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>.
■ ' fc •
l! '•■ • -
U^
- -^^
. V" . . . .
JOHN WILEY Sl SONS PUBLISH
^ The American House Carpenter.
A Trciitise on the Art of Building, comprising Styles of Arcliitec
ture, Strength of Materials, and the Theory and Practice of th
(^onstructionof Floors, Framed Girders, Roof Trusses, Rolled Iro;
Beams, Tubular Iron Girders, Cast-Iron Girders, Stairs, Doort
Windows, Mouldings and Cornices, together with a (yompend o
Mathematics. A manual for the i)ractical use of architect's, cat
penters, and stair-builders. By R. (i. Hatfield, architect. Re-writ
ten and enlarged. Numerous nne wood engravings. 8vo, cloth, §;:
The Theory of Transverse Strains,
And its Ap])lication to the (-onstruction of Buildings, including
full discussion of the Theory and (Construction of Floor BeaniH
Girders, Headers, ('arriago Beams, Bridging, liolled Iron Beams
Tubular Iron Girders, Cast-iron Girders, Framed (iirders am
Roof Tresses, with Tables calculated expressly for the work, etc
By R. G. Hatfield, architect. Fully illustrated. Second editio
with additions. Svo, cloth, $c
Cottage Besidences.
New edition. A series of Designs for Rural Cottages and Cottag
Villas, and their Garden Grounds. By A. J. Downing. Contain
ing a revised list of Trees, Shrubs, ajid Plants, and the most recen
and host-selected Fruit, with some account of the new st^Me of (Jar
dens. By Henry Winthrop Sfirgent and Charles Downing. Wit!
many new designs in rural architecture. By George Harney, at
chitect. 4to, cloth, $f
Carpenters' and Joiners' Handbook.
Containing n Complete Treatise on Framing Hip and Valley Roof.>
together with much valuable instruction for all mechanics an<
amateurs, useful Rules, Tables never before i)ubli8hed, etc. B
H. W. Holly. New edition with additions. 18mo, cloth, 75 centt
The Architect's and Builder's Handbook-
Containing Original Tables and Valuable Information for Arch:
tects, Builders, Kngineers,' and Contractors, fully illustrated wit
plates. By F. E. Kidder. Put up in pocket-book form. Thir
edition, revised and enlarged. Morocco flaps. $3.5(
%* Mailed, prepaid, on the receipt of the price. Catalogue of
our publications gratis.
ARCHITECT'S AND BUILDER'S
POCKET-BOOK
OP
MENSURATION, GEOMETRT. GEOMETRICAL PROBLEMS, TRIGO-
NOMETRICAL FORMULAS AND TABLES. STRENGTH AND
STABILITY OF FOUNDATIONS, WALLS BUTTRESSES,
1 PIERS, ARCHES. POSTS, TIES, BEAMS, GIRDERS,
TRUSSES, FLOORS, ROOFS, ETC.
IN ADDITION TO WHICH IS
A GREAT AMOUNT OF CONDENSED INFORMATION:
^ STATISTICS AND TABLES RELATING TO CARPENTRY, MASONRY,
DRAINAGE, PAINTING AND GLAZING, PLUMBING, PLAS-
TERING, ROOFING, HEATING AND VENTILATION,
WEIGHTS OF MATERIALS, CAPACITY AND
DIMENSIONS OF NOTED CHURCHES,
THEATRES, DOMES, TOWERS,
SPIRES, ETC.,
WITH A GREAT VARIETY OF MISCELLANEOUS INFORMATION.
BY »-''
FRANK EUGENE KIDDER, C.E.,
OON8ULTINO AUCHITECfJTWBTON.
iLLUSTRATED WITH 423 ENGRAVINGS, MOSTLY FROM ORIGINAL DESIGNS.
'; THIRD EDITION, REVISED AND ENLARGED.
/
NEW YORK:
JOHN WILEY & SONS,
15 AsTOR Place.
1880.
THE NEW YORK
PUBLIC LIBRARY
1»30
Copyright,
By F. E. KIDDER,
1884.
BLBCTROTYPED BY
RAMD, AVBBY. AND COMPANY,
BOWTON.
.
Efjts Booft
IS RESPECTFULLY DEDICATED TO THOSE WHOSE KINDNESS
HAS ENABLED ME TO PRODUCE IT.
TO MY PARENTS,
WHO GAVE MB THE EDUCATION UPON WHICH IT IS BASED;
TO MY WIFE,
FOR HER LOVING SYMPATHY, ENCOURAGEMENT, AND ASSIST-
ANCE;
TO ORLANDO W. NORCROSS
OF WORCESTER, MASS.,
WHOSE SUPERIOR PRACTICAL KNOWLEDGE OF ALL THAT
PERTAINS TO BUILDING HAS GIVEN ME A MOKE
INTELLIGENT AND PRACTICAL VIEW OF
THE SCIENCE OF CONSTRUCTION
THAN 1 SHOULD OTHERWISE
HAVE OBTAINED.
Oi
•
PREFACE.
In preparing the following pages, it has ever heen tlio aim of
the author to give to the architects and builders of this country
a reference book which should be for them what Trautwine's
"Pocket-Book" is to engineers, — a compendium of practical
facts, rules, and tables, presented in a fonn as convenient for
application as possible, and as reliable as our present knowledge
will permit. Only so nuu'h theory has heen given as will render
the application of the formulas more apparent, and aid the stu-
dent in understanding, in some measure, the principles upon
which the formulas are based. It is believed that nothing has
been given in this book but what has been borne out in practice.
As this book was not written for tntjineerH, the more intricate
I' problems of building construction, which may fairly 1m' said to
come within the province of the civil engineer, have Imm'u omitted.
Desiring to give as much information as possible likely to l)c of
s«^ice to architects and builders, the author has borr()\\(Hl and
quoted from many sources, in most cases with the i)ennissiun of
the authors. Much practical information has been derived from
the various handbooks published by the large manufacturers of
rolled-iron beams, bars, etc. ; and the author has always found the
publishers willing to aid him whenever re(| nested.
Although but very little has been taken from Trautwhie's
"Pocket-Book for Engineers," yet this valuable book has served
I the author as a model, which he has tried to imitate as well as the
difference in the subjects would i>ermit; and if his work shall
prove of as much value to architects and builders as Mr. Traut-
wine's has to engineers, he will feel amply rewarded for his
labor.
CONTENTS.
PART I.
PAO
Arithmetical Signs and Characters
Involution
Evolution, Square and Cube Root, Rules, and Tables .
Weights and Measures 2
The Metric System a
Scripture and Ancient Measures and Weights .... 3
Mensuration fl
Geometrical Problems 6
Table of Chords 8
Hip and Jack JEIafters fl
Trigonombtry, Formulas and Tables S
PART II.
Introduction 12
CHAPTER I.
Definitions of Terms used in Mechanics 12
CHAPTER II.
Foundations 113
CHAPTER III.
Masonry Walls 14
CHAPTER IV.
Composition and Resolution of Forces. — Centre of
Gravity
X CONTENTS.
CHAPTER V.
PAOB
Betaikiko Walls 161
CHAPTER VI.
Strength of Masonry 165
CHAPTER VII.
Stability op Piers and Buttresses 178
•
CHAPTER VIII.
The Stability of Arches 185
CHAPTER IX.
Resistance to Tension 197
CHAPTER X.
Resistance to Shearing 213
CHAPTER XI.
Stbbnoth of Posts, Struts, and Columns 217
CHAPTER XII.
Bbnding-Moments 250
CHAPTER XIII.
Moments op Inertia and Resistance, and Radius of Gy-
ration 2^*7
CHAPTER XIV.
General Prinoiplks op the Strength op Beams, and
Strength of Iron Beams 280
CHAPTER XV.
Strength op Cast- Iron, Wooden, and Stonb Beams. —
Solid Built Beams 307
CHAPTER XVI.
'•» AND DKFLECTIOti OF BrAMS 318
CONTENTS. Xi
CHAPTER XVII.
PAGE
Strbngth and Stiffness of Continuous Girders .... 327
CHAPTER XVIII.
Flitch Plate Girders 336
CHAPTER XIX.
Trussed Beams 33<.)
CHAPTER XX.
Riveted Plate-Iron Girders 345
CHAPTER XXI.
Strength of Cast-Iron Arch-Girders 350
CHAPTER XXII.
Strekqth and Stiffness of Wooden Floors 363
CHAPTER XXIII.
PiKB-PRoor Floors 364
I
^ CHAPTER XXIV.
Mill Construction 375
I CHAPTER XXV.
i Matkrials and Methods of Fire-Pkoof Construction for
Buildings 383
CHAPTER XXVI.
Wooden Roof-Trusses, with Details 392
CHAPTER XXVII.
Ibon Koofs and Roof-Trusses, with Details of Construc-
tion 415
CHAPTER XXVIII.
Theory of Roof-Trusses 426
CHAPTER XXIX.
Joints . . .
Xii CONTKNTS.
PART III.
PA<
Classical Moul1>ings 41
Characteristics of Mouldings 4'
Heat and Ventilation 4'
Ventilation of Theatres 41
(■HIMNEYS 41
Proi'oktions for Boiler Chimneys 41
AVrought-Iron Chimneys 41
Flow of (jtas in Pipes 4'
Gas Memoranda 4'
Stairs 4'
Tarlk of Treads and Risers 4'
Seatinc-Space in Theatres 4}
Spaces occupied by School-Skats 4^
Symbols ehr the Apostles and Saints 4i
AVeight of Bells 41
Dimensions of the Principal Domes 41
Heights of Columns, Towers, Domes, Spires, etc. . . . 4^
Capacity of Churches, Theatres, an-d Opera-Houses . . 4^
Dimensions of Theatres and Opera-Houses 41
Dimensions of English Cathedrals 41
Doiensions of Obelisks 41
Miscellaneous Memoranda 4)
Lead Memoranda 4!
Weight of Wrought-Iron (Rules) 4!
Weight of Flat, Square, and Round Iron 4!
Weight of Flat Bar Iron 4!
Weksht of Cast-Iron Plates 4!
Wkkjht of Lead, Copper, and Brass 4'
Wkkjiit of Bolts, Nuts, and Bolt-Heads 41
AVkight of Iron Rivets 4!
Nails and Spikes i^
Tacks y<
AV eight of Plain Cast-Iron Pipes 5<
AVeight of Cast-Iron Pipes in General 5<
Weight of Cast-Iron Water-Pipes 5<
Wrought-Iron Welded Tubes 5(
American and Birmingham Wire Gauges r)(
Galvanized and Black Iron r>(
Corrugated Iron 5(
Memoranda for Excavators, etc 5(
Memoranda for Bricklayers 5
Drain-Pipe .5
Table of Board Mkasurk 5
IfTLUlOa SEDUCED TO BOARD MEASURE 6
CONTENTS. xiii
PAGE
plianks reduced to board measure ......... 521
Nailing Memoranda 527
Memoranda for Plasterers - 528
I ^Iehoranda for Roofers » 52f)
I Plumbing 533
I Hydraulics of Plumbino 534
r' Memoranda for Painters 541
Window-Glass 542
Price-List of Polished Plate-Glass 544
asimialtum 548
CAPAciTi- OF Freight-Cars 549
Weight of Substances 549
Weight of Buildings 551
Cost of Public Buildings 551
Wear and Tear of Building Materials 552
Capacity of Cisterns and Tanks 55;>
Weight and Composition of Air 554
Comparison of Thermometers 554
Colors of Iron caused by Heat 555
IMeltikg-Point of Metals . 55()
Linear Expansion of Mp^tals 55(>
Properties of Water 557
Consumption of Water in Cities 550
Co-efficient of Friction oTjO
To MAKE Bluf^Print Copiks of Tracings 560
Mineral Wool 5()2
Rrlative Hardness of Woods 5()3
Hard-Wooi) Lumber Grades 5<)4
List op Noted Architects 5(54
Scale of Architects' Charges . 570
Horse-Power 572
Weight and Shrinkage of Castings 572
Speed of Dri ms and Pulleys 57;»
Weight of Grindstones 573
American Works of Magnitude ........... 573
I^IMENSIONS AND WEIGHT OF ChURCH BELLS 550b
i^IMENSlONS OF PlANOS, SCHOOLROOMS, ETC 577
^'MENsioNs OF Fire-Engines and Ladder and Hose Car-
RUOES 577
Dimensions of Carriages 578
Weight of Sash-Weights, Lumber, etc 578
^^[PLosivE Force of Substances ol9
Force of the Wind 580
^^ Five Orders 580
Cost of Roofing-Slated 593
Measurement of Stonk-work » . . »
^^ASUBBMEST OF BrICK-WORK • . . •
XIV
CONTENTS.
PAei
Table of Bricks required in setting Boilers 507
Dimensions of Tubular Boilers 599
Dimensions of Registers and Ventilators 601
Capacity of Pipes and Registers 603
Dimensions and Description of Radiators 603
PART L
PRACTICAL
Arithmetic, Geometry, and Trigonometry.
Rules, Tables, and Problems.
PEACTICAL
ARITHMETIC AND GEOMETRY
SIGNS AND CHARACTERS.
The following signs and characters are generally wsoA to (U*not
and abbreviate the several mathematical operations : —
The sign = means equal to, or equality.
— means minus or less, or subtraction.
-f means plus, or addition.
X means multiplied by, or multiplication,
-r means divided by, or division.
2 ( Index or power, meaning that the numl>^r to whic'
8 I they are added is to be squared (2) or cubed (^).
: is to ^
: : so is [ Signs of proportion.
: to J
J means that the square root of the number befor
which it is placed is required.
A^ means that the cube root of the number bcit'or
which it is placed is required,
the bar indicates that all the numbers under it ar
to be taken together.
( ) the imrenthetiiH means that all the nimibers betweei
are to be taken as one quantity.
. means decimal parts; thus, 2.5 means 2n7, 0.4
means -^^^(i.
° means degrees, ' minutes, " seconds.
. *. means hence.
INVOLUTION.
To square a number, multiply the number by itself, and th
product will be the square; thus, the square of 18 = is x is = :324
The cube of a number is the product obtained by nuilti
plying the number by itself, and that prodwet V^\j vW \\\\\\>J«i^
ajraiii; thns, the cuho of /4 = 14 X 14 X 14 = riA^.
EVOLUTION.
The foiirtli power of a number is the prwiiirt obtain)
by iiiiilU|ilyinc iIip iluiiiIh'I' liy lixcir fiiiir times: tliiia, tiie fuuf
L
EVOLUTION.
; Koot.— liiilt for iletci'ininiiig tlip square root o
ttlinilwi'.
1st, Diviili- tihf. given nuiiilicr Into iierloils of two figures eao
(Wiiiiiu'iii'iug lit the right if It la a wliole uuniber, iiml at tj
ilec!liiml-i)Oint JF tliere are ilecitiiiila; thus, 1
'2d, F'Jiid tlie largest tKjiiare In tlie left-hoad period, and placai
root in till' (|Ufitient; aulitraet tlie said aqiiare from the left-ba
l»rlod. and to the remainder bring doivii Hie next period for a n
dividend,
S<I. DoiibiK tlie root already found, anil annex oub cipher fa
trial divlsur, ave liow nutiiy times it will go In tiie (tlvideud, s
pill till- number In tlif quotient; aUo, in plaee of the cipher In t
divisor, multiply this Biial divisor by the number in the quotit
just found, and subtract the product from the dividend, and to t
reniainder bring down the next period for a new dividend, .
proceed as before. If it shouli! be found that the trial dlvli
cannot Iw contidned In the dividend, bring ilown the n
for H new dividend, and annex anotUer cipher lo the trial divix
and put a cipher in the quotient, and proceed as before.
EsAMPi.i:, i(ri3«.8iyii ( 101.17 square rot-i
I
20227 ) l.-woal
144-'l7
Cube Root.— To extract the nihe root of a number, point
tho nuinlier from right lo left Jnto periods of three figures eai
and, if theiv 1^ a decimal, couuuence at tlic decliual-point. and pol
ofT into periods, going Intb n-aya.
wRain the hlgliest root of tlie Brat perlnl, and place to d|
r, w In long division; cube the root thus found, a
it perkKl; to Ihi^ remainder anneN the next peril
t alrendy fouml, and m\dX\\-\^' V's Wvtec, sad ann
CUBE ROOT.
two cipliers for the trial divisor. Find how oft^'ii tliis irial (li>
is contained in the dividen<l, and write the result in ilu* root.
Add together the trial divisor, three times the proihut of the
figure of the root by the second with one eijdier annex^'d, and
square of the second figure in the root; niultiidy th«* sum i>y tli<'
figure in the root, and subtract from the dividend; to th<« ivn
der annex the next period, and proceed as before
AVhen the trial divisor is greater than the divid«Mi<l. w rite a n
in the root, annex the next i)eriod to the dividend, and prortM*
before.
Desired the ^403039.
4S)m]\) (1\) ci\\ye root.
7X7X7 = :>4:5
7 X 7 X :} = 14700 Io00:i0
7 X <) X :j =: 1S90
9 X 1> = SI
1
>
\
vMra
Desired the ^'40:5:)S:J.4U).
150o:ji»
4<«r>S;}.4lO ( 7^].0 cube root,
7x7X7 = o4;}
7 X 7 X a = 1470<J
7 X 8 X :; = tm
•i A .> —
153:39
73 X 73 X 3 = 1598700
73 X 9X3= 19710
9X9= 81
1618491
Desired the ^158252.6:^2929.
005s;]
40017
14506419
145(H)419
15S252.(>)2929 ( 54.09 mhit rooi
5 X 5 X 5 = 125
5 X 5 X 3 = 75(X)
5X4X3= (>00
4X4= 16
•)•>.>.>-
')')j,ji')
81 1()
540 X 540 X 3 = S7480000
540 X 9 X 3 = 1458(M)
9 X 9 = SI
32404
7SS632929
.^'7025881
7SSi>:V2\VH\
TABLE
OP
, SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, ANJ
RECIPROCALS,
From 1 to 1054b.
The following table, taken from Searle's "Field Enginocring,'
will be found of great convenience in finding the square, cube
square root, cube root, and reciprocal of any number from 1 to 1054
The reciprocal of a number is the quotient obtained by dividing
by the number. Thus the reciprocal of 8 is 1 ^ 8 = 0.V2').
8
SQUARES, CUBES, SQUAKE KOOTS,
Xo.
Squares.
Cubes.
1
Square
Koots.
•
Cube Roots.
RecipxxKViis.
1
1
1
1.0000000
1.0000000
1.000000000
2
4
i 8
1.4142i:W
1.2599210
.500000000
3
9
27
1.7320508
1.4422496
.333338383
4
16
64
2.0000000
1.5874011
.250000000
5
25
125
2.2360680
1.7099759
.200000000
6
36
216
2 4494897
1.8171206
.166666667
49
343
2.6457513
1.9129312
.14285n48
8
U
512
2.8284271
2.0000000
.125000000
9
81
729
3.0000000
2.0800837
.111111111
10
100
1000
3.1622'm7
2.1544347
.100000000
11
121
1331
3.3106248
2.2239801
.090909091
12
144
1728
3.4&41016
2.2894286
.083333333
13
169
2197
3.6055513
2.3513347
.076923077
14
196
2744
3.7416574
2.4101422
.0714285n
15
225
8375
8.8?29833
2.4662121
.066666667
16
256
4096
4.0000000
2.519W21
.062500000
ir
289
4913
4.1231056
2.5712816
.058823529
18
324
5832
4.242t>407
2.6207414
.05.5555556
lU
361
(i859
4.3588969
2.6684016
.052631579
20
400
8000
4.4T21360
2.7144177
.050000000
21
441
9261
4.5825757
2.7589243
.047619048
22
484
10648
4.6904158
2.8020393
.045454545
23
529
12167
4.7958315
2.8438670
.043478261
24
576
13824
4.8989795
2.8844991
.041666667
25
625
15625
5.0000000
2.9240177
.040000000
26
676
17576 •
5.09C0195
2.{;624960
.038461538
27
729
196aS
5.11X51524
8.000COOO
.037037037
28
784
21952
5.2915()2()
3.a3C5^'89
.035714286
29
841
24389
5.3851048
3.0723168
.034482750
30
900
27000
5.4772256
8.1072325
.033333333
31
961
29791
5.5077644
8.1413806
.032258065
32
1024
32768
5.6568542
8.1748021
.031250000
33
1089
85937
5.7445026
8.2075343
.030803030
34
1156
39304
5.8309519
8.2396118
.029411765
35
1225
42875
5.9160798
8.2710663
.028571429
86
1296
46656
6.0000000
8.3019272
.0277771'7B
37
1369
50653
6.0827025
8.3322218
.027027027
38
1444
54872
6. 1044140
8.3619754
.026315789
39
1521
59319
6.2449980
8.3912114
.025641026
40
1600
64000
6.3245553
8.4199519
.025000000
41
1681
68921
6.4031242
8.4482172
.024390244
42
1764
74088
6.480740r
8.47GC266
.023809524
43
1849
79507
6.5574385
8.5033981
.023255814
44
1936
85184
6.6332496
8.5303483
.022727273
45
2025
91125
6.7082039
8.5508Ca3
.022222222
46
2116
97336
6.7823300
8.5830479
.021739130
47
2209
103823
6.K556546
8.(5088261
.021276600
48
2304
110592
6.9282032
8.6342411
.020833383
49
2401
117649
7.0000000
3.6593057
.020408163
50
2500
125000
7.0710678
3.6840314
.020000000
61
2601
132651
7.1414284
8.7084298
.019607843
52
2704
140608
7.2111026
8.7325111
.019230769
53
2809
148877
7.2801099
8.7562858
.018867925
54
2916
157464
7.34S4692
8.7797631
.018518519
55
3025
166375
7.4101985
8.8029525
.018181818
56
8136
175616
7.4833148
8.8258624
.017857148
57
3249
185193
7.549«U4
8.8485011
.017543860
58
.3364
195112
7.6157731
8.8708766
.017^1879
69 j
3481
205379
7.6811457
3.8929965
.016848153
60
3600 I
216000
7.7459667
\ %.9\A8fe1^
v .^<y«««s?
61 /
3721
226981
7.8102497
\ ^.«ai?AV»^
\ .QVSJSeWfii-
62 1
3844 /
238328
7.8740079
\ a.^'wa\?>
\ QVSfiWSfc
CUBK ROOTS, AND KECIPKOCALS.
l»
No.
Squares.
Cubes.
Stjuare
Knots.
Cube Roots.
1
Reoiproi'als.
03
3969
250047
7.9372539
3.9790571
.015873016
64
4096
262144
8.0000003 i
4.0000000
.015825(»00
65
4225
274625
8.0622577 \
4.«tt07258
.015:384815
66
4350
287496
8.1240384 1
4.0412401
.(Mr,l5ir)15
67
4489
300763
8.1853528
4.1K>15480
.(U4;»i"):i73
68
4824
314432
8.2482113
4.0816551
.014705^2
69
4761
328509
8.3036239
4.1015881
.014492754
70
4900
343000
8.3886003
4.1212KV3
.011285711
71
5041
357911
8.4281498
4.1408178
.(H4(>84r)(»:'
72
5184
873248
8.4852814
4.1801878
.01:38888^9
73
5329
389017
8.5440037
4.1793:390
.0138988:30
74
5476
405224
8.8023253
4.198:>3()4
.0135ia')14
75
5C25
421875
8.860-^40
4.2171():3:3
.oi:j:3:33:3:3J
76
5776
438976
8.7177979
4.2:r>S2:36
.(U:5l.57H«r)
77
5929
45653:)
8.7749644
4.254:3210
.012: H7(>i:J
78
6084
474552
8.83178()^
4.2728586
.012*^2051:5
79
6241
493039
8.8881944
4.2908404
.012858228
80
6400
613000
8.9442719
4.3088605
.0ie50(X)00
81
6561
531441
9.(KK)0000
4.:52()71X7
.012;5J:>()79
82
6724
551368
9.055Ca")l
4.3444815
.012195122
83
6889
5717H7
9.1104S'W
4.3(520707
.(rr.»01H193
84
7056
592704
9.1051514
4.:3795191
.01M»01782
85
7225
614125
9.2195445
4.35)6S2i»8
.01i;'81708
86
7396
636056
9.2r:J(;lK>
4.4140(M9
.011()2;SK)7
87
7569
658503
9.3.>7trj)i
4.4:il0n8
.011191253
88
7r44
681472
9..*i;v');vii.-,
4. 44798! ni
. 011:3(5:3(5:3(5
89
7921
704989
9.4;j3y8ii
4.4647451
.011235955
90
8100
729000
9.48883:30
4.4814047
.011111111
91
8281
75u571
9.5::X<J20
4. 1'.n'Jl 14
.(»10:tH5»011
92
^464
77868S
9.59100:30
4.5i4a:>r4
.OiO.^O'.CH).')
93
8649
804057
9.6438508
4..">:j(KkM9
.010752(588
94
8886
830584
9.6953597
4.548.>3."i9
.(M(-<i-J82US
95
9025
857375
9. 746794:$
4.r):>:K>28
.01(52(5:31(5
96 .
9216
8847;%
9.7979590
4."iKC,rO
.01011(5()C)7
97
9409
912673
9.8488578
4.. 59470! >9
.01o:5(K>278
98
9804
941192
9.89941M9
4.(5101:303
.O10->01082
99
9801
970299
9.9496744
4.8280850
.010101010
100
10000
1000000
10.0000000
4.8415888
.010000000
101
10201
1030301
10.0498756
4.(r>,eM)<»5
.00:>.aH)<.>;»;)
108
10404
1061208
10.0995049
4.072'>v>H7
Mr.Mn^zi
103
10609
1092727
10.1488916
4.(5"?75482
.<KK ; 087:38
104
10816
1124884
10.1980390
4.';v>2(5(»14
.(WKM5153K5
105
11025
1157625
10.2469508
4 7178940
.00!C):::i810
106
11236
1191016
10.2956:301
4.73282:35
.0(»;>i.j;3'.X)2
107
11449
1225043
10.3440804
4.7474594
.m.)V^:i7\)i
106
11(584
1259712
10.3923048
4.78220132
.00;i2."){fc»59
109
11881
1295029
10.4403085
4.7768582
.009174312
110
12100
1331000
10.4880885
4.7914199
.000090000
111
12321
i;%7631
10.5356538
4.8058955
.OOOOOIKKK)
112
12>44
1404928
10.5830052
4.8202H45
.008i)C85il
113
12769
1442897
10.6801458
4.S:i45881
.(KW-; :955s
114
12996
1481544
10.1770783
4.8488076
.(K)S7 71930
115
13225
1520675
10.7238053
4.8<529442
.(KW;0.5852
116
13456
1560896
10.7703296
4.K709990
.(KXv;:.2081K)
117
13689
1601613
10.8166538
4.8fK)9732
.(KK")17009
118
13924
1643032
10.862780.->
4.IK)48881
.008174578
119
14181
1685159
10.9087121
4.9186847
.008403361
190
14400
1728000
10.9544512
4.93243^2
.008333333
m
14641
1771561
H.OOjOOOO
4.9480874
Amz'SiAm
1^
14884
J5139
lHt5H48 1
11.0453610
4.05%7^'J
JJiS
mme? \
11.0905365
4.«7^\?S»
1 4.9ftWa\Q
j/ssre I
190(^24 '
11. ia55287
\ .Wf»Qfe«iV?»
>
12
SQUAUKS, CUBES, SQl'AUK UOOTS,
Square
lioots.
No.
Squares.
Cubes.
Cube Boots.
Reciprocals.
2i9
o-:jji
15438219
15.779r338
6.2911916
.004016064
250
ceooo
1562.70.K)
15.8113883
6.2996053
.004000000
5^51
O.JOl
15613251
15.8429795
6.3079935
.00o9840i>4
2.32
63504
16003008
15.8;'450i9
C.ai6;i596
.00&868254 !
253
61009
16194277
15.9050737
6.3:^7035
.005952569 ^
254
64516
16387064
15.93r:i;75
6.3330256
.003937006
255
65025
165813V5
15.908;i9l
6.3413257
.003921669
256
65536
16777216
16.0000000
6.3490042
.008906250
257
66049
16974593
16.0)12195
6.:3578011
.003891051
258
66564
1717:3512
I6.oo.:;^i84
0.:3()Ol!'.;08
.0G.S8759G9
259
6708t
173r3979
16.09o4709
0.3743111
.00:3861004
260
67600
17576000
16.12451.55
G. 3825043
.003846154
261
68121
1^779581
16.1554044
0.:e900705
.003831418
262
68044
14 984728
16.1804141
6.;39b8279
.00S8167W
263
69169
18191447
16.2172747
6.40()0585
.003802281
264
69696
18399744
16.2480708
0.4150087
.00:3787»79
265
70225
18609625
16.2788206
0.4231583
.003773585
266
70756
18821096
16.3095004
0.4312270
.003759396
267
71289
1J034163
16.3401346
0.4:302^.07
.003745318
268
71824
1924a«2
16.3707055
0.4473057
.003731343
269
72361
19465109
16.4012195
6.4553148
.008717472
270
72900
19683000
16.4316r07
0.40.33041
.003703704
271
73441
19902511
10.4620776
6.4n21-30
.003690037
2?2
73984
20123018
16.49^4225
0.4;02;;:36
.00:3676471
2;3
74529
20346417
16.5227116
6.4871541
.003663004
274
75073
20570824
16.5529454
0.4950053
.003649635
275
75625
20796875-
16.5831240
6.rA)29.'>72
.003036364
276
76176
21024576
16.6132477
6.5ia*300
.003623188
277
10729
21253933
16.6433170
0..51t;0ci39
.003610106
278
77284
21484i;52
16.673a320
6.520,->189
.003597122
^9
77841
21717039
16.7032931
0.5343:351
.003584229
280
78400
21952000
16.7332005
0..^>421.326
.003571429
281
78961
22188041
16.7630546
6.. 54991 16
.003558719
282
79524
22425703
16.?028V>6
6.. 5570722
.003546099
283
80089
22665187
10. 82200.38
6.. 50.54 144
.003533569
284
80656
22900: JO 4
10.852v>905
0..573i:3K5
.003621127
285
81225
23149125
10.88194:30
6.. 5808443
.003508772
286
81796
23393656
10.9115:345
6.-5885323
.003496503
287
82369
23639903
10.J)410743
«..50j202;J
.003484321
288
82944
2;S887872
16.9705(527
«.fK);J8545
.00:341^2222
289
83521
24137509
17.00000iX)
0.0114890
.003460208
290
84100
24389000
17.0293804
6. Gl 91 060
.0034-48276
291
84G81
24042171
17.0581221
0.0207054
.00:3430420
292
85264
24897088
17.0880075
6.6342874
.00:3424658
293
85849
25153157
17.1172428
6.0418522
.(K)3412969
294
86436
25412184
17.1404282
6.0493998
.0a3401361
295
87025
25672375
17.1755040
6.<>.569302
.00:3389831
296
87616
25934Ji36
17.2046505
6 0644437
.003.378378
2})7
88209
26198073
17.2330879
6.07194(K3
.00:3:367003
298
88804
20403592
17.262()7()5
6.6794200
.003:355705
299
89401
26730899
17.2910105
6.6608831
.003344482
300
90000
27000000
17. .3205081
6.G943295 '
.003333333
301
90001
27270001
I7.:349.i516
C. 7017593
.003322259 ,
302
91204
27543008
17.3781472
6.7091729
.0a3311258
303
91809
27818127
17.40689.52
6.7166700 1
.0033(J0330
304
92416
28094404
17.4355958
6.7239508
.00.3289474
305
93025
28372625
17.4642492
6.7313155
.00:3278689
306
93536
28652616
17.4928557
6.1-386641 ;
.003267974
307
^4249
2893444:)
17.5214155
6.7459967
.0a3257329
308
94mi
29218112
17.549«2«^
ft.'isaatai
.00:3246763
309
9^81 '
29.'50?3(J29
I7.r>7»;3<.>r^
ft.lftW^VASS
310 /
Oinod
29791000
17.WX*Ml>«
*i.w1WM»
CUBE ROOTS,
AM) UKCIPIIOCALS.
1 •"*
No.
1
Squares.
Cubes.
Siiuara 1
hoots.
1
Cube Root it.
ReoipnH'iils. \
311
96721
30080231
17.6351921
6.7751UiJ0
.«io:fc.M:4:ii
312
973W '
80371328
17.6635217
6.7WSM220 .
.00:320t.lu>
313
9r»69
80664297
17. 6918m JO
6.780661 i
.00:U04S^8
314
98596
80959144
17.7200451
6.70ti8844
.00:3184713 ;
315
99225
81255875
17.7482393
6.8040921
.003174»J0:3 '
31tt
99856
81554496
17.7763888
6.8112847
.OlWlt>45.")7
31T
100489
81855013
17.8044938
6.8184620
.Oo:31.>4.>74
818
101124
32157432 '
17.8325545
6.825(i.»42
.Oi«144»»."V4
319
101761
82461759
17.8605711
6.8;i^l4
.0O3134?J0
3^
103400
82768000
17.8885438
6.8399087
.0O312.")0tW i
3:21
1U3041
83076161
17.9164729
6.8470213
.00:31 1.-)265
3:22
103684
33386;M8
17.9443584
6.8541240
.00:3105.">{W
as3
104329
33698267
17.97^K)8
6.8612120
.00:300.5075
324
104976
84012224
18.0000000
6.8682855
.00:308<)420
a^
105625
84328125
18.0277564
6.87.'>;i443
.0(K307002:3
326
106276
84645976
18.0554701
6.8823888
.(Kt30674K'.
327
106929
84965788
18.0881413
6.8894188
.00:HV)8HU
328
107584
35287552
18.110770:j
6.8!M>4345
.00:31 Mi-r8i>
329
10tJ241
35611289
18.1383571
6.9034359
.003030514
330
106000
85987000
18.1659021
6.9104232
.Oa'3030303 I
331
109561
36264691
18.1934054
6.9ir30t>4
.00:3021148
332
110224
86594368
18.22086?^
6.9243.V>6
.00:3O12i>48
333
110889
86926037
18.2482870
6.981:3008
.00:i(K.):30o:i
334
111556
87259704
18.27566<J9
6.9:382321
.0<n.»j)040i-,>
335
112225
87596875
18.30:30052
6.9451496
.((L»iKi07.->
336
112896
87933066
18.330:3028
6.0520533
.0021>;G15H)
387
113569
88272753
18.357555W
6.9580434
.(H)20<)7:355)
338
114244
880144?2
18.384776:J
6.965Hli>8
.(H)20r)K")8()
330
114921
38958219
18.4119520
6.0726820
' .W)20408o;i ■
810
115600
89304000
18.4390880
6.979.5321
.0^^291117^.
811
116281
89661821
18.466185;^
6.9863681
.0(^>0:32551
342
116964
40001688
18.4932420
6.9931006
.00202:307:
843
117649
40353607
18.5202.VJ2
7.0000000
.(K)2<>i:>l5-.i
844
118386
40707584
ISSATSiTO
7.0067962
.lKh>00«07;
815
119025
41068625
18.5741754J
7.0135791
.(K)2808"i51
846
119716
41421736
18.()0107n2
7.020345K)
.00280017:3 ;
847
120409
4178192:i
18.627{)oW)
7.02710.58
.0028818J4
848
121104
1 421441S2
18.65475H1
7.0338407
.0028r<350.i
849
121801
42508549
18.6815417
7.0405806
.002865:330 '
850
122500
42875000
18.7062860
7.04^.2987
.(;028,-)7143
851
128201
43243551
18.7;i4{KM«)
7.0540041
.(K)2H400i.):3
852
123904
43614208
18.7(}1()(>:^)
7.060C0()7
.(NJl^yOOOO
858
vzvm
43966977
18.7882042
7.0()737C7
.0028:32801 '
854
126316
44361864
18.8148877
7.0740440
.(K)28248VJ ;
85ft
126025
44738875
18.8414487
7.080G088
.00281G})01
356
12Gr36
45118016
18.807%2J
7.0873411
.(X)2808080 i
857
127449
454992!K)
18.8(M4J:^)
7.00397(K)
.0028011-00
358
128164
45882712
18.92UM70
7.1005885
.OO270:320<J
859
128881
46268270
.H. 947205.]
7.10710:37
.002785515 1
S90
129600
46656000
18.9736(>.»
7.11.378()G
.002'i7i i78
861
130321
47045881
19.0000000
7.1203(574
.im77{)<>\ :3
36v>
131044
4743792K
19.0262970
7.1200:3()0
.0027024/:!
Ul
131769
47832147
19.0525580
7.1.33402.-)
.0027-54821
364
132496
48228544
19.0787840
7.1400:370
.00274725:3
365
1832:£S
48627125
19.1049r32
7.1465005
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366
133956
40027896
19.13112a5
7.1530001
.0027:32240
867
134689
494:*H>J
19.1572441
7.1505988
.00;>7247!X>
868
135424
49836<K«
10.18;W2(}1
7.16609.57
.000717:301
869
136101
60243409
10.20937X»7
7.17^25809 1
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870 i
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190000 1
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19.2353841
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1098304
iiaioaawj
100
1100101
83 3H«1,!B
lino
33 4087035
10 16S9IWt
nwani
1I6043K.11
83 4111301
lOlffTlRBS
1100704
iifniswoa
K434WB5
oixiwHna
lOM
3£44llfl<iia
imiwaen
^
ITW
IllOflIB
IlTOBOWSl
33 4653001
10 1708538
a<nu^
1
ET
1
WEIGHTS AND MEASl RES. ^^^T^fl^B
■WEIGHTS AND MEASURES.
Measures of Leiigtfi.
12 Inches = 1 loot. J
8 feet =1 yaril = ;mi lii.lie*, 1
iS yards = 1 roil = I IW indies - IftJ (1, 1
tt rods - 1 furlong = IIMI iiichi'fl = IJHO ft. = 220 yiis.
8 mrloiisp = 1 mile = UaatiO liicliei. = ri2W ft. = 1760 yds.
1 yard = IKICKCfiHl! of a raik. | = rial rodn.
k GrSTKL's 0»A<N. J
^B T.DS indws = 1 link. 1
^H 100 links = 1 clmln = 4 rorl» = <i() feet. 1
^H 80 diainH = 1 mile. 1
6 fept = 1 fHtliuiii. 120 fatliuiiis = 1 falil.-'s l.^iiglh.
Stable ahowing Inches expressed in Decimals of a
Foot.
' i!^L;!_! _v'_'.' ' ' v'..' 'A 1 i_" '_!_' '"' " ^jul
x..'^ ■:;;■■■ ^'. ■ ' ii
W' 17'^ 3-8'
, li^'rj -■■ iV IS-W
le-:i-i !■..■. ■ J- .■'■.. ■'■■ . -■• .1 . 1 i . 1 ■■>ii] 19-3-.;
IM1 .■■■■ . -■ -7 1"
aa-iii: ■ ■ ■ ■ii'ii
Bi_i-: .i ' . -"" imi .T.i:4.fi3u;|.Bui.WT'
3i-M
25-32
13-lfl
a7-32
39-3!
I5-W
1
^- .. , , . ■■ - . ^ .\w\^^^
J
m^ %
24
SQUARES, CUBES. SQUARE ROOTS. ETC.
No.
Squares.
Cubes.
HilUHIt*
Roots.
Cube Roots.
Keoiprucftls.
093
980049
97914ttV57
81.5119025
0.9766100
.001007049
991
9Sd03(}
9^«1077K4
31.5277ri.V,
0.0790590
.Ui)lUUJU»i
095
990025
9H.J074875
81..Vi;*)20ti
0.9833055
.(li)10U3U£)
09G
092010
9Krt0479:)(i
31..V>94<)77
0.9H6<MM
.0010^916
097
994009
99102097.)
31. 57531 *W
0.9K<K)9aO
.001000009
0!H
9J6004
9940119S^2
31 5!)113N0
0.9033280
.001002001
0J9
90S001
!r^7002;>99
31.(MN{%13
0.9966056
.(K)1001001
1000
1000000
lOOOOOOOJO
31.G22T7JHi
10.0000000
.OOIOOOOU)
lOvlI
1002001
10O»0:3001
81.(«85K10
10.0033322
.oooeooooio
lOJJ
10>1004
10060120.M
31.654:jH:ki
10.0060622
.0009UH001D
100)
1006009
1009027027
81.0701752
10.0099800
.0000070000
1001
1006016
1012 480G4
31.685ir><H)
10.0183155
.0000960150 ,
1005
1010025
10l50r)125
31.7017:J49
10.0166389
.0000960248 ,
lOOG
1012030
1018108216
31.717503:) ,
10.0190601
.0009910658 <
1007
1014049
1021147313
31.73:fc»J3.3
10.0232791
.0000080^7
lais
1016064
1004192512
31.7490157
10.0365058
.0000020635
1009
loiHasi
1027*13729
81.761760:J
10.02JK)104
.0000010808
1010
1020100
103)301000
31. 78049 W
10.08:30228
.0000000990
1011
1022121
1033361331 1
81.?J<i22<W 1
10.0365:330
.OX)OflOll97
101^
lOt^lU
103643;)?28
31.8119474
10.089(^10
.0001)^142}
1013
1006169
1039509197
81. 82766* » .
10 013146i)
.0009871668
1014
1008196
1042.590744
31.8433066
10.0101506
.O0O9H6l8n
1015
1030225
101567H:)r5
31.8500646
10.0497521
.OOOi)8S0217
1016
1032256
1048772096
81.8747549
10.0580514
.OOOgtM25dO
1017
1034280
1051H71913
81.8904374
10 0568485
.0009832813
1018
10:)63»4
ia")i9rrK32
81.9061123
10.0500185
.0009»i!31K3
1019
1088361
lOsso-fiK-yj
31.1«17794
10.0629364
.(MXIOHI^IS
lOiO
1010400
10612080J0
81.9:i74388
10.0662271
.OOOOHOaOtt
1021
101:^1
1064332201
31.9530900
10.06051.50
.0009704819
10;^:$
1044484
10«74(i261S
31.9»W7:U7
10.0?2802)
.00007847SI '
1033
1046529
1070591H67
31. 9S 13712
10.070086)
.000977Sin
10:21
1048576
1073741821 ■
32.(l);K)i)iU
10.0798(S81
0009765003
10»
1050625
10r<»S90625
32 0150212
10 0826481
OOO97560U
10;»
1052676
1080015576
32 0Jl-J:ilS
10.0859262
.0009746660
10i7
1054729
10«32;)G<iS)
32.0M5S1;)7
lO.OKSttOlO
OOOTlTSnM
10J8
1056TH4
10S6:573J>:i2
^.0;i24m
10.09*1755
00007?rOs«
1029
1058841
10^{)517:)<9
32. 078)2.) <
10.0957469
.000!r7l8l73
1010
1000900
1092727003
32 09:)61.)1
10.0990163
.0009708793
1031
1062981
10ir)912791
32 10918S7
10.1023835
.ooooooosn 1
1012
1065024
109910 170S
32. 121751) <
10.ur>5487
.00 9689032 '
10:38
1 10670.S:)
1102*tt5«7
:«. 110317.)
10.1088117
.0:H»68051i
1034
; 1009156
lia")507:J01
32.1.558701
10.1120726
.0009671180
10:i5
i 10ri2i)
1108717875
:)2. 17141.59
10.1153314
.0009661886
1036
1073296
111198»r)6
32.18<;a5:)9
10.1185880
OOOAWSIO
ia37
. 1075369
1115157653
32.2021X11
10.121W28
.O000O13WS 1
10:«
1077444
1118.^5^2
32.218»K)71
10.12.V)953
.0000638011
1019
. 1079521
112Hi22JI9
82.2:);iV229
10.1-2S3457
.OOOOftU680
1010
1081600
1124864000
32.2190310
10.1315941
.OOOgOIRMS i
1011
1083681
1128111021
82.2045316
10.1.^)48403
.0009606148 '■
1012
1 10a5764
11313li()iW8
32.2S<X)2W
10.1:380845
.0009500889
1043
1087849
113W2<».><>7
32.2aV)105
! 10.1413206
.0000587788
1044
. 1089936
113789:)IS1
32.3109888
10.1445667
.0000578544
1045
1092025
. 111116('il25
32.82<>1.598
10.1478017
.0000560878
1 1046
' 1094116
lU1445ri«
32.aiH>2:i:)
10.1510406
.ooooseossi
; 1047
. 1096209
11477:«K23
32 .357:)?.U
10.1.M2744
• .0000651008
• 1(M8
1098304
11510225«)2
: 32.372St«I
10.1575<Mi2
.oooouioes .
1049
1100401
115432l)(W9
82.3H82lHr»
in.Ui07:i59
.000058SaRR
1050
11025013
j 1157025000
82.4(W7ar>
10 1039636
.0000608810
1051
1104601
ll«0935*r)l
■ 82.4101.301
10. 1071893
0000614748 i
1052
1106704
1161252»K)8
, 32 431511I5
10.I7(U129
a)0950S7tn
J0S3
1108809
, n«7575877
1 82.44WH)U>
\V> AT.VV.su
.VX\(WU9Q676
2:iU
1110916
JI7090W(M
1 a2.4tt5:%»Vi
\0 .llW^y^^
<Mo»Msnmk
WEIGHTS AND MEASURES.
^TmOHTS AND BtEABURBB.
Meattiires of Length.
12 Inches = 1 foot.
a feet = I yard = 3(1 in<:h«a.
5t yards = 1 rocl = HO inches = lOi ft.
4;i rods = 1 furionj; = 7it20 inclii's = 1(00 ft. =
t* furlongs = 1 mile = 83380 Inclips = -laso ft. =
I).()I)U>8H^ of a mile.
I (rhain = 4 rods = 88 feet.
6 feet = I futhoiil. 120 fatlioiiiH = I cuble's length.
'able Bhowing Inches expressed in Decimals of
Foot.
i;I't>
ii-i«
a-i
I3-I'i
19^:-
p
^T OF WEK^^^^^^^H
1
18 ilnu:l.in» = 1 ouiil-t, (oa.). j
■
10 ounces = 1 ponnil, (lb.).
I
100 pounds = 1 limidivil wpigliL (cwt. ).
1^
20 bundrml w i-iuljL = 1 ton.
■ In
ollprting dutieti upon rorfign goods nt the United S
-■T'"
i-hi>usea, and tilBo In freiglitlng ciml, and aelllug it by w
2M iioimds = 1 quarter.
4 quarters, or i 12 lbs. = 1 hundretl weiglil.
■M hundrral iieigiil — 1 long ion = ±.'41) i>oiiada.
A atone = 14 iwunds.
^
A quintal - 1(X) iionnUa.
The
32 pounds uf OHts = 1 llllshel. ^
.
40 poiuKis of T1iiiuii>y-sc<id = 1 busbel. ;^^H
48 pounds of hnr[vy - I busheU^^H
,,
60 pounds of rye = 1 buslid, ^^^|
50 |>uundB of in<li»n L'urn =1 bushel., ^^H
1
SO pounds o( Indian meal = 1 bushel. |
OU potuids of whenl = ] bushel.
UU puiuida of dover-aeett = 1 bushel.
(to pounds of potntoes = I bushel. „^^J
■
50 pounds of butter = 1 Urkin. ^^H
100 pouixls of nienl or Hour = 1 saek. ^^^|
100 iKiunds of grain or Hour = 1 I'entsL ^^^H
100 poiuids of dry lisli = 1 quintal, ^^H
100 poLuids of nail" 1 >-ask. ^^^|
intl pounds of Hour = i burel. ^^1
aOO pounds of bwt or imrk = 1 barrel. ^^^|
^
Tro]' Wei^lit. ^^H
■
V8E1> IN WRIoHtSn iiOLU Olt SILVEB.^^^H
Si grains = 1 penn;>relght |pwt^^^|
iO pi>uuy\v>>ii>lit8 = 1 ounce (oz-i^^^^M
l^ouuees = 1 |>ouud (Ib.).'^^H
' .-1 eaml at \iw jewtieiTa. for pivc-litim stoiiPs. Is. in the O]
; 8(««, 3.2 gmiiist 111 I-oiHloti, :!.ngrBius, in Paris. 3.18 gi»i«
j^^glHl
yato 4 jewellera' smlns. In troy, apolliecarie*', mkLC
■
Bdlts, Uif grain is thu mow. "^^M
MEASURKS OF VALUK AND TIMK. 29
Apothecaries' Weljflit.
SED IN COMPOirXDINO MEDICINKS, AND IN PITTINC4 ri»
MEDICAL PRKSCRIPTIOXS.
prains (gr. ) = I scruple ( 3 ).
cmples = 1 drachm ( 3 ).
8 drachms = 1 ouucc (oz.).
12 ounces = I iiound (lb.).
Measures of Value.
UNITED STATES STANDAKI).
mills = 1 cent,
cents = 1 dime.
10 dimes = 1 dollar.
10 dollars = 1 eagle.
le standard of gold and silver is OCX) parts of pure metal and
>f alloy in 1000 parts of coin.
le JineneHS expresses the quantity of pure metal in 1000 parts.
e remedy of the mint is the allowance for deviation from the
I standard fineness and weight of coins.
Weight of Coin.
Double eagle = 516 troy grains.
£agle = 258 troy grains.
Dollar (gold) = 2.5.8 troy grains.
Dollar (silver) = 412.5 troy grains.
Half-dollar = 102 troy grains.
5-cent piece (nickel) = 77.10 troy grains.
3-cent piece (nickel) = 80 troy grains.
Cent (bronze) = 48 troy grains.
Measure of Time.
seconds = 1 minute. ' 8(55 days = 1 common year,
minutes = 1 hour. ! 3<i6 days = I leap year.
hours = 1 day. I
Holar day is measured by the rotation of the (^artli ui)on its
with respect to the sun.
agronomical compatalion and in nautical time, the day com-
ixes at noon, and in the former it is counted throughout the "2-1
s.
ciril computation the day commences at midnight, and Is
led into two portions of 12 hours each.
ifolar year is the time in which the earth makes one revolution
nd the sun; and its average time, called the mean nolar year,
5 days, 5 hours, 48 minutes, 40.7 seconds, or nearly 865i days.
mean lunar month, or lunation of the moon, is 29 days, 12
•8, 44 minutes, 2 seconds^ and 5.24 thlrda.
t'Al,KNDAK. — A>"GL'[.Alt .IJKASl'RK
TUe Caleudiu-, Old niid New Style.
■^ Tlif JiUiiM Calendar was pstalilislu' I l>y -liUius Cr
nnil liy It one day was inserted in every fgurth yitar.
aame thing as assuming tliat the tengtli of tite solar ye*r in
tiays. a hdiirs. [iistead of thi! value given above, thus fntmj
an a<rciimulBtivp error of 1 1 iiiimites, 12 aeconds, ever? year. '
calendar was adopted by the church ii) 325 A.D., at the Com
Xlue. In Llie year 1562 the annual error of I i minutes, 12 aee
liad aiiioiiiitiTl toft perioilof Itl (lays, which, hy order of Pope<
ory XIII., was suppressed In the, calendar, and the 5th of C
rui'koueil as tlie Mth. 'I'o prevent the repetition of thia tn
waa ilecidt>il to leave out thre« of tlie Inserted days evray 400 j
and to make thia omission in tlie years which are not exactlj d
Ue by 400. 'riiiia, of tlie years 1700, 1800, IBOO, 2000, all of n
are leap years according: to the Julian Calendar, only the last
leap year acconling to thn Ili-Jimiie'l or Vi-fyiiriua Calendar.
Reformed Calendar was not adopte<l tiy En(;land until
II days were oiultted from the calendar. The two calftoilMi
now often called the OOl N'i/(c and the Neie Stule.
The latter style is now mlopteU in every Clirlstian country el
Russia.
Circular and Angular Measures.
-TWl degrees — I cirfumference (C. ).
SeconilAaK usually subdivided into tenths and hundredths.
A iiiiniile of Ihe circumference of the earth la a geographVi
Degref^ of the earth's circiliiiferpniie on a meiidian aveiage ViW
upon a unit called a
THE METKIC ST STEM.
teui of wci^lits and measures
easures \»m
nee fran^fl
ceuttejfl
THE METRIC SYSTEM. .Ml
Tlie names of derived uietric denominations are formetl by pre-'
ixing to tlie name of the primary unit of a me^asare —
Milli (niiire), a thousandth, j Hecto (liek'to), one h unci red.
Centi (sent'e), a hundredth, Kilo (kil'o), atliousand,
Deci (des'e), a tenth, Myria (mir'ea), ten tliousand.
Deka (dek'a), ten, I
This system, first adoi)ted by France, has been extensively adopted
:>y other countries, and is much used in the sciences and tlie arts.
tt was legalized in 18116 by Congress to be used in the United States.
%nd is already employed by the Coast Survey, and, to some extent,
by the Mint and the General Post-Office.
Linear Measures.
The meter is the primary unit of lengths.
Table.
10 millimeters (mm.) = 1 centimeter (cm.) = 0.3937 in.
10 centimeters = 1 decimeter = 3.937 in.
10 decimeters = 1 meter = 39.37 in.
10 meters = 1 dekametei: = 393.37 in.
10 dekameters = 1 hectometer = 328 ft. 1 in.
10 hectometers = I kilometer (km.) = 0.02137 mi.
lO kilometers = 1 myriameter = (i.2137 mi.
The meter is used in ordinary measurements; the centimeter oi-
willimetet', in reckoning very small distances; and tlie k'Hoim^tcr.
for roads or great distances.
A centimeter is about ^ of an inch; a jnHer is about 3 feet 3
inches and I ; a kilometer is about 200 rods, or f of a mile.
, Surface Measures.
The Miuare m^ter is the primary unit of ordinary surfaces.
The are (air), a square, each of whose sides is ten )neters, is
the unit of land measures.
Table.
100 square millimeters (sq. mm.) = 1 square I — q J55 g^ jj^^j^
centimeter (sq. cm.) ) *
100 square centimeters = 1 square decimeter = 15.5 sq. inches.
J 100 square decimeters = 1 s'luare I ^.^ ^^^ ^^ ^^^ ^ ^^
^KTKB (sq. W,) )
38
MENSURATION.
An eUiptfe is the section of a cone when cut by a plane paMiif
obliquely through both sides, as at ab. Fig. 21.
A pavaholu is a section of a cone cut by a plane paralld to iti
side, as at cd.
A hyperbola is a set^tion of a iH>ne cut by a pUme at a greater
angle through tlie l^ase tlian i» made by the side of the oone, is
a' Hi.
In tlie ellipse, the inuwter^t axi«, or lowj
diameter, is the longest line tliat can be drawn
through it. The cot^jnyate axin, or short di-
ameter, is a line drawn through the centre,
at right angles to the long diameter.
A Jrntftum of a pyramid or cone is tint
which remains after cutting off the upper part
of it by a plane parallel to the base.
A Hphere is a volume boimded by a curved
sui'facc, all points of which are equally dis-
tant fi*om a i)oint within, called the centre.
i>leiisliratioii treats of the meanarement qf lines, ntirfiMtti
and r(dnnten.
KUL£8.
To co)apute the area of a aqaare, a rectanglCf a rhombus, W o
rhondjoid.
lU'LE. — Multiply tb«» length by the breadth or height; thus, to
ritlior of V\ii^. 2*2, 2:3. 24, the area = ah X hr.
^Flg.21. ^
Fig.23
Fift.24
To compute the area of a triangle.
c RrLE. —Multiply the base by the altS-
tudt^. and divide by 2: thus, in Fig. :S,
ab X vd
area of a be
*}
i Titjind the length of the hypothemuse tfti '
ji(//it-antjl** triaucil*' \rl^e\i HotK cidai
are fcaoicu.
ANCIENT MEASURES AND WEIGHTS.
38
Table.
10 milligrams (mg.) = 1 centigram
10 centigrams
10 decigrams
10 grams
10 dekagrams
10 hectograms
10 kilograms
10 myriagraiiis
10 quintals
= 1 decigram =
= 1 GRAM (g. ) =
= 1 dekagram =
= 1 hectogram =
= 1 KILOGBAM (k.) =
= 1 myriagram =
= 1 quintal =
0.1543 troy grain.
1.543 troy grains.
15.432 troy grains.
0.3527 avoir, ounce.
3.5274 avoir, ounces.
2.2046 avoir, pounds.
22.046 avoir, pounds.
220.46 avoir, poimds.
= 1 TOXNEAU (t. ) = 2204.6 avoir, poimds.
The gram is vised in weighing gold, jewels, letters, and small
quantities of things. The kilogram, or, for brevity, kilo, is used
by grocers; and the tonneau (tonno), or metric ton, is used in find-
ing the weight of very heavy articles.
A gram is about 15^ grains troy; the kilo about 2^ pounds avolr-
<lupois; and the metric ton, about 2205 poimds.
A kilo is the weight of a liter of water at its greatest density; and
the metric ton, of a cubic meter of water.
Metric numbers are written with the decimal-point (.) at
the right of the figures denoting the unit; thus, 15 meters and 3
centimeters are written, 15.03 m.
Wlien metric numbers are expressed by figures, the part of tha
expression at the left of the decimal-point is read as the number
of the unit, and the part at the right, if any, as a number of the
lowest denomination indicated, or as a decimal part of the unit;
thus, 46.525 m. is read 46 meters and 525 millimeters, or 46 and 525
thousandths meters.
In MTiting and reading metric numbers, according as the scale is
fO, 100, or 1000, each denomination should be allowed one, two, or
hree orders of figures.
SCRIPTURB AND ANCIENT MEASURES AND
TVEIGHTS.
Scripture Longr Measures.
Inches.
Feet.
Inch en
Digit
= 0.912
Cubit
= 1
9.888
Palm
= 3.648
Fathom
= 7
3.562
Span
= 10.044
Egyptian Long Measuvei^.
kJjud cubit = 1 foot 5. 71 inches. Royal cubVt = \ IoqX.^.^ Vaj3as*
AKlUENT MKASilRKS AS!) WEIOHTS.
Grecian Limu; MeaNiiroH.
— ().7.Ki4 Slmliiini = (Ml
= 1 O.LH75 I MiW = -INl
= I I. .IBS*; I
JeivlHli Lonff MciiNnr^s.
- 1.824ft. I Mile ^ :
mnir>j- = :«148 it. 1 Day's jimnipj- = :i:l
Komuii Loiiti; MeiiHiireH,
■iMgll - U.-ar.T". Cubit
Uncia (inch} = (1.1X17 I'lusus
Pea (toot) ^ ll.iHi; I m]e (tnlllai'lii
Konuii) Weight.
Andent liblim = O.TOIM jioimil
Ancient WeiKlitx,
04 nd
1
L 3i.a
ilriiiirlus (ltofnan)= | i|2.|^
Atlic ilrftciiMia = I r^l.ll Di'imHi
I mt I 415.
Egyptiaii mini = K.aae Oim.'.- = ] 437.
Ptolemaic miim = S.II85 I 431.3
L««Ber mliia - 3.8112 Drwdiin = 14fl.6
Greater nilna = t\i uf l^rac^llTJla.
Tfttntt = ttO tiiliite = no poumU
round = 1 2 Koman oimcna.
In Ihli \m\. Ublo, wIktl- Iwii or lonre vxIdim Qra |
iIkv uc Iruiu illffunul uulliiirltlua uii tbo riibji-cl.
Mlficellaiieoiis.
=a
-i/aWan toot — l.llll'i Hpliri?« lim. -..-^
ffaby/otilan foul = 1.14(1 I HeXirvw iwUv =\a(i
MENSURATION. - DEFINITIONS.
dd
MENSURATION.
m
DefinitioDH.
A point U that which has only position.
A plane is a surface in which, any two points Iwini? taken, tlie
ralght line joining them will be wholly in the
irface. ^ Fiji
A curved line is a line of which no portion is ^ Curved Line
traight (Fig. 1).
Parallel lineit are such a^ are wholly in the same plane, and have
\w same direction (Fig. 2).
A broken line is a line compos(\l of a
A*ries of dashes; thus, -. . f«9-2
An amfle is the opening l>etween two ParuUei Linen.
hues meeting at a point, and is termed a r'lyht anylf when the two
hues are perpendicular to each other,
»n active angle when it is less or
sliarper than a right angle, and oh-
tiuse when it is greater than a right
angle. Thus, in Ftg. 3,
A A A A are acute angles^
0 0 0 O are obtuse anglea,
^^ K R R are right angles.
Polygrons.
^polygon is a portion of a plane bounded by straight lines.
♦"^ triangle is a polygon of three sides.
^fcalene triangle lias none of its sides equal: un /.sr>.s(v7^.«< tri-
'^yie has two of its sides equal; an ev'f/-
"'^cra/ triangle has all three of its sides
«mai.
, ^ ^yht-angle triangle is one which has a
'■'ght angle. The side opposite the right Fig. 4.
"l? ^® called the hypothenuse; the side on Right angle TriuDgie.
^^h the triangle is supposed to stand is called itb ^(^s(^ and the
'"'**»• side, its altit;ude.
FI0.B.
eealme Trtaogle.
Fig. 6. "tXv"^-
I»oscelett Trtau^fcW. \S»^u\\a.vviX«\ '^^\»»
36
GEOMETRICAL TERMS.
A fitififlfilntffral is a polygon of four sides.
(juailrilaterals are (Hvided into classes, as follows, — the trope-
limn (Fig. 8), which has no two of its Mdes parallel; the tn^^ezoU
I Fig. 0), which has two of its sides |)aralU'l: an<l the parallelogram
I Fig. 10), whi^li in imiindeil by two i^irs of parallel sides.
\
\
/■
L
7
Fig. 9.
Fif. 10.
A i»anill<'lo«;nuii wliosc' sides an* not equal, and its angles not
ri^lit aimU's. is culled a rhnmhoid (Fig. 11); when the sides are all'
«f|iial. hilt th<' :iii<:l('s are not riglit angles, it is called a rAoii»6irji
r Fig. VI) \ and. when the angles an^ right angles. It is called a reeUut-
ifle ( Fig. l'{). A rcelungle wluyse sides are all equal Is called a 9quart
{ Fig. 14). Polygon* whos*' si<l«»s an» all oqnal are called reffular.
/
I
Fig. 11.
Fig. 12.
Fig. 13.
FI9. 14.
IJesides tlie S(iiiar<» ami wiuilateral triangles, theje are
'Ihf in'ntafjnn (Fig. 15), which lias five sidf»s:
The hexuiion (Fig. 10), which has six sides:
The hi'ittainm (Fig. 17), wliich has seven sides;
'I'lie orUnjitn (Fig. 1?^), which has eight sides.
Fig 15.
Fig. 16.
Fig. 17.
FI1.I8.
'I'lie f'lnirdifon has nine sides.
The dccdifon lias ten sides.
T'lie doilecayon has twelve sides.
For nil poly frons, the side upon w\V\e\\ W \r %wvv^^««^\av^k&^^
caJItni its banc ; tlw ]>eri)eudicular disiauce ivoia WwiVii^^vsaX^N^*
GEOMETRICAL TERMS.
37
Sngleto the base (prolonged, if necessary) is called the altitude ; and
a line joining any two angles not adjacent is called a diagonal.
A pefimeter is the boundary line of a plane figure.
A circle is a portion of a plane bounded by a curve, all the points
of Which are equally distant from a point within oalle<l the centre
(Fig. 19).
The circumj'erence is the cun'e which hounds the circle.
A rrtcZt?(« is any straight line drawn from the rentre to the cir-
ciitiiference.
' Any straight line drawn through the centre to the circumferemo
on each side is called a diamete^r.
An urc of a circle is any part of its circumference.
A chord is any straight line joining two points of the ciirumfer-
elni:e, ^i hd.
A segment is a portion of the circle
included between the arc and its
rhord, as A in Fig. U).
A sehtor is the space included ho-
tween an arc and two radii drawn to
its extremities, as B, Fig. ID. In the
figure, ab is a nidins, al a diameter.
and (lb is a chonl stiblcrtding the arc
bed, A tai^genf is a right line which /
in passing a ciu've touclu'S without
cutting it, as ./>/, Fig. \\).
Fig. 19.
\
I
Volumes.
\priAin is a vohune whose emls are equal and parallel polygons.
and Whose sides are parallelogi-ams.
A pHsni is triangular^ rectangnl<n\ etc., according as its ends
are trian^/leitf rectamjles, etc.
A cube \s a rectangular prism all of whose sides are squares.
A cylindf^r Is a vohune of uniform diameter, boiuided by a curved
suiface and two equal and parallel circles.
A. pyramid is a volume whose base is a polygon,
and whose sides are triangles meeting in a point
<*Alled the vertex-.
A pyramid is trlangidar, qiiadrangnlar, etc., ar-
wrding as its base is a triangle, (juadrilatei-al, etc.
A rout is a volume whose base is a circle, from
^hich the remaining surface tapers unifonuly \u
spo/iji or vertex (Fig. HO). ^^^' '^^•
^(9Ji/c ffdctwHtf are the figuren made by a plane ewVWw^ ?k. cow'^;.
MENSUHATION.
An cUipiie Is tbe section of a ci
nlTtlquely through bolb s1<]c«. u a1
A parabi'lii is a sei-lioii of a i\
e wlipn cut by a ]>laiii> pamiiM
6, Fig. 21.
e uut liy n plane juirallel U
A linperbuhi Ih a aeuUuu uf h rviw out lij' a plane Mag.
niigle througli t.lm tvasv tliaii Ik iiiaiie by r.lie hIiIv of the c
111 tlw ellipse, llie IraiiHrei'nr uxi», t
ilhiwelrr. is the longest line tliat <An be
Lliiiiiigli it. Tbe euvjunatu uxln. or a/i
■imcti'r. la a line drawn tbroiigh tlie c«BUi
at light angles to tlie long illaineter.
A /niHl.iiiti of ft pyrilmUl o
u'liicli remains after entting aft the upper {1
nf it by B. plane parallel to the base.
A "iifivi'p is a voluuii* botiniiwi by a can
siLi-fac-e. all iwints of which are equally d
liiiii trorii a point witlilii, called the centre.
To coiiipute the (irff it/ n m/Fuirr, 'i i-pctannle,
rlioiiibuid.
llVLB. — Slulliply tbe lengtb by tbe hreaiUlu
i-illier of Fit!'- '^i. ■^^. ^4. Ibe an-a = iili x l,r.
mp na.23
— Multiply ilie base by tl
i divide by 2; thus. In I
ah X c<I
1 of tibc = 2
fi\i'l tlie l«iti|t)i of' tliv hui>uMi«auMt^
i-i)/ Jil-nivjjl'' IvlniigV" ""
ui-e Iciiouin.
MENSURATION. — POLYGONS.
89
Rur.E:. — Square the length of each of the sides making tlie right
Ligle, add their squares together, and take the ^^
^iiare root of their sum. Thus (Fig. 26), the
sngtli of ac = 8, and of bv = 4; tlien
o/j = 3 X 8 = 9 + {4 X 4) = 9 + 10 = 25.
^25 = 5, or ab = 5.
^o find the length of the base or altitude of a riyJtl-angle triangle,
when the length of the hypotlienuse and one side U known.
Rule. — From the square of the length of the hypothenuso
iibtract the square of the length of the
)tlier side, ajid take the square root of
he remainder.
To find the area of a trapezium.
Rl'I.k. — Multiply the diagonal by the
siiui of the two perpendiculars falling
upon it from the opposite angles, and
divide the product by 2. Or,
ah X {cf -f- di)
2
= area (Fig. 27).
To find the area of a trapezoid (Fig. 28).
RuLK. — Multiply the siun of the two par-
allel sides by the perpendicular distance between
them, and divide the i)roduct by 2.
To compute the area of an irregular polygon.
Kiii.E. — Divide the polygon into triangles
l)y means of diagonal lines, and then add to-
ilet her the areas of all the triangles, as yl, J^,
and C (Fig. -21)).
7'o find the area of a regular pob/y on.
Rule. — Multiply the length of a side by
I he perpendicular distance to the centre (as
ttOy Fig. 30), and that j^roduct by the number
of sides, and divide the result by 2.
7o compute the area of (( regular polygon
ichen the length of a side only is given.
JiULE. —Multiply the square of the side b>j
thp wiililpl/er opposite to tlie name oK the
noiy^rojj in coluwn A of iho folJowino; table; —
^vV*^^
50
MENSURATION. — CIRCUMFERENCES-
CIRCUMPBRBNCBS OP CIRCLBS.
(advaxcixcj hy kkjiitiis.)
CIRCUMFERENCES.
Dian.
0.0
0
0.0
1
3.141
2
6.283
3
9.424
4
12.56
5
15.70
6
18.84
7
21.99
8
25.13
9
28.27
10
31.41
11
34.55
12
37.69
13
40.84
14
43.98
15
47.12
16
50.26
17
53.40
18
56.54
19
59.69
20
62.83
21
I 22
' 23
I 2>
26
27
28
29
30
; 31
i 32
33
34
35
I 36
I 37
' 38
: 39
i •*»
I
' 41
' 42
/ 44 !
t'J
65.97
69.11
72.25
75.39
78.54
81.68
84.82
87.96
91.10
94.24
97.39
100.53
103.67
106.81
109.96
113.10
116.24
119.38
125.66
128.81
131.95
h'i/i. 09
i:iH.'j:i .
I4j.:i7 I
i
o.i
I
0.3927
3.534
6.675
9.817
12.95
16.10
82.07
85.21
88.35
91.49
94.64
97.78
100.92
104.07
107.21
110.35
113.49
110.63
119.77
122.92
126.06
129.20
132.34
135.48
l:iS.62
14h76
19.24
22..38 i
25.52 I
28.66 ;
31.80
34.95
38.09
41.23
44.37
47.51
50.65
53.79
56.94
60.08
63.22
66.36
69.50
72.64
75.79
78.93
I
o-i I o.|
0.7854
3.927
7.068
10.21
13..35
16.49
19.63
22.77
25.91
29.05
32.20
35.34
38.48
41.62
44.76
47.90
51 .05
54.19
57.33
60.47
63.61
66.75
69.90
73.0 1
76.18
79.32
82.46
85.60
88.75
91.89
95.03
98.17
101.32
104.46
107.«)0
110.74
113.SS
117.02
120.17
123.:51
126.45
127.59
132.73
135.S7
139.02
142.10
1.178
4.319
7.461
10.60
13.74
16.88
20.02
23.16
26.31
29.45
32.59
:i5.73
38.87
42.01
45.16
48.30
51.44
54.58
57.72
60.80
64.01
67.15
70.29
73.43
76.57
79.71
82.85
86.00
89.14
92.28
95.42
98.57
101.71
104.85
107 .iH)
111.13
114.28
117.42
120.50
123.70
126.84
129.9S
133.13
136.27
139.41
I42.r>r)
98.96
99..35
102.10
102.49
105.24
105.64
108.39
108.78
111.53
111.92 '
114.67 '
117.81
120.95 ;
124.09 '
127.24 ■
130.38
133.52
13r>.66
\
115.06
118.20
121.34
124.49
127.63
130.77
133.91
137.05
99.75
102.80
106.03
109.17
112.31
115.45
118.60
121.74
124.88
128.02
131.16
134.30
137.45
o.i
0-1
0.J
o-l
1.570
1.963
2.356
2.748
4.712
6.105
5.497
5.890
7.854
8.246
8.630
9.(BS
10.99
11.38
11.78
12.17
14.13
14.52
14.02
15.31
17.27
17.67
18.06
18.45
20.42
20.81
21.20
21i9
23.56
23.95
24.34
24.74
26.70
27.09
27.48
27 J8
29.84
30.23
30.63
zm
32.98
33.37
33.77
34.16
36.12
36.52
36.91
37JD|
39.27
39.66
40.05
40.44
42.41
42.80
43.10
43.58
45.55
45.94
46.33
46.73
48.69
49.08
40.48
49.87
51.83
.52.22
52.62
53.011
54.97
55.37
55.76
56.15
58.11
58.51
58.90
50.29-
61.26
61.65
62.04
62.48
04.40
64.79
65.18
65i8
67.54
67.93
68.32
68.72
70.68
71.07
71.47
n.86
73.82
74.>2
74.61
75.00
76.96
77.36
77.75
78.14
80.10
80..'>0
80.80
81.28
83.25
83.64
84.03
84.48
86.39
86.78
87.17
87.67
89.53
89.92
00.32
90.71
92.67
93.06
93.46
03.85
95.81
96.21
06.60
96.99
100.14
103.29
106.42
100.56
112.n
115.85
118.99
.122.18
125.27
128.411
131.55 ;
134.70 :
137.84!
140.96 1
MENSURATION. - CIRCLES.
Til
AREAS AND CIRCUMFERENCES OP CIRCLES.
From I to 50 Feet.
(ADVANC'IXO by t)XE INCH.)
ArM.
Cirenm.
Feet.
Ft. In.
0.7854
3 4}
0.9217
1.009
3 8
1.2271
3 11
1.3002
4 2
1.5761
4 5
1.7671
4 8
1.9689
4 11
2.1816
5 2
2.4052
6 5
2.6398
5 9
2.8852
6 2i
3 0 '
1
"l
3
4
5
6
7
8
9
10
11
4 O
1
^^ I
3 I
4 I
5
V\
8 ;
9
10 I
7
3.1416
3.4087
3.6869
3.976
4.276
4.5860
4.9087
5.2413
5.585
5.9395
6.8049
6.681ft
7.0686
7.4666
7.«767
8.2957
8.7266
9.1683
9.6211
10.0846
10.5591
11.0146
11.5409
12.0481
12..W64
13.0952
13.6353
14.1862
14.7479
15.8200
15.9043
16.4986
17.1041
17.7205
18.3476
18.9868
13 4i
13 74
Dim.
Arei. • rirnim.
Ft.
5 0
1
2
3
4
5
6
<
8
9
10
11
6 0
1
2
^3
4
6
s
10
11
7 0
1
2
3
4
;') I
a .
7 i
^ I
10
11
8 0
1
•)
4
.')
()
7
8
9
10
n
Feet.
19.635
20.-2947
20.96.56
21.6475
22.34
23.0437
2:J.7583
24.4835
•25.2199
25.9672
26.7251
27.4943
28.2744
29.0649
29.8668
30.6796
31.5029
32.3376
33.1831
34.0391
34.9065
35.7847
36.6735
37.5736
38.4846
a9.406
40.:W88
41.2825
42.2.'W7
43.2022
44.1787
45.1656
4.i.l(>:J8
47.173
4S.1962
4!t.2-236
r)0.-2»>56
51.:U78
52.3816
5:i.4562
54.5412
55.6377
•'>♦>. 7451
.')7.Srt28
5S.992
60.1321
61 .2826
62.4445
Ft.
15
15
16
16
16
17
17
17
17
IS
IS
IS
18
19
19
19
19
20
20
20
20
21
21
21
21
art dirt
22
22
2;i
%\
2:i
2:i
24
24
24
24
25
25
25
25
2t)
2t»
2t>
2«>
2.
2
/w.
8|
111
9
3j
6i
n
^
?!
1
4j
10|
A\
s)
11;
•)j
5«
111
22 3
^\
9J
2i
9f
Ij
4i
log
'i
11
. ..]
Dian.
Ft.
9 0
1
2
3
4
5
6
7
8
9
10
11
10 0
1
2
3
4
5
0
7
8
9
10
11
11
0
1
2
3
4
5
6
7
8
9
10
11
12 0
1
•>
art
3
4
5
6
Arei. i Cirrum.
'id
"A
K
9
w
Feet.
63.6174
64.8006
65.9951
67.2007
68.4166
69.644
70.882:$
72.1309
73.391
74.662
75.943:i
77.2362
7S.54
79.854
SI .1795
82.516
S.S.8627
85.2211
S6.590:l
S7.J>697
89.^608
V.0.7627
92.1749
93.5986
95.o:m
96.478,3
97.9347
99.4021
100.8797
102.:J689
103.8691
105.3794
lort.wia
10S.4342
109.9772
111.5319
l]3.0i»76
114.0732
116.2607
117.S)9
119.4074
121 .0.^76
122.7187
124.3598
120.0127
127.6765
Ft.
2S
2S
28
2^»
2i>
29
2<»
30
30
30
30
31
31
31
31
32
32
32
32
-n
68
9
*-'
10|
i!
4g
7A
lit
U
5
K
111
'^i
•H
Hi
33
'■^l
3.3
H
3;i
•'!
34
rt
34
34
34
H
34
9^
3.'>
3)
;i
3')
35
10 j
1.
3(i
3»5
■»1
36
''J
.30
m
37
'^
37
•>i
37
S|
37
11
3S
3S
5i
3S
^^
I'f.*
0
39
.39
39
40
V^
\
54
MENSUKATION. — CIUCULAU ARCS.
Areas and Circumferences of Circles (Feet and Inches).
Area. Cireum.
; Diam.! Area. Cirenm.
Ft.
43 0
1
•>
3
4
5
ft
7
8
<l
10
11
44 0
1
•>
3
4
5
6
<
R
9
10
11
45 0
1.
o
md
3
4
5
6
8
9
10
11
Feet.
14.V2.20.>
1457.836
146.3.483
1469.14
1474.804
1480.48:^
1486.173
1491.870
1497.582
1503.:}05
1509.a3ft
1514.779
1520.534
1.526.297
1532.074
1537.862
1.54:3.658
1549.478
1.5.55.288
1.561.116
1566.959
1572.812
1578.673
1584.549
1590.4:r)
1596.329
1602.237
160S.1.55
1614.0S2
16-20.023
1625.974
1631.933
1637.907
1643.891
1649.883
1655.88)
In.
1
4;
I
lOJI
1J
n
11
2J
5I
8^
n«
I 138 25
I 138 5|
' 138 9
i 139 k
139 3 J
139 6g
139
140
Ft.
135
135
135
135
13t>
136
136
136
137
137
137
137
95
' 140 33
' 140 7A
141 lOf
141 U
141
141
141
142
142
142
142
143
143
14:5
14: J
144
43
lOi
n
'4
llj
I
Ft.
4(i 0
1
3
4
5
6
7
8
9
10
11
47 0
1
o
6
7
8
9
10
11
48 0
1
•>
3
4
5
6
t
8
9
10
11
Feet.
1661.906
16<i7.9.31
1673 97
1680.02
1686.077
16«,»2.148
lfl98.-231
1704.321
1710.425
1716..54!
1722.663
1728.801
1734.947
1741.104
1747.274
17.53.455
1759.643
1765.845
1772.0.59
1778.28
1784..515
17{«).761
1797.015
1803.283
1809.562
1815.848
1822.149
IS 28.460
1834.779
1841.173
1847.457
1853.809
1860.175
1866.552
1872.937
lS79.:i35
147
'\
147
11
148
2,
148
54
148
8|
148
149
'^\
149
^l
149
82
150
1.50
1.50
I
Diam.
^7.
49 0
1
2
3
4
5
6
7
8
9
10
11
.50 0
Area.
Feet.
1885.745
1892.172
1898.504
1905.037
1911.497
1917.961
1924.426
19.30.919
1937.316
1943.914
19.50.439
1956.969
1963.5
157 i
Circular Arcs.
To ,find the len'jf/i 0/ a rircitlar arc when iff( chord and heiyhtyOr
versed sine is (/irm; hy tiik following tablk.
Ki'LK. — Divide the height by the chord: tiiid in the eoluimi of
heights the number ecjuai to this quotient. Take out the coiTe*
sponding number from the cohinm of lengths. Multiply this
number by the given chord.
ExAMPLK. — Th«» chord of an arc is SO and its versed sine is 30.
what is the length of the :irc ?
Ans. :]() ^ SO - 0.:^.'). The length of an arc for a height of 0.375
we find fro.Ji table to be 1.34003. 80 X 1.340C3 = 107.2504 =:•
Jejigth of arc.
MENSURATION, - cmCLES.^^^
^i
A&BAB AND CIRC UMFE RENO BS OF CIBCLEB.
|.-i.jiic».f;,ii/(-w rt.././.«.i
h
tm. Ci»iR.
Di...j irw.
titrun. \t\iM.\ km.
CirtH.
i
IMM.-UO
Si?
icisjais
rK,.o\>..r.a
,,,,.,
"-1 :ag4U7iJ
l71.7K7a
173.101;
I7*AIM^
\
VHA.OTOa
l«47.4Sze
iwLiTus
Jl
ai)ia.Bj>u
IMlaTBT
:!
Mj4!aa''ii
I74.K7^
174.Mfl;
1J6.S0IW
MJI
UtB.lWOI t'H.ni74
1«3.I«« 11A.455T
.a
A.
IKS
3i)«.»!Ma
an4.«io*
iai:4i7B
1
wmunhj
llfiiHSS
17«.U7a
1
1
i
tIlS.M1l)
iSS!
l«J(g41
M7illffi3
i
.6
Slis!ft5*3
iia!;s4.j
:« ai4v:Hia>
17J.SO0O
I7S4MU
iTei'enia
W7JHB0
1
awiiswu
iiia.41770
ISl.OTll
!a
2661 .7^86
26M.0B71
-JI'IR.OWB
3l>«7.<MeJ
ITU.OTOfl
a
,.IM.A3nR
IhJiJiu'waa
1
■iW1.7W7
iai)!s»7
»W.MT4
1H-7MI
in.73»
1
aaoB.iKM
22M.I110Q
iwlweit
'.2
.A
3m:iS3i
J,
iro^Tse
ins.nsie
IW.MTJ
l».H14
143.6Ba
.&
;«
iJ7^liS;a
SMI. 74*6
ISll^j;:
III
iBsinqas ;
»J)
lMl.lM:i 1».9«IU
,3
a».23io
330T.2171
J3W;i7M
imiwvrj
IM^SIIW
^
MB.SOM J«.«»«
tK.*m IS6.TtS6 f
.»lmi.ma in.53W
-7/2Mn.saW 171.S451
.«;aMS.s«a 172.1583
.« Me7.1B7e I72.4T35
■
b
1
MENSVllAllON. - CIKCULAR ARCS.
Table of Circular Aros ( ' iIcJ).
Lnflb. l|Ui. Li^lkl '
urn
1'nUe of Leiigtbs of Circular Arcs whose Badlos
iti 1.
KuLK. — Knowing the nicMiii'e of lliu cii'clf and the measnieof
iliii arc In degrees, niiniites, ttnd Becouilii; take from the table tie
kitjitlis opposite the inunbur of tlegrecs, niiimles, tind sttconds fi'
tUi> arc, and multiply tiieii' sum liy the railitis of the ch'de.
EXAMi'LK. — Wliat h the length uf an arc Huhtending an angle
of 13* 37' 8", with a I'adius of 8 fi'et.
Ann. Lfiifilh for l;l=> = 0.2268828
■•-'= 0.0078340
S"= 0.0QQ0388
13''arK"= 0.2347850
»^
MENSURATION. -CIRCULAR ARCS.
LengthB of Ciroular Arcs ; Badius = 1.
5
lrl[lb.
Kl
U^i.
_v
wt. .
hf
Ml.
,
o.onoouis
,
O.OIKKWM
0.0174OM
fll
.OWftVIS ■
0.W23.WU
.OBOj>.i74
n.UIMUlM
.1170107
«.oon4-w
oiuiiniKO
.10»:iT0«
D^IOUSW
oJ3Da-Jn.i
.18«!Uai
o.ooooua
oifloanimi
n.DooolU
O.DO-JBOM
'.■ii\:i!>!.
0.0000633
U.OOSIUHR
O.IftlOtKU
li
o.oowoo;
O.WM3fflS
7i
l!266«37I
oioiHimo
0j)oa78i-i
0.4208*28
.«40PIM
O.OiNlmTfi
o!oo43*;w
u!-jei709i
75
:30§BWl!l ,
.3281.WJ '
a!oi>0O83(
0!0OtM.^I
.3788101
f
0.0001 01 »
!"
D.OOOIOHT
O-WMOM
80
1.8B62f(H
03838124
i!*sinoo
li
owwilli
w
oioSa
^
M
i!4eao7W
UJIUUIWO
■la
DJMOIMO
30
1.Bil8'>4M
.«0.'p702»
m
onuoiS^s
M
olooesHOj
M
osteHiio
w
oioouiaiti
39
oioiodflsa
!fiMOI^
o!oiios3s
oiaiKiaiai
!7ioi4r [
40
oioHKisn
n
ti
0.0002080
uiDD02133
0.00031W
4.i
o!7N.W9W
\.sism7,-
«
M
48
l.BSOIHB"!
4B
48
10D
4t
40
W
o.«»24Ta
SI
o.ni4ii:i;«i
M
0,87»018
no
ICI^
o.oooMai
M
iW-BM 1
13
1.H-J3221 1
o!d002S18
o.0OnMM
M
0>15WSH
at
I'mm-n
lis
1.ftH9<l7£-1
S.0O7121«
«
f.
S7
oSwMn
ill
0.{K(^V2
\'.HV1»W
\w
I'jHWWh l^
sj
coaasBo
m
, \w
\ ^inwww. \
"'"^1
zl
n..J7*-,3a
00
I'.lMlWlft
\"
\ l»«IM.v\
so
MENSURATION. — CmCUMFERENC^^^H
CIHCUMPBBENCBS OF
CIRCLES. '
CIRCUMFERENOES.
lu>
0.0
O.J
">■*
0-1
0.1
0-1
O.J
' 1
gJM
0.39m
0.7S.M
1,178
1.S70
1.08S
fi.106
iiisa
^
B
16.70
ia.io
KA9
l)1.!S3
17.27
i-:fl7
isiiw
e
10
ia.M
22 ja
18.53
IS
2BJ1
1».46
20.70
27.(»
30.21
21.20
24 JU
1
13
43!a8
47.12
asloB
3(.34
4fl:ia
30.12
42!41
is.as
3*. 62
4a:B4
»a.M
43!lB
13.M
I
ssiaa
1
If
01/^
a2.M
64:79
83.04
86.18
i
Ti.-a
72.64
faM
Toiin
7a!s2
7ll07
68.31
TI.47
BoiiO
»
iifia
hbIiis
ai.4e
att!7i
89.14
ssiue
sbIbi
i
SI
32
3S
«.39
87.78
imi-ii
ii
11
ii:p
108JS
09.76 ]
101.39
looiij
113.31 ■
3e
30
40
113.411
113.S8
va.s\
m.4s
114.28
1^3^70
II
1 15.08
IISJS
128.02
1
I
I3S.82
135'.gT
12B.M
s
130.3S
\^
m 1
MENSURATION. - CIRCLES.
f)!
A.IIBAS AND CIRCUMFERENCES OP CIRCLES.
From I to 50 Feet.
(advancino by one inch.)
IHii.
Area.
Cirenm.
Diam.
Area.
Cirniin.
Ft. In.
Diam.
Area.
Cirfum.
Ft.
Feet.
Ft. In.
Ft.
Feet.
Ft.
Feet.
Ft. In.
10
0.7854
3 If
3 4!
5 0
19.635
15 8g
9 0
63.6174
2M \\\
1
0.9217
1
20.2947
15 11
1
64.8006
2H (58
2
1.009
3 8
2
20.9656
10 23
2
65.9951
28 \\\
3
1.2271
3 11
3
21.6475
16 53
3
67.2007
29 1
4
1.3962
4 2|
4
22.:W
16 9
4
68.4166
29 \\\
5
1.5761
4 5,
5
23.0437
17 1
5
69.644
29 7
6
1.7671
4 8l
6
23.7583
17 lil
6
70.882.3
29 lOj
7
1.9689
4 11
7
24.4835
17 6}
7
72.1309
30 1 1
, 8
2.1816
5 2,
8
25.2199
17 n
8
73.391
30 4i
i »
2.4052
5 5|
9
25.9672
18 i{
9
74.662
30 '\
10
2.6398
5 9
10
26.7251
18 31
18 7i
10
75.9433
30 11^
1 "
2.8852
6 2\
11
27.4943
11
77.2362
31 \\
20
3.1416
6 3i
6 0
28.2744
18 lOJ
10 0
7S.54
31 5
1
3.4087
6 6}
1
29.0649
19 I4
1
79.854
31 K
2
3.6869
6 91
2
29.8668
19 42
2
SI. 1795
31 11',
3
3.976
7 i
-3
30.6796
19 75
3
82.516
32 2g
4
4.276
7 3J
4
31.5029
19 10|
4
83.8627
32 -A
5
4.5869
7 7
5
32.3376
20 1^
5
85.2211
32 K|
6
4.9087
7 lOi
6
33.1831
20 4|
(>
8»5..)903
32 11 1
7
5.2413
8 1
7
34.0391
20 s|
7
ST. 9697
33 2]
8
5.585
8 44
8 7|
8
34.9065
20 n^
8
89.3008
3.', (5]
9
5.9395
9
35.7847
21 2g
9
i:0.7t527
33 It',
10
6.3049
8 lOjj
10
36.6735
21 5^
10
92.1749
34 I
11
6.68i&
9 n
11
37.5736
21 Sg
11
93.5986
34 3^
30
7.0686
9 5
7 0
38.4846
21 111
11 0
95.03:U
34 Hg
1
7.4666
9 83
1
39.406
22 3
1
96.4783
34 \y\
2
7.8787
9 11
2
40.3388
22 6S
2
97.9347
3:. I
3
8.2957
10 2
3
41.2825
22 9.
3
99.4021
3-) \\
4
8.7265
10 5f
4
42.2:^67
23 i
4
100.8797
3:. :•,
5
9.1683
10 8}
5
43.2022
23 2k
5
102.3689
3:. 10.^
:}(5 1 \
6
9.6211
10 llj
6
44.1787
23 05
6
103.8691
7 ;
10.0846
11 3
7
45.1656
23 9|
7
105.3794
3(5 4^
8
10.5591
11 6
s
4o. 1(538
24 Ig
8
10r).t>013
30 7^
9
11.0446
11 91
«>
47.173
24 4a
9
1 08.4342
3t) 10]
10
11.5409
12 5
10
4 S. 1962
24 7,
24 lOi
10
10;>.9772
:57 2|
11
12.0481
12 3
n
4it.2236
11
lll.r)319
:57 .-.i
40
12.5664
12 6|
8 0
•)(). 2(556
25 li
12 0
113.0976
37 Sg
1 1
13.0952
12 9}
1
51.3178
25 4t
1
114.(5732
37 IH
2 '
13.6353
13 1
'2
52.3816
2:. 7^
0
1 1(5.2*507
3S 23
3
14.1862
13 4i
13 n
13 loj
3
53.4562
25 n
3
117.S-)9
3s :^l
4 1
14.7479
4
54.5412
2t) 2^
4
119.4(574
3S s„^
5 '
15.3206
.')
5.'..rt377
2») ;■) ',
5
121.0S76
:?,t 0
6 '
15.9043
14 1
14 4
t)
.'>«■), 7451
2(5 sg
6
122.7187
39 3i
••
1 '
16.4986
^
(
.')7.S62S
2t5 114
7
124.3598
39 (5§
8 ■
17.1041
14 7/
H
.').s,<m2
Ti -11
\ ^
\ \iC^.^\Tv
\\^> ^\
.<>/
]7.720rt 1
U 11 ,
U 1
00.1321
27 :>\
\ ^
\ Vl"X"v^^
V \^ \
70/
1S.3476 j
U 2i /
10
HI .2820
*
\ ^^
i \ V2».^vi^
>\ V \^ '?i
"1
18.0868 1
lo 5i
11
1
♦52.4445
0.) ■i
'\~
\
-
1
\
.
^^^^^^ MiJNSUlCA-nO\. -L-tltL-UI.AK AHul^^^H
Din
Am. ' rlrrnn.
ninigJ 'Aru.
c„...
DllU
km.
Ci!
M.
/;»(, Ft- /«.
^V, ^w/.
A'', h.
«~
A«(
Ft
144 u
ia8s!74B
iiMisaB ik 4)
144 1>
1IW2
IT!
IS
a
1463483
1«M
KM
13^ 'l
3 ■ 16811.02
4 lesB.on
14S fl
407
IS
14§o!46»
isH J
16IK.148
14,-| li
llffl
Wl
nwiaai
1««
IB
187 6
171b!.U!
mw
IS7 8
lTJ2.fl63
147 ll
147 4
l»56W
IM
iszo.sat
1S8 2J
IM 6i
i^Im
130
1750<:l
1S4»!*T8
189 8
H« 11
tamiim
HO 3
u
i-^vsioiA
!« '"
im.on
iwa.Ms
160 «
49 0
IM (■
1 iiM.:!«a
141 10
18^0^ ' iS J'
tlwi!;7B
I.pI fi
iBj5:«l Hi 11
isl':!!?
I'si 1
B
VSSi'mi 143 s
1M3.W1 143 S
I«5i!«B) ' 144 tl
1
IsiB^^l
1M 4
Ciifiilai- Arcs.
To .piid llie l<-'\ulh of « ,-h-riil,i,- on: irl.tn it" .hord nn'l Mgk
rerwd Hhip iK'jireii; hv the Foi,LO«-iN<i table.
Rl-le. — TJivide the lieigbl hy the cliortl; linrl in the ixAvn
lieights tLe number eijual to tills quotient. Take out the (
numljer hy the givpn rhord.
Ex.iHPLK. —Tile phonl of an sro is MO anil its versed sine t
what is the lenfitli of the ire :'
Ans. 30 -^ «0 = O.in-l. Tlie l.Tigtli of au aiv for n height of i
' H-e.Snd ljxi:n tahk lo be IJJWffi!. SO ■^ l.;UO<ia = 107.258
Je^gtl, of an:
m^) M
MENSURATION. — SPHERES AND SPHEROIDS.
Gl
To compute the surface of a segment of a sphere.
Rule. — Multiply the height (he. Fig. 33)
jy the circiunference of the sphere, and add
^lie product to the area of the hase.
To find the area of the base, we have the
liameter of the sphere and the length of the
versed sine of the arc abdy and we can find
the length of the chord ad by the rule on
p. 56. Having, then, the length of the chord
nd for the diameter of the base, we can easily Fig. 33
find the area.
Example. — The height, />c, of a segment abd, is 36 inches, and
the diameter of the sphere is 100 inches. What is the convex sur-
ftw*, and what the whole surface?
Ans. 100 X 3.1416 = 314.16 inches, the circumference of sphere.
36 X 314.16 = 11309.76, the convex surface.
The length of atZ = 100 — ;56 x 2 = 28.
V1OO2 — 2^ = 96, the chonl ad.
96^ X 0.7854 = 7238.2464, the area of base.
11309.76 + 72:38.2464 = 1854a0064,
the total area.
To compute the surface of a spherical
zone.
Rule. — Multiply the height [cd. Fig. 34) «
•y the circumference of the sphere for the
onvex surface, and add to it the area of
be two euds for the whole area.
Fig. 34
Spheroids, or EHipsoids.
Definition. — Spheroids, or ellipsoids, are figures generated by
he revolution of a semi-ellipse about one of its di<»meters.
When the revolution is about the short diameter, they are pro-
xte ; and, when It is about the long diameter, they are oblate.
'o compute the surface of a spheroid lohen the spheroid is prolatv.
Rule. — Square the diameters, and niulliply the square root ot
talf their sum by 3.1416, and this proiliict by the short diameter.
Example. — A prolate spheroid has diameters of 10 aud 14
QcbeSy what is its surface ?
Ans. W= 100, and 142 = 196.
Tlieirsnm = 296, andw^-7^ = \^\^^.
12.1655 X 3.141(5 X 10 = 'iS2.\^\ %c^\Ma.xfe \\i<3ftRSi'
MEMSUltATlOlS. - LKNGTIIS
Tu nmiimte the chunJ of an arr icAci. the rJioM qf hnif the
e jiierii. (The vi
^^.JL..,^^ slnp is tlie iwrpeniliciilar Im, Pig. 31.
Xn HiiLK. — From tlie s<i«iire of the clioi
pi'' 31 ball' tliu Hi'<; Kulil.rucl tlie square of Lhe v(
^^ siiiL-, auii u<in,>- iwki! Itie s^iiare root of
^Bfaiu ill tier.
^B ExAMi'LE. —Till! cliora iif lialt tlie art- Is ffli, and the vffl
^Btoe Sn, wliat Is llR' leugtli of Uit^ clionl uf the arc ?
^K vl.i«. W-3tP = a;J04, and V^304 =
and 4B X 2 = tW, the chord.
To coiiipate tl,e chnvd qf an arc icflen the iUimetey and v
Sfultlply tliu versed slue by S and siibt a t Ih produ 1
llie dlniiit^ter; then snbtract th i]iia of ll a d r
llie square of the diameter, and -ak 1 e |u re oot of tha
liiaindei'.
Example. — The diamotpr of a i le is 100 and the v(
sliic of tut are 3(1, what Is the fhord of the an- ?
Ahs. 3(ixa = 12. 100-72-28. 100i'-28' = Oni
V'uaia = m. Uie chonl of the arc.
To coinpule the third qf half an arr xehen the r/turil iif the I
(tad the itcrned Hint lire yiteu.
Rri.K. — Take tlie sqiiai-e root of tlie sum of the squares ofl
versed siimand of half the chord of the arc.
EXAMl'LB. — The chor.1 of an are Is KG, and the versed sine^
wlial Is the chord of halt the arc ?
Aux. \'-M'' + ^ = lA.
TV) tomptttf the chord nf half lui nn- ir/icii tlif ilkiwrter and ntr
nine oi'c yiren.
Bulb, — Mullipl.v the dlanielrr l)y the versed sine, anil lake i
sqiiare root of i.heir [iroiliici.
To cui.iiJMtc II dUiiiiflrr.
RiTi.K I.— nivhle the sqiiare of the chord of half the awM
MENSURATION. — ARCS AND VERSED SINES. '»1>
Example. — Wliat is the i-adius of an arc wIkwm* chonl is 1H5, and
lose versed sine is i]i\ ?
Ans. 482 4- :^j2 = ;j60(). 30OO -r :)6 = 100, tlic dlaniet«T,
and radius = 50.
0 compvfe the versed sine.
Rule. — Divide Uie square of tlie cliord of half tlie arc by tin*
lameter.
""o coiiiijitte the reraed sine irhen the chord of the arc. and thr
diduietfr are yicen.
RiLK. — From the square of the diameter subtract the wjuan'
rf tlie chord, and extract the square root of the remainder; sub-
bact this root from the diameter, and halve the remainder.
"0 coinpnte the length of an arc of a circle when the ninuber of
(JeyrecH and the radint* are f/irf^ij.
UiLE 1. — Multiply the number of degiee^s in the arc by :>. 141(1
multiplied by the radius, and divide by IJSO. The result will Iw tin-
fngth of the arc in the same unit as the radius.
Rile 2. —Multiply the radius of the circle by 0.01745, and thr
'xxluct by the degrees in the arc.
Example. — The number of degrees in an arc U 60, and the
^U8 is 10 inches, what is the length of the arc in inches ?
Ana. 10 X 3.141« x (JO = 18H4.JM) -f IM) = 10.47 inches:
or, 10 X 0.01745 x (K) = 10.47 inches.
o compute the length of the arc of a circle when the lent/ih is
, yiten in degreen^ minuten, and necondx.
Rule 1. — Multiply the number of degrees by 0.01745321), ami
le product by the radius.
Rile 2. — Multiply the number of minutes by ().(KK)21>, and thai
deduct by the radius.
RiLEn.— Multiply the number of seconds by ().0(HKK)44.^ timrs
lie radius. Add together these three n\sults for the length of tli»'
trc'.
'Sw also table, p. 57.
Example.— What is the length of an arc of (K)o 10' 5", the
■^^lius being 4 feet ?
Ann. 1. ()(;o X ().0174:):J29 X 4 = 4.lSvS789 feel.
J. !(/ X ().(M)()-i<) X A = VVCNWVN \vjv-\.
S. r/' X ().(HMHH>4S X A — V>.CVC^>K>X> V^v-V-
MENSrUATION. - CONES AS!) I'YUA.Mll)^
'o enmimle the gur/ufe of a uplieroid vhen tltf *iifieroid in e
e thf( (liaiiielerB, and multiply [lie $<iunre
■ liBlf Ctieir suiu^.-i-UlH, biuI Lliis product dy lUe loug dlam
■ Til •■oinpule tl.p xiirJilKn of a .yllMh'r.
' Rule. — Mii!iiply tlie length l>y ilm drcuiiifMunee for ll
vex stirfacc, mjrl ftdil to the- tirodAct tlM
tlie two ends for the whole surface.
To cimiiitle the Hfulhmal area of n ci
HHg(Ffg.35). ■ '
fittLK. — Find the area of liotli circt
.iiibtract tlie area of llie smaller from l|
of the larger; the rtiiiiahider will be t!ie/
a the ring.
in tlis mirSiio: of a ttim.
— Multiply the periffietei' or circiiiiiferenep of
one-half the slant height, or side of the ronp, flit- the convei
Add to this the area of the hase, (or the ivliol* dre*.
ExAMfLE. —Tlie diameter of the base of a rane is 3 inch*
the slant height lo inches, what is the area of the cone 1
An9. 3 X 3.H1II = e.424S = circumference of
D.ii48 X 7J - Ttl.flW) scjiiaiij iiiclies, the convex
3 X 3 X 0.78^ = 1.0SS square Inrlies, tlie area of t
Area of (.'Oue = T7.7->1 square Inches,
pj 3g To enmpute the urea of Uic surface if
I , H|ii.B.-t~UultJp|y the liim of the peril
of tlie two ends by thi' siuiit height of lb
turn, and divide by 2, tor tlie conv
Add the area of the top and bottom stuH
To comimte the (wr/uce if u iiyriuniit.
I'l.t — Multiply the perimeter of t^
me-lmlf the slant height, and, »dd|
f product the area of lliK base.
lompide m .^"rf'ice iif ^'^'t^
''"• '■■'■ a
Kri.K. — Multiply llie sum of ih« perimeters of ^he two fl
ilie slant height of the frustum. \ia\v« rt\B ■pwAiMA, askl (diS
i-esull the area of the two elida.
MENSUUATION. - PRISMS.
63
BffENSURATION OF SOLIDS.
pule the volume of a prhm,
:. — Multiply the ai-ea of the base by the lielglit.
nile applies to any prism of any shape on the base, as long
op and bottom surfaces are parallel.
pule the volume of a prmnoid,
NiTiON. — A prismoid is
having parallel ends or
[issiniilar in shape with
itoral sides.
:. — To the sum of the
f the two ends add four
Lhe. area of the middle
pai*allel to them, and ^
y this sum by one-sixth
peri)endicular height.
ipr.E. — What is the vol-
a quadrangidar prismoid, as in Fig. .37, in which ah = 0",
, ac = he= 10", ce = 8", ef= 8", and Ui = 6" ?
Ans, Area of top = ,^ x 10 = .50.
Area of bottom
2
8 + 6
2
X 10 = 70.
Area of middle section = — ^ — x 10 = 60.
|50 + 70 + (4 X 60)1 X igQ = 600 cubic inches.
— The length of the end of the middle section, ae nui lu Fig. 37 =
C
I the volume of a prisvi
ncated obliquely,
•:. — Multiply the area of
e by the average height
idges.
iiPi.E. — What is the
of a truncated prism,
Fig. .38, where ef = 6
^7i = 10 inches, ta = 10,
, (7/1 = 8, andy7> = 8?
Fig.38
^. Area of base = a x lo = 00 square 'u\c\\os>.
A verage height of tul^os ~ - -^ Z^^-J-^ - ^^ \xv<cV\^'s
A
66 MENSURATION. — SPHEROIDS, PARABOLOIDS, ETC.
the square of tlie radius of the base phis the square of the hei^
1G3 X 4 X 0.5230 = .^11.3872 cubic hicheBTol-
ume.
Second Solution. — By the rule for find-
ing the diameter of a circle when a choid
and its versed sine are given, we find tint
tlie diameter of tlie sphere in this case is U,&
inclies; tlien, by Rule 2, (3 X 16.25) — (2X4)
= 40.75, and 40.75 X 4» X 0.5236 = 341.88fi2
Fig. 41. cubic inclies, the volume of the segment
To i^owpitfe the volume of a spherical zone.
Definition. — The part of a sphere ia-
cluded between two parallel planes (Fig.
42).
Rule. — • To the sum of the squares d
the radii of the two ends add one-thiid
of the square of the height of the lone;
multiply this sum by the height, and that
Fig. 42. product by 1.5708.
To compute the volume of a sphei'oid.
Rule. — Multiply the square of the revolr-
ing axis by the fixed axis, and this product by
0.5236.
To compute the volume of a paraboloid of revo-
lution (Fig. 43).
Rule. — Multiply the area of the base by haM
Fig.43 the altitude.
To compute the volume of a hyperholoid of revolution (Fig. 44).
Rule. — To the square of the radius of the
base add the square of the middle diameter;
multiply this sum by the height, and the prod-
uct by 0..5236.
To compute the volume of any figure df rew-
lutlon.
Rule. — ISIultiply the area of the generating surface by the ci^
cumference described by its centre of gravity.
To compute the volume of an excavation, where the ground is irreg-
vlar, and the bottom of the excavation in level (Fig. 45).
JiuLE. — Divide the surface of the gco\mOL\.o\i^ «xjcw«X«^\s^
9guaJ squares of about 10 feet on a aide, a\iCL aacftt\».\xL \i>i xasa
Fig.44
MENSUltATlON. — EXCAVATIONS.
67
a
a
a
6
3 i
C
e;
C <
b
8
i
t
3
d
i
d
d
d
1
7
I
3
6
i
c
i
3
i
I 1
a
1
")
Fic
).45
>
a
a
oifalevd the height of each comer, «, a, a, 6, 6, 6, etc., above the
■ tevel to wliieh the ground is to be excavated. Then add togothor
the heights of all the comere that only come into one square.
fet take twice the siun of the heights of all the corners that come
b two squai-es, as &, &, 5 ;
; Aext three times the sum
of the heights of all the
comers that come in tluee
jBquares, as r, c, c ; and
then four times the sum
3f the heights of all the y
Gomel's that belong to foiu*
Jcjiiares, as (7, ff, rif, etc.
Vdd together all these
luantities, and multiply
heir sum by one-fouith
he area of one of the squares. The result will be the volume of
be excavation.
Example. — Let the plan of the excavation for a cellar be as in
he figure, and the heights of each corner above the proposed bot-
oni of the cellar be as given by the numbers in the figure, then the
olume of the cellar would be as follows, the area of each square
leing 10 X 10 = 100 square feet: —
Vohuue = \ of UX) (a's + 2 6's + :^ c's -f 4 (Z's).
The «'s in this case = 4 + 6 + 3 + 2+1 + 7+4 = 27
2 X the sum of the ?;'s = 2 X (3 + 0 + 1 + 4 + ;^> + 4)= 42
3 X the sum of the c*s = 3 X (1 + 3 + 4) =24
4 X the sum of the (Z's = 4 X (2 + 3 + 0 + 2) =52
145
Volume = 25 X 145 = 3625 cubic feet, the quantity of earth to be
Lcavateil.
GEOMETRICAL PEORLEMS. ^^H
To coMtruet aa aiii/le er/iial lo a gieeti ttitt
With lliP point '^. «t Ihe Apex Of tM
angle, tis a eentre, anil any rodliis, Aeiat
are BC. Then wltli the point a, at the-rt
the new angle, as a centre, and with IH
I'adius as before, deseribe au are Hke BC. '
with lie as a radius, and 'i as a centre, A
an arc cutting the other at r, Tlien will
equal to the given angle CAB.
I'BOBLEU 0. — From a point on a ijiq
to draw a line makiny an angle qf 60° V
cmiine(Fig. 54).
Take an; distance, as ab, as a radiua, and, wltli u ae a cent
KCvWte the arc 6c, Than with 6 as a tentre, aad tha same:
cutting Ihe lirat one at c. Draw from a
tliraugh e, and it will make with ub aa angle of 60°.
Pkobleh 7.-
Flfl.55
II tlieen. point, A, on a gicen line, .
'otc a Hnt makinij an tttujU o/4S° viUh the given line (Pig.
Measure off from A, on AE, any distance, Ab, and at b
line perpendicular to AE. Measure off on this perpendim
equal to Ab, and draw a line from A lliruugh r, and U*H
an angle witli AE of 4.5°. - 1
PB0B1.EM 8. — FYiiiii nnij point, A. on n nivpn line, to drffl*
whiiih thall make nay Avaireil angle icilh the j/ioen line (Flgj
To perform this problem-we mnac
table of chords at hand ( such aa la fa
pp, 8o-))S], which we ose as folloW
in the table the length of clionl tOl
1, for the ^ven aiiglp, Thentifte^
^ illuH, ail iarge as convenient, deae^
c of a circle he wltli X as a centra^
lionl of flic Hliglc. touuil \i\ U\e \a\>\e.,\vj thieleiigU
4t»f with ihc iiroiluciasanewt&ft\\\B,Knfi.>i*'i
'uttiiig be In '1. Dvaw aWnis *nl«^'*
lie the lieaired ansle wHbDE.
Fig. SB
l/j'O-L
GEOMETRICAL PROBLEMS
71
Example. — Draw a line from A on DE^ making an angle of
SoLimoN. — We find that the largest convenient radius for our
fcvs 8 inches: so with ^ as a centre, and 8 inches as a radius, we
-cribe the arc he. Then, looking in the table of chords, we find
tte chord for an angle or arc of 44° 40' to a radius 1 is 0.76. Mul-
tiplying this by 8 inches, we have, for the length of our new radius,
J.08 inches, and with this as a radius, and 6 as a centre, we describe
n arc cutting &c in df. Ad will then be the line desired.
Problem 9. — To bisect a given
ngle, 08 BAC (Fig, 61),
With ^ as a centre, and any radius,
escrlbo an arc, as cb. With c and b as
entres, and any radius greater than
ne-half of cb, describe two arcs inter-
ecting in c?. Draw from A a line
hrough d, and it will bisect the angle BAC,
Problem 10. — To bisect the angle contained between two lines,
IS AB and CD, when the vertex of the angle is not on the drawing
:Fig. 58)
Draw fe parallel to AB, and cd parallel to CB, so that the two
lines will intersect each other, as at i. Bisect the angle eid, as in
the preceding problem, and draw a line through i and o which will
bisect the angle between the two given lines.
Problem 11. — Through two given points,
fi and C, to describe an arc of a circle with
^ given radius (Fig. 59).
With B and C as centres, and a radius
^ual to the given radius, describe two arcs
^^tersecting at A, With A as a centre, and
fe same radius, describe the arc he, w\uc\\
7 be found to pass through the given pouiU, B ^m^ ^.
^\^^,^^
TO
fiEOMErillCAL PROBLEMf.
ac; bisecLncbyaperpendifwlnr. The inWrseftioiiot this line «j
llie perpeniifi-ular f'/J will lie llie requireii ceotre of tlip c
arc. Tliroiigli il ami h draw Hie linea Be and I)t' ; from n
nilh llie givpn rullus, pquaJ t« ..4n, 7J&, describe the strea At^m
He; from D Ba a, (.'eiilre, aiid C'i> as a radius, describe llie arc a
wlik'h coiupletea the curve required.
Phoblesi 18, — Til tonnlrufl a Iriangie iijimi ii f/iceii Hra^
line irr bane, the leiiath nf the Iwo niileii iKing i/ieeii { Fig. IX).
Fimi (an equllateml triangle, Pig, Baa>.— With the e
A and B of the given Hue a» cetiti'es, ami .'IB as a radliis, des
ar:;s culliug each other at C Join AC aud lit'.
Second (wlieu the sides are unequal, Fig. Deb). —Let ADbetiv
given base, and the otlier two sides be eqiial to C and B. WItb.A
aa a centre, and a ratlius equal lo (', deiifrihe an imiefiuite an
With ^ as a centre, and B as a railius, deM'ribe an nrc cutting Ul
tirst at E. Join E nith A and D, and it will give the requin
triangle.
Problem JO. — To describe a circle about n Irlnagle (Fig. 01
lliseet two of the sides, ns AC and CB, of the Irianglu, and I
ilieir centres erect perpendicular lines, as fie and he, intersecting i
e. Willi I? aa a centre, and eC as a radius, describe a cirele, h
"111 be fiiunU lo pass Ihrough A aud Ii.
PSOBLEX 20. — To inscribe a circle in a triangte {Fig. CS).
^Sieet two of the ttagles, A and B, ot l^\u U\»v%\« Vj \n\«9, cm
With o as a centre, and ue aa a. ta&nia, iiiaR#ft«>
ij-WlU he fotind to iuat toucU V.\u^ ot^ittv ^?^<A|^|^^
GEOMBTBICAL PROBLEMS.
75
Problem 21. — To inscribe a square in a circle, and to describe
n circle about a square (Fig»69).
To inscribe the square. Draw two diameters, AB and C7), at
right angles to each other. Join the points -1, 1), By C, and we
liave the inscribed square.
To deifcribf the circle. Draw the diagonals as before, intersecting
at Ef aiid, with ^ as a centre and AE^9ls a radius, describe the
circle.
Fig. 70.
I
Problem 22. — To insa'ibe a circle in a square, and to describe
a square about a circle (Fig. 70).
To inscribe the circle. Draw tlie diagonals AB and CD, inter-
secting at E. Draw the perpendicular EG to one of the sides.
Tlien with ^ as a centi-e, and EG as a radius, describe a circle,
which will be found to touch all four sides of the square.
To. describe the sqiutra. Draw two diameters, AB Rud CD, at
i*iglit angles to each other, and prolonged beyond tlie circumference.
I)ra\v the diameter GF, bisecting the angle CEA or BET). Diaw
lilies through G and F perpendicular to GF, and terminating in
t-he diagonals. Draw AD and CB to complete the square.
Proble:m 23. — To inscribe a pcnta-
fioriina circle (Fig. 71).
Draw two diameters, AB and CD, at u
J'ight angles to each other. Bisect ^10
at E. With ^ as a ceqtre, and EC as a A
ladiiis, cut OB at F. With C as a ct;ntre,
^nd CF as a radiua, cut the circle at G
*nd 77. With these points as centres, and
ihesauic isLdiiis, cut the circle at / and
'^ Jo/n I,J,If,G, aj2d C, aiul we then
^ve Inscribed in tiie circle a regular pentagon.
aKUME-rKlCAL PUOBLEM8.
PROBLEBCB ON THE ULUPSS. TBB PASABOii,
THE HYPBRBOLA, AND TUB CTCLOU).
elltpiii: Dip length awl lirmdlli,*
IBT MmroD
(Fig. 7ft, tlie two
axes, vlB and CU,
being giv
On AB anit C'Dj
as diamct«n, tni
from the Btuuc
centif, O.descrili'!
tlie circles AGBII i
and CLVK. T»kf
any convenioii
number of polutt
on tlie drcuttifn-
euce of the oaUT
circle, as h, If,
b", ett,, and trwn
them draw IliM
to tlie eeutre, 0,
cutting the Inntf
drclp at the points
III the points 'i, h', cte., ilrawUues
il from the p()lnta ii, a', etc., dim
lines parallel to the longer
nxis, and Intersecting tli'
nnt set of lines at <■. r",
<■", etc. These Usrt pirfnts
will be ixilDts in the el-
lipse, and, by obtaining!
6 stifficlent n umber of tlioBi
the ellipse enn eaallj bt
2d Mktiiod {Fig. 80|.
— Take the Stndgbt edge
of a, stiR piece of paptSi
f'9-80 cB\i\\)o».n\, uT ^uA^w'^
tp point, as '(, niarkofE <i!j eiiual U)\vaM.'.\ied»irt«i'i«»
GEOMETRICAL PROBLEMS.
79
L ac equal to half the longer diameter. Place the straight
tliat the point h shall be on the longer diameter, and the
on the shorter: tlu^ will the point a be over a point in
pse. Make on tlie paper a dot at or, and move the slip
always keeping the points 6 and c over the major and
.xes. In this way any number of points in the ellipse may
Ined, wlilt'h may be connected by a curve drawn freehand.
ETHOD (Fig. 81, given the two axes AB and C7).) — From
nt i> as a centre,
idius AO^ equal to 0
f of AB^ describe
cutting AB at F
These two points
led the foci of the
[One property of
lipse is, that the
f the distances of
vo points on the
iference from the
. the same. Thus
5 + GF,^ Fix a
: of pins into the axis A B at F and F', and loop a thread
i upon them equal in length, when fastened to the pins, to
0 as, when stretched as per dotted line FI)F', just to reach
[tremity D of the short axis. Place a pencil-point inside
ord, as at E, and move the pencil along, always keeping the
tretched tight. In this way the pencil will trace the outline
: ellipse.
»BLEM 32. — To draw a tange/it to an ellipse at a given point
curve {Fig.
it be re-
1 to draw a
It at the
E on the
! shown in
i2. First
he foci F
*', as in the
uetbod for
'ngan el-
ea from
ilEOSIKTHICAl. HROBLKMS ^
L^draw Hum EF nml EF'. Pi'olong EF' lo n, su lliM j
■.equal EF. Bistcl llio angle nKFas at '', aiid llirui:^ h
"iiie toudiing llie curve at E. Iliis line will be tire T
«(]iiijiMl. If ^t were ik'siii-U lu dmiv a. liof Dontial to i
it £:', as, for iDstautv. ilio jutnt uf aji elliptical an.'h, bisi
' oiigle FEZ", BJiil draw lli« liiswliiig liiiu lliroiisU E, ami ili
the normal Ifl the ciirvw, anil llip proper linp for Ibe joiuB
elliptical arch at that point.
Problem 33. — r.i dmio a liinf/pnl lo na ellipse /rom a
point viUhout tlie eiirni- (Fi^. R^).
^^^^a-^H
From the poiDl Tas a centre, and a radius equal t
■ to the nearer tocua F, describe a circle. From F' as a centi
A radius equal to the length of the longeraxis, describe fu
the cin'le Just described at ii and b. Draw lines from Ji" ta|
h, cutting the circumfereuce of the ellipse at K anil O. DnN
from T tbii>ugli E and G, and they will l>e tlie langents requ
Prouleu 31. — To describe an eilipse approxliwilelg, bj/i
i(f circular area.
F^rst (with arcs of two radii. Fig. M). — Take half the dlHl
of the two axes AB and CD, and set it olf from tbe cenlre t
and e nn OA and OC; draw ar, and set off half uc to il;
parall^'l Ui ac; set off Oe e<iual to Od; join ei, and drav em m
parallels to ili and le. On in aa a centre, with a radios mC, d
an *fe Ihmiigh C, tei'minating iu 1 and'.!; and withiMKt
UK/ /tiMSfirailiua, describe au arc Uiv(mg\\ U, t^irmiinUta^Vi
Ou il and e m centres deserW^ atta vXitw
f the jwiats 1 and 4, 'i vaA 3. Ilift ^^
GEOMETRICAL PROBLEMS.
83
The Hyp^bola.
The hyperbola possesses the characteristic that if, from any point,
\ two straight lines be drawn to two fixed points, F and F'j the
[, their difference shall always be the same.
Pboblem 37. — To dencribe an hyperbola throwjh a fjiren tertex,
r, with the given difference ab, and one of the foci, F (Fig, 87).
y
Fig. 87.
Draw the axis of the hyperbola AB, with the given distance ah
and the focus F marked on it. From b lay off bF^ equal to aF
^ lor the other focus. Take any point, as 1 on AB, and with a\ as
radius, and JP as a centre, describe two short arcs above aiul
ibelow the axis. With 61 as a radius, and F' as a centre, describe
arcs cutting those just described at P and P'. Take several points,
as 2, 3, and 4, and obtain the corresponding points P2, P3, and P4
in the same way. Join these points with a curved line, and it will
be an hyperbola.
iTo draw a tangent to any point of an hyperbola, draw lines from
the given point to each of the foci, and bisect the angle thus
formed. The bisecting line will be the tangent required.
GEOMETRICAL rllUI
Ti
point ID the (■iivuiftT&^
" Eircli' ti)l1iag ill a. sintiglit linti
l'm)iii.EM ;J8.- Ta deaeHi
Dmw llit^ xtrJglit line .11
iM-to. Describe tlie senentLiq
Uiigeiit Id ihia line iit Lhe eei
tliroitgli the ce'iliT of ilic c
dniw tlie loie EE paralle! K t
Let fall H pfirpcndicular from
ilio base. Diviilfl the aeiui'dr
euee into any nitiuber of 6
for instance, six. I^tiy off on .
. CE distances G'l', 1'2', etc., i
j<s the dlvisinns of the circnni
J Draw the chords Dl, ZH, etc.
theix)hilal',2',3',oi " '■ "
radii equal to the generating
desci'ihe ares. From the point
.y, 4', 5'. oLi the line li
radii cijiial respectlTely ti
01. m, m, Di, D5, dMcefl
culling the preceding, and li
seetlons will he points of ttui
required.
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86
GEOMETRICAL PROBLEMS.
Table of Chords ; Radius = 1.0000 {contimied).
