Full text of "Cyclopedia of civil engineering; a general reference work on surveying, highway construction, railroad engineering, earthwork, steel construction, specifications, contracts, bridge engineering, masonry and reinforced concrete, municipal engineering, hydraulic engineering, river and harbor improvement, irrigation engineering, cost analysis, etc."

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THE LIBRARY

THE UNIVERSITY
OF CALIFORNIA

LOS ANGELES

GIFT OF

G. J. Cummings

Cyclopedia

Civil Engineering

A General Reference Work on

SURVEYING, HIGHWAY CONSTRUCTION, RAILROAD ENGINEERING, EARTHWORK,

STEEL CONSTRUCTION, SPECIFICATIONS, CONTRACTS, BRIDGE ENGINEERING,

MASONRY AND REINFORCED CONCRETE, MUNICIPAL ENGINEERING,

HYDRAULIC ENGINEERING, RIVER AND HARBOR IMPROVEMENT,

IRRIGATION ENGINEERING, COST ANALYSIS, ETC.

Prepared by a Corps of

CIVIL AND CONSULTING ENGINEERS AND TECHNICAL EXPERTS OF THE
HIGHEST PROFESSIONAL STANDING

Illustrated with over Two Thousand Engravings

NINE VOLUMES

CHICAGO

AMERICAN, TECHNICAL SOCIETY
1917

BY
AMERICAN TECHNICAL SOCIETY

AMERICAN SCHOOL OF CORRESPONDENCE

Copyrighted in Great Britain
All Rights Reserved

Cff

Authors and Collaborators

FREDERICK E. TURNEAURE, C. E., Dr. Eng.

Dean of the College of Engineering, and Professor of Engineering, University of

Wisconsin

Member, American Society of Civil Engineers
Joint Author of "Principles of Reinforced Concrete Construction," "Public Water

Supplies," etc.

FRANK O. DUFOUR, C. E.

Structural Engineer with Interstate Commerce Commission Division of Valuation,

Central District

Formerly Assistant Professor of Structural Engineering, University of Illinois
Member, American Society of Civil Engineers
Member, American Society for Testing Materials

WALTER LORING WEBB, C. E.

Consulting Civil Engineer

Member, American Society of Civil Engineers

Author of "Railroad Construction," "Economics of Railroad Constr

W. G. BLIGH

Inspecting Engineer of Irrigation Works, Department of Interior, Canada
Formerly in Engineering Service of His Majesty in India
Member, Institute Civil Engineers (London)
Member, American Society of Civil Engineers
Member, Canadian Society of Civil Engineers

ADOLPH BLACK, C. E.

Civil and Sanitary Engineer, General Chemical Company, New York City
Formerly Adjunct Professor of Civil Engineering, Columbia University

EDWARD R. MAURER, B. C. E.

Professor of Mechanics, University of Wisconsin

Joint Author of "Principles of Reinforced Concrete Construction"

AUSTIN T. BYRNE

Civil Engineer

Author of "Highway Construction," "Materi

Authors and Collaborators — Continued

A. MARSTON, C. E.

Dean of Division of Engineering and Professor of Civil Engineering, Iowa State College
Member, American Society of Civil Engineers
Member, Western Society of Civil Engineers

De WITT V. MOORE

Consulting Engineer and Architect
District Engineer— Central District Division of Vak
Interstate Commerce Commission, Chicago
Member, American Society Engineering Contractor:
Member, Indiana Engineering Society

W. HERBERT GIBSON, B. S., C. E.

Civil Engineer

Designer of Reinforced Concrete

C. D. RAWSTORNE, C. E.

Consulting Engineer, Civil Engineering Department, American School of Corresponden
Formerly Superintendent of Construction, John M. Ewen Company

HENRY J. BURT, B. S., C. E.

Structural Engineer for Holabird and Roche, Architects

Member, American Society of Civil Engineers

Member, Western Society of Civil Engineers

Member, Society for the Promotion of Engineering Educate

RICHARD I. D. ASHBRIDGE

Civil Engineer

Member, American Society of Civil Engineers

HERMAN K. HIGGINS

Civil Engineer

Associate Member, American Society of Civil Engineers

Member, Boston Society of Civil Engineers

Member, New England Water Works Association

Member, American Railway Bridge and Building Association

ALFRED E. PHILLIPS, C. E., Ph. D.

Professor of Civil Engineering, Armour Institute of Technology

Authors and Collaborators— Continued

H. E. MURDOCK, M. E., C. E.

Head of Department of Agricultural Engineering, Montana State College, Bozeman,

Montana
Formerly Irrigation Engineer, U. S. Department of Agriculture

A. B. McDANIEL, B. S.

Assistant Professor of Civil Engineering, University of Illinois
Member, American Society of Civil Engineers
Member, Society for the Promotion of Engineering Education
Fellow, Association for the Advancement of Science
Author of "Excavating Machinery"

GLENN M. HOBBS, Ph. D.

Secretary and Educational Director, American School of Correspondence
Formerly Instructor, Department of Physics, University of Chicago
American Physical Society

THOMAS FLEMING, Jr., B. S., C. E.

With Chester & Fleming, Hydraulic and Sanitary Engineers
Associate Member, American Society of Civil Engineers
Member, New England Water Works Association
Member, Engineers' Society of Pennsylvania

CHARLES E. MORRISON, C. E. , Ph. D.

Formerly Instructor in Civil Engineering, Columbia University

Associate Member, American Society of Civil Engineers

Author of "Highway Engineering", "High Masonry Dam Design"

EDWARD B. WAITE

Formerly Dean, and Head, Consulting Department, American School of Correspondence
American Society of Mechanical Engineers
Boston Society of Civil Engineers

HAROLD W. ROBBINS, M. E.

Formerly Instructor, Lewis Institute, and Armour Institute, Chicago
Past Secretary, The Aero Club of Illinois
Special Writer and Technical Investigator

JESSIE M. SHEPHERD, A. B.

Head, Publication Department, American Technical Society

Authorities Consulted

THE editors have freely consulted the standard technical literature of
America and Europe in the preparation of these volumes. They de-
sire to express their indebtedness, particularly, to the following
eminent authorities, whose well-known treatises should be in the library of
everyone interested in Civil Engineering.

Grateful acknowledgment is here made also for the invaluable co-
operation of the foremost Civil, Structural, Railroad, Hydraulic, and Sanitary
Engineers and Manufacturers in making these volumes thoroughly repre-
sentative of the very best and latest practice in every branch of the broad
field of Civil Engineering.

WILLIAM G. RAYMOND, C. E.

Dean of the School of Applied Science and Professor of Civil Engineering in the State

University of Iowa; American Society of Civil Engineers
Author of "A Textbook of Plane Surveying," "The Elements of Railroad Engineering"

JOSEPH P. FRIZELL

Hydraulic Engineer and Water-Power Expert; American Society of Civil Engineers
Author of "Water Power, the Development and Application of the Energy of Flowing
Water"

FREDERICK E. TURNEAURE, C. E., Dr. Eng.

Dean of the College of Engineering and Professor of Engineering, University of

Wisconsin
Joint Author of "Public Water Supplies," "Theory and Practice of Modern Framed

Structures," "Principles of Reinforced Concrete Construction"

HENRY N. OGDEN, C. E.

Professor of Sanitary Engineering, Cornell Uni
Author of "Sewer Design"

DANIEL CARHART, C. E.

Emeritus Professor of Civil Engineering, University of Pittsburgh
Author of "Treatise on Plane Surveying"

HALBERT P. GILLETTE

Editor of Engineering and Contracting; American Society of Civil Engineers; Formerly

Chief Engineer, Washington State Railroad Commission
Author of "Handbook of Cost Data for Contractors and Engineers"

CHARLES E. GREENE, A. M., C. E.

Late Professor of Civil Engineering, University of Michigan

Author of "Trusses and Arches, Graphic Method," "Structural Mechanics"

Authorities Consulted— Continued

A. PRESCOTT FOLWELL

Editor of Municipal Journal and Engineer; Formerly Professor of Municipal Engineer-
ing, Lafayette College
Author of "Water Supply Engineering," "Sewerage"

IRVING P. CHURCH, C. E.

Professor of Applied Mechanics and Hydraulics, Cornell University
Author of "Mechanics of Engineering"

PAUL C. NUGENT, A. M., C. E.

Professor of Civil Engineering, Syracuse University
Author of "Plane Surveying"

FRANK W. SKINNER, C. E.

Consulting Engineer; Associate Editor of The Engineering Record
Author of "Types and Details of Bridge Construction"

HANBURY BROWN, K. C. M. G.

Member of the Institution of Civil Engineers
Author of "Irrigation, Its Principles and Practice"

SANFORD E. THOMPSON, S. B., C. E.

American Society of Civil Engineers

Joint Author of "A Treatise on Concrete, Plain and Reinforced"

JOSEPH KENDALL FREITAG, B. S., C. E.

American Society of Civil Engineers

Author of "Architectural Engineering," "Fireproofing of Steel Buildings," "Fire Pre-
vention and Fire Protection"

AUSTIN T. BYRNE, C. E.

Civil Engineer

Author of "Highway Construction," "Inspection of Materials and Workmanship Em-
ployed in Construction"

JOHN F. HAYFORD, C. E.

Expert Computer and Geodesist, U. S. Coast and Geodetic Survey
Author of "A Textbook of Geodetic Astronomy"

WALTER LORING WEBB, C. E.

Consulting Civil Engineer; American Society of Civil Engineers

Author of "Railroad Construction in Theory and Practice," "Economics of Railroad
Construction," etc.

Authorities Consulted — Continued

EDWARD R. MAURER, B. C. E.

Professor of Mechanics, University of Wisconsin

Joint Author of "Principles of Reinforced Concrete Construction"

HERBERT M. WILSON, C. E.

Geographer and Former Irrigation Engineer, United States Geological Survey; Ar

Society of Civil Engineers
Author of "Topographic Surveying," "Irrigation Engineering," etc.

MANSFIELD MERRIMAN, C. E., Ph. D.

Consulting Engineer

Formerly Professer of Civil Engineering, Lehigh University

Author of "The Elements of Precise Surveying and Geodesy," "A Treatise on Hy-
draulics," "Mechanics of Materials," "Retaining Walls and Masonry Dams,"
"Introduction to Geodetic Surveying," "A Textbook on Roofs and Bridges," "A
Handbook for Surveyors," "American Civil Engineers' Pocket Book"

DAVID M. STAUFFER

American Society of Civil Engineers; Institution of Civil Engineers: Vice-President,

Engineering News Publishing Co.
Author of "Modern Tunnel Practice"

CHARLES L. CRANDALL

Professor of Railroad Engineering and Geodesy in Cornell University
Author of "A Textbook on Geodesy and Least Squares"

N. CLIFFORD RICKER, M. Arch.

Professor of Architecture, University of Illinois; Fellow of the American Institute of

Architects and of the Western Association of Architects
Author of "Elementary Graphic Statics and the Construction of Trussed Roofs"

W. H. SEARLES, C. E.

Author of "Field Engineering" and "Railroad Spiral"

HENRY T. BOVEY

Late Rector of Imperial College of Science and Technology, London, England
Author of "Treatise on Hydraulics"

WILLIAM H. BIRKMIRE, C. E.

Author of "Planning and Construction of High Office Buildings," "Architectural Iron
and Steel, and Its Application in the Construction of Buildings," "Compound
Riveted Girders," "Skeleton Structures," etc.

Authorities Consulted— Continued

IRA O. BAKER, C. E.

Professor of Civil Engineering, University of Illinois

Author of "A Treatise on Masonry Construction," "Engineers' Surveying Instruments,
Their Construction, Adjustment, and Use," "Roads and Pavements"

JOHN CLAYTON TRACY, C. E.

Assistant Professor of Structural Engineering, Sheffield Scientific School, Yale

University
Author of "Plane Surveying: A Textbook and Pocket Manual"

FREDERICK W. TAYLOR, M. E.

Joint Author of "A Treatise on Concrete, Plain and Reinforced"

J. B. JOHNSON, C. E,

Author of "Materials of Construction;" Joint Author of "Design of Modern Frame
Structures"

***

FRANK E. KIDDER, C. E., Ph. D.

Consulting Architect and Structural Engineer; Fellow of the American Institute of
Architects

Author of "Architect's and Builder's Pocketbook," "Building Construction and Super-
intendence, Part I, Masons' Work; Part II, Carpenters' Work; Part III, Trussed
Roofs and Roof Trusses," "Strength of Beams, Floors, and Roofs"

^«

WILLIAM H. BURR, C. E.

Professor of Civil Engineering, Columbia University; Consulting Engineer; American

Society of Civil Engineers; Institution of Civil Engineers
Author of "Elasticity and Resistance of the Materials of Engineering;" Joint Author of

"The Design and Construction of Metallic Bridges," "Suspension Bridges, Arch

Ribs, and Cantilevers"

WILLIAM M. GILLESPIE, LL. D.

Formerly Professor of Civil Engineering in Union University

Author of "Land Surveying and Direct Leveling," "Higher Surveying"

GEORGE W. TILLSON, C. E.

Past President of the Brooklyn Engineers' Club; American Society of Civil Engineers;

American Society of Municipal Improvements
Author of "Street Pavements and Street Paving Material"

<*»

CHARLES E. FOWLER

Consulting Civil Engineer; Member, American Society of Civil Engineers
Author of "Practical Treatise on Subaqueous Foundations"

W. M. PATTON

Late Professor of Engineering at the Virginia Military Institute
Author of "A Treatise on Civil Engineering"

Fore wor d

all the works of man in the various branches of en-
gineering, none are so wonderful, so majestic, so awe-
inspiring as the works of the Civil Engineer. It is the Civil
Engineer who throws a great bridge across the yawning chasm
which seemingly forms an impassable obstacle to further
progress. He designs and builds the skeletons of steel to dizzy
heights, for the architect to cover and adorn. He burrows
through a great mountain and reaches the other side within a
fraction of an inch of the spot located by the original survey.
He scales mountain peaks, or traverses dry river beds, survey-
ing and plotting hitherto unknown, or at least unsurveyed,
regions. He builds our Panama Canals, our Arrow Rock and
Roosevelt Dams, our water-works, nitration plants, and prac-
tically all of our great public works.

C, The importance of all of these immense engineering
projects and the need for a clear, non-technical presentation of
the theoretical and practical developments of the broad field
of Civil Engineering has led the publishers to compile this
great reference work. It has been their aim to fulfill the de-
mands of the trained engineer for authoritative material which
will solve the problems in his own and allied lines in Civil
Engineering, as well as to satisfy the desires of the self-taught
practical man who attempts to keep up with modern engineer-
ing developments.

€1. Books on the several divisions of Civil Engineering are
many and valuable, but their information is too voluminous to
be of the greatest value for ready reference. The Cyclopedia of
Civil Engineering offers more condensed and less technical
treatments of these same subjects from which all unnecessary
duplication has been eliminated; when compiled into nine
handy volumes, with comprehensive indexes to facilitate the
looking up of various topics, they represent a library admirably
adapted to the requirements of either the technical or the
practical reader.

C, The Cyclopedia of Civil Engineering has for years occupied
an enviable place in the field of technical literature as a
standard reference work and the publishers have spared no
expense to make this latest edition even more comprehensive
and instructive.

C, In conclusion, grateful acknowledgment is due to the staff
of authors and collaborators — engineers of wide practical ex-
perience, and teachers of well recognized ability — without
whose hearty co-operation this work would have been im-
possible.

Table of Contents

VOLUME VI
MASONRY AND REINFORCED CONCRETE . . .

. By Walter Loring Webb and W. Herbert Gibson^ Page *11

Masonry Materials: Natural Stone— Testing Stone— Building Stone— Bricks-
Concrete Blocks— Cementing Materials— Cement Testing: Chemical Analysis,
Specific Briquette, Molds, Mixing, Molding, Storage of Test Pieces, Tensile
Strength— Constancy of Volume, Broken Stone— Mortar: Properties, Mixing and
Laying, Concrete, Waterproofing, Preservation of Steel in Concrete — Fire Pro-
tective Qualities— Methods of Mixing Concrete, Steel for Reinforcing— Types of
Masonry: Stone Masonry — Brick Masonry — Concrete Masonry — Rubble Concrete
—Concrete Under Water— Clay Puddle— Foundations: Character of Soil— Prepar-
ing Bed— Footings— Pile Foundations— Types of Piles-Construction Factors-
Cofferdams— Cribs— Caissons— Gravity— Retaining Walls— Bridge Piers— Abut-
ments— Culverts— Concrete Walks — Concrete Curbs — Reinforced Concrete Beam
Design: Theory of Flexure— Percentage of Steel— Resisting Moment— Calcula-
tion and Design of Beams and Slabs: Slab Bar Spacing, Simple Beams, Bonding
Steel and Concrete, Slabs on I - Beams— T- Beam Construction— Flat-Slab Con-
struction: Method, Placing Reinforcing Bars, Rectangular Panels— Reinforced
Concrete Columns and Walls: Flexure and Direct Stress— Footings: Simple,
Compound— Reinforced Concrete— Retaining Walls— Vertical Walls— Culverts-
Girder Bridges— Columns— Tanks— Concrete Construction Work: Machinery for
Concrete Work: Concrete Mixers — Sources of Power — Hoisting and Transporting
Equipment — Construction Plants — Forms: Building Forms, Forms for Sewers
and Walls, Forms for Centers of Arches — Bending of Trussing Bars — Bonding
Old and New Concrete— Finishing Surface of Concrete — Representative Exam-
ples of Reinforced Concrete Work — Concrete Arch Design and Construction:
Theory of Arches — Voussoir Arches: Distribution of Pressure, External Forces,
Depth of Keystone, Voussoir Arches Subjected to Oblique Forces, Illustrative
Examples — Elastic Arch: Advantage and Economy, Mathematical Principles,
Illustrative Example (Segmental Arch of 60-Foot Span, Depth of Arch Ring,
Loads of Arch, Laying off Load Line, Trussed, Shear, Moment, Temperature
Stresses, Combined Stresses)— Hinged Arch Ribs

REVIEW QUESTIONS Page 461

INDEX Page 473

* For page numbers, see foot of pages.

t For professional standing of authors, see list of Authors and Collaborators at
front of volume.

MASONRY AND REINFORCED
CONCRETE

PART I

MASONRY MATERIALS

Masonry may be defined as construction in which the chief
constructive material is stone or an artificial mineral product such
as brick, terra cotta, or cemented blocks. Under this broad defini-
tion, even reinforced concrete may be considered as a specialized
form of masonry construction.

NATURAL STONE
BUILDING VARIETIES

Limestone. Carbonate of lime forms the principal ingredient
of limestone. A pure limestone should consist only of carbonate of
lime. However, none of our natural stones are chemically pure,
but all contain a greater or less amount of foreign material. To
these impurities are due the beautiful and variegated coloring which
makes limestone valuable as a building material.

Limestone occurs in stratified beds, and ordinarily is regarded
as originating as a chemical deposit. It effervesces freely when an
acid is applied; its texture is destroyed by fire; the fire drives off its
carbonic acid and water, and forms quicklime. Limestone varies
greatly in its physical properties. Some limestones are very durable,
hard, and strong, while others are very soft and easily broken.

There are two principal classes of limestone — granular and
compact. In each of these classes are found both marble and ordinary
building stone. The granular stone is generally best for building
purposes, and the finer-grained stones are usually better for either
marble or fine cut-stone. The coarse-grained varieties often dis-
integrate rapidly when exposed to the weather. All varieties work
freely and can be obtained in blocks of any desired dimensions.

2 MASONRY AND REINFORCED CONCRETE

Marble. When limestone is wholly crystalline and suitable
for ornamental purposes, it is called marble; or, in other words, any
limestone that can be polished is called marble. There are a great
many varieties of marble, and they vary greatly in color and appear-
ance. Owing to the cost of polishing marble, it is used chiefly for
ornamental purposes.

Dolomite. When the carbonate of magnesia occurring in lime-
stone rises to about 45 per cent, the stone is then called dolomite.
It is usually whitish or yellowish in color, and is a crystalline granular
aggregate. It is harder than the ordinary limestones, and also less
soluble, being scarcely at all acted upon by dilute hydrochloric acid.
There is no essential difference between limestone and dolomite with
respect to color and texture.

Sandstone. Sandstones are composed of grains of sand that
have been cemented together through the aid of heat and pressure,
forming a solid rock. The cementing material usually is either
silica, carbonate of lime, or an iron oxide. Upon the character of
this cementing material is dependent, to a considerable extent, the
color of the rock and its adaptability to architectural purposes. If
silica alone is present, the rock is of a light color and frequently so
hard that it can be worked only with great difficulty. Such stones
are among the most durable of all rock, but their light color and poor
working qualities are a drawback to their extensive use. Rock in
which carbonate of lime is the cementing material is frequently
too soft, crumbling and disintegrating rapidly when exposed to the
weather. For many reasons the rocks containing ferruginous cement
(iron oxide) are preferable. They are neither too hard to work
readily nor liable to unfavorable alteration, when exposed to atmos-
pheric agencies. These rocks usually have a brown or reddish color.

Sandstones are of a great variety of colors, which, as has already
been stated, is largely due to the iron contained in them. In texture,
sandstones vary widely — from a stone of very fine grain, to one in
which the individual grains are the size of a pea. Nearly all sand-
stones are more or less porous, and hence permeable to a certain
extent by water and moisture. Sandstones absorb water most
readily in the direction of their lamination or grain. The strength
and hardness of sandstones vary between wide limits. Most of the
varieties are easily worked, and split evenly. The formations of

MASONRY AND REINFORCED CONCRETE 3

sandstone in the United States are very extensive. The crushing
strength of sandstone varies widely, being from 2500 pounds to
13,500 pounds per square inch, and specimens have been obtained
that require a load of 29,270 pounds per square inch to crush them.

Conglomerates. Conglomerates differ from sandstone only
in structure, being coarser and of a more uneven texture. The
grains are usually an inch or more in diameter.

Granite. The essential components of the true granites are
quartz and potash feldspar. Although the essential minerals are but
two in number, granites are rendered complex by the presence of
numerous accessories which essentially modify the appearance of
the rocks; and these properties render them important for building
stone. The prevailing color is some shade of gray, though greenish,
yellowish, pink, and deep red are not uncommon. These various
hues are due to the color of the prevailing feldspar and the amount
and kind of the accessory minerals. The hardness of granite is due
largely to the condition of the feldspathic constituent, which is valu-
able. Granites of the same constituents differ in hardness.

Granites do not effervesce with acids, but emit sparks when
struck with steel. They possess the properties of strength, hardness,
and durabilty, although they vary in these properties as well as in
their structure. They furnish an extensive variety of the best stone
for the various purposes of the engineer and the architect. The crush-
ing strength of granite is variable, but usually is between 15,000
and 20,000 pounds per square inch.

Trap Rock. Trap rock, or diabase, is a crystalline, granular
rock, composed essentially of feldspar and augite; but nearly all
contains magnetite and frequently olivine. It is basic in compo-
sition and in structure; as a rule, it is massive. The texture, as a
general thing, is fine, compact, and homogeneous. The colors are
somber, varying from greenish, through dark gray, to nearly black.
Owing to its lack of rift, its hardness, and its compact texture, trap
rock is generally very hard to work. It has been used to some
extent for building and monumental work, but is more generally used
for paving purposes. Within the last few years, on account of its
great strength and fire-resisting qualities, it has been extensively
used in concrete work. The crushing strength of trap rock or dia-
base is usually between 20,000 and 26,000 pounds per square inch.

4 MASONRY AND REINFORCED CONCRETE

CHARACTERISTICS

From the constructor's standpoint, any stone is good which
will fulfil certain desired characteristics. These various charac-
teristics are not found combined in the highest degree in any one
kind of stone. It is essential to learn to what extent these various
desirable characteristics are combined in the various types of stone
which are quarried. At the same time, it should not be forgotten
that stones of the same nominal classification vary greatly in the
extent of their desirability. The chief characteristics to be con-
sidered by the constructor are cost, durability, strength, and appear-
ance. Although in some cases this represents the order in which
these qualifications are desired, in other cases 'the order is indefinitely
varied. For example, in a high-grade public building or monument,
a good appearance is considered essential, regardless of cost. In a
subsurface foundation, appearance is of absolutely no importance.

Cost. The cost of any stone depends on its intrinsic valua-
tion in the quarry, the cost of quarrying and dressing, and the cost
of transportation from the quarry to the site of the structure. The
cost of transportation is often the most important, and this con-
sideration frequently decides not only the choice of stone but even
the type of construction— whether stone masonry or concrete.

To give some idea of the cost of stone quarrying, a few approxi-
mate costs will be given. The cost of quarrying limestone and
sandstone for heavy retaining walls will be from 40 to 75 cents per
ton loaded on cars; but if this same stone is wanted for dimension
work, the cost of quarrying will be increased on account of more
regular shaped stones being required, which will cause more or less
waste. The cost of getting out and loading granite will be from
90 cents to $3.00 or $4.00 per ton, depending on the location of the
quarry and the size and shape of the stone required.

Stone that can be quarried by the use of wedges or a little black
powder can be marketed at a small cost, but when more expensive
means are required, the cost of the stone will be increased. Trans-
portation is generally an item in the cost of stone that must be
considered and often it proves to be a serious one.

Durability. Under many conditions the most important quali-
fication is durability. The -lack of it is also the most seriously
disappointing quality. Rocks which have remained hard and tough

MASONRY AND REINFORCED CONCRETE 5

for unnumbered ages while covered by earth from air and frost, will
disintegrate after a comparatively few years' exposure.

Atmospheric Influences. A very porous stone will absorb water,
which may freeze and cause crystals near the surface to flake off.
Even though such action during a single winter may be hardly per-
ceptible, the continued exposure of fresh surfaces to such action may
sooner or later cause a serious loss and disintegration. Even rain
water which has absorbed carbonic acid from the atmosphere will
soak into the stone, and the acid will have a greater or less effect on
nearly all stones. Quartz is the only constituent which is absolutely
unaffected by acid. The sulphuric acid gas given off by coal will
also affect building stone very seriously.

Fire. Natural stone is far less able to withstand a conflagration
than the artificial compositions such as brick, concrete, and terra
cotta. Granite, so popularly considered the type of durability, is
especially affected. Limestone and marble will be utterly spoiled,
at least in appearance, if not structurally, by a hot fire. Sandstone
is the least affected of the natural stones.

Hardness. The durability of a stone is tested by its resistance
to abrasive action in pavements, doorsills, and similar cases. The
value of trap rock for macadam and block pavements is chiefly due
to this quality.

Strength. In some structural work (as, for example, an arch)
the crushing strength of the stone is the primary consideration.
The average crushing strength of various kinds of stone will be
quoted later. The tensile strength should never be depended on,
except to a very limited extent, as a function of the transverse
strength. Even this is only applicable to such cases as the lintels
over doors and windows, the footing stones for foundations, and the
cover stones for box culverts. It is usually true that a stone which
is free from cracks and which has a high crushing strength also, has
as much transverse strength as should be required of' any stonel

Appearance. It is seldom that an engineer need concern
himself with the appearance of a stone, provided it is satisfactory in
the respects previously mentioned. The presence of iron oxide in
a stone will sometimes cause a deterioration in appearance by the
formation of a reddish stain on the outer surface. It usually happens,
however, that a stone whose strength and durability are satisfactory

MASONRY AND REINFORCED CONCRETE

TABLE I*
Physical Properties of Some Building Stones

KIND OF

STONE

LOCALITY

if*

SPECIFIC
GRAVITY

WEIGHT PER
CUBIC FOOT ||

RATIO OF
ABSORPTION

(Ibs.)

Granite

Grape Creek, Colo.

/Bed
\Edge

14,492
17,352

2.603

163

.048

Granite

Stony Creek, Conn.

/Bed

\Edge

15,000
16,750

2.645

165

1
201

Granite

Milford, Conn.

22,610

Granite

City Point, Me.

Bed

15,046

2.65

'l6C

Granite

East St. Cloud, Minn.

/Bed

\Edge

28,000
26,250

2.609

163

Diabase

New Duluth, Minn.

/Bed
\Edge

26,250
26,250

3.005

188

338

Limestone

Bedford, Ind.

6,500

147

Limestone

Bedford, Ind.

10,125

152

Limestone

Greensburgh, Ind.

16,875

170

117

Limestone

Conshohocken, Pa.

15,150

Limestone

Stillwater, Minn.

25,000

2.762

173

1
251

Limestone

Stillwater, Minn.

/Bed

\Edge

10,750
12,750

2.567

161

Sandstone

Buckhorn, Larimer Co., Colo.

fBed
\Edge

18,573
17,261

2.379

168

.040

Sandstone

Fort Collins, Larimer Co., Colo.

/Bed
\Edge

11,707

10,784

2.252

141

.072

Sandstone

Brandford, Fremont Co., Colo.

fBed

\Edge

3,308
2,894

2.004

125

Sandstone

Marquette, Mich.

Bed

6,323

2.166

135

~2~0~

Sandstone

Kasota, Minn.

Bed

10,700

2.630

164

1
56

Sandstone

Albion, N. Y.

Bed

13,500

2.420

151

1
44

Sandstone

Cleveland, O.

Bed

6,800

2.240

140

1
37

Sandstone

Seneca, O.

Bed

9,687

2.390

149

'From Merrill's "Stone for Buildings and Decoration".

MASONRY AND REINFORCED CONCRETE 7

will have a sufficiently good appearance, unless in high-grade archi-
tectural work, where it is considered essential that a certain color or
appearance shall be obtained.

Seasoning of Stone. Stone, to weather well, should be laid
with its bedding (lamination) horizontal, as it was first laid down
by Nature in the quarry. The stone, moreover, will offer greater
resistance to pressure if laid in this manner, and, it is said, will stand
a greater amount of heat without disintegrating. This is important
in cities where any building is liable to have its walls highly heated
by neighboring burning structures.

Some stones that are. liable to be destroyed by the effects of
frost on first being taken from the quarries, are no longer so after
being exposed for some time to the air, having lost their quarry
water through evaporation. This difference is very manifest between
stones quarried in summer and those quarried in winter. It has
frequently happened that stones of good quality have been entirely
ruined by hard freezing immediately after being taken from the
quarry; while, if they are quarried during the warm season of the
year and have an opportunity to lose their quarry water by evapora-
tion prior to cold weather, they withstand freezing very well. This
particularly applies to some marbles and limestones. This change is
accounted for by the claim put forward that the quarry water of the
stones carries in solution carbonate of lime and silica, w^hich is depos-
ited in the cavities of the rock as evaporation proceeds. Thus
additional cementing material is added, rendering the rock more
compact. This also will account for the hardening of some stones
after being quarried a short time. When first quarried they are
soft, and easily sawed and worked into any desirable shape; but after
the evaporation of their quarry water, they become hard and
very durable.

Table I gives the physical properties of many of the most
important varieties and grades of building stone found in the United
States.

TESTS

Of the above four qualities, only two — durability and strength
— are susceptible of laboratory testing, and even for these qualities
the best known laboratory tests are not conclusive. The deteriora-
tion and partial failure of the masonry in some of the best known

8 MASONRY AND REINFORCED CONCRETE

cathedrals of Europe, which commanded the best available talent
in their construction, are startling illustrations of the impractica-
bility of determining from laboratory tests the effect on stone of
long-continued stress, combined perhaps with other destructive
influences. Although the best technical advice was obtained in
selecting the stone for the Parliament House in London, and the
stone selected was undoubtedly subjected to the best known tests,
it was apparently impossible to foresee the effect of the London atmos-
phere, which is now so seriously affecting the stone. Several of the
tests to be described below should be considered as negative tests. If
the stones fail under these tests, they are probably inferior; if they
do not fail, they are perhaps safe, but there is no certainty. A long
experience, based on a knowledge of the characteristics of stones
which have proven successful, is of far greater value than a depend-
ence on the results of laboratory tests. The tests attempt to stimu-
late the actual destructive agencies as far as possible, but since a
great deal of stonework, which was apparently satisfactory when
constructed and for a few years after, has failed for a variety of
reasons, attempts are made to use accelerated tests, which are supposed
by their concentration to affect the stone in a few minutes or hours
as much as the milder causes acting through a long period of years.

Absorption. It is generally said that stones having the least
absorption are the best. The absorptive power is measured by
first drying the stone for many hours in an oven, weighing it, then
soaking it for, say, 24 hours, and again weighing it. The increase
in the weight of the soaked stone (due to the weight of water ab-
sorbed), divided by the weight of the dry stone, equals the ratio of
absorption. The granites will absorb as an average value a weight
of water equal to about 7|o of the weight of the stone. For sand-
stone the ratio is about /f.

The test for absorption has but little value except to indicate
a closeness of grain (or the lack of it), which probably indicates some-
thing about the strength of the stone, as well as its liability to some
kinds of disintegration.

