355, 359, 361
highway bridges 107, no, 115
Inspection of 67, 146, 518
joist. 138
Steel mill buildings, Allowable stresses in, 8, 57
Cost of 433. 436
Design of 7
Erection plan of 408. 441
Estimates for 425
Examples 49, 53, 54
Steel, Minimum thickness of 210
Steel office buildings 69, 70, 81, 103
Erection 105
Specifications for 103
Weight of 70
Steel plate flooring 34
Steel railway bridges 149
Specifications for 209
Weight of 151
894
INDEX.
PAGE
Steel reinforcement 272, 507, 509
Specifications for, 62, 105, 213, 272, 363,
383
Steel stand-pipe 365> 387
Steel, Strength of 62
Steel tank 365, 380, 381
trestle 150, 158
tubular piers. . . .255, 262, 263, 264, 265, 478
Stiffeners, 58, 61, 65, 142, 145, 207, 212, 216,
221, 423
Stiffeners in bins 327, 333
Stile 38 to 43
Stirrups 547
Stiff -leg derrick 468 469, 470, 471, 478
Stone, Amount of 240
Stone bins 312
Stone masonry 269
Straight 278
Strain 527
Strength of cast-iron 65, 488
chains 451
concrete 520
masonry 237
Portland cement 523
steel 62, 494, 508, 509
steel castings 496, 511
timber 298
wire rope • 341, 443, 444
wrought iron 65, 491, 492, 496
Stress 527
Stress diagram 173, 174, 389, 422
Stress due to weight 57, 142, 222
Stresses 531
Alternate 57
Allowable, 8, 62, 80, 105, 115, 205, 209, 362,
379, 382, 387
Diagram for 173, 174, 422
Impact 161, 205, 208
Maximum 160
Stresses in beams 529, 536 to 545
bins 299
bridge trusses 558, 559 to 569
circular girder 367
columns 368
deep bins 319
elevated tanks 366
end-post 222
eye-bar 586
flat plates 313, 535
framed structures 552
grain bins 319
hooks 533
lacing bars 598
masonry 56, 75
office buildings 76, 79
pins 584
pipes 534
portal 563, 569
riveted joint 366, 370, 532
rollers 534
roof trusses 552
shallow bins 307
stand-pipes 365
steel buildings 57
PAGE
Stresses in, suspension bunker 309
timber floors 35
transverse bent 556
trestle bent 563, 569
wire rope 344
Stretcher 268, 270
Stringers, 138, 177, 199, 212 216, 222, 277,
283, 284, 297, 434
Strut 593
Strut, Single angle 575, 576
Structural drawing 389
Structural mechanics •. 525
Structural steel, Cost of 428
Erection of 441
Estimates of 425
Specifications for, 62, 105, 213, 497, 499,
502, 505
Structural timber, Defects of 277
Structural timber, Definitions of 278
Stub abutment 245, 246
Sub-purlin 3, 18, 31
Sub-sill 277
Sulphur. . .62, 213, 488, 494, 497, 499, 502, 505
Summer wood 278
Suspension bunker 309, 316
Sway bracing 149, 223, 277, 296
Swing door 43
Swedge bolt 95
T Abutment 245, 246
Tackle 449, 450
Talbot, A. N., Formula for waterway by, 250
Tank details 373, 374, 375, 377
Erection of 441
Painting 387
Shop cost of 433, 434
Taper plates 431, 432
Tar and gravel roofing, 4, 29, 32, 60, 74, 440
Tar paint 178, 180, 576
Tees 417, 418
Templet shop 390
Tension 531
Test of cast-iron 489
Tests, Impact 162
Tests of steel, 62, 63, 67, 105, 214, 272, 384,
386, 497, 500, 503, 504, 507, 509
Tests of wrought iron 491, 493
Theorem of three moments 543
Thickness of walls. 75
Three-hinged arch 13, 14
Through traveler 472, 474, 475
Tie plates 61, 143, 211
Tie rods 430
Ties, 117, 138, 177, 179, 180, 199, 202, 204,
208, 277, 282, 283, 297, 593
Tile roof 4, 18, 31, 56, 428, 440
Timber 66, 520
Vimber, Allowable stresses in 298
Timber ballasted floor 179
block floor 33, 126
bridges, 277, 285, 286, 287, 290, 291, 293,
294, 295
buggy 459
columns 298
INDEX.