M. 11* !»•
.1M9
.1952
.1955
.1957
.1960
.1963
.1966
.1969
.1972
.1975
.1978
.1981
.1983
.1986
.1989
.1992
.1995
.1998
.2001
.2004
.2007
.2010
.2012
.2015
.2018
.2021
.'2024
.2027
.20:t3
.2036
.2038
.2041
.2044
.2047
.2050
.*2a'>3
.2056
.2059
.2062
.2065
.2067
.2070
.2073
2076
.2079
.2082
.2091
.2093
.2096
.2099
.2102
.2105
.2108
.2111
.2114
.2117
.2119
.2122
.2125
.2128
.2131
.2134
.2137
.2140
.2143
.2146
.2148
.2151
.2154
.2157
.2160
.2163
.2166
.2169
.2172
.2174
.2177
.2180
.2183
.2186
.2180
.2192
.2195
.2198
.2200
.2203
.2206
.2209
.2212
.2215
.2218
.2221
.2224
.2226
.2229
.2232
.2235
.2238
.2241
.2244
.2247
.2250
.2253
.2255
18»
.2264
.2267
.2270
.2273
.2276
.2279
.2281
.2284
.2287
.2290
.2293
.2296
.2299
.2302
.2305
.2307
.2810
.2313
.2316
.2319
.2322
.2325
.2328
.2331
.2383
.2336
.2339
.2342
.2345
.2348
.2351
.2354
.2367
.2350
.2362
.2365
.2368
.2371
.2374
.2377
.2380
.2383
.2385
.2388
.2301
.23d4
.2307
.2400
.2403
.2406
.2400
.2411
.2414
.2417
.2420
.2423
.2426
.2429
14»
.2258 / .2432
.2261 .2434
.2264 / .2437
.2437
.2440
.2443
.2446
.2449
.2452
.2455
.2458
.2460
.2463
.2466
.2469
.2472
.2475
.2478
.2481
.2484
.2486
.2489
.2492
.2485
.2498
.2501
.2504
.2507
.2510
.2512
.2515
.2518
.2521
.2524
.2527
.2530
.2533
.^2586
.2538
.2541
.2544
.2547
.2560
.2553
.2666
.2659
.2561
.2664
.2567
.2570
.2573
.2576
.2679
.2582
.2585
.2587
.2500
.2503
.2596
.2509
.2602
.2005
.2608
.2611
16*
.2611
.2613
.2616
.2619
.2622
.2625
.2628
.2631
.2634
.2636
.2639
.2642
.2645
.2648
.2651
.2654
.2657
.2660
.2662
.2665
.2668
.2671
.2674
.2677
.2680
.2683
.2685
.2688
.2691
.2604
.2697
.2700
.2703
.2706
.2709
.2711
.2714
.2717
.2720
.2723
.2726
.2729
.2732
.2734
.2737
.2740
.2743
.2746
.2749
.2752
.2755
.2758
.2760
.2763
.2766
.2769
.2772
.2775
.2778
.•2781
.2783
\
16*
.2783
.2786
.2789
.2792
.2795
.2798
.2801
.2804
.2807
.2800
.'2812
.2815
.2818
.'2821
.'28-24
.2827
.2830
.2832
.2835
.2838
.2841
.2844
.2847
.2860
.2853
.2855
.2858
.2861
.2864
.2867
.2870
.2873
.2876
.2878
.2881
.2884
.2887
.2»H)
.2893
.2896
.2899
.2902
.2904
.2907
.2910
.2913
.2916
.2919
.29'22
.29*25
.2927
.2930
.2933
.2936
.2939
.2942
.2945
.2948
.2»&0
.2d5d
.2056
ir
18*
.2956
.8129
.2950
.3182
.2962
.8134
.2965
.3187
.2968
.8140
.2971
.8143
.2973
.8146
.2976
.8140
.2979
.8162
.'2982
.3155
.2985
.3167
.2988
.3160
.'2991
.3163
.2994
.3166
.2996
.3160
.'2999
.3172
.3002
.3176
.3005
.3178
.3008
.8180
.3011
.3183
.3014
.3186
.3017
.8189
.3019
.8102
.3022
.3196
.3025
.8198
.3028
.8200
.3031
.3203
.3034
.3206
.3037
.3209
.3040
.3212
.3042
.8215
.3045
.8218
.3048
.8221
.3051
.3223
.3054
.3226
.3057
.3229
.3060
.3232
.aMa
.3235
.;{065
.3238
.3068
.3241
.3071
.3244
.3074
.3:U6
.3077
.3249
.3080
.3252
.3083
.3255
.3086
.3*258
.3088
.3261
.3091
.3264
.3094
.8267
.3097
.3269
.3100
.3272
U5103
.3275
.3106
.8278
.3109
.3281
.3111
.3284
.8114
.3*287
.3117
.3289
.3120
.3-292
.avtt
l:S]!)b
19*
.av2ft \ .Ms»
.3801
.3804
.3807
.3810
.3312
.3316
.8818
.3321
.8824
.8327
.3380
.3833
.8836
.8888
.8841
.3844
.8847
.8860
.8868
.3866
.3868
.8861
.8304
.8867
.8370
.3878
.3876
.8878
JS3SI
.3884
.8887
.3300
.3303
.8306
.8808
.3401
.8404
.3407
.3410
.3413
.8416
.3419
.3421
.3424
.3427
.8480
.3488
.3186
.3489
.8441
.8444
.3447
.3460
.8463
.3466
.3460
.3462
.3464
80*
.3473
.3476
.8470
.8482
.8484
.8487
.8480
.8403
.8486
.8489
.8602
.8804
.8607
.8610
.3618
.8616
.8610
.3622
.8626
.8627
.8680
MS&
JU»
.8680
.8642
.8646
.8647
.8660
.8663
JS666
.8660
41602
.8666
.8607
.8670
.8678
.8676
.3679
JI662
.3666
.8687
.8600
.8603
.3606
JUOO
.8002
.8006
.8608
.8010
.8018
.8016
.8010
.8026
.8080
14
H
M
tt
.«
AVl^X MMkX 2»!^
JSOSD
V
«!•
.3045
.3046
.8660
.8663
•MUUt
JaOOn
.80&8
.3002
.8806
HfUlfi
JaOOO
.8070
.8073
.8076
.8079
,8088
JMBO
.8089
41702
.8706
.8700
J710
.8718
.8710
41719
.8782
.8726
.8728
41710
.STO
jTao
4na9
41742
.8746
.8748
.3760
.8763
.8766
.8768
.8702
.3706
.8708
41770
.8778
.8770
.3779
41782
41796
•STfO
.819
.8808
.8806
v
1
211
3!
4
i
6
7
8
9
14
11
U
IS
14
U
16
17
U
19
»
81
8t
81
82
3S
34
41
«t
U
44
4i
m
^^r r.KUMUTKlCAL
PROKLF.MS. ^^^^
Table of Chorda: Radius
= 1.000O {wrdiiiited).
98-
S3'
«*•
8S*
M'
aT US-
«o-
so-
31-
sa-
M.
.ssie
■tmi
^is8
4318
^4W
^
4838
~6(io8
~^
^613
0*
.asm
At
.3822
lama
8*4
.3SZ£
40
.3828
4340
40«
I
.3830
.3833
!40ut
:J5
4M
.46
46H.
JO
.3830
.4007
WH
^ I
•3342
.41
43&
4842
K.
.M
|10
.3848
.4018
.41 UU
43ft
1 «3
IS
1 j4S
la
13
.3U3
«UI,
u
B
iJmu
.41S8
jf
1
.4039
,430
Jf
S4
S90
'jsm
«iso
^70
M
AM
.38T3
.4330
m
20
1
jwjo
AX
4MM
In
^7B
4311
.46*
a
la
Ait
1 1 24
64V8
23
|H
^se
A*a
438
24
U
.4UM
AtH
IW
m
Iw
A-ax
4403
2e
in
A3»&
us
6888
»
ASUS
.*m
,4678
.4B17
.5088
.6264
.6423
28
»
,4a2l)
.hum
.8428
29
Itu
aaia
A-tU
!4H4
.4823-
AiM
.6428
ao
.aeon
,41120
.3908
Atia
.46BI)
,41«9
.Htm
iw
.9910
A3i2
Afii
.4N»
.4UJ2
'■^'^
16437
33
.4U8J
ASm
.mb
.4h:h
.6W0
A-JhS
.4SU8
laeie
'aiW
Asni
JHOl
:(7
•airii
.WW
.4404
.4773
AWi
:S14S
16013
las
'ahoh
.4437
w
isn^i
^40B8
AMD
.4llW
!8464
!m22
41
.3KIS
^Wl
.*JT2
.4445
.4012
;*78!
!48S1
.4IIM
.6120
'.t2S»
.M67
.Mflu
.SfflW
41
43
-43714
.4867
.6402
iaew
411
«(
JBao
AUU
.44.^1
14821
AW
W7
.640.1
.6833
43,
Jtua
'.ma
.^494
.MlIU
.M3fl
M
»VI
Mm
«
Mn
.*m
.443U
AIM
!.W74
«
.»M
.4181
.ASKl
A*iri
'.¥a-2
..\-IU8
.JH7B
tt
.Wfi3
.4«ie
.446.1
«
Mim
-UeB
Aiaii
;4877
isosu
GO
.a)M
.4130
.4800
.4641
!8488
60,
.Kfe
at
!447n
!4a4e
.WM
!m90
ss
.»»7
'Axm
.Mm
.4849
iwiB
'.6W!>
:s«ei
«I0
Mli
r84W
u
jsn
Ami
.64W
•ane
!4858
.6602
ST
.3R»
AIM
Aim
Isios
.B8.1B
.56M .6011
ts
.*IU
.4403
^4863
.itm
.Mil .ws!»\,i>wr,\.'^i%\i*\.l
.atss
.4I3S 1 .«M
.48011
!483«
.MXK, 1 .6114 V ,S1*1\ .-a6\«\ .W%\»a
imri-""!
A^IA4^}.^
.4838
.5C08 \ j,-^j^\ .^\ .1*^ .w«\«|
1
■
■
1
=^=^
8S
GEOMETRICAL PKOBLKMS.
Table of Chords; Radius = 1.0000 (conthnted)^
M.
0'
1
2
3
4
f)
0
«
K
',»
10
11
VI
13
14
lo
16
17
18
19
au
21
22
23
24
25
26
27
2H
2«
3()
31
32
3:1
34
3r)
:U'>
'37
38
39
40
41
42
4:*>
.44
.45
•46
147
!48
149
|50
51
52
53
54
55
56
57
'/SS
59
33* 34* 35*
.5680
.r>683
.5686
.5689
.5691
.:)694
.5697
.5700
.5703 _
.5705 ■
.5708 I
.5711 I
.5714
.5717
.5719 I
.5722
.5725
.5728
.5730
.57351
.5736
.5739
.5742
.5744
.5747
.5750
.5753
.5756
.5758
.5761
.5764
.5767
.5769
.5772
.5775
.577S
.5781
.5783
.5786
.5789
.5792
.5795
.5797
.5800
.58a3
.5806
.5808
.5811
.5814
.5817
.5820
.5822
.5825
.5828
.5831
.5834
.5836
.5839 ,
JiM'J I
.684:'} j .
r,st7 ; .
.5847
.5850
.5853
.5866
..5859
..5861
.5864
.5867
.5870
.5872
.;>875 !
..5878
..5881
.5884
..5886
..58S9
.5892
.5895
.5897
.5900
.5903
.5906
.5909
.5911
.5914 i
.5917
.5922
.5925
.5928
.5i>31
.5934
.5936
.59:i9
.5942
.5945
.5947
.5950
.595.3
.5956
.59.59
.5961
.59tU
.5967
.5970
.5972
.5975
.5»»78
.5J»81
.5984
.5986
.5989
.5992
.5995
.59i»7
.♦JOOO
.({003
.6(K)6
.tJiKHf ,
.wn .
tm4 I
.6014
.6017
.6020
.6022
.6025
.6028
.6o:n
.6034
.6036
.♦V042
.6045
.6047
.6050
.605:1
.6056
.60.58
.wm
.6064
.6«W7
.6070
.6072
.6075
.6078
.6081
.6<)83
.608li
.6089
.6(K)2
.60i)5
.6(H)7
.6100
.614M
.6106
.6108
.6111
.6114
.6117
.6119
.6122
.6125
.6128
.6130
.613:)
.6136
.6i:{9
.6142
.6144
.6147
.6150
.6153
.6155
.6158
.6161
.6164
.6166
.6169
.6172
.6175
.6178
.6180
36* 37* : 38* I 39* i 40*
1"
.6180
.6183
.6186
.6189
.6191
.6194
.6197
.6200
.62(V2
.6205
.6208
.6211
.6214
.6216
.6219
.6222
.6225
.6227
.6230
.62: J3
.6236
.6238
.6241
.6244
.♦R247
.6249
.♦J252
.6255
.6258
.6260
.6263
.6266
.6209
.6272
.6274
.6277
.6280
.6283
.6285
.0288
.6291
.(:^'94
.6296
.0299
.6302
.6:105
.6307
.6310
.6313
.6316
.6:118
.6321
.6:124
.6:127
.6:1:10
.6332
.6335
.<\338
.6341
.6:143
.6:140
.6.346
.6349
.6:W2
.6354
.6.157
.6361):
.6:m:i
.6:i«l5 i
.6:168!
.6371 .
.6374
.6:176
.6379 I
.6:i82
.♦1385 .
.6:J87 '
.631N) ■
.6:19:1 j
.6:i*Ml I
.♦UWS
.6401
.6404
.6407
.6410
.W12
.6415
.6418
.W21
.642:1
.6426
.«>429
.6432
.64:14
.♦1437
.6440
.6443
.6445
.6448
.6451
.6454
.6456
.6459
.6402
.fU65
.6467
.6470
.6473
.6476
.6478
.6481
.&484
.6487
.6489!
.♦U92i
.6495 :
.6498
.6500
.65o:i
.6506
.65«)9
.6511
.6511 !
.6514
.6517
.6520
.6522
6525
.6528
.6531
.65:1:1
.6.5.-36
.65:W
.♦1542
.6544 I
.6.547
.6550
.655.1
.6555
.6558
.6561
.6564
.65^)6
.6569
.6672
.6575
.6577
.6580
.658.'}
.6586
.6588
.6591
.6694
.6597
.6599
.6602
.6605
.6608
.6610
.6613
.6616
.6619
.16621
.6624
.6627
.66:10
.6632
.66:15
.6(K18
.6640
.6643
.6646
.6649
.6651
.6654
.6657
.DOW
.6662
.66^15
.667 1 \
.Wi'i \
.6676
.6679
.6682
.6684,
.6687
.♦M90
.6t$93
.6695
.6698
.♦1701
.6704
.6706
.6709
.6712
.6715
.6717
.♦i720
.6723
.6726
.6728
.6731
.6734
.6736
.6739
.6742
.6715
.6747
.6750
.♦i75:i
.675*1
.6758 I
.6761 :
.6764
.6767
.6769
.6772
.6776
.6777
.6780
.6783 1
.6786 1
.♦•788 !
.6791 I
.6794:
.6797 i
.6799
.6802
.68(»5
.6808
.6810
.6813
.6840
.6843
.6846
.6840
.6861
.6864
.68.57
.6860
.6862
.6865
.6868
.6870
.6873
.6876
.6879
.6881
.6884
.6887
.689«)
.6892
.6895
.6898
.♦KN)1
.6908
.6906
.09(»9
.6911
.6914
.6917
.♦H»20
.6922
.6925
.6028
.6631
.6033
.6096
.60:»
.6941
.6044
.6047
.6060
.0062
.0966
.6058
.6061
.6963
.tWDO
.OWJlf
.6971
.6974
.6977
.6816 j .6980
.6819 ! .6982
.6821 ■ .6985
.68*24
.6827
.6991
.6829 : .6993
.6832 ! .6996
.6835 I .6099
\ .*Sft40\ .-V^A\ ."WW
41' . 48* j 4S* M.
.7004
.7007
.7010
.7012
.7016
.7018
.7020
.7023
.7026
.7029
.7091
.7034
.7087
.7040
.7042 i
.7046
.7048
.7060
.7063)
.7066
.7050
.7061
.7064
.7067
.7000
.7072
.7076
.7078
.7080
.7083
.7086
.7080
.7001
.7004
.7007
.7000
.7102
.7106
.no6
.7110
.7118
.ni6
.7118
.7121
.7124
.7127
.7120
.7132
.7136
.7137
.7140
.7143
.7146
.7148
.7151
.7164
.7166
.7150
.7162
.7167 I
.7170:
.7173
.7176
.n78
.7181
.7184
.7186
.7180
.7102
.no5
.n«7
.7200
.7203
.7206
.7208
.7211
.7214
.7216
.7210
.7222
.7384
.7827
.7230
.7882
.7236
.7238
.7241
.7243
.7246
.7240
.7261
.7264
.7857
.7860
.7202
.7866
.7888
.7870
.7878
.7878
.7870
.7381
.7384
.7387
.7380
.7393
.7306
.7398
.7300
.7308
.7800
.7^
.7311
.7314
.7316
.7310
.7822
.7336
.733U
A-
.7385
.7338
.7841
.7344
.7346
.7810
.7362
.7364
.7367
.7300
.7808
.7385
.7368
.7371
.7373
.7376
.7370
.7381
.7384
.7387
.7390
.7882
.7305
.7308
.7400
.7408
.7406
.7408
.7411
.7414
.7417
.7410
.7422
.7425
.7427
.7480
.7433
.7435
.7438
.7441
.7448
.7446
.7440
.7468
.7464
J467
.7400
.7402
.7405
.7408
.74n
.7478
.7470
.7470
.7481
.7484
.7487
\.T48Blw
^H GKOMETKIUAI. PROJILKMK. ;-
Table of Chords Radius = 1 OOOO {<• I'ued)
!)0
GEOMETRICAL PROBLEMS.
Table of Chords ; Rculius = 1.0000 (continued) .
61*
1 ^
55" 1 56'
T
.U23'»
.<»2:i8
.0-2-U)
.924:1
.92-40
.^♦248
.92.10
.92r>6
.<t2.'>8 I
.9261
.926:i
.9266
.9268
.9271
.9274
.9276
.9279
.9281
.9-284
.9287
.9289
.9292
.9294
.9297
.9299
.9302
.9305
.9307
.9310
.9312
.0315
.9317
.9320
.9323
.9:i25
.9328
.9330
.93:»
.93:to
.93:^8
.9341
.934;{
.9346
.9;J48 ,
.9351
.9:io:j .
.93545 I
.9;y)9
.9361
.9364
.9:J66
.9:i69
.9371
.9374
.9:J77
.wm
.W«2
.f/;m
57* , 58* : 60*
I
_ I
04)1 .u:UiUi
.9389
.9392
.9395
.9397
.9400
.9402
.94a5
.9407
.9410
.9413
.9416
.9418
.9420
.9423
.9425
.9428
.9430
.9433
.9436
.9438
.9441
.9443
.9446
.9448
.9451
.9464
.9456
.9459
.9461
.9464
.9466
.9469
.9472
.9474
.9477
.9479
.9482
.9487
.9489
.9492
.9495
.9497
.9500
.9502
.9505
.9507
.9510
.9512
.9515
.9518
.9520
.9523
.9525
.9528
.9530
.953:i
.95.36
.95i)» j
.9o43 I
I
.954:t
.9546
.9548
.9.551
.9553
.9566
.9559
.9661
.9564
.9566
.9569
.9571
.9574
.9576
.9579
.9581
.9584
.9587
.9589
.9592
.9594
.0597
.9699
.0602
.9604
.9607
.9610
.9612
.9615
.9617
.9620
.9622
.9625
.9627
.9630
.96:»
.9635
.9638
.9640
.9643
.0645
.9648
.9650
.965:)
.9665
.9658
.9661
.966:$
.9666
.9668
.9671
.9673
.9676
.9678
.9681
.9vo»»
.96»i
.9689
.9691
.1*694
W96
I .5»l'
.9696
.{N)99
.9701
.9704
.9706
.9709
.9711
.9714
.9717
.9719 j
.9722 j
.9724 I
.9727
.9729
.97:J2
.97:44
.97:J7 '
.9739 I
.9742 I
.9744
.9747
eo*
.9750
.9752 ,
.9755 I
.9757 i
.9760
.9762
.9765
.9767
.9770
.0772
.0775 '
.0778 ,
.0780
.0783
.9785
.9788
.9790
.979:)
.9795
.9798
.9800
.0803
.0806
.0810
.9813
.9816
.9818
.9821
.9823
.9826
.9828
.9K:il
.98:»
.98:J«
.98:58
.9841
.9843
.9846
.9848
.9848
.9861
.9854
.9856
.9859
.9861
.9864
.9866
.9860
.9871
.9874
.9876
.9879
.9881
.9884
.{m86
.9889
.9891
.9894
.9897
.9899;
.0002
.0004.
.99074
.0909
.9912
.9914
.9917
.9919
.9922
.9924
.0927
•99a9
.9932
.9934
.9937
.9939
.9942
.9945
.9947
.0050
.0052
.0055
.0957 1
.9900
.0062
.0065
.9967
.0970
.9972
.9975
.9977
.9980
.9982
.W85 ,
.1*987
.9990,
.991»2!
.9995 ;
.9998;
l.lKHWi
1.<NNN)
l.ooo:)
1.0005
1.0008
1.0010
1.0013
1.0015
1.0018
1.0020
1.002:)
1.0026
1.0028
1.0030
1.0033
1.00:15
i.oo:)8
1.0040
1.0043
1.0045
1.0048
1.0050
1.005:i
1.00.'>5
1.0058
1.0060
1.006:1
1.00«)5
1.0068
1.0070
1.007:J
1.0075
1.0078
1.0080
1.008:t
1.0086
1.0088
1.0091
].009:t
1.0096
1.0098
1.0101
1.0103
1.0106
1.0108
i.oni
1.0113
1.0116
1.0118
1.0121
1.012:)
1.0126
1.0128
1.0131
1.0i:)3
1.0136
1.0138
1.0141
1.014:)
1.0146
1.0A4H
l.OAiA
IJdUl
1.0153
1.0166
1.0168
1.0161
1.0163
1.0166
1.0168
1.0171
1.0173
1.0176
1.0178
1.0181
1.018:)
1.0186
1.0188
1.0191
1.0193
1.0196
1.0198
1.0201 I
1.020:) I
1.0206;
1.0208
1.0211 ,
1.0213
1.0216
l.(»218
1.0-221
1.022:)
1.0226
1.0228
1.0231 I
1.02:):) i
i.02:)6.
1.0-238 I
1.0-241 i
1.0-243'
1.0-246
l.(r248
1.02:)t
1.025:)
1.02.=)6
1.0-258
1.0261
1.026:)
1.0-266
1.0-268
1.0-271
1.0-273
1.0-276
1.0278
1.0281
1.(»-28:)
1.028()
1.0-288
1.0-291
1.0-21*3
1.0296
\\.VV2»H
1.0301
1.0309
1.0306
1.0308
1.0311
1.0313
1.0316
1.0318
1.0321
1.0323
1.0326
1.0328
1.0331
1.0333
1.0336
1.0338
1.0341
1.0343
1.0346
1.0348
1.0361
1.03.'i3
1.0366
1.0368
1.0361
1.0363
1.0366
1.0368
1.0370
1.0373
1.0876
1.0378
1.0880
1.0383
1.0386
l.o:)88
1.0390
1.0393
1.0395
i.o:)e8
1.0400
1.0403
1.0405
1.0408
1.O410
1.0413
1.0416
1.0418
1.0420
1.0423
1.0425
1.0428
1.0430
l.(U3:)
1.0435
1.0438
1.0460
1.0453
1.0457
1.0460
1.0402
1.0406
1.0407
1.0470
1.0472
1.0475
1.0477
IMSO
1.0482
1.0485
1.0487
1.0400
1.0482
1.0485
1.0187
1.0600
1.0602
1.0604
1.0607
1.0600
1.0512
1.0614
1.0617
1.0610
1.0622
1.0524
1.0627
1.0682
1.0534
1.0637
1.0542
1.0644
1.0647
1.0648
1X)661
1.0554
1.0556
1.0558
1.0661
1.0664
1.0566
1.0508
1.0571
1.0574
1.0676
1.0578
1.0561
1.0584
1.05R6
1.0440 j 1.0688
1.044:) 1.0501
1.0446 1.0503
\.v\U1 \\.Q!Aft
1.0506
ijomi
1.O008
1.0006
1.0606
1.0611
1.0613
1.0616
1UM18
1.0621
1.0083
1.0626
1.0086
1.0690
1.0033
1.0085
1.0088
1.0040
1.0048
1.0045
1.0648
1X050
1.0058
1.0055
1.0056
1.000U
1.0002
1.0065
1.0067
1.0070
1UM72
1.0675
1.0077
1.0060
1.0062
1.0665
1.0067
1.00B0
1.0602
1.0604
1.0607
1.0600
1X1702
1X704
1X707
IjOTOO
i.on«
1X714
1X717
1X710
1.0721
1.0724
1.0726
1.0720
1X731
1.0734
1.0730
1.0730
1.0741
1X744
1
^^^^ GEOMETRICAL PROBLEMS.
*^^^
Table of Chords; Radiua = 1.0000
{mntln-'ied) .
1
M-
««■
ea"
«■
es"
6»"
Til-
■IV
73-
M.
!
.OTM
jnss
.ores
i.osea
LflSBS
LOftM
1.0B1U
11
1.1328
i.im
l!llffi4
l.W^
\.\W<<
i.isoa
I
i
I.OfB7
\wn
lim
Lissa
.1M»
'iMO
.1780
I.ISW
U
1
10
.onw
;-^
l.IOM
i'lni'i
'iftll
1.1988
w
M
MM
'l^
'ml
■iBlil
119M
■M
M
MK
11114
i.ii&a
.1B2S
30
M
11™
iilij
lisw
. «w
■j^
I'l^
»
VI
1.113B
l.l-JKU
I.IMB
i.Toe
4U
I.IMHI
M
n
11019
1.11W
'"'alw
1.1450
i.isfe
i.ijM
1. UTS
i.aitis
"
i.emji.jvssfi.ni4l
l.UJ-i I l.lflU^ 1.1166
\,.,»,\««
««■
J
1
I
*J2
GEOMETRICAL l»UOBL£MS.
Table of Chords; Radius = 1.0000 (continued).
I
M.
74°
75'
76*
KY
1.2o:i»i
1.2175
l.-2:n3 I
1
1.20:w
1.2178
1.2316 1
2
1.21V41
1.2180
1.2:118 1
'j
1.204:i
1.2182
1.2:)'20 1
4
1.204«
1.21JS4
1.2:J22 1
5
1.2t»4S
1.2187
l.-2:i25 1
n
1.2o:»o
1.21 SO
1.2:J27 , 1
1
1.2iC»:5
1.2191
1.2:i-29 j 1
K
1.20'»5
1.2194
l.-2:W2 ! 1
\\
1.2i»",7
1.21:m
1.2:m : I
10
1.20«0
1.21*W
1.-2336I 1
11
1.20H2
1.2201
1.23.38 I
12
1.20JU
1 .220.3
l.'2:Ul 1
\'\
1.20«56
1.2205
1.2343 1
14
l.-iOfK*
1.220S
1. -2:145 1 1
i:)
1.2071
1.2210
1.2348 1
Irt
1.2073
1.-2212
1. -2:150 1
17
1.21)70
1.2214
l.-2:i^>2 1
18
1.2078
1.2217
1.-2.354 1
1J»
1.208JI
1.2219
l.-2:{57 1 1
20
1.20S;5
1.2221
l.-2:i59 , 1
21
1.20S.-»
1.-2224
l.-2:«l 1 1
22
1.2087
1.2226
l.-2:)64 1
2:i
1.2090
1.2228
1.2366 : 1
24
1.2092
1.2231
1.-2368 I 1
25
1.2«>94
1.2233
1. -2:170 1 1
2r)
1.2097
1.2235
1.-2373 1
27
1.2099
1.2237
1.-2375 1
2S
1.2101
1.-2240
1.-2377
1
2it
1.2104
1.2242
1. -2:180
1
:i()
1.2im»
1.-2244
1.-2:182
I
:n
1.21 OS
1.2247
1.2:184
1
'.VI
1.2111
1.2249
1.2:186 . 1
:«
1.211.3
1.2251
1.2:189 ; I
:m
1.2115
1.2254
1.-2391 : 1
:j.'»
1.2117
1.2256
1.-2393! 1
:jt)
1.2120
1 .2258
1.-2396 1
:J7
1.2122
1.2260
1.-2:198 1
:js
1.2124
1.2263
1.-2400 1
:ii»
1.2127
1.2265
1.-2402 1
40
1.2129
1.2267
1.2405 1
41
1.21.31
1.2270
1.2407 I
42
1.2134
1.2272
1.-2409 1
4:J
1.21.36
1.2274
1.-2412 1 1
44
1.2138
1.2277
1.-2414 , 1
4')
1.2141
1.-2279
1.-2416 ■ 1
4(i
1.214:5
1.2281
1.-2418 1 1
47
1.2145
1.228:J
1.-24-21 1 1
4S
1.2148
1.2286
1.-24-23 ! 1
49
1.2150
1.2288
1.-24-25! 1
50
1.21.52
1.-221K)
1.-24-28
1
. 51
1.2154
1.2293
1.2430
1
52
1.2157
1 1.-2295
1.-2432
1
! 53
1.2159
' 1.2297
i.-24:i4' 1
, ^
1.2101
1 1.2299
1.-24:17 i 1
• 55
1.2164
1.2:M)2
1.24:19! 1
50
1.2166
1.2:J04
1.2441 1 1
57
1.2168
i 1.2:J06
1.-244:1 , 1
/ ^^J
1.2171 ,
1 i.2:i0ii
1.2446 ' 1
/ r>9 1
1.21 7:i
i.'Jiiii
L2:ii:i
1.244«. 1
i *
90 1 i
L2lTr,
1.2450
1
.'24.')0
.-24.5:1
.-2455
.-2457
.24.59
.2462
.2464
.2466
.-2468
.2471
.2473
.-2475 1
.-2478 ;
.2480 I
.-2482 i
.2484 :
.-2487 I
.2489
.2491 I
.2493
.-2496;
.-2498
.2500 .
.-2oO:i
.'2505
.-2507
.-2509
.2.512 ■
.2514
.-2516
.-2518
.2521
.-25-2:1
.25-25
25-28
.-2530
-25:12
.•2'y.u
2537
.2539
.-2541
.-254:1
.-2.546
.-2548
.2.5.50
.-25.52
.*25o5
.-2.567
.2559
.-2562
.2564
1.2566
L.-2568
I .-2571
[.-2573
1.-2575
[.2577
.-2580
1.-2582
[.-2.)84
[.-2586
1.-2586
1.-2589
1.-2591
1.2593
1.2595 I
l.'2.')98 !
1.-2600 I
1.-2602
1.-2604
1.2607
1.2609
1.2611
1.-2614
1.-2616
1.-2618
1.-2620
1. -26-2:1
1. -26-25
1. -26-27
1. -26-29
, 1.-2632
1.-2634
. 1.-26:16
1.-2638
1.-2641
1. -264:1
1.2645
■ 1.-2648
1.-2650
1.-2652
1.-2654
I 1.-26.56.
1.2659
; 1.-2661
1 1.266:1
1.-2665
, 1.-2668
1.-2670
; 1.-2672
' 1.-2674
1.-2677
I 1.-2679
I 1.-2681
. 1.-2683
1.-2686
1.-2688
' 1.-2690
I 1.-2692
I 1.-2695
. 1.-2697
' 1.-2699
1.-2701
1.-2704
1.2706
1.-2708
1.-2710
1.2713
1.-2715
1.-2717
1.-27 1ft
A.Trl'l
79*
80*
1. -27-22
1.-2S56
1. -27-24
1.-2858
1.-27-26
1.2860
1.-2728
1.2862
1.-2731
1.-2865
1.-2733
1.2867
1.-2735
l.-28d9
1.-2737
1.2871
1.-2740
1.-2874
1.-2742
1.2876
1.-2744
1.2878
1.-2746
1.-2880
1.2748
1.-2882
1.-2751
1.2885
1.2753
1.2887
1.2755
1.2889
1.-2757
1.-2891
l.-276(>
1.2894
1.-2762
1.2896
1.-2764
1. -281^1
1.-2766
1.-2900
1.-2769
1.-2903
1.2771
1.2905
1.-2773
1.2907
1.-2775
1.-2909
1.2778
1.2911
1.2780
1.2914
1.-2782
1.-2916
1.-2784
1.-2918
1.-2787
1.-29-20
1.-2789
1.-29*22
1.-2791
1.29-25
1.-2793
1.-29-27
1.-2795
1.-29-29
.1.'2798
1.-2931
1.-280O
1.-2934
1.-2802
1. -29:16
1.-2804
1.-29:18
1.-2807
1.-2940
1.2809
1.-2942
1.-2811
1.2945
1.2813
1.-2947
1.-2816
1.-2949
1.2818
1.-2951
1.-2820
1.-2954
1.-28-22
1.-2956
1.28-25
1.-2958
1.28-27
1.2960
1.-28-29
1.-2962
1.-2831
1.-2965
1.-2833
1.-2967
1. -28:16
1.-2969
1. -28:18
1.-2971
1.-2840
1.-2973
1.2842
1.-2976
1.-2845
1.2978
1.-2847
1.-2980
1.-2849
1.-2982
1.-2851
1.-2985
^ A.*ZHv»4
' \.-2»«k
81* 82°
1.-2989
1.-2901
1.2993
1.-2996
1/2998
1.3000
1.3002
1.3004
1.9007
1.3000
i.aoii
1.31-21
1.312S
1.3128
1.3128
1.3130
1.3132
1.3134
1.S137
1.3130
1.3141
1.3143
1.3013
1.3145
11
1.3015
1.3147
12
1.9018
1.3150
13
1.3020
1.3152
14
1.30-22
1.3154
15
1.9024
1.3166
16
1.3027
1.3158
17
1.3020
1.3161
18
1.3031
1.3163
19
1.3033
1.3165
20
l.-2H^ft
1.3035
1.3038
1.9040
1.9042
1.9044
1.3046
1.3040
1.3051
1.3053
1.3055
1.3057
1.3060
1.3062
1.9064
1.9066
1.3068
1.3071
1.3073
1.3075
1.3077
1.3070
1.9082
1.3084
1.3086
1.3068
1.3000
1.9003
1.3005
1.3007
1.3000
1.3101
1.3104
1.3106
1.3108
1.3110
l.:in2
1.3115
1.3117
M.
1
2
3
4
6
7
8
9
10
1.3167
1.3160
1.3172
1.3174
1.3176
1.3178
1.3180
1.3183
1.3185
1.3187
1.3180
IJIIOI
1.3103
1.3106
1.3108
1.9200
1.8202
1.3204
1.3207
1.3200
1.3211
1.3213
1.3215
1.3218
1.3220
1.3222
1.9224
1.3226
1.9228
1.9231
1.3233
1.3235
1.9237
1.3280
1.9242
1.3244
1.9246
1.3248
21
22
23 ,
24
25 I
26 .
27 i
28;
29 '
3U i
31
32
33
64
35
36
37
38
3»
40
41
42
43
44
45
46
47
48
48
50
51
52
63
54
55
56
57 !
58 I
GEOHBTRICAL PROBLEMS. 93
Table of Chor^B ; Radiua = 1.0000 jvoiiduded) .
'/J^l
94
HIP AND JACK RAFTBR8.
Lengrtlis and Bevels of Hip and Jack Raftefrs.
The lines ab and be in Fig. 89 represent the walls at the angle
of a building; be is the seat of the hip-rafter, and fl/of a jack-rafter.
Draw eh at right angles to be, and make it equal to the rise of the
roof; join b and h, and hb will be the length of the hip-rafter.
Through e draw di at right angles to be. Upon b, with the radius
bh, describe the arc hi, cutting di in i. Join b and i, and extend gf
to meet bl in j ; then (ij will be the length of the jack-rafter. The
length of each jack-rafter is found in the same manner, —by ex-
tending its seat to cut the line bi. From/ draw fk at right angles
to fg, also fl at right angles to be, Make/fc equal to /Z by the arc
Ik, or make gk equal to gj by the arc jA; ; then the angle BtJ will be
the top bevel of the jack-rafters, and the one at k the down bevel
Backing of the hip-rafter. At any convenient place in be (Fig.
89), as o, draw mn at right angles to be. From o describe a circle,
tangent to bh, cutting be in s. Join m and 8 and n and s ; then
tAese lines will form at a the proper ang\eioT\)«>i^\Tv%^'fe\jQi^<ii
tJie hip-rafter.
TRIGONOMETRY. 96
TRIQONOMETR7.
lot the purpose of the author to teach the use of trigonom-
what it is; but, for the benefit of those readers who have
acquired a knowledge of this science, the following con-
formulas, and tables of natural sines and tangents, have
iserted. To those who know how to apply these trigono-
functions, they will often be found of great convenience
lity.
3 tables are taken from Searle's "Field Engineering," John
h Sons, publishers, by permission.
96
TKIGONOMETRIC FORMULAS.
Tri(m)komictkic VvvcnoKs.
Let A (FI|?. HYT) - an^le BAC ~ arc lih\ and let the radius AJi^ « AB -.
AH= 1.
W« then have
sin .4
^BG
008-4
= AO
tan A
^ DF
cot A
-HG
sec .4
■^ AJ}
cosec A
■-: AG
versin A
:^ CF = BE
covers A
-^ BK =.- HL
exsec -4
= BI)
coexsec A
= BG
chonl A
-^ BF
chord 2 -I
'.= Bl ^ 2BC
In the riufht-angUMl triuuKle ABC (KIjj:. 1()7)
Let AB --- c, .4 6* - />, and i^C - «.
We then have :
I'-
U.
I
3.
4.
5.
6.
7.
8.
9.
10.
sin A
cos - (
tan -4
cot A
sec .4
a
c
h
c
a
b
h
a
c
b
cosec -4 — —
a
vers A —
exsec A =
c -b
c
c -b
b
covers A -- — -
c
coexsec A— - —
u
u- sin B
=^Vi>tB
--- tan B
— cosec B
— sec/?
= covers B
= coexsec B
= versin ^
= exsec B
L
Pio. 107.
11. « = c sin ^ r^ ft tan >4
3'**. 6 = c eos^ = a cot -.4
13. c =
14. a = c cos B —h <r<>t -B
a
sin A
h_
COS A
15. b
Ifi. c
17. a
= c sin i? = a tan B
^ a _ fc
COB B Bin B
= V (o"Hr ft>(c '-^fef
]«. b = t^(c-f a) (c-o)
19. c = V'aa'-hfc*
a). C' = W»s=w4f4-i?
21. area = - ,,-
TRIGONOHETIUC FORMULAS,
1)7
Solution of Qbu^ub Trianolks.
Fig. 108.
OIVEN. fU)r»H7.
FOKMrLuK.
5«
2:i
24
25
26
27
28
29
80
81
A, H,a
n
A^ a, 6
88
C, 6, c C = ]H<i° - (,4 -I- B\ b z= . ■ . sin />',
sill -4
a
<• -^ . , sin (-4 -f //)
sm ^
B, C, c Kill B = ®*" '"*- . />,
a
C= lH<)°-Ll-f-/^j,
a
c ~ . : . sin C
sm A
C\ a,b H(A-^B) l^(A + B)- (M)° -^C
imA- B) tan H M - /») = " ,-*/ tan i^ (.4 + //;
I It -r u
a,b,c
A,B
I
area
A
A = }4(A-\-B)-hH{A -B\
B = }^(A-\-B)-}4(A-B)
. , .cos%(A-l-B) ^ , sinK'(.l+^)
' cxs&\^<A~B) %\\i\%A—B)
^ = ^ a 6 sin C.
Let« ~}^(a-\-h-\-c)\fA\\yiA = i /
>
sin^
j 6c
(«'-/>) («-r)
6c
■(s-6)(»-r)
A,S,C,a
area
area
vers A ~
be
2(8- b) (h- c)
be
K — 4^« {h — a) (a — "6/"(« — r)
/ jp, __ a*^ sin fi . sin C
/ ^ 2 sin A
98 TRIGONOMETRIC FORMULAS.
OKNKRAL FORMULA
34
35
37
38
39
40
41
cosecui
sin A = 2 sin ^ A cos %A = vers A cot ^ A
sill -4 = l/Hversa^ = V^a~co8 2-4)
1
cos -4 =- J = 4/I— sin«.4 = cot ^ sin ^
8ec A
cos A ~ l-vereX = 2cos«^>4 — 1 = 1— Sain*^^
cos^ - co8« ^ ^ — 8in« H ^ = VW+H<^^~A
* « 1 sin ^ - _— . ^
tan ^4 = — :-■ - = — _ = y aec^ A~~ I
cot -4 cos -4 ^
y cos^ ^ cos
tan^ = A/-:-.- - 1 = ..L^cos^^ ^ .-f'-''-^-^—
cos^ l + cos2^
.» I * t 1— cos 2 -4 vers 2.4 . ^,, ^
A-i I tan -4 = - . „ . = - -^ \. = exsec ^ cot V4 ^
sin 2^ sin 2^ ^^
43
44
46
47
48
49
50
51
1 cos A
cot -4 s= == ^ — • = A/cosec''^ — 1
tan A sin A ^
sin 2 ^ sin 2 ^ 1 + cos 2 A
cot A —
1 — cos 2 A vers 2 ^4 . sin 2 A
ei^sec^
vers ^ = 1 — cos A — sin -4, tan ^ ^ = 2 sin^ ^ ^
vers -4 — exsec -4 cos A
exsec A — sec A — 1 = tan A tan \^A — - ' -. - •
^" cos A
versX
' -i/ A . /l — cos X ^ /
sm Ji^ = |/ g = |/. 3
sin 2^ = 2 sin A cos ^i
/^
, - . / * + COS -4
COS f^ u4 =j ' ^ '
62 coa_2A = 2cosa-4 — 1 = cc^^A — s\n'*A «= \— ^^sd^A.
TRIGONOMETRIC FORMULAS. 0\
Gknkral F6Bifuii&
54. tAB !l^ =
2tan>A
1 —
50. cot. H^ - v^^ - ginU * oosec^-coti
56.cat2^ = «>*'^-*
57. ▼ersH-^ =
2cot^
H vers ^ 1 — 008 A
1 + ^l — H verTI 8+ ^2(1 4-"co8l5
sa vers 2^ = 2 sin* A
t — co&A
50. ezsec ^A =
60. exsec 2 ^ =
(1 + oo« -4) + Vsj (1 4- cos -4)
tan*^
1 — tan« yl
61. sin M ± B) = Bin^.cos^± sin ^. cos ^
62. cos {A ±B)=:co&A, cos B T sin ^ . sin ^
63. sin^ + sinf = 2sinH(4 + ^)cos^(^ — B)
64.sin^ — sinf=:2oosH(^ + f)sin^(^ — S)
65. cos A 4- cos B = 2 cos y^iA-{- B) cos ^ (4 — 5)
66. cosP — cofl^ = 28in^U + f)sIn^(^-.B)
67. 8in« 4 — 8in« B = cos« B — cos« ^ = sin {A + B) sin (4 — B)
6a C08« -4 — sin* B = cosiA -\' B) co9{A — B)
69. tan^ + taiiB = -^"i^^^^
' COS A . cos B
Z
TO. tanU-tea^=-'^i^--^^
cos^. COS B
466^ri^
^^^^Ir GEOMETKICAL ntOBI.KMs. 1
m^
Table of Chords ; Hadius = l.OOOO {conlinHB^
u
»■
,»•
13-
14-
.«■
17-
18"
19-
«r
^
ion
.20B1
Mftl
~
2«11
~
.2968
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~~
.3413
«•
'2287
^2440
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iwm
.2370
.2443
.2448
'mib
'.i.m
.2062
.3134
33U7
.3479
55
.2102
.3440
!2BC8
,3313
.lau
JMl
.2109
12270
.2452
12825
.2»71
.3143
.331&
.IBM
.2108
.2281
.24B3
.3828
.2801
.2073
.3140
a4!«l MtH
.2384
.3458
.3378
.3321
.2187
!2e34
.2879
.3324
!34M
.^m
.2200
.283H
.2082
.3156
J1S37
.3409
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10
IMO
^aiK
.2203
.2298
.2488
.2839
.2812
.2085
.2988
.3330
.3333
.3504
■^
1
12
.22S9
,3163
.1607
3«7»
'iMI
■2181
:247B
■2flSI
'Mil
!290e
!333B
3affl
i
^_
IS
18
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:2m
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!i«ai
12834
;3887
.2909
.3172
.3344
.1616
3m 1
K'
'.wee
i21«l
'.Xi3
!2a«u
.3003
.3360
H
J11U
.2918
12480
.2682
.3383
.8635
18
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.2310
.2838
.3336
w
SO
.2ee8
J63D
.1878
Jlfil
.2325
.3408
.2an
.3344
.jon
.8180
.3181
J633
12
.2847
.3384
33
!2aat
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.2£07
!ZS63
.3108
.3370
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j«83
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.3028
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JS73
jam
38
.2389
.2883
.3031
.3203
.3378
.864^
!lM6
.3888
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.3034
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w
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In 72
[iiia
.1884
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.3200
.3381
.3863
»
.3001
.3040
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90
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!3624
.36»7
.3042
.3387
•3563
81
.aoo7
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.2354
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.3700
.2373
.3044
.3300
.8641
K
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.21S3
.2703
J04S
J231
.3303
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S3
sua
.2350
U
.3180
.2382
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!2«81
.3054
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3743
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.2386
.2433
Ji711
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.3401
.3373
3141
s?
.2024
21W
.2388
.1541
.2544
.aoBO
.3083
.3232
.3404
3748
3761
ss
.2027
.'muu
.2374
.2*47
'siw
.3803
JOBS
.3333
.3410
.3683
.2377
.28H
.3413
.3685
!2Ura
'.2208
.2380
!25a3
.2800
.3241
3687
!n«
«1
JttOB
.2209
.2668
.3218
.3419
j»m
«2
.2385
.3077
.3688
!221»
.2383
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.3424
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.3218
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!2737
12910
.3355
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4»
,2047
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48
!z2ze
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■^\l ^^
.3381
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^
W
!20se
.2230
.2922 .3004
.3367
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J»10
40
.2ase
.3097
.8441
.9813
.a»2
!2236
.2400
!26B2
!2027
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3»e
(1
.2238
.2758
.3U7
3819
37«
.2311
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.3822
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jiog
.3281
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3026
M
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J311
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.2030
.3284
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3828
3T*»'
1
.3508
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.3387
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jtmM
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.2945
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J
/i5f/s
.3432
.3434
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li^i^
■
J
GKOMETKICAL rROI3LKMS,^^^^^^^H
Table of Chorda; Radius = l.OOOO {wntmiml).
».
9V 1 as-
«•
«B-
M'
87*
as- ' 89-
.to-
31' 98'
u.
lO"
Mio Laser
41W
iste
.4408
'tme
.4S3S
.um
smi
~~^
0-
\i ran sm
4 .38X1^
!4M6
M76
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.1608
MTl
,4880
■Jsw
iUio
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.4«II3
.0U22
434a
.4888
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.4348
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.:*iaB
S
^6378
,M>43
H|
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Am
43
'.^
:4114
^4884
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:Si
Imsi
:mh
^^H
.was
"mm
■^
'.iK6
■&M
S
isoao
,6568
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:*«3
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'.fm
.5566
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.6669
20
.421S
.4988
.6238
,MIH
.6671
21
.■K»l
.4681
.fr238
22
.4KB
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;4i4o
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.6247
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27
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s
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.6609
30
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.4U32
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Urn
.■M54
AMI
:47!m
,4980
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iw
.&2II7
.a4S8
44
.44Se
!&3U3
46
.^■■i; 'iKs..*'**
.44aB
AtltA
!47»ll
.63(16
^6641
vi.i-i ii:i .tiW
.441)2
.1832
.4802
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!547e
■im
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I&t82
401
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;4,;ji j-i.. .I'.;.. Ml- .wiJ
ti"
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!.«.<*
1 a
.4138
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66
.44B8
.4BSh .4s.:;7 i .4m 1 .i.m \ Asat \ Ji!«i\ awift\»\
*;S'
■—i,'
«?5
.4830
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■"»
■»»«
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m
\\
\Awn\.wt«.\iA\
.4838 .SO08 .M16\.63*6\A!.-Va\*WftV
^^^^^r 1>K0III.F.M.S. ^^^H
i
Table of Chords ; Radius = 1.0000 (coRj(nN4|
1
"
.3- 1 34*
3S-
3fl" 37"
1„-
39*
*o-
*!•
♦a-
1
»oan
W4-
B014
1 «.^„
eeu
6878
6«4n
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71BI
1
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MV
8017
ami 6341
K,U
6819
664.1
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1
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MB)
s
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B 0(
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63 1
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83 4
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BSTf
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MM
9218
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8226
17
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mid
1
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GEOMETKILA]. PROUI.KMS.
e Of Chorda; RadiaB = 1.000O (otilinued).
H"'
«8' 4T
4S'
40-
«r
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H'""
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J
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10
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96
TRIGONOMETRIC FORMULAS.
Trigonometric Functions.
Let A (Fifr. 107) = angle BAC = arc BI<\ and let the radius A^^^ABt
AH=:i.
W% then have
sin .4
= BG
cos^
= AG
tan^
^DF
cot--l
'-=Ha
sec A
= AD
cosec A
--=AG
versin A
= CF^ BE
covers A
= BK=HL
exsec A
-BD
coexsec A
= BG
chord A
== BF
chord 2 X
~^BI^ 2BC
In the right-angled triangle ABC (Fig. 107)
Let AB =:c,AC= b, and BC - a.
We then have :
1. sin A
2. cos A
8. tan A
4. cot A — ~
5. sec A
6. cosec yl = — =:
7. vers A =
8. exsec A =
a
c
b
c
a
h
h
(I
c
£
a
c -b
c
c -b
b
9. covers A = — - =
c — a
c
10. coexsec A= - — =
/
c — a
a
— COS B
= sin B
= cot B
- tan/?
^ cosec B
sec J?
covers B
c«>exsec B
versin B
exsec B
Fio. 107.
II. rt =c»in>4 — fetan^
12. b ^ c cosX = a cot A
13. c
14. a = c cos B ~ b tnyt B
a
sin A
cos^
15. h
16. c
17. a
— c sin B = rt tan ^
_ a ft
~ cos i? ~" sin P
3H. 6 = ♦'(c-f a)(c-o)
10. c = Vaa-f fta
20. C' = W» = -4.-f J»
21. area = - ^-
ah
TKlCK)NOJ(tETlUe FORMULAS.
1)7
r
Solution of Qbuc^ub Triamolks.
Fig. 308.
GIVEN. eoroHT.
roHMVLM.
22
A, B,a
23 I A,a,b
24
25
a
C\ b,c ; C = ]S(i° - (,4 H- Ti\ b ~ . • . .sill />',
sm -1
c ^ ,^ , sin(A-\-B)
sin A
B, C, c I sin i? = . />.
a
C^ m)°-(A-{-B},
a
c — - , - . sin <?.
sm A
27
28
29
ao
81
C% a,b }4U-\-B)^%{A-{-B) = fHi° -i^C
I
\%{A- B) tan i^ (yl - />) = ^-^^ tan J^ (^ + //;
.4,i^
a, 6, <?
area
A = yiU + B)-\-\i{A- B\
B=-^(A-\-B)-yiU-B)
^ = ^" + '^>cas>^(.r-/?j - ^" - ''' sinK>(^ -"^)
JS: = ^ a 6 sin C.
Let a = ^ (a -f- '^ + c) ; sin ^ A — \/
S
«(« — «)
cos y^A—A'^' , . ; tan }4A =
\ be
2i
sin A —
vei*» -<4 ^
'{8-h) (8-C)
be
(S--h){H-C)
/(s-ft)(*
y His—
a)
2\^:i (« - (1) (f(—b)(ft — c)
be *
2 ( « — b) (s — c)
be
area
K " ^ H{ii — a) (a — b) (^s — c^
» A, ^, O, a area / K = « - ^^ ^ - «"^ ^
/ / ;2 sin >1
lOG
NATURAL SINES AND COSINES.
0
1
2
8
4
5
6
7
8
9
10
80*
Sine CoBin
.60000
.50025
.50050
.50070
.50101
.50126
.50151
.50176
.60201
.50227
.50252
11 .50277
12 .50302
.50327
.508^
.5ftJ77
.60403
17'.50i2«
18 1.5045.')
19 ' .60478
20,.60S03
13
14
15
16
21 I.6062R
22 .50563
23 1.50678
^.60603
25 1.50628
26
27
.50654
.60679
28 .50704
29;. 50729
30.. 50754
81'
81 1.50779
32!. 50804
.60829
.60854
.60879
.50904
.50929
.50954
.50979
.51004
33
34
35
36
87
88
39
40
41
42
43
44
45
46
47
48
49
50
■ r>2
r>3
54
. .^5
56
57
58
..M029
.eift-vi
.61079
.61104
.61129
.61154
.61179
.51204
.51229
.61254
.81279
.51304
.61829
.61854
.51879
.51404
.61429
.61454
.86603
.86588
.86573
.86559
.86544
.86590
.86515
.86501
.86486
.86471
.8&457
.86442
.86427
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.86398
.863H4
.86369
.86354
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.86810
R6295
.86281
.86266;
.86251 1
.86287;
.86222
.86207
.86192
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.86163
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59 [ .61479
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/ ■
59^^
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.61877
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.61927
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.62126
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.62374
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Cofdn
.86717
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.86161
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88*
SS«
Sine 'Cosin
6i»ae .84806'
68017 .84789 ,
68041 .84774
63066 .84759
58091 .84748
58115 .847S8
63140 .84n2
63164 .84697
68189 .84681
.'>8214 .84666
63238. .84660 '
68268
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64000
54024
54049,
64073
64097;
64122,
54146;
54171 1
54195
6^220
I
'I
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.84<n*2 -■
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Sine^l
64464
64488
64518
64587!
M661
64586
64010
64685
64650
64683
64708
64782^
&475C
647811
M805
64829
64854
64^^78
M902
M927'
64»61
64976'
64990
&yi24
65048
65072
65097
65121
65145
65169
&51»4
.85851' .62770 .84948 • .64:M4'. 84009 : .55702 .88060
KfifflKS .52794 .84JW8 .M2»J9 .KMWW .65?^ .88084
.K'i821 .62819 .84913 .64293 .88978 .65750;. 88017. 1
.85806 .62844 .84897, .54317 .83JHJ2 .56775 .88001
.85792 .62869 .84882 1 .64842 .Kii^lO .55799 .82966
.85rr7 .62898 .84806 .54366 .839:)0 .55828 .82969
85702 .62918 .84851, .648911.83915 .55847 .828581
.8')747i .62948 .84836 .64415 .838<K) .65871 .82986 j
,.a5732, .62967 .84820 .64440 .8388:) .65895 .82920 i
.8,m7 /^6^J .84805 .544C>4 .KWl)? .55919 :.8B8904 !
Bine , Cosin | Sine' Cosin ^ bm© Co^Ti\«taMk \;
Oosin
.88807
.88861
.88885
.88819
.88804
.8K88
.88779
.83iS6;
.88740
.887^
.88706
S4*
.88678
.88660
.88646
.88029
.89618
.88507
.83581
.88666
.88548
65218.
65242
r5266
65;S)ll
55315;
N5389i
55363'
55388'
.'>5412:
55486
.836171
.88601
.83485
.83469 !
.88468
.88487
.88421 If
.88405
.83888
.88878
.88856
65460
554H4
55509'
6;>533-
65r»67|
565811
55605'
65630
65654
65678
.88840
.88324
.888061
.88202!
.8&2716!
.88260
.88244
.8a8a»M
.88913!'
.88195
.88179
.88168,;
.88147! I
.88181 !■
.88115 1 i
.88098
.88082 I
.88066 I
Sine jOotin
66819
66048
66868
66888
66016
66010
66064
66068
66US
66186
66100
66184
66806
66M0
66806
66858
56877
66401
66485
66148
66478
66497
66an
66545
66669
66588
86617
66641
66718
66786
66760
66784
66808
86686
86804
66888
86876
87000
67tl84
67tM7
67071
67085
07118
9n4S
57167
6n81
67815
67888
57808
67966
67810
67884
5r866
60
.8»B7 6fl
.898n 66
.68856 67
.8aB»:«
.BBBBE 00
.8»06 M
.82700 SI
.88778 88
.88757 51
.8R41 60
.88781 48
.88308,48
.8U88'47
.0675 46
.88058 45
.88648 44
.88086 48
.88610141
.8K88I4I
.8B677j40
.8K6] tt
.88544 »
.8B586 17
.8XUII86
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.88478 84
.aOM 8
.88446 81
.88489 81
.88US;80
.8BK8 87
.8047, »
.88880:81
.88814:84
.8880710
.88881 S
.88854 81
.88848 »
.88881 19
.88814 18
.88198 17
.88181 16
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.81815; C
Qoiagk\«tBft I, ^
58*
5T
b^
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NATt'KAI, SINES ANIJ COSINES.
^
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17
-■V :>J" j> f OTAXi
NATURAL TANGENTS .'
PART II.
Strength of Materials, and Stability of
Structures.
INTRO DTI CnOK.
In the (.'hapters raDstittiLlng this pari of the book, the a
I lias enileavoreil to preaent to archltocU and builders handy tui
reliable rules and tablm tor deteraiinlng the strength or stability o'
any piece of work they may have In hand. Every pains has beei
l&ken lo present the ruleH In the Klmplcat form couslsleiit witi
their accuracy', and It \a believed that all constants and theoriei
advanced are fully up to the knowledge of the present day, aonii
of the constants on transverse strength having bu£ recently Iveet
determined. The rules tor wrought-lron columns have lately beei
slightly changed by some engineers; hut ae the question ot tin
strength Of wrougbt-iron columns has not yet been satisfactorily
settled, and as the formnlas herein given undoubtedly err on tin
ante side if at all, we have thougtit best not to change them, espe
(•ially as they are still used by many bridge engineers.
The quesiion of tlie wln(l-pre«sure on roofs has not been talcei
up ill as thorough manner as would he needed for pitch roofa oi
very great span ; but for ordinary wooden roofs, and Iron roofs otr
exceeding one hundred feet span, the inelho<t given in Chap,
XViri. is sufficiently acciuntc.
.Viiy one wishing to study thf most accurate ujcthod of ol>talnln(
t|]f! effect of (he wind-pressure on toots will find It In ProfeiWI
<;ri:!en's excellent work on ''(iraphlcal Analysis uf Roof TrusMt."
Id wncloaion, the author recommends these chapters as present
lug accurate and modem rules, especially adagited to tlie requlMf
ments of American [>ra(^tlce, i
M
124 EXPLANATION OF SIGNS AND TERMSL
EXPLANATION OF SIQNS AND TERMS USED IN
THE FOUiOlTTINa FORMUIJLa
Besides the usual arithmetical signs and characters in general
use, the following characters and abbreviations will frequently be
used : — I DiS
The sign V^ means square root of number behind.
^ means cube root of number behind.
( ) means that all the numbers between are to be
taken as one quantity.
• means decimal parts; 2.5 = 2^^^^, or .46 = iVb-
The letter A denotes the co-efficient of strength for beama one
inch square, and one foot between the sapgoiU,
C denotes resistance, in pounds, of a block of any
material to crushing, per square inch of section.
E denotes the modulus of elasticity of any material,
in pounds per square inch.
6 denotes constant for stiffness of beams.
F denotes resistance of any material to shearing, per
square inch.
It denotes the modulus of rupture of any materiaL
S denotes a factor of safety.
T denotes resistance of any material to being pulled
apart, in pounds, per square inch of crosa-eection.
Breadth is used to denote the least side of a rectangular piece,
and is always measured in inches.
Depth denotes the vertical height of a beam or girder, and is
always to be taken in inches, unless expressly stated otherwise.
Length denotes the distance between supi)orts infeety unless
otherwise specified.
Abbreviations. — In order to shorten the formnlaa, it has
often been found necessary to use certain abbreviation8;iiacha8
bet. for between, hot. for bottom, dist. for distance, diam. fbr
diameter, hor. for horizontal, sq. for square, etc., which, however,
can in no case lead to uncertainty as to their meaning.
Where the word ** ton " is used in this volume, it alwaya meana
2000 pounds.
SBF1MITI0M3 OF TEBMS.
CHAPTER I.
rZORS OF TERMS USEID UT UBGHASICS.
a frftcjuently oecur in treating of mpoliaiii.^l
I, and it is essential that tlieir meaning be well un<ler-
ibanics is the science wlilcku-eats of the action of forcen.
ilied Mechanics treats of the laws of meclianins which
a works of human art; such as beams, trusses, arches, etc.
t Is the relation between two points, when the stralglit line
them does not change in length or direction.
dy la at rest relatively to a point, when any point in the
at rest relatively to the Brst-ioentioned point.
ion is the relation between two points, when the straight
ning them changes In length or direction, or in Ixith.
dy moTea relatively to a point, when any point in the body
relatively to the point first mentioned.
ce Is that which changes, or tends to change, the state of a
1 reference to resi or motion. It is a cause regarding the
i1 nature of which we are Ignorant. We cannot deal wttli
jroperly, but only with the laws of their action.
llllbriiiin is that condition of a body In which the forces
upon It balance or neutralize each other.
tlco is that part of Applied Mechanics which treats d^^^|
onsof equilibrium, and is divided Into:— ^^^|
^tics of rigid bodies. ^^H
ydrostatlcs. ^^1
diding we have to deal only with the former.
ictures are artlflcial constructions in which all the parts
ended to be in equllibrlnm and at rest, as in the case of a
r consist of (wo or more solid bodies, called pieces, wlileh
inected at portions of their surfaces called joints-
e are three conditions of equilibrium in a structure; vii.; —
be forces e\erti!d on the H'hole structure must iNilance each
These forces are: —
be weight of the st
iHoaait auTles.
fi nKFlNlTlONS lif TJiUMS
t. The supporLlnj! |>rtasuivs, iir reKlslMnc-i' of the faundi
\rd external forces.
[I. The torceia exeiiecl >m ««i-li piece must biUaure Mch 41
I, The weight of the pie<Mv
•>. The load It carries.
r. The reBislance of its joint*.
ULThdforfiM eiC£7ted on each of the parts IntowMeli H
»ui Ditty b(^ supposed to be ilnided uitist balnnce pacli otht^r.
Stability ouuhIbU iu the fulliluient of condiuone I. an
U Is, tlie ability of tlui Uru(.ture to resist dis^ilat-enient «C H
Struii)Etl> I'otuilttts in tlie tulfllnieiit of foiidilioii U(-tt4ii*'K
a ttbllity of a jilace to J«sl8l breaking
Stiffuess consists iu tlie ability of n piece to resist beniling.
i'he theory of Ntni<:titrt» is divided into two parts; vii. : -^ .
I. TliRt whii-l) treats of strength and stitfusss, deailng only, wllh
igle jiieia-s, and seueraily kiuiwit us Htrengtli of iuaterltti>> |
IL 'I'hat which IreaCs of aLabilJty, dualing with strut
StrCMS. — The load or systfrn of forues acting on a)i> pitwnf I
ilerlal in nftiin deiiot«(l by tlie tenu " xtrt^s,'' and the u'oi'd will |
■g used in tlie following pages.
The iiiteimitii of the ntfnn per square incli ou any iionual >i
ic of tt solid is Uie total sireaa dividvil by tlie area of tlt« «ectioo |
squari! ineliM, TbiiB. if we bad a bar ten feet long and l"" j
2tu» oqiuire, with a load of SOOU iwunds pulling in the (tiiecliou 1
Its length, the stress on any normal section of the rod would !•« 1
30 pounds; and tlie Intensity of the stress per square inch wovi^ \
«(KKI T 4, or 20011 pounds.
HtriUil. — When a solid body Is sulijecte<i to any kind of i1
alteration la produced in the volume and figure of the liwily. Hi**
is alteration is called the "strain." In the cose of tlie IimbIv*'^"
ove, the strain would lie Hie anionnt that Ibe Imt would str*!*"^ '
4er Its load.
The Ultimate Stvengrth, or Brcnkiitj; Load, of a ba*^ '
the ImmI ruqniriHl to produce frai^uiv in home specified way.
The Safe Loatl is the lond that a iilece can support witlM^~*
,|ittirin)i Itsstri'iit^ib.
Facton of Safet.V. — Wlien not oiberwise specified, a/oct-
mtf'fli/ means the rarlo In nllicli ilir lireaking looil exceeds U
fe load. In designing a [il<uv of niateilal U> sustain a o
W'. /( la reqiilnti that it shall lie \ierliH'.Hs "^'^ \hi4m b\\ <i
!'««,- ami hi'iiiv ft is necpjtsary to mat.- »n B.\\r<»
uuati'Hal, worktiiauBliip. e.l>\ \\,\mi\i\
TtSED IN MK<'II.\M<'S. ^^^
nuterials of diSerant composUion, ilirrerent fncton of sRf(«t7 will
be required. Thus, iron being more homogeneoun than wtxMl. and
l«si liable lit defects, it does not require bo great a faetor of safety.
Aad, again, different kinds of strains require difTerent fuclors of
safety. Thus, a long woodrai polumu or stmt roqulres a |Te*ter
fiwlor of safety tlian a wooden beam. As llie (acMirs thus vary
for dlffUent kl:idii of strains and rnaterials, we will give tliir proper
fkct^irs of safety for the different strains when connldertng tlie
resistance of the uiat«rial to those strains.
Dlfitinctioii between Dead and Live Ixiad. — Tlie
t«rm "dead load," as used In mechanics, means a ioad that is ap-
plied by imperceptible degrees, and that remains steady; s«r-h as
the nelght of the structure itself.
A "live load" is one that Is applied suddenly, or aeeompaniefl
with Yibrations; such as swift trains travelling over a r«ilw(iy-
bridge, or a force exerted in a moving machine.
It has been found by experience, that llie cIToel of n live load on'
a beam or oilier piece of material is twice as serere a» that of ai
dead loail of the same weight; lienee a piece of material designed
t« carry a live load should liave a factor of safety /wice an largd
as one designeil to cany a dead load.
The load produced by a crowd of people walking on a floor Is
naually considered U> proiluce an effect which la a, meitn between
that of a dead and live load, and a Factor of safety is adopted
accordingly.
The Modulus of Rupture is a constant quantity found In
the formulas for strength of iron beams, and is eighteen times the
value of the constant " A."
Modulus of Elasticity. — If we take a har of any etaslic
material, one inch square, and of any length, securetl at one end.
and to the other apply a force pulling In the (llrection of its length.
weshallflnd by careful nieasuremeut that the Imr has been stretched
or elongated l^ the action of the force.
Now, if we dtride the total elongation in inches by the original
lengtli of the bar In inches, we sball have the elongation of the bar
por nnit of length; ami, if we divide the pulling-foree per square
inob by this latter qoantity, we shall have what is known aa the
modulus of elasticity.
Hence we may define the modiihin qf el'inticity a» the pulling or
ctymprexmnsi /'»'<■'■ I"^' """ if "ccd'on dhideil by (he dotiffottoa
or comprejiMon per •mil •>( I'^ngtli.
Aa an examiile of the methotl of determining tlie modulus of~
tgarJty of any matfrial, we will lake the (oWowUv^-.
""'" ■■ - j^jatr of wrotijrlit-lron, two me^
128 nEFlNITlONS OF TERMS.
ten feet long, securely fastened at one end, and to the other
we upplr n puiliug-torce of 40,000 pounds. Tills force caiUM
bar to stretch, and by earcfiU measurement we find the elongatl
to be 0.0414 of an iiicb. Now, as the bar is ten feet, or 120 incli
long, if we ilivide 0.0414 by 120, we shall have the elongation at
bar per unit of length.
Performing thiit operation, we have as the result 0.00034 of
inch. Ah the bar is two inohes square, the ares
is four square inches, and hence the pulUng-force per square ii
is 10,000 pounds. Then, dividing 10,000 by 0.00034, we have as ■
modulus of elasticity of the bar 29,400,000 pounds.
This is the method genenUiy employed to determine the inodn
of elasticity of iron ties; but It can also be obtained froni i
deflection of beams, and it is in tlmt way that the values of i
modulus for most woods have i)een found.
Another definition of the modulus of elasticity, and which is
natural consequence of the one just given, is the number i
pounds that would be required to stretch or shorten a l>ar oae iiw
square by an amount equal to Its length, provided that the Uw<
perfect elasticity would hold good for so great a, range. The Dia
ulus of elasticity is generally denoted by E, and is used In >!
determination of the atiffnesa of beams.
Moment. — If we talce any solid tiody. and pivot it at any
point, and apply a force to the body, acting in tmy direeticit'
except in a line with the pivot, we shall produce rotation uf tit*
body, provided the force is sufficiently strong. This rotation id
produced by wliat is called the moment of the force; and Iks
moment of a force about any given point or pivot is the prodoc*
of the force Into the perpendicular distance from the pivot to the
line of action of the force, or, in common phrase, the product of
llie force into the arm mitk loAicA it acta.
The Centre of Gravity of a body is the point thmngh
whidi the resultant of the weight of the body always acts, no mtt-
ter in what position the body be. If- a body be suspended at It*
centre of gravity, and revolved in any direction, it will always Iw
in equilibrium.
(Forcentreof gravity of surCftcea, lines, and solids, see Chap. IT.)
J
FOUNDATIONS.
/ Kadi ai th«8e two great clfteaes iqaj be subdlTlded i
I '"vulona: —
1 "- Foundations In situations where wnler offers no iuijietliini
■ ^ the execution of tbe work.
■ A. Foandallona under water.
■ Itisspldon) tbat architects design tiuildingk whosi; T
W *rp under water; and, a* this division of the STilijet-t pn
f 'Iwply into the science of pngim^ring, we siiall not disf ubs It hers.
Foundations on Sand. — Before we cmi decide «liat kind
I of foiuidation it will be necesHary to bnild, wp must know tht! nature
I (if tlie subsoil. If not already Itnown, this is deterudneil. ordinarily,
b; digging a trench, or makings pit, close U> the site of the pi'opoaed
I works, to a depth suEFicient to allow the different strata to be «een.
' For important structures, the nature of the subsoil is often d*-
I temiined by boring witli the tools usually employed for this pni^
poae. When tbls method is employed, the different kinds aat,
thickness of the strata are itelemiined by examining tbe epeo^
mens brought up by the anger iLse<l in boring.
Fouitdatioiis of the First Clastt. — The foundations in-
clnded under this class may be divided into tno cases, accordinji to
the diSerenl kinds of soil on which the foundation is to be built: —
Cask I. — Foimdatiiiim on »oil e'imponeii nf matfrialt tphom
UaMlity In aot nfftcled bs luttvratwn with icater, and trhirh are
firm enough lo aa/iporl the aelyht of the itriiHurf.
Under this case belong, —
Fiiuniintimi» iin It'irlr. — To prepare a rock foundation for being
built upon, all that is generally required is to cut away the loose
and decayed portions of the rock, and to dress the rock tu a plane
mrface as nearly perpendicular to the <iirection of the pressure as
Is practicable; or, If the rock fomis an inclined plane, to mit a
series of plane surfaces, like those of ateiia, for the wall to rest on.
If there are any tissiu%s in the rock, they sl:oii1d be tilleil n 1th con-
eret« or rubble masonry. Concrete la betiw for tlils purpose as.
when once set. it is nearly InconipreBsible under any thing short of
I crusblng-force; so that It forma a liase alnunt as «o11d as the
Ttn-X itself, while the compression of the mortar joints of the
masonry is certain to cause some Irrexuiar settlement
If it is unavoidably nernasary that some parts of the foundation
shall start from a lower level than otheis, care slioul<l he taken to
lf«ep the iDortar joints as close as possible, or to execute the lo«or
portions of the work In cement, or some hard-setting mortar: othe-T-
wise the foundations will settle imequally, anii thus cMttw nuu-.K
Injury ta tlie aiiperstriietutv^ The load placeA on V\ie TticV AwnW
^ta^n cIhh' fxiivit <jii,--eighth of ilmt iii-ccKB»r^ I,
FOUNDATIONS. ^^H
feasor Ranklne gives tlie following examples of tlie actual
of the pressure per square foot od some existing rock
Average of onlinary cases, the rock being at least as stro
as the strongest red bricks
Pressures at the base of St. Rollox cbinmey (450 feet beli
the summit)
()n a layer of strong concrelfi or beton, 6 feet deep , . ,
Oil sandBtoiie below the bcton, eo soft that it crumbles in t
The last ejtample shows the pressure which li safely
practice by one of the weakest substances to which the
Tock can be applied.
, Jules Gaudard, C.E., states, that, on a roeky groi
Roquefavour aquwiuct exerta a pressure of 26.800 pound
-square foot. A hed of solid rock is unyielding, and nppeai
sight to offer all the advantages of a secure foundation. 1
erally found in practice, however, that, in large buildli^
the foundations wilt not rest on the rock, but on the adjac
and as the soil, of whatever material it may be composed, I
be compressed somewhat, irregular settlement will almost in
take place, and give much trouble. The only remedy In boi
o make the bed for tbe foundation resliiig on the soil a
possible, and lay the wall, to the level of l.lie rock, in ee
' lard-setting mortar.
Foundation tin Compact Stoni/ Earlhn, such (is Gravel *
— Strong gravel may he considered as one of the best soils
npon; as it is almost incompressible, is not atfected by eif
the atmosphere, and is easily levelled.
Sand is also almost inmnipressible, and forms an excellc
flation as long as it cm be kept from escaping; but as il
cohesion, and acts like a fluid when exposed to running ■
should Ik treated with great caution.
The foundation bed in soils of this kind is prepared by d
trench from foiu- to six feet deep, so tiiat tlie foundation
Started below the reach of the disintegrating effects of froel
The bottom of the trench is levelled; and. if parts of it are
to be at dllTercnt levels. It is broken into steps.
Care should be taken to kee^) the surface-water from mm
iJie trench; and, if necessary, drains ahould be made at Ou
to carry awtiy (lie ivater.
3^~f^ — '"bt resting on the bottoni o^ l\\e Menc\\ ftwso
e reslslancp of Ihi" ii\»l«r\sil IotoAwr tt«;^
Ht. Gaiulanl snyft that a load of 1U,5IH) to 18,:iOU pouiidB per '
Que fool has been jilit upou cloae aaud in l.lio fi>uili<at1ona or
arai Uriilge, and on gravel in the Lock Ken Viafliicl at Borileatui.
Ill the bridge at Nantes, tliere is a load of l!),2U0 pounds to tbe i
]iure foot on aand^ but some settlement has already taken place.
Rankine gives the greatest intensity of pressure on foundations
n Bnn earth at from Z500 to 3500 pounds iter square foot,
tn order to distribute the pressure arising from the weight of the
Rructure over a greater surface, it is usual (o give a<ldltional breadtli
k> tbe fouadalion I'uurses: this increase of ttreaiUli is called Uip
ipTMil. Ill ronipa^l, strong varlli, the tiprciKl Is iiiitde one and a
UF limes Ilie tliii^kness of tlic wall, aiid, in ordinary earth or sand,
twin tliftt tliitJuiess.
Case II. — Foiiiidationa on mU» firm iiioayh tii sii^'imrt lln'
wAjht q/' the atructare, hut inltoae atdtiiUty l» effected tiff water.
The principal soil under tlUs class, with wliich we have to do, is
In tills soil the bed is prepared by digging a trendi, ae in rooky
xhIi: Slid the fotuidation must be sure to start below the frost^line,
lor iiie effect of frost in clay soils is very great.
Tlie soli is also much affected by tbe aetion of water; and hence
lilt ground should be well drained before tie work is begun, and
6m trenehi:s so arraoge<l [Jiat the water shall not remain In Cheni.
ilml, in general, the less a soil of this kind is exposed to the tvir ami
"'■Stlier, aud tbe sooner it is protecleii from exposure, the belter for
'lie work. In biiiltUng on a clay bank, great caution should be used
''I secure thorough drainage, that the clay may not have a tendency
'*> slide (luring wet weatlier.
Tlie sate load tor stiff clay and marl is given by Mr. Gaudard at
rom 5500 to 1 1,000 pounds per square foot. L'nder the cylindrical
'Ipis of the Sz^iedin Bridge In Hungary, the soil, consisting of
lay intermixed with Hnc sand, bi'ars a loud of ]3,.^00 pounds to
lie square foot; but it was ilr.'incd inimiIIi li( In incireasc its sniv-
Jorting jiower hy ilrH'(Jig .soiiu- |iili- in iIj.' linr of the cylinder,
inilatso to protpi'l Ihe cylimln' i.\ -li -rnii- niii-iili-.
Mr. McAlpine. M. Inst. C.V... iii luiililiu^ j. Iii;.'h wall at Albany,
N'.V., Bucircedud In safely loading a wtI cliiy huil with two to
lliii sijuare foot, but with a settlement dei)piiding on tlic depth of
t'i« excavation. In order to prevent a great InBux of ualej
<'<HIKquent wflening of tlu; soil, he surrounded the exi-HTatton <
"ithapitddle treneli (h/i feel high and loiw !ee\,'w\Ae,MAV*»!wi J
/■ra*/ a iuyer of amraa gravel on ilie VjotHnu.
f'^^j^'" *"' ^''"■'/"'. — There are. Wirvevnn.'Lm*^*"
r'Ol'NlMTlONS,
Whkiiever material is employed, the bed Is first prepHreil by ea
vating n trench BuHJeientl; ileep to place tlie roimiiHtiua-couC
below the a<^tion ot frost and rain. Great cslitinn shuuld be a
iti eases of this ktml to prevent uneqiia] settling.
The bottom of the trench is made level, and eoyered witb »1
c.f stonea, wnd, or confrrete-
Stones. — When stonw is used, the bottom of the trench si
1w paved with rubble or eolible stones, well settled in pltee
ramming. On this paving, a betl of concrete is then laid.
Sand. — in all situations where the ground, although soft, is
Hufdeient consistency to confine the sand, tiiis material may be in
with many advantages as regards both the coat and the st>bllftj<
the work. The quality which sand possesses, of distributing t
pressure put upon It, In both a horizontal and vertical dtrectiA
iimkeH it especially valuable for a foundation bed in this kind
soil ; as the lateral pressure exerted against the sides of Die tonti
lion pit greatly relieves the Iwttom.
There are two methods of using sanil; viz.. in layers aiidaspll*
In fonuing a utratiim of sand, it is spread In layers of aliout nit
Inches in thickness, and each layer well rammed before the na
one Is spread. The total depth of sand used should be suffldetl
to admit of the pressure on the upper surface of llie sand bdid
distribntcd over the entire Imttom of the Irencli.
Sahd-plling is a very economical and efficient method of foni
a foundation under some circumstances. It would not, howc
be effective in very loose, wet soils: as tlie sand would work InW
the surrounding ground.
Sand-piling is executed by making holes in the soil, i
iHtllom of the trench, about six or seven iiiehra In diamet«r, ixS
about six feet deep, and lilting lliem with damp sand, well nnBWl
so as lo force it into every cavity.
In situations where the stability of piles arises from the pressure
of the ground around them, sand-plies are found of more servi"'
than timl>er ones, for the reason that the timber-pile tranimlB
pressure only in a vertical direction, while the sand-pile tranimlui'
over the whole surface of the hole it Rlls. tluis acting on a buS*
area of bearing-surface. The ground above the piles should M j
covered with planking, conorele, or masMiry, lo prevent its be(jjJ
forced up by llie lateral pressure exiTted by tlie piles: and. on Ufc^
stratum thus formed, the foundation walls may be l)«llt in the usmI '
. fottndHtions on Plica. — Where v\w soW w^"*^ ■«\;\i?i\*'
M|b to bulhi is not firm enougli lo s«\nni« t\w lQwmft».*:wi«.«
^gioioul fonmion metlioiK ot fnrm\Hg a '«>\\A ^u'^'^***'*^
^^^^r rot'MiATIOHSi.
ng wooden piles iiiEo the soil, and placing tlir [niiiidbtioii
pon these.
illea are generally muud, and li&ve n leogth of a1>oiit iweiily
heir mean diameter ot cross-aectioii. The lUameter of the
uicH from nine to eighteen Inches. The piles aiiould be
t grained, and free from knots and ring strokes. Fir, beach,
ul Floriila yelloW'pine are Ihe best woods for plied: though
aiid liemloek are very coinnioiily used.
Te piles are exposed to tide-water, they art.' generally itriveu
neir barli on. In other cases, it is not essential.
I which are driven through hard grouuil, generally requin^ to
n iron hoop fixed tightly on their heads to prevent them froni
ig, and also to be nlwl with ii'uti shoeij. either of I'ust or
5 piles may be divided into two classea, — those whieh trani-
e load to a Srra soil, thus acting as pillars; and tliose where
le and its load are wholly supported hy the friction of the
m the sides of the pile.
rder to ascertain tlio safe load which it will do to put upon
of the drat class, it is only necessary to calculate the safe
Pig-strength of the wood; but, for piles of the second and
■onuuon class, it is not so easy to itetemiine the maxitnuut
lllcli they will safely support.
y writers have endeavored to give rules for caleulsting the
if H given blow in sinking a pile; but Investigations of this
re of little practical value, because we can never lie in pos-
L of sufficient data to obtain even an approximate result.
leet of each blow on tlie pile will depend on the uioinentuin
blow, the velocity of the ram, the relative weights of tiie
id tlie pile, the elasticity of the pile-head, and the rcslstanca
I hy the ground timiugh which the plM is iiassing; and. ns
t-oami^d eoudttions cannot well be ascertained, any i^leula-
n which they are only assumed must of necessity \>i: mere
id Oil Piles. — Professor Rankiiie gives the ilnilts of the
ad on piles, basml uiion practical e^xainples. as follows: —
piles driven till they reach the tirin ground, IWH) pounds per
inch of area of hrad.
lilies standing in soft groiuid by friction. 2(NI iHiuiids per
incli of area of head.
as, in the latter case, so much depends upon the character of
/ lu which the piles are driven. Biic\v a ig,ea*«.\ TvA%»a'C>.'»i
• hardly to be recoiiitiientU-il.
tmiln for tin- iif:
cing-loiwl ow iiU** Xvft.Ne
Vi^t^dcdl
^■^^P FOUNDATIONS,
founded upon practical experience; and they nre probably the
Lliat we can rely upon, wltll our present knDwle<lge of the sUb}
Perhaps the rule most commonly glren is that of Major Sani
United-Statea Engineer. He experimented largely at Fort I
ware, and in 1351 gave the foUowlng rule aa reliable for ordii
pile-driving.
Sanders's Rule for determining the load for a <
wooden pile, driven until it sinks tlirougli only small and nei
equal distances under 8ueoe&3ivi> blows:—
hSafe load in lbs. =
relght of hammer in lbs. x fail in inche*
a X sinking at last blow
^■tKr. Jolm C. Trautwine, C,E., in his poeket-l>ook for
^^nea a rule which apt>ears to agree very well with actual result)
^Kiliis rule is expressed as follows;
le load in _
< 0.02!
tons of 2240 lbs. I..ast sinking In inches + 1
For the safe load he I'econimenda that one-half the extreme M
should be taken for piles thoroughly driven in tlmi soils, and Ml
fourth when driven in rlver-muit or raarali. '
According to Mr. Trautwine, the French engineers conaidet
pile safe for a toad of 25 tons when it refuses to sink under a hail
mer of 1344 pounds falling 4 feet.
The test of a pile having been anfficiently driven, accordizigl
the best authorities, Is that it shall not sink more tlinn one-SfthJ
an inch under thirty blows of a raui weighing 800 pounds, falHj
5 feet at each blow.
A more common rule Is to consider the pile fully driven wherf
does not sink more than one-fourth of an Incli at iIih last bit
ram weighing 2500 pounds, falling 30 feet. *"
in ordinary pile-driving for buildings, however, the piles oft*'
sink more than this at the last blow; but, as the piles aresddoK
loMled to their full capa<;ity. it is not necessary to be so particular •
in the fotmdattons of engineering Btnietim-s. A common prariM
with architects Is to specify the length of tlie jiiles to be used, aM
the piles are driven until their heads Bn; Just above ground, tM
then left to be levelled off afterwards. 4
Exantple of Pile Foundation.— As an example irf tH
iiiptlioii o( ilftemiluing the necessarj n«H\\wr (it ^Va \« f'^mM
t/fii-Mi litiili)ing. »'e will ileti!nTi\ne t^»' nmii^wt ol -(W** '"'^
FOUNDATIONS.
} shown in Fig. 1). The walls are of brick, and the wei|
•e* taken at 110 pounds per cnbic foot of masonry.
i piles are to be driven in two rows, two feet on centres; a
>und that a pile 20 feet long and 10 inches at the top will si
Fig. 1.
fncb under a liiOO-pound hammer f aWiwj; "iS^S \^eX. «A\«« >iJftfe
^n entirely driven into the soil. W\\al <\\s\«.\\ov- ^\w^
v- on rrnti^s Ienirth^^^isi' of the v.'h1\ ?
V6S FOUNDATIONS.
By calculation we find that the wall contains loT^ cubic feet
masonry per running foot, and hence welglis 17,906 pounds.
The load from the floors which comes upon the wall is: —
From the first floor 1500 lbs.
From the second floor 1380 lbs.
From the third floor 1380 lbs.
From tlie fourth floor . T90 lbs.
From the fifth floor T20 lbs.
From the sixth floor 720 lbs.
From the roof 240 lbs.
Total e7301bs.
Hence the total weight of the wall and its load per running foot
24,(m pounds.
The load which one of the piles will support is, by Sanders's ra
1200 X 240 _
— g ^ . — = 36000 pounds.
By Trautwine's rule, using a factor of safety of 2.5, the safe lo
would be
fi^ X 1200 X 0.02:J
— 25 X n + 1) ~ ^*"* ^^^ ^^^ ^^ pounds), or 33600 pouni
Then one pair of piles would support 72,000, or 67,200 poun
according to which rule we take.
Dividing these numbers by the weight of one foot of the w
and its load, we find, that, by Sanders's rule, one pair of piles v
support 3 feet of the wall, and, by Trautwine's rule, 2.8 feet of wt
hence the piles should be placed 2 feet 9 inches or 3 feet on centr
111 very heavy buildings, heavy timbers are sometimes bolted
the tops of the piles, and the foundation walls built on these.
In Boston, Mass., a large part of the city is built upon rm
land, and hence the buildings have to be supported by pile foun
tions. The Building Laws of the city require that all buildii
*• exceeding thirty-five feet in height (with pile foundation) si
liave not less than two rows of piles under all external and pa
walls, and the piles shall be spaced not over three feet on cent
in the direction of the length of the wall."
As an example of the load which ordinary piletf in the mj
land of Boston will support, it may be stated that the piles un
Trinity Church in Boston support two tons each, approximateh
For engineering works, various kinds of iron piles are used; '
iJiey are too rarely used for foundaUotva ot \>>i\\dLVc^g^ \a ^m^
within the Hi'oi>e of this cha\>tt'r. VTor a v\ttWYV0.\.\swi ol N
VOUNU Alius S,
resder should consult some standard work on engineering'
Tery gwid deacriplion of iron piles la ^ven in "Wheeler's CMki
Ingltieerlng," and also in " Trautwine's Handbook."
Concrete Foundation Beds.— Cuncreie u lately iutd<
lor foundation beds In soft soil, and is a vi^ry valuable nmlerial fiim
this purpose; as it affords a linn solid bed. and van Iw spread cnt'
I as to distribute thK pressure over a large area.
Concrete is an artitli;ial cumponud, generally nuule by nilxtiig-|
lime or foment wltii sHnd, water, and noine hard material, as brokeQ'
■tone, Blag, bits of brick, earthenware, liiunt day, shingle, etan
if tluire it any ctaoiee of tlie maLerials forming the base of Ibl
*'oncrete, the preference should be given to fragments of a aomA
What porous nature, such as purees of brick or limestone, rathej
than to those with smooth surfaces. i
The brofceD matertal itse^l in the concrete \a Koimttlines, for con
Tfnience, called the uijiirenate, and the mortar in which It Is incased
the matrix. The ag^gate Is generally broken so as to pu
tlirough a 1^ or ^ incli mesh. <
In damp ground or under water, hydraulic lime sliould of couMj
be used In mixing the concrete.
Laying: Concrete. — A very common practice in laying eon
cr«t« is lo tip the concrete, after mixing, from a height of six
eight feet Into the trench when; It la to be de|>osil«d. This pr
Es objected to by the best authorities, on the ground that
and light portions separate while falling, and that tlie
tlicrefore not imiform throughout ita mass.
The best method is to wheel the concrete In harrows, Imi
ately after mixing, to the place where it la to be laid, gently tip]
it into position, and carefully niinmiufi into layers about tweh
inches thick. After each iByer has lieen allowed lo a«t, it shouUt]
l>e swept Mean, wetted, and mii<le rough, by means of a pick, for tlril <
next layer. 1
Some contraclort make the concrete courses the exact width,
spectfled, keeping up the sides with hoards, if the trencii is tocu
wide. Tills ljt a baii practice; for when the sides of the foundlitj
tlon pits are carefully trimmed, and the concrete rammed up solliltf j
against them, the concrete is less liable to l>e cniaheil and brokesu
before it has entirely ronaolidatei). It iii therefore dealnible tItM_
the spectHcatlons for coiKrete work should rei|Uire that the wludel
extent of the exeavatlon be tilled, and that, If the trenches awj
excavated too wide, the extra amount of concrete he fumislied a^
the contractor^ exjieiiae. J
Concrete imile with hydi-aniic lime \9 soweVmwa AaA^WA-^
m
140 FOUNDATIONS.
The pressure allowed on a concrete bed should not exceed on^
tenth part of its resistance to crushing. Trautwine gives as the
average crushing-strength of concrete forty tons per square foot
Foundations in Compressible SoiL— The great diffi-
culty uiet with in forming a finu bed in compressible soils arises
from the nature of the soil, and its yielding in all directions under
pressure.
There are several methods which have been successfully em-
ployed in soils of this kind.
T. When the compressible material is of a moderate depth, tbe
excavation is made to extend to the firm soil beneath, and the
foundation put in, as in firm soils.
'J'he principal objection to this method is the expense^ which
would often be very great.
II. A second method is to drive piles through the soft soil into
the finn soil beneath. The piles are then cut ofif at a given level
and a timber platform laid upon the top of the piles, wiiich serves
as a support for the foundation, and also ties the tops of the piles
together.
III. A modification of the latter methoil is to use shorter piles,
which are only driven in the compressible soil. The platform is
made to extend over so large an ai-ea that the intensity of the press*
ure per square foot is within the safe limits for this particular
soil.
IV. Another mo<lification of the second method consists in
using piles of only five or six inches iu diameter, and only five or
six feet long, and placing them as near together as they can be
driven. A platfonn of timber is then placed on the piles, as in the
second method.
The object of the short piles is to compress the soil, and make it
firmer. '* This practice is one not to be recommended ; its effect
being usually to poun<l up the soil, and to bring it into a stato
which can best be described by comparing it to batter-pudding.'* ^
V. Still another method is to surround the site of the work with
sheet-piling (flat piles driven close together, so as to fonn a sheet),
to prevent the escaiw of the soil, which is then consolidated by
driving piles into it at shoit distances from each othen The piles
are then sawn oif level, and the ground excavated between them
for two or three feet, and filled up with concrete: the whole is then
planked over to receive the superstructure.
The great point to be attended to in building foundations in soils
of this kind is to rii'.s tribute the wi'\*T\\t o^ Uve sUwcture e<iually
' I)(>hK(Mi on Kov\m\;v\\tu\H.
fOUNUATIONS, 141
iver the foundation, which will then settle in a vertical direction,
tnd cause httle injury; whereas any irregular settlement would
Knd the work from top to bottom.
Platiking for Foundatloa Beds. ~ In erectii^ buildings
01 soft grotmd, where a large bearing-surfai«; is required, planlting
■ttj be resorted to with great advantage, provided the timber I'an
be kept from decay. If the ground is wet and the timber goiMl,
(here is little to fear in this respect; but in a dry situation, or om-
exposed to alternations of wet and dry, no dependence can lie
placed on unprepared timber. There are sererat methods em-
iloyed for the preservation of timber, such as kyanizing or crt-o-
loting; and the timber used for foundations should be treated by
me of these methods.
The advantage of timber is, that It will resist a great cross-strain
vith very trifling flexure; and therefore a wide footing may be oli-
ained without any excessive spreading of tlie bottom courses of
he masonry. The best method of employing planking under nails
8 to cut the stuff into short lengths, which sliould be placed
itroas the foundation, and tied longitudinally by planking laid to
be widtii of the bottom course of masonry in tlie direction of tlie
ength of the wall, and flrmly spiked to the lx>ttom planking.
Another good method of using planking is to lay down sleepers
in the ground, and (ill to their top with cement, and then place tlie
ilanking on tlie level surface thus formed. For the ei'oss-timbers,
Dur-inch by six-inch timber, laid flatwise, will answer in ordinary
Foundations for Clifmneys — As examples of the foun-
ations required for very high chimneys we quote the following
rom a treatise on fouii iations iu the latter part of « work on
' Foundations and Foundation Walls by Geoige 1 Powell.
Fig: Smpreaenta the lase of a chimney erecU-A hv VSft Ins 'Ont
•fcago ReSniiig f ompany 151 feet high and liSpi^ w\w>.ie».fOw
142
HIUNDATIONS,
foot, Tlie base, iiiurcly two ruui-!H'» of hettvy (limeiulon stone, m
shown, is bedded upon the Burfat^e^nivel lieu the nioath of tba
river, there recently deposited by the lake. The mortar empjofed
in the joint between the stone is rooHng-gnvel Id cement. Tha
Area of the base is 256 square feet, the weight of chlinney, incloslve
of base, t)25 tons, giving a pressure of ^ pounds to the sqiure
ineh. This fouDdatlon proved to bt iwrfeot.
Fig. 3 represents the base of a eliinincy erected in 1873 fortlie
McComiicli Heaper Works, C'liii.'aeo. whith is lao feet high, 14 feH
square at the foot, with a rounil ftiu' of tt feet 8 inches diameter.
Fi 3
The base poiers (12.1 s<|iiare feet tlie ^el^,llt of tike chinuw^and
base is approximate]) I KNI tons Ili< i ressure upon the grOQsd
(dry hard clay) is therefori m poun Is to the square Inch. Thi>
foundation also proied to bv perfect iii eiiry respect.
TABLK
aiioiriny the perminHlUe lonil* iiiioii rnrimm kiiidt <if foundation
hcila, /)(T •iquare foot.
Roek foundations . . . 4000 to 40,000 Ills., average, SO.OOO lbs.
Coarse gravel and sand 2-500 to 3500 lbs.
Clay 4000 lb*.
CoucrpW 8000 lbs.
Piles In artin<'iaUciil, tor eaeli pil<' 4000 lbs.
Piles 111 flrni soil, (or '^h pile ^,000 to 140,000 lbs.
^m CHAPTER III.
J MASOITRY' WALLS.
Footing CoDrses. — In cMrmnencing ilm foundation i
of a building, It is ctistoinary to apreiid the bottom courses of the '
nuuonry ronsiderabl; beyond the face of the vihH, whatever b« tlie
cbuBCt«r of the fonndation bed, unless, pei'hnps, it be a solid rock
lied, in which case the spreading of the walla would be useless.
Tbese spread courses are technically known m '' footing courses."
They answer two important purposes: —
1st, By distributing the weight of the structure over a larger
xrea of bearing^urface, the liability to vertical sKttlemeut from
the compression of the ground is greatly diminished.
2d, By increasing the area of the base of tlie wsll, tliey aitil to
its stability, and form a protection against the danjter of the work
being thrown out of "plumb" by any forces tlial may act against
it.
Footings, to have any useful effett, must I* securely bonded into
the body of the work, anil liave suHicient strength to resist the
violent cross-strains to which they are exposed.
Footings of Stoue Poiiiidatioiis. — As. the luwi'r any
titone is placed in a huildiug, the greater the weight it has to sup-
port and the risk arising fitim any defects in the laying and dress-
ing of the stone, the footing courses should be of strong stone
laid on fted, with the upper and lower faces liriasefi true. By laying ■
on fted Is meant laying the stone the same way that it lay liefoni >
quarrying.
In laying the fooling courses, no bark joints should be alloweil
beyond the face of the upper work, except where the footings are
in double courses; and eveiy stone should honil into the body of
the work several inches at least. Unless this is atl«nrle<l to, the 1
footings will not receive the weight of the superstnictiuy, and will ^
be useless, as Is shown in Pig. 1.
In proportion to the weight of the sui>erslnicture. the projection
of each footing course beyond the one above it must Iw reduced, or
the cros.'^strain thrown on the projecting portloti of tlic masonry i
wWiepJ it from top to bottom, as shown 'm F\^ 1.
' ' work. sw\i a* Wii- »\*oV
MASONRY WjSI
brldgps and the Hke, the proportionate increase of bo
obtained by the foolinga is very slight, and there u ge
risk of tlie latter beiug broken off by t^^»
13
1 —
1 -_
N
-
5.-^
of the WDi'k, as in Fig. 2.
give rery tittle projection
the work with a battering-face,
Fia- 2.
therefore usual in tl
the footing ci
V
Fig. 3.
Footings of undresseil rubble built I:
never be used for buil<l}iigs of any importance, as the
of the mortnr is sure to eause movemeuts in the su;
If rubble must be uaeil, it should be laid with cemei
that the whole wil! form a solid mass; in which case
shape of the stoue are of little consequence.
In general, footing atones should be at least two by I
the bottom, and eight inches tliick.
The Building Laws of the city of New York reqi
footJD^ ujider all foundation walls, und under all |^i(
posts, or plllitra resting on the earth, bVibH \>e ut aW««
Unxlern ft) mutation wall tlie !oot\nBiv"wt\>e«'^\wM*
Ifie Iwtlom wiatli of l\ie waW, anfl ra^tej
MASONRY WALLS,
145
or pillars, at least twelve inches wider on all sides than the
a width of the piers, columns, posts, or pillars, and not less
dghteen inches in thickness; and, if built of stone, the stonos
not be less than two by three feet, and at least eight inohos
base-stones shall be well bedded, and laid edge to edge; and,
' walls are built of isolated piers, then there must be invortod
s, at least twelve inches thick, turned under and between the
or two footing courses of large stone, at least ten inches
in each course.
e Boston Building Laws require tiiat the bottom course for all
lation walls resting upon the ground shall be at least twelv(>
» wider than the thickness given for the foundation walls.
)otingrs of Brick Foundations. — In building with
:, the special point to be attended to in the footing cours(!s i»
i BRICK
.■«w'*v — =1
i^£
^ ^y.
'^>. "■=^.
ti BRICK
<<^
fyCyy^ .
^=5=-^ ^^yZ^y^. ^
•^1 ,-=^
U,l
/V> —:=-
"^v
Fig. 4. Fig. 5.
eep the back joints as far as possible from the face of the
:; and, in ordinary cases, the best plan is to lay the footings in
2 BRICKS
"^yy.m
'nil"" =
^^//y^
'V//
Wf
v/m.^^
m
\\\\
El
yjl////'^ I //////,; ^'■-
''///«
Fig. 6.
courses; the outside of the work being \sv\eL a.\V \i«w^x^, wnja.
w projecting more than one-f ourUi brvc^L \>eioTA \Xi& ^^u
. except in tlie ease of an eiglit-incYi >wa\\.
MASONRY WALIS.
brick t
f
Rg-T.
The bricks used for footings slionlil be. tlii^ liai'dest and S
that caj) be obtained. Tlie botloiii I'ourse sliould in all ntaeu be
double one.
Too much care cannot be Watowcd upon thi' fooling coursGi (
any liullding, us upon them depends tiuicIi of the stability of tl
work. If the bottom (;oiir»e.i 1)^ not solidly Ixnlded. if an; n
or vacuities an: left In the Ik'cIh of the masonry, or if the n
themselves be unaound, or badly put together, tlie effects of tat
carelessness are arire to ihow lljeiiiselves sooner or laMr, an
almost always at a period when remedial efforts are useless.
Inverted Arches. — in struetures where the weight of d
superstructure is sustained by a number of piers, It Is often adnu
tageous lo rounect the base of the piers by means of invcrU
artthes; as they serve to distribute the weight of the slnu-im
evenly over the foimdatlon tieil.
The form of the arch is eonunonly that of a si']|u-4-llip9<>
approach In^' to it.
The arcliPs. If of brick, should be at leiwtt twelve inches think.
Tn using Inverted arches, rare shonld lie taken that the outflf
arches have sufficient abutments, otherwise the thrust of the ai
may push the wall against which it nbnls out of a perpendiculir. ,
Founillltioii WhIIh. — Foundation walls should start belo*
the reach of frost, and should be carefully bonded together, U
made as solid and compact as possible.
The bottom courses are often laid dry. and the remainder U
cement mortar. It made of stone, tliej should not be lesa tlU
tfenCy Inches thick, and. It o< hrick, n.-v.>T\eBs (.Viaa^wA-jt'--*-^*
^ tb/ckneas. fn orclinnry (onndaHons U \ft om\^ \w«w
ing^ a wati am Bhall not l» cr\w\if^ \j^ ^^w ■«fe\*«. <*
q)cr9tmctnre. the working-atrength of the /oundtttlon witll <-hti
wily be determine"! by multlplyiiifc the area of ilB upper 8ur(»fB
t Mjuare feel by six tons for brick-work, two and & half tons for
Bmmon nibble, and, for good couruKl mbble, by one-fifteenth of
hs cmshJDg-strength of tli« itoue It is built wllb.
)^r wouden btiltdingti. lui eighteen or l.uuiity in<'li J'iil>l>l(' Hull,
IT twelvMnrb brirk wall, is generally used.
In aoilx of sand, gravel, or loam, the wall is generally liuill nith
bath Bides lertieal : is clay soils either tlit Inside or initsidi' of the
tall Is generally batterm],
In such a case It would, of coiirae, be beti«r to batter Lhe wall on
Hw biside. if the room is of no valae.
For brick and stone buildings, the foundation wallx are. generally |l
iho0i eight to twelve inches thicker than tlie wall next above them.
In New-York City the laws require that all foundations shall be ||
iMlt of stone or brick, laid in ceinent mortar. ,,
' Stune tounilations shall be at least eight inches thicker than thf) [
PMll next above theiu, to a deptli o( sixteen feet below the curb f
llttel, and shall be [ncrcAsed (our indim In thlcknens for every li
[rtlltlonal five feet in depth below the salil sixteen fet^t. Founila-
tkiiu of brick shall be at leant four Inches thicker than the wall
Iwn Khove them, to a depth of sixteen feet below the curb level, I'
Wil iliall be increased four Inches In thickness for every additional |
[■re feet in depth below the said siileen feet. i
I the Boston Bnllding Laws make the following requireinents in
ngkrd to foundations : —
De'H(ii(A-//'"'WJ*. — Uwellings not exiweding thirty-fiTe feet in
V^: tbe foundation walls, laid with block stone with horlKontal
"Nines, or with brick la cement, shall not be less than sixteen
fches thick. Walls excaseding thirty-five feat, and not exceeding
Iftj-Sve feel; foundation walls, if of block stone, not less tlian ]
■igbteen inches thick, and, if of brick, not less Ihan sixteen incliaa
Uiick, and laid in ceinent. I
Walls exceedii^ fifty-five feet In height: founihitlon walls, laid
"Itb block stone or winent. not less than twenty inchas thick. I
Foundation walls lal<l with Irregular i-ubble-work shall be one- {
Ditrtb greater in thicluiess than that reiiiiired for block stone walls, i
BviMings <ith«r Uian DinfUhifi'IIoiiiiPH. — Walla not exceeding
hlity-five feet in height: foundation walls shall be of block stone, i
a liorlKontal courses, not less than twenty-four inches thick. |
Walla exceeding Ihlrty-Hve feet in height: foundation walls of ]
lock stone, oal leaa tlmn (wenty-eight inches iMcV. i
roumbulon walls of (HilldJngs Other than .\we\\mft-\va\«Ki, koM
V^gdlng Mrty-Uve feet in height, \n Uve Mt^j o^ T
148 MASONKY W\LI;S.
b« liuilt of ItTTftular rubhie-stone, one-fourtb Lhleker tl
stonr; walla, proDliJi'd, that, when a\mh foundation walla m
piliig, tbe lower (?o'jrse shall be of block stone.
Brick aod St<»ne Walls.— Very little is known
tbe Btitbllity of walls of biii 111 Ilia's, beyond what haa beeo g,
precliual experii'ticii. Tbe only strain which comes upon any In
xaatai section of such a wall, which eaii lie estltnut«il, is tlie din
u'el){lit of tlie wall above, and the pressure due to the Soora and ro
But [t l9 generally found necessary to make the wall thicker ti
the considerations of the crushing-strength alone would require. .
With the same ainoimt of material, a hollow wall is more sta
than a solid one, and it also possesses many other advanta)i;es a
solid walls. The atrengtii of a brfck wall depends vtry much uf
the bond. In this country it la a general rule among imuona
use as few headers, or bond brick, as tbey can possibly get ah
kvitb. The common custom is to make every ninth or tenth cou
of headers, and build Iho remainder of the wall of stretdH
firick bearing-walls of buildings should never be less than m
inches thick below tbe top Hoor, and atone walls not leas than I
teen Inchea.
The thickness of the walls required by the laws of the cltjw )
New York and Boston are shown by the tables on pp. 14i), ISO.
The height of the wails is in all cases measured from the ouri
The New- York Law further reads : " It is imderslood that til
amount of materials specified may be used either In piers Drba
tresses, provided the outside walls between tbe samn sliall in D
lase be less than twelve Ini'bea in tbicknesB to the height of fM
feet, and. If over tliat height, then slxte(>n Inches thirk; but inn
rase shall a party-wall between the piers or buttresses of a bulldini
be less than sixteen Inches In thickness.
" In all bniidings over twenty-Gve feet In width, and nc
either brick [lartitloii walla or ginlera supported by eolui
ning from front to rear, the wall shall be increased an addltiuntl T
four inches In thickness, to tbe same relative thickness in h
as required by the table given, for every additional ten feet i> I
width of said building, or any portion thereof.
" In all buildings hereafter erected, situated on the street-comK'i I
the bearing-wall thereof (that Is, the wall on the street upon which I
the beams rest) sliall l>e four Inches thicker in all cases than ^ I
otherwise pro\'iAei!l for by tliis Act. All walls other than beari»?- fr
nails niHy be four inchea less \li iWckneas ttia.'tv i«\m\iiA \Tl >1«
TOWs/ons of this Aet (and lUe tab\el,v«>''\^«*^'*'*i*'*^,''*^***'***.
'Blrelnebea In thickness."
"I
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MASONRY WALLS.
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M.^s(l^Ry walij*.
In addition to the requlivmentB lndlrat«d in the Ubie, the F
n BuUding Laws make the following: "VniiltP'l pnrtihur
M used, i&atead o( sulitl walU. Thuy slutll h« built itt lom
» thick from the foundation wolb to lUe under side of t
lot-boarding. !Said walls flinll be coiutructed ot two «
if equal tiiiekiiess, with an air-space iKtweeii ilieni of four Inr.hes
■knd tiMi together perpendioulurly with continuous widtlis of h
■ tiumHl hrick of good quiillty, wldch shall be nut more thmi t
Vifi«t Bparl. The air-space shall be smoothly pinslc-i'ed.
'Every building hereaftererected, more thmi thirty feet in v
, I'butrlies, theatres, rallroad'Statiou buildings, and other pult-
Inikllngs, shall have one or nion^ brick or stone partition walla,
big from front U> rear, and carried up lo a height not less thaa
■top of the second-story lloor-joista. Said wall or walls may bf i
IT inches less in thickness than is called for by the tables. TIteM
i >iJla shall be so located, that the spaci^ between any two of the tioori
I bHtliig-walls of the building shall not be over twenty-live feet. 1
"Exterior walls faced with stone shall have a backing of not*
a than eight inches of tmrd brick-work, laid in mortari bnt In
DO case 9)iall the thickness of stone and backing, taken together,
I lie less than the thiekness rer^uired for a brlrk wall of the saow
I lidglit. :
"In every brick wall, every ninth course of l)ric'k Hhall be k-
I heading course, except in walls built with sonie Iwnd, In which wj
IS every ninth course l!i a heading course; and except whers
ire faced with face-brick, in which case every ninth courw
alull be bonded with Flemish header, or by cutting the course of tlw
Ixn-brick, and putting in diagonal headers iKhInd the same, or \ij
iplittlng face-iirick in half, and backing tlie surue by a continuons
I row of headers.
" .411 iieailing courses shall be of good, hard, perfect brick."
COMPOSITION OF FORCES, ETC.
CHAPTER IV.
d
Lbt ub fmaglim a round ball platpd on a |.lane aiirfaoe at A (H
1), the surfaw. being perfectly level, so that tlie lall will havol
tendenpy to move imtil some force ia imparted to It. If, now, 'i
Impart a force, P, to the ball in the direction Indicated by tj
arrow, the bat) will move off in the same direction. IT, imUid I
Imparting only one force, we Impart two forces, P and Py. tall
E □ iKill, it will not move In the dirwtion I
fiither of the forces, but will move off t
the direction of the resultant of Ihei
fon'Bs, or in the direction Ah In the fignnt
If tlie magnitude of the forces PandJ*
1b indicated by the length of the arrov^'
^/^X then, if we complete the jMiralli
' / ^ ^BCI>,thediagomilD^ will represenlilifi
\i \ direction and magnitude of a force whii'li
Fig. I. will have the same effect oti the ball M 111"
two forces P| and P. Tf, in addition to the two forces Pj and ?>
we now apply a third fonr. P„ thr liall will move In the dliwti*
of the resultant of all three forces, which can be obtained by mhH-
pleting the parallelf^ram A DEF, formed by the resultant DA »ni
the third force P,. The diagonal J} of thlBBeronf
paralleh^rram will he the resultant of alt thrw ol
tlie forces, and the ball will njovc in the direecion
Af. In the same way we could tind the resalUit.
of any number of forces.
Again ; suppose we have a bail suspended In i^
air, whose weight is indicated by the line W (Fisi
2). Now, we do not wish to suspend this ball byl
vertical line above it, but by two inclined HnesH
forces, P and P ,. What shall be the
of these two forces to keep the ball suspended in just this podtionl
We have here jaat the opposite of omt \iffX. c&se', and, instead oCi
Undlng the diagonal of the resultant, wi' liave the AVaeirai, ■«>iiM
/« t/tp fine ir. and wish to find tlie sidts ot V\\s \ni.rsine\oBr«Mi.
^^^^aiflontt P and P,, and froiu H ilrn-A \\w» VMsStaA «i '
Fig. 2.
Fi|. 3.
eOMPONlTlON OF I'OR'-B
3 'tmiplele ttie parallelogruin. Then will CA Iw ll
nagniiiiile for P, and t'B tor P,.
Tliiu we see how one force can lie mailr (o havi* Ihi- .
Ui iiuvny. or many can be made to do tlie woi'k of one. Braritig
Die above In njiliid, we are now prepared to ntudy the following
propositions : —
L A force majf be repregmted lig n utralffht. Une.
In considering the action of forc(«, either In relation ti
jtnres or by themselves, It is very convenient to represent the force |
Lfnplllcally, whlcli can eoail^ be (lone \\y a straight line having an
tKTOw-hwuJ, as in Fig. 3. Ttie length of the
Hjit. If drawn to n ficale of pounds, shows
llw value of the force In pounds; the itiree-
: Vvn of the line indicates the direction of the
: foree; the arrow-head shows which waj it
, wis; and the point A denotes the point of
»I>pliiiition. Thus we bavf the ([irecllon, magnitude, and ywiiit
ol ipplicatioti of the force represented, which is all that we need
Parallelogram of Forces. — II. V lux/ force* nppUviI nt
Slit point, anil aciin.;/ In the same planf, be TppTmented hy tao
tniljikt liifK iftcifiieii til each other, thfir remillnnl. fill he equal
h Ihf diayoaal (ff Ihf parallelo</rain formeil on Ihfni- /m<-«.
Tlina, if the lines AB and AC (V\g. 4) represent two forces act-
ing on one point, .4, and in the same plane,
tlwn, to ohiain the forci; which would have the
*ame *lfwt oa the two forces, we complete the
E»rrilelo;?ratii AISIJt,\ and draw the diagonal
'il). This line will then represent the result-
»iit of the two forces.
When the two given forces are at right angles
♦HinlUint Will, by geometry, be equal to the nqai
it the sqnares of the other two forces.
•nie Triangle of Forces.— IK. ^
line forcex actiny oti ii point he reprt-
•fited III mafinifvilr iinil iliri-i-linii h>j llie
*(te» ((/" a Irlani/lp taken In orili-r, Ihe-y
till keep the ptAvt In pi/^irllbrlnni.
Thus let P, Q. and n (b'ig. h) rel,r.^.-|.nl
tliiw forces acting on the point O. Now,
if H* can draw a triaogli: like that sliown
" e/ie light of Fig. S, whoti- sides »hal\ ^^i-
^e^velfparklM to ihe for.-os, auri s\,aA\
.tluT
ivs v\i
158
f'KNTRKS OF (JRAVITY.
and triangles, and, the (r«*ntn« of i^i-avity of each being found, tbe
(«ntre of gravity of the whole may lie detenuined by treatiiig thb
centres of gravity of the separate parts as particles whose weij^
are proportional to the areas of the parts they represent.
Triangle, — To And the centre of gravity of a triangle, draw a
line from each of two angles to the middle of the side opposite: the
intersection of the two lines will give the centre of gravity.
QuadrilaleraL — To iind the centre of gravity of any quadrilat-
eral, draw diagonals, and. from the end of each farthest from their
intersection, lay off, towanl the intersection, its shorter segiiit*nt:
the two points thus fonmnl with the point of intersection will fonn
a triangle whose centre of gravity is tliat of the quadrilatenl.
Thus, let Fig. 11 be a quadrilateral
whose (rentre of gravity is sought
Draw the diagonals A I) and BC, and
from .1 lay off AF= ED, and from
n lay ofif BII = EC, From E draw
P a line to the middle of FH, and from
F9. line to the middle of EU, The
l)oint of intei'section of these two lin^s
is the centre of gravity of the quadri-
lateral. This is a method commonly
used for finding the centre of gravity of the voussoirs of an arch.
Table of O'hirvH of Gniriiy. — Let u denote a line
drawn from the vertex of a figure to the middle point of
the base, and 1) the dist^ncn* from the vertex to the cen-
tre of gravity. Then
In an isosceles triangle 1)= \a
chord^
in a segment of a circle 7> = io x area
In a sector of a cinile, the ver- 1 d — j> x ^ ^ clionj
tex being at the crentre S '* ^ *^
In a semicircle, vertex l)eing at ( 7> = 0 42^)H
the centre i
In a quadrant of a circle /> = j|ii
In a S4»mi-<4lipse, vertex \H*\\i<i [ /> = 0 426fl
at the centre i
In a parabola, vertex at intersection of ( D = hi
axis with curve) ^
In a cone or pyramid I> = i«
In a frustum of a cone or pyramid, let h = height of complete
cone or pyramid. //' = hejght of frustum, and the vertex be at apex
of ('ompJet4' cone or pyramid; then 1)= ^j^^ __ l^»7\
Sector.
FIg.S
VL If i\v.y itMmher qf parallel /oreM ttr.t wi a hoAy la opjHMfMJ
dirpelttiiM, than.fiir the body to he in fiiitUbrluin, the man nf the
uiunients teadinQ to turn the hoilg In ime itlrettioa muni (^uo)
tliF mm <if thf momeatA lunding to Jnm thf fiuilu !n thr ojiimiili-
tHreetion about mij/ i/lven point.
Thus let Fig. i< represent tbree parallt^l
forces acting (HI a iiirt All. Then, for the
Ml lo be In fMiiiililirliiiM, the aum o( thf *- ]
lurew F, uHil F.I niu«t l>e equal tii F,. \
Also. If we lake lUe t^iiil of thi- roil. .1.
lur iiiu- axis, tbeii must tlie niuuienl of F,
Iff equal to tile siun uf the moments i>f
. t\ Mill F, alwut thnt t>o1nt, tieeaiise the
UNUwnt of F| lends to turn tbe roil ilowii
Wmjbe HgliL. and tLe nioiueuts uf F, and F, lenil lo turn the nxl
^Bo the Wt, and tiii-iv should bi: no mure t^ndenry to turn tlie
H^eue way tban Uie other. For example, let the forces F,, Ft,
^Cb be represented by 5, iind let the distance Aii be repreeenteil
1i)'2,and the distance .^c by 4. The force F| must eqiiAl the sinii
of the forces F, and F,, or 10; and its moment must equal the
■Uta of the momeuta of Fj and F,. If we take the moments aroniid
.1, llwn tlie moment of F, = .'i x 2 = 10. and of F< = i x 4 = iS).
Tb»lr aum equals 30: hence the moment of F, nmst be .10. Divid-
ing tlie moment .■» by the force 10, we have for tlie ann 3; or
tbe force F, must act at a illslaiice 3 from A to keep the rod in
rqallfbriom.
I If we tJK)k om- nmmenta orounil 'i, tlien the force F, would have
ngtnomttnl, not Imvlng any arm, and so the moment of F, about
i niut eitual the moment of F, aliout tbe wnie point ; or, as in this
i^uethe foreea an' equal, they must both In- applied at the same
illnam'e from li, Hhriwing that >• must be lialfway between ti and e,
M was piwved before.
The Prliici|i]e of tlie Lever.—
'Iliis prinriple is IbisciI upon the two pie-
'wling propositions, and is of great im-
portance and convtmlence.
VII. //■ thrf-c piiTnIM firrcm nettny in
imt plare halanev fiiifk other, then each "j
farce mwit he proportional (u (Ae distance
Utween the other two.
Tlius, If w iMvo a rml AB (Flga, 9a,
Bb, Mild He), with tlinv fones, P,, P,,
JV.tMffgonit.ibM thB rodsliall l«ba\anw.i.\. ■«em»*-^>»'"**d
FIb.Si
^^^^^^ (COMPOSITION 01' FOKCE.S.
following relation bptw«!n tlie fon^s and t.lipir points of api
-~ ' " Zi . .^. . A .
L CJJ ■ AU • vie
P^ P, : P, ; Pa :: BC : AB : AC.
This Is tlie e^e of tlie conmion lever, and gives the nieal
de1«Fmin[ng Iww much a ei^«" lever will raise.
I
I'lli: ]ii'oportLoii 1h also triuj fnr any airan^iiient
{as shown in Figs, a, h, anil c), provided, of course, tlm forces .
lettered in the onier sUown In the figuras.
BxAHPi.K. — Let the dislance AC huB implies, and the dliUl
C7i be 12 implies. If a weight of -lOn pounds is applied at the po
B, bow much will it raise at tli« other fnil. and what support 1
be required at C (Fig. fibl?
Ann. Applying the rule just aiven. we liave the proportion; —
: (/',)::
T 12.
Hence P, = liHMI pouiuis; or 50U pounds applied at B frill lift 10
RUspPndnl at A. The supporting force at ('must, hy propoBitt<l
v., be equal to the sum of the forces F, anil P„ or
<u this case.
Centre of Gravity. — The lines of action of Uie foMI
gravity convei^ towards tile (mntre <if the earlii; but the dial
of the centre of the eartli from the bodies which we have »
to consider, compami witli the size of those bodies, is so great, tt
we may consider the lines of action of the forces as parallel. 1
ni'unber of the forces of gravity acting upon a iMxly niay be conri
<vr^ as iv/iial to (Jie ntiini>er of particVes coro^oalug the body.
/»f rm/rp qf iji-iitiUj of a body -awi fee Acftwi aa X.\w v>«S
ihrmtfih vbidi the resultant of the paraWel lorcea cA gc*N\Vi,»iAii
u/K'ii IhpiMtily. passes in everv jiosiHim o? VW AxwX-j. , ^^^^
BBTAININQ WALLS. 161
CHAPTER V.
RETAINING WALLS.
JL Betainingr Wall is a wall for sustaining a pressure of
earth, sand, or other filling or backing deposited behind it after it
Is built, in distinction to a breat or face wall, which is a similar
Btmctore for preventing the fall of earth which is in its undis-
turbed natural position, but in which a vertical or inclined face
bas been excavated.
Fig. 1 gives an illustration of the two kinds of wall.
Retaining Walls. — A great deal has been written upon the
theory of retaining walls, and many theories have been given for
computing the thrust which a bank of earth exerts against a re-
taining wall, and for determining the form of wall which affords
the greatest resistance with the least amount of material.
' There are so many conditions, however, upon which the thrust
exerted by the backing depends, — such as the cohesion of the
earth, the dryness of the material, the mode of backinfi: up tlie
' Wall, etc., — that in practice it is impossible to deterinine tlie exact
thrust which will be exerted against a wall of a i^iveii height.
It is therefore necessary, in designing retaining walls, to be guided
^y experience rather than by theory. As the theory of retainiuij;
'Walls is so vague and unsatisfactory, we sliall not offer any in tliis
Article, but rather give such rules and cautious as have been estab-
• llshed by practice and experience.
In designing a retaining wall there are two tUiugs to b^ Q,ovvs.vi
^redf—the betaking and the wall.
T^e tendency qf the Ocwkiiiy to alq) is very \\u\c\\ \q?.s nnAww WNs
Utt.j * *■
1«2
hbtainino wai.ia.
in a [Iry kIbIc lliaii when It Is filled with waler, iind hence era;
pi'i'i'iitition .--hoiiliJ be taken to accure gooil drainage. Besides id
face drainage, there should be openings left In the wall for Aa
water which may accuninlate behind it to escape aod mo off.
Tilt niawifr in wliich tlie material ia filled against the wall alia
atfeets the stability of the backings. If the ground be made ln^[ii-
lar, as in Fig. 1, and the earth well rammed in layers Incllned,frMt
the wall, thu pressure will be very trifling, provided that atlentlnn
be paid to drainage. It, on the other hand, the earth be tipped, it
the usual manner, in layers sloping toicartU the wall, the full pies>-
ure of the earth will be e^ierted against il, and it oiust be made of
corresponding sti'ength.
Fig.4
FTs-a
Tho Willi. — Itetaiiiinj; walla are generally buill with a batter
ing (sloping) faee, as tlils l.t tlin ^ti'ongest wall for a given amanDt
of mal^^rial; and, if the coureea are inclined tow*ards the back, tlM
tendency t« slide on e&ch oClier will be overconii
'y dt depeuil upon the adhesion of the iv
Fia-s
Fig.S
The importance of making llie resifsLBriif independent of ti»
iufhesion of the morUr In obvlou9\^ v<'i-\ nii^U as it woMid oUW
wise he necessary In ilclay Imckmg np » "«»\\ \ra'\\ rt» wio*:
lliorousbly sc(, whkli might r<t\WTe wv'^vX imwAV*.
WKTAININO WAIJJ*.
l«:i
tack of the Wall sliould be left Uougli. — lu
c it would be well to let evury third or fourtii tuiinw
a inch or two. This Increases tlie Motion of the earth
le back, and thus causes tlie resultant of tlitt forces ftctliig
le wall to become more nearly vertirul, and to fall fartlii-i'
le base, giving increased stability. It hIbo cimduces lii
not to make each c^uurse of unifonii iieiglit tlniiiigliout llic
I of the wall, but to have soiiLi> of tlu> dIouch, i?H]HH'inlly ni-ar
, siilHciently bigli toreaclnip tliruu):li 1w»or lliiiv I'ounies.
ueaos the wliole masonry becoints uiori^ elfi'i-tiuilly inter-
' bonded togetlier as one mass, anil less liable lo bnlgit.
deep freezing occurs, the back of the wall slioiild be sloped
for three or four ftet below its top,asat 0(,'(FiK, 2), which
•e quit* smooth, so as to lessen tlie hold of the frost, and
displacement.
'., 4, 5, and C show the relative sectional arenas of walls of
shapes that would be required to resist the pressure of a
earth twelve feet high {"Art of Building," E. Dol>so)i,
The lirst three examples are calculated to resist the luaxi-
rust of wet earth, while the last shows the modified form
idopted In practice.
8 for the Tliickness of the Wall.— As has been
he only practical rules for retaining walls which we have
Irical rules based upon experience and practice.
ohn C. Trautwine, C.K., who is considered authority on
ing subjects, gives the following table in his " t'oi^kel-Book
neers," for the thickness at the base of vertical retaining
th a sand-backiug deposited In llie usual uianner.
if Uiv waW-. wVwVW
104
UETAININO WAVLS.