Test for Frost. The only real test is to wash, dry, and weigh
test specimens very carefully; then soak them in wrater and expose
them to intensely cold and intensely warm temperatures alternately.
Finally wash, dry, and weigh them. If the freezing has resulted in

MASONRY AND REINFORCED CONCRETE 9

breaking off small pieces, or possibly in fracturing the stone, the loss
in weight or the breakage will give a measure of the effect of cold
winters. However, as such low temperatures cannot be produced
artificially except at considerable expense, and as a sufficient degree
of natural cold is ordinarily unobtainable when desired, such a test
is usually impracticable.

An attempt to simulate such an effect by boiling the specimen in
a concentrated solution of sulphate of soda and observing the subse-
quent disintegration of the stone, if any, is known as Brard's test.
Although this method is much used for lack of a better, its value is
doubtful and perhaps deceptive, since the effect is largely chemical
rather than mechanical. The destructive effect on the stone is
usually greater than that of freezing, and might result in condemning
a really good stone.

Chemical Test. The most difficult and uncertain matter to
determine is the probable effect of the acids in the atmosphere.
These acids, dissolved in rain water, soak into the stone and combine
with any earthy matter in the stone, which then leaches out, leaving
small cavities. This not only results in a partial disintegration of
the stone, but also facilitates destruction by freezing. If the stone
specimen, after being carefully washed, is soaked for several days in
a one per cent solution of sulphuric and hydrochloric acid, the liquid
being frequently shaken, the water will become somewhat muddy,
if there is an appreciable amount of earthy matter in the stone. Such
an effect is supposed to indicate the probable action of a vitiated
atmosphere. Of course it should be remembered that such a con-
sideration is important only for a structure in a crowded city where
the atmosphere is vitiated by poisonous gases discharged from fac-
tories and from all chimneys.

Physical Tests. A test made by crushing a block of stone
in a testing machine is apparently a very simple and conclusive test,
but in reality the results are apt to be inconclusive and even decep-
tive. This is due to the following reasons, among others:

(a) The crushing strength of a cube per square inch is far less than that
of a slab having considerably greater length and width than height.

(6) The result of a test depends very largely on the preparation of the
specimen. If sawed, the strength will be greater than if cut by chipping. If
the upper and lower faces are not truly parallel, so that there is a concentration
of pressure on one corner, the apparent result will be less.

10 MASONRY AND REINFORCED CONCRETE

(c) The result depends on the imbedment. Specimens which are rubbed
and ground with machines that will insure truly parallel and plane surfaces
will give higher results than when wood, lead, leather, or pi aster-of -Paris cushions
are employed.

(d) The strength of masonry depends largely on the crushing strength of
the mortar used and the thickness of the joints. Other things being equal, an
increase in the crushing strength of the stone (or brick) which is used does not
add proportionately to the strength of the masonry as a whole; and if the mortar
joints are very thick, it adds little or nothing. Since the strength of the masonry
is the only real criterion, the strength of a cube of the stone is of comparatively
little importance.

In short, tests of two-inch cubes (the size usually employed) are
valuable chiefly in comparing the strength of two or more different
kinds of stones, all of which are tested under precisely similar con-
ditions. A comparison of such figures with the figures obtained by
others will have but little value unless the precise conditions of the
other tests are accurately knowTn. Under any conditions, the results of
the tests will bear but little relation to the actual strength of the
masonry to be built.

Quarry Examinations. These are generally the surest tests and
they should never be neglected, if the choice of stone is a matter of
great importance. Field stone and outcropping rock, wrhich have
withstood the weather for indefinite periods of years, can usually
be relied on as being durable against all deterioration except that
due to acids in the atmosphere, to which they probably have not
been subjected in the country as they might be in a city. On the
other hand, however, large blocks of stone can seldom be obtained
from field stones. If a quarry has been opened for several years, a
comparison of the other surfaces with those just exposed may
indicate the possible disintegrating or discoloring effects of the
atmosphere. A stone which is dense and of uniform structure, and
which will not disintegrate, may be relied on to withstand any
physical stress to which masonry should be subjected.

BRICK

Definition and Characteristics. The term brick is usually
applied to the product resulting from burning molded prisms of
clay in a kiln, at a high temperature.

Common brick is not extensively used in engineering structures,
except in the construction of sewers and the lining of tunnels. Brick

MASONRY AND REINFORCED CONCRETE 11

is easily worked into structures of any desirable shape, easily handled
or transported, and comparatively cheap. When well constructed,
brick masonry compares very well in strength with stone masonry,
but is not as heavy as stone. Brickwork is but slightly affected by
changes of temperature or humidity.

Brick is made of common clay (silicate of alumina), which
usually contains compounds of lime, magnesia, and iron. Good
brick clay is often found in a natural state. The quality of the brick
depends greatly on the quality of the clay used, and equally as much
on the care taken in its manufacture.

Oxide of iron gives brick hardness and strength. The red color
of brick is also due to the presence of iron. The presence of car-
bonate of lime in the clay of which brick is made is injurious, since
the carbonate is decomposed during the burning, forming caustic
potash, which, by the absorption of water, will cause the brick to
disintegrate. An excess of silicate of lime makes the clay fusible,
which softens the brick and thereby causes distortion during the
burning process. Magnesia in small quantities has but little influ-
ence on brick. Sand, in quantities not in excess of about 25 per
cent, will help to preserve the form of the brick, and is beneficial
to that extent; but in greater quantities than 25 per cent, it makes
the brick brittle and weak.

Requisites for Good Brick. Good brick should be of regular
shape, with plane faces, parallel surfaces, and sharp edges and
angles. It should show a fine, uniform, compact texture; should
be hard and, when struck a sharp blow, should ring clearly; and
should not absorb more water than one-tenth of its weight. The
specific gravity should be 2 or more. Good brick will bear a com-
pressive load of 6000 pounds per square inch when the sides are
ground flat and pressed between plates. The modulus of rupture
under transverse stress should be at least 800 pounds per square inch.

Absorptive Power. The amount of water that brick absorbs
is very important in indicating the durability of brick, particularly
its resistance to frost. Very soft brick will absorb 25 to 30 per
cent of their weight of water. Weak, light-red ones will absorb 20
to 25 per cent; this grade of brick is used commonly for filling interior
walls. The best brick will absorb only 4 to 5 per cent, but brick
that will absorb 10 per cent is called good.

12 MASONRY AND REINFORCED CONCRETE

Color of Brick. The color of brick depends greatly upon the
ingredients of the clay; but the temperature of the burning, the
molding sand, and the amount of air admitted to the kiln also have
their influence. Pure clay, or clay mixed with chalk, will produce
white brick. Iron oxide and pure clay will produce a bright red
brick when burned at a moderate heat. Magnesia will produce
brown brick; and when it is mixed with iron, produces yellow brick.
Lime and iron in small quantities producer cream color; an increase
of lime produces brown, and an increase of iron, red.

Size and Weight. The standard size for common brick is
8j by 4 by 2\ inches; and for face brick, 8| by 4-| by 2j inches.
There are numerous small variations from these figures; and also,
since the shrinkage during burning is very considerable and not
closely controlled, there is always some uncertainty and variation in
the dimensions. Bricks will weigh from 100 to 150 pounds per
cubic foot according to their density and hardness, the harder bricks
being, of course, the heavier per unit of volume.

Classification of Common Brick. Brick are usually classified
in three ways: (o) manner of molding; (6) position in kiln; (c) their
shape or use.

(«) The manner in which brick is molded has produced the
following terms:

Soft-Mud Brick. A brick molded either by hand or by machine, in which
the clay is reduced to mud by adding water.

Stiff-Mud Brick. A brick molded from dry or semi-dry clay. It is
molded by machinery.

Pressed Brick. A brick molded by machinery with semi-dry or dry clay.

Re-Pressed Brick. A brick made of soft mud, which, after being partly
dried, is subjected to great pressure.

(b) The classification of brick with regard to their position in
the kiln applies only to the old method of burning. With the new
methods, the quality is nearly uniform throughout the kiln. The
three grades taken from the old-style kiln were:

Arch Brick. Brick forming the sides and top of the arches in which the
fire is built are called arch brick. They are hard, brittle, and weak from being
overburnt.

Body, Cherry, or Hard Brick. Brick from the interior are called body,
cherry, or hard brick, and are of the best quality.

Pale, Salmon, or Soft Brick. Brick forming the exterior of the kiln are
underburnt, and are called soft, salmon, or pale brick. They are used only for
filling, being too weak for ordinary use.

MASONRY AND REINFORCED CONCRETE

(e) The classification of brick in regard to their use or shape
has given rise to the following terms :

Face Brick. Brick that are uniform in size and color and arc suitable for
the exposed places of buildings.

Sewer Brick. Common hard brick, smooth and regular in form.

Paving Brick. Very hard common vitrified brick, often made of shale.
They are larger than the ordinary brick, and are often called paving blocks.

Compass Brick. Brick having four short edges which run radially to an
axis. They are used to build circular chimneys.

Voussoir Brick. Brick having four long edges running radially to an axis.
They are used in building arches.

Crushing Strength. The results of crushing tests of brick vary
greatly, depending on the details of the tests made. Many reports
fail to give the details under which these tests are made, and in that
case the real value of the results of the test as announced is greatly
reduced.

The following results were obtained at the U. S. Arsenal at
Watertown, Mass., by F. E. Kidder. The specimens were rubbed
on a revolving bed until the top and bottom faces were perfectly true
and parallel.

MAKE OF BRICK

No. OF SPECIMENS

PRESSURE AT
WHICH SPECIMENS

ULTIMATE
COMPRESSION

ESTED

BEGAN TO FAIL

(per sq. in.)

Philadelphia Face Brick
Cambridge Brick

3,527 Ibs.
4,655 "

5,918 Ibs.
12,186 "

Boston Brick

7,880 "

11,670 "

New England Pressed

4,764 "

12,490 "

The following results were obtained by C. Y. Davis, the tests
being made at the Watertown Arsenal:

KIND OF
BRICK

COMPRESSION
(per sq. in.)

KIND OF
BRICK

COMPRESSION
(per sq. in.)

KIND OF
BRICK

COMPRESSION
(per sq. in.)

Red

9,540 Ibs.
*8,530 "
6,050 "
6,700 "

Pressed

. 6,470 Ibs.
*9,190 "
5,960 "
6,750 "

Arch

7,600 Ibs.
* 10,290 "
6,800 "

These specimens were tested to select brick for the U. S. Pension Office at
Washington, D. C. The specimens tested were submitted by manufacturers.

Fire Brick. Furnaces must be lined with a material which is
even more refractory than ordinary brick. The oxide and sulphide
of iron, which are so common (and comparatively harmless) in

* Indicates the brick selected.

14 MASONRY AND REINFORCED CONCRETE

ordinary brick, will ruin a fire brick if they are present to a greater
extent than a very few per cent. Fire brick should be made from
nearly pure sand and clay. There is comparatively little need for
mechanical strength, but the chief requirement is their infusibility,
and pure clay and silica fulfil this requirement very perfectly.

Sand=Lime Brick. Within the last few years, the sand-lime
brick industry has been developed to some extent. The materials
for making this brick consist of sand and lime; and they were first
made by molding ordinary lime mortar in the shape of a clay brick,
and were hardened by the carbon dioxide of the atmosphere.

There are two general methods of manufacturing these bricks:

(a) Brick made of sand and lime, and hardened in the atmosphere. This
hardening may be hastened by placing the brick in an atmosphere rich in carbon
dioxide; or still less time will be required if the hardening is done with carbon
dioxide under pressure.

(b) Brick made of sand and lime, and hardened by steam under atmos-
pheric pressure. This process may be hastened by having the steam under
pressure.

When sand-lime bricks are made by the first process, it requires
several weeks for the bricks to harden; by the second method
it requires only a few hours; the latter method is the one generally
used in this country. The advantages claimed for these bricks are
that they improve with age; are more uniform in size, shape, and
color; have a low porosity and no efflorescence; and do not disinte-
grate by freezing. The compressive strength of sand-lime brick of
a good quality ranges from 2500 to 4500 pounds per square inch.

CONCRETE BUILDING BLOCKS

Types. The growth of the concrete block industry has been
rapid. The blocks are taking the place of wood, brick, and stone
for ordinary wall construction. They are strong, durable, and cheap.
The blocks are made at a factory or on the site of the work where they
are to be used, and are placed in the wall in the same manner as brick
or stone. There are two general types of blocks made — the one-piece
block, and the two-piece block. The one-piece type consists of a single
block, with hollow cores, making the whole thickness of the wall. In
the two-piece type, the front and back of the blocks are made in two
separate pieces and bonded -when laid up in the wall. The one-
piece blocks are more generally used than the two-piece blocks.

MASONRY AND REINFORCED CONCRETE 15

Size. Various shapes and sizes of blocks are made. Builders
of some of the standard machines have adopted a standard length of
32 inches and a height of 9 inches for the full-sized blocks, with
width of 8, 10, and 12 inches. Lengths of 8, 12, 16, 20, and 24
inches are made from the same machine, by the use of parting plates
and suitably divided face-plates. Most machines are constructed so
that any length between 4 and 32 inches, and any desired height,
can be obtained.

The size of the openings (the cores) varies from one-third
to one-half of the surface' of the top or bottom of the block.
The building laws of many cities state that the openings shall
amount to only one-third of the surface. For any ordinary pur-
pose, blocks with 50 per cent open space are stronger than neces-
sary.

Materials. The material for making concrete blocks consists
of Portland cement, sand, and crushed stone or gravel. Owing
to the narrow space to be filled with concrete, the stone and gravel
are limited to one-half or three-quarters of an inch in size. At least
one-third of the material, by weight, should be coarser than | inch.
A block made with gravel or screenings (sand to f-inch stone), with
proportions of 1 part Portland cement to 5 parts screenings, will be
as good as a block with 1 part Portland cement and 3 parts sand. •
These materials will be further treated under the headings of "Port-
land Cement", "Sand", and "Stone".

Proportions. The proportions generally used in the making of
concrete blocks vary from a mixture of 1 part cement, 2 parts sand,
and 4 parts stone, to a mixture of 1 part cement, 3 parts sand, and
G parts stone. A very common mixture consists of 1 part cement,
2| parts sand, and 5 parts stone. A denser mixture may be secured
by varying these proportions somewhat; that is, the maker may
find that he secures a more compact block by using 2f parts sand
and 4| parts stone; but a leaner mixture than 1:2^ : 5 is not to be
recommended. In strength, this mixture will have a crushing
resistance far beyond any load that it will ever have to support.
Even a mixture of 1:3:6 or 1:3|:7 will be stronger than necessary
to sustain any ordinary load. Such a mixture, however, would be
porous and unsatisfactory in the wall of a building. Blocks, in being
handled at the factory, carted to the building site, and in being

16 MASONRY AND REINFORCED CONCRETE

placed in the wall, will necessarily receive more or less rough han-
dling; and safety in this respect calls for a stronger block than is
needed to bear the weight of a wall of a building. For a high-
grade water-tight block, a 1:2:4 or a 1:2$: 4 mixture is always
used.

Amount of Water. Blocks made with dry concrete will be soft
and weak, even if they are well sprinkled after being taken out of
the forms. Blocks that are to be removed from the machine as
soon as they are made will stick to the plates and sag out of shape,
if the concrete is mixed too wet. Therefore there should be as much
water as possible used, without causing the block to stick or sag out
of shape when being removed from the molds. This amount of
water is generally 8 to 9 per cent of the weight of the dry mixture.
To secure uniform blocks in, strength and color, the same amount
of water should be used for each batch.

Mixing and Tamping. The concrete should be mixed in a
batch mixer, although good results are obtained in hand-mixed con-
crete. The tamping is generally done with hand rammers. Pneu-
matic tampers, operated by an air compressor, are used successfully.
Molding concrete by pressure is not successful unless the concrete
is laid in comparatively thin layers.

Curing of Blocks, (a) Air Curing. The blocks are removed
from the machine on a steel plate, on which they should remain for
24 hours. The blocks should be protected from the sun and dry
winds for at least a week, and thoroughly sprinkled frequently.
They should be at least four weeks old before they are placed in a
wall. If they are built up in a wall while green, shrinkage cracks
will be apt to occur in the joints.

(b) Steam Curing. Concrete blocks can be cured much more
quickly in a steam chamber than in the open air. They should be
left in the steam chamber for 48 hours at a pressure of 80 pounds per
square inch. By this method of curing blocks they can be handled
and used much quicker than when air cured. Their strength is then
much higher than the air-cured blocks when six months old. When
a large quantity of blocks are to be made, the steam curing is more
economical than the air curing, even considering the much more
expensive plant that is required. See Technologic Papers, Bureau of
Standards, (U. S.) No. 5.

MASONRY AND REINFORCED CONCRETE 17

Mixture for Facing. For appearance, a facing of a richer
mixture is often used, generally consisting of 1 part cement to 2 parts
sand. The penetration of water may be effectively prevented by
this rich coat. Care must be taken to avoid a seam between the two
mixtures.

Blocks are made with either a plane face or of various orna-
mental patterns, as tool-faced, paneled, rock-faced, etc. Coloring
of the face is often desired. Mineral coloring, rather than chemical,
should be used, as the chemical, color may injure the concrete or fade.

Cost of Making. The following is quoted from a paper by
N. F. Palmer, C.E.:

Blocks 8 by 9 by 32 inches; gang consisted of five workmen and a foreman;
record for one hour, 30 blocks; general average for 10 hours, 200 blocks. The
itemized cost was as follows:

1 foreman @ $2.50 $2.50

5 helpers @ 2.00 10.00

13 bbls. cement @ 2.00 26.00

10 cu. yds. sand and gravel @ 1 .00 10.00

Interest and depreciation on machine 2 . 00

$50.50

This is the equivalent of $50.50 -J- 200, or 25£ cents per block; or, since the
face of the block was 9 by 32 inches, or exactly 2 square feet, the equivalent of
12.6 cents per square foot of an 8-inch wall.

Another illustration, quoted from Gillette, for a 10-inch wall,
was itemized as follows, for each square foot of wall :

Sand 2.0 cents

Cement @ $1.60 per barrel 4.5 cents

Labor @ $1.83 per day 3.8 cents

Total per square foot 10 .3 cents

This is apparently considerably cheaper than the first case, even after
allowing for the fact that the second case does not provide for interest, depre-
ciation on plant, etc., which in the first case is only 4 per cent of the total. This
allowance of 4 per cent is probably too small.

CEMENTING MATERIALS

The principal cementing materials are Common Lime, Hydraulic
Lime, Pozzuolana, Natural Cement, and Portland Cement. There
are a few other varieties, but their use is so limited that they need
not be considered here.

18 MASONRY AND REINFORCED CONCRETE

Common Lime. This is produced by burning limestone
whose chief ingredient is carbonate of lime. Except in the form of
marble, a limestone usually contains other substances — perhaps up
to 10 per cent of silica, alumina, magnesia, etc. The process of
burning drives off the carbonic acid and leaves the protoxide of
calcium. This is the lime of commerce; and to preserve it from
deterioration, it must be kept dry and even protected from a free
circulation of air. When exposed freely to the air for a long period,
it will become air-slaked; that is, it will absorb both moisture and
carbonic acid from the air, and will lose its ability to harden. The
first step in using common lime is to combine it with water, which
it absorbs readily so that its volume is increased to 2\ to 3| times
what it was before. Its weight is at the same time increased about
one-fourth; and the mass, which consisted originally of large lumps
with some powder, is reduced to an unctuous mass of smooth paste.
The lime is then called slaked lime, the process of slaking being
accompanied by the development of great heat. The purer the lime,
the greater the development of heat and the greater the expansion
in volume. It is soluble in water which is not already "hard", or
which does not already contain considerable lime in solution. A
good lime will make a smooth paste with only a very small per-
centage (less than 10 per cent) of foreign matter or clinker. By
such simple means a lime may be readily tested.

The hardening of common lime mortar is due to the formation
of a carbonate of lime (substantially the original condition of the
stone) by the absorption from the atmosphere of carbonic oxide.
This will penetrate for a considerable depth in course of time; but
instances are common in which masonry has been torn down after
having been erected many years, and the lime mortar in the interior
of the mass has been found still soft and unset, since it was hermeti-
cally cut off from the carbonic oxide of the atmosphere. For the
same reason, common lime mortar will not harden under water and,
therefore, it is utterly useless to employ it for work under water or
for large masses of masonry.

When the qualities of slaking and expansion are not realized or
are obtained only very imperfectly, the lime is called lean or poor
(rather than fat} and its value is less and less, until it is perhaps
worthless for use in making mortar, or for any other use except as

MASONRY AND REINFORCED CONCRETE 19

fertilizer. The cost of lime is about CO cents per barrel of 230 pounds
net.

Hydraulic Lime. This is derived from limestones containing
about 10 to 20 per cent of clay or silica, which is intimately mixed
with the carbonate of lime in the structure of the stone. During
the process of burning, some of the lime combines with the clay
(or the silica) so as to form the aluminate or silicate of lime. The
excess of lime becomes quicklime as before. During the process of
slaking, which should be done by mere sprinkling, the lime having
been intimately mixed with the clay or silica, the expansion of the
lime completely disintegrates the whole mass. This slaking is done
by the manufacturer. The lime having a much greater avidity for
the water than the aluminate or the silicate, the small amount of
water used in the slaking is absorbed entirely by the lime, and the
aluminate or the silicate is not affected. The setting of hydraulic
lime appears to be due to the crystallizing of the aluminate and
silicate; and since this will be accomplished even when the masonry
is under water, it receives from this property its name of hydraulic
lime. It is used but little in this country, and is all imported.

Pozzuolana or Slag Cement. Pozzuolana is a form of cement-
ing material which has been somewhat in use since very ancient
times. Apparently it was first made from the lava from the volcano
Vesuvius, the lava being picked up at Pozzuoli, a village near the
base of the volcano. It consists of a combination of silica and
alumina, which is mixed with common lime. Its chemical composi-
tion is therefore not very unlike that of hydraulic lime. It also
possesses the ability to harden under water. Its use is very limited,
and its strength and hardness relatively small, when compared with
that of Portland cement. It should never be used where it will be
exposed for a long time to dry air, even after it has thoroughly set.
It appears to withstand the action of sea water somewhat better than
Portland cement; and hence it is sometimes used instead of Portland
cement as the cementing material for large masses of masonry or
concrete which are to be deposited in sea water, when the strength
of the cement is a comparatively minor consideration. Artificial
pozzuolana is sometimes made by grinding up blast-furnace slag
which has been found by chemical analysis to have the correct
chemical composition.

20 MASONRY AND REINFORCED CONCRETE

Natural Cement. Natural cement is obtained by burning an
argillaceous or a magnesian limestone which happens to have the
proper chemical composition. The resulting clinker is then finely
ground and is at once ready for use. Such cement was formerly
and is still commonly called Rosendale cement, owing to its having
been produced first in Rosendale, Ulster County, New York. A
very large part of the natural cement now produced in this country
comes from Ulster County, New York, or from near Louisville,
Kentucky. Cement rock from which natural cement can be made
is now found widely scattered over the country.

In Europe, the name Roman cement is applied to substantially
the same kind of product. Since the cement is made wholly from
the rock just as it is taken out of the quarry, and also since it is cal-
cined at a much lower temperature than that employed in making
Portland cement it is considerably cheaper than Portland cement.
On the other hand, its strength is considerably less than that of
Portland cement and the time of setting is much quicker. Some-
times this quickness of setting is a very important point — as, for
instance, when it is desired to obtain a concrete which shall attain
considerable hardness very quickly. On the other hand, the quick-
ness of setting may be a serious disadvantage, because it may not
allow sufficient time to finish the concrete work satisfactorily
without disturbing the mortar which has already taken an initial
set. Natural cement is only used on account of its cheapness, and
especially when the cement is not required to have very great
strength. The disadvantage due to its quick setting (when it is a
disadvantage) may be somewhat overcome by the use of a small per-
centage of lime, when mixing up the mortar.

It is not always admitted, at least in the advertisements, that a
given brand of cement is a natural cement; and the engineer must
therefore be on his guard, in buying a cement, to know whether it is
a .quick-setting natural cement of comparatively low strength or a
true Portland cement.

Portland Cement. Portland cement consists of the product
of burning and grinding an artificial mixture of carbonate of lime
and clay or slag, the mixture being very carefully proportioned so
that the ingredients shall "have very nearly the fixed ratio which
experience has demonstrated to give the best results.

MASONRY AND REINFORCED CONCRETE 21

"If a deposit of stone containing exactly the right amount of clay, and
of exactly uniform composition, could be found, Portland cement could be
made from it, simply by burning and grinding. For good results, however,
the composition of the raw material must be exact, and the proportion of car-
bonate of lime in it must not vary even by one per cent. No natural deposit
of rock of exactly this correct and unvarying composition is known or likely
ever to be found; therefore Portland cement is always made from an artificial
mixture, usually, if free from organic matter, containing about 75 per cent
carbonate of lime and 25 per cent clay." — S. B. NEWBERRY, in Taylor and
Thompson's "Concrete, Plain and Reinforced."

As before stated, Portland cement is stronger than natural
cement; it sets more slowly, which is frequently a matter of great
advantage, and yet its rate of setting is seldom so slow that it is a
disadvantage. Although the cost is usually greater than that of
natural cement, yet improved methods of manufacture have re-
duced its cost so that it is now usually employed for all high-
grade work where high ultimate strength is an important con-
sideration.

In a general way, it may be said that the characteristics of
Portland cement on which its value as a material to be used in con-
struction work chiefly depends may be briefly indicated as follows:

When the cement is mixed with water and allowed to set, it
should harden in a few hours, and should develop a considerable
proportion of its ultimate strength in a few days. It should also
possess the quality of permanency, so that no material change in
form or volume will take place on account of its inherent qualities
or as the result of exterior agencies. There is always found to be
more or less of shrinkage in the volume of cement and concrete
during the process of setting and hardening; but with any cement
of really good quality, this shrinkage is not so great as to prove
objectionable. Another very important characteristic is that the
cement shall not lose its strength with age. Although some long-
time tests of cement have apparently indicated a slight decrease in
the strength of cement after the first year or so, this decrease is
nevertheless so slight that it need not affect the design of concrete,
even assuming the accuracy of the general statement.

To insure absolute dependence on the strength and durability
of any cement which it is proposed to use in important structural
work, it is essential that the qualities of the cement be determined
by thorough tests.

22 MASONRY AND REINFORCED CONCRETE

CEMENT TESTING

All cement should be tested. On large operations a testing
laboratory can be fitted up and all cement tested at the site of the
operation. On smaller jobs the tests are generally made by pro-
fessional laboratories. The cost of these tests is small. The pro-
fessional laboratories keep men at all the big cement plants so that
they can secure samples when the shipments are being made. Often
by the time that the cement is received at the job and unloaded the
report of the seven-day test will be also received at the work.

Standard Tests. The following method of testing cement is
taken from the "Final Report on Tests of Cement" made to the
American Society of Civil Engineers by a committee appointed to
investigate and report on that subject, and is copied here from the
proceedings of that Society by permission of their secretary, Charles
Warren Hunt. The report on "Methods of Testing Cement" is
printed in Vol. LXXV and the "Standard Specifications" is printed
in the February, 1913, number of the proceedings of that society.

Methods for Testing Cement*

SAMPLING

1. Selection of Sample. The selection of samples for testing
should be left to the engineer. The number of packages sampled
and the quantity taken from each package will depend on the
importance of the work and the facilities for making the tests.

2. The samples should fairly represent the material. When the
amount to be tested is small it is recommended that one barrel in ten
be sampled; \vhen the amount is large it may be impracticable to take
samples from more than one barrel in thirty or fifty. When the
samples are taken from bins at the mill one for each fifty to two
hundred barrels will suffice.

3. Samples should be passed through a sieve having twenty
meshes per linear inch, in order to break up lumps and remove foreign
material; the use of this sieve is also effective to obtain a thorough
mixing of the samples when this is desired. To determine the accept-
ance or rejection of cement it is preferable, when time permits, to test
the samples separately. Tests to determine the general character-
istics of a cement, extending over a long period, may be made with
mixed samples.

'Accompanying Final Report bf Special Committee on Uniform Tests of Cement, dated
January 17th, 1912.

MASONRY AND REINFORCED CONCRETE 23

4. Method of Sampling. Cement in barrels should be sampled
through a hole made in the head, or in one of the staves midway
between the heads, by means of an auger or a sampling iron similar
to that used by sugar inspectors; if in bags, the sample should be
taken from surface to center; cement in bins should be sampled in
such a manner as to represent fairly the contents of the bin. Sam-
pling from bins is not recommended if the method of manufacture
is such that ingredients of any kind are added to the cement subse-
quently.

CHEMICAL ANALYSIS

5. Significance. Chemical analysis may serve to detect adul-
teration of cement with inert material, such as slag or ground lime-
stone, if in considerable amount. It is useful in determining whether
certain constituents, such as magnesia and sulphuric anhydride, are
present in inadmissible proportions.

6. The determination of the principal constituents of cement,
silica, alumina, iron oxide, and lime is not conclusive as an indication
of quality. Faulty cement results more frequently from imperfect
preparation of the raw material or defective burning than from
incorrect proportions. Cement made from material ground very
fine and thoroughly burned may contain much more lime than the
amount usually present, and still be perfectly sound. On the other
hand, cements low in lime may, on account of careless preparation of
the raw material, be of dangerous character. Furthermore, the
composition of the product may be so greatly modified by the ash
of the fuel used in burning as to affect in a great degree the signifi-
cances of the results of analysis.

7. Method. The method to be followed should be that pro-
posed by the Committee on Uniformity in the Analysis of Materials
for the Portland Cement Industry, reported in the Journal of the
Society for Chemical Industry, Vol. 21, page 12, 1902; and published
in Engineering News, Vol. 50, p. 60, 1903; and in Engineering Record
Vol. 48, p. 49, 1903, and in addition thereto, the following:

The insoluble residue may be determined as follows: To a
1-gram sample of the cement are added 30 cu. cm. of water and
10 cu. cm. of concentrated hydrochloric acid, and then warmed until
the effervescence ceases, and digested on a steam bath until dissolved.
The residue is filtered, washed with hot water, and the filter paper
and contents digested on the steam bath in a 5% solution of sodium
carbonate. This residue is filtered, washed with hot water, then
with hot hydrochloric acid, and finally with hot water, and then
ignited at a red heat and weighed. The quantity so obtained is the
insoluble residue.

24 MASONRY AND REINFORCED CONCRETE

SPECIFIC GRAVITY

8. Significance. The specific gravity of cement is lowered by
adulteration and hydration, but the adulteration must be consider-
able to be detected by tests of specific gravity.

9. Inasmuch as the differences in specific gravity are usually
very small, great care must be exercised in making the determination.

10. Apparatus. The determination of specific gravity should
be made with a standardized Le Chatelier apparatus. This consists
of a flask (D), Fig. 1, of about 120 cu. cm. capacity, the neck of
which is about 20 cm. long; in the middle of this neck is a bulb (C),

Fig. 1. Le Chatelier Apparatus for Determining Specific
Gravity of Cement

above and below which are two marks (F) and (E); the volume
between these two marks is 20 cu. cm. The neck has a diameter
of about 9 mm., and is graduated into tenths of cubic centimeters
above the mark (F).

11. Benzine (02° Baume naphtha) or kerosene free from water
should be used in making the determination.

12. Method. The flask is filled with either of these liquids to
the lower mark (E), and 64. grams of cement, cooled to the tem-
perature of the liquid, is slowly introduced through the funnel (B),

MASONRY AND REINFORCED CONCRETE 25

(the stem of which should be long enough to extend into the flask to
the top of the bulb (C) ), taking care that the cement does not adhere
to the sides of the flask and that the funnel does not touch the
liquid. After all the cement is introduced, the level of the liquid
will rise to some division of the graduated neck; this reading, plus
20 cu. cm. is the volume displaced by 64 grams of the cement.

13. The specific gravity is then obtained from the formula

Specific gravity Weight of cement in grams

Displaced volume in cubic centimeters

14. The flask, during the operation, is kept immersed in water
in a jar (A), in order to avoid variations in the temperature of the
liquid in the flask, which should not exceed ^° C. The results of
repeated tests should agree within 0.01. The determination of
specific gravity should be made on the cement as received; if it
should fall below 3.10, a second determination should be made after
igniting the sample at a low red heat in the following manner: One-
half gram of cement is heated in a weighed platinum crucible,
with cover, for 5 minutes with a Bunsen burner (starting with a low
flame and gradually increasing to its full height) and then heating
for 15 minutes with a blast lamp; the difference between the weight
after cooling and the original weight is the loss on ignition. The
temperature should not exceed 900° C., and the ignition should
preferably be made in a muffle.

15. The apparatus may be cleaned in the following manner:
The flask is inverted and shaken vertically, until the liquid flows
freely, and then held in a vertical position until empty; any traces
of cement remaining can be removed by pouring into the flask a
small quantity of clean benzine or kerosene, and repeating the opera-
tion.

FINENESS

16. Significance. It is generally accepted that the coarser par-
ticles in cement are practically inert and that only the extremely fine
powder possesses cementing qualities. The more finely cement is
pulverized, other conditions being the same, the more sand it will
carry and so produce a mortar of a given strength.