PACK
Timber, Defects in 278
doors 43. 45. 60
ll<».rs 8, 33, 34, 35, 126, 176, 177
hook 458
Hour truss 288
joist 138
pili-s 57
Etirlins 62
tresses in 35, 58, 138, 204
Specifications for 144
travelers 474, 475, 480
trestles 277, 282, 283, 284
Weight of 69, 204, 208
Tin roofing 4. 31. 44°
Tobin bronze , 520
Tongs 456
Tools for erection of steel, 67, 105, 463, 464,
465, 466, 467
Top chord 195, 222, 397
Torsion in shafts 533
Towers 137, 222, 434
Tower struts 212
Translucent fabric 41
Transverse bent, 3, 7, 9, 12, 14, 17, 18, 49, 54,
77. 556, 590
Transverse bracing 18, 212, 223
Traveler 468, 470, 472, 478
Traveling crane 12
Trestle . . 150, 277, 282, 283, 284, 441, 563, 569
Trestle towers 137
Trestles, Weight of steel 158
Trimmers 453
True stress 534
Truss, see und2r bridge, roof, etc.
Tubular piers 255, 435, 437
Turnbuckle 572
Turned bolts 65, 145, 216
Two-hinged arch 13, 14
U abutment 245, 246
Ultimate deformation 528, 532
Ultimate stress 527
Uniform loads 151, 159
Unit stress 527
Universal mill plates 415, 420, 421, 422
Upsets for bars 383
Upset rods 61
Ventilators. .3, 12, 29, 43, 44, 59. 423. 425
Ventilator, Monitor 3, II
Ventilating buildings 9
Viaducts, Erection of 441
Voussoirs 268
Wall anchors 105
Wall plates. . 104, 105, 144, 212
Walls, Details of 96
Mill building 7
Thickness of 75
Wane 278
Warren truss 108, 109, 565
Washers 287, 297
Water jet 279
Water, Weight of 69
PACE
Waterproofing, Cost of 440
Waterproofing floors, 35,76,1120, 178, 179, 1 80,
181, 182
retaining walls 243
Watertight joints 370
Waterway for bridges 250
Web plates. . . .58, 65, 142, 145, 216, 220, 432
spiice 583, 596
stiffencrs, 58, 61, 65, 145, 207, 212, 216, 221
Wedge 287, 458
Welds 66, 146, 216, 217
Weight of ashes 69
ballast 179, 204, 208
bars 572,573
beam bridge 113
bracing 4
building materials 69
cast iron 69
coal tipples 360
columns 4
concrete 69, 204, 208, 381
conductors 26
corrugated steel 4, 15, 25
covenng 56
draw spans 157
electric railway bridges 115
girts 4
gutters 26
head frames 347, 348, 350
highway bridges 1 10, 1 15
hoisting engines 443
locomotives 154, 205
louvres 24
masonry 237
materials 4, 69, 73, 146, 311
office buildings 70
plate girders, 112, 150, 151, 152, 153, 155,
15.8
purlins 4, 56
. rails and fastenings 139, 204, 208
railway bridges, 150, 151, 152, 153, 154,
155. 156, 157, 158
railway viaduct 158
ridge roll 24
roof arches 13
roof covering 4
roof trusses 3, 55
roofing 74
sheathing 56
slate 4, 30, 56
skylight glass 4
signal bridges 157
skips 350
snow 4, 69
steel 69, 217, 384
tiles 31
tile roofing 56
timber 204, 208
trestle towers 158
tin 4
wrought-iron 69
Weight, Stress due to 57, 142, 222, 589
Wheel guards 138, 177, 208, 281
896
INDEX.
PAGE
Wheel loads, 153, 162, 163, 164, 165, 166, 167,
168, 169, 170, 171, 172
Whipple truss 109
White lead 514
Wind bracing 97. 98, 100, 101, 102
loads, 5, 56, 71, 72, 103, 140, 205, 209, 379
shake 278
stresses, 76, 78, 141, 209, 327, 379, 553, 556,
589
Width of angles 41 1
Windows, 8, 36, 37, 38, 60, 96, 329, 422, 427,
440, 481, 545
Wing abutment 245, 246
Wing wall 268
Wire glass 8, 38, 54, 60, 69
netting 8, 28, 29, 52, 53, 59
rope. 341, 440, 443, 444, 480
Wood sash 36, 37
Wooden doors 43, 45, 60
floor 8, 34
trestle 277
Work 528,535
Winch 442, 443
Wrench 453, 455, 461
Wrought-iron, 65, 69, 215, 297, 487, 489, 491,
492
X-brace 277
Yellow pine 298
Yield point 528
Zees 417, 418, 514
Zinc 519
Zinc paint 514
AND THE CALCULATION OF
STRESSES IN FRAMED STRUCTURES
THIRD EDITION. ENLARGED.
By MILO S. KETCHUM, C.E., M.AM.Soc.C.E.