Ib assumed to be 1, so tliat the table begins with backing of Um
same height as the wall. These vertical walls may be battered to
any extent not exceeding an inch and a half to a foot, or 1 in 8,
without affecting their stability, and without increasing the base.
ProiM>rtion of RetaininiT Walls.
Total height of tbo earth oon-
Wall of
Good mortar,
Wall of
pared with the height of the
cut stone
rubble.
good, dry
wall above grouud.
Id mortar.
or brick.
nibble.
1
0.35
0.40
OiO
1.1
0.42
0^7
0.57
1.2
0.46
0.51
0.61
1.8
0.40
0.54
0.64
1.4
0.51
0^
0.06
1.5
0.52
0.57
0.67
1.6
0.54
0^
0.60
1.7
0.55
0.60
0.70
1.8
0.56
0.61
0.71
8
0.58
0.63
0.73
2.5
0.60
0.65
0.75
8
0.62
OJN
o.n
4
0.63
0.68
0.78
6
0.64
0.60
0.79
BrCHt Walls (from Dobson's "Art of Building").— When
tli(>. groiiiid to b(i supported is firm, and the strata are horizontal,
Um^ of1i(M; of a brcst wall is more to protect than to sustain the eartlL
It sliould \h\ borne in mind that a trifling force skilfully applied to
iuil>r()k('.n f]:roun(I will keep in its place a mass of material, whicb,
if oncci allowed to move, would crush a heavy wall ; and therefore
i;n*iit care should be taken not to expose the newly opened grooiMl
to the influence of air and wet for a moment longer than is requisite
for sound work, and to avoid leaving the smallest space for motion
Ix^tween tlie l)aek of the wall and the ground.
The stHMii^tli of a brest wall nmst be proportionately increased
when the strata to be supported inclines towards the wall: where
they in(']in<^ from it, the wall need be little more than a thin facing
to protect the ground from disintegration.
The i)re.servation of the natural drainage is one of the most im-
portant points to be attended to in the erection of brest walls, as
upon tins their stability in a great measure depends. No rule can
l)e given for the best manner of doing this: it must be a matter for
attentive consideration in each particular case.
BTBBNQTU OF HASOMBY.
CHAPTER VI.
STRENGTH OF MASONRT.
D " Strength of masonry " we nteai
e, as that is the only force to which niasoniy shoulil
The Ktrengili of the difFerent atones .and materiaU
Miry, as detennined by experinieDt, is given in the
le:~
tJTOKEB, Etc.
lOOOU.
Art llint, S garla KraTsl, three v
,ent. b«t>:iiKH.h-
00k. oM} .
KM
3.m
2.4S0
li'rl
riiwU-r, N.V
I2.BW
riiwU-r, N.V.
■ompaTiy)
h It.)- lj.iarr)-, Wl.
M«; STilKNCiTIl OF MA.SONUY.
Tiic sUjiu's ill this tabic are supposed to be on bed, and the height
lo Ix' not niont than four times the least side. Of the strength of
iiihl)le niiLHonry, Professor llankine staU^s that '*the reslstaneB
of */noii foursfrtl ruhhU' masonry to crushing is about four-tenths of
that of single blocks of tlie stone it is built with, llie resistanee
I if roniinoii nihblf Xo crushing Is not mnvh greater than that of the
iMoiiar which it contains/*
Stonos generally <*ommenrc to crack or split under about one-hilf
of tlicir rnishing-loiul.
Crii.sliiii{;-Hei|?lit of Brick and Stone. — If weaasomi
tli(> \v(M<<:ht of brickwork to l)e 112 poiuids per cubic foot, and tbifc
it would crush under 4.>() pounds i)er square inch, then a vertictl
uniform column r>8(> feet high would crush at its base under its own
wciglit.
Average sjindstoiics at 14r) {Hmnds per cubic foot would requivB
a <M>lumn 5i)r»o f(><>t bigh to (Tush it; and averages granite atl(B
|M)unds {HT cubic f(M)t would re<iuirt^ a column 10,470 feet higLj
The Mci-ciiants' shot-tower at Baltimore is 246 feet high, and its
base sustains a pressure of six tons and a lialf (of 2240 pounds)
)H'r square foot. The base of the gnuiite pier of Saltash Bridge (by
lininel) of solid masoniT to tht> height of iH\ feet, and supporting
tlie einls of two iron si)ans of 4.V) feet each, sustains nino tons
aud a half )MM'S(|uaiv foot. 'I'be highest pier of Rocquefavour stone
atjuediict. Marseilles, is iVXi feet, and sustains a pressure at the base
«»f iblrteeii tons and a half |K'r s<iuan» foot.
\Vorkiiig:-Strt*ng:tli of Masonry. — The working-strength
ot masoiirv is i^enerallv taken at fnwii one-sixth to (m«*-tenth of the
ciusbiug-load for piers, column^, etc.. ami in the cast* of arches a
ta«-tor of sat'etv «»f twenty is «»fien recnmiiu luh^l for computing the
it"»i>lance of the \«»ussnirs to crushing.
Mr. rrauiwiue states that it cannot 1k> considered safe to expanc
c\en lirsi-class ]»reNS<*«l brickwork in rtimut to more than thirteen
or sixteen ton^* pn-ssuiv \m'v square fi«ot. or giHxl hand-niouldeii
lMi«k \i nuMi' than two-ibiivU a«i much.
>bect lead i«» M»nictinu> ]»lao*il ai ilu* joints of stone coluniiis
wiiba \iew lo iipiali/e the pn's^iorc, and tliU'* incrt^ase the strength
oi the colun.p.. V\|Hriuiiiir>. Iiowi-mt. mm-iu to show that tin'
irt*e*'t is tiiri-itix ilii- ri\iM-v.\ and ilia! ibe •-olumn is materially
WiakciH'i! ;!n !-<l»\ .
PitM'N. - ^l.^'»on:■\ ;i»a! i'» >o bc.i\i]\ loaile,! that it is iiM^essary
i.« piv.A'itio;: i: in i-e^ar.l to ;;<« '«ir«M:::li ii» r«-'»is; crushing, is. as a
jLv:.'r.*. r.;!i. ■. :1ji lorn: ot i»i«'i-s. ei'lu-r i«f brick or stone. As
STltKNOTH OF MA.SONKY. 167
piers are often in places where it is desirable tliat they should
Mxsupy as little space as possible, they are oflea loaded to the full
Imit of safety.
The material generally used for building piers is brick : block or
vat stone is sometimes used, for the sake of appearance; but rubble-
i^ork should never be used for piers which are to sustain posts,
[)illai*s, or columns. Brick piers more than six feet in height
should never bv^ less than twelve inches square, and should have
properly proportioned footing courses of stone not less than a foot
thick.
The brick in piers should be hard and well burned, and should
be laid in cement, or cement mortar at least, and be well wet before
being laid, as the strength of a pier depends very much upon the
mortar or cement with which it is laid: those piers which have to
sustain very heavy loads should be built up with the best of the
Rosendale cements. The size of the pier should be determined by
calculating the greatest load wliich it may ever have to sustain, and
dividing the load by the safe resistance of one square inch or foot
of that kind of masonry to cnishing.
Example. — In a large storehouse the floors are supported by a
girder running lengthwise through the centre of the building. The
girders are supported evei^ twelve feet by columns, and the lowest
row of columns is supported on brick piers in the basement. The
load which may possibly come upon one pier is found to be 55,000
pounds. What should lie the size of the pier ?
Alls. The masonry being of good quality, and laid in cement
iiioilar, we will assume that its crushing-strength is fiOO pounds per
square inch; and, taking one-sixth of this as the working-load, we
find that the pier must contain 65000 -r 100, or ()50 square inches.
This would require a pier about 24 X 27 inches.
it is the custom with many architects to specify bond stones in
brick piers (the full size of I he section of the pier) every tliree or
four feet in the height of the pier. These bond stones are gener-
ally about four inches thick. The object in using Humh is to
distribute the pressure on the pier equally through the whole mass.
Many first-class builders, however, consider that tlie piers are
stronger 'without the bond stone; and it is the opinion of tiie
writer that a pier will be just as strong if they riv. not used.
Section 8 of the Building Laws of the city of New York requires
that every isolated pier less than ten superficial fe(»t at the base,
and all piei*s supporting a wall built of rubble-stone or brick, or
under any iron l)eani or arch-girder, or arch on which a wall rests,
or hntel supitortmg a wall, shall, at iulerva\s o^ wot X^'g*^ Wi^w W\\\\^
tjc'/jtis in hfiifiht, hava built iir.o it a \)mu\ sVmvo. u^^V V.'?>f. \\\v\
STRENGTH OV MASONRV.
four inch« thick, of n diameter (incli way prjiml to the dliil
of the pier, except tliat in piers ou the stiwil front, abovs
curb, the bond stone may be foiu' inches less than the pU
diameter-
Piers which support colnmns, posts, or pillars, should have ^
top covered by a plate of stone or iron, to diatribtite the prei
over the whole cross-BBCtioii of the pier.
Id Boston, It is required that " all plRrs shall be built of g
hard, well-bumed brick, and laid in clear cenieut, and all h
used in piers shall be of the hardest quality, an<l be well wet wl
laid.
"Isolated brick piers under all lintels, girders, iron oroUierflj
umns, shall have a cap-Iron at least two inches thick, o
cap-stone at least twelve inches thick, the full size of the
" Piers or coluums supporting walls of inasoury sliatl Iiare ft
footing course a broad leveller, or levellers, of block stone notfl
than sixteen inches thick, and with a bearing sni'face equal In M^
to tiie H(|iiare of the width of the footing course pltu
required for a wall of the same thickness and extent as t
by the pier or column,"
For the Strength of Masonry Walls, see Chap. m.
The following tables gi?e tlie results of some tests on l
brick piers, and stone, made uuder the direction of fl
author, in 1>ehalf of the Massachusetts Charitable Mechanics Ai '
elation.
The specimens were tested in the govemment lesting-ni
at Watertown, Mass., and great care was exercised t
tests as perfect as possible. As tiie parallel plates between w
tlie brick and stone were crushed are Bxed ii
necessary iliat the specimen tested should ha
The bricks which were tested were ruiibed u
until the top and bottom faces were perfectly tj
The preparation of the bricks In this way requii'eil a great dl
of time and expense; and it was so dlHicult to prepare soineof 4.
harder brick, that they bad to be broken, and only on&juU W
the brick prepared at a lime.
g-maol^
e position, Hi
p perfectly pandW
a revolving HI
le and parallel. ,'
J
STRENGTH OF MASONRY.
169
TABLE
UUimate and GrtiekiTig Strength of the Brick, the
Size and Area qf Face.
or Bbiok.
Size.
Area of
face in
sq. ioB.
Commenced
to crack
under lbs.
per sq. inch.
1
Net
strength
lbs. per
sq. inch.
6,062
5,831
5,862
5,918
9,825
12,941
11,681
14,296
12,186
13,839
11,406
9,766
11,670
10,270 ;
13,530
13,082
13,085
12,490
Face Brick . . .
• • «
II <i
• • •
Whole brick
Whole brick
Whole brick
33.7
32.2
34.03
4.303
3,400
2,879
3,527
8,670
7,760
3,393
3,797
4,655
11,.518
8,593
3,530
7,880
3,862
8,180
2,480
4,535
4,764
$rick (Ea«tem) .
<i II
II II
II <i
Half brick .
Whole brick
Half brick .
Half brick .
10.89
25.77
12.67
13.43
kCottaCo.'B Brick,
II II II
11 II II
Half brick .
Whole brick
Whole brick
11.46
25.60
28.88
dPreesed Brick .
II II
•
II II
•
•
Half brick .
Half brick .
Half brick .
Half brick .
12.95
13.2
13.30
13.45
idelphia Brick used in these tests were obtained from a
ler, and were fair samples of what is known in Boston
)hia Face Brick. They were a very soft hrick.
bridge Brick were the connnon brick, suoli as is made
ton. They ai-e about the same as tlie Eastt^n Brick.
on Terra-Cotta Compani/.f Brick were nianufactm*ed of
e clay, and were such as are. often used for face brick.
-England Prensed Brick were liydraulic pressed brick,
most as hard as iron.
►f tlie Streuj^th of Brick Piers laid with
Hf OrtarsJ — Tliese tests w(>re made for the pui*pose of
strength of brick piers laid ui) with different cement
\ compared with tliose laid ui) with ordinary mortar,
ised in the piers vv«?re proctured at M. W. vSands's brick-
l)ridge, Mass., and wcie good ordinary brick. They
the same lot as the samples of common brick referred
»ove tabid.
of thene tvntf wa^ firnt published \u VW. .\v\\<iT\c»\\ N.T'Sli^
Thfl plum vnem 8" by 12". mh\ nine couwm, or alioiit £H" |
[ni^ptiiig the Aral, whlcli waj hut eight iwiirM-a hi^h. They
JmlU Nov. 20, 1881, In one ot the atAn-houiHS nt ihit Uatl(44
In Vla1«novu, Masi. In onler U> hnve thi- two e
M lArm pnrf(<ctly parnllel mirfacm. n iimt n( ntioHl b>If w
lick (il pi)rt> l\irtland cenii^nl wan put nii thf top of eaci
U Ihf foot waagrmnntl In tlie»m<: (.vnii-nt.
Marfli tt. INH2, thrw months nnil five ilayn later, the topa ol
iHMi were i1r>!H«ei1 lo plani' aurtiiL-pa nt rlnlit auRlea to tbe ri
le |ii>>ni. (.>ii al.[4tin])tlllg t'> drtiis the lower ends nf the fiea
ownt Kniiil (iceleil off, hckI it wm neciwaary in reiuove It eiil||
id put oil « layer nf ''eiiii.'nt nlniilar to lliul on tiic top ol tbe p
btit WHS Hlluweil to lianlun fur one ntonth luiii aixteen days, <^
M p\en yicte tested. At that time the plera were four nionthii
ranty-slx dsys old. As the plors were built lii cold weathwj
rMa wiiru not wet. |
Tho pit!)-!' wp.n' liullt. by a iildlltHi liriek-lnyer, and the ma{
(ire mixed under his superintendence. 'I1ie tejits were mnile i
M ^ivrrnmnnt teBtlng-moehine at tlie Arsenal. -I
Plpr Nn. 1 (brleks laid In oommon lime mortar two days olj
hi* mortar was jwirt of a lot prepared for use iu the erectioa<
rutlding then being t>itllt in llo.ston, niid was such as la eoitiiq
led In building.
S\tv of pier »" *. Vi" A rea (Kl sq, Inchi!*,'
Lfnglh H uoursex -M ineheg. i
Wi>iglit 144 pounds. |
Age -I iiiouliis, :jtt days.
l'1tliunti?atrenKtli l.')O.UO() pounds. ,|
Time tif ttwt 4.'i iiiinules. j
I'ndprnlrMdof FIO,n(HI pounds, n longlludlnal enck was ojli
(ll tlr"i ami speond eniu-aea: 1(0,000 pounds extended the 4
,, also opening emek on the opposite aide dl
inii'ses. The pier suslalnwl lhem«xlmuiii'|
•t minutes, rapidly ih-veloplng loiipitndiual eincks. and r™!
ini« of the iirieks. l]
Pier No. t (hriek iuid In nnirlxr <'nii>i»>>.<-d i.f one part I'ori
«nt and thiw parts iimo tnoriar). '
Slwof iiliT8"x 12" Ari'alKi sq. Ineliei.
length D eoiinteii . 2*^1 inchos.
Wnlghi Itii pound*.
■HuiJttV\vs,^ 4i!I»,
iiivuyili ...... ■&«.»« 1
£
*« ^pOTW^
STKKNGTli OF MASONRY. 171
A load of 180,000 pounds opened a longitudinal seam in the fourth
coarse. Sustained the maximum load one minute. The pier failed
by opening longitudinal seams^ and did not break up when removed
from the machine.
Pier No, S (brick laid In mortar composed of one part Newark
and Rosendale cement and three parts lime mortar).
Size of pier 8" X 12" Area 96 sq. inches.
Length 9 courses 22^ inches.
Weight 159 pounds.
Age 4 months, 26 days.
Ultimate strength 245,000 pounds.
Time of test 20 minutes.
At 130,000 pounds' compression, longitudinal seams appeared
in the second and fourth courses. Rapid development of seams
♦Hvurred under 220,000 pounds. The pier sustained the maximum
'oad one minute, failing bjj^splitting and crushing the bricks.
Pier No. 4 (brick laid in mortar composed of one part Orchani
Homan cement and three parts lime mortar).
Size of pier 8" x 12" . , . • . Area 96 sq. inches.
Length 9 courses • • • 22^ inches.
Weight 158 pounds.
Age 4 months, 26 days.
Ultimate strength 195,000 pounds.
Time of test 25 minutes.
At 100,(KX) pounds* pressure three bricks cracked, and at 150,000
ounds' pressure there were cracks in siglit on each of tlie four faces.
t sustained the maximum load one minute, and failed l)y crackinf^
rid crushing the bricks.
/*ier No. 5 (brick laid in cement mixed in tlie propoition of one
dft Portland cement and two parts sand).
Size of pier 8" x 12" Area 90 scj. inclies.
Length 9 courses 2:> inches.
Weight 10(5 pounds.
Age 4 montlis, 2<5 days.
Ultimate strength 240,000 ponnd.^.
Time of test :]0 minutes.
At l^5,(X)0 pounds' pressure, a crack appeavoA \w Wx*? NXCvc^ ^^'^^ks?^^
/ one in tho fifih course, l^he \)iev f aWoA \>»^ o^^nvvw^ V^'^^ -"^'^^^^
ns. It ilUl nut />/vak up when reuxownX Uvuw V\\«i^ vw.w^xvnx^^-^I
STKKNnTH OF MASOl
impiit eoinposeil of one imit Nov
opni'lssnnil).
Size of ptt-r 8" X 12" Arejidfl sq. inches.
englti 9 courses 23i inches.
[ WelgliL . 1117 pounds.
. 4 months, 20 days.
Ultimate strength 205,00(1 pounds.
Time of test '20 miaales.
At (18,000 poiuida' preaaure, cracks were irerceived in the thirf;
rotmes troui each end. Failed by opening lougitudiual si
Pier Nu. 7 (brkk laid In cement composed of one part Ordiinl
ItoiiMii cement and two parts saud).
»Slw! of pier 8" X 12" .... Area 90 aq. Indies.
Length 0 iiouraes 23^ inches.
Weight 104 pounds.
Age . 4 muntlii!, 20 days.
TJItfiUHte strength 185,000 i>ounds.
Time of teat 20 TQliiiites.
Commeneeil to crack when under 170,000 pounds' pKa\
Palled by opening longitudinal seams, and crushing the bricb.
Pier did not break up wlicn taken from the lesting-mHehinB.
Pier No. S [four courses laid in Newark and Rosendale cemool
one part, anil sanilone part; remaining flveponrses laid InPorllMid
cement one part, to two parts of aani!).
SlJie of pier fl" X 12" Area Ofl sq. Inches.
Lengtli tl courses 2;l,',- inehea.
Weiglit . . . wn pounds.
Age 4 months, 2C days
U1ttinnt« strength 2Sr).000 pounds.
Time of T«at i^ minutes.
I'niler 131^,000 pounds' pre:9sure, the third course, laid In Nen
and Hoiiandale eejiient, began to crack off. When the pier MMA
the (ind laid In Newark and Rosendale cement was tborouglQl:
CMickcil, while the opposite end (laid in Portland cement) 1
four longltiudlnal m^inis, — one In each fane. This shows thattU
Iili)rt«r eanip(>.''ed of ojie )ian I'ortland cement to two pvM of SM
AstrongtfF t/i«l tlint of Newark and Uou9u\K\e. ccn\«ita mixed I
e part ccnienl \(t on* ol b»u«\.
r table Is arranged ko hb to »\»n«
tlpU-r-i lai'l Willi lli.- .lifE.ivut hkhvav
t««dy means of comparliioi). It is iiitensthig lo compare tlie BguroB
Qbt^ed ftum the Lests wilh tliose given in the haDithooks. Mr.<
Out ordinary brick-work cracks w[lli 20 to 30 tons per square foot,
wUeli is equivalent to 311 U> 40B pounds lo Ihe sqnare inch. Th*
I'lTKcr mmibpr is less Ihnii half the pregsun; per square ineli, whicb
VraluceJ the first track In the pier laid with lime mortar.
Common brklu MA !a —
1
^1
Mi
II
,b..
l.BJfi
I.SM
I.7J0
1,662
3,020
1,662
1«7
UmB mortsr. 3 t»na; PoUlnnd CTmcnl, I ptrt .
rjme niorlar, a parM; Newark anU Koaetulale
IM,000
LJmemonar.aparta: nomauwment.lpon . .
i'onlMidMnwnl.lparli Mnd.SpofM ....
Nuwuck and RaseiuUle cemeiila, 1 pan; umd, 2
Komancemeiit.Ipart; und.a'purU
For first-rate brick-work ineement, Mi'. Trautwine gives niim- ]
bere which correspond to 770 to 1088 pounds to the square inch.
the tests of the piers laid in cetniMit. The Portland cement used' *
in building these piers was the Iciml known m Brooks, Slioobrldge, '
* Co.!s cement; and this with li\e other brands were ftimislied tor
ilie tests l>y Alessrs. Waldo Brothers, Boston, Muss.
Actual Tests of tlie Cnishing-Strenffth of Marble
uud SaiHlNtone (made under the direction of Ihe author for tM'
were raa4e with the government lesting-niacliine at the Unitetl-
StWes Arsenal. Walertown, Mass., and every precaution was taken
to seeure accurate and reliable results.
StrrnERi.AKU Falls Vehmii-jt Mabhlf, (white). —This maW
l)le is iitiarrieil by the V(>nrtont Marble Company. Centre liutland,
Vt.
Block No. i.~No. I (|(ia(ity, ■■ V " la^ur. 'Wti^Vw. VSft ■'jd-MiSa.
<ya<u«{BeA«, UUimaLe strength 404,000
powndLs VVVfl
a^y^
TKMNCTII til- MA«)NR1
This block uoiiini.-iii'.il lo era-
pounds' pri'B3urp(!>T5«pi>iunlB [i
tindei' 404,01X1 pounds.
Bioct JVo.fi. — Same kind and qimlityaa No, 1. Siw!a"xe*y
ao^. Sectional area S0.12 square iudi«s. UUImatc iH:
370,000 iHinnilH (10.243 poiimU per sgiiiire inebf.
This black did not crack nl ull until U gavo way entlrcily u
pressure of ^70.000 imiiiuls,
Urownstone fkom thk Bav iiir Vvmiv QvAHRVixa
PANY. — Samples of the three following varieties of brown
Btonu were fui-nished for [fstiiig by the Boston agents of the Ba;a
Fundy Quarrying Company.
Makv's Point (N.B.) Stohh. —This stone Ia « Biie-graiudM*
brown sandstone.
liloek No. 1 nwasiirwi 4.04" X i.W X S". Beetiuiial a
square inches.
Thin i«tone coniitienced lo ciiiek at the turners and ftlong tlM,
edges under lOS.iXXi pounds' preswire, and Continued crackiog imUl
11 suddenly broke into a number of pieces under 127,600 pound*
pressure, or IfliS pounds per square Inch.
Blaek No. « riieaaiired 4" x J. 75" X 7". Swlloual area 15 squsn
inches.
The stone ronnnenc'ed to fi'ack near one comer nnder a preMM
Of 31,000 [wunils, iiud under "7,0IM pounds it w<vs bftdly cracked
It dew from the inachini' in fragments when the pressure reacbei
113,800 iHiunds, ur 758<> poniids per s()unre inch.
Woon's Point {N'.U.) Sanostomk. — This stone is of about *?
same I'Olor as the Mary's Point atone, hut it has a much CMr»<6
grain, and Is not very hard.
Bli'nk JVo. 1 measured 4.03" X 4.0:!" X S". Seetloiial
square Inches.
Coniuiencat to crack at 50,000 pounds, on tti^ coniera, and eatt.
tinuetl cracking along the e^lges and at tile comers, until It
crushed under W) 000 lbs presbure, or 4ll3s! llis. pi-r square incli. i
SIimJc Vo I measuietl 4 x ( OH" >c T.'i-')". Secllonal
■qiMre mthes.
Tills qt >ni Kinirnenieil to tntek nnder a pi'essnre of M,<lt
pounds and fHJIni imdei h presiiurc iif ti^.oOO pounila, or SBT^
poiuuls per W|URr lULh
LoNOMrtiiiit '5ri si- — lli liay of Fiindy Qnim-ying C<m
pttny itl>^i 'I'Mrn a tarietj of llii lAingiiu-aduw i,>[ass. | samlsLoM
Wbli'h lia nvlilMi binnn in ml
.M'irt Af 1 itit>Haitr(.>d .1 "^
1- /m (..■«.
M
Sl'KKNOTII OY MASONilY. 175
Ills stone sliowed no cracks whatever uiilll the pressure bad
lied 152,000 pounds, when it commenced to crack at the cor-
I. When the pressure reached 200,000 pounds, the stone sud-
ly flew from the machine in fragments, giving an ultimate
tngth of 13,596 pounds per square incli.
'his stone did not fit into the machine very perfectly.
Slock No, t measured 3.39" x 3.97" x 7.5". Sectional area 15.6
lare inches.
rhe stone commenced to crack along the edges under a pressure
47,000 pounds. Under 78,000 pounds, a large piec^ of the stone
lit off from the bottom of the block, and xmder 142,300 pounds*
essure, the stone failed, cracking very badly. Ultimate strenyth
r square inch 9121 pounds.
Brown Sandstone from East Longmeadow, Mass. — Quar-
d by Norcross Brothers & Taylor of East Longmeadow. This firm
trks several quarries, the stone differing in the degree of hard-
58, and a little in color, which is a reddish brovvn. Tli<^ different
"ieties take the name of the quarry from which they come.
)0FT Saulsbitrv Bijownstone. — This stone is one of the
lest varieties quarried by this firm, although it is al)oiit as hard
the ordinary brownstones. The specimens tested were selet^ed
the foreman of the stone-yard without knowing the purpose for
ich they were to be used, and were rather below the average of
3 stone in qimlity.
^lock No, 1 measuretl 4" x 4" x 7.08". Area of cross-section 16
are inches. Ultimate Htreinjth 141,000 po*/jj(/.s, or 8812 j>o»7Ji(/.s
square inch,
•tone did not commence to crack until the pressure had reached
,000 pounds.
ihck No, t measured 4" X 4" x 7.S."i". Area of cross-section \i\
are inches. Ultimate streuyt/i 12i>,CK)0 ymwiKM, or 8062 />oj/><</x
square inch,
'liere were no cra<?ks in the specimen when it was umler KM^iMJO
inds' pressure.
Card Saulsburv Brownstone. — This Is one of tlip hardest
1 finest of the Longmeadow sandstones.
ilock No. 1 measured 4.16" x4.16" x 8". Sectional area 17.3
are inches. Ultimate strenyth 283,(K)0 j)o{f»f/.s, or \?tjy20 pou ads
square inrh.
tone did not commence to ciack until the J^'fissure had reaclu'd
,000 jK>ni)d«, almost the cnisliln2:-stren<i\\\.
/oc^ ATo. S measured 4.[.>" x 4.ir>" X S". SeeVXiiwA livx^vw V\a
V fncJifs. UltiiHfUv sfn-nyth 252,000 pouiuU, OY U,^5^ Vi>\xw.^
17*
STUBNOTH OF HASOHUY.
Tills spacimen did not coiunienra lu ci«ck nnUI Lbe pimmre hi4
n:u:Li!tl 240,000 pounds, or 13,053 puiiiids to the sqiure Iticli.
Tlic followlug labl« is armngeil to sliow tlie aectloiul art* auil
stn-iigth of rarli ^pt^imi^n, mill tlie avenge for escb vuMj ol
f-l •■ Tlic i-mL-kiiitf-sli'L-iigili, so to ^{KAk, of the stone, U of con-
hi<li!riil)le hii|M)i'liiU(t!, for, afler a stone liaa couiiiienceJ tocrack,!!*
IHTDiHiifUt stivii^li Is probably njafbitl; fur, if t1ii> load wblcUcauMd
it ii> cratk were uUoweil tu remain on Llie sluni:. It would proUblj
lu tiiiu- (.Tiisli lliu sloii«. Id tesUiij; tUe blocks, lioui'Vcr, some lii-
cijiiulity in llie faces of tlie block might cause one cornfi' to L'r>i'k
H liun tlie stuiie Itself had Dot coninieiiCMl to weaken.
».„.,.„...
i
1
li
1"
P
1
S
■3
jj
MARBI,!.
is"
"■f?
10,746
7,707
4,45*
13,W8
11,358
8,i37
13,M0
14,085
S.730
9,986
2,346
2,903
10,SM
6,672
7,375
13,334
!SS
so,ooo
HIJW
i-2a,iii»
BlDck N". 1
BluckNo.a
IS
H-BOiVi, IMul.
1B.»
/.<„(V""rr.'o;i' 5(o«' [Bnj- of Fun
,i,.jiiiiurrjLui(Cumi«iny'.).
i;s
H..PT 8*0Laai,'n« 8tome.
BlnqkNo.]
K
■ >'... B.„,„„.
llKKkNo.1
IlluckXu. -i
17.20
IC-
Ofii. Q. A. GiUmore, a few yeara ago, lwX*4 tt* iM«iu^li of
UMiiy varieties of saiiilstouc by c'msli'i"B vwioAwAi-wiSx*. '^^i* «
STRENGTH OF MASONRY. 177
>^ined by him ranged from 4350 pounds to 9650 pounds per
ii^ch. Comparing the strength of the stones tested by the
with these values, we find that the specimens of Hard
uy sandstone had a strength far above the average for sand-
and the other specimens have about the same values as
•tained by Gen. Gillmore.
lould expect, however, smaller values from blocks 4" x 4"
m from two-inch cubes; for, as a rule, small specimens of
Qy material show a greater strength than large specimens,
iteresting to note the mode of fracture of the blocks of
ine, which was the same for each specimen. The blocks
by the sides bursting off; and, when taken from the ma-
e specimens had the form of two pyramids, with tlieir
eeting at the centre, and having for their bases the eom-
iids of the block. The pyramids were more clearly shown
pecimens than in others, but it was evident that the mode
e was the same for all specimens.
Sandstone. — In 1883 the writer superintended the
' two six-inch cubes of the Kibbe variety of Longmeadow
J, quarried by Norcross Brothers. One block withstood a
[)f 12,590 pounds to the square inch before cracking, and
did not commence to crack until the pressure had reached
ainds to the square inch. The ultimate strength of the
c was 12,619 pounds, and of the second 12,874 pounds, per
ch.
■mte Mis a •Min' >M*. k is cntaB
■iMiK Mf tte OnK af *c pur •»•« Mf pMR !■ the odU
tte lis ahil Ml oHMwl Ac MMMM «i Ik «ti^ of 111
l4t w» ' II II AM tt* fiar iWHnw tte font at a I
«Ucfc «Mn» > itowi r n ite *«ebM .ABL Ite toda
Hit a— Ht wji t* MCMM A« pier M wtMt «lmai ibl
r X «>,.«,«, br^lkr KB. Nwr.ikMthepin-dMlblf
MHE O^pF BBt jut «tal rN«>,. TW WCJ^ of Ifel |
«a. •< (BHW. act Onvg* Ikr «■>!* of ^nlt; a< the fkr lid
■ the kw« aMWMMl OnM, or the m
he oC «< the oMtar vigt. ««rti enw Ac |wr to muic: bM
to ikvr tbe fin !■ mte d^vMRiaH. «« «Ht OK aoae fMU
•*tj.
TKi h icwtalT *wr ^ ■nkt^ dw MH(M «( the wri^ ^
W that df ihe thcwl «1M« nlMnl 1ft k v«Wl In \W bnttaH «f 1
Am dfaoace tor pi«» or b«m«wMihMUM.>K^iB.
STABILITY OF P1EH8 AND BUl^l'BESSES.
17G
Kepreseiitiug this point in the tigure hy b, we have the necessary
equation for the safe stability of the pier,
£ <lenoting the width of the pier.
We cannot fix)ni this equation detenniue the dimensions of a
pier to resist a given thrust; i)ecause we have the cli stance ah, /.
aud W, all unknown quantities. Hence, we must first guess at thi
'-Bize of the pier, then find the length of the line ah, and see i1
the moment of the pier is equal to that of the thrust. If it is not,
must guess again.
T/B
A
c
•
/
8
7
,r>
C
8.2
Graphic Method of deteriniiiiug: the Stability of f
Pier or Buttress. — When it is desired to detennint' if a i^ivoi
pier or buttress is capable of resisting a given thrust, the problen
can easily be solved graphically in the following manner.
Let ABCD (Fig. 2) represent a pier which sustains a giver
thnist T at B.
To determine whether the pier will safely sustain I his thrust, w<
pipceed as follows.
Draw the indefinite line EX in the direction of \\w thrust
Through the centre of gravity of the pier (which in this case is ai
the centre of the pier) draw a vertical line until it intersects tin
line of the thrust at e. As a force may be considered to act any
where in its line of direction, we may consider the tluiist and th*
weight to act at the point e; and the resultant of these two forces
can be obtained by laying off the thrust T from e on cA, and tin
weight of the pier IF, from e on the line eV, both to the sam<
scale (pounds to the inch), completing the parallelogram, and draw
ing the diagonal. If this diagonal prolonged ew\>aX\\vi\i^&^*A \X>
pier at less tlmn one-fourth of the width ot t\\e \)a?k^ itowxWv^ vsv\
edge, the pier will be umtahle, and its din\euH\o\\a \\\\x?\.\yi Ocva.v\
r/^e siafjilUif of a pief- may l>e Increased V>>^ aA^\\\% vci \V^ >*
n'ABlLri'Y OF PIKRS AND BUTTHESSE8.
Kl60
^wlfby pUciug some lieav; innterjnl on top), or by Increasing its ll
^P It the base, by means of " aet-ofFs," ns In Fig. 3.
' Figs, a (A and It) sbow Che method of determining tlie stall
of a buttress with offsets.
The &rst step la to lind tlie vertical line passing througb'
centre of gravity of the whole pier. Tliis is bust lione by divfl
Ibe buttress up Into quiuirilalerals. as AISCD, liEFO, and OB
|Fig.:IA|, Hndlng tlie centre uf gravity of each qiiadrilateid 9
Die methort oF diagonals, anil llieii measuring the perpenilicali
distant-es .I'l, X,,.rj, from the different centraaof gravitylofli
line Kl.
Multiply liiQ area of each i|uadri I literal by the distance of;
centre of gravity from the line KI, and add Uignther the n
and tlie products. Divide the sum of tho Utter by the sum of
former, and the result wilt be the distance of the centre of gm
aS the whole buttress from Kl, This dlBtance we denote by X
F19.3H
EXAMi-LK I. — Let till! buttress shown In Fig, 3 A have I
illmensions given twtween tlio cross-marks. Then the areil
tlie qua<trllateruls and the distances from their centres of gmvltj
Kl would be as follows:
Total area, fil) sq. ft. Total moments, ISS.."*,
The sum of the moments Is If.S.S.'j; aftA.AViUVwg Hife by the l>«i
a/KB, H'O fiBve 2.2,5 as the distftiuio X„. TAeBavuVn^ftAsXiifSst^*
of the drawing from KI, we \iavK b. 'po\n\. ftvTwx'^ ■tfUieQ.'i
M^Uciif line passing tlirougU llie cenlie ol pwi\\.T ■»»*. 1
Uf I'lEKS ANli DIVITIIK!
e is founil. tlie nwthod of delemiining llw sUbility of
t same aa Uinl given fur Die pier In Fi|j;. 2. KIg. 3B
riflliwi. If thi? butLress is more tliiiii ont! fool
Mit angles to tlie iiliiui; of llie paper), tlin cubii' cuiilenls
<t be otitajneil to diul tlie wttigtil, It la eusi?r,
Ib^tiviile tile mal tltriist by tiie tlik-kuesH of the buttress.
m the tlirusi per foot of Inittress.
of Resistance. — U-Jtaltiini.. TIu: line of resl!itan(«
jssurea. of a pier or bultresB, U a line drawn tltrougli the
f pitBSkii'y of eajJi Joint.
wiilre iif jirexifure of aiiy joint 'm tlie point where the
t of iha forces acting on that portion of the pier alwve
DC of pressures, or of resistHnce, when drswii in a pier,
»w near the greatest stress on any joint coinKs to tlit eilges
be drawn liy Ihc following niPthod.
{BCD (Fig. 4) be a pier
ine of i-esistance we wish o-
FirsI divide the pier iu
into portions two or three
h, hy drawing horizontal
It is more ronveiilent lo
e portions all of the same
ig the line of the thrust,
w a vertitiil line through
.re of sravily of tlie pier,
Ing the line of thrnHt at
t IK From a lay off to a
. thnlal T and tlie weights
fferent jiortions of the pier,
eing with the wei)(ht of the
■rtion. Thus, HT] represents
hi of the portion above the
t; le, represents the weight
eeond portion; and ao on.
.1 of the lo's will ecjiial tlie
eight of the pier,
Bl proceeded thus far. eoiiipleti' a pHrHllelograiii.
,a two aiilea. Dmw [he diagonal, aiuH pri^Xon^
■lie Best Joint will be a point in Uie Vvvw «^
•therpamllpJogmm, with Tanrt m^ + m, tor V
j^mprsecting the second joiiiL 9i,
t82
Aiin.r
Jill wny, wbeii Lliu last ilia(,'aniil will intersect the boae In 4
.c polnti 1, 2, S, and 4. hikI the resiilUng line Will be tlie
B hnvi; tftkcn tliu almiilesC case as an t^xample; but lli
Irltielple li irws for any cbk,
Klioiild tlie line of reR)sl»ncit of n pier at any point kp
<iutB<[li- edge of the jolul nearer than one-quarter the
f lilt.- joint, the plnr slioulit lie consiilereil unsafe.
n example embraeing all tlie jirlnriplea given above,
l*ke tlio following case.
Mfi.K TI. — Let fig. 5 represent the section of a ai
pt a eliurcli, with it buttress against it. Opposite the buttti
^e Inglde of t)ie wall, is a haiiimer-beain truss, which we «
m" tKi-ne an outwanl tbrtut on ilie walls of the church a
g lu aboui IWOO [loniiiis. We will further t-onsider tt
taultnnt of lUe thrust ai-(« at P, anil at an angle of BO"
!borii!onial. The tliuietiBions of the wall ami Ijultress are g\
l- riA, and the buttress Is two feet thiuk.
' QitKHTioN. — Is tbe buttress sufficient to enuble tlie \
wlthaiaiiil the thrust of the truss ?
The first point \o decide Is if tlie line of resistance ei
Joint CD At a siife distance In from C. To asoertain this, ««
•llnrt the centre of gravity of llie wall and buttress above lli«
We can find tids cosiest by the method of mome
Jf'f (Fig. .^A), as alre&dy explaine<t.
Tli« distance A', Is, of course, half the thickness of the'
■ foot. We next And tlie centre of gravity of llie
^fY> IFig. 5A|, by the ineilioil of diagonals, and, scallq
ttitfiOf A',, we lind it to be 2.1*5 feet,
IIm ariNt of CKFG = .1 , = Ul »|iiar<' fet4 ; nud of GIKL
JW sqiwre ft*t-
'riKii wo liave,
.Vi = I
: Jii A,
.r„ = 1.5
Or Ifce CMitn- of gravhy is al a dislanre I.'i tool fmiu
■' Kf) (FIf. S). Then nil Fig. r> nirasure the distance X, = IJH
ami Ihnmgtt the point ii draw a venkiA Uiw inwtVMtii
of a^ tlinist prolonfcnl M <>. Sow. W rtw v>w«A 1b ^
for M batlmsa two ttvi Ihk-k. ii wonW W Vi».W rtiax, at
^^^MUn^ oite foot thick. We w^W c»a Oi^
THE STABILITY OF AliCUEiJ.
187
dd of hoop-iron bond, Sir Mai*c-l8ainbanl Brunei built a
of bricks laid in strong cement, which stoo<l, projecting
biitnient like a bracket, to the distance of sixty feet, until
troyed by its foundation being undermined.
w-York City Building Laws make the following require-
arding brick arches : —
ches shall be at least four inches thick. Arches over four
shall be increased in thickness towartl the haunches by
of four inches in thickness of brick. The first additional
sliall commence at two and a half feet from the centre of
tlie second addition, at six and one-half feet from the cen-
e span ; and the thickness shall be increased thence four
• every additional fotti* feet of span towards the haunches,
aid brick arches shall be laid to a line on the centres with
int, and the bricks shall be well wet, and the joints filled
:?nt mortar in proportions of not more than two of sand
cement by measure. The arclies shall be well grouted
id, or chinked with slate, and keyed.''
r Radius of Brick Arches. — A good rule for the radius
ital brick arches over windows, doors, and other small
is to make the radius equal to the icidth of the openiny.
;s a good rise to
md makes a pleas-
rtion to the eye.
ften desirable to
lings in a wall by
an arch, when
ot sufficient abut-
) withstand the
kick of the arch,
case, the arch can
I on two cast-iron
s, which are held
>y iron rods, as is
Fig. 2.
his is done, it is necessary to proportion the size of the
ic thrust of the arch. The horizontal tlirust of the arch is
ly represented by the following formula: —
load on arch X span ,
Horizontal thrust = h X rise of arch in feet*
tension rods are used, as is geneva\\>f Wve e^'&ft, NX^fc ^Nasssfc-
rod can he detenninoA by the toWowm^ T>3\e.*. —
V Hi X rise, oi avc\\ \\\ ^'^AiV V.'Ve^'^^
JT
1S8 THE STABILITY OF ARCHES.
Tf only Olio rod is iis(h1, 8 should Ix* substituted In tlie place of | '^'''
Uk in tli<' diMioiiiinator of the al>ove rulti; and, if three rods are
ummI, 24 should Ih^ ummI instead of 10.
Centres for Arelies. — vl centre is a temporary stnictnre,
pMUM-ally of tluilMT, hy which th<* voussoirs of an arch are sup-
liortod whil(> the arch is InMng huilt. It consists of parallel frftmes
or rihs, ]>Ia('(Ml at convenient distances apart, curved on the outsklc
to a line parallel to that of the soffit of the arch, and supportin;;
a series of transverse i)lanks, upon which the arch stones rest
The most common kind of centre is one which can be lowered. or |^'
sti lU'k all in one piece, hy driving out wodgt»s from below it, sou
to rem(»ve tlie sup]K)rt from ever\- jwint of the arch at once.
The centre of an arch should not be struck imtil the solid partof
the bar'king has l>een huilt. and the mortar has had time to set and
harden ; and, when an arch forms one of a series of arches with
piei*s iM'tween them, no centre should Ih» struck so as to leave a pier
with an arch abutting against one side of it only, imless the pier bas
sufficient stahilitv to act as an abutment.
WluMi possible, the centre of a large brick arch shoiiUl not be
struck for two or three months after the arch is built.
Mecliaiiical Principles of the Arch.— In designing an
arch, the first (luestion to he settled is the form of the arch; and in
regard to this there is generally but little choice. Where the abu^
ments are abundantly large, the segmental arch is the strongest
form; but, where it is desired to make the abutments of the an'li
as light as possible, a pointwl or semicircular arch should be used.
Depth of Kei/f<fone. — Having decide<l uix)n the form of the arcli.
the depth of the arch-ring must next be decide<l. Ttiis is generally
determined by computing the requirtnl depth of keystone, and
making the whole ring of the same or a little larger depth.
In considering the strength of an arch, the depth of tlie keystone
is r'onsidenMl to be only the distance f^om the extrados to the intra-
dos of tlie arch: and if the keystone projects al)ove the arch-ring,
as in Fig. 1, the projection is considered as a imrt of the load on
the arch.
Then* are several rules for determining the depth of the key-
stone, but all are empirical; and they differ so greatly that it is
difficult to recommend any particular one. Professor Ranklne*8
IJule is oft.<*n quoted, and is probably true enough for most arches.
It applies to both circular and ellipticjil arches, and Is as follows: —
Raiikine's Rule. — For the depth of the ket/stone, take a
}))ofin ;>;7>portional between the inside radius at the crown, and
o. /y of a foot for a jsijigle arch, and 0.\T oi ^ iooX. \ot «liv m^\\^x\\v
Oj^^ one of a m^r'ivs. Or, if repnn*eu\e\\ Vj'^' ?». ^oy\\\\\\^.
THE STABILITY OF ARCHES. 189
' keystone tor a single areh, In feet
= >/ (0.12 X radius at crownl.
keystone for an arch of a series, in feet
= ^ (0.n X radius al crown).
i seema to agree very well with actual cases in urchea of
ind. By it, however, the depth of keystone is the same
f any length, provided the radius is the same; and in this
it aeema to us, the rule is not satisfactory.
vine's Rule. — Mr. Trautwine, from calculations intule
number of arches, has deduced an original rule for the
eystone, -which is more agreeable to theory than Ran-
is rule Is, for cut stone,
of key, in feet =
nd-ctaa» work, this depth may be increased about one-
:, or, for ftricil or fair rubble, about one-fourth,
iwing table gives a few examples of the depth of keystone
listing bridges, together with the depth which would be
I Trautwine'a or Rankine's Rule. From this table It will
it both rules agree very well with practice.
TABLE I.
yradlus -j- half span
i) + 0.!
2 foot.
ng Depth of Keyato
ne of Some ExMing Arehe*.
1
i
,
t
■s
■5
1
CilcuTuud
X."'
Engtonr.
Utif.
ai«le.
Stcelf.
; (draitar »re).
h
e
ft.
■i,«
h.
4.11)
.n, WMhIngton
Brid^,Clic.ier!
u/Tiirii. ItBly :
feMBtddBcl'hU.
brick In cem=nl.
a, Bdd IteulliiK
B 'ud 'Reading
aoo.o
3U
30.05
IS.UO
ft.
140.00
4.M
3.00
\
dpD TMK. UTAIIIMTV tIK AKcnr;s.
Ti.ble n„ Ukeii from T«Ht wine's "Civil Knginwrs' Huidbod
given llli' deplli of keystone fur arelies ot firal-class cut-stol
iwi-onlliig lo Traulwiiie'B Rule. For se^^o^a-claBs tul-stone, »
ttlioiil ojie-eiglith jtart, mid, for gooil rubble or brick, about og
(our III part.
TABLE 11.
rnhht ./ KmtoiifxM ^rehM cif Ki-«(-CW» 0K^8to»^ ■
>,.„
Itiss m rABTs or ms BfAX, ^M
IMI.
' i
i
1
i
t .
i
^
]
'It
"S"'
'"it
V'
';&"■
7«"-
"aJ
Ml
OM
d'm
oiss
iiW
o!bt
ua
.03
i.oa
l-W
":w
IJB
i.n
IJH
JIO
3
w
.49
J.W
•it
1.70
U>
K
tM
u
i!ss
!w
4JH
xu
4U
!.0G
U3
Ut
m
aias
:*4
iM
80
s'm
2.M
3.H
100
a^TII
i.;a
zIm
.09
a.a
120
bIm
a.w
3.8T
t.ii I
ino
sign
1
IBO
alas
4!06
4!ss
1
•M
:i.iifl
4,ii
4.1»
1
140
i.m
tioci
1
mi
4!m
■
m
■
m
4.M
4.62
4.W)
Jl
n«ving deeidBd what tlie thickness of the ai'eh-ring will Iw. <l|
mmains to determine wliether such an arcli woulil be stable B,
built.
this point: -
EXAHI'LE I.— Untnailed Hnniclifiilar arch ijf tO fool nfOtu
nrst, to Hud the depth of keystone, we will tnke Kankine'»Bnler
Uld by it we have,
Depth of key = \J»A'i X 10 = Vl.ii = I-l fool.
T/nulwiiie's Rule would givi' WM\'i \\w same, ot, J
, l/i!Lti? + „.,,„i»,.a„»,v. J
fllTY '
)i|.;s
mi
, if w«shiiiitd rompiit* tlir sluhlHty of u si'iriic-iri'ulnr areh nf
t span, anil 1,3 fnol rlpiitli of ki-y^'Mii'. wi- ulioiild flnii t.ljnr
oh was very unstiihlp: hencp. In tliip I'Kw. we :iiust|tbrow ilii'
lalde, anil ^ by our own jittfgmmt. In the opinion of thi'
r, sncli an arth shonlil liavp at leaat 3) feet dnptli of arcli-
and we will try the stability of the an-li wltli that thickness.
»11 calcnJallons on the arch, it is eiistoniary to consider On-
to be one fool thick at right angles to its face; forit iseviileiil.
if an a,reh one foot thick is nlahle, any niinil>erof ai'cliwiof llii'
rtiniensions built ftlongsidi^ of it woiilil h" stable.
■aphic Solution of tlie Stability of the Arcli.—
most ponveniwil nirtlio"! of ilelerminin}! Uih Btnhililyof tin-
is by the gtiiphic nietlio<t. as it is called.
r Step. — Draw one-half the arrli to sb large ii scnb- na con-
nil, and divide It up into voitssoirs of pijual sixe. In this
iple, shown in Fig. 3. we have divided the arcli-ring into ten
1 vouBBoirs, (It is not necessary that these should lie the
il voussoirs of which the arch Is built, ) The next step ]» to
ihH area of each vousaoir. Where the amti-ring Is divided into
salrs of equni sixe, this Is easiest done by computing the area
Auch-rinB, and dividing hy the number of voiivsolrs.
Flg.3
tefOT rti-en i.f ane-h'ilf •>/ arck-rhin is as follows: —
» in square feet = 0,7854 X (outnide radius squared -- inside
B squared).
this example the whole area equals 0.1854 X (12.6^ ~ 10=) =
quare feet. As there are ten equal voiissoii's, the area of each
oir is 4.4 square feet.
'iBgdmwa oat one-half of the arch-ring, -we a\\\C\c. wuJ* ^■vft,
x; equal pans; ami from the pomt A l,T\g. ■?.^ -wft'V*-! 'A^
IIP. IwloNxtheoOawiO ""
ttoaret
^^^^^P^ THE STABILITY OF i
with thp top vouasoir. The whole length of the line^ff will
liie whole area (irawii to 3»nie scale.
The npxt step is to tind the vertical line passing throogli
centre of gravity of the whole arch-ring. To do this, it is
necessary to draw vertical lines through the centre of gravis
each TousBOlr. Tlie centre of gravity of one voussuir may b« (a
hy the method of diagonals, as in the second vouHSolr from the
( Fig. 3). Having the centre Of gravity of one voussoir, the eenl
of iiravity of the others can easily he obtained from It.
Next, from vl and £ (Pig. 3] draw lines at 45° with AE, id
secting at O. Draw 01, 02, 03, etc. Then, where AO InteM
the Hrst vertical line at 0, draw a line parallel to Ol,
the second vertical at h. Draw he {nraliel to 02, cd parallel U'
and BO on to kn parallel to 010: prolong this line downward B
it intersects AO, prolonged at D. Then a vertical line ilri
through I> will pass through the centre of gravity of the arch-rii
2d IjTBr. — Draw a horizontal line through A (the upper pMt
the middle third), and a vertical line through Z); the two
intersecting at C (Pig. 3). I
Now, that the arch shall he stahle, it is considered necessary tbi
It shall be puasihie to draw a line of resistance of the arch nitUl
the middle third. We will, then, lirst assume that the line (ji
resistance shall act at A, and con
Then draw the line CB, and a horizontal line opposite the
10, between Q an<) P. This horiEontal line represents the 1i
zontal thrust at the crown.
Draw AF equal to yP, and the lines PI, P2, P3, etc.
Then, from the point where AC prolonged
vertical, draw a line to the second vertical, parallel
this point a line to the -third vertical, parallel to P2 ; and
The last line should pass through it. If these lines, which we
call the line of resistance, all lie wltldn the middle third, the
may bt: considered to be stable. Should the line of resistance ;
outside of the an-li-ring, the arch should be considered mut
In Fig. 3 this line does not all lie In the middle third, and we
see if a line of resistance can yet be drawn within that limlL
2u TuiAL. — The line of resistance in Fig. 3 passes lartbest
the middle third at the seventh joint from the top; and
pass a line of resistance llirongh A and where the lower Una Ol
middle third cuts Uie seventh joint, or at 1) (Fig. 4),
To &o this, we must prolong the line gh, parallel to OT f Fig.'
^Igiff-^auaraecta AO. lu this case "rt ^nVeratscVa \v. «)i.O:\»&'i
MHhMffili ooJaciileiicc; it would not b.\'n&-ib &o
^^^H(aH{cBJ interaecUng PA. pcoVon&eA n.l, G. 'Qtv»
TUB STABll.l-1
ARCHES.
rough C and D, and the horizoDtnl line pi}, opposite the point 7:
!s line represeatfi tlie new hortzontSil ttinisC H\. Draw
a,»nd the lines PI, P2, etc; then draw the line o[ realaWwe
t before. It alionld pass through D if drawn eorreeily. ThLs
ime we see timt the line of resistance lies within the middle third,
s«ept jnst a short distance at tlie springing; am) hence we may
nnsider the arch stable. If It Iiad gone outside the middle third
iUe time, to any great extent, we should have considered the ftrch
nnetable.
The above is the method of determining the stahllity of an
unloaded eemfclrcular arch. Snch a case very seldom ocean In
pnctlce; but it is a good example to illustrate the metliod, which
Itflles U) ail other cases, with u little diSerence in the method of
nmlnlog the centre of gravity of loaded arches.
Fig,4
EtAHPi,E n. — Loaded or mtrcharued semiclrculnr arcli.
We will take the same arch as in Example 1., and suppose It to
w loaded with a wall of masonry of the same thickness and weight
per square foot aa that of the arcb-rlng; the horizontal surface of
"w wall being 3 feet 6 inches" above the arch-ring at the crown.
IstStep. — Find centre ofgratity.
Commencing at the crown, divide the load and archning Intft
•Wps two feet wide, making the last strip the width of the arcli-
'^ at the springing. Tlien draw the joints as shown in Fig. U.
Measure with the scale the length of each vertical line, Au, Rli,
^.; llien the area of A'llili Is equSl to the length of Aa + Bb, as
lie distance between them is jnst two feet. The area of SfKk Is.
'f course, fjCx. wiihh of arch-ring.
In this case, thearcHsof the slices areasabavitiVjAit'Si^Teaiw.
XowdMile the arcli-ring into thirds, and ^rom ft\e \ws «A "Oj
Jl^fW.at H, toy off in aucco.ssiow, to a a?a\fi,\>\e ««*
194
THE STABILITY OF ARCHES,
AtA I''
oghtb
the alices, comDumciDg with the flist slice from the crown, JtBL |
Th<!se areas, when meaaured ofF, will be represented by tha tb
£1,2,3. . .6 (Fig. 5). From the extremities of this line, Bull, I
ilraw lines at 45° with a vertical, intersecting at O. From 0 di
Itnca to 1, 2, 3, 4, 6, and 6. Next, draw a vertical line thraoghtb
ivntre of each slice (these lines, in l^'ig. 5, are numbered 1,%!,
etv. ). From the point in which the line RO interaecU verticil I,
draw a line parallel to 01, to the line 2. Frorn this point dr»Bi
line to vertical 3, parallel to 02. and so on. The line panlld Is
05 will intersect vertical 8 at Y. Then through T draw a
downwards at 4b°, lutersectlng OB at X. A vertical line dnwi -
tlirough X will pass through the centre of grsvlty of the arctHlni
aud Its load.
iTtSzsP. — TofindthethruHat the crown and M Ui» aprinsiiit-
To find the thrust at the crown, draw a vertical line through X,
an<l a horizontal line through K, intersecting at V. Now, the weight
of arch and load, and the resultant thrust of arch, must act tbrongb
this polnL We will also make the condition that the thrust shall
pass through Q, the outer edge of the middle third. Then tb«
(lirust of the arch must act in the line VQ. Of^mslte 6, on the '
vertical Hue through R, draw a horizontal tine H, between VX '
and VQ. This horizontal line represents a horizontal thrust at B,
which would cause the resultant thrust of the arch to paas throng
(>. Now draw tlie horizontal line ItP. equal in length to B, and
f/vm J" liraw lines l,2,:i . . . n. Th«l\w. l'ftTe¥T«»wo.1»\hftthnut
of the arch at (Ite springing. Its amowW m cvftAc \vA. cA xoMneri
c»a be detfmtlneit by iiieasiiriiiit its Vi-nii?.\\ lo \-\»- vv«vv »"*<-
^ THE STABILITY OF AEfUKS, ^^^^^^^
'nf-.p. — To dram the line <tf' resistance.
liaes PI, P2, 1% eu-., represent, the iiiagniLuilc mid iljrcc-
: the thrust, U eiuli joint of tlie arch. Thiu /'I represents
rust of the first voossoir &nd ita loud ; P2, that of the first
lUBSoirs and their loads- and so on. Then from the point a',
the line RP, proionged, inleraectB the vertical Une I, draw
a'li' pumllel to PI; from &', on 2, draw a liiu' ''V purallpl
and ao on. The last Une aliould pass throtifh fj. and Ih-
■I to Fa.
; it we eonneet the points whura tlie lines a'b', li'e', eW., cot
nts of the arch, we shall have a broken line, wlilch is known
line of resistance of the ai^:b. If this line Ues within the
: third of the areh, tlien we conclude tliat the ardi is st^le.
line of resistance goes far outside of the middle, we must see
B possible to draw another iine of resistance within the mid-
ird; and if, after a tiial, we iUid that It is not possihie, we
conclude that tlie arch is tiot safe, or unstable,
lie example which we have just been discussing, the line of
nee goes a little outside of the middle tltird; but it is very
lie Chat on a second trial we should Bnd that a line of resist-
jtssed through S and Q* would He almoat entirely within the
: third.
methoil of drawing the second line of resistance was
iii-d uadet' Example 1. ; and, as the same inetliod ajiplies to
es, we will not repeat it.
method given for Example n. would apply equally viell for
-elliptical areh.
iMPL£ in, — Segiiimiial arch, icilb load (Pig. (1).
Stbp. — To determine the centre df gravity.
his case we proceed, the same as in the latter, to divide the
ing and its load Into vertical slices two feet wide, and compute
3a of the slices by measuring the length of the vertical lines
f), etc. Having computed the areas of the slices, we lay them
order front j;, to a convenient scale, and tlien proceed
pi as in Kxaniple il., the remaining steps determining the
; and the lines of resistance are also the same as given under
Jle li.
flat segmental arch, there is practically no need of dividing
:h-riiig Into voiissoire by joints radiating from a centre, but
Blder the joints to he vertical. Of course, when built, they
teniado to mdlaie.
(t shows the eouiputalion for an arch of -Ut-Coot s^ton, and
Joarf I3i fft-t h/gJj at the centre, 't^vv, iVv^-V q\ >3sv'e.'M'ift-
mtiuvn. Htm til.- .-iirvp ot p\vssi«i-.s Vws eWVXteVj ■*i'.''N^
TMi StAUlLlTY OV \liCHK3,
KU>e middle ttiinl; and hence the nreh is nbnndantly si
Ktt should be remarked, that the line of resistance in a
Lkrch flhoiild be drawn IhrQUgh the low^ edge of the K
I U the sprlugiug.
iy safe, ori
e in asegn
the MMMj
4
It will be noticed that the horizontn] tliriut, and the tbM
Mt the springing, are very great as compared viith ttaoMinftl
ll*n:b; and hence, allhougli ttie aewoMOsJ. «t^^
t tbe two. It requires muc\\ \\ca.v\et dD<ia.Tiraia».
s examples sfrve. to s\idw Uie weVhcAot 4sMI
y-Md tl*r.Wt of nny «r.,U mw\> a^ \a vwi \tv\mH
which any material offers to being pulled aparl
tenacity of Ita fibres, or the cohesion ciC the partictes
composed.
it that the amounl of resiatanee to tension which any
of a body will exprt depends only upon Ihe tenacity
'Of the cohesion oC ita particles, and upon the number
irticles, in the cross-section.
iber of the fibres, or particles, in the section, la pro-
tlie area, the strength of any piece of material must be
t its crosB-aectlon; and henra, if we tnow the tenacity
lal per aiiuare Ineh of cruas-Hei^loti, we ciin obtain the
h by inidtiplying It by the area of the section in
tty of difFerent building-materials per square inch has
tg pulling apart a bar of the material of known dimen-
Hviding the breaking-force iiy the area of the cross-
yes the average values for the tenacity of huildlng-
determined by the most reliable experiments.
tenacity of one square Inch of Ihft material, all
to determine the tenacity of apieceof any uniform
hlply the area of its croBs-sectlon, in square inches, by
the table opposite the name of the material. This
K weight that would just break the piece; but, as what
safe toad, we must divide the result by a factor of
engineers advise using a factor of safety of five foj'
'ftltliough tlie New-York City and also tbe Boston
require a factor of six,
fftCtor of safety by S, and the tenacity by T,
I
KKSlSlANC't; TO
STONKB, IjRroKS, AND
OetLnl, PonlBoci' (Eni.)
Csmentt l*ortlaiid (^ayJot'i
Uortu, hydiaullo!
Uorur, EDmmon. ili
Mm-ble, CbiuiiplulD, varle
gated
UBrfali!, Lee, Mhu.. whJLe
UhtIiIi, UanclUHtor, Vt. .
Uarble, Tonnone«, varte<
rtd
u>, ioaia»ii. . .
— - M-adii, woilfM .
-_..,, Dhlu . ■ . . .
LnhlBli ....
Met* 1.1.
-BnuawIrD, utwniiMted, .
Cuppsr, aheit , . . . .
Metals (coHtlnutd).
t'lHt-Iron, Engltih . .
CaM-lron. onJioary pig . )
WroiigbMrou, rollnl ban,
Wrougiil-lraD platra ! '. '.
Steel, Bmsemir ....
etfol bara, rolled nnd ham
Fir, New -England
Hi-mlock ....
Hlokary, Ameduan
Maple, white . .
Oad, while . . .
» roiiiiil Imr,
Safe loitd =
0.78fi4 X ilianieter stiuared >
Si
m
3
T
- m
ExAMPi.K I. — Wliat is the safp load for a tie-bar of vUteiJ
8 by 6 indies? t
Ann. Here the brt-ailtli and ileplii both equal ll iiicheB, T =
&nd we win let .S = 5; then,
Kafe load =
< B X 7)HMI _
riO4O0 1bs.
RESISTANCE TO TENSION. 199
^ the size of the bar is desired, we haye.
8 X load
>readth = j
For a round bar,
The breadth = 5^^^^^^ (3)
S X load
Diameter squared = 0 7854 x T ^^'
Example II. — It is desired to suspend 20,000 pounds from a
)x>und rod of wrought-iron : what shall be the diameter of the rod
*o carry the weight in safety ?
An8. In this case T = 50,000; and taking S at 6, we have
5X20000
Diameter squared = 0.7854 x 50000 = ^'^'
The square root of this is 1.6 or If inches nearly: therefore
the diameter of the rod should be If inches.
Tensile Strengrtli and Quality of Wrouglit-Iron.
The best American rolled iron has a breaking tensile strength of
'from fifty thousand to sixty thousand pounds per square inch for
-specimens not exceeding one square inch in section. Ordinary bar-
iron should not break under a less strain than fifty thousand
pounds per square inch, and should not take a set under a stress
less than twenty-five thousand pounds per square inch. A bar one
inch square and one foot long should stretch fifteen per cent of its
length before breaking, and should be capable of being bent, cold,
90° over the edge of an anvil without sign of fracture, and should
show a fibrous texture when broken.
Iron that will not meet these requirements is not suitable for
structures ; but nothing is gained by specifying more severe test s,
because, in bars of the sizes and shapes usually required for such
work, nothing more can be attained with certainty, and conscien-
tious makers will be unwilling to agree to furnish that which it is
not practicable to produce.
The working -strength of wrought-iron ties in trusses is generally
taken at ten thousand pounds per square inch. In places where
the load Is perfectly steady and constant, twelve thousaud pounds
may be used.
The extension of iron^ for all practical purposes, is as follows : —
IVrougbt-iron, rwooTf of its lengtli per tow \)et ^c\y\axfe \wOcv.
Cast-iron, ^nftru of its length per ton per acvwar^ vc\e\\.
204
RESISTANCE TO TENSION.
Table VII. gives the weight and proof, or safe strength, of chaiiu
manufactured by the New-Jersey Steel and Iron Company.
TABLE II.
Strength of Iron Rods,
Safb Tbnsilb Strbnoths of Round Wrought-Irok Rods i to 4 Ixchib
IN Diameter, and the Wbiohts per Foot, the Safb Strength bei»«
TAKEN at 10,000 Pounds per Square Inch.
Diameter in
inches.
Weighto
per foot.
Safe
strengths
in lbs.
Diameter in
inches.
Weighto
per foot.
Safe
•trength
in lbs.
:
1
1
1 »
1
M % 9 9 m •
-
1 • . . . .
> 11
■MM • • • • •
ll
1 ij * • • • •
1
! 2 ! ! ! ! '.
1
I
1
0.041
0.165
0.872
0.661
1.04
1.49
2.08
2.65
3.35
4.13
5.00
5.95
6.98
8.10
9.30
10.58
123
491
1,104
1,963
3,068
4,418
6,013
7,854
9,940
12,272
14,840
17,670
20,730
24,050
27,610
31,420
2|
n
2|
2i
2|
23
2|
3
3|
H
Si
3i
H
3i
31
4
11.05
18.80
14.02
16.58
18.23
20.01
^1.87
23.81
25.88
27.94
30.13
32.41
34.76
37.20
89.72
42.88
85^
80,760
44,800
40,080
54,110
59,860
64,910
70,680
76,690
82,950
89,460
96,210
103,200
110,4W '
117,080
125,660
RESISTANCE TO TENSION.
205
TABLE III.
Safe Strength of Flat Rolled Iron Bars,
1 .
Width in iDches.
i1
' a
■ ••«
1"
ir
ir
1}"
2"
2f
2f'
2}"
3"
3f'
ibe.
Ibe.
Ibe.
ibe.
Ibe.
ibe.
lbs.
IbB.
lbs.
lbs. :
tV
630
780
940
1,090
1,250
1,410
1,560
1,720
1,880
2,030
i
1,250
1,560
1,880
2,190
2,500
2,810
3,130
3,440
8,750
4,060
ft
1,880
2,340
2,810
8,280
3,750
4,220
4,600
5,160
5,630
6,090
i
2,500
3,130
3,750
4,380
5,000
5,630
6,250
6,880
7,500
8,130
A
3,130
3,910
4,690
5,470
6,250
7,030
7,810
8,500
0,380
10,200
)
3,750
4,690
6,630
6,560
7,500
8,440
0,380
10,300
11,300
12,200
ft
4,380
5,470
6,560
7,660
8,750
0,840
10,900
12,000
13,100
14,200
i
5,000
6,250
7,500
8,750
10,000
11,300
12,500
13,800
15,000
16,300
ft
5,630
7,030
8,440
9,840
11,300
12,700
14,100
15,500
16,900
18,300
i
6,250
7,810
9,380
10,900
12,500
14,100
15,600
17,200
18,800
20,300
H
6,880
8,590
10,300
12,000
13,800
15,500
17,200
18,900
20,600
22,300
i
7,600
9,380
11,300
13,100
15,000
16,900
18,800
20,600
22,500
24,400
i«
8,130
10,200
12,200
14,200
16,300
18,300
20,300
22,300
24,400
26,400
J
8,750
10,900
13,100
15,300
17,500
19,700
21,900
24,100
26,300
28,400
H
9,380
11,700
14,100
16,400
18,800
21,100
23,400
25,800
28,100
30,500
1
•
10,000
12,500
15,000
17,500
20,000
22,500
25,000
27,500
30,000
32,500
ft
10,600
13,300
15,900
18,600
21,300
23,900
26,600
29,200
31,900
34,500
li
11,300
14,100
16,900
19,700
22,500
25,300
28,100
30,900
33,800
36,600
ift
11,900
9
14,800
17,800
20,800
23,800
26,700
29,700
32,700
35,600
38,600
It
12,500
15,600
18,800
21,900
25,000
28,100
31,300
34,400
37,500
40,600
li
13,800
17,200
20,600
24,100
27,500
30,900
34,400
37,800
41,300
44,700
li
15,000
18,800
22,500
26,300
30,000
33,800
37,500
41,300
45,000
48,800
If
16,300
20,300
24,400
28,400
32,500
36,600
40,600
44,700
48,800
52,800
1}
17,500
21,900
26,300
30,600
35,000
39,400
43,800
48,100
52,500
56,900
11
18,800
28,400
28,100
32,800
37,500
42,200
46,900
51,600
56,300
60,900
'/
20,000i
26,000j
30,0001
SOyOOO
40,000
45,000
50,000
\!>b,OK»W,WftVNb^^
\
BESI5TANCK TO TENSION.
Table VII. gives the weight anil proof, or safe strength, a
manufacttireiil by the New-Jersey Steel and Iron Campanr.,
TABLE II.
Strength (if Iron Hoc
ISTHB or Round WROcaBi
THB WeICIHTS FSH f DOT, 1
inNon PER SqcARi Imcu.
Bsfo
RESISTANCE TO TENSION,
TABLE III.
aaf« Strength <^ Flat Boiled Iroa Ban.
WIdlh Id iDchH.
1"
11"
H"
11'
2"
2J'
2i"
ar
a-
3f'
1
ItHk
1.880
J,SOD
3,130
4,3Sa
s.eai
8,260
e.8«i
T.5O0
8,130
8,5fl)
9.3SO
10,000
[3,800
15,300
7i(,S«
•o.oaol
AO
340
SM
470
030
810
MO
200
500
,300
flOO
900
Ibg.
1,8BD
3,1»U
4,000
8,600
0,380
10,300
11,300
14,100
15,000
16,000
18,800
20,800
21,600
W,400
SSMK
Rm.
1,000
2,190
3,280
4,380
6,470
7,«W
8,750
9.840
10,900
13,100
14,200
18,400
n,5«o
19,700
24.100
28,300
28,400
30.1100
32.800
3,760
8.250
8,760
10,000
11,300
12,600
10,300
18,800
22.500
27,600
32,600
1,411)
2,810
5.B30
7.030
9,840
14,100
18,900
10,700
25,300
2S,100
30,900
38,800
42,200
45,000
Ibg.
3,130
0,260
10,900
16,800
20,aoo
23,400
25,000
20,800
28,100
29,700
40,800
\w.00
1.7M
3.440
fl,8flO
8,690
12,000
20,800
22,300
25,800
27,500
E
37,900
41,300
14.700
A
880
750
BUO
800
100
000
900
800
600
400
300
000
OOO
BOO
500
300
800
8
'-*
:»
S2
!8
10
S2
M
hO
12
200
200
401)
500
500
800
800
^
1
soa
RESISTANCE TO
TENSION. ■
i
1
(7p«el .Sei-eio
En<la. 1
1
-""— ■
~ J
h
11
1
1
lis
!i
IJ
i
1
1'
jl
= ■3
.3
1
i^
1^
1
f
2
^g
"
ss
^£
M
mi
^
u*
s
5
?
5'
l»«h».
Inchei.
[noha.
no.
perceni
i.cb»
Inoheik
DO
per-,
2*
%
2.550
4
t
2.754
ij
18
4
4
2.5S0
22
2.879
2S
iJ.
3
3*
3'754
3
28
1
3.004
3.004
1}
2«
IS
2i
3|
2.754
3*
21
3»
3.100
n
21
A
3!
2.87«
«1
26
31
3.225
24
?!»
3
2.879
a.004
?t
20
25
1
3.225
3.317
i*
SO
ifi
tl
y.004
■H
19
1
3.442
3
23'
3.100
3i
3.442
3
18.
S,
sj
3.225
it
26
8^67
3
21
31
3.225
21
«*
3.ii»2
3
24
3
1
3.317
3
22
3
3.692
3
IS
3*
3.442
3
21
21
24
1
4
3.667
3
20
!|
4.028
if
21
<lt
3.692
3
20
4.153
U
H
ii
3.798
4.028
1!
IS
^3
3»
J}
4.15;i
1
23
»«
4.255
21
:
Rb:
.HKB.-
•trenglh ol Itod, bkn IWTlaa: IM
'"«"
n UMtlHl to dHlninllon, wl
■ Iheretora ueouAry uj idk
r Ih« bar tiivarlBbly hmk \\ m
lioui d<.vel<»>liig ibi^ futi >tnag
ke up for tiJs loM In Mniwtl^
ol 111 Ihu upwl Bcrew-ODds
ovi.rlh.llnlhel».r. ^
u» Mia on flulihcd tNiniudlt
TlH,
/
,i£S«^/
nlDnc 1
he^r to'C/k'n xh^^"
/ TAB
rewjii In above utile an tVi
uFi™v.\\\>\mi&\.«o.Aj™&»A. -t
1 Tom
nke OH
uuul end tot live Inobt
A£»
rod ad
r
1
r
^
BE818TAHCB TO TENSION.
TABLE T.
Strength <if Iron and Steel Wire Rope»,
KUETACnrBID BT THS JoBH A. ROEBLIMS'a SOUS Co., ITlW TOBK.
IK
^
~~c^
TB«-.
Wtigbl
Tnule
pr f«,l 1.1
Proper
Proper
midilsr.
iDcbea.
'»"■""•■
in'^u".
worlitne
lu'™!.-.
7S,'
Wl7
B NmlTEEK
THE 8TB
AXD.
1
St
8.00
74.00
15.00
i-mo
2(1.0
2
6.30
fB.OO
13.00
IO0.(J
21.0
3
5.2.->
.'■.4.00
11.00
78.0
17.0
4
4.10
44.00
U.00
w.o
13.0
5
a.M
30.00
8.00
M.O
11.0
Si
1
3.00
3:j.00
0.50
6
2.50
27.00
.'>..W
30.0
8.0
7
2.00
20.00
4.00
:f0.0
li.O
8
1.58
10.01)
3.00
ai.o
5.0
9
i
1.20
11.50
2,.M1
20.0
4.0
. 10
I
0.88
KM
l,7.'i
13.0
:!.0
, '*>*
4
0.70
.1.1:!
hir,
0.0
2,0
1 !S!
0.44
4.27
».r>
J. 5
?
0.:ti
a.48
0..50
r,'.'b
1.0
r
w
TU 8ETEH W
UK Htrar
».
3.37
30.00
0.00
67.0
10.00
12
2.77
30.00
7.50
55.0
1:i..-iO
13
2.28
25.00
B.25
45.0
10.00
14
1.82
20.00
5.00
36.0
8,00
15
l.-W
10.00
4.00
30.0
0,50 1
m
1.12
i2.ao
3.00
22.0
17
a88
8.80
2.2.1
17,0
3>.0
18
0.70
7.»0
2.00
13.5
3.0(j
1»
I
0.67
5.80
1.50
10.0
2.25
20
0.41
4.10
1.00
8.0
1.75
21
0.31
2.83
0.75
0.0
1.2S
22
0.23
2.13
0..W
-
23
0.19
1.65
4
1.00
'H
0.18
1.38
3
0.7fi
25
a
0.126
1.03
\ ",.
^"
•1
210 RESISTANCE TO TENSION.
Ropes, Hawsers, and Cables.
(UASWKLL.)
Ropes of hemp fibres are laid with three or four strands of
twisted fibres, and run up to a circumference of twelve inches.
Hawsers are laid with three strands of rope, or with four rope
St rands.
Cables are laid with three strands of rope only.
Tarred ropes, hawsers, etc., have twenty-five per cent less
strength than white ropes: this is in consequence of the injury
tin* fibres receive from the high temperature of the tar, — 290°.
Tarred hemp and manila ropes are of about equal strength.
Manila ropes have from twenty-five to thirty per cent less strength
than white ropes. Hawsers and cables, from having a less pro-
portionate number of fibres, and from the increased irregularity
of the resistance of the fibres, have less strength than rox)es; the
difference varying from thirty-five to forty-five per cent, being
grt;atest with the least circumference.
Kopcs of four strands, up to eight inches, are fully sixteen per
cent stronger tlian those having but three strands.
Hawsers and cables of three strands, up to twelve inches, are
fully ten per cent stronger than those having four strands.
The absorption of tar in weight by the several ropes is as fol-
lows : —
Bolt-rope . . . .18 per cent
Shrouding . . 15 to 18 per cent
Cables 21 per cent
Spun -yarn . . 2.5 to .30 per cent
AVhite ropes are more durable than tarred.
The greater the degree of twisting given to the fibres of a rope,
etc., the less its strength, as the exterior alone resists the greater
portion of the strain.
To compute the Strain that can be borne Mith
Safety by New Ropes, Hawsers, and Cables,
<leduce<l from the Experiments of the Russian
Government upon the Relative Streugi^h of
Different Circumferences of Ropes, Hawsers,
etc.
The Vni ted' States navy test is 4^00 pounds for a white rope^ oj
three strands of best Riya hemp, of one and three-fourths inches in
circvmference (/.e., 17^000 pounds per square inch); bvi in thefd-
lowing table 14,000 pounds is taken as the unit of strain thai can
V ^me with /tafety,
"'TL.K. — Square the circumferenw, ol Wve, to^>\wi(^»^^Xft«^«&&.
'i following units lot oTvWwwt^ xoie«»^ '^fc*
BB8ISTAMCB TO TENSION.
TABLE
howinif the Unltt for crmtpntii'a the Si^e Strain that •>
borne Ajr RnprK. llamxfrii, nnd CaNf».
ao„..
"'-■•■
Cab
...
w.,„.
r.™,.
While
T»r-.l,
4Sn
Whit«.,Tl>rri
1
s
1
1
1
i
1
■1
1
4«l
iil
CIreumtcrence In Ipo.
WMW rope, 2.5 to 8 111..
Whlw ro]*, B lo s liiM. .
»UtaroU«^t<^l|l|iB.
VTMleropelMio-Mlu.!
Tir»dro|)«,2..Tlo-'iin».
I.mdm^;8WK']«:
TiiTedropc,12lol>tlnt
Twredrope.lSloSOln..
ll"llaro^;iaioia(n!:
ll>nll(rope,l8Ui:Miiis.
llw.
1.14(1
ew
S33
1
11...
■a
I
■1
:
Wbea it is reqiilreil to ascertain the weight or atruin Ihiit run
>« borne by ro]ie«, etc.. In generai use, tbe above units slioiikl Ix^
'educed one-third, in order to meet the reduction of their atrfngt)!
>y chafing, and espo3ur« to the weather.
TABLE VI.
Strength and Weight of Manila Rope.
d
g
d
1
K
*
■*■
s
2
^
:3
°
-
3
E=
c
is
In<
Inn.
Ih.
ion..
,n.
l».
lU.
'-" /
IL
10.97
\"
\...\^.-V-
RB81STANCE TO TENSION.
TABLE VIL
Weight ond Proof Strength of Chain.
IflHVTACTIIRBD BT THB NEV-JKBBCT STICL AKD IboH C
Stud Cuain.
Suon
T LINK OUAtN.
X.B.Cr.«i|
aiiB
BTrighl pcT
Proof.
B1z«
'w'i2S°
I'roof
I'roof
tuthDID.
faltaDDi.
1 ma
JIM.
Lon,
iDdlHI
Itaa.
^.«
lOB.
33
38
43
10 '
12
14
a'
7
T
i
50
Ifl
i
»i
2
U
1
58
18
12
4
65
eo
15
*1
4)
72
2;i
19
5i
1?
80
88
20
28
A
25
30
7
7
81
es
81
35
8
10
no
2A
40
»t
lit
114
37
47
11
13
127
54
I2J
14i
138
1
61
14
la
ifi
150
48
Si-
68
16
19
157
52
76
18
21
ISi
no
5t)
ll'k
85
20
23
184
00
95
23
25
ils
200
64
103
24
37
314
tiM
113
26
20
2
2^0
72
123
31
I
250
60
13:J
SO
33 1
2U0
ss
BBSIBTANCE TO SUEAKUIG.
CHAPTER X.
RB8I8TAITCZI TO SHEARHTO.
ir abaaiag ig meant the pushing of one part of a piece b; the
er. Hog in plg, i, let abed be a beam resting upon the aup-
9 SS, which are very near togpther. If a aufflciently heavy
resistance of a body V
a, directly proportional tt
/ere placed upon the beam, it wouiU cause the beam to brealc,
* beuding, but by poabing tne whole central part of the beam
;li between the ends, as represented in the figure. Tliis mode
;ture is called "shearing."
0 shearing is, like its resistance to
,he area to be sheared. Hence, if
8 square inch of tlie material to
ng by F, we shall liave as (he safe resistance to shearing,
Safe shearing ( _ area to be sheared X F
strength t ~ ~ « " ' ' '
oting factor of safety, as before
ieee of timber may be siieared eilher Inngittichnally or Irans
y; and, as the resistance is not the same m both cases, thf
o( F will be different m the two cases Hence, m sulisti
; values for F, ne must distinguish nhtther the force tends
ear the piece longitudinilly (lengthwise.) or transit rsilj
a).
le I. gives the value of F, as determineA \>^ ex'^\\m«w\.,VOT
•si common njaienaN employed \\\ arctaWt^vwsOi s.ca*sx).
ILKS1STA^■CE TO aHEAEING,
uofiiff the RegUUinne of Materials to Sfteorinff, both 1
dinally and Transverselj/, or the VtUuet tf F.
«.„..„.
V.lu-offf
c:„,.,„„
■as
610 <■
4-0 d
732*
lla.
Si
s:
There are but few cases In ai'cliitectural construction in wbicli
Llie resistance to shearing has lo be piwiiled for. The one WM
frequently met with Is at the em\ of a tie-beam, as Id Fig. S.
The i-afii^r / sa 1 & ul 1 t da o p isU or shear oft tb
ilece Alien, &ml ilic area of the section at CD should offer enoug
u keep tlie rafter in place. Tlils area U eqoal to d
b Klrkaldy. c Trmtwlue. inntfitW. 'V^ijM&SuahQiIii*
RES18TANCE TO SHKAKINU.
215
times the breadth of the tie-beam; and, as tlie breadth is fixe<l, wo
have to determine the length, CD, If we let // denote the hori-
lontai thrust of the rafter, then, by a simple deduction from
formula 1, we have the rule: —
length of CD in inches = yi^^-^u^^^Tl' <2)
F, in this ease, being the resistance to shearing longitudinally.
Example 1. — The horizontal thrust of a rafter is 20,000 pounds,
the tie-beam is of Oregon pine, and is ten inches wide: how far
should the beam extend bt^yond the point D f
Ann. In this case // = 20,000 pounds, and from Table I. we find
that F = 840; 8 we vnll take at 5. Then
5X20000
= 10 X 840* ^^ nearly 12 inches.
Practically a lai^e part of the thrust is generally taken up by an
iron bolt or strap passed tlirough or over the foot of the rafter and
tie-beam, as at ^ (Fig. 2). AVhen this is done, the rod or strap
should be as obliquely inclined to the beam as is possible; and,
Whenever it can be done, a strap should be used in preference to
s rod, as the rod cuts into the wood, and thus weakens it.
Another common case in which the resistance to shearing should
be considered is in the cas<^ of iron pins and wooden tree-nails.
If we have three bars fastened together by a pin, and each pull-
ing in the direction indicated by the arrows in Fig. 3, they will
tend to shear off the pin at the sections a u.
11
I I
' bun J'
Fig. 3.
If the puU exerted by the tie B be denoVed \^^ H^ ^Xv^'cl «m3ci
action of the pin wiW have to resist one-VvaVi H, ^ >Xv«^
Diameter of wooden pin in inch««
216 RESISTANCE TO BHEARING.
^Bl»o ieipUons to rt^isi ilir whole. TIipm. fmiii Rule t,
^bw follow!
I
= yjiM
Diameter of wronglil-iTOn pin in inches ^ W.--^^ (41
- / "
forninla 8, F is the resUlanct: lo sliearint; transversely.
II. — Suppose the liar U 1b pulling wltli a force
.STi pounds: WhaX should Im' the diiinietei' of an iron [un
resist it ?
lji:!72 .
Ans. Diamei*r — Siiuare root "i
^iw
l.iTilS ~
square root o;
'. "These are tJxmt the only two i;nsK» in wliltli nipture bj
Is liable lo take place in arphileelural construction.
Btrengtli of riveted joints Involves the consideration of she
but the architect seldom has occasion to calculate tlie stren
■uch Joints: and, as the iiuestion of rivets is a ratli^r comid
one, it win not be discussed in this chapter. A description
more common forms of rivet«d joints will, however, 1ie [ounA
Chap. XXIX. Occasionally a large beam of short span, siwUi
ten by ten Inch beam, two feet long, needs to be computed Hi
reference to shearing at the points of support: but such heamii
not occur in building construction; and, where they do occur, 111
can btt computed by fonimla !.
STRENGTH OF POSTS, STRUTS, AND COLUMNS.- 217
CHAPTER XL
RISNGTH OF POSTS, STRUTS, AND COLUMNS.
.8 the strength of a post, strut, or column, depends primarily
>n the resistance of the given material to crushing, we must
t determine the ultimate crushing-strength of all materials used
this purpose.
?he following table gives the strength for all materials used in
Iding, excepting brick, stone, and masonry, which will be found
Chap. VI.
TABLE I.
erage Ultimate Crushing-Loads^ in Pounds per Square Inchy
for Building-Materials,
Material.
Crushing
weight, in Ibfi.
per sq. loch.
Material.
Crushing
weight, in Ibe.
per sq.inch.
)r Stone, Brick,
»nd MA80MRT, see
Chap. VI.
Metals.
Bt-iron ....
rought-iron . . .
ie\ (cast) ....
Woods.
\h
C.
80,000
36,000
225,000 a
8,600 a
Woods {continued).
Beech
Birch
Cedar
Hemlock
Locust
Black walnut . . .
White oak ... .
Yellow pine . . .
White pine ....
Spruce
a
9,300 a
11,600 a
6,500 a
5,400 b
11,720 b
5,090
3,1 r)0 to 7,000
4,400 to 6,000 ;
2,800 to 4,500
'he values given for wrought and cast iron are those generally
d, although a great deal of iron is stronger than this. The
lies for white oak, yellow pine, and spnice, are derived from
eriments on full-size posts, made with the government testing-
3hine at Watertown, Mass. ; the smaller value representing the
tngth of such timber as is usually found in the market, and
larger value, the strength of thoroug\\\^ sea.?>ow^^ ^X.'m^ssXi-
led timber. For these woods a smaller iactoi ol §>«A^Vj xsNa.^ \*
• Trautwine.
V> HiMf^eXA,
*TREN(iTH Of WOOUKN fUSTS
^^Bed than for llie others. Ihe slren!.ali of wliich whs derived D
^HRperimenU on sinall pit'ces.
^™ The values for wood ai'e (or dry tiinlwr. Wet timber U <
about one-lmlf as strong to resist compruwiun » dry timber,;
this fact should be talcen Into account wlien using green tlmba
The flreni/lh qf a column, pnat, or atrul depeuils. In a 1
measure, upon the proportion of the length to the dinmetcf
least thickness. Up to a certain length, they break simpl},
uonipressiou, and above tlutt they break by tlrst bending siden
and tlien breaking.
^V 'Woodi-n Columns.
*^ For woodun columns, wheie the length is not more than fli
times the least thickness, the strength of tile column or
may be computed by the rule,
^Biiei
^Tabl
fa<^tor of safely
«re C denotes the strength of the given mnterisl a
,ble I.
nit factor qf 6(i/eti/ to be used depends upon the place vrbi
the eoluiun or strut is used, the load which comes upon it, tt
quality of the material, and, in a large measure, upon the r,
taken for C. .
Thus tor whit« oak, yellow pine, and spmce, the value C la U
actual crushing-strength of full-size posts of onlinary qualltf
lience we need not allow a factor of safety for these greater ItW
four. For tlie other woods, wo should use a factor of safety Otii
least six.
!/ the load iijiiiii tlit eoliitnn or post is such as come* upon tk
floor of H niachine-sliop. or where heavy uiacliinei^ is used. Olf;
the strut Is for a railway-bridge, a larger factor of safety shoO]
be used in
If the qvality qf the Hmlier is exceptionally good, we may uset
larger values for the constant C, in the case of the last four w
given in the table. For ordinary hard pine or oak posts, multt
tlie area of cross-section in Inches by 1000; for spruce, by 800, ■
Sot white pine, by 700 pounda.
, EXAMPi.t: I, — What Is the sate load tot a Imrd-plne post itfj
^picliea, 12 feel long ?
mKtt% -Area of ci
^^V h<10,OOU pouwh
STRENGTH OF WOODEN POSTS AND COLUMNS. 219
ExAMPLK II. — What is the safe load for a spruce strut 8 feet
long, 6" X 8" ?
Ana, Area of cross-section = 48; 48 x 800 = 38,400 pounds.
Columns and struts over fifteen diameters long, or where the
length is more than fifteen times the least thickness of the post or
strut, are liable to break by both bending and crushing. In speak-
ing of the length of a column as affecting its strength, we mean
the greatest length of the column which is unsupportetl sideways.
Thus we may have a column forty feet long ; but if it is securely
braced every ten feet, so that it cannot bend, it will be just as
strong as though it were but ten feet long.
The column must, however, be prevented from bending in any
direction; for, if it were only braced in two ways, it would be no
stronger than if not braced at all.
For columns over this length, the following fomuila, deduced by
Mr. Lewis Gordon from Mr. Hodgson's experiments, has been for
a long time in use, and it probably answers better than any other
formula: —
For rectangular ) breaking- _ C X area of cross-section
pillars and struts y load, in lbs. "~ sg. of length (2)
^ ■'" sq. of breadth ^ ^'^^
For cylindrical 7 breaking- C x area of cross-section
columns > load, in lbs. / . sq. of length \ (^\
' * 1.7(1 -^ — — 2__ y nnoil (tJ)
/ sq. of length \
• '\^ ^ sq. of breadth ^ "'"^/
In these two formulas the length is taken in inches.
The value of C is the crushing-strength of the particular kind of
timber used for the strut.
Mr. C. Shaler Smith, a prominent engineer, determined from his
own experiments that the value of C for hard pine should be about
5000, and that is the value generally used by engineers.
For white pine or spruce we should use 3000 for C. With these
values, a factor of safety not larger than six may be used for almost
any case in building-construction, and in many cases a factor of
safety as low as four might be used.
Example III. — What would be the safe load for a hard-pine
strut 15 feet long, 6" x 8'' ?
Ans, The ratio of length to least thickness is in this case 30 :
so we should employ fonnula 2. Then
5000X 48
Breaking-weight = zr^i^ =^Wl^^\x\A^x
1 -f- i^ X 0.004
6^
220 STRENGTH OF HARD PINE AND OAk S 1 li I I -
Taking one-slslh of Ihls, we have for the sate load, 8006 poiuiiJ*
Example IV. — Wli»t would Iw lln- saft load forarumed whfl
plue column 12 feel long, aw! 6 Inclips in diameter at its sumlli
pan?
Aim. Using formula 3, we have.
P 3(100 X 2S.3
Breaklng-Ioa(l = — -; -rrr^ -r — 1513-1 pound
As in thia case the pine woulil prolialily l>e of very good quallt]
Mill dry, and tlie load not being very severe, we may use a factort
safely of four, which would give a safe load of 3783 pounds.
The application of Table I. is obvious. To use TaWe II., flml
first the ratio of the length to the diameter of the column, bo
being taken in inches. Look in the table, and Dnd the safe lo
per square inch for that ratio, and multiply by the area of tilt
smallest croas-section of the posL
Example. — Take the same case as in Example III. Here tie
ratio was 30, and looking in Table II., op|>oslte 30, we finil I09T.
Multiplying tliia by 48, the cross-aectiou of the post, we liave CS,11I
pounds for the bi'eaking-load, as before.
/ran capit/or Umber plUars are often used in impe
Nt ructions, and are an excellenilnvi'nllon. as they serve to dlstriba
rlie thrust evenly through il'c pillar, ami also fonn a bracket, whli
1^ often desirable, for »{Upi>ui'tlng Lhi' eiidK of ginlem wliere a u
jjost rests on lop of (he liral. Fig. 1 Btio*B \.te w
the beat forma oi caps.
8T&BMGTH OF WOODEN POSTS AND COLUMNS. 22 i
TABLE IL
Habd-Pin£ and Oak Posts.
Breaking-Loads, in Tons {of £240 pounds), qf Square Posts qf
moderately Seasoned Hard Pine or Oak, flnnly fixed and
equally loaded.
Side of square post or strut In inches.
6
39.7
35.0
30.9
27.4
24.3
21.7
19.4
17.5
15.8
14.3
13.0
11.9
10.9
9.2
62.4
56.0
50.3
45.1
40.6
36.6
33.1
30.0
27.3
24.9
22.7
20.9
19.2
16.3
14.1
12.2
10.7
8
90.8
83.5
75.3
68.9
62.5
57.2
51.9
47.6
43.4
40.0
36.6
33.8
31.1
26.8
23.2
20.1
17.7
9
124.4
115.1
105.8
9C.4
87.0
81.5
5.2 0.4 15JB
64.0
59.5
55.0
51.0
47.0
40.0
36.0
30.0
28.0
25.0
10
163.0
152.5
142.0
132.0
122.0
113.5
7(3.0 10").0
70.0 ! 97.5
90.0
84.0
78.0
73.0
68.0
59.0
52.0
49.0
41.0
11
207.0
12
255.0
195.0
242.5
las.o
230.0
171.5
217.0
100.0
204.0
150.0
192.0
140.0
180.0
131.0
169.5
122.0
159.0
114.0
149.5
100.0
140.0
99.5
132.0
93.0
124.0
82.0
109.0
72.0
97.0
64.0
87.0
14
367.0
353.0
339.0
16
500.0
483.0
466.0
323.0 449.0
307.0
432.0
292.0 ; 414.5
I
277.0 I 397.0
203.5
250.0
237.0
224.0
212.5
201.0
182.0
163.0
148.0
JHO.O
503.0
U7.0
331.0
310.0
301.0
274.0
249.0
226.0
34.0 \ U.q\ '^^.Av^'^A^^'^^^
1
SM STRBMOTH of wooden posts and rOI.LMiSK. |
^^^^^^^^^^^^tSm.E III.
^m Hard-Pink Pillams ano Posts. 1
1
^klna-Loadf, in, Poitnrfs per Si/uoTe Inch of Cro*«-S*r(«B
MflwHABivPiMi! Pii.LAR9«n<i Posts whofte llelgiiU art- m^nrnm
r*V the Difimeler or Least Side. M
Length 111
lnGb» iDvlcled
by ]««i tiijck-
1
l.^g\h In
UoudJ.
rJ
15
l&w
2631
34
323
B89I
IS
1453
2470
35
498
S4T 1
n
13fi4
2319
36
476
son 1
18
1-28 1
^'178
37
4.->4
77-2
19
1203
-'046
38
434
7:!-S 1
20
1131
1923
39
415
700
21
1064
1809
40
39S
67lJ
22
1002
1703
41
381
047
23
B44
1606
4^
365
021
24
830
1513
43
351
m
26
841
1429
44
336
.i7a
20
794
1350
4S
323
.■>50
27
750
1376
46
311
528
28
711
1200
47
200
508
29
674
1148
4S
287
489
30
ftlO
1087
40
278
473
31
607
1032
50
288
455
/
32 1 577
ie\ \ h\.
\ ^ V «.J
L_Z 1 "
933 \ S-i
\ ,«» \ ^
lk& -J
STRENGTH OF CAST-IRON COLUMNS.
223
Cast-iron Columns.
For cast-iron columns, where the length is not more than six or
dgiht times the diameter or breadth of column, the safe load may
le obtained by simply multiplying the metal area of cross-section
ay h^ tons, which will give tons for the answer.
Above this proportion, that is, where the length is more than
Bigbt times the breadth or diameter, tlie following formulas should
be used. These formulas are known as Gordon's and Kaukine's.
Formulas —
For solid cylindrical cast-iron columnsy
Safe load in lbs. =
Metal area X 133.30
sq. of len«jth in inches
14-
sq. of diam. in inches x 2t50
For hollow cylindrical columns of cast-iron^
Safe load in lbs. =
Metal area x 13330
1 +
sq. of length in inches
400 X sq. of diam. in inches
(4)
o
(5)
For hollow or solid rectangular 2><7/(e/-.s
<tf cast-iron.
Safe load in lbs. =
Metal area x 133;)0
sq. of length in inches
500 X sq. of least side in inches
1 +
For cast-iron posts, the cross-section being a cross
of equal arms.
Safe load in lbs. =
Metal area x 1.3:330
sq. of length in inches
1 +
(6)
-. (7)
133 x sq. of total breadth in inches
Example I. — What is the safe load for a hollow cylindrical
cast-iron column, 10 feet long, 6 inches external diameter, and 1"
thickness of shell ?
Ans, We must first find the metal area of the cross-section of
the column, which we obtain by subtracting the area of a circle of
four inches in diameter from the area of one aVx \Tic\v^"9»\\v^vNK!vR\f8t,
77ie remainder will be the area of the meta\. T\\^ ^xi^-sv. '^\ ^ ^''--
iDcb circle is §8,27 aqvuure inches, and of a iowT-mc\v,\'i.'i^^^S!»2
8cft»; and the meUl area of the column \a \b.n\ ^<\\vwce Vcvv^xsa.
226
STRENGTH OF CAST-IRON COLUMNS.
Besides this table, we have computed Table V. following, which
gives at a glance the safe load for a cast-iron column coming within
the limits of the table, and of a thickness there shown.
Thus, to find the safe load for the column given in the last
example, we have only to look in the table for columns having a
diameter of 10 inches and a thickness of shell of 1 inch, and oppo-
site the length of the column we find the safe load to be 104 tons,
the same as foimd above.
The safe load in both tables is one-sixth of the breaking-load.
TABLE IV.
Strength of Hollow Cylindrical or Rectangular Cast-iron Pillan
(Calculated bt Formulas 5 and 6.)
Length
Breaking-weight in pounds
per square inch.
Safe load in pounds
dividcKl by
per square inch.
external
breadth or
diameter.
Cylindrical.
Rectangular.
Cylindrical.
Rectangular.
6
75,294
76,190
12,549
12,698
6
73,395
74,627
12,232
12,438
7
71,269
72,859
11,878
12,143
8
68,965
70,922
11,494
11,820
9
66,528
68,846
11,088
11,474
10
64,000
66,666
10,666
11,111
11
61,420
64,412
10,236
10,735
12
58,823
62,111
9,804
10,352
13
56,239
59,790
9,373
9,965
14 ■
53,859
57,471
8,976
9,578
15
51,200
55,172
8,533
9,195
16
48,780
62,910
8,130
8,817
17
46,444
50,697
7,741
8,449
18
44,198
48,543
7,366
8,090
19
42,050
46,457
7,008
7,743
20
40,000
44,444
6,000
7,407
21
38,050
42,508
6,341
7,085
22
36,200
40,650
6,033
6,775
23
34,455
38,872
6,742
6,479
24
32,787
37,174
6,464
6,195
25
31,219
35,555
6,203
5,926
26
29,741
34,014
4,957
5,669
27
28,343
32,547
4,724
6,4*23
28
27,027
31,152
4,504
6,192
29
25,785
29,828
4,297
4,971
80
24,615
25,571
4,102
4,761
81
23,512
27,310
3,918
4,818
82
22,472
26,246
3,746
4,374
83
21,491
25,172
8,681
4,196
84
20,565
24,154
3,427
4,020
86
19,602
23,188
8,282
8,864
STRENGTH OF CAST-IRON COLUMNS.
227
TABLE V.
*hoioing Safe Loud in Tons for Cylindrical Cast-Iron Columns,
Thickness op Shell 3 Inch.
Length
of
column.
Diameter of col
umn (outside).
Gins.
7 ius.
8 ins.
9 ins.
10 inn.
11 ins.
12 ins.
Tons.
13 ins.
Feet.
Tons.
Tons.
Tons.
Tons.
TOHB.
Tons.
Tons.
6
60.6
78.1
94.0
110.8
128.6
144.9
161.7
180.0
7
55.7
72.2
88.9
106.9
124.2
140.1
156.4
176.0
8
50.7
66.3
83.8
101.1
117.7
135.2
151.1
170.3
9
45.8
61.9
78.7
95.2
113.4
130.4
145.8
164.5
10
40.8
56.0
73.5
89.4
106.8
123.2
140.5
158.7
11
37.1
51.5
68.4
83.6
100.1
118.3
135.2
153.0
12
33.4
47.1
63.3
79.7
95.9
113.5
129.9
147.2
13
30.9
44.2
58.1
73.9
89.4
106.3
124.6
141.4
14
27.2
39.8
54.7
70.0
85.0
101.4
119.2
135.6
15
24.7
36.8
49.6
64.1
78.5
96.6
114.0
129.9
16
22.3
33.9
46.2
60.3
71.9
91.8
108.7
124.1
18
—
29.0
41.0
52.5
67.6
84.5
103.4
118.3
20
•~
24.4
36.0
44.7
63.3
77.2
98.1
112.5
Metal
area of
croessecliou.
80. ins.
12.37
sq. ins.
14.73
sq. ins.
sq. ins.
sq. ius.
sq. ins.
sq. ins.
sq. ins.
17.10
19.44
21.80
24.15
26.51
28.86
Thickness of Shell 1 Inch.
Length
of
column.
Feet.
6
7
8
9
10
11
12
13
14
15
16
18
20
Diameter of column (outside).
6 ins.
Tons.
77
71
64
58
52
47
42
39
35
31
28
25
22
Tins.
8 Ins.
9 ins.
10 ins.
11 ins.
12 ins.
Tons.
Tons.
Tons.
Tons.
Tons.
Tons.
100
121
143
167
188
211
92
118
138
161
182
204
85
108
131
153
176
197
79
101
123
147
. 170
190
72
95
116
138
161
183
66
88
108
130
154
175
60
81
102
124
147
169
67
75
95
116
138
162
52
69
90
110
132
155
47
64
83
104
126
148
43
59
78
96
119
142
39
53
68
88
105
128
35
46
58
79
94
114
13 ins.
Tons.
234
230
222
215
207
200
192
184
177
170
162
151
136
Metal area of cross-section.
1
§g. iiMklM. Ids. jsq. ins.
U,71 18,82 / 22.00
2B.21 \ ^\.4\ \ ^Afe \ ^'V.'V'^i
\
238 STKEMti'l'lI OV CAST-IRON COLTnHI^|
TABLE V. Iconliiined).
■ Safe Loud in Tons for CyHiidrlrat Cast-iron Columt
Thickmeb* Of Shell 1] Ihchks.
Tliu.
aiDi.
Bl™.
10 1™.
ni«.
12 IP.
an
^
St
1«
IM
3
*l
73
DB
63
M
109
IW
i
199
0
m
13V
Mi^tal area of erOM-KcilQii, 1
v.r
ii.38 ' 5l.62
V.!S-
■ss-
■3i.sr
«.
THlCKSHSa OF HnEii, H Ihchbb. i\
Lcnslh
Dlamclar of column (olitddo). i
S iM.
Oi.,.
ID1,».
11 [«.,
ISfnt. [iSlii^
Ul».
Fwt.
Ton-.
'^OTl'"
■"■^■g"-
Tone.
''»
Te™. ■
I
IM
18*
219
3»
133
ira
i
120
150
lis
Si
2S&
EM
di
m
M
IW
IIR,
au 1
j ] MMaV area ol MOM-wtlton.
ipfei;--|^5-- -a-V^a-Vva-VsX-ta
^H
STRENGTH OF CAST-IRON COLUMNS.
229
TABLE V. {concluded).
8<tfe Load in Tom for Cylindrical Cast-Iron Columns,
Thickness of Sheli
. 2 Incues.
liength
Diameter of column (outside).
of
•olumn.
Sinfl.
9 ins.
10 Ins
11 ins.
12 ins.
13 ins.
14 ins.
15 ins.
Ilbct.
Tons.
Tons.
Tons.
Tons.
Tons
Tons.
Tons.
Tons.
f e
•207
251
296
3:39
38:}
428
467
514
7
200
242
286
328
371
421
459
502
1 8
185
229
271
316
358
408
445
490
' 9
173
215
258
305
34:)
393
432
474
10
162
202
245
291
3.W
380
422
462 •
11
151
189
231
277
320
366
409
450
12
141
178
221
265
307
352
396
438 ,
18
131
167
206
249
295
3:J9
38:3
424 ;
14
122
158
196
237
28:j
325
369
412 1
15
112
145
183
226
270
311
354
398 1
M
102
136
170
215
2:)7
297
339
384 ;
18
90
119
155
189
'2ii'2
276
314
359
20
79
101
142
170
207
249
286
332 1
Metal
area of
crosH-Hcction.
sq. ins.
37.70
sq. ins.
43.98
sq. ins.
50.266
sq ins.
56.55
sq. Ins.
62.84
sq. ins.
. 69.11
sq. ins.
75.40
sq. ins.
81.68
Note. —If the breaking-load is desired, multiply ttie safe load by 6.
Wrought-Iron Posts and Columns.
In trusses, roofs, etc., built of wrought-iron, the pieces in com-
pression are usually made of wrought-iron, as well as the pieces
which ai-e in tension. Wrought-iron is also used, to some extent,
for columns in buildings; the column being made up of three or
oiore sections of wrought-iron bolted together.
In using wrought-iron to resist compression, any shape may be
ttsed which offers a resistance to bending. Four angle-irons bolted
Ogether in the form of a cross make a good strut, or two channel-
'X)ns bolted together, back to back. In the latter case, the great -
St strength propoilionate to the weight of the bar is obtained
viien the channels are separated, so that the distance from the
'Vitside edge of one to the outside edge of the* other shall be ecpial
O the widtl) of the cbanne}.
I-beams are also suitable to resist comprossvow, \>vyX. \\v\.nq. n\\^
f(^l/on that they cannot readily be rivo.U^d \.o oV\\vi.v v^^^^ ^
tntss or frame.
232
STRENGTH OF WROUGHT-IRON STB0TS.
TABLE VL
WROUGHT IRON STRUTS.
ULTIMATE PRESSURE IN LBS. PER SQUARE INCH,
Length
Flat
Fixed
Hinged
Round
XJSAST RADIUS
or GYRATION.
Eni>s.
Ends.
Ends.
Ends.
20
46.000
46.000
46,000
44,000
80
43,000
44,000
48,000
40,250
40
40.000
40,000
40,000
86,500
50
8S,000
38.000
88,000
83,500
60
36,000
36,000
83.000
80,590
70
84,000
34,000
83,750
27.750
80
82,000
3-2.00O
81,600
25,000
90
80,900
31,000
29,750
22,750
100
29,800
80,000
28.000
20,500
110
23,030
29,000
26,160
18,500
120
S6,300
28,000
24,900
16.500
lao
94.900
26,730
22,660
14,660
140
23,500
25,500
21,000
12,800
150
81,750
24,230
18,750
11,150
100
20,000
23,000
16,500
9,500
170
18,41)0
21,500
14,650
8,500
180
16,800
20,000
12,800
7,500
190
15.650
18,750
11,800
6.750
200
14,500
17,500
10,800
6.000
210
13,600
16.250
9,800
5,500
220
12,700
15,000
8,800
6,000
280
11,950
14,000
8,150
4,650
240
11,300
13,000
7,600
4,300
260
10,500
12,000
7,000
4,050
260
9,800
11,000
6,500
8,800
270
9,150
10,500
6.100
8,500
280
8,500
10,000
5,700
8,200
390
7,850
9,500
5,350
8,000
800
7,200
9.000
5.000
2,800
810
6,600
8,500
4,750
2,650
820
6,000
8,000
4,500
2,500
880
5.550
7,500
4,250
2,300
840
5,100
7,000
4,000
2.100
850
4,700
6,750
8,750
2,000
860
4,300
6,500
3.500
1,900
870
8.900
6,150
3,250
1,800
880
3,500
5,800
3,000
1,700
890
8,250
5,500
2,750
1,600
400
8,000
5,200
2,500
1,500
410
2,750
5,000
2,400
1,400
420
2.500
4,800
2,300
1,800
480
2,350
4.550
2.200
440
2,200
4,300
2,100
460
2,100
4,050
2,000
460
2,000
3.8CO
1,900
470
1,950
^'S2
460
1,900
1,800
STRENGTH OF WROUGHT-IRON STRUTS.
233
TABLE VU.
GREATEST SAFE LOADS ON STRUTS.
reatest safe load in lbs. per square inch of crosu section for vertical stmte.
h ends are supposed to be secured as indicated at the head of each col-
a.. If both encte are not eecared alike, take a mean proportional between
values given for the classes to which each end belongs. If the stmt Is
ged by any uncertain method so that the centres of pins and uxis of titnit
y not coincide, or the pins may be relatively small and loosely fitted, it is
t in such cases to consider the strut as '* round ended/*
LSNGTH
Flat
Fixed
HiNOED
Round
LEAST BADIUS
car GTRATION.
Ends.
Ends.
Ends.
Ends.
20
14,380
14,380
13,940
18,830
80
13,090
13,^30
12,460
11,670
40
11,700
11,760
11,110
10.140
50
10,8«0
10,860
10,180
8,930
en
10,000
10,000
9,230
7,820
70
9,190
9,190
8,830
6,850
80
8,420
8,420
7,500
5,950
90
7,920
7,950
6,840
5,230
100
7,450
7,500
6,220
4,560
110
6,840
7.070
5.620
8,980
120
6,260
6,670
5,060
3,440
130
5,';90
6,820
4,580
2,960
140
5,340
5,800
4,120
2,510
150
4,830
5,390
3.5T0
2,120
160
4,350
5,000
3,060
1,760
170
3,920
4,570
2,640
1,530
180
3,500
4,170
2,250
1,310
190
3,190
3,830
2,0»')
1,150
200
2,900
3,500
1,800
1,000
' 210
2,f.70
3,190
1,590
890
S20
2.440
2,880
1.400
790
230
2,850
2,640
1,260
720
940
2,070
2,410
1,140
650
^
1,910
2,180
1,040
600
1,750
1,960
940
550
870
1,610
1,840
870
50O
880
1,460
1,720
790
440
290
1,330
1,610
730
410
800
1,200
1,500
670
370
810
1,080
1,390
620
350
•820
970
1,290
580
320
880
880
1,190
540
290
840
800
1,(W0
490
260
850
720
1,040
450
240
860
650
980
420
230
870
580
920
380
210
880
510
850
340
200
800
470
800
310
80
«> ^
' 430
740
\ «»
^ »
236 STRliNGTH OF WROUGIIT-IIION SIKl'JS.
Table IX., p, 239, also shows llie dislance required tietween ll
backs of oliai)n<<U usc<l as poxts lo give equal stifTni'ss parnllel wll
and at rlgliL angles lo Ihe weh.
TLus if wc wisk lo use two fl-lnch TU-pound channels, plan
back to back, for posts, they should he placed 4.n incliea apiirt <
ha.ve the same stilTnesa in either clireelion. In this way we gul tl
most strength out of llie ii'on used.
Wllb faced or fixed ends,
ife load In tons ~ .j .
f
With hinged ends.
Safe load in tons =
n which L dcuoles the length of the Etrut ii
Anolk-Bars with Evkn Leos.
DesignatloD Wclgli
DhIouiUou 'WeiBhl per
orb»n fool In ll*.
l^K:
IJ lo 2}
Akgle-Barb witu Um^ven Less.
■::.V
6 iDcb wif
4 ■■ "
|:i :
STRENGTH OF WROUGHT-IRON STRUTS.
231
Tee-Bars.
rxesisnation of bar.
Weight per foot
in pounds.
a.
)
r.
371
175
4 inches
X 4 inches
12i
3.75
Vertically
Kidcwirto
3^ "
X 3i "
9.6 and 10.8
2.87
284
133
VcMtically
hfidewirto
3 "
X 3 "
7.0 and 9^
2.11
\
2U9
97
Vorticaliy
Sidewino
2i "
X 2i "
5.0 and SJ
146
145
68
Voiticaliy
SidewiHC
2
X 2 "
Z\ and 33
0.94
92
43
Vertically
Sidewiho
5 "
X 21 "
11.7
3.50
107
363
Vertically
fldewlrte
3
X 2 "
4.8 and 6.8
1.45
81
117
Vertically
Side wise
2 "
X U "
3.00
0.91
47
50
\'crtically
Sidewiso
2\ "
X li "
2.40
0.74
21
61
Vertically
Sid ('Wise
2 "
X 1 inch
2.15
0.65
17
53
Vertically
Side\vis('
n "
X 1 «'
1.86
0.56
i
17
31
Verti(rally
Sidowirto
If it is desired to use Phoenix or Pencoyd beams or bars, or thosi
of the Union Iron Mills, for reason either of cost or convcnic^nce
the strength of those beams or bars should be the same as Trentoi
beams or bars of tlie same loeUjht and outside dimensions. Tin
strength of iron struts of the same outside dimensions is propor
tional to their weight.
The tables for Trenton beams and bars used as posts are basec
upon the metal resisting with safety 8000 pounds to the square incl
for short pieces.
ttuiio of Length of Posts unsupported Edrjewise to Length unsiip
j)orted SidewlsBy giving Same Strength.
Beams.
Channels.
Size.
Ratio
Size.
Ratio
3.82
Size.
Ratio
Size.
Ratic
15 in. 200 lbs.
6.07
8 in.
65 lbs.
15 in. 190 lbs.
4.26
0
in. 45 lbs.
3.20
15 *• 150 '•
5.83
7 "
55 "
3.:i7
15 •« 120 '♦
5.10
6
'• 3:1 " 3.65
12 \ " 170 "
12i " 125 '•
lOi " 135 ••
3.91
6 *«
120 "
1.S7
12\ ♦• 140 '*
4.04
6
" 22.{ " 4.27
4.96
6 "
90 «'
2.15
12', ♦• 70 ••
5..56
5
<( I.) «
4.04
3.82
6 «'
50 "
3.23
10^ *« 61) *•
4.80
4
•• 16.^ •'
3.49
lOl " 105 *«
4.40
6 •♦
40 •'
3.77
9 " 70 ••
3.92
3
« 15 i<
2.59
lOi" 90 "
4.48
6 «'
40 '•
3 01
9 " GO "
AAZ
1
; 9~ " 126 " / 3.64 1 5 "
30 "
3.38
8 •' 4b " \AAV»,\
^T^JAi*^ "^K\5A.
1 9 " 85 " 3.90 4 "
37 «'
2.29
8 «» S'i " \^."H
19*' 70 " 4.37 4 "
SO '* 2.50
7 " oO ** \o.Vl\
^ \\\. n:l Vvs>«.\'?
8 *' 80 ** 3.29 4 *'
18 " 4.21
7 " ^l)>i" \4.v>b
V Vi '>'• V?*
^^ \
lilii'"'^
TABLE VIII. ■
/
ail?
Isi III 1
MiiiiF
li^
S.8S8SSil83S38?8S3SS!SMS
i
ip|ip|5ppppp|5|
i
=
i|i|lP|,!p|3p|S|3p|
■AI iiQinio^ ni n
S8=3SS38?S38SSt:S!iiSSSS5
™
'
sffrrrrs-rrrg
■Mi«apii
qiBoang -msiiw "!
H00|^ puB^-^qouit Jq^..U!
^Mi«aap3^qi8u9j^a ' =
ipppppi^ppisisi •
■qiSnai jo i>|pp|ni
n gis.tij iCii paooiiujM
wn in,,-'Il .,3au»q:.
•0 Msq 1I14J1— '.nqi
4l>iniao] P4I3.1J1 WW! QM.l,
=
iii|iiii^i'i"Pi»i5P|
•spiiinaiunB -JKiiiiBnie
■^
ipisiiisppiJijppi
g
1
11
nil
Iiiiliiiiii
_i/
1 s .-••- — - -i
1
■E — ~ j^m
STKENOTH OF WEODGHT-IRON STRUTS. 239
XAUPLE. — Wliatls Uie safe load, as a strut, of a pair of flve-
1 nineteen-pound cliannels, six feet long, riveted together one
1 apart, and baving fixed ends ?
4 X 3.62 X !tOj
tns. Safe load = — av-va>. • = la.flo tona.
TABLE IX.
rming Distance regtured from Back to Back of Channels
ormlns Post* to (ilee Equal SliffneBu ParalUt toith mid at RirjM
AngUa to the Web.
lii!!!!
Ihtbf
Sue op Cdahnel,
ill
1
M
m
S inchhenvy. 1M lb., per jnrd-
1 :: "£■ 1 ;i !: i:
B " buorr. ™ " " ■'
i : £!??'■ S' •" " :
« " iigbi,' as " " "
< " ei.Hght, 33i
! : S:!S!; !? « ~ ~
i.W
DJfl
iii
1
B.ro
aim
sis')
■24.68
5o!t»
14 !w
l-iiM
t!6o
t ncMdlDg Ihu bere raqotred.
etlng Songe lo Oaiige will h«v«i widUi out t«
I'llUtNlX WUOUGHT-IHON COLUMNS.
^V P)in.>ntx Wrougltt-Iron Columns.
^ The rolled segment coliimiiof tln-'I'liiBnU Irou Company iitl
Ing into quite f^enei-ai use for v«rtiral struU in iron bridges, tioi
columns it) buildings. For volunins whose lengtli is motet
nftcen limes tlie diameter, lliey possess greater sirengtb per sri
iticii of metal tLaii cast'iron, uni
leas liable to contain any flaw Hi
Tliey c-m also l)e palnteil on
inalde, before the column Is pitt
to protect tbeiu rroiu nny ilam
in tlie fttiuospliew, which :
cause rust.
These columns are made i
the rolled segments "C," wlileh
riveted together, l)y rivets aboitt
inches apart, by means of fli
aloug their sides, )is shown at '
Between every two segments an
. bar is fistiuenliy hiserteil, tlirw
whicli the rivets puss. These b
! they are called.
e the
J the c
iroiumna, or the table i
jiaiilar table for cast-iic
: — and contribute mneh to the stn
of tlif pillar. The columns are
with casi-lron raps and bases. Tat
X.. pp. 242, ^4:!. gives the sizes ofU
colmnns I'olled by the Phu^nix Do
Company, as pnbllshed in th^r I
of seelions. These cohiums ■
from llie small four-s^ment coh
i'ii Inches InsMe >)1ameler, and («p
ble of Btipporthig a load of 7} Una
wftli safety wiieii twenty feet kail
to the massive eigtit-segmenl trin
ic G (143 Iiiebes Inside diameter, aUti
strenf^h siitReient to bear safcljrtfB
tons when of the same lengtli),
^ The Btrenglli tff these eolaiiint
be compute<l by means of the fonuidfe
lov liottov) C^\\V\ftT«;!i «1
1 p. 244, v;\i\c\i a wsei tt« i
KBTSTONE WROUOHT-IRON COLUMNS.
241
kMPLE. -+ What is the safe load for the four-segment column
g inches internal diameter, i inch thickness of shell, and 2()
ng?
. From Table X., p. 242, we find the outside diamcttM- of this
n, with a tiiickness of half an inch, to be (i.O inches, which
make the ratio of the lengtli to the dianiPt<M' of the column
85 to 1. Then, from Table XI., p. 244, we tind the safe
►er square incli for a cylindrical colunui of that length to be
K)unds. The metal area of cross-section of the column is
juare inclies: hence the safe load for the colunm is 13.8 x
■ 1(K3,662 pounds, or 51.8 tons. If we compare this with a
on column of the same dimensions, we find, from Table V..
st-iron columns, p. 227, tliat a seven-inch column thr(»e-
s of an inch thick (which is as thin as columns should l>e
ind twenty feet long, will only support 24.4 tons, or less than
hat the wrought-iron coluuni supports with less metal.
m"/^/////////^
Fig. 5.
5ssrs. Caniegrie Brothers & Co. also manufacture
;ht-iron cohunns of two patterns, which answer the same
•se as the Ph<vnix wrought-iron columns.
.' first pattern is that known as the Keystone Octaproii
m, of whicli a section is shown in Fig. 5. They are rolled
jments as shown, and fastened together by rivets.
ole XII. gives the diameters, areas, and weights of tbes«»
ims as rolled. In comi)uting their strength, they should
nisidered as square colunnis, the diameter given in the tables
J the outside diameter of the colunnis.
■
^^v*
'
E
W^^ PHtENIX WKOUGHT-niON CO
,l-MN.s
1
^^
TABLE
t.
Sizes qf Pluena ColttlMts
OsS SBUJlltllT.
Ohb Coi-oaN.
Mjbb.
"v^uT
Wetghl
•■'"»
in ivebcf.
twrjBni,
«i.i.,U
111 imnudB
"
A
ft
9i
3.8
12.0
4.(«
4 segment.
i
13
4.8
16.0
X
14i
5.8
lfl.3
ar inter, diani.
1
17
8.8
aa.8
4:«
i
18
11.4
21.3
5.31
B'
ft
m
7.8
2(1.0
5.44
»
2.^
«.2
3o.a
5.5a
i segment.
ft
2Bi
10.0
35.3
5.9W
4ii" inter, dlam.
i
ft
30
1S.0
13.4
40.0
44.8
5.810
5.941)
5
■■ii
14.8
40.3
8.000
^
18
7.4
24.(1
8.440
B»
2^
0.0
30.0
0.580
211
10.8
35.3
s.m.
4 aegment.
.30
12.2
40.6
8.810
5+i" Inter, diani.
ft
:i4
13.8
15.4
48.0
51.3
7.0tU
'
4!^
17.0*
58.6
7. ISO
A
2-5
10.0
33.3
iM
.*W
12.0
40.0
T.**!*
.*i
14.0
4e.«
7.1*
16.0
53.3
8.IWI1
-15
18.0
60.0
Kino
C
48
!».£
64.0
8.:ilO
4 segment.
21.2
23.3
70.8
77.3
8.440
8..iB0
7-ft" Inter, dlam.
i
(S
25.2
84.0
8.««
+a
68
27.2
110.6
8.810
i
7a
29.2
97.3
8.«30
8;i
.^.2
110.6
9.1»
/
■
li
fl.1
37.2
124.0
B.440
U \ 1«1
\ 4\.-l
\m.%
^,«
\
1
I
H
PH<BNIX WROUGHT-IRON COLUMNS.
243
TABLE X. — Concluded,
Sizes of Phoenix Columns,
Onb 8e
IGMBNT.
Mark.
. .
Thick ncfM
ill inches.
Weight
ill poundH
per yard.