17. Apparatus. The fineness of a sample of cement is deter-
mined by weighing the residue retained on certain sieves. Those
known as No. 100 and No. 200, having approximately 100 and 200
wires per linear inch, respectively, should be used. They should
be at least 8 inches in diameter. The wire cloth should be of brass
wire and should conform to the following requirements:

MASONRY AND REINFORCED CONCRETE

No. of Sieve

Diameter of Wire

MESHES PER LINEAR INCH

Warp

Woof

100
200

0.0042 to 0.0048 in.
0.0021 to 0.0023 in.

95 to 101
192 to 203

93 to 103
190 to 205

The meshes in any smaller space, down to 0.25 inch, should be
proportional in number.

18. Method. The test should be made with 50 grams of
cement, dried at a temperature of 100° C. (212° F.).

19. The cement is placed on the No. 200 sieve, which, with pan
and cover attached, is held in one hand in a slightly inclined position
and moved forward and backward about 200 times per minute, at
the same time striking the side gently, on the up stroke, against the
palm of the other hand. The operation is continued until not more
than 0.05 gram will pass through in one minute. The residue is
weighed, then placed on the No. 100 sieve, and the operation re-
peated. The work may be expedited by placing in the sieve a few
large steel shot, which should be removed before the final one minute
of sieving. The sieves should be thoroughly dry and clean.

NORMAL CONSISTENCY

20 Significance. The use of a proper percentage of water in
making pastes* and mortars for the various tests is exceedingly
important and vitally affects the results obtained.

21. The amount of water, expressed in percentage by \veight of
the dry cement required to produce a paste of plasticity desired,
termed "normal consistency", should be determined with the Vicat
apparatus in the following manner:

22. Apparatus. This consists of a frame (.1), Fig. 2, bearing a
movable rod (B), weighing 300 grams, one end (C) being 1 cm. in
diameter for a distance of 0 cm., the other having a removable
needle (7)), 1 mm. in diameter, 0 cm. long. The rod is reversible,
and can be held in any desired position by a screw (/£), and has mid-
way between the ends a mark (F) which moves under a scale (gradu-
ated to millimeters) attached to the frame (A). The paste is held
by a conical, hard-rubber ring ((/'), 7 cm. in diameter at the base, 4 cm.
high, resting on a glass plate ( //) about 10 cm. square.

23. Method. In making the determination, the same quantity
of cement as will be used subsequently for each batch in making the

*The term "paste" is used in this Deport to designate a mixture of cement and water, and
the word "mortar" to designate a mixture of cement, sand, and water.

MASONRY AND REINFORCED CONCRETE

test pieces, but not less than 500 grams, with a measured quantity
of water, is kneaded into a paste, as described in paragraph 45, and
quickly formed into a ball with the hands, completing the operation
by tossing it six times from one hand to the other, maintained about
6 inches apart; the ball resting in the palm of one hand is pressed into
the larger end of the rubber ring held in the other hand, completely

Fig. 2. Vicat Apparatus for Testing Normal Consistency of Cement

filling the ring with paste; the excess at the larger end is then removed
by a single movement of the palm of the hand ; the ring is then placed
on its larger end on a glass plate and the excess paste at the smaller
end is sliced off at the top of the ring by a single oblique stroke of a
trowel held at a slight angle with the top of the ring. During these
operations care must be taken not to compress the paste. The
paste confined in the ring, resting on the plate, is placed under the
rod, the larger end of which is brought in contact with the surface
of the paste; the scale is then read and the rod quickly released.

MASONRY AND REINFORCED CONCRETE

24. The paste is of normal consistency when the cylinder
settles to a point 10 mm. below the original surface in one-half
minute after being released. The apparatus must be free from all
vibrations during the test.

25. Trial pastes are made with varying percentages of water
until the normal consistency is obtained.

26. Having determined the percentage of water required to
produce a paste of normal consistency, the percentage required for a
mortar containing by weight one part of cement to three parts of
standard Ottawa sand is obtained from Table II, the amount
being a percentage of the combined weight of the cement and sand.

TABLE II

Percentage of Water for Standard Mortars

Neat

One cement,
three standard

Neat

One cement,
three standard

Neat

One cement,
three standard

Ottawa .sand

Ottawa sand

8.0

9.3

10.7

8.2

9.5

10.8

8.3

9.7

11.0

8.5

9.8

11.2

8.7

10.0

11.3

8.8

10.2

11.5

9.0

10.3

11.7

9.2

10.5

11.8

TIME OF SETTING

27. Significance. The object of this test is to determine the
time which elapses from the moment water is added until the paste
ceases to be plastic (called the "initial set"), and also the time until
it acquires a certain degree of hardness (called the "final set" or
"hard set"). The former is the more important, since, with the
commencement of setting, the process of crystallization begins. As
a disturbance of this process may produce a loss of strength, it is
desirable to complete the operation of mixing or molding or incor-
porating the mortar into the work before the cement begins to set.

28 Apparatus. The initial and final set should be determined
with the Vicat apparatus described in paragraph 22.

29. Method. A paste of normal consistency is molded in the
hard-rubber ring, as described in paragraph 23, and placed under
the rod (B), the smaller end of which is then carefully brought in
contact with the surface of the paste, and the rod quickly released.

30. The initial set is said to have occurred when the needle
ceases to pass a point 5 mm. above the glass plate; and the final set,
when the needle does not sink visibly into the paste.

MASONRY AND REINFORCED CONCRETE

31. The test pieces should be kept in moist air during the test;
this may be accomplished by placing them on a rack over water con-
tained in a pan and covered by a damp cloth; the cloth to be kept
from contact with them by means of a wire screen; or they may be
stored in a moist box or closet.

32. Care should be taken to keep the needle clean, as the col-
lection of cement on the sides of the needle retards the penetration,
while cement on the point may increase the penetration.

33. The time of setting is affected not only by the percentage
and temperature of the water used and the amount of kneading the
paste receives, but by the temperature and humidity of the air, and
its determination is, therefore, only approximate.

STANDARD SAND

34. The sand to be used should be natural sand from Ottawa,
111., screened to pass a No. 20 sieve, and retained on a No. 30 sieve.
The sieves should be at least 8 inches in diameter; the wire cloth
should be of brass wrire and should conform to the following require-
ments :

No. of Sieve

Diameter of Wire

MESHES PER LINEAB INCH

Warp

Woof

0.016 to 0.017 in.
0.011 to 0.012 in.

19.5 to 20.5
29.5 to 30.5

19 to 21
28.5 to 31.5

Sand which has passed the No. 20 sieve is standard when not
more than 5 grams passes the No. 30 sieve in one minute of con-
tinuous sifting of a 500-gram sample.*

FORM OF TEST PIECES

35. For tensile tests the form of test piece shown in Fig. 3
should be used.

36. For compressive tests, 2-inch cubes should be used.

MOLDS

37. The molds should be of brass, bronze, or other non-
corrodible material, and should have sufficient metal in the sides to
prevent spreading during molding.

38. Molds may be either single or gang molds. The latter are
preferred by many. If used, the types shown in Fig. 4 are recom-
mended.

*Thi3 sand may be obtained from the Ottawa Silica Company at a cost of two cents per
pound, f. o. b. cars, Ottawa, 111.

3f> MASONRY AND REINFORCED CONCRETE >

Fig. 3. Diagram Showing Form and Dimensions of Standard Cement Briquette to be Used for

Testing

Fig. 4. Types of Briquette Molds

MASONRY AND REINFORCED CONCRETE 31

39. The molds should be wiped with an oily cloth before using.

MIXING

40. The proportions of sand and cement should be stated by
weight; the quantity of water should be stated as a percentage by
weight of the dry material.

41. The metric system is recommended because of the con-
venient relation of the gram and the cubic centimeter.

42. The temperature of the room and of the mixing water
should be maintained as nearly as practicable at 21° C. (70° F.)

43. The quantity of material to be mixed at one time depends
on the number of test pieces to be made; 1000 grams is a con-
venient quantity to mix by hand methods.

44. The Committee has investigated the various mechanical
mixing machines thus far devised, but cannot recommend any of
them, for the following reasons: (1) the tendency of most cement is
to "ball up" in the machine, thereby preventing working it into a
homogeneous paste; (2) there are no means of ascertaining when the
mixing is complete without stopping the machine; and (3) it is diffi-
cult to keep the machine clean.

45. Method. The material is weighed, placed on a non-
absorbent surface (preferably plate glass), thoroughly mixed dry, if
sand be used, and a crater formed in the center, into which the
proper percentage of clean water is poured; the material on the
outer edge is turned into the center by the aid of a trowel. As soon
as the water has been absorbed, which should not require more than
one minute, the operation is completed by vigorously kneading with
the hands for one minute. During the operation the hands should
be protected by rubber gloves.

MOLDING

46. The Committee has not been able to secure satisfactory
results with existing molding machines; the operation of machine
molding is very slow, and is not practicable with pastes or mortars
containing as large percentages of water as herein recommended.

47. Method. Immediately after mixing, the paste or mortar is
placed in the molds with the hands, pressed in firmly with the
fingers, and smoothed off with a trowel without ramming. The
material should be heaped above the mold, and, in smoothing off,
the trowel should be drawn over the mold in such a manner as to
exert a moderate pressure on the material. The mold should then
be turned over and the operation of heaping and smoothing off
repeated.

48. A check on the uniformity of mixing and molding may be
afforded by weighing the test pieces on removal from the moist

MASONRY AND REINFORCED CONCRETE

closet; test pieces from any sample which vary in weight more than
3% from the average should not be considered.

STORAGE OF THE TEST PIECES

49. During the first 24 hours after molding, the test pieces
should be kept in moist air to prevent drying.

50. Two methods are in common use to prevent drying: (1)
covering the test pieces with a damp cloth, and (2) placing them in a
moist closet. The use of the damp cloth, as usually carried out, is

Fig. 5. Diagram Showing Construction of Metal Clip for Holding Cement
Briquettes under Test

objectionable, because the cloth may dry out unequally and in conse-
quence the test pieces will not all be subjected to the same degree of
moisture. This defect may be remedied to some extent by immers-
ing the edges of the cloth in water; contact between the cloth and
the test pieces should be prevented by means of a wire screen, or
some similar arrangement. A moist closet is so much more effective

DRIVING A "RAYMOND" CONCRETE PILE
The pile is here being driven into the previously driven steel shell.

MASONRY AND REINFORCED CONCRETE 33

in securing uniformly moist air, and is so easily devised and so
inexpensive, that the use of the damp cloth should be abandoned.

51. A moist closet consists of a soapstone or slate box, or a
wood box lined with metal, the interior surface being covered with
felt or broad wicking kept wet, the bottom of the box being kept
covered with water. The interior of the box is provided with glass
shelves on which to place the test pieces, the shelves being so arranged
that they may be withdrawn readily.

52. After 24 hours in moist air, the pieces to be tested after
longer periods should be immersed in water in storage tanks or pans
made of non-corrodible material.

53. The air and water in the moist closet and the water in the
storage tanks should be maintained as nearly as practicable at 21°
C. (70° R).

TENSILE STRENGTH

54. The tests may be made with any standard machine.

55. The clip is shown in Fig. 5. It must be made accurately,
the pins and rollers turned, and the rollers bored slightly larger than
the pins, so as to turn easily. There should be a slight clearance at
each end of the roller, and the pins should be kept properly lubricated
and free from grit. The clips should be used without cushioning at
the points of contact.

56. Test pieces should be broken as soon as they are removed
from the wrater. Care should be observed in centering the test
pieces in the testing machine, as cross strains, produced by imperfect
centering, tend to lower the breaking strength. The load should
not be applied too suddenly, as it may produce vibration, the shock
from which often causes the test piece to break before the ultimate
strength is reached. The bearing surfaces of the clips and test
pieces must be kept free from grains of sand or dirt, which would
prevent a good bearing. The load should be applied at the rate of
600 pounds per minute. The average of the results of the test
pieces from each sample should be taken as the test of the sample.
Test pieces which do not break within | inch of the center, or are
otherwise manifestly faulty, should be excluded in determining
average results.

COMPRESSIVE STRENGTH

57. The tests may be made with any machine provided with
means for so applying the load that the line of pressure is along the
axis of the test piece. A ball-bearing block for this purpose is
shown in Fig. 6. Some appliance should be provided to facilitate
placing the axis of the test piece exactly in line with the center of
the ball bearing.

34 MASONRY AND REINFORCED CONCRETE

58. The test piece should be placed in the testing machine,
with a piece of heavy blotting paper on each of the crushing faces,
which should be those that were in contact with the mold.

CONSTANCY OF VOLUME

59. Significance. The object is to detect those qualities wrhich
tend to destroy the strength and durability of a cement. Under nor-
mal conditions these defects will in some cases develop quickly, and

HEAP OF TESTING MACHINE.

Fig. 6. Part Section of Head of Machine for Making Compression Tests
on Cement Blocks

in other cases may not develop for a considerable time. Since the
detection of these destructive qualities before using the cement in
construction is essential, tests are made not only under normal
conditions but under artificial conditions created to hasten the
development of these defects. Tests may, therefore, be divided into
two classes: (1) normal tests, made in either air or water maintained,
as nearly as practicable, at 21° C. (70° R); and (2) accelerated
tests, made in air, steam, or water, at temperature of 45° C. (113°
F.) and upward. The Committee recommends that these tests be
made in the following manner:

MASONRY AND REINFORCED CONCRETE 35

60. Methods. Pats, about 3 inches in diameter, \ inch thick
at the center, and tapering to a thin edge, should be made on clean
glass plates (about 4 inches square) from cement paste of normal
consistency, and stored in a moist closet for 24 hours.

61. Normal Tests. After 24 hours in the moist closet, a pat
is immersed in water for 28 days and observed at intervals. A
similar pat, after 24 hours in the moist closet, is exposed to the air
for 28 davs or more and observed at intervals.

riv^..;

DETAIL OF COVER

o . . .0

'*\*.

PLAN VIEW

CONSTANT- LEVEL BOTTLE

Top edge turned on

\ \ i TTI

is"

ZO- Gaje Copper, tinned on
inside. Use hard solder only

FRONT VI £\

\ 11 :-l 1 1

\ ^ REAK.V/EW
^/ Pipe for connection fo

Je yet bottle

WlKE SHELF

Fig. 7. Details of Apparatus for Making Accelerated Tests on Cement Blocks

62. Accelerated, Test. After 24 hours in the moist closet, a pat
is placed in an atmosphere of steam, upon a wire screen 1 inch above
boiling water, for 5 hours. The apparatus should be so constructed
that the steam will escape freely and atmospheric pressure be main-
tained. Since the type of apparatus used has a great influence on
the results, the arrangement shown in Fig. 7 is recommended.

63. Pats which remain firm and hard and show no signs of

3f> MASONRY AND REINFORCED CONCRETE

cracking, distortion, or disintegration are said to be "of constant
volume" or "sound".

64. Should the pat leave the plate, distortion may be detected
best with a straightedge applied to the surface which was in contact
with the plate.

65. In the present state of our knowledge it cannot be said that
,a cement which fails to pass the accelerated test will prove defective

in the work; nor can a cement be considered entirely safe simply be-
cause it has passed these tests.

George S. Webster, Chairman.

Richard L. Humphrey, Secretary.

W. B. W. Howe,

F. H. Lewis,

S. B. Newberry,

Alfred Noble,

Clifford Richardson,

L. C. Sabin,

George F. Swain.

Standard Cement Specifications*

GENERAL OBSERVATIONS

1. These remarks have been prepared with a view of pointing
out the pertinent features of the various requirements and the
precautions to be observed in the interpretation of the results of
the tests.

2. The Committee wyould suggest that the acceptance or re-
jection under these specifications be based on tests made by an
experienced person having the proper means for making the tests.

SPECIFIC GRAVITY

3. Specific gravity is useful in detecting adulteration. The
results of tests of specific gravity are not necessarily conclusive as
an indication of the quality of a cement, but when in combination
writh the results of other tests may afford valuable indications.

FINENESS

4. The sieves should be kept thoroughly dry.

TIME OF SETTING

5. Great care should be exercised to maintain the test pieces
under as uniform conditions as possible. A sudden change or wide
range of temperature in the room in which the tests are made, a
very dry or humid atmosphere, and other irregularities vitally
affect the rate of setting. -

'Adopted August 1C, 1909, by the American Society for Testing Materials.

MASONRY AND REINFORCED CONCRETE 37

CONSTANCY OF VOLUME

6. The tests for constancy of volume are divided into two
classes, the first normal, the second accelerated. The latter should
be regarded as a precautionary test only, and not infallible. So
many conditions enter into the making and interpreting of it that it
should be used with extreme care.

7. In making the pats, the greatest care should be exercised
to avoid initial strains due to molding or to too rapid drying-out
during the first 24 hours. The pats should be preserved under the
most uniform conditions possible, and rapid changes of temperature
should be avoided.

8. The failure to meet the requirements of the accelerated tests
need not be sufficient cause for rejection. The cement, however,
may be held for 28 days, and a retest made at the end of that period,
using a new sample. Failure to meet the requirements at this time
should be considered sufficient cause for rejection, although in the
present state of our knowledge it cannot be said that such failure
necessarily indicates unsoundness, nor can the cement be considered
entirely satisfactory simply because it passes the tests.

GENERAL CONDITIONS

1. All cement shall be inspected.

2. Cement may be inspected either at the place of manufacture
or on the work.

3. In order to allow ample time for inspecting and testing, the
cement should be stored in a suitable weather-tight building having
the floor properly blocked or raised from the ground.

4. The cement shall be stored in such a manner as to permit
easy access for proper inspection and identification of each shipment.

5. Every facility shall be provided by the contractor, and a
period of at least 12 days allowed for the inspection and necessary
tests.

6. Cement shall be delivered in suitable packages, with the
brand and name of manufacturer plainly marked thereon.

7. A bag of cement shall contain 94 pounds of cement net. Each
barrel of Portland cement shall contain 4 bags, and each barrel of
natural cement shall contain 3 bags of the above net weight.

8. Cement failing to meet the 7-day requirements may be held
awaiting the results of the 28-day tests before rejection.

9. All tests shall be made in accordance with the methods
proposed by the Special Committee on Uniform Tests of Cement of
the American Society of Civil Engineers, presented to the Society
on January 17th, 1912, with all subsequent amendments thereto.

10. The acceptance or rejection shall be based on the following
requirements:

38 MASONRY AND REINFORCED CONCRETE

NATURAL CEMENT

11. Definition. This terra shall be applied to the finely pul-
verized product resulting from the calcination of an argillaceous
limestone at a temperature only sufficient to drive off the carbonic
acid gas.

FINENESS

12. It shall leave by weight a residue of not more than 10%
on the No. 100, and 30% on the No. 200 sieve.

TIME OF SETTING

13. It shall not develop inital set in less than 10 minutes, and
shallnot develop hard set in less than 30 minutes, or more than 3
hours.

TENSILE STRENGTH

14. The minimum requirements for tensile strength for bri-
quettes 1 square inch in cross section shall be as follows, and the
cement shall show no retrogression in strength within the periods
specified :

Neat Cement

AGE STRENGTH

24 hours in moist air 75 Ib.

7 days (1 day in moist air, 6 days in water) 150 Ib.

28 days (1 day in moist air, 27 days in water) 250 Ib.

One Part Cement, Three Parts Standard Ottaica Sand

7 days (1 day in moist air, 6 days in water) 50 Ib.

28 days (1 day in moist air, 27 days in water) 125 Ib.

CONSTANCY OF VOLUME

15. Pats of neat cement about 3 inches in diameter, \ inch
thick at the center, tapering to a thin edge, shall be kept in moist
air for a period of 24 hours.

(a) A pat is then kept in air at normal temperature.
(6) Another is kept in water maintained as near 70° F. as
practicable.

16. These pats are observed at intervals for at least 28 days,
and, to pass the tests satisfactorily, should remain firm and hard
and show no signs of distortion, checking, cracking, or disintegrating.

PORTLAND CEMENT

17. Definition. This term is applied to the finely pulverized
product resulting from the calcination to incipient fusion of an
intimate mixture of properly proportioned argillaceous and cal-
careous materials, and to which no addition greater than 3% has
been made subsequent to calcination.

MASONRY AND REINFORCED CONCRETE 39

SPECIFIC GRAVITY

18. The specific gravity of cement shall be not less than 3.10.
Should the test of cement as received fall below this requirement, a
second test may be made on a sample ignited at a low red heat.
The loss in weight of the ignited cement shall not exceed 4 per cent.

19. It shall leave by weight a residue of not more than 8% on
the No. 100, and not more than 25% on the No. 200 sieve.

TIME OF SETTIHG

20. It shall not develop initial set in less than 30 minutes;
and must develop hard set in not less than 1 hour, nor more than
10 hours.

TENSILE STRENGTH

21. The minimum requirements for tensile strength for bri-
quettes 1 square inch in cross section shall be as follows, and the
cement shall show no retrogression in strength within the periods
specified :

Neat Cement

AGE STRENGTH

24 hours in moist air 175 Ib.

7 days (1 day in moist air, 6 days in water) 500 Ib.

28 days (1 day in moist air, 27 days in water) 600 Ib.

One Part Cement, Three Parts Standard Ottawa Sand

7 days (1 day in moist air, 6 days in water) 200 Ib.

28 days (1 day in moist air, 27 days in water) 275 Ib.

CONSTANCY OF VOLUME

22. Pats of neat cement about 3 inches in diameter, \ inch
thick at the center, and tapering to a thin edge, shall be kept in
moist air for a period of 24 hours.

(a) A pat is then kept in air at normal temperature and
observed at intervals for at least 28 days.

(6) Another pat is kept in water maintained as near 70° F.
as practicable, and observed at intervals for at least 28
days.

(c) A third pat is exposed in any convenient way in an atmos-
phere of steam, above boiling water, in a loosely closed
vessel for 5 hours.

23. These pats, to pass the requirements satisfactorily, shall
remain firm and hard, and show no signs of distortion, checking,
cracking, or disintegrating.

SULPHURIC ACID AND MAGNESIA

24. The cement shall not contain more than 1.75% of anhy-
drous sulphuric acid (SO3), nor more than 4% of magnesia (MgO).

MASONRY AND REINFORCED CONCRETE

Test Machines. There are many varieties of testing machines
on the market. One very common type of machine is illustrated
in Fig. 8. A reservoir contains a supply of shot, which falls through
the pipe closed by means of a va^'e at the bottom. The briquette
is carefully placed between the clips, as shown in the figure, and the

Fig. 8. Cement Testing Scales with Briquette in Position
Courtesy of Fairbanks, Morse and Company

wheel below is turned until the indicators are in line. A hook lever
is moved so that a screw worm is engaged with its gear. Then
the valve of the shot reservoir is opened so as to allow the shot to
run into the cup, a small valve regulating the flow of shot into

MASONRY AND REINFORCED CONCRETE 41

the cup. Better results will be obtained by allowing the shot
to run slowly into the cup. The crank is then turned with just
sufficient speed so that the scale beam is held in position until the
briquette is broken. Upon the breaking of the briquette, the scale
beam falls, and automatically closes the valve. . The weight of
the shot in the cup then indicates, according to some definite
ratio, the stress required to break the briquette.

SAND

Sand is a constituent part of mortar and concrete. The strength
of the masonry is dependent to a considerable extent on the qualities
of the sand and it is therefore important that the desirable and the
defective qualities should be understood, and that these qualities be
always investigated as thoroughly as are the qualities of the cement
used. There have been many failures of structures due to the use
of poor sand.

Object. Sand is required in mortar or concrete for economy
and to prevent the excessive cracking that would take place in neat
lime or cement without the use of sand. Mortar made without sand
would be expensive and the neat lime or cement would crack so
badly that the increased strength, due to the neat paste, would be
of little value, if any, on account of it contracting and cracking very
badly.

Essential Qualities. The word "sand" as used above is intend-
ed as a generic term to apply to any finely divided material which
will not injuriously affect the cement or lime, and which is not subject
to disintegration or decay. Sand is almost the only material which
is sufficiently cheap and which will fulfil these requirements,
although stone screenings (the finest material coming from a
stone crusher), powdered slag, and even coal dust have occasion-
ally been used as substitutes. Specifications usually demand that
the sand shall be "sharp, clean, and coarse", and such terms
have been repeated so often that they are accepted as standard,
notwithstanding the frequent demonstration that modifications
of these terms are not only desirable but also economical. These
words also ignore other qualities which should be considered,
especially when deciding between two or more different sources of
sand supply.

42 MASONRY AND REINFORCED CONCRETE

Geological Character. Quartz sand is the most durable and
unchangeable. Sands which consist largely of grains of feldspar,
mica, hornblende, etc., which will decompose upon prolonged expos-
ure to the atmosphere, are less desirable than quartz, although, after
being made up into the mortar, they are virtually protected against
further decomposition.

Coarseness. A mixture of coarse and fine grains, with the
coarse grains predominating, is found very satisfactory, as it makes
a denser and stronger concrete with a less amount of cement than
when coarse-grained sand is used with the same proportion of cement.
The small grains of sand fill the voids caused by the coarse grains so
that there is not so great a volume of voids to be filled by the cement.
The sharpness of sand can be determined approximately by rubbing
a few grains in the hand or by crushing it near the ear and noting if a
grating sound is produced; but an examination through a small lens
is better.

Sharpness. Experiments have shown that round grains of
sand have less voids than angular ones, and that water-worn sands
have from 3 to 5 per cent less voids than corresponding sharp
grains. In many parts of the country where it is impossible, except
at a great expense, to obtain the sharp sand, the round grain is used
with very good results. Laboratory tests made under conditions as
nearly as possible identical, show that the rounded-grain sand gives
as good results as the sharp sand. In consequence of such tests,
the requirement that sand shall be sharp is now considered useless
by many engineers, especially when it leads to additional cost.

Cleanness. In all specifications for concrete work, is found
the clause: "The sand shall be clean." This requirement is some-
times questioned, as experimenters have found that a small per-
centage of clay or loam often gives better results than when clean
sand is used. "Lean" mortar may be improved by a small per-
centage of clay or loam, or by using dirty sand, for the fine material
increases the density. In rich mortars, this fine material is not
needed, as the cement furnishes all the fine material necessary and,
if clay or loam or dirty sand were used, it might prove detrimental.
Whether it is really a benefit or not, depends chiefly upon the rich-
ness of the concrete and the coarseness of the sand. Some idea of
the cleanliness of sand may be obtained by placing it in the palm of

MASONRY AND REINFORCED CONCRETE 43

one hand and rubbing it with the fingers of the other. If the sand
is dirty, it will badly discolor the palm of the hand. When it is
found necessary to use dirty sand, the strength of the concrete
should be tested.

Sand containing loam or earthy material is cleansed by washing
with water, either in a machine specially designed for the purpose,
or by agitating the sand with water in boxes provided with holes to
permit the dirty water to flow away.

Very fine sand may be used alone, but it makes a weaker con-
crete than either coarse sand or coarse and fine sand mixed. A
mortar consisting of very fine sand arid cement will not be so dense
as one of coarse sand and the same cement, although, when measured
or weighed dry, both contain the same proportion of voids and
solid matter. In a unit measure of fine sand, there are more grains
than in a unit measure of coarse sand and, therefore, more points of
contact. More water is required in gaging a mixture of fine sand
and cement than in a mixture of coarse sand and the same cement.
The water forms a film and separates the grains, thus producing a
larger volume having less density.

The screenings of broken stone are sometimes used instead of
sand. Tests frequently show a stronger concrete when screenings
are used than when sand is used. This is perhaps due to the vari-
able sizes of the screenings, which would have a less percentage of
voids.

Percentage of Voids. As before stated, a mortar is strongest
when composed of fine and coarse grains mixed in such proportion
that the percentage of voids shall be the least. The simplest method
of comparing two sands is to weigh a certain gross volume of each,
the sand having been thoroughly shaken down. Assuming that the
stone itself of each kind of sand has the same density, then the
heavier volume of sand will have the least percentage of voids. The
actual percentage of voids in packed sand may be approximately
determined by measuring the volume of water which can be added
to a given volume of packed sand. If the water is poured into the
sand, it is quite certain that air will remain in the voids in the sand,
which will not be dislodged by the water, and the apparent volume
of voids will be less than the actual. The precise determination
involves the measurement of the specific gravity of the stone of

44 MASONRY AND REINFORCED CONCRETE

which the sand is composed, and the percentage of moisture in the
sand, all of which is done with elaborate precautions. Ordinarily,
such precise determinations are of little practical value, since the
product of any one sand bank is quite variable. While it would be
theoretically possible to mix fine and coarse sand, varying the ratios
according to the varying coarseness of the grains as obtained from
the sand pit, it is quite probable that an over-refinement in this
particular wrould cost more than the possible saving is worth. Ordi-
narily, sand has from 28 to 40 per cent of voids. An experimental
test of sand of various degrees of fineness, 12| per cent of it passing
a No. 100 sieve, showed only 22 per cent of voids; but such a value
is of only theoretical interest.

BROKEN STONE

Classification of Stones. This term ordinarily signifies the
product of a stone crusher or the result of hand-breaking by hammer-
ing large blocks of stone; but the term may also include gravel,
described below.

The best, hardest, and most durable broken stone comes from
the trap rocks, which are dark, heavy, close-grained rocks of igneous
origin. The term granite is usually made to include not only true
granite, but also gneiss, mica schist, syenite, etc. These are just as
good for concrete work, and are usually less expensive. Limestone
is suitable for some kinds of concrete work; but its strength is not so
great as that of granite or trap rock, and it is more affected by a
conflagration. Conglomerate, often called pudding stone, makes a
very good concrete stone. The value of sandstone for concrete is
very variable according to its texture. Some grades are very com-
pact, hard, and tough, and make a good concrete; other grades are
friable, and, like shale and slate, are practically unfit for use. Gravel
consists of pebbles of various sizes, produced from stones which have
been broken up and then worn smooth with rounded corners. The
very fact that they have been exposed for indefinite periods to
atmospheric disintegration and mechanical wrear is a proof of the
durability and mechanical strength of the stone.

Size of Stone and Its Uniformity. There is hardly any limita-
tion to the size of stone which may be used in large blocks of massive
concrete, since it is now frequently the custom to insert these large

MASONRY AND REINFORCED CONCRETE 45

blocks and fill the spaces between them with a concrete of smaller
stone. But the term broken stone should be confined to those pieces
of a size which may be readily mixed up in a mass, as is done when
mixing concrete; and this virtually limits the size to stones which
will pass through a 2|-inch ring. The lower limit in size is very
indefinite, since the product of a stone crusher includes all sizes
down to stone dust screenings, such as are substituted partially or
entirely for sand, as previously noted. Practically the only use of
broken stone in masonry construction is in the making of concrete;
and, since one of the most essential features of good concrete con-
struction is that the concrete shall have the greatest possible density,
it is important to reduce the percentage of voids in the stone as much
as possible. This percentage can be determined with sufficient
accuracy for ordinary unimportant wrork, by the very simple method
previously described for obtaining that percentage with sand —
namely, by measuring how much water wrill be required to fill up the
cavities in a given volume of dry stone. As before, such a simple
determination is somewrhat inexact, owring to the probability that
bubbles of air will be retained in the stone which will reduce the
percentage somewhat, and also because of the uncertainty involved
as to whether the stone is previously dry or is saturated with water.
Some engineers drop the stone slowly into the vessel containing the
water, rather than pour the water into the vessel containing the
stone, with the idea that the error due to the formation of air bubbles
will be decreased by this method. The percentage of error, however,
due to such causes, is far less than it is in a similar test of sand, and
the error for ordinary work is too small to have any practical effect
on the result.

Illustrative Example. A pail having a mean inside diameter of
10 inches and a height of 14 inches is filled with broken stone well
shaken down; a similar pail filled with water to a depth of 8 inches
is poured into the pail of stone until the water fills up all the cavities
and is level with the top of the stone; there is still 1\ inches depth
of water in the pail. This means that a depth of 5f inches has been
used to fill up the voids. The area of a 10-inch circle is 78.54 square
inches and therefore the volume of the broken stone was 78.54X14
= 1,099.56 cubic inches. The volume of the water *used to fill the
pail was 78.54X5.75, or 451.6 cubic inches. This is 41 per cent

46 MASONRY AND REINFORCED CONCRETE

of the volume of the stone, and is in this case the percentage of voids.
The accuracy of the above computation depends largely on the
accuracy of the measurement of the mean inside diameter of the pail.
If the pail were truly cylindrical, there would be no inaccuracy. If
the pail is flaring, the inaccuracy might be considerable; and if a
precise value is desired, more accurate methods should be chosen to
measure the volume of the stone and of the water.

Screened Stone Unnecessary. It is invariably found that
unscreened stone or the run of the crusher has a far less percentage of
voids than screened stone, and it is therefore not only an extra
expense, but also an injury to the concrete, to specify that broken
stone shall be screened before being used in concrete, unless, as
described later, it is intended to mix definite proportions of several
sizes of carefully screened broken stone. Since the proportion of
large and small particles in the run of the crusher depends consider-
ably upon the character of the stone which is being broken up, and
perhaps to some extent on the crusher itself, these proportions should
be tested at frequent intervals during the progress of the work; and
the amount of sand to be added to make a good concrete should be
determined by trial tests, so that the resulting percentage of voids
shall be as small as it is practicable to make it. It is usually found
that the percentage of voids in crusher-run granite is a little larger
than in limestone or gravel. This gives a slight advantage to the
limestone and gravel, which tends to compensate for the weakness
of the limestone and the rounded corners of the gravel.