Professor-in-Charge of Civil Engineering, University of Pennsylvania; Sometime Dean of
College Engineering and Professor of Civil Engineering.
University of Colorado; Consulting Engineer
Cloth, 6^x9 Ins., pp. 562+xiii, 66 tables and 270 illustrations
Price, $5.00 net, postpaid.
TABLE OF CONTENTS
PART I.— Loads. Chapter I. Dead Loads. II. Snow Loads. III. Wind Loads.
IV. Miscellaneous Loads.
PART II.— Stresses. Chapter V. Graphic Statics. VI. Stresses in Framed Struc-
tures. VII. Stresses in Simple Roof Trusses. VIII. Simple Beams. IX. Moving Loads
on Beams. X. Stresses in Bridge Trusses. XI. Stresses in a Transverse Bent. XII.
Stresses in Portals. XIII. Stresses in Three-Hinged Arch. XIV. Stresses in Two-
Hinged Arch. XV. Combined and Eccentric Stresses. XVx. Graphic Methods for Cal-
culating the Deflection of Beams.
PART III.— Design of Mill Buildings. Chapter XVI. Framework. XVII. Cor-
rugated Steel. XVIII. Roof Caverings. XIX. Side Walls and Masonry Walls. XX.
Foundations. XXI. Floors. XXII. Windows and Skylights. XXIII. Ventilators.
XXIV. Doors. XXV. Shop Drawing and Rules. XXVI. Paints and Painting. XXVII.
Estimate of Weight and Cost.
PART IV. — Miscellaneous Structures.
APPENDIX I. Specifications for Steel Frame Mill Buildings.
APPENDIX II. Calculation of 22 Problems in Algebraic and Graphic Statics.
APPENDIX III. Structural Drawings, Estimates and Designs.
COMMENTS OF THE PRESS.
COMMENTS OK THE PRESS ON FIRST EDITION.
Professor Ketchum's work is the first book on the design of steel frame mill buildings;
in thoroughness and clearness it does full justice to its subject. It is the result of both
theoretical and practical acquaintance with the type of structure treated. It will prove of
value as well to the designing engineer as to teachers and students. — Engineering News,
Oct. 15. 1903.
It covers a broader field than its title indicates, as it is in reality a treatise on framed
structures. — Railroad Gazette, Nov. 21, 1903.
The book is new and presents the best modern practice and should be found valuable
to architects as well as engineers. — Architects and Builder's Magazine, Jan., 1904.
COMMENTS OF PRESS ON SECOND EDITION.
This is the second edition of a well known treatise, which has already met with well
deserved appreciation among engineers. — Engineering and Mining Journal, Nov. 17, 1906.
The main impression we have derived from a survey of the contents of this book is
that it is of a sound practical character. — Mechanical Engineer (London).
The first edition of this book was issued in 1903. It was promptly received with
favor by engineers because it supplied for the first time a systematic treatment of the
details of American steel mill buildings. Valuable information was published regarding
cost analysis of such structures that is not generally available to engineers, especially to
the younger ones outside the estimating departments of bridge works. — Professor H. S.
Jacoby in Engineering News.
McGraw-Hill Book Company, New York
DESIGN OF WALLS, BINS
AND GRAIN ELEVATORS
THIRD EDITION, ENLARGED
By MILO S. KETCHUM, C.E., M.AM.Soc.CE.
Professor-in-Charge of Civil Engineering, University of Pennsylvania; Sometime Dean of
College of Engineering and Professor of Civil Engineering,
University of Colorado; Consulting Engineer
Cloth, 6^x9 ins., pp. 556+xix, 40 tables, 304 illustrations and
2 folding plates. Price, $5.00 net, postpaid.
TABLE OF CONTENTS
PART I. — Design of Retaining Walls. Chapter I. Rankine's Theory. IA. Rankine's
Theory Modified. II. Coulomb's Theory. III. Design of Masonry Retaining Walls.
IV. Design of Reinforced Concrete Retaining Walls. IVA. Effect of Cohesion; Stresses
in Bracing of Trenches; Stresses in Tunnels. V. Experiments on Retaining Walls. VI.
Examples of Retaining Walls. VII. Methods of Construction and Cost of Retaining Walls.
PART II.— The Design of Coal Bins, Ore Bins, etc. Chapter VIII. Types of Coal
Bins, Ore Bins, etc. IX. Stresses in Bins. X. Experiments on Pressure on Bin Walls.