28
i
D
■k
32
;egiiient.
36
40
ater. diaiu.
i
44
fs
48
28
i
■h
32
i
36
i'«
40
C
i
44
^uient.
t
48
53
Qter. diam.
H
58
i
m
H
68
I
73
1
83
30
1*6
J
35
^
40
i
45
f«
50
G
{
55
segment.
1
65
inter, diam.
+?
70
5
75
1
85
li
95
H
ia5
n
115
One Column.
Area ill
sq. inches.
14.0
16.0
18.0
20.0
22.0
24.0
W.8
19.2
21.6
24.0
26.4
28.8
31.8
34.8
37.8
40.8
43.8
49.8
24.0
28.0
32.0
36.0
40.0
44.0
48.0
52.0
56.0
60.0
68.0
76.0
84.0
92.0
Weitfht I
in }M)U(idr«
por f(M>i.
46.(5
(»6.()
66.6
73.3
80.0
56.0
64.0
72.0
80.0
88.0
96.0
106.0
116.0
126.0
136.0
146.0
166.0
80.0
93.3
106.(i
120.0
133.3
146.6
1()0.0
173.3
186.6
200.0
226.6
253.3
280.0
306.6
\
T^onut
OutHidc
diameter
in incheH.
9.625
9.750
9.870
10.000
10.125
10.250
11.5(K)
11.625
11.750
11.875
12.000
12.125
12.250
12.375
12.5(K)
12.625
12.750
13.000
15.000
15.125
15.250
15.375
15.500
15.625
15.750
15.875
16.000
16.125
16..S75
16.625
16.875
17.125
\
^
— The weight of livet-heads adds from two \o tVvft v^t cetvV vo\Xift^«\'^
t co/umoM. 1
/
242
FHCENIX WROUOHT-IRON COLUMMBi;
TABLE X.
8\tu qf Pkanix ^ .
rowf/ZiMrOR
.)
Mabk.
Ohk BBsm*
I
TUflkner
In
A
4 a^^ment*
inter, dlar >j;
33,58.2
33,327
S3,0rU
.SI. 'J 15
r.l.tilO
;n.-Jft8
i:7.'.«-'n»
■JT.'k'o
..- .1-, I
•■'■.■ I
• -I,! t
•-■.ITl
14.i4'.
-•.." ' '
1 •.4. ■
• . ■ ■ .1
.- . i-t '
•.■:,4'«''
* • p. ■ " •
=.4 •:.\.^\'
...,0-2t)
36,;V_»rt
3.'>,2SS
;i'.,oia
:«,'»Gl
a4,»;ns
34,527
34,:i4ri
34,155
33,957
3:},750
3:j,:i:J5
33.313
33,0S3
32,>4G
3J,t>)4
32,3'>4
32, HH)
31. MO
."1.574
31.:W4
31.<»:w
3<».7.'-9
:vi.4«'.0
"^M'*4
■J".' ■"5
■J-.'.-il'J
2".«>17
•>.71'.»
•>.4:i
-T.^Jl
■_:..' ".1
L'..' !•;
-■ .' :4
■-• .: IJ
•_■• .'■:!
. ■: • • .1
_ '.-r . «
■■".■' i.;
•_4.-..'^
■-....• 4
i' •*
_ ■ '^ ~
■_• .• •■♦
.fti load in iwuikIk
'- |H2r square inch.
lliidric.ll.
li(MMaii(nil
8,874
8,Wi
8,842
S.SW
8,804
8,S52
8,764
8,^22
8,721-
8,789
8,074
8,753
8.(i24
h,715
8,571
8,»i74
8,515
8,»>J2
8,457
8,5S0
8^95
H,.539
8,:i32
8,489
8,265
8,437
8,197
S,3S4
8,126
>,32S
8,0.-.:j
^,271
7,979
8,211
7,9u-2
8,151
7,H24
s,oss
7,770
b,025
7,C*l."i
7.«.«W
7,5s:j
7.s<i3
7,.'»IHI
7.'»26
7,416
1 1 1 «> 1
7,.'J31
V(2.
7,246
1 ,*>77
7,1. •-»
7,.-rl'3
7,U77
7.47'i
0.9^7
7.4"!
6.'.«H
7.:;2S
%,<\:\
7.2.'.4
6.7J.;
7.1 7'.'
p.'-.:;.'
7.:-.
ri..*.'.2
7,":'i
6. 4'.".
i.,"«."i.'i
€.'.7'*
\\<-
e.--".':;
«".MIi
6.2* »•;
•!.72'«
t..l21
»^.«'-»;
€.'»■;•.
»■■. '.7'»
r..v:2
C.'-^-l
r»,^ 1 •
.-..42^
."•.T****
.-..VJ
•'.■'» 1
I.J7S
6.2m
:..-.4i
r-.i.j'
r-.4- i
|..",V.
t — "2
r-.'.'^-.
.-..:.. 4
5.1-1'.'
:>.--j'i
'o>".>
\
KEYSTONE WROUGHT-IRON COLUMNS.
245
•5?X
)
9
m
m
I
9
>
I
0
>
>
P
9
J
9
9
J
r
>
•oiqx i g «if-^ -^"x r^-». sjf-^ I I I
'^
is
g
o
O
H
o
n
O
a
•4
O
o
B
O
^^-
' =i co"^ oo xi-
?C (N l- CO Ci
• _• m • m
O/
•*
• • • • • • •
I I
r I
.5 "^iO
S
9
(IS
.a
•mm
if
HI • •
CiO
^fi
cc;o
cc-t
53
iS2 S?.
^ot-
ooo
?2S
Ct -71
I-CC
to
•s o a
s
s
CD
I 'a
CO o oc »-o <?! c: o -t
S5
S«
<
$00
S« $5: 8S
2 « =
JS I
•&
I II I I >
I I
11 II
II II
II II
«M xo 'Nc: cc?! c:co
£ IX ©^ co-r «x c:^ I I
I I
I •
OX XX I'- 1- -tC O CO i-t
• • •• •• •• ••
— cc »r: I- c: — cr i.o i- ct
CO ^o ctt- o-r co5^
5 ' ' ?LS S.- SS as 22S I
rl
i ^
?
'!<K *« 5>o '"ftv^ o^
i-* ,-^ *-* "^x 0'X'>\ ^^v*?^ nftnft
I I
-'*
^«c
r 244 STRENGTH UP WROliGHT
H
TABLE XI.
StreiKith of lloli'iii' CyliinMcrtl or
Seetangulfir
Wroiwhl-^
Pillai-K.
(UALCULATED BY FuBMlTL
AB B ANIl tl.}
r„„r
Bn.'ii*iiig.v.e[|thl.ln riouiid.
tialii load In nouiub 1
pur Hiuora Udi. |
dlvldjid by
Uj-ltodrld.
RHtoiigular.
Cylluclrte-l.
R«i.Dr>|
5
a5,«5
8i.aw
8,874
,m
3»,3OT
.s»
3Ei,21T
.m
3i,061
,821
IS
84>1
,780
IS
»4,B07
34:801
8.71S
M.3Sfl
34.flB8
8,874.
11
33,K!T
34,627
g,Sl&
8.031
8,688
S3,SM
34,155
8^
s3,:iM
33.057
B,332
,4M
M
d.aes
.437
ss^Ase
8,1BT
.384
■a
3a,HM
33,313
8.120
n
8,053
.171
32;84B
7,9;i>
3i
31.010
32,604
7,002
M
ai.j08
32,354
7.8J4
27
7,770
.Mf
3S
ailsjo
7,00a
»m.
suiasi
J,6M
m
30
7.000
M,twa
3i;030
jn
zo,aM
30,-58
,ng
33
M,M1I.
30,400
7,218
,on
2§,e42
-648
SS,3B7
^.D■:^
->7«
au,fios
0,887
'^
27 .SM
as^DH
Mt3
IS
TO
28.900
mIsst
ai.7iB
0,720
lis
20,aw
KX»
la
»,0S2
Sl.f21
0,405
8.378
;IS
26,111
■^%^s
><
V4,827
i'.-XB
7»
4B
W,486
au,oi4
0,121
MU
.Ml
M;809
1 m
S3,41i>
26,-11
e,ssB
1^-
HI
!3,U-l
S,-M
tm
SI
m
M,48B
aj,8ifl
8W
u
22.184
24,sa)
0,641
CW.
u
6,401
B.OU
aiisja
6.asa
ISa
/
Se S1.2I5
■£1,M2
6.301
8,810
/ 17 j i»,W9
i!a,Wi*
i;ta.
«Mi
Ki.uai
\ b.\s«
\ ««.
L" "■*"
» / M,MS
\ bfICO
\ ^
I
r
^YSTONE WROUGHT-IRON COLUMNS.
245
0
0
lb
u
0.
h
X
UJ
o
ij z
8'
JZ UJ
h
<l O
H
O
a.
CO
bJ
o
o
0
o
z
<
CO
bJ
CO
CO
u
z
o
\^
mvwx
•
ja
to
^^•RJx
1 1
1 1
•
.a « a
•
D
^^1
•
• •
• •
00 t-
• •
1 1
1 1
r f
■J
^
0
•s.
•
oco
(Mb-
CO O
B
O
•
1
1
co«o
1^ ^H
S?5
ss
1 1
1 1
1 1
z
§>
M
■*
"*
1
•
a
3S
• •
• •
8S
1 1
1 1
1 1
<
?
CC^
;Otr-
ooo
•
i
• •
• •
t-QO
00^
• •
COCO
<N*CO
1 r
f 1
•
p
1-^
1-H 1^
ij
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o
ja
1^00
050
^5^
COTji
n
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00
I
:?
sss
S^
00 ^
• •
1 1
1 1
1
<o
^
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•
o
82
• •
• •
• •
t-CO
1 1
1 1
<
7
Olr-
ooo
1-1 CO
"^CO
s
T-t
^^ 1^
1—1 1^
•s! <u ti
JO ^ o
•
5
1 q6
00 »o
<N05
• •
CO ^
CO(N
<©od
c5^
r 1
•
1—1
1-H 1-^
rl 1—1
ri(N
ij
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ja
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coo
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as
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05-^
co>o
tH 1-t
tH 1—t
ri<N
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•
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cox
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c: -«
coo
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C-2 y^
gg
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m
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cor-
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1-H
rH T-H
z
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• •
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f
^^ 00^ ca^ ^j<3l '^^Sl
-maajiomx
>c
-^«,
^w*« »-^-^ s^'f^**' ^Ilr-*^
«n^
v-»!»»
246
RIVETI.ESS WROUGHT-IRON COLUMNS.
*w
2"i
Inch.
"C-K
«prt»
-?t
1 1
•
l-
•
5
QO
•
1
i 1
1 1
1
5foJ
"^
A
•
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c4 CO
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to
1 f
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k
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fie
•55
5:
1
^0
1-1 S
t-CC
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558
• •
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s 1
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1-
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a
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PKTLESS WROUaHT-IBON COMIM^■
urecj by
.VETLBSS C01.UMS. also inaiiiifiii'turecj I
Carnegie Brothers & Co.. Is a wroiigln-lron (-ijluirin rolled
enta, l>ut. faslcncil (ogetlifr by tneans of ^-roovwl luttens
'-er tlie flanges nf Itie Ht-'ginenls. The olijet^l of this Is to
iniiin which shall be morf pleasing In apin'srance than the
coluimis. Both of tlieac forms of roliuiins mtiy, at coursa,
k with caat-iron uaiu auil bases.
\ anil the table following show the form nf the colitmn, iinil
meters, areai), Ihlrknpss, uiil weights, rolled, These I'oluiiins
hv cunsiileri^il aa hollow cylindrical wroiighc-lron (-oliiiniis,
.meter given in th^ Uible being for the oiitNiileor the column.
umiiB exposed bi tliu weather should be kepi thor
covered with a gowl ihuk
( paint thai mixeil wltli red
lelug prefei'able
it is impossible Ui iciialiit ihe
surface of closed iHiluniua >i
at this Is attended with niucti
ilty and expen<ie such cohuiint
d preferably be usi i only In
nterlot of buildings nhere thi.
ges in temperatui'e are not con
ible and the air is couipam
! ilr\ Id places eiposei! to
puirpiiies of t«iu{>er Ltiire, and
Dte<ted from the rain ihe paint
le inner surface of the columns will si
Fig 6
ir later cease to
proleclion to the iion from the moisture of Uie aliiioephere
T loiToslon will itl in and once begun ndl co(iti«w*
long as tliere is unoxidlMd metal left in ^^^ |
y tiniei
oil) inn
tigs 7, S md il repre»ent tjpps of polmons '
open secuon^, whicli adnLit of repainting at aW '^
and are tlieivfore suitable foi outdoor Borlt tins
Wrou^t iron coiimins fail, either by ''^**"^„ o
Wdilj .,at of ihe sinieht line, or by the hu^K^'^
lUe meUl betW^"
orothtr
ilae\t.
. Vroviii^.^^
©■■^
BENlllSG-MUMENTS.
CHAPTER Xir.
BCHDUTG-MOMENTa.
beniting-iiionipiif of a beam or truss represents llje ilMtn
tlve enei^y of the loail on tlii> l>eiiiu or trais nt nny point for w '
tlip bending- moil lent Is ronipiitMl.
Tlie moment of u, foree aroimil any givpn nxis is the prochMl^
tlie toitx Into tlie perpendicular dislaiiee between tlie line of «
of tli« foree and tlie axis, or the proilurt of tlie force into ita mul
In a beam the forces or ioada are all vertital and the arms h
Konlal.
The bending-inoment at any eross^-ctioii of a beam is Ihen^
Inhale sum of tlie nionients of tlie forces tending to tiini the btt
:trouud the horixoutal axis pasalng tliroi;gh the centre of gruU):
of tile section.
i. — Suppose we have a beam with one end sectirtiT
lixed Into a wall, and the othe
0^
^^Z
end projeetlng from it, as in Fig. L
I Alt us now suppose we
weight, which, if placed ai
iif ihebeam, will cause it
ai (lie point of support.
Then, if we were to ]
■eislil ■
tlie I
near the wall, the beani <
support the weight easily; but,i
we move llie widght towanb »
outer end of the beam, the l«
; and, alM
veight ia at the >'ud, tlie inM
hrnaks. as shonn by the dotted lines, Fig. I.
Now, it is evident that the ilestniclive enei^ of the wd|^ I
greater, the farther the weight is removed from the wall-«nil o( th
beam, though the weight itself remains Che same all tlie iM
Tlie reason (or tliia is, tliat the nioiuent of the weight lends i
tiim tbebi-nm about the point -4, aivi\V\\iia vt«i\w» * V»'i'> '>^ 'HI
upper Sbrea of the bi'ani, and coinpTPBae*V\ve\o'M>«%!iWB
l« nioml out on Hie U-a«>.\*s ««),«™v\«*;an«»B
a the i,»ll and .oiLi'v^-^^*"" "" ^^"' ^*"-*' *'"'
upper norea
BENDING-MOMENTS.
251
iient of the weight produces a greater tension or compression
the fibres tlian they are capable of resisting, they fall, and t1i(?
,m breaks. Before the fibres break, however, they commence to
itch, and this allows the beam to bend: hence the name " bend-
;-moment" has been given to the moment which causes a beam
bend, and perhaps ultimately to break.
rhere may, of course, be several loads on a beam, and each one
vlng a different monuint, tending to l)end tlio beam; and it may
K) occur that some of the weights may tend to turn the beam in
fferent directions: the algebraic sum of their moments (calling
ose tending to turn the beam to the right -h, and the others — )
)nld be the bending-moment of the beam.
Knowing the bending-moment of a i)eam, we have only to find
e section of the beam tliat is capable of resisting it, as is shown
the general theory of beams, Cliap. XIV.
To determine the bending-moments of beams mathematically,
quires considerable training in mechanics and mathematics; but,
most beams may be placed under some one of the following
ses, we shall give the bending-moment for these cases, and then
low how the bending-moment for any other methods of loading
ay be easily obtained by a scale diagram.
Examples of Beiicling^-Moraeiits.
Cask I.
Beam fixed at one end, and loaded
Ith concentrated load W,
Bending-moment = W X L, (L
iiy, or may not, be the whole length
the beam, acconling to where the
iight is located. )
Case 11.
Beam fixed at one endy loaded icith
lUtrihuted load W,
h
Bending moment = ^1^ x ^ '
^Xv*^
BENDING-MOMENTS.
253
Cask VIT.
ea^n supported at both end.% loaded with two equal concen-
ed locLdSy equally distant from the centre.
'nding-moment
= W X m.
m-^
W@
<rm
Fig.8
Pw
rrom these examples it will l^e seen that all the quantities which
Ler into the bending-moment are the weight, the span, ami thc^
itance of point of application of concentrated load from each
A,
The bending-moment for any case other than the ahove may
isi\y be obtained by the graphic method, which will now be
xplained.
Graphic Method of Determiiiiiigr Bencling'-
Momeiits.
The bending-moment of a beam supported at both ends, and
loaded with one concentrated load, may be shown graphically, as
follows : —
Let W be the weight applied, as shown. Then, by rule under
^'aseVI.,thebending-
'foment directly under
„. ?w X n
^^ = ]Vx — g— •
'^'*aw the beam, with
'^e given span, accu-
^tely to scale, and
'i^n measure down
'le line AB equal
^ the bending - mo-
ment. Connect B
'itli each end of the beam. If, then, we wished to find the bending-
loment at any other point of the beam, as at o, draw the vertical
ne // to BC ; and its length, measured to the same scale as ABj
ill give the bending-moment at o.
Beam with two concentrated loads,
fo draw the bending-moment for a beam nv\W\ \>^o cQ.weft?cv\x"?>.V^
fs, first draw the dotted lines ABD and ACB, ^vNVtk%NXvi ^>^>^'
BEKlM.Nti-MOMEXTS,
of llie Vmliiig-tiimnpnt for each loiul «ipfir»tply;
rl Ff fiiiml to /' X
Fig. 10
Now, thft benrting-iiiotneni at tlie pciiit Keqiwis EB, ilne'
load Tl', ami Eh, due to the load P: lienoe Uie liendfng-moid
£ should be ilraivn tqual lo EI!+ Eh = EBi ; and at Fthe
lug moment aliould equal FC+ Fir = FC\. The outline U
bendliig-moinent das lo both loads, Ihcii, would be tlM
AB,C'xD, and tlie greatest bundiug-iiiQiui^nt would in llUB (
lebefT',.
Beam with lli
■nffid h/i'iK.
Proceed as In the laat caae, and draw the bending-mmUt
each load separately. Then make A l> = At + AS + AS, i
' Bl +?l2 + nS,and(:F=Cl + (."i + CA. The line HDJS*
llien bf CJiB oiiHIiic for IhpbfwWng-irQTnenV A^vaWi A\ftia^
The tiending'momi^m tor a Iteaui \oai\eiV *\V\i mvs wvoftwn^
^UeU wnighla may be drawn In the w
BENDIN0-H0HENT8.
uniformly diiiiHbiiled load.
i 171 W representing thp wliolf i1Utril>uU>(l loail.
the points C, B, i) by a parabola, and il wilt give
{ the bending-monienta. If, uow, kk tvanteii tlie
lat at the point a, we bave only to draw Lhe vertical
leasure It to tb^ aaitie scale aa AB, and It will be ttie
Hi. Methods for drawing the parabola may be fouiiil
cal Problema," Part I.
d with both iliflribnteil and enni:eatrated toads.
nding lines.
<, the bendmg-momenl ai X wovM \»e BE. Twtv*-
tteet ben(Jing-nioment wiU depend u-ponfla* V*"**
■atal loatlH, and it may and msk^ twA <i«k>m »*•'
256
BENDIXG-MOMENTS.
Example. — What is the greatest l)ending-moment in a beam of
20 feet span, loaded with a distributed load of 800 pounds and a
concentrated load of 500 i)ounds (J feet from one end, and a con-
centrated load of 600 pounds 7 feet from tlie other end ?
I
Arts. 1st, Tlie moment due to the distributed load is W^ ^ ^'
800 X 20
or
8
2000 pounds. We
therefore lay oft
to a scale, say
4000 pounds to
the inch, Bi =
^^p" 2000 pounds, and
>//^^ draw a parabola
between the
points A, l?,and
C.
2d, The bend-
ing-moment for
the conctnitrated load of 500 pounds is
500 X 6 X 14
20
, or 2100 pounds.
Hence we draw E2 = 2100 pounds, to the same scale as Bl, and
then draw the linos A E and CE.
8d, The bending-momcnt for the concentrated load of 600 pounds
(>0{) X 7 X l;5
is -—- , or 2780 pounds; and we draw DZ — 2730 pounds,
and connect 7) with A and C
4th, :Mako Ell =2 — 4, and T>G-'^ — 5, and connect Q and II
with C'and A and with each other.
The greatest bending-monicnt will he represented by the longest
vtM'tical line which can be drawn between the parabola AJIQ and
\X\(\ broken line AllGC. In this example we find the longest verti-
cal line which can he drawn is xy ; and by scaling it we find the
greatest bending-nioment to be 5550 pounds, applied 10 feet 11
inch(!s from the point A.
In this case, the position of the line X// was detennined by
drawing the line TT^ parallel to IIG, and tangent to ABC, The
line Xy is drawn through the point of tangency.
MOMBNTS OF INEBTIA AND RESISTANCE. 257
CHAPTER XIII.
IBNTS OF INERTIA AND RESISTANCE, AND
RADIUS OF GYRATION.
Moment of Inertia.
strength of sections to resist strains, either as girders or as
lepends not only on the area, but also on the form of the
action. The property of the section which represents the
)f the forai upon the strengtli of a beam or post is its mo-
f inertia, usually denoted by 1. The moment of inertia for
►ss-section is the siun of the products obtained by miiltiply-
! area of each particle in the cross-section by the square of
mce from the neutral axis.
. — The neutral axis of a beam is the line on which there is neither
lor comprcBsion; and, for wooden or wrought-ii-on beaniH or poPts, it
all practical purpooee, be couHidered a» patiF<ing through the centre of
>f the crosH-section.
most forms of cross-section the moment of inertia is best
by the aid of the calculus; though it may be obtained by
15 the figure into scpiares or triangles, and multiplying their
>y the squares of the distance of their centres of gravity
le neutral axis.
Moment of Resistance.
resistance of a beam to bending and cross-breaking at any
Toss-section is the moment of the two equal and opi)osite
consisting of the thiiist along the longitudinally compressed
and the tension along the longitudinally stretched layers,
moment, called "the moment of resistance," is, for any
Toss-section of a beam, e(iual to
moment of inertia
extremis distance from axis
le general formula for strength of colunms, given on p. 2ol,
ect of the form of the colunm is expressed by the st\uai"('.
radius of gyration, which is i\\e iwowwwv ol m'cx'Ovs^vA
ion {livided by its area; or -7 = r-. T\i^ \\\'a\!WKvAa» «
■■ the i^nncipal clenientarv seeUoiva, -awOl ^ ^vi\N e.os«e
MOMENTS OP INEHTIA AND RESB^H
fomiB, are given below, which will enalile Lhe momeni
given neutral &xH for any otiier aectlon to Ite readll]
by merel; adding together ilie momenta about the gl'
the elementary sections of whlcli it is eonijioited.
In the case Of hollow or re-entering sections, the mot
hollow portion ia to l>e suhl.Liicterl from LhAt of the encti
Homents of Inertia and Resistance. an<l
OjTtitlon.
/ = Momeni of ii
R = Moment, of r
a = Radius of gyretion.
A = Area of the section.
Position of neuLral asis represented by broken li
I ■■
Bam [anothiT formula).
1 denote area of one flaiigi-,
i' denote area of web,
f = effective deplli betwwr
of gravity o
the formula generally u»eii bj iA\c iiv\^neet»
MOMENTS OF INBETIA AND RESISTANCE. 2(W
>5»..|
v-t— <
3^2
K ■«-^-.— —
,-«»».. .^-.»«»»»-fl
ii
:i
h
\^ — ^ — *i
3
7
7 :
7
G2
I
36'
37_6d^
2(?"" 24'
/ _d^
A ~ 18'
12*
6
= T'
dP
I
R
3
I
d
7
— h^/f «
b)d^
I = 0.7854r*.
7? = 0.78r)4r8.
G2= 4-
7 = 0.7^54 (r*-r/).
For tlie sectiona of rolled Iron beams anit bars to be found Ind
nwrlCRi. the moiiientj! of Inertia are given in the "Book of .Sectioifl
Iron Company, tlie Pho'iiix Iron Comimny, and Messrs. Cua^
BrotliiTS & Co. The weighia for tlie beams and cliannels are in M
casta in ii'ii'iiiU ]>er yard for the anglt- and T bars, in some ciM^
in imMiil' i»-r foot.
MOMKNTS OF INERTIA, AND BADH OF GYRATIOS
OF PEXCOYD BEAMS.
1
1
1.
n. 1 m.
.. 1 .1
B<x.^|p^t-rd-
AkooI
Uomuuf of InetUa.
liodllof gfnUcnk'l
iwidw.. 'P^^""-
«|. Ins.
A.l.AB.|Axllt:ri.
AibAB
Al1>01
18
201X0
iB.eo
082.08 : 28.50
5.S6
1.20
»
145.0
i4.5r>
521.19 ' 10.91
5.98
l.«
la
108.0
16.89
37l.i)8 23.19
4.69
1.1T
12
120.0
11.05
272.80 1 12.22
4,78
1.01
lOi
iie.ft
11.8fi
30tl.r,.-i . 14.24
4.17
t.oe
lOJ fil.O
9.-0
HiS.2:'. 9. as
4.16
OfH
10 112.0
11. n
i7;i.'is LO.m
3.94
ans
10 1 no.o
fi.04
U'^,:!! : 8.0B
i.0.1
0.B5
0 00.0
B.07
118.1*1 1 S.44
S.«2
0.«l
9 ' 70.0
Q.e8
H4.44 1 5.59
3.88
as»>
8 1 81.0
8.14
8.1.H3
7.23
8.SI,
aH
1 8 ! 65.0
H.M
09.17
5.02.
3.25
ast(
1 7
05.0
fi.fi8
49.73
4.15
2.75
aw
' 7
52.0
ri.14
4:i.08
3,43
2.89
aeii
tl
S0.0
5.04
ae-oa
2.15
2.31
ao5
! i:
40.0
J.OS
24.10
1.80
2.43
o.He
1 -'
34.0
3.38
1.3.40
1.21
1.99
o.ea
f,
-mo
2.94
i2..'iO
1.00
2.m^
aeO'
i
38.0
2.00
■:m
i.n
l^^
O.AS,
3 1 sa'o
i.eo
5.14 \ tt.w \ \41fc V asivj
2.25
a.2« \ «.n \ <^ \ ^a|
^J^ml 17.0
■ Ml
2.W \ O.Aft \ \fS>\^
m
|^^K__
BABII OF GYRATION.
261
have given in each case all the information furnished by the
!tive companies; and although it would be very desirable to
the same information for all the sections that is given for the
>yd sections, the author has thought it best not to complete
kbles by his own work.
owing the strength of a Pencoyd section, it will be very easy
dge of the strength of another similar section of the same
me dimensions and area, or weight. For the Pencoyd and
Q Iron Mills sections, the radii of gyration are also given.
ENTS OF INERTU, AND RADII OF GYRATION,
OF PENCOYD DECK-BEAMS.
fl '^
tl <^ ■! ' l|H
<y
ID
S.
Weight
per
yard.
Ibe.
I.
Area of
cro«B-
BectioD.
sq.infi.
10.38
9.06
8.02
7.17
6.11
5.21
4.18
II.
III.
MoraentA of Inertia.
Axis A B.
221.98
164.09
118.22
9.33
7.64
6.19
Radii of gyration.
Axis
C D.
84.77 4.92
57.66
34.40
21.95
3.63
4.62
4.25
8.84
3.44
3.07
< Difltance
I d from
base to-
neutral
axis.
2.59 I 2.57
3.S7 I 12.04
/
1.64
0.<^8
0.95
0.92
0.87
0.8.*)
0.77
0.71
2.20
\,^9>
5.24
4.08
4.27
4.00
3.50
3.20
0.63 2,65
Fbr ibr •rrtiaiki tt raOad triw bnaa aed tanM V
■■ritet. tbetaoiaau of tnrrtia *t* givm is th<> **P'
foUBtonl bj th« BMiMbirliiRrv Tbr Mtm*'
noownts nf iaenia for the tieaiiv>. <->riTi9'-i
■Bannfaftimd bj A. & I*. ICobats a ' <>.. i'
Iron (VimjMiij, UkeFluvnix Iran * >.-u.|-'
Bnchpn A Co. Tba ««^u for Um- bi
emsea in /'•i<j»b (<r jr«nt tor the car
^Dll OF GYRATION.
26a
'^ iheetia, and kadu of gyration,
^ pencoyd angle-bars.
LEGS.
•
■
■ eight
per
yard.
Monie
inei
Axis
A B.
17.68
m.
IV.
Radii of
V.
VI.
Ilttf of
tia.
Axis
C 1).
gyration.
Distance!
d from
base to
neutral
axil*.
Axis
A B.
Axis
0 D.
6 X
ii
.50.6
7.16
1.87
1.19
1.66
6 X
1
110.0
3.5.46
1.5.00
1.80
1.17
1.86
5 X
A
41.8
10.02
4.16
1..56
1.00
1.41
5 X
1
90.0
19.64
8.67
1.48
0.98
1.61
4 X
28.6
4..36
1.86
1.24
0.81
1.14
4 X
54.4
7.67
3.45
1.19
0.80
1.27
3i X
24.8
2.87
1.20
1.07
0.70
1.01
3i X
.ms
4..S:^
1.85
1.04
0.69
1.10
I
3 X
14.4
1.24
0.51
0.93
0.60
0.84 1
3 X
3:5.6
2.62
1.15
0.88
0.59
0.98
2J X
13.1
0.95
0.39
o.a5
0.55
0.78
2? X
2.5.0
1.67
0.72
0.82
0.54
0.87 1
21 X
11.9
0.70
0.29
0.77
0.50
0.72
2i X
22.r>
1.23
0..54
0.74
0.49
0.81
2i X
10.6
0..50
0.21
0.69
0.45
0.(J5
21 X
A
17.8
0.79
O..34
0.(i7
0.44
0.72
2 X
•h
7.1
0.27
0.11
0.62
0.40
0.57 ;
2 X
I
1.S.6
0..50
0.21
0.61
O..39
O.M :
IJX
?6
6.2
O.IS
0.08
0.5:j
0..^>6
0.51 1
IJX
K
11.7
0.:U
0.14
0.51
0.35
0.57
Ux
1%
i».;j
0.11
0.05
0.46
0.31
0.44
li X
i
9.H
0.19
0.09
0.44
0.31
0.51
U X
i
3.0
0.05
0.02
0.41
0.26
0..36
U X
i
5.0
().()H
0(>4
0..38
0.26
0.40
/ X
'
2.0' .
0.02
i o.oi
\ 0.*^
\ ^.^
\ ^5$:^^
' X
4.4
o.(y4
'; O.0f2
\ (i.^
\ ^.«
\
A ^:>;:>
/
\
\_..
R.
MOMENTS
OF INERTIA,
m
1
MOMENTS
OK INERTIA. AND RADII OF GY
H
OF I-ENCOYD CHANNELS
i
,|U-
r-%
'
I.
o.
m.
IV.
V.
a
i-
D4
BI»ln
Wetgh
Am. of
Ifantenta
f lDerU>.
lUdllnf
gynllon
Axil A B.
a'^'.
&t.
IB
14S.O0
14.8«
451.51
10.06
5.S1
1.13
t
' IS
88.50
8.8.3
182.71
7.43
4..15
0.98
i
13
*).Ofi
T,M
123.71
3.22
4.50
0.74
i
10
80,on
r>.i»
»2.08
4.29
3.92
084
i
10
49.00
4.8B
73.01
2.33
3.89
0.89
0
9
54.00
5.40
(W.34
2.47
3.45
0.68
0
i
g
37.00
3.7a
43.05
1.31
3.43
0.59
0
P
8
43.00
4.25
40.00
2.17
3.00
0.71
0
■
8
mou
2.UU
28.23
1.08
3.09
o.tto
«
7
41,00
4.10
20.51
1.71
2.08
0.65
^
1
au.oo
2,64
iy.4fi
0.00
2.IU
0.58
a
6
33.00
3.-29
18.37
).40
2..3<(
0.67
a
a
33.00
2.27
11.67
0.59
2.27
0.51
a
3
27.30
2.73
HI. 20
OM
l.lt:j
0..W
0,
19.00
i.sa
(1.07
0.37
1.88
0.4.'>
a
4
4
21.50
2Afi
5.10
a54
l.->)
0.50
°i
17..W
I.IT,
4.14
0.41
]..>t
0.48
J
3
15,00
1.52
2.03
0.32
1.16
a4a
/ «/
11.30
1.13
Q.m
\ 0.-i\ I «.«.
■
s
S.75
0,8S
V>M
\ O.ftS \ tt.14
^
^
1
RADII OF GYRATION
SNTS OP INERTIA, AND KAIili vx
OF PE\r;OYD A.VOLE-EAiit
-A
LVL.v :.>.,-
Size, in incfaa*.
4 .r>^.Tm
•-*. .' r -«
3 X 6
tt X fi
5 X 7}
5 X ;-)
4X4
4X4
X
X 1
X
X 1
X
X
3i X ;5i X
3i X :i\ y
•>
•J
X
'> y
•»
X
'-*» ^
>>3
-4
X
•^:- -
2}
X
•j! X
iii
X
-s ^
X
■-'. X
21
X
- - '
-4
X
-. '
'>
/
'1 ^
2
X
— *
Ij
X
a
• •
15
X
^ /
1;
/
'. . '
1*
/
' /
li
/
^ _ #
1
/
; _ /
;
y
.■
/ .
r
_.
p •
4:>
."4
• •
-:y
••■ t
.fw
264
MOMENTS OF INERTIA.
MOMENTS OF INERTIA, AND RADII OF GYRATION,
OF PENCOYD ANGLE-BARS.
UNEVEN LEGS.
I.
I!
r
41.8
II.
III.
IV.
V.
VI. VI.
1
■<
Size, iD iDchee.
Momeuta
inertia.
of
Radii of gyration.
Distance
from base to
neutral axes.
1
Axis
A B.
Axis
C D.
5.60
Axis
E F.
3.55
Axis
AB.
Axis
CD.
Axis
E F.
d.
0.96
6 X 4 X
T%
15.46
1.92
1.16
0.92
1.96
6 X 4 X
1
90.0
30.75
10.75
7.46
1.85
1.09
0.91
2.17
1.17
5 X 4 X
1
32.3
8.14
4.66
2.47
1.59
1.20
0.87
1.53
1.03
5 X 4 X
1
80.0
18.17
10.17
6.10
1.51
1.13
0.86
1.75
1.25
5 X 3^ X
■i
30.5
7.78
3.23
1.95
1.60
1.03
0.80
1.61
0.86
5 X 3^ X
0
J .
58.1
13.92
5.55
3.72
1.55
0.98
0.79
1.75
1.00
5 X 3 X
\
28.0
7.37
2.04
1.42
1.61
0.85
0.70
1.70
0.70
5 X 3 X
i
54.4
13.15
3.51
2.58
1 .55
0.80
0.69
1.84
0.84
4i X 3 X
«
26.7
5.50
1.98
1.27
1.44
0.86
0.69
1.49
0.74
4i X 3 X
f
43.0
8.44
2.98
2.04
1.40
0.83
0.68
1.58
0.83
4 X 3i X
^
26.7
4.17
2.99
1.44
1.25
1.06
0.74
1.20
0.95
4 X 3i X
4;i.0i 6.37
4.52
2.34
1.22
1.03
0.73
1.29
l.W
4 X 3 X
3
24.8
3.96
1.92
1.10
1.26
0.88
0.67
1.28
0.78
4 X 3 X
39.8
6.03
2.87
1.69! 1.23
o.a5
0.65
1.37
0.87
3^ X 3 X
'A
21.2
2.5:3
1.72
0.86! 1.09
0.90
0.64
1.07
0.82
3| X 3 X
mri
4.11
2.81
1.49! 1.06
0.87
0.64
1.17
092
! 3 X 2i X
h
16.2
1.42
0.90
0.47' 0.94
0.74
0.54
0.93
0.68
3 X 2^ X
\
25.0
2.08
1.30 0.72 0.91
0.72
0.54
1.00
0.75
i 3 X 2 X
i
11.9
1.09
0.39
0.25 0.96
0.58
0.46
0.99
0.49
1 3 X 2 X
{
22.5
1.92
0.67
0.47 0.92
0.55
0.46
1.08
0.58
3i X 2.^ X
A
17.8
2.19
0.94
0.56, 1.11
0.73
0.56
1.14
0.64
3| X 21 X
{
27.5
3.24 1.36
0.871 1.08
0.70
0.56
1.20
0.70
6 X 3.^ X
f.'
39.6
14.76 3.81
2.68! 1.93
0.98
0.82
2.06
0.81
6 X 3i X
1
a5.o
29.24
7.21
5.751 1.86
0.92
0.81
2.26
1.01
6i X 4 X
-h
44.0
19.2i)
5.72
3.87i 2.09
1.14
0.94
2.18
0.93
6i X 4 X
1
95.0
;38.66
11.00
8.35j 2.02
1.08
0.93
2.38
1.13!
j 5i X 3i X
a
h
32.3
10.12
3.27
2.14 1.77
1.05
0.81
1.82
0.82
1 51 X 3i X
^
52.3
15.73
4.96
3.35; 1.73
0.97
0.80
1.91
0.91
; 7 X 3^
s
61.7
30.25
5.28
4.45! 2.21
0.92
0.85
2.57
0.82
7 X 3i X
' I
95.0
45.37
7.53
\ ^.IC
\\ l.\V^
\
WA4
y*in\
Uar;
\
B&DII OF OTRATION.
"^ '' INERTIA OF TRENTON BEAMS.
-%.,
,.
*'i
in.
Wdghtiw
Ar»^™r
Uomenui
of loerlU.
jUhM.
Ita.
■q. Inx,
Alia AH.
A.U O D. '
" "" '
16
200
ao,02
707.1
27.48 i
16
120
15.04
r,23..>
i5.2e
ISi
170
16.77
:H)I.2
2.^41
m
125
12.33
288.0
11.54
10*
135
lase
23.1.7
15*)
10*
105
10.44
185.0
0.43 \
10*
BO
B.go
11(4.0
8.00
e
12G
12.33
150.8
11.23
9
95
8.50
111.9
7.35 I
9
70
7.00
93.il
4.92 1
6
80
8.03
iM.9
7.W 1
8
65
B..n
(0.4
4.55
7
as
5.50
44..1
3.80
«
lao
11.84
rt4.fl
18.51)
6
90
8.70
49.M
10. 7h
0
BO
4.fil
20.0
2,74
0
40
4,01
;il.5
1.11]
5
40
3.»)
15.4
\.W
5
ao
■im
12.1
1.04
4
37
■AM
0.2
1,74 ,
4
30
2.91
7.3
i.n :
' /
„
1.77
V.
\ ^■■•^^ \
266
MOMKMTS OF INSKTIA.
MOMENTS OF INERTIA, AND RADII OP 6YRATI0K,
OF PENCOVD T-BARS.
c
^fe
UNEVEN LEOS.
61m, In Inches.
4^ X
4 X
4
4
4
8
L
X
X
X
X
X
X
:j X
:{ X
2^ X
2 X
2 X
2 X
22 X
2i| X
r> X
5 X
2i X
3i
3i
2i
2i
3
3
U
u
u
r'c
Weight
per yard.
II.
III.
MoroentM of Inertia.
AxIm a B.
Axis O D.
44.50
5.27
41.80
4.05
30.70
1.01
3:3.00
l.tW
25.90
1.94
25.25
2.09
20.40
0.08
28.25
3.12
23.H0
1.38
11.20
0.19
9.10
0.10
8.75
0.10
7.(K)
0.05
5.88
0.01
18.75
0.50
21.00
0.83
48.44
5.37
44. 10
0.24
rt.50
0.01
3.66
3.23
4.01
4..58
2.18
1.69
1.68
1.06
0.94
0.50
0.33
0.18
0.17
0.17
0.(J2
0.(«
5.31
5.25
0.24
IV.
V.
Radii of gyration.
Axis A B.
1.09
1.05
0.72
0.70
0.86
0.91
0.58
1.05
0.70
0.41
0.33
0.43
0.26
0.13
0.55
0.0;}
1.05
1.19
0.12
Axis C D.
0.91
0.88
1.14
1.17
0.92
0.82
0.91
0.61
0.63
0.71
0.60
0.45
0.49
0.54
0.58
0.55
1.04
1.09
0.61
VI.
DifltaoM
ditom
baaeto
neutral
axis.
1.10
1.09
0.67
0.64
0.77
0.84
0.54
1.10
0.82
0.37
0.32
0.43
0.27
0.17
0.66
0.75
1.05
1.08 )
0.18
RADII OP GYRATION.
267
FOMENTS OF INERTIA OF TRENTON BEAMa
Inches.
>
5
4
4
4
-€-
fV
\f
B
Weight per
yard.
Ib0.
I.
Area of croM-
section.
sq. ins.
200
20.02
120
15.04
170
16.77
125
12.33
185
13.36
105
10.44
00
8.90
125
12.33
85
8.50
70
7.00
80
8.a3
65
6.37
55
5.50
120
11.84
90
8.70
50
4.91
40
4.01
40
3.90
30
2.99
37
3.66
30
2.91
« 1
1.77
A
li
^— o
Momenta of inertia.
Axis A B.
707.1
523.5
391.2
288.0
233.7
185.6
164.0
150.8
111.9
93.9
83.9
67.4
44.3
64.9
49.8
29.0
23.5
15.4
12.1
9.2
7.5
4.?>
Axis O D.
\
27.46
15.29
25.41
11.54
15.80
9.43
8.09
11.23
7.35
4.92
7.55
4.55
3.90
18.59
10.78
2.74
1.61
1.68
1.04
1.74
1.11
— I
268
MOMENTS OF INERTIA.
MOMENTS OF INEKTIA OF TRENTON CHANNELS.
Size, in
inches.
15
15
12i
12i
lOi
9
9
8
8
7
7
6
6
6
5
4
3
4-4---%
;b
Weight per
yard.
Ibe.
Area of
croes-
eection.
Bq. ins.
U.
in.
Momentu of ioerlia.
18.85
12.00
14.10
7.00
6 00
7i)2
5.08
4.48
3.30
3.60
2.54
4..32
.3.20
2.25
1.92
1.65
1.45
Axis A B.
586.0
37ao
291.6
153.2
88.4
82.1
58.8
44.5
32.9
27.1
17.3
21.7
17.2
12.6
7.2
3.9
2.0
Axis C D.
32.25
14.47
17.87
5.04
3.84
5.35
2.53
2.54
1.44
1.96
0.83
2.12
1.30
0.70
0.44
0.32
0.29
VI.
DistaDce d
from baae
to neutral
axis, in
inches.
1.260
0.950
1.120
0.756
a628
a850
a&so
a760
a580
0.715
0.511
0.725
0.630
0.540
0.464
O.460
O.510 ■
65
55
Deck-Beamr.
6.20
5..35
Note. — The weights of the c\Minue\ft tot e^tVi «\i*i ^nqc^ ^^w$s% xq«X 1*
iacrows^i'il within certain limits by ro\V\ug v\\v; \)ai WucVvt.
MOMENTS OF INERTIA.
269
q^TS OF INERTIA OF TRENTON ANGLE-BARS.
nches.
Weight per
foot, in Um.
I._
Area of
crosB-
sectloD,
in
sq. ins.
II.
Moment
of Inertia.
VI.
Dittance
d from
base to
neutral
axis,
In inchee.
EVEN
LEGS.
X 6 in.
19 to 32i
5.75
19.910
X 4^ "
12i to 20J
3.75
7.200
X 4 "
9i to 18
2.86
4.360
X 8i ''
8i to 14i
2.48
2.860
X 3 "
4.8 to 12
1.44
1.240
X 2f "
5.4 to 9i
1.62
1.150
X 2i "
3.9 to 7i
1.19
0.700
X 2i "
3i to 6
1.06
0.500
X 2 "
3i to 4i
0.94
0.350
X U "
2 to 3
0.62
0.180
X li "
13 to 2i
0.5iJ
0.110
X li"
1 to If
0.30
0.044
X 1 "
i to l|
0.23
0.022
X ^"
0.6 to 1
0.20
0.014
X i "
rVto 0.8
0.17
0.009
1.685
1.286
1.138
1.013
0.842
0.802
0.717
0.654
0.592
0.507
0.444
0..358
0.296
0.264
0.233
Axis A B
ii
n
n
ii
li
ii
n
ii
li
II
' II
II
n
k<
n
a
li
ii
li
ii
a
ii
ii
UNEVEN-
LEGS.
X 4 in.
X 3i "
X 3 "
X 3 ''
X U"
14 to 23
10.2 to* 19i
9 to 14i
7 to 14i
4.0
418
3.05
2.67
2.09
1.11)
j 15.460
I 5.600
j 7.780
I 8.190
j 5.490
] 1.080
] 3.370
I 1.640
1.5(J0
o.no
X 2i 'Y 4i to 9i I 1.31 i ^-^
< 2
ft
4 to 7i 1.19
40
] 0.:^90
1.964
O.iHU
l.()10
0.860
1.490
0.740
1.260
0.7(50
1.320
0.320
C D
A B
170
OF INsi^l^^^^^^
MOMENTS OK INKItTIA OF TRKNTON T-BAI
m . N
c
=J
^ — ,
^|L
3
■>
D
L
I..
VL
Bl», lo lD.be..
^ItfS.
m,%,.
MOIDDIX
of Inerlln
d from
JeSL
4 In. X 4 in
m
3.75
1 2.620
! 1-180
(Axl
81 " X ar
9.B anil 10.8
2.87
i 1,630
[ 1.030
( ;;
8 " X 3 '
7 and 9i
2.11
( 1.780
) O.»70
|o.8»0
( ;;
2i " X 2t '
6 and 5^
IM
I 0.850
) 0.400
{ 0.740
( " '
2 " X 3 '
Si and 3J
0.94
( 0.350
j aieo
} 0.590
5 " X2l'
11.7
3.50
I 1.500
J Q.OPO
j 0.010
3 " X 2 '
4.8 and 5.S
1.4S
( 0.470
i aeao
j 0.620
1 ■■
2 " X U '
3.00
0.91
( aiTO
1 0.180
|o.Nm
i ;; ;
21 " X li '
2.40
0.74
1 0.060
1 0.180
1 0.390
2 " X ] '
2.15
O.R'i
( 0.040
) 0.140
1 0.2*10
/
If XI "
i.se
\ O.WS
\
Vw,
V1
Jl
MOMENTS OF INERTIA.
271
IftOMSNTS OF INERTIA OF PHCENIX BEAMS.
•C-
IV
/
B
4
I.
II.
Moment of inertia.
*A fn 4n/>(iAa
Weight per yard,
Total area of cross-
section, in sq. ins.
1
t
Axis A B.
16
200
20.0
707.0
15
150
15.0
531.0
12
170
17.0
398.0
12
125
12.5
288.0
lOi
185
13.5
239.0
lOi
105
10.5
189.0
9
150
15.0
194.0
9
84
8.4
112.0
9
70
7.0
96.5
8
81
8.1
87.5
8
65
6.5
68.5 :
1
7
69
6.9
57.0
7
55
5.5
43.5
1
6
50
5.0
31.0
6
40
4.0
24.6
5
36
8.6
15.0
5
30
8.0
12.5
4
30
3.0
8.0
1
18
1.8
4.5
ilfoTB. — As the HmmiIv Iron Company do not give \,h« tuom«k\!L\>ot iaerUa for
r ebmonel and aai^mmm, ■ we do not give it here. 'Fot 9^ \MbX cA xXikfe «»&» ifiafc
weight it woahhW too9tmh ^* the same m the TTQii\A\i\»x%.
MOMENTS OF INERTIA.
-fr-H-
I.
11. 1 in.
IV.
■V.
Biie. Id
15
Wrfgbl
Ana of
UoiMiil-ot Iwntta.
iUdliof
nntto.
Ail< A B,
530.0
All! 0 D.
18.30
A.I. A B.
AitiCS
150.0
15.0
5,94
1.04
15
1M.0
1U.G
HI 4.0
20.00
5.61
1.01
15
201.0
20.1
877.0
25.40
5.S0
1.12
15
240.0
24.0
750.0
29.90
G.50
1.12
12
lii)].0
12.8
275.0
11.00
4.88
aw
12
1S0.0
18.0
340.0
15.50
4.35
0,03
lOJ
B4.5
0.5
!6r,.0
8.01
4.17
0,ffi
m
las-u
13.5
201.0
10.70
3.86
0.S9
10
00,0
i1.0
150.0
TIH
4.09
0,M
10
135.0
13.5
1S7.0
11, .10
3.73
0,91
g
70.5
7.0
07.5
5.48
3.73
0,88
B
99.0
0.0
117.0
7,U
3.44
0,8,i
1)
1M.0
13.5
I5U.0
14,0
8.42
1.01
»
150.0
15.0
1011.0
15.7
3.34
1,03
8
0(1.0
CO
OD.O
4.57
3,25
0.8.1
a
105.0
10.5
4)0.4
ft, 06
2.04
0.82
7
54.0
5.4
45.8
3,72
2.1)1
ass
7
75.0
7.5
54.-1
4.87
2.80
asi
6
40.-1
4.1
24.5
2.00
2.48
0.7D
6
54.0
5.4
28.4
2,51
3.30
ass
6
ao.o
3.0
12.3
1,08
2.03
O.B0
5
31).0
3.0
14.2
1.S4
I.Bl
aso
4
24.0
2.4
8.10
0.71
l;61
0.56
4
30.0
3.0
6.00
0.87
1.53
0.54
3
21.0
2.1
3.00
a55
Lei
aB5
^/
27.0
2.7
3,54
\ 0.?A
V ■ \.%
V"
s
RADII OP OTR&TIOH.
.(L
1.
11.
IV.
VI.
Monumtn of
Radii ot
Dinlann o(
liicnU.
T^S^'^v,
of KcTlon.
•S2t
Ali, A B,
AxU A H.
web.
120.0
12.00
3.W.0O
5.47
0.82
180.0
18.00
471.00
5.12
0.88
ao.0
t!.OI)
110.00
4.40
O.011
77.fi
e.75
140.00
4..'-.0
0.74
00.0
0.00
108,00
4,;il
0.72
B0.0
It.OO
170.00
4,42
0.72
150.0
15.00
243,00
4.07
0.8:1
4e.o
4.ao
62.-T0
3,01
0.55
S2.5
5,25
75.60
3,711
O.U:J
90.0
11.00
10fl.t*0
3.44
0,00
60.0
0.00
8(1.40
3,S0
0.70
105.0
10.50
120.1)0
8.48
0.115
43.5
4.;!5
3.30
0,58
64.0
6.40
iw.no
3.40
ao8
no.o
(1.00
8<>.1<I
3.15
0.73
37.n
.^73
:t4,so
3.03
0,53
46.5
4.S.'>
3il.20
2.H0
0.53
4S.(I
4.S0
4.i.ao
3.07
aiut
S4.(l
S.40
64,50
2.77
0.73
:ji.;>
a. 15
22.40
2.07
0.52
40.r,
4.05
20,10
■ISA
0,53
42.0
4.20
30,00
2.70
O.IW
80.0
0.00
37.1>0
0,08
22.:*
2.25
1-2.10
2,:t2
0.48
28.5
2.83
KJ-JW)
2,2t
0.47
aao
:i.00
10.00
2,35
0.00
■i8,n
4.80
22.00
2,14
0.(i:!
1S.5
l.lffi
7.00
I.IH)
0.44
■Ai.r>
L'..-i.'i
8.2.1
I.NO
0.44
ai-ii
2,10
10.22
t.|L4
aoi
42.U
4.20
i;i.:il
1,78
i).04
1H.0
1.80
4.11
1,51
0,40
SLO
2.10
4.51
1,47
0.40
21.0
2,10
4,iia
\M
0,54
27.0
2,70
G,T8
1.40
aso
15.0
1.00
2.04
i.n
Q.SV
_[
JAO
180
2.27
\ ^-^
\ ''■'•" \
274
MOKIENTS OF INBBTIA
MOMENTS OF INERTIA, AND RADII OF GYRATION, OF
UNION MILLS ANGLE-IRONS.
For miDimam and maximum thickness and weight.
EVEN LEGS.
1
•
VI.
II.
IV.
Size, In
inches.
Weight per
foot, in Ihs.
Area of
cross-
section, in
sq. ins.
Dietan
centr
gravity
outsic
flange,
Min.
1.68
ice of
e of
' from
leof
in ins.
Max.
Moments of
inertia.
Axis A B.
Radii of
gyration.
Axis A B.
Min.
Max.
Min.
Max.
Min.
Max.
Min.
Max.
6X6
19.2
39.2
5.75
11.75
1.96
19.900
43.100
1.90
1.90
4x4
9.5
19.5
2.86
5.86
1.14
1.35
4.860
9.550
1.20
1.30
3^X3^
8.3
17.0
2.48
5.11
1.01
1.22
2.870
6.380
1.10
1.10
34x3^
7.7
15.8
2.30
4.73
0.95
1.16
2.270
6.100
0.99
1.00
3x3
5.9
12.2
1.78
3.65
0.86
1.04
1.510
3.350
0.92
0.96 1
2ix2J
5.4
8.8
1.62
2.65
0.80
0.91
1.150
1.990
0.84
0.87
1
2|x2i
4.9
8.0
1.46
2.39
0.74
0.85
0.850
1.490
0.76 j 0.79 ;
2|x2i
3.5
7.3
1.06
2.19
0.66
0.79
0.500
1.130
0.09
0.72 I
2 X2
3.1
5.6
0.94
1.60
0.59
0.70
0.350
0.680
0.61
0.63 1
i|xii
2.1
5.0
0.62
1.50
0.51
0.64
0.180
0.480
0.54 j 0.56
U^U
1.8
8.6
0.53
1.09
0.44
0.55
0.110
0.250
0.46 ! 0.48
1
Ijxlj
1.0
2.0
0.80
0.61
0.35
0.43
0.044
0.008
0.38
0.40
lixil
0.9
1.8
0.27
0.55
0.32
0.39
0.032
con
0.84
0.86
1X1
0.8
1.2
0.23
0.36
0.30
0.33
0.022
0.036
0.80
QJSl
t
SADII OF QTB&TIOH.
.^J,^
i-
II,
.V.
VI,
MoraenWof
lladll of
niMnnoe of
eiiE, Id
SSK.
o?«™.
lUPlTll.
(UmlloH.
iira'l'wrein
A%\i A 11,
All. A B.
w«b.
16
120.0
12.00
359.00
0.47
0.82
16
180.0
18.00
471,00
5.12
0.88
12
60.0
(i.Ol)
119.00
4.46
0,69
la
77.5
6.75
140.00
4.56
0.74
12
B0.0
9.00
108.00
431
0.72
12
fl0.0
9.00
176,00
4.42
0.72
12
14O.0
15.00
248.00
4.07
0.8:1
10
48.0
4.80
H2..i0
3.61
0..55
10
W.5
5.25
7.i..^)
3.711
O.IW
10
IW.O
9.00
106.80
3.44
0.66
10
60.0
6.00
89.40
3.S6
0.70
10
105.0
10.50
12tl.i>0
3.48
0.65
e
43.5
4..'H
47.40
3..?0
9
64.0
5.40
tM.SO
3.46
0.68
9
(ao
9.00
61). 10
3.15
0.7il
B
37.5
3.75
:{4.rri)
3.m
0.53
8
48.5
4.05
311.20
2.90
0.53
e
48.0
4.80
45.30
3.07
0.66
8
M.O
8.40
64.50
2.77
0.73
7
31.5
3.15
22.40
2.U7
0.52
7
40.5
4.05
20.111
2.54
0..^,2
7
42.0
4.20
.■W.(HI
2.70
0.66
7
80.0
0.00
37.90
2.51
0.(18
0
22.5
2.25
12.10
2..12
0.48
6
28.5
2.S5
13.90
2.21
0.47
B
30,0
;i.oo
it!.ni)
■>.Ai
0.'ill
6
48.0
4,80
22.00
2.U
11.62
0
19.5
I.!)5
7.00
1.90
0.41
&
25.5
2,5.')
8.25
I.WI
0.41
G
27.0
2.70
10.22
1.H4
O.Kl
5
42,0
4.20
l;!.3.-.
1.78
0.64
4
18.0
1.80
4.11
I.5I
0.4ii
4
21.0
2.10
4.51
1.47
0.46
4
Ul.O
2,10
4.1)8
l..'i4
0.54
i
27.0
2.70
5.7*
\.4a
I (i.TA
? /
IS.O
l.-Hi
2.04
\ \.Yl
\ q,-;a \
J-/
)S.O /
J 80
■2.21
\ \.Vi
\ RJ.-A
1
876 MOMKN-rs 1)1. INEllTIA
1
^K FROrEKTlES OF IINIUN MILLS T-IItONS. M
K
M
■
1
■
1
ll
-J|^
r-^
'^
3
1
1
1
1
..
ii. IV.
ni.
4
1
i
is-
Axl. A B.
Aula (7D, ■
i-
111
it
pi
m
1
0 «a
13
3W
«Ta
£.eu
oeo
6.-0
-ao
„
6 -n
lot
1.40
0.86
i.sn
11 -SI
19
4,M
1.13
fl.SO
2. IK
l.OT
S.90
1.70
0J9
* x6
"*
i-s;
IO.M
3.06
1.67
2,70
1.40
0,M
4 -11
ISl
3.(111
1.19
7.80
iA»
I.ffl
iZ
;;»
D«
« k3
B|
X.IS
o.eo
£.10
0.9D
O.ST
S.,10
t.io
«,»
71
61
I.Sj
H.O-J
1.10
0,«1
0.70
a.™
1.00
0.0
S1-*
Im
\m
a^M
I;^
1,D!I
i!m
1.00
0.W
S
ilxa
n
2.78
rt,«s
114
1.00
0,88
1.80
O.M
V.Zf
t '*
121
3.A8
1.3S
5.M
2.10
1.S1
i.qo
o.r;
u^
» xai
iM
I.OD
I.W
2.29
I.B9
U.BI
M3
»i4
3 .2i
81
l.SO
o.m
].«
0.81
0.70
».77
O.SI
o.n
(l-ij
1.B3
O.Sfl
i.39
0,T4
0,IU
D.S&
a.44
D.)l
Hi "21
o.d
•4"U
0.26
«j|
■ 1
■.
KoTE. — Tbe momenw ot inettta »nd iubumwc, an4 raMfcffl
Bw Ubfe does uot iiicludt ull biicb inwmfa>Miit»4.
~1
ll _
J
BAUII OF GYRATION.
277
For compound sections made up of two or more beAms or bare,
the moments of inertia are found l)y combining those of the several
shapes as given in the preceding tables. Thus: —
/ =
G2 =
Twice the moment of inertia
for beam a (col. II.) + tliat for
beam b (col. III.).
/
simi of are^s of beams a and b
(col. 1.)
/ = Twice area of beam a (col. I. ) x
cP + twice moment of inertia
for beam n (col. III. ) + that for
beam /> (col. II.).
I
c? 4- i width flange of beam a
L
sum of areas of beam<^ a and b
(col. I.)
^ a
^ f>f^
=^--«-
JL.
1 = Twice area of channels (col. I.)
X cf^ + moment of inertia (col.
III.), in which d = distance of
centre of gravity of the channel
from centre line of the combi-
nation.
J
area of the two channels (col. I. )
r;:*
i- I
1
■ II 11 nmmnyt
Ledtiee
I = Twice the moment in col. II.
9^ = Same as for single channel.
When a section is employed alone, either as gird(T or jiost, the
neutral axis passes through its centi-e of gravity. WhtMi rigidly
jonnected with other si^ctions fonuing Y^vK, ol a v:ou\v*.a\\\<\ s^vNaqw.
h€' neutral axis fiasscs through tlie ceulti* ol ^yanWn o'i W\« ^tssw
pound ^rtlan; ami [liorefore thp niiiiiiciit nf iRertia of M^^l
tu7 snnion will nol be Ihnt around Its own centre of SfV^^I
arounil an axis Ht a distance from that i»olnl. The atOMHl
inertia u/ a nection iibuiil o» nxis ulher Ihou that tlirough lb fl
tre <^ gravitg is equal to llie nioinenl about the ftxls tbrough
cenire of gravity plus ihe product of the area of ibe secllon by
square of tlie distani-e of Its centre of gravity from the nxia ili
wliich the ntoiueiit of inertia is souglii.
Tlie llrst step, then. In Unding tlie moment of inertia, is to f
the position of tlie centre of granty of the section. For all )]
■iietriiTHl wrtions, tlil«, of course, lies at tiie middle of the A^
For triangles, it is found on a line parallel with tlie base, and i
tant one-third the height of tlie triaiigle above tlie base. For ot
.lections, It is found bj supposing the ares divided up into elem
tarj sections, aud uiultiplyiug the area of each such section bf <
dlfitaiKW of its rcntre of gravity from any convenient line. 1
suin of these producis divideil by the total area of the section i
give the ctistjtnce of the centre of gravity from the Hue from nil
the distancea were tuea-suml.
ExAUPLB. — Find the neutral axis of a J. section having Ibi
folloiving dimensions : width, 8 inches ; depth, 10 Inches ; tbick-
neas of melnl. 2 inches. The ai'ea of the vertical flange, considerUf
itasniniting tbrough to the twttouiof the section, would belOxS,
or 30 square inches; anii the distance of Its centre of gravity abOT*
the bottom line, 5 inches. Tlie product of these quantities, then-
fore, is 100. The area ot Die liottom flange, not Included in Clx
vertical flange as above taken, is It limes 2, or 13 sijuare iuchei; tlM
distance of its centre of gravity above the bottom line,
llif product of the two. therefore, 12, Tlie sum of these proJtuM
divided by the total area is ^, or 3..') inches, which Is the distwre
of the centre of gravity almve the bottom line of the SH^tlon.
Having fomid the neutral axis of this section, lis momejil of
Inertia is readily found by the formula before given. Thus, \n ^
case just supposed, li woulJ l)e 10 — l.o = '6Ji, d, = 3.E; d., = 1.6;
and the moment would be (see p. 250),
, rix ((..vi + it
I
The iiiinni'Mt of resistance ot this section as a girder voM M
gjf . or 44f: and if a str»Sn on l.\ie ft\>wa lA V\w \™b. (A \M» }
oiiiiJs jier square Inch be alloivetl. l\ie". »^>"
rt«*nce of (he girUer tiuilllv"«'l ^^ *'^"'^" **^ «i«»^
MOMENT OF RESISTANCE. 279
una] the bending-moment of the load, it will be able to support a
Md whose bending-moment is 44} times 12,000 pounds, or 536,000;
Af if used as a girder secured rigidly at one end, and loaded at the
4hery it would support a load, in pounds, of
536000
length in inches
Jt if supported at both ends, and the load uniformly distributed
^▼er the span, it would support a load eight times as great; the
bending-moment in such case being one-eighth that in the former
(see pp. 251, 252).
Note. — Tho formulas and figures on pp. 258, 259, and 277, are taken, by per-
■iMioD of The New-Jersey Steel and Iron Company, from a handbook which
th^ publish, entitled "Useful Information for Engineers and Architects," and
taining full information pertaining to the forms of iron wliich they maoufac-
CHAPTER XIV.
Bt the terra "beam" is raeaiiL ajiy piece of material «
ppoi'ts A load whose tendency is to break tlie piece across.
:bt angles to, the fibres, and whloh also causes the pleiy lo ba
Fore breaking. When a load of any kind is applied to any bi
fflll cause it to bend b; a certain amount; and as It Is impoull
bend a piece of any material without stretching the fibres {
1 outer side, and compressing the fibres on the inner aide, II
nding of the beam will pivdoce tension in its lower fibres, u
:upression in its upper ones. This tension and compresslini U
o greatest in those fibres which are the farthest from the nt
in of the bean. Tlie neutral axis Is the line along which ll
res of the beam are neither lengthened nor shortened by Ibe IM
; of the beam. For I)eam9 of nrought-iron and wood the nei^
is practically passes through the centre of gravity of the CK
:tion of the beam.
To determine the strength of any beam to resist the effecU ol
y load, or series of loads, we must determine two things: Bm,
s destructive force tending ta bend and break the beam, i '
led the "bending-nioment;" and, second, the combined ri
ce of all the fibres of the beam to being broken, which is e
i "moment of resistance."
The methods for finding the lien ding-moments for any load. kE
■les of loads, have been given in Chap. SII. ; and rules for flnd
i moment of resistance, which Is ec|ual to the moment of inertkl
'Ided by the distance of the most extended or compressed AbmC
im the neutral axis, and the quotient multiplied by the strengUl
the material, have been given In Chap. Xlll.. together vilbl
lies of the moment of Inertia for rolleil iron sections of the usull |
Now, that a beam shall just be able to resist the load, and n
^k, we must have a condition where the bendtng-moment
lieam is eqnal to the moment ot TCB\aW.tw;a ^n<o\\.\9\\^<ni^'0».l
rigth of (he roatei-ial. ThW \.\ie \«a.TO
w/sl Ihf gi^■en load, tlie inomenv "1
PRINCIPLES OF THE STRENGTH OF BEAMS. 281
rength of material must be several times as great as the bending-
loment; and the ratio in which this product exceeds the bend-
i^moment, or in which the breaking-load exceeds the safe load,
I known as the ** factor" of safety.
By ^* the strength of the material *' is meant a certain constant
[oantity, which is determined by experiment, and which is known
» the ** Modulus of Rupture.'' Of course this value is different for
hah different material. The following fable contains the vahies
I* this constant divided by the factor of safety, for most of the
iMterials used in building-construction. The moment of resistance
iitUtipUed by these values will give the safe reaiaUng-poY/er of the
ham. •
L
Modulus of Rupture for Safe Strength.
Material.
I^t-IroD
kVrought-Iron . . . .
Steel
American ash . . . .
American red beech .
American yellow birch
American white cedar .
American elm . . . .
New-England fir . . .
Hemlock
American wtiite oak
Material.
American white pine . .
American yellow pine . .
American spruce . . . .
Michigan pine
Blueetone flagging (Hud-
son River)
Granite, average . . . .
Limestone
Marble
Sandstone
mate
Value of
R,
iu lbs.
1440
2250
16-20
1530
375
300
270
300
150
900
The above values of R for wrought-iron and steel are one-fourtli
hat for the breaking-loads; for cast-iron, one-sixth; for wood, one-
hinl; and for stone, one-sixth. The constants for wood are based
ipon the recent tests made at the Massachusetts Institute of Tech-
nology upon full-size timbers of the usual quality found in hui Ici-
ngs. The figures given in the above table are believed to be amj)ly
afe for beams in floors of dwellings, public lialls, roofs, etc.; but,
or floors in mills and warehouse-floors, the author recommends
hat not more than two-thirds of the above values be used. The
afe loads for the Trenton, Phcenix, and Union Iron Mills sections,
sed as beams, are all computed with 12,000 pounds for the safe
alue of li, or with 12,000 pounds flbre strain, as it is generally
Ailed.
There are certain cases of beams which \v\o§>V it^.^<^w\.Vi ^s^ysxsK
buihling'ConstriiL'lion, for which formvAas cawXie, ^vsexvVj'^^cvOei
- 8Rfp loads for the beams may be detevvwYW^^ <i:vc^eV\^vV\>\.
vi lmpi)ens thai we may have either a rei^wXaxX^ ^\yavv^^ ^
2«2 PRINCIPLBS OF THE STRENGTH Of ilKAMS,
irregularly 1ob(I<>(I, or a beam ot irregular wctlon, but with ■ «;
mail melliod of loniliug, or botb; and in siicli CAsta il is neeoH
to determine llie bending-moment, or uiotueut of resistance, tt
rind llie beam whose iiioinent of resistance iniillijilied by R
equal to tbls IwDding-ULoinent, or what Jood will give a bendli
inoment equal to the moment of resistauce ol a beam multlpQ
by /e.
For ftawple. BU|iiHwe we have a reetangulnr beam of yellil
)>lne loadeil al irregular points with irregular loads; wliat ditw
nions shall llie l>eam be to carry these loa<ls ? We will suppose Lt
we have fotini) the beniling-moinent caused liy tiieae loads lo
JtfO,0(X) incli poundB. •
Then, as bunding-iiionient equals nioinent of resistance mnltipfl
by /{.
/[ X If
480.1)1)0 poiiiuls = — y — X 2-J50 = B X D* X 375;
480000
Bx Di= -_y^ = 12S0.
If we assume D = 12 inelies, then B = -rrr ~ 0 incliea, or I
lieam should be 9 Inches by 12 inebes.
If, instead ot a liard-pine tieain, we sbould wish to use an In
beam to carry our loads In lUe above example, we must Qnd>^
lieaui whose nionient of resistance nuiltiplied by 12,000 eqnd
480.00C) Inch pounds. We ran only do this by trial, and for tl
first trial we will take (he Trenton ISV-lnch 125-poutid Itesiti. Tt
inonienl of Inertia of tliis b<;aui Is given as 283; and its moiiK^nlt
reslNlanue is one-slxtli of ttiis, or iS. Multiplying this by 12,0081
we have riT0,<X)O pounds as tlie n?sisting-rorce of this beam, tf
US,llOI) pounds over the bending-inontent. Hence we should pnit>-
ably use this beam, as the next lightest beam would probably puI
be strong enough. In this way we can And the strength of a beam
of any cross-section to carry any load, however Irregularly dispuwd
It may l>e.
It Is very seldom that one needs to compute the strcngUi of
wrou^it-irnu beams, channels, etc. ; because. It he uses one of Uw
regular aectiuns to lie found In the uiarbel, the compuLalions hate J
mlrendy liwii iiiaile by the uianutacVvaeis, s
lianrilKMik. Tlieiv niiitht, however. Vie cases wXwm V
^im*ry lu make llic caleukHons Uiv any v»«-\cKiM\»Ba-,i
bJpeJl uiSL's wi' givu the IoHovj\H5 Votuvull
PRINCIPLES OF THE STRENGTH OF HKAMS. 283
Beams fixed at one eiul, and loaded at the other (Fig. 1).
Safe load in pounds =
1000 X moment of inertia
length in feet X y
(1)
Beams fixed at one endy loaded with uniformly diHribufed load
(Kg. 2). ^
Safe load in pounds =
2000 X moment of inertia
length in feet X y
(2)
Fig. 2.
Beams supported at both ends, loaded at middle (Fig. 3).
W
Safe load in pounds =
Fig. 3.
4000 X moment of inertia
(3.
span in feet X y
Beams supported at both ends, load uniformly distributed
(Tig. 4).
Sufe load In pounds =
Rg. 4.
8000 X motuewt o\ \w<?xW'a.
span Vn ieviX. X -y
V^
286 STRENGTH OF IRON BEAMS.
Another important advantage in the use of deeper beams isltheir
{greater stifi^ess. By referring to the tables, it will be«>ee&
that a beam twenty feet long, under its safe load, if )
f
6 inches deep, will deflect .... 0.95 inch, i
9 inches deep, will deflect .... 0.63 inch.
12i inches deep, will deflect .... 0.46 inch.
15 inches deep, will deflect .... 0.38 inch.
i
A floor or structure forjned of deep beams will therefore be ituch
more rigid than one of the samus strength formed of smaller
sections.
There are, of course, cases where the use of deep beams would be
inconvenient, either from increasing the depth of the floor, or from
the fact, that, with a light load and short span, they would have to
be placed too far apart for convenience. In general, however, H
will be best to employ the deep beams.
Inclined Beams, — The strength <ff beams inclined to the horizon
may be computed, with sufficient accuracy for juost purposes, by
using the formulas given for horizontal beams, taking the horizon-
tal projection of the beam as its span.
Strength of Trenton, Pencoyd, Phoenix, and Union
Iron Mills Rolled Beams, Channels, Angle a^d
T Bars.
The following tables give the strength and weight of the various
sections to be found in the market, together with the generai
dimensions of the I-beams.
The tables are in all cases made up from data published by the
respective manufacturers. The deflection of the beams under their
maximum safe distributed load is also given in the last four tables.
These latter tables will be found very convenient, for they can
be used for the spans indicated, without any computations what-
ever.
■
.
STRENGTH OF IRON BEAMS.
285
ABiPLE 2. — A 12-inch heavy Union Iron Mills channel-bar,
ling 90 pounds per yard, and having a clear span of 24 feet,
>rts a concentrated load at two points, 6 feet from each end.
t is the maximum load that can be supported at each point
stent with safety ?
1000 X 168
18, Safe load at each point = — q~x1\ — ~ ^^^ pounds.
te moment of inertia for channels and angle-bars, and other
ons, will be found in Chap. XIII.
I>eepest Beam always most Economical.
henever we have a large load to carry with a given span, it will
)und that it can be carried with the least amount of iron by
g the deepest beams, provided the beams are not too strong for
load. Thus, suppose we wish to support a load of 9 tons with
an of 20 feet, by means of Trenton beams. We could do this
3r by one 121-inch beam at 125 pounds per yard, or by two
;h beams at 85 pounds per yard. But the 12Hnch beam, 21 feet
, would weigh only 875 pounds, wliile tlie two 9-incli beams
Id weigh 1190 pounds; so that, by using tlic deeper beam, we
315 pounds of iron, worth from tliree to five cents per pound.
C
he following table, under tlie heading ,^-, gives the relative
igth of Trenton beams in proportion to their weight, thus
biting the greater economy of tlie deeper patterns.
Trenton Rolled I-Beams.
KENOTH OF EACH BeAM IN PROPORTION TO ITS WEIGHT.
Beam.
inch, heavy . .
light . . .
heavy . .
light . . .
heavy . .
light . . .
extra light .
extra heavy
heavy . .
[igbt . . .
heavy . .
<t
t(
it
((
t<
ti
i(
w
37.41
36.76
28.41
30.64
26.64
27.20
27.78
21.44
23.41
23.86
20.99
Beam.
8 inch, light
I
6
6
6
6
5
5
4
4
4
t(
((
((
<(
(<
(t
((
(i
T).) pounds .
120 «'
90 *'
heavy . . .
light . . .
heavy . . .
UghX. . . ,
bea\^ » . .
UgYvV . .
20.75
18.37
14.33
14.67
1.5.36
15.65 i
12.27
2«8 STRENGTH OF IRON BEAMfl.
J
1
CHANNEL-BARS AND DECK-BEAMS.
1
'■
II.
...
IV.
y-m
DsaignallDn or bar.
Bate
dl»trlbiited
lund, In lb>.
of lncr[li>
Widlh of
flauge,
Inla9
C„,.»..B„.,
\
IG iBcb, havf . .
190
effi,i»o
^.0
*i
!«,»
Jight . . .
120
«1.1»0
ij-«.o
4
I2«t
I!|
bmvy . .
140
asi.floo
aoLB
1
14.lt
13)
llghl , . .
se
aw.ioo
181.9
3
s.«
lOi
haivy . .
90
134,7^0
8§.4
3)
9,W
hCBvy . .
TO
11B.0«W
82.1
n
M»
Ughl , . .
M
,«,000
sa.8
21
6.09
[.gbl , . .
49
8B,B50
44.S
n
4,48
Mr™ light
M
66,800
32.9
i.i
3.30
IlKhi . . .
3S
82,000
27.1
II
3.»
<..im ll^ht .
251
M,500
17.3
1
2JH
hcaiy . .
4u
68,300
111.7
21
4.al.
light . . .
fit™ llehi .
i-il
46.TO0
12^8
2J
cii™ llMhl .
W
ti.>m
7.2
It
1.M
«imllghi-
161
1B,700
3.9
l(
141
«<tnL IlKhl .
15
10,500
2.0
4
1.41
)
DeCKBE.MB. 1
Slncb
. \ -.^'« \ --^
\'^
:
^ J
8TBBNGTH OF IRON BEAMS.
289
STRENGTH, WEIGHT, AND DIMENSIONS OF TRENTON
ANGLE AND T BARS.
I^gnation of
bar.
I.
Weight
per foot,
in lbs.
IT.
Bafc
dlHlributcd
load for one
foolof npan,
iu IbH.
Angles Even Legs.
6 in. X 6 in;
4) » X 4i "
4 " X4 ««
3i «i X 3i ««
3 « X 3 ««
2j «. X 23 "
2i " X 2i '»
2] » X 2i "
2 «« X 2 '*
13 « X 13 ««
IJ " X 14 «
1| " X 1) "
I " X 1 "
I " X I "
J " X 3 '•
19.00
12i
04
8i
4.80
5.40
3.00
3.50
3.13
2.00
1.75
1.00
0.75
0.60
0.56
36,900
18,000
12,184
9,200
4,611
4,710
3,156
2,530
1,970
1,150
832
393
246
186
133
Designation of
bar.
Weight
per foot,
in lbs.
IT.
Safe
diHtributed
load fur one
fuotof Kpan,
ill lbt«.
Angles Unequal Legs.
6 in. X 4 in.
5 " X 34 *'
44 " X3 "
4 «« X 3 "
3i " X l\ "
3 •• X 2i "
3 " X 2
cc
14.00
10.20
9.00
r.oo
4.00
4.37
4.00
T-Bars.
30,680
14,7.'>0
18,:r)3
9,651
14,580
7,020
9,850
5,871
5,515
1,143
4,490
3,233
4,:m
2,080
Note. — Nearly all of the above bars can be rolled wHK %x^siAKt vViltiktaiaa \*
igind, aad the atrengtb would increase iu proporliotk. TYi^ «)c^on<&\«X^m»
* the lightest weight of the bars.
^K^^^K OP ti^oN'^m^^^^^H
STRENGTH, WEIGHT. AND DIMENSIOJJS OF VlM
IRON-MILLS BULLED I-BEAMS. 1
I-
11.
m.
IV.
7
WHgh.
Moment
Width of
An
4
V
U <a
b. iigbt . . .
lao
MB.MO
fi30
00
s.oa
~i
Ifi
IlKht .
IBS
esB.000
614
00
00
fi.Xt
I
Ifi
heuvy
£J0
800,011«
760
00
S.81
91
1-J
light .
180
4H,0110
MO
00
♦.N
U
101
IlKbl .
U5
2=1.000
lOi
DO
4.M
ft
inj
hnivy
llghl .
h««vy
!:
uo,onu
201
N
UO
00
4.32
ft
s
llgbl .
JO
174,000
B7
M
4.01
1
e
bfivy
as
ao8,oaa
in
00
4.33
«
,
««™ llghL .
ISO
»00,DDO
1»
w
4.M
IW
8
ligbL , . .
80
140,«W
88
90
a.Bi
u
s
bBuvy
105
lai.onn
MJO
*M
IM
I
lighl .
M
iwi.ooo
tS.80
3.01
54
T
b«.vy
75
124,000
M
30
3.B1
JM
g
light.
41
6s,aoo
M
w
3.24
44
a
boBvy
M
7B.9O0
28
M
3.48
M
'
Ughl.
30
44.600
IJ
iW
a.73
U
U
«
tight .
24
34,800
8.10
2.48
14
■
J
UBiiy
30
■M,oon
«.M
UB
M
/ = ■
Ugbl .
.,, \ ,«.^ \, .» \ *«. \ ^
, - ,„,,
« \ «-•» '^
^^ yt^^
■
tf
■
■
STBENGTH OF IRON BKAMS.
2i» I
fniENGTH, WEIGHT. AND DIMENSIONS OF UNION
^ IRON-MILLS CHANNEL-BARS.
lYeslgnation of bar.
•
Weight
per
yard,
in Ib8.
Safe dis-
tributed
load for
one foot
of span,
in Ibp.
DeHignation of bar
Weight
l)er
• yard,
in llw.
Safe dis- j
tribuled i
load for ;
one fo<tt '■
of HpiUl.
in IbH. '
15 in.
, light . . .
120.0
382,000
7 in., light . . .
31 .f)
~ 1
;> 1,300 '
15 "
heavy . .
180.0
602,000
7 " heavy
4().r)
59,700 1
12 "
one weight,
60.0
159,000
7 •• light .
42.0
60,800
12 «
light. . .
67.5
187,000
7 " heavy
60.0
86,400 i
12 "
heavy . .
90.0
22:i,000
6 •' light .
22.5
32,:joo i
12 "
light . . .
90.0
235,000
6 " heavy
28.5
:57,100 ,
12 "
heavy . .
150.0
331,000
6 " light . ,
30.0
44,200 i
1
jlO "
one weight.
48.0
100,000
6 *• heavy .
48.0
68,600 I
M "
light . . .
52.5
121,000
5 ♦• light .
19.5
22,400 i
» "
heavy . .
90.0
in, 000
r> " heavy
25.5
26,400
10 «
light . . .
60.0
143,000
5 ♦• light .
27.0
32,700
10 ««
heavy . .
105.0
203,000
5 " heavy
42.0
42,70(»
' ^ tt
one weight,
43.5
84,000
4 •• light . .
18.0
16,5(K)
9 •*
light . . .
54.0
115,200
4 *' heavy ,
21.0
18,100
9 "
heavy . .
90.0
158,400
4 " light . ,
21.0
19,900
8 "
light. . .
37.5
68,900
4 " heavy
27.0
28,100
8 "
heavy . .
46.5
78,500
3 " light. .
15.0
lO.iHK)
8 "
light. . .
48.0
90,400
3 " heavy
18.0
12,100
8 "
heavy . .
84.0
129,100
I
FRENGTH, WiEIGHT, AND DIMENSIONS OF IMON
IRON-MILLS ANGLE-IRONS.
ANGLES WITH EQUAL LEG 8.
Size.
Bize.
Weight
per foot,
in lbs.
Safe dis-
tributed
load for
one foot
of span.
36,800
6 inch X 6 inch
19.2
n
4 " X 4 ««
9.6
12,000
2
3| •' X 34 "
8.3 ! 9,600
n
8| " X 31 "
7.7 7,900
n
3 ** X 3 " / 5.9 ' 5,700
u
^ " x2i '' 6.4 ' 4,700
u
S^ " X 2i **
4.9 I
1
1
3,80(1
1
2\ inch X 2\ inch
" X 2 "
" X 11 «•
" X 1^ «'
•• X \\ "
*• X \\ **
" X \ ♦•
Weight
per foot,
in IbH.
3.5 1
I
3.1 I
2.1 ;
1.8
Rafe dis. 1
tributed \
load for '
one foot ;
of Hpan.
__ ._l
2,600 i
2,000 I
1.120
800
^
i\>-i S'lliKNGTK OK IHON IIKAMS.
w
■Strength, wkkiiit. and dimexsions oi- vm
K lliOX-MILLS ANGLE-niOVS.
1
ANOI.KB WITH [TNEQLAI. l,Etl8. ■
p
Bl>e,
iulUa
Ptth rltn
IrilailflJioniJ
foi om- fool
ol ipilll.
Siie.
;s-a.
'=||
»,««
3i,a.x3in.
e,oifl
H,JO0
10.8
ti!»U9
3J " >■ 3 "
1.S
a^nM '
S ■' » 31 ..
10.S
,!:S
3 "-SI"
/«
U.'iw
4;tB
2JM»
* ■■ X 34 "
s.e
11 1(120
EJ ■■ « 9 ..
3.1
s
4" -3 ..
8.3
1 'is
■i "Xll"
■■"
w
Note. -Tim abme m<i for tbt lout ihlcknui itaoi iho aii)jlc-irD.i. n.g' loul
STHEXUTU, WEIGHT, AND DIMEN'SIOXS OF PHC£)fl
KOLLED I-beam;^. ■
I.
11.
III.
IV.
J
Mwnt
^
^^■p|)Ih^
lllHri'hS.Hl
Wiriihef
.™<
Deaiguolion of btani.
^'J^"-
'"'uTiS!""
(iBUg.-.
s
IS Inch, hrovy . .
inn
ssn.noo
70TJ
0.30
MA
IS :: e; ■ : :
3m!t
b.'M
1»
n " iiiihi . . .
4in,'«So
aaK.0
lii
? ;: S,:,,-
S3t)4>
111
ns
aiu,<ioii
laui
iM
IM
191.0
s.a7
lU
I ;; '£'":':
7n
iinlooo
m1
s
S " llv«vy . .
SI
tssimK)
tM
7 " &■ ■ ■
DQ
l4l!oQ0
KO
4JW
§
7 •; iiifhi . '. '.
wis
3.HI
tJ
Wl
31,11
3^
»A
D - liKbl . ! !
TIMIilU
la
•iM
i.
i \ =\^^^\%v^
■
STRENGTH OF IRON BEAMS.
293
ni, WEIGHT, AXD DIMENSIONS OF PENCOYD
I-BEAMS.
ition of beam,
iu ina.
i^ heavy sect'n.
1^6 ligbt
(«
» 3
I 6
U heavy
7 *«
l^ light
,^6 heavy
(i
3
4
light
n
I heavy
ki ligbt
J. 3 heavy
4
iK light
ii heavy
i "
ti
((
(»
((
(i
(i
ti
<(
(t
«(
(»
<i
«i
(»
i»
(4
tt
<t
200.0
2:3:3.0
145.0
201.0
1C8.0
194.0
120.0
163.0
119.0
I60.O
97.0
136.0
112.0
137.0
90.0
UKi.O
00 0
322.0
70.0
88.0
81.0
HM)0
Oo.O
75.0
II.
Safe di8-
ti-ibutcd
load for
one foot of
span, in
net toD8.
III.
424.41
324.30
280.32
212.22
ia3.50
140.54
162.02
138.43
123.21
07.04
07.02
80.70
Moment
of inertia.
Neiilral
axirt
I)er|>en
dicular to
web.
682.08
521.19
371.08
272.80
206.55
168.23
173.58
148.31
118.81
04.44
83.03
IV.
Width
of
flange,
in ins.
53
m
5i
5i
55-3
m
4; ,
H
4t
4}
4-3
4-3
455
4J
41
41 :j
-\ ^
V.
Area of
croms-
section,
in lUB.
. ^V
19.90
23.30
14.55
20.10
16.89
19.40
11.95
16.30
11.89
16.50
9.70
13.60
11.17
13.70
0.04
10.60
0.07
12.20
6. as
8.80
8 14
10.00
w
IKON fl^^l
m
1
BTIlK\<i'riI. WKKiHT. ANll
1>I1KAM»
IHMKNSKIVH
OK f-K'M
1
I.
...
ni.
IV.
1
WMKht
e»u ciii>
liiliuinl
Iwrifur
•iKiii, in
.^rzt
flwU
Al
NEuinl
T X A liwvy inrt'u
113.0
(W.38
411.78
SIS
T X 1 ■■
Kfi.(l
41
T X II llgW •■
61.0
n7.44
4:t.09
■■in
L
T X ( ■■
88,0
^
■
• X il Im,, ■■
r.0.0
41.87
Sfl.l)2
iiA
r
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•W-ll
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34.0
ai.01
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21)
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11.7
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i
i
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WlMUWVV
^
STUENGTH OF IRON BRAMS.
295
ENGTH, WEIGHT, AXD DIMENSIONS OF PEXCOYD
DECK- BEAMS.
I.
II
III.
IV.
V.
leBigtiation
of bar
Weight
per yard,
iu lbs.
Safe dis
tributcd
load for
oucfootof
Bimu, iu
net toils.
Moment
of iuertia
1.
Width
of
llauge,
iu ius.
Area of
cross-
scclioUt
iu ius.
inches
X
Ml
inch.
104.0
172.60
221.98
53
10.40
««
X
a
C(
138.0
6^f
13.80
««
X
i
ii
91.0
139.50
164.09
5i
9.0(5
««
X
i
14
118.0
53
11.80
««
X
i
((
80.0
110.30
1 18.22
5i
8.02
«(
X
i
i(
105.0
04
10.50
ct
X
•
i
t»
72.0
87.90
84.77
5
7.17
1
X
8
»»
04.0
01
9.40
J "
X
a
<i
61.0
07.30
57.60
43
0.11
i "
X
i
(i
84.0
4y
8.40
I "
X
H
(t
62.0
45.80
34.40
4J
5.21
7 "
X
i
it
72.0
m
7.20
6 "
X
ft
t*
42.0
34.20
21.95
33
4.1S
6 '*
X
u
1(5
ii
57.0
4
5.70
5 ''
X
■h
»(
34.0
22.40
12.04
»>4
3.37 '
5 "
X
(1
44
4(5.0
ol
4.00 i
i
Note. — Bfinimum and ma\imii)n thicknoHHes givou : intermediate Bcctioiin
• be rolled. .Snfe yoadH giveix arc for irou •. Blei:\ \)ea\\ift tvxv\ vxWi ^a^i xv^\vA«
■996 STKENG'i'il 01
IKON' BEAMS, 1
STliENGTIl, WEIGHT, AND UIWENSJONS OF PENCI
CHANNEI^BAKS. ]
I.
11.
m.
IV.
^B
irtbiiletl
■IBID. <u
Momem
SE
■s
J5 X s
148.0
280.94
451.51
4
H
15 X 1
204.5
43
X
13 X iJ Ueayy Bect'n.
8S.5
142.11
182.71
S)!
s
12 X J "
160,0
3H
u
]a X ,^ Ught ■•
60.0
96.22
123.71
2ii
s
12 X S "
101.5
2H
la
10 X f, heavy "
60.0
85.94
92.08
alS
9,
10 X i "
100.0
»,'.
m
10 X J light
49.0
68.08
73.91
2i
«
10 X 5 "
8C.5
2i
&
ft X A heavy "
51.0
66.73
(UM
2/.
<s
S X } "
S3.0
21
8,
B X is light "
37.0
45.27
43.65
W<
ai
II X i '• "
01.0
2ii
6.'
8 X j'i heavy "
43.0
4«.60
40.00
^A
4'
e X J "
80.5
21
SJ
8 Xi^Iighl "
30.0
32.04
28.23
2
3j
8 X J "
54.0
21!
^
7 X4S heavy ■•
41.0
3«.35
20.51
2li
i
7x3-
73.0
2i
7jl
7 x^, light •■
26.0
21.(11
18,40
HI
2.
7 X i "
40.0
"
2»'.
i
■
^■Krolled. S^U laa<U give.
STRENGTH OF IRON BEAMS.
207
NGTH, WEIGHT, AND DIMENSIONS OF PENCOYD
CHANNELr-BAKS {concluded).
I.
II.
111.
IV.
V.
signatlon of bar.
In ins.
Weight
per yard,
In lbs.
Safe dis-
tributed
load for
one fool of
span, in
net tons.
Moment
of inertia
I.
Width
of
flange,
in ins.
Area of
cross-
section,
in ins.
X i heavy sect'n.
32.90
28.58
18.37
2i
3.29
X S "
55.40
25
5.54
X \ medium
32.00
2i
3.20
X ^ «
54.50
2i
6.45
X 3^^ light
22.70
18.16
11.67
13
2.27
X i «
w
39.60
2-A
3.96
X J heavy
27.30
19.21
10.29
2
2.73
X 4 "
46.00
n
4.60
X ^2 light
18.80
12.45
6.67
It
1.88
X i "
32.90
m
3.29
X i heavy
21.50
12.03
5.16
m
2.15
X i "
31.50
m
3.15
X ^\ light
17.50
9.65
4.14
ll^6
1.75
X i "
23.70
m
2.37
X A
15.20
6.32
2.03
ii5
1.52
xii
18.00
I'ii
1.89
X 1
11.30
3.33
0.80
li
1.13
X A
8.75
2.25
0.48
1-3^.
0.88
^h
10.00
-^h
1.00
x^^i
\
.3.50
\
\ "^^
\ ^:?^
— Minimum and niaxlrmnu lh\cUuc%ecH %\v<iu '. vvvvs \wVtiVVwv<SN''>^^^^
Ifo rolled.
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^■VK IJISTKlltt'lKD LOAns AND I>I!;KI,Pa:TI(i\S <iH
W^ TKENTOS BEAMS. ■
IM» liad* IB Ml ion, ev™ly ai.lrlbuWO (In -WlUun lo wHsbl of IMM]. nfl
cauoeiiirunl load In middle, illoir OM b.ll of tliii girn, tu uWvMo*. H
B=- =
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VMON HKiX-MlLL.- l:EAM^.
1> SR M fl
38.1.: solw 3$
s iA^; viM ujif VIM '
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re (be dcneetiniM, li
3(U
BEAMS SUPPORTING BRICK WALLS.
Beams Supporting: Brick Walls.
Ill the case of iron l>eams supporting brick walls having no
openings, and in which the bricks are laid with the usual bond, the
prism of wall that the 1>eani sustains will be of a triangular shape,
the height being one-fourth of the span. Owing to frequent irregu-
larities in the bonding, it is best to consider the height as one-third
of the span.
1
1 1 1 1
■■ 1
"
III 1
1
1
' 1 1 1 1
1
-T-^
III!
1
1 1 1 1
1
1 1 1 1
1
1 y^>^ 1
•
i 1 ^^''P . "Sv
r
1 j.^' 1 o^.^^ 1 -V 1
— J--
\ ^ \ .1 1
N.
1
^^" 1 I.I
1-^
y 1 1 .1 1
^^-
1
^-1 1 I.I
1
1
•
o
1
0
1
- 1
b^^pk;.
^
aWlrWiM
1
1 1
1
1 1
1 1
1
Fig. 7.
The greatest bending-stress at the centre of the beam, resulting
from a biick wall of the above shape, is the same as that caused by
a load one-sixth less, concentrated at the centre of the beam, or
two-tliirds more, evenly distributed.
Thn w<Mght of brickwork is very nearly ten pounds per square
foot for one inch in thickness ; and from this data we find thai
the boniling-stress on the beams would be the same as that causec
by a uniformly distributed load equal to
25 X square of span in feet X thickness in inches
Having ascertained this load, we have merely to determine fron
the proper tables the size of beams required to carry a distributei
load of this amoimt.
Example. — It is proposed to support a solid brick wall 1
"•es thick, over an opening 12 feet wide, on rolled iron beams
shonhl bp. the size and woAg\\l o^ \>evv,w\s'?
le given abovo, V\\o. \]lw\^wvw\>3 (i\?A,vCwi\ft\ Vs
FRAMING AND CONNECTING IRON BEAMS.
305
ivould produce the same bending-stress on the beam as the
equals
25 X 144 X 12
9
= 4800 pounds.
e wall is twelve inches thick, it would be b<ist to use two beams
1 side by side to support it, as they would give a greater area
ild tlie brick on ; then the load on each beam would be 24()0
ds, or 1.2 tons. From the preceding tabhis for safe distributed
on beams, we ftnd that a 4-inch heavy beam would just about
ort this load; but as a 5-inch light l)eam would not weigh any
i, and would be much stiffer, it would be better for us to use
5-incli light beams to support our wall.
a wall has openings, such as windows, etc., the imposed weight
he beam may be greater than if the wall is solid.
3r such a case consider the outline of the brick which the beam
ains to pass from the points of support diagonally to the out-
! comers of the nearest oi)enings, then vertically up the outer
of the jambs, and so on, if other openings occur above. If
re should be no other openings, consider the line of imposed
jkwork to extend diagonally up from each upper comer of the
lbs, the intersection forming a triangle whose height is ouii-tliird
its base, as described above.
Vhen beams ^are used to support a wall entirclij (that is, the
ims run under the whole length of the wall), and the wall is more
m sixteen or eighteen feet long, the whole weight of the wall
)uld be taken as coming upon the beams; for, if the beams should
ad, the wall would settle, and might push out the supports, and
18 cause the whole stnicture to fall.
Framiugr and Connecting Iron Beams.
iVhen beams are used to support walls, or as girders to carry
)r-beams, they are often placed side by side, and should in sn(!li
Fig. 8. Fig. 9. Fig. 10. Fig. 11.
es be furnished with cast-iron separators ^VWw^ \^^v««^^\\ v\\v\
^es, so as to firmly combine the two beams. 'V\\^'5»v.\ ^^:\s'^\^d\»\^
he placed from four to six feet apart. ^\\e\\ -axv ^\t^"^'?.^:w^>j
?iK/i by Figs. 8 and K), Figs. 9 and \\ s\\ovj\ti^ \w\\vf> c>,\ ^v
■D6 FIlAMi.NO AMI CUSM.
ittlure uBimlly viuployed; tlint tviili iwn liuli-lioles iN-Jiig ii>m
llip 15-lm'ti and 121-inth beam?, luid tli.it witli a singlii itoli
anialler sixes.
FiB.ia. Fig. 13.
WtiL-ii Ijcanis an- ivqniretl to be fraiutil togelliL-r, it in
(lonp as shuwii by tjie at'compaoylng cuts, in wLii'li l-'j^'. I
two beatna uC Ihe aaiiie sjzti fitted togetlier. Fi]U. 1.1 sbuu-^
fitted Hush wIlli the boLWmi (lange ot a beam of larp-r slw^. Ri
14 *howR a smaller beani fitted lo the Btein of a hirp-r
the lower Hantce.
^ I
Fig. 14.
Wfitiali liraiiin may be aiicwre.kl W an iniii j^iiiier in the a
Kp*Mi iron beam, by Ivai«lafti\w wv\,ai«\wiivrfsw!.^W
'4lCel; or an ang\e4ion v\\a^\» VivvWi \n Vt«-«^4
IT to affoi-a a Hat WarVng on -wVwV 'Aw^
fcjn Fig. K,.
STRENGTH OF CAST-IRON BEAMS.
so:
CHAPTER XV
STRENGTH OF CAST-IRON. TVOODEN. AND STONE
BEAMS — SOLID BUILT BEAMS
Cast-iron Keanis. — Most of <m\ knowVM'j^o of tlio strcngtli
tif cast-iron bo.iins is derived from the experiments of Mr. Eaton
Hoilgkinson. I'rom these experhnents he found that the form of
cross-sortion of n beam which wiU resist
the greatest transveiso sti'ain is that shown
in Fig. 1, in which the bottom (lange con-
tains SIX times as much metal as the top
flange.
When cast-iron b<»ams are subjected to
very light strains, the areas of the two
flanges ought to be nearly e(|ual. As in
practice it is usual to submit beams to
strains less than the ultimate load, and yet
beyond a slight strain, it is found, that
when the flanges are as 1 to 4. we have a pr()])orti()ii whicli
approximates very nearly the re(iuirenients of practice. The thick-
ness of the three parts — web, to]) flange, and bottom flange —
may with advantage be made in proportion as .">, (J, ami s.
If made in this proportion, the width of the loj) tlange will be
equal to one-thinl of that of the bottom flange. As the icsnli of
liis experiments, Mr. Ho<lgkinson gives the following rule for the
breaking- weight at the centre for a cast iron beam of the above
form : —
Fig 1
Breaking-load in tons
Area of hot. flange depth ^ ,. ,.,,.
in square inches in ins.
clear span in feet
(1)
Cast-iron beams should always be tested by a load e(iual to that
which they are designed to carry.
IVooden Beams. — Wooden beams are almost invariably
square or i-ectangulai shai)ed timbei-s, ami we s\va\\ V\w\^Xsyc^ mw'
suJer only thsit shaiw in th<' following vuW.s vv\u\ Uw\w\\«k».
312 STKKNGTH OF MtiUi'i.N 111-;aM~
sirong as a, square beam wliose aiilr is iN)iin1 In Die iliaioeierari
circle, ilencc, lo Hutl One loud for a cylinili'lcal be.tiu, Rrsl
Ihe proper load for the coiresponding aijiiarc beam, aiiil Uieo dli
it by 1.7.
The bearing of the ends of a beam on a wall beyond a
amount does not atrengcbcn Clie beam any. In general,
sbould liave a bearing of four tnchoa, ibougU, if the beam be
Bbort, tlie bearlDg may be less.
Weiijhl Iff Uif Beam iUeif to be Irtken Into ^ccoiitil,— 'I
nuias we have given for tbe sLrenglh of beams do not U
account llie weiglit of the lieani itself, and lienee the safe
tbe formulas includes both Ibe cxUtrnal load and tlie weiglit of
material in tbe beam. In small wooden beams, the weight'
the beam is generally so small, compared wfth the external
that it need not be taken into account, llul Iti larger wooden
and in melal and stone beams, the weight of the beam slioujil lt|
subtracteil from tbe safe load if tbe lond is distributed; sod IfJ
the to:«t is applied at tbe centre, one-bait the weight of (be
should be subtracted.
The weight per cubic foot for different kinds of timber naj'
found in tbe table giving llie Weislit of .Siibstimee", Part IIL
Tallies for the streiigtli of hard pine, Hpmce,
oak lieatns, are given below, for beams one inch wide.
To And the strength of a given beam of any other breadth, 111!
only necessary to mnltliily the strength given in the table by lb*
brea<Uh of tbe given beam.
Example. — What is the safe load at the centre for a yellow-piiu
beam, supported at both ends, 8 inches by 12 inches, 20 feel dew
Alls. From Table II., safe loail for one inch thickness li WKi
pounds. IXK) X 8 = T2V) pounds, salt? load for beam. For n ihr
trihuted load, multiply these figures by 2.
To find tbe size of 11 lienm ilml will support agiven load wlUi.
given span, find the safe load for a lieam of au assumed deptb OD
inch wide, and divide the given lo.id by this strength.
ExAHPLK. —What size spruce beam will be required tocuiTi
distributed load of S&40 pounils for a clear span of 18 feet ?
An». This load would correspond to a load of 4320 pounilal
the centre of tbe beam. From the table wo find that a beam 1
inches deep and 1 inch thick, IS feel, span, will support 720 pounfi
and dividing Uie load, 4:]20 i>otnids, l>y 720, we have tt for li
breadlb of (lie beam in incheBi \»encKU\c\»aTO»\«ya\i\»i!il«i'
Inches, lo curry a dialribuled loaA o* S*W> ■po™A»"«\to *. «?«
I/' flH-l. '
RELATIVE STRENGTH OF BEAMS. 311
. KxAMPi.E 1. — What load will a hard-pine beam, S inches by 12
tclies, securely fastened into a brick wall at one end, sustain with
fety, 6 feet out from the wall ?
- -/4r.s. Safe load in pounds (Formula 2) equals
8 X 144 X 125
r T-TT-a = (W(K) lbs.
'. 4 X b
: Ex AMPi.K 2. — It is desired to suspend two loads of 10,000 pounds
ieach, 4 feet from each end of an oak beam 20 feet long. What
^lould be the size of the beam ?
Ans. Assume depth of beam to be 14 inches; then (Fonnula 13)
L 4 X 10000 X 4
^Hreadth = — 196 x 105 ~ ^ inches, nearly : therefore the beam
•bould be 8 X 14 inches.
Relative Streugrtli of Rectaiigriilar Beams.
From an inspection of the foregoing fornuilas, il will be found
tliat the relative strength of rectangular beams in different cases
Ib as follows: —
I Beam supported at both ends, and loaded with a uniformly
f distributed load .1
Beam supported at both ends, and loaded at the centre ... ^
Beam fixed at one end, and loaded with a uniformly distributed
load i
'} Beam fixed at one end, and loaded at the other ^
Also the following can be shown to be true : —
^m firmly fixed at both ends, and loaded at the centre . . 1
^m fixed at both ends, and loaded with distributed load . . 1^
These facts are also true of a uniform beam of any form of cross-
st'etion.
}Vheu (I Miuare becwt is .supported on Us e<1f/(f, instcail of on its
^ide, — that is, has its diagonal vertical, — it will bear almiil st'vcn-
t^nths as great a breaking-load.
The stronf/esi beam which can be cut out of a ^jnlZZl^^
^und log is one in which the breadth is lo ihc
<iepth as 5 to 7, very neaily, and can be founci
graphically, as shown in margin. Draw any
diagonal, as ah, and divide it into three c(|ual
^rts by the points r and </ : from these points
^raw perpend iculat' lines, and conned the \h)\\\\,^ " ^ "^^
<? aiKiywith ft and h, as shown. * Vx^^.
Cylixdhk'al /iKAMs. — a <:yliiu\v\ca\ W-aiwx '\^ viwM \:
314
STRENGTH OF OAK BKAMS.
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STRENGTH OF SPRUCE BEAMS.
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■nfi SOLID UUILT WOODMN lil'lAM:^
Till' foregoing UblpB for strengtli of hi>«ins mi- coiiijinlPil (r
tli« iIhUi givi-n In llils diaplcfi Wkitig llii> sMnit'ili nf t.lir WMil
given In llx' Uible fur I'u-efflolenU.
TlicBC tsbW ure as aLvuraleiM (i«[i lie (wiupiitixl with our prat
kiiowlnlgp; and. »s tlii.' ra-efflolenls are basoil upon oxperlnw
uti full-slKcd limlH'rs, ii would seem m ttioiigU lllt^ laltltw slioiilil
almost nbsoluli'ly currwt,
itTOKK I)kam», — TUl' siiMiii roniiulits aii[>ly tOBkini'iisio wooil
bwttnt, oniy tlie v»lwa of tliu co-officli-nl A arc only f roiti ono->ll
to oiiQ-tpiilli of blinking Iniuls. ShihIbIoiie bpttiiia sliuiilil ii«v«r
stibjectiid to any very bnnvy lonils; but, wlicre iisnd as tlnteli, I
Atone should be relioviid by Iron bcuns or brick arcliei bick
ihe aton^.
I
Sollil lliiilt Beams.
A HOlld livaill iE> orii*nllnii>s ri'<fiiire(i of gi'PUCer br««dth i
thickness than Uiill of sny single piece of tlinl>er. To provide MM
a lieaiii, it Is ncceKsiLry to use ei ronihlnntion of pieces, ransiningi
several layers of timber laid In jii\tnv«isil.ion, nml llnnly
together by holts, straps, or othi<r iiK'niis, so ibnt the whole sli*
aei M a single pleeo. This is termed it hoIUI bullt heaiii.
When two pleeus of limber are hiiill Into oni- beam having twit*
Iha deplh of either, keyn ol hard wood ure nsud to resist Ihe shau'-
ing-strain along the joint, as shown in Fig, 0.
Treilgotd gives the rule, tliat Ihe hrcjidth of the kry ahoiiM bf
twiee Its depth, and the sniii of the deptlis shonhl bn equal lo oiui
and u third the total depth of the Ikmui.
It hits been rueonimeticlud to have the bolts and the key* on lli>
right of the eenlre make an angle of forly-flve degrees with Ibti hkI'
of the beam, and those on the left to make the suppteinent of llii>
angle.
The keyn are soniutlniei) made of two wudgisshnpeil ploera. tot
dill imrpose of nmkmg Iheni fit the nntehc-a moiH- aniigly, ami, b
riue uf slirinkage !ii the timber, to nlluw of easy re-«djustnwnt.
When Ilin ili'ptli of ilii' licani in rei|iiiriit to be luu than Iheiuw
cif ll>e dt-i'llii "f 111.' 1«o |ii.>cc.», thi'y .ire ofleu hnlH Into ombl
iii.lrnihiM Ihi'iii, clir. priijirrii.ns ..f iIk' mie litlliig aeciirawly In*
M.i> ii.ik'lii'« iii:i<l.' ii] lb.' .illKT.iiiid Ihr I W.I lirnily rnsleilud l«g«lkir_
hS liah» or snap.1. Tim httlll hi'nw slw*n In Flft. 10 tllustntea It" '
nieUiod. In Mii»< pjirticnilar exaiu\i\f \.\w \»»w Vn.vwk'iWfta'i"
^gaililille to the eii.l»; bo {\\n.\. V\»' ivm ^"^TO\* «>*1 ^■«*'^^
SULLU BUILT WOOUEN HKAMB.
"817
n a beam Is built of several pieces tn length as well as in ■
they should break Joints with each other. The layers below
utral axis should be lengthened by the scarf or fish joints
>r resisting tension; and the upper ones should have the ends
gainst each other, using plain bull joints.
8!
i ill
.ny builders prefer using a bvUl beam of selected timber to a
! solid one, on account of the great difllfulty of getting the
■, when very lai^, free from defect? moreover, the strength
e former is to be relied upon, although it catmot be stronger
the correaponding soJid one, if |;iertecl\^ aounii.
rTTAPTER XVI.
STIFFNESS AND DEFLECTIOH OF BBAHELl
Ik Clmiw. XIV. and XV. wi> liavi> cwisideri'il tlie sLrengtJiJ
to nmisl brvAkiiin only : but in all limUcluss bulldjliei
desired thai those beams wlilrli show, or wliicli suiiporl a « ~
slioiilil not only hate BiiDIpIetit strenglli to curry tlie load i
safety, but sliould iln bo wIiIiouL betidln); enoU(;h to prrsKnlft
Hppuai'Bniw lu tiie eye, ur to craek the celllnjj: : lieii<^, I
lallng llie diniensioiie of such beams, we ehou]<] rttit only imkd
tliem Willi regani lo llieir resietance to breaking. Imt also U
ing. Uiifortitnati^ly, we liave ut pn^tnt no iiii<tUod of comlrinil
tbe two palciiktions in one operutlou. A In'ain upiiort.ianed Iq
rules for strength will not beml so as to strain the Itbrea hrjie
their elastic limit, but will, in many cases, bend n
regard for appwu'anee will justify.
llie amouat whicb a beam bends under a given load Is raJlol N
diction, and its resistancre to bending is trailed Its rtifitat
hence the stiffness is inversely as the deflm-tlon.
The rules for the stiffness of beams are derivi^il froiri I
Hie deflection of iieama; and the latter are derived partly Iroi
malhi'inatical reasoning, and partly from (>xp«riintints.
V/v iMU find tlie diJIeHion <it the cimtre, of wii/ Iwaoi iiol striiw
beyond the elastic limit, by llie following formula: —
_ load ill lbs. X culic of span in inehea x c
Def, in inches - ^lojuiug ^f t^la^tic^lty X (nonmiit of inerti»'
The values of r, are as follows : —
Btsam Bujiporletl at hotli endn.
fHtrlnl at
luiCormly loaded
« llw otlier .
!■ l.F<
SHli^VU
STIFFNESS AND DEFLECTION OF BEAMS. VA'J
dwing formula for a rectawjular beam support nl <it. both eiiil%
loftded at the cfnitre: —
load X cube of span X 172^.
Def. m inches = llTtoSulth x .•uhe of .U-ptii x'a:' ''^'
Span being taken in feet. From this formula tiie valur of the
dulus of elasticity, F, for different materials, has been cah-u-
pd. Thus l)Qp,ms of known dimensions are snpi)()rte(! at each
1, and a known weight applied at the centre of tlie f)eam. Tin'
fteetion of the beam is then carefully measured; and, substituting
ise known quantities in Formula 2, the valu<» of E is easily
tained.
1728
Formula 2 may be simplified somewhat by representing 4 x'/' '^^
r, which gives us the formula
If X //
Def. In inches = Ji'x J^^'yTf* ^'^^
•^or a distributcnl load the deflection will be five-eighths of this.
Note. — The constant /'correspondH lo IlatruMd'H F, in hiHTriinsvcrHt' ^StrainK.
If we wish to find the load which shall cause a given deflect ion,
wi* can transpose Fomuila 2 so that the load shall form the left-
hand mend)er. Thus : —
Load at centre _ '^ ^ breadth X cube of dei>th X (U^f. in ins. X K
in pounds ~ cube of span X 172S * '
Xow, that this fonnula may b<^ of use? in determining the load to
put upon a beam, the value of th(^ deflection must in sonic way be
fixed. This is generally dom* by making it a certain pi()])()!ti()i>
of the span.
Thus Tredgold and many other authorities say, that, if a flooi-
^eam deflects more than one-fortieth of an inch for every foot of
span, it is liable to crack the ceiling on the under si(h'; and hence?
^his is the limit wiiich is generally given to the deflection of beams
n first-class buildings.
Then, if we substitute for ''deflection'' the value, length in feet
-r 40, in the above fomuila, we have,
breadth x cube of <lepth X c
Load at centre = 1. 1 :r,~ > (">)
^^11 i-i^ square of length ^ '
K
etting e = j^.^^^y
Many engineers and architects think U\a\, (»ae-lh»r\\v,v:\v ^>S atv\?(vc'>
r foot of span is not too much to aUow U>y \\w v\v-^^^oW>\\vA '^
:\2()
STIFFNESS AND DEFLECTION OP BEAMS.
beams, as a floor is seldom subjected to its full estimated load, and
then only for a short time.
If we adopt this ratio, we shall have as our constant for deflec-
E
tion, e, - j29(Jo-
in citlier of the above cases, it is evident that the values used for
Ky b\ i'y or f 1 , should be derived f mm tests on timbers of the same
siz(; und (quality as those to be used. It has only been within the
last three or four y(?ars that we have had any accurate tests on
the strength and elasticity of large timbers, although there bad been
several made on small pieces of various woods.
The values of the various constants for the first three woods in
the following table have been derived from tests made by Professor
Lanza and .his students at the Massachusetts Institute of Tech-
nology, and the values for the other woods are about six-sevenths
of the values derived from Mr. Ilatfield^s experiments. The author
believes that the values given in this table may be relied upon for
timber such as is used in first-class construction.
TABLE I.
Vidne.H of Constants for Stiffness or Deflection of Beams.
K '-- Modulus of elasticity, pounds per square inch.
F ~- Constant for deflection of beam, supported at both ends, and
loaded at th(i centre.
" - Constant, allowing a deflection of one-fortieth of an inch per
foot of span.
r I = Constant, allowing a deflection of one-thirtieth of an inch per
foot of span.
Material.
Cast iron . .
\V roil gilt-iron
Steel . . .
Yellow pine .
Hpruce . . .
AVIjite oaii .
White pine .
Hemlock . .
Wiiitewood .
ChcHtiiut . .
AhI) ....
Muple . . .
E.
15,700,000
20,000,000
31 ,000,000
1,780,000
1,294,000
1,240,000
1,073,000
1,045,000
1,278,000
944,000
1,482,000
1,902,000
/ =
432*
36,300
60,000
71,760
4,120
3,000
2,870
2,480
2,420
2,960
2,180
3,4.30
4,400
^« ~ 12960'
1210
2000
23.')8
137
100
05
82
80
98
72
114
146
STIFFNESS AND DBFLECTlun ^.
Rules for Stifitaess of Beams.
ing the deflection caused by a weight at the centre of a
.nd the ratio of other deflections, caused by diiferent modes
ing and supporting, we can easily deduce the formulas for
ferent cases considered under the strength of rectangular
These cases are —
Beams Supported at Both Ends.
ided at the centre,
breadth X cube of depth X e
Safe ^0^ = square of length ' »«'
load X square of length
Breadth = "^j;^ ordepUrxT"- '""
oaded at a point other than the centre, m and n heimj the
nienta into which the beam is divided ,
breadth X cube of depth x square of length X r
Safe load - HTx ,,^2 x u^ ' ^^^
«
__ load X m' x n^ x 16
Dreadtb — ^^y^ of depth x s^iuare of loiigth x e* ^^^
Load uniformly distributed,
8 X breadth x riibo of depth X e
Safe load = rrx "^are oH^nith ' ^ ^^
_ 5 X load X square of loiigth
Breadth - 8 x cube^oYdcplh x~e~~* <^
Inclined beam, loaded at the centre,^
__ breadth x cube of depth x e
Safe load — lengtlTx hor. dTstT bet wee n~ supports' ^
_ load X length x hor. dist. between supports
Breadth - ""^be^f doptfrx "^ •
Beams Fixed at One End.
Loaded at extreme end,
^^^^<^^^^ X cube of de\)U\ x e
Safe load = i^ri: T\ :\ >
16 x square oi \eTV^X\\
' Tredgold*a Elemenls of CarpeuUv > V- ^'
^.
1
STIFFNESS AM) DEFLECTION- ■ .:-•.'- J
Load xtnifoniily diatribKttd,
breiull.b X cnlip of depth X e
Safe load =
< square of length
< load X SFjUiti'e of
cube of (leptU X
Tables.
^^B TflbleH II., Ill,, and IV. have been prepared so as tosl
^l^glanca llie grealest load tbnL a beam one Inch Lliick will
without exceeding tlie iimiL of deflecLioa or llie safe a
Tlu-y give llie sarae resulla as would be obtained by using t]
formulas.
Ratio of the Stiffness of
If the stiffueas of a bcAtn, supported at Iwlh ends, and loadetl
tlie centre be called ...
Tiien liiat of tlie same beam, with the aame load uniforfl
disti-ibiiled, nlU be
Firmly flxed at both ends, and loaded at the centre, accoidl
lo IiItKjeloy
Firmly fixed at both ends, and imlformly loaded ....
Fixed al one end, and loAded al tlie other
Fixed at one end, and uniformly loaded
The Btilfest rectangular beam containing a given amo
material is tliat in which the ratio of depth to breadth ia as 1
hence, in designing beams, the depth and breadth should bt
to approachaa near this ratio aa is practicable.
Example 1. — What itt tht gi'ealeat diatiibuled load thai t
10 Inch white-pine girder of 12 foot clear span will supportt
out deflecting at the centre more tlian ^^i of an inuh per 1
Ann. This girder cornea under the case of a beam s
both en<ls, and loaded with a unifoiinly distributed load, s
should be calculated by Formula 10. Substituting the gWt
aloiis III Formnla 10, weliave.
STIFFNESS AND DEFLECTION OF BEAMS.
323
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STIFFNESS AND DBFLBCTIOir OF BBAMfl.
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STIFFNESS AND DEFLECTION OF BEAMS.
325
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ExAUI-Li; 2. — Wliftt «hi>«lil l« Ibe dimeusionS of a yirlloi
beam of 1(1 fool span, U> siipiiott a conccntraieil load of 4aO<J pc
witboiit ilellecLiDg mure ilian i of an incb at ilie centre V
Ana. A JetleL-Cion of } of an fui:h in aspaii of lU feet is in
prop<irtiun of yr, of an indi per fool of span; an.
rouceDtralLHi, and apiilled at the cenLre. we should use Formul
employing tor e the valuu given In tlie fourtli column, oppo
ycUon' pine.
FuniiulHTgiv-esthedlmenaloDsof the breadth, and loobtAlnl
must assume a value for Llieileplh. Fur this wu u'il! Grst li'yKln
tSubati luting in Formula 7, ne have,
4250 X nm
"^'i'*' = 512 X m = " ■"'■■'"'«■ '"^^'■'y-
This wouli] give us n beam 0 by 8 luche«.
KxAHPLi! S. —Whal \s the iargesL load tbat an inclined s|i
beam H by 11! inches, 12 teel long between supports, wDI c-in
ibPL-eulre, cunsislenlwithatiffneaa, the borlKontal disUiace iKtu
the suppuKa being 10 feel i*
Aan. Formula }2 ie tbe oUr to lie employed; and we will uc
vahio of e given in tbe tljiiil culnnin, o|>posile spi-uce,
the proper subxliluliona, we liavi?,
Safe load = ■ ^.^ ^ ^^ -' = mtli pounds.
Cjiliidriciil BeaniN.
For cylindrical beams tlie same ffjiiiiuiaa niay be iiniplojeil
for reclangular beams, only, liislead of ' , iiae 1.7 X r. ; tliat 1
I'ylrndfiCHl beam bends l.T times as miieb as ihe
iiiclaiigle.
Detleetioti of Iron Beams.
For rolled-iron ijeanis tlio delleetioii is most aciHiratdy Ol
by Foriinda L. 'Hie follovi'liig approximate formula gives t
fleclioris ijuiie aceurately fur tlie maxlniuni safe loads,
. , , wiUHi-Rof span in feet
D.i1l«Llou m indies = 7,, ^ the depth of bean.'
The deftei'tlons foi- tlie Fhmiix, I'lnmiiid. Tri-nluti, awl P**
Jrou-MHlH tjeums, are given In Liu: tallies tor strength of bGsn»>>'T
ChMp. XIV. I
_Jn UMliig iron beams. II aliou\il \*: \\:Wf.\-a\va*&. ^.\^»^. Avt 4W*'
y aJwa vs ttitf mosl evovioii"ea\\ u.»w\ v.\w «.\Biv«« «\ ».^'
^ «ter wh^n ^ ..vU^bW »uuv\,ev ,A .V.v^W™**««J
CONllNUOUS GIRDERS. 327
CHAPTER XVII.
ITGTH AND STIFFNESS OF CONTINnOUS
GIRDERS
ERS resting upon three or more supports ai-o of quite fre-
•ccurrence in building construction ; and a great variety of
s is held as to the relative strength and stiffness of continu-
. non-continuous girders; very few persons, probably, having
rect knowledgtf of the subject,
most every building of nnportance, it is necessary to employ
resting upon piers or columns placed from eight to fifteen
irt; and in many cases girders can conveiuenlly be obtained
will span two and fven three of th(^ spaces between the piers
imis. When this is the case, the question arises, whether it
lietter construction to use a long continuous girder, or to
ich girder of only one span.
architects are probably aware that a girder of two or more
s stronger and stiffer than a girder of the same section, of
le span, but just hovj much stronger and stiffer is a question
e unable to answer.
is seldom that a girder of more than three spans is employed
iiaiy buildings, we shall consider only these two cases. In
lotures, the first pohit which shouUl be considered is the
ice required of the supports, and we will first consider
istance offered by the supports of a continuous girder,
lis chapter we shall not go into the mathematical discussion
subject, but refer any readers inttMested in the derivation of
mulas for contiiuioiis girders to an article on that siibject,
author, in the Junti (J881; number of Van Nostrand*s
neering Magazine."
Sii/>porting Forces.
-*• (^f Two SpauH, ioadea at the Centre of Ea<iK ^\>aw..— ^
»/ two spans, I an,! /. , is loaaed al VA^e o^ewVxe o\ VV^^V*
L
828 CONTINUOVS GIRDER-S.
wiih If pounds, and ul llii' f^cnirc of ', wlih W, poaiab,
re-actioD of the support It, will W represented by llio fontruU
Vi\V-:iW,
re-action of the support [t.^ by
of r.he supiwrl fii by Ihe formula
L i.)n',-;jir
■ «" = a2 — ■
If iV = W,, Iben each of tbe end supports would have to s:
-^ of one of Ihe loads, and the centre support V o( IT, Werel
giiiler cut so as lo make two girders of one span nacli, then tbe I
supports wonlU tarry ior t^ 11', and the eenti-e support +8 'f'l*
we see, that, by having tlie ginler continuous, we do not reqnii
much resistance from tlie end supports, but more from tlieea
support.
Girder iif Tivo Spnns, unifor^iil!/ Diiilrihiiled Load o
Span. — Loud ovHi' each span equals lo pounds per unit of kngii.