Broken stone is frequently sold by the ton, instead of by the
cubic yard; but as its weight varies from 2200 to 3200 pounds per
cubic yard, an engineer or contractor is uncertain as to how many
cubic yards he is buying or how much it costs him per cubic yard,
unless he is able to test the particular stone and obtain an average
figure as to its weight per unit of volume.

Cinders. Cinders for concrete should be free from coal or soot.
Usually a better mixture can be obtained by screening the fine stuff
from the cinders and then mixing in a larger proportion of sand,
than by using unscreened material, although, if the fine stuff is
uniformly distributed through the mass, it may be used without
screening, and a less proportion of sand used.

As shown later, the strength of cinder concrete is far less than

MASONRY AND REINFORCED CONCRETE 47

that of stone concrete; and on this account it cannot be used where
high compressive values are necessary. But on account of its very
low cost compared with broken stone, especially under some con-
ditions, it is used quite commonly for roofs, etc., on which the loads
are comparatively small.

One possible objection to the use of cinders lies in the fact that
they frequently contain sulphur and other chemicals which may
produce corrosion of the reinforcing steel. In any structure where
the strength of the concrete is a matter of importance, cinders should
not be used without a thorough inspection, and even then the unit
compressive values allowed should be at a very low figure.

MORTAR

Kinds of Mortar. The term mortar is usually applied to the
mixture of sand and cementing material which is placed between
the large stones of a stone structure, although the term might also
be properly applied to the matrix of the concrete in which broken
stone is embedded. The object of the mortar is to furnish a cushion
for the stones above it, which, as far as possible, distributes the
pressure uniformly and relieves the stones of transverse stresses and
also from the concentrated crushing pressures to which the projecting
points of the stone would be subjected.

Common Lime Mortar. The first step in the preparation of
common lime mortar is the slaking of the lime. This should be
done by putting the lime into a water-tight box, or at least on a plat-
form which is substantially water-tight, and on which a sort of pond
is formed by a ring of sand. The amount of water to be used should
be from 2| to 3 times the volume of the unslaked lime.

The "volume" of unslaked lime is a very uncertain quantity,
varying with the amount of settlement caused by mere shaking which
it may receive during transit. A barrel of lime means 230 pounds.
If the barrel has a volume of 3.75 cubic feet, it would be just filled
by ,230 pounds of lime when this lime weighed about 61 pounds per
cubic foot. This same lime, however, may be so shaken that it will
weigh 75 pounds per cubic foot, in which case its volume is reduced
to 81 per cent, or 3.05 cubic feet. Combining this with 2^ to 3 times
its volume of water will require about 8| cubic feet of water to one
barrel of lime. On the other hand, if the lime has absorbed moisture

48 MASONRY AND REINFORCED CONCRETE

from the atmosphere, and has become more or less air-slaked, its
volume may become very materially increased.

Although close accuracy is not necessary, the lime paste will be
injured if the amount of water is too much or too little. In short,
the amount of water should be as near as possible that which is chem-
ically required to hydrate the lime, so that on the one hand it shall be
completely hydrated, and on the other hand it shall not be drowned
in an excess of water which will injure its action in ultimate harden-
ing. About three volumes of sand should be used to one volume of
lime paste. Owing to the fact that the paste will, to a considerable
extent, nearly fill the voids in the sand, the volume obtained from one
barrel of unslaked lime made up into a mortar consisting of one part
of lime paste to three parts of sand, will make about 6.75 barrels of

mortar, or a little less than one
cubic yard.

Natural Cement Mortar. This
is used, especially when mixed
with lime to retard the setting, in
the construction of walls of build-
ings, cellar foundations, and, in
general, in masonry where the
unit stresses are so low that
strength is a minor consideration,
but where a lime mortar would
not harden because it is to be under water, or in a solid mass
where the carbonic acid of the atmosphere could not penetrate
to the interior. When natural cement is dumped loosely in a
pile, the apparent volume is increased one-third or even one-half.
This must be allowed for in mixing. A barrel averages 3.3 cubic
feet. Therefore a 1:4 mortar of natural cement would require one
barrel of cement to 13.2 cubic feet (about one-half a cubic yard) of
sand. A bottomless box similar to that illustrated in Fig. 9, and
with inside dimensions of 3 feet X 2 feet 6 inches X 1 foot 9 inches,
contains 13.2 cubic feet. It is preferable to use even charges of one
barrel of cement in mixing up a batch of mortar, rather than to
dump it out and measure it loosely. If the size of the barrel varies
from the average value given above, the size of the sand box should
be varied accordingly. The barrels coming from any one cement

Fig. 9. Botto

Box for Measuring Sand

MASONRY AND REINFORCED CONCRETE 49

mill may usually be considered as of uniform capacity. Since it is
practically somewhat difficult to measure accurately the volume of
a barrel, owing to its swelling form, it is best to fill a sample barrel
with loose dry sand, and then to measure the volume of that sand by
emptying it into a rectangular box whose inside area, together with
the height of sand in it, can be readily measured.

Portland Cement Mortar. A barrel of Portland cement will
contain 370 to 380 pounds, net, of cement. Its capacity averages
about 3.3 cubic feet, although with some brands the capacity may
reach 3.75. The expansion, when the cement is thrown loosely in a
pile or into a measuring box, varies from 10 to 40 per cent. The
subject will be discussed further under the head of "Concrete".

Lime in Cement Mortar. Lime is frequently employed in the
cement mortar used for buildings, for a combination of reasons:

(a) It is unquestionably more economical; but if the percentage added
(or that which replaces the cement) is more than about 5 per cent, the strength
of the mortar is sacrificed. The percentage of loss of strength depends on the
richness of the mortar.

(b) When used with a mortar leaner than 1 : 2, the substitution of about
10 per cent of lime for an equal weight of cement will render concrete more water-
tight, although at some sacrifice in strength.

(c) It always makes the mortar work more easily and smoothly. In
fact, a rich cement mortar is very brash; it will not stick to the bricks or stones
when striking a joint. It actually increases the output of the masons to use a
mortar which is rendered smoother by the addition of lime.

The substitution of more than 20 per cent of lime decreases the
strength faster than the decrease in cost and therefore should not
be permitted unless strength is a secondary consideration and the
combination is considered more as an addition of cement to a lime
mortar in order to render it hydraulic.

Effect of Re=Qaging or Re=Mixing Mortar. Specifications and
textbooks have repeatedly copied from one another a requirement
that all mortar which is not used immediately after being mixed and
before it has taken an initial set must be rejected and thrown away.
This specification is evidently based on the idea that after the initial
set has been disturbed and destroyed, the cement no longer has the
power of hardening, or at least that such power is very materially
and seriously reduced. Repeated experiments, however, have shown
that under some conditions the ultimate strength of the mortar (or
concrete) is actually increased, and that it is not seriously injured

50 MASONRY AND REINFORCED CONCRETE

even when the mortar is re-gaged several hours after being originally
mixed with water.

Effect on Lime Paste. Such a specification against re-mixing is
never applied to lime paste, since it is well known that a lime paste
is considerably improved by being left for several days (or even
months) before being used. This is evidently due to the fact that
even during such a period the carbonic acid of the atmosphere cannot
penetrate appreciably into the mass of the paste, wrhile the greater
length of time merely insures a more perfect slaking of the lime.
The presence of free unslaked lime in either lime or cement mortar
is always injurious, because it generally results in expansion and
disruption and possibly in injurious chemical reaction.

Effect on Portland Cement. Tests with Portland cement have
shown that if it is re-mixed two hours after being combined with
water, its strength, both tensile and compressive, is greater after
six months' hardening, although it will be less after seven days'
hardening, than in similar specimens which are molded immediately
after mixing. It is also found that the re-mixing makes the cement
much slower in its setting. The adhesion, moreover, is reduced by
re-mixing, which is an important consideration in the use of rein-
forced concrete.

Effect on Natural Cement. The effects of tests with natural
cement are somewThat contradictory, and this is perhaps the reason
for the original writing of such a specification. The result of an
elaborate series of tests made by Mr. Thomas F. Richardson showed
that quick-setting cements which had been re-mixed showed a con-
siderable falling off in strength in specimens broken after 7 days and
28 days of hardening, yet the ultimate strength after six months of
hardening was invariably increased. It is also found that for both
Portland and natural cements there is a very considerable increase
in the strength of the mortar when it is worked continuously for
two hours before molding or placing in the masonry. Such an
increase is probably due to the more perfect mixing of the constitu-
ents of the mortar.

Conclusions. The conclusion of the whole matter appears to be
that, when it is desirable that considerable strength shall be attained
within a few days or weeks (as is generally the case, and especially
so with reinfo reed-concrete work), the specification against re-mixing

MASONRY AND REINFORCED CONCRETE 51

should be rigidly enforced. For the comparatively few cases where
a slow acquirement of the ultimate strength is permissible, re-mixing
might be tolerated, although there is still the question whether the
expected gain in ultimate strength would pay for the extra work. It
would be seldom, if ever, that this claimed property of cement
mortar could be relied on to save a batch of mortar which would
otherwise be rejected because it had been allowed to stand after
being mixed until it had taken an initial set.

Proportions of Materials for Mortar. Lime Mortar. As previ-
ously stated, p. 47, a barrel of unslaked lime should be mixed with
about 8? cubic feet of water. This will make about 9 cubic feet of
lime paste. Mixing this with a cubic yard of sand will make about
1 cubic yard of 1:3 lime mortar. This means approximately
1 volume of unslaked lime to 8 volumes of sand.

Cement Mortars. The volume of cement depends very largely
on whether it is loosely dropped in a pile, shaken together, or packed.
The practical commercial methods of obtaining a mixture of definite
proportions will be given in the following section. Natural
cement mortars are usually mixed in the 1 : 2 ratio, although a 1 : 1
mixture would be a safer mixture to use. Portland cement will be
used to make 1 : 3 mortar for ordinary work, and 1 : 2 mortar for very
high-grade work. As previously stated, a small percentage of lime
is sometimes substituted for an equal volume of cement in order to
make the mortar work better.

CONCRETE
CHARACTERISTICS AND PROPERTIES

Concrete is composed of a mixture of cement, sand, and crushed
stone or gravel, which, after being mixed with water, soon sets and
obtains a hardness and strength equal to that of a good building
stone. These properties, together with its adaptability to mono-
lithic construction, combined with its cheapness, render concrete
very useful as a building material.

Principles Used in Proportioning Concrete. Theoretically, the
proportioning of the sand and cementing material should be done
by weight. It is always done in this way in laboratory testing.
The volume of a given weight of cement is quite variable according
as it is packed or loosely thrown in a pile. The same statement is

52 MASONRY AND REINFORCED CONCRETE

true of sand. A barrel of Portland cement will increase in volume
from 10 to 30 per cent by being merely dumped loosely in a pile and
then shoveled into a measuring box. In measuring the materials
for concrete the cement should be measured in the original packages
as it comes from the manufacturer, but the sand and stone should
be measured loose as it is thrown in the measuring boxes. To a less
extent uncertainty exists regarding the conditions of the sand.
Loose dry sand occupies a considerably larger volume than wet
sand, and this is still more the case when the sand is very fine.

Ideal Conditions. The general principle to be adopted is that
the amount of water should be just sufficient to supply that needed
for crystallization of the cement paste; that the amount of paste
should be just sufficient to fill the voids between the particles of
sand; that the mortar thus produced should be just sufficient to fill
the voids between the broken stones. If this ideal could be realized,
the total volume of the mixed concrete would be no greater than that
of the broken stone. But no matter how thoroughly and carefully
the ingredients are mixed and rammed, the particles of cement will
get between the grains of sand and thus cause the volume of the
mortar to be greater than that of the sand; the grains of sand will
get between the smaller stones and separate them; and the smaller
stones will get between the larger stones and separate them. Experi-
ments by Prof. I. O. Baker have shown that, even when the volume
of the mortar was only 70 per cent of the volume of the voids in the
broken stone, the volume of the rammed concrete was 5 per cent
more than that of the broken stone. When the theoretical amount
of mortar was added, the volume was 7.5 per cent in excess, which
shows that it is practically impossible to ram such concrete and
wholly prevent voids. When mortar amounting to 140 per cent of
the voids was used, all voids wrere apparently filled, but the volume
of the concrete was 114 per cent of that of the broken stone.

Conditions in Practice. Therefore, on account of the imprac-
ticability of securing perfect mixing, the amount of water used is
always somewhat in excess (which will do no harm); the cement
paste is generally made somewhat in excess of that required to fill
the particles in the sand (except in those cases where, for economy,
the mortar is purposely made very lean) ; and the amount of mortar
is usually considerably in excess of that required to fill the voids in

MASONRY AND REINFORCED CONCRETE 53

the stone. Even when we allow some excess in the above particulars,
there is so much variation in the percentage of voids in the sand and
broken stone, that the best work not only requires an experimental
determination of the voids in the sand and stone which are being
used; but, on account of the liability to variation in those percentages,
even in materials from the same source of supply, the best work re-
quires a constant testing and revision of the proportions as the work
proceeds. For less careful work, the proportions ordinarily adopted
in practice are considered sufficiently accurate.

Proportions. On the general principle that the voids in ordinary
broken stone are somewhat less than half of the volume, it is a
very common practice to use one-half as much sand as the volume
of the broken stone. The proportion of cement is then varied
according to the strength required in the structure, and according
to the desire to economize. On this principle we have the familiar
ratios 1:2:4, 1 : 2| : 5, 1 : 3 : 6, and 1:4:8. It should be noted that in
each of these cases, in which the numbers give the relative propor-
tions of the cement, sand, and stone respectively, the ratio of the
sand to the broken stone is a constant, and the ratio of the cement
is alone variable, for it would be just as correct to express the ratios
as follows: 1:2:4; 0.8:2:4; 0.67:2:4; 0.5:2:4.

Cinder Concrete. Cinder concrete has been used to some
extent on account of its light weight. The strength of cinder con-
crete is from one-third to one-half the strength of stone concrete.
It will weigh about 110 pounds per cubic foot.

Rubble Concrete. Rubble concrete is a concrete in which
large stones are placed, and will be discussed in Part II.

Compressive Strength. The compressive strength of concrete
is very important, as it is used more often in compression than in any
other way. It is rather difficult to give average values of the compres-
sive strength of concrete, as it is dependent on so many factors. The
available aggregates are so varied, and the methods of mixing and
manipulation so different, that tests must be studied before any conclu-
sions can be drawn. For extensive work, tests should be made with
the materials available to determine the strength of concrete, under
conditions as nearly as possible like those in the actual structure.

A series of experiments made at the Watertown Arsenal for
Mr. George A. Kimball, Chief Engineer of the Boston Elevated

MASONRY AND REINFORCED CONCRETE

Railway Company, in 1899, was one of the best sets of tests that have
been published, and the results are given in Table III. Portland
cement, coarse sharp sand, and stone up to 2% inches were used; and
when thoroughly rammed, the water barely flushed to the surface.

TABLE III
Compressive Strength of Concrete*

Tests Made at Watertown Arsenal, 1899

MIXTURE

BRAND OF CEMENT

STRENGTH (Pounds per Square Inch)

7 Days

1 Month

3 Months

6 Months

,„,[

1:3:6]

{

Saylor
Atlas
Alpha
Germania
Alsen

Average

Saylor
Atlas
Alpha
Gormania
Alsen

Average

1724
1387
904
2219
1592

2238
2428
2420
2642
2269

2702
2966
3123
3082
2608

3510
3953
4411
3643
3612

1565

2399

2896

3826

1625
1050
892
1550
1438

2568
1816
2150
2174
2114

2882
1538
2355
2486
2349

3567
3170
2750
2930
3026

1311

2164

2522

3088

The values obtained in these tests are exceedingly high, and cannot be
safely counted on in practice.

Tests made by Prof. A. N. Talbot (University of Illinois, Bul-
letin No. 14) on 6-inch cubes of concrete, show the average values
given in Table IV. The cubes were about 60 days old when tested.

TABLE IV
Compressive Tests of Concrete

University of Illinois

No. OF TESTS

MIXTURE

STRENGTH (Pounds per Square
Inch)

1:2:4

2350

i:3:5£

1920

1:3:6

1300

With fair conditions as to the character of the materials and
workmanship, a mixture of 1:2:4 concrete should show a Compressive

•From "Tests of Metals", 1899.

MASONRY AND REINFORCED CONCRETE 55

strength of 2000 to 2300 pounds per square inch in 40 to 60 days;
a mixture of 1 : 1\ : 5 concrete, a strength of 1800 to 2000 pounds per
square inch; and a mixture of 1:3:6 concrete, a strength of 1500 to
1800 pounds per square inch. The rate of hardening depends upon
the consistency and the temperature.

Tensile Strength. The tensile strength of concrete is usually
considered about one-tenth of the compressive strength; that is,
concrete which has a compressive value of 2000 pounds per square
inch should have a tensile strength of about 200 pounds per square
inch. Although there is no fixed relation between the two values,
the general law of increase in strength due to increasing the per-
centage of cement and the density seems to hold in both cases.

Shearing Strength. The shearing strength of concrete is
important on account of its intimate relation to the compressive
strength and the shearing stresses to which it is subjected in struc-
tures reinforced with steel. But few tests have been made, as they
are rather difficult to make; but the tests made show that the shear-
ing strength of concrete is nearly one-half the crushing strength.
By shearing is meant the strength of the material against a sliding
failure when tested as a rivet would be tested for shear.

Modulus of Elasticity. The principal use of the modulus of
elasticity in designing reinforced concrete is in determining the
relative stresses carried by the concrete and the steel. The mini-
mum value used in designing reinforced concrete is usually taken as
2,000,000, and the maximum value as 3,000,000, depending on the
richness of the mixture used. A value of 2,500,000 is generally
taken for ordinary concrete.

Weight. The weight of stone or gravel concrete will vary from
145 pounds per cubic foot to 155 pounds per cubic foot, depending
upon the specific gravity of the materials and the degree of com-
pactness. The weight of a cubic foot of concrete is usually con-
sidered as 150 pounds.

Cost. The cost of concrete depends upon the character of the
work to be done and the conditions under which it is necessary to
do this work. The cost of the material, of course, will always have
to be considered, but this is not so important as the character of the
work. The cost of concrete in place will range from $4.50 per cubic
yard to $20, or even $25, per cubic yard. When it is laid in large

56 MASONRY AND REINFORCED CONCRETE

masses, so that the cost of forms is relatively small, the cost will
range from $4.50 per cubic yard to $6 or $7 per cubic yard, depend-
ing upon the local conditions and cost of materials. Foundations and
heavy walls are good examples of this class of work. For sewers and
arches, the cost will vary from $7 to $13. In building construction —
floors, roofs, and thin walls — the cost will range from $14 to $20 per
cubic yard.

Cement. The cost of Portland cement varies with the demand.
Being heavy, the freight is often a big item. The price varies from
$1 to $2 per barrel. To this must be added the cost of handling.

Sand. The cost of sand, including handling and freight, ranges
from $0.75 to $1.50 per cubic yard. A common price for sand
delivered in the cities is $1.00 per cubic yard.

Broken Stone or Gravel. The cost of broken stone delivered in
the cities varies from $1.25 to $1.75 per cubic yard. The cost of
gravel is usually a little less than stone.

Mixing. Under ordinary conditions and where the concrete
will have to be wheeled only a very short distance, the cost of hand-
mixing and placing will generally range from $0.90 to $1.30 per
cubic yard, if done by men skilled in this work. If a mixer is used,
the cost will range from $0.50 to $0.90 per cubic yard.

Fonns. The cost of forms for heavy walls and foundations,
varies from $0.70 to $1.20 per cubic yard of concrete laid. The cost
of forms and mixing concrete will be further discussed in Part IV.

MIXING AND LAYING CONCRETE

Practical Methods of Proportioning. Rich Mixture. A rich
mixture, proportions 1:2:4 — that is, 1 barrel (4 bags) packed Portland
cement (as it comes from the manufacturer), 2 barrels (7.6 cubic feet)
loose sand, and 4 barrels (15.2 cubic feet) loose stone — is used in
arches, reinforced-concrete floors, beams, and columns for heavy
loads; engine and machine foundations subject to vibration; tanks;
and for water-tight work.

Medium Mixture. A medium mixture, proportions l:2i:5 —
that is, 1 barrel (4 bags) packed Portland cement, 2| barrels (9.5
cubic feet) loose sand, and 5 barrels (19 cubic feet) loose gravel or
stone — may be used in arches, thin walls, floors, beams, sewers,
sidewalks, foundations, and machine foundations.

MASONRY AND REINFORCED CONCRETE

TABLE V

Proportions of Cement, Sand, and Stone in Actual Structures

STRUCTURE

PROPORTIONS

C. B. & Q. R. R.
Reinforced Concrete Culverts. . . .

Phila. Rapid Transit Co.
Floor Elevated Roadway

1:3:6

i:3:6
1:2.5:5
1:3:6

1:3:5
1:4:7

1:2:4
1:2:4

l:4:8orl:9.5
1:2:4
l:3:6orl:6.5

1:4:7.5
1:3:6
1:2:4

1:2:4
1:3:6

1:2:4
1:2.5:5
1:2:4
1:2.5:5

1:2.5:4

1:2:4
1:3:6

1:2: 3 Trap rock

Engr. Cont. Oct. 3, '06
" Sept. 26, '06

Cement Era, Aug. '06

Eng. Record, Sept. 29, '06

11 29, '06

" March 3, '06
" 3, '06
3, '06

" Oct. 13, '06
Eng. News, March 23, '05

[Walls

Subway {™g

C. P. R. R.
Arch Rings
Piers and Abutments

Hudson River Tunnel Caisson
Stand Pipe at Attleboro, Mass
Height, 106 feet.

C.C. & St.L.R.R., Danville Arch
Footings

Arch Rings

Abutments, Piers

N. Y. C. & H. R. R. R.

/-> • • (Footing. .

Ossmmg Walls.S

lunncl {Coping

American Oak Leather Co.
Factory at Cincinnati, Ohio.

Harvard University Stadium

New York Subway
Roofs and Sidewalks
Tunnel Arches

Wet Foundation 2' th. or less. . . .
Wet Foundation exceeding 2'. ...

Boston Subway . .

P. & R. R. R.
Arches. .

Piers and Abutments

Brooklyn Navy Yd. Laboratory
Columns

1 • 3 ' 5 Trap rock

Roof Slab

1-3-5 Cinder

Southern Railway.
Arches. .

1:2:4

Piers and Abutments

1:2.5:5

58 MASONRY AND REINFORCED CONCRETE

Ordinary Mixture. An ordinary mixture, proportions 1:3:6 —
that is, 1 barrel (4 bags) packed Portland cement, 3 barrels (11.4
cubic feet) loose sand, and 6 barrels (22.8 cubic feet) loose gravel or
broken stone — may be used for retaining walls, abutments, piers,
and machine foundations.

Lean Mixture. A lean mixture, proportions 1:4: 8 — that is, 1 bar-
rel (4 bags) packed Portland cement, 4 barrels (15.2 cubic feet) loose
sand, and 8 barrels (30.4 cubic feet) loose gravel or broken stone — may
be used in large foundations supporting stationary loads, backing for
stone masonry, or where it is subject to a low compressive load.

Tendency Towards Richer Mixtures. These proportions must
not be taken as always being the most economical to use, but they
represent average practice. Cement is the most expensive ingredi-
ent; therefore a reduction of the quantity of cement, by adjusting
the proportions of the aggregate so as to produce a concrete with
the same density, strength, and impermeability, is of great import-
ance. By careful proportioning and workmanship, water-tight con-
crete has been made of a 1 :3:6 mixture.

In the last few years the tendency throughout the country has
been to use a richer mixture than was formerly used for reinforced
concrete. The 1:2:4 mixture is now used practically for all build-
ings constructed of reinforced concrete, even if low stresses are used,
but theoretically a 1:2^:5 mixture should have sufficient strength.

In Table V will be found the proportions of the concrete used
in various well-known structures and in Tables VI to IX the amounts
of materials used per cubic yard for various proportions.

Proper Proportions Determined by Trial. An accurate and
simple method to determine the proportions of concrete is by trial
batches. The apparatus consists of a scale and a cylinder which
may be a piece of wrought-iron pipe from 10 to 12 inches in diam-
eter capped at one end. Measure and weigh the cement, sand,
stone, and water and mix on a piece of sheet steel, the mixture having
a consistency the same as to be used in the work. The mixture is
placed in the cylinder, carefully tamped, and the height to which
the pipe is filled is noted. The pipe should be weighed before and
after being filled so as to check the weight of the material. The
cylinder is then emptied and cleaned. Mix up another batch using
the same amount of cement and water, slightly varying the ratio

MASONRY AND REINFORCED CONCRETE

TABLE VI
Barrels of Portland Cement Per Cubic Yard of Mortar

(Voids in Sand Being 35 per cent and 1 Bbl. Cement Yielding 3.65 Cubic Feet
of Cement Paste.)

PROPORTION OF CEMENT TO SAND

1:1

1:1.5

1:2

1:2.5

1:3

1:4

Bbl specified to be 3 5 cu ft. . .

Bbls.

4 22

Bbls.

3 49

Bbls.

2 97

Bbls.

2 57

Bbla.

2 28

Bbls.

1 76

"38 "

4 09

3 33

2 81

2 45

2 16

1 62

" 4.0 "

4.00

3.24

2.73

2.36

2.08

1.54

" 4.4 "

3.81

3.07

2.57

2.27

2.00

1.40

Cu. yds. sand per cu. yd. mortar. .

0.6

0.7

0.8

0.9

1.0

of the sand and stone but having the same total weight as before.
Note the height in the cylinder, which will be a guide to other batches
to be tried. Several trials are made until a mixture is found that
gives the least height in the cylinder, and at the same time works
well while mixing, all the stones being covered with mortar, and
which makes a good appearance. This method gives very good
results, but it does not indicate the changes in the physical sizes of
the sand and stone so as to secure the most economical composition,
as would be shown in a thorough mechanical analysis.

There has been much concrete work done where the proportions
were selected without any reference to voids, which has given much
better results in practice than might be expected. The proportion
of cement to the aggregate depends upon the nature of the con-
struction and the required degree of strength, or water-tightness,
as well as upon the character of the inert materials. Both strength
and imperviousness increase with the proportion of cement to the
aggregate. Richer mixtures are necessary for loaded columns,
beams in building construction and arches for thin walls subject to
water pressure, and for foundations laid under water. The actual
measurements of materials as actually mixed and used usually show
leaner mixtures than the nominal proportions specified. This is
largely due to the heaping of the measuring boxes.

Methods of Mixing. The method of mixing concrete is imma-
terial, if a homogeneous mass, containing the cement, sand, and
stone in the correct proportions is secured. The value of the con-
crete depends greatly upon the thoroughness of the mixing. The
color of the mass must be uniform and every grain of sand and piece
of the stone should have cement adhering to every point of its surface.

MASONRY AND REINFORCED CONCRETE

TABLE VII
Barrels of Portland Cement Per Cubic Yard of Mortar

(Voids in Sand Being 45 per cent and 1 Bbl. Cement Yielding 3.4 Cubic Feet
of Cement Paste.)

PROPORTIONS OF CEMENT TO SAND

1:1

1:1.5

1:2

1:2.5

1:3

1:4

Bbl. specified to be 3.5 cu. ft

" 3.8 "
" 4.0 "

" 4.4 '

Bbls.
4.62
4.32
4.19
3.94

Bbls.
3.80

3.61
3.46
3.34

Bbls.

3.25
3.10
3.00
2.90

Bbls.

2.84
2.72
2.64
2.57

Bbls.

2.35
2.16
2.05
1.86

Bbls.

1.76
1.62
1.54
1.40

Cu. yds. sand per cu. yds. mortar.

0.6

0.8

0.9

1.0

TABLE VIII
Ingredients in 1 Cubic Yard of Concrete

(Sand Voids, 40 per cent, Stone Voids, 45 per cent; Portland Cement Barrel
Yielding 3.65 Cubic Feet Paste. Barrel Specified to be 3.8 Cubic Feet.)

PROPORTIONS BY VOLUME

1:2:4

1:2:5

1:2:6

1:2.5:5

1:2.5:")

1:3:4

Bbls. cement per cu. yd concrete.
Cu. yds. sand
stone

1.46
0.41
0.82

1.30
0.36
0.90

1.18

0.33
1.00

1.13
0.40
0.80

1.00
0.35
0.84

1.25
0.53
0.71

Proportions by volume

1:3:5

1:3:6

1:3:7

1:4:7

1:4:8

1:4:9

Bbls. cement per cu. yd. concrete.
Cu. yds. sand
" stone " "

1.13
0.48
0.80

1.05
0.44

0.88

0.96
0.40
0 93

0 82
0.46
0 . SO

0.77
0.43

0 86

0.73
0.41
0.92

This table is to be used when cement is measured packed in the barrel,
for the ordinary barrel holds 3.8 cubic feet.

TABLE IX
Ingredients in 1 Cubic Yard of Concrete

(Sand Voids, 40 per cent; Stone Voids, 45 per cent; Portland Cement Barrel
Yielding 3.65 Cubic Feet of Paste. Barrel Specified to be 4.4 Cubic Feet.)

PROPORTIONS BY VOLUME

1:2:4

1:2:5

1:2:6

1:2.5:5

1:2.5:6

1:3:4

Bbls. cement per cu. yd. concrete.
Cu. yds. sand
stone

1.30
0.42
0.84

1.16
0.38
0.95

1.00

0.33
1.00

1.07
0.44
0.88

0.96
0.40
0.95

1.08
0.53

0.71

Proportions by volume

1:3:5

1:3:6

1:3:7

1:4:7

1:4:8

1:4:9

Bbls. cement per cu. yd. concrete.
Cu. yds. sand
" stone " "

0.96
0.47

0.78

0.90
0.44

0.88

0.82
0.40
0.93

0.75
0.49

0.86

0.68
0.44

0.88

0.64
0.42
0.95

This table is to be used when the cement is measured loose, after dumping
it into a box, for under such conditions a barrel of cement yields 4.4 cubic
feet of loose cement.

[Tables V to IX have been taken from Gillette's "Handbook of Cost Data".]

MASONRY AND REINFORCED CONCRETE 61

Wetness of Concrete. In regard to plasticity, or facility of
working and molding, concrete may be divided into three classes:
dry, medium, and very wet.

Dry Concrete. Dry concrete is used in foundations which may
be subjected to severe compression a few weeks after being placed.
It should not be placed in layers of more than 8 inches, and should
be thoroughly rammed. In a dry mixture the water will just flush
to the surface only when it is thoroughly tamped. A dry mixture
sets and will support a load much sooner than if a wetter mixture
is used, and generally is used only where the load is to be applied
soon after the concrete is placed. This mixture requires the exercise
of more than ordinary care in ramming, as pockets are apt to be
formed in the concrete; and one argument against it is the difficulty
of getting a uniform product.

Medium Concrete. Medium concrete will quake when rammed,
and has the consistency of liver or jelly. It is adapted for construc-
tion work suited to the employment of mass concrete, such as retain-
ing walls, piers, foundations, arches, abutments; and is sometimes
also employed for reinforced concrete.

Very Wet Concrete. A very wet mixture of concrete will run
off a shovel unless it is handled very quickly. An ordinary rammer
will sink into it of its own weight. It is suitable for reinforced con-
crete, such as thin walls, floors, columns, tanks, and conduits.

Modern Practice. Within the last few years there has been a
marked change in the amount of water used in mixing concrete.
The dry mixture has been superseded by a medium or very wet
mixture, often so wet as to require no ramming whatever. Experi-
ments have shown that dry mixtures give better results in short time
tests and wet mixtures in long time tests. In some experiments made
on dry, medium, and wet mixtures it was found that the medium
mixture was the most dense, wet next, and dry least. This experi-
menter concluded that the medium mixture is the most desirable,
since it will not quake in handling but will quake under heavy
ramming. He found medium 1 per cent denser than wet and 9
per cent denser than dry concrete; he considers thorough ramming
important.

Concrete is often used so wet that it will not only quake but flow
freely, and after setting it appears to be very dense and hard, but

62 MASONRY AND REINFORCED CONCRETE

some engineers think that the tendency is to use far too much rather
than too little water, but that thorough ramming is desirable. In
thin walls very wet concrete can be more easily pushed from the
surface so that the mortar can get against the forms and give a smooth
surface. It has also been found essential that the concrete should
be wet enough so as to flow under and around the steel reinforcement
so as to secure a good bond between the steel and concrete.

Following are the specifications (1903) of the American Railway
Engineering and Maintenance of Way Association:

"The concrete shall be of such consistency that when dumped
in place it will not require tamping; it shall be spaded down and
tamped sufficiently to level off and will then quake freely like jelly,
and be wet enough on top to require the use of rubber boots by
workman."