XI. The Design of Bins. XII. Examples and Details of Bins. XIII. Cost of Bins.
XIV. Methods of Handling Materials.
PART III. — Design of Grain Bins and Elevators. Chapter XV. Types of Grain Ele-
vators. XVI. Stresses in Grain Bins. XVII. Experiments on the Pressure of Grain in
Deep Bins. XVIII. The Design of Grain Bins and Elevators. XIX. Examples of Grain
Elevators. XX. Cost of Grain Bins and Elevators.
APPENDIX I. — Concrete, Plain and Reinforced. Chapter I. Concrete. II. Data
for Design of Reinforced Concrete Structures. III. Formulas for Design of Reinforced
Concrete. IV. Specifications for Reinforced Concrete Construction.
APPENDIX II. Definitions of Masonry Terms; Specifications for Stone Masonry.
APPENDIX III. Specifications for Material and Workmanship of Steel Structures.
COMMENTS OF THE PRESS.
Those familiar with Professor Ketchum's book on Steel Mill Buildings will welcome
this pioneer treatise on bin design, which is characterized by the same thoroughness, clear-
ness and logical and systematic arrangement displayed in the former volume. ... A
valuable feature of the book is to be found in the tables of costs of actual structures which
are included wherever possible and analyzed so thoroughly as to be of the greatest assistance
and value. For practical data and scientific and theoretical accuracy, Prof. Ketchum's
book can be recommended to the student and practicing engineer alike. — The Engineering
Magazine, November, 1907.
This book will be welcomed by the constructing engineer as the first authoritative
and elaborate contribution to technical literature on the perplexing subject of the design
and construction of coal and ore bins. . . . The portion of the book which relates to
coal and ore bins is the largest, and this will make it appeal especially to mining and metal-
lurgical engineers. They will find the admirable study of retaining walls to be scarcely
less useful.
Professor Ketchum is well known as the author of "The Design of Steel Mill Build-
ings," which won high appreciation because of its eminently practical character. His
present work is one of the same order, and will take a high place. — The Engineering and
Mining Journal, June 8, 1907.
McGraw-Hill Book Company, New York
THE DESIGN OF
HIGHWAY BRIDGES
AND THE CALCULATION OF
STRESSES IN BRIDGE TRUSSES
By MILO S. KETCHUM, C.E., M.AM.Soc.C.E.
Dean of College of Engineering and Professor of Civil Engineering.
University of Colorado ; Consulting Engineer
Cloth, 6^x9 ins., pp. 544+xvi, 77 tables, 300 illustrations in the text
and 8 folding plates. Price, $4.00 net, postpaid.
TABLE OF CONTENTS
PART I. — Stresses in Steel Bridges. Chapter I. Types of Steel Bridges. II. Loads
and Weights of Highway Bridges. III. Methods for the Calculation of Stresses in Framed
Structures. IV. Stresses in Beams. V. Stresses in Highway Bridge Trusses. VI.
Stresses in Railway Bridge Trusses. VII. Stresses in Lateral Systems. VIII. Stresses
in Pins; Eccentric and Combined Stresses; Deflection of Trusses; Stresses in Rollers, and
Camber. IX. The Solution of 24 Problems in the Calculation of Stresses in Bridge Trusses.
PART II. — The Design of Highway Bridges. Chapter X. Short Span Highway
Bridges. XI. High Truss Steel Highway Bridges. XII. Plate Girder Bridges. XIII.
Design of Truss Members, XIV. The Details of Highway Bridge Members. XV. The
Design of Abutments and Piers. XVI. Stresses in Solid Masonry Arches. XVII. Design
of Masonry Bridges and Culverts. XVIII. The Design of Timber and Combination
Bridges. XIX. Erection, Estimates of Weight and Cost of Highway Bridges. XX.
General Principles of Design of Highway Bridges.
PART HI.— A Problem in Highway Bridge Details. Calculation of Weight and Cost
of a i6o-ft. Span Steel Pratt Highway Bridge. The Calculation of the Efficiencies of the
Members of a i6o-ft. Span Steel Pin-connected Highway Bridge.
APPENDIX I. General Specifications for Steel Highway Bridges.
COMMENTS OF THE PRESS.
Professor Ketchum has done the profession a real service in presenting to civil en-
gineers and students this masterly and complete work on highway bridges. The author
has a plain way of getting his ideas before the mind of the reader. — Ernest McCollough, in
The Contractor, Dec. i, 1908.
The reputation for practical book writing established by the author in "The Design
of Steel Mill Buildings" and "The Design of Walls, Bins and Grain Elevators" is upheld
in his most recent work. Altogether we do not know where bridge designers can find
elsewhere so much good practical information as is given them in this book. — Engineering
Contracting, Dec. a, 1908.