Re-action of left support,
''' ~ -'L 4'i(+',u-
Re-action of central sU[)l>oi'l.
/.■.-"■i/-i-M-n,-n,.
Re-action of right support.
yfhea both spau.i are equal lo f, i.\»e re-iM:Uoi\ ot each end auiipvi
Yi»ifl, , and of llie central support, ^i lul ; Xvetw* \.\« ^T4ra.\nV
WtMUnittHts. fcliieee lliP re-action o( \\ve tnAsuvVM^^*"*^
]
CONTINUOUS GIRDEBS. 829
€Ihntinnous Girder of Three Eqval Spans. Concentratal Load </
"^ Pounds at Centre of Each Span.
lie-action of either abutment,
He-action of either central support,
/?, = «! = f J ir; (SI
Of the re-action of the end supports is lessened three-tenths, and
^Hat of the central supports increased three-twentieths, of that
'Which they would have been, had three separate girders of the same
^^ss-section been used, instead of one continuous girder.
D
Fig.2
Continuous Girder of Three Equal Spans uniformly loaded v?ith
'W Pounds per Unit of Length,
Re-action of either end support,
i^.=/?♦ = !w^• (9)
Re-action of either central support,
7?g = i?3 = |i ,rf; (10)
hence the re-actions of the end supports are one-fifth less, and of
the central supports one-tenth more, than if the ginler were not
continuous.
Strength of Continuous Girdn'i<. — Having determintMl the re-
action of the supports, we will now consider the strength of the
ginler.
The strength of a beam depends upon the material and sha]>e
of the beam, and upon the external conditions imposed upon th(»
beam. The latter give rise to the bending-moment of the beam, or
the amount by which the external forces (such as the load and
supporting forces) tend to bend and break the beam.
It is this bending-moment which causes the difference in the
bearing-strength of continuous and non-continuous girders of
the same cross-section.
Continuous Girders of Ttro Spans. ^Whon a rectangular beam
is at the point of breaking, we have the following conditions : —
Bending- _ Mod, of rupture x breadth x s<|. of <l(^pth.
moment "" 6 '
jtntf, that ilte b&tm may carry its load w\V\\ \i*iT\e^\. ^a&viVTj > ^^ v»»Bi
tlivitle the looii by a proper factor of saie.V'^.
330 CONTINUOUS 0IRDSH8.
Hence, if we oui determine the bendin^momeiit of abetm uder
any conditions, we can eaftiiy determine the required dimenslomof
tlie l)eam from Fonnula 11.
Tlie greatest bending-moment for a continuous girder of two
spans is almost always over the middle support, and is of the oppfh
site Iciiid to tliat which tends to break an ordinary beam. ■
hiHtribuied Load. — The greatest bending-moment in a contina-
OILS girder of two spans, / and / 1 , loaded with a unifonniy distributed
load of w pounds per unit of length, is
Bending-moment = q«^ . ■ > * (IS)
V/hen f = (i, or both spans are equal,
tol*
Bending-moment = -g-, (]2a)
which is the same as the bending-moment of a beam supported it
both ends, and uniformly loaded over its whole length: hmces
continuouH girder of two »pawt uniformly loaded Us no 9troi^tr
than if non-continuous.
Concentrated Load. — The greatest bending-moment in a con-
tinuous girder of two equal spans, each of length /, loaded with W
))Ounds at centn^ of one span, and with Wi pounds at the centre of
the other span, is
Bending-moment = A f ( M^ + Wi ). (IS)
Wluiii \V = ir,, or the two loads are equal, this becomes
Bending-moment = rfe If^/, (ISfl)
or ontsfourth less than wliat it would be were the -beam cut at the
ini<l(lle support. •
('t)ntinnou» Girder of Three Spantt^ Distributed Load. — The
<;roat<'st bending-moment in a continuous girder of three spam
h)a<le(l with a uniformly distributed load of w pounds per unit of
length, the length of each end span being /| and of the middle
simn ly is at either of the central supports, and la represented by
the formula,
Bending-moment = ^T^^jZf^T]' ^^^'
When the three spans are equal, this becomes
wP
liending-moment = Tq, (14a)
'Mth tea than what it wou\d \i^ ^«c« >>Mb Xvcmbl ^mijl ^5»r
CONTINUOUS GIRDERS. 331
Concentrated Loads, — The greatest bending-moment in a con-
t.inuon.s girder of three equal spans, each of a length /, and each
loaded at the centre with W pounds, is
Bending-moment = /„ IF/, (15)
or two-fifths less than that of a non-continuous girder.
Deflection of Con tin nous Girders.
Continuous Girder of Two Equal Spans. — The greatest deflec-
tion of a continuous girder of two equal spans, loaded with a
uniformly distributed load of w pounds per unit of length, is
wl*
Deflection = 0.005416 ^. (16)
(^denotes modulus of elasticity; /, moment of inertia.)
The deflection of a similar beam supported at both ends, an<l
uniformly loaded, is
wl*
Deflection = 0.013020^.
Hence the deflection of the continuous girder is only about two-
fifths that of a non-continuous girder. The greatest deflection
in a continuous girder is also not at the centre of either span, but
between the centre and the al)utments.
The greatest deflection of a continuous girder of two equal spans,
loaded at the centre of one span witli a load of W pounds, and at
the centre of the other span with \Vi pounds, is, for the span with
load ^K,
{2^W -{)}¥,) l^
Deflection = 15:^6^7 ' ^^'^^
for the span with load IF,,
(23 W^, -dlV)l^
Deflection = 1536 El * ^ '
When both spans have the same load,
7 IF P
Deflection = ^^.^ V/ • (1*6)
The deflection of a beam supported at both ends, and loaded at
the centre with W pounds, is
Deflection =
48^/'
or the defection of the continuous gVrdet \a oxvVj ^N«l^r^'«^w
>/ the DOD-continuous one.
MKS CONTINUOUS (ilidiEUf'.
CoiUinnous driler of Tliire Eqml Spn„t. — rnifuniily rfiKitt
uUid load of K pounds jilt iinil of Itngili,
^V Greatest ileflection in eiul epeias = li,iXKiSS4 ^
or the greatest dcflecfioii In the girder Ik only nboiit oaeAi
of a non-conlinuous ginler.
Coucentmlei] load of II' poiinils at i-entre of each sptm.
1 WI^
~ m) EI
11 M'l>
Uenwtion at ei-olre of enil sjianR — ^%~ri
From tlie foregoing we (■an liraiv many olxtervatioiiB iinri fonf
along, wlikli will be of great use In dei-iiting whetber it will br b
In any given case to use a contiDuous or non-con tinuo lis glnler.
Firtt an to the SupiiorU. — We see from llie forniuliis given
tlie re-aetloii of the snpporMng forces In the (iifTerenl wiHfls, tbMlii
nil caa*>s tlie end supports do not 1ihv<! as niticli loiul brought apon
tiiciii wben tbe girder Is eoiitinuoiis u when It Is not; but of i
tlie illflerence must be niadit up by the other snpparts. This
often Ih> desirable In buildings uliere the glnlers run acTO
buililing, the ends resting on the side walla, and the girders
aupported at Intermedials points by coluuins or piers. In snclii
i»s(', by using a continuous girder, part of the load could be talq
from tlie walls, and transfeiTinl to the irolumiu or jiierB.
liiit there is anolher question to lie rousidrered in sucb a cat
Aiul thai is vibration. Should Ilie building lie a mill or factory'
wliieli [he ginler^ had to support maeliines. tlien any vi
l^veu to the udddle span of the lieani would be carried to the
walls if the beam were conlinuoiis. while if separate girders
iiseil, with tlieir enils an inch or so apart, but little if any
wouM tie carrieil to ihe sidi- walls from tlie mhklle span-
Ill all cases id JDiiionant con^Iruci ion. the (tipponing fofM
MhauU be carefidls looked ahm.
— As Uie retanVse sUvnvWv sS wwAVtuiim* a^A.
Virn.^ir U-.«r..v^ «.<>»">>^^- '• • "--^^-i ^^^
CONTINUOUS OIRDER8. 833
h of a continuous girder, knowing the fonnulas for its bend-
ment. From the values given for the bending-nionients of
*ious eases considered, we see that the portion of the girder
trained is that which comes over the middle supi)ort8; also
xcept in the single case of a girder of two spans uniformly
, the strength of a girder is greater if it is continuous than if
)t. But the gain in strength in some instances is not very
although it is generally enough to pay for making the girder
uous.
ness, — The stiffness of a girder is indirectly proportional to
ection; that is, the less the deflection under a given load, the
the girder.
, from the values given for the deflection of continuous
J, we see that a girder is rendered very much stiffer by being
continuous ; and this may be considered as the principal
;age in the use of such girders.
often the case in building-construction, that it is necessary
beams of much greater strength than is required to carry
perimposed load, because the deflections would be too great
beam were made smaller. But, if we can use continuous
J, we may make the beams of just the size required for
bh; as the deflections will be lessened by the fact of the gird-
ing continuous. It should therefore be remembered, that,
great stiffness is required, continuous beams or girders
be used if possible.
Formulas for Strength and StifTness.
convenience we will give the proper formulas for calculating
rength and stiffness of continuous girders of rectangular
ection. The formulas for strength are deduced from the
la,
BX D'^X R
Bending-moment = .. * (22)
U is a constant known as the modulus of rupture, and is
m times what is generally known as the co-efficient of
til.
ENOTH. — Continuous girder of two equal spanSy loaded
mly over each span,
2X BX D'^X A
Breaking-weight = j ^ V^\
ff denotes the breadth of the gm\eY, I) \X\«. ^^^nX>^^^^S|
^tb in inches), and L the \eugtVi oi otv^ %\>^^> VuSeeV., "^
values of the coDstanl. A ale Cliree times ilir values given in 1
I., p. 310. For yellow pliie, U75 pouiiils; tor spruce, 270 poan
auti for wliite plnii. 240 iMHinda, — may ba takeu as reliable vaWl
tor A.
Coalimtont yirier of twu uqttal hihiiih. Imulfii ei/uallg a
centre iif eaek epaii,
^t Bi-eaking-weiglil = ^'X j^ ■
f
K e
E ei/""/ njmi
iiileil Miifnrmlf n
rf rf/uiilly (li
B X If X
St ne
beam wU
earli epoii.
Continvovg ijinltT uf iwo egitul xpiiiis, iuadeii erjually ai
(i/ eocA span,
16 B X I3« X e
Load on one spun = -=- X tj -■
Contuiuoits girdw of thkeb eiiuiil spiini. loiuieil iii'iloru
each span,
'HitER efiuiif HimiiK lontlnd egvallj/ at Hi
20 B X D'X e
The valiif^of the miiHUiU '' Ih I2.»«)0, divldeU liy Ihe modulull
ehutlcityi and, for the Ihrw woovVs ransv conunuv.V'j -omAiAban
the following values may \ie lakfu ; —
^Mlow phiK, i:l7; wliiW pine, »'i-, «vvuee, V«l. _^,
CONTINUOUS GIKDERS. 385
r iron beams we may find the bending-moment by the for-
ts given, and, from tables giving the strength and sections of
d beams, find the beam whose moment of inertia =
bending-moment X depth of beam
2000
in the bending moment is in foot pounds.
'or example, we have a continuous 1-beani of three equal spans,
ded over each span, with 2000 pounds per foot, distributed.
eh span being 10 feet, then, from formula 14(/, we have
2000 X 100
Bending-moment = Tq = 20000.
20000
Moment of inertia = "ij/jTviT x depth of beam;
),000 -r 2000 = 10, and we must find a beam whose depth multi-
lied by ten will equal its moment of inertia.
If we try a ten-inch beam, we should have 10 X 10 = 100; and we
e from Tables, pp. 260-272, that no ten-inch beam has a moment of
ertia as small as 100: so we will take a nine-inch beam. 9 x 10
90, and the lightest nine-inch beam has a moment of inertia of
'<: so we will use that beam. In the case of continuous I-beams
three equal spans, equally loaded with a distributed load, we
ay take four-fifths of the load on one span, and find the iron
am which would support that load if with only one span.
Example. — If we have an I-beam of three equal spans of 10
et each loaded with 20,000 pounds over each span, what size
(am should we use ?
Ans. t of 20,000 = 16,000. This would be for one foot of span.
,000 X 10 = 160,000.
From Tables, Chap. XIV., we find that the beam whose co-efli-
ent is nearest to this is the nine-inch light beam, — the same
jam which we found to carry the same load in the preceding
sample. For beams of two equal spans loaded uniformly, the
rength of the beam is the same as though the beam were not
ntinuous.
The formulas given for the re-actions of the supports and for the
flections of continuous girders with concentrated loads, were
tified by the author by means of careful experiments on small
•^1 bars. The other formulas have been verified by comparison
th other authorities, where it was poss\\i\^ lo ^o ^q\ >OLVQvy^ cswji
tfro of the cases given, the author has nevet ^^eiv ^\%R>issfc^\s
work on the subject.
__FUTCU I'LATK aiKD£RS.
CHAPTER XVm.
FLITCH PLATE GIRDERS.
Ik framing large buildings, it often occurs that the floora m
supporterl (ipon girilere. nhich themsehes rest upon column;
It is required tiial the columns shall be spaced farther apan Ihi
would be allowable It noodpn girders were used. In sn'A\ <
the Flitch Plate girder luay bu imn puie
used, oEtentimea witli advan- ^f-f ^^~ •'.- ~Z
tage. A section and elevation of ^^ fe--^"~ ty ' ^'-1=3
a Flitch Plate girder is shon-n in
Fig. 1. flfl- 1-
The difEerenI; pieces are bolted together every two feet by A
fom'ths-lnch bolts, as shown in elevation. It lias been foond 1
practice tliat the thickness of the iron plate should bi
twelfth of the whole thickness of the beam, or the thickness ot Id
wood ahoutd be eleven times the thickness ot the iron. As llie d
licit; of iron is so much gi'eaCer than lliat of wood, we must pnp
lloii the load on the wood so thai it shall bend the same amoaal
IhQiron plate: otherwise the whole strain might he thrown OH tl4
iron plate. The modulus of elasticity of wrought-iron is about UA'
teen times that of hard pine; orabciim ofhard pine ons Inch wA
would bend thirtuca tiuic:9 as much as a plate of iron of the si
size under the saiiic loail. Ilenc-e, If we want the hard-pine be
to bend the same as the Iron plate, we must put only one-tUirteeiilli|
as much load on it. If the wooden beam is eleven times a!
as the Iron one, we should put eleven-thtrteenlhs of its safe load d« I
It, or, wliHt niitounls to the same thing, use a constant only eleven- i
tblrteenihs of the strenglli o( Ibe 'Nood. OaLhis basis the b
lag fru-iimlas have l>een maxle up (ov t\w*WttTi^\vo\ Y^\\^^
Inlera, lit nUMi the thickness ot Uie \toi^. "''^ <iTvt-Vn^ViJi (?
f (Ik; beam, aiiproxiiiiaWls ■ —
FLITCH PLATE OIRDEBB. ^^7
•t D = Depth of beam.
B = Total thickness of wood.
L = Clear span in feet.
t = Thickness of iron plate,
f = i 100 pounds for hard pine.
~ » 73 pounds for spruce.
W = Total load on girder.
lien, for beams supported at both ends,
afe load at centre, In pounds = j{fB-\-V)Ot), (1)
Me distributed load, in pounds = -£- {fli + 7500. (2)
/ yvL
For load at centre ^ ~ \~fli + irATt' ^"^^
As an example of the use of this kind of girdor, we will tak<i tlu^
ee of a railway-station in which the second story is devoted to
fices, and where we must use girders to support tlie second floor,
twenty-five feet span, and not less tlian twelve fe(?t on eenlr(»s, if
e can avoid it. This would give us a floor area to \h) supported by
e girder of 12 X 25 = 300 square feet; and, allowing 105 pounds ])er
uare foot as the weight of the super! inposcnl load and of tln^ floor
telf, we have 31,500 pounds as the load to be supported by the
rder. Now we find, by computation, tliat if w(» were to us(» a
lid girder of hard pine, it would require a seventeen-incb by four-
tin-inch beam. If we were to use an iron beam, we find that a
teen-inch heavy iron beam would not bav(i the requisite, strmgtb
r this sx)an, and that we should be obligcnl to use twolwelve-incb
tarns.
We will now see what size of Flitch Plate girder wr would
'.quire, should we decide to use such a i^irder. We will assunn'
le total breadth of both beams to be twelve inches, so that wr can
setwo six-inch limbers, which we will have hard pine. The tliick-
ess of the iron will be one inch and ontMiighth. Th(?n, substi-
Ulng in Fommla 3, we hav*;.
I SirAH) X 25 , —
we we shAll require a twolve-in(Ai V)y iov\rleev\-\v\e\\ %\v^vix. ^^
for a compAriBon of tlie cost of the Ihree girders we have «nuM
ill lliLS Pxaiiiplp. The sevenlpen-incli by foiirtm^a-ijich bant
girder would contain 515 feet^ioard measure, wliicb, at
foot, would aiiiuiuil («»25.70.
Two twelve-Inch Iron beaiiiB 26 (««t 8 Im-lies long will m
•AtaS pounds; and, At four cents a [wuud. they would con
The Flitch-PlaM girder would eontain 364 feet, tHNird n
whicli would <!OBt t\S.W. The iron plute woul<l wi^h II
pounds, which would cost $52.5(1; making the lotal cci
^rder (70.70, or $13 less than the iron Ivauis, nnit #45 ii
the solid bard-pine b^ams. Flitch-Plate beainit also jk
advantage that the wood ahnosl entirely pratects the imi;
that, in case of a fire, the hent would not probably affect tba i
^tll the wooden iKams were badly burned.
h
TRUSSED BEAMS.
839
CHAPTER XIX.
TRUSSED BEAMS.
ENEVER we wish to support a floor upon j^inlers having a
>f more than thirty feet, we must use either a trussed girder,
^ed iron-plate girder, or two or more iron l)eams. The clieap-
id most convenient way is, jM'obably, to use a large wooden
, and truss it, either as in Figs. 1 and 2, or Figs. :} and 4.
ill these forms, it is desirable to give the girders as much depth
: conditions of the case will permit; as, the deeper the girder,
ss strain there is in the pieces.
the belly-rod truss we either have two beams, and one rod
I runs up between them at the ends, or three beams, and two
running up between the beams in the same way. The beams
d be in one continuous length for the whole span of tin* girder,
?y can be obtained that length. The requisite dimensions of
ie-rod, struts, and beam, in any given case, nuist be deter-
d by first finding the stresses which come upon these pieces.
lien the area of cross-section re<|uired to resist these stresses.
SINGLE STRUT BELLY-ROD Tiu'ssES, sucli as is represented
ig. 1, the strain upoi\the pieces may be obtained by the follow-
brmulas : —
>r DiSTKiBUTEi) LOAD W ovet' whole (jirder.
Tension in T
8^ , length of T
10 " ^ length of C
5
Compression in (' = -w W.
Compression in B =
8
8 \env;aA_olB^
(1)
340
TRUSSED BEAMS.
For COKCBNTRATED LOAD W over C,
Tension in T
_W length of T
" 2 ^ length of Cr
Compression in C = W.
W length of J?
Compression in » = -g x ^^^^^^
For girder trussed as rejyresented in Fig, t under a distbibi
LOAD W over whole girder,
3 length of 8
Compression m S = j^ IT x j—gtirSTC-
Tension in i? =
Tension in B
A MTV length of B
10 "^ ^ length of C
For CONCENTRATED LOAD, W at centre,
, . ^ W length of 5
Compression in S = -^ x ^^^^^f^-
Tension in 1? = ir.
Tension in B
_W length of B
- 2 ^ length of C*
For double strut belly-rod tnifis (Fig. 3), with distrii
LOAD W over whole yirder,
£^
^
B
Fig.3
Tension in T
= 0.367 W^ X
length of r
length of C
Cbmpresslon In C = O.^enw.
nomp. hi U orD = O.WW ^.y^tv^\vq1C
TRI7SSED BEAMS.
341
length of C ^^^^
07' c?ONCENTRATET> LOAD W over each of the struts C,
length of T
Tension in T = w X "^
Compression in C = W.
length of B
Comp. in B or tension in D = W x |^j[^^j7^f7;* (IS)
'br girder trvssedy as in Fiy. 4, vnder a disthibuted load M'
r 10 hole girder.
Compression in S
Tension in R
Fig.4
= 0.367 [V X
length of *S
length of R'
= 0.3(h!!'.
. , h»ngth of B
Tension in B or comp. m 1) = 0.367 M x | ^^^^. of^'
(14)
(15)
Tnder concentrated loads W apj^lied at S and S.
Compression in S
Tension in R
= ir X , -
length of 8
length of R
= W.
length of B
Tension in B or comp. in I) = W x . , , „«
(16)
(17)
>usses such as shown in Figs. 3 and 4 should be divided so that
rods /?, or the struts C, shall divide the length of the girder into
ee equal or nearly equal i)arts. The lengths of the pieces 7\
B, Rf »S\ etc., shoidd he measured on the centres of the pieces,
us the length of 7»* should he taken from the centre of the tie-
m B to the centre of the strut ]) ; and the length of C should be
isured from the centre of the rod to the coutre of the strut-
m J^.
.fter determining the strains in the pieces by these fornuilas,
may compute the area of the cross-sections by the following
couip. in strut
Area of cross-section of strut = -
C
Diameter of single tie-rod ^
=V
tension in rod
VWiTi
(18)
fio»
' Allowing 12,000 ])OJiMd8 nafc touHlon per «<c\\i&tc Vwi\vVa>i»t'
= 1000 pouuils iKt square Inch /or hunl pine And ink,
8O0 poiinils per square iiicb for spnice,
TOO poiiiiils pci- si|«ai* Incli for wliite pine,
13,000 poiiiuls per square inrli for ruuiivn.
T = 2000 pounds per sqiinii: inih for hard pine,
1800 pounds per sqiiant int-h for spi'itce,
1500 iwiinJs per sijuare liipli for wliite pine,
10,000 pounds yiev sqimre ini-li foi' wroiiglil-iron,
A = 125 poiitiils i^er square inch foj' Imnl pine,
lOi) iHXiLirls \K-i' s<|iiare rliull fill' o:ik,
1)0 iiouuds ]ier Mgluiti: iiieh Em' spruce,
iSO [Kiiiiiils (HT si|imre iiieli for wlilU: pine.
E\AMi'i.Es. — To illiistmtf llie iiu'IIkhI of computing [be dJ
sloiisof Lhe (lilTen>n[ |Nirls of ^'inlerK uf thl!« kiiiil, we will u'
1. — Co'm'iitniimi Jne n ginler mcIi n» is Kliamn in Fig. 1,
spftn of 30 feet, the Iniss to lip 13 feel on cciilrfs. Mill nt
a Hoor for whii'li we alioiilil nllow IIHI ixiitii'ls tx-r square fooL
girtler will i'uii«ist of three slnit-lH-HNis nnd two rods. W<
allow ilii^ l>etly-i'od 7' to puine i«ri fivt Iwluw lliP beiiniB
will Msiuiie tliat the depLli of the lieariia H will lie 12 tnelie*;'
IHe length of C (which is iiieaaurw\ Ivow \\se eeitlre of tbe ti
mhl be 30 Indies. "Uw lenEl\i oH B woaVA. rf i;oraM4\>t'i
coiiipuwiioii, or by sc«Vme< ''** **'** ^^ ^'*<^
^/Jiolies. ^^H
tueKi
— WOUUI
TRUSSED BEAMS. 843
The total load on the girder equals the span multiplied by the
Lance of girdere on centres, times 100 pounds = 30 X 12 X 100 =3
OO pounds.
Chen we find, from Fonnula 1,
_ , 182i inches
Tension ni rod = Vi) of 36000 X qq fnpiTir" ~ 05604 pounds;
[1, from Formula 20,
V()5($(U
iSSbii ~ ^8 inches, nearly.
The strut-beams we will make of spruce. The compression in
e two strut-beams = y^, of 36000 X ^^„^ = 64800 pounds, or 21600
•mids for each strut. To resist this compression would require
600
QQ , or 27 square inches of cross-section, which corresponds to a
am 2i inches by 12 inches. The load on /y = ^ of ;J(i000, or 18000
mnds: and, as there are three beams, this gives but 6000 pounds'
ad on each beam. Then, from Foruuila 22,
6000 X 15 ^, . ,
^ = 2 X 144 X 90 = ^^* '"^'*^«'
od, adding to tliis the 2^ inches already obtained for compression,
•ehave for the struf-beams three 53-iueh by 12-inch spruce beams.
*he load on C= ^ W, or 22.500 pounds. If we are to have a num-
er of trusses all alike, it would be well to have a strut of cast-iron;
ut, if we are to build biU one, we might make the strut of oak. If
22500
►feast-iron, the strut should have fonQT)? or 1.8 S(|uarc inches of
ross-sectiou at its smallest section, or about 1 inch l)y 2 inches, if
•22500
>i oak, it w(mld rerjuire a section e(|ual to Voom • <>'" 22^ s«|u;u(!
Holies. = 4^ inches by 5 inches, at its smallest section. Thus we
lave found, that for our truss we shall require thre(» sirut-heams
Hnches by 12 inches (of spruce), about i]l feet lonijj, two belly-rods
'S inches diameter, and a cast-iron strut 1 inch by 2 inches jii the
•nullest end, or else an oak strut 4i inches by 5 inches.
2. — It is (h'sired to suppoit a floor over a hH'tun^-rooni forty fe<»l
'''(le, by means of a trus.sed ijirder; and, as the room above is to be
sed for electrical purposes, it is desired to have a truss with very
ttle iron in it, and hence w(^ use a truss such as is shown in Fig. 4.
^'bere the girders rest on the wall, there will be brick pilasters
nv'inga, projection of six inches, \v\uc\\ w\\\ \\\^V.v^ W\v^ 's^'^w <5>\ Sivw-
tssSOfovl: am/ we wiW space tlie rods \\ U sv^ v\?»\,o OC\n\v\s^'«\\v^<v^
m into threa equal spans ot V-MoeV »j*Ae\\, 'V\\v\ Vw-Vv-.ww n
islBt of two hsrd-piiii.' lieaotB, hHIi thp stmts coming bi
Ihein. We will liave l«o rwU, insteail Of imp. hI if, comlnj
eEich side of tliu stmt, niiil passtug llii'ougli an iron casllngj
the beams, forming EU()ports for lliem. Tlie iieighl of iriui
centre to cenlie of timbers we diusI llniit lo IS inulies. luuX f
space Uie trusses S fcret on (vnU'es. Then Hie total nooiNird
ported by one girder equals S fcvt by 39 feet, eqiutl to Si2 ■
feel. The lieavlcat load lo which the floor will be subjfrt^
be the weiii;UL of students, tov Mhicli Tii pounds per sqiuq
will be ample allowaiiee; and liii: weight of the floor itself ij
abotu 25 pouniU; so that Hie tuUil weight of tlie floor and \ai
be 100 poimds per square foot. This makes the total weight
to come on one girder 31,200 pounds.
Then we find, Fonnula 14,
CompressioD in sinits =
Tension in bolh tie-beams = 0.367 II' x 'j'^'-'^-j^" - lOfiOOO p^
Tension in both rods H - 0.;Jff7 \V = 1 1450 pO
The timber in the ti-uss will be hard pine, and hence we mnli^
100800
-jnjTg-, or 107 square Inches, ai^ea of cross-.settion in Iha
which is equivalent to a 0-inch by I2-incli timber . or, as N
not a mercbanlable size, we will use tt 10-inch liy 12-meh .
The tie-lieama will each have lo earr; one-balf of lOnOOO, or
pounds ; and the area of cross-svction Co resist Ibis equals -s
27 inebea, or 2^ inches by 12 inches. The distrilinted lA
out section of each tii!-l»ani coming ft«ni the floor-joist i
■ la X S X lOU = 10400 pounds; and from Formula 23 \ee^
2 X ir X i, 2 X 10400X1^ '
■** = ha D^X A ^ ■•■ X 144X12U - 3|)intlieB. Tlii.nll.>.bi
of each tie-beam must Ik Zi inches + '2i inches = -ij l)iui|
say 6 inches: lience the tie-beams will be (t Inches by 13 i
Each rod n'Ml have to cari'y 5725 pounds, anU their cU|
VSTM 11
g^ =^ f inch, nearly. '
Thus we have found, for the dimensions of the various jdf
the girder: —
Two lie-beams 0 inches by 12 iuebes; Iwu rods al each ]l
and strut-pieces U) Inches by 12 inches.
traD_PW.TE.lHON QIKUEItS.
CHAPTER XX.
RIVETED PLATE-IBON OIRDEHB.
IVhbmkver llie load upon a girder or llie span Is loo great Lo
mil of using an Iron beam, anil tht? use of h trussed wooden
der is impi'acLicable, we iiiiuC employ a riveleil iron-piale glidei'.
iders of this kiuil are t]\tHa commonly used at lUe present day ;
they can easily \>e made of any strenxlli, anil jMlapted lo any
in. They are not generally useil in ijuildmgs [or a gn-aler span
Ml Bistj feet. These giixlers are usually nmhi eillicr like Fig. 1
r
Fig. 2, in aection, wiili vertical stiffeners riveted to the web-
Ltes cvei7 few feel along ihcir lengtb. Tlie vertical plates, (.-ailed
web-plates," are madi? of a single plate of wrouglil-ij'on, rarely
s than oue-fourtli. or itjut-e llian flve-eigUlhs, uf an inch thick, i
d generally thrue-i-iyliiiis ot an inch thick. ITniter a ilistrihulod j
kd, (he web of llii-cr'-i'tghtlis of an inch thick is generaity luffi- ]
^ntly strong lo i-csisl. (lie shearing-stress in the girder wllboni ]
cIcUng, provided lliaL two vertical pieei^of angle-iron ai
llie well, near each ejiil of the giri\vr. t\vesB \eAV«C\ \y*s«» <J
rie-lroa or T-irou, whichever is waed, ate i:a.\\ei\ "^A'Rwp
lltlteglnlur is (oathid al ilii! cenUe, a-u-S. w\ft*'ai
under ft (llalHbiit^iI louil. It in nwi'SMtry lo lis
■ III' vihiiW iMipUj i>f l\ie glnlfr, iiIhl'Iii;; Llieni h ilisliuu'e'8
Hi [III- li''ii|;lil of ilic Kinkr, 'I'll*? wab is only asaiu
111" slii'iLniig-ati'ttw in iIir giiilor. Tlifi lop %n<\ Itultotn p
jfitilor. u')ii(Oi ha.ve In Ix' proporlloiiHl U) lliv loaiU. Bpan, Mid li«l
arc (ttsiciioj lo iliP web liy itiiutnn of unglp-iroua. It hw been (i
ilinl in neurly ull rnwii l.h<; be.aL proportions for theangle-lrc
:i Ini'licji by;i inc-lii<N by 1 liii'li. wIiIpIi gives Uik sectional amofc
nng1'-!i ftvi* itiiii a Imif sqimii' im'lic-a. Till? two aiigies
uki-n logi'tliiT form liir flange; the upper ones bein; ralied t
"upper flange," anil l.lie lower ones the " lower flange."
Iltviirs. — Tiin rivnta wilit which Die jiiaies anil sn^le-iroiu I
joined togrtlii<r siiouiil Iw three-fourths of an ineh i
unless the ginlcr is light, when Bve-e.lgblbs of an Ineh mayliesu
dent. The spaeing ouglit not to exteod six inclies, and ahonU
closer for lieavy flanges : and in ail caws It ehould not iie more I
three iuf lies for a disianr* of eighteen inches or Iwo fi^ei (roiii
end. Klvetx bIiouIiI aiw not be sptieeil Hoser llian Iwo anit I
times llieir diameter.
Rules for the Strenfjfth of Riveted Girders.
In calciiUting the strengtii of a riveted ginler, it Is eustomirj
eonsidor tlmt the Hangi^ renl.tt Ilie tmnaversc strain In thetiltd
and that ttie web resists Itie shea ring-Hl ruin. To eaictiial* I
strength of a riveted ginler very aeciimlpiy, we shoiUd allow I
till' rivi'l-lioles in tlic flanite.a and arLgle-trona ; lilll we can m
piUe liie strengtii (if tUe girder wltb suffleient accuracy by UM
Ibe slr<'n;:lb of the iron at ten tbouaand pounds p«r si|Uiir» )»
Iii)il''iid of <»'<'W<' tbnusaiii] [lounds, which is useil for rolleil ilM
ami disreKiiidiui; lh« Hvet-lwles. Proceeilirtgon this consii)»ntk
we liiivi- ihi' fiillowlng rule for the strengtii uf thegliiier : —
^. , , , , , H' X ai'ea of one Han«e x height
bafe loail iL, tons = :i x span in feet —
Area of one flange I ^ ■' " '"^^ >< spa" '» fort
in square ineliea ) 10 x iieight of web In inches'
Tliif helijlil of liie girder in nieusiired In inehes, anil is tlw t
of the weli-plale, or tlie distance litticeen the flan)^pUt«s.
web we may make either one-balt or lhree-«lKlitfax of an
thick ; ami, (f tlie ginler U loai.\ei\ v,\\.\\ a. cow;
V or any other point, we slmuVA vwe NevV\c«\ tt.\%ei\cn^
tof the girder, siiacetl Uveliwift^i'-o' *-'\^»''&''^^^^ "
UIVETKD PLATE-IKON (5IR1)KRS.
Ml
If the load is distributed, divide one-foiu11i of the whole load on
! girder. In tons, by the vertical sectional area of the web-plate ;
d if the quotient thus obtained exceetls the figure given in
» following table, under the nund)er nearest that which woul<l
1.4 X lieiglit of girder
obtained by tlie following expression, " Tl7l7kness of welT"'
en stiffening pieces will be required up to within one-eighth of
e span fmnj tlie middle of tlie ginler.
30
35
40
46
•W
55
60
«:»
i
70 : 75
80
85
90
3.08
2.84
2.«1
2.3»
2.18
1.99
1.82
1 .♦>»!
1
1.52 1.40
1.28
1.17
1.08
95 100
l.OOl 0.92
ExAMPLK. — A brick wall 20 feet in length, and weigliiiig 40
jns. is to be supi)orted by a riveted plate-girder with one web.
lie girder will be 24 inclies liigli. VVliat should be the area of
acli flange, and the tliickness of the web ?
8 X 40 X 20
Auit. Area of one flange = — lO x"*i4~ ~ ^^ square inches.
Subtracting 5 square inches for tlie area of two 3-incli by .'J-inch
ingle-irons, we have 5 square inclies as the area of tlie plate. It"
vemake the plate 8 inches wide, then it should be 5 -f 8, or } of an
nch thick. The web we will make | of an inch thick, and put two
tiffeners at each end of the girder. To find if it will be necessary
3 Use more stiffeners, we divide { of 40 tons, ecpial to 10 tons, by the
iva of the vertical section of the web, which e(|uals | of an inch x
* inches = 9 square inches, and we obtain 1.11. T1h> exi)ressi()n
4 x height of girder
"Trn:;; ~~ y ,., i , in this case, equals SO.O. The number iirar-
thickness of web ' ' '
t this in the table is 00, and the figure under it is 1.08, which is a
tie less than 1.11 ; showing that we must use vfrtical stificuiTs
> to within .'> feet of the ccntic of the gir(l<*r. These vertical slit!"
lers we will make of 2i-inch by 2.J-inch angle-irons. From the
nnula for the area of flanges, the following tables has been coni-
ited, which gi'eatly facilitates the process of finding the necessary
iSL of tlanges for any given ginler.
RIVETED PLATE-iaON OIRDERS.
C(>«IBcient for iletemtiDin); the area required in fla:
10,000 pounds per iquartt itich of croas-sectioa fibre at
RuLK. — Multiply the loail, In tone of 2000 poun
iliBtrlbuted, by the co^tBcient, and divide by 1000
ijiiotlent will be the gross artn, in square Inches, req
Dl.».«
Urixli nr glrdur, out to oul of web, iu In
■UK
1*
11
Ifl IK
'»
35
34 W
3«
1.
10
E50
air
ISS
w
~60
IM
lie 1 116
«
100
iTiS
i»d
^
m
Sfl
t»
IMI^M
IB
i67
an
1W
&1
30
14
8»
M
6*8
^
10
361
]TS 1 IM
14U
n
229
M
361)
z(io' lih
«t
»M
zte
234
m
IM
182
IS
3M
KOO
*«
401
2tt5
IW
238
lie
HU
jao
»
439
son
2SI
223
£1
471
4lS
AW
1iM
S*l
493
24fl
M
4U1)
»UU
Sfe
ixa
638
-489
-417
376
341 1 3ia
ZBB
SS8
■M
3U
STR
1!7
4M
IK
aDo
4aY
430
KH
■Saa
as.-. 1 :ui:] a:K
all
30
m
«13
,W3
-Si»
460
40B i ;;;5 .thi
S4I
Sdo
KSfl
«ao
4H0 ( 4iiil . -IHI 1 :lliO
3M
»
S66
7»
nsg
5«T
sio 4tH 1 va, ' m-i
384
iuo
3H
STfi
t&ii
-^i5 477 ' 4^Ut ' Jill
Pl
mb
inW
«M
flJS mb 411:1 ' 4-J7
Kt3
M
M6
8»
?3l
AM j wii 1 m ■ 4,>o
4K
3S0
Example. — Let its take the sanir ainlcr that <
rximpttled. Here tlie span was 20 fei't, ami the dtpil
inches. From tlie table we find Ihe oo-c flic lent to
"••iit}p}yiag ihiB by the load, 40 tons, imil dividing
'iBqamre Inches as Uie aiva oi owv fta,ttiip,\K
obbilned before.
RIVETED PLATE-IRON GIRDERS 349
Girders intended to carry plastering should be limited in depth
It to out of web) to one-twenty-fourth of the span-length, or
If an inch per foot of span: otherwise the deflection is liable to
the plastering to crack. In heavy girdei*s, a saving of iron
ly often be made by reducing the thickness of the flanges towards
ends of the girder, where the strain is less. The bending-
»ment at a number of points in the length of the girder may be
(miine^l, and the area of the flange at the different points niadci
Proportional to the bending-moments at those points. The tliick-
^Qss of the flanges is easily varied, as required by foiming them of
^ sufiBcient number of plates to give the greatest thickness, and
••^lowing them to extend on each side of the centre, only to such
distances as may be necessary to give the required thickness at each
N>int, The deflection of girders so formed will be greater than
^M)se of uniform cross-section throughout.
CA«T-IKUX Ai;;
ClIAI'TKK XXI.
Cast-Irov arcli-(,'ii-(l<'i's ari
snppurl tliP front nr rrnr wiill
iisiinl lonii of aiich ik glnlcr
being sliowii ill Fig. 2.
liri- cNli-ni'lvdy Hmplojl
liiiiMiiii;s, Klg. I eliow
fiiiii of Ilie <-iisIiii){ Nut
FIB- 1.
Flj.1.
tilt
The costing in mailp in uiie piece wlUi box eniJB, the latlpr
grooves anil »e*ts to n-ufiive tlie wi^it«hl-lroii tie-rod.
Tlip t.le-roil is niiicli^ fmiii une-«-lgl]tli to thre^-t^ighthii of ul
Hhori.er timn the i-nstlng. nnd huN wjusn.- cnils forming Hbw '
HO as to tit into llie caatings. Th« rod iuts iisitally one wcbl
lengtli, and great care should be talien thttt tiiis weld ba ftrtt
The rod is expanded hy heat, and tlicn plaeni in poritimi I
eautiiig, and allowed to pontracl in cooling; thus tying the two-i
or the eaatliig together to form abntnienta for rei«iving tbe:
zoQtal tlimst of thi- an-1i. If tlie rod Ik too long. It will not iw
the full proportion of ilie strain until the i-asir-iron has so fi
tlecud, that its lower edge is sul)jecteil to a sevure t«luUe »trm
nhidi cMWron i-an fi-e»ilj vesWi. \t v\wL\.\i^-tQ4\a
nlag la raniliered up, anrt » iwvpvi' \v.\V\r\
c--«S( anil wroiiRlil ir..n. f
i-vVVh Vi(A>yVh[
CAST-IEON ARCH-GIRDERS.
351
« The girders should have a rise of about two feet six inches
pngth of twenty-five feet.^
les for Calculating^ Dimensionft of Girder and
Bod.
ast-iron arch-girder is considered as a long column, subject,
ertain amount of bending-strain ; and the resistance will be
ned by the laws affecting the strength of beams, as well as
)se relating to the strength of colunms.
Fig. 3.
we regard the arch as flexible, or as possessing no inherent
ess, and the rod as a chord .without weight, we can deduce the
i^ing formula for the horizontal thrust or strain : —
r. thrust __ '®*^ P^^ ^^^* ^^ span x s])an in feet, squared
strain "" 8 x rise of a^irder in feet ' '
)m this rule we can calculate the required diameter of the
)n-rod, which may be expressed thus : —
Diameter in inches
=V
load on girder X span in feet
8 X rise in feet X 7854
(2)
e rule generally used, however, in proportioning the wrought-
;ie to the cast-iron arch is to allow one square inch of croHs-
m of tie-rod for every ten net tons of load imposed upon the
of the arch.
? following table, faken from Mr. TrjeT^a^iOoVow^" KxOwXfc^s.-
tectural Iron-Work for BuildlnRK. — Wli.i.lA«. 3 . ^«.^^^. ^^^' '^^"^
& p&nlc or some uoiiaual flrcumBUnce, is U posijbin tj
on llie floor of one liuinln-tl nml iwimtj poiindH
The folloH'tng lalile givi's llie nclglit |ht squure foot fl
bo Agsiimed, in ailililloa to the weight of the tiooi, for tlwsirn
Kor street bridges for general public rraffic, 8(i Hts. per sqtawl
For Buors of (twfUinga 40 Ilia, per iqiwm 1
Kor (■hiirclins.thealreB.nnJIiiill rooniB.SOidlMO lbs. pur iwiiwrst
Kor scIiooIh VO lbs. per wiiurc I
Kor luiy-ltifta SO lbs. per MtiMK I
Korsli)rage ol gr;im lUO ihs. pertquaiv.
Tot wareluiiues ami p^neral jiii^n.'liandiBP^ Hhi} lbs. perKqnuv-i
Koc fEwtorifV) 100tn40lilbs. jiersqiu
Warehouse-floors are aometlmes very lieavily loaded, i
thane u sptcbl eoiiipulatton slioulU Iw mtule in caeh case
"Wcinlit of the Floor itself.— 11 nving decided upmv
span of the floor beams anil upon the euiierinpofied loait, wei
next (.■oDsiJer the height of the floor itseif.
Wooden floora in dwelhngs weigh, on tlie Average, Troui s«ie9l
to twooty two pounds per square foot of floor, inciudln:^ lh*«
of llic plAsici'ing on the unUec side. For ordinary spans tlie wt
may be talceu at twenty pounds per square foot, and, for long sp
twenty two pounds per square foot. For floors in public bnlliUl
the weiglit per square foot seldom exceeds Iwenty-fivc jKiunds, I
it may safely be assumed at that amount.
In wurehoiiBP- floors, which have to sustain very heavy Imuls,
weiglil per square foot may sometimes be aa gr<!at us forty ■»
pounds ; and in such cases the approximate weight of the floor
nquaro foot should !» first calculated.
Factor of Safety to be used.— in conslderint; th* 1
un a floor, it should be remembered tliat the effect of a
denly applied upon a beam is twice as great as that of tlie M
loBil gradually applied; and hence tlie factor of safely usn) for
fonner should be twice as great as that for tlie latter,
eaiised by a crowil of people Is usually considered to prodttn
effect which is a mean lietween that of the same load when gnAQ
ally and when snildenly applied ; and hence a factor of stfKj 'ift
employed whicli is a mean Ix^tween that for a live tuiil fnr « Wl
load. i
' 'TOtfMton of safety (or l\oov-\.^m^)ctBa^o\«v.^\\l■J^^us\lP«.«l^^
} bom S to o. For B\iort. avan* '™ of\%nM^ *'*!^^
~ dings, and stores, S \s pvobB.W"i wm^-JJ ~-»—
WOODEN FLOORS. 35.">
V«ngth ; bat for long spans, and flooi's in factories and machine-
I0p6, a factor of safety of 5 should often be use<l.i
Rules for the Strength of Floor-heaiiis.— In ronsid-
Hng the strength of a floor, we assume it lo he (equally loaded over
■a whole surface, as this would \ye the severest strain lo whicli i\w
kmbers could Ik; subjected. Hence, in calculating t lie dimensions
f the floor l)eams, we use the formula for a dislribut<»d load. Thai
prmula i^ for rectangidar beams,
2 X breadlh X <le])th s(|uan'd x .t
Safe load = span in feet X .s' H)
i being the factor of safety.
For floor beams the safe load is reiM-i'sciitod by llie sn)»erini])ose(l
oad and weight of floor supporte<l by each beam.
The area of floor supported by each beam ecpials ibe length of
Seam multiplied by the distances ImM ween centres. If we let ./* de-
aoto the weight of the superimpose<l load per sfpiare foot of floor
Wrface, and /' the weight of one scpiare foot of the floor itself, then
Lhe total weight per square foot will be (/ + /') i)onn(ls. and the
total load on each beam will erjual
Length of beam x distance between centres x (/+/').
JHow, if we substitute this expression In place of the safe load in
•he above fonnula, ami solve for the depth, we shall have,
Bqiiare of _ *^ ^ *^^^^- ^^'^' (^^^tres X length sipiared x (./'+./')
•depth ~ ~ 2 X breadth X A
<>r, if we solve for the distance between centres, w<» shall ba\ e.
Distance between _ 2x ^J'.^^.^lt'L^-!i*'l^^^\^^^H^''^!^l^ r^
centres in feet .S x h^igth scpiared x ( /'+ /')
(2)
(3)
N.B. — The length and diPtance beiwoen centron niiisi bo tsikcn iii./Vr/. and
thfe length raeanB oniy the distance between suppoiU, or iho clear npan.
The values of the constant A for the four woods n\ general use
we as follows : —
Spruce 270
Hard pine 375
Oak 3l."i
AVhite pine .... 240
formulas 2 and 3 apply to all floors sup])orted by rectangidar
^ms, whatever be the factor of safety employed, the weight of
' Vn\\\ very recently it has been (»ur custom to use facloiR of safety twice an
Bteatas tbe»»e, but, aft we have had oeeasion lo reduce \\\e t^u*\a.\\\i^ ^v»\ 'A\«t^'^\
o about one-bait of thai tonnerly tiHed, we have ved\\ce«\ V\\t Vvvv;v<.%x«^ v^^ «a^«e\>5
^cordia/fiy. It will be ioiiiid thai the re»ull is lhe »u\ue a» v\\wv vi\>Vi4.\\viCv. Xs.^ >^
'(he of other writen.
the auperinipoaed load, or of tile floor itself. To jlltutril'' 11
application cif l.lieM formulas, we will give two examples ouchi
nre conatniitly occurring In practice.
ExAHi'i-e 1. — \Vhat slioult! be tbe dimensions of the *pr«
fkior-beaius lii a ilwelllnj;. ttie lieams to liave a sp&n of 15 fret, H
lo bii placeil 111 inflies, or li feet, on centres?
Ann. lu Ihia cas« we would use a factor of safety of 5:/bIukI
be taken at 40 pounds, /* at 20 pounds, nnd A is 270 pauiul& i
SU1I1EI i iticlitia fur lliu breiulth. Tlieu, by Foruiutii ^,
Square of depth
5X l.i xaSXiH] _
" i X a X 270
The deptU = v''^= » Utile over 9 inches. Hence, to btve
requlBite Blreuj-th, the beams should be a X 10 incliea.
ExAUPLK S. — It Is deslreU to iise 2 by 10 inch
bvaiiis In the (toor of a church, the beams to liave a span ni
feel. Wliat distance should lliey be spaced on centres ?
Ant. Here .H — H.J'— 100 pounds,/' = 25 pouuila, and A =!
poundB. 'Fhoii, by Formula 3, we have
Distance between ci
_ 2 X 2 X 1(K) >i
375
-O.S4fi.,orllli
Ilcnce the floor will be sufBcienlly strong tt the beams are placnl
incb.a on centres.
Hrlilf^iiig: of Ploop-beaiiis.— ISy "bridging" Ie mei
system of bracing floor-hi
eitlier by means of sinnll s:
as in Fig. 1, or by means of slii|
piecea of boards at right a
to tlie joists, and Dtting ti
The effect of this bracing is4
ciiii'dly lii<nefie<nl in sustain&H
any > ouccnlralei! weight open*
floor; but it does not maUiii]]!
sticngthen a floor to resist a na
fornily distributed toad. Tt
bridging also stitTens tlie joMl
and prevents them from tundtj
aidcwiac. ]l Is ciislonuty I
Vnsert. TQ^a (rf cnns-bridgin^ I
ttoni evBT^ ¥«e \n <» A^ \«t)i.\a4
bof f lie beams ; ai.d lo\ie eKePlWett^B^ ^\YQ\Ai\w\ai*
Hong the floor, so lliat .-adi s«>iV nw-j o\>«X 4\TOtfAi'
WOOl^EN FLOORS. 363
Ans. We have simply to substitute our known quantities in
Fonnula 7, assuming the depth at 10 inclies, and taking the value
of e at 100 pounds, the beams being of spruce.
Performing the operation, we have,
5 X H X 153 X (40 + 20)
Breadtli = 8 x 10^ X 10<) = 1.08 inches.
This gives us about the same dimensions that we obtained wlien
considering tlie beam in regard to its strengtli only : hence a beam
two by ten inches would fulfil both the conditions of strength and
stiffness.
In the case of headers, stringers, etc., where the joist has to carry
Hot only a distributed load, but also one or more concentrated loads
applied at different points of the beam, the required dimensions
can best be obtained by considering the beam to be made up of a
number of pieces of the same depth, placed side by side, and com-
puting the required breadth of beams of that depth to carry each of
tile loads singly, and then taking the sum of the breadths for the
breadth required.
The formula for stiffness of plank-floors has already been given
oil p. 359.
The Irlmiiierii, A H unit CD, liavf tn anpi>orl ontshaK i
MiiTicd by £F pliw oiip-tialf lUe loml f«rrl«l by OU, an
balf oF tlie loful Hiip|>ortvi] by tiie onliuary juUt. The i
w1j1i:h lu I'alclilate aa('lj a Irlmnier la to consiilor ll Lo I
of Iwu buuiiis plficeil si'le by siilc, tine lo i^airy lUe end o
■■ra ifFnnil Gfl.mA tlie sei'oiiil being oiie'lialftliE Lhlch
wxlliiivry joist. Tile lire«iiih of the part carrying il
till! tniniiiers coulil tlicti Ik (.akiilatnl by Formula It, <
and lliL' tolal brpadtli of the trimmers fnuiid by aiidii
tlie bri'adtlia of Uie t«u v"'!^ i"'*" "hiili il is siipp
divided ^Vt! Imve nut Llie epai.<? li«rc lo lOUsiUer :
stiingtli of lieadors and Lriniinera, but »uiild lefer i
desiring further iiifoi malioii uii tlieaubiuct to liatHult:
verse btraids." wliere lUey will liiid tlic siibjiil fidly ilii
il
Fifl.3
Stlmip-lroiis.— At the iioint of i-onnection of
tlip hMdev wiib ilie irlmniiT, llie load on the trinm
from the beadt-i- Isa ccnoenirHi^l one ; and al) luortii
point, lo reci'lve the lietuJer, sliould be avoiileil. II b n
loni, m f)r«i-<'laHS ronsimolion. to support the end> af
means of stliTup-<rons, as shown In Fig. 3. The Baato
Yorh Huilding I^ws require thai "every trlnuncvar I
tliuii four feel loni;, iised \n ws^ XiivWiWi^L e^tevL » dw
In Blliiup-iroiis ol s«.U<iW« \\i\cVL\wssa Itw Mm
ileiit Ihm e».l. v,-trieaV \«TVo* »
tMM
WOODEN FL00R8. 359
*ty one-fourth of the load on the header-; and we can easily
*luce the rule,
load borne by header
Area of cross-section of stirrup = 40000 * ^^^
fca stirrup-irons are generally made of iron bars about two inches
^t^and three-eighths or one-half inch thick.
Tlie headers are also generally bolted to the trimmer, as shown
^ the same figure; so that the trimmers shall not spread, and let
^ headers fall.
Girders. — Formulas 2 and 3 will also ap]>ly to wooden girders
Qpporting the floor-joist, neglecting the weight of the girder itself.
Kl this case the distance between centres would, of course, nu^an
he distance between the centres of the girders. The application
'f th<3se formulas to girders being the same as for the floor-joist, it
eenis hardly necessary to illustrate by (»xampl(»s.
Solid or Mill FloorK.
Bjf Solid or Mill Floors we mean a floor constructed of large
eanis spaced about eight feet on centres, and covered with plank
<f suitable thickness, and this, again, covered with maple or hard-
•faie flooring as desired. Such floors will be found fully described
tt Chap. XXIV.
For cnlcnlatinfj the Irmje timhersy the best method is to compute
he greatest load that the beam is ever liable to carry, and then*
ietermine the necessary size of timber by means of the proper
Dnnula, which may be found in Chap. XV. ; or if tlu; beams are
paced a regular distance apart, and have only a iniiformly dis-
ibuted load to carry, they may be computed by Formulas 2 and .5,
ven above.
The jfooT'iAiink may be computed for their strength by the fol-
wing fonnula, supposing the load to be uniformly <listribut(Hl: —
V weight \wv scpiare foot X /> x N
_. ^ _^.^ ^ . 15)
ley would, however, bend too nuich, when proportioned by this
nnula, for us(; in mills, and in buildings where the under side of
3 plank nmjst be plastered.
For such buildings the thickness of the plank should be propor-
ned by the formula for stifl'ness, which is.
Thickness of plan k= V ~ \ i\~C^ O ^^
ing the constant for dethiction <'lv*>u \i\ CA\a\>. ^"S\.
Briek ArvlieM.
B vaj of uiaJuug ■ lire-|in>(tf Door (if brick it U
llie space betweui tbv joists willi bfitk archer, reallng «u Uie ka
flui£C9 afnisst terra-ootta or l«ick akewbacka. n*]ii-x
U punned, rare $Ih>uM Ik: lakeu tbat ilie bri<.'k» of Viliii;li thfin
are oomiKkted are of gonl 8ba[ie, and very tiaril. Tli«y ibouH
laid in contact with ear\t otlirr, fiilioui uiortar; and all the^
sboQhl be fillti} «ith lh<- Wal wiiu-jit gruui. xnd Ir krj^l Ml
The arcbes ni?ed nol bv over four iin'Ti>« tbii>k fur sjians be
bU and eiglil £e«t, except for about a. foot iit. wtch Bprlnging, ulni
they ahonia be eigbt hichts thick for spuiis lwtwe<-n six and w(^
feet, care being taken to form the ski-wbac-ksijult^ solid, briIm
lo the line of pressure. The rise of tlie arch should be abotlM
i-iglith of tlie span, or an inch and n hstf to the foot;' sDdIi
most desirable span is bptivi'fn foiir and six Feet.
I'
ri r)Trj7Rj-jvv
^ — -
Above the arth the spare Is fille<i intli ttnient itmrete inw'
wooden strips, three inches by four Inches, are einbeddsi ft
nailing the flooring to. The thrust of the arches ii
hy a series of lie-roilti, usually from lliree-quarl^rs t
In diameter, placed iu lines from sU to eight feet apart, i
tvaoing from beam lo beam ti-om oue end of the liulldinKieD'
^Wler, being anclion»i\ into ea.\i ei«\ waft «Vftv %uiu.>. >i«A<«;a|
FIRB-PROOF FLOORS.
367
gle-bar or channel serving as a wall-plate for distributing tlui
"Hin produced by the thrust of the first arch (Fig. 7).
The weight of a brick arch with cement filling is alK)iit seventy
•'Unds per superficial foot of floor.
•rehes of Hollow Brick, Teil Hollow Blocks, and
Hollow Tile.
Owing to the great weight of brick anihes and the necessary
Hng, together with the expense of furring to obtain a flat ceiling,
It arches of hollow brick, or of hollow blocks of fire-proof mato-
il, are now quite generally used. These arches, being mucli
?hter than brick, admit of the use of lighter l)canis, an<l thus
feet a saving in the thickness and cost of the floor. They also
ve a level ceiling, dispensing with the necessity for furring or
thing, and possess several other advantages, described in Cliap.
XV. If segmental arches are desired, however, they can be
ade of either of tliese materials.
Fig. 9.
The voussoirs of the flat arches are cemented together with
ints inclined to a common centre, as in a segmental arch. The
^ewbacks take the form of the iron beams agahist which they
«t, and each block keys with the adjacent; ones no two joints
iing allowed to be parallel, as this Would endanger the safety of
ie flat arch. The lower surface of the flat arch descends about
ae-lialf or three-quarters of an inch below the flanires of the iron
earns; and the bottom of the latter is cemente<l over to i)r()tect
aem from fire, and to form a flat ceiling, which is then n^ady for
lastering. The danger of cracks in the ceiling at the joint of the
at arch and iron beam is avoided, as the beam is cemented over
•efore the plastering is put on.
Fig. to.
Big. 10 shows a section of a flat arch oi Wvft w^^x-aX \QrKv>
' The cats used In tbU chapter aro taken, vjUb VY\e\tpetvtt\%%\oxiA^^^^'^^
Iron Compmny'M book of I reef u I hiformalVon tot KteYsW^fceVv. iwv^^>^^^«^
* of Iwllow bloein (or 111
e Tie Fin-Pfw^ BmihBns droipaug of >'«w Tork; I
Kontoa ItvUam *ui4 Pcmw Brtd- Cumjhikv. also of »« VOI
Uw j^Hwr FirfPnif ContUveHtm Compaag of Chicago; ■
til"? HrjW Firr-PronfiM3 VatufMKg of Clliuago and New In
Theae nMnjvuiws Rnunbettm Uocki for various depUis and ap
u4 anlwB, and o( vsrioii* wci^iU per fqnare foot. The follow
tal4u, coBiiilkd bmo «bU oUsined fiom (tie printed einndia
Ike nrioBs ouiii{Miiie*, abow the Miura of arcbe» maunbctiit
UirJr weight {er ■qoate lool, mhI In some cases the loada wU
Uber will naUin.
n.AT AIICHES,
abjiht Flt«.pn>a[ BBiidiug Cnmpuny nl
HOIXOW FlHB-CLAV Bmicki.
SwMbcisocu Dcirthol '
np lo 3 f I. 0
Ten. Hollo* BLOcn>
Daplh of Wer^hi por 8»fe lewf t
3 ft. SIq..
. f t " V
FIBE-PROOF FLOORS.
369
PLA-r ARCHES OF HOLLOW TERRA-COTTA TILE,
Murafaetared by the Pioneer Fire-Proof ConHtmictioii (-orapany.
Spans between beams.
2ft
8 " 10^ in. to 5 ft.
4 •• 0 ♦' to 6 "
6 " 0 " . . .
6-»« 0 " to 7 ft.
« " 0 " to 10 ♦•
Depth of arch.
W
'^ei^ht per
8q. ft.
4 in.
16 IbH.
« "
22 ••
9 *•
28 ♦'
12 "
:« "
9 -
.34 "
ir)*-
r>o "
The flat arches manufactured by The Fh'f- Proof Buildhuj Com-
tny, both of hollow brick and hollow teil blocks, from two feet
►an to four feet span, have been tested with fliirtoon hundred
>unds per square foot, and from four to six feet span, with two
Lousand pounds per square foot, without dt^flection or <T.'icks.
A six-inch flat arch of hollow terra-(!Otta tile, manufactured by
le Pioneer Fire-Proof Construction Company, having a span of
wee feet eight inches, was loaded with :^:J50 i)oun(ls on one scj^uare
K)t in the centre, without the arch showing any (^viden(;e of weak-
ning under the severe strain.
All the tile in the tables given above have ])een tested by a(!tual
se in floors of a variety of buildings, showing conclusivi'ly that
beir strength is more than fully equal to the demands.
Rules for Determining tlic Size of £-Bcanis, etc.
The method of computing the size of the iron beams ustul in
Ire-proof floors is merely to determine the exact load that thc^y will
lave to support, and then to find the rciiuired size of beam to carry
hat load.
The weight of a brick arch with ctnnent filling is generally taken
it seventy pounds per superficial foot of fioor. The superimposed
oad will of course be the same as that foi- wooden floors; viz.,
iighty to one hundred poimds per square foot for floors in i)ublic
>uildings, forty pounds for floors in dwellings, and two hundred
•nd fifty pounds for floors in first-class stores and warehouses,
^he weight of the iron lx*ams themselves is so considerable that it
iUst be subtracted from the safe load to get the true bearing-load.
The load that the beams will have to sui)port in a floor con-
ructed with brick arches may be represented by the expression,
Diat, between centres X length X (/ -V "VS) -V \\V. vi^ \>^5v\\\\\a>v^Si^
vbich/ denotes the superimposed load vex ^wvv^tSx^XA ^^<^^..
'Vta FIRE-rROOF PI
U Ihe floot' were conatntcteil of the ft
tablis give.n above, the weight ot the h
bt Biibstituteil ill piat'e of tlie liutitbei' '
»liove Bxiirwslon.
HnviiiK obtainwl tlie valup of this i'
llie liettui, we must procued to Hnd the slur- of Uie Ih-mui wlili
carry tills IohiI. TIw safe i[lstrlbut«i| lotui in puumU for«4
<niie fool of TretiUin, Tlniaii Mills, l>hu>niK. niiil feneiiyil I
I fa given In Ihe tables Id (^iit|i. XIV.; mill, tu ulitaiii the si|
I'lor any spun, ll, is only nccttssiiry to divide the safe load furM
' by the ^vini s|>aii in fett. Tim saft; dintrlllliteiT loail for a ^
'«□>■ tiHit wp will i^all Llie cn-egicieiit of tlie beam ; Uihii. fn
49i)nslili>rallons |j;iven above, we have.
Dist. I)etween ^ co-efflcient in pounds — weight of beaj
.■eiiLrcs ~ span squared X (_/'"+ 70) l
A.I an illiislration of the method of cali'uliiting the requU
of Ihu I-beiinis, we will take Ihe following : —
ExA»ii>i.ii I, — What slxed Trent<»u I-beuni would be li
in the floor of a first-cla.S5 store, the beams to have n spal
feet, to be 4 feet afiart, attd to be Riled in betwi>pn witb
Ans. By Fonnida I we find that the co-^Hiclent minus M
the Iwam = 4 x 144 X (iJO + TO) - 1R1,320 pounds. Now,
look in the table giving Llie sirengtli of Trenton beams, we shr
tltal the beam whose ea-«ffici«iit I'otnes next abcve 184,330 ]
is the " {t-iui-h heavy," whose co-efBcient is 1»1»,000 poundi
weight of the beam woiUd be 'HI} pounds: )ic.>n<-e ihe l)-iudi
lieaoi is amply strong enough (or the pur|>ose-
Iron beams for floors with arebes shouhl have a liearing
wall of at least six ij)eh«s.
To save the trouble of goiug through the above work etct
it is desired to find the size of beam nested in a so-callvit lU
store, tbe foUowuig t^ble, showing the si»> of rolled T-4«a
floors In that class of buildii^, for dlstaiu'es between o
four, five, and six feet, has been ealculateil. The ^
table is too simplu to require eiiplur-atlou.
•1. Theunliaaai
J
Mes showing Hie Retiuired Siz« of UoI1<m1 I-ltuHiiiN
ir Brifk Ai-died Floors in FirHt-clusK NKirt-s aixl
Careliouaes.
eutated to vtteUtin a load on tkejtvar nf SSci poiiiiih fr
rial /""', t.lie strenolh of the ieome helnii Ihiinr
It miiHu.ftirturrrs.
TKEX'roN ROLLED l-l!KAMS.
'
Tcr
«'■
Staohhravy,
«oo
a ;; ji^t" ■
W,3
B ■■ M lb*:
8 1' OT lbs.
xxt.o
I '■■ b^JJ;
Mtio
101 ■' itghi :
lOl ■■ hB>vy.
720.0
m;; liRhi .
70S-1
loso.o
I^" ^^^.
1076.1
iT;- iiehi .
idoo.u
14U0.0
\l '■'■ bSivJ;
Ifi ■' heavy,
.
".re;:"
<llncbll|[h1 .
S :: SlVb^:
fi •' UU tin.
01 jj Hghi":
iii '■ haivj,
2} ■■ heavy.
ft ■■ beavy,
! " ES:
wa.o
1208.7
]4Uo!d
"he table on the following page sliows the sizii of Phtrnix boami
aired to support a floor with the diffwent spans anil iHslancM
rt ttiere Indicated, the total weiglit of floor and Usui iH-inj; taken
ine hundred and forty iioimds pf r square foot, whii'h for a floor
irick arches would leavi' seventy [ioillni» for thi' H;i()eriiii]josed
I.
'his Luhle is taken direct from tli<' I'htenix ('iniipHny's "Book of
iful Information." All of the hundlKioks ]ii<1ilished by the four
ling companies mentioned ubov c:ontaiu tahles rednelng tbe
'igstirj calculations for deterriiiniut; the si/i' of lniu.ii] to bo used
uy givra floor, to s miuiiuuiii.
^^ PHCENIX BEAMS
THEIR ADAPTATION AND DUTY AS FL
1
}ORING JOIST&
S' sV 1 6^
apart apart apart
7,000 7.7«J^40«
«<. , e« 1 7.
?o'| 77 1 «4
9,800 io,7Bo »,7a)
1 ,"»
80 ; 88 ; 9«
.■.ioo».|^.3^
^ ! 99 1 .=«
11.600 13.860; i5,uii
Ckar
Span.
3' 1 3W
■part 1 apart
4.aoo 1 4,900
aptt _.;^
L-oad Iba.
36 n' 1 4»
S,o<o ^■ao
6«J"
4» t H
6,710 7.560
.7" .
S6 j «3
7,V «.»»
.^ W9"«
" 64 ■ TJ
8,960 10,080
,"W 1 9"
Lo«IU».
Load Iba.
6,J» 1 7,840
8"
■Slbct.
S4 0' S3
7,360 B,a>o
B^r,"™ 9'
/-i""-
»f«L.
I.oad Ibi.
.iftoT,
l.<M>dlba.
Load Iba,
1
6.0' 1 ,. I So 1 9=
8,400 B.S™ ".«» '».*«■
B-^'-'HI .0^1' ™_
9,140 10,780 ii,jio 13,860
.oW">»
"" 1 '•" i ™
.4,000: . 5,400 rt,8»
1 ":'.'»
<B.'ttoO;.B,^«^A
18,140 1 10.0.0:11 AK
Ot,5"l!0 |,5._a.
.4^ 1 ".54 1 .M
19.600 aijBolujM
j>n' 84 9S 1 .08
10,080 i..7«o 13^0 15,110
>BI«t.
L^adlbs.
Load lbs.
JBD' 1 9, 1 .^ 1,7
10,918 ia,74o 1 i4.!fio 16,380
84- D 1 9' 1 '" i "6
Load Ibt.
I
11,60a 14,700 l6,Soa 18,000
.5» j 16= 1 ,8,
..,ooo,.j,ioo|»5,aB»
loabov
1
table the loid is »»V.-:ft M !<=.*«. Sf
Disflectioii of Rolled l-I
on 1-beajua can be i^oiiipute<l liy Foi
^n«, C'liap. XVI.
According to tlie calculations of the uojiueer of tlie New-Jersey
teel and Iron Company, tlie b^aiug in tbe Uible on p. 371 st'iU not
eflect over otie-tbirtieth of lui ineli for every foot of sjian, iijiili^r
^load wliicli they have betn caJculated to siippcrt.
Tle-Hods.^Tie-rodn fromflve-eightlisto one inch in iliuiricl^r
Keanlhiaiily employed to take tlU! tllniat of the tirlrk an'li<-«. anil
U adil to tllti security of the floor. The^e may be spiiceil from
Kilt to teirtlnjea the depth of the beams apart, and the holes for
Km should always be pUDched at the t^viitre of the depth of thn
■tin. The formula for tlie diameter of the tie-rod for any floor
Diameter Bquari'd =
W X span of nrtrli, il
02832 X rise of an-hT
. feel
[31
''denoting weight of floor, and superiiiipuBeil load I'esting on the
cti halfway between the tie-rods on each side.
fi&AJUPi'E. — What should l>e the iliameter of the tii'-rfid In lake
e thrust of the arches in Example 1. the rods to hi- Hjiai'-'d 7 feet
In thib
le llie span = 4 feci, nearly; H' ^
321) X
H-iKfi X i "
UO; and !■ = J of span = i fool. Then tfi =
D = 1 inch, nearly.
Of iK>urae, where arches abut against each aide of a beam, there
no need of rods to take tlie thnmt of the archer; but it is always
Fer to use them, as the outside biiy of the floor might he pushed
f aidewlse if the whole were not tied tbroi^h ; also, it one of tlie
Ches should fall, or break through, the r<>rl<' would ktvp the
ber arches in place.
S:x|)criments «» the Strength of Itiiok atul Flat
.rches. — Kither of the forms of floor mentioned above is
ifliefenLly strong to support any Mejuly weight that is liable to
yme upon it; bnt for concentrated live loads, and partli'ularly for
Mrs where heavy boxes are to be movetl. the brick arrli appears
I be the besL
The following experiments, conducted by Mr. F, C. Merry, archi- '
*l, at tlie lime of the enn'tion of the Western Union Telegraph 'j
uildlng in New-york City, show very coi\c\\iH\NftVj ft« «ra>ws^a»» J
-*• alrengih of (he different floors we have «\e\i\,\awi >» * '
niililpiily-appllod Inntlx. Esfiprlinpnlol floora www corwlnii
h nn-he*. flat nTf]i<v i.f liollow terta-«nil,a r.ile, dtiil tlnil
uf III)' ii'il liollow bliK-kfi. HUjipui't'Ml l>y i.r>ti Ixmiis pliuwd^
I' ftwt H[Hirt. Thesu nivlies van; Irstutl by allowing h ft
giraiiiti* flftwii InpLien -wiiuirR »nd lour fwit Long, with th»
n>iiiiik-il, tu full froui dirrerent helglits bo ua to strlltv ihi
■quarcly ui> une of its ttu-«e. Tliv mv)ii« were covered widt
■ hiyvr of innciuto, Init withuut any b«Hir>l.s ur ntlier Riateri*L
The i>fln't ut til* fHlUng we[|;ht on the door constnir^ind.
tnrhi'jt uC txll hollow liloclis was to jiunch a, hole Ihrouiilj ihi
klnioHt iixarU)- thi^ sixo uf the stone, the rest of the floor ri'n
liitM-t. Thn effco.t on ilie liolluw term-colla arch was W
ilown III)' iip|«r lutrl of thv hollow l)lo«ka, thoiigli it tuuV
minus Hinount of iioundiu-; lo hn'Kk It riowii." 1i tiM
muiuinbt'ml. Imwever. In ■■onnm'tloii wltli the terra-cuttji iiri
Ihp i-xiM-rinii'mul floor whs vry cnrafnlly conatriifli^, iinj
[wrHonal suitPfvUloii of Mr. .Merry, so that the JointH vli^
«•; whll«> in onliimry wnatniL-tioii thit loeuliantis are not,
esui'tui to |iul ilio pliis's in tli« i)ro])ur plawa, aiiil llitw
«curv fXivut joliils.
The briok an-ht« aiooil the t<wt the beUi of all. The welj
klloweil lo ftiii Ihnui^li it hfljjilit of thrve f<^t, on the fiiMt
out fniclurhig ll Iti tho h«st. At last, after severe poUtrf
«ttui<! placr, one brick at a time was knockttd out ol
■huwliig tliat tite only way lu whicli the hrick arehes caii bel
Id hy breaking the intllviilual l>rleks Into fragniciit.''.*
CHAPTER XXIV.
MILI. CONSTBOCnON.'
Ir Ihls chapter It la proposed to describe tlie principal eoiui
jf-f««tnTea o( what, in the Eaatem States, is known as thc! ''
Utructlon," or "Slow-burning Construction.'' It Is a nmtblH
EDDBtructlon brought about largely through the Influence <jI tbi
mutnal Insurance I'Oiupanles, aiul eHpeciallf through t
B of Mr. William B. Whiting, wbuse meciianicftl judguiea
'mcK, and skill as a manufacturer, hare been devoted formal
o the Interesta of the factory mutual companies and to tl
'ement of factories of all kinds. Mr. Edward Atkiim '
Bidcnt of the Boston Maiiufaclureia' Mutual Insurance I'a
ig', hua also done a great deal towards influencing the public
irof ihisraoiipof construction.
wifpi-i/dwi in thla mode of construction la to have h hmUi
H Vbose outside wails sliall Ix: built of niiiaonry (generally of briekj]
uilrated In piera or luittresROS, with only a thin wall contatnrij
^he winitows between, and the Hoors and roof of which ahmlli
gonstrucled of large timbers, covered with plank of a auItaUtj
Kfcness; the girders being aiipported between the walls b; woodetti
Jitt furring or concealed apacei are allowed, and notliii^
JSpamiitted which will nUnw of the accumulation of dirt, the otH^''
cealntent of Rm, ur, in slmrt, any thing that is not needH. ti^
'Mr. ''- J- H. Woriilliiiry, iiiBpwtor fur the factory mutual HtM^
inaumiice conipaniejj oF Massachusetla, who has uritlen a veijl'''
able book on the " Fin' I'ltittH'lion of Mills" (pubilsheil by John
Wiley ifc Son» of ttnv ^ork), lias given sui^h coiicis<> and clear
i( wlinl dotet and what does not constitute safe con-
a tor iiiilla .in'l waroliouses, that wilb Wa \FW^»ftSin.-»»
laote them rfrfi/'thrr fivnii liia work.
(.Jul
B W ortiiors' » Bi»
4 CX}N5'l'KEJCT]0rF.,^|
"PrcvniliiiK Features uf Bad Con
Mills and Storeliuusus. — Tlie Kxperiuiii:?
UutualB lias liliown Lliat in uiUI aud Btorehoii
where i.'onsldcrations of safety, convcniuni'e, and
B«ntlal, the following prevalent features of bud coi
he omitted; —
" Bad roofs,
" Haftera of plank, eighteen to twenty-four
tetiln'*, set eilgiiwlse,
"Any roof-iilsnk Ims tlian Iwo inches thick (t
ferred) ; any coverin); which la nut grooved udJ sp
" Any hollow apace Of an Inch or more in a rool
" Any and every mode of sheatliing on the Inait
as to leave a hollow space.
" Any and every kind of meml roof, f xi^pt a tin
ing on plank.
'■ Boxed eomlues of every kind.
" Bad floors containing liollow spaces or uune':e
" Thin or tliirk tloors resting on plank set edgei
Iwenty-foui' inches i>elwoen cei
" Alt sheatlilng naiie<l to the under side ol [
tiiahing a hollow floor.
" Bad Hnisli, leaving hollow spaces, c
" Alt inside flnt.ih whluli Is fumnl off *
Mween the finish and the wall.
'■ Wooden dodos, if fun-ed oft.
" Open elevators.
"Iron doors, iron shntti-rs,
"Any and all concealed 8|)ai.-eH, wooden t
tllators of every kind, In which fire can InrkOTBpl
lepteil from water.
" Any and all openings trout one floor to anotl
departiiiunt to another, except such as are abaoln
the conduct of the business (all necessary opening
l«cCed by 8«lf-<-losing hatcliea or shiittei's, or by a
Hre-duors ciiveii^cl with tin; automati<- d»ors pr«
plaeis.).
"Esseutial Features for tlie Hafe <
of nilllM and Storehouses. — solid beitnia, ■
bolted near together, eight lo ten feet belween ooi
palntal. varnished, or 'flUed' lur oV \v»8b ticttw
",18 flnished, lest dry-rot r\iiihV\ «\«m*.
i-by an inch air-spw* va.-\v sh\.^ \w Oaj
L. I., a... •f,...i.„r^ tt.il ii.[>nv« ttlKj
side ol f
1
t1«Hrly flat. 'riiiiWrv V
ttiy
project eighteen to thirty-sis Indies, as may be ilesired, serving
brKcketa. Plank laid to the ends of the ItmberB, Neither
Bor boxed tomiceg of any kind. Woodei] [wsts of suitable siM^
not tapered, unless when single i>09ta tumwi froiii the trunks of
trees with the heart as a centre, rollowing the natural tapej-. Core*
Cored one and a half inches dianieler ; two Iialf-inch holes tnuiM
[rt'taely through the post near U)\i and bottom for Terililatlon. \
"Floor-planks not less than three inches tliiek for eighl-foot
bays, tlu'ee and a Iialf to fonr for wider bays.
beams bttve-been placed twelve feet apart, with four-inch plauk fot.
the floor ; but in such cases a careful computation of the strengtlt
«hould Iw made, liaseU upon the load to be placed thereon, beforf
ft wide a space between beams is adopted, lest tliere should he exf
■e tieflectlon. The belter method, where lUe arrangement M
Winery requires such wide biiys, U lo alter the plan of floor*
Top floor one and a quarter Inch boards of Soutliern
^ maple, or some hard wooit. The best cnnstruction requires
a top Boor to be laid over three-quarter inch mortar, or twA
I thicknesses of rosia-stzed sheathing-paper, cerl&in grades of whien
we uow made especially for this purpose. I
" All rooms in which special dangers exist, such as hot drying
to be protected overhead with plastering on wire-lath, following the
line of wriling and"timber, thus avoiding any cavity in the celling.
In such rooms, the wooden poals should also be protected with tin;
care tteing taken lo leave tlie half-inch holes through the posta
tje&r the top and ha.w uncovered, so that dry-rot may not takQ
Fig. 1 represents the proper constroction of one bay of a tlues-
Btory mill, each bay iieing like the others, and the building beirg;
lOnneil of any number of such bays placed one after the other.
Sucb a building cannot be cotisidered as fire-proof: hut the tD»i
lerinl is in such a shape that It would not readiij take lire, and
would bum slowly eveii Mien. Moreover, the construction Is such,
that any part of llie building can be easily readied by a slreara o(
water ; so that a fire <.'an lie readily e^xtln^dshed before It has
gained inudi headway.
In a brick building no yraitUe tliould be lined, except for stepa
and underpinning, as it splits badly when ex^iosed to heat, and ia
tberefore unsuitable for sills or lintels, or any work liable to b«!
«xp09ed to any Intense Iieat in case, the baMVn^^VtwA&^ie. cia%s^
77ie beet qaalilim of brown sandstone, mais >ift ivwA ^cb *»fc,'
/ar olber places it would be better to use \>T\iti ot wm^r*
Moalrletl brfckn ar« now nianufactmed \iv » grc»lv«Aa^'
S78
MIIJ, CUNSTEUCTION.
The iMwt fuRturim aiiil woollen inllh in MAasacliiuettt are no
generally Imill willi the l>eainB eight feet ftpart from centres, u
with a :i|)iin uf luvuty-Hvi' ur twenty-four feet, thei« i>elng one <
mon- ruHN of imihIh aii'onliiig lu the size of the mill. Fig. 1 repr
!ti><:tii>ii of a mill liaving two rows of posts.
'i'lii' fl'>c)r-l>i'anis art- iisiiully twt-lve inclifs by fourteen Inobn
lianl-|.iii.. tiiiilH-rM.! wliiili irsl oil twi-iily^ni'li brick piers In llw
hnsi'ni.-n[, anil mi w<MHl>-n ihihis and tl tNiile walls In the ol
sliirirs. The PTnU wliirh n-*t on thi' iintsiili' wall are arrange*
ii)> l<i liHvo nil itlr-NiKii'i- nroiiiid t1i<; nml of tlie timber, nnd arr
uiieli»n-i1 lo tlir whII )iy a rHM-iron plate on which tiie beam r
'['liiH piali-. sluiwn in (Ij;- -■ hiis a transverse projection on
ii|i|H'r snrraii'. ultii'li Ifis Into a srtmvf tn the bottom of the beam.
:inil is tiimni down xlxiut six in<'lii-s into tiic lirickwork at Itir
■'nil. 1'1i<- l>r<i-kw(irl( for about Hvi' iiiurw» above the beiun shoiihl
\k- kttil ilry. jMnl till- upper edge of lh<' end of the beam Bllghlli
ninnileil, in <•»»■ of tile |iosslb)e liiimlng of the beam, this vouhl
Dillon til.' be»in lo fall without Ihniwin.i; out tlie wall.
Th-- fi-«>f on lop of these bcanm i* rr.nstructed, first, of thrw
ini-li planlcs, not over nine inclii'M wiile. planed both sides, and
■rri«>\<»l iiu iKitli fAuf*. whli'h are (illnl with splines of hard wooJ
(f!i-iUT.ll]y Ji;inl ptn.O almiU U«W-iimT«\* <A mv WcXiNi-j wo, ludi [
' /(*«,
Ih^-„
e
A« -KfA V»
> that, It
>ih
for b«mH and
rlHlO. A
.</«
ow
* tlio machine
y
V) vuu e»»W
I liair. Ill nulling tli« plunks, it in Iwlter to ■'liili
f ftfter tlie maniipr or iiniliiig iiiaU^hiMl floors in dweiling-liniu
; that Is, ilrli-lng ihe naiU oblligui^ly thmugli the gruovJ
I the ftpline is piiL in : this alluws tli« ptank lo shrink a
without oratkini;. and witliunt npllllliis tlii? npllni-s.
Fl«.2. , I
Of i.'aurae, when planks arc nailed in this way, lUK^h plunk inuit '
be nailed before the nest is put du*H. This takes ronsidembte'
Uae; BOtJiataome huildern lay i immlH-r of planks, wedge theiiiij
up, and then drive in the sphn^^ from oiii' end and nail directly 1
UuouKh thp planks into the lloor Cimbera ]
ng, 3.
ThB uppfir duurlng in smierally uf some hani wool, an inch an^
a quarter thiiik, ineruly juinteil.
"The floorsshould be rendereti water-tight by three-fourths of N
inch of mortar between tliu upper and lower floors. Tlie layer rf
mortar preaervea the hiuiber from decay, preventu the floor troi^
beaming aoaked wRti oil, and is so slow burning tliat it Is i
nearly ttrc-prouf than uiiy other practical nii>tliud of eiinatni^-
FJg. ■iabows a section through siwUa floor ».s"«ft\^ai'^ftiftKSKW
TAa roqt la generally formed of im-vncU Vi^ t'MftVi«A»tV\ffl««
.*i«0 MILL C0N8TKUCT10N.
timbers placed the same as those below; and the outside <
allowed to project over the wall from eighteen inches to two
forming brackets to support the eaves. These timbers are cc
with two and a half or three inch spruce plank, groove(
s])lined the same as for the floors. The plank extend to the <
the overhanging timbers, and form the eaves to the buildir
l>oxed cornice being allowed. If the roof is flat, as is ger
the case in mills and factories, the plank should be covere(
tin, gravel, or duck.
If tin is used, it should be the best "M. F." tin, paint
tiie imder side with two coats of red-lead, and well dried befo
sIk ets are laid.
if a gravel roof is used, it should be equal to th^ best qua
tar-and-gravel roofing over four thicknesses of the best roofin
('oiton duck is gradually coming into use as a roofing materia
has for a long time been used for covering parts of vessels,
light, durable, does not leak, and is not readily inflammable.
The material should be twelve-ounce duck, weighing s
ounces to the square yard, and should l>e thoroughly stretche
tacked with seventeen-ounce tinned carpet-tacks, the edges
lapped about an inch. If the roof-planks are rough, or not
even thickness, a layer of heavy roofing-paper should be laid
the duck is put down. After the duck is laid, it should be thorc
wet, and then painted with wliite-lead and boiled linseed-oil
it becomes dry; which makes it water-proof. To protect froi
give it two more coats of white-lead, and over this a coat oj
clad paint. Instead of the four coats of white-lead and o
duck may be saturated w itli a hot application of pine-tar tl
with boiled linseed-oil. This has been found to work per
The ironclad paint should be applied, whichever method is u
rf the roof is nitched. it should be covered with shins^les a
Mtr.T, CONRTRLi
Itjrd; Uiese being IJu> least dlamel^rs of the uoliuiina. tf Itiu
nns are tiii>ered, they mny be ba\f an inrh Ips^ in illaineter ■
op, and oiif inch moiv nt Mic luitlniri, iiialcing the taper gi
b of the coliiraii thrve-fonrlbs of jiti inrli. Tlmj shoitW
F either liard-pine or otik tiiiiUer, thorn iiglily scoMiiied, and
Id have cores bored one and a half iiK^hes in ilianieter, with
half-inch bole? tranRTerself through the post, near top and
an, for ventilatioD and to prevent dry-rot. The colunins ore
[ded with cast-iron caiis, as shown In Fig. 4, wtilcli support
nda of the Boor-baBms; and, where there la a VPrtlral tine of
hIwh'. Til.- (IiJb hF Ifii' pdilKw'ariiritiii "inii^ |>1iM?R~agiln!
Ilii^y <vst shoulil >H' tiirnnl tnw. »<> liml tliu ■.'(iiitiu.'t will l>r unl
(Drill. V\K- ■*> ruprcHt-iilB h vf rtiinl iieotlon throiL)ih tbv fluor w
Ilic i-cntni of t.lie i-uliiitiiin. unil Hg. (1 Bbow» n pi-rqin-tivc v1f« c
» iiliitk ivltli Llie iHue o[ Itie ujjpir I'uliutui i-oiiiing down mrt '
Uip. The tirick plurs iii tlie batwnicjit Bniiiioriliifi l.lw- ciilni
shoiilif be (■Bpjied wilti HI) iron platt twp.nry iticlir» li,v twr
ini'lies, an Inrh anil three-f»iirtliB IhU-k.
'I'lic nliiivt' is the most appi-nveil iiiethoil of (-onitCriK'IJini iini
Mii^iK' rill* inilh, fsi-Utrle», aiiH storeiioiiMiB; anil tin- iliiiicns'
glv«D ror thfl various parte will aoswur for any col
or woollen facTory whore Ihe. bays are nut morr I
eight fi^t lung rrom n'Jitiva. Wliere the layt *l
morn than Unit, or the loa^ia on tlii- Hoors are giwW
HS may hi- the nasu In HlorelioiiwH, tin- floor-planli U
timbers slioulil he iiroiHirtiomii ai.'contilig to the nd
tor Htrenitlli hiiiI slitTnras given in f'liap. XXIL,!!
thi> I'oliiiiina |irO[iorlloji<"l ar'i'onllng to Ihe rulegiv
in Cliap. XI.
II' piirlili'iHH /ire di'flred In sinOi a mill or ul*
houae, tliey alioulil l)« built of Iwo-lm^li tonguwl •
groovod |)liiiik plaii^l U))(<Hlier on <'ml (fonnlngaw
partition), itml [ilHsti'n:cl both Men, eittier on wJn,
on ilavetallril iron lath. Such partUiuiu Mve U
founil to niiT'k hi'II after a trial ol twelve yean.s
offer effi-i'liiul ifsiittHncR to Are.
Mill tlf,.,>-t iljxl nln'tU-rii should lii' luiilr of d
thickiies»it's of inrli bonnln, I'overiHl on ult nMm nl
tin, aa (ieairl iMid In (."hap. XXVI.
For a thorough deserlpllon of tlie avparatiiB and applianc™ urf
for the Dm protection of inllU, and for a thorough UIkvumIij" "'
tlw vibration of inilln, tlm deflection of the floor-|ilanlts. kji'1, '
fapl. every thing that refers to the conBtruRtlon anil prHtectii''
of mlllB and factorieB, tlm reailer Is referre<l to Mr. Woodbtur''
work on the " Fins Protwtioii of Mills." mentioned a'
Thf cokI pvr aguiiri- /not of toUl floor art-a of mill* and ta«o»W
at the prcNent lline (IHhU), aptonJinK i" Mr. Kdward AtkinBWi.U
Mill with three atorleB for maphinery. iiiirt a hase-
wcnt for inlBTollaneoiiB jinrposj')'
Mill with tuo HtorieB formai'hin<>ry, and no bBBement
Mill with one story, ol aI«>Hi. «in-. wtv «1 ftw«, -«VAv
/WTOinent for hcatmn ami AvrUvh*'- otA-j . . . A»tt.«!|
FIfl. fl.
Wmliov Is for
1.1 ?H«
i.-IiA|iUir, to n&j all tliHL
■.e fii'<j.]iroof o
ice we shall confine ourselves lo merely suting wliat experi«np«
I ehown to be fauts, nnil ilewrihiuj; Uiv uieiliods of fire-proofing,
1 Ere-prooHng buildinj", iiow in use.
It may safely he staled ihM For h building to lie tirc-froof in
Jity,—
Irt, Tlw I'ulBlde vfilU !-lwuUl b« of im'unru or irnn.
"A, No coiiniivctite Kifidaork *h<iiild lie f:rpo&ed. (Thla, of
mui^ does not indude caBiiigB. wliiiOi fould be easily re-
placed if destroyed.)
id, A"o cotiilruetire irowrork Kliotilil liv tJ-/iowd,
tth, JVo wioii piirliliiiiiM (unless protected by fire-proof mate-
rial) niu! no icuut'/iiirmf/shoiUdbe allowed in the building.
th, Tlierf s'lniilii hf no toneealed spaces to which fln: might
^ find its way, and where it eouid not he reached with water;
« hollow wooil floors, liollow wood furrings, etc.
a be lire-proof, a tmildiny uliould be an itenr rermlii-proul'
Tw is pomible.
le sis conditions are strictly observed, a fire migbl bum all
ii> furniture and goods the boilding contained, and then die out
IT wfuit of fuel, with no damage to the hnilding. except to the
Itiide <'oat of plastering, tlie doors, wood-casings and finish, sash,
withe upper flooring. These would probably have to be renewed;
n the structural part of the buildini:; would renkain uninjured.
If to the above, all the rioore in the building were tinned, both
Tinned Doors. — Thus tar no fire-proof door hw bei
wliioli is so saCisfBCtory In every respect (tmleaa It be in aps
»g M iloor maile of two thicknesses o( tongueil and groove
eighths liieh boiinta laid diagonally aerosa each other, ui
wtth wrought-lron nails dritvn flush, and clinched on t
side. Tlie itoor la then covered on the sides and edges vil
of tin kK'ked together like a tin roof. If a swinging c
hinges Bliould be bolted on. and not put on with scren
door was designed fortbc use of mills; hut it has worked
factorily, that it is generally adopted wherever a Rre-proo
wanted. Fire-proof shutters are also made in the same w
Tu fulh! the second, third, and fourth of the six conditi<
tloned above, numerous methods a:id materials have been I
and companies have been formed for their manufacture ai
cation. Of these, the timterials most frequently used ai
bumt-claj tile, porous terrar-cotta tile, hollow blocks mai:
hydranllc lime of tell, and hollow blocks composed of Uin
and ashes, cinders, etc. All of these materials possess tlUf
of resisting fire, and are poor conductors of heat. J
PoroilH teira-COtta, in places where strength la w^
is undoulitedly one of the best Arc-resisting materials 1
posses. It Is composed of a mixturtt of clay luid any <
ble material, such as sawdust, charcoal, cut straw, tMi4
^^^£-1
-PROOF CONSTRUCTION FOR BUILDINOS. 386
■ orSbiarSl}/ ennntrTietfJ, stores, warehouses, public buildings,
A all large buildings In (■itirs, liuve oittai'b walls of maaunry or
tak, wtLli pi^rliaps the. prltidiiul pnrUtions nf lii'i<*k, jtiil Ihr. r
Uxtiog partitions, wltli tlic Roots and roiif. ui winni I'uii'i.riii'tiiii
breover, tliR brick walli siiil imnitiuuii mi; ulti'n tL;ri'i><l with
^o^, for tbe plastering; so that tin: wliole buUiliug iibuiuiiU with
Eng^plucGs iu which fire can cmiceal iUL-lf umil it brttaks out
Buch toree as lo be alniOHt iineontrullitblc. There arr, n
ing companies, such as the Wlylit Flri^Froiifing Cnmpiiiiy of
Bw York and Chii'agfi- who Wl'l taku such a building hefon
[trad, and guarantee to make it absolutely fire-proof.
iTRie floors may be rpndereil flrc-proof by means of jwrous terras '
Oto lilea fastened to tbe under side of the n'owlen joist, and a i
^Kx of cement one Inch or more In thickness spread between
^der and upper flooring. Tbe under side of the roof is protected
I, tlie same way. The wooden partitions iiiii//il be pi'otei -ted with
jfcrouB terra-eotta; but It would be elieaper and better lo build llifi
F botlow briak, with porous tile iuaerted wherever It Is desired to
■iVe n^llngs, Suck a partition is more Qre-proof tliuu a
krjr brick partition, as the hollow bi'lck are niade of clay, whiek
HI resist a more intense heat than the ordinary brick. The out-
de walls may either receive the plastering direct, with no furring,
r else be furred with hollow tile; the latter being much the better
leUiod.
If there are any iron columns or beams in the building, tliey must
C protected by porous terra-cotta, or some other (ire-]>roof and
iDD heat-H:on ducting material.
The whole bnllding is then plastered in tiie usual manner,
Ifrectly upon the tiles; and a fire may he kindled in any part of tlie
nilding without reaeliing any of Its constnictive parts. Instead
>l protecting tlie under sides of the floors and root with i>oroiu
•rra-cotta, teire-talhiuij may he used. This i.ithing, or wini-rlolh,
■ kept three-fourths of an inch from all woodwork, by pieces of
Uop-Iruii, placed on edge, and held by niciins of staples ilrlven
>^er tiie hoop-iron, and into the wood. Tiie plastering Is then
tpplicdtothewire-clotli; and, if done in a tliorouj;]! manner, it will
1^ any ordinary fire to injure the floor-timbers. See p. 391-
In place of the cement between the floorings, sheets of m^neso
i^aldte (which la absolutely fli-e-proof) one-fourth of an inch thick
nuy be used. While a liuilding supIi as lias been described can b
made absolutely flre-pi'oof by these uiethuila, it is very difflcult to di
K, beoause of the siiuiherless comers, nng\e%, imvtUt, t
^oon, etc, which mmt be eery cai-e/ullu 8.\,Wv\te\ \j
^A^McegetSn between the floot-jDlBVa,Vi.')^%^^
386 FIRE-PROOF CONSTRUCTION FOU BUILDINGS.
through the floor, where it could not be detected until it had nearly
consumed the timbers. The difficulty in fire-proofing such buildings
is, therefore, that some careless workman may not l>e as particular
with his work as he should, and thus allow a loopliole through
which the fire might find its way.
It is much better therefore, and not nuich more expensive in tiie
end, to build the floors either of fire-proof material filled in bf-
tween iron beams, or of plank, three or more inches thick, siij;-
ported on heavy timbers i)laced from seven to eight feet apart, after
the mill-patteni. If built in the fonner way, it is only necessary
to protect the lower flange of the iron beams to get a thoroughly
fire-proof floor, which there is no possibility of destroying by fire
(or water, if hollow fire-clay tile are used). All the bearing parti-
tions of a building should be brick, and shoidd be at least twelve
inches thick. The plastering should be applied directly on the
brick, or, if it is desired to take extra precautions against any
destruction of the building by fire, the brick partitions should be
lined with porous terra-c^otta furring-blocrks. All other partitions
should be built of hollow brick or hollow blocks of some fire-proof
material.
The ouUide walls of the biulding should be either furred with
fire-proof furring-blocks, tile, or bi*ick, or the inner four inches of
the wall may be built of hollow burnt-clay brick, of the same size
of ordinary brick, and the i)lastering ai)i)lied directly to the wall.
This saves the cost of furring, and prevents the moisture from
striking through the wall. In no case should the walls be furred
with wooden strips, as is the custom in many parts of the country.
Tlte r(K\t\ If Jlaf, may be constructed in the same way as the
floors, only the weight to be provided for will not be as great, and
hence the beams and arches may be made lighter.
ff ffifrhed, the roof may be constructed with I-beams or channel-
bars placed from eight to ten feet from centres, supporting two and
a half or three inch ±'s, which are placed sixteen or twenty inches
ai)art. The I-beams or channels may be covered with porous
terra-cotta, and tlu^ roof formed by setting fire-j)roof blocks be-
tween the I's. The blocks (.'an then be plastered on the under
side, and covered on the outside with slate nailed to the blocks.
In Mansard roofs the I's may be set vertically, and the blocks
set in between them in the same way. There are various forms of
fire-proof blocks and tiles manufactured for this purpose; some
being intended to set in between 1-bais, and some to be built in
between small I-beams. They are all constructed on the same
'inciple, however. If it is dvisVvtt«\lo\vA.Nv> ^ \>vw^\ tv><s^,^ without
Wngr tijiished off on the VnsVAe, \Ave toc^^ im.^ ^J^^ v»5\nsXx\mAr^ '^
PROOF CONSTRUC'llON fH
, angle-irniiH. wtth the sltitr fitstitiKHl
MVf a IittrixuiiUl cvlilnK
g-bliiL-lu aiispeiidBil
liiKouetlieBre-proof
I pre vim C tlic nuiiius or
tting into tlic^ ruof, mi
i> in the roof wniilrl
H protected.
le building, tliey miisl
by Hi'p-prDof blocks,
I used, plasti^rint! on
may be uswl. )
lumilK. — Tlif (le-
jron raluuiiiii by in-
tBS been thv rniuiiiuu
loas of vast ainounls
ever since iron tgl-
l>e«n osetl. Their
Joringfii'ea, in biiild-
to be flre-proof a
pinbustible matma
Ion liave befn xif><
^D iiKcraBity for I)
tram the effi-ctH
i under all L-Ircii
disMtrous e^e
UeiulGed by the si d
Of cold water ugii
amiig, causing lliin
d4>ly by cMttrarii
„ H'l'l'-h WHter
eoneequiinUy to lirealt
^lOadB. 1 he exgia
foiron (?o!<ui
WVe been ni^kn^ I
la anoIli«r u
The first
Is to raise tbi
cf, ftiaarauLU as the atraiin ieiiu\x
^Pait that riee<led to \ki\i\ tA\em
■ I much grealur \ini\er suiAi
.vAm:^^
3«tl
'IRB-FBOOV COHSTltUCllON FOR BUHJUNGS.
Tilt" prevailing metUix) for fire-proofing iron columns Is
tlieni wilh flri'-proof blocks of nitlier porous t«rre-cotta orliollow
tilv, mill I1i(!ii finish tki'iii witl) cement.
Aniiiiig tlie first Inventions for fire-prootinK li^'> ''oInninH in Cbis
way is lliBt sliown In FJ;;*. I. 2, 3, anil 4, whifili rpprRsimL" WisUt'ii
patent process for flre-prooliiiff tlin I'lKi'nlx wroii!;l it-iron iiJuiiins.
Fi;;. 2 is a pcrspct^ive view of tin: column, sliowiii^ it in the van-
mis stages of coiupletiou. Fig. 1 is a section on tlie line ab. Fig.
:t is u vidw iif one of the ]>latis eiilai^cl; and Fig. 4 shows one of
tlif liloi-ks. The Pioneer Fire-Proof Coiixtriictioit Company Ifflvt
a similar mutlio J of fire-proofing iron columns by
• means of iiollow tile. These nipthotls ran be
applied to coluKuis of almost any shape.
Iron columns may also lift protecteil by easing
them with wooii covereil with plastering lipLl on
by wirc-latliing. Fig. 5 shows a combination iron
I and wood column deviserl by Mr, P. B. Wglil,
(leni'xal manager of the AViglit Fire-Proofing
Company, an I formerly a consulting architect.
Tlie iron i ore of the column has o cross-section
n.semblm!{ i Creek cross, with projections fiB
LliG sid<s, to liolil in placn the four wood-sectoi?
which arc driven in from the upper end. Thf
'paces between the wood, over the ec^s of the
nun core, arc filleil with plaster, which is covered
nith stiips of slieet-Iron nailed to the eiigea «f
Ihi noot sictora. If this column were eovemi
mtli plastir on iron-1atb:ng, It would undoulit-
edly be pcrftctly fire-proof; but for some reaaon
(probably till trouble .and expense of making) it
IS not >eiy < \tcnsively used.
llie pKcifiling itiHliod of finishing fire-i>ro(^
ijihimiia IS to work a moulded base and dado
with Keone's cement (which has the appearance
i>f j.liiHt.er and the hardness of marlile), and above the ilailo 10
liiiiih ill plaster, with any amount of elaboration. The plain sliafta
may be of superfine Keenc's cement, colored and polished.
IVroiijihl-iron beams used tis girderx arc either protected by
liorou!< lerra-cotta blocks or tile, or by covering with plaster on
wiriv'latliing.
Fiiis. tl iind 1 show forms of jxirous terra-cotta blocks manufic-
red by the liaritaa Hollow uud Purou* Hricfc Company tor pro-
"■ «;lrders. Other conipaiuesa.\wiVHa.iva.^MX.\a«,\jE(attte
e. The figures ou v. 8S» *vo-« m^\u>6& (>\ %x*rv^
Fig. B.
IF CONSTUtlCriON FOIt lUTU.niNRS.
islmctign for varigus parte of « liiiilillTij", iis eiiiiiluyiil by t.
■f-Proqf' Buitilinii Compiinj/ <lf A'fif Viirk.
THE FIRE PROOF BUILDING CCMPAWY OF NEW YORK.
Fire Proof ConaUQClion *ilh Iron and HoUowBncl..
rimUfKOOl' rONSTRV' I I .,-
t Harllan IMloui ami t'nriian IMfk Compntiy nf Snt
aw.iati.\iv \MT\msu-ot lire-proof pkrllLlnnf. Iiollowt
:* of \t,v\o\.vi iliiiM-nsiotut anil tlik'kiu'.ssiu
I'.iiuin^ini-iiti. 'i'lir^Kiv llglit, vvruiiii-jir<H»f, doiMCU
III, liMtt, or souii'l. am) ■'hii Ih! »t up by nny iiripUaytr.
T L-ONSTRIJOTrON I
UINOS.W
tlitlDiis fonncil fif Ute»e liiHck, plHstcreit iMth si Iks nitli bh ii
btlis Inch plasterini;, Is, fiir Fig. X, forty |>niitii1s hl^ ) rliirty
ands, anil for Fl){. 10, l.nenty-five pounds. TIil shuih LOtiipan;
D manufaetiire liollow liHck o[ porous terr*-eolU of llie same
e» as U>e bumt*lay bricks sliowu In the figures mentigned
fig, 11 tiliows tlio poroiis lerra-fotta ceiling-blocks minufiutiirpd
APPENDIX.
Wire Ijiltliinu:. — An iitiproveii form of wire latliing ie now
tde by tlip Stanley Corrugated Fire-Proof Latliing Company of
!* Tork, which has a narroiv corrugation every six indies, whick
lU ^uRiclent apace for A coiitiniious key, and yet liringa tbc
uter HO near to the beams that they are actually seale<t, and all
MiMlily of uorrents of air between is prevented,
rills latliii^ can readily l>e applied to ceilings, biiania, columns,
I., without the tii-cesslty of furring. Tlie manufarturers claltn
tt their lathlns liaa been largely used with satisfaction, both in
li cuiintry anil l>y the M<-Lro [Kill tan lloaiil of Works of Loudon.
rOODBN HOOF.TRDSBES, ^TITH DETA:
WHENEVt:riltis required to root a Imll, room, or huilding
the cleftr spun h more Ibtui tweuty-tive feet, tlie roof slu
Biipported by a triiBS of soma fonn. Tlie various lormsor
li tor thin purpoKc Imvc c'prtalu (»!iiiiin;B ruid princlplflsl
I, (liffcriiiK trom tbosf in bridge and floor trusses, «
I whk'h arc discusM^ in anothw tlmptPf, In the
lat«8 and Canada, whore thwe luv oftrai Ijcovy snow-
ttce has taught that tht- beat, fonn of r<iof for a
t, perhaps, in lar^ cities, is tlie A, or pitch rODf.
lattonR of the roof iDny vary from twcnty>s1x (tegreui,
,0 the foot, lo sixty degrees, or twenty-onK luetics to
'i, Init should not be teas than six inches to the foot for
pvered with slate or shingles. For roofs covered with coni-
rootlng, tin, or copper, the inclination iimy \ie aa iittleas
n inch to the foot.
^Ue«t form of pitch roof la that nhown In Fig. 1. It con-
HgF of two by ten or two by twelve inch rafters, supported
lower ends by the wall-plate, and holding themselvee up at
hy their own stiffness and strength. A piece of hoard,
he ■' rldge-pIate," is generally plitced between the upper
the rafters, and the rafters are nailed t^i it. In some locali-
1 ridge-piece is not used, but the upper ends of each jmlr of
ire held together liy a piece of Imarii nailed to tbu side of
prs before they are raised,
rails of the building are prevented frdm being pushed out-
r the floor of' ceiling beams, wliich are nailed lo tin: plate.
ters are p]u<^ about two feet, or twenty Inches, on centres,
boarding la nailed directly on the rafters. The Itorisontal
npport the attic-floor and tlic celling of the room below.
rool cau only be usmI, Imwever, vXvxa "Oa/). i\'AiiXiix.\i&iVi,isl>^
-pIMes is nut iiioni limn Iwcnl-s-^owc \eA", ^w""
pan (()*■ r«rt>;rs, unlfSH made exWmwVj "^^euw-J , '
g°«»-
iDl'.N RLiiJI-'-l Itrs.sK.s.
L KJnir Post Tpiiss. — Whenever we wish LO roof a boll
B wLlch tlie waJ]-|>lat>'s are more thun tweniy-four fwt t^M
nust luliiiit s<iiiie inellioil for supporting llie roft^'s at, ibe <X
Tilt- lUBtlioii geiiemlly eiiiployni {sliown hi Pig. ii} Is to luetn
like tlial bIkiwii in [lie (igure, ajuuvil itliout twi>1ve (eet apart lA
l»ii((tl] of ilif liiiiliUiig, anil on i.lipsi' plaoi' laigt- beams, callwl "]
I
Fig. 3
liiis," wliieti s[i]»]iort tlie roof , or jacic-rafters. Aslheiiistwurfn
one purlin to tlie next is not centrally mure than aix or p(gbt
I he Jaeli-rafters may be made as aiuall as two inches by six la
When the span of the tniss la more than thirty-four feet, two
litis miglit tie placed on eanh sltle of the truss, or at A and A.
is always heat, however, to place the purlins only over tiie end <i
brace, or al a Joint, wlien it can be so arranged. Tlie ceiling of II
room covered by the I'oof is framed with light joists «upport»dl
the tie-lieara of the tnisa. These I'Si ling-joists sltoiild n
tiMd Into the tie-beam, but should rest on a two-inch by fon
" ^iKJt^ to llift tle-beani an shown in Fig. 3.
IQSpiUi of thelruaa exceeiia tti.VT*,'j-&»i* li»^,\x.\» B
te tlmbei^ long enQi^\i tor tt\et\'i-\iPB.w«\iSMmft.«i
%eMe on(5 of thi! lipsl meQuift* »< \i->iaa.'ai«,'a*'«
1 from the to
gh. If they we
iceil togolhPi
WOODBN HOOF-TRII8BES, 395
n Is to make It of two-Inch plank bolteil together, thu pli-ops
dring Joint, so that no two joints sbatl b« opposlt« pach other.
fl form of truss Is very rarely usecl where the tinihers may Id-
iin below, and they are therefore generally left
ire to be ptaneil, anri maile a part of the Hnlsli of
wouM be neeessary to iuu> xotid tle-beanis
jrelse builiHUe tnuMiif liniil piiii'. of whirh wood.
iber« may be obtaineil fifty or sixty fi*l loiijj. Tlie form of truss
>wn In Fig. 3 is the modem form of the »lil ktii^ i>ost truss,
iwn in Fig. 4, which was made wholly iif wimmI, .-xceptitiK tlie
n straps usefl to connei-l the pietcs at the jniiiti.
IJueen Post TriiiM>— ^Vhentbesi)aii tolH'r»rift;il is ))etu'<i'n
irty-fiveantl forty-Hvi!
% a truss such as is
own In Pig. T, is pref-
sbie, for ."everal rca- ^ -^
ns, lo the king post '
It consists of a, iiori-
intal straining-beam,
iparatlng tlie upper
Ids of the principal
ifters, and a rod at
■eta end of the stralu-
g^beara, leaving a
■Be space in the een-
- of the l>eam clear.
>ia is a great ailvan-
lere it Is desired to
ilize the attic for
lids form of truss
Mild not be used for
span of over forty
!L For spans from
ty feet to fifty feet,
other, form of the
no truss, shown in
(. a, should be used.
lis is a very stroiiK form of tniss, and leaves considerable clear
ice ia the centre. In this trtisa the vt\twA?a.\ wtosi *»i'ii^^«*.
te ot two pieces, — one. running to thft «)'e, ft«i «i*«.t 'it^i:!''
itralnlne^teAm. Tliis gives the greatftsl wonowvi V"*. ws«*"
396 WOODBN ROOF-TBUMB8.
tian, and allowa of fonnlng a pn^w jtini at B.
borne tn mind tbat the ■trengtii of a troM dependi
the way In which the (decea are Johud togetliw, and thatftl
may fail, simply throagh bad and hnproper jolnta.
Fig. 7 ahowi a tniaa lued In on« of tbe old baUdingg in Li
OTer a room dxt; feet wide. It is built of oak, and ha* w
ties in place of Iron tie-rods ; but In principle it la the Haioe as tbi
trusa shown in !1g. It. The actual dimenalona of the varluiis pieca
of tlie truss are given in the figure.
ng. 8 shows' a queen
post truss supporting
;i poitlon of the roof
of the Maasachusetts
Charitable Mechanics'
A.ssociation bnlldlng In
Boston, Mr. William G.
Preston, arehit«ct. The
timbers, which are of
liani pine, have the <Ii-
meosiona shown in the
figure.
Fig. 9 shows a queen
post roof-truss, adapted to the sia-
pension of a floor from the johits o(
the tniaa. As It was necessar; to
liave the centre rod to suppwt thft
floor beneath, it then became neces-
^ry to put In the braces B, B. The
k *''\\\\W ""■' tjraees G C would only come into j^
k *^i\vC\ ' V" when one of the extreme rodi.wM
loaded, and none of the otbem.
These braces are called "conntof'
braces." T\ie vivnMMT in irtAdi te
toot ol 1-l\ft ^ufA^A
DemjaOolM
A (Flg.»).
WOODBK aOOF-TRUSSES. 31tY
inluged deUll of It U shown In Fig. 10. This tnua Is
I HuReam of Pine Arte, SL LouU, Mo., Messrs. Peabodf &
architects, Bo«ton, Mass.
For spans of from fort; to eighty feet, a truas kucI) as Is shov
g, 11 is one of the beat forms to adopt, wliere a [litoh ro
sired.
The stmts should be largest tl>»'a^tfl the centre, and tlic tli
TLe main rafter, on the contrary, and U\e
tieat Blrala at the joint A. Tfiga, 12 and \^ Awi-m
,\
«ven grtaiter, wl^ ,( I,
"M to ],.,,. p|„„^.
At till' jinsuiji ilay, t^-
''"Pt-, flat ,^f, (,„ ,
t^te'v-ly UM.1: Mil whaii
Im'",',,'","'''',''"-'™!
3
WOODBN KOOF-TRUSHBH.
Tke fonn of tnui geatrMj employed for flat roofs U thai shown
^ Vlg). 14 and Ut. IUb truM nuiy be adapted to any ipan froiu
-■*:niy to one liundred feet, by shiiply
'auging the height of the truss ami the
Uiiber of brrw^. and proportioning
b« various parts to tlif sti-ains wliich
hey carry. Tlie height of tlie truss be-
wp*n the centres of the chonis ought
^Mm
">t d, be leas tlian ont^-t^l)■llth of the span, and, if iKis»lt>le. »1ioiil<l
« made one-seventh, as the higher the tniss, the less will lie the
'fain on the chords.'
It should be noticed, that in this truss the hra(-<>s are ineliniHl in
•e opposite direction to that in which they are plaewl in the
li ihe "tbotil'
" Vftev
400
WOODBM BOOF-TmU0BB&
<ft '".*•■'*''•■*
tnuses prarkyiitly ihowiL Hie diiteaoet between Oe
rods should be so emaged thai Ibe bnces dull not HMike
of more than forty-five degrees with a horiaontal line.
Fif.l6
DETAIL OF JOINTS "A** ft-*B> FIO. IS.
Fig. 16 shows the best method of forming the Joints^ A^A^A
By B, By etc (Fig. 15), although not very frequently used in nofr
trusses. For spans over forty feet, the tie-beam should be made q
of plank bolted together, as shown in Fig. 8, unless it is poflsibh
to have the tie-beam in one piece. This is a good form of truss Id
theatres, and large halls where there is a horizontal ceiling.
^^unter-Braces.—If it is desired to load the trass at a
oikot than the centre ^IYl ^ eoTi»&Tk\x«iu»l VmA^ — as; i
iDRN ROOF-TRUSSES.
fi tniM alioiild kave additional brH»!a, called ''
a the o]iiH)site directioa to llii' liran's sbown.
T-lirocea neoil only lit used ivLim iIih riMsa in uiiejiii-
ny loaileii.
s witb Iron TleH> — In all truwieB where
II of the Iram is not horiuiiitul, Imt highfi' in tlia centre
the eods, it is better to stibslitute Hii iron ti« for tlie wooden
.7 shows B form of truss very well suited foi' the roofs of
:-houseg, stablea, or any place wliej-e It ia desired lo liave
rable lieight in tlie centre of
II, and a ceiling is not desired,
lorlzonlal Iron rod is fastened
t thcii' (>nc1s, and
L^wo rods are fastened otdy
~ 1, and merely run over
t in a groove. The iron
itened by means of the
Piles shown on the drawing.
allows a detail of tlie upper joint A. A better way o(
the joint wonid be to have an iron box cast to reeeive the
ihe rafters, and fasten tlie ends of tlie tie.
iied Trusses with Iron Tie-Rods. — For buildings
0 have tlie trimsea and roof-tiiubers show, with
mt that fonneil liy the roof a very pretty and gracefnl
Mis obtained by the use ot arched nbs, either for Iha
liSiordB of the truss, or for braces In aucli trusses an
i^roA adds to the grace and apvarcnl \iv,\\Wie** <A \fe.tWaaB,^
ybe Kcty conveniently used. ¥1k Yi a\iO')>RB.\oTTO.oV'Woa» i
support t()e roof of the MelvopoV\\.B.u l^owceA aiSi-.'*«*jj
6. George B. Post, architect, T\ie a-pvo. ol \\ftW»»«J
402
WOtniEN KOOF-THl'SSES.
tb»t hulldlne Is about fifly-f'inr fn-l. m
M shown in Pig. lil.
rub between the rafter ami Llir
III is umniuentei] with fiawiil
work. Tht! truBB has a v«ry light nni)
ftiry appeamnce, besides enibodyinp
»ll tb« Btrength tliat cau be desired in
Tl«' tie-ruj Is kept from sagging liy
e of the areb. Fig. 20 shows
rib, iiisipful of 1
itiid ati iron tte-ni
.1 to rs. Thiitj
niuy either he h
the wooden bfl
Hnd D. for a d
or only aliout Vt
or, wimt would ]
ler, run elear U
the wooden be^
the outside ufthi
For truBst<B of yi
slderable span, ^
arched trusses I
used wltli ei'ouM
effect.
Figa. 21 and '
guud examples {
form of criis*.
arctied rllM sup]
till.- luod tlmt
uiion the triM
tile Ue-nxls |in!*
enrif of i)ii' are
spreHilhig, OS w|
the I'ase If tlial
nil lie-roila.
The bracing I
the arched ribs'
ply W
s tha
WOODEN R00F-TRU68B8.
40
^ purlins aud raftera, and only carries t\w load direct)
. It does not assist the truss in anv wav in carry in
lioil of sup-
roof of the
11 H' lliding-
i-York(nty,
M'i'uliar and
)us; and. as
client exani-
; advantage
led form of
liall give a
ption of tlie
[I of tlie roof
ipports. A
riding-room
ted by Fig.
ooni is one
id six feet
long, and
ee feet wide. <5*
is kept en- to
of posts or
md the en-
s supported
rge trusses,
ch is shown
The roof
:he trusses
:her side is
by smaller
ing on these
3S ; but each
irge trusses
carries a
iual to about
i feet, and a
uit of extra
I. It was de-
>vide for the
hesi^ large aiciics without having yovVs vXwimw^Nsw
the method adopted is very \ugev\\o\\v^. V^vv<^^
>/ the iron posts which receive Uw wv^\\v»A \\V>%«
04 woonR
Irula, whkh ore helil In plavi hy Iron tio-bara Mid b»t]f
Mni8, wlili-h tof^lier fomi k ImrUontal tru^s at eacb aid.
pn-veiitM frani being puslied out by twi
1^ oiie-tiirb irp-buTR in such side wall sliijun in l.lii; |)lar
Tlii< Iwttoma of the two Iron posts are tied together by ira
nmiiing iindiT tbe floor the wlioli; li-ngth of the room. AH*
Uilc ^vus for tliu tii^-ruda iif eiK'li trnsB two liars three Inc
oae Inch, and an ludi iini\ % \^a.V1 liou rod, which ^
Pt to two tle-l«T8 lUvi'C \ut\\eB vn\A fl
lirged scctlonB ol V\ic tWi*, \\\*\\a\v\«, «*-^
rtfi. 22. It sl.onV\ W- noU.-oA\.W>, -*--«<-*-■
WOODKN ROOF-TBU88KS.
403
>nd ties, by having iron rode tliroiigli tlmir ii'iitrf holding
■ibs hither.
eliowH a detail, or enla^^ied view u[ Hit: iron skewtiack
at each end of tite tnisg shown In t ig 22
< shows the luetliod adopted for supporting tlif roof aitd
f the City Arniory at Cleveland O
i-Timber Trdsses. — Oni> of the iirini:li»tl rliaracier-
th(! GotliLC style of arrliiu^'tin'e is tliat of miikliig tliP
il portions of the building ornamental, and ex|ii>sing the
onsLnirtion of an eilifire to view : and, as tlii' jxiinteil
.nd steep roufe were developed, tiii' riiof-ti'usa Iwami' an
^t featiiri' In llic omainenliitioii of llii> iiitc-rioi- of the
trusses were built almost entirely of wihhI, ami gi'nerally
beavy timbers, to ffive the appeivriHViMj «l ^c^^. *M»ti^!^.
le simplest fonm of these trnaaea ]» »V«'m«'™'*\?,"»>- *''
en in the li^niiv. tin- triiaa is reaWy ^wl miwAv i.'ftv's* *■■**
.10r>
WOODKN ROOF-TRUSSES.
beam braced by bra(*k«»t.s at the ends, though it (loos not, in its
appoarance to the ey*», offer any suggestion of a beam. Fig. '27
shows another form of a small roof-trnss ornamented according
to the Gothic style.
,:^^^./\-J^m2kj:i2k-. u^m rius is in principle a
king post truss witli
brackets at the sui>-
ports.
Fig. 28 shows an
early fonn of what is
known as the "ham-
mer - beam truss/'
from the beam //.
called the ''hamiuer-
beam."* This truss
differs in principl»»
from all the trusses
we have thus far de-
scribed, in that it lias
no tie-beam, or no
substitute for one.
The rafters are con-
nected near the top of [
the truss by a short
tie - l)eain ; but thin
would offer Imt little
resistance to the raf-
ters spreading at their
lower ends: hence the
truss must dei)enil
upon some outside
force to keep it intact.
This outside force is
generally the resist-
ance of the masonry
m^ZEj^im^^^^^ «'hioli support
the truss. These walls
are ixenerally very heavy, jind are often re-enforced on the outside
by hiitt losses built aj^aiiist the wall directly opposite the roof-
trnsscs. In most eases suc\\ a waW \>o?>?.^?fi>«i9» «v\^^.Wut stability
to withstiind the thrust of l\\vi Vy\\s*, ^\vv\ \\^\v^<iNX\^.\:\^.-Vvsa.\v\v^a5s
Oe dlriprnsed with ; \mt in a nvooAotv \>\\\VVvw^ \Xv^ >«^\%. ^"^fcx ^vj
^Jslance wiiatever to being Uuvxsl ^>^^^> '"''Y''™ txvt^^^^^
i
WOOBEN ROOF-TRUKSES. 407
WOODES ROOF-TRUSSES.
should be nsed in such a bnitdlne. It is therefore inipnKtiQtUef
aae a haimu^r-beun Irura in a wotxlcn building. In rooli vM^
this form of truss is used, the ceiling is geDerslly formed of m
itwatbing u&iled to the under side of ttie jack-rafters lietweoi li
porlins, tbus alloning them to l>e seen. The purlins i
decontled: ami false ribs are often plae«d vi-rtii<Blly l>«[«eeu tlioi
1 1 I iftci'9 sliould be made very large t
iireaking at tLe point A.
Fig. 30, r)al« I. , sliows a liiimmer-lwaiu tv
^jU^Jbat sliown in Fig. 'ISi, ovt\^ s. WuV
^^^^ter omaiTisnUd. TUU ftguv>^ aVvo** Uic e^ita »?B, -^
irOODEPt ROOK TKIJSSES.
■ Fig. !JI) represi^tits lialf of one of Ihe lru«sea in Ihe Pint Cbl
liaatoo, Mass., Messrs. Wnte &\'B.nBTttiA,B.n\',HKn»«. Ttafl|
^^BUfug: or falsework. IL s\ioiilA \>e no\.\iia
WOODBN BOOP-TBlI86Efl.
411
Tied eolnmn, *t th« upper part of the tniss (Pig. DO), llierc in an
D rod (Fig. 31 ) which hokis up the Joint A.'
in this form of tnua the ontwan] thrust of thit arch cniitrs the
11 jott kbove the corbi>^ K; and, as the ilii>HaUiii of the ilinut Is
'lined only about thfny ilf^ifes from a vnrik-al, the lendnncy
licb It has to overthrow tlie wall \s not very jiim'hI. and may be
lily resisted byaw&ll twenty inches ur l«r. fi-el tliii;lc, re-e.itort-ed
a buttress ou the outHitle.