Transporting and Depositing Concrete. Concrete is usually
deposited in layers of 6 inches to 12 inches in thickness. In han-
dling and transporting concrete, care must be taken to prevent the
separation of the stone from the mortar. The usual method of trans-
porting concrete is by wheelbarrows, although it is often handled by
cars and carts, and on small jobs it is sometimes carried in buckets.
A very common practice is to dump it from a height of several feet
into a trench. Many engineers object to this process as they claim
that the heavy and light portions separate while falling and the con-
crete is therefore not uniform through its mass, and they insist that
it must be gently slid into place. A wet mixture is much easier to
handle than a dry mixture, as the stone will not so readily separate
from the mass. A very wet mixture has been deposited from the
top of forms 43 feet high and the structure wras found to be water-
proof. On the other hand, the stones in a dry mixture will separate
from the mortar on the slightest provocation. Where it is necessary
to drop a dry mixture several feet, it should be done by means of a
chute or pipe.

Ramming Concrete. Immediately after concrete is placed, it
should be rammed or puddled, care being taken to force out the air
bubbles. The amount of ramming necessary depends upon how
much water is used in mixing the concrete. If a very wet mixture
is used, there is danger of too much ramming, which results in wedg-
ing the stones together and forcing the cement and sand to the

MASONRY AND REINFORCED CONCRETE

surface. The chief object in ramming a very wet mixture is simply
to expel the bubbles of air.

The style of rammer ordinarily used depends on
whether a dry, medium, or very wet mixture is used.
A rammer for dry concrete is shown in Fig. 10; and
one for wet concrete, in Fig. 11. In very thin walls,
where a wet mixture is used, often the tamping or pud-
dling is done with a part of a reinforcing bar. A com-
mon spade is often employed for the face of wrork,
being used to push back stones that may have sepa-
rated from the mass, and also to work the finer por-
tions of the mass to the face, the method being to
work the spade up and down the face until it is thor-
oughly filled. Care must be taken not to pry with the
spade, as this will spring the forms unless they are
very strong.

Bonding Old and New Concrete. To secure a water-tight joint
between old and new concrete requires a great deal of care. Where
the strain is chiefly compressive, as in foundations, the surface of the
concrete laid on the previous day should be washed with clean wrater,
no other precautions being necessary. In walls and floors, or where
a tensile stress is apt to be applied, the joint should be thoroughly
washed and soaked, and then painted with neat ce-
ment or a mixture of one part cement and one part
sand, made into a very thin mortar.

In the construction of tanks or any other work
that is to be water-tight, in which the concrete is
not placed in one continuous operation, one or more
square or V-shaped joints are necessary. These joints
are formed by a piece of timber, say 4 inches by 6
inches, being imbedded in the surface of the last
concrete laid each day. On the following mornmg,
when the timber is removed, the joint is washed and
coated with neat cement or 1:1 mortar. The joints
may be either horizontal or vertical. The bond be- FJ^ n^ ^mmer
tween old and newr concrete may be aided by rough-
ening the surface after ramming or before placing the new con-
crete.

64 MASONRY AND REINFORCED CONCRETE

Effects of Freezing of Concrete. Many experiments have been
made to determine the effect of freezing of concrete before it has
a chance to set. From these and from practical experience, it is
now generally accepted that the ultimate effect of freezing of Port-
land cement concrete is to produce only a surface injury. The
setting and hardening of Portland cement concrete is retarded, and
the strength at short periods is lowered, by freezing; but the ultimate
strength appears to be only slightly, if at all, affected. A thin scale
about Y6 inch in depth is apt to scale off from granolithic or concrete
pavements which have been frozen, leaving a rough instead of a
troweled wearing surface; and the effect upon concrete walls is often
similar; but there appears to be no other injury. Concrete should
not be laid in freezing weather, if it can be avoided, as this involves
additional expense and requires greater precautions to be taken;
but with proper care, Portland cement concrete can be laid at almost
any temperature.

Preventive Methods. There are three methods which may be
used to prevent injury to concrete when laid in freezing weather:

First: Heat the sand and stone, or use hot water in mixing the
concrete.

Second: Add salt, calcium chloride, or other chemicals to lower
the freezing point of the water.

Third: Protect the green concrete by enclosing it and keeping
the temperature of the enclosure above the freezing point.

The first method is perhaps more generally used than either of
the others. In heating the aggregate, the frost is driven from it;
hot water alone is insufficient to get the frost out of the frozen lumps
of sand. If the heated aggregate is mixed with water which is hot
but not boiling, experience has shown that a comparatively high
temperature can be maintained for several hours, which will usually
carry it through the initial set safely. The heating of the materials
also hastens the setting of the cement. If the fresh concrete is
covered with canvas or other material, it will assist in maintaining
a higher temperature. The canvas, however, must not be laid
directly on the concrete, but an air space of several inches must be
left between the concrete and the canvas.

The aggregate is heated by means of steam pipes laid in the
bottom of the bins, or by having pipes of strong sheet iron, about

MASONRY AND REINFORCED CONCRETE 65

18 inches in diameter, laid through the bottom of the bins, and fires
built in the pipes. The water may be heated by steam jets or other
means. It is also well to keep the mixer warm in severe weather,
by the use of a steam coil on the outside, and jets of steam on the
inside.

The second method — lowering the freezing point by adding
salt — has been commonly used to lower the freezing point of water.
Salt will increase the time of setting and lower the strength of the
concrete for short periods. There is a wide difference of opinion as
to the amount of salt that may be used without lowering the ultimate
strength of the concrete. Specifications for the New York Subway
work required nine pounds of salt to each 100 pounds (12 gallons) of
water in freezing weather. A common rule calls for 10 per cent of
salt to the weight of water, which is equivalent to about 13 pounds
of salt to a barrel of cement.

The third method is the most expensive, and is used only in
building construction. It consists in constructing a light wood
frame over the site of the work, and covering the frame with canvas
or other material. The temperature of the enclosure is maintained
above the freezing point by means of stoves.

WATERPROOFING CONCRETE

Concrete Not Generally Watertight. Concrete as ordinarily
mixed and placed is not generally water-tight, but experience has
shown that where concrete is proportioned to obtain the greatest
practicable density and is mixed wet the resulting concrete is imper-
vious under a moderate pressure. With the wet mixtures of con-
crete now generally used in engineering work, concrete possesses far
greater density, and is correspondingly less porous, than with the
older, dryer mixtures. However, it is difficult, on large masses of
actual work, to produce concrete of such close texture as to prevent
seepage at all points. It has frequently been observed that when
concrete was green there was a considerable seepage through it, and
that in a short time all seepage stopped. Concrete has been made
practically water-tight by forcing through it water which contained
a small amount of cement or cement and fine sand.

Nature of Waterproofing Methods. Compounds of various
kinds have been mixed with concrete or applied as a wash to the

66 MASONRY AND REINFORCED CONCRETE

surface to make the concrete water-tight. Many of the compounds
are of but temporary value and in time lose their usefulness as a
waterproofing material. ,

Effect of Steel Reinforcement. Reinforcing steel properly pro-
portioned and located both horizontally and vertically in long walls,
subways, and reservoirs, will greatly assist in rendering the concrete
impervious by reducing the cracks so that if they do occur they will
be too minute to permit leakage, or the small cracks will soon fill up
with silt.

Coatings Applied on Pressure Side of Walls. Several successful
methods of waterproofing will be given here, and most of these
methods will also apply to stone and brickwork. In the operation
of waterproofing, a very common mistake is made in applying the
waterproofing materials on the wrong side of the wall to be made
water-tight. That is, if water finds its way through a cellar wall,
it is useless to apply a waterproofing coat on the inside surface of
the wall, as the pressure of the water will push it off. If, however,
there is no great pressure behind it, a waterproofing coat applied on
the inside of the wall may be successful in keeping moisture out of
the cellar. To be successful in waterproofing a cellar wrall, the
waterproofing material should be applied on the outside surface of
the wall; and if properly applied, the wall, as well as the cellar, will
be entirely free of water.

In tank or reservoir construction, the conditions are different,
in that it is generally desired to prevent the escape of wrater. In
these cases, therefore, the waterproofing is applied on the inside
surface, and is supported by the materials used in constructing the
tank or reservoir. The structure should always be designed so that
it can be properly waterproofed, and the waterproofing should
always be applied on the side of the wrall on which the pressure
exists.

Waterproofing Methods. Plastering. For cisterns, swimming
pools, or reservoirs, two coats of Portland cement grout — 1 part
cement, 2 parts sand — applied on the inside, have been used to make
the concrete water-tight. One inch of rich mortar has usually been
found effective under medium pressure.

At Attleboro, Mass.-, a large reinforced concrete standpipe, 50
feet in diameter, 106 feet high from the inside of the bottom to the

MASONRY AND REINFORCED CONCRETE 67

top of the cornice, and with a capacity of 1,500,000 gallons, has been
constructed, and is in the service of the waterworks of that city.
The walls of the standpipe are 18 inches thick at the bottom and 8
inches thick at the top. A mixture of 1 part cement, 2 parts sand,
and 4 part broken stone, the stone varying from £ inch to 1| inches,
was used. The forms were constructed, and the concrete placed, in
sections of 7 feet. When the walls of the tank had been completed,
there was some leakage at the bottom with a head of water of 1QO
feet. The inside walls were then thoroughly cleaned and picked,
and four coats of plaster applied. The first coat contained 2 per
cent of lime to 1 part of cement and 1 part of sand; the remaining
three coats were composed of 1 part sand to 1 part cement. Each
coat was floated until a hard dense surface was produced; then it
was scratched to receive the succeeding coat.

On filling the standpipe after the four coats of plaster had been
applied, the standpipe was found to be not absolutely water-tight.
The water was drawn out; and four coats of a solution of castile soap,
and one of alum, were applied alternately ; and, under a 100-foot head,
only a few leaks then appeared. Practically no leakage occurred
at the joints; but in several instances a mixture somewhat wetter
than usual was used, with the result that the spading and ramming
served to drive the stone to the bottom of the batch being placed,
and, as a consequence, in these places porous spots occurred. The
joints were obtained by inserting beveled tonguing pieces, and by
thoroughly washing the joint and covering it with a layer of thin
grout before placing additional concrete.

Alum and Soap; Linseed Oil. Mortar may be made practically
non-absorbent by the addition of alum and potash soap. One per
cent by weight of powdered alum is added to the dry cement and
sand, and thoroughly mixed; and about one per cent of any potash
soap (ordinary soft soap) is dissolved in the water used in the mor-
tar. A solution consisting of 1 pound of concentrated lye, 5 pounds
of alum, and 2 gallons of water, applied while the concrete is green
and until it lathers freely, has been successfully used. Coating the
surface with boiled linseed oil until the oil ceases to be absorbed is
another method that has been used with success.

Hydrated Lime. Hydrated lime has been successfully used to
render concrete impervious. The very fine particles of the lime fill

68 MASONRY AND REINFORCED CONCRETE

the voids that would be otherwise left, thereby, increasing the
density of the concrete. For a 1 : 2 : 4 concrete hydrated lime amount-
ing to six to eight per cent of the weight of the cement is used.
When it is used in a leaner mixture the percentage of lime is increased,
that is, for a 1:3:6 concrete a percentage of lime up to 16 or 18 per
cent is sometimes used.

Sylvester Process. The alternate application of washes of
castile soap and alum, each being dissolved in water, is known as
the Sylvester process of waterproofing. Castile soap is dissolved in
water, f of a pound of soap to a gallon of water, and applied boiling
hot to the concrete surface with a flat brush, care being taken not to
form a froth. The alum dissolved in water — 1 pound pure alum in 8
gallons of water — is applied 24 hours later, the soap having had time
to become dry and hard. The second wash is applied in the same
manner as the first, at a temperature of 60 to 70 degrees Fahrenheit-
The alternate coats of soap and alum are repeated every 24 hours.
Usually four coats will make an impervious coating. The soap and
alum combine and form an insoluble compound, filling the pores of
the concrete and preventing the seepage of water. The wTalls should
be clean and dry, and the temperature of the air not lower than 50
degrees Fahrenheit, when the composition is applied. The composi-
tion should be applied while the concrete is still green. This method
of waterproofing has been used extensively for years, and has gener-
ally given satisfactory results for moderate pressures.

Asphalt. Asphalt is laid in thicknesses from \ inch to 1 inch
as a waterproofing course. It is usually laid in one or more con-
tinuous sheets. It is also used for filling in contraction joints in
concrete. The backs of retaining walls, of either concrete, stone, or
brick, are often coated with asphalt to make them waterproof, the
asphalt being applied hot with a mop. The bottoms of reservoirs
have been constructed of concrete blocks six to eight feet square
with asphalt joints f inch to | inch in thickness and extending at
least halfway through the joint, that is, for a block 6 inches in
thickness the asphalt would extend down at least 3 inches.

Asphalt is a mineral substance composed of different hydro-
carbons, which are widely scattered throughout the world. There
is a great variety of forms in which it is found, ranging from volatile
liquids to thick semi-fluids and solids. These are usually inter-

MASONRY AND REINFORCED CONCRETE

mixed with different kinds of inorganic or organic matter, but are
sometimes found in a free or pure state. Liquid varieties are known
as naphtha and petroleum; the viscous or semi-fluid as maltha or
mineral tar; and the solid as asphalt or asphaltum. The most noted
deposit of asphalt is found in the island of Trinidad and at Ber-
mudez, Venezuela, which is used extensively in this country for
paving and roofing materials. The bituminous limestone deposited
at Seyssel and Pyrimont, France; in Val-de-Travers, Canton of
Neuchatel, Switzerland; and at Ragusa, Sicily are known as rock
asphalt and are perhaps the best for waterproofing purposes.

In the construction of the filter plant at Lancaster, Pa., in 1905,
a pure-water basin and several circular tanks were constructed of
reinforced concrete. The pure-water basin is 100 feet wide by 200
feet long and 14 feet deep, with buttresses spaced 12 feet 6 inches
center to center. The walls at the bottom are 15 inches thick, and
12 inches thick at the top. Four circular tanks are 50 feet in diam-
eter and 10 feet high, and eight tanks are 10 feet in diameter and 10
feet high. The walls are 10
inches thick at the bottom, and
6 inches at the top. A wet mix-
ture of 1 part cement, 3 parts
sand, and 5 parts stone was
used. No waterproofing mate-
rial was used in the construction
of the tanks; and when tested,
two of the 50-foot tanks were found to be water-tight, and the other
two had a few leaks where wires which had been used to hold the
forms together had pulled out when the forms were taken down.
These holes were stopped up and no further trouble was expe-
rienced. In constructing the floor of the pure-water basin, a
thin layer of asphalt wras used as shown in Fig. 12, but no water-
proofing material was used in the walls, and both were found to be
water-tight.

Felt Laid with Asphalt Alternate layers of paper or felt are
laid with asphalt or tar, and are frequently used to waterproof floors,
tunnels, subways, roofs, arches, etc. These materials range from
ordinary tar paper laid with coal-tar pitch or asphalt to asbestos or
asphalt felt laid in coal-tar or asphalt. Coal-tar products have

Fig. 12. Floor of Pure-Water Basin

MASONRY AND REINFORCED CONCRETE

come into very common use for this work but the coal-tar should
contain a large percentage of carbon to be satisfactory.

In using these materials for
rendering concrete water-tight,
usually a layer of concrete or
brick is first laid. On this is
mopped a layer of hot asphalt;
felt or paper is then laid on the
asphalt, the latter being lapped
from 6 to 12 inches. After the
first layer of felt is placed, it is

Fig. 13. Method of WaterProofing Reservoirg mopped OVCr with hot asphalt
by Means of "Hydrex" Felt . , , , -

compound, and another layer or

felt or paper is laid, the operation being repeated until the
desired thickness is secured, which is usually from 2 to 10 layers —
or, in other words, the waterproofing varies from 2-ply to 10-ply.
A waterproofing course of this kind, or a course as described in the
paragraph on asphalt waterproofing, forms a distinct joint, and the

Fig. 14. Section Showing Method of Waterproofing Concrete
Courtesy of Barrett Manufacturing Company

strength in bending of the concrete on the two sides of the layer must
be considered independently.

MASONRY AND REINFORCED CONCRETE 71

When asphalt, or asphalt laid with felt paper, is used for water-
proofing the interiors of the walls of tanks, a 4-inch course of brick is
required to protect and hold in place the waterproofing materials.
Fig. 13 shows a wall section of a reservoir (Engineering Record, Sept.
21, 1907) constructed for the New York, New Haven and Hartford
Railroad, which illustrates the methods described above. The
waterproofing materials for this reservoir consist of 4-ply "Hydrex"
felt, and "Hydrex" compound was used to cement the layers together.

Fig. 14 is an illustration of the method used by the Barrett
Manufacturing Company in applying their 5-ply coal-tar pitch and
felt roofing material. It illustrates in a general way the method
used in applying waterproofing. The surfaces to be waterproofed
are mopped with pitch or asphalt. While the pitch is still hot, a
layer of felt is placed, which is followed with alternate layers of
pitch or asphalt until the required number of layers of felt has been
secured. In no place should one layer of felt be permitted to touch
the layer above or below it. When the last layer of felt is laid and
thoroughly mopped with the coal-tar, something should be placed
over the entire surface waterproofed to protect it from being injured.
For roofing, this protection is gravel, as shown in Fig. 14. In water-
proofing the back of concrete or stone arches usually a layer of
brick is placed and then the joints between the bricks are filled with
pitch. Brick used in this manner also assist in holding the water-
proofing in place. Five layers of felt and pitch should be a sufficient
protection against a head of water of ten feet.

PRESERVATION OF STEEL IN CONCRETE

Short Time Tests. Tests have been made to find the value of
Portland cement concrete as a protection of steel or iron from cor-
rosion. Nearly all of these tests have been of short duration (from
a few weeks to several months) ; but they have clearly shown, when
the steel or iron is properly imbedded in concrete, that on being
removed therefrom it is clean and bright. Steel removed from con-
crete containing cracks or voids usually shows rust at the points
where the voids or cracks occur; but if the steel has been completely
covered with concrete, there is no corrosion. Tests have shown that
if corroded steel is imbedded in concrete, the concrete will remove
the rust. To secure the best results, the concrete should be mixed

72 MASONRY AND REINFORCED CONCRETE

quite wet, and care should be taken to have the steel thoroughly
imbedded in the concrete.

Cinder vs. Stone Concrete. A compact cinder concrete has
proven about as effective a protection for steel as stone concrete.
The corrosion found in cinder concrete is mainly due to iron oxide
or rust in the cinders, and not to the sulphur. The amount of sul-
phur in cinders is extremely small, and there seems to be little danger
from that source. A steel-frame building erected in New York in
1898 had all its framework, except the columns, imbedded in cinder
concrete; when the building was demolished in 1903, the frame
showed practically no rust which could be considered as having
developed after the material was imbedded.

Practical Illustrations. Cement washes, paints, and plasters
have been used for a long time, in both the United States and Europe,
for the purpose of protecting iron and steel from rust. The engineers
of the Boston Subway, after making careful tests and investigations,
adopted Portland cement paint for the protection of the steel work
in that structure. The railroad companies of France use cement
paint extensively to protect their metal bridges from corrosion. Two
coats of the cement paint and sand are applied with leather brushes.

A concrete-steel water main on the Monier system, 12 inches in
diameter, 1.6 inches thick, containing a steel framework of |-inch
and ^ inch steel rods, was taken up after 15 years' use in wet ground,
at Grenoble, France. The adhesion was found perfect, and the
metal absolutely free from rust.

William Sooy Smith, M. Am. Soc. C. E., states that in removing
a bed of concrete at a lighthouse in the Straits of Mackinac, twenty
years after it wras laid, and ten feet below water surface, imbedded
iron drift-bolts were found free from rust.

A very good example of the preservation of steel imbedded in
concrete is given by Mr. H. C. Turner (Engineering News, January 16,
1908). Mr. Turner's company has recently torn down a one-story
reinforced-concrete building erected by his company in 1902, at New
Brighton, Staten Island. The building had a pile foundation, the
piles being cut off at mean tide level. The footings, side walls,
columns, and roof were all constructed of reinforced concrete. The
portion removed was 30 by 60 feet, and was razed to make room for
a five-story building. In concluding his account, Mr. Turner says:

MASONRY AND REINFORCED CONCRETE 73

"All steel reinforcement was found in perfect preservation, excepting in a
few cases where the hoops were allowed to come closer than f inch to the surface.
Some evidence of corrosion was found in such cases, thus demonstrating the
necessity of keeping the steel reinforcement at least f inch from the surface.
The footings were covered by the tide twice daily. The concrete was extremely
hard, and showed no weakness whatever from the action of the salt water. The
steel bars in the footings were perfectly preserved, even in cases where the con-
crete protection was only | inch thick."

Tests by Professor Norton. Prof. Chas. L. Norton made
several experiments with concrete bricks, 3 by 3 by 8 inches, in which
steel rods, sheet metal, and expanded metal were imbedded. The
specimens were enclosed in tin boxes with unprotected steel and
were exposed for three weeks. One portion was exposed to steam,
air, and carbon dioxide; another to air and steam; another to air and
carbon dioxide; and another was left in the testing room. In these
tests, Portland cement was used. The bricks were made of neat
cement of 1 part cement and 3 parts sand; of 1 part cement and 5
parts stone; and of 1 part cement and 7 parts cinders. After the
steel had been imbedded in these blocks three weeks, they were
opened and the steel examined and compared with specimens which
had been unprotected in corresponding boxes in the open air. The
unprotected specimens consisted of rather more rust than steel; the
specimens imbedded in neat cement were found to be perfectly
protected; the rest of the specimens showed more or less corrosion.
Professor Norton's conclusions were as follows:

1. Neat Portland cement is a very effective preventive against rusting.

2. Concrete, to be effective in preventing rust, should be dense and with-
out voids or cracks. It should be mixed wet when applied to steel.

3. The corrosion found in cinder concrete is mainly due to iron oxide in
the cinders, and not to sulphur.

4. Cinder concrete, if free from voids and well rammed when wet, is about
as effective as stone concrete.

5. It is very important that the steel be clean when imbedded in concrete.

FIRE PROTECTIVE QUALITIES OF CONCRETE

High Resisting Qualities. The various tests which have been
conducted — including the involuntary tests made as the result of
fires — have shown that the fire-resisting qualities of concrete, and
even resistance to a combination of fire and water, are greater than
those of any other known type of building construction. Fires and
experiments which test buildings of reinforced concrete have proved

74 MASONRY AND REINFORCED CONCRETE

that where the temperature ranges from 1400 to 1900 degrees
Fahrenheit, the surface of the concrete may be injured to p, depth
of \ to | inch or even of one inch ; but the body of the concrete is
not affected, and the only repairs required, if any, consist of a coat of
plaster.

Thickness of Concrete Required for Fireproofing. Actual fires
and tests have shown that 2 inches of concrete will protect an I-beam
with good assurance of safety. Reinforced concrete beams and
girders should have a clear thickness of \\ inches of concrete outside
the steel on the sides and 2 inches on the bottom; slabs should have
at least 1 inch below the slab bars, and columns 2 inches. Structural
steel columns should have at least 2 inches of concrete outside of
the farthest projecting edge.

Theory. The theory of the fireproofing qualities of Portland
cement concrete given by Mr. Spencer B. Newberry is that the
capacity of the concrete to resist fire and prevent its transference
to steel is due to its combined water and porosity. In hardening, con-
crete takes up 12 to 18 per cent of the water contained in the cement.
This water is chemically combined, and not given off at the boiling
point. On heating, a part of the water is given off at 500 degrees •
Fahrenheit, but dehydration does not take place until 900 degrees
Fahrenheit is reached. The mass is kept for a long time at com-
paratively low temperature by the vaporization of water absorb-
ing heat. A steel beam imbedded in concrete is thus cooled by the
volatilization of water in the surrounding concrete.

Resistance to the passage of heat is offered by the porosity of
concrete. Air is a poor conductor, and an air space is an efficient
protection against conduction. The outside of the concrete may
reach a high temperature; but the heat only slowly and imperfectly
penetrates the mass, and reaches the steel so gradually that it is
carried off by the metal as fast as it is supplied.

Cinder vs. Stone Concrete. Mr. Newberry says: "Porous
substances, such as asbestos, mineral wool, etc., are always used as
heat-insulating material. For this same reason, cinder concrete,
being highly porous, is a much better non-conductor than a dense
concrete made of sand and gravel or stone, and has the added advan-
tage of being light."

Professor Norton, on the other hand, in comparing the actions of

MASONRY AND REINFORCED CONCRETE 75

cinder and stone concrete in the great Baltimore fire of February,
1904, states that there is but little difference in the two concretes.
The burning of bits of coal in poor cinder concrete is often balanced
by the splitting of stones in the stone concrete. "However, owing
to its density, the stone concrete takes longer to heat through."

Fire and Water Tests. Under the direction of Prof. Francis C.
. Van Dyck, a test was made on December 26, 1905, on stone and
cinder reinforced concrete, according to the standard fire and water
tests of the New York Building Department. A building was con-
structed 16 feet by 25 feet, with a wall through the middle. The
roof consisted of the two floors to be tested. One floor was a rein-
forced cinder concrete slab and steel I-beam construction; and the
other was a stone concrete slab and beam construction. The floors
were designed for a safe load of 150 pounds per square foot, with a
factor of safety of four.

The object of the test was to ascertain the result of applying to
these floors, first, a temperature of about 1700 degrees Fahrenheit,
during four hours, a load of 150 pounds per square foot being upon
them; and second, a stream of water forced upon them while still at
about the temperature above stated. A column was placed in the
chamber roofed by the rock concrete, and it was tested the same way.

The fuel used was seasoned pine wood and the stoking was
looked after by a man experienced in a pottery; hence a very even
fire was maintained, except at first, on the cinder concrete side, where
the blaze began in one corner and spread rather slowly for some time.

The water was supplied from a pump at which 90 pounds pressure
wras maintained, and was delivered through 200 feet of new cotton
hose and a l|-inch nozzle. Each side was drenched with water while
at full temperature, apparently; and the water was thrown as uni-
formly as possible over the surface to be tested, for the required
time. The floors were then flooded on top, and again treated
underneath.

Inasmuch as the floors and the column were the only parts sub-
mitted for tests, the slight cracking and pitting of the walls and
partition need not be detailed.

The column was practically intact, except that a few small
pieces of the concrete were washed out where struck by the stream
at close range. The metal, however, remained completely covered.

76 MASONRY AND REINFORCED CONCRETE

On the rock concrete side, the beams showed naked metal up to
within about 7 inches of the ends on one beam, and about 2 feet
from the ends on the other beam. The reinforcing bars were de-
nuded over an area of about 30 square feet near the center; but no
cracks developed, and the water poured on top seemed to come
down only through the pipe set in for the pyrometer.

On the cinder concrete side, the beams lost only a little of the
edges of the covering, not showing the metal at all. There were no
cracks on this side either, and the water came down through the
pyrometer tube as on the other side. The metal in the slab was bared
over an area of about 24 square feet near the center.

During the firing, both chambers were occasionally examined,
and no cracking or flaking-off of the concrete could be detected.
Hence the water did all the damage that was apparent at
the end.

During the test the floors supported the load they were designed
to carry; and on the following day the loads were increased to 600
pounds per square foot.

The following is taken from Professor Van Dyck's report:

"The maximum deflection of the stone concrete before the application of
water, was 2^ inches; after application of water, 3^ inches; with normal tem-
perature and original load, 3^ inches; deflection after load of 600 pounds was
added, 3xi inches.

"The maximum deflection of the cinder concrete before the application
of water, was 6rg inches; after application of water, 6| inches; with normal
temperature and original load, 5H inches; deflection after a load of 600 pounds
was added, 6 inches. These measurements were taken at the center of the roof
of each chamber."

Results Shown in Baltimore Fire. Engineers and architects,
who made reports on the Baltimore fire of February, 1904, generally
state that reinforced concrete construction stood very well — much
better than terra cotta. Professor Norton, in his report to the
Insurance Engineering Experiment Station, says:

"Where concrete floor-arches and concrete-steel construction received the
full force of the fire, it appears to have stood well, distinctly better than the
terra cotta. The reasons, I believe, are these: The concrete and steel
expand at sensibly the same rate, and hence, when heated, do not subject
each other to stress; but terra cotta usually expands about twice as fast with
increase in temperature as steel, and hence the partitions and floor-arches soon
become too large to be contained by the steel members which under ordinary
temperature properly enclose them."

MASONRY AND REINFORCED CONCRETE 77
METHODS OF MIXING

Two methods are used in mixing concrete — by hand and by
machinery. Good concrete may be made by either method and in
either case the concrete should be carefully watched by a good fore-
man. If a large quantity of concrete is required, it is cheaper to
mix it by machinery. On small jobs where the cost of erecting the
plant, together with the interest and depreciation, divided by the
number of cubic yards to be made, constitute a large item, or if
frequent moving is required, it is very often cheaper to mix the
concrete by hand. The relative cost of the two methods usually
depends upon circumstances, and must be worked out in each
individual case.

Mixing by Hand. The placing and handling of materials and
arranging the plant are varied by different engineers and contractors.
In general the mixing of concrete is a simple operation, but should
be carefully watched by an inspector. He should see

(1) That the exact amount of stone and sand are measured out;

(2) That the cement and sand are thoroughly mixed;

(3) That the mass is thoroughly mixed;

(4) That the proper amount of water is used ;

(5) That care is taken in dumping the concrete in place;

(6) That it is thoroughly rammed.

Mixing Platform. The mixing platform, which is usually 10
to 20 feet square, is made of 1-inch or 2-inch plank planed on one
side and well nailed to stringers, and should be placed as near the
work as possible, but so situated that the stone can be dumped on
one side of it and the sand on the opposite side. A very convenient
way to measure the stone and sand is by the means of bottomless
boxes. These boxes are of such a size that they hold the proper pro-
portions of stone or sand to mix a batch of a certain amount. Ce-
ment is usually measured by the package, that is, by the barrel or
bag, as they contain a definite amount of cement.

Process of Mixing. The method used for mixing the concrete
has little effect upon the strength of the concrete, if the mass has
been turned a sufficient number of times to thoroughly mix them.
One of the following methods is generally used. (Taylor and
Thompson's "Concrete".)

(a) Cement and sand mixed dry and shoveled on the stone or gravel,
leveled off, and wet as the mass is turned.

7S MASONRY AND REINFORCED CONCRETE

(b) Cement and sand mixed dry, the stone measured and dumped on top
of it, leveled off, anil wet, as turned with shovels.

(<l) Cement and sand mixed with water into a mortar which is shoveled
on the gravel or stone and the mass turned wHh shovels.

(e) Stone or gravel, sand, and cement spread in successive layers, mixed
slightly and shoveled into a mound, water poured into the center, and the mass
turned with shovels.

The quantity of water is regulated by the appearance of the
concrete. The best method of wetting the concrete is by measuring
the water in pails. This insures a more uniform mixture than by
spraying the mass with a hose.

Mixing by Machinery. On large contracts the concrete is
generally mixed by machinery. The economy is not only in the
mixing itself but in the appliances introduced in handling the raw
materials and the mixed concrete. If all materials are delivered
to the mixer in wheelbarrows, and if the concrete is conveyed away
in wheelbarrows, the cost of making concrete is high, even if machine
mixers are used. If the materials are fed from bins by gravity into
the mixer, and if the concrete is dumped from the mixer into cars
and hauled away, the cost of making the concrete should be very
low. On small jobs the cost of maintaining and operating the mixer
will usually exceed the saving in hand labor and will render the
expense with the machine greater than without it.

Machine vs. Hand Mixing. It has already been stated that
good concrete may be produced by either machine or hand mixing,
if it is thoroughly mixed.

Tests made by the U. S. Government engineers at Duluth,
Minn., to determine the relative strength of concrete mixed by hand
and mixed by machine (a cube mixer), showed that at 7 days, hand-
mixed concrete possessed only 53 per cent of the strength of the
machine-mixed concrete; at 28 days, 77 per cent; at 6 months, 84
per cent; and at one year, 88 per cent. Details of these tests are
given in Table X.

It should be noted in this connection, that the variations in
strength from highest to lowest were greatest in the hand-mixed
samples, and that the strength was more uniform in the machine-
mixed.

MASONRY AND REINFORCED CONCRETE

TABLE X
Tensile Tests of Concrete*

AGE, AND METHOD OF MIXING

HIGH

Low

AVERAGE

Age 7 Days
Machine-Mixed Sample
Hand-Mixed Sample

260
159

243
113

253
134

Age 28 Days
Machine-Mixed Sample
Hand-Mixed Sample

294
231

249
197

274
211

Age 6 Months
Machine-Mixed Sample
Hand-Mixed Sample

441
355

345
298'

388
324

Age One Year
Machine-Mixed Sample
Hand-Mixed Sample

435
369

367
312

391
343

The mixture tested was composed of 1 part cement and 10.18
parts aggregate.