Altogether the work embodies a fortunate blending of the rational with the thoroughly
practical. — Journal of the Franklin Institute, Jan., 1909.
McGraw-Hill Book Company, New York
THE DESIGN OF
MINE STRUCTURES
By MILO S. KETCHUM, C.E., M.AM.Soc.C.E.
Professor-in-Charge of Civil Engineering, University of Pennsylvania; Sometime Dean of
College of Engineering and Professor of Civil Engineering,
University of Colorado; Consulting Engineer
Cloth, 6^x9 inches, pp. 46o+xvi, 65 tables, 265 i lustrations in the
text and 7 folding plates. Price $5-°° net, postpaid.
TABLE OF CONTENTS
PART I.— Design of Head Works. Chapter I. Types of Head Works. II.
Hoisting from Mines. III. Stresses in Simple Head Frames. IV. Stresses in
Statically Indeterminate Structures. V, Stresses in Statically Indeterminate
Head Frames. VI. The Design of Head Frames. VII. The Design of Coal
Tipples.
PART n. — The Design of Mine Buildings. Chapter VIII. Stresses in Roof
Trusses and Frame Structures. IX. The Design of Roof Trusses and Steel Frame
Structures. X. The Design of Bins and Retaining Walls. XI. The Design of
Coal Washers. XII. The Design of Coal Breakers. XIII. Miscellaneous Struc-
tures.
PART m. — Details of Design and Cost of Mine Structures. Chapter XIV.
Details of the Design of Steel Structures. XV. Estimate of Weight and Cost of
Mine Structures.
APPENDIX I. — Specifications for Steel Mine Structures. Part I. Steel
Frame Buildings. Part II. Steel Head Frames and Coal Tipples, Washers and
Breakers.
APPENDIX n. — Specifications for Timber Mine Structures.
APPENDK III.— Reriforced Concrete Structures. Chapter I, Data for the
Design of Reinforced Concrete Structures. II. Formulas for the Design of Re-
inforced Concrete Structures. III. Specifications for Plain and Reinforced Con-
crete Structures.
COMMENTS OF THE PRESS
It is a pleasure to record the publication of another book by Professor Ketchum.
His books are always examples of what technical treatises should be, and this volume
is no exception to the rule. This volume is a self-contained, concise and valuable text-
book for the student or structural engineer who wishes to become familiar with the
design of mine structures. — Canadian Engineer, July 4, 1912.
This is a new book in a field never previously covered in a satisfactory manner.
The various subjects described and illustrated are based on good practical working
plants and make them particularly valuable for reference. The author is to be highly
commended for producing so useful a book. — Mining and Scientific Press, July 6, 1912.
So far as we are aware this book has no counterpart in recent technical literature.
— Mines and Minerals, July, 1912.
McGraw-Hill Book Company, New York
SURVEYING MANUAL
A MANUAL OF FIELD AND OFFICE METHODS
FOR THE USE OF STUDENTS IN SURVEYING
FOURTH EDITION
By PROFESSORS WILLIAM D. PENCE AND MILO S. KETCHUM
Leather, 4^x7 ins., pp. 388 + xii, 10 plates and 140 illustrations in,
the text, and 130 pages of tables. Price, £2.50 net.
TABLE OF CONTENTS
Chapter I. General Instructions. II. The Chain and Tape. III. The Cora-
pass. IV. The Level. V. The Transit. VI. Topographic Surveying. VII.
Land Surveying. VIII. Railroad Surveying. IX. Errors of Surveying. X.
Methods of Computing. XI. Freehand Lettering, Logarithmic and Trigono-
metric Tables.
COMMENTS OF THE PRESS.
The object of the authors as stated in the preface, is first "to provide a simple and
comprehensive text, designed to anticipate, rather than replace, the usual elaborate
treatise; second, to bring the student into immediate familiarity with approved surveying
methods; third, to cultivate the student's skill in the rare art of keeping good field notes
and making reliable calculations."
In this the authors have succeeded admirably. As a pocket guide to field practice
for students, probably nothing better has been produced. Especially are the instructions
in regard to keeping field notes to be commended. Many engineers have found that it
has taken years to obtain this art, so generally neglected in the work of engineering schools.
— Journal of Western Society of Engineers.
The scope of the book is large, and the various subjects included are treated not in a
descriptive but in a critical manner. The book is well arranged and is written in a clear
concise manner, which should make its study easy and pleasant. — Engineering News.
It gives the student just the information he needs. The book is a gratifying indication
of the importance attached to the cultivation of habits of neatness and celerity in the
authors' methods of instruction. — Engineering Record.
McGraw-Hill Book Company, New York
PLEASE DO NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET
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