I trusses of this liinil, the pie<'es sliiuild Iw aw:urely fasteiuil
4h«r whenever they '"roiw or touch each other, and the whole
i8 made as rigid as i)OMsilil<'. No dependence for extra stre.iiKth
uld bu made on the ciLsin^'H nnil panel-work.
ig. Si sliowB a triiRs derived from a liamniei^bpam tniss, in
ch lliB eeiJing is inadi- to take Hie lovin ol a saMiX., '^raasss, tA
mftBM of thin
niM are two flve-Vncb \)1 tti\*«*o-*«*.^«*.^
Pig. 33 shows a forui of LriiHs used in EinnuiQUet Cbiirch Alf
biirne Falta, Mass., Wi:9srs. Van Uriint & Howe, archlt«ct«, Bci
This truss was iirobably derlvH] from the liaiiiiiier-beaDi ti
possesses an advantage uvtr tliat truss in tliat it U
trussed rafter, so timt there Is [lo-danger of thi' rafter being b(^
and, if the truss h spciirely lioltnl lu^^'llti'i- »I all Its jolnta, it (
tiut very little tlinist on the walla. The rafturs and ctowM*
formal ol two plei^es oE Uutber \>oUj?A ui^uvWi, ami ^04
iipiight piet-es run lu bel*eei\ Uieni.
UMes in tlie ihuryli at SVveWiutiw ¥a.\\« 'taMl^
»♦.! t
■'-I'l*'
'WM'^J»gj|
WOODEN ROOF-TRUSSES.
413
• ^ allows a form of hammer-beam trass sometimes used in
•<^en churches. The braces BB are carried down nearly to the
% 80 that no outward, thrust is exerted on the walls.
is generally better, however, in wooden buildings, to use a
with a tie-rod ; and, if an iron rod is used, it will not mar the
; of the height of the room seriously. If the roof-trusses are
d only about eight iieet apart, the roof may be covered with
and a half inch spruce plank laid directly from one truss to
ther without the intervention of jack-rafters or purlins. The
iing can then be covered with slate or shingles on the out-
and sheathed within. Fig. 34 shows the roof covered in this
Purlins are put in, however, flush with the raftera of the
to divide the ceiling into panels.
5. 35 shows a section through the rooi oi ^t. »^«KiSA*%»<o\!NSRja-^
t Yarmouth, Eng,
t span is thirty-three feet, and iVie Uxxa'&^'a «^x^ ^^-w^fe^ ^fiow
eet apart from centres.
i\6 IRON HOOPM AND HOOF-TRUSSES.
onnilitioDs of epan, load, height, etc, and of these the lollowli
exiim]ilea have been foiiiid to be the best and most eptinomicnl.
Ik'I'ore proiieedln^' tu describe these various forms of tniMi^, i
woiiUl C&11 the reniler's attention Co the sections of beams, tufi
irons, T and channel bars, shown in Fig. 1. It will trequpntlj]
necessary to refertd these seetlons; as they are the principal sh
of rolled iron eutering into the construction of Iron ruofa, and
Is of great Importance that an arcbltei't or builder be familiar vi
their forms and names.
For convenience in descriliing llie different forma of iron rool
we shall (Uvlde them Into the following classes; —
1st, Trusg-riKil's vilUi Uraifiht rufUrn, which are simpl; bnn
frames or girders.
2d, BoiBalrina-ro<ifa leilh cureeii rafters at sniaU rigidity, u
witb a tie-rod and bracing.
!id. Arched roofa. In which the rigidity of the curved nftai i
Hufflclent to resist the distorting Influence of the load wIthDi
additional bracing.
Trussed Roofs.— For small spans, the moat economical u
simplest form ot tniss is that represented in Fig. 3, (Owing » 0
nB.2.
small scale to which It Is necessary to draw these llgures, ire
represented the pieces by a single line, wlUch has been drawn heavi
for strut-pieces, and light for ties and rods. )
This trass was hnlll by the Phcenlx Iron Company for tlie roul
of a furnace-building. It consists of two straight rafters of riiu-
oel or T bars, two struts supportinf- Che rafters at the ceolR.*
main tie-rod, and two inclined ties assisting the tie-rod to support
the end of the struts. The lines on the top ot the truss reptiwni.
IlUon of a monitor on Vh,e roof, '«\tlclv la not a part of ttH
■f only supported by It. ^
W the great merits ot l\v\s troaa \» *.^ia.V. "A^saaViS, Vi« -^m
tf«Mloli, Viz.. the raitera Jind \,vjo a\,I^tta■,•^l\l.V^Q.^a■^«|
ntON ROOFS AND ROOF-TBUSSES.
417
retj desirable In iron trusses, owing to the fact that wrought-
resists a tensile strain mnch better than a compressive one,
hence it is more economical to use wrought-! ion in tlie fonn
es than in the form of stmts.
shonld be borne in mind tliat for ties, rods or flat bars of iron
ihe most suitable; while for struts, it is necessary to use some
1 of section that offers considerable resistance to bending, such
T-iron, or four angle-irons riveted together in the form of a
s; for wrought-iron struts always fail by l)ending or buckling,
not by direct crushing. In Figs. 2-10 the pieces whicli are
ts, or resist a compressive strain, are drawn with heavy lines,
those pieces which act as ties are drawn with a light line.
Fig. 3.
'ig. 3 represents a truss similar to that in Fig. 2, but having two
Its instead of one, which is more economical where the span is
T fifty-six feet, for the reason that it allows the rafters to be
de of lighter iron.
^or spans of from seventy to a hundred feet, the form of truss
wn in Fig. 4 has been found to be about the most economical
I satisfactory in every respect.
I ■
NKW MILL, PHCBNIX IRON -WORKS, ROCK-ISLAND ARSENAL.
Fig. 4.
he rafters in this truss, for moderate spans, may be T-irons;
for larger spans, channel-bars and the ties and struts may be
3d to the vertical rib. For very large spans, channel-bars may
sed, placed back to back, with the ends of the bracing bars be-
tn them. I-beams are also used lor t\\e T^AtOits., \i\iX. \}Q!e^ \ssw^
objection of not being in a 8liax>e to eoTVxves^ v%"8»i^^^ ^NSQv^. \5m
forma of iron. The flanges of an l-\>^d.\w (^o tvqX. o-'^^c ^» ^
porfunity for riveting as do Uiose ol «lxv^\^ «.xv^ '\^ Vtwsa.
wblcb were conatructed b^ ibe P\\i\?nt(. Iton Compiuii ol Ptdll
L These inay be conaWevtiA -ab \,\w n\oi\AeM. V
loofs.
_ prfllfipal us. of Uh- \K>waVrta?,-i«o\ \w<.v™ ■« %
ntON R00F8 AND ROOF-TKt> 8SES.
419
e areas in one span, such as is often desired in railway-
skating-rinks, riding-scliools, drill-halls, eti\
LET-HOUBB, TWELFTH AND MARKET «TRKBTN, PHILAOKLPHJA.
Fig. 8.
represents the diagram of a bowstrlng-trnss of a hun<lred
-three feet span. The tnisses in this particular case are
venty-one feet six inches apart. The arched rafter con-
wrought-iron deck-beam nine inclies deep, with a plate,
3s by an inch and a foiiitli, riveted to its upper flange.
the springing, this rib was strengthened by ])lates, seven
seven-eighths of an inch, riveted to tlie deck-beam on each
Fig. 9.
ruts are wrought-iron I-beams seven inches deep. The tie-
} six and a half square inclies area, and the diagonal tension-
•e an inch and a fourth diameter. These trusses are fixe<l
id, and rest on rollers at the other, permitting free expan-
contraction of the iron under the varying heat of the sim.
Fig. 10.
shows a similar truss having a »\mi\ o\ Vwc> \\\W!k.^s»^ ^
t It consists of bowstring pTVtve\vaA» v^vav*^*^ ^^'^
4-20
IRON ROOFS AND ROOF-TRUSSES.
four fppt apart. The rise \s one-fifth the span, the tie-rod rising
sevi;ntiH>it feet In the middle above the springing, and the curved
rafter rising forty feet and a half. The rafter is a flfteen-tnrii
wroHght-iron I-bcani. Tiie tie is a round rod in short lengths,
tour inches diameter, thicltened at tlie joints. The tension-bara
of tlie bracing are of plate-iron, five inelie't to three inclies in
wldtli, and flve^ightlis of an inch thicli. Tiie Estruts are tornieil
of bars having tlie form of a cross.
The following table, taken from Unwin's " Wrought-Iron Itridgss
and lioofs," gives the principal proportions of some notatile l>aw-
atriiig-trussK), mostly in England: —
PKOPORTIONS OF 1SOWSTRIN(J-KOOFS.
LocBtlon.
l:s
i
1
KiFTlB.
»
H3
1
I
!
101
p'
<;Bnnoti Htreet ....
liju" kfHur's Bridge '. '.
i53i ao'
1 si'
I'i
1
"1,
Foi' spans much exceeding a liundred and twenty or a hundred
and thirty feet the bo wst ring-truss is luucli tlie most eeouomical.
mid ailvantageous to luc.
Ai'CliCtl Roofs. — Tliese roofs consist of trusses in i\k fom
III' an areii, iiaving braced ribs, which possess sufficient rigidit; Id
(licinselvca to resist the load upon tlieni. Tlic ttirust of these lai^
ribs, iiowever, lias to be provided for, as In tlie case of masoarj
arches, either by heavy abutments or by tie-rods. As these trasses
embrace the most difficult problems of engineering, and are rawlj
tiSBil, we have thougiit best not to give any examples of such trnsses.
If any reader should have occasion to visit the Boston and Provi-
dence Bailroad Pepot at Boston, he can there see an admirable
r aMMm^e ol this form of truss.
• Al iprlDiUig lUTOlj-aVB «\11l»\MlU».
IBON ROOKS AND ROOF-TKUSSKS.
42:
Details of Iron Trusses.
After deciding upon the form of truss wliicli it will be best to wae.
"the shape of the iron to form the different members is a matter t<
1)6 considered. There are many practical reasons which make i
<lesirable to use certain shapes of iron in construe tinjjj iron trusses
even though those shapes may not be tlie most <U\siral)lr in n^j^an
to strength; so that a knowledge of the details of iron trnss<'s i
requisite for any one who wishes to become a mast^»r of bnildinj
construction.
By far the best way to study the <letails of construction is to ob
eerve work already built and that whi(*li is in process of construe
tion; but this requires considerable time, and often th<' thing on
vants cannot be found at hand. The following details of th
various ways of joining the different members of iron tiu'«4scs wil
^ found useful.
There are two general methods of constructing iron trusses
One is to make all the parts of the truss of combinations of angle
^t)n8, channel-bars, and flat plates, and rivet them togt^ther at th
joints, so that the truss will consist of a frame-work of iron bai*s al
'■Jveted together. The other method is to use channel-bai-s, T-irons
^•beams, etc., for the rafters and struts, and roils for the ties, whicl
^J* connected at the joints by eyes ami pins.
HEELS.
Fig. H.
In the first method the ties are either made of flat bars or angle
irons.
Fig. 11 shows two ways in which the tie-rod is secui-eil to th
foot of the rafter in the second method of construction. A casting
forming a sort of "shoe," is made, in which the rafter (its, and th
tie is secured to the " shoe" by means of au e\fe-eud aud \)u\v c^r
jj)Bte may be bolted to eacli side, and t\\e \\\\oV> y^^V w\vja\vc«>\^^
Of course the tie must in either case c.o\\a\^\ o\ Vnsh> \vA.Yd«.vyw
i'Hrrli side of the slioe.
IKON BOOKS ANT* R00F-TKUS8M. ^^
Fig. 12 Ulnstrates two ways of fastening llie npper rnda Ol
buta to tbp rafters. In the first tnctho<l the casting Is nuuIeW
bside thi> strut, and is lM>lt«<l to the liottoni of tiK rattur.
Fii;. l-'i sliiiws tliB proportifHis for I'yiM nn'l srrew ""nila fori™
, @ n 4
l»
tiaiifJ ill this mRllin-^ ni lymaUutUDn.
IBOH ROOFS AND ROOF-THU88E8.
I. IS ukd 17 show the niarmer of (ormlng the joiuM In the
lethod of coiutruction. fig. 16 represnnU the joint at the
Fig. IS.
I of the main rafter; and Fig. 17, th<^ joint nhere a raltir,
ng-beam, tie, and Btnit come together. All the pieces are
ly riveted to a piece of plate-iron, »hich thus holds Ihem
er. The other joints are formed In a ainiilar nay. Which
letter method of constnictlon depends very much on circum-
oofs of wide span, provision for expansion of the iron, due
nges of teiiipfratin-e, may l>e made hy resting the skewback of
lit of the truss on a cast wall-plate, with rollers interposed to
> of the sliding of the shoe without sti'aining the wall, as in
i; but this preoantiou is not ni><^RSsary in roofa of sixty feet
rless. farefLilexiMTJiiients have proved that an iron rod one
ed feet long will vary alwut a teuUi of a toot for a change
iperaturc ot a liunihiicl and fifty clegrees F.; and, i
iBs(£s( nuige to ivliicli iron lte&\\\K a-tii tote ai. '
irobably be subjected in tUiB c\\\wa,\ft, w
would be suflicicnt for all purposes. "Bot a\Y.Vi V
424
4R0M KOOFS AVD BOOF-TB0B8E6.
the vibration of each wall would tlien he only fit
of a foot either way from the perpendieolar, — a variaUon » i
and so gradually attained, that there is no danger in impo^i
upon the side-walls by firmly fastening to them each shoe of
rafter. Expansion is also provided against by fastening down
shoe with wall-bolts, and allowing the other to slide to and fro
the wall-plate without rollers.
If
If
Fig. 13.
After the trusses are up, there are various ways of constraetlBg
the roof itself. If the roof is to be of slate, it is best to space thBj
trusses about seven feet apart, and use light angle-irons forpuriinB,
which are spaced from seven to fourteen inches apart, according to
the size of the slate. On the iron purlins the slate may be laid
directly, and held down by copper or lead nails clinched around the
Fig. 19.
angle-bar; or a netting of wire may be fastened to the purlins, an
a layer of mortar spread on this, \tv N\\vve\\ >i>afc «\^\aa are beddei
^n greBter intervals are uae(\ \tv *\>vui\iv^T«.\\«»,\Xi^Vsa\«A\s
* ftuitened on tx»\> or v^g^\iv»\ t\w 9\^ea^1^E>afc\iecw5
mON ROOFS AND ROOF-TRUSSES. 425
brackets, allowance always being made for longitudinal ex-
ion of the iron by changes of temperature. On these purlins
astened wooden jack-rafters, carrying the sheathing-boards or
i, on which the metallic or slate covering is laid in the usual
ner; or sheets of corrugated iron may be fastened from purlin
arUn, and the whole roof be entirely composed of iron,
ben the rafters are spaced at such intervals as to cause too
h deflexion in the purlins, they may be supported by a light
Q placed midway between the rafters, and trussed ti-ansversely
I posts and rods. These rods pass through the rafters, and have
lied washers, screws, and nuts at each end for adjustment. By
Hating the trusses on each side of the rafter, and slightly in-
sing the length of the purlins above them, leaving all others
I a little play in the notches, sufficient provision will be made
iny alteration of length in the roof, due to changes of tem-
ture.
Fig. 20.
ben wooden purlins are employed, they may be put between
*afters, and held in place by tie-rods on top, and fastened to the
jrs by brackets; or hook-liead spikes may be driven up into
purlin, the head of the spike hooking under the flange of the
a, spacing-pieces of wood being laid on the top of the beam
I purlin to purlin. The sheathing-boards and covering are then
id down on top of all in the usual maimer.
426
THSOBY OF BOOF^IBUSSBS.
CHAPTER XXVHL
THBORT OF ROOF-TRUSSBa
In this chapter it is proposed to give practical methods for
puting tlie weight of the roof with its load, and the proportion
the truss and its various parts.
The first step in all calculations for roofs is to find the exact lotd
which will come upon each truss, and the load at the different jolnto.
The load carried hy one truss will be equal to the weight of t
section of the roof of a width equal to the distance between the
trusses, togetlier with the weight of the greatest load of snow that
is ever likely to come ux)on the roof. In warm climates, of comae,
the weight of snow need not be provided for.
It is a very common practice to assume the maximum weight of
the roof and its load at from forty to sixty pounds per square fbot
of surface ; but, while this may be sufficiently accurate for wooden
roofs, it would hardly answer for iron roofs, where the cost of the
iron makes it desirable to use as little material in the truss as will
enable it to carry the roof with safety, and no more. The weight
of th<' roof itself ('an be easily computetl, and a sufficiently accu-
ratt» jiilowance can be made for the weight of the truss ; and, if
the roof is to be in a climate where snow falls, a proper allow-
ance must be made for that : and, lastly, the effect of the wind on
the roof must also be taken into account.
Mr. Trautwine says, that within ordinary limits, /or spans not
(.rreedirifj about ncxeniy-jive feet, and with trusses seven feet apart,
tite total load p<^r square foot, including the truss itself, purlins,
etc. , complete*, may be safely taken as follows : —
iioof covered with corrugated iron, unboarded
If plastered below the rafters
Roof covered with corrugated iron or boards .
If plastered below the rafters
Koof covered with slate, unboarded, as on laths
Roof covered with slate on boards li inches thick
Roof covered with slate, if plastered below the rafters
'^ covered with shingles on laths 10
fj^kutered below the i-af tera, or beVow \.\ei-\««m . ^
'lingles on Vwic\\ boax^ . , * , Yl^
8 pounds.
18
11
18
13
16
26
u
Vk
THEORY OF ROOF-TRUSSES. 427
For spans of from seventy-five to one hundred and fifty feet, it
Vlll suffice to add four pounds to each of these totals.
The weight of an ordinary lath-and-plaster ceiling is alx)ut ten
^KWnds per square foot; and that of an ordinary floor of an inch
iaid one-fourth boards, together with the usual three by twelve
Eoist, fifteen inches apart from centre to centre, is from ten to
twelve pounds per square foot. Wliite-pine timber, if dry, may be
Esonsidered to weigh about twenty-five pounds ; Northern yellow pine,
fchirty-five pounds ; and Southern yellow pine, forty-five pounds per
Knbic foot. Ordinary spruce may be considered to weigh twenty-
■Ix pounds per cubic foot. Oak may be reckoned at from forty
"•o fifty pounds ; cast-iron, at four hundred and fifty pounds ; and
"wrought-iron, at four hundred and eiglity pounds \wr vnhle foot.
For flat roofs, the weight per square foot of the various loofing
Uttterials on seven-eighths inch boards, not inrltnJin(/ tlu' rafters
or joist, may be taken as follows : —
Roof covered with tar and gravel over 4 thic^knessi's of felt, i)i lbs.
•• u» a ^ Y, tin ^ . :Ji ••
** " " cotton duck (12 oun<re) * . 2i| '*
" "* •* lO-ounee copp*^' ',j'i "
From this data the weight of the roof itself may be easily com-
puted, and we have then only thti weiij;ht of the snow and efi'eot of
'v^inds to allow for.
Snow* — Any allowance for the weight of snow nuist depend
ipon the latitude. It may accunmlate in considerable (juantities,
becoming saturated with watei*, and turnni«< to ice. The weight of
I cubic foot is veiy various. Freshly fallen snow may weigh from
ive to twelve pounds. Snow and hail, sleet or ice, may weigh
'rom thirty to fifty pounds per cubic foot ; but the quantity on a
'oof will usually be small. Snow saturated with water will usually
dide off from roofs of ordinary pitch. An allowance of from
[.welve to fifteen pounds per square foot of roof will sutiiee for
most latitudes.
Wooden trusses frequently support an attic-floor, and in such
cases the weiglit of the floor and its greatest probable load should
be considered as applied at the joints of the truss.
Wind Pressure. — The load on the roof, thus far considered,
is a steatly dead load, which of course acts in a vertical direction.
But roofs are frequently subjected to great pressure from the foree
of the wind ; and, as this (;an act only ou one side of the roof at
» time, it is an unsymmetrical load, awOi wwit^oN^x \\. ^s^v?*^ \\v>\. ^.v\.
ertically. The pressure of the wind o\\ ^w *vw^^vv'^^^ ^wxV^*
ways normal to tlie surface, no luaUet vj\\^\. NXv^- v\\\vyv\XvA\
m HUM UM
Till' purllri« C uml /' wtmlil nlso oupliorl, Lho m
r-tf. 1
IE we ounsiilur llir ivof i.i> Ih' 8l»l«<l on tioi^iilii tm Innh'
Iimrtli tlilck. wn shall Iiavi^ for llie weight uf unc sioufl
|iuurida 1 allowing fui* snow, 15 imunils ; nomiiil pn-MUiv nf
'■. Uitul wi'liihlorluHil (in on? Hitiiiru roul, 117 fxiiiitils; UiUt
fiililJiirUHl liy one Crusi, 07 x u76 = 3t<,rAK! pouiitis ; toW M
iC t!)idi of ihn pulnta B, C, and £), one-fotirth of SH,^^
w liMwl ntmiiiK ut J und E is Bu])ijort«rl dlrucUy by Uhj '
till' bullcllii)(. unil uee<l nul be uuusiilered hs t'uuiing; ou (Iwl
Jill. If, niiw. wi> draw n vi^liwl lliiti ou our pii|H.-r. hiuI. c-muii
Kt thu iiiiiHT t-nil, ky uff UI14K puiiudH at sotiib i-unvL'nlMiI h
hUX) pounds to the Inch (In thu fotlowliii; Jl^mti lURtmni
hAvn Ihsi'Ii UBCit i.i> kwp the itlagrams witliln Ihi- limits u( tl
hnt wnrf lint drawn in b Iui^ btkIo to get tliirs tnwa«s niM
rairly), nnd then oni>-fiitlf of \WAfi pounds, or 4H24 pouodi
1^ sgbIi', wi' stmll Imvu tlii' line re- (Fig. lif) re))r«s>nd
half ih" loud on thu iniss, or [lie IohiI I'Oiiiing on *wli
support B,
Now, tllfti till' til MI'S lu-Unginllie mfter and tii-lwwu, I
Hiipportin^ foii'KH. nit I'ondng togi^ther at tin- |H>ijil A, sllall
(u-li othui', tlify ntuot tm In siirh a pruiHirtiun, tlmt If va
lliii' from It lAmllel to tlie rafter, and a line throujt-U r. pal
ilie tle-be»in, the line lul lutiat represent the tlinist in tb
piu'l of ih<^ rafter, and tlie line <lf, the pull In tite tle-bwin.
next I'onsider the foi'ceH acting on tlio Joint li, rommend
the mfiLT, nnd going aronnd i.i> tiie riglit, we find tlutt I
foree whicli we know, la the foive in the rnftiT. n^nse
Vig. 1(1 hy the line Jd. Next wis have the wulght. IKMfi '
aellng down, represiiUloil by the line ali, aiul there mmi
unknown forcus. — tlial in the upixsr part ut the rafter andt
In the strut.
To ohtMln ltat!«e forces, draw a lino tlirougli l> (Fig. l<i)i
lu tlif mflHT. and a Uni^ throngli if, parallel i.o the strut.
tviii linea will lulersecl in r; an<1 the line Iw will represent tj
in tliu rafter, and tin- line i-il the foree lu the Urul- Furtli
If we follow till' <l1rectlon tii whieh the forres act, we abtU^
the foren tla arts up ; heni^ the rafter is In oonqveMdM
nuualnlng forcos inuHl n>-t Hniinirl In order ; liencs ttb kcH
!««•(* t0WU>dB the jiiluv. tvnd iil wu viv ^id'«»^ Uva ^iHtai
PMea »nj tn eoiuvir»»iiVm.
talat (he ro«s« BwHwanvvW- vonAt:. ■"C\vi i™
M. which &cts«V- \wnV»i-\wve\A»'*o>'r"" "
THEORY OF ROOF-TRUSSES. 431
vhich would extend beyond ctof; then there remain the forces
n the rafter to the right, and the vertical tie, which are determined
>y drawing a line through / parallel to the rafter, and a line
.lirough e parallel to the tie. These two lines intersect in i; and
rbe line %f will represent the force in the rafter, and ei will repre-
sent the pull in the tie. We have now only to measure the lines
ji our diagram of forces, and we have the forces acting in every
>art of the truss; as, of course, the ('orresiwnding pieces on th«»
lifferent sides of the truss would Im» similarly strained. Measuring
the different force-lines by the same scale we used in laying otf th*»
weight, we find the strains as shown by tlic figiu-es on the lines.
Fig. la.
Having foimd the strain-pressure in tlie different parts of the
truss, it is very easy to determine what shoidd be their dimensions.
Thus the compression in the foot of the rafter is 20,750 pounds.
Now, if we wish to make it of hard pine, we know that hanl pine
will safely bear 1000 pounds to the square inch: and hence we shall
need W(f(P = ^1 square inches area in the rafter. This would
require only a 3 by 7 timber ; but, as the rafter will need to be cut
into more or less, we will give it more area, and caII it a 6 by (5.
The short struts have a pressure of 1:5.750 i)ounds, and hence
need not be larger than a 3 by 0, excejjt. that, being so thin, it is
liable to l)end; and so we will make it 4 inches by 0 inches. The
tie-beam resists a pull of 14,7(K) pounds: and, as hanl pine will
safely withstand a tensile strain of 2(KK) jwiuids, we should only
need about eight square inches of area : but, while this would resist
the pull, we must add enough more to allow for cutting into the
tie at the joints, and for sagging imder its own weight ; so that we
will nuike the beam out of a 6 inch by (» inch timber.
The centre tie, which has to resist a pull of 9648 pounds, we will
make of wrought-iron instead of wood, as shown in Fig. 4, Cha]).
XXVI. ; and, as wrought-iron may be safely trusted with a pull of
10,000 j)ounds to the square inch of cross-section, we shall need a
rod having a sectional area of not quite oTie square inch, or a rod
of an inch and an eighth, or an inch and a fourth, in diameter.
If the rafter and stnit had been of spruce, we should have divided
the strain by 800 poimds, or 700 if of white pine ; and for the tie
we should have divided the pull by 1800 if spruce was to be used,
and by 1500 if we intended to use white pine.
■ It will be noticed, that, while we determine the size of our tim-
bers mathematicaUy, it ofUm happens t\vat \\v^ Ttvw?>V twsOrr. SX^kcdl
considerably larger to prevent their Y>eTiAViv^ w\v\^x \>cv^xx ws:
\reigbt, and to allow for cutting, borVng, r\>Vw\xv^, *?u •% -s^ XX>»8
rill not do to di^pend entirely upon n\at\\eiu«iWc»\ As»VwqNa««cb»
482
TUEOBT OF ROOF-TBUSSBS.
these should be sappkmented by % practical knowled^ of
subject.
The methods of determhiing the strains in this tntss i^pU<
all trusses properly put together, and which do not exert an
ward tlimst on their supports.
Example 2.— For further illustration we will take the t
shown in Fig. 5, Chap. XXVI., and of which a diagram is g
18.8M
Fig. 2.
Fig. 2s.
in Fig. 2. We will assume that it has a span of 45 feet, and <
dimensions as given in the figure ; also that the trusses are p
12 feet apart from centres. By glancing at Fig. 5, Chap. X^
it will be seen that the purlin at 2 (Fig. 2) carries the weig
that portion of the roof extending from halfway between pi
1 and 2 to the ridge of the roof, and in this case equal to 13^
= J62 square feet. 'The purlin at 1 supports the roof for 4j
each side of it, or 0 X 12 = 10& ac^xwitfe iefcX.. TNaSu^ ^^s^^
a pressure of 10,8i>4 pounds at. t\ie ^omX. % «iA ^Vififc v^v'
Joint 1. Besides this, we liave a ce?v\Vn% w\&va^^^ Vwsov
b^^ma of the truss, whlcli wou\4 weV^Yv aXwAxX. vn^iVi vs«:
THEORY OF EOOF-TRUSSES. 433
iquare foot more. This weight would be supported one-third at
Bach of the joints 3 and 4, and one-sixth at earli end of tlie truss.
The weight of the ceiling, coming at joints .'3 and 4, may be assumed
to be hung from joints 2 and 5 by means of tlu; vertical rods : so we
can add the weight coming from the ceiling to the weight of the
roof, and consider it as applied at the points 2 and 5. The whole
area of the ceiling is 12 X 45 = 540 square f<»et, and its weight
about 9000 pounds ; making 3000 pounds applied at ;j and 4, and
the total load at 2 and 5, 13,854 pounds. The load at 1 we have
already determined to be 7236 pounds. Tliis gives us sufficient
data with which to draw om- diagram of strains.
As in Example 1, first lay off the loads on a vertical line, to
some convenient scale ; thus, ad (Fig. 2c/), load at first purlin, 1,
and de, the loads at 2 and 3 combined. Then ae represents half
the weight supported by the truss, and also the load coming upon
each support.
To draw the strains, first draw ah (Fig. 2n) parallel to A B (Fig. 2),
and a horizontal line through e, intersecting ah in h ; nt^xt go to
the joint 1, and we have the force />a, acting upwards ; then the
Joad ad ; then from d, the stress in DC, which must act in a direc-
tion parallel to it, and the stress in BC, also acting paralhil to it.
These last two stresses are found by drawing a line through d
parallel to DC, and a line through h parallel to BC.
KoTE. — In Fig. 2 the linee are denoted by the letters either side of them;
^Us the bottom of the rafter on the left is called AB^ and the brace BC; the
'eft upright tie is denoted CF, and the right one FG. In the diagram of strains,
'he line representing the strain in any piece is denoted by the same letters as the
Piece, with the difference that small letters are used for the strain diagram, and
^he letters oome at the ends of the lines. This method of notation (known as
'* Bow's Notation") is very convenient, and aids greatly in following out the
'trains.
Next take the strains in the pieces at the joint 3. We know
Uready the strains kb and 6c, and drawing the line cf parallel to
Of, and kc parallel to KC, we have the strains in the remaining
>ieces. It will be noticed that the line ^ lies over the line eh; but
t should be kept in mind that they represent two separate strains,
md should be measured separately.
Considering next the strains at joint 2, we find we already
lave/c, cd, and de (13,254 pounds), leaving only kf to close the
igure ; thus showing that the strain in the beam EF is the same
iS that in the tie FK, tliough the f onuet \a ^ evi\\:v^\^^"^\N«^ -sNxassv^
nd the latter a pulling one.
We BOW have the strains in all t\\e pieces oi >i\x^ \xv\a&>^«^
ited by the corresponding lines In FVg. ^a, «i.xi^, x«ve».'^>a2t\»% ^^
ir aailp f pou is wd ftn J i] )■
p 1 iiiw in tl stnii %ni a
en It tl e n M H n- I In-
1 WM
Sin
>(IH()I
ging et ac
« u hes )
roUs ha e u I
n tl
m'
tl e en f U It K UH i g In** >•
n n H fy I o all \t f r utMng ]u1nUr>
ng to o J dgmen Tl us wf »oull iii»k«i
ingirea a fis by 1 Ind ps tite il*-ii
e^ftd elrasHlnlt y inJi-s. 1
of 'nm po u di pi I c li w p II of 3
)n tic rod whi 1 uouldnqt
ExAi
Fig. 3i.
Example 3. — Take tbe uubb w\iciMMtuied by the diagram »ho«« I
[. 3, loaded wltli tUe weViCo^ ot "Uw twft, ««& «x^*K>Nw(,'te (
iiow by nieana ot rods sviapew\c4Umv» yAvA*?.^:^ '"*'-■ "^
tlie various j<.ii»i^ v, "VvW >»■ »i«>v^\. » fr"**^
THEORY OF ROOF-TRUSSES. 43.'i
To draw the strain diagram, draw a vertical line, and, comnien-
'ing at the top, measure off to a proper scaU* the line ac (Fig. .')</)
ftqual to load at 2, q/" equal to load at o and 4 ronibined, Hn<l
fi equal to load at 5.
Xow, as the joint 5 is at the centre of the truss, it is evident that
only half of the load at that joint will come on either sni)]»ort: so
our supiK)rting force at 1 will e<|ual «o, and not (d. ConsichM-ini:
now the strains at joint 1, we have first the sn]>i»(>rtiu.Lr torre ao.
acting upwards, the stress ab, in the rafter, actin«r lUtw iiwuds, and
the pull ob, in the tie, which makes a closed triangle. Next go to
joint 2, and we have ba, and nc equal to load at *J. aii.l rd and Inl
closing the figure.
At joint 3 we have three unknown forc(?s : so we must go first to
joint 4, where we already have dr and c/, e<iual to load at ',] and 4
combined : draw fe and dc to close the figure. Now, going to
joint 3, we have o6, bd, and dc (which we alrea<ly know), and
<lraw eg and 0(j to close the figiin». In this case the point </ ha^)-
pens to come at the ix)int b, so that one lays over th<' other. At
joints we have ye, ef,fi (equal 12,()00 pounds), and drdw ih and
///< to close the figure. There would be no strain on the central
rod other than the direct pull of 12,000 pounds, which it <'arries
from the floor below. It should also be remembered that ilu' tie
^a has, hesides the strain shoM*n in the diagram, a direct ]»ull of
^5,600 pounds from the weight of the tloor suspended from it ; so
that the two should be adde<l to show the totiil pull in the rod.
'Hie strains, in i>ounds, in the various pi(MH»s. are given in ninnhers
On the corresponding lines in the strain diagram (Fig. 8r/).
Example 4. — Take the skeletcm tniss rei)resented in Kig. 4.
loaded as there shown (by the weight of the roof above and a ceil-
*lig below).
To draw the strain diagram we first lay off the load jA- (Fig. 4(./),
^lual to the sum of the weights at joints o and I (113,820 pounds),
^l = 18,320, Im = 1:3,320, and mo = one-half of 13.320 = (MUiO. Then
iraw the lines ja and oa, and we have the strains jit tln^ support.
\.t joint 1 we know <{} and ./A*, and draw kr and ar to close the figure.
there will be no line in the strain diagram corresponding to A A,
Or there is no strain in that tie excepting the direct i)ull of 3()00
>ounds. At joint 2 we have on and r(r, and draw rd and od to (jlost^
he figure. At joint 3 we have dc, rh\ and kly and draw Ic and dc
\.t joint 4 we already have od and d(\ and find ef and o/ by drawing
Xnes from e and o parallel to the respective pie(«e6 in Fig. 4. At
oint 5 we have/e, e/, and Im, and draw )//// and/f/. We must next
fo to joint 7; for a,t joint (> we would have 1\\t^v* *VriC\\\^ \» ^^^^,
nd by the gnphic method we can find onV'^ Iv^o «X «k. NXsafc-
THEORY OF ROOF-TRUSSES.
■*37
!ioas, that, as far as finding the strains is concerned, it
iifference whether the truss be of iron or wood ; the dH-
the material only being taken into account when the
' varioas pieces are deterrnined.
.B 5 (Tna* mith Horizontal CkonlH). — For the next
'c will take a truss like that shown in Pig. 15, Cliap.
id of which a skeleton is shown in Fig. 6. This truss is
of sixty-four feet, and supports a flat roof and plaster
ow the tie-beam, and also a gallei'y betow on eaeli side.
at Uie different joints wou1<l be about as indicated in
I draw the strain diagram (FSg. Tia^, Wj Qtt\.\\tVfli»\%«OTi.»,
0, commencing first with the XtoAs, ive».t^V,ft«. wassv*-
nals foad at joints 1 and 2,(icei(oa\a\oaSia*- V****^'*"
foad at joints 5 and 6, and do awA oe «>cV<»^!ai^«
IRY OF KOOF-Tlll'SSKS,
<--l>air of lliJA loul 'abt
f nf looila n
ai joint, .., «■!■ liaiT r,Li- sHpporUnfj (ort
'en* ill i.hi; ntftiT "/<, and tlie streos in Llie IIhi ;it>. diwiii
, AC }oliit t wf. ktiiiw fill auil iif<, mill ilraw r>H and pa, A
At juinL '2 we know nfi Hntl />ii alremly. hiiiI dnl
At juiiit H we. kmiw »iii, n'>, »il<l '»', and dniw o'M
It joints fi ami It are foiuid in tlii' K
at joint 7 we. know the strains hi. i<I. anil '(>■. an
(1 /(/: Thi! I'l'iitro rod //// Iiuh no strain i'X(r],tinM
11 of 2100 [Kjuiidfl.
XHBORY OF ROOF-TRXJSSES.
439
PiiE 6. — Tniss such as shown in Fig. 17, Chap. XXVI.,
•ombination of iron and wood truss, suitable for a large
tables The skeleton of this truss is shown in Fig. 6; the
his example being forty feet, and the rise fifteen feet. The
•m the weight of the roof would be about as indicated in
lere generally being no ceiling in roofs of this kind,
iagram of strains is shown in Fig. 6a. ab equals load at
nd bo equals one-half load at joint 3; oa^ ae, and oe repre-
strains at joint o ; ea, aft, bf, and/e, the strains at joint 1;
fyfth and (JO represent the strains at joint 2, completing
trains in the truss. The complete diagram of strains for
IS of the truss is shown in Fig. 66.
Fig. 6b.
PLK 7. — Iron truss (Fig. 7), span 80 feet, pitch 30 degrees,
between trusses from centres, 20 feet,
•ads for the truss with a slate roof on an inch and a quarter
iron purlins, would be about as indicated on drawing,
aw the diagram of strains, lay off the loads on a vertical
one-half of the truss, which would give ao (Fig. 7a).
•aw on parallel to ON, and an parallel to AN, then hni
to BM, and nm parallel to NM ; next draw ml x)arallel to
ni draw ci and dh. and draw Ih in line with ntn; 'then draw
el to LK, and ik parallel to IK. Draw h<j parallel to HG;
Irawn right, it will pass through k. Draw og intersecting
This will give all the strains in the truss.
liJd be noticed tiiat hg lies over ky, \svi\. ^«^ ^ws^^\sfc
' as two separate lines. Tins ioxm oi troaa \s» ^'^k^^
7y of iron. The strains are fvgvire^ m vovwv^^ wv^\V
ko
THEORY OP ROOF-TR(;;sSEfe,
and tlic site of llie various pieces ..ray be con.i.nleJ by ihf ndal
atmW and ties. In Fig. 7 Uie pieces Mi, J,'/, ffc „„,] j,e ^
tlht. principal tie, are all ties; the other pieces being in compn^
The piece GG is only a light rod whieh is used to pn.vent lb,. .
Example 8 (/roii BoioMri.ufl TtusbV— Ss^mi rt ^TOia,-*!-,-*:.
[nee hetween trusses, !nm> cwitrw, m lew,-, ^^ iA «
0 ftifl.
THBOBT OF ROOF-TRUSSES.
» fcom of tnuB, rapreaented by Fig. B, is one of the n
mtcat of tniMes for yerj great spans.
llle truKais: »<> wi- iijua^ lemvi^ lliniii uill ill drawing tl
To ilmw tLe atraiu iliagralu, Iny off tUe IuhiIs i
ill »ll tlie pri'vious esaiuplea, and reiuetnber that the
1h^ IJHlfway iKtneen t and/ (Fig. Rir) ; then oa wiU bet|
in^ i»Ki: nt joint I. In drawing ilie straina at the dilUt
ilmw flrst the strains at joint 1, Hiidtlimat joints S,
in the onter in wlikh tliej' »re nuniWred (Fig. 8).
To coitiineiire the strain diagram, we have on equ^
porting Sorve at joint 1, and from a draw ■ line paralM
friira 0 a line parallel to OG. Tliese two lines Iiit«i|t
■liftwliig linus pai'allel to tlie curved lines of the tn
strain ]ii»^ parallel to a linn connecting the turo ends i
oliorU. Thua III/ should be ilmwn parallel fo 1-3, an
tu 1-2.) At joint 2 we alrejiilj have o;;, and from $
parallel to Gil, and from » a line parallel to OH {i-4
tlif liiittsoA andijA.
At juint 8 tlia strains are liy, \iii, the load ah, ami ffil
At joint 4 we now liavp oh ami hi. and draw it ant
stralna at jniiite IS aiid 8 are drawn in a ainlilitr way, ail
-I, T, and 9. aiiiiilaily to those at joint ii. After draniDj^
at joint U, go to joint ID; and, after drawing the stM
THEORY OF ROOF-TftUSSES. 443
e in tension, excepting the upiwr chord, which, of course, is in
tnpression. We might analyze the way in wliicli the strains act,
saying tliat the upper chont carries all tlie load, like an arch,
id is prevented from spreading out at the ends by the lower tie.
ae object of tlie bracmg and vertical pieces is only to keep the
5 in its curved position, and not allow it to come down flat, and
us allow the ends of the arch to spread out.
Example 9 {The llatnmer-Beam Truss). — As this truss is so
equently used by architects for supporting the roof of churclies
id large halls, we have devoted considerable space to it.
As generaily constructed, hammer-beam roof-trusses exert a more
' less horizontal pressure upon the walls supporting them, recjuir-
g that the walls shall be heavy, and re-enforced by buttresses on
le outside. In churches where the walls are low. this horizontal
trust of the truss is easily taken (a,i*c of ; but in many cases it is
*sirable to do away with it entirely if possible. In order better to
nderstand the action of the stresses in this truss, we have pre-
tnted first a truss (Fig. 9) whic^h has all the features of the hannner-
3am truss, excepting the lower braces, and yet exerts no horizontal
trust against the wall.
The truss is supposed to be built like the ordinary hanmier-beam
•uss, excepting the omission of the lower braces, and putting in
ax)ng timber-ties, IW and PO, in place of the ornamental curved
ieces usually employed. In this particular example we have
ssumed the span, of the truss as 60 feet, the rise as 35 feet, and
le distance between centres of trusses 15 feet. This would make
le loads at the different joints about as is indicated in Fig. 9.
To draw tl^e strain diagram, lay off the loads on a vertical line
I the usual Way, the centre coming at o (Fig. 9(f) halfway between
and e. Now at joint 1 we have the strains oa, (ff, and fo ; at
lint 2, fa, ahy by, and f(j ; at joint 8, of^fih f//^ and o//, oh actinij
om h to (/, and hence is a pulling strain. At joint 4 we have h\i,
>, he, ci, and hi to close the figure: /// is also in tension. At joint
we have ic, cd, dk, and i^. At the top joint 0, the strains are hi,
?, tlj and kl, which (completes the strain diagram for one-half of
le truss, which, of course, is all that is needed. Exan'iining.
)w, the diagram, we find that the strains are in general much
rger than would be the case if there were a horizontal tie across
e truss: still, if we make the pieces large enough to withstand
ese strains, the truss will be stable, and ext;rt no outward thrust
1 the walls.
Looking at Fig. 9 we see that OF, 11, P, -awvV B, \Q>rKv ^ v^w^ysv.-
'23 tie, only it is pulled up in the centto \tv W\e \oxidl\ ^o^^. ^'
. 9a we see tlmt the strain in tlie Ue-rod KT. \aN^\^ ^x^-^^v^^
THEORY OF
ve mmgiDu th,. tie ifi ,„ be cutin (»
I
THEORY OF BOOF-THrSSES. 44^
^^ joint, the main nflen von]*] hre^'k m the jomx^ 4 xth\ *>.
'^ tbe bottom portion imniodiau*ly «-lidf ontiranls;. <mighi4'-Timg
^^ tbe main tie, and allowing ibe top of iLt- iniss to fail thn^Ticrh.
-having seen that a hammer-beam truss r'-nh.] Itr biiih in \khioJi
'^I'e is no horizontal thrust. v«' vill now tvniMdrr iho haniirn-r-
'-ain truss j.s usually built, in which a liC>rizc»nial thnisi i?
^pectPtl. The diagram of such a truss is shewn in Fiii. 1»». in
^lich tlie curved braces usually built in the o-iiire of the truss
'^ not shown; as they are c<:»nsiden-l to I if ]»urt'ly omamontal,
id have no strains in them. The brace OM is lirawn as thouirh
Were straight : Imt a cur\t*il brai.-H can W u>f J a> well, without
tering the diagram; for the rea>on that tin* strain in the ciin'eil
ece acts in a straight line connecting the centres of each end of
le brace.
To draw the strains in this truss we must first find the horizon-
■1 thrust of the truss against the wall.
To do this we have to consiiW that all the piece from joints n to
•int 4 simply form a framed brace supporting the upjx^r ix>rtion
• the truss at joint 4, or that a single brace, shown by the dotted
ae 04, would have the same effect on the wall as all the pieces
It together in the framed strut; that is, we may consider the
Uss to have the same horizontal thrust as the truss shown in Fig.
)«. The load at joint 4 would evidently be 12,000 pounds plus
ad at joint 5, plus half-load at joint 0, and half-load at joint 2 ;
aking in all 36,000 pounds. To draw tlui horizontal thrust and
rains we proceed as follows : —
liay off ah (Fig. 10b) = load at joint 2, be = load at joint 4, rd =
ad at joint 5, and de = load at joint 0. Then the load at joint 4
^ig. 10a) = ^ab+ be + cd + ^dp ; an:l if we draw from x a hori-
^utal line to the left, and from the c(»ntre of nb a line panillel to
1: (Fig. 10a), these two lines will intersect at I, and Ix will be the
:irizontal tlirust exerted on the wall at the point o.
Having obtained this tlirust, it is easy to determine the strains in
ke pieces.
At joint 0 we liave the thrust IXy the vertical supporting fort^e xa,
ad the stresses ao and mo closing the figure. At joint 1 we have
n, of, and of, as the strains in O/, AF^ and FO.
At joint 8 the strains are wo, o/,/(/, and mg ; at joint 2 they are
a, abj bg, and gf; at joint 4 the strains are m//, f/b ; be and ci
losing the figore. It will be noticed that the figure closes witlioiit
Hewing any line to be drawn i)arallel to ^fT: hrmce there lii IK
^nsional strain in 3//. There must be, however, a tufm^nm
rain on Jfl equal to the outward thrust cm tVife iir«iV^\ Vo^
4 shown In tbe stnin diagram.
■UC THBOHY OF R(l(.]--Tin>M -
Al joints wi- )iavi' tlw Hlrntn» iV. cd. 'Ik. »d(I l-I, !inilM>)iM|
we have kd, dr. el. uiiil ii: u liiG)ii-on>plet«sUie strains turou
of the IrusB, wliirli is nil wi.- tu-inL
r
Fig. 101.
Comparing, now, the iliRgrani of strains. Fig. lOfc, witU Plfr
ivt find Ihat ill gpiiHral the strains in tlif, truss, Fig. 10, u« i«
leas than in llic triisn, Vi^. !>: whili'. oii the other hand, the iBd
tnaa exerts no oiitwai-il lUciwt on tUa wallfi, hh Ib the hh»
K«^. 10.
By biiiHing n tnisB Ukr F\K' ^*>- "'^'^ V"VWvv
and I J to johit, I'i, we c
KVYw'owrae W» *A'
THEORY OF BOOF-TBUSSES.
449
train diagram complete for one-half of the truss; and that is all we
equirOy as the stresses in both sides of the truss will be the same.
18,100
13J00
Fig. 12.
Fig. 12a.
Applying,, now, our scale to the linea Vn \^i^ ^-^.^KfiCDL <5\ ^xssicBS
Fig. 12aJi, we and the stress in tlie raiUr AB to\>% ^.^'^^^-^siS
^gured on the line ab, the stress in AD V> ^i^ Y^^'^ ^^\5S>aa
timbers of Ute truss will be planed, it nill be liardly «>f
8 b; 8 timber; and, as the uext largest merchaut si
will me that size.
The Btrewi lu the section of the raft«r CD Is 52,41
for this an 8-inch by 8-lnch timber will be more than «|
As the stress in GF Is still less, we will make the i
one piece of eight-inch by elghl--lnch timber, with a
eight-iuch plank bolted to the under aide of it in the
as shown In Fig. II.
Brakes.— The stress in the braee or strut AD is 13,1
and for this we will use a foiur-iiii'ii by six-inch tiinb
inch plank being liable to spring lor bo long a length.
The strut EF has only 17,400 ponuda' stress on It; bi
long, we will use a (oiir-inch by elght-inuh timber (or H
Tie-Beani.— I'he niaKlraoni strain in the tIe-bM
puuriils ; anil, its httrd pine muy safely be truat«d with ]
lier squitrt! iitt'li tensile strain, we need only have 2S «i
at timber in tlie least cross-section of the tie-beam; bvi
have to cut into it some, and the rods must go tbrou^'
beam should be as ivide as the struts and rafters in on
a good joint, we will make the lle-beain of one piece ol
by eight-inch hard pine. If it is found impraeticat
THEORY OF ROOF-TRUSSES.
451
ghths in diaineter if the screw-end is upset, and two and
th inches if the end is not upset.
we have determined the dimension of eacli piece of our
td may feel sure that there will he no danger of its falling
long as the timber remains sound.
Purlins. — Having decided upon the proportions of our
e will now decide what we will use for the purlins. To
gilt appearance to the roof, and also keep it good and stifl',
sagging between the trusses, we will use a trussed purlin,
t shown in Fig. 13. The load upon i^ach purlin we have
iound to be 18,100 pounds; and it can be proved, that, with
supported at four points, the load (doming on each of the
die points of support will be 0.367 of the whole weight on
1. Then, denoting the weight over one of the struts 8 by
value would be 0.367 x 13,100 = 4807 pounds, or, for prac-
'poses, 4800 pounds.
68"
-1-
1
g'b" 4
- C ti'
B r ^
Cx8' J
.^^
V
^44
s
1 — (m
S
^
;^
Fig. 13.
Fig. 14.
the strain in the tie /? is to the strain on 8 as the length of
he height of the truss from centre of rod to centre of beam,
make this height 3 feet, and we find the length of A\ by
fi, to be 7 feet 4 inches ; then.
Strain in li : 4800 pounds : : 74 * 3,
7'^ X 48(K)
Strain in /? = o = 11,733 pounds.
uld require a rod an inch and one-fourth in diameter with
w-ends upset. The rod should have a turn-buckle at T.
)eam B wouJa have a compveaaWe a\,t%\Tv — ^ — —
w/iic/5, which would require a beam aXiowV \\ \\\Ocv\s^
lit, as the beam has also to earr>f t\\e \Nfe\?Nv\ ^^ ^^^ "*
452
THEORY OF E00F-TRUSSB8.
■
rafters between two points of support, we sluill be obliged tc
six-incli by eight-inch timber for the straihing-beftm of our i
I^V THEORY OF UOOl-'-TKUSSE.S. 453
e stnitB we will make, as Ghown in Fig. 14, of ra^l.-iron. I.hn
^^^^ess of the iron being one-half ol an iiicli.
tfon Truss. — For an iron truss requiral lo meet tJie condi-
du of this case, a form such as is shown in Kig. IS will be found
t most economical. The tie-rod is raised eliglitlj In the eentro,
tl llie bracing is arrangcil so as lo bring the alnitK nearer at right
gles with the rafters.
I'lie Icjiglh of the raftera. poRition of the purlins, and dlstant'e
tweeii trusses from centres, are the same us in the i-aae of the '
K>den truss; hence the loads on the truss will l)c the SHine. Aa
> have slightly changed the position of till' lie and liraclng. Iiow-
er, we shail tic ohtiged to make a new strain .sheet.
The niethoil of drawing it is so similar to tliiit for the woodsn
las, that we shatl not describe the necessary sKpe. It ihonlil he
ticed, that, where we had one vertical tie at the (■sntre of the
Oden truss (Fig. Ill, wp have two in the iron ln«», sllghtl.v
kilned: hence the strain on each one in only/i (Pig. 16«), a
tie more than (me-half of the strain on the rod Fl (Fig. 12).
le stresses In the different pieces of the truss are indicated by
t figures on tlie corresponding lines (Fig. 15a).
[r Fig. In the heavy lines denote the pieces wiilcli arr In ri>in-
sssion, and the light lines those which are In tension. The
tied lines refer only to the meiisur«inents. Tatlng (iret th«
tees which arc in coinpresslon, we find the grealpRl compresrion
any part of the rafter is 65,300 pounds on the lower length, and
iSOO pounds on the upper length. We shall probably Knd that
a best way in which to build up Ihe rafter will be to use two ][
Cfe to bark, which are (apable of rcoisting Uie-comprBssion uu
a middle length, anil bolting a plate ou each sidr to give the
ilitlonal strength required in the lower length.
Por tliis truss we will use the Trenton nbapcK of rollnt iron.
To compute the required (limenaions of tlie clianiiflB tor our
fter. we have the formula (p. 235). ,
Safe load = ■ r j . ~ ■
V values of II and r we Hhal) find in tlje last column of the table
I p. 238, as we sliall keep the channels an inch apart. Tlie
ngtbot each section of the rafter is ll.!3 fp«t.
We will first atsmnc two heavy nine-lni'b channelH. and see If
ley will answer. For these we have,
4 X I2,!)() X 68T ^ ^
'4^4 THliOltY OF KOoi
ini'h lleht <'1iHniiel9. TU«aP we Sad, only have n sate ImtA of I
Ions, or !iil,OIKI poiinilsr so we nuisC uae the nine-int^h henvj rh
iii'Is, whii.-h are strong enough for uiy purt of the rafter. T(
ulisohitely aure that our rafter has sufildent strength, hoireyn, '
will riviU a six-Inch hy [lin.-c'-pightlis of an Inch plat« to tlie iq
lUiigw or the channels, for the lower li^iigth ot the rafter.
The MlTUl EF has 17,0011 pounds' ronijiri'ssion upon it, and is
Afciiming tn-o Four-inch xUteen and a half |)iiuiiil I'lixiinil
1>iiii-i»l an InHi »parl, buu'k to back, we dnd their
4 X 3.07 )t 21t4
Siiln load. In tons = — '|on"+"ei)4 " ~ '' ^"»i "r I^"' pi'Ms.
Tht-«i we will theKfoi-R uue.
*l1ir'.slrul,<ii>haa but 13,11X) pouuds' noiiipi'uaaloii ii|>on ii.in
■inly aDvpp fael long; au chat, for this, two llirt!i^ini.-|| t'lUUD
]J...v,J twiJtlo lw<-k will 1.K aii]])ly surHcirtiit.
For the ties w.' will use angle-irons- The grailesl alntlaln
main tit; i«74.r>il(i iiomuls. which requirus only savi'ii scjiiarel*
i.{ r'nws-scctiuii ; mid lii'nue, if we use for our inniii lie l«'(i G
liiiir-iiiHi U> six-iiii'li ungltui, we shall liavu ampin striatgiti U
Fur lUr tie Fl we will use two bars three IntTbua by «
inch, giring a total cross-section of three siiuare ini'hes.
Kor the tie DE we will use two bars two innhos by t!
of an iiioli.
The joints of the truss will be formed by rlvi^ling a thluk |i
of iivii plate between the channels, and riveting the slniltandl
to tlial, mfKr the method shoKii in ¥ig^ Itt tutd 17, Cliap. XXT
With this cxutiiple we liiavti tlie stdijeut of n>of-triisse5. A*
liiivi' stated before, the inetlnxl of finding the strains due to w
liressnre alone we liave not given, because, hi the trusses nil
conn- especially before the architect or builder, the metlioJi U
l^veii we believu sufficiently accurate. Any one wishing U
the niethoii of drawing the diagram of straius due to wind I*
alone will find it fully eKplalned in Green's ■■ Graphical A
of Ruof-TruHsoH." '
' I'ubll^hod hy .Jqha W»ry k Sous. Nsw Votk.
JOINTS. 455
CHAPTER XXIX.
JOINTS.
The stability of any piece of frame-work depends in a very
iat measure upon tlie manner in which the joints are made. It
therefore very important, that in drawing trusses, or fraine-
»rk of any kind, the designer should liave a good knowledge of
a fundamental principles upon which every joint should be con-
ducted, and of the most approved methods of forming the prin-
>al joints found in frame-work. ^
J'ointS are the surfaces at which the pieces of a frame touch
ch other. They are of various kinds, according to the relative
aitions of the pieces and to the forces which the pieces exert on
Ch other.
Joints should be made so as to give the largest bearing-surfaces
kisistent with the best form for resisting the particular strains
:^ch they have to support, and particular attention should be paid
the effects of (!ontraction and expansion in the material of which
ey are made.
In planning them the purpose they are to serve must be kept in
Ind, for the joint most suitable in one case would oftentimes be
e least suitable in another.
JOINTS IN TIMBER-WORK.
In frames made of timber, the pieces may be joined together in
ireo ways, — by connecting them ;
1. End to end;
* As the author could think of no better way in which to present the uubject,
i has taken, by permission' of Professor Wheeler and of the publishers, the
tUowing chapter on joints from the text-boolc, on Civil Engineering, prepared
V Professor Wheeler for the uhc of the cadets of the United-States Military
cademj^, and published hy John Wiley & Soi^ii ol Iscnn Xox>s.. T>c\fe waJOsssix
nrtlly recommends Profesnor Wheeler's work to l\ve attYvW^^V. c>t Xsvx-CAfcx ^"^^
Abb to obtain a thorough knowledge of cot^ftUucWow *xv^ >2W!v \w»x»^'»
toyed therein.
^B 2. The eii<l of one piece ri'.sLiiig iiih>ii or iii>IHiv(l inLn the iuxfl
Poolb.,; «,1 ■
^^ 3. Tlie f^es resting on, or uol^lieil into vuvh otlii-r. H
I. Joists of Beams united End to End, the uofl
tbe beams Iwlng in the same straight tine. H
J7Mt, Suppose the pieces are required lo resist stwiiiB li hI
1
1
— i ^
J
1
ll
1
1
..
I
K
■y ^
\ ^
i
'^
:.
1 !
H
1
1
•o
s
!l
1 ^'-
H
~
.:::T:i.
^' .
J| 4
u
c'
■ iJ
tJ
-. = 1 —
-- 111
is
' h
= st
^
=-.===.:
{1
ii.
1
•«
■-■.^
::::=:
1^
J
> s
2 =
£
i
1
X
i
i -f
:.;::-..
1
-
' I
?
/^^
r ^
^
1
Tills case occurs, when, in large or long fratiies, a single plMJl
tbe required length cannot be easily procured. fl
The ueuoJ method of lengttietiXns te ^u lb.i» cose b; Jtthlna
^jgOfOMM by n conibinaliow ol ttw two. ^
^^^^Moints. — WhcnUwAieam»a.\jWiew4«.im&,»sii.i«a
^^K'piecos of wo.^\ or iv..u v\-'^'-'\ ™^ ™=^^ «.\a*H~^
JOINTS.
457
0 the timbers, the joint is called a fish-joint, and the beam
o he fished.
joint is shown in Fig. 1, and makes a strong and simple
ion.
the beams are'used to resist a strain of compression, the
es should be placed on all four sides, so as to prevent any
lovement whatever of tke beams.
iw'*^^
.\^.^..\
4"-''--t'
^''"''-^
J strain be one of tension, it is evident that the strength of
t depends principally upon the strength of the bolts, assisted
riction of the fish-pieces against the sides of the timber,
lependence upon the bolts may be much lessened b"^ notcb-
Gsh-pieces upon the beams, as sho^'iv on >iXxfc w:^'^'^ ^^'^ ^"^
? in Fig. 3 ; or by making use oi \Le^^ oxXiViOta ^\\v«
irted in shallow notclies made. \iv \)oW\ VXv^ \ie»^ ^^^ ^
itown on tJie lower sido oi t\\e vW^e \\\ X\\^ ^^^^^^^ "^^'^
Care should be taken not to place tbe bolts ti
e pieces. Tbe sum of the uruas o! cross-aiHitlons uf Uw h
■hould not Im leas than one-fifth that of tin: beain.
Scarf -iToints. — In these joints llie i>lKn» overlitp twdltll
luu) are bolted together. The form of lap depends upon Itw 1
at strain to wliicii the lieani Is to be subjected.
r^-'
1^
"'"I
IVM
Fig, 4 Is an example of a simple Bi'arf-joiiii that is sometimes
when the 1>eaiu is to be subjected only to. a slight strain of ^
slon. A key or folding wedge is (i'e<piently added, notched K
In botli beams at the middle: it servos to bring the surfacea q
Joilit Ughtlf together.
J^tg Joint is often uiadttby uvtUVng^.'Vtc^ws.vaKVa 'suc'b ». n
^«Jtt^j^m projections wliicli fil Vnlo potwHvo^vSni^ \i "
m/^^g^tople, in which two ot vXiwe no\*;\iK» m*^
JOINTS. 451^
\\ lap shown in this figure is ten times the thickness of the
id the depth of tlie notches at A and B are each equal to-
1 that of the beam. The bolts are placed at right angles
icipal lines of the joint.
a good joint where a strain of tension of great intensity
listed, as, by the notches at A and 7^, one-half of the cross-
the beam resists the tensile strain.
illation of Fish and Scarf Joints. — The joint
Fig. 6 is a combination of the fish and scarf joints, and
sed to resist a tensile strain.
Suppose the pieces are required to resist a transverse
!ase the scai*f-joint is the one genei-ally used, and it is then
rnetimes by simx^ly halving the beams near their ends, as
re usual and the better fonn of joint for this case is
pper portion of this joint the abutting surfaces are per-
' to the length of the beam, and extend to a depth of at
bird, and not exceeding one-half, that of the beam. In
Q portion they extend one-third of the depth, and are
liar to the oblicpie portion joining the upper and lower
er side of the beam is bshed by a piece of wood or iron
•ed by bolts or iron hoops, so as to better resist the tensile
iiich this portion of tli<i beam is subjected.
Fig. 8.
. Hcarf-joint arranifod to rcHJHt a croHS-Htraiii and one of extension,
n of the joint in fished by an iron i)late; and a folding wedge inserted
I to bring all the eurfaces of the joint to their bearings.
Suppose the piece required to resist cross-strains combined
sile strain.
it frequently used in this case is shown in Fig. 8.
revious cases the axes were regarded as being in the same
le. If it he required to unite t\\e eI\^?.,^w^>aaN^•<^\^^»5^s.
ngle with each other, this ma^ be <\oxve Vj \a\Ni'\»% "<^^^
je ends, or by cutting a mortV^ei \xv Wvfe e-^-^Nxfe ^"^ ^
end of the other to fit, and iaateuKw^ \Xv^ fe\v^9.\JCi%«a
by pina, bolts, Btraps, or other devices. The joints nstd in
latter ctise we termed "raortise" and " tenon joints." Thfirf
wiil depend upon the angie Iwtween the axes of the beams,
II. Jointsof Beams, tht! axes of the liouiis making in t
wltli ew-'ti other.
Murtise and Tenon Joitits.— Wlien tlip axes i
liicuiar to each other, the (uorlisa Is cnt in tlie face of
Inanis, and the ejid of the other t>eani is sliajieJ into
lit the mortise, as shown in Fig. Q.
r
f
lugrth^r.
When tlie axes are obiique to each other, one of the most oiui-
mon joints consists of a triangular notch cut in tite face of
tlie beams, with a, shallow mortise cut in the bottom of the
the end of the other heaiii Ixting ciU to lit the noi.eli anil luurllMi
as shown In Fig. 10.
kV
Ldicular to each other when prafiticable; and the thickness of
t«non H shnidrt be about one-flfth of that of the beam A. The
XL .thaulJ be left a Utile u]>en at c u> allow for sutllmg uf the
me. The distance from b to the end D of the beam sUouUt be
BdeoUy great to resist aafely the longitudinal a hearing-strain
ised by the thrust of the beam A against the mortise.
tnppose the axes of the beama to be horizontal, and the beain
io be subjected to a croas-stmin ; the circujnstaneea being auclk
.t the end of the beam ^ is lo be connected with the face of the
ler beam B.
a this case a mortise and tenon joint is used, but niodiSed in
m from those jnat shown.
Co weaken the innln or siiiiportitig lieani as little as possible,
[ mortise shoiiid be cut near the middle of Ma dupth ; that ia, the
itre of tbe mortise should be at or near the neutral axis. In
Urthat the tenon should have the greatest strength, it should be
or near the under aide of the joint..
ilnce both of these conditions cannot be combined in the same
nt, a modlQcatloD of both is used as shown in Fig. i 1 .
B
i
riie tenon lias a depth of one-sixth tliat of the croas-beam A, and
ength of twice this, or of one-third tlie depth of the beam. The
>er side of the erosa-beam la made into a ahonlder, wbicli is let
u tlie main beam one-lialf the length of the tenou.
double tenons have been considerably used in carpentry. As a
Gi they should neeer be used, as both are seldom in bearing at tbe
II. Joints used to connect Beams, the Faces rest-
g on or notclied into I^cb Otiier. — The simplest and
ingest joint in this case is made by cutting a notch in one or
h beams, and fastening the fitted beams together,
f the beams do not cross, hut have tlie end o^^«vftU^tM.t^«5Bm.yM.
er, a dove-tail Joint is sonip.times uaei. In VVa V>'\^V'
SiJaJ/nform, is cut In the supporting \«aatt,M*i'*fc<^
rlwam /a fitted Into tliis uotcU.
It of the sfarinkige of limber, tlie dove-lall joint
T \jv iweil. excppt in cases wiierc tiie ahrink^e b tlieiUilt
"patta counleract KaiAx oLher.
It is a joint mucli ua«d in joiner's work.
The jolnia used in timbei-worit an- );enerelly coniposrd of (ib
siirfavea. ( 'iirved oi>«b luive titicn recotniiiendeil tor stniu, but I
expitrinients ot Hcklgltinson -would hardly justify tlieii nu 1
simplest forms are, a.s a rule, the best, hs they afford Ili« <wl
nicatis <if Httiiig tiie parts together.
Fastenings.— The pieces of a frame are held lagetliPrW
joints by fastenings, whieli uiay Ije classed as follows: —
I. PiiiK, including' aaila, itiiilces, screws, bolts, and WNdgee;
a. Straps and tit— bftrs, inthiding stirmpB.
.; Mui
■g, S<»cketi4.
These are so Mi'll Icnowii tliatadi'seripliouof ihejii Ism
In iilHiiiiing anil i-senitiiiB joints am) faulpiiings llie folio
Beii«ral principlus alioxdd he kept in view: —
I. I'o arrange the joints and fastenings so as to weiili^u u
as possible the piei^es wiiieii are to be coaiiucled.
II. In a joint subjei'Ied to (.'ompressiun to plaec the abo
gnrfiices as nearly as possible parpendieiilar to the ilireclinn ot
III. To give to such joints as great a surface as |>ractiislilr.
IV. To proportion the fastenings so that they will Im uqii
strength to the pieces tbey eonnect.
V. To place tlie fastenings so that there shall be no'ilangei' of
joint givinti; way l)y the fastenings shearing, i»- crusitlng tl
JOINTS FOK IROy-WOKK.
The piec*i3 of an iron frame are onlinurily joineil hj meant d
rivets, pins, or nuts and screws.
Blveted Jotuts. — A rir-el is a short headed boll o. ,■■—,.
iron or other nialliAhle material, niaile so tiiat it can be liuvtu
into boles la the pieces to Vie laslvneA Ui^<Oa«, uu\ V^aii Vw qdll
of the boh can be spn'ail out ovViiftVen v\o'«i\ rto-cVf uv»<\«mi
AKpM-saure or h.-iniinerln?. 'n.\» i>v«r»v\o« \'i U-tow4 ■* Awl
s |)f rforuicd by hanJ i
^^^^^B JOINTS.
•-^i a hanuner by a succeselon of blows : by raachlneiy, tui ordlna-
-"S^ us^l, lli(> heate'1 bolt Is both pressed Into tlie hole, and riveted,
" « single stroke. If a lunpiiiae tises a sttceeBsiou uf blows, the
*«Bntion Is tlien Icnowii na "anap-riveting.'' By mauy it is claimed
k^t machine riveting poasesseg great superiority over that by hand,
IK' the reason that the rivets more completely lilt tha holes, and in
k^way become an Int^^l part of the structui'e. It is doubtful If it
6*WMses the advantage of superior strength to any marked dt^ee.
1 does i-ertainly possess, howevpr. tha advantage of beinR nioiti
««.fckly exeoutwl without liariiage lo the heads of the rivets.
' TTie holes are generally made by punching, are about one-twen-
i^Xh of an inch larger than the diameter of the rivet, sni) are
U^Ily conical. Thcdlameterof t)ie rivet is eKtiersllygre.ater than
kk« thickness of the plate through wliloh the hole Is to lie punched,
«M«,use of the (llfAculty ot punching botes of a smaller slxe. Piinch-
l^lnjiires the piece when the latter Is of a hard variety of iron;
taad for this reason euglnfers often require that the holes bedriDed,
i>rilling seems lo he the betrjjr method, especially when several
bleknesses of plates are to be i;oiinected, as it insures the precise
lEutching of thp riyet-hol>». The appearance of the iron around a
M/fHe made by pimching gives a very fair test of the quality of the
When two or more plates are to be riveted, they are placed togetlier
iB the proper position, with the riveUholes esactly over one anotlier,
*ai(l screwed together by temporary sci'ew-bolts inserted through
■WW! ot tlie lioleg. The rivets, heated red-hot, arc then inserted
>Xito the holes up to tlie bead, and by pressure or liamniering Uiit
Iniull end Is beaten down fast to the plate. In a good joint, eape-
Bially when newly riveted, the frit-tlon of the pieces Is very great,
being Bufiicient to sustain tlie working-load without calling into play
KJiesbearing-resistanceof the rivets. In calculating the strength of
Ule frame, the strength due to friction is not considered, as It cannot
be relied on after a short time in those cases wliere the frame i4
•objected to shocks, vibrations, or great cliangus of leuperature.
Ifumber aiul Arrane'emeDt of Blvetx.
The general rule determining the number is, that the aian (^ the
weaa <tf the cram-aections ^f the ritels shall he equal to the ^ffet-
tive teetiouat nrea 0/ the plate after the holes have been putieheS,
This rule is baaed on the theory that the resistance, to ibeactn^
■train la the rivet is equal to the tenacity <i\ ttw, 9\i.\)e.
2b determine (Ae proper diatance hetviten tUBrtutlaVft^JB*-
JHU^j' row. so that the strength ol tUe viNeX,* \ti a.'ft'i *™
464 JOINTS.
shall be equal to the strength of the section of the plate along tUi \h
row after the holes have been punched, let
(/, be the diameter of the rivet; "^
c, the distance from centre to centre of the rivets;
(If the area of cross-section of the rivet;
A', the effective area, between two consecutive rivets of tha
cross-section of the plate along the row of rivets; and
ty the thickness of the iron plate.
T, the tenacity of iron.
.S, the shearing strength of rivets.
It has been assumed that
and the rule requires that
T a
TA' = Sx a, or ;^ = 2;: = 1.
We have
whence
_a i^rcP _
A'" tic-d)"^*
c = i^^ -r a
i
for the distance from centre to centre of the consecutive rivets in
any one row.
English engineers, in practice, use rivets whose diameters are t,
f, I, 1, H, and H inches, for iron plates t) it» t> i> 8> and } inches
thick respectively, and take the distance from centre to centre at
two diameters for a strain of compression, and two and a half
diameters for extension. The distance of the centre of the ex-
treme rivet from the edge of the plate is taken between one and a
half and two diameters.
Instead of assuming the resistance to shearing in the rivet equal
to the tenacity of the iron plate, a better rule would be to make the
product arising from multiplying the sum of the areas of the cross-
sections of the rivets by the amount of shearing-strain allowed on
each unity equal to the maximum strain transmitted through the
joint.
If the strain was one of compression in the plates, and the ends
exactly fitted, the only riveting required would be that necessary
to keep the plates in position. As the workmanship rarely, if ever,
admits of so exact fitting, the rivets should be proportioned by the
ra/es just given.
735« j»/2r<? nf t/ie head of a rWet Aepen^a xv^TLXJaa Qia.\&sSu^ <st the
ally circular in iorra, ^ttiA. ^ovjCAXsan^ ^ ^^skcbj^^^
JOINTS.
46{
than twic«, and a tlilckBesa at tlie centre not leu than one
; diameter of the rivet.
is method! are need in tliearrangementof the rivets. Thi
nent often used for lengthening a plate is shown in Fig. 12
thod ia known as " dialn-rivetii^."
)
<
}
ooo
oo
ooo
--V
^^V/^
K-n
Ir^
3 sliows another method used for the same purpose, li
le number of rivets ia the same as in the previous example
e is a hetter disposition of ttiem.
U and 15 show the arrangement of the rivets often used ti
.es to a plate.
10, 17, sod 18 sliow in plan tbe tonna ol wN«&''£a^a
■jlnte.
abowa the single ahear-JoVnt or a\n^ft\a.V-ifi^'°^
Fig. 17 shows the ordinary fish-joint. In Uils joint tte A
cover plates are placed on each side, and have a lluciness of
ttiBt of the plates to be CMinectedt sometimes only one oowi^
ll nseil, and then the eonnfiction is known as the " bnltjoint''
When several plates are to be fastened t<^ether, the mef
ihown In Fig. 18 is the one ordinarily used.
The proportions tor eyes and pins, and for screio end* and ^
lor teosion-rDds, 'will he found In Chap. IX. ^
PAHT III.
Rules, Memoranda, and Tablk^
V8BPUL IN
Designing, Estimating, and Building.
> ♦
CLASSICAL MOULDINOa
ouldingrs are so called because they are of the same shape
ighout their length as though the whole had been cast in the
mould or form. The regular mouldings, as found in remains
assic architecture, are eight in number, and are known by the
wing names : —
[
]
D
innulet, band, cincture, fillet,
Ustel, or square.
Astragal, or bead.
)
L
Tome, or tore.
Scotia, trochilus, or mouth.
'volo, quarter-round, or echinus.
Cavetto, cove, or hollow.
/
Inverted cymatium, or cyraa-reverBa.
Cymatinm, or cy ma-recta.
last two are both called ** ogee."
me of these terms are derived thus : Fillet, from the French
Jily "thread;" astragal, from astragalos, "a bone of the
" or "the curvature of the heel;" bead, because this mould-
when properly carved, resembles a string of beads; torus, or
the Greek for rope, which it resembles when on the base of a
nn ; scotia, from akotia, ** darknea^,^^ \ieic».\\afc q.1 \J^^ ^tass?
•IK which its depth produces, and \ii\i\s\v V& Vsv^x^ass^'^
tion of the torus above It \ ovoVo, ii^Tcv oxu\u. '''" ^s^
■frO HEAT AND VBNTILATIOK.
which this meulxir resembles, when carved, u in the li
capital ; caretto, from caeits, "hollow;" cymatium, from b
Characteristics of Mouldings. — Neither of these m
lng3 is peculiar to any one of the orders of arcliitecture ; i
aithoii^ each has its appropriate use, yet It is iiy nc
flued to aiiy certain position, in an assemblage of inoiUdings. '
use of the Hllel, is to bInU the ports, as also that of the ai
and torus, which resemble rupee. The ovolo aud cyma-reyemaj
strong at their upper estremitiea, and are therefore used U
projecting parta above them.
The cyma-rccta and cavetto, being weak at tlieir upper extnuni' 1
ties, are not used as supporters, but are placed uppermost to a
and slicltcr the upper parts. The scotia is introduced in tlie bi
of a <:oiiirnn to separate the upper and lower torus, and to pi
n pleasing variety and relief.
The form of the bead and that of the torus Is the s«n
reasons for giving distinct names to them are, that the toma, I
every order, is always eonsiderably larger than the bead, and I
placed among the base mouldings, whereits the bead is never place
there, but on the capital or entablature. The torus, also, is aeldo
carved, whereas the bead is ; and while the torus, among ll
Greeks, is frequently elliptical in its form, tlie liead retains I
circular shape. While the scotia is the reverse ol tlie torus, tb
cavetto is the revei'se of tlm ovolo, and the cyma-r^cta and cym)
reversa are combinations of the ovolo and cavetto.
HEAT AND VENTUiATIOIT.
The eaiisfs of the lose of heat in ventilated rooms are, (I) uniti
of heat required to warm the passing air, (2) imlts of heat abs«M'
by walls, (3) units of heat absorbed by ceiling, (4) units o(
absorbed by floor, and (5) units of lieat aiisorbed by windoin.
The sources of heat in rooms are, (1) units of heat generated bgr
Uie occupants, (2) units of heat generated by lights, and (3) unl
of heat generated by fires or heating apparatus. An adult nn
requires for respiration and transpiration hourly 215 cubic feet<
utmospheric air, or Si-'i X 0.077 — tO.ri pounds, and generates alw
$Bb units of heat, 100 units ot w\i\o\\ pp tattiR focraatlon of rapC^
4£e other 190 units being iUaa\pat*y\ V>^ raA:\«t\mv\n'flBJi
*^ Bctfl, and contact wWi t\\« coWei a.\T. TVb «xi»fljs«.'
X, .nd the heat g-ncT^t.-d, U^ ?pA\%\v« ^■«.i\« "
HEAT AND VENTILATION.
iL'iHc gravitn
mfficiently near for practical purpcsea thus ; The spetillc
nf ^s IB iLbout lialf that of atiuosplieric air, or 0.()3S t>oundB p^'
cwbic foot, and rtqiiirus for complete coiubiiBlion 0.038 X iT = 0.64
pennda of air, orj^ = 8,44 cubic feet. Each cubic toot of ~
'burned emits about GOO units of heat. An oil-lamp with a gool|
-Wick eoDBunies about ir)4 grains iier hour, equal to 36 lamps p^
^poond. Each pound of oil requires 150 cubic feet of utr for
^^e combustion, und generates about ltt,00t) units of heat, c
^er lamp. CiiDiUe; six to the pound may be reekoiied the sai
nlamp I'onsuming oil, each candle bumin); about I'll grain
TABVLATED IN BOUKD NU-MUE«3.
An adult man vUialBS |ipr hour (cubic feetl
Eadi cubic foot of ga.* bunicil " "
Each pound of oil burned " ■'.,...
Each pound of candles '' "
Units of heat generated by a nian per hour
Units <)f heat generated by one cubic foot of gas ... i
ITnits of heat genuraWJ by one pouud of oil or candles . lQ,i
An average gaa-burner consumes about four feet of gas per hour.
Windows, as ordinarily constructed, will admit ai>out eight Rublo
feel of air per minute.
Ventilation of Tlieatrcs.
ExAKPi.GS oi- Theatue Ventilation. —The plenum pvin-
cipie (of forcing pure air into Ihe building, and driving out the-
Impure air) has b<^en introduucd into the Metropolitan Openi
House, New York, where every fixed chair in the house has »iS
admitted to it. A very full and Interesting account of the ventihb'
tlon of tills house Is given in the " Sanitary Engineer " of Dec. 0^
1883.
The object being to have an excess of air entering the bnildi^
Iteyoud that escaping liy the regularly provided foul-air outlet
thus Insuring an lutenial atmospheric pressure slightly in ei
of the air withuut tin' building. This maintains an outward
rent through crevices of doors, windows, and otlier openings, M
aecomplisli which in a practical manner a blowing ei^.ne is UM
and the supply of air is almost unlimited. A contn^Iing T&lre
fitted In the centre of the auditorium ceiling, by the adjustment i
mii!eb the pressure within the house \Btega\a.\ftA,a.iii.'CMs.MKJSii
of pieauia maintained under the vMy'wift^Teasmsa'ai-^M'^Sft-^
"" '~'ga[ieed of the fan.
■T"
»
472 CHIMNEYS.
The plenum principle is also employed in the Madison-Sqnaie
Theatre, New York. The inlet for fresh air (s by a descending
flue, which is six feet square, lined with wood, and in this is placed
a conical cheese-cloth bag forty feet deep. This filters the air,
which af ton^'ards passes over ice in siunmer, foiu* tons l)eing used
t'lich night, — two tons before, and two tons after, the air pasMs Ir
the fan at the bottom of the inlet shaft. The fan forces the nir ft:
into a brick (iu(rt, from which sheet-iron pipes lead the air into fonr
brick casings, which surround the steam radiators used for 'wann-
ing the air in the winter. The auditorium has four sections of
ninety scats each, and from the steam chambers direct to each
of these seats a four-inch tin circular pipe conveys the air. In
addition to these, special ducts from the fan are usetl in the sum-
mer to pour an extra supply of cooled air to various parts of tlie
auditorium. Tests used to prove the efficiency of this system have
given satisfactory results.
A tiUHpcrature without draughts, and not exceeding sixty-five
degrees F., is the most desirable in a theatre; and it should be the
aim of every theatre-builder to attain tliis result, which will at
times necessitate cooling the incoming air during the summer
months.
CHIMNEYS.
[From the " Building and Engineering Times.**]
The oi)joct of a chiiimoy is to produce the draught necessary for
the proper combustion of the fuel, as well as to furnish a means of
disrliaigiiipj the noxious products of combustion into the atmos-
pliere at such a heiglit from tlic ground that they may not be con-
sidcreil a nuisance to people in the vicinity of the chinmey.
Kc2:ardin,£j tiie second of the above purposes for which chimneys
are built, it need only l)e said, that it is of secondary importance
only, and that where due attention is given to the proper methods
of setting boilei-s, and proportionating grate areas, furnaces, and
rate of combustion, the smoke nuisance is comparatively unknown,
and is of no practical importance whatever.
The main points to be considered in designing chimneys are tlie
right proportions to insure, first, a good and sufficient drauglit,
and, second, stability. |
Without entering into any demoTisXT^AAow q\ >:?ftfcN^^<sv\j^^VS&&
aow of the heated gases tllTougU\.\vei^mv^e^^.xv^^^^«^V»^xs^^
UP the chimney, ^ e ^VW ^tiefl^ ^^^ ^ ^^^ !^^ "^"^^ ^^^^"^
^ CHIMNEYS. A
'wliich xvroduces the dniiigfat is the action of gravity upon the <
ference in the specific gravities of the heated column of the gasc^i
? combustion inside the chimney, and the atmosi)here at Its non
\ temperatnre ontside of the chimney, by wliich the former is for
up the flue ; and the laws governing its velocity are the same
tliose governing the velocity of a falling body; and it can hi* pro^
"tliat its velocity, and, consequently, the amount or volume of
4mwn into the furnace, and which constitutes the (Irau<^'lit, in
I^Toportion to the square root of the height of the cliiinney. It i
Common error that the force of the draught is in <iir(*ct i)r<)iK)rt
to the height; so that, with two chiinn(»ys of the sani<* arra of fl
One being twice the height of the other, the higher one would j
flnce a draught twice as strong as the other. The intensity
draught under these circumstanc<».s would be in the i>roiM>rt
^f the square root of 1 to the squan^ root of 2, or as 1 to 1.42.
double the draught-power of any given (.'hininey by adding
"the height, it would be necessary to build it to four tinicvs Mu- or
Hal height. Practically there is a limit to the Ii<>ight. of a eliinn
<rf any given area of flue, beyond whi(rh it is found that tlic^ a<!
tional height increases the resistance due to the velocity an<l fi
tion more rapidly than it iner'^ases the flow of cold air into
furnace. For chimneys not over forty-two inches in diamel
the maximum admissible height is about three hundred feet.
From an investigation of the same laws w(^ find that tli<^ velot
of the flow of cold air into the furnact? is in proportion to
square root of the ratio between the density of the outside air £
the difference in the densities of the outsith* air and the he^
gases in the chimney; from which we may deduce the fact that v
little increase of draught is obtaine«l by increasing the teniperat
of the gases in the chimney above r)50 or COO deijrees F.
raising the temperature of the flnc from 000 to IL'OO degrees
would increase the draught less than twenty per cent, while
waste of heat would be very considerable. C:!onversely, we n
reduce the temperature of the flue about one-half, wlu^n the t(
perature is as high as six hundred degrees, by ni<*jins of an eco
mizer or otherwise, and the reduction of draughf-fonte would
only about twenty per cent, as before.
It is found that the principal causes which act to impair
draught of a chimney, and wliich vary greatly with difi'enmt ty;
of boilers and settings, are the resistance to the passage of the
offered by the layer of fuel, bends, cYbow?^, ?cv\v5i Oi\a.ws^^ \cl
diinenaions of the flues, roughness oi tYve Auacav^wc^ ^i \stv3«-
hales in the passages which allow t\\e ewU^^wcOi o\ ^^^^^ ^
generally, any variation from a straiglit, a\Y-t\^\\. V^i**^*®^^'^
474 CHI1IIIB78. .
■
size from oomlnutioEHduuiiber to diimney-fiae; .and the resfiptoiiee
to draught ts in direct {iroportion to the magnitude^ and numlier of
such vari&tfonB.
In designing a chimney, it is, therefore, always necessary to con-
sider the type of lx>iler, method of setting, arrangement of boUen
and flues, location of chimney, and every thing which will be likdy
to in any way interfere with its efficient perfcMmance. Much, of
course, depends upon the judgment and experience of the designer,
and it would be impossible to give any general rule which would
cover all cases. When only one boiler discharges into a chimney,
for instance, the chimney requires a much larger area per pound
of fuel burned than when several similar hollers discharge into a
chimney of the same height; and, taking all these varying dream-
stances into consideration, a great deal of judgment is, in many
cases, required to determine the proper dimensions.
It is a common idea that a ** chimney cannot be too large :" in
other words, the larger the area of the flues, tl^e better the drauj^
will be. But this is not always the case. In many cases where a
chimney has been built large enough to serve for future additions
to the boiler-power, the draught has been much improved as addi-
tional boilers have been set at work. The cause of this is to be
found in the increased steadiness of draught where several boilers
are at work and are fired successively, as well also as in the better
maintenance of the temperature of the flue; as the velocity of the
gases necessarily increases with the increased amount required to
be discharged, and they do not have time to cool off to so great an
extent as when they move more slowly.
General Rules for Brick Gldmnesrs.
[From Molesworth*8 " Pocket-Book.'*]
The diameter at the base should be not less than one-tenth of the
height. J
Batter of chimneys, 0.3 inch to the foot.
Thickness of brick-work, a brick from top to twenty-^ve feet
from ditto. A brick and a half from twenty-five to fifty feet from
the top, increasing by half a brick for each twenty-five feet from
the top.
If the inside diameter at the top exceeds four feet six inohes» the
top length should be a brick, aad «k\i<BM. \^0k»
0HIMKST8.
47r
H
T
i
V
Velocity qf Artificial Draught
Height of chimney In feet.
Temperature of air supplying tlie cliimney.
Temperature of air at top of cliimney.
Velocity in feet per second.
F
h
HP
A
V = 0.3tJ5 ylH(T-t),
Area of Chimneys,
Quantity of coal consumed per hour, in pounds.
Height of chimney, in feet.
Horse-power of engine (indicated).
Area of chimney at top, in square inches.
15 F 150 HP
A =
0^
Sj'h
Proportions for Boiler Chimneys.
[From "The Builder."]
For marine boilers the general rule is to allow fourteen square
inches area of chimney for each nominal horse-power: for station-
ary boilers the area of the chimneys should be one-fifth greater than
the combined area of all the flues or tubes. In boilers provided
with any other means of draught, such as a steam-jet or a fan-
blower, the dimensions of the chimney are not so important as la
cases where the draught is produced solely by the chimney.
Rule for finding the Required Area for any Chimney, — Multiply
the nominal horse-power of the boiler by 112, and divide the prod-
uct by the square root of the height of the chimney in feet. Tlie
quotient will be the required area, in square inches, at top of
chimney.
TABLE SHOWING DIAMETER AND HEIGHT OF CHIM-
NEY FOR ANY BOILER.
Hone-
power of
boiler.
Height of
chimney,
in feet.
Interior
diameter at
top.
Horse-
power of
boiler.
Height of
chimney,
in feet.
Interior
diameter at
top.
lFroni"Tho Build
T/'J
nelKht □
Prwaiiro liue
in Jlw. per fool.
n,U«.p,rho«.|
.
Id
SO
M
476
fUGHT OF CHIMNRYS FOR DIFFERENT aEIGHIi
Wroiiglit-Iroii Clilmiieyf^.
The Pennsylvania Sleel Conipiiiiy bad tbe following
iron cliimncy-alac^ka in use in 18tt3; suid, according to Mt.
the BUperinteuOent, tliey iiave provn] Ixith durable and
Blast funiacp No. 2, Whitewell Hluve-stack, (i feet (1 incli«s ill)
eter; IfiS feel liigh- lined with nine-inch Hre-brick for iW f
four-fnclj r«l brick for IM feet. Ejected 1877.
0. H. furnace stack, diaineter 7 feet; height 135 feet; lined a
as above. Erected 1(*80.
Hail Mill boiler-stack No. 2, 0 feet diameter: 112 feet h^
Erected I88I.
Whitewell atove-Btnck, 0 feet 6 inches (liBmetur; htM(;hl \10 M
lined BanLe as above. Erected 1881.
Furgfi boiier-Htack, 7 feet diuueter; inside shell lined wilb alii
inch tire-brick for 30 feet, then four-inch red brick i<
feet high from base-plate. Erected ISflO.
Rail Mill boiler-sta^k, 7 feet diameter; 110 fuct high;
above., Erectiid 1874.
Rail Mill gas-furnace stack, same u Rail Mill boiler
Erected 1875.
Rail Mill gas-furnace stack, saiae as lUil HUL Erected ISO.
OAS MEMOItANDA.
V FLO'W OP GAS IN PIPES.
[From BaiwolL'i " Kn^noc
the flow of gns fa (iiiterniinisd by tlie same rTiles as govern lh»t
the flow of water. The proeaure aiiplieil Is inrii.aled and esH-
kted tn inches of water.
l.iingib, la
The volumes of gases of tike apeclflc gravities illsclinrged In equal
lines by a liorUontal pipe under the same pressure, and for diffei^
Bt lenstlis, ara Inversely as the square roots ot the lengths.
The loss uf volume of dlschat^e by triction, In a pipe six Indira
ti diameter and one mile In length, is estimated at nlnety'-five per
rat.
Gas Memoraufhi.
In distilling fifty-six pounds of coal, tlic volume of gns produced
11 ciibic feet, when thw distillalion was cffcfled in three hours, was
U.8; in seven bours, 37.-j; iii twenty hours, 33,5; and, In twenty-
Ive hours, 31.7.
A retort produces about six hundred cubic feet of gas in live
Murs, with a cliai^ of about one and a half hundred- weight of
Oal, or 2800 cubic feet in twenty-four hours.
A cubic foot of good gas, from a jet oue-tliirty-tliird of an inch
1 diameti^ and a flatiie ot four inches, will burn sixty-five min-
ims.
Xatemal lights require four cubic (eel, aiii eit.\e.tt\^ \vgL\Va,
eeubkifeet, per hour. When large ot ^.TgciuWi^im^"^
Mte to ten cubic feet will be retniVtfeA.
STAIRS.
Wooden Htairs are generally built with twi>tadi
HtrlngerN tmi^lied nut on tbe upper aide to form the tlqa,
(-i)vurud with plocisof boarda, whose length is equal to Uie it
of Ihu BlalrK. 'I'he horkunta.! tiuards upon which Ihe fnt
placed arc callivl the treads; anil the vertical boanls, the ril
In tlnt-clua wurk, the treiuhi ahontd be an inch and a qi
rlih'k, anil the riHere aeven-eighllia of an Incli llUcfc, aad
shuiitd l>e of some hard wood. The etringera fhould not be p
over sixteen Inches apart from ecnlrea, and twelve inches 'a b
Tile treads generally project an inch and a half beyond tbel
of the rlscra, forming a nusing.
A good mle lor the proportion of risers and treads is tfe
sum of the rise and trea<l shall equal seventeen Inches and :
Tims, If the rise Is six Inches, the tread should be eleven IndiH
u half (plus the width of the nosing): or, If the rise Is eight:
till' ireail should be hut nine Ineliea and a half.
The rise is always measured from top to top o( treads; and
tread, htsui face tti faee of risunt. The following table sbi
giants how nmny risers or i.reads there will be in any gfi
twice.
EXAMPLic, — In a ci/rtain building the height from the W
the flrst floor to the top of the second Is 18 feet. How ntanj d
will be required, and what will they be?
Ana. Find In the table the heights coming nearest i
atid tlien notice the height anil number of risers necessary to «1
thin height. Thus, in the column headed 71 Inches, at the M
we And IS feet H Inches, showing that 30 riscra 71 inches
will give 18 feet ll inches. If we used a rise of 7j inches, 2U i
would also give ua IS feet IJ inches. Hence we shall need ritlM
ur U(l rluen, according as we wish our rise li or T^ Inches. If
use a rise of T] Inches, we Khali only require 28 risers. The
bur of treads In a given distant^ can be found in the same tnj.
^^^^^r
^^^^^^^ »rAIRA. ' VIS 1
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SEATIHO-SPACE IN THEATHBB.
[Kroin lymiloii " Bnlldlrig Tlm<;»."l
e qiiRtllon o( seating 1b one upon whli^h a mumper uA I
Uic arc apt to diffur.
! requirciiu^nls of the. Mctrupolltaii lioiirJ of Woito Vl
'Aspect to seating are, that " the area to be assigned toeoehioi
shall ncit be leas than one (oot eight inches by one foot six incll
In the gallery, nor less tlian two feet four implies by one (aot^
inches, <n tlie oilier parts of the liDUse, room, or other plue
public resort," 'I'lieae conditions It Is perhaps liardly newM
to say are not coniplied with in any theatre miiler the jurladlfli
of the Boanl.
Until tbenlrea are licensed to bold a certain number, or oti
le^l restrictions enforced, an architect, in calculating tli« Mlb
napaclty for Llie cheaper parts of bis theatre, must be gnlddl
past experience. In Llie upper drcle, pit, and gallery, irhwtl
seats are not divided off, the audience will [lack Itself in an Uli
Isliing manner, when a calculation is madtt of the space in 1K
occupied by each person.
Froju average ca.lculatiaus made in London theatres, th« vli
of leat required !n the uniiumbenid parts of a tlieatn^ is as
ii])per circle, eighteen Inches; pit, sixteen inches; amphltbi
BlxLw'n Int-'hes; gallery, fonrt«en indies. It is not Intended
uclvouate a nilninium space for the seats; on the contraTy, tb
cannot be a doidit but tiiat, if the miniinuiu of eighteen inc
were strictly enforcetl, It would he a most desirable innovation.
The several divisions of tlxt auditorium arc provided wlUi a
or less luxuriant seats according to the price [lafd for admission.
Tlie stalls are usually fitted with arm-oliairs,
TliK wUilh of seat, and the space allowed between each roir,
considerably, according to the degree of comfort and
In any case, Cbe space allotted to each seat in the stalls Is gm
than that given in any other part ot a theatre. The width of
Scats a<lopled vaj'ies from twenty inches to twenty-four inches; i
the distancn from back to back, from tbn<e feet to live feel, '
■tall-scats sliould Tie the very embodiment of an easy anu-dn
& very frequent fault residts from tiin seat being too high, an)
back not suthciently inclined, li should not he forgotun >
the occupants of tlic stalls have to look up lowanls Ibi^
Tlicy should lie able to recline Etaslly in the clialr ut an angle nit
lo theifneof vision. To B\t \iisoTOtta\*iJ.\»'i»\.o\»s.\at».*.i([
a H\a^ aT^iC t-Kim
Iwpniforl ot Slall-se
I k should endeavor Vi
?\T9,\.\'), V\\e.ft«rt A
tDlHfl
1
SPACES OCCUPIED BY SCHOOL-SEATS.
481
slionld not be sunk too low. It should never be more than four
"f^et below the highest point of the stage-floor. Secondly, the seat
should not be too high, and the back sufficiently inrlincMl for the
occupant to accommodate himself to the angle of vision. As
instances of comfortable stall-chairs, the following dimensions are
t;hose of seats in two representative theatres. Width, twenty-one
Inches; depth, sixteen inches; height of seat from floor, sixteen
inches; height from floor to top of back rail, two feet ten inches;
distance from back to back, three feet ten inches. In the other
case the seats are continuous, and *' tip up." Width from centre
to centre of arms, twenty-three inches; depth, twenty-four inches;
height from floor, sixteen inches; inclination of back, 115 degrees;
and the distance from back to back, three feet.
I>ress-Circle. — The seats in this part are similar to those in
the stalls; but the inclination of the backs should be slightly less,
unless the circle is low, and not much in height above the stage-
level. It is also advantageous to make the seat one or two inches
higher than the stall-chairs. In the theatre previously alluded to,
the dress-circle seats are twenty inches wide, eighteen inches deep,
eighteen inches high, and inclination of back 115 degrees. The
width of the steps upon which the seats are fixed ranges from three
feet to three feet six inches.
Upper Circle. — The steps in this part may be reduced to two
feet six inches. This reduction in width is imperative at each
level: otherwise the height of the steppings would be inconvenient.
The seats should be divided by arm-rests, and have back rails.
They should be eighteen inches wide, fifteen inches deep, eighteen
inches high, and about 100 degrees inclination of the backs.
SPACES OCCUPIED BT BCHOOL-SEATB.
SIZES OF CHAIRS AND DESKS FOR SCHOOLS AND
ACADEMIES.
Age of scholar.
16 to 18 years.
14 to 16
12 to 14
10 to 12
8 to 10
7to 8
6 to 7
5to 6
4to If
II
II
t»
II
It
II
tt
163 inches.
Height of denk
(next scholar).
29i inches.
28
27.
26|
25J
24
22^
21
19
K
<(
((
<C
<<
(i
Space occupied by
desk and chair
(back to back of
desk).
2 feet 9 inches.
2
2
2
2
2
9
8
7
5
4
1.
vv
\
vv
~— — -^ . _: . . I J —
DeakM tor two McholAn are three feet ten Incliea \onfi, wx^Iot «.«Nsv^ ^^
ro feei long.
404 HBIGHTS OF OOLUMirS, TOWBBS, Am> BOMBfl.
HEIOHTB OF COLUMNS, TOWBEUI, DOMBE^ BPIBBBi
COLUMNS.
Name.
Alexander «...
Bunker Hill » . . .
Chimney (St. Rollox).
I Chimney (Musprat's).
City
July
Napoleon . . .
Nelson's . . .
I Nelson's . . .
Place Venddme
, Pompey's Pillar
' Trajan. . . .
I Washington . .
' York . . . .
Place.
St. Petersburg . .
Chariestown, Mass
Glasgow .
Liyerpool
London
Paris .
Paris .
Dublin
London
Paris .
Egypt.
Rome .
Washington
London .
TOWERS AND DOMES.
/
Tower . . . ,
Tower . . . ,
Capitol . . .
Cathedral
Cathedral . .
Cathedral . .
Cathedral . .
(Cathedral . .
Cathedral . .
Cathedral . .
lieaning Tower ,
Porcelain . . .
St Paul's. .
Stnahonrg .
JCark'0 .
Feet
Babel
Baalbec
Washington . . .
Antwerp
Cologne
Cremona
Escurial
Florence
Milan
St. Petersburg . . .
Pisa
China
ItOTVioi^
"VetAcfe , . , ,
^^i^ ...
176
4m
m
m
132
171
196
114
145
656 >
138
CAPACITY OF CHURCHES, THEATRES, ETC, 485
HEIGHT OF SPIRES.
ty Church . . .
.trade of Notre Dam
des Invalides .
iild of Cheops .
nid of Sakara .
.CITT OF SEVERAL CHURCHES, THEATRES,
AND OPERA-HOUSES,
CHURCHES.
.1;., Kom* .
0
Je
a7,mw
33,0IKI
36,800
THEATRES AND OPE K A- HOUSES.
UIM1',.NS1()\9 01' l-|llv\TKl>, i-yr
I DIMENSIONS or THEATRES AND OPEHA-HOITa
The roJlowIiig an! the dimensions of r.ome of tlio proml
theatres In IbU country iind lu Europe : —
>!Ie [f nclli-il«t. I'gr
<)l»ra-HDiu>e. l-lil
a&bo'L'b«aln,'Ua
tllf
=l!li
t ToliiJdeplh'of nudlloiiua
'.' Toul width Df uidiUriun
at betnecn tho frxHllRtili to
DDCEMSIONS OF ENGLISH CATHEDRALS.
487
S
o
H
OS
M
QQ
*2
H 00
s
33
X
X
X
>
•<
5C
v a
§ S
5 .
I
5 •
go
^1
9* 9» ay Qi Qi
U P fc. t.
30
CI
Im fc. u
i-H r^ 1-1 O* ©< 0< i-H ^ 0^ i-H iH ri i-i i-H i-i I— I i-H rn ?-• i-i i-(
|i-i<»"^i-i»r-l^l®i:-^l I I I IrT
fOOQQOa I ri 00 ■^ r-i » r- 1^ i S^^
I I I I
??
I I I I I I I I I I r-> I I I
eooSweo l«neo-tr-5i-iSS8eooo iSeo looo
OOOQe^O»COrHOO-»<< It- I I l!r®«r°2^ li-iOOeOr-J
SeOOr^ACOCDOOCD I -f t- r^ OO i-l "t t- 00 CO »5 »-"?« »« ^
»— t-o>5ooost-t- 00«O»— I— Ot-00»-CDt-»-t— o
•*c^i-ieo«o Icoeo^ ir-r-i«i-HQi-OJ^ lift leoot-
C^eOC^eOC^ fHC<C^ ri C^ frl CI fl i-< r-i iH rH ri i-i
it-»tOQOQOO>Oe^Ppr-ir^O^O»-'Ooe»eOO»0"^
/
as
a
3
DlMESSIONg OF VAIUOrS OBELISKS.
fmoved lo Rome by Vaa-
bl Pliny lo
ON'lliki of NecUnsbli, cncled near tbc Tomb ot
Ar>lni>€ by rtolemy Fbilodulpbus
OlwUik dF ConelsnUui, rSBtoml sud erected In
front of S. Qlovanul Lulermip. a( ligme . . .
P>r1 of one of Uieobollalu of llw son of SeHOatrlB,
In the cculni of the plain In front ot »l. Peter's,
Ik of A
Mailiat
leEDa, rron the CIroug . .
In the nni£B del PopdlB n
u>, raised by PIub V.
Pluudi Monte Cilortt
Two lAeMtkt: one at Aleiandrli, vul^rly Mllcd
aeopulni's Needle, nnd the oLher nt HellopOlb .
Obellak by Pliny, nttrlbuted to Bothi*
Two obellik* In the mini nt Tbebeg
Oroa obollik at Ooniunllnaple
Obellak In the Plaiia Xaroua. n-moved from the
Obelisk 11 A
tr"
OhellBk from
the U
n».l.^
BOfA
nwin
imnt of Ih
<:hun
h of
dta. Uarlu JUggi
re, at
« <i«
leoH
f Sallu
t, a
ronl
nir in
MercaU
Oballak at Bljlje, In
BmM obella:
at Con
flyl-
lln. . . .
Tbe Ba>berl
iObel
k. .
M1SCEIXANE0U8 MEMORANDA. 48
mSCELLANEOnS BflEMORANDA.
Weight of Men and Women, — The. average W(;ight of twent
thousand men and women weighed at Uoston, 1864, was, — niei
^^H pounds; women, 124i pounds.
Snialleat Convenient Size of slab for a 14-inch wasli-bowl, 21 b
^ inches. Height of slab from floor, 2 feet 0 inches. Very snia
(12-lnch) corner wash-bowl ; slab, I foot 11 inches o.av.U side.
f^H)irti« should be 2 feet 2 inches between partitions; partition
^ ^eet high.
^pace occupied by Water-CloMeLs, 2 feet (\ inches wide, 2 fe(
^eep.
I^lmemdouH of Double Bed, — 6 feet 0 indues by 4 feet (i in(!hes.
^meiisions of Hlmjle lieda (in donniiories). — 2 feet 8 inches b
^ ^«et 0 inches.
^imennions of a Bureau. — 3 fe(it 2 inches wide, 1 foot (\ incrhc
*"*ep^ and upwawls.
^^HmenslonH of a Wasfistaml (common chainl)er-sets). — 2 fe«
inches wide, 1 foot 0 inch(js dtK'.p.
^Mmen»iorni of a Barrel. — T)iani<^t(T of head, 17 inches; bung, 1
^^hes; length, 28 niches; volume, 7^iH0 cubic; inches.
^^MmenHiouH of Billiard-TablcH ((jollender). — 4 fe(»t by 8 feet,
^^t 2 inches by 9 feet, and 5 f(»et by lOfec't. Size of room reqiiirec
^^ feet by 17 feet, 14 feet by 18 feet, and 15 fe(^t by 20 teet respc(
^^Vely.
^lorHe-Stalls. — Width, 8 feet 10 inches to 4 feet, or (^Ise 5 fe(
^'^ over in width, 9 feet long. Width should never be between
^*^cl 6 feet, as in such cases the; horse is liabl(» to cjust himself.
Z)ijnensionH of l>rawimjH for Patent h {\]mUM\ States). — 8.5 b
^^ inches.
J*itch of Tin, Copper, or Tar-and-( travel Roof. — Five-eightl
^' an inch to the foot, and upwards.
A full of onevtenth of an inch in a mile will producer a current i
^^rsern.
Melted snow produces from one-fourth to oncMiighth of its bul
*^ water.
At the depth of forty-five feet, the temixTatun^ of the earth :
Uniform throughout tlui y(iar.
A spermaceti candle, 0.85 of an inch in diamet<'r consumes a
inch in length in an hour.
Velocity of nound in water, 470H feet per scM-ond.
Avenues qf City of New York run ^ZH^ r>Vi' WW vi.^'sX vA \V3itCii..
Averm/ff Height of Hand Unil to Stairs 'm A^umWVwsx^.— ^^
7 inrlirs from top of step on Vnu' nvU\\ t\sv'Y.
I.EAD MEMORANDA.
u
par roufs iini) glitters uaf T-pollTiii Itviil.
For hlpa and rldgea use ll-poiiiid lend.
For tlasliiii^ use 4-pnimd lend.
Gutters aliould liave a fall of at least one inc'li In 10 feet.
. Ko slieet of lead should be laid In greater length tlian tei
ivelve feet without a drl]i to allow of expansion.
A pig of lead la about three feet long, and weighs from x I
~ reil-weight and a. fourth to a hundred-weight and a half,
Spanish pigs aie about a liundred-weJghL ^
Joints to lead pipes require a pound of solder for evprj' lad
I diameter.
WEIGHT OP WEOUGHT-IHON.
OeiieiiU KuleH fur iletei'iiiiiiiufT tliu Weiglit of I
Piece of Wrouglit-Iroii.
One cubin foot of wrought-lron weiglu
One square foot one inch thick *' VV
One square inch one foot long "<,... }3
One flipiare inch one yard long " . . , . ilj X 3
Thus it appeam tluit tliu weight of any plere of wroiight-inll
pounds per yard is equal to tell times its area in square inaliM< i
For round iron, the weight pei' foot may be found hy taking]
diameter in quarlei'-inchea, squaring it. and dividing hy 0,
BxAHPLic. — Wliat Is the weight of 2-iiich round Iron? '
2 inches = 8 quarter-Inches. 8' = 84,
"u' = 1')^ [lis. per foot of 2-iiich round.
ExAiHpLti;. — What is the weight of i-inch round iron t t
t Inph = S quarter-inches. 3^ = 8,
'^; — 1 i lbs. iier foot of i-inch round.
Tha aljovu ruhst are vers umvwiVen^, ».iiA cWAeTOeWAJ
t to i>e (iu.lcU.\v C.\>U\KVA ^^■\tt^ w
WEIGHT OF FLAT AND BAR IRON.
491
IGHT PER FOOT OF FLAT, SQUARE, AND ROUND
WROUGHT-IRON.
tlCRNSaS OB DiAMKTEU.
WeiKht of
a Mquare foot,
in IbH.
Wbiwht 1
Hquare bar,
in IbH.
»KR Foot.
liound bar,
in IbH.
0.0026
1 inches.
In decimals of
a foot.
v»
0.002(5
•
1.263
0.0033
1^
0.0052
2.526
0.0132
0.0104
A
0.0078
3.789
0.0296
0.0233
i
0.0104
5.052
0.0526
0.0414
A
0.0130
6.315
0.0823
0.0646
A
0.0156
7.578
0.1184
0.0930
»V
0.0182
8.a41
0.1612
0.1266
i
0.0208
10.100
0.2ia5
0.1653
A
0.0234
11.370
0.2665
0."2093
ft
0.0260
12.6;^0
0.3290
0.2583
U
0.0287
13.8^)0
0.3980
0.3126
0.0313
15.160
0.4736
0.3720
a
0.0:i3l)
16.420
0.5558
0.4365 !
iv
0.036.">
17.680
0.644()
0.5063
a
0.0391
18.950
0.7400
0.5813
i
0.0417
20.210
0.8420
0.6613
i»«
0.0469
22.730
1.06<)0
0.8;^70
«
0.a521
25.260
1.31()0
l.a330
H
0.a573
27.790
1.5020
1.2500
i
0.0025
30.310
1.8950
1.4880 '
n
0.0677
32.840
2.2230
1.7460
I
0.0729
35.370
2.5790
2.0250 ,
n
0.0781
37.890
2.9600
2.3250
1
0.0833
40.420
3.3680
2.6450
lA
0.0885
42.940
3.8a30
2.9860
H
0.0938
45.470
4.2630
3.3480
lA
0.0990
48.000
4.7500
3.7300
U
0.1042
50.520
5.2630
4.1:^30
lA i
0.1094
53.050
\ ^.^J^>P»i
V N.:^^^
« /
0.1146
55.510
\ e».^^^»<i
\ ^.^
^■F
WEIGHT OF FLAT AND BAR IROS. 1
WEIGHT I'Ell FOOT OF FLAT. SQUARE, AXD BOOH
WKOUGHT-IKON iCniUliuledj. ■
TuiCKHKBe .
n DliMKTRH,
Wolgbtot
a tqmre foot,
Wiioar
PES Fom.
In iDohw.
afool-
equare Inr,
[touiHl tm^
1t^
O-llOfl
58.10
6.WV\
6.«fl
ii
11,1250
00.93
T.5T8
6.9dS
IS
11.1354
05m
8.893
em
li
0.145S
70.73
10.310
8.101
IS
0.1Wia
75.78
11.840
9.3(10
2
0.10U7
80.83
13.470
mm
3!
0.1771
ffi.89
13.210
11.960
21
O.IS75
itOM
17.050
13.3W
2i
0.197S
»5.ve
19.000
I4.BM
2*
0.20S3
101.0(1
21.(B0
ie.m
2fi
0.2188
106.10
a3.aio
18.2W
2i
0.22!»2
111.20
25.470
S0.010
2i
O.S.tdO
Illi.W
27.840
si.m
3
0.2500
121. ;to
30.310
23.810
H
0.2CU4
im.3o
32,8(10
S5.eS(l
31
0.27(8
131.40
35,570
27.M0
3i
0.2813
13«.40
38.370
30.130
3i
0.2917
141.50
41.260
32.41(1 '
3i
0.3021
146.50
44.260
34.7fl'l
3S
0.312.^
151.60
47.370
3ri.sm
as
0.322fl
156.60
60.670
311.730 1
«
O.^Tt:i
161.70
B3.8B0
42.380
*i
0.3438
166.70
67.310
46.01(1 ,
*i
0.3.>J2
171.80
60.840
47.781
4i
0..'i(l4ll
176.80
64.470
sasN
4i
0..'i750
ISl.OO
W".200
53.ST0
45
0.3.V>4
180.1)0
72.050
6fl.590 1
4*
0.3«r>8
Iftl-W \ 1&.W0
6».e» 1
/
0.4()03
\ \ffl.Wl
\ «.J«»
\"^
^^
WEIGHT OF PLAT AND BAR IBON.
nOHT Mat FOOT OF FLAT. SQUARE, AND ROUND
WROUGHT-IRON [CoMclvded).
^BICKHIBS OR SuaETEB.
WHighi at
Weiuht
ER PnoT.
In incbe».
Id dccLnu.1. at
fil^H^tor,
RouDd b.r,
6
0.4161
aiai
84.20
00.13
5*
0.4271
207.1
RS.47
89.48
51
0.4375
212.2
02.83
72.01
51
0.4479
217.2
07.31
78.43
51
0.4.583
222.3
101.00
8o.oa
51
0.4(188
227.3
100.U0
83.70
5J
0.471ffl
232.4
111.40
87,48
51
0.4800
2.37.5
110.30
91.31
•
0.5000
242.5
121.30
95.23
M
0.5208
252.6
131.80
103,30
U
0.5417
2(12.7
142.30
111.80
M
o.5ea5
272.8
153.50
120.50
1
0.5833
282.0
105.00
129.60
71
0.0M2
203.0
m.oo
139.00
71
0.8250
.303.1
189,50
148.80
7i
0.S438
313.2
202.30
158.00
8
0.86fl7
323.3
215.60
189.80
81
0.B87B
333.4
229.30
180.10
81
0.7083
3i3.5
243.40
191.10
8i
0.7202
353.0
247.90
202.50
e
0.7500
.^03.8
272.80
214.30
IH
0.7708
.373.9
288.20
226.30
W
0.7BI7
384.0
304.00
238.70
al
0.8125
30i.l
320.20
251.60
10
0.33;S!!
404.2
830.80
284.50
Ml
0.8750
424.4
371.30
201.80
U
0.01(17
44J.8
407.60
320.10
III
0.0583
4&1.Q
V&.tiS
\ 'iSftSi
" /
1 foot.
485.0
\ ««,(»
\ ?»R.SSl
WEIGHT OF PLAT lEOH,
WEIGHT. PER FOOT, OF FLAT IRON.
1
TmcKBEaB. IK ■FBiOTlOH* or iBCHlta.
— --
A
*
A
i
A
!
A
*
A
)
11
,
oan
o.«t
O.M«
0.«39
ij»
MS
LflT
18S
UK
5*
14
oloi
lUH
ft.™
t.ta
lilT
1.41
111
2.34
1]
o.aM
rtjui
*.I8I
-iSM
l.iW
IJt*
1.M
ios
2.34
!J!
11
04tH
O.SJJ
0J«
1.1<0
ITi
i.3e
1i
0.313
fl.Ba
1.150
l.U
1.8g
%jn
^f
bJHi
1.US
Law
l.m
1.37
i.o&
Sm
3.1)
1)
i).ate
1.090
Lm
3.38
5i
0.3P1
D,7M
Lira
i!d6
».U
3«
O.J)T
fl.SS!
1.4*0
.«<
jXi«
2.ftO
3.M
S.B»
4JJ
4^
^1
".4*S
1.3i0
3.»8
4«
2!
«.M9
oiMt
4.22
ix
3)
«,4«
flJHO
lAsa
iImo
S.17
1^7
■i.ta
3Jo 1 4.4ft
iJ&
H
u.ait
1AM
\JM
S^Mo
g.eo
ZXb
i.n
2
l.(WO
iMa
a.iw
4.Wi
■i
«:aM
1J»
i.ax)
tK
an
aiw
Siw
4.'ao
*.6S
*.70
S.1fi
JI.W
5.30
i/»a
IJ80
a.$oo
4.3S
CjH3
«.£>
m
^
1.3M
UH
aTK
e.77
H
4.ue
^M
»Jo
«!h
7.ai
B.n
3!
O.TU
i!«a
im
«.:is
TJt3
o,faa
\x;<i
u»
SJM
4.IT
7J0
«.«
41
aJ«
*.*«
6,5.
41
lISM
3.810
7.M
«.3»
4I
li.iim
I.Deo
i«0
«:oft
8.M
4.t0
IM
i.\x
4.n(
B.M
7.W
10.41
llJ*
rij
LUM
IZiK
4
almo
1.4U
4!m(
sja
a!sB
lolsi
MM
1S.«
H
3.400
&liU
.L.i9a
5.10
8.3»
1S.1
S} 'lisM
sioio
\z.a
14^
n
I.SS0
I.™
4m«I)
6:*«
s:i3
loiai
lU
4
U.l»
llW*
71
1.4M
aiwu
iS
fliM
7.»
».7fi
iHI
ii.n
1-J.08
IsifiB
14.81
BJ1
tI
a.iai)
4.aw
<1.M(
vi
3.'230
4.B40
11.30
lS.li
l.fl50
3.3M
S.Oft)
46«
1S.M
15.00
1B.«
isa
SI
$.100
10.,1l
12.03
"I
t!»s(
13.40
1»!4
il
i!s-jo
i.m
i.m
fi»
uIm
ia!4i
I8'.33
aoj»
t.OW
U.OD
n.n
«i
l^ftM
5.™
tItk
17.34
le!?
31.31
4
ij*a
Z3«a
6.940
i.w-a
iilss
u.sa
17.81
i».Tl
ai.r
»'
J.O30
4.060
B.iaui 10.18
i4.sa
w.»
Xl.tl
2UI
in)
%siaa
4!™
C-IUI
»;*» {^;j2
ii™
HM
S
is
a).s
KM
loj
a.l»
*,S80
laiis
laisi
IfM
31 .«
na
/UJ 2^40
J.4sn
n.Bj
aoaa
32.40
11 2.200 4.6Sn
11 13.340 l4.em
bIsso. l\.T^\■v*J»\wAA■**\'°^\'*'^\*•
' h-MO l-n^
B.5a^^'■ll.0R\v.aa\■^6-.■^V*■■«\■!^M'\■!a»\lI
k
^/
••^
7!340
7.6(M
^jsg^^p^
WEIGHT OF FLAT IRON.
WEIGHT, PER FOOT, OF FLAT IRON.
fHICKNEBS, IN FBACTlONa Or I?<CIIE>>,
1 H I ! 11 1 ii".- 1! lA 1 H ift li ;
t n
ti
■ata
"9 IT
"l "■^ 33 1
i9 (» 1 J7 *)
m IT I aoM
_ n
_ 1
l«i*
W.W.
\'?,:'ii-.
496
WBIQHT OF CA8T-IB0K PIATSS.
WBIOBT OF CABT-IROir PLATB8.
WEIGHT, IN POUNDS, OF CAST-IRON PLATES ONE
INCH THICK.
(OaUmlated at 450 lbs. per cubic foot.)
B a
5a
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
36
Width, iir Ihohbs.
•
8
10
IS
14
u
18
80
6.25
8.3
10.4
12.5
i4.e
16.6
18.7
80.8
9.87
12.5
15.6
18.7
21.8
25.0
28.1
81.8
12.50
16.6
20.8
25.0
29.1
88.8
87.4
41.6
15.60
20.8
26.0
81.2
86.4
41.6
40.8
62.0
18.70
25.0
81.2
87.5
48.7
40.9
56.2
62.4
21.80
89.2
88.4
48.7
61.0
68.8
66.6
72.8
24.90
38.3
41.6
50.0
58.8
68.6
74.9
68.8
28.10
37.5
46.8
56.2
65.5
74.9
84.2
03.6
31.20
41.6
52.0
62.5
72.8
83.2
93.6
104.0
34.30
45.8
57.2
68.6
80.1
91.5
103.0
114.4
37.50
50.0
62.4
75.0
87.4
99.8
112.3
124.8
40.60
54.0
67.6
81.2
94.6
108.2
121.7
135.2
43.60
58.2
72.8
87.5
101.9
116.5
131.0
145.6
46.80
62.4
78.0
93.7
109.2
124.8
140.4
156.0
49.80
66.6
83.2
100.0
116.5
183.1
150.3
166.4
56.10
75.0
93.6
112.5
131.0
150.0
168.4
187.2
84
85
88
60
68
76
88
100
118
125
138
150
163
175
188
200
225
SI
47
68
n
94
K6
125
140
156
172
187
203
218
234
250
881
MTEIGHT OF LEAD, COPPER, AND BRA^S.
497
a
V
QQ
QQ
C4<DQ9 MtOCj <o CD <0 <0 CD tD
CO rH m 00 n r^ CO •i* pH Op pH C4 ri op i-H -vf ri 00 ri QT -t QO C^
00 T»< 00
«r5 Ml-
(N
•o o
5 o
I-
•Oi-^5l-+SoC0 1^l^C>-+OOp^-r*l-I^Ci -♦QCCl— COa-QCl-
SoOOOOrHrHi-iC^fiOiSl'-Or-rrcCOCr-'tQCW-trtCO-l'COai
— OOOOOOOOOOOOOi-tr-ir-<^C^'MCICC>^O>O»^000Si
._'l
,Q O
eS O
op
2. I
« o
PS
pa
o
— <OOOOOOOOO®OOOi-«rHrHi-<ci0*c6c»5 '*iOOl-^OJCci
S bo
« a
.Q o
»""
e8 Q
CO rH
a; O
ft
CDS'
$
^SQ^'OtOOOOOpOOOOQOQQ
,j5^obcot-c^Or-<traTfeoc4i-<oo»i-So^eo
oooooooco
ri 00 « eo
i.-^ o I— o CO I
j3i-i(Nri?iot-o6oi-Hr^i-^QcocboPi-H-iii--ocotoc^r--eoa>'rao50oi
p
eS a
x> o
1°
3»ft-<<i-(iAr-r-'<*i-(oo«p^oooooi
•-HCO«OO:eO00'^0f)Hi'^l'-«'N-1<O>l-(
Soooooi-ir-ic>ieo«<?t-oJc5u;o6i-iOi
ooooooooooo
-, ^ ^ » - w v^ . - v-^ .• --' -I M- . - . . -.- 1- w. . - 00 (N o (N n; t— I- w OJ !•- «c>
Soooooi-ir-ic>ieo«<?t-oJc5u;o6i-ioojTj«o>ojo«»^-;_:*.^
— OOOOOOOOOOOOrHrHi-iC<<NC<leoeO^®t-QOrHr-ii-i,-(
£ do
£::
eS o
go
COlH
»-<©OOOOOOOOOOrHi-ii-iC<»C^eOW"^'<*«Ct-0>rHeCOl— 0>
as
3 g
a, >H
-a 2.
ffi
®<M00'^OOOOi
ooi-to^eooiooii
eoi
'OOOOOOOOOOOOOOOO-
'00«o'MO»®eOf-"0»coj'*ooeoi'-oo
,OrHCO«Ot^Oii-HeO^OO
i-(eO^OOC^«00>COI'-0-*QOC^®OJ«0^»-"0>«0-!t<iMO>
rii-ti-triC^C^(NC»5c0'<*'^-T|<iOi0iO©t»00000>Oi-lr-i
^
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§
C4 CDC4 (
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l(D<M (0 (O <0 „ <D (0 CO
) iH CO ^ i-t 00 iH C4 rH op pH <f p^ 00 iH OP^OOe^QQ^OP
iW WEIGHT OF ItnLiS, MJ1>, AM> L.i H 1- i!!-.Ai':^
WEIGHT OF ONE irUNDRED BOLTS WITH SHX
HEADS AND NUTS,
80.110 '
•1^
WEIGHTS OF NUTS AND BOLT-HEADS. IN PO'
iFc<f(hi or to
Dtmnelor of bait. In iDcbM.
WEIGHT OF IRON RIVETS.