STEEL FOR REINFORCING CONCRETE

Quality of Reinforcing Steel. Steel for reinforcing concrete is
not usually subjected to as severe treatment as ordinary structural
steel, as the impact effect is likely to be a little less; but the quality
of the steel should be carefully specified. To reduce the cost of
reinforced concrete structures, there has been a tendency to use
cheap steel. This has resulted in bars being rolled from old railroad
rails. These bars are known as rerolled bars and they should always
be thoroughly tested before being used. If the bars are rerolled
from rails that were made of good material, they should prove to be
satisfactory, but if the rails contained poor materials the bars rolled
from them will probably be brittle and easily broken by a sudden
blow. Many engineers specify that the bars shall be rolled from
billets to avoid using any old material.

The grades of steel used in reinforced concrete range from soft to
hard, and may be classified under three heads: soft, medium, and hard.

Soft Steel. Soft steel has an estimated strength of 50,000 to
58,000 pounds per square inch. It is seldom used in reinforced
concrete.

*(From "Concrete anc

iforced Concrete Construction", by H. A. Reid.)

80 MASONRY AND REINFORCED CONCRETE

Medium Steel. Medium steel has an estimated strength of
55,000 to 05,000 pounds per square inch. The elastic limit is from
32,000 to 38,000 pounds per square inch. This grade of steel is
extensively used for reinforced concrete work and can be bought in
the open market and used with safety.

Hard Steel. Hard steel, better known as high-carbon steel,
should have an ultimate strength of 85,000 to 100,000 pounds per
square inch; and the elastic limit should be from 50,000 to 65,000
pounds per square inch. The hard steel has a greater percentage
of carbon than the medium steel, and therefore the yield point is
higher. This steel is preferred by some engineers for reinforced
concrete work, but it should be thoroughly tested to be sure that it
is according to specifications. It is often brittle. This is the grade
of steel into which old rails are rolled, but it is also rolled from billets.

Processes of Making Steel Reinforcing bars are rolled by both
the Bessemer and the open-hearth processes. Bars rolled by either
process make good reliable steel, but bars rolled by open-hearth
process are generally more uniform in quality.

TYPES OF BARS

The steel bars used in reinforcing concrete usually consist
of small bars of such shape and size that they may easily be bent
and placed in the concrete so as to form a monolithic structure.
To distribute the stress in the concrete, and secure the necessary
bond between the steel and concrete, the steel required must be
supplied in comparatively small sections. All types of the regu-
larly rolled small bars of square, round, and rectangular section,
as well as some of the smaller sections of structural steel, such as
angles, T-bars, and channels, and also many special rolled bars,
have been used for reinforcing concrete. These bars vary in size
from I inch for light construction, up to 1^ inches for heavy beams,
and up to 2 inches for large columns. In Europe plain round bars
have been extensively used for many years and the same is true in
the United States, but not to the same extent as in Europe; that is,
in America a very much larger percentage of work has been done
with deformed bars.

Plain Bars. With plain bars, the transmission of stresses is
dependent upon the adhesion between the concrete and the steel.

MASONRY AND REINFORCED CONCRETE 81

Square and round bars show about the same adhesive strength, but
the adhesive strength of flat bars is far below that of the round and
square bars. The round bars are more convenient to handle and
easier obtained, and have, therefore, generally been used when plain
bars were desirable.

Structural Steel. Small angles, T-bars, and channels have been
used to a greater extent in Europe than in this country. They are
principally used where riveted skeleton work is prepared for the
steel reinforcement; and in this case, usually, it is desirable to have
the steel work self-supporting.

Deformed Bars. There are many forms of reinforcing materials
on the market, differing from one another in the manner of forming
the irregular projections on their surface. The object of all these
special forms of bars is to furnish a bond with the concrete, independ-
ent of adhesion. This bond formed between the deformed bar and

Fig. 15. Square Twisted Reinforcing Steel Bar
Courtesy of Inland Steel Company

the concrete is usually called a mechanical bond. Some of the most
common types of bars used are the square twisted bar; the corrugated;
the Havemeyer; and the Kahn.

Square Twisted Bar. The twisted bar, shown in Fig. 15, was
one of the first steel bars shaped to give a mechanical bond with
concrete. This type of bar is a commercial square bar twisted
while cold. There are two objects in twisting the bar — first, to give
the metal a mechanical bond with the concrete; second, to increase
the elastic limit and ultimate strength of the bar. In twisting the
bars, usually one complete turn is given the bar in nine or ten diam-
eters of the bar, with the result that the elastic limit of the bar is
increased from 40 to 50 per cent, and the ultimate strength is in-
creased from 25 to 35 per cent. These bars can readily be bought
already twisted; or, if it is desired, square bars may be bought and
twisted on the site of the work.

Corrugated Bar. The "corrugated" bar, which has corruga-
tions as shown in Fig. 16, was invented by Mr. A. L. Johnson,

82 MASONRY AND REINFORCED CONCRETE

M. Am. Soc. C. E. These corrugations, or square shoulders,
are placed at right angles to the axis of the bar, and their sides

Fig. 1C. "Corrugated" Bar for Reinforcement of Concrete
Courtesy of Corrugated Bar Company

make an angle with the perpendicular to the axis of the bars not
exceeding the angle of friction between the bar and concrete. These
bars are usually rolled from high-carbon steel having an elastic limit
of 55,000 to 65,000 pounds per square inch and an ultimate strength
cf about 100,000 pounds per square inch. They are also rolled
from any desired quality of steel. In size they range from \ inch to
1| inches, their sectional area being the same as that of plain bars
of the same size. These bars are rolled in both the common types,
round and square.

Havemeyer Bar. The Havemeyer bar, Fig. 17, was invented by
Mr. J. F. Havemeyer. This has a uniform cross section throughout

Fig. 17. Havemeyer Bar for Reinforcement of Concrete
Courtesy of Concrete Steel Company

its length. The bonding of the bar to the concrete is uniform at
all points, and the entire section is available for tensile strength.

Fig. 18. Kahn Trussed Bar for Reinforcement of Concrete
Courtesy of The Kahn System

Kahn Bar. The Kahn bar, Fig. 18, was invented by Mr. Julius
Kahn, Assoc. M. Am. Soc. C. E. This bar is designed with the
assumption that the shear members should be rigidly connected
to the horizontal members. The bar is rolled with a cross section

MASONRY AND REINFORCED CONCRETE

TABLE XI
Standard Sizes of Expanded Metal

GAGE

WEIGHT IN LB.

SECTIONAL AREA

INCHES

No.

PER SQ. FT.

1 FOOT WIDE
IN SQ. IN.

.30

.082

.625

.177

.86

.243

as shown in the figure. The thin edges are cut and turned up, and
form the shear members. These bars are manufactured in several
sizes.

Expanded Metal. Expanded metal, Fig. 19, is made from plain
sheets of steel, slit in regular lines and opened into meshes of any
desired size or section of strand. It is commercially designated
by giving the gage of the steel and the amount of displacement
between the junctions of the meshes. The most common manu-
factured sizes are given in Table XI.

Fig. 19. Example of Expanded Metal Fabric
Courtesy of Northwestern Expanded Metal Company

Steel Wire Fabric. Steel wire fabric reinforcement consists of a
netting of heavy and light wires, usually with rectangular meshes.
The heavy wires carry the load, and the light ones are used to space
the heavier ones. There are many forms of wire fabric on the
market.

Table XII is condensed from the handbook of the Cambria Steel
Company and gives the standard weights and areas of plain round
and square bars as commonly used in reinforced concrete construc-
tion:

MASONRY AND REINFORCED CONCRETE

TABLE XII
Weights and Areas of Square and Round Bars

(One cubic foot of steel weighs 489.6 pounds)

THICKNEBHOR
DIAMETER

(Inches)

WEIGHT OF
SQUARE BAR,
1 FOOT LONG
(Pounds)

WEIOHT OF
ROUND BAR,
1 FOOT LONG
(Pounds)

AREA OF
SQUARE BAR
(Sq. In.)

AREA OF
ROUND BAR

(Sq. In.)

ClRCUM. OF

ROUND BAR
(Inches)

.213

.167

.0625

.0491

.7854

.332

.261

.0977

.0767

.9817

.478

.376

.1406

.1104

1.1781

.651

.511

.1914

.1503

1.3744

.8.50

.668

.2500

.1963

1.5708

1.32S

1.043

.3906

.3068

1.9635

1.913

1 . 502

.5625

.4418

2.3562

3 . 4(X)

2.670

1.0000

.7854

3.1416

4.303

3.379

1.2656

.9940

3.5343

5.312

4.173

1.5625

1.2272

3.9270

7.650

6.008

2.2500

1.7671

4.7124

10.41

8.178

3.0625

2.4053

5.4978

13.60

10.68

4.0000

3.1416

6.2832

SPECIFICATIONS FOR REINFORCING BARS

Process of Manufacture. Steel may be made by either the
open-hearth or Bessemer process.

Bars shall be rolled from billets.

Chemical and Physical Properties. The chemical and physical
properties of reinforcing bars shall conform to the limits as given in
Table XIII.

Chemical Determinations. In order to determine if the ma-
terial conforms to the chemical limitations prescribed in the above
paragraph, analysis shall be made by the manufacturer from a test
ingot taken at the time of the pouring of each melt or blow of steel,
and a certified copy of such analysis shall be furnished to the engineer
or his inspector.

Yield Point. For the purpose of these specifications, the yield
point shall be determined by careful observation of the drop of the
testing machine, or by other equally accurate method.

Form of Specimens, (a) Tensile and bending test specimens
of cold-twisted bars shall be cut from the bars after twisting, and
shall be tested in full size without further treatment, unless otherwise
specified as in (c), in which case the conditions therein stipulated
shall govern.

(b) Tensile and bending test specimens may be cut from the
bars as rolled, but tensile and bending test specimens of deformed

MASONRY AND REINFORCED CONCRETE
TABLE XIII

PROPERTIES CONSIDERED

STRUCTURAL STEEL GRADE

HARD GRADE

Plain Bars

Deformed Bars

Phosphorus, maximum
Bessemer
Open-hearth

0.10
0.06

Ultimate tensile strength, pounds
per square inch.

55,000 to
65,000

85,000 to
105,000

Yield point, minimum pounds per
sq. in.
Elongations, per cent in 8 inches,
minimum

Cold bend without fracture:
Bars under | inch in diameter or
thickness

33,000

1,250,000
tensile str.

180°, d = 1 1.

33,000

1,250,000
tensile str.

180°, d = 1 1.

52,000

1,200,000
tensile str.

180°, d =3 t.

Bars f inch in diameter or thick-
ness and over

180°, d = lt.

180°, d = 2t.

90°, d=3t.

bars may be planed or turned for a length of at least 9 inches, if
deemed necessary by the manufacturer in order to obtain uniform
cross section.

(c) If it is desired that the testing and acceptance for cold-
twisted bars be made upon the rolled bars before being twisted, the
bars shall meet the requirements of the structural steel grade for
plain bars given in this specification.

Number of Tests. At least one tensile test and one bending
test shall be made from each melt of open-hearth steel rolled, and
from each blow or lot of ten tons of Bessemer steel rolled. In case
bars differing f inch and more in diameter or thickness are rolled
from one melt or blow, a test shall be made from the thickest and
thinnest material rolled. Should either of these test specimens
develop flaws, or should the tensile test specimen break outside of
the middle third of its gaged length, it may be discarded and another
test specimen substituted therefor. In case a tensile test specimen
does not meet the specifications an additional test may be made.
The bending test may be made by pressure or by light blows.

Modification in Elongation for Thin and Thick Material. For
bars less than fg inch and more than f inch nominal diameter or

86 MASONRY AND REINFORCED CONCRETE

thickness, the following modifications shall be made in the require-
ments for elongation:

(a) For each increase of f inch in diameter or thickness above
f inch, a deduction of 1 shall be made from the specified percentage
of elongation.

(b) For each decrease of ^g inch in diameter or thickness below
A inch, a deduction of 1 shall be made from the specified percentage
of elongation.

Number of Twists. Cold-twisted bars shall be twisted cold
with one complete twist in a length equal to not more than 10 times
the thickness of the bar.

Finish. Material must be free from injurious seams, flaws, or
cracks, and have a workmanlike finish.

Variation in Weight. Bars for reinforcement are subject to
rejection if the actual weight of any lot varies more than 5% over or
under the theoretical weight of the lot.

MASONRY AND REINFORCED
CONCRETE

PART II

TYPES OF MASONRY

INTRODUCTION

Definitions. In the following paragraphs, the meanings of vari-
ous technical terms frequently used in stone masonry are clearly
explained :

Arris. Arris is the external edge formed by two surfaces,
whether plane or curved, meeting each other.

Ashlar. Ashlar is a style of stone wall built of stones having
rectangular faces and with joints dressed so closely that the dis-
tance between the general planes of the surfaces of the adjoining
stones is one-half inch, or less.

A x or Peen Hammer. A peen

hammer is a tool, Fig. 20, which is 4. _^

similar to a double-bladed wood ax.
It is used after the stone is rough-

. , j , , j », , , , Fig. 20. Ax or Peen Hammer

pointed, to make dratts along the

edges of the stone. For rubble work, and even for squared-stone

work, no finer tool need be used.

Backing. Backing is the masonry on the back side of a wall; it
is usually of rougher quality than that on the face.

Batter. Batter is the term used to indicate the variation from
the perpendicular, of a wall surface. It is usually expressed as the
ratio of the horizontal distance to the vertical height. For example,
a batter of 1:12 means that the wall has a slope of one inch hori-
zontally to each twelve inches of height.

MASONRY AND REINFORCED CONCRETE

Fig. 21. Bushh

Bearing Block. The bearing block is a block of stone set in a
wall with the special purpose of forming a bearing for a concentrated
load, such as the load of a beam.

Bed Joint. A horizontal joint,
or one which is nearly perpendicular
to the resultant line of pressure, is
called a bed joint. (See Joint.)

Belt Course. A belt course is
a horizontal course of stone extend-
ing around one or more faces of a building; it is usually composed
of larger stones which sometimes project slightly and is, in most
instances, employed only for architectural effect.

Bonding. Bonding is the
system according to which the
stones are arranged so that they
are mutually tied together by
the overlapping of joints.

Bushham me ring. Bushham-
mering is a method of finishing
stone by which the face of the
stone, after being roughly dressed
to a surface which is nearly
plane, is smoothed still more
with a bushham mer, Fig. 21. The
face of the bushhammer has a
large number of small pyramidal points, that, in skillful hands,
speedily reduce the surface to a uniformly granular condition.

Buttress. A buttress is a very short projection, Fig. 22, built
perpendicular to a main wall which may be subjected to lateral
thrust, in order to resist, by compression, the tendency of the wall
to tip over. (See Counterfort.)

Cavil. A cavil is a tool which
has one blunt face, and a pyramidal
point at the other end, Fig. 23. It
is used for roughly breaking up
stone.

Chisel. A chisel is , a tool made
of a steel bar that has one end Fig. 23. Cavil

Fig. 22. Buttres

100

MASONRY AND REINFORCED CONCRETE

Fig. 24. Chisel

forged and ground to a chisel edge, as shown in Fig. 24. It u used
for cutting drafts for the edges of stones and is usually driven by a
mallet or hammer.

Coping. The coping is the course of stone which
caps the top of a wall.

Corbel. A stone projecting from the face of a
wall for the purpose of supporting a beam or an
arch which extends out from the wall is called a
corbel.

Counterfort. A counterfort is a short projection'
built behind a retaining wall in order to relieve
by tension the overturning thrust against the wall.
(See Buttress.)

Course. A course is a row of stones of equal
height laid horizontally along a wall.

Coursed Masonry. Masonry having courses of equal height
throughout is termed coursed masonry.

Coursed Rubble. Rubble masonry (see Rubble), in which the
stones in each course are roughly dressed to nearly a uniform height,
is designated as coursed rubble.

Cramp. A cramp is a bar of iron, having the ends bent at
right angles, which is inserted in
holes and grooves specially cut for
it in adjacent stones in order to
bind the stones together. When
carefully packed with cement
mortar, these iron cramps are
effectively prevented from rust-
ing.

Crandall. A crandall, Fig. 25, is a tool made by fitting a
series of steel points into a handle, using a wedge; by means
of this device a series of fine picks at the stone are made with
each stroke, and the surface is more quickly reduced to a true
plane.

Crandalling. Crandalling is the system of dressing stone by
\vhich the surface, after having been rough-pointed to a fairly
plane surface, is hammered with a crandall, such as is illustrated in
Fig. 25.

Fig. 25. Crandall.

101

90 MASONRY AND REINFORCED CONCRETE

Dimension Stone. Dimension stone is the cut stone whose pre-
cise dimensions in a building are specified in the plans. The term
refers to the highest grade of ashlar work.

Dowel. A dowel is a straight bar or pin of iron, copper, or even
of stone, which is inserted in two corresponding holes in adjacent
stones. The dowels may be vertical across horizontal joints, or
horizontal across vertical joints. In the latter case, they are fre-
quently used to tie the stones of a coping or cornice. The extra
space between the dowels and the stones should be filled with melted
lead, sulphur, or cement grout.

Draft. Draft is the term applied to a line on the surface of a
stone which is cut to the breadth of the draft chisel.

Dry-Stone Masonry. Dry-stone masonry is masonry which is
put in place without mortar.

Extrados. The extrados is the upper, or outer, surface of an
arch, especially the upper curved face of the whole body of voussoirs.
(Compare Intrados.}

Face. The face is the exposed surface of a wall.
Face Hammer. A face hammer, Fig. 26, is a tool having a ham-
mer face and an ax face. It is
used for roughly squaring up
stones, either for rubble work or
in preparation for finer stone
dressing.

Feathers. See Plvgs.

Fig. 20. Face Hammer

Footing. The footing is the

foundation masonry for a wall or pier, usually composed, in stone
masonry, of large stones having a sufficient area so that the pres-
sure upon the subsoil shall not exceed a safe limit, and having
sufficient transverse strength to distribute the pressure uniformly
over the subsoil.

Grout. Grout is a mixture of cement and sand (usually 1 part
cement to 1 or 2 parts sand) made into a very thin mortar so that it
will flow freely into interstices left between stones of rough masonry.
Grout is used to great advantage in many lines of work.

Header. A header is a stone laid with its greatest dimension
perpendicular to the face of a wall. Its purpose is to bond together
the facing and the backing.

102

MASONRY AND REINFORCED CONCRETE 91

Intrados. The intrados is the inner, or under, surface of an
arch.

Jamb. The jamb is the vertical surface on either side of an
opening left in a wall for a door or window.

Joint. The horizontal and vertical spaces between the
stones, which are filled with mortar, are called the joints. When
they are horizontal, they are called bed joints. Their width or
thickness depends on the accuracy with which the stones are
dressed. The joint should always have such a width that any
irregularity on the surface of a stone shall not penetrate com-
pletely through the mortar joint and cause the stones to bear
directly on each other, thus producing concentrated pressures
and transverse stresses which might rupture the stones. The
criterion used by a committee of the American Society of Civil
Engineers in classifying different grades of masonry is to make
the classification depend on the required thickness of the joint.
These thicknesses have been given when defining various grades of
stone masonry.

Lintel. The lintel is the stone, iron, wood, or concrete beam
covering the opening left in a wall for a
door or window.

Natural Bed. The surfaces of a stone
parallel to its stratification are called the
natural bed.

One-Man Stone. One-man stone is a
term used to designate, roughly, the size
and weight of stone used in a wall. It
represents, approximately, the size of stone
\vhich can be readily and continuously Fig. 27. pick

handled by one man.

Pick. A pick is a tool which roughly resembles an earth
pick, but which has two sharp points. It is used like a cavil
for roughly breaking up and forming the stones as desired,
Fig. 27.

Pitch-Faced Masonry. Pitch-faced masonry, Fig. 28, is masonry
in which the edges of the stone are dressed to form a rectangle which
lies in a true plane, although the portion of the face between the
edges is not plane.

103

MASONRY AND REINFORCED CONCRETE

Fig. 28. Pitch-Faced Masonry

Pitching Chisel. A pitching chisel is a tool which is used with
a mallet to prepare pitch-faced masonry. The usual forms are
illustrated in Fig. 29.

Plinth. Plinth is another term for Water Table, see page 94.

Plug. A plug is a truncated
wedge, Fig. 30. Corresponding
with it are wedge-shaped pieces
made of half-round malleable
iron. A plug is used in connec-
tion with a pair of feathers to
split a section of stone uniformly.
A row of holes is drilled in a
straight line along the surface of
the stone, and a plug and pair
of feathers are inserted in each hole. The plugs in succession are
tapped lightly with a hammer so that the pressure produced by
all the plugs is increased as uniformly as possible. When the pres-
sure is uniform, the stone usually splits along the line of the holes
without injury to the portion split apart.

Point. A point is a tool made of a bar of steel whose end is
ground to a point. It is used in the intermediate stage of dressing
an irregular surface which has already been roughly trued up with a
face hammer or an ax. For rough masonry, this may be the finish-
ing tool. For higher-grade masonry, such
work will be followed by bushhammering,
crandalling, etc.

Pointing. Pointing is the term applied
to the process of scraping out the mortar for
a depth of an inch or more on the face of a
wall after the wall is complete and is sup-
posed to have become compressed to its final
form; the joints are then filled with a very
rich mortar — say equal parts of cement and
sand. Although ordinary brickwork is usually
laid by finishing the joints as the work pro-
ceeds, it is impossible to prevent some settling
of the masonry, which usually squeezes out some of the mortar and
leaves it in a cracked condition so that rain can readily penetrate

Fig. 29. Pitching Chisel

104

MASONRY AND REINFORCED CONCRETE 93

through the cracks into the wall. By scraping out the mortar,
which may be done with a hook before it has become thoroughly
hard, the joint may be filled with a high grade of mortar which
will render it practically impervious to rainwater. The pointing
may be done with a mason's trowel, although, for architectural
effect, such work is frequently finished off with specially formed
tools which will mold the outer face of the mortar into some
desired form.

Quarry-Faced Stone. Quarry-faced stone is stone laid in the
wall, in the condition in which it comes from the quarry. The
term usually applies to stones which have such regular cleavage
planes that even the quarry faces are sufficiently
regular for use without dressing.

Quoin. A quoin is a stone placed in the corner
of a wall so that it forms a header for one face and
a stretcher for the other.

Random. Random is the converse of Coursed
Masonry; masonry which is not laid in courses.

Range. A range is a row or course with the
horizontal joints continuous. Range masonry is
masonry in which each course has the same thick-
ness throughout, but the different courses vary in
thickness.

Riprap. Riprap consists of rough stone, just
as it comes from the quarry, which is placed on
the surface of an earth embankment.

Rough-Pointing. Rough-pointing is dressing
the face of a stone by means of a pick, or perhaps
a point, until the surface is approximately plane.
This may be the first stage preliminary to finer
dressing of the stones.

Rubble. Rubble is the name given masonry
composed of rough stones as they come from the quarry, without
any dressing other than knocking off any objectionable protruding
points. The thickness may be quite variable, and therefore the
joints are usually very thick in places.

Slope-Wall Masonry. Slope-wall masonry signifies a type of
wall, usually of dry rubble, which is built on a sloping bank of earth

Fig. 30. Plug and
Feathers

105

94 MASONRY AND REINFORCED CONCRETE

and supported by it, the object of the wall being, chiefly, to protect
the embankment against scour.

Sjmlls. Spalls are small stones and chips, selected according
, to their approximate fitness, which are placed between the larger,
irregular stones in rubble masonry in order to avoid, in places, an
excessive thickness of the mortar joint. Specifications sometimes
definitely forbid their use.

Squared-Stone Masonry. Squared-stone masonry is masonry in
which the stones are roughly dressed so that at the joints the
distance between the general planes of the surface of adjoining
stones is one-half inch or more.

Stretcher. A stretcher is a stone which is placed in the wall so
that its greatest dimension is parallel with the wall.

Stringcourse. A stringcourse is a course of stone or brick,
running horizontally around a building, whose sole purpose is archi-
tectural effect. (See Belt Course.}

Template. A template is a wooden form used as a guide in
dressing stones to some definite shape, as illustrated in Figs. 33
and 34.

Two-Man Stone. Two-man stone is a rather indefinite term
applied to a size and weight of stone which cannot be readily handled
except by two men. The term has a significance in planning the
masonry work.

Voussoir. A voussoir is one of the tapering or wedge-shaped
pieces of which an arch or vault is composed. The middle one
is usually called the keystone.

Water Table. The water table is a course of stone which projects
slightly from the face of the wall, and is usually laid at the top of
the foundation wall. Its function is chiefly architectural, although,
as its name implies, it is supposed to divert the Wja'ter wliich might
drain down the wall of a building, and to preventjt from following"'
the face of the foundation wall.

Wood Brick. Wood brick is the name for a- block of wood
placed in a wall in a situation where it will later be convenient to
drive nails or screws. Such a block is considered preferable to the
plan of subsequently drilling a hole and inserting a plug of wood
into which the screws or .nails may be driven, since such a plug may
act as a wredge and crack the masonry.

106

MASONRY AND REINFORCED CONCRETE

STONE MASONRY

Classification of Dressed Stones. Stone masonry is classified
according to the shape of the stones, and also according to the
quality and accuracy of the dressing of the joints so that the joints
may be close. The definitions of these various kinds of stonework
have already been given in the previous pages, and therefore will
not be repeated here; but the classification will be repeated in the
order of the quality and usual relative cost of the work.

The term rubble is usually applied to stone masonry on which
but little work has been done in dressing the stones, although the
cleavage planes may be such that very regular stones may be pro-
duced with very little work. Rubble masonry usually has joints
which are very irregular in thickness. In order to reduce the amount
of clear mortar which otherwise
might be necessary in places
between the stones, small pieces
of stone called spalls are placed
between the larger stones. Such
masonry is evidently largely de-
pendent upon the shearing and
tensile strength of the mortar
and is therefore comparatively

weak. Random rubble, Fig. 31, Fig. 31. Random Hubble

which has joints that are not in

general horizontal or vertical, or even approximately so, must be
considered as a weak type of masonry. In fact, the real strength
of such walls, which are frequently built for architectural effect,
depends on 'the backing, to which the facing stones are sometimes
secured by cramps.'

The'.next grade in quality is squared-stone masonry, which refers

to«~the accuracy in dressing the joints and may be applied to
coursed, range, ahd random work. The term ashlar refers both
to the rectangular shape of the stone and the accuracy of dressing
the joints; it may be applied to coursed, range, and random work.

Cutting and Dressing Stone. Many of the requirements and
methods of stone dressing have already been stated in the definitions
given above. Frequently a rock is so stratified that it can be split
up into blocks whose faces are so nearly parallel and perpendicular

107

96 MASONRY AND REINFORCED CONCRETE

that in building a substantial wall with comparatively close joints
the stones may be used with little or no dressing. On the other
hand, an igneous rock such as granite must be dressed to a regular
form.

Rectangular Blocks. The first step in making rectangular
blocks from any stone is to decide from its stratification, if any, or
its cleavage planes, how the stone may be dressed with the least
labor in cutting. The stone is then marked in straight lines with
some form of marking chalk, and drafts are cut with a drafting chisel
so as to give a rectangle whose four lines lie all in one plane. The
other faces are then dressed off with as great accuracy as is desired,
so that they are perpendicular, or parallel, to this plane. For
squared-stone masonry, and especially for ashlar masonry, the
drafts should be cut for the bed joints, and the surface between the
drafts on any face should be worked down to a true plane, or nearly
so. The bed joints should be made slightly concave rather than
convex, but the concavity should be very
slight. If the surface is very convex, there
is danger that the stones will come in con-
tact writh each other and produce a concen-
tration of pressure, unless the joints are
made undesirably thick. If they are very
concave, there is a danger of developing
transverse stresses in the stones, which
might cause a rupture. The engineer or

Fig. 32. Defective Work contractor must be careful to see that the
bed joints are made truly perpendicular to

the face. Careless masons will sometimes use the stones in the
form of truncated wedges, as illustrated in Fig. 32. Such masonry,
when finished, may look almost like ashlar; but such a wall is
evidently very weak, even dangerously so.

Cylindrical Surface. To produce a cylindrical surface on a
stone, a draft must be cut along the stone, which shall be parallel
with the axis of the cylinder, Fig. 33. A template made with a
curve of the desired radius, and 'with a guide which runs along the
draft, may be used in cutting down the stone to the required cylin-
drical form. A circular template, swTung around a point which may
be considered as a pole, may be used for making spherical surfaces,

108

MASONRY AND REINFORCED CONCRETE

Template

Fig. 33. Template for Cutting Cylindrical
Surface

although such work is now usually done in a lathe instead of by
hand.

Warped Surface. To make a warped surface or helicoidal
surface, a template must be
made, as in Fig. 34, by first cut-
ting two drafts wThich shall fit a
template made as shown in the
figure. After these two drafts
are cut, the surface between
them is dressed down to fit a
straightedge, which is moved
along the two drafts and per-
pendicular to them. Such stone-
work is very unusual, and almost
its only application is in the making of oblique or helicoidal arches.

Economical Size of Blocks. The size of the blocks has a very
great influence on the cost of dressing the stones per cubic yard of
masonry. For example, to quote a very simple case, a stone 3 feet
long, 2 feet wide, and 18 inches high has 12 square feet of bed joints,
6 square feet of end joints, and 4.5 square feet of facing, and con-
tains 9 cubic feet of masonry. If the stones are 18 inches long, 1
foot wide, and 9 inches high — just one-half of each dimension — the
area of each kind of dressed joint is one-fourth that in the case of
the larger stones, but the volume of the masonry is only one-eighth.
In other words, for stones of sim-
ilar shape, increasing the size
increases the area of dressing in
proportion to the square of the
dimensions, but it also increases
the volume in proportion to the
cube of the dimensions. There-
fore large stones are far more eco-
nomical than small stones, so far

, „ . . . „ Fig. 34. Template for Warped-Surface Cutting

as the cost ot dressing is a factor.

The size of stones, the thickness of courses, and the type of
masonry should depend largely on the product of the quarry to be
utilized. An unstratified stone like granite must have all faces of
the stone plug-and-f eathered ; and therefore the larger the stone, the

109

98 MASONRY AND REINFORCED CONCRETE

less will be the area to be dressed per cubic foot or yard of masonry.
On the other hand, the size of blocks which can be broken out from
a quarry of stratified rock, such as sandstone or limestone, is usually
fixed somewhat definitely by the character of the quarry itself.
The stratification reduces very greatly the work required, especially
on the bed joints. But since the stratification varies, even in any
one quarry, it is generally most economical to use a stratified stone
for random masonry, while granite can be cut for coursed masonry at
practically the same expense as for stones of variable thickness.

Cost of Dressing Stone. Although, as explained above, the cost
of dressing stone should properly be estimated by the square foot of
surface dressed, most figures which are obtainable give the cost per
cubic yard of masonry, which practically means that the figures are
applicable only to stones of the average size used in that work. A
few figures are here quoted from Gillette's "Handbook of Cost Data" :

(a) Hand Dressing — Wages, 75 cents per hour. Soft, 38 to 45 cents; medium,
60 to 78 cents; hard, $1.12 to $1.20 per square foot of surface dressed.

(b) Hand Dressing — Wages, $6.00 per day. Limestone, bushhammered,
50 cents per square foot.

(c) Hand Dressing Limestone — 32 square feet of beds and joints per
8-hour day (or 4 square feet per hour); wages, 75 cents per hour, or
19 cents per square foot.

(d) Hand Dressing Granite — For J-inch joints, 50 cents per square foot.

(e) Sawing Slabs by Machinery — Costs approximately 30 cents per square
foot.

Constructive Features. Bonding. It is a fundamental prin-
ciple of masonry construction that vertical joints, either longi-
tudinal or lateral, should not be continuous for any great distance.
Masonry walls — except those of concrete blocks — are seldom or never
constructed entirely of single blocks which extend clear through
the wall. The wrall is essentially a double wall \vhich is frequently
connected by headers. These break up the continuity of the longi-
tudinal vertical joints. The continuity of the lateral vertical joints
is broken up by placing the stones of an upper course over the joints
in the course below. Since the headers are made of the same quality
of stone (or brick) as the face masonry, while the backing is of com-
paratively inferior quality, it costs more to put in numerous headers,
although strength is sacrificed by neglect to do so. For the best
work, stretchers and headers should alternate. This would usually
mean that about one-third of the face area would consist of headers.

110

MASONRY AND REINFORCED CONCRETE

TABLE XIV
Mortar per Cubic Yard of Masonry

GRADE OF MASONRY

VOLUME OF MORTAR PER CUBIC YARD OF MASONRY

Ashlar
Squared-Stone
Rubble

1 to 2 cubic feet
4.5 to 7 cubic feet
5.5 to 9 cubic feet

One-fourth or one-fifth is a more usual ratio. Cramps and dowels
are merely devices to obtain a more efficient bonding. An inspector
must guard against the use of blind headers, which are short blocks
of stone (or brick), which have the same external appearance on the
finished wall, but which furnish no bond. After an upper course has
been laid, it is almost impossible to detect them.

Amount of Mortar. For the same reasons given when dis-
cussing the relation of size of stones to amount of dressing required,
more mortar per cubic yard of masonry is needed for small stones than
for large. The larger and rougher joints, of course, require more
mortar per cubic yard of masonry. In Table XIV are given figures
which, for the above reasons, are necessarily approximate; the larger
amounts of mortar represent the requirements for the smaller sizes
of stone, and vice versa.

The stones should be thoroughly wetted before laying them in
the wall, so that they will not absorb the water in the mortar and
ruin it before it can set. It is very important that the bed joints
be thoroughly flushed with mortar. All vertical joints should like-
wise be tightly filled with mortar.

Allowable Unit Pressures. In estimating such quantities, the
following considerations must be kept in mind:

(1) The accuracy of the dressing of the stone, particularly the bed joints,
has a very great influence.

(2) The strength is largely dependent on that of the mortar.

(3) The strength is so little dependent on that of the stone itself that the
strength of the stone cannot be considered a guide to the strength of the masonry.
For example, masonry has been known to fail under a load not more than five
per cent of the ultimate crushing strength of the stone itself.

(4) The strength of a miniature or small-scale prism of masonry is only
a guide to the strength of large prisms. The ultimate strength of these is beyond
the capacity of testing machines.

(5) So much depends on the workmanship, that in any structure where
the unit stresses are so great as to raise any question concerning the strength,
the best workmanship must be required.

Ill

100 MASONRY AND REINFORCED CONCRETE

Judging from the computed pressures now carried by noted
structures, and also from the pressures sustained by piers, etc., which
have shown distress and have been removed, it is evident that,
assuming good workmanship, the allowable pressure on masonry is
as follows :

Granite Ashlar up to 400 pounds per sq. inch

Limestone or Sandstone Ashlar up to 300 pounds per sq. inch

Squared-Stonc up to 250 pounds per sq. inch

Rubble up to 140 pounds per sq. inch

Somewhat larger pressures may be allowed on the different
grades of stone masonry when Portland cement is used in the mortar
instead of common lime.

Cost of Stone Masonry. The total cost is a combination of
several very variable items as follows:

(1) Value of quarry privilege

(2) Cost of stripping superincumbent earth or disintegrated rock

(3) Cost of quarrying

(4) Cost of dressing

(5) Cost of transportation (teaming, railroad, etc.), from quarry to site

of works

(6) Cost of mortar

(7) Cost of centering, scaffolding, derricks, etc.

(8) Cost of laying

(9) Interest and depreciation on plant
(10) Superintendence

Some of the above items may be practically nothing, in cases.
The cost of some of the items has already been discussed. The cost
of many items is so dependent on local conditions and prices that the
quotation of the cost of definite jobs would have but little value and
might even be deceptive. The following very general values may be
useful to give a broad idea of the cost of stone masonry:

Rubble and Masonry in Mortar $3.00 to $ 5.00 per cubic yard

Squared-Stone Masonry 6.00 to 10.00 per cubic yard

Dimension Stone, Granite Ashlar up to 60.00 per cubic yard

BRICK MASONRY

Many of the terms employed in stone masonry as well as the
directions for properly doing the work are equally applicable to
brick masonry and, therefore, will not be here repeated. The follow-
ing paragraphs will be devoted to those terms and specifications
which are applicable only to brick masonry.

MASONRY AND REINFORCED CONCRETE 101

Bonding Used in Brick Masonry. Some of the principles
involved in the effect of bonding on the strength of a wall have

( II II II 1 1

I II 1

i II 1 II II 1

1 II \

ii i i ii in

i ii ii n

II 1

Fig. 35. Common Bond

already been discussed. The other consideration is that of archi-
tectural appearance. The common method of bonding, Fig. 35, is
to lay five or six courses of brick entirely as stretchers, then a course

i ii ii ii a i ii i ii

J I I I L

Fig. 36. English Bond

of brick will be laid entirely as headers. There is probably some
economy in the work required of a bricklayer in following this policy.
The so-called English bond, Fig. 36, consists of alternate courses of

J L

Fig. 37. Flemish Bond

headers and stretchers. If the face bricks are of better quality
than those used in the backing of the wall, this system means that
one-half the face area of the wall consists of headers, which is cer-

113

102 MASONRY AND REINFORCED CONCRETE

TABLE XV
Quantities of Brick and Mortar

MORTAR

THICK-

No. OF

(Cubic Yard)

KIND OF BRICK

(Inches)

JOINTS
(Inches)

PER CUBIC
YARD

PER CUBIC
YARD OF

PER 1,000

MASONRY

Common brick

8} X 4 X 2J

}

430

.34

.80

Common brick

8J X 4 X 2|

516

.21

.40

Pressed brick

8f X 4| X 2i

544

.11

.21

tainly not an economical way of using the facing brick. The Flem-
ish bond, Fig. 37, employs alternate headers and stretchers in each
course, and also disposes of the vertical joints so that there is a
definite pattern in the joints, which has a pleasing architectural effect.

Constructive Features. On account of the comparatively high
absorptive power of brick, it is especially necessary that they shall
be thoroughly soaked with water before being laid in the wall.
An excess of water can do no harm, and will further insure the bricks
being clean from dust, which would affect the adhesion of the mortar.
It is also important that the brick shall be laid with what is called a
shove joint. This term is even put in specifications, and has a definite
meaning to masons. It means that, after laying the mortar for the
bed joints, a brick is placed with its edge projecting somewhat over
that of the lower brick and is then pressed down into the mortar
and, while still being pressed down, is shoved into its proper position.
In this way is obtained a proper adhesion between the mortar and
the brick.

The thickness of the mortar joint should not be over one-half
inch; one-fourth inch, or even less, is far better, since it gives stronger
masonry. It requires more care to make thin joints than thick
joints and, therefore, it is very difficult to obtain thin joints w7hen
masons are paid by piecework. Pressed brick fronts are laid with
joints of one-eighth inch or even less, but this is considered high-
grade work and is paid for accordingly.

Strength of Brickwork. As previously stated with respect to
stone masonry, the strength of brick masonry is largely dependent
upon the strength of the mortar; but, unlike stone masonry, the
strength of brick masonry rs, in a much larger proportion, dependent
on the strength of the brick composing it. The ultimate strength of

114

MASONRY AND REINFORCED CONCRETE 103

brick masonry has been determined by a series of tests, to vary from
1,000 to 2,000 pounds per square inch, using lime mortar; and from
1,500 to 3,000 pounds per square inch, using cement mortar — the
variation in each group (for the same kind of mortar) depending on
the quality of the brick. A large factor of safety, perhaps 10, should
be used with such figures.

Methods of Measuring Brickwork. There has been a consid-
erable variation in the methods of measuring brickwork, due to
local trade customs, but the general practice now is to measure
brickwork by the 1,000 bricks actually laid in the wall. Owing to
the variations in size of bricks, no rule for volume of laid brick can
be exact. For bricks that measure 8| inches by 4^ inches by 2f
inches the following scale is a fair average:

7 bricks to a superficial foot for 4-in. wall = 40 Ib.
14 bricks to a superficial foot for 9-in. wall = 94 Ib.
21 bricks to a superficial foot for 13-in. wall = 121 Ib.
28 bricks to a superficial foot for 18-in. wall = 168 Ib.
35 bricks to a superficial foot for 22-in. wall =210 Ib.

Common hand-burned bricks weigh from 5 to 6 pounds each.
One thousand bricks, closely stacked, occupy about 56 cubic feet.
Table XV shows the quantities of brick and mortar for both common
and pressed brick.

Cost of Brickwork. A laborer should handle 2,000 brick per
hour in loading them from a car to a wagon. If they are not un-
loaded by dumping, it will require as much time again to unload
them. A mason should lay an average of 1,200 brick per 8-hour
day on ordinary wall work. For large, massive foundation work
with thick walls, the number should rise to 3,000 per day. On the
other hand, the number may drop to 200 or 300 on the best grade of
pressed-brick work. About one helper is required for each mason.
Masons' wrages vary from 50 to 75 cents per hour; helpers' wages are
about one-half as much.

Impermeability. As previously stated, brick is very porous;
ordinary cement mortar is not water-tight; and, therefore, when it
is desirable to make brick masonry impervious to water, some
special method must be adopted, as described in Part I, under the
head of "Waterproofing".

Efflorescence. Efflorescence is the term applied to the white
deposit which frequently forms on brickwork and concrete (see

115

104 MASONRY AND REINFORCED CONCRETE

page 08, Part I). The Sylvester wash has frequently been used
as a preventive, and with fairly good results. Diluted acid has
been used successfully to remove the efflorescence. These methods
have been described in Part I.

Brick Piers. A brick pier, as a general rule, is the only form of
brickwork that is subjected to its full resistance. Sections of walls
under bearing plates, also, receive a comparatively large load; but
only a few courses receive the full load and, therefore, a greater
unit stress may be allowed than for piers.

Kidder gives the following formulas for the safe strength of
brick piers exceeding 6 diameters in height:
Piers laid with rich lime mortar

(a) Safe load, Ib. per sq. in. = 1 1 0 — 5 —

Piers laid with 1:2 natural cement mortar

Piers laid with 1:3 Portland cement mortar

(1)

In the above formulas, // is the height of the column in feet
and D is the diameter of the column in feet.

For example, a column 16 feet in height and 1| feet square, laid
with rich lime mortar, may be subjected to a load of 65 pounds per
square inch, or 9,360 pounds per square foot; for a 1:2 natural
cement mortar, 90 pounds per square inch, or 12,960 pounds per
square foot; and for a 1:3 Portland cement mortar, 146 pounds per
square inch, or 20,914 pounds per square foot.

The building laws of some cities require a bonding stone spaced
every 3 to 4 feet, when brick piers are used. This stone is 5 to 8
inches thick, and is the full size of the pier. Engineers and archi-
tects are divided in their opinion as to the results obtained by using
the bonding stone.

CONCRETE MASONRY

Concrete is extensively used for constructing the many differ-
ent types of foundations, retaining walls, dams, culverts, etc. The
ingredients of which concrete is made, the proportioning and the
methods of mixing these materials, etc., have been discussed in

110

MASONRY AND REINFORCED CONCRETE 105

Part I. Methods of mixing and handling concrete by machinery
will be discussed in Part IV. Various details of the use of concrete
in the construction of foundations, etc., will be discussed during the
treatment of the several kinds of work.

RUBBLE CONCRETE

Advantages over Ordinary Concrete. Rubble concrete includes
any class of concrete in which large stones are placed. The chief
use of this concrete is in constructing dams, lock walls, breakwaters,
retaining walls, and bridge piers.

The cost of rubble concrete in large masses should be less than
that of ordinary concrete, as the expense of crushing the stone used
as rubble is saved, and each large stone replaces a portion of cement
and aggregate; therefore, this portion of cement is saved, as well as
the labor of mixing it. The weight of a cubic foot of stone is greater
than that of an equal amount of ordinary concrete, because of the
pores in the concrete; the rubble concrete is therefore heavier, which
increases its value for certain classes of work. In comparing rubble
concrete with rubble masonry, the former is usually found cheaper
because it requires very little skilled labor. For walls 3 or 3^ feet
thick, the rubble masonry will usually be cheaper, owing to the
saving in forms.

Proportion and Size of Stone. Usually the proportion of
rubble stone is expressed in percentage of the finished work. This
percentage varies from 20 to 65 per cent. The percentage depends
largely on the size of the stone used, as there must be nearly as much
space left between small stones as between large ones. The per-
centage therefore increases with the size of the stones. When "one-
man" or "two-man" rubble stone is used, about 20 per cent to 25
per cent of the finished work is composed 'of these stones. When
the stones are large enough to be handled with a derrick, the pro-
portion is increased to about 33 per cent; and to 55 per cent, or even 65
per cent, when the rubble stones average from 1 to 2 \ cubic yards each.

The distance between the stones may vary from 3 inches to 15
or 18 inches. With a very wet mixture of concrete, wrhich is gen-
erally used, the stones can be placed much closer than if a dry mix-
ture is used. With the latter mixture, the space must be sufficient
to allow the concrete to be thoroughly rammed into all of the

lit

106 MASONRY AND REINFORCED CONCRETE

crevices. Specifications often state that no rubble stone shall be
placed nearer the surface of the concrete than 6 to 12 inches.

Rubble Masonry Faces. The faces of dams are very often
built of rubble, ashlar, or cut stone, and the filling between the faces
made of rubble concrete. For this style of construction, no forms are
required. For rubble concrete, when the faces are not constructed
of stone, wooden forms are constructed as for ordinary concrete.

Comparison of Quantities of Materials. The mixture of con-
crete used for this class of work is often 1 part Portland cement, 3
parts sand, and 6 parts stone. The quantities of materials required
for one yard of concrete, according to Table VIII, Part I, are 1.05
bbls. cement, 0.44 cu. yd. sand, and 0.88 cu. yd. stone. If rubble
concrete is used, and if the rubble stone laid averages 0.40 cubic
yard for each yard of concrete, then 40 per cent of the cubic contents
is rubble, and each of the other materials may be reduced 40 per
cent. Reducing these quantities gives 1.05X0.60 = 0.63 bbl. of
cement; 0.44X0.60 = 0.26 cu. yd. sand; and 0.88X0.60 = 0.53 cu. yd.
of stone, per cubic yard of rubble concrete.

The construction of a dam on the Quinebaug River is a good
example of rubble concrete. The height of the dam varies from 30
to 45 feet above bed rock. The materials composing the concrete
consist of bank sand and gravel excavated from the bars in the bed
of the river. The rock and boulders were taken from the site of the
dam, and were of varying sizes. Stones containing 2 to 2| cubic
yards were used in the bottom of the dam, but in the upper part of
the dam smaller stones were used. The total amount of concrete
used in the dam was about 12,000 cubic yards. There was 1| cubic
yards of concrete for each barrel of cement used. The concrete was
mixed wet, and the large stones were so placed that no voids or
hollows would exist in the finished work.

DEPOSITING CONCRETE UNDER WATER

Methods. In depositing concrete under water, some means
must be taken to prevent the separation of the materials while
passing through the water. The three principal methods are as
follows :

(1) By means of closed buckets

(2) By means of cloth or paper bags

(3) By means of tubes

118

MASONRY AND REINFORCED CONCRETE 107

Buckets. For depositing concrete by the first method, special
buckets are made with a closed top and hinged bottom. Concrete
deposited under water must be disturbed as little as possible and,
in tipping a bucket, the material is apt to be disturbed. Several
different types of buckets with hinged bottoms have been devised
to open automatically when the place for depositing the concrete
has been reached. In one type, the latches which fasten the trap-
doors are released by the slackening of the rope when the bucket
reaches the bottom, and the doors are open as soon as the bucket
begins to ascend. In another type, in which the handle extends
down the sides of the bucket to the bottom, the doors are opened
by the handles sliding down when the bucket reaches the bottom.
The doors are hinged to the sides of the bucket and, when opened,
permit the concrete to be deposited in one mass. In depositing
concrete by this means, it is found rather difficult to place the layers
uniformly and to prevent the formation of mounds.

Bags. This method of depositing concrete under water is by
means of open-woven bags or paper bags, two-thirds to three-quar-
ters filled. The bags- are sunk in the water and placed in courses —
if possible, header and stretcher system — arranging each course as
laid. The bagging is close enough to keep the cement from washing
out and, at the same time, open enough to allow the whole to unite
into a compact mass. The fact that the bags are crushed into
irregular shapes which fit into each other tends to lock them together
in a way that makes even an imperfect joint very effective. When
the concrete is deposited in paper bags, the water quickly soaks the
paper; but the paper retains its strength long enough for the con-
crete to be deposited properly.

Tubes. The third method of depositing concrete under water
is by means of long tubes, 4 to 14 inches in diameter. The tubes
extend from the surface of the water to the place where the concrete
is to be deposited. If the tube is small, 4 to 6 inches in diameter, a
cap is placed over the bottom, the tube filled with concrete and
lowered to the bottom. The cap is then withdrawn, and as fast as
the concrete drops out of the bottom, more is put in at the top of
the tube, and there is thus a continuous stream of concrete deposited.

When a large tube is used to deposit concrete in this manner,
it will be too heavy to handle conveniently if filled before being

119

108 MASONRY AND REINFORCED CONCRETE

lowered. The foot of the tube is lowered to the bottom, and the
water rises into the chute to the same level as that outside; and into
this water the concrete must be dumped until the water is wholly
replaced or absorbed by the concrete. This has a tendency to sepa-
rate the cement from the sand and gravel, and will take a yard or
more of concrete to displace the water in the chute. There is a
danger that this amount of badly washed concrete will be deposited
whenever it is necessary to charge the chute. This danger occurs not
only when the charge is accidentally lost, but whenever the work is
begun in the morning, or at any other time. Whenever the work is
stopped, the charge must be allowed to run out, or it would set in
the tube. The tubes are usually charged by means of wheelbarrows,
and a continuous flow of concrete must be maintained. When the
chute has been filled, it is raised slowly from the bottom, allowing a
part of the concrete to run out in a conical heap at the foot.

This method has also been used for grouting stone. In this
case, a 2-inch pipe, perforated at the bottom, is used. The grout,
on account of its great specific gravity, is sufficient to replace the
water in the interstices between the stones, and firmly cement them
into a mass of concrete. A mixture of one part cement and one part
sand is the leanest mixture that can be used for this purpose, as
there is a great tendency for the cement and sand to separate.

CLAY PUDDLE

Clay puddle consists of clay and sand made into a plastic mass
with water. It is used principally to fill cofferdams, and for making
embankments and reservoirs water-tight.

Quality of Clay. Opaque clays with a dull, earthy fracture, of
an argillaceous nature, which are greasy to the touch, and which
readily form a plastic paste when mixed with wrater, are the best clays
for making puddle. Large stones should be removed from the clay,
and it should also be free from vegetable matter. Sufficient sand
and wrater should be added to make a homogeneous mass. If too
much sand is used, the puddle will be permeable; and if too little is
used, the puddle will crack by shrinkage in drying. It is very impor-
tant that clay for making puddle should show great cohesive power
and also the property of retaining water.

120-

MASONRY AND REINFORCED CONCRETE 109

A simple test to find the cohesive property can easily be made.
A small quantity of the clay is mixed with water and made into a roll
about 1 inch in diameter and 8 to 10 inches long; and if, on being
suspended by one end while wet, it does not break, the cohesive
strength is ample. The test to find its water-retaining properties
is made by mixing up 1 or 2 cubic yards of the clay with water,
making it into a homogeneous plastic mass. A round hole is made
in the top of the mass, large enough to hold 4 or 5 gallons of water.
The hole is filled with water, and the top covered and left 24 hours;
when the cover is removed, the properties of the clay will be indicated
by the presence or absence of water.

Puddling. The clay should be spread in layers about 3 inches
thick and well chopped with spades, aided by the addition of suffi-
cient water to reduce it to a pasty condition. Water should be
given a chance to pass through freely as the clay is being mixed.
The different layers, as they are mixed, should be bonded together
by the spade passing through the upper layer into the under layer.
The test for thorough puddling is that the spade will pass through
the layer with ease, wrhich it will not do if there are any hard lumps.

When a large amount of puddle is required, harrows are some-
times used instead of spades. Each layer of clay is thoroughly har-
rowed, aided by being sprinkled freely with water, and is then rolled
with a grooved roller to compact it.

Puddle, when finished, should not be exposed to the drying
action of the air, but covered with dry clay or sand.

FOUNDATIONS

PRELIMINARY WORK

Importance of Foundations. It would be impossible to over-
emphasize the importance of foundations, because the very fact that
the foundations are underground and out of sight detracts from the
consideration that many will give to the subject. It is probably
true that a yielding of the subsoil is responsible for a very large
proportion of the structural failures which have occurred. It is
also true that many failures of masonry, especially those of arches,
are considered as failures of the superstructure, because of breaks
occurring in the masonry of the superstructure, which have really

121

110 MASONRY AND REINFORCED CONCRETE

been due, however, to a settlement of the foundations, resulting in
unexpected stresses in the superstructure. It is likewise true that
the design of foundations is one which calls for the exercise of experi-
ence and broad judgment, to be able to interpret correctly such
indications as are obtainable as to the real character of the subsoil
and its probable resistance to concentrated pressure.

CHARACTER OF SOIL

Classification of Subsoils. The character of soil on which it
may be desired to place a structure varies all the way from the
most solid rock to that of semi-fluid soils whose density is but little
greater than that of water. The gradation between these extremes
is so uniform that it is practically impossible to draw a definite line
between any two grades. It is convenient, however, to group sub-
soils into three classes, the classification being based on the method
used in making the foundation. These three classes of subsoils are:
firm; compressible; and semi-fluid.

Firm Subsoils. These comprise all soils which are so firm, at
least at some reasonably convenient depth, that no treatment of the
subsoil, or any other special method, needs to be adopted to obtain
a sufficiently firm foundation. This, of course, practically means
that the soil is so firm that it can safely withstand the desired unit
pressure. It also means that a soil which might be classed as firm
soil for a light building should be classed as compressible soil for a
much heavier building. It frequently happens that the top layers
must be removed from rock because the surface rock has become
disintegrated by exposure to the atmosphere. Nothing further
needs to be done to a subsoil of this kind.

Compressible Subsoils. These include soils which might be con-
sidered as firm soils for light buildings, such as dwelling houses, but
which could not withstand the concentrated pressure that would be
produced, for example, by the piers or abutments of a bridge. Such
soils may be made sufficiently firm by methods described later.

Semi-Fluid Subsoils. These are soils such as are frequently
found on the banks or in the beds of rivers. They are so soft that
they cannot sustain, without settlement, even the load of a house, to
say nothing of a heavier structure; nor can they be materially
improved by any reasonable method of compression. The only

122

MASONRY AND REINFORCED CONCRETE 111

possible method of placing a heavy structure in such a locality
consists in sinking some sort of a foundation through such soft soil
until it reaches and is supported by a firm soil or by rock, which may
be 50 or even 100 feet below the surface. The general methods of
accomplishing these results will be detailed in the following pages.

Examination of Soil with Auger. The first step is to excavate
the surface soil to the depth at which it would be convenient to place
the foundation and at which the soil appears, from mere inspection,
to be sufficiently firm for the purpose. An examination of the
trenches or foundation pits with a post auger or steel bar will gen-
erally be sufficient to determine the nature of the soil for any ordi-
nary building. The depth to which such an examination can be
made with a post auger or steel bar will depend on the nature of the
soil. In ordinary soils there will not be much difficulty in extending
such an examination 3 to 6 feet below the bottom of the foundation
pits. In common soils or clay, borings 40 feet deep, or even deeper,
can readily be made with a common wood auger, turned by men.
From the samples brought up by the auger, the nature of the soil
can be determined; but nothing of the compactness of the soil can
be determined in this manner.

Testing Compressive Value. In order to test a soil to find its
compressive value, the bottom of the pit should be leveled for a
considerable area, and stakes should be driven at short intervals in
each direction. The elevations of the tops of all the stakes should
be very accurately taken with a spirit level. For convenience, all
stakes should be driven to the same level. A mast whose base has
an area one foot square can support a platform which may be loaded
with several tons of building material, such as stone, brick, steel,
etc. This load can be balanced with sufficient closeness so that
some very light guys will maintain the unstable equilibrium of the
platform. As the load on the platform is greatly increased, at some
stage it will be noted that the mast and platform have begun to sink
slightly, and also that the soil in a circle around the base of the mast
has begun to rise. This is indicated by the rising of the tops of the
stakes. Even a very ordinary soil may require a load of five or six
tons on a square foot before any yielding will be observable. One
advantage of this method lies in the fact that the larger the area of
the foundation, the greater will be the load per square foot which may

123

112 MASONRY AND REINFORCED CONCRETE

be safely carried, and that the uncertainty of the result is on the
safe side. A soil which might yield under a load concentrated on a
mast one foot square would probably be safe under that same unit
load on a continuous footing which was perhaps three feet wide;
and if, in addition, a factor of safety of three or four was used, there
would probably be no question as to the safety. Such a test need
be applied only to an earthy soil. It would be practically impossible
to produce a yielding by such a method on any kind of rock or even
on a compacted gravel.

Bearing Power of Ordinary Soils. A distinction must be main-
tained between the crushing strength of a cube of rock or soil, and
the bearing power of that soil when it lies as a mass of indefinite
extent under some structure. A soil can fail only by being actually
displaced by the load above it, or because it has been undermined,
perhaps by a stream of water. A sample of rock which might crush
with comparative ease, when tested as a six-inch cube in a testing
machine, will probably withstand as great a concentration of load
as it is practicable to put upon it by any engineering structure.
Even a gravel, which would have absolutely no strength if an
attempt were made to place a cube of it in a testing machine, will be
practically immovable when lying in a pit \vhere it is confined
laterally in all directions.

Rock. The ultimate crushing strength of stone varies greatly.
The crushing strength is usually determined by making tests on
small cubes. Tests made on prisms of a less height than width
show a much greater strength than tests made on cubes of the same
material, which shows that the bearing strength of rock on which
foundations are built is much greater than the cubes of this stone.
In Table I, Part I, the lowest value given for the crushing strength
of a cube is 2,894 pounds per square inch, which is equal to 416,736
pounds per square foot. This shows that any ordinary stone which
is well imbedded will carry any load of masonry placed on it.

Sand and Gravel Sand and gravel are often found together.
Gravel alone, when of sufficient thickness, makes one of the firmest
and best foundations. Dry sand or wet sand, wrhen prevented from
spreading laterally, forms one of the best beds for foundations; but
it must be well protected from running water, as it is easily moved
by scouring. Clean, dry sand will safely support a load of 3,000 to

124

MASONRY AND REINFORCED CONCRETE 113

8,000 pounds per square foot; and when compact and well cemented,
from 8,000 to 10,000 pounds per square foot. Ordinary gravel, well
bedded, will safely bear a load of 6,000 to 8,000 pounds per square
foot; and when well cemented, from 12,000 to 16,000 pounds per
square foot.

Clay. There is great variation in clay soils, ranging from a
very soft mass which will squeeze out in all directions when a very
small pressure is applied, to shale or slate which will support a very
heavy load. As the bearing capacity of ordinary clay is largely
dependent upon its dryness it is, therefore, very important that a
clay soil should be well drained, and that a foundation laid on such a
soil should be at a sufficient depth to be unaffected by the weather.
If the clay cannot be easily drained, means should be taken to pre-
vent the penetration of water. When the strata are not horizontal,
great care must be taken to prevent the flow of the soil under pres-
sure. When gravel or coarse sand is mixed with the clay, the bearing
capacity of the soil is greatly increased.

The bearing capacity of a soft clay is from 2,000 to 4,000 pounds
per square foot; of a thick bed of medium dry clay, 4,000 to 8,000
pounds per square foot, and for a thick bed of dry clay, 8,000 to
10,000 pounds per square foot.

Soft or Semi-Liquid Soils. The soils of this class include mud,
silt, quicksand, etc., and it is necessary to remove them entirely or
to reach a more solid stratum under the softer soil; or, sometimes,
the soil can be consolidated by adding sand, stone, etc. The manner
of improving such a soil will be discussed later. In the same way
that water will bear up a boat, a semi-liquid soil will support, by the
upward pressure, a heavy structure. For a soil of this kind, it is very
difficult to give a safe bearing value; perhaps 500 to 1,500 pounds
per square foot is as much as can be supported without too great a
settlement.

Improving a Compressible Soil. The general method of improv-
ing a compressible soil consists in making the soil more dense. This
may be done by driving a large number of piles into the soil, espe-
cially if the piles will be always under the water line in that ground.
Driving the piles compresses the soil; and if the piles are always
under water, they will be free from decay. If the soil is sufficiently
firm so that the pile can be withdrawn and the hole will retain its

125

114 MASONRY AND REINFORCED CONCRETE

form even temporarily, the pile may be drawn and then the hole
immediately filled with sand, which is rammed into the hole as
compactly as possible. This gives us a type of piling known as
sand piles.

A soft, clayey subsoil may frequently be improved by covering
it with gravel, which is rammed and pressed into the clay. Such a
device is not very effective, but it may sometimes be sufficiently
effective for its purpose.

A subsoil is often very soft because it is saturated with water
which cannot readily escape. Frequently, a system of deep drainage,
which will reduce the natural level of the ground water considerably
below the desired depth of the bottom of the foundation, will trans-
form the subsoil into a dry, firm soil which is amply strong for its
purpose. Even when the subsoil is very soft, it will sustain a heavy
load, provided that it can be confined. While excavating for the
foundations of the tower of Trinity Church in New York City, a
large pocket of quicksand wras discovered directly under the pro-
posed tower. Owing to the volume of the quicksand, it was found
to be impracticable to drain it all out; but it was also discovered
that the quicksand was confined within a pocket of firm soil. A
thick layer of concrete was, therefore, laid across the top, which
effectively sealed up the pocket of quicksand, and the result has
been perfectly satisfactory.

PREPARING THE BED

Preparing the Bed on Rock. The preparation of a rock bed on
which a foundation is to be placed is a simple matter compared
with that required for some soils on which foundations are placed.
The bed rock is prepared by cutting away the loose and decayed
portions of the rock and making the plane on which the foundation
is placed perpendicular to the direction of the pressure. If the rock
bed is an inclined plane, a series of steps can be made for the sup-
port of the foundation. Any fissures in the rock should be filled
with concrete.

Whenever it is necessary to start the foundation of a structure at
different levels, great care is required to prevent a break in the joints
at the stepping places. The precautions to be taken are that the
mortar joints must be kept as thin as possible; the lower part of the

126

MASONRY AND REINFORCED CONCRETE 115

foundations should be laid in cement mortar; and the work should
proceed slowly. By following these precautions, the settlement in
the lower part will be reduced
to a minimum. These precau-
tions apply to foundations of
all classes.

Preparing the Bed on Firm
Earth. Under this heading is
included hard clay, gravel, and
clean, dry sand. The bed is
prepared by digging a trench
deep enough so that the bot-
tom of the foundation is below Kg 38 Drainage for Foundation Wall
the frost line, which is usually

3 to 6 feet below the surface. Some provision, similar to that shown
in Fig. 38, should be made for drainage.

Care should be taken to pro-
portion the load per unit of area so
that the settlement of the founda-
tion will be uniform.

Preparing the Bed on Wet
Ground. The chief trouble in mak-
ing an excavation in wet ground is
in disposing of the water and pre-
venting the wet soil from flowing
into the excavation. In moderately
wet soils, the area to be excavated
is enclosed with sheet piling, as in
Fig. 39. This piling usually consists
of ordinary plank, 2 inches thick
and 6 to 10 inches wide, and is often
driven by hand; or it may be driven
by methods that will be described
later. The piling is driven in close

contact, and in very wet soil it is Fig.39. sheet Piling in Foundation
necessary to drive a double row of

the sheeting. To prevent the sheeting from being forced inwards,
cross braces are used between the longitudinal timbers. When one

137

116 MASONRY AND REINFORCED CONCRETE

length of sheeting is not long enough, an additional length can be
placed inside. A more extended discussion of pile driving will be
given in the treatment of the subject "Piles".

The water can sometimes be bailed out, but it is generally
necessary to use a hand or steam pump to free the excavation of
water. Quicksand and very soft mud are often pumped out along
with the water by a centrifugal or mud pump.

Sometimes, areas are excavated by draining the water into a hole
the bottom of which is always kept lower than the general level of the
bottom of the excavation. A pump may be used to dispose of the
water drained into the hole or holes.

When a very soft soil extends to a depth of several feet, piles are
usually driven at uniform distances over the area and a grillage is
constructed on top of the piles. This method of constructing a
foundation is discussed in the section on "Piles".

FOOTINGS

Requirements of Footing Course. The three requirements of a
footing course are:

(1) That the area shall be such that the total load divided by the area
shall not be greater than the allowable unit pressure on the subsoil.

(2) That the line of pressure of the wall, or pier, shall be directly over
the center of gravity — and hence the center of upward pressure — of the base of
the footings.

(3) That the footing shall have sufficient structural strength so that it

can distribute the load uniformly over
the subsoil.

When it has been determined
with sufficient accuracy how
much pressure per square foot
may be allowed on the subsoil
(see pages 112, 113), and when

the total load of the structure has
been computed, it is a very sim-
ple matter to compute the width
of continuous footings or the area
of column footings.

, The second requirement is
very easily fulfilled when it is possible to spread the footings in all
directions as desired, as shown in Fig. 43. A common exception

Fig. 40. Construction Where Lines of Dow
' Pressure <
, Coincide

yard and Upward Pressure on Footings
Do Not r '

128

MASONRY AND REINFORCED CONCRETE 117

tmttmttmttm

Fig. 41. Transverse Stresses in

Footing Determining Ita

Thickness

occurs when putting up a building which entirely covers the width of

the lot. The walls are on the building line; the footings can expand

inward only. The lines of pressure do not coincide, as shown in

Fig. 40. A construction as shown in the

figure will almost inevitably result in cracks

in the building, unless some special device

is adopted to prevent them. One general

method is to introduce a tie of sufficient

strength from a to b. The other general

method is to introduce cantilever beams

under the basement, which either extend

clear across the building or else carry the

load of interior columns so that the center

of gravity of the combined loads will coincide with the central

pressure line of the upward pressure of the footings.