499
IRON RIVETS.— WEIGHT PER HUNDRED.
h
DlikMBTERS.
r
i
1
*
1
a
4
26.49
i
89.8
1
i
1.895
4.848
0.966
16.79
55.2 '
2.067
5.235
10.340
17.86
27.99
41.4
57.9 ,
2.238
5.616
11.040
18.96
29.61
48.5
60.7 j
2.410
6.003
11.780
20.08
81.18
45.6
63.4
2.582
6.402 ' 12.480
21.04
82.74
47. S
66.2
2.754
6.789 '■ 18.120
22.11
84.25
49.9
08.9
2.926
7.179
18.810
28.21
85.S6
52.0
71.7 i
3.098
7.566
14.500
24.28
87.87
54. J
74.4
3.269
7.956
15.190
25.48
38.99
56.8
77.2
3.441
8.348 lo.a^O
2(5.56
40.40
58.4
79.9
3.613
8.783 16.570
27.65
42.11
60.5
82.7
3.785
9.120 , il.-^V,:)
28.78
4:3.67
62.(i
85.4
3.957
9.511 ! 17.950
29.82
45.24
(54.8
88.2
4.129
9.898
18.640
80.90
46.80
(5(5.9
90.9
4.301
10.290
19.380
81.99
48.86
69.0
98.7
4.473
10.670
20.020
38.08
40.02
71.1
96.4
4.644
11.060
20.710
34.18
51.49
78.8
99.2
4.816
11.440
21.400
35.27
58.05
75.4
101.9
4.988
11.840
22.090
36.85
54.61
77.5
104.7
5.160
12.230
22.780
87.44
56.17
79.6
107.4
5.332
12.620
23.480
38.52
57.74
81.8
110.2 1
5.504
13.010
24.170
89.60
59.30
83.9
112.9
5.676
18.390
24.860
40.69
60.86
86.0
116.7
5.848
18.780
25.550
41.78
02.42
88.1
119.4
6.019
14.170
26.240
42.87
68.99
90.8
121.2
6.191
14.560
26.930
48.94
65.55
92.4
128.9
6.363
14.950
27.620
45.01
67.11
94.5
126.6
1.
0.519
1.74
4.14
8.10
^3.99
22.27
38.15
uh of rivet required to make one head =1^ diameters of
ar.
NAILB AMD SFIEIia.
SIZE, LENGTH, AND NUMUEU TO THE POUNfli
Cumterlxwl Null and Iron Ci»ni«nr. ,|
UUO.«..,.
c..«™.
F,...,...o. :
Slia.
I JIDBLli, ' No. to
Inlndtu. iiDuiHl.
•2
No.io
m
«..^- i.ML;;:
2d
I
719
fill
if
SB8
448
%
133
Gd li i
4(J
*lt}
72
:!l(i
■i
6d
IHfl
31
4It
12(i
2
2
lis
04
•Ml :IS
3
sod
4
2+
4()d
4
17
6d
60d
e
14
ed
2
eod
6i
10
3
40
lOd
12d
20d
2
3
3
LianT.
Mfikee..
SOd
4
4(1
6d
a
373
272
iva
31
4
10
15
13
10
e
WH
WHL
il 1
5'
BtATf.
3d
!^ \
lOd
12(1
3i
w.
74
fiO
B...T.
ri
li 1 206
od
TACKS.
f
SutobBi
SItn
t
Niimbo
Ri,«
1 "-
pound.
J
pmiiid
1 M.
A
iaoof>
4 0/
,',r
4000
14 ox
U 1
lOOW ft •• \ i^s \ "WW
la "
t 8000 \ 8 " \ 4 \ •iMS>\W. ~\ KM,
■. i
t sA\v:.\i\^sVAN;^
ft ' ^m
EIGHT OF PLAIN CAST-IRON PIPES.
501
I^HT OF PLAIN CAST-IRON PIPB8.
OF A LINEAK FOOT WITHOUT JOINTS.
Tiircf
iNEMS O
1 fi
Ibi^.
p Metal^ in Incheh.
1 '
1 "
llm.
I
1
lbs.
lbs.
i
1
lbs.
'^ i
lbs.
lbs.
1
Ibft.
8.7
12.3
16.1
20.3
24.7 29.5
;U5
39.9
1
10.6
14.7
19.2
24.0
29.0 .34.4
40.0
4(J.() 1
12.4
17.2
22.2
27.6
32.3
45.(i
52.2
14.3
19.6
L.').3
31.3
37.6
44.2
51.0
.58.3
16.1
22.1
28.4
35.0
41.9
49.1
56.(J
(W.4
18.0
24.5
31.5
38.7
4() 2 1 54 0
62.1
70.(J
19.8
27.0
.34.5
42.3
50.5
59.9
67.7
7(J.7 1
21.6
29.5
37.6
46.0
.54.8
63.8
73.2
H2.9
23.5
31.9
40.7
49.7
59. 1
(W.7
7H.7
HO.O
27.2
36.9
46.8
57.1
67.7
7S.5
89.8
101.0
30.8
41.7
52.9
64.4
76.2
88.4
101.0
114.0
34.5
46.6
59.1
71.8
84.8
98.2
112.0
126.0
38.2
51.5
65.2
79.2
93.4
lOS.O
123.0
1.38.0
41.0
56.5
71.3
86.5
102.0. IIS.O
134.0
150.0
45.6
61.4
77.5
93.9
111.0
12H.0
145.0
163.0
49.2
06.3
83.6
101.0
119.0
138.0
15({.0
175.0
52.0
71.2
80.7
109.0
128.0
147.0
167.0
187.0
j
50.6
76. 1
95.9
116.0
136.0
157.0
17S.0
199.0 1
60.3
81.0
102 0
123.0
145.0
167.0
189.0
212.0
67.7
90.0
114.0
13^.0
162.0
187.0
211.0
2.36.0
75.2
101.0
127.0
153.0
179.0
20(^.0
233.0
261.0
S2.6
lU.O
139.0
168.0
197.0
22(5.0
255.0
285.0
80.0
12').0
151.0
182.0
214.0
245.0
278.0
310.0
97.3
131.0
164.0
198.0
2iJ1.0
266.0
300.0
335.0
05.0
140.0
176.0
212.0
249.0
286.0
323.0
1360.0
12,0
150.0
188.0
221.0W(5ft.Q\%^.^
\^^
:. — F
'or each
I joiia.
adc\ a
loot V.O
\ex\ti^Vv
m^
602 WEIGHT OF CAST-IRON PIPES IN GENBRAL.
WEIGHTS, PER FOOT, OF CAST-IRON PIPES IS G
ERAL USE, INCLUDIiVG SOCKET AND SPIG
ENDS.
[Dennis, Tx>ug, & Co.]
Diuineter.
Thick uertH.
WelKhl
piT foot.
DlaiiH'UT.
Thicl,
>iie«*n. ■
Wei«l
per fo
2 iiicht's.
{ + inch.
0^4 n»s.
14 inches.
I inch. ;
l:iS 11
91 "
10 "
i
**
85
2 •'
■i ••
14 "
10 **
^
108
:3 "
1+ '•
11 "
10 '*
3
4
129
I •'
m "
10 "
1
152
:{ "
i "
18 "
16 **
1
175
:\ "
5 a
23 ''
18 '*
n
114
4 *'
2+ "
lOi •'
18 '*
3
137
4 *
i "
28 **
18 **
7.
101
4 ''
;]i "
20 *'
8
182
IJ •'
3 ••
25 "
20 "
1
100
rt "
i "
3:3 "
20 *'
i^
197
(5 *'
5 "
42.1 "
20 "
1
215
() "
r)2 *'
24 *'
150
s ••
.1 -i
40 "
24 "
3
4
100
S **
i "
48^ ^*
24 "
224
H *•
s
50 "
24 '*
1
257
S ''
4
08 ''
;J0 **
3.
4
2:^7
10
1 0^
50 '*
80 *^
7.
277
10 ••
.1 ii
■I
54 "
80 ''
1
810
10
\ .■<
()S '•
;;o ^*
1^«
800
10 '•
■\ "
SO •'
80 *'
J
\2 '^
1
1)7 ••
80 "
1
881
1:3 •'
S2 '•
:J(} •'
u
42ir
12 ••
90 '*
80 •'
11
470
12 '•
7 .i
117 "
48 "
1
512
14 •*
1 t»
74 *'
48 "
u
584
14 ''
A *<
94 ''
48 **
li
085
14 "
J u
113 ''
48 ''
li
775
WEIGHT OF CAST-IRON WATER-PIPES.
503
WEIGHTS OF CAST-IRON WATER-PIPES.
In ponnds, per foot rnn, including belle and Bpigots.
uneter.
Philadel.
phla.i
Chicago.'
Cincinnati.' .
Stand-
ard.'
Light.'
Weight.
Thickness
2 ins.
—
—
—
—
7
6
3 "
15.000
—
17
i inch.
15
13
4 '*
21.111
24.167
23
i "
22
20
6 **
aO.106
36.6(J6
50
i -
33
30
8 **
40.683
50.000
65
* "
42
40
.0 "
52.075
65.000
80
J «
60
0.)
.2 **
69.162
83.333
100
f "
75
70
6 "
102.522
125.000
130
i ''
—
—
10 **
147.681
—
200
I- "
—
54 «
-
250.000
224
7. U
—
to "
-
-
300
1 "
-
—
t6 **
—
450.000
430
H "
—
-
rater-pii)e is usually tested to three hundred pounds' pressure
square inch before delivery, and a hammer test should be made
lie the pipe is under pressure.
'he Philadelphia lengths for each section are, for three and four
ti pii)e, 9 feet; all larger sizes, 12 feet 3^ inches in length.
'he Cincinnati lengths are uniform for all diameters, — 12 feet.
Jliicago, same as Cincinnati,
tandard lengths are, for two-inch pipe, 8 feet, and all other
js, 12 feet.
!'he thickness of the lead joint ranges from one-fourth inch on
ill sizes to one-half inch on the large sizes.
SIGHTS OF LEAD AND GASKET FOR PIPE JOINTS.
[Dennis, Long, & Co.]
'iameler
►f pipe.
2 inche.4
3 '•
4 "
6 '•
8 ••
7 *'
I
T^cad.
2.^) lbs.
:j.5 "
4.5 •*
0.5 "
9,0 "
13.0 "
' Frvm Traatwino.
(Jsisk<-t.
I). 1-25 lbs.
0.170 "
0.1 70 "
0.200 ♦'
0.300 "
0.250 *«
Diameter
of pipe.
12 inches.
14
16 •♦
\% "
20 '»
1.') lbs.
18 '»
22 '•
0.250 lbs.
0.375 "
0.500 "
« I)enti\a»l.ovi%,%t.Co.,\.oNv^*^'^'^'^^-^'5
WBOUGHT-IRON WELDED Tl
gill
^'i'
,1 I
1|4
s-'-'i''-'-
1
||j|SE|||5Sjpi|S3
|||||||i||jj||l5p
|||||||jl®||||lil
i§S|Sj|i58iiS8l5!3
si|gm^ss^g§^gii^
3Si!|SI?S^fSia!i||
|ii|iSi;m>ISil!|
gfl!=3Sa35SJB?||SS
iiilHIiisllfiiil!
WKOUGHT-IROH AND LAP-WELDEI) TUBES.
sr?"'
Jiuincler,
THICKKSe
, IS Inch
..
.UTdAL .
7itHE»'
iuchrai.
s;;.
Blrong.
"
Eitru ,in
■«:""S,
1 1
oiflTS
IS
!
Lap-welded amekicax charcoai. ikon lioir-Eii-
TUHES.
etcodnnl dImelulaiiB (Table of Munis, Ta^tkcr. K^ Co.. I.iiiilli'il).
J-
i
^*
M
^■H
^?=
■s
11
1-
u
is
P
|L
lii
1
S'^P
ii
Il'ISi
]"■'.'',
■" "i-'i
I'll
1
H.IOJ
2.-iKI
il:«i
1:17'
PJ
SilJO
!i.SI»
H.lIiT ' »-«il
CAM
0.7Ut
J
^h"
Il.-i4.-i
iu
«JH
H.673
30.074
ai.4ie ; auiHi
O.liHJ
TLB
106 GALVANIZES ANI> BLAcS^^^^^PH
AMERICAN AND BIRMINGHAM WIRE aAOtl
i
I
'rillCBNSM, IK
i
1
■s
■^nS-J^'"
1
•3
ISCHII.
Amfciran *[<
■»r;£"
AnuTlMii
Binning.
»oo
0.4(IIMI
0.454
11
0.1HIOT
0.120
•Jf,
aono
0,1
000
0.4mm
0.4:i5
12
aosos
0.10»
•Mi
0.011)0
ftl
OO
o.;i(i4w
0.38(1
13
0.0711J
aoio
■21
0.0142
«J
0
0.!Ji4H
0.840
U
0.0(141
0,0ft:3
Si*
o.oiai
u
1
0.2S();!
0.:MK)
!.■>
0.03T0
0.072
St
11.0112
a
z
0.a5TQ
0.2S4
10
0.0508
0.0(15
.10
0.0100
0.
0.22R4
0.251i
17
0.0452
0,058
.^1
0,(mB9
IK
*
0.2(M3
0.23S
18
0.04(r.
0.040
32
0.(1071'
<L
0.1S1I)
0.?20
10
O.O.TW
0.042
SI
0.0070
n
0.]<I2fl
0.2*)
20
0.031(1
0.0)15
.14
o-iKxa
0.
0.1443
0.180
21
0.0284
aoa2
;i5
O.l)0Sfl
a
0.1285
0.1li.'i
■22
0.[)2.-.;l
0.028
.1(1
O.«(B0
a
«
0.1144
0.14S
2A
0.022S
0.023
1
|,0
o.ioii)
0.134
24
0.O2OI
0.022
^
GALVANIZED AND BLACK IHON.
Weight, in i-omi(h, jifi' nqiiiirc fool, qf giihanUeJ eheel-ir<m„
Jtul. nnd r<iyriigatri2.
Tli<! niinibprs aw] lhU-kr\ensi-3 arc tliose of t.lio Iron tM>tor»|
ga)v»nize<]. When Kllula\tM:l lt.\\e«itdtnftrv sise o[ wUcltln
tieo teet (o two fwt and a haW ^n ■w\&\.\.,\i^*i.Ms«*e.J
J&iBil>)ln converted Into & totit ^^s^^B& ow, Va^x ™^ggg|
CORRUGATED IRON.
507
mon size), its width is thereby reduced about cnr^-tenth
i, or from thirty to twenty-seven inches; and consequently the
jht per square foot of area covered is increased about one-nintli
.. When tlie corrugated sheets are laid upon a roof, tlie over-
)ing of about two inches and a lialf along their sides, and of four
les along their ends, diminishes the covered area about one-
inth part more, making their weight per square foot of roof about
-sixth part greater than before. Or the weight of corrugated
I per square foot, in place on a roof, is about one-tliird greater
1 that of the flat sheets of above sizes of which it is made.
Weight of Iron peii Square Foot.
>
Black.
Galvanized.
) Flat.
Corru
I^bs.
gated.
Flat.
Corru
gated.
1
Lbs.
On roof.
On roof.
Lbs.
On roof.
Lbs.
On roof.
0.485
0.566
0.539
0.647
0.818
0.954
0.896
l.OS
0.520
0.614
0.583
0.701
0.859
1.000
0.954
1.14
0.565
0.659
0.628
0.753
0.898
1.040
0.997
1.20
0.646
0.754
0.718
0.8r)l
0.979
1.140
1.090
1.30
0.723
0.842
0.802
0.963
1.01)0
1.240
1.180
1.41
0.803
0.942
0.897
1.070
1.140
1.330
1.270
1.52
0.889
1.010
0.907
1.180
1.220
1.420
1.360
1.62
1.010
1.180
1.120
1.350
1.340
1..560
1.490
1.79
1.130
1.310
1.260
1.510
1.4(50
1.700
1.620
1.95
1.290
1.500
1.4.30
1.720
1.630
1.900
1.810
2.17
1.410
1.640
1.560
1.880
1.7.")0
2.040
1.940
2..33
1.690
1.970
1.880
2.250
2.030
2.370
2.260
2.71
1.980
2.310
.2.200
2.6 iO
2.320
2.700
2.580
3.09
2.340
2.730
2.600
S.120
2.6S0
3.120
2.980
3.57
2.630
3.070
2.920
3.510
2.96)
3.4.50
3.290
3.95
2.910
3.390
3.230
3.880
3.250
3.790
3.610
4.33
3.360
3.920
3.730
4.480
3.690
4.300
4.100
4.92
3.840
4.480
4.270
5.120
4.180
4.870
4.640
5.57
OTE. — The galvanizing of Bheet-iron adds about one-third of a pound to
eight per square foot.
YSTONE BRIDGE COMPANTB CORRUGATED
IRON.
he Keystone Bridge Company's corrugations are 2.425 inchea
5, measured on the straight line. The>f Tftc\\x\v^ ^ \^\\^Vv <5.i vt<5P5i
. 725 inches to make one corrugaUow, anCi V\\«i (^fe\lOi\ ^A ^«t\>a^
is S\
ieet.
25 indies to make one corrugaUow, anCi V\\«i (^fe\lOi\ ^A ^«t\>a^
h inch. One corrugation is aWoweCi ioT \^>^ Vw ^^^ ^N-^^
et, and six inches in the leiiglA\, iov W\^ \3fi.\vaX \>\^Ocv ^V ^
nigateil sheet No. 20, two feet wide, six feet long bcM
supijorts, [oiuleil uuifoiuily wUli ftre-clay.
MEMORANDA FOR EXCAVATORS, ETC.
509
ICBMORANDA FOR EXCAVATORS AND WELI.-
DIGGER8.
Excavating is generally done by the cubic yard, or square; a
fnbic yard being twenty-seven cubic feet; and a square is generally
iwkoned as eight yanls, or a cube six feet by six feet by six feet.
Wells 3 feet clear diameter and i brick thick will
require the net excavation, per foot in
depth, of
3
feet 6
4
((
4
It
6
5
(<
5
n
6
6
ti
6
tl
6
7
(i
7
«
6
8
«
8
«{
6
0
((
10
«
10
<(
6
11
{{
11
((
6
12
«
<(
n
(C
«
<(
CI
«
• • • •
s diameter,
{ brick thick . ,
a
i
44
a
i
* fc
n
i
fe i
• »
i
k 4
n
i
n
11
ti
it
tt
It
tt
It
tt
t(
It
11 cubic
feet.
Hi
17J
^n
26
30
3()
m
5(5
m
71
7Si
80i
104
113
1221
132}
143i
From 13 to 15 cubic feet of chalk
17 to 10 " " clay
18 to 24 " " earth
18 to 20 " " gravel
19 to 25 " " sand
= 1 ton weight.
Or an average for general calculations may be taken as follows:—
14 en. feet of chalk weigh 1 ton
18 " " clay ** 1 "
21 " " earth '* 1 "
10 cu. feet of gravel weigh 1 ton
22 " " sand " 1 "
A cubic yard of earth in orlgliuiV v^^^*^^ ''•^ "*
bic yard and a fourth to a cable yatd toj^ ^\a^
I
HENOtCAN'IM Xilt rUtlCKI.A
MEMORANDA FOR BRICKLAYERS
STITY OF BRICK-WORK IS ltAJ{l!I!I^DHAIN3
WELLS,
luclxdlng tvailagc in c)iii[iii>g Bround Uk cunet.
Thickncw of brick-
A toad of mortar lueasurea a cubic yard, or Iwonty-seveu CT
teei] requires a cubic yard of sand aud nlue busliels of liiiu^i
will fill tliirty lioda.
A bricklayer's Iiod, measuring 1 foot 4 Indies byS iuuhes I
inches, equals 1200 cubic liu^lieH in capacity, and c
bricks.
A single load of sand and otiipr materials equals a i-ublv j«ri
twenty-seven cubic feet; and a double !oad equals twice tliat q
tity.
A raaianre of lime h a single load, or cubic yard.
One thousand bricks closely BtacltiHl occupy about fifty^Is ■
feet.
One tlioiisand old bricks, (;|[>ane<l and loosely stacked. (K
alioiii seventy-two cubic ted.
Uiie auperfleial foot of gang«\ wtbea vcn^ixve* \.ii;n\rfij3Hfc
^m wejflcial fool nf lacVugs veti«\vea aea<
DRAIN-PIPE.
511
e yard of paving requires tliirty-six Mock bricks laid flat, or
two on edge, and lliirty-six pamng bricks laid flat, or eighty-
)ii edge.
,e bricks of different makers vary in dimensions, and those of
ame maker vary also, owing to the different degrees of heat to
li they are subjected in burning. The memoranda given above
rick-work are therefore only approximate. The following table
the usual dimensions of the bricks in various parts of the
try : —
Oeecription.
imore front
adelphia front,
rainglon front .
iiton front . .
ton
ibaugh . . .
Incb?8.
y 8.1 X 4i X 2g
ix
|x
X 2
X 2
Description.
Maine . . .
Milwaukee .
North liiver
Trenton . .
Ordinary
Inches.
1
si
8
6
n
X 43
X 41
X 24 ins.
X 2( ins.
«. K^^fc S Valentine's (Woodbridge, N.J.) . . . . 8|
re-oncB j Dowulng's (Alleutowu, Penn.) 9
16 weight of the smaller sized bricks is about foiu* pounds on
iverage, and of the larger about six pounds.
•y bricks will absorb about oue-fifteenth of their weight in
r.
DRAIN-PIFR
lere are three kinds of drain-pipe offered in the market; viz.,
It Glazed Vitrified Clay-Pipe," "Slip Glazed Clay-Pipe," and
raent Pipe." The name of the latter sufficiently indicates
I it is without any description.
16 "Slip Glazed Clay-Pipe" is made of what is known as "tire'*
h as fire-brick) clay, which retains its porosity when subjected
le most intense heat. It is glazed with another kind of clay,
vn as " slip," which, when subjected to heat, melts, creating a
thin glazing, which, bemg a foreign substance to the body of
tlpe, is liable to wear or scale off.
Salt Glazed Clay-Pipe " is made of a clay, which, when subjected
Q intense heat, becomes vitreous or glass-like; and is glazed
he vapors of salt, the salt being thrown in the fire, thereby
ting a vapor which unites chemically with the clay, and forms
azing, which will not scale or wear off, and is impervious to
action of acidSf gases, steam, or ai\^ oWifct "Vavcrww ^\:^:3^'mns»^
iJtes with the clay in such a manner aa Vci iotw\ v^tI <4 ^
/?/• ///^> p/;ie, and is theiefore iniVc&tvucUVA^.
I^t^liued pipe cnn only be made from c\a,j thu «
thni is, wben siibjectttd to an intttnsn heat will etttae-
cniu[>ai't ImhIj, not I'ltroiis. Anil it should be hurnc in
"slip glazing" l« only rtsorUrl to when the clays aie
oature tliat they will not vitrify.
The mnUrtal of ilraia-piiies should be a liard, vitreous
not porous, since Lliis would lead to the abaorptioB of I
contents of tlie drain, would ba»e less actual slrengl
pressut«, would be mora affecleil by tlic frosl, or by
tion of crystals in (■ouneciion witli certain dicmical cor
or woidd be more susceptible to tlic chemical action i
BtitiienlB of the sewerage.
"Mueli experience with cement scwer-pipes seems to d
that they are not siiflJciently onitorm in quality, nor
strong anil durable, to be used with conBdenee In anj
work, whetlier public or private, ifewfr-pipn ihoutd bei
aa this requlrra tliem to be subjected to a mticli more h
Chan la needed for ' allp ' glazing, and thus secures a Its
rial."
TUe standard salt glazed sewer and drain pipe msnul
tlie Akron Sewer Pipe Company of Akron, O., has I
to anawer all ruquireraents, and is one of the best drain-
found in the market.
The foUomm!/ table glvea Ihe capacity of tlie dllTere
drain-pipe for different inclinations. Data for com
amount of rain-water to be prodded for over any pre*
la also given.
CAP.4C1TY OF PIPE.
The niasinium r»lnfa\\, aa skowWVj f.vu.\^<%,\« vSa
■ (except (luring -sery \icavj ftUiniM.'i, e«eaA.WZ
re, or aiT gaUona ^v-v*»**«
w
TABLE OF BOARD MEASURE.
513
>^ng to various obstructions, not more than fifty to seventy-five
• cent of the rainfall will reach the drain within the same hour,
I allowance should be m&de for this fact in determining size
pipe required.
TABLE OF BOARD MEASURE.
SxPLANATiON. — The length of the board is given, in feet, in the
tr-hand column; the width is given, in inches, in the upper row
figures; and the contents are given under the width, and opposite
i length. Thus, the contents of a board 13 feet long and 7 inches
3e will be found under 7, and opposite 13, and is 7 feet 7 inches.
A
Width, in
Inches.
%
6
7
8
9
10
11
12
13
14
ft. in!
ft. in.
ft.
in.
ft.
in.
ft.
in.
ft. in.
feet.
ft. in.
ft. in.
1
0 6
0 7
0
8
0
9
0
10
0 11
1
1 1
1 2
2
1 0
1 2
1
4
1
6
1
8
1 10
2
2 2
2 4
3
1 6
1 9
2
0
2
3
2
6
2 9
3
3 3
3 6
4
2 0
2 4
2
8
3
0
3
4
3 8
4
4 4
4 8
5
2 6
2 11
3
4
3
9
4
2
4 7
5
5 5
5 10
6
3 0
3 6
4
0
4
6
5
0
5 6
6
6 6
7 0
7
3 6
4 1
4
8
5
3
5
10
6 5
7
7 7
8 2
8
4 0
4 8
5
4
6
0
6
8
7 4
8
8 8
9 4
0
4 6
5 3
6
0
6
9
7
6
8 3
9
9 9
10 6
LO
6 0
5 10
6
8
7
6
8
4
9 2
10
10 10
11 8
11
5 6
6 5
7
4
8
3
9
2
10 1
11
11 11
12 10
12
6 0
7 0
8
0
9
0
10
0
11 0
12
13 0
14 0
13
6 6
7 7
8
8
9
9
10 10
11 11
13
14 1
15 2
14
7 0
8 2
9
4
10
6
11
8
12 10
14
15 2
16 4
15
7 6
8 9
10
0
11
3
12
()
13 9
15
16 3
17 6
16
8 0
9 4
10
8
12
0
13
4
14 8
16
17 4
18 8
17
8 6
9 11
11
4
12
9
14
2
15 7
17
18 5
19 10
18
9 0
10 6
12
0
13
6
15
0
16 6
18
19 6
21 0
[Q
9 6
11 1
12
8
14
3
15
10
17 5
19
20 7
22 2
20
10 0
11 8
13
4
15
0
16
^
18 4
20
21 8
23 4
n
10 6
12 3
14
0
15
9
17
6
19 3
21
22 9
24 6
12
11 0
12 10
14
8
16
6
18
4
20 2
22
23 10
25 8
iS
11 6
13 5
15
4
17
3
19
2
21 1
23
24 11
20 10
>A
12 0
14 0
16
0
18
0
20
0
22 0
24
26 0
28 0
>J6
12 6
14 7
16
8
18
9
20
10
22 11
25
27 1
29 2
»
13 0
15 2
17
4
19
6
21
8
23 10
20
28 2
30 4
rr
13 6
15 9
18
0
20
3
22
6
24 9
27
29 3
31 6
SB
14 0
16 4
18
8
21
0
23
4
25 8
2S
30 4
32 8
>9
14 6
16 11
19
4
21
9
24
2
\1^ n
\o
15 q
17 6 20
0
22
G
25
i:
V^n '
V
15 6
18 1 20
8
23
*3
\\ 25 V
q\ 2"^
b\ 'i\\ '^
n^^
1
514
TABLE OF
.1
■
■
^H
TABLE OF BoAJtn MBAernK (ConUnued)- 1
fel
Width, is Ikcuk
-
1
:; =
>
10
11
IS
a
■0
SI
n
n
(1.
In
(I. In
(t. In
ft.
ft.
In
ft.
in
ft.
In
ft. in
iti
i
3
i ■
1 5
7
8
1
!«) 1 10
i
a
»
2 S
2 10
3
3
2
3
'
s
1^ 3 ft
3
3
i
4 C
4 3
4
4
9
5
fi
3i 5 e
i
5
0
5 -1
B 8
0
6
4
0
t
0 T 4
a
G
3
H g
7 1
7
II
fi
8
0 9 S
0
7
0
H (1
8 0
1)
0
0
10
(
10
(Ml m
7
8
9
!) 4
10
11
1
(
13
12 10
8
1(1
0
10 N
11 4
12
12
8
13
14 8
0
11
3
12 (1
12 U
13
14
3
15
(
15
i
16 8
10
12
0
13 4
14 2
15
15 10
16
8
ft
18 4
11
13
fl
14 8
15 7
16
17
6
13
4
10
3
20 2
SI
12
15
0
18 0
17 0
0
19
0
20
0
21
0
22 0
23
Vi
16
3
17 4
18 5
19
20
21
22
23 10
21 1
14
n
6
18 8
Id 10
21
22
2
23
4
24
6
25. 8
SO 1
15
IS
9
20 0
21 3
22
B
23
9
25
0
26
3
27 6
2!*
lit
20
0
2i i
22 8
24
0
25
4
26
s
2fl
11
2B 4
.19
17
21
3
22 «
24 1
2a
a
26
11
28
4
31 2
32
16
22
(J
24 0
25 C
27
0
sa
30
0
81
33 11
«4
19
23
S
25 4
26 11
6
30
31
K
&i
3
At 1(1
36
20
25
0
20 8
30
0
31
8
33
4
35
0
36 8
38
21
2(1
3
29 9
31
6
33
3
3fi
0
30
0
as 6
40
22
27
6
29 4
31 2
33
0
34
10
39
8
38
a
40 4
42
23
0
30 6
32 7
34
(i
3i(
6
38
4
40
3
42 ••
44
24
SO
0
32 0
34 0
30
;js
0
40
0
42
44 «
411
26
31
3
■13 4
an 5
;!7
7
41
8
+?
9
45 10
47 1
116
32
6
Zi S
36 10
nil
41
2
43
4
45
6
4T 8
-191
27
33
I)
m 0
38 3
4a
9
45
47
3
4B «
51
28
33
0
37 4
39 8
42
44
4
46
8
49
51 4
53
20
3<)
3
38 8
41 1
4;l
45
11
48
4
50
m 2
55
30
37
G
40 0
42 (1
45
47
0
BO
1)
52
II
5r> Q
57
i
31
1
3S
1
9
1
41 4
\
43 11
46
49
51
8
54
3
5a 10
SO
8CANTL1NQ8 KBUUCEU TO BOAULl HKAISUllE. dl.'>
Scantllngrs reduced to Bonr«1 Mensiiri
Exn-ANATION 111- 'l'AHI,E. — At tllC luft-llimil of tllG IKIKC will ^H•.
lonnd the lengCli of «ach scanning, in feet. At tlir htail cif cftch
of tbe remaining coluiiiiia will be found Ihe bwa-h, bi'liig Llic wliUh
Mid thickness, in incbes ; and o|>pD3ite tllt^ given li'ii^li of uai'li
will be found the contents. of each scantling.
Il
ixt
B"8
«xs
a
4
SX6
BX6
h
XlChH.
llnAes.
liich«. liichw.
iiichei.
InchM
ft. in.
ft. Jn
ft In ' (I
in. f., 1„.
feel.
2
0 «
0 H
i o'
1 N
2
3
0 9
1 0
1 a
•i
■i 0
3
4
I 0
1 4
2 0
2
3 4
4
5
I 3
] 8
2 6
3
4 2
e
6
1 e
2 0
3 0
4
fi 0
a
7
1 9
2 4
3 6
4
5 10
7
8
2 0
2 .H
4 0
G 8
8
g
2 3
3 I)
4 C
0
7 9
0
10
2 6
3 i
5 0
0
8 4
10
11
2 0
3 S
5 9
7
9 2
11
12
3 0
4 [>
6 0
it
10 0
12
13
3 3
4 4
6 9
8
10 10
13
14
3 0
4 S
7 0
11 8
14
15
3 9
5 0
7 6
10
12 9
1»
16
4 0
>> 4
8 0
10
13 4
10
17
4 3
5 9
8 9
It
14 2
17
18
4 0
S l>
9 0
12
iT, a
1ft
19
4 g
Q 4
9 6
12
Vi 10
19
20
3 0
a 9
10 0
13
Ifi 8
'2f)
21
6 3
7 0
10 n , 14
17 C
21
22
5 0
7 4
It (1 , 14
22
23
5 g
7 9
11 f. ' l.i
19 2
2:t
24
e 0
8 0
12 0 1 I'l
•M 0
24
25
6 3
8 4
12 (5 1 19
:J0 10
25
26
Q 0
8 3
13 0 1 17
21 8
m
27
6 g
g 0
13 9 18
22 9
27
28
7 0
g 4
14 n ] 18
■a 4
28
20
7 3
9 8
14 9 19
•a 2
29
90
7 6
10 0
15 0 20
■i.'> 0
W
31
7 9
111
HI 4
IS « 20
8
2o 10
V *^
"I
0 8
16 0 21
4
1»»
\ ^1
£
!
3
4'
'i 1
4
r>
'li
8
]()
(J
Vi 10
14
15
2
10
4
17
18
8
i'.l
10
21
0
22
2
2:1
4
24
2.'>
29
10
2ft
29
2
;<o
4
31
fi
32
8
;)3 10 1
V^.
^\
\'S\ *.\«. •*.
516 8CAirruii08 Kia>vcs» to boarp nbasubi
SCANTLI2IG8 RKDUCHfiD, KT€. ( CoiUfllUed).
ii
8xf
tx
10
txii
tlxft
t|x6
t|x7
n^s
Sl'^t i
ia
iiicbes.
inehet.
iuoiies.
toches.
iuches.
Inohes.
inclies.
iDdin. ■
ft. in.
ft.
in.
ft. in.
ft.
in.
ft. in.
ft. iu.
ft. in.
ft. Id.
2
3 0
3
4
8 8
2
1
2 6
2 11
34
'i 9
3
4 6
5
0
5 6
8
2
89
4 5
5 0
5 8
4
6 0
6
8
7 4
4
2
50
5 10
68
7 •
5
7 6
8
4
9 2
5
8
68
7 4 j 84
9 5
6
9 0
10
0
11. 0
6
8
76
8 !) 10 0
11 8
7
10 6
11
8
12 10
7
4
89
10 3 11 8
13 2
8
12 0
13
4
14 8
8
4
10 0
11 8 t 13 4
15 0
9
13 6
15
0
16 6
9
5
11 8
13 2
15 0
16 11
10
15 0
16
8
18 4
10
5
12 6
14 7
16 S
18 9
11
16 6
18
4
20 2
11
6
18 9
16 1
18 4
20 8
12
18 0
20
0
22 0
12
6
15 0
17 6
20 0
22 6
13
19 6
21
8
23 10
13
7
16 8
19 0
21 8
24 5 '
14
21 0
-23
4
25 8
14
7
17 6
20 5
2:^ 4
26 8
15
22 6
25
0
27 6
15
8
18 9
21 11
25 0
28 2
16
24 0
26
8
29 4
16
8
200
23 4
20 8
80 Q
17
25 6
28
4
31 2
17
0
21 8
24 10
28 4'
81 11
18
27 0
30
0
33 0
18
9
226
26 3
300
88 0
19
28 6
81
8
34 10
19
10
289
27 9
31 8
85 8l
20
30 0
33
4
m 8
20
10
25 0
29 2
33 4
87 6
21
31 6
35
0
38 6
21
11
26 3
30 8
35 0
39 5
22
33 0
36
8
40 4
22
11
27 6
32 1
30 8
41 8
23
34 6
38
4
42 2
24
0
28 9
33 7
38 4
43 2
24
30 0
40
0
44 0
25
0
300
35 0
40 0
45 0
25
37 6
41
8
45 10
26
1
31 3
36 6
41 8
46 11
26
39 0
4.3
4
47 8
27
1
32 6
37 11
4;^ 4
48 9
■ 27
40 6
45
0
49 6
28
2
3;^ 9
39 5
45 0
50 8
; 28
42 0
46
8 * 51 4
29
2
35 0
40 10
46 8
52 6
20
43 6
4S
4 ! 53 2
m
3
363
42 4
48 4
54 5
:}() j 45 0
50
0
55 0
31
8
37 6
43 9
50 0
56 3
:n
46 6
51
8
56 10
32
4
38 9
45 2
51 8
58 2
1 :)2
48 0
53
4
58 8
33
4
41 0
46 7
fAi 4
60 1
1 II 2i X 10
2ix
11
2i X 12
8>
:8
8x4
3x5
8 x«
8x7
' ij c inbhes.
jm 1
inches, inches.
inches.
inches.
inches.
incbeB.
ft. in.
inches.
!
i
ft. in.
ft.
in.
ft. in.
ft.
In.
feet.
ft. in.
ft. in.
2
4 2
4
7
5 0
1
0
2
2 6
3 0
3 6
3
6 8
6 11
7 6
2
3
3
3 9
4 6
5 8
4
8 4
9
2
10 0
3
0
4
5 0
60
7 0
/ 5 / /O 5
11
6
12 6
3
0
5
6 3
7 6
8 9
6 12 e
13
9
15 0\ 4
ft\ ^
\ n V\\^<^<i
Uo 6
7 14 7/16
4
n tt \ ?
r ^\ n
\ % v^\\^^\vt %^
4-
2Q -Ol (
22 iO ^
1
BCANTUNG8 REDUCED TO BOARD MEASURE. 517
ScANTWNGS Reduced, etc. (Continued).
8|x 10
«4x
11
84x
12
8x
8
8x4
8x
6
8x6
iDches.
inches.
inches,
ft. in.
inches.
inches.
«
inches.
inches,
ft. in.
ft. in.
ft.
in.
ft.
in.
feet.
ft.
in.
20 10
22
11
25
0
7
6
10
12
6
15 0
22 11
25
3
27
6
8
3
11
13
9
16 6
25 0
27
6
30
0
9
0
12
15
0
18 0
27 1
29 10
32
6
9
9
13
16
3
19 6
29 2
32
1
35
0
10
6
14
17
6
21 0
81 3
34
4
37
6
11
3
15
18
9
22 6
;« 4
;w
8
40
0
12
0
16
20
0
24 0
35 5
39
0
42
6
12
9
. 17
21
3
25 6
37 6
41
3
45
0
13
6
18
22
6.
27 0
39 7
4:^
7
47
(\
14
3
19
23
9
28 (S
.41 8
45
10
50
0
15
0
20
25
0
:\0 0
43 9
48
2
52
()
15
9
21
26
3
31 6
45 10
50
5
55
0
16
6
22
27
6
liS 0
47 11
52
9
57
6
17
3
23
28
9
:14 6
50 0
55
0
60
0
18
0
24
30
0
36 0
52 1
57
4
62
6
18
9
25
31
3
37 6
54 2
59
7
65
0
19
6
26
32
6
39 0
56 3
61
11
67
6
20
3
27
33
9
40 (}
58 4
64
2
70
0
21
0
28
35
0
42 0
60 5
66
6
72
6
21
9
29
36
3
4;j 6
62 6
68
9
75
0
22
6
30
37
6
45 0
64 7
71
1
77
6
23
3
31
38
9
46 6
66 8
73
5
80
0
24
0
32
40
0
4^ 0
8x7
inches.
ft. in.
17 6
19 3
21 0
22 9'
24 6
26 3
28 0
29 9
31 6
m 3
;J5 0
m 9
38 6
40 3
42 0
43 9
45 6
47 3
49 0
50 9
52 6
54 3
56 0
8x8
inches.
feet.
4
6
8
10
12
14
1(»
18
20
22
24
26
28
30
82
34
3x9
3 X
10
8 X 11
inches.
inches.
inches.
fl. in.
ft.
in.
ft. in.
4 6
5
0
5 6
(J 9
7
6
8 3
9 0
10
0
11 0
11 3.
12
(\
13 9
13 6
15
0
16 6
15 9
17
()
19 3
18 0
20
0
22 0
20 3
22
()
24 9
22 (•>
25
0
27 6
24 9
27
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SCANTLINGS REDUCED TO BOARD MEASURE. 519
Scantlings Reduced, etc. (Continued).
4 X
7
4x8
inches.
inches.
ft.
in.
ft. in.
m
0
72 0
(i5
4
74 8
ca
8
77 4
70
0
80 0
72
4
82 8
74
8
85 4
4x9
inches.
4x 10
inches.
4x 11
inches.
feet.
81
84
87
90
93
96
ft. in.
90 0
93 4
96 8
100 0
103 4
106 8
ft. hi.
99 0
102 8
lOG 4
110 0
113 8
116 4
4x 12
inches.
feet.
108
112
116
120
124
128
6x6
inches.
ft. in.
56 3
58 4
60 5
62 6
64 7
m 8
6x6
inches.
ft.
67
70
72
75
77
in.
6
0
6
0
()
0
6 X
7
inches.
ft.
in.
5
10
8
9
11
8
14
7
17
6
20
5
23
4
26
3
29
2
32
1
35
0
37 11
40
10
4:3
9
46
8
49
52
00
.58
(U
64
67
70
72
75
78
81
84
87
90
93
6
4
•>
.>
2
1
0
11
10
9
8
7
6
O
4
6x8
inches.
ft. in.
6 8
10 0
13 4
16 8
20 0
23 4
26 8
30 0
33 4
36 8
40 0
43 4
46 8
.50 0
53 4
56 8
60 0
63 4
66 8
70 0
73
76
4
8
/
80 0
83 4
86 8
90 0
93 4
96 S
KK) 0
103 4
106 8
6x9
inches.
ft. In.
7 6
11 3
15 0
18 9
22 6
26 3
30 0
33 9
37 6
41 3
45 0
48 9
52 6
56 3
60 0
63 9
67 6
71 3
75 0
78 9
82 6
86 3
90 0
93 9
97 6
101 3
105 0
lOS <)
112 ()
116 3
121) 0
5 X 10
inches.
ft. in.
8 4
12 6
16 8
20 10
25 0
29 2
33 4
37 6
41 8
45 10
50 0
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58 4
62 6
m 8
70 10
75 0
79 2
83 4
87 6
91 8
95 10
100 0
104 2
il08 4
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IK) 8
|12i) 10
125 0
129 2
133 4
6x6
inches.
feet.
6
9
12
15
18
21
24
27
30
33
36
39
42
45
48
51
54
57
60
63
66
69
72
75
78
81
S4
87
90
93
m
6x7
inches.
ft. in.
7 0
10 6
14 0
17 6
21 0
24 6
28 0
31 6
35 0
38 6
42 0
45 6
49 0
92 6
56 0
59 6
63 0
66 6
70 0
73 6
77 0
80 6
84 0
87 6
91 0
94 6
98 0
101 6
105 0
108 6
\Vi ^
6x8
inches.
\\Vi ^ \
feet.
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100
104
108
112
116
120
124
7 y 7
inches.
ft. in.
8 2
12 3
16 4
20 5
24 6
28 7
32 8
36 9
40 10
44 11
49 0
53
57
1
2
61 3
65 4
69 5
73 6
77 7
81 8
85 9
89 10
93 11
98 0
102 1
10() 2
110 3
114 4
118 5
122 6
126 7
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ISO.
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PLANK MEASURE.
Plunk Measure.
Board measure ia the basis of ptank measure; that Is, a plank
hro inches thick, and thirteen feet long, and ten inches wide, con-
tains evidently twice as many square feet as if only one incii thick:
(berefore, in estimating the contents of any plank, wc llrst find
tbe contents of tite surface taken one Inch tliick, und then. If tiie
plank be one inch and a quarter thick, wu add onu-quurter of
Mm contents to U«elf, whicii gives the contents (in lioani Mieasuie)
Of tbe plank.
CoNTl
' Planks i
Bo A I
I McAsuiii
s«, li
?
WiuTH IS Inches.
J
J_
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s
s
10
11
n^
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17
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h.
feet
(wt
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set.
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s
21
11
1
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2
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27
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10
12
13
33
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11
12
14
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18
11
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16
30
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41 M\^.\r*V'.\*\«V
1
PLANK MEASURE.
PLANE MEASURE iCoiit!niit4)-
V Plamks in Boaiii) Mi!:A>^i'Ith:. Tdk^kvcss,
IB IT ts'.n]
?.
i
n
fli
4
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76 ,1
4H|62
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78 68
r Board Measitre. Tttn.'Ki'KSS
PLANK MEASURE,
PLANK MEASURE {Cmitlt
p Planks (n Boarci Mkasu
^.H
E,.
,;
Hi
»
1B|.0
1H ID
to
fn,t
f.-H
few fe.t
fnt
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^f PLANK MF.ASUKB.
^r PLANK
MEASURE {0..,II.Kieai.
■«.»„„. „
Planks
IS BoAKi) Xkasuiib. Thick.vbm
■
I.VCHtS.
1
1
1
W«,TH. .K Inch...
.
.
8
s
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17
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57
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5.1
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67
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41
45
50
54
02
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70
74
78
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30
35
38
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52
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78
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27
32
36
40
45
54
77
81
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25
28
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47
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til till
70
75
80
84
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43
411
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78
83
88
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30
35
41
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31
37
42
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30
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31
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32
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70 77 «3 8» 06 102 108 aaimNH
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53
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72 70 85 02 08 105 112 US ISSp^
:...r«»™o.
Planks
IN UOARl. MEABUBE. TlilCKNKaB
1
1
W.DTU, IN rKCBB*.
1
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7
S
B
10
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teel.
led
t«t
15
feet.
la 17
IS II
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31 ™
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21
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30
32
34
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41 Um
12
18
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23
25
28
m
33
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13
10
22
24
27
311
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35
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41
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17
21
25
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18
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PL\NK HRAStJRR.
PLANK MEASURE {Continued).
Width, in Jncheb.
•
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9
i»
11 ; 13
f k
IS U 16
77 1
Ifl 17
18
IB
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,
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i
rl""!
to 15
\''\'vr\A^
PLANK MEAHUItK (CwUlHuefi),
('.INTKNTS ;v ]'[,A>K» 1.1 ItlJARD MKAHUKB. TUICKN!
iNClim 1
li'"' ^
WlOTH. IK INCOIB.
1
•1
fl
7
8
9
10
11
13
13
I*
Is
10
11
18
i
1 'ft-
~
Bt
■1
■M ait
4(1
52
5
i.
T*
i
-27 40
47
54
0
68
9
28 42
41)
56
63
70
77
20
43
51
58
05
7
HI
30
45
53
UO
03
31
40
54
70
8
32
48
56
64
72
80
88
33
48
58
66
74
•y
oil W9
34
50
HO
68. 7
94 J
I 19 128 lit 45 Id
35
52
HI
TOI 7
t^S
W On
i U 1 140 49 58114
CoBTKNTa f>F PLANKa IN BOAni> MKAsrilB. TfllCKKl
Inches.
' r*
WlDIH, IK INOBHS.
1
1
10
fl.
7
20
8
20
10
29
II
(eei
32
It
35
1)
It
IS
44
» 17
,.
I
38
41
f»l
,».
tHt.
h
47
50
as
11
m
22
24
29
32
35
38
41
45
47
61
54
B7
1
12
20
25
35
3»
42
40
49
B3
56
60
63
]
13
23
27
30
34
38
42
40
40
53
B7
01
84
08
25
29
m ' 37
41
45
49
53
57
01
05
«9
74
15
W
31
*j 1 :i9
44
48
5:5
57
61
06
70
74
79
18
2S
3:5
371 42
47
51
56
61
65
70
15
70
84
n
30
35
40 1 45
50
55
00
04
69
74
79
84
80
18
32
37
42' 47
53
58
63
(8
74
79
84
89
«.-.
10
33
39
44; 50
55
61
07
12
78
B3
89
!M
>(»
1
20
;15
41
47, 5:1
58
64
70
76
82
88
93
ill
lOfl
1
21
37
4;!
49 1 55
01
67
74
80
80
92
98
104
no
22
3S
45
51 58
04
71
77
83
90
96
io:i
imi
no
1
23
40
47
54' 00
07
74
81
87
(14
101
107
114
121
1
24
42
49
50 1 CA
77
M
(11 IIR
inr.
112
119
126
1
25
44
51
58
(ifi
7:i
80
ii:> ,1(12
im
117
124
181
1
20
45
53
01
OS
76
III
ini ;ll«
114
121
129
137
27
47
55
(13
71
70 87
192 1110
118
126
134
14S
40
57
65
7*
82. W\\!R\V«i\\U
123
131 Im
147
r
/2tt 5i
m
68
70
8.=. \ pR\vni\\\ft\u?.'ft«i'>ft9Sv'A*fcNca.^
_£
HI
70 j 7B
\ «^\ \ttiyv-,v\\\\\^Y^'^\'?^
■r
t
1
■
■
1
NAILINO HEHORANDA. 527
PLANK MEASURE (Concluded).
OF Planks in Board Measure. Thicknrhs, ^
Inciieh.
r
W.UTH, ™ iNCnEB.
i
.
'
»
11
ia
13
U
15
la
£
30
f,
I
4\:{
U<)
m
U*)
I4n
Ifni
rtii
7.i
Hi
MM
1*.
141)
ir,«
n
AT
nut
IIH
llW
l^y
m
IH!i
4
At)
W)
7"
ir<u
KM'
\m
b
til
11
lUli
Uli
1!1U
m
15}l
Ittil
114
m
104
■ilH
HAILINa MEMORANDA.
[9rom "Ballder's Qulde, aod EatlioBtor'a Price-Book."]
Qoantity of Tfails for Different Kinds of Work.
ir 1000 shiDglea allow 3Ho 5 pounds 4<I. naila, or
1000 laths about i
1000 feet clapboarda
1000 " covering boards . . .
1000 " " "...
1000 " upper floors, sq. edged,
1000 " "
tfuwi " " ( matched and 1
^*" 1 blind nailed (
1000 " " "
10 partitions j^j,,jj,j,gf
1000 " furring, 1 by 3 . . .
1000 " " 1 by 2 . . .
1000 " pineflniBb ....
"ity 'plain work' ia meant stralgliC Burfauea (likeu]
tinil ceilings], witliout regard to tlie slyle or qualUyo
Upon (be job. Any panelled worli, whether o:
run with n inotilJ, would be rated by the foot si
" Different metliods of valuing plastering find favi
portions of the eouutry, The following general r
to be equitable and jusl to all parties: —
'^Flrst, Measure on all walls anil ceilings the s
plastered, without deducting any grounds (
extent than seven superHcial yards,
" Second, lieturns oF chimney-breasts, pilasters,
of plastering lesa than twelve Inches in width, i
Inches wide; and wliere the plastering is finished down
Hurbase, or wainscoting, add six inches to height of wal
" Third, In closets, add one-halt to the measuremq
ceiiinga, and soffits of stairs, add one-half to the a
circular or etlliiticHl work, chat^ two prices; dotM
I'eiiings, three prices. 1
" Fourth, For each twelve feet of interior work.dou
tlie ground tliui the first twelve feet, add five per ceoB
work, add one percent for, each foot that the work 9
the first twelve feet. I
MEMORANDA FOR ROOFERS. o29
Useful Memoranda.
*he following facts may often prove of use to the plasterer: —
>ne hundred yards of plastering will require fourteen hundred
is, four bushels and a half of lime, four-fifths of a load of
d, nine i)ounds of hair, and five pounds of nails, for tM'o-coat
pk.
''hree men and one helper will put on four hundred and fifty
ds, in a day's work, of two-coat work, and will put on a hard
sh for three hundred yards.
I load of mortar measiu*es one cubic yard, or twenty-seven cubic
t, requires one cubic yard of sand and nine bushels of lime, and
1 fill thirty hods.
L single load of sand and other materials equals one cubic yard.
twenty-seven cubic feet; and a double load of sand equals twice
t quantity.
L measure of lime is a single load, or cubic yard.
i bushel of hair weighs, when dry, about fifteen pounds.
3iIEMORANDA FOR ROOFERS.
Slate Roofs.
The pitch of a slated roof shouUl be about one in height to four
length. The usual lap is about three inches, but it is sometimes
r inches. Each slate should be fastened by two threepenny
:e-nails, either of galvanized iron, copper, or zinc. On roofs of
-houses the nails should be of copper or yellow-metal.
L square of slate is one hundred superficial feet, allowances
ng made for the trouble of cutting the slates at the hips, eaves.
nd chimneys, etc. The sides and bottom edges of the slates
uld be trinnned, and the nail-holes punched as near the head
possible. They should be sorted in sizes, when they are not all
>ne size, and the smallest placed near the ridge. The thickness
slates varies from three-sixteenths to five-sixteenths of an inch.
I their weight from 2.6 to 4.53 pounds per square foot.
lUastic Cement. — In first-class work, the top course of slate
ridge, and the slate for two to four feet from all gutters, and one
t each way from all valleys and hips, should be bedded in elastic
lent.
loofiiJ/^-Papej'. — Koof-boards s\\ovM \>ci con^x^O^ V\^\ v^\^s^
wo thicknesses of tarred felt roofiug-papeY,\ifeio^^ W\vi,«N»Xfc^
Xo dry or rosin-sized felt should \>e M^feA ow Yc>oi'&. ^
:);50
MEMORANDA FOR ROOFERS.
Flasliiiigp*.— By *' flashings" are meant pieces of tin, zinc, or
oopiHT, laid over slate, and up against walls, chimneys, copings,
etc.
Coiiiitor-tlasliiiigrs are of lead or zinc, and are laid I)etweeD
tlh' courses in brick, and tiu^ned down over the flashings. In flash-
inj:; against stone-work, grooves or reglets often have to 1h» cut to
nM'eive the counter-flashings.
C'lose and Open Valleys.— ^1 close rdllci/ is where the
slat I' are mitre J and flashed in each course, and laid in cenienL
In such valleys no metal can be seen. Close vallevs shoiiUl only
hv used for pitches above forty-five degrees.
.1/* npcH Kdllci/ is where the valley is formed of sheets of copper
or ziu<* fifteen or sixteen inches wide, and the slatt* laid overtliese.
Rule for computing: the Number of Slates in a
Square.
Subtract three inches, or the amount of head-cover, fi-om the
leiijilh of the slate, nmltiply the remainder by the width, and
divide by two. This will give the nmnber of square inches covered
per slate ; divide 14,4(X) (the number of square inelies in a square)
!)> the inind)er so found, and the result will be the niunber of slates
rt'i|uiiTil.
The tnllowinic table ijjives the number of slates per square for the
iisiial >ize>. allowiui^ three inches for head-cover : —
\i .Mi?i:i: or Slatks vvai Sqiaiik.
Si/.c, ill
; ri(
ci's per
Si/.c. ill
I'lt'ct'H ])('r
Size, ill
Pieces jwr
ilu•ln•^.
fi(
jiiai'i-.
iiH-lu'H.
H(|uart'.
inches.
wjuare.
• ■. ■ IJ
.'»;;;;
s < 16
•J77
12 X -JO
141
: • IJ
4:)7
'.t ^ IH
246
14 X' 2(>
121
^ • 1-J
,
4'M)
111 X irt
221
11 X 22
1:57
',• • V2
.■'„'>.'>
'.t ■ IS
213
12 X 22
126
7 ■ 14
:i74
1(» ^ IS
W2
14 X 22
108
s ■ 14
:527
\1 ' IS
lOO
12 X 24
114
H -■ 14
1
21»1
10 X I'O
im
14 X 24
98
lu - 14
1
'itil
1 1 X 20
1;)4
IG X 24
; 86
riic \vri«,^ht of slate per cubic foot is about 174 pounds, or, per
(Uare t"c)ot of various thicknesses, as follows : —
ThickneHH, in inches i
Wciuht, in pound» 1-?1
:i.
1
3
1 »;
4
K
2.71
3.62
5.43
i I
Tlw weight of slating \a'u\ pev ^v^vv^t^^ loox. o\ ^\vc\^M5fe <i,w«d
win, of course, depend ontlve sUe \vsoa\. '^\v^ >«v\^xv cA \^\s^
MEMORANDA FOR ROOFERS. 531
!, three-sixteenths of an inch thick, for exanii»l«*. i»**r ««iuare
of roof, would he 5..S<> pounds.
a experienced roofer will lay. on an average, two sMiiiarvs «>f
5 in ten hours.
pdinary roofing-paper weighs ahout tift»vn poiintls jn-r JM^nare.
averages ahout fifty pounds in a roll.
t the present time |1884| the additional ro<Jt of layinj: >hiU- in
tic cement varies from thirte«^n to fift»*en jH'r cent.
Sliing^Ies.
he average width of a shingle is fcnir inclu>« : lu'iir*', \vli»'n
igles are laid four inches to the weather, earh shiiiirl*' av»-raL;»**«
een square inches, and IHKj are required for a *;<|uare of rnotinj;.
If 4i inches to the weath«'r, 8<K) will cov»t a sijuare.
5 '* " •* 720
5i ** ** •• CuV) *'
s is for common gable-roofs. In hip-roofs, where tli«* shiiiuh's i\ vo
more or less to fit the roof, add five per cent to abovr fimiifs.
carpenter will carry up and lay on the roof from fiMccn Inin-
l to two thousand shingles per day, or two S(iiiares in twO
ires and a half of plain gable-roofing.
ne thousand shingles laid four inches to the wcatlicr will re-
•e five pounds of shingle-nails to fasten them on. Six pounds
ourpenny nails will lay one thousand split pine shingles.
Roofing-Tiles.
iles are thin slabs of baked clay. They an; extensively used in
ope for roofs, gutters, and house-siding, and, to some extent,
his country,
lain roofing-tiles are usually made i of an inch in tln<*kness,
inches long, and i'>\ inches wid(\ They weigh from 2 to 2.1»
nds each, and exjmse about one-half to the weather. 740 tiles
er 101) superficial feet. They are hung upon the lath by two
pins inserted into holes made by tht^ moulder. Plain tiles are
f made with grooves and fillets on the edges, so that they
laid withoiU overlapping very far, the grooves leading ti»o wafj»r.
8 is economical of tiles, and saves half of t'
jeet to leak in drifting rains, and to injury h
•aij-tjles, first iiseil in Flanders, luive
9n and hein*j: overlapped by, the
532 MKMOKAHtit]
Tlwy are made 141 '•>' '"ii esixw tini UicJips t
weigh from r. Iu6i iioimils (wli, l7lli-ovnrllll»s<|u«t» feet ot^
Crown, riilg^ liiji, am) \t\lvy tilea aif seiui'-cyUudriail, |
nieuts of L'ylin<It^rs, ii»^1 for tlie piirtwses indicated. A gul
lias beeii introUui-ed in Eiiglaiiil, forming ttie Ioh"^ eouru
nalli'il to the lower sliealliing-l»oiird or lalli, |
Siilliig-tik» are iisetl as a substitute for weatlie.r-boardingii
ait! made in tlif lu wheu moulding, and tliey are ncvurMl lo tl
by flut-lii-aJed nails. Tbe gage, or expostnl fan*, is soil
liidniilwl to represent courses of brick. Fine ntortnr ii iiitr
Iwtween lliem wLeii tliey res! uiion each otlier. Siilliig-d
sumetitrtes called " weatlier-tiics" and ^' matkeniBtical tiles."
names are derived from their exposure or markings. Tl
varioiisiy formed, having curved or creuated edges, aail 1
ornaments, either raised or encaustic.
TIw g1aie<l tiles are inferior to slatie, as liiey iinlii1)n alxn
aevenlli of their welglit of water, and tend to rot the ialli oo
liiey Hre laid. Good roofiug-aiale oidy lmbil>es one two-lnin
piirt of its weight, and is neariy waterproof.
Tin Roofs.
[From " C'arlienWii' and BulUtore' Journal."]
A tin roof pitjperly put on, and kept properly painted, »
alKiut thirty yeai'H. A tin roof o<i<rht not to be painted for t
time until it has been on about tiiirty days, so as to get tiie
off tlie tin ; and ail the rosin should lie carefaily scraped off
it is sometimes necessary, on building where there li
didnpness or steam, as stables, )>lacksuiltii-ahops, round 1
eU'.. to paint tlie tin one toal on tlie under side before,
After llie roof lias l>een painted tlie first coat, il should be't
again in alwtil a year, and, after tliat. once in three ]
'i'iien.' Ale two kinds of tin ; one, the coating of which it
tiiat la, the tlu pivper, sometimes called " bright tin ; " th|
the coating of whlcli is a composition, port tin and part iei
is called "tern," "leaded," or "roofing" tin. This htst la
clieaper than the "bright," and will not rust any quicker;
tliink, as do many others, tiiat (lie sulphiu* in otu- softMMial
eats through tlic "leaded" coating sooner tluiu thrM
"tinned."
Ottin llicre are two a^iea, \(1 \rj U Inches and 14 by stf
jT^des a.6 to l\i\ckne9ft, IC v\it\\^. kq& VS.'OB«i\l
steep roof |o\ie-a\x.W\ pVW^ ov '
if liigh liV. ■w\\pre \v\.V\e «m
01 tin tl
PLUMBING. 538
low down, where much smoke will get to it), put on with a stand-
g groove and witli the cross-reams put together with a double
ek, makes as good a roof as can l>e made.
For flat roofs, the lK»st roof is made with the IX (10 hy 14)
bright*' tin, laid with cleats ; hut the others make gootl roofs,
id any of them will last twenty-five years at least.
All tin roofs should l>e laid witli cleats, and not by driving tli<'
lils through the tin itself.
PLUMBING
The following is a portion of ** An Ordinance for the IJegnlatioii
f Phunbing,'* passed by the Boston City (»overnment, March,
?83. It is recommendeil as worthy of observance by architects
id plumbers elsewhere.
"Section 3. — Every building shall be separately and independ-
itly connected with the public sewer when such sewer is pro-
ided, and, if such sewer is not provided, wfth a brick ami cement
?sspool of a capacity to be approve<l by the inspector.
**Sect. 4. — Drains and soil-pipes through which water and sew-
ge is used and earned shall be of iron, when within a building, and
)r a distance of not less than five feet outside of the foundation
'alls thereof. They shall be sound, free from holes and other
efecls, of a iniifonn thickness of not less than i of an inch for a
iameter of four inches or less, or j'V of an inch for a diameter of
ve or six inches, with a proportional increase of thickness for a
reater diameter. They shall be securely ironed to walls, iaid in
vnches of uniform gmde, or suspended to floor-timbers by strong
on hangers, as the said inspector may direct. They shall Ih» sup-
lied with a suitable trap, placed, with an accessible clran-oiit,
ther outside or inside the foundation wall of the building. They
lall hav(? a proper fall towards the drain or sewer ; and soil-pipes
tall, be carried out through the roof, open, and undiminished in
ae, to such height as may be <lirecte«l by the said inspector-, but no
il-pipe shall be carried to a height less than two feet above the
of. Changes in direetiou shall be made with curveii pipes, and
iinections with horizontal pipes shall be nuule with Y branches.
**.Sect. i}. — Rain-water leaders, when <()iiiiected wiili sdil or
ain pipes, shall be suitably trapped.
*'.Skct. 6. — Sewt'i\ soil-pipe, or \vasVe-v\v*.' \v.wV\\^vw*» -^wxWxxviV
constructed of bv'nk, slieet-niriul, ov e'AvV\w\\v<-^\«j,'8^>^"^^^'^'^^'^'^'^'^^
'S shall not ho iisi'tl as vucli ven: WiUoys.
• )•> I
PLUMIJING
"Skct. 7, — Iron piix^s, Ix^fore Iwing put in i)laco, shall befinl
lc?%ltMl by the water or kcioseiio lest, aiul llieii coalinl inside and
out Willi coal-lar pitch applied hot, or with paint, or with some
e(|iiivah*nt suhstanee. Joints shall 1m> rmi with iiioltcii load, anil
t horou^hly ealked and made tight. Connections of lead pipes with
iiMii pijM's shall l)c made with bi*ass ferrules properly soldereil and
raikfd to the iioil.
••Sk(T. s. — Every snik, hasin, bath-tub. water-closet, slop-hop-
[MM. jiikI each set of trays, and every fixture having a waste-pipe,
shall hi* furnished with a trap, which shall be placed as near as
practitiihle to the fixture that it serves. Traps shall be prolet'ted
from siphonage oi air-pressure by special air-pipes of a size not less
than llic waste-pipe ; but air-pii>es for water-closet traps shall l*
of not less than two-inch bore foi" thirty feet or less, and of not less
than three-inch bore for more than thirty feet. Air-piix»s shall be
run a> direct as practicable, ami shall Ik* of not less than four-incli
bon* where they pass through the roof. Two or more ali-piprt
may be connected together or with a soil-pipe; but, in every case of
connection with a soil-pipe, such couuectioii shall be above tin f-
upper fixture of the Hmilding.
••si:( T. 1>. — Drip or overflow pii>es from safes under water
cl(>Nrt> and other lixtures, or from tanks or cisterns, shall l)e run
to soiin- pla( (' ill open siglil ; and in no case shall any such pipe
lie couui'cied tlireclly with the drain, waste-pipe, or soil-pipe.
••M.( T, 10. — Waste-pipes from refrigerators, or other recepta
clr^ in which provisions are stored, shall not be connected with a
drain, soil-pip*', or other waste-pipe, unless such waste-piix^s are
provide. I with tiai)s suitably ventilated; and in every case llieif
sliall Im- an ojK'n tray between the trap and refrigerator.
•■ Sh< 1 . 1 1. — Kveiy water-closet, or line of water-closets, on i\w
saint' tln(»i, >hall be supplied with water from a tank or cistern; ami
til.' t!u>liinii-[)i[)e shall not be less than one Inch in diameter."
Hytlraulies oi Plumbing.
The followinii i)anes on the hydraulics of plumbing are, withlbe
(•((useiit ot the author, taken directly from the fifth edition (I81M)
of an rxcellcni work on " II(»use-l)rainage and Water-.Service,"^by '
.lames C. IJayles, Ksc)., editor of *' The Iron Age" and ** The Metal-
Worker.'^
If'ff/rr Js piacticaUy vm \\wo\\\vyv^'s^A>V ^^^^^^^^ ^^\%V\vu«j^^ at llie
' l'uhli..hvd hv DaVKl ^V^Uum^*,HV^\\ovvvW^V^^^^^^>^v^;^ ^^^>^. '\\.^ '^>^<5.
rocotiimt-mi^ thirs wot k lo iiienvv«.'cvs •.vm\ V a\w
'«e on til,- /nini.hiujjj i..! vivy 'AmV cov\uV\'i \uu\>^t..
PLUMBING. 53;")
rage temperature of sixty dcgrws F., al)ont 02.3 pounds to tlio
lie foot, and 8.3 pounds to the gallon. These figures are sul)jert.
$Ught variations incident to changes in teniiMM'aturc.
i colunni of water twelve inches high exerts a downward press-
• of alK)nt 0.4:J of a pound to the 8(|uare inch. A colunui two
I high exerts a pressure of about ().tM\ of a pound, or just twiei*
t exerted by a cohunn oiu' foot high. This pressure per square
h, due to head,* is irrespective of volume, or any thing else
'ept vertical height of column. With these figures in mind,
calculation of the pressiu'e per square inch due to any head is
imple matter. The following rules will be found valuable for
erence ; —
To Fixi> PiJEs.sruE IN Poinds pek ►Squahe Inch kxeuted
A Column of Watei:. —Multiply the height of the colunni,
feet, by U.43.
To FIND THE Head. — Multiply the pressure, in pounds per
lare inch, by 2.31.
Pressure oi Water. — The weight of water or of other
aids is as the quantity, but the pressure exerted is as the ver-
al heis:ht.
Fluids press equally in all directions: hence any vessel or conduit
itaining a fluid sustains a pressure on the bottom tHjual to as
my times tlie weight of the column of greatest height of that fluid
the area of the vessel is to the sectional area of the column.
Lateral Pressure. — The lateral pressure of a fluid on the
i»s of the vessel or conduu in which it is contained is cfiual to
.» product of the length multiplied by half the square of the
pth and by the weight of the fluid in cubic unit of dimensions.
le following formula is simple and satisfactory : multiply Uw.
mierged area in niches by the pressure due to one-half the depth.
"submerged area " is meant the surface upon which the water
»sses ; for example, to find the lateral pressure upon the sides
a tank twelve teet Uniii by twelve feet deep : 144 X 144 = 2()T.'J()
lies of side. The pressure at the bottom will be 12 X 0.4:] = .5. 10
.inds, while the pressure at the top is 0, giving us, say, 2.() imuiids
the average : therefore 20T.'>0 x 2.0 = ;");]*) 14 pounds.
f>iscliarge of Water. — The quantity of water discharged
ing a given time from a given orifice, under different heads, is
U'ly as the square roots of the corresponding heights of the
ler in the reservoir or conlaining vessel above the surface of
orifice.
Iniall orifices, on accouni of fricliou, d"vsQ\\^Y2,'i \)XQr^\\\QWi^s\N
.1 beuJ uf ». If IT equals th«- Iv.iuhl Ihal \h*; wvvVct \\*o% vv\>ov v.> \\\v' vixVCv^*.'
536
PLUMBING.
It'ss than tlioso which aro larger anil of the same shape nnder the
sain«» pr»*ssiin».
rin-iilar ai)ertiire8 are the most efKcacioiis, having less surface in
pn>iK)rtion to area than any other form.
If a cylindrical horizontal tnbe through which water is disoliargei
l)«* of jrrcater length tlian its diameter, the discharge is mncli in-
<Teaseil. It can be lengthened with advantage to four times llie
diameter of the orifice.
To FIND THE XUMBEK OF rXITED-SXATHS GALLONS COS-
TAINED IN A FoOT OF PiPE OF ANY DlAMETKlL — Square tllC
diameter of the pipe in inches, and multiply the s<iuare by 0.(HU8.
Velocity of Flow of Water. — Water which hasaoliance
to flow downward does so with a velocity in exact proportion to its
liead. Tlie following table gives the velocity of flow of water due
to heads of fmm one to forty feet : —
Vrbn'Utj In Feet per Second due to Heads of from 1 to 40 FceM
Head.
o.r)
1.0
1..')
•j.o
•J..'>
:;.()
4.0
4.:.
:..()
."i . .')
r..<»
♦>.:"»
7.!)
".')
H 0
S..'»
•.».<)
10.(t
Vfloeity.
lli'ud.
5.67
10.5
8.0-2
ll.O
9.82
11.5
U.34
12.0
12.68
12.5
13.89
13.0
1.'>.(K)
13.5
10.04
14.0
17.01
14.5
17.93
15.0
18.81
15.5
i<».n4
10.0
20.44
10.5
21.22
17.0
21 .90
22. OS
2; '..38
24.00
24.72
25.36
17.5
18.0
18.5
19.0
19.5
20.0
25.98
26.60
27.19
27.78
28.35
28.91
29.46
30.00
30..54
31 .0»)
32.08
32..")8
:'»3.oO
33.55
;U.02
34.49
:U.96
35.41
35.86
Head. | Velocity
20.5
21.0
21.5
22.0
22.5
23.0
23.5
24.0
24..T
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
36.31
36.75
37.18
37.61
38.04
38.46
.38.88
39.29
39.69
40.10
40.50
40.89
41.28
41.67
42.05
42.44
42.81
43.19
43.56
43.92
Head.
Veloctty.
30.5
31.0
31.5
32.0
32.5
:i3.0
i«.5
34.0
34.5
35.0
35.5
36.0
36.5
.37.0
37.5
38.0
38.5
39.0
39.5
40.0
44.29
44.65
45.01
45..37
45.72
46.07
46.42
46.76
47.10
A'M
47.78
48.12
48.46
48.78
49.11
49.44
49.7t)
50.08
50.40
50.72
In pliiinhiiig-woik wo <'aniiot secure this velocity in the flow of
water through pipes, l)ecause of the friction which constantly tends
to diniinlsli it. The longer the pipe, the greater the friction and
constMiucui retardation of tlie flow. In the followmg table we have
the hinid of water consumed by friction in pipes one yard long and
from one to four inches in diameter. This table shows the headol
water reciuired to produce a given flow per minute. By means
of tlie rules given on p. ">o8 it is made applicable to any length o!
;>//>c; and a variety of prob\e\\\s voV^iuvj; to lengths and diameter
of l)i}H\ </i.s(]iarge in gaUous, a\u\\wM\\w\^^v, wtt^^N^Xx'iW.
^ WoxV \\\i\v.\\\ \c.-
PLUMBING.
/>37
ad of Water ronxuiiied by Frh'tion in Pipfn out. Yard Lomj,^
Diameter of
' THE Pipe, in Ix< h»>.
1
U
S
Water,
Z
IN Feet.
1
Heai^ of
0.0041
0.00054
0.00012
0.00iK»42
0.rNiooi6
fi.(Ml(i(Nl|
0.0164
0.00216
0.00(k5l
0.000168
0.000067
fi.((N4i:ii:i
4i.(r4Ni|t;
0.037U
0.00487
0.00115
0.000379
0.<irK)I52
IM>4l'H»7(ii
it.f¥*Ht.:ti
0.0658
0.00867
0.00*205
O.00O674
o.jirirr27i
(l.<M4l]J.',4l
(Mlf4lll''.l
0.10-28
0.01354
0.00321
0.00H)63
0.(NM»42:i
o.iNHii'.i:>
O.lNNlllNI
0.1481
0.01950
0.0IU63
0;4»01517
O.OfHM'ilKi
O.HN»2ll2
O.OOOIll
0.2016
0.02855
0.006.30
0.002061
(MKi4ik:ui
(l.dtKC'Xi
O.OOOl'M*.
0.2633
0.03468
0.00823
0.002696
o.(ir)H»s4
O.lKMI.'Ol
O.iKNrJ.'iT
0.3.^33
0.04389
0.01041
0.00:J413
0.(iOI:i7J
<i.ii('<tt'i.;i
u.t**t:;2-'
0.4110
O.OMIO
0.01286
0.004210
O.OOltMMl
{i.HHiTs;;
0,(>.>4lJU|
1.64
0.21670
O.a5140
0.0>«Vh)
li.(Mr>770
u.fMi .l;
n.'4i|t,4Ki
.1.70
0.48770
0.115
0.f«7J»20
0.01 .'.J
t).ii(i7(i7
(i.(iti:',i;|u
6.58
0.86700
0.-205
0.0674-20
o.iniTi
(».nl2.'i;;
o.oot;i;;o
10.28
1.35
0.:«1
o.la'iri
(MUJ:;
(i.ni'.Os
o.oiooio
14.81
1.95
0.46:i
0.1.517
OAH^ti.k
•j.irihjp
0.014 Wt
20.16
2.65
0.630
(».2(»U
O.OXid
o.uts;','*
O.Ol'.iliiM)
2rt.:j3
3.46
0.82:i
o.2*K»6
O.IOM
o.n.'>oi4
o.«»2.',7..'o
:«.:«
4.38
1.041
0.3413
0.i:i72
o.(»»i;{|«;
o.o.{2.V.o
41.1
5.4
1.28
(».421
0.1 tiO
o.(»7'»
o.Oh'l
49.7
6.5
1.55
0..509
(».20.'i
1 1.094
0.0 |H«;
59.2
7.8
1.85
0.606
0.24:;
0.112
0.o.i7n
69.5
9.1
2.17
0.712
0.2WJ
0.1 :t2
0.(Mi7'»
80.6
10.6
2.52
0.825
0.3.32
(J.153
o.07hh
92.5
12.1
2.89
0.948
o.:i81
(M76
O.OINii
10,>.3
13.8
3.-29
1.078
0.4.13
0.2(10
0.102K
118.9
15.6
3.71
1.217
0.485
0.22«1
o.lK.I
133.3
17.5
4.16
l.:j«Wi
(».549
0.2;'.:;
o.i:{i2
148.5
19.5
4.64
1..521
(».61 1
(».2H2
(• i4.'>o
164.6
21.6
5.14
1.68:.
0.677
o.:u;!
O.U'p(»7
181.4
23.8
5.67
1 .k:)K
0.747
o.;w:.
0.1772
199.1
26.2
6.-22
2.039
0.819
U.'M'.i
0.MM5
217.6 *
2H.6
6.80
2.229
O.SIMJ
0.414
0.2126
2-57.0
31.2
7.40
2.427
0.975
0.4;. 1
0.2:1 U
2:)7.1
33.8
8.03
2.6;j.3
1.0.5K
0.4W
0.2.'ill
278.1
36.6
8.69
2.848
1.1 4:>
0.!VJ«.»
0.2716
2«»9.9
.39.5
9.37
3.071
1 .234
0..571
0.2*.t2«»
322.6
42.4
10.08
3.:{o:i
l.:i28
0.614
o.:'.i;iO
346.0
45.5
10.81
3.;'»44
1.424
O.ImS
o.:t;7M
370.3
48.7
11. .58
3.7^»2
l.:)24
(».7o:.
o.;mii7
.395.4
,52.0
12..%5
4.019
1.627
O.7.V.'
o.:'.ir,-j
421.3
55.5
13.16
4.21 :>
I.7:t4
O.W>2
0.4 1 1.-.
448.1
.59.0
14. go
4.589
1.844
O.S.'^J
o.4;;7»i
475.6
62.6
14.87
4.871
1.9oS
O.tKJ.'i
0.4«".4.'»
.504.0
66.3
15.7.-)
.5.162
2.075
O.O.'iO
0. I9j:i
.533.3
70.2
16.66
5.461
2.1W
1.01:.
o.:.J4s
563.3
74.1
17.60
5.769
2.:j:i«J
1 .(►72
o.:.:.o2
.594.2
78.2
18.57
6.085
2.44<i
1.i:n
o.fiKo;;
625.8
82.4
19.56
6.408
2.. 576
1.191
0.('.1I2
6.58.4
86.7
20..57
6.742
2.710
1.2.53
o.r.4:io
691.7
91.0
21.61
7. 08: J
2.H47
i.:n7
(».67a.'»
725.8
95.5
22.68
7.43:?
2.988
i.:i82
0.7089
760.8
100.1
2:J.80
7.790
3.i:m)
1.448
o.74:u>
796.6
104.9
24.80
8.150
3.270
1.516
0.77SO
833.2
109.7
26.00
8..530
3.4.30
1.586
0.81.30
870.7
114.6
27.'20
8.910
3.580
1.667
0.8600
909.0
119.7
28.40
9.300
3.740
1.730
f
948.0
124.8
29.60
9.700
3.900
1.806
988.0
130.1
30.HO
10.110
4.060
1.881
JO-Jfi.7
UVk4
32.10
! 10.530
\ Ai.*r»
\\r'-
1 RoxV l1y<\rau\Vc«.
;)3S IM.UMBIXCi.
Tlio practical application of this table will W fouml in the fol
lowing rules : —
To F!xi> THE Head of Wateij, aviien Diametek asi»
Lencjtii of Pipe, axd Xumbek of Gallons disc HAUOEf* peh
Mini Ti:, are known. — In the al)ove table the head due to a length
of ()n«» yard is found opposite the number of gallons. Multiply tlial
nunilxT by the given length in yards, and we have the required head
in feet. Thus, to tind the head necessary to deliver i:>0 gallons per
minute by a j)ii)e 4 inches in diameter, rM) yanls long : opix)site 190
i^allons in the table, and under 4 inches in diameter, is 0.(>70, which,
nudti plied by HOO, gives 339 5 feet, the head souglit.
To FlNf) THE DIA.METEK OF THE PlTE, WHEN IIeAI), LeNGTH
OF IMte. and the NrMHEi: of (Gallons DisciiAKCiEi) peii Min-
itj:, AUK KNOWN. — Divide tlie head of water in feet by the length
of the pipe in yards, and the nund)er nearest to this in the table
opposite the number of gallons will be found under the i^eqiurwl
(liametiT.
To FIND THE Xl'MBKU OF GALLONS DISCHAIUJED. AVI! EN THE
Head, LENcrni of Pipe and its Diameter, are known.— Di-
vide the head of water in feet by the given length in yards, and the
ne.'irest number thereto in the table under the diameter will be
t'ouiul opposite the re(|uired nund)er of gallons.
To iiM) THE LENfrrn, when the Head, Xumher of Oal-
I,0.\-« I'll: MlMTK. AND DlVMETER OF PiPE, ARK KNOWN. —Di-
vide til*' Ljiven head by the head for one yard, found in the tahlt
uudt'i- the ixiven (liame,ter and opposite the given number of ir^l
lolls. ;nul the result is tiie required length.
'I'lie actual discharge of pipes is easily calculated with approxi-
mate accuracy bv Proiiv's fonuula. In using this fornuda. find tlic
discliai'm' in gallons ])er minute by nudtiplying the head in indu's
l>y the (11 nncter of the pipe in inches, and divide the i^roduct by
/// X (]\
the lenLiili ot the pipe in inches ( - — 1. In the following tabK
tind the number nearest to the cjuotient thus obtained in the firsf
i'olunin, and the dischari^e in gallons per minute will be foiuul
opposite it, under the diameter of the pipe used.
The dis('harg<^ of small pipes may be calculated with sufticieni
accuracy for practical purposes from the following convenient
tal)le, sliowiuii: the <piantity of wati'r that will flow through a pip'
')(/(} /ec/ lonii: in '2A hours, \\\U\ a pnvssure due to a head of tt'ii
HncU "... l.ir,0 - \ V--^; ';^ ■ • ^1^^ ^-
PLrMHINO,
Tiisthftr^e of Pipes hi/ Prnny'K FormtiUi.
I>ljlHKTIiR or
I " I ' ' •' ! ° I " I ' I ' I
Ml
UlU 1 1M iJMb
nvm 1 981 iM*
4 DttlU
06W. OBSIU 1J6J IttJU J55
OMtt 1-MI 1 RhI i4V< 110
I HL23 jiajw
HI IU91 (
lint n;: lelpniiiiieil 11 ] lessuii hit lo 1 i.n I uilh uliid 1i lias
to (teal ail 1 tlic SI4C of II \\n needed I o I sclinice n ^ncn | laii
iity ma giieii time, tlic p]iiiiil)«r iiuisl enleiiliile tin sl]iii!;;ih nlikh
his piiu' niu'.L iWKsess to i-eslst IliU pressiiic iiiider all I'ciiKUtioiis.
Tills lie iieeil not iln with nbsoliili> acriirary, for tlic reason lliat li'.'
liliist l1Sl^ llii> pipe lie fiiiiU in tlie market ; but Ilie strenglli of tlie
«izea In the niarkel is kiumii. aii<) on llie basis o( this knouleilue
be can (l«teni)liie tlie welglil of pipe lie re<|iilres. In nil rhcIi eai-
enlatioiis, lionevcr. tlieiv slioulil be a lilH'ral nmi^iii fur aaf<>ly.
'Hie pipe niay conude. external iiiHiieiices may weaken it. nivl
extraordinary pressiii'es may be bruiiglil tulienr upon it, — as by the
sndJeti doting of a rock, ivliieli. owiu5;\.ol\\e\\\i;owi\i\i«aMif«i»Mw*'
of water, causes it lo strike a povi<tYi\\\ hVvx.-Xwv \.<--> Ww «,>j!>;
trresleif iiiojiietJIiitii of iIn' eiillio i-iAivmtt (i^ \\!Ai.'V "v^ *^
MO
n.t'HRIKO.
Tliia uflcn Inints pipe* which are *ntp1y ■Irong to retiitkpN
ileitl more llisn tlic iioniiKl preuure la wliiuli Lliey are tnbJecUi
Otiiei' cauae* abo operate ta Increase Che preanire, and tax tfc
rcjIsUng power*, of llic pipe; aiid tl uiiut be strong enongli to bci
(liMit wllboul (training. The following table give» the tebllMi o
lize and thickiicw to strength In staiulanl lead pipes. Tbite h
urea are compiled from tlie tesulta of careful tests.
IKe^U and Strength t)f Xrad PfjMa.
e Hi?"-
?i
IS
MEMORANDA FOR PAINTERS. 541
'Oiig^t-iroii pipes suitable for water service range in
ter ifroni half an inch to sixteen inches. The tables on pp.
)5, show the weiglit of the various sizes manufactured,
sre. Tasker & Co., of the Pascal Iron-Works, Philadelphia,
•t the pipes which they manufacture to the following tests: —
-half to one and one-fourth inch, butt- welded, iWK) i)ounds
idic pressure i>er square inch.
and one-half to ten inch, lap-welded, 500 pounds hydraulic
ire i)er square inch.
?tically they are strong enough to bear any pressure with
the plumber has to deal. The same is tnie of drawn brass
»pper pipes.
e pressures to be dealt with in American plumbing prac-
ary through a wide range. In cities supplied by what are
1 as gravity- works — i.e., where dependence is placed on
il head at the distributing reservoir, as in New York — the
ire of water is often very light.
»re pumping machinery is used, and a high head is main-
in tall stand-pipes, or the pumps deliver directly into the
, we sometimes get pressures of one hundred pounds to
uare inch, and upward.
MEMORANDA FOR PAINTERS.
[From '• liuilUerrt' (luide and Price Book."]
Puiiitiiigr.
iters' work is generally (\stiniate<l by the yard, and the cost
(Is ui)on the number of coats applied, besides the quality of
ork, and the material to be i)ainted.
! coat, or jyrintiiifjy will take, for 100 yards of painting, 20
Is of lead and 4 gallons of oil. Two-coat work, 40 pounds of
nd 4 gallons of oil. Three-coat, the same quantity as two
; so that a fair estimate for 100 yards of three-coat work
be 100 pounds of lead and 16 gallons of oil.
gallon priming color will cover 50 superficial yards.
"- white zinc "
" white paint
" lend color
" black piiint '*
stone color ''
a
50
i<.
((
44
a
((
rA>
\,\
«.<.
44
(
vv
vv
-4 3tip<'rticial yanls
IMHIW- GLASS.
yftllKWlwinr. will c
lihvc. ciilor ''
(,Teen iMini "
briglit emeraltl green '■
bronze green ■'
e pound o( paint will cover about 4 siijM'i'lii.'iiil yanla rip' fin
t, anil about 6 each addlttoiial i^oat. Une i>oiiiid of iiuUy, h
stopping, (.'very 20 yurds. One gallon of tar and 1 pound uf iilu
Mill cover ,J2 yards superficial tliu Drat coat, anil n yaoil* m
Additional coat.
A square yard of new brick wall requires, for tlte lirat vuat '
liHint In oil, j of a pound ; and for the second, 3 poiuids ; andfc
the thini, 4 puunds.
A (lay's work un tlie outside of a building is lUO yards ul Sr
coat, and SO yards of eitlier second or third coat. .In ordmB
door, luchidhif; casings, will, on bolL sides, make S to 10 yacdsi
painting, or about .5 yards to a door without the caBiU]^ An onl
nary window niukes about 2^ or ti yards.
Fifty yaiilsof common graining is a [lay's work for a graineru
one man to rnl> in. In imlnting blinds of ordinary size, 1^ i* ■ h
day's work for one coat, and i) iiounds of lead and 1 gallon ot «
will paint I hen I.
■WINDO'W.GLAaS.
Polialied FreiR-li plate wiii<luu->g:laK8, which Is roit
sidered to 1>e the highest grade of window-glass iii the market, mi
be abtaine<l in lights varying in size fi-om a piece one inch mtm
to a Ilglit eight feet wide and fourteen feet long. Owing to It
extra cost of rolling targe lights, the price per s<juare foot n( lu]
lights is sometimes twice that of smaller liglits; so lliat clie coMt
plate-glass must beestlmatt^d by a price-list, giving tliecotitoirevs
different size of light. Such a price-list is given below. 'FblaS
remains the same from year to year, and Is known as the "itMM
ant" list for polished plate-glass. Tlie nuctiiations in the prIcvM
glass are arranged liy means of a illscoiint, which is tlir sa
all sixes. At the present tlini' the discount on large lota of pU*-'
glass Is a!)out lifty per i^'vit. 1
WISDOW-GLASS.
■.»M
MM
41*0
KM 1 W.
Uw
:)44
WINDOW-GLASS.
Price-List of I*tiLisiiKi> I'LATK-(ir.Ass (f'ou tinned).
SizeA. ill iiK'he«: priccH, in dolkrH and cents.
•• I
;;n
4J
44
4'i
4^
.HI
.'••J
.'.4
.Vi
.'iS
♦i«)
•iJ
04
tJS
TO
-.>
74
T'i
7S
so
s\
s';
^^
'.'0
'.*J
lO'J ,
02 i
04 '
')^
ll»
IJ
It
I-l
l^
•JO ;
• >•>
•Jt
•J'l
■J'>
:;■•
•■■>
S4»
]1.4'»
1 •-'.<».'»
IJ.T'.
i.:.4it
14.10
U.T'i
l.'i.4.'»
I'i.lO
J-J.Jt)
•j:;.lo
•j:;.'.«.'i
•Ji.N'l
Ji.T'i
•J7.:m)
•JS.40
20.:m)
:iO.'JO
:;i.o.i
:;i .'.»:i
:;j.s:>
.■;:;.7."i
;;4.»V)
;;:...")0
:;r>.4o
o7.:;o
■ {S.l.')
:;o.0">
• ;'.».o.'>
11.70
PJ.OO
j:;.'.'t
41.40
1. "..•_'. I
l«i.I.'»
17.0.)
J7.'».'i
l-^.^o
10.70
.■,0.1 10
..|..»o
■■>'.•■'.■>
■.:•,. -J.')
.■-1.1.')
.i.'i.O.'i
.i.'».'.t >
•'■7.70
.■)S.iiO
V.t.4'i
til).:;;
I
i:'>s I iil.-j.->
NO : lij.i.t
144 I i;:i.{U)
ij.i.i
14.:{i»
I.'kUo
\ •*.''*
21. SI
22.70
•24.«il
2.'>..V»
2t5.'»0
27.4.1
2S.4<)
2'.t.:J.'>
:;o.:iO
:!1.2.'>
:;2.20
.•;:;.l.')
:U.10
:;.i.iri
Sii.OO
:5s. so
:50.7.'>
4m. 70
41.»J:»
42.»>0
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44. .'.0
4.').4.")
40.40
47.:i.')
4S.:iO
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$4
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l:t.7»
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l.'i.2i>
l.'i.l(;'»
22.i:»
2:i.ir»
24.1:»
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27.150
28.10
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40.40
41.00
42.70
43.Ji')
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70.40
71.40
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74.20
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27.20
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27.35
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42.20
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47.20
48.45
49.70
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73.30
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52.05
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61.20
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07.70
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70.:iO
71.00
72.9<i
74.2(»
7n..=>0
7t).H0
78.10
79.40
80.70
82.00
83.30
84.60
90.00
92.00
93.00
31.30
32.0.)
:W).40
;Mi.75
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40.S.T
42.20
4:t:t.')
44.90
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49.<»0
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54.45
55.80
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0S.05
09.40
70.75
72.15
73..>0
74.85
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7 7..') 5
7S.95
80.30
81 .05
s:i.oo
84.3.')
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92. (M»
93.iK)
94.00
9fi.00
97.00
99.00
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41.2«t
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71.(Ki
72.40
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7.').2''»
76.7i»
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79.0O
80.y:.
82.35
8:i.80
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93.K1
94.1R'
96.«»0
97.««»
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102.0()
103.«X^
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vv
v^
WINDOW-GLASS.
60
as
u
W
JM
su
et
M
m
as
70
IB
38
«
~
4?
■"?
43
«
:
:
2
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63
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64
sa
110
00
M
BO
86
t
72
-
03
M
OS
m
63
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88
88
i^
w
74
78
■n
81
ni
89
83
«
83
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60
?J
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70
81
IS
8b
«i
b4
34
bi
94
«i
89
™
75
77
SO
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r
101
73
78
B'
M
100
10
Ta
16
91
lOS
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log
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's
:i
i
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9*
M
W
08
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131
133
91
W
9S
i
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S4
M
10.}
m
fl7
101
141
1 s
°
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g
M
143
181
m
«a
102
ISJ
too
104
IM
1 a
123
131
189
M
l«z
lis
JS7
105
136
IS)
IM
l!i6
139
36
14S
joa
IflT
111
116
138
1«
JtW
136
iw
m
11!»
lia
160
1<M
137
41
IM 1
114
m
]tX
1^7
n*
m
148
^
169
i''
140
113
i
167
78
188
w 1
138
iiiii
is'
1"
187
m
i-i
\i
\*J
v^
j,w ; ui j iJH
l£4
100
lOi
171
\™
\ ^*
i\ 1.
^^
'[
-7"7"1
«^
S8
eo
SS
AI
3i
A,
^
-.^\1
646
WINDOW^LASS.
PKIOE-Llf«T OF PoiJHIIKn Pl.ATK-i;i.AS8 {CouchtiM).
tjlzea, ill iocbeii: iiriem, in doliara.
r
1
74
76
78
1
H*
84
86
88
to <
fS
H
^
^ -
74
HI
^
1
... ^..
—
1
7«",
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^
1 ^
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—
^
. i
7h
•.»o
92
95
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1 -
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-
- .
-
- - ;
-
Mi
*.♦*-
(♦5
97
100
^
^^
^
_ 1
•
1
-
s-j
iJ
97
90
102
105
.
«
^
^
_ 1
* 1
Ki
f»7
99
102
105
107
110
^
^
,
^
1
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H4»
W
1«»2
104
107
110
112
115
M
- i
^
-
■■
KH
101
104
107
110
112
115
118
120
-
-
1
1
90
104
106
100
112
116
118
120
123
126 .
_
"
92
1(W
]<K)
112
114
117
120
128
126
129
132
^ 1
-
94
108
111
114
117
120
123
126
129
13-i .
i:i5
137 , - ,
_
90
111
11.1
« 116
119
122
125
128
131
134 '
137
140 143 1
9H
IVi
116
119
122
125
128
131
184
137
140
143 14«1
100
lli'i
1IK
121
124
128
131
VM
137
1441
143
146 m 1
10*2
117
121
124
127
130
i:»
136
140
143
146
149 ' ISJ ■
104
120
12:(
126
1-29
K0
VM
i:{9
142
146
149
152 : 1» ■
106
122
125
129
132
136
l:)9
142
145
148
152
155
158 >
JOK
124
128
131
134
138
141
144
148
151
155
158
iei|
no
127
1.10
133
137
140
144
147
151
154
157
161
IM
112
129
ia2
136
139
143
146
160
158
157
160
164
WI
114
l.'Sl
]:i:>
138
142
145
149
153
156
160
163
167
17D
110
l:U
m
141
144
148
152
165
159
162
166
170
178
IIH
V.W
140
143
147
161
154
158
162
165
169
178
m
TJu
I'M
142
146
140
153
157
161
1»14
168
172
175
179 ! 1
. 122
140
144
148
152
156
159
16:i
167
171
175
17H
m 1
VH
i4:i
147
150
154
15H
10-J
^m
170
174
177
196 ' 200 1
1 I2t\
145
149
153
157
161
H)5
169
172
176
195
199 203 1
12S
147
151
155
159
16:j
167
171
175
179
198
'202 . 207 1
i:n>
150
154
158
162
\m
170
174
178
197
201
' '205
'21U 1
l.Ti
152
166
l»iO
164
16S
172
177
195
200
204
, '209
213 1
i:m
1;54
158
hVi
167
171
175
194
198
20:i
207
•212
216 f
i:m
157
161
165
169
173
178
197
•201
206
210
215
219
i:5s
159
16:i
167
172
176
195
199
204
209
213
1 218
223
140
mi
166
170
174
179
198
202
207
212
216
'221
1 226
M'J
U'^\
KM
172
177
196
2(K)
205
210
215
220
224 21S»
144
Km
170
175
179
198
203
208
213
218
223
227 ,232
14(1
ItiS
173
177
196
201
200
211
216
221
•226
•231 23fi
US
170
175
194
im»
•204
2l>9
214
219
224
•229
234 |239
Ifxt
I7:i
177
197
202
207
212
217
222
227
'232
' -237 iii
l.VJ
ISO
194
199
204
209
215
220
225
230
235
•240 304
l.)4
192
197
202
207
212
217
223
228
233
23K
:u)2 ! 3DS I
1 ITirt
194
11W
204
210
215
220
225
231
236
'241
:km> • zvi
158
196
202
•207
212
218
223
228
234
239
3a:i
:i09 316
liVO
199
2«>4
210
215
220
226
231
237
242
307
313 331
ItiJ
201
207
212
21S
22:j
229
234
240
904
310
317 334
I«W
204
209
215
220
226
232
237
301
307
314
321 . 828
1(Mi
2tMi
212
218
223
229
•234
240
304
311
318
325 ! 332
IrtS
2i»«.»
215
220
226
232
•237
301
306
315
322
329 336
: 17U
211
217
223
229
235
240
305
312
319
326
333 310
/
76
1
i 78
1
1 80
\ H»
\
1
\ ^
\»'
\»
■'\^
1
The above table waa kindly turiAUVxeA vY.« ,.vxxW >..j \^«^*«.t^.\\\\\^ -^v^^
Bottton, Mam., Importer* and aeaxerik
^^^H^I.ASS. ^Gl
ASS t'OK SKYLIGHTIJ. ^^H
V OrtliiDiry WhxIow-aiwiH.
^^InxH is gold by Hie l>o«, whi.-h contaiiifi, n* nearly ui
S, nfty square leel, whaleTer may be tlie siae of tlie panes.
thicknesB of ordinary, or
"Bingle tliick,'' window-glaas, is
one-Bix teen til of an ini.'h
and, of "double thick," nearly
[lith of an inch.
tensile utreiiglli of eoiiinH
lU giatts varies from axxi i«ninily
) iHiniuls pur aquan; inch
and lie crufiliinK Hti't'iijJtli tmni
iiinilB to 10,000 potinds.
following tal)le gives the
miiibin- nf panes ttf «ti»<inir-;/fr(jwr
f<« OTMsMt.—
r^
iK 111
Ihiuw
«i«. 1„
Pan*
Ni'.L', III
l.l.=»
- ii»
™;h™.
bl,"-
Im^fa^^P.
hlli.
ll».h«.
lol.
g
»
2'ta
a
fl'W
K\
■J4X44
12-at
30
axxt
20
0
Iffl
sa
2X23
2S
■a
0X3«
if
2BX4U
'Jti K4H
axai
20
2ax4l>
a«n
SXffl
20" 4B
T w
30X4U
;-*>
l«x-W
10.^41
311" 4(1
4,
■IxiB
i
aiK2»
]l
M>X thl
:«■ 44
"
46
J>U
^
Hx'S
13
4>! IB
Six W)
J
68
4«ao
ra
zo-ae
10
32'M
^
»
4>JiM
H
ao^44
^
34 -4(1
»
44
4 X40
14
2^»:i4
em -in
»
a4 X M)
6> M
43
6xffi
My Ml
KB ' bit
6X30
24X30
ae-flo
I
u
24X33
M'M
8
S3
«-is
26
114 XS8
"
40X80
GlaNS for
Skylighte.
. 1
re gkyllgbU are ^ittzwl w
Ill aeai M Ao>MW v\iv«t ^6»>*^^
use*/ in Jen^liH of from h
xtfti'.v Lo ittt^^ \at\v*»>« «-^^B
^M- ti< fifteen irioliea. J
Ui. ol •Aafta*VAtt.w«V»ip^™
Ill uepessary for all Joints. This is the cheapest taade of g
Tlie best, Iiowever, tor skyHglit purposes, is fluted or rouglj
' gliUB. 'Oif followini; ililoktic'ta^a are recorauiended us prop
12 ini'lies by 48 tni'lii's is llie extent for glass ^ incb tltiuk
20 '■ lOU ■' " ■' i " '^
WeUjht of So'djh OIum per Square Fo'it.
ThickneHS - . ■ ■ i I's t ( i * i 1 iw
W«lght 2 21 4 5 7 8i 10 12Jpoi
ASPHALTUM.
(For Rock Aapbalt, bbb pDge 5et.)
AapliBltiim is nsed eNttinalvely fur composition rooftng,
Mine purpose as tar.
Aspboituiu, or solid bitimien, U a natural pitch, found In
eiiL couul riea. Tbe most acceseiMp luiil erunomieO) for use
L'nitcd States is obtained from the " Great Pitch Luke," & i
able and Ineibaitstiblii deposit In tbe Island of Trinidad.
It is impervious to water, and is one ot tie moat iwch>
anU dnritble substances known, — quaJitios which, togetj
its tenacity, adhesiveness', and resistance to the ejects of 6
extreniu chaises of beat and cold, make it a cementtng mri
the greatest value for raofs, pavements, and various other p|
The principal advantages claimed for asphaltura aa a'
material over pitch and coal-tar, arise from the fact that t!
mlt)ous tii».tt('r of the asphalt \s not volatile at any tempea
the snn's lieat. and Is therefore pennancnt; while In all i^
manufactured from coal-tar tliere are volatile oils, whlct
evaporate on es[>usure to the sun and air, destroying the fll
nnd life of the material. The fact is now well known. Id
]iitcb or cement manufactured from coal-tar thus gradiiall]
urates, until, in the course of years. It l)eeomes brittle, aw
bles away; and tliat felt saturated with coal-tar in like'
hardens, until it becomes brittle and finally worthless.
Asplialted slieatliliLg-felt, for roohng purposes,
r shinelea, sVaUia, cXa^i^ioMds, etc., la aJso ml
j^%iannor to the tavted ■pa.'pcra mote asrowwt&i ii!
Bofh l\vese matjerttiB ifta.ij \» ^"^T^
li eonditinn reaiVy (or msp..
WEIGHT OF CUBIC FOOT OF SUBSTANCES.
$4»
CAPACITT OF FREIGHT CARS.
[ProiD the "American Archilecl."]
A ear^ad is nominally 20,000 pounds. It is also 70 barrels
•* salt, 70 of lime, 90 of flour, (JO of whiskey, 200 sacks of flour, 6
Ords of soft wood, 18 to 20 bead of cattle, 50 to 60 bead of hogs,
O to 100 hea<l of sheep, 9000 feet of solid boards, 17,000 feet of
tding, 13,000 feet of flooring, 40,0(K) shingles, one-half less of hard
timber, one-fourth less of green lunil)er, ont*-tenth of joists, scant-
l»ig, and all other large timbers, tUi) bushels of wheat, 400 of coin,
^^50 of oats, 400 of barley, 300 of flax-seed, 300 of apples, 4:^0 of
i^Hsh potatoes, 360 of sweet potatoes, 10(K> bushels of bran.
"MrmOHT OF A CUBIC FOOT OF SUBSTANCES.
Names of Substances.
Anthracite, solid, of Pennsylvania
broken, loose
" niodei-ately shaken
heaped bushel, loose
^Ahy American white, dry
^phaltum
Brass (copper and zinc), cast
" rolled
Brick, best pressed
" common hard
** soft, inferior . .'
Brickwork, pressed brick
** ordinary
Cement, hydraulic, ground, loose, American, Hosen-
dale
" hydra«li<', ground, loose, American, Louis-
ville * .
" hydraulic, ground, loose, English, Portland,
Cherry, dry .
Chestnut, dry • .
Coal, bituminous, solid
broken, loose
heaped bushel, loose
C/oke^ loose, of good coal
be&ped bushel
it
Average
weight, it) lbs.
\
tt
\
r)4
80
;i8 .
87
504
524
150
125
100
140
112
56^
50
90
42
41
84
49
14
WEIGHT 01^ CVaiC VOOT OP Sl^l',s|\M li.-i,
H'eight of Cubic Foot qf Bubitancea [Cmtinard).
LI loam, dry. loosu .......
'■ '■ " mtKli^ralJ:ly miimmil . .
a aofi, flowing iiiiiil
Ebony, dry
Elm, dry
Flint
iilaaii, •'onimon window _ . . .
Gold, taat. pure or 24-i-Ariil.
" pore, liaiiiiiii:r)iil
Rravel, HlHiiit lilt sHiiii^ a^ sand
Hemlock, dry
Ulckory, dry
Hombli^nde, black
Ivory
l.lBnilm vRh-. dry ! . . .
J.ime, qiiltk, (•rDiiiid, loiwn, or <n small liiiiip« . .
■' ■' ■' ■' tliorouglily aliskui . .
■■ ■' ■' " per struck busliel . .
Llmnatiinwi .ind nmrbles
■' " " lootie. In irregular fragiiieiiu.
Mahogany. Spanish, dry
■' Honduras, dry
Msple, dry , ,
Marbles, (Sue Limestones.)
MMonry. of granite or limestone, welklresflod . .
" " tnortnr rubble
■' " dry ruhWe
^^ "' "' sandstone, -DeW-ATewwA
^feksury, at '.i'i? Fnhrc.nlie.it
Id
m.
WEIGHT OF CUBIC FOOT OF SUBSTANCES. 550a
Weight of Cubic Foot of Substances (Concluded),
^AMKS OP SL'BSTANCEU.
Average
weight, ill lbs.
pa
»rtar, hardened . . .
id, dry, close ....
' wet, fluid, maximum
k, live, dry
white, dry ....
other kinds ....
:roleum
le, white, dry ....
yellow, Northern; .
** Southern . .
.tinum
artz, common, pure . .
»in
t, coarse, Syracuse, N. Y. . .
Liverpool, fine, for table nse
id, of pure quartz, dry, loose .
well shaken
perfectly wet
idstones, fit for building . .
iles, red or black
7er
te .
)w, freshly fallen .......
' moistened and compacted by rain
nice, dry
el
phur
lamore, dry
1, cast
rf or peat, dry, unpressed
.Inut, black, dry
.ter, pure rain or distilled, at 60 degrees F.
' sea
J&y I/CC9 ............
c or spelter
18: J
80 to 110
120
59
5?
32 to 45
55
25
34
45
ia42
165
09
45
49
90 to 106
99 to 117
120 to 140
151
162
655
175
5 to 12
15 to 50
25
490
125
37
62
459
20 to 30
38
62i
64
60.5
497
Oreeu timlten uau<y weigh from one-fVUbU> o)a!&-Y»MTfiAX«>S&M&^XH<
IMhNSlONS OF CllTKL-K ISlil.U-.
B AHD WEIGBT OF CHlIRCa BE
1
.JMtTDBK
D BT WlU.IAa B1.J1KE id Cai., IlllHuS.
B<u ot frame
BHT.
TODB.
DliuoeUir.
Iitamfi
«
21 ill.
42 X 32 In.
M
2aiin
46 X-S6in.
3H
E
24 in
46 X 36 in.
38
aaw
DS
26 in
46 X 36 in.
3»
400
D
27Jin
53 X 40 In.
44
500
CH
2» la
53 X 40 in.
44
800
c
Hi in
60 X 4» in.
41
700
B
.^ in
HO X 41S ill,
4!
Win
AS
.S4iin
00 X 4S in:
41
WKI
3A ill
70 X rrt in. 1 :rf
1000
A
:t7 ill
70 X M in. 1 rtf
IIOO
Git
;i81in
7fi X 57 ill. 1 (-
1300
m in
76 X 57 In. 1 <k
1300
40 in
70 X :>•! in. ^i■
1400
0
41 in
70 X 57 in. ft
1500
42 in
7fl X .'■.7 in. , ft
1601)
43iin
KH X (W in.
7
■ 1700
Ffl
44iiTi
KH X ilrt ill.
7
1B50
F
4(1 in
Hli X (tt in.
7
2000
47 in
iH y in in.
7
saw
E
4^ in
!»1 X 07 in.
7
,2500
D||
51 in
100 X 70 in.
ft
3(KNl
^3 in
112 X 73 ill.
11
- 3300
L
a.i in
112 X Ti in.
■ 11
4000
t-H
58 in
■ 124x78 in.
1'
6000
C
IK! in
" 124 J^ 7!S in.
"
ir bells of l(«s than 500 pouwia
'■ <• pjvi to 800 pouuilB .
k inch d
WEIGHT AND COST OF BUILDINGS. dOi
T77JEMGHT OF BUILDINGS.
[From the "American Architect."]
been calculated that the pressure per square foot of the
acture upon the foundation walls of a few of the beM-
juildings is as follows : —
? of United-vStates Capitol at Washington, 18,477 pounds
•d College, Philadelphia i;{,44(>
'eter's, Rome ;j;J,:j:i<>
.^aul's, London 8l),4:>(>
Senevieve, Paris (M),()()0
Toussaint, Angers <.K),(MM>
• the pressure upon the earth i>er square foot in the case of
'auFs, London, is 42,9o() poiuids.
COST OF PUBLIC BUILDINOS.
An experienced architect and surveyor, on the H)th of February,
79, prepared, and presented to Gen. Meigs, Quart (^rnaster-Gen-
al, the estimate which follows of the cost of various pul)lic and
•ivate buildings in this coimtry, the (•oiiii)ari8on Iwing by cubic
et, exterriardimensions : —
lb-Treasury and Post-Office, lioston, Mass *$2,080,50'
nited-States Branch Mint, San Francisco, Cal. . . . 1,500,00
iistom and Court House and Post-Office, Cairo, 111. . 271, Of
istom and Court House and l*ost-()ttice, (/Olumbia,
s.c:. ;^l,f
nited-States building, I )es Moines, lo 221,*
nited-Stat<^^ building, Knoxville, Tenn 398,
nited-States building, Madison, Wis 82^).
nited-Stateg building, Ogdensburg, N.Y., 216
njted-Statea building, Omaha, Neb. ....... i]:i4
nited-States building^ Portland, Me im
erman Bank, Fourteenth Street, Newport, R.I. . . . 47
aats-Zeitung, New-York City 47
estem Union Telegi-aph, New- York City 1,4(
asonic Temple, New- York City 1,9
^ntenniaJ building, Shepherd's, comet T^w^VWv «cA
^ewnsy/ van /a Avenues, WaslVmgto\^,l>.C. ....
/ to this the United-States "NaUouaX ^\\\^>x\\\, ^^c^b-
oofliii/W/n^, at Washington, D.C •
552 WEAR ANJl liau OF BL'M.lTlNn M \
1
•■THE WEAR AND TEAR OP BUILDING MA- ]
■ TERIALB.
At tlie tUDlU Kiuiiuil iiieuting of Die Flif Uiide
rvrlU-n' Aasod
tioii of llie Norlli-weat, lisld at Cliirago In Si-ptei
Liber, IHTfl, Mr..
W, Spalding reail a paper on the wear anil le*r o
biUmiug nuUa
ils, and labulal^id the reaull of his Investigation
emu : —
s 111 tlie follawt
Vnnie
d veiling.
Brie*
dvulllng
Friiin
....„
^
\"i"Jit,'.
1
ill
1
'le
i"
^i
i ."i
II
P
III
tt
ill
M
'■
£
£
-:
£
™.i..
SO
.
so
3
.
;
u
M
1
milting, aauide . .
»
20
Piklnllng, iDBidt) . . .
»
Corn?ce '.'.'.'.'.'.
1
40
?
M
n
M
1
4
Weiuher-boardlns . .
30
^hntblog
M
Flooring
30
txion, ooraplclo . . .
ao
30
ih
30
i
Wlndowa. Domplele .
ID
Bu>lr.W<»«^ . .
iio
30
B»»
30
ai
30
It
30
»t
M
Bi'llrUng bsrdnK '. '.
r
PbllUliBIKllWRho .
30
to
t
UuUilds imi>a> . . .
«
l>J^onl'u«be'r : '.
«
1
40
3
a
n
ao
H
i
frotn ilw iTplh
wtwl will, ta
d towtw ol l|
elevtiti Western States.
CAPACITY OF CTSTKKNS AND TANKS.
55;5
• •••••••••••••••••••••••••••••
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i4
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00
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')r>.SA
(ArAClTY OF CISTKUNS AM) TANKS.
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CAPACITY OF CISTERNS AND TANKS.
553b
PACmr OP CISTERNS AND TANKS.
OF Barrels (3H Gals.) in Cisterns and Tanks.
—
6
Diameter, in
Feet.
n
112.8
12
1.34.3
13
157.6
1
7
8
59.7
9
10
93.2
33.6
45.7
75.5
40.3
54.8
71.7
90.6
111.9
1.35.4
161.1
189.1
47.0
64.0
83.6
105.7
130.6
1.58.0
188.0
220.6
J 53.7
73.1
95.5
120.9
149.2
180.5
214.8
2.52.1
60.4
82.2
107.4
136.0
167.9
203.1
241.7
283.7
67.1
91.4
119.4
151.1
186.5
225.7
268.6
315.2
73.9
100.5
131.3
166.2
205.1
248.2
295.4
346.7
80.6
109.7
143.2
181.3
223.8
270.8
322.8
378.2
87.3
118.8
155.2
196.4
242.4
293.4
349.1
409.7
94.0
127.9
167.1
211.5
261.1
315.9
376.0
441.3
100.7
137.1
179.0
226.6
289.8
338.5
402.8
472.8
107.4
146.2
191.0
241.7
298.4
361.1
429.7
504.3
114.1
155.4
202.9
256.8
317.0
383.6
456.6
535.8
120.9
164.5
214.8
272.0
335.7
406.2
483.4
567.3
127.6
173.6
226.8
287.0
354.3
428.8
510.3
598.0
5 i 134.3
182.8
238.7
302.1
373.0
451.3
537.1
630.4
DiAME
TER, IN
Feet.
20
373.0
15
16
238.7
17
18
19
21
22
i
209.8
269.5
302.1
336.6
411.2
451.3
J
251.8
286.5
323.4
362.6
404.0
447.6
493.5
541.6
)
293.7
334.2
377.3
423.0
471.3
522.2
575.7
631.9
t
335.7
382.0
431.2
483.4
538.6
596.8
658.0
722.1
)
377.7
429.7
485.1
543.8
605.9
671.4
740.2
812.4
)
419.6
477.4
539.0
604.3
673.3
746.0
822.5
902.7
46L6
525.2
592.9
667.7
740.6
820.6
904.7
992.9
i
503.5
572.9
646.8
725.1
807.9
895.2
987.0
1083.2
>
1
545.5
620.7
700.7
785.5
875.2
■ 969.8
1069.2
1173.5
;
■587.5
668.2
7.54.6
846.0
942.6
1044.4
1151.5
1263.7
\
629.4
716.2
808.5
906.4
1009.9
1119.0
12.33.7
1354.0
)
671.4
773.9
862.4
966.8
1077.2
1193.6
1315.9
1444.3
\
713.4
811.6
916.3
1027.2
1044.6
1268.2
1.398.2
1534.5 ;
)
755.3
859.4
970.2
1087.7
1211.9
1342.8
1480.4
1624.8
»
797.3
907.1
1024.1
1148.1
1279.2
1417.4
1562.7
1715.1
839.3
954.9
1078.0
1208.5
:tek, in
1346.5
1492.0
1644.9
1805.3
DiAMI
Feet.
24
25
582.8
26
27
28
29
80
»
537.1
630.4
679.8
731.1
784.2
839.3
»
6U.5
699.4
756.5
815.8
877.3
941.1
1007.1
i
752.0
815.9
882.5
951.7
1023.5
1097.9
1175.0
; 859.4
932.5
1008.6
1087.7
1169.7
1254.8
1342.8
1
966.8
1049,1
1134.7
1223.6
1316.0
1411.6
1510.7
•
1074.2
1165.6
1260.8
1359.6
1462.2
1568.2
1678.5
t
1181.7
1282.2
1386.8
1495.6
1608.7
1723.0
1846.4
1
1289.1
1398.7
1512.9
1631.5
1754.6
1882.2
2014.2
i
1396.5
1515.3
1639.0
1767.5
1900.8
20.39.0
2182.0
: 1503.9 1
1631.9
1765.1
1903.4
2047.1
2195.9
2343.9
1
1611.4
1748.4
1891.1
2039.4
2193.3
2352.7
2517.8
1
1718.8
1865.0 ,
2017.2
2175.4
2339.5
2509.6
2685.6
; 182«.2 1
1981.6 i
214:3.3
2311.3
2485.7
2666.4
2853.5
' 1933.6 /
209«.l i
2269.4
2447 .S
L 'l«i\.^
\ 1^^:.^
\'?JJ^1X2»
\ ^
/ 2041.1 ;
2214.7 '
2395.4
2f)8'.\.'i
\ t;"9>.\
\ *lVH"5»>i.\
\*?;s!^;
/_
2l4S.r) j
2321.2 1
2521..')
\ TiVi.l
\ ^mi\A
. \ iV.Vi .
^^'SJKX
^-^
jat are tapering, raeaHure tbe d\aTOe\.ev \o\^x-V^\\V^^&^XQ.v«i\>iX%'^•
; OK [IIERMOMT^IKI
VTBiaHT AND COUPOBITIOH OF
1 cubic foot of air at 32 ilugiti-s F., iiiidiT a iireasiii
pounds per sqiian- Inch, wciglis 0.0S0728 of a poitnd.
Therefore 1000 cubic feet = 80.728 imunila.
OF AIEL
L iireasiirr ul I
1 cubic foot = i.aaa o
53.85 cubic feel of air eootain
J as pfir ccnl oxre™-
I T7 per I'ttnl nilrc^n.
J 0.20716 ounce oxyga}
1 0.!W4Ht ounce nitrogM
i.aaaoo total weight [■
1 0.0185725 pound oi|(
I 0.0821.555 pountl dIIH|
0.08OT2S pounil.
1 1.000 [louni] oiygen.
t 3.347 pounds nitrogM
4.;X7 ponnda.
= CO, = 22.
C^arlmuic acid
C = II. 0 = & 0, = Ifl.
For coiiibustion to cai-tonii' acid, 1 (loimcl of coal lefullj
pounds of oxygeo, or 148.(1 cubic feet of air, supposing ■11 (|
osygen to combine with the coal. 2S0 lo .TOO onltic feel of d
pound of coal is the usual allowance for Imperfect combnsUoi;
li.ad pounds of air for perfect cominiBtton.
34.00 poLitids of air for Imperfect couihuslion.
OOMFABIBON OF THERMOBIZrrERS.
To eiiiifert the degreea qf iliffei'eiit Ihermomelfri- from «M
the otiier, use the folloiciny formula: —
F stands for degrees of Fahrenheit, or 212» 1
C '• '• C;elsius,' or I0(>o >- bolliu^poini.
B " " Reamur, or 30° >
i'R BC
F = -j- + 32, and F= r + 32 for degrees aitove freexiug-fl
BK 9C ',
F= 4-32, and F= "s" — 32 for degrees below freezlng-fl
C= Q , and R = j; for degrees above fi
n.\ K =
tor ftcfnMVidcnt ti
COLORf$ OF IRON CAUSED BY HEAT.
565
) of Celsius or Reamiir = + 32^ Fahrenheit. Zero of Fah-
it = - 17.770 e, or - 14.220 R,
low miwh Is 8® Celsius above Zero in Fahrenheit ?
» X 8 72
F = — j— = -5 = 14.4 + 82 = 46.4° above.
low much is 8° Celsius below Zero in Fahrenheit ?
V = ^-^-^ = ^ = 14.4 - 82 = 17.6° above.
)A8E8 WHBKB THK PKODUCT IS SMALLER THAN 32, IT INDI-
\ THAT THK T)E»KKB 18 AliOVE ZeRO OF FAHRENHEIT; SEE
PLE 2.
low much is 10** Celsius below Zero in Fahrenheit ?
« X 19
F =
- 82 = 84.2 - 82 = 2.2 below Fahrenheit.
■BRUNT COLORS OP IRON CAUBEO BT HBAT.
[Poulllet.]
Fab.
410©
430
403
502)
080)
032
077
1202
1472
1657
1832
2012
2102
J 2782?/
/ 291 2 f
Color.
Pale yellow.
Dull yellow.
Crimson.
'Violet, purple, and dull blue; between 201® and
370® C. It passes to bright blue, to sea-green,
and then disappears.
Commences to be covered with a light coating of
oxide, loses a good deal of Its hardness, becomes
a good deal more Impressible to the hammer, and
can l)e twisted with ease.
Becomes nascent red.
Sombre red.
Nascent cherry.
Cherry.
Briffht cherry.
Dull orange.
Bright orange.
White.
Brilliant white, welding heat«
Dazzling white.
t
1$ MELTING-POINT AND FXT'ANSIUN ill Mk
MBLTnrO-POIHT OF MBTALB.
Pktliia . .
Antimony
BUmiith . .
Tin (average I
\
.1822 to 2013, white)
2012 to 2192. gray (
2733, welding heat.
53
LINEAR EXPANSION OF METALS.
Tin .' ." .'
Copper, yell I
'' red
Forged iron'
Steel' , .
Cast-iron ' .
0,003S4
0.00222
0.00188
U.00171
U.00I22
0.00114
0.00111
0.0000122
aooooiu
0.00001 u
For a i^haiige of 100° P. a bar of iron, 1475 feet long will e
one foot. Similarly, a, bar 100 feet Ions will pxtend O.IWK
foot, or 0,81.% of an inch.
Aeconling to the experiment; of Dulong & Petit, we Iiit
mean expansion of iron, copper, and pluUnuin hetwetn (f
100° C. and 0° and 300° C, us below.
THE PROPEKTIES OF WATER.
r>57
law for the expansion of iron, steel, and cast-iron at very
emperatures, according to Rinman, is as follows : —
From 26* to bib" C, red
heat, = 6W C.
For V C. r Pah.
ron . . .
' 0.00714
0.01071
0.01250
0.0000143 = 0.0000080
0.0000214 = 0.0000119
0.0000250 = 0.0000139
From 25* to 1300*, nascent
white, = 1275' 0.
• • • • •
• • • • •
ron • • .
0.01250
0.01787
0.02144
0.00000981 = 0.00000545
0.00001400 = 0.00000777
0.00001680 = 0.00000933
From 500' to 1500', dull
red to white heat, = 1000°
C, difference.
ron . . .
0.00535
0.00714
0.00893
0.00000535 = 0.0000030
0.00000714 - 0.0000040
0.00000893 - 0.0000050
) OP Expansion in 100 Parts, assuming Forge-Iron
TO EXPAND BETWEEN 0° AND 100° C, = 0.00122.
-
From 0° to
100*.
25* to 525'.
25' to 1300°.
500* to 1500'.
ron • • • .
100 per ct.
93 "
91 "
117 perct.
175 **
205 "
80 per ct.
114 **
137 "
44 per ct.
58 **
73 "
THE PROPERTIES OP WATER.
TEB was supposed to be an element, until Priestly, late in the
jenth century, discovered, that, when hydrogen was burned in
5 tube, water was deposited on the sides. (It has been shown
he combustion of hydrogen requires eight parts, by weighty
jg&n ; and vapor of water is the resuU."^
as not, however J until Cavendiab and "La-NoVaNfeT \sss^s*\^
hAt its chemica,] composition was deletmvn^*
The several eoniliCi'tilB uf water am usually atuleil »
l;41ic licjuitl, an<i llit gaseous. Two L'oiiJitioiia are iMvered ^
)l tvi'iu; mill waler slioulil betinilerstood ascSipable uf e)
ur (tiff«i^iit cuiulitioiis. — till; solid, the liquid, the vkpunit
t gftBeoiis. Al nnd below 32° V. water exists iit the solidj
111 is kiiovt'ii as ice. AeconlluR to I'lofessor Kankiiie. icol
IS H. spepiHi- giiivitj ot 0.02, Thus a eubie tool at ice ITMglu
VjnuniLs.
^V'lieu water puxsea from Che sotUI U> the liquid stale, 1
r required for I i<|uef action Bui[li.'ieiit to elevate the leuipenU
} pound of water 143= F. This is termed the lairait
of liquefaction. According to M. Person the specific heat
is 0.504, and the latent lieat of liquefaction U2.iy>.
Prom 32° to 39° the density of water increasi's ; iklxMiB llie
temperature tlie density diminishes.
Water is said to In; at its maximum density al 39" F., aw) I
pressure of one atmosphere weighs, according to Beriii'lim, I
pounds per cubic foot.
Water is said to VHporiM at 213° F., anil pressure of a
} phere (14.7 ]M>uniU); but Faraday bus showu that va|N>tll
It all temperatures from absolute zero, and tliut tlie ill
vaporlstalion is the diMpi>earani.'e of beat. Dalion obtaiiri
following experimental reHults oti evaporation below liu b
temperature : —
■r-fT-
U^.Ur.
212
1.00
2a.pa}
180
0.50
11270
164
0.33
lasoo. .
152
0.25
t.«W- '
144
0.20
S.IS8'
1.38
0.17
5.36r>
n
From Ibis the genfral law is ilcduued, that the
evaporation is proportional to tlie elastic force of the vapor. 1
Tlius. suppose two tanks of similar sorbce dlmensioi
to tile atmosphere, one containing water maintaineil a
•212° F.. and the oilier containing waler at 144° P.
Then, for em-h pound of wWet: w&tiorateil in the last U
pounds will be evaporaiei\ m Uw to?*- XawV.
^ Jt should be underelood Uia(. v\ve\u.-« o\ P»>.\aft Vri>^tj|
H[ dry air ; and v,lteu Oie aVr "<
CONSUMPTION OF WATER IN CITIES.
5.09
e equal to that of the vapor of the water, the evaporation
es.
he boiling-point of water depends uiwn the pressure. Thus at
atmosphere (14.7 pounds, 29.22" barometer) the temperature of
llition is 212**.. With a paitial vacuum, or absohite pressure
ne pound (2.037" of mercury), the boiHng-point is 101.40 F.
pon the other liand, if the pressure be 74.7 pounds absohiU*
pounds by the gauge), the temperature of evaporation becomes
> F.
he vaporotis coftditioh oTf Wat^r is limited to saturation; that is
ay, when waler'has bfeeA converted" by heat into vapor (steam),
when this v&pdr has'befen furnished with latent heat sufficient
render it arfliyflrcJus," the 'vaporous condition ends, and the
ious state beginS.
uperheated steam is wat^r in the gaseous state,
he temperature of the gaseous state of water, like that of the
oroUs, depends lipon the imposed pressure. Under pressure of
atmosphere, water exists in the solid state at and below :>2° F. ;
a 32® to 212^ it exists in the liquid state; at and above 212°, in
vaporous fetate;'arid above saturation, in the gaseous state.
had bfeen stated that water boils at 212°; but MM. Magnus
Donnfey have shown, that, when water is freed of air, it may
levated in' temperature to 270° before evaporation takes place,
he Specific heat of Water under the several conditions are as
)ws : —
d
lid
0.504
1.000
Vaporous
(raseous
0.475 to l.DOO
. . . 0.475
CONSUMPTION OF TTSTATER IN CITIES.
)AiLY Average Numbp^k of Gallons of Watkk pek
Capita ix the Cities named.i
ihington, I
).C. 158
r York .
. .100
Dklyn .
. . 50
ladelphia
, . 55
iimore .
. . 40
2ago .
. . 75
ton . .
. . 60
any, N.Y.
. . 80
poit . . .
. 8S
Jersey City, X.J. JH)
Buffalo, X.Y. . (51
Cleveland ... 40
Columbus . . .80
Montreal . . . 55
Toronto ... 77
London, Eng. . 29
Livei-pool ** . . 28 .
Glasgow, Scot. . oQ \
Edinbm-gh, Scot. . ;i8
Dublin, Ireland . 25
Paris, France .
Tours, " .
Toulouse, ** .
Lyons, ** .
Leghorn, Italy
Berliiv, Pt\3®5Aa*
"il^ATvXiWC^s ''''
*s>
28
22
2()
20
30
' Jacladiag water used fdr manufaclunni^, iouuVAatoitfc, Wiii ^%aX»«
I^FRIM COPIKS Ol- TltAriNGS. 5(}1
li to Iny the BeDsillr«d papiT ami trai'Iiip:
k double^bick window-KliuA, ot f(ooi) qtial-
ptbB tracing wliicli It is wislicil to copy.
Bi« toko^litlii' It's i-in;{ anil HcnsitiiK^ p«|>er
d Ui)^llier while [Timing.
ItlOT senaltizinc the i«|H!r. Tliewt consiHi
%.in w^iK'tt, of citrate of in>n ami annnoiiln.
^.pOttiBti. 'J'liiisu can he obiainctl at any tWug-
'a not Iw over i>i(tht or li'n ci<ntit per oiiuce
W giasR liottle h> ki4-|i t)ic Holiitiun of thp
, If there in but little <'i>]iyinj{ to ilo, an onli-
P^, anil Lhi! solution iimili' rri'^li whi'iii'vi-r it
irthi^n ilieh in which to plaii' Ili<; Kottitlon wluni
iner-plat? Is as gooi) ns any thing for this
t.pasl«'bnii>h about four inrlic-s wiili-. If the
T in which til wash llic ii^iii'!. aflcr Ihcy
iiinlighl. 'i'lii; (nillot of an onllniiry Blnk
Ing a piecoof ]Kti)i'r over It wii.li a winulit on
r (town, anit tlie sink filtctl with watiT, if the
tkto Ifty the copy in. If it h uou it woiilil be
ir-tlght box alHJiit live or six inches ili'i>i>. aiiil
id loiigur tlian tliu ilruwiiig to lie co|iiiil,
y of white: book-[i!t)N!r.
I cold water in the follou'lii!: projioT-
Bvt (iltraU: of Iron aiid ammonia, one iinnceof
Mhi eight ounces of water. 'I'liey may all !»>
r. and eliaken U[>. 'I'eii miniiti's will stiftici-
It tMiwr ID Im: Mtnsitiii^l on » smooili table or
U»ot'llie solution into tliu eartliKn lUiih or plaie.
II coKtinft of It to the iKigHT with thp hniHli :
> a iHHinl by two a<ljaiX!nt cunicrs, and set it
Bdry; one hour is snHidcnl for thn ilrylng; then
I siite up, on the Imiril on which you liavc
d the whiti* Hatiiu^l cloth; lay your tnu'inu which
.-opy on top ot it; on lop of all la^ tlu> iiiam ijla9j&,
tluu pajwr and tnMiinn av« Vn>\.\» «\\o<i\>.\»sA\t\\«A«»-
mch otIiiT. urid lay l\\<- w\»o\v Uhws, w\\ '\vv 'A'* ""^
een eleven ami iwo o'tUwVi ii\ V.\w h«wvw"'-'Oi.«>«>*>
r
TO MAKK lil.I 1- I'KIM- '■■I'm:'^ -!!■ in.\r:
CO-BPnCIBNT OF FRICTION.
TliB ratio oblalucd by illvlding tlio cnLiru toitx of friclloft bjl
nominl pressure Ib calliiO tlie co-efflclBnt of frlclion; lienw irtK
dofliKi llie mtit or no-rditiL'nl of Jrlctlon to be tlio trktlwi duel
nnmiftl i)resBuri' of one pound.
This ccMifflvU'iit ts iM follows : for
JniTi on link ■ SS
CsBt-iroii on oak • ■ > ■ • IS
^L Oak on oak, fibres parallel 48
Cast-iron an caHt-lron . . .
Wrougbt^Iron on wrougbt-tro
Brass on Iron ,
Wrouglit-irou on cast-iron 11
Cast-iron oil elm . . IB
Soft limestone on tlie sitnie M
Hard llnicalonG on tlic same 3S
Leather bolts on wooden pulleys 47
Leather bulta on cast-iron pulleys !S
Cnst-iron on casl-irun, greased , , . 10
Pivots or axes of wrouglit-irou or cast-iron, on brass or eulri
pillows : —
Ist. When constantly supplied With Oil 06
2d, Wlien greased fiom time to time
3d, Witliout any application
TO MAKB BLUB-PRmr COPIBB OF TRACIIfOl
Tlie following directions, taken from the "Locomotive,"
the whole ground. Tho sensitized paper can be procured at i
whore artists' materials are sold, all prepared, so that Llie pi
of preparing the paper by means of chemicals can then be on
The materials required areas follows : —
1st, A board a little larger tlian the tracing to be copied.
(Jrs wing-board on whicU the drawing and tracing arQ mad
alwaya bo used.
2l}, Two or tlireo. lWcl[iiCB5P.aolftm\i\c\ot oS.\\M w:m,"ii\M*
Ib t,o besmootWy tac\tPJiW3X.\veB!aw*
TO MAK!': UH'K-l'ltEN'r I'OPIKS Ul- TTlAI.'lNtiS. 561
well surface, on wliicli r.o Inj the nensltli^vd luipcr iiml tniriiig
bile prinUng.
ISd, A plate of wnumon iloubln-Uiick winclow-j^liuts, of gotx] qual-
1, slightly larger thaiv the tracing which li is wished tu copy,
ion (if the glass is to kivp ttii^ tracing and gcnsitiMil pa|)er
aely and smoothly pressed Cogctlier while printing.
I tth. The chemicals for sensitizing the paper. These consist
ntply of equal parts, by weight, of citrate of iron Knd ammonia.
d red prussiale of potash. These can be obtained at any ilmg-
Tlie prite should not !«• ovi-r eight or ten cents per otmei-
M-eiicli.
liGU), A stone or yellow glass bottle Hi liei^p the snhition of the
boTp cbeniicnls in. If tliere Is but little ropyiti); to do, an <
Uy glass bottle will do, and the sotution uiutle In'sh wiienev
wanted for immediale use.
Qtb, A shallow eartbon dish in wliich Co plan.' the suliiiion when
UDg it. A eonitiion dinner-pla(« Is as good as any thln(c tor tUs
TOt. A bnish, a soft past^bnisli about four im'lic* wid«, i
Bst thinji wf know of,
8Hi, rii-nty of cold ivatcr in which to wash tiic inpii's afwi
Me been exposed to ttie sunlight. Tile oiitM of an orilinary sink
ay be closed by placing a, piece of pai)er over It with a woi^lit on
>p to Iceep the paper <town, and the sink lilted with water, if the
ak Is Urge enough to lay the copy in. IF It is no!-, it would ba
etter to make a water-tight box atiout hvc or six Inches drap. and
X inclies wider and longer tluui tlie druwing tu lie cuiiied.
9th, A good (|uality of white book-paper.
Dissolve the chentlcals m cold watur in the folIowinB propor-
oita : One ounce of citrate of iron and ammonia, one ounce of
nI [H-ussiate ol potash, eight uun<!(» of water. They may all bt
at intoahottle togetlier, and shaken up. Ten iiilnutea will ■□tticp
I tlissolve thein.
J. ay a sheet of the paper to he sensitized on a sitioolh table or
mrd ; pour a liule of 'the sohitlou into tJie Garilun itish or plate,
id apply a good even coating of it to the i>apcr witli Hif hrusli:
en tack the paper to a lioard by two adjacent corners, and set it
a dark place lo dry ; imv hour is sulflcienl for the drying; tHea
Kce its sensitized side dp, on the Iniaril on wlrich yon have
noolhiy tacked tlie while liaiiiicl cloth: lay your tracing wliiek
,u wish to copy on top of it; on top of all la^ tlva t;).Asa \JMbu,
!iD£ careful tiiat paper an<l Imdngare VmU\*ww!»ii»»4\ti'>(«fl»«^
iitact Willi each other, iind lay the vj\\qW \\\\\\9, "'
r,l. Betwi-pn etcvt'u mid two o'l-tacV. \u U*v swvftWissAi
exAiU|^
c^leur ilay, from bIk to t«n minutes nill b« 3Htficlentt]r li
exprisr' it; At other sea-wns a lorigpr tirii^ will bv mjtilm], ]
1o<vtion does not &<liii1t of <Hr«pt tiunllelit, Ihe priuting nuy j
done ill tlie sliaile, or even on a eloudy day; but from o
lioiira ami a hnlf will be reijnireil for exiiosure. A little experiKH
will soon I'lialile anyone to Judge of the proper lime tores
(111 iliffeiwit llays. After exposure, place your print iu the sink
liTjiigli of wat^r Iwfore nipnllonetl, and wash tlwiwughly, MUsj
suuk from lliree to five lUiniiles. I'pon iiiimeraion in Uie w.
llie ilrawiiig, hardly visible before, will uppear in clear while lii
on a dark-blue ground. After nasUlng. tack up against the «!
or other convenient place, ^y the eomi^rs. to ilrj-. This finishes t
operation, which is veryaiuiple and tliorough.
After the copy is dry, it can lie written on uiiii a con
and a solution of common soda, h liicii iiives n white line.
MINERAL WOOIk
[Mwi
iwny.l
lilast furnacea converted inln M
» in subjecting a small slmni of I
force of 11 jet of steam or com- 1
nnumerable aniatl shot or iplKcJ
Mineral w<ki1 is the
fibrous elate. Tiie process consists
the mo)t<?n siag to the impelling fore
pressed air, whicli divides it into Iniiumerable
nles, forming a spray of spark-like objects. The threads are:
out immediately upon the detaehilient of Ihe slag particles
the main body of the Htivani, their length and fineness being
liendeut upon the fluidity and couiposltlon of the material in
treatment. When the slag is of tlie proper <-onslslency, the t^
ules are small at the outset, and are to some extent absorbed I
the lil>re; liut In no case will they disappear entirely, so lb
great portion of the wool contains tliem, and is only geparst«d f
them by riddling. That jJoKion of the mineral wool which !•■
ricd away from the shot by air-<iirrent8 is very light (;
pounds per enhic foot), anil fonns an fflm urade; while the
ance has a working-weight of twenty-four ponnils jx-r cubic I
and is callH /lyillnnrji mineral wool.
The frtrii grade of mineral wool contains about ninety-thr«e
c«nt of its volume of air. and the ordinary mineral wool
eight i)er cent.
Tliis air circulates w\l\> aviijta ft.\Wv'™Vt'j fti»^^wl^!«*^« '
gnff prevent l\iepBa5».a,eo^\*ea.'i..TOi\|Crteja.'
RELATIVE HARDNESS OF WOODS.
563
enl wool Is uaed in biukliBg* to ID brtwrn tbe scad»
ists. to keep ont the roM in winter and b(«& in sommer. md
tally closing; np all passages in vfairfa rermin and inseets
illy make their homes, and fires are eonintanirat^l without a
ility of arrest.
; peculiarly adaptetl for deafening floors: becan^ie it b nsed
nd is inelastic, ami therefore does not tnuismit the Tibra-
lecessary to the conimiinication of soiumL
eral wool is also nsed largely for parking around steam and
Iter pipes to prevent loss of heat l>efore reaching the radi-
inary mineral wool weighs abont 34 pounds per cubic foot,
put np in bags containing from (^ to 90 pounds in each bag.
s at the works, in Stanhope. X. J.. 1 cent per pound, and at
n New- York City. l\ cents per poun^l.
ra mineral wool weighs alM»iit 14 pounds per cubic foot, and
up in bags containing from 25 to -l.'i pounds in each Ijag. It
at the works. 3 cents per pound, ami at the store, Xew-York
(^ cents per pound.
UJ,
ATIVE HARDNESS OF T^OODS.
ing shell-bark hickon- as the highest standard of our forest-
and calling that 100, other trees will compare with it for
»8S as follows : —
>ark hickory . . .100
t hickory .... 96
oak 84
ash 77
)od 7*1
oak T'\
hazel 72
-tree 70
ik 69
beech 65
walnut 65
birch 62
Yellow oak 60
Hani maple fii]
White elm 58
lied cedar ....... 56
Wild cherry 55
Yellow pine 54
Chestnut 52
Yellow jx)plar . . . • . .51
Butternut 4:;
White birch 4:\
White pine no
-i
&&1
LIST OK ^OTKU AirCHlTECTS.
-WOOD LUMBER ORADBB m BOSIOir.
Tlie Boston law for Uie survey of black walnut xiid Cliert;, id
oak, poplar, and buLt^rnnt, requires tliat the vi'ooiis be dividtdin
three eiwles, — number one, noiuber two, and culls.
Number ona includes ail boards, plank, or joist llj&lare (tee fin
rot and uliakes, and nearly free rrom kools, sap, and bwl U
tbe knots must be small and sound, and so few tliat tbey vml
not ciiusQ waste for the best kind of work. A split in a boantii
plunk, if parallel with the edge of a piet'c. is classed nnmber aoe
Number two includes all otlier deecriptious, except wlien a
tliii-d is u'ortlilesB; when a botvrtl, plank, or joist conlaint a
knots, splits, or any other Imperfections combined, ntakit^ li
than one-third of apiece unfit for good work, and only fit for or
Dury purposes, it is niiuiber two; when one-third is worthier, it
a cull, or refuse, liefuse or cull hanl wood JDclndes all b
plank, or joist tliat are mauufactured badly, by bein;; sawol i
dianionil shape, smaller in one part than iu anothej*, splil
ends, or with splils not parallel, large and bad knots, worm-bolt
sap, rol, shakes, or any imperfections wliicli would ciiuse apivwl
Imiiber to be one-third woi'lliless or waste.
All hard woods are measured from six Inches up; aud all luinba
sawed thin is inspected the same as if of proper thickness, Iml
classed as thin, and sold at tbe price of thin lumber.
There is no snch thickness as J-lnch lumber: the regnlar i
are i, I, Ij-, li, 2, 2i, it. 4 inch, and up, on even inches. Tbe n
ular lengtlts are 12, 14, and 10 feet^ shorter than 12 does not ec
luand full market-price.
LIST OF NOTED ARCHITECTS.
[OWILT.]
Before CiiRtST.
Itlluai. ot A
7lfa Labyrlnlb at Lcm
id Iho Temple of JspluT'
Kin u, Mlww, Tomplo »> *^"" I
LIST OF NOTED ARCHITECTS.
,0G5
Before Christ.
Naxe ov Architect.
<3illicrateB, of AtbenR.
Moesicle«i, of AtbeoB.
Dioocrates, of Macedonia.
AndroDkus, of AtbcDB.
CiUimachoB, of Corinth.
SofltratuB, of Cuidns.
CoBBuliue, of Rome.
HermodoruB, of SalamlB.
Fkwritlos, of Rome.
rrinciiMil works.
ABsisted IctinuH in the erection of the
Parthenon.
Propylaea of the Parihciion.
Rebuilt the Temple of Diana ai Kpheaufi,
engaged on workn at Alexandria, was
the author of the proponliion to trann-
form Mount AthoM into a colossal
figure.
Tower of the VVindH at Athens.
Reputed inventor of the (Corinthian
order.
The l*haroH of Alexandria.
DetsiKu for the 'i'emple of Jupiter
OlympuB at Athens.
Temple of Jupilor Blator in the Forum
at Rome, Temple of Mars in the Cir
CUB FlaminiuR.
Several buildings at Rome; the firRt
Roman who wrote on architecture.
After Christ.
Name or Abchitect.
VfitmviuB PolUo, of Fano.
MetrodoruB, of Persia.
AloisiuB, of Padua.
Antbemlas, of Trales, of
Lydla.
Bazalphue, Abbot of I'etcr-
borough, afterwards made
BiBbop of Lichfield, of
England.
Bgbert, ArchbiBbopof York,
of England.
KomualdtiB, of France.
I^rincipal works.
Basilica J UKtitiuB at Fano; a great writer
on archil <*<*lu re.
Many bnildings in India, and some
at ConHtaiitinoj)Ie; the firnt-known
Christian architect.
Assisted in the erection of the cele-
brated rotunda at liavenna, the cupola
of which is said to have been of one
stone, thirty -eight feet in diameter
and fifteen feet thick.
Bt. Sophia, at Constantinople.
Built the Monastery of Medeshamp-
stede, afterwards called Peterbor.
ough.
Rebuilt York Cathedral.
The Cathedral of RheimB^ tbe catllMt
cxan\v\e. oi UoVYi\*i ^xvt^\\Vft^^x^
!■• NOTED AltCSj
Aftkk Chhist.
(Mr
dIUiUiiibrr.utSiHlii.
mt
inc. Arelibl<bdt> Dt
Cm
(irbiir)-. of Palilalia.
BmlHltu. BiKlup uf Lla
col
or EiiKlnnd.
lyu, Btihup of Win
iih«
irr. ur KhkIhuI.
■ 1.1
lux, KLtiup of I^K
of KiihIbiiiI.
!«i.
udsr, Bi-hol. of r,L.i.
Tli« CuthrdiHl nr Duunu at 111
uwli^aliiiniciil aiyle of urcliiUeta
woi liulli 111 IDie.
Uathedrul of Chitrea.
(.Itolrur CaiiltrtillryCullnlnl.tl
[t uf Lincoln Culitdriil.
Id Id bave creeled the old»t p
Biilll old Si. I*aiil'B. In HWJ
Rcbulll Unculn H'uLtaodtal.
t^iilii. tn«wurkiwur«
lurd atj'k-, mul weta dtc
TlwTu'
riy teei •qiiBi'e. built tn
fi.r eiilar^ni, Uw Clw
Unrl. Hi^ore. ■( Finn
LIST OF NOTED AUCIIITECTS.
567
Aftek Christ.
E OP Architect.
'd'Urbino, of Urbino.
W., Prior of St.
ioIoraew*8, of Eng-
iii Gil de Hontanon,
aiu.
[ Angelo di Baona-
of Florence.
o de Gainza, of Spain.
ca, of Spain.
)re Havens, of Eng-
Century.
16th
16th
16th
16th
16th
16th
16th
Principal workn.
Continued the erection of St. Peter's at
Komo after the death of Bramante,
his master in architecture; engaged
on the buildings of the FarneHe I*al-
ace; Church of Santa Maria, in Navi-
cella, repaired and altered ; stables of
Agostino, near the Palazzo Farnese;
Palazzo CafPareili, now Stoppani;
the gardens of the Vatican; the
fagade of the Church of Ban Lorenzo,
and of the Palazzo Uggoccioni, now
PandolAni, at Florence. '
Supposed to have designed Henry VII. 'h
Chapel, where he was master of the
works.
Plan of the Cathedral of Salamanca,
etc.
Library of the Medici, generaliy called
the Laurentian Library, at Florence;
model for the fa9ade of the Church of
San Lorenzo, commonly called the
Capella dei Depositi; Church San
Giovanni, whicli he did not finish;
fortiti cat ions at Florence and at Monte
San Miniato; monument of Jnliut*
II., in the Church of San Pietro in
Vincoli, at Rome; plan of the Cam-
pidoglio, Palace of the Conservatori ,
building in the centre, and the flight
of steps in the CampidogUo, or Cap-
itol, at Rome; continuation of the
Palace Farnese and several gates el
Home, particularly the Porta Nomen-
tana or Pia : steeple of St. Michaele,
at Oetia; the gate to the Vineyard del
Patriarea Grimani; Tower of 8. Lo-
renzo, at Ardea; Church of Santa
Maria, in the Certosa, at Rome ; many
plans of palaces, churches, and chap-
els. He was employed on St. Peter's
after the death of San Sallo.
The Chapel Royal at Seville.
Uoyal Palace of Granada.
Cains (^ollege, Cambridge. A good
apec\me\\ ot V\v« wc^VW^fcVwx* 'A ^^wt
day.
W ArrjcR Chkirt.
.„„.„.,„„
Oninry-
PrtoQlpal .«*!
1 tarlo Uadcniu. nl l^ni
tai-dy.
Sir H. Wallpn. o! Engtand.
imgoJone.,ol Eugludd.
( Claude I'erraull, of France
EuBlund.
France.
Ale.flndQr JcBii B=pU«B le
Biond, of France.
aalltdaBlbbleiu, n[ Italy.
Jntn« Gltobn, of Beolland.
Bir Wtlll&m Cbamiiors. of
Eti^land-
Robert Adaoi, ol Soollnnd.
mib
Alicnd lOduKlAnKeto'et
Lalln «o«i U-p^ th
Urban VIII.
Aulbor nf "Tbe Klnnen
tenure," j.iibli.bHl In
lun; Burgcoiu- Hall; i
vent Qarden, London;
BU(Bbi.rofoibcrim|iorU
F^txJeofLhol^uvIv.Chat
Uha(»l of KolreIWu»l
or lbs P«lia Ptraa.
St.Piiul'a; lilnnued the nil
after ibt Uro, n»rly all
iborfin, llampion Court,
I'lie dufliu of the Udtol d
lli.lleH^du1'nlBi.l{uy(1
I.ouIb dc (Irand, that d
etc. He wa. the .»|>l».
USDiurd. ibe repnled Id
L'HOlet do V«iidOnie. In tl
fL-r,aII>arl.. Hevuani
tnltu«ial.yl>e(ertbeG
Tbi«tre at Vpmna, ihsmr
aulbor vf two bnoka ou i
Bade;iffe-. Libtao", O.R,
Uic-FieMa; Kliig-i Co
IJlirai-y. and t)c»lr 1
Urldne.
Bamctw'l llouHnamliuany
Arebllen to Oeorge in.;
prlneli*! works are the K
HI Edinburgh, loflrmai;
Ibd Ediu burgh Unlw
nouK.-, Adolphi Temu»
Biuk of Kngland, Buan
Bir Jobn eoimu.of England.
Cbatln Pereter, of Ftmwe.
\
^ ^
LIST OF NOTED ARCHITECTS.
569
After Christ.
p Architect.
s, of Englaud.
Century.
18th
tt, of England.
E^]^, of Eng-
of England.
ckman, of Eng-
Ich Schlnkel, of
land, of United
Abel Blouet, of
rich Zwirner, of
18th
18th
19th
19th
19th
19th
19th
19th
Priucipal work.
The earlieBt, lu modern times, who prac-
tised solely mediaeval art ; restoration
of Ely and other cathedrals; altera-
tions at various colleges at Cambridge
and Oxford.
The Pantheon Assembly rooms, palace
at Kew, Fonthill Abbey, Doddington
Hall, Ashridge House, and many res-
torations.
Published ** Specimens of Gothic Ar-
chitecture," *< Examples of Gothic
Architecture," «• Antiquities of Nor-
mandy," and other works.
Brighton Pavilion, Haymarket Theatre,
Buckingham Palace, Regent's Park
and its terraces of dwellings. Regent
Street and the Quadrant improve-
ments.
New court of St. John's College, Cam-
bridge; restoration of the Bishop of
Carlisle's palace, Cumberland; up-
wards of twenty-five churches in the
midland counties, several private
dwellings. Published " Attempt to
discriminate the Styles of Architec-
ture in Englaud."
Hauptwache Theatre and Museum,
Werder-Kirche (Gothic), Bauschule
and Observatory at Berlin, theatre
at Hamburg, Schloss Krzescowice,
Charlottenhof, and the Nicolai-
Kirche at Potsdam. Published tiis
designs, many of which were not
executed.
Pittsburgh Penitentiary; Eastern Peni-
tentiary at Cherry Hill ; Hall of Jus-
tice, New York; Naval Asylum,
Norfolk; New-Jersey State Peniten-
tiary and many others, with jails,
asylums, and county halls.
Published supplement to Roudelet's
"L'Art de Bfttir," and revised the
tenth edition of that work.
Restoration of Cologne Cathedral,
churcYi aV \\j(^tasi^«,Ti.
1
370
SCALE OF AKCHUrECTB' CHAKOE8.
AftbiT Chkist.
Same or Abchitbct.
Centory.
Principal works.
David Hamlltoii, of 8oot-
Uth
Tha Netoon Honament, tlK Bo;
lu&d.
dMnge, the Western Club-hoa
other buUdiugn at Olatfow ; A
Palace and Lennox Caitle, Sec
Mr. JowphGwUt.
IMh
Compiler of the **£ncjelopf
Architeelure.''
8CAZ.E OF ARCUITBCTB'
Charges aud Professional Practice of Arcliit
A« Indomctl hy the American Institute of Arehtteeta.
For full professional services (including supervision), 5 ji
upon tlie cost of the work.
1*AUTIAI. ISEUVICE as FOLLOWS.
For preliminary studies 1 p
For preliiuinary studies, general drawings, and specifi-
cations 2^ p
For preliminary studies, general drawings, details, and
specifications SJ p
For warehouses and factories, 3i per cent upon the cost,
in the above ratio.
For works that cost less than $10,000, or for nionunien
decorative work, and designs for furniture, a special rate ii
of the above.
For alterations and additions, an additional charge to 1
for surveys and measurements.
An additional charge to be made for alterations or addi;
contracts or plans, which will be valued in proiwrtion to tl
tional time and services employed.
Necessary travelling expenses to be paid by the client.
Time spent by the architect in visiting for professional c
tion, am] in the accompanyuvg tTO.vel, whether by day oi
wiJJ be charged for, whether or wox. «^w>j twDLToNss^ovv, v^
office work or supervising worV^, Va ^Vvew.
^h^ ^rehitecVs payments are sueee^v\xA>3 v\vx^^^ \
- fn tlie order of tHe aboN-e ^X^^sxW-^uctv^.
B ov AliciiriKi-r
iTntn RH'iU'tual eBtiiiisUi is rei'dv^U, tliu rlmt^'b niv liasril uiii
b p\t>[M3Svi\ 1-ost of tlis wnrks, ami tliu iiftyiiii?nl« arc n^elved us
>Ulnients of llic entire fee, whli-h ia Uisnl upon the actual fost.
X'he |trchltei;t bases his professional cliarge upon ttiu aalire i.'Osi,
'the owner, uf the building wlien completed, Ini-lmlllig all lli«
tUTM necessKry to I'endei' it fit for occupation, ajid h vntitked to
tair additional eonipeusatiou for fui'uilui'e or otiii'j' artii'li's
Bdgoed or pun-linsed by tile an-bitect,
[f uiy material or work iiseil in the congtrnetiun uf tlie hulliliii^
already upon tlie ground, or come into possession of the owner
tliout expen^ to blni. tlie value of said material or worb is to Im'
dod lo the sum actually expended upon the building before the
Ehilect's eonfmiasion is couiptilud.
Dntwliiga, as inslniments of service, are the proiieriy of tbe
chltei^.
Sf re itl NT K N D K NCK.
■'It Is the opinion of the Boanl of Trusted of Ibc Aiiierienii
«titule of Architects, tliat tbe supervision or sujieiinlendence of
k Bivhitect, as dlstiugulsbed from the superintendence of a clerk
the works, means such occasional inspection of a building in
QCesB Of erection, or of other work, as tbe archll^-cr, personally
by deputy, finds necessary to insure Its lieing executed in con-
rmity with his designs and ap«cltlc«tlons or itlrectFons, and
lable him to decide when the suixesslve iiulalments provided for
the agreements are due and payable. It incUules, oinong hln
liei' duties, the esercise of authority to stop tlie progress of work
ihdeiuned under it, to decide in constiiictive emergencies, ana to
der neeessary changes."
AODITtONAL ChAIIOES ASO PBALTICK AI'PilOVED UY TllK
Boston So(!1btv op AKCiirrfcicrn.
For all works in wliicli the expenditure is mainly for skilled and
tlstic labor, as for litliiigs and fumituiti, ujiiral or luusaii; decora-
m, Ecnlptnre, staiued glass, or like works, and for selection of
itte and other matcriala. the architect's charge is not made iy
l,y of eommlsaion on tins cost, but should be regulali^I by sjitifM
vumstonces and conditions.
When several similar but distinct buildings ant t^i'ected at the
me time from a single speclficatiiin and one set of divwlngs, and
ider one contract, the commission is chargeil un tbe cost of one
ch building, and a sjicfial charge in made in iTspect to the
rheabove chm-ges do not cover niatcrisA a.\\eiMA*«a
j^^ient (isa agreed to the ileaign, «it\\M \<etotfc W <aM9^i
572 HORSE-POWER, _ WEIGHTS OF CASTlNa'^,
tract is \jrepaTfii\, or of iiiakin^ surveys aad plans of liiiRclfnp Ui]
alUreil, or of arraiiglng for rights <in paily walls or bOtI
ilenta! ami consHiuenl upon a failure of builders whllsl curryf
out work, tior iii cases of Biibseqiient litigation; bu; aB «ii*li I
be cimrged for in addition.
HORSE-POWER.
A tiorse can travel 401) yaitls at n walk In 4^ inliiuten, ntiki
til 2 II I inh Lea, anil utngiiloii in I iniiiiite; he oociipies in ■ i
troin 'M to 4( feet front, ami at b picket J feet liy 0) ouii Ills ii
Hge wulglit equals 1000 pouuds.
A hwse carrying 22& pounds can travel 25 miles In a il«l1
8 hours.
A Arniitild-horee cad ikaw 1000 pounds 2.'! miles a day, w«l^4
carriage included.
in (i ItorKi-iiiill a lioi'sc moves at tlie rata of 0 fi?et In a i
Tlie lilanieler of the track should not be less than 2^i IccL
A liofne-imieir, in niachlnery, is estimated ml '.iii,<XQ pOiud
raised I foot in a minute; lint m a Iioi'sc can exert tluU foM b
six hours a day, one luacliinery Iiorse^xtwer Is equivnlenl br U|
of 4j horses.
The Ktreiiglli oj a hovse la equivalent to that of five men.
The daily alluuanee of water for a horse should be (our gillDN
RUIiiiS FOR wmaHTS OF CASTINQS.
UulLiply Hie weight
of the pattern by
and the product!:
weight of the i!»sl
Reduction Tor Roiiud Cores and Core Print&
Rule. — Multiply the square of the diameter by tlie lengtli
the core in Indies, auil Llio product multiplied liy 0,017 b
weight of the pine core to be deducted from the weight ol
Shrlnkaj^e in Castings.
f Cast-iron, \ ]
.nil ^^^^\ ' ' \ U^ "^ 'net 'on««
V Z\nc . . ?,
V'ORKS Of MAONITI'DE.
The dlwueter of Hie ili-iver iKiit'j j/ireii, In find iln numlier iff
!^ HfLK. — Multipl; tbe diameter of tlie driver by llie number of
revolutlunB, anil divide the product by tlie dUnietcr of the
Iven : the quotient will be the numbi'i' of revolutions of
t Urlvcii.
fy. tliameler and re-eolutiong of the driier being pirni, to find
S iliau'eler qf the driuen that ihall make any given number of
nbitions in the name time.
RuLK. — Multiply the diameter of tbe driver by its number of
^Volutions, and divide tbe product by tlic number of revolutiona
W ilie driveu : the inwtient will be its diameter.
Tq ascertain the xize qf the drifa:
Rci.E. — Multiply the dianieti'r of tlie driven by tbe number of
^Volutions you wish it to make. hiiiI divide tbe product by tlie
li*olutlons of tlie clriver : the (jiiotlent will be tbe diameter of
*e iWver.
Jt. B. —Id ordering pulleys, be careful to give the exai^I size of
*»e aliaft on which they are (o go; also state how you wish them
bilabed on tbe tnw,—fint fnif for shifting belt, rounding for
'On-shifting belt.
WHIGHT OF ORINDSTOimS.
RvLB. —Square tbe diameter (io incbea), multiply by thickneK
E| iDcheg), then multiply by decimal 0.063<)3.
SxAMi'LE. — Find the weight of astoue4feet 0 Inches diameter
il<l T inches thick.
4 feet fi inches = 54 inches; square of 54 = 2910; multlplietl by
= 20412; multiplied by 0,00383 = Ann. 12^8.815 poirnds, which
' iveiglit of stone.
AMERICAN WORKB OF MAOIDTUDE.
Crotoil Aqueduct, N.Y. — Has ii capacity of 100,000,000 to
l-S.OOti.OOO gallons per day, aud from dam to receiving reservoir is
^134 miles In Jeji^-tb,
Suifpenifiou Britlgv:, Niagara Kiver.—'W«e,*^i^'»S»^3-'
.V^
"4 AVi.JJ'AN A^KK> <^J M-UiNnil^t.
■; ■ - . f» .:.;; <uTi<>c«> ivl&:ixi^Ui iIj- '^•iiMni«-iJ<tu m1 :be Brook*
•.•■• .- fc.-*- :*i*-T2 f!r*Ui "Tb*" &t*.i4t:j H^-nili] :'* —
^ ■ ■• V-u-V-.rk • • wi6- - 2««r ivr-i >>> ITJ i«-r-i.
N- ■ "i :i :■ »-: •^■ZllAlll* 4*'«.-*4-"» •■n>>ii- vanK *.*{ Miasonn".
J,- . . . •■•»-; rO-Uili:* ^.:!14 tiil»i«- xarS ••! lii^K^nn'.
.',- : J": • •■-■■ r-*jAi:. ICi*-*; f*^l «> ill* Lr*'. |\
' - ■ .-...•■' N - ^\ - V •>rk » j«i irc«^?h . 1 -">5:f fe<ei • • i m li***.
J -..a. ,►;..-:;- ": ^rIJc*r. iA^* iv^,
'■'' . ::. ■ i Tlij-. ?-Jfrrt,
\ ■•■:■■■ ■■.!"'■;•-*. 4.
J*.i.. -'.•■; •'*. •-vi; "-aM*-. lOi ini-lirs.
■-'."■•. J :.: >•: luiir '-alil*-*. inclusive of wra]»jiiiig:-win*. .*>.>5S: ions.
'.::::.*•> «*ir»-ii2r:h of «ifh oaWe. 12.2iii» inns.
\V-!.'l;! <fi w:r»*, ii»-ariy 11 f«*rt iier pound.
Krt< :. '-a)!!*- i-ontAin^ •yJ'.*» ]<iralle1. not twist^^l, p:alvauiznl fUfA
.. /- .-.-.I \\:r»-*. 'I'l^r-Iv wrappeil to a M»li«l i-y1in<It'r I't'i inrlies is
. 1...- *■ ;.
>../.. ,,] r,,\\.'i-^ ,x'. iiijli-\\at»-r liii*'. 'ill f«-»*i l»y 14n tVi-l.
"^./- '»! •.•■.\t :•« ul i«»«»l-<-oiir>»'. ,V; ft^t I IV l:>i fet't.
'I ■.'..! i.»:jl;* <'T t«A..-r- ai^iv*- high water. 2T>S ft'et.
' .'If lit-i^'lit *»t l'ri<li!»- ill ••♦.'litre of river-.Ni>au aljovi* high ^'ater
>• >''- v.. ]:;:. t.M-r.
II. -jiit ni tl'ior at luwHi's above hiijrh water, 111» feet :] inches.
'.jM<li' i»i r».i;i<lway. ^^ i».-»-t in Hi^> feet.
^■./.'- of ;iii<'ljorai:»*> at haM'. IIU feet hy 120 feet.
^iz«' oi ainiiora;r«"* at i«jii. 1«>4 feet by 117 fet»t.
Hi'iu'Iit of ain'horai:»'>. >0 feet front. >v) feet rear.
\V<iL'ht of «*arh an<-]ior-i»lat«\ *2:> tons.
ri)«' jibovr jliMn'n>ion'H «lo not make this the longest bridge in \\)f
\\orM. Hut tlH'H' i> no >:n;:lr ^jl>an whicli approaclies the central
-|»;m o\rr tln' Ka^t IJivrr. It is half as long again as Koebliug's
< iiHinnati bridj^** (lor»7f«M't b«*t\v«'en towers), and nearly twi(*e as
l<»im as \\\i' sann* engineer's Niagara bridge (821 feet). Noteworthy
suspension-biidgrs in KnrojMi are Trlford's, over the Menai Straits
/.'fSO fot't), /inlslio<l in lS-2:)-, rXxaVyv* \i\:\^%^ ^\.^\Vwswxi^ (^870 feel),
/Jnishoil In IHIM; and T\er\\e^ ^ Vay^* s \>t\^^v w^\- v\w x^^^v^ssft.-.
AMERICAN WORKS OF MAGNITUDE. 575
\PPENDIX TO THIRD EDITION.
i^lie Wa8hiiigrtoii MoiiUiueiit, at Washington, D.C, is
feet 5 inches high, and has a base of 5r> feet, with an entasis
1 foot in every 34 in heiglit. The monument is fa<*ed with
tte marble and baekecl with bhic granite to the height of 452
-; above that the walls are entirely of marble. The average
element of the structure at each corner is 1.7 inches. The
K&ument is a simple plain obelisk with no embellishments what-
r.
^lie weight of- the monument is 8(),47() tons, or :>.(> tons per
^re foot; the area covered by the foundation being 22,4(X)
i«ire feet.
^e comer-stone of the monument was laid July 4, 1S48, and
cap-stone was set Dec. (J, 1.S84.
Iftetropolitaii Opera-House, New York; .J. c <'ady,
sv York, architect.
^he building fills a square 200 X 2()0 feet; the size of the audi-
Inm is 85 feet 8 inches X 95 feet 0 inches; the stage is IK) fe(»t x
feet, and 150 feet from top to bottom; the seating capacity is
0; there are 5 stories of balconies.
^he trusses used for roofing the auditorium antl stage are 8 pan-
id Belgian trusses, having a span in great part of 106 feet. They
13 feet from centres over the auditorium, and 8 feet from cen-
* over the stage, where they have to carry the weight of the
g;ing-loft and the great fire-tank, in addition to the roofing. The
b of the trusses on one side are moiuited on carriages to allow
contraction and expansion. They are secured by lines of swa,>j
-ces, while purlins of angle-irons rul\\V\l\^\)e\>^'e^\\\\\«^\\\\^<^«^^<^
buJJding-hlocks, which in turn reeexve i\w sXvtWwe.. V w^^"^ ^
e of the stRrrp roof is suspen<le<\ a t\re-taT\\t oK Vwv\\v-v-\v«vv w-^
L
57G NOTEU AMKRU-AN BB
blitig n:i ordinary boiler; its leiifj^lli Is 78 feet It wns biUH
position, and tubes were built in Ht intervals to allow mat
the roof-t Hisses to [Miss througli it. Underneath tlie whj
large pan to receive any possible leakage. I
This tank supplies the automatic aprinldera nhich guj
wlioit- stage area, and also the various lines of flre-hose. '
3 over the pruseenlum opening has a span of S^
79 feet aLwve the stage, ami earries a brick wall 40 feet in
is wait Is stayed, not only by tUe roof masses, but by a 4
compensating liraces and ties.
The. stage-auppoKs are of iron, iastead (as usuully) ul
They are made In sertians easily taken apart to admit'
desired cliange in the stage or the space under it. Tlierr i
StM} separate pieces of iron-work in this part of tile stniell
of the buildingpropervBsMSl, 333.41; eosi of ^
veiTtllation. seating, deeoratlon. carpets, and furniture, f I id,
[^ostol8(*nery. costumes, properties, music library, etj?.,fl4H
New City Hall, Phtlailnlpliiu ; John M.-Artluii
art'liitect.
iifiin-Hiidinji o/ BiiUdiiiff.
From north to south -iHO feet S
" east to west 470 feel.
Area 4S seres
Number of I'ooms iu tniilding 520.
Total amount of Hour-roum 14} acrm
Height of main tow.'r 537 feet 4'
IVidth at base IX) feet,
Centre of clock-face abofe pavemnil .... 301 fwt, '
DiametPr of clwlt-faee 20 feet-
State Capitol, Hartford, Conn, j R. M. Tpjohn,
lecl. Xew-York City.
EWerior is of marble; liuildiug is of (i reproof ci
brick and iron floors.
Ditnenniona t(f Biittdiny.
Length -IM feet.
Depth 1 . . . liW feet.
Height to lop of roof .... HO feet.
Height to top of figure on dome, '2-")fj feet.
,s<'uale chamber vfi ItA y; 40 ft
/fejtresenUtivea' ball *\ ^f^'- "*
kCoiirl-room . . . -
f ImiUliny. *'J.rw.tWvuo.
DIMENSIONS OF PIANOS, WAGONS, ETC. 577
Dimensions of Steiiiway Pianos.
andparlor, 7 -octave, 6 ft. 0 in. x 4 ft. 8i in., to
7 ft. 3i in. X 4 ft. Si in.
andparlor, 7i-octave, 8 ft. 10 in. x 5 ft. 0 in,
uare pianos . . . . (5 ft. 8 in. x i) ft. 4 in.
and square . . . . 6 ft. 11 i in. x 8 ft. i) in.
)right piano . . . 4 ft. 10 in. x 2 ft. :^ in. x 4 ft. 0 in. higli.
)riglit grand .... 5 ft. 1 .J in. X 2 ft. 4 in. X 4 ft. 5i in. liigh.
Heigrht of Blackboards in Scliool-Houses.
Primary Schools,
ird class, chalk moulding .... 2 ivet 1 incli from floor.
:ond class, chalk moulding ... 2 feet 2.^ inches from floor.
8t class, chalk moulding .... 2 feet 4 inches from floor.
ight of boards 5 feet, to allow for mottoes,
rramnmr Schools. etc., at top of board.
p of stool moulding 2 feet (> inches from floor.
ight of board 4 feet (» inches.
''he alM)ve are the heights adoi)t(Ml in the Boston schools.
>iniensions of Sclioolroonis, Boston Schools. — The
« of the rooms in the Boston schools, as ailopted hy the
lool Board, are: for grammar schools, 28 fee: x :}2 feet X 18
; (J inches high; for primary schools, 24 fe«»t X :J2 feet x 12
;. This accommodates 5(3 scholars i)er room, in each grade,
»wing 216 cubic feet per scholar in the grannuar schools, and
cubic feet in the primary gradt*.
Minensions and Weigrht of Fire-Enj^ines. — From
isurements of different fire-engines belonging to th«» city of
jtoni it was found that the greatest length, including pole, was
feet 6 inches. The widths varied from 5 feet to 5 feet 1 1 inches,
average height being 8 feet 8 inches.
lie average weight of 2.) engines is 80(M) p<mnds; th(» irreatest
ight being i)420 pounds, and the least 4780 ponn<ls.
dimensions and Weight of Hose Carriages. —
treme length, with horse, lt> feet 6 inches; without horse, 17
t 6 inches. Width, '> feet 0 inches to 7 feet 0 inches; height,
m 6 feet 8 inches to 7 feet 0 inches; average weight of 11 car-
ges, 2D4i} pounds; greatest weight, i^'iOO; least weight, 2120.
[>inieiisions and Weight of lia<\<lex ^^'^^we^^ —
igth of truck f ;« feet; total leu£;t\\, >n\\\\ Va.\\vV\s v>\\. V.>» \^^v,
th, 6 feet 2 inches: average \vei*:\\t oi v> w^VLS^^v"^. ^*^^'^^^ ^'^^'^^'^
test weight, SH(H): ]<^ast. 4:^50.
DIMENSIOKS OI' I
MlltlA
\ I>iiiieiUfiou8 of Carriages.— Covered Bagvf \G«ii«i
otfr nil, 14 feel; utdtli, 5 feel.; heigbt, T feet 4 ind
n siJBOe from U W 20 feet aqusre. according to skill
. Vau\>i. — Lcnglli ovi>r >U, IS feet; wi<UI), li feel; lielgbi.t
y [Plum .Bw). — Length over all, 14 feet i wulttl,itei
uu. — l.engtli over all, 19 feet II inches: wliltb. 0
blches; lielglit, (! feet 3 iuelies; length of pole. 8 fwl 0 iiwliM.
Stuahape Gin (« Whnlii). ^Length ovw all. 10fr«t KiM
width, 5 fpet S iuehett; lieiglit. 7 fe«t a Int-lifs.
rietorift. — Length, without jiole, 9 feet II inches; hof
pole, 8 feet; width over all, 5 feet 4 indies.
I.iillil Brniiiihai'i. — Length, nilljuut pole or Khafl. I) tni
L ieei : wiillh ov.t all, ."■ fi-ci 4 hiclips; lioijilit. (i fi-.'r 4 inclws.
28. iB'
34.81
40.^
47.28
r4.oo
6I.IKI
:rr.in
44.38
WBIQHT OF LTTMBIUt PER THOUSAHD
<U) H
''EIGHTS OF CORDWOOD. — EXPLOSIVES.
579
"VTEIGRTS OF CORDWOOD.
maple
-pine
Lb8.
Car-
bon.
4468
100
2864
r>8
3-234
64
3449
79
2368
49
1903
4.3
1 cord Canada pine
1 " yellow oak .
1 " white oak .
1 " Lombardy pop
lar . . .
1 ** red oak . .
rVE FORCE OF VARIOUS SUBSTANCES
USED FOR BLASTING, ETC.
(Builders' Guide and PHec Book. —-Hodgson.)
Substances.
)ow(ler . . ' . . . .
powder
powder
nitrate of soda for its
?hIorate of i)otash for
m
il
)tash
m mixed with clil orate
di
d mixed witli €lik>rate
di
lixed with chlorate of
serine
Heat.
5m>
(508
('41
764
(i87
578
142()
1424
1422
i;I20
Volume of
ga«i.
0.17:nitre.
0.225 ^'
0.210 ''
0.248 '•
0.:^,18 ''
0.801 ''
0.780 *'
0.586
j Keti mated
I explosive
force.
((
0.484 "
0.408
((
0.8.^,7 "
0.710 ''
88
187
180
190
809
472
5;^
(\80
080
582
478
989
e table is by the celebrated M. Berthelot, who further
itro-glycerine " as really the ideal of portable force. It
detely without residue; in fact, gives an excess of oxy-
elops twice as imich heat as powder, three and a half
' gas. and has seven times tUe e'si^Xo^xN^. l<yt<ifc^^^5«giJ^.
and. taken voliimo for vo\ui\\e,\\,"^o%^^!aa«^V«^^N^>&«B«*
." From the extreme i\au«;eY o\ W\^ ^oxVl., xv^t^^^»«^
leniist slioul.l attoiu\>t to \\\au\\laeV\vf^ \V. ^
■6H0 I'ORCE Uf IIIE WISL
FORCE OF THE VriJSD.<^
(Bulldcn' Oiildr^ and Pricn Book.)
2200
2640
3080
O-OtiTi
0.030)
. 0.07B I
0.1*f (
a4ii2 [
runt
l.lWil
3.0071
4.42U [
«.(127(
7.870 (
•xmy (
i3.;jw
n.7;w (
24.15:1 [
41(.aM) (
IlArdlyiwtflif
Jiiat perae|)tlli(
lien tie bntat.
TiHsk gate.
lligli wind.
Vtrj h^ Willi
THE CLASSICAL ORDERS.
The tenii "order," in tu iirchlU!(;tur>l meaning, n^m
syaleni of eolumnlalioii iiroctisec] b; the Greeks unit KomU
in empioyeil to deoote the iwlumiia atiil enuliluuirr iq
These Lwo (livislo&a combined eonBtitiitB an onier, anil Mi
ordera are ahke; bat, aa Ilierc were c«rtAin ilisthict atybs'
limns and enUblaturea employed by ttie (Intelis aiul Rom*
orders have beeiL ilirlded Into five elassea, which wv cdb
known as tiie Ftee Ordem.
The plainest and simplest of the onlera its the TrscAK.
which was used l>y the early liomaiis, and siippiwed tu bal
liorrowed by them fHini the Etrmeans; the next Ihnw.
Vbi., tbe Dome, lonw, v.m\ Zv,v.\xiva.i.n. were origiiii|
pHlSeoUd by tlie GreeVB", ani\ lAw \»«" f« *:mi«m»v«. «rt
THE FIVE ORDERS. 581
The ancient Greeks and Romans, using these orders continually,
ought them to i)ei*fection ; and the best examples of the different
ders have in modern times served as guides in designing classi-
1 buildings.
As has been stated, an order consists of two divisions, the
•lumn and entablature; and each of these is subdivided into
.ree distinct parts or members, — viz., the column, into bane,
oft, and capital ; the entablature, into archltrace, frieze, and
nnice.
That those who wish to employ any of the orders in their designs
ay readily draw tliem in the right proportions, the different
xlers have been analyzed, and a certain size given to each part in
-mis of the diameter of the column. For thife purpose the lower
iameter of the column is taken as the proportional measure for
1 the other parts and members of an order, for which purpose it
subdivided into sixty parts, calleil minutes. Being proportional
measures, diameters and minutes are not fixed ones like feet and
lehes, but are variable as to the actual dimensions which they
cpress, — larger or smaller, according to the actual size of the
iameter of the column. For example, if the diameter be just five
iet, a minute, being one-sixtieth, will be exactly one inch.
In the following engravings which are taken fi-om Hatfield's
House Carpenter," the numbers in cohnnn H denote the height
f the parts opposite them in minuter ; and the numbers in column
' denote the projection of the corresix)nding part from the axis of
le column, also in minutes.
Some writers give the proix)rtions of the parts in diameters,
odules, and mimites; the module being half a diameter, or thirty
linutes. Its use, however, rather complicates the measurements,
istead of simplifying them.
The following definition of the five orders is taken from " The
ouse Carpenter" (John Wiley «fe Sons, publishers), and corre-
onds with what is generally given in other architectural works.
The TuscAiT Okdek (Fig. 1) is said to have been introduced
the Romans by the Etruscan architects, and to have b'^en the
ily style used in Italy before the introduction of the (trecian
ders.
This is the plainest order used by the Romans, it having but few
ouldings, and no cjirving or enrichments. The shaft was more
mder than the Doric, and had a base consisting of a plinth and
perincombent torus, connected with t\\e \>o^^ q>\ V\\<^ ^waW >^i^ -^
^et Although the capital had the same \tvv\\n\\\\\8\ tv\«v^^\^^^ "»-'
f Dtfiic, they did not project nearly as \aT, T\\v- w^^^- '^^ '^^^^'^ "^"^
TtrJywas vory limited, owing to \ls Y\\vV\\e?>"*>\ voa^- *^ "^^^"^
TUB FIVB OBDBB&
kDOWB eoanfniiig It k from Tttroriiu, no mnklm of tatU
in thia Uyle belug fouoil ■BMWg ladent ruUtk
^^^
^^
IL
.-
^^^rrh^°*^=^
*
j:l
^~^-^^^^C^^TC^"'*°*=^^ 1
1
s
1
U 1 J l-l'"M -1
p
»
1
•
•
a
4
-
^ ^
-
i
"r
1
1 ^
1
^
J — n
C )
»
-
1 . 1
Thi-: Dohk; Okdi£k (Fig. 2) is the oldest and simplest
Oreek orders. Its principal tea.lux«&, a;a -weft ut <iA mouldii
omAnuvits,«re simple; ltsc\»rac**i\*w:NfeTfc,sm4\\,\*»K»\
ut the iupreas of repose, soWAU7,aw\»we«*^. -x^ifc'
TIIK FIVK OKDKItH.
e sliart anil tlie rapiul, aud rest imm^iBtely, H'ithoiit bue, on
e upper step, which serves as tlie ground Aoor of the temple.
lie sliaft is cftantipllnl perpendwu\ar\N \Wo v«
Iff a s/wrp edgi- „r arris: and is grVRrt^ AVmii
1. »o (list !)]!■ .(iamctpr alwve is «>ivcV V*-
This tapering i\i>m n»t lakp placo in a straight I
lint ilfc^rrase iu n gentli^ imrabutii' i-iirvo, u'liii'l
The arcliitravi' is a itM.-l«iigu1ar block sepuraleil by w projwll
ailet from the frieze. The frieie of the Dorii? Order \s ii<
up with aculptiin* in unint«miplMl sui^LtuBiun; hiti it n
);roups, Kit ivgulur iii[«rrals, separated by featittvs calleil iri^yp
nlilrh nre (|iiaiIraiieiilBr [irojectlng slabs, iifglier tiian tlii'y i
Inoiul. witli perpeniliciilBr i^lianiiels, and an' to l>e ronslilcml
supports of the comi»>. Ttiey ftre distribtited in sueL a tvaj' ih
one occurs over tlie miilille of eai'li Foliitnn, ami of each int«nt
iiLg space; in tlie case of the cornpr colnnins, liowevcr, ti
giyijhs are introduced at the ooreerg, and not over tbe ci!t
tlie cohinin. The spaces fonti«tl between the triglyplis arc
metopes. They are pitlier s<|iiaiV8, or olilongs of greater bi
than height, and were arifrinally oiien. Aflei' tlLcy were (
Hlto-reliefs were generally introduced, which In the larger l«n(l
represented the deeds of gods an.) hei'oi's, and in tii<> smaller ul
the skulls of anltnals.
The Doric was much niori' larRsly iisiul in I Inly and Sicily ll
uitlier of tlie odier ordei-a, and In the clHSSlsal bidliUiigs of niotli
times it is vei'y cominuidy found. It is very suitable for the In
stoi-y of u fa^e whicli luks two or nioi-e orders, one aboTP I
The Ionic OnuKti (Fig. 3) did not mme into use until I
Doric had l)een jjerfected and in uae lor a long time. -Veeurilliig
lustorians, it was invented by HeniiogeHtw uE Alalunda: aui
Iwing a native of <^'arla, then In liie possession of tlic loiiinii»
order was called the Ionic.
The difitingulshiug features of this oriler arc the voliiira nr
rals of the capital, ami the dentils amonn; llie lied-moiddin^
the cornice; althoiigli, in some instancKS. duntlls are
The Ionic OiiieralM) lias nioreinouUlngslhsn the Dori.-;
an' richer and niore elegant; anil, as a style, it is lighter
graceful than tlie Doric. The Doric Order lias l>een eompiinti
the male and the Ionic lo the female figimr. The Ionic
lias a less diminlshp^l shaft, and a .Hinaller parabolic eun*e. than ll
Doric. It is like the Doric, channelled ; the timings, nliieh ■
twenty-four in number, are separated by annulets, and are th«
fore narrower but at the same tlin? deeper than the Doric, i
wa termlnateil at ihe toy an<.\ \>ov\o\u ^ a final curvature.
^iHAUa|eF differs from 1.\w Uov\>;,a^w>,\'w^as.s\'a]t>■^wK.^'dl
THE FIVF ORDRRR.
K Ionic Vom-tk. — Draw a perpeiidiciilur from
» (Fig. 4). and make an ciiiial to 'JO inln., or to ? of the whole
; draw so at right angles to na, anil equal to It miii.;
— Grecian Ionic.
o, with 2i alia, for radiiis, rteacrVoft V\ie e-jC lA "Cas, •i'^nM),-
o, the centi-i- of the i-ye, draw Uic. *^a!Me vWl, ■«''>'0t\ *A
uUail t(,« .Jiiimpt,.rot tli.- ey.-. \\l.,.'iSi w«\..'ixv^ «■"''*
586 TBK FITS ORDERS.
Into UA e^aal pwto, h ■bown «t lig. S. Ilta Mvenl eeabnl
raUtion sn Kt Um an^M fonnod by tba haiTT Unea, m flgm^l
8, S, 4, t, S, eW. The pMftian trf thCM aa^ U detonliwd k
comsMnctiig at tbe p<diit 1, and making eacb heavy tine cm |«
leu Id hngUi than the iveoading one. No. 1 1* the centre for A
arc 06 [Fig. 4); 81i theceBmEwttaaKfte; and so on to the Iw
Volute.
The inside spiral line is to be described from the centres r, .
etc (Pig. 5), being the centre of the first small square towatdi
middle of the eye from the centre for the outside arc. The bre
of the fillet at ly is to be made equal to 2fis min. This is
splnl of thri-'' revolutions; \)VA one ol avi^ uTcmber of revolut
JM rf or tf, nmy be drawn, by i\"K\\ft* "f V?'WE>-W\VtA*,».wsrt™
/n^niiinber of equal v»rt*. Then^\■J\&».ftvft■s«^.^««««.^^
SsiNTHiAN OiiiiEit (Fig. Ill Is In geneml like llie lontt,
ts prujKirtions are light^T Btiil more slfiiitt!i', niiil lite liidl-
Brts are more riL'Ii SI11I (Jegajit, 'I'lii' (liJitingiiiRliIng te»-
he order is its bemittlr»l MpiWl, which liiis tlic sliaiie of an
d ealyK, Its rurin Ixsing tmn'oweil from orgaiili? nature. Tlie
t, or bnink-iirsini!, is iiniMlnl In llie litavtx, sa well as In
I ami Btftlks. Tike abiieUH is square lii shape, wltli Its
'Ved Into a retrenCiiig semlclrele, anil ils tniiinal«il i'omero
by the volutes shown In tlie engraviuj|(. 't\w Attic bnae Is
vi with this order, Chn same as with the Ionic, although a
base Is shown In the cut.
AM OKDEKM .UOI>lFIliII BY TUK IIoM AN». — The OrdBDl
s were Introduced into Rome In all their |)errei'tion, lint
irlouB Romans, not satislied with the sinijile i>le4;iitH-e of
ued proportions, sought to improve itjiun tliem by Uvi^
of ortuuiienl. They [ransforiiied in many instaitCM tlw
{anee of the Grecian art into a gaudy splemlor, better
their less refined taste. The Itoiiians remodelled each ot
ni. The Dorle was nicxlilied by increasing the height
oluiun to eight diameters; by changing the CL-hinus of
al for an ovolo, or quarter-round, and adding au astragal
[ below it; by placing the cejiCi-r-, instead of one edge,
TSt triglypli over the centre of the column; and intro-
lorizoittal instead of inclined mutules in tli« comloe,
WHIP instances dispensing wlUi t,\v«iv B.\\fiiB«Cnwi. "^a
' modltieil hy lUininiahing tlic uSiif ot "l\*« \iA\*R»,w
wen- Jiaf^iinlly itrrangi'il. Thl* ni^w I'HiilUtl ba» bM tn
iixjem lunii'. Tlie fat'orit« iiriler at Itoiiii' niiil ht^r i>i>loDi*!
tliQ C'orliitliian, lint litis onler tlip Kudwu urtisls, In tl
..PpASJiil^
searcli for Sort>l(y, siibjeoted ti> iiuiiiy ftltemtiuna, cspecUIlT %
fuUage of its (^aiiital. Into Lite uppur iiui of Ihts Uiey il
th(^ iiiiiilitiml loaXv i;apila,\-, thus cQinbintiig tli« twa In »
^lUtlon of the CoMi'oMTR Onutw. iSk ^b "
ill v\i.' M'''\i "i ■V'\u\a ^«\s
■PTIAK Stylk. — Till! arcliitectiire of the ancient EgypllBns
r>CFterf«ed by boldnesR of outline, solidity, tind gnuulfUT.
. principal fwitiires of tlie Egyptian style of arcbitectwre are :
inily of iilnn. never ilevlHllug troni rigUl Unea ».w.\ 'Mi^fiev-
«-HlJs. Ii^iuii-: llie iiritiT surface sWghfl's ^\«x\«^\^^^ V««w»-1
I,-- /».-i7»'i(i(ii'iil(ir; tlip whole buWWng Vmw. too^ %sXiJ'
I ."in,,-.'. r-:,rhiiii!: ii, Oil.' viw.> troTv\p><^vU*V^''^.*»«~'
Buppaned by i^iioriuDtis columns, very sioui lii iimportion Ui
.height; thi: sliafL soiut^ClmeB polyguiiiil, liuvitii; no basu, but^
'jgreat variely of liaodsoins raiiitals, lln- fiiliogi' of Uvsv bi
llli' paliii, lotiis. Bnil otiier Iwiimb: nihililHLiiri's haiin); Biinfl
-I--B-
■ \
i
i
i
i
m
if
T i
1 1 :i
architrave, trowned with a huge cavetlQ omaiuenied wilJil
ture; and tbc in1«rcoluniiii!itioD very narrow, usually 1} dilij
and seldom Hxceeittng2i- In Uve Kinnlns of a temple
B-erc fdinid Co be ^ teei tViioVi-, miA «. v\» www. -A "^
, wads at the foundalioii *««, W* l«*- *;«^^ »* S
■ toniieHB- stones oi w\v\Ay X.'hase, '
HOCK ASPHALT. 5!a
lerally, were built, had botli their inside and outside surfaces
ed, and the joints throughout the bo<Iy of tlie wall as perfectly
se as upon the outer surface.
rhe dimensions and extent of the buildings may be judged fi'om
1 Temple of .Jupiter at Thebes, which was 14(K) feet long and ;i(M)
t wide, exclusive of the porticos of which there was a j;i-eat
niber.
^ great dissimilarity exists in the proportion, form, and i^ener; 1
lures of Egyptian columns. For practical use the colunin shown
Fig. 8 may be taken as a standanl of the Egyptian style.
ROCK ASPHALT.
Hock asphalt is a lime ore impregnated naturally, by a geological
enomenon still but imperfectly explained, with bitumen in the
^portion of <5 to 10 for 10(). It is found in strata like coal.' It
LSts in Eurojw in many i>laces, and is a material relatively rare,
t of great value. It is mined princii»ally at Seyssel and Pyri-
►nt, in the valley of the Rhone, France, and in the Val de
Bvers, canton of Xeuchatel, Switzerlan I.
[f apiece of asphaltic ore be exposed to a temperatun* of from
^ to 100® centigi'ade, it will become powder. The bitumen,
uch serves to keep together the moler-ules of lime, softened by the
at, begins to melt; and, their cohesion thus destroyed, the grains
lime, each coated with a i)ellicle of bitumen, se])anite, and form
!hocolate-colore<l powder. If, while it is yet hot, this powder is
t into a mould, it will re-assume, as soon as it is cold, its former
nsistency; and the block of ore will have been reconstructed with
same grains, and, in general, its sann* properties. It is ui)on
B singular property that the princi])le of laying roadways of ro///-
€Hsed asphalt is founded.
[f, instead of treating asphalt as explained above, it should after
ing broken be heated in kettles (in which a little bitumen has
en first put to serve as a foundation) for five or six houi*s, there
11 be obtained a sort of black semi-liquid paste, wbic'h is imistic
phalt This is the material which, being mixed with a little
ivel, is used for laying walks, floors, roofs, etc. In this opei-a-
n the bitumen which is fii*st i>ut in the k(»ttle plays the same
rt as grease in a frying-])an. It stops the asphalt from burning
fore it is melted, while at the same time it restores the* bitumen
It the asphalt has lost by evaporaticm.
The paste referred to is tlien put in tUe mo\\V\?^,N'^\*Yvcv^*vcv'^^'*^^?^
onling to the use for wliich the as\>\\aAt \s \w^V?^^*^^* ^"^^*'^^^"*^
of t ho cakes thus fornuMl bears \\\e iuaww^^cWW'^^'' "^ ^^"^^^
whi(^h U of giMit use in delertiiie frauds, for nothing is vaxin
itiiitute tlian real ninstic asphnlt. With a. little bitumen aod m
tnni'ailalil jKiwiler, any iinr can make u block tlial tLe moU pRWtH
eye cannot tvll rrotiithcf^eiiiiine. It ia time alone wliich ileiKKUI
tlie iniposLun-, iiml ufti-ii M n ilisaatrouB prii-e to tliosi> sf
Uuiiipi-etted iMp'uiU hwc l>e«n long ii»nl in Eiiro[H.- fi>
ways, sidewntk's, and miirlyanls, suliject to cunsiil^rable tntlBf'.
Mr. E. r. North, C.E,, tneniber of A.S.C.E., in liis repurt m
l»venieiiU of London and Paria (''Tranaactinus American Sod
of Civil Enginaera," elxxx. |). 126), saya -'From a saniLary jn
of vifw, asphalt is without :i i«.i.-r. lis surfiice in siuoutli. ngul
and non-abeurbeut, witli nu vavitiea iir rmcks of any kiTiil lo nil
. the infectnl inuil and dust of thesti'eeta, and tube soil lienntlti It
kept dry. It is niore thoroughly cleaned, either by sweeidBg
wiuhing, tluui any othur pavement. Its (rciNJoin from noise. «a
other exctillMires, are faat placing It in all llie business ami In
ing streets of the eity of London, where it seems to be sufienn
all other i«veuienls. In njuiparison with gran lie, itsgrealemni
is to lirain- workers anil th-.- iiwners of horses." In an arlifit 1
Joimson's 1 "ydopiedia, fJi'jl, tj. A. liillmore says of the "mm
rotk asphalt," —
"It must be conceded that nothinj; lias jtl been il
which can replace with entire aatisfattion ttie blttuuiiiaiB lla
stones of Seyssel anil Val de Tracers. In the natural asplutltic IM
thecalcareousniattejissu intimately and impalpublycuiulilnnlvl
tlie bitumen, resists so thoroughly the lU-'tlon of air and w»l«rtl
even muriatic aoid, is so entirely free from nioisture, -
due. perhaps, to tlie vast [iressuru im<l intense lieat undent!
the ingredients liave been iuwriwrated by nature. — that*''*
forced to attrilmte tiie excellence of this mateiial t "
<if I'ertain natural uonditions which llie most skilful i
iiietliods fall lo rfprwlnce."
liliintir asphtUI is used for floors of cellais, storw, IjrdB-prii
malt-houses, hotel kitchens, stables, laundries, (■onservatorii
public buildings, currlage-faetories, siigar-refiuerles, millSi I*
etc ; and tor any place where a hard, smooth, clean, dry. Hm
water proof, odorless, and durable covering of a light color ii
cjuired, either in basement or upper stories. It can be laid elll
over cement concrete, brick, or wood, in one sheet without Hta
also over cement concrete for roofs, tor fire-prc«)f bulhlings. f
'/H-«Iling--houBe eeHars, ea'pec^aW^ m\ innlst or (illod land. Il
^^l^ial is especially ivda-VM, \iem6 ■caWitJJi^v, t.
^^^m mould onlusl, ini'pev\vo>iftWse^«i^«ift«..wAV«'»^»»!
^^^^s invaluable.
COST OF U00FING-SLATi:>5. 'jOS
MastH.' asphalt i» al^o vahiahle for domf rtturx*}* «>Vfr U*\\n la-
tions, and for covering vaults and arches iindergnuuid.
The line of asphalt for ron/x is extending, many of the princij^l
buildings in London and a large niimU^r in this i*ountry InMug
covered with it. It possesses esjHH'ial advantages for this purjMise
from the fact tliat it is Iwth fireproof an«l fire-ivsisting.
Architects and builders desiring to employ asphalt for any of the
above purposes should b*» careful to secure tlu' irenuiiic Val-ili-
Tratera or Seytuffl rock asphalt, as tlieif are imitation.s whi<'h an*
of but little value.
For floors of cellars, courtyanls, t;tc., laid on the ground, a Imse
of cement concrete '3 inches thick should th'st he laid: and over this
is put a layer of asphalt from f to \\ inch thick, acconling t(» tlu'
use to which it is to be put. For ordinary cellar floors, the asphalt
need not be more than f inch thick: for yanls on which heavy teams
are to drive, it should i»e \\ inches thick. In spivifying asphalt
pavement, both the thickness of the c(mcrete and of the asphalt
should be given : it should also be rememhereil, ** asphalt pa viMuent "'
•<loes not include the concn»,te foundation unless so siM'cilied.
In laying asphalt over plank or lM)ards, a layer of stout, f/r//
(not tarred) sheathing-iwiper should first be put down, ami the
agplialt laid on this. Asphalt floors for stables should he at least
1 inch thick. The coi*t of rock asphalt in the large cities varies
from 20 to 26 cents per squai-e foot in jobs of 2(KM) feet and u\ov.
This does not include the concrete foundation. Iniitatioii asphalts
are laid for as little as one-half this amount, and (jeniiaii and
other cheap asphalts for about two-thirds the al)ove priec.
Comparative Cost of .Different Sizes of Koofiiif^-
Slate.
The following table shows the prices for No. i Monsou (Mnhif)
oofing-slates delivered on wharf in Hoston. May 20, jssr,. It. will
e seen that the moiVnun mIzps, such as \i\ X |o. ir. x H. |s x U),
iMt the most; and, as the sizes increase or diminish from thene,
le price decreases. The price of liroirnriHf I Mniiif) slal«'< are in
II cases *1 ]>er square umrp thati the MiMi'^oii slatr-s.
The price of Bangor (Pennsylvania; slat4»s in liostoii. at the
line date, is very nearly the same as for Monson slat****, exeept for
t X f<'8, whivh are *I a wpiare les«.
KiHi ffUktes t-ofit from */2 t4> ^I'^.Tii) yv v<\uav«-.
I S!>4 MEASlKKMIi.NT Ul
PRICES OF MOKSON IICAINII) OLATEA
an K 10 ! teM
18 X 11 1 fi ift
18 * in 1 t-.i
l'rl«c iwf
la . B j »j on
14- u , au
14 - T ' AM
Snx, ^
Measiirenieiit uf St«ue Work.
Slwiitt walls arw genorully iiioasiiivil iiy llii; inin'li, «liiM
^ left (I \m\ufs liuif;, IK Imrlira llili-k, und 12 Inehfa liigli, m
i8:Mj ciiliir fnct. It 1b gpiif-ntlly r»rkuiie<l. tif>nxv«r,M:i
:. Ill sotne loi<BlltlHs, ^2 i-iibic fivt. ur Hi fn-t II im-liet
iii'lies wule X l:j inclii-a liigli. i» calleil a pvn'li. wliMi im
h III tlie wuU. OtYaaioiially atuiif work is nieusuiiHl by \ht
yaril of 37 ciibic fi'i-t.
<{et inejuiireiiieiit In tlmt nUfre nil openings tUmiigli
' ileductei], anil 24} ciibiir feet allon-ml tii oui: |>eR^li.
iri««eiireinent i» iliat whert; nu openings iiniler
UeiliH'tetl, and 25 mbk' feet allowed lo one prn'li. When Op
are deiliicteil, it is generally agreed to allow ti conipeiisMl
phiiiibiiig and a(|UHriiLg tin* janilis. an<l for sills mid Ijitlt^Is.
tstime ttulU less tlian HI inches lliii'k are reekoiiHl »s i( lA
tliick by iiiasoiiB. and over HI iiiolii's thit-k each aildilioiwl
nxiiited. Kiibblc walla are Bometinies nieaBnr<-il by Hie rani
eiibic feet, Fdiitliig ™nrit« are always iiieaauri-il
Filer foffr of a superior kind of nibble iiiaaoiiry is iu«
si'iiarately anil ilescrllied.
i^NniB c^ntifit of seleeted atones aw. ftlloweil as blork slO«
other dressings In a similar manner.
Walihisi of blork nUiiif Is eliar^d at [ler i:uhk' foot, ai>Mnl
deseriptlon, similar to aalilar pr^iiared and set. Including al
and joints; hut Hie face is charged extra per foot sup
according to the way in which It may be dresseil.
(iranlte, freestone, limestone, etc.. useil for trimming, is
ally sold in rough blocks by the cubic foot. Ashlar, ptalfi
STB j^nerally measnre>l b^ U\e b<v'^"' foot; belt
etc.. by the lineal tool; »\w ¥t\io AKvenSTO^ i\\eift. *«
Bnmldiittl», eti'. Mariilc, \>\\ve«ovve. »x»\ a\««: W«,
■MMfdol. lliei.ri.-evari\HSu.>>»t.\""6^
MEASUUEMENT OF BRICKWORK. 59r)
Measurement of Brickwork.
•ickwork is generally measured by the one thousand bricks,
in the wall, and sometimes by the cubic foot, in estimating
16 one thousand, the contractor figures on what the bricks will
<lelivere<l at the site of the building, and adds to this the cost
lying in the wall, including the cost of the mortar,
le general custom in measuring the exterior brick walls of
lings is to compute the total number of brick in the wall, and
the number of face or outside brick that will be required,
difference will be the number of common brick. The outside
ic generally cost more than those used for the interior, have to
uUed, and the labor in laying costs more.
. measuring brickwork, it is customary to deduct all openings
loors, windows, archways, elc. : but not for small flues, ends of
8, boxes of window frames, sills, or lintels, etc., on account of
y^'astage of material in clipping around or filling in such parts
he work, and the increased amount of time required.
Uere ai-e different methods of computing the number of brick
ny given quantity of work. Some contractors will compute
total numl)er of cubic feet of brickwork in the buiUling, and
tiply by the number of brick contained in a cubic foot, allow-
for wastage, etc. This is probably as iiccurate a niclhod as
be followed. The larger number of mii'^ou!^, however, compute
superficial area of the walls, and multiply by the number of
k in the wall to one scjuare foot of surface; the numl)er. of
•se, dei>ending ui>on the thickness of the wall.
I the EaMteim States, the following scale will be a fair average: —
ich wall, or ^-brick .... 7i bricks per superficial foot.
ich '' " 1 -brick .... 15 *' ** "
ich " " U-brick .... 221 " "
ich " " 2 -brick .... 80 *'
ich '' " 2j-brick .... iill *' " "
ich *• " ;5 -brick .... 45 ** " " *'
. the Middle and Western States, the bricks are larger, and
following scale will bo more correct for that section of the
itry:^
Inch wall, or -J-brick .... 7 bricks per superficial foot.
inch " '* 1 -brick .... 14 *' "
inch " *' li-brick .... 21 '' *' "
inch " *' 2 -brick .... 28 " " " "
inch ** " 21-brick .... 85 " " " "
seven bricks additional for each half-brick added t<i t\jkk?Kssfts»s.
le following fable shows the iwrnxV^ev o\ \iT\vYs \w ^v^ ^«xn
from 4 hwlwfi to 24 inches i\\ t\ue\av^»^, «^^^ ^^"c Vcw«v \ >
upetficial fVef.
JUt; TABLE 01
NUMBER OF BHICKS IS A WALL.
TABI£ TO FIND KUMBBR OF BRICRB IN A WALl]
AppU«ib]«uiEuU
mSuiw^
or W«t«rn tHato.. .Hit.™ I.y unr-Jifleenlb. i
"^^.l
1'^
or Bbickb tu Tbi
™..„ II
eet of
.
..
2in
«
1 •*
11
^
to
«
2 n
3(
4-
BO
J;
i u
4.
B
«
1 3
i:«
4 »
20
1.0
1*1
o 38
y
188
^
45
flO
IM
180
225
*70
63
106
210
263
3l3
t- ao
120
-40
M)
360
H8
%
-aj
27
ite
m
W
225
soo
17
450
1 ■*
<wo
+.0
KM)
7*
fillO
^ 22!)
4.10
WH
12.
4 30(1
100
KK
1201
IHWi
n
5(
112
liOO
S 5
asol
H 4.)<
HOI
IJ.>0
l^W
22^
27001
7
525
Iftrf)
ln7i)
3100
21 2o
SI60I
SI
(lO
IJOI
1800
2400
«I00
.■WOO.
K)
67
IW
J02.
2 01
in
4W(I:
Tio
IrfK
A ViU
.1 4.71(1 1
IK
i(X
UIOl
i.-m VM
Mn imi
KK
221^
4.,on
BTrf »n
x I.110U !
W
aom
lOlH
nooo 2000
.IKH l!>O0U
■1 ■«
.01
1J2A ilKK
ri ll-ml
n
4500
250
KKKl
'\5
"iivHI
;j
O-K
"!!-
4- KK
HKKK
HHXK
iOO(
2.>1K
IKKMII)
i;i-.ono ,
41KM
><HX)(
H)lK)0
I8O0O0'
MHM
7 KM}
■-■iJOOO
U)IK
4- KJI
HKKIO
KX)
ISOOOl
2ai)000
■r,mfi\
HJI
2. K
MX
7 K)
210001
'H2.)00
31.JO0«
bOOl
BOO(K
20000
MOOOO
2400(K
iOOOOO
;160iKK)
KK*
67)00
iOlfl
202(00
27)001
i.7iO0
405000
KKM
7m
2 KXI
WOOIK
7.000
VAWi
Application ok Taiii.e. — How many bricks will Ihere be in
9846 superficial feel of waU 16 \nc\\w v\\\cW
Answer. — In 0000 squaw XtfX ftwvp. aw.'ri^R.\nW»».,
40 '
6
Uw
BRICKS KEQUIKEI) IN SETTING BOILEIIS.
r>y
TABLE OF NUMBER OF BRICKS REQUIRED IN THl
SBTnNG OF HORIZONTAL TUBULAR BOILERS.
Compiled by Mr. Arthur Walworth, Engineer of the Walworth
Manufacturing Company, Boston.
^
The uamber of bricks are for double 8-iiich Hide and rear wallH, with air 8pac
between. If one of the 8-inch Bide walls be omitted, deduct the number o
bricks in the iast coiumn.
Diameter of Boiler, 24 Inches.
Length of
Boiler.
Length of Grate.
Feet.
6
7
8
9
10
11
Firebrick.
2 ft.
•2 ft. 6 in.
Bricks.
2427
2728
3029
3330
3631
3932
127
Bricks.
2407
2708
3009
3:J10
.3611
3912
143
.-Jft.
Bricks.
Bricks
•2387
£Wi
2688
2668
2989
2969
:j-290
3270
.3591
3571
.3892
3872
169
176
3 ft. 6 in. 4 ft.
Bricks.
2347
2648
2949
32.T0
3.551
3852
101
Bricks
in outside
wall.
.735
610
685
760
835
910
Diameter of Boiler, 30 Inches.
Length of
Boiler.
Feet.
6
7
8
9
10
11
12
13
14
Firebrick.
2 ft. 6 in.
3 ft.
3 ft. 6 in.
Bricks.
Bricks.
Bricks.
3367
:{344
:»2i
3755
3732
3709
4143
4120
4097
4631
4508
4485
4819
4896
4873
6307
6-284
.5261
6695
6672
5649
6083
6060
6037
6471
6448
6425
178
197
216
Length of Grate.
4 ft. 4 ft. 6 in.
Briclis.
3298
3686
4074
4462
4850
.52.38
.5626
6014
6402
236
Bricks.
3275
3663
4051
44:39
4827
5215
.5603
.5991
6:i79
264
5 ft.
Bricks.
3252
3540
4028
462K
4804
5192
5580
.5968
6:i56
273
Bricks in
one out-
riide wall.
699
797
895
993
1091
1189
1287
1385
148:}
Diameter of Boiler, 36 Inches.
Length of
Boiler.
Length or Grate.
2 ft. 6 in.
3 ft.
/
I / Firchiick.
3 ft. 6 in.
Bricks.
l^ricks.
4270
4244
4665
4639
5060
5034
5455
.5429
58.50
5824
6245
6219
6640
6614
7036
7009
74.')0
7404
24 1
26'J
4 ft.
Bricks.
4218
4613
5008
.5403
5798
«\^;^
, 283
Bricks in
one out-
side wall.
Bricks.
4192
4587
4982
5:«7
5772
304r
.'>W BltlCKS ItKyl-lKKl) IX RETTING imil.KHfl
J
Table of
DlAMBTRII OF UOILER, -t^ IX( UK". 1
Lknuth or Qbatk.
BlU.1
'&5ler.
,ES
Bh.
ft. n IB.
tn. 4ft. a In.
-Wt.
ari-niB.
F«t.
Brioki.
Briok..
Brlok..
Briek..
Brick..
Brick..
11
enH
fliS
•l»'
MSB
BIW
0««
S
W
eiw&
M5!I
ns»B
6571
SMS
«!.%
Hfl
18
JOfti
TBOS
T8§8
HMM
is™
73113
TfflS
S
«355
irasB
S«l
Ml
aaat
»I2^
UK
nrebrkk.
M77
S
ajfl
aW
ass
-
DiAUKTUH OF UOILKIt, 48 l.VCIIKH. J
l-BNOTU IIP IIRATI
,«J
'i£.e'
si
a f I. B 1,1
4(1.
4 ft. 0 in
fifi-
1
F«t.
BrfckK.
Urlcko.
Brick,.
Brlcli..
Brick.. Brick.
i"
8T-J1
?m
88.iB
noft
7i>w Ta»
i4i:
ji
tl846
mu
Illa'J
Moa
S5S1 MM
imu-j W7I
ITS
mo;
Mi
HUSH
fill
ittso:
Flnhrick.
^l!l
SS5
^IJO .»(.»
DiAMKTKH or Bttll.BR, 54 INCIIBB.
Length ot
LlNOTR or Oun.
il,Kk."
.IdfH^
4 ft.
4 ft. n In.
ah.
Sft-otn.
eft.
Fern.
Brlok..
774«
Briokt.
1200
TTI3
Brli^kn.
Brkk>.
TftlT
tIu
IM)
8-« w^j
MM
1II»
S-iKS
I^J1B 1 HIM
VtK,
1,-,N I »«H
n«
Si s\ ^^^\^i\^
/ "
/ "
■
sri
^aw I "-T
m >^ 4» .^
-^^^
^
1
k=
■
STEAM HEATING. - BOILEKS.
r>9i»
HORIZONTAL TUBULAR BOILERS.
Manupactubed bv Kendall &. Roberts, Camrkiduk, Mass.
I
V,
*^ .'
^ h.
^^ .* c
u
84
n
O
u
o
3
0
si
16
o
I
S
X
.£ •
•
u
k
Se-
ts
02
5 i
558
e ^ 3 •
-III
E.5 5 i
188
24:^2
14592
U
16
188 3
15
.V
2270
151
58
522
i:^$20
78
17
164 3
16
A
2132
142
54
4S<J
127J>2
78
16
164 < 3
15
Ve
2011
VU
50
450
12(KMi
72
17
140
3
16
1880
125
48
4;{2
11280
72
16
140
3
15
f
1765
117
44
396
10590
66
17
117
3
16
>«
1538
im
40
:W0
9228
66
10
117
3
15
3
1442
m
m
324
8(J52
eo
18
65
•1'
17
3
1074
72
28
232
6444
6()
17
$)2
3
16
3
X
1229
82
32
288
7374
(M)
16
92 3
15
3
s
1152
77
30
270
(J912
m
15
92 3
14
3
1075
72
28
252
6450
60
14
92 i 3
13
3
998
(H
26
2^U
5988
54
18
50
«i
17
A'
IKK)
($0
2(J
234
5400
54
17
72
3
16
fV
977
<$5
2(J
2:J4
58(J2
54
16
72
3
15
A
917
01
2(J
234
5502
54
15
72
3
14
f\
857
iw mm
24
210
5142
54
14
72
3
13
h
797
53
24
210
4782
54
13
72
3
12
,V
735
49
24
210
4410
48
17
49
3
16
A
ti84
4(;
20
180
4l(U
48
16
49
3
15
?.
042
43
18
152
:^52
48
15
49
3
14
A
iy^)
40
IS
152
:^J00
48
14
49
3
13
h
m ^ m
37
18
152
:^^iO
48
13
49
3
12
A
513
34
18
152
^5078
48
12
((5
2J
11
A
542
m
18
152
3252
42
16
38
3
15
i
508
;J4
10
144
:1048
42
15
38
3
14
J
476
32
10
144
285<J
42
14
3S i 3
13
i
441
;J0
16
144
2(W0
42
13
;{8 3
12
4
408
27
14
12(J
2448
42
12
45
2J
11
i
390
26
14
126
21^40
42
11
45
2i
10
1
4
355
24
14
12(J
2130
42
10
45
2i
9
\
320
22
12
108
1920
42
«
45
2i
8
^
285
liJ
12
108
1710
m
13
28
3
12
1
4
im
20
12
108
183(J
36
12
34
2i
11
i
2i«$
20
12
108
1788
36
11
U
2i
10
i
271
18
10
90
1626
36
10
M
^
9
i
244
16
10
90
146-1
36
9
U
8
i
211
14
8
72
1266
36
8
34
2i
7
i
190
12
8
72
1140
30
9
30
2
8
i
152
10
i <^
, 54
912
30
'1
iiO
2
7
.1
4
ir>^,
\ '
\>^
\ ',A
\ 'X^*^
Tbicknetui of hoatln one-eiKhlh Inch v;Te«LU't VYvwxv \\v\vV.\\v*>*' <^^ ^*'^*
Tbtg ItMt thref coVumna addeOL\>v vVvvs ^wVXvot.
<)(>(>
STEAM HEATING. — BOILERS.
TJPRIGHT TXTBITIiAR BOILERS.
Manufactured by Kisndall & Kobbhts, Cambridueport, Mass.
1
Diameter
Height of
Number
Diameter
length of
Heating
Hone- ■
of shell.
shell.
of tubes. ;
1
of tubes.
tubes.
surface.
power. 1
1 ins.
ft. ill.
iu.
ft. In.
fl.
1
; IS
4 0
40
I
•
0 ;«
—
-
IS
4 «
40
1
■
0 89
—
-
\ 18
5 0
40
1
•
0 45
—
-
! 24
:> 0
2r>
•>
8 6
52
^
i 2-*
5 0
25
2
4 0
58
8}
24
6 0
25
2
4 6
64
4
1 30
5 0
45
2
8 0
80
5
i 80
5 0
45
2
8 6
90
6
IM)
0 0
45
►>
*«
4 0
102
H
i
:i0
0 0
45
2
4 (>
114
80
1
7 0
45
2
5 0
125
^
m
i) 0
65
2
4 0
145
^
m
H 6
65
2
4 6
162
n
;U)
7 0
65
2
5 0
ISO
12
m
7 H
65
*>
--
5 6
195
lo
:M\
S 0
65
2
6 0
210
14
1
42
() 6
lOi)
2
4 ()
240
16
42
7 0
1(X)
2
5 0
268
18
1 42
7 (J
100
2
5 (>
298
lof ;
42
8 0
KM)
2
() 0
818
; 21
1
! 4S
7 0
120
2
5 0
820
21
; 4s
7 0
120
2
5 6
850
2:5
: 48
S 0
120
2
6 0
, :580
25
.■>4
8 ()
186
2
(» 6
IRK)
' 4()
r>4
<) 0
186
2
7 0
($75
! 45
:>4
0 ()
186
2
7 6
720
i 48
VA)
10 0
250
2
7 6
975
! 65
m
11 0
250
2
8 6
1100
! "^'^
00
12 0
250
2
9 (>
1224
81
KK<iISTKRS AXf> VKNTILATORK.
UEMSIOHS OF REGISTERS AND VENTILATORS,
""„
.J Jii iJ<"Jr or
lleglslcr t^ux.
"'C
:L
w.""
01»«i.
>• Bi
^x e|
6 X 7(
a xiii
-16
4 ^IS
6 Xlflj
* »1T|
6 XIBI
fll« 81
7 X B|
BJx 9
7 xlOi
a|"io
T X13
(U-iai
R X15t
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fli-id
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111 ' -^i
s " s
8 <11}
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eix u|
mi X loj
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D .lai
10] X laj
3i
fl - 13i
Hi H ISi
^1 1
ai 1
101 X 1UJ
^1 ■
UJ X 131
a
lUl X 141
iH . 151
^ ;
10 1 l«
'•^ 1
3j 1
121 ■< liJ
lai X 19}
■ii ;
12) X 171
2) 1
1-4 X 18J
2j ■
uixi»l
HJ X 21
2J
13i - 25i
2i
I4J X 141
lS|K|fl|
2|
Ul K Wj
leixiiot
2t
141 XM
104X241
2J
X3t
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171 ' 271
IBi-iaj
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<»l
181X201
171-221
IBJxMl
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a>!-aoi
221X821
3|
22JX86
S|
"M
aOi X 281
221X281
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sn) x3»
231 X 81S
sflixaai
Si
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\
a.) - w\
\ n \
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Mi - -m
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131 X laj
m - 171
141 X 181
141 " m
15| X 1«|
161 " 21i
171 " I7|
. ,
vIM.rrv
AM> WQ^^^^H
ESTIMATED
CAFACITT OF PIPEIS AND 1
RBOISTBRS. 1
'T;:=;rTd
iMI.lBClW-.
■rfplp..
-1. loetH..
of pipe.
--■"I
Iliidiea
la luchH
U'l
» 1
U "
W
3M
s .. »|
ItKCTAMGlIl:.AR PIFBS. 1
.™,.
■g. illcbci.
ut pipe.
rfpll*
L 4.«
■i-
180
K' W
1 i
•*
lai
U 9;w
0 H
lAI
18(1
m
10 ao
»
B 6
■"
«i«
IB^I 1 " - M
11KG18TKKH. 1
HI«ot
optnlng.
•^^si^r:
S1.g nr
oponlng.
■■^irr"
S. i^
a "10
10:<U
10
».., -1
lOxlJ
WXW
ROUND BEGISTERS. |
. sua of
■S'SC
opfning.
'i'lX"
is,s. isaJ
I -v*
.OVM—. _J
'1
4S
V" ■• \ "
X.._y|
.^_^M
DlBKCT Reltasi
1
Tu.«l«
Burf»Gu,
length.
WWth.
v.,„.^. 1 j
each row.
In tq. ft.
B»ppiy.
RUuni.
1 X 4
1 X a
1 X s
1 X 10
1 X 1-i
1 X IB
1 X 20
1 X 24
] X 28
] X 33
4
12
1(1
20
24
28
3a
,'JS
1 21
1 101
2 2i
2 !l>i
3 Hi
4 2i
ft
0 l\\
41
4i
4i
41
-11
■li
-11
41
41
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riHh,
fa ^H
■
^P*
^
■
B__
IHM
'
•^ 1
^r
r. -J
^_
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r
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S -
^T
s ■
■ g
=:
■ ^
2
T £
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, 1-
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= ■
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3 ■ ■
3 ' ir
,;
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^
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4s : nn
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i
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II
1
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u
1
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1 •
« X 33 1 IM r. Hi
»i
«
I'
S X 3B 1 lU fi «i
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tt
'
<X 4 Id
s m
10
1
1
4 X ft
52
I 81
10
1
1 ,
i
4 X 12
48
2 2i
10
1
i 1
&
4 X lit
04
a loi
10
n
1
1
4X 20
80
3 6i
10
u
4X 24
ee
4 2i
10
n
" 1
4X S8
113
4 101
U)
li
li
tj
i X H2
law \ 5 ft^
\» ^''
V'
■
^^ Tin »l»tn* »f« '■" ™»""
«»v«*-^s^^^^
DIMK»IO!C:* OF PIPE R^iDlATOELs.
t;or)
flKUCXAR.
Surface, tfixe,
a sq. ft. diameter.
Valvtttt
in -Mi. ft. liiaiiiHti'v
Svppiy . E&Kam. Snijoiy. Ri^'.i"m.
ft.
in.
inch.
1
iaefc.
In ha
!v»*M III m
jproii :;.:
18
1
i:
••
•
4
i i
<'i»lrjm n
"«.
:50
1
^
I ■
«
I :
ft. :a.
.'irh.
54
1
in
1
I ,
">i
- ■-?
«
1 *
72
2
n
1
i !
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- +s
•
102
2
lOi
It i
I
l'>2
-* ^i
1 ..
* 4
130
3
2 ,
H ;
U
l:;i)
;*. J
I4
160
3
2
'' 1
1
1*1*)
:5 J
li
ji'h.
lymRKiT F*ii'p. n.vrirAri'i:^.
4 /: iL'.
Xo- of tu**#.
Square feet. '
I>»n4jrth of
fr. in.
-lipp-.y.
iriih.
i:.-t:r:i.
i'lih.
4X4
16
0
^»>
7;
I
t
4 X «
24
1
1/
7;
1
i
4 X .s
:52
1
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7;
1
t
4 X 10
40 ,
1
U^
7;
1
4
4 X 12
48 !
2
ly
7^
u .
1
4 X 16
fW
2
f»i
71
n 1
1
4 X 2f)
f¥) -
0
">V
-\
\ w
\
4 X 24
ift;
4
n
1-v
w
V
4 X 2<^
112
4
^^
"^
\\
V V^
...
■ ^— . •
\
\ _
^MOt> IllMK.NSIONs I'l- l.\MliiO;v i;aih\iij1;-
H DIBIBNaiONS OF CLOG8TONS PATENT CASt
V mON RIMG RADIATOR.
M.M,*,T,,U.„ BV ls,M..,- ,v NKNr,,,.,,., s, l!,..,„v
^n .^■.^s^S^B.S
w
£
ff
Diittcr liAiuATiiu.-. 1
Arn.ii^odfor(iBallnKwnhliiBhurlow;.r,- .|.i„n J
of
Tuli™ In
eanhniK
fuwln
Kl.fBlt.
Leiiph
I
"L
Tuhi.111
fmut II.
^
.J
] X 4
1
1 8
0
2X4
40
1 s I
1 -K
i.
0
(1
2X1
m
2 » 1
1 X I
JO
2 4
8
2X11
<w
8 1 3
1 X
%
J 8
6
I X 7
70
2 R If
^
1 X '^
40
3 0
fl
2X8
RO
!t a »j
£
1 X i)
4j
% 5
A
2
2X9
1X1
A A t
Ji
1 X 10
lO
3 t)
f)
:!
^x 10
100
S 8
s
1 X II
1 11
8
i X 11
110
3 11
■lA
I X 1
!0
4 4
0
Q
2 X 12
120
4 4
1 X H
at
4 8
tl
2x n
130
4 e
1 X 14
70
1 1
2 X 14
140
a I
1 X 1,
75
5 5
(1
' X I
150
n s
1
1 X 1(1
•«
■5 n
(1
2 X 10 1IU>
3 u 1
1
^^U|l|ltl, Ukc Tiiiir i^tihK ol Ok BtK->
"1
m
■
h. Vwt
cast-iron pin railiator shown in tlii' almce cut is probably
ixtensivBly iisiil than any otliar form of imlliwl milinliir,
lonaUlerwl by many steam himtfirs lly best indirect nwliKlor
iniloubtiHlly lias tlie urea
t of space CliaL it occii]nfA.
siugtbis radiator great jiivmu
frois dirt, and it is well to wi
nulUtor la modo In sections ci
t lieatiiig capai-il] foj' ilie
111 should bp taki'ii t<i ki-cp
1 it Uioroii^'lily with n liose
itamlng noiiiiiially M
' nuHatiiig-surface, but tictiially only about S} Hi|iiari' trel.
It above allows seven sections: the sections made by llii' IT,
tliCotQpany are 41 incites lung, flj Inches high, and :i liii-hea
«ch section having 01*2 pinK, wtiicli are |^ inch lung, i iiicb
t the base, and I inch at the top.
width of the otiter sections is :ii inches.
Caht-Ikon Rino Kaoiatohs (indlrecl).
following cut represents six spctiims of ■'Clogston's" paliait
>n bxllrect raUlator, manufaclDred by Ingalls & Kendricken
iton. Similar forms of radiators nre used by other Hthib.
articular pattern is made in sections 4'i inches long, 8 inch<«
I the centre, and 4jr inches wi<le; each section containing 111
feet of heating surface. The same Ann also inannfacturcs a
f size of tlu- same radiatiir. wWch is 30 iin'hes long, 8 hicliea
Old 4i incln's widii. and coiitaiiia W> w^UMte. ^tes. (A \»*oi«»v
These, nnjiators can be usw\ iin: \\ov-'»
610 INDEX.
Blne-prfnt coplo« of tracfn^rH, to make ....
BlueAtone, rtrengtb of
Board nMmture, table of ... . ....
Boiler tulK'M
BowMtrfng roof-tniMieM
Box-j¥inl<*rM
Brent walirt
Briek arobei* for floont
Briok plem, Htreiifrtb of
Brick wallA
Bricks, dimeiMiotiii of
*' strength of
Brick-work, Htrength of
Brick- work in draiiiM and welU
Bricklayeni* ineraomiMla
Bridging of floor-bennis
Brooklyn Bridge, the
Boilt betuns, solid
Bureau, dimenaionK of a
.ButtreMies, stability of
Tablei*
Calendar, the old and new
Canterbury Cathednil
Capacity of churphet*, theatres, opcra-houecA, etc.
** of eisterni* and tanks
" of dndn-|)i|w«
" of frt'ight-can*
OaiThi^e-lH'uniri
Cant-lron arch-»<irderM, Htrcn^th of
OaHi-iroii iK'aniH, strength of
Cant -Iron coliimnH, Htreni^th of
(*a!«l-iron pipex
CaKtingM, shrinka^' In
'• wei^ht of
Cathedral, .VmicnR
'• Cantfrlmry
*' Lincoln
Salisbury
Ht. I*aurrt
York
of (-hatres
'• of rit»a . . . . ;^
" of KheimM
" of ToltHlo
CalhttdralH, Eiii^iMh, diineiirtionrt of
f Vnient*, streniifth of
Centre of gravity, diifiuiltow*, eVc
*• " *' examv>\e«
Centrt*n for archcH
ChAliim, strength and welviVxl of • • • • •
Obimnvya, boiler, proporXiou* ^ov .
•* brick, ru\e« for
circular area, lengtb of .
ClrCDlar ««clo™, ana uf
CIMenu and UBkn, caiuiclly of . .
Uo-effldeni for Inanw, table of . ,
Oo-effident of (rioilcm
Coln,wHBhInf
CoJon of Inni chdhcI by best . .
Coluram. uat-livn. nipa and baaea
*■ wrouffhl-lnn, Blre«gth of
GofDpantKe nriatance lo cniifhliia
CompaTfaon of tbennomeleTs • .
COmpoallkni of forcea
Conente, atniifth ot . .
Condnuoua ginlera. nnugl
norrngaled aliMt.irDn : .
Oort of Jlllhlte bUlWtTlKK .
OaMparaqnare'tODtof fact
Cmlon «ini.-dgn, K.Y . .
CmUaB belgbl of brick an
CrnaUiiB ilrtnElh of mater
Mrength of alone.
Cube nwt.nile for dctermli
fjfuloia. lo deteriW n . .
BeOtctloo of Imutu . ,
ih-plBle girders 336
wooden, loads on SM
.uffnew of ' . . aei
of water S36
iDBCoprem m
«, deanllkin o( lib
« 162
ndstton wall Hfl. 118, lift
HdiUoni 130
■ch plate wlndow-glsM, prlce-llBt MI>
Uon, co.efflcleatof HO
memomnda «I
plp« 601
Hon of g»B In «T
lera, imnliimom 32T
aiUh-plBle 33e
forfloo™ 360
riveted plate Iroo 3U
• for skylight* 647
ilta, strength of ' IW
lUcal analyal* of roof-truwei ttH
■Itj, centre of 138
Ian long meunres St
dslooes, weight of 6^
<er> clwln 3^
mer-beam roof-iraBaee, annljel* of 443
" " descrlptlDn 400
hiaof columne (moQumeiilal) 484
of iplrH 486
of lOTen and domes 484
iw brick arolwe 367
brick partttfoDS. 3S6,390
describe an
decimals of a foot, ti
■i
'll'l INPEX.
Urtolulion of torcot
^
, ,'"" - ■ -
' ■ ' gjM
SbIdw, .ymboli tor ihe -
:lill\:l
K™ilB({..p8(jelll.cb(»l
*
^>»d (•( dnimi and pu1l«yfl
ii-:^uv:.-
, . - , »v^
INDEX. ^17'
PA OB
Square root, rule for determining 4
" '♦ table of 7
Stability, detiuition of 126
Stability of arche« 185
•• of pierH, buttresses, etc 178
Stairs 478
Statics, definition of 125
Steam -pi pes 504
Stiffnet*n of beams, general formula ,318
" of beams, ratio of 322
" of continuous girders 334
♦♦ of cylindrical beams 326
♦* of hard-pine beams 323
" of oak beams 325
" of rectangular beams, formulas 321
** of spruce beams 324
Stirrup-irons 358
Strain, definition of 126
Strength of beams, general principles 280
** ** •• iron, formulas for 283
" *' ** supporting brick wall 304
" of cast-iron beams 307
** of cast-iron columns 226, 227
'* of chains 212
** of continuous girders 329, 333
** of cylindrical beams 311
*♦ of flat rolled iron bars ; . 205
" of hard-pine beams, table 313
*< of hemp and Manila ropes 210
** of inclined beams 286
" of iron and steel wire ropes 209
of masonry 165
of mortars 165, 170
of oak beams, table 314
" of Pencoyd beams, channels, etc 293, 301
" of Phoenix iron beams 298
" of pins and tree-nails 215
" of posts, struts, and columns 217
" of rectangular beams, diagonal, vertical 311
'* of solid timber and plank floors 361
" of spruce beams, table 315
'* of Trenton beams, channels, etc 287, 802
" " •♦ " proportional to weight 285
'' of Union Mills beams, channels, etc. . 290, 808
" of wooden beams 307
" of wooden floors 353
*• of wrought-iron (tensile) 199
♦• of wrought-iron rods 204
Stress> definition of . . : - '^^E®*
Structurea, detinition of ....««»* ^
irtruts, i!i«rd-p/ne and oak, strength of * *
" w^roiijrbtfron, strength of
vmipi™, afnmtinn 'i
Wiitw-ptuxeU, ■paw tar
»«««
Weight, BpolhissrH.- .
■' itvDlnlii[«lf. .
KiDBUriib
■' uiKl ■tceriglb of U
of idr
xidvip*'
™u™t,«..e
-pipes
cocper, brsM,
HDdl»d
n«iindbar1n!
id guket for [ilpo joints .
WrigblB,
WBll-dlgg
Wludpre
BdUgM,
Win
■Wire
Wooden buaniB. atrengtb of
W<»duD eDlumiui ....
VraughlJroii chimney* .
Wroughl-IcDn, Imcluml eiirfa
Wruugbt-lroD poslg aoii eoli
" wiiter.pIpBi
welded tnbu
York OMbedi
ll
INDEX. G21
IXDEX TO ADDITIONS.
PAGE
, rock rm
imeiiKioiirt and weijfht of 5o(»n
>ards, height of . 577
etting, miinhor of bricks loquired 597
y of i)ii)('rt and rt^j^intcrs 602
i«<. (MinenHionn of 578
roofiiig-Klatow 593
i(»iis of bfllw 550b
of cairiaijert 578
of Connecticut State Capitol 576
of tire-engine8 577
of hose-carriagert 577
of ladder- wagon « 577
of Metropolitan Opera House 575
of Philadelphia (Mty Hall 576
of radiators 603
of registevH and ventilators Oni
of t«choul rooms 577
of Steinway pianos 577
of Washington Monument 575
^ es 579
cini^H, dimensions and weight (;f 577
f the wind 580
tal tubular boilers .599
rriages ^ 577
wagons, dimensions of 577
?ment of l)rick-wo»k 595
' of stone-work 594
»litan Opera House, dimensions of 575
'I'iie l^Mve .')S0
phia City Hall, ^limen^ions of 570
dimensions of 577
rs, diinencions of 603
•s. ca[)a('ity of 602
dimensions of 601
phalt 501
ight8, load, dimeiifiions of 57S
>ofu8, dimensionH of .'»77
•ofing, cost of 593
ork, measurenieiit of 594
boilers, horizontal 599
" upright 600
ttihular boilers 600
i;ton Monument, dimeDaious of .)75
of bells ' .550b
of compressed lead Bash-weightd 578
of cord-wood 579
of fire-engines ,...».,. ^"v
»/■ /jON." rvirr/ages ,, '^"v
■/' /.i</<ier-\vago/jH ,,».•»«••** ^^^^
* .iim'n-. /XT M • ^
rv of ....-•*
GUARANTEED
Roofing Plates
Every sheet of our Guaranteed Roofing
Plates is now stamped, not only with
the name of the brand, but also
with the thickness, 10 or IX.
" GILBERTSON'S OLD METHOD"
Extra Heavily Coated Roofing Plate.
W'v %Mi,iranUM* this to Ix' a l>etter and heavier coated i)late than
*• M. v./' "Old Styli^," or any other extra-coated plate; ami, if
ii«»i Unuid so, all boxes may be held subject to our order.
' CAMARET
f f
Guaranteed Roofing Plate.
Tlif larixr and inrirasini^ demand for this ])lato, which is sold hy
IIS iindci' a positive and (ielinite i^uaranty as to material, coatinij.
■.u\-[ '-.tt' ml assortment, is sullicicnt evidcmu' of tht^ apprecMation ot
•> 111!'- !>' lilt' 1 rade at laru<'.
\vdr]\ and (>vt'r\ box «)f both of the above brands is strapped with
linop irn;i. and contains a card with the nanie of the assorter.
r.otl, iIm *'<;ill)erts<)irs Old Method" and the "Caina-
r<'t " tr<' niadr of the v<'rv best (juality of Siemens Mjirtin sleel.
till' only ditference ix'inn that th(^ former is far more heavih
riy.y' cd.
We keej) both the above brands in stock in \ew York and Clii-
eaL,M>, as \vt»ll as in Philadelphia.
We can furnish Till Sliiiijfles made from our guaranteoil
brands of lloolini; IMates.
Merchant & Co.,
525 Arch Street, PHILADELPHIK.
SO Beekman Street, NEW XORK.
135 Lake Street, CHVCN^Q. W
PIONEER
preproof Construction!
Vpatentees. Manufacturers, and Contractors.
HOLLOW. SOLID, AND POROUS
[FIRE-CLAY TILE
jireproofing Buildings.
W/ow Tile, Floor Arches, Partitions, Walls, Roof^
Furring, Vault Lining, Column and
Girder Covering.
ife-proof Protection for Iron and Wooii Con-
struction in Every Form.
FIRE-CLAY TILE. SUSPENDED CEILIHGS. ETC.
T lllnstraieil Catalogue a.
CLARK AND SIXTEENTH STREETS.,
CHZCiiCO, IIXU.
^e/ephone 8iS3.
I
IMPORTED SnSSEl MD NEUCUTEl
Natural Rock Asphalt
FOR FLOORS.
Tfl K :ittoiitioii of architectrt and owiieni of buildingK li« callwl to Imported
K<H'k Asphalt, for floon of (VI Lin*. HturpM, Ijaniidrlets CoDaenratoiie*,
I*n'weriei«, KltcheDi* of IloteU nnd rnhlic J nutltottona, Kugmr ReRiiMiet,
Siuhlin*. ICliikH, Maiiufactorfeii, vtc, or in any plac« where a smooik,
Imrd. dry. Hr«*pn>of aiHl wateri>roof, odnrleM, an<i durable coverii»,
fret* from dui«t, Ik rtHiuinil, cither over cfinent, concrete, briclc, or wood,
ill OIK* H)toi>t, without HeamH; aliK>, over ooncrete, for roofa for flreproof buiU>
iim^. For liweliinK-hoitiM' oellan*, especially on inol«t or fille<l land, tnts matciU
it ('ri|Ht'iully udupteil, t>eiMg water-tlinit, Don-alworlient, free from mould onkiM,
imiKTvioiiH to ■»ewi'r-v»>««*'*. and for sanitary puHMttmn invaluable, it !« eqaiilljr
wHi :td:ipttti for UoiidwayH and Walki*, an it will wlthi4and the hardeot vtmffi.
'j'liii* urtirU*. Uiut; in UfH' in Kurope, where It* great value ha« been proved, U
Natural liiH'k Asphalt, and containit no coaUtar or artlticial products, haudew
ininuMliat(>ly, aind in ready for umh within a few hours after being laid.
Wt' ha\('*iii our employ fori'it^n exiierti* of long exi>erience, and are ready to
promptly till ordern for an v work in this line.
Althoi'iuh wi> carry the cheaper grades in stock, and are prepared to give ei4i-
mati'rt tor such work, the standard brands, Seysael and Neuchatel (Val deTn-
viTM;, II, r kintirn to be much superior in all respects.
\\\' append a list of a few samples of our work in Boston and vldnity.
BA8KMKNTS.
F. L. .\m4>'« Itulhliii:;. isomer Kingston and Bedford Streets, Boston, Msm. E
II. Iiirharil!40ii. ArchitiH*!.
M.)M'.H Kimball r.uililiii«, 'M\ Oliver Stre<'t, ISoston, Mjws.
r.o^l.m Daily AdvcillmT Iluilding. Washinifton Htreet, Hoston, Mus!<.
Ili-iuiiu'iiway Itiiililiiiu. coriu'r Court and Treniont Streets, Boston, Mass. Brad-
U'> . \Vi:i!*lttw, it Withert'll, A ri-hlteets, Boston.
Ma^oiii*' r.-mplr. rttnit-r Tremonl and Boylston Streets, Boston, Mass.
Ilvdt' School. llammniHl Street, Boston, Mass.
New ^«li<> >l hoiiHf. r>lortrt()in Street. Boston, Mass.
ll;ii\;ii:l \le«Ui-al Srhool, llosloli, Mass.
STABLES.
H;irv;ii<l W'UMiiiaiy School, Village Slre<»t, Boston, Mass. W. Whitney Lewi*,
Arcliilect.
A(l;iin«- llxpresf* Stable, Villaife Street. Boston, Muss.
ArliiiirtoM ('lull Stable, Chesinut Street, Boston, M.oss. Sturgis & Brigham.
.\rchiti'cl-».
MISCELLANEOUS.
S.h.H.l di' 'IVH'hnolony, Boylston Street. Boston, Mass. I'pper floors.
Fasiciiil Hall Market", Bost'jui, Mass. Passoucway. ^
M«Mh:iiii«- Charitable Association. Boston, Mass. Kitchen doors.
WilN Mt'inorial liisiitiite. Morton, Mass. Water-closets and bathrooms.
T. M. D.ivir*. Newport, IM. IJoof.
v.. 1» Sawyer, Cambridife, Mass. House cellar.
Mr. r.rown, «.i^l Beacon Street, Boston, Mass. House cellar.
Ito^toM v<: .Xlbaiiy Kailroad. Walks around station, South Framingham, Maiu*.
IVpperell Maiiiifacturintr Co., Bitldeford. Me. Yard.
Hoti-I Wentworth, Newcastle, N.H. laundry tloor.
Para Kiibbcr .-ihoe Co., South Framingham, Mass. Floors.
Saiuples may be seen at our otiices, and work In use will be cheerfully shown
on a]>j>lication.
SIMPSOH B^OT^^^%.
22 Millt Street, ^oaXoo-^^^ftaa"
'5, 159 La SaWe ^tx^^^-^ ^"^^^^^^
I
^^TSOORD^^^
No. 387 Harrison Avenue, BOSTON.
METAL
5KYLIGHTS»i VENTILATORS,
Garry's Patent Iron Roofing,
ORRUGATED IRON rOR ROOriNG AND SIDING. AND MONTROSS'S
PATENT METALLIC SHINGLES.
lornices, Window-caps, Bay and Oormer Windows, etc., in t
Galvanized Iron, Copper, and Zinc.
BOSTON ARCHITECTURAL
Sheet Metal Works, ,
METAL WORK <°> BUILDINGS. {
i'oppt'i- lift}/ Whiihtir-- • i|
'^iiti'tlx. Coi-iticcM, Giittet-M, t'otHfifftors, t
Whufoif Cups, i'f<',
Galvaraj Iron SlyliMs aai Teiitilatflrs.
No. 5 MOTTE STREET,
r Harrison Avenue. B Q ^^ ^ Vk -J
HENRY MAURER,
lUHUTACTDBBB OT
HOLLOW BRICK
or EVERY DESCRIPTIOM FOR
IFratEKln of Ins B«uu, FitnM ivu 3d, ISBL)
SllflllJ. PAI1III1«5S. FIBEIB. b. POROIS WIERIAl ofiSia
420 East 23d St., New York.
Corrugated Wire Lathing,
FBOTECTION TROM FIBE.
Perfect freedom from cracked or falllngf plaster. I
GivG'i a contlniiouii key to mortar, without furrlne of an; I
kind. I
Seal^ faces of beams. preveatlDff all circulation of air. '
(( risiill iKit iittiihutt irfterr f'lirrliiff imd fint trhe I
r/<,tli ine iixvil.
la thorouglily simple and convenient to handle and applr
A8 it can be uaed directly on the tace of wood sheath-
lni2. it is particularly adapted for plaeteriHK exteriors of
frame houses.
Delivered In flat sheets inquiring' no furring or atretcti-
Ing.
THE STANLEY COBRVJGWtO ?WtVMiW VWYNftS. -Wv.
230 Broa«l>Na^, He>w '<wV.
^-«OLD MEDAL, CHRIST CHURCH, N.ZF"""
SILVER MEDALS, Highest Award.
Amsterdam, IS83. Calcutta, 1884.
Brooks, Shoobridge, & Co.
BEST ENGLISH
PORTLAND CEMENT.
CHARLES J, STEVENS, Agent, 7 Bowlicg Green, N.Y.
Works: Craya, Ess«x, England.
JOHN FARQUHAR'S SONS
Slate, Copper, Tin, and
Gravel Roofing.
Nos. 20 and 22 EAST ST., BOSTON.
Ordcf box It Matter Builders' Association, 164 DCVOItSHIfle ST.
SPECIAL ATTENTION GIVEN TO REPAIRS OF ALL KINDS.
1
Inventori atid on'iiere of Furq nhBrV Pi.tenl B\irto»»»\onEY»,lO(W»w*?»n. *««
p
Benjamin H. Shoemaker.
Foreign Window Glass ; French Plate Glass
Cathedral Glass. English and Scotch;
» Rough and Ribbed Skylight Glass;
French Window Glass (extra double thick);
Enameled and Colored Glass;
German Looking-Glass ; Beveled Edge Mirpors.
A FULL STOCK ALWAYS IN STORE. TOGETHER WITH
AMERICAfJ WINDOW GLASS, COACH. CAR, and CHURCH GLASS,
CUT 10 A^Y SIZE OR PATIERN.
205, 207, 209, and 211 NORTH FOURTH ST,
FIIZZ<ADSI<FSL&.
Electric Valve Service
FOR AUTOMATIC REGULATION DF TEMPERATURE.
Aulomalrc, EconDmical, Neiuleu, Ml
Elicienl.
THE
Johnson Electro- Pneumatj
VALVE SYSTEM
ti
■criutlve
t\>\<\iau,l
A. H. AHDRt>N% «L CiiCk.
•?rlJ«ulkHn Street, BOSTQW. w^ Nt)toMVV.-.*wi*.ww*
'^ ) Bo.a S»ee<. HtHi -(OTV.
1
ABSOLUTELY
K-P/fOOF CONSTRUCTION.
CLINTON WIRE LATH,
In use for 25 years.
jUifD. No building protected by this LATH
has ever been destroyed by fire.
SEND FOR CIRCULAR.
CLINTON WIRE CLOTH CO.,
■S Beekman Street. 137 Lal<e Street, 23 Court SIr«el, Main Office,
NEWYOflK CHICAGO, BOSTON, CLINTON. MASS.
INGALLS & KENDRICKEN.
Steam- Heating Apparatus,
far Warming and VentHaiing Dwel/mg-Houses, Public
Buildings, Hospitals, School-Houses, flail-Road
Stations, Mills, etc.,
(Elogston'5 jpntcnt Steam Babiators,
WE ALSO MAHUrACTURC SECTIONAL SAFETY STEAM BOILERS,
BOTH FOR POWER AND HEATING.
OFFICE ma MANUFSCTORY;
80 and 82 SULBTJUX ST^-EER.,
A IKOA,,^ (CODMAN BUlLDmG.I t-rVCTTC
MlWIA A; REBER
PATENT
EXPANDING WATER CONDUCTOR.
S. S. S. Conductor Co.
1 63 Lacock Street,
AU^GHEKT, PA.
iJU)«a of i
8 ruNlCL
6-FOOT LENCTI
SINGLE SWEET
SOFT STEEL.
CALVANIZEO,
KALAMEINED,
SOLDERLESS
STANDING SEA
CONDUCTOR CO^
lii:i Lacut'k Slrrt-t
llip whII lo miiko riDy tivcr-
Ikiw Troni tlic eave pipe m
]jcu(l, rim down the sp.iiit.
:iud not the wull ; anU w 1 1 1
open, iu ciise of freeKinu-.
Kt) ua 10 prevent bursiirin,
.ind cm rmuiin lioiibli;
Ji.uktduad wulur-tiglit.
09^_
New England Felt Roofing Co,
BEE-HIVE BRAND
F®£T HOOFIN(
Approved by Ihe best architects and contractors.
insured at same rates 3s metal or slate.
The "Standard " in use by most of the prominent manufact
companies in New England.
" Bee-Hive Brand," Basin Sized Sheathing.
" Standard ftl " Tarred Paper. tK^
Office: 22 MLlIiK. STBEEra, ■BSi^T:i3&
IronlBp^n
loenix Iron
^o. 410 WALNUT STREET,
PHILADELPHIA. PENN..
^ACTURE ROLLED BEAMS. CHANNELS, ANGLES.
T-SHAPE AND BAR IRON OF ALL SIZES.
1 Trusses, Girders, and Joists for Fire-Proof
Maildings, framed and ffited as per plans.
WKOKJHI' IltON COrUMSfii OF ALL SIZHS.
Die-forged Weldless Eye-Bars a Specialty.
Htiiuitli-H I'umlitliill bit npptimliOH.
y 30.000 Tons. Established 1852.
\
A. & P. Roberts & Co.,
PENGOYD IRON WORKS.
OFFICE: 261 SOUTH FOURTH STREET,
PHILADELPHIA. PENH.
XB-O^ OR STEEL
teams, Channels, Deck-Beams, Angles, Tees,
Plates, and Merchant Bar,
TJARANTEED TO COMPLY WITH SPECW^CS^-VCfS*
£
to/terf m dammereil lite M "iiw*®
'POSITIVE yENTILilTII
OF
PUBLIC BUILDINGS,
POSITIVE CHANGE OF AIR
II nf w
L«hnnk'Hl »p-iil, wiioaii Hction i- us rPliaMf ns tint of a |i
I »iniiviiij[ wnter.
Sueh an »)t<>iit. i nielli gently KTitiiloyeil, tan alouu aolvl
' pnilili-iti o(
PERFECT VENTILATION.
CONTRACTS TAKEN
School-Houses, Halls, and Church(
CORRESPONDENCE INVITED.
N.y.
45 Fulton Street, 32 OUvor Street, j
>
Wanitary Appliances.
■THiii. II 11/ • II iii:i: t i.ii.\ET,
■•C.ISCAIH:'- WATIilt CLOSKT.
'• MOU'HA UK •• WASH-OUT CLOSKT,
■ Uiii'/iK','' " Gothtim " and "SiaiidHcrf," Imiff
tiiHl tt/ioft Ho/titet'K,
"jVch' neptti-fiu-e " Vnliv Basin.
~A» IheMgqcKl- are InrKtlj' O'fil IhrauKliiiut Ihc l'"tmi SlaU-n, m«i Man.t hidlily
lllustrntod cin^nlare on ai'ipA'cMliri.
SEITKV UTTSBK <£ CO.,
Manufacturers.
SHOW-KOOMS AND OFFICES AT
ID BEEKMAN ST., 235 WASHINGTON ST.,
NEW YORK. - BOSTON.
PATENT
Soapstone Finish,
For Finish or skim coat on walls and ceilings,
ym not absorb. Will not chip or crack. Can be
vraBhed. Groves extremely hard ^rith age.
Potter's Colored Mortar.
Makes a strong joint, will not absorb, and
therefore holds its color.
END FOR CIRCULARS
American Soapstone Yvi»^ ^^-.
^ NASHUA., N.V\.
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