The third requirement practically means that the thickness of
the footing (be, Fig. 41) shall be great enough so that the footing can
resist the transverse stresses caused by the pressure of the subsoil on
the area between c and d. When the thickness must be made very
great, such as fh, Fig. 42, on account of the wide offset g h, material
may be saved by cutting out the rectangle ekml. The thickness
mo is computed for the offset go, just as in the first case; while the
thickness A; m of the second layer may be computed from the offset
kf. Where the footings are made of stone or of plain concrete,
whose transverse strength is always low, the offsets are necessarily
small; but when using timber, reinforced
concrete, or steel I-beams, the offsets may
be very wide in comparison with the depth
of the footing.

Calculation of Footings. The method
of calculation is to consider the offset of
the footing as an inverted cantilever which
is loaded with the calculated upward pres-
sure of the subsoil against the footing. If Fig' ^J&tftJSlf* in
Fig. 41 is turned upside down, the resem-
blance to the ordinary loaded cantilever will be more readily appar-
ent. Considering a unit length I of the wall and the amount of the
offset o equal to dc in Fig. 41, and calling P the unit pressure from

/I— \m

o h

129

118 MASONRY AND REINFORCED CONCRETE

TABLE XVI
Ratio of Offset to Thickness for Footings of Various Kinds of Masonry

MODULUS or

0£

PRESSURE ON BOTTOM OF FOOTING

RUPTURE

s •< —

(Tons per Square Foot)

KIND OF MASONRY

*>&:

and Maximum

«»~

Values)

***« <
O2

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Granite

1.200-1,365

1,280

130

2.5

1.8

1.45

1.25

1.1

1.0

0.95

Limestone

450- 900

675

1.8

1.3

1.05

0.9

0.8

0.75

0.7

Sandstone

135-1,100

525

1.6

1.15

0.95

0.8

0.75

0.65

0.6

Ccncrete (plain)

1:2:4

400- 480

440

1.9

1.35

1.1

0.95

0.85

0.75

0.7

1:3:6

213- 246

230

1.4

1.0

0.8

0.7

0.6

0.55

0.5

the subsoil, we have Pol as the pressure on that area, and its lever
arm about the point c is \o. Therefore, its moment equals \Po'tl.
If t represents the thickness be of the footing, the moment of
resistance of that section equals | Rlt2, in which R equals the unit
compression (or unit tension) in the section. We therefore have
the equation

By transposition

Ajor-2-.J.*

The fraction — is the ratio of the offset to its thickness.

(2)

The solution

of the above equation, using what are considered to be conservatively
safe values for R for various grades of stone and concrete, is given
in Table XVI.

Example. The load on a wall has been computed as 19,000 pounds per
running foot of the wall, which has a thickness of 18 inches just above the footing.
What must be the breadth and thickness of granite slabs which may be used as
a footing on soil which is estimated to bear safely a load of 2 . 0 tons per square
foot?

Solution. Dividing the computed load (19,000) by the allowable unit
pressure (2.0 tons equals 4,000 pounds), we have 4.75 feet as the required width
of the footing.

J (4.75 - 1.5) = 1.625 feet, the breadth of the offset o

From the table we find that for a subsoil loading of 2.0 tons per square foot,

1.625

the offset for granite may be 1.25 times its thickness. Therefore,
1.30 feet = 15.6 inches, is the required thickness of the footing.

1.25

130

MASONRY AND REINFORCED CONCRETE 119

The computation of the dimensions of such footings when they
are made of reinforced concrete is taken up during the development
of this specialized form of Masonry in Part III.

Although brick can be used as a footing course, the maximum
possible offset, no matter how strong the brick may be, can only be
a small part of the length of the brick — the brick being laid perpen-
dicular to the wall. One requirement of a footing course is that the
blocks shall be so large that they will equalize possible variations in
the density and compressibility of the subsoil. This cannot be done
by bricks or small stones. Their use should therefore be avoided in
footing courses.

Beam Footings. Steel, and even wood, in the form of beams,
are used to construct very wide offsets. This is possible on account
of their greater transverse strength. The general method of calcu-
lation is identical with that given above, the only difference being
that beams of definite transverse strength are so spaced that one
beam can safely resist the moment developed in the footing in that
length of wall. Wood can be used only when it will be always
under water. Steel beams should always be surrounded by concrete
for protection from corrosion.

Using Wood Beams. If we call the spacing of the beams s, the
length of the offset o, and the unit pressure from the subsoil P, the
moment acting on one beam equals %Po2s. Calling w the width
of the beam, t its thickness or depth, and R the maximum permis-
sible fiber stress, the maximum permissible moment equals £ Rwt*.
Placing these quantities equal, we have the equation

$Po*s = $Rwt* (3)

Having decided on the size of the beam, the required spacing may be
determined.

Example. An 18-inch brick wall carrying a load of 12,000 pounds per
running foot is to be placed on a soft, wet soil where the unit pressure cannot
be relied on for more than 2,000 pounds per square foot. What must be the
spacing of 10- by 12-inch footing timbers of long-leaf yellow pine?

Solution. The width of the footing is evidently 12,000 -5- 2,000 = 6 feet.
The offset o equals 3 (6 — 1.5) =2.25 feet = 27 inches. Since the unit of
measurement for computing the transverse strength is the inch, the same unit

must be employed throughout. Therefore, P = -TTT-; R = 1,200 pounds per

131

120 MASONRY AND REINFORCED CONCRETE

square inch; w = 10 inches; and t = 12 inches. Equation (3) may be rewritten

Substituting the above values, we have

_ 1,200 X 10 X 144

9 nnn
3 X =£r X 729

144:

This shows that the beams must be spaced 56.9 inches apart, center
to center. These beams should be underlaid with thick planks,
or even beams, laid close together, parallel with the wall, and for
the entire width of the footing, for the double purpose of providing
the full pressure area needed and also to tie the beams together.
The span of the crossbeams is 56.9 inches or 4.74 feet. The clear
space is 4.74 — .83 or 3.91 feet. The working span is a little more
than this, say even four feet. Then M= (2000X4) X 48 -5-8 or
48,000 inch-pounds. Placing this equal to (Rbh2}-t-6, in which
6=12, then ^ = 4.48 inches. Allowing a little for outside deteriora-
tion, the "planks" should be 5 inches thick.

Using Steel "L-Beams. The method of calculation is the same as
for wood beams, except that, since the strength of I-beams is
more readily computable by reference to tables in the handbooks
published by the manufacturers, such tables will be utilized. The
tables always give the safe load which may be carried on an I-beam
of given dimensions on any one of a series of spans varying by
single feet. If we call W the total load (or upward pressure) to be
resisted by a single cantilever beam, this will be one-fourth of the
load which can safely be carried by a beam of the same size and on a
span equal to the offset.

Example. Solve the previous example on the basis of using steel I-beams.

Solution. The offset is, necessarily, 2.25 feet; at 2,000 pounds per square
foot, the pressure to be carried by the beams is 4,500 pounds for each foot of
length of the wall. By reference to the tables and interpolating, a 6-inch I-beam
weighing 12.25 pounds per linear foot will carry about 34,860 pounds on a 2-
foot 3-inch span. One-fourth of this, or 8,715 pounds, is the load carried by a
cantilever of that length. Therefore, 8,715 -=- 4,500 = 1.936 feet = 23.25
inches, is the required spacing of such beams.

When comparing the cost of this method with the cost of others,
the cost of the masonry-concrete filling must not be overlooked. A
thick layer of concrete should be placed on the leveled subsoil; the

132

MASONRY AND REINFORCED CONCRETE 121

steel should be immediately placed at the proper spacing; then the
spaces between the beams should be filled in with concrete, care
being taken to ram the concrete so thoroughly as to prevent voids.
The concrete should extend up to a level at least two inches above
the beams so as to protect the steel from rusting. In this case the
spacing is 23.25 inches, and the net clear space about 20 inches.
Since the concrete will be deeper than this, we may say, without
numerical calculation, that the arching action of the concrete be-
tween the beams would be ample to withstand the soil pressure.
The spacing of the beams should be neither so wide as to preclude
safe arching action — which is unlikely — nor so narrow as to hinder
thorough tamping of the concrete between them.

Design of Pier Footings. The above designs for footings have
been confined solely to the simplest case of the footing required
for a continuous wall. A column or pier must be supported by a
footing which is offset from the column in all four directions. It is
usually made square. The area is very readily obtained by dividing
the total load by the allowable pressure per square foot on the soil.
The quotient is the required number of square feet in the area of
the footing. If a square footing is permissible — and usually it is
preferable — the square root of that number gives the length of one
side of the footing. Special circumstances frequently require a
rectangular footing or even one of special shape. The problem of
so designing a footing that the center of pressure of the load on a
column shall be vertical over the center of pressure of the subsoil
is solved in detail under "Column Footing", Part III, page 252. A
column placed at the corner of a building which is located at the
extreme corner of the property, and which cannot extend over the
property line, must usually be supported by a compound footing.
The principles involved are discussed in detail, under "Compound
Footings", Part III, page 256.

The determination of the thickness of a footing depends some-
what upon the method used. When the grillage is constructed
of I-beams, as illustrated in Fig. 43, the required strength of each
series of beams is readily computed from the offset of each layer.
If the footing consists of a single block of stone or a plate of concrete,
either plain or reinforced, the thickness must be computed on the
basis of the mechanics of a plate loaded on one side with a uniformly

133

122 MASONRY AND REINFORCED CONCRETE

distributed load and on the other side with a load which is prac-
tically, concentrated in the center. This problem is taken up under
"Simple Footings", Part III, page 249.

Example. A column with a base 3 feet 4 inches square, carrying a total
load of 630,000 pounds, is to be supported on a soil on which the permissible

Fig. 43. Grillage of I-Beams

loading is estimated as three tons per square foot; an I-beam footing is to be
used. Required, the design of the I-beams.

Solution. The required area of the footing is evidently 630,000 -4- 6,000 =
105 square feet. Using a footing similar to that illustrated in Fig. 43, we shall
make the lower layer of the footing, say 10 feet 6 inches by 10 feet wide. The
length of the beams being 126 inches, and the column base being 40 inches

134

MASONRY AND REINFORCED CONCRETE 123

square, the offset from the column is 43 inches, or 3 . 58 feet on each side. Look-
ing at a table of standard I-beams, we find that a 9-inch beam weighing 21
pounds per Linear foot will carry 50,320 pounds on a span of four feet. For a

span of 3.58 feet, the allowable load is |^jj X 50,320, or 56,220 pounds. Tak-

O . do

ing one-fourth of this, as in the example on page 120, we have 14,055 pounds
which may be carried by each beam acting as a cantilever. The upward pressure
of an offset 3.58 feet long and 10 feet wide, at the rate of 6,000 pounds per
square foot, would be 214,800 pounds. Therefore, 15 such beams, each 10 feet
6 inches long, would be required in the lower layer. The upper layer must
consist of beams 10 feet long on which the offset from the pier is 40 inches on
each side. The group of beams under each of these upper offsets- carries an
upward pressure of 6,000 pounds per square foot on an area of 10 feet 6 inches by
3 feet 4 inches; total pressure, 210,000 pounds. The total load on each foot
of width of the upper layer is 63,000 pounds. Looking at the tables, a 15-inch
I -beam weighing 42 pounds per foot can carry a load, on a 10-foot span, of
62,830 pounds. The permissible load on a cantilever of this length would be
one-fourth of this, or 15,700 pounds. The permissible load on a cantilever
3 feet 4 inches long will be in the ratio of 10 feet to 3 feet 4 inches, or, in this
case, exactly three times as much, which would be 47,100 pounds. The total
of 210,000 pounds, divided by 47,100, will show that although five such beams
will have a somewhat excessive strength, four would not be sufficient; therefore
five beams should be used. The lower layer of beams have a flange width of
4.33 inches each. The 15 beams, distributed over a space of 10 feet, or 120
inches, would be about 8 inches apart, leaving 3.67 inches net space between
them, which is sufficient for ramming the concrete. The five upper beams
each have a flange width of 5 . 5 inches, which would use up 27 . 5 inches of the
40 inches width of the column base, leaving 12 . 5 inches for the four spaces, or
3| inches per space, which is again sufficient, although it is about as close as is
desirable. It should not be forgotten that surrounding all these beams in both
layers with concrete adds somewhat to the strength of the whole footing, but
that no allowance is made for this additional strength in computing dimensions.
It merely adds an indefinite amount to the factor of safety.

PILE FOUNDATIONS

Piles. The term pile is generally understood to be a stick of
timber driven in the ground to support a structure. This stick of
timber is generally thought of as the body of a small tree; but timber
in many shapes is used for piling. Sheet piling, for example, is gen-
erally much wider than thick. Cast iron and wrought iron have
also been used for all forms of piling. Structural steel has also been
used for this purpose. Within the last few years, concrete and
reinforced concrete piles have been used quite extensively in place
of wood or cast-iron piles.

135

124 MASONRY AND REINFORCED CONCRETE
TYPES OF PILES

Cast=Iron Piles. Cast-iron piles have been used to some
extent. The advantages claimed for these piles are that they are
not subject to decay; they are more readily driven than wood
piles in stiff clays or stony ground; and they have a greater crushing
strength than wood piles. The latter quality will apply only
when the pile acts as a column. The greatest objection to these
piles is that they are deficient in transverse strength to resist sudden
blows. This objection applies only in handling them before they
are driven, and to those which, after being driven, are exposed to
blows from ice and logs, etc. When driving cast-iron piles, a block
of wood is placed on top of the pile to receive the blow; and, after
being driven, a cap with a socket in its lower side is placed upon
the pile to receive the load. Generally, lugs or flanges are cast on the
sides of the piles, to which bracing may
be attached for fastening them in place.
Screw Piles. This term refers to a
type of metal pile whose use is limited,
but which is apparently very effective
where it has been used. It consists essen-
tially of a steel shaft, 3 to 8 inches in
diameter, strong enough to act as a col-
umn, and also to withstand the twisting
to which it is subjected while the pile
is being sunk, Fig. 44. At the lower
end of the shaft is a helicoidal surface
having a diameter of perhaps five feet.
Such piles can be used only in compara-
tively soft soil, and their use is practi-
cally confined to foundations in sand-
banks on the shore of the ocean. To
sink such piles, they are screwed into
place by turning the vertical shaft with
a long lever. Such a sinking is usually
assisted by a water jet, which will be
described later.

Disk Piles. A variation of the screw pile is the disk pile, Fig.
45, which, as its name implies, has a circular disk in place of a heli-

Fig. 44. Screw Pile

Fig. 45. Disk Pile

136

MASONRY AND REINFORCED CONCRETE 125

coidal surface. Such a pile can be sunk only by use of a water 'jet,
the pile being heavily loaded so that it shall be forced down.

Wood Bearing Piles. Specifications for wood piles generally
require that they shall have a diameter of from 7 to 10 inches at the
smaller end, and 12 to 15 inches at the larger
end. Older specifications were quite rigid in
insisting that the tree trunks should be
straight, and that the piles should be free
from various kinds of minor defects; but the
growing scarcity of timber is modifying the
rigidity of these specifications, provided the
most essential qualifications of strength and
durability are provided for. Timber piles
should have the bark removed before being
driven, unless the piles are to be always under
water. They should be cut square at the
driving end, and pointed at the lower end.
When they are to be driven in hard, gravelly
soil, it is often specified that they shall be
shod with some form of iron shoe. This may
be done by means of two straps of wrought
K ..^^ ^ ...J iron, which are bent

'2WJJ&** i1 over the p°int so as.

to form four bands radiating from the point
of the pile, Fig. 46. By means of holes
through them, these bands are spiked to the
piles. Another method, although it is con-
sidered less effective on account of its liabil-
ity to be displaced during driving, is to use
a cast-iron shoe. These shoes are illustrated
in Fig. 47. It is sometimes specified that
piles shall be driven with the butt end, or
larger end, down, but there seems to be
little if any. justification for such a specifica-
Fig.47. cast-iron Pile-shoe ^^ r^^ resistance to driving is consider-
ably greater, while their ultimate bearing power is but little if any
greater. If the driving of piles is considered from the standpoint of
compacting the soil, as already discussed on page 113, then driving

Fig. 46. wrought-iron

137

126 MASONRY AND REINFORCED CONCRETE

the piles with the small end down will compact the soil more effec-
tively than driving them butt end down.

White pine, spruce, or even hemlock may be used in soft soils;
yellow pine in firmer ones; and oak, elm, beech, etc., in the more
compact soils. The piles are usually driven from 2| to 4 feet apart
each way, center to center, depending on the character of the soil
and the load to be supported. Timber piles, when partly above
and partly under water, will decay very rapidly at the water line.

Fig. 48. Single and Double Sheet Piling

STRINQEK "^

Fig. 49. Triple Sheet Piling for Cofferdams

Fig. 50. Bevel Point for
Sheet Pile

This is owing to the alternation of dryness and wetness. In tidal
waters they are destroyed by the marine worm known as the teredo.

The American Railway Engineering Association recommends
the following specifications for piling:

Piles shall be cut from sound, live trees; shall be close-grained and solid;
free from defects such as injurious ring shakes, large and unsound knots, decay,
or other defects that will materially impair their strength. The taper from butt
to top shall be uniform and free from short bends.

All piles except foundation piles shall be peeled.

Sheet Piling. Ordinary planks, 2 or 3 inches thick, arid wider
than they are thick, are, w:hen driven close together, known as sheet
piling, Fig. 48-a. The leakage between the planks may be greatly

138

MASONRY AND REINFORCED CONCRETE 127

reduced by using a second row of plank, breaking joints with the
first row, as shown in Fig. 48-b. When it is required that the sheet
piling shall form a water-tight wall, such as a cofferdam, three thick-
nesses of plank are generally used with joints as arranged in Fig. 49.
Sheet piling is usually driven in close contact, either to prevent
leakage, to confine puddle in cofferdams, to prevent the materials
of a foundation from spreading, or to guard a foundation from being

Fig. 51. Types of Sheet Steel Piling, (a) Carnegie Steel Company;

(b) Jones and Laughlin; (c) Lacka wanna Steel Company

(Arched Web Section); (d) Lackawanna Steel

Company (Straight Web Section).

undermined by a stream of water. To make wood piles drive
with their sides close against each other, they are cut obliquely at
the bottom, as shown in Fig. 50. They are kept in place, while
being driven, by means of two longitudinal stringers or wales. These
wales are supported by gage piles previously driven, which are sev-
eral feet apart. '

The increased cost of timber and the large percentage of dete-
rioration and destruction during its use for a single cofferdam

139

SECTION a a

128 MASONRY AND REINFORCED CONCRETE

have developed the manufacture of steel sheet piling, which can be
re-drawn and used many times. The forms of steel for sheet piling are
nearly all patented. The cross sections of a few of them are shown
in Fig. 51. One feature of some of the designs is the possible flex-
ibility secured in the outline of
the dam without interfering with
the water-tightness.

Concrete and Reinforced=
Concrete Piles. Concrete and
reinforced-concrete piles may be
classified under two headings : (a)
those where the piles are formed,
hardened, and driven very much
the same as any pile is driven;
(6) those where a hole is made in
the ground, into which concrete
is rammed and left to harden.

Reinforced-concrete piles
which have been formed on the
ground are designed as columns
with vertical reinforcement con-
nected at intervals with horizon-
tal bands. These piles are usually
made round or octagonal in sec-
tion, and a steel or cast-iron point
is used.

Fig. 52-a shows a type of pile
that is commonly used when con-
structed in forms, hardened, and
driven the same as a wood pile.
These piles must be reinforced
with steel so that they can be
handled.

Fig. 52-b shows the general plan of a type of pile that has been
used to some extent along the seashore where piles can be jetted.
They are usually molded in a vertical position and as soon as they
can be handled are jetted in place. These piles are not dependent
on the friction of the surface of the concrete with the sand but can

Fig. 52. Reinforced-Concrete Piles

140

MASONRY AND REINFORCED CONCRETE 129

convey the load direct to the sand under the enlarged end. Piles
of this type have been used for loads of 50 to 60 tons. They cannot
be used in clusters but each pile must be of sufficient size to support
the entire load at any given point.

Raymond Concrete Pile. The
Raymond concrete pile, Fig. 53,
is constructed in place. A col-
lapsible steel pile core is encased
in a thin, closely-fitting, sheet-
steel shell. The core and shell
are driven to the required depth
by means of a pile driver. The
core is so constructed that when
the driving is finished, it is col-
lapsed and withdrawn, leaving
the shell in the ground, which
acts as a mold for the concrete.
When the core is withdrawn, the
shell is filled with concrete, which
is tamped during the filling proc-
ess. These piles are usually 18
to 20 inches in diameter at the
top, and 6 to 8 inches at the
point. When it is desirable, the
pile can be made larger at the
small end. The sheet steel used
for these piles is usually No. 20
gage. When it is desirable to
reinforce these piles, the bars are
inserted in the shell after the
core has been withdrawn and before the concrete is placed.

Simplex Concrete Pile. The different methods for producing
the Simplex pile cover the two general classifications of concrete
piles — namely, those molded in place, and those molded above
ground and driven with a pile driver. Fig. 54 shows the standard
methods of producing the Simplex pile; A shows a cast-iron point
which has been driven and imbedded in the ground, the concrete
deposited, and the form partially withdrawn; while B shows the

Fig. 53. Raymond Concrete Pile

141

130 MASONRY AND REINFORCED CONCRETE

alligator-point driving form. The only difference between the two
forms shown in this figure is that the alligator point is withdrawn
and the cast-iron point remains in the ground. The concrete in
either type is compacted by its own weight. As the form is removed,
the concrete comes in contact with the soil and is bonded with it.
A danger in using this type of pile is that, if a stream of water is

-PULL/US CLPHPS

fTOPOf CONCRETE FlUINlj

CAST IKON POINT DRIVING ran* /t

OPERATION FINISHED riU O

(") (B)

Fig. 54. Standard Simplex Concrete Piles

encountered, the cement may be washed out of the concrete before
it has a chance to set.

A shell pile and a molded and driven pile are also produced by
the same company which manufactures the Simplex, and are recom-
mended for use under certain conditions. Any of these types of
piles can be reinforced with steel. This company has driven piles
20 inches in diameter and 75 feet long.

Steel-Shelled Concrete Piles. In excavating for the foundation
of a 16-story building at 14th Street and 5th Avenue, New York, a
pocket of quicksand was discovered with a depth of about 14 feet

142

MASONRY AND REINFORCED CONCRETE 131

below the bottom of the general excavation. A wall column of the
building to be constructed was located at this point, with its center
only 15 inches from the party line. The estimated load to be sup-
ported by this column was about 500 tons. It was finally decided
to adopt steel piles which would afford the required carrying capacity
in a small, compact cluster, and would transfer the load, as well as
the other foundations, to the solid rock. These piles, 5 in number,
were driven very close to an existing wall and without endangering
it. Each pile was about 15 feet long, and was made with an outer
shell consisting of a steel pipe, f inch thick and 12 inches inside
diameter, filled with Portland-cement concrete, reinforced with
four vertical steel bars, 2 inches in diameter. This gave a total
cross-sectional area of 27.2 square inches of steel, with an allowed
load of 6,000 pounds per square inch, and 100.5 square inches of
concrete on which a unit stress of 500 pounds was allowed. This
utilizes the bearing strength of the external shell, and enables the
concrete filling to be loaded to the maximum permitted by the New
York Building Laws. The tubes and bars have an even bearing on
hard bed rock, to which the former were sunk by the use of a special
air hammer and an inside hydraulic jet. The upper ends of the
steel tubes and reinforcing bars were cut off after the piles were
driven. The work was done with care, and a direct contact was
secured between them and the finished lower surfaces of the cast-
iron caps, without the intervention of steel shims.*

Gushing Pile Foundation. A combination of steel, concrete,
and wood piles is known as the Gushing pile foundation. A cluster
of piles is driven so that it may be surrounded by a wrought-iron
or steel cylinder, which is placed over them, and which is sunk into
the soil until it is below any chance of scouring action on the part
of any current of water. The space between the piles and the
cylinder is then surrounded with concrete. Although the piles are
subject to decay above the water line, yet they are so thoroughly
surrounded with concrete that the decay is probably very slow. The
steel outer casing is likewise subject to deterioration, but the strength
of the whole combination is but little dependent on the steel. If such
foundations are sunk at the ends of the two trusses of a bridge, and
are suitably cross-braced, they form a very inexpensive and yet

*Condensed from Engineering Record.

143

132 MASONRY AND REINFORCED CONCRETE

effective pier for the end of a truss bridge of moderate span. The
end of such a bridge can be connected with the shore bank by means
of light girders, and by this means the cost of a comparatively expen-
sive masonry abutment may be avoided.

CONSTRUCTION FACTORS

Bearing Power of Piles. Pile foundations act in a variable
combination of two methods of support. In one case the piles are
driven into the soil to such a depth that the frictional resistance of
the soil to further penetration of the pile is greater than any load
which will be placed on the pile. As the soil becomes more and more
soft, the frictional resistance furnished by the soil is less and less;
and it then becomes necessary that the pile shall penetrate to a
stratum of much greater density, into which it will penetrate but
little if any. Under such conditions, the structure rests on a series
of columns (the piles) which are supported by the hard subsoil, and
whose action as columns is very greatly assisted by the density of
the very soft soil through which the piles have passed. It prac-
tically makes but little difference which of these methods of support
exists in any particular case. The piles are driven until the resist-
ance furnished by^each pile is as high as is desired. The resistance
against the sinking of a pile depends on such a very large variety
of conditions, that attempts to develop a formula for that resistance,
based on a theoretical computation taking in all these various fac-
tors, are practically useless. There are so many elements of the
total resistance, which are so large and also so very uncertain, that
they entirely overshadow the few elements which can be precisely
calculated. Most formulas for pile driving are based on the general
proposition that the resistance of the pile multiplied by the distance
which it moves during the last blow equals the weight of the hammer
multiplied by the distance through which it falls. Expressing this
algebraically, we have

where R is resistance of pile; s is penetration of pile during last
blow; w is weight of hammer; and h is height of fall of hammer.

Practically, such a formula is considerably modified, owing to
the fact that the resistance of a pile, or its penetration for any blow,

144

MASONRY AND REINFORCED CONCRETE 133

depends considerably on the time which has elapsed since the previous
blow. This practically means that it is far easier to drive the pile
when the blows are delivered very rapidly; and also that when a
pause is made in the driving, for a few minutes or for an hour, the
penetration is very much less (and the apparent resistance very
much greater), on account of the earth settling around the pile during
the interval. The most commonly used formula for pile driving is
known as the Engineering News formula, which, when used for
ordinary hammer-driving, is

This formula is fundamentally the same as the above formula, except
that R is safe load, in pounds; s is penetration per blow in inches;
w is weight of hammer in pounds; and h is height of fall of hammer
in feet.

In the above equation, w is considered a free-falling hammer
(not retarded by hammer rope) striking a pile having a sound head.
If a friction-clutch driver is used, so that the hammer is retarded by
the rope attached to it, the penetration of the pile is commonly
assumed to be just one-half what it would have been had no rope
been attached, that is, had it been free-falling.

Also, the quantity s is arbitrarily increased by 1, to allow for the
influence of the settling of the earth during ordinary hammer pile
driving, and a factor of safety of 6 for safe load has been used. In
spite of the extreme simplicity of this formula compared with that
of others which have attempted to allow for all possible modifying
causes, this formula has been found to give very good results. When
computing the bearing power of a pile, the penetration of the pile
during the last blow is determined by averaging the total penetration
during the last five blows.

The pile-driving specifications adopted by the American Rail-
way Engineering Association, require that:

All piles shall be driven to a firm bearing satisfactory to the Engineer,
or until five blows of a hammer weighing 3,000 pounds, falling 15 feet (or a
hammer and fall producing the same mechanical effect), are required to drive
a pile one-half (J) inch per blow, except in soft bottom, when special instruc-
tions will be given.

145

134 MASONRY AND REINFORCED CONCRETE

This is equivalent to saying (applying the Engineering News
formula) that the piles must have a bearing power of 60,000 pounds.

Examples. 1. The total penetration during the last five blows was
14 inches for a pile driven with a 3,000-pound hammer. During these blows the
average drop of the hammer was 24 feet. How much is the safe load?

2wh 2 X 3,000 X 24 144,000

FTT= a x 14) + 1 =-^s~== 37'895 pounds

2. It is required, if possible, to drive piles with a 3,000-pound hammer
until the indicated resistance is 70,000 pounds. What should be the average
penetration during the last five blows when the fall is 25 feet?

™ nnn _ 2 w h 2 X 3,000 X 25 _ 150,000

70,001 -—p^- s+ i ~TTT

-1 -2.14-1 -l.Hincta

The last problem suggests a possible impracticability, for it
may readily happen that when the pile has been driven to its full
length its indicated resistance is still far less than that desired. In
some cases, such piles would merely be left as they are, and addi-
tional piles would be driven beside them, in the endeavor to obtain
as much total resistance over the whole foundation as is desired.

The above formula applies only to the drop-hammer method of
driving piles, in which a weight of 2,500 to 3,000 pounds is raised
and dropped on the pile.

When the steam pile driver is used, the blows are very rapid,
about 55 to 65 per minute. On account of this rapidity the soil does
not have time to settle between the successive blows, and the pene-
tration of the pile is much more rapid, while of course the resistance
after the driving is finished is just as great as is secured by any other
method. On this account, the above formula is modified so that the
arbitrary quantity added to s is changed from one to 0.1, and the
formula becomes

Methods of Driving Piles. There are three general methods of
driving piles — namely, by using (1) a falling weight; (2) the erosive
action of a water jet; or (3) the force of an explosive. The third
method is not often employed, and will not be further discussed.
In constructing foundations for small highway bridges, well-augers

146

MASONRY AND REINFORCED CONCRETE 135

have been used to bore holes, in which piles are set and the earth
rammed around them.

Drop- Hammer Pile Driver. This method of driving piles con-
sists in raising a hammer made of cast iron, and weighing 2,500
to 3,000 pounds, to a height of 10 to 30 feet, and then allowing it
to fall freely on the head of the pile. The weight is hoisted by
means of a hoisting engine, or sometimes by horses. When an
engine is used for the hoisting, the winding drum is sometimes merely
released, and the weight in falling drags the rope and turns the hoist-
ing drum as it falls. This reduces the effectiveness of the blow, and
lowers the value of s in the formula given, as already mentioned.
To guide the hammer in falling, a frame, consisting of two uprights
called leaders, about 2 feet apart, is erected. The uprights are
usually wood beams, and are from 10 to 60 feet long. Such a
simple method of pile driving, however, has the disadvantage, not
only that the blows are infrequent — not more than 20 or even 10 per
minute — but also that the effectiveness of the blows is reduced on
account of the settling of the earth around the piles between the
successive blows. On this account, a form of pile driver known as
the steam pile driver is much more effective and economical, even
though the initial cost is considerably greater.

Steam- Hammer Pile Driver. The steam pile driver is essen-
tially a hammer which is attached directly to a piston in a steam
cylinder. The hammer weighs about 4,000 pounds, is raised by
steam to the full height of the cylinder, which is about 40 inches,
and is then allowed to fall freely. Although the height of fall is far
less than that of the ordinary pile driver, the weight of the hammer
is about double, and the blows are very rapid (about 50 to 65 per
minute). As before stated, on account of this rapidity, the soil does
not have time to settle between blows, and the penetration of the
pile is much more rapid, while, of course, the ultimate resistance,
after the driving is finished, is just as great as that secured by any
other method.

Driving Piles with Water Jet. When piles are driven in a situ-
ation where a sufficient supply of water is available, their resistance
during driving may be very materially reduced by attaching a pipe
to the side of the pile and forcing water through the pipe by means
of a pump. The water softens and scours out the soil immediately

147

136 MASONRY AND REINFORCED CONCRETE

underneath the pile, and enables the pile to settle in the hole easily.
The water returns to the surface along the sides of the pile and
assists in reducing the frictional resistance. In very soft soils, and
in sand, piles may thus be jetted by merely weighting them with
a few hundred pounds while the force pump is in action. When the
pile is practically down to the depth to which it is to be jetted, it
should be struck a few blows with a light hammer to settle it firmly
in the bottom of the hole. Of course, the only method of testing
such resistance of the pile is by actually loading a considerable
weight upon it. This method of using a water jet is chiefly applica-
ble in structures which are on the banks of streams or large bodies
of water.

Splicing Piles. On account of the comparatively slight resist-
ance offered by piles in swampy places, it sometimes becomes neces-
sary to splice two piles together. The splice is often made by
cutting the ends of the piles perfectly square so as to make a good
butt joint. A hole 2 inches in diameter and 12 inches deep is bored
in each of the butting ends, and a dowel pin 23 inches long is driven
in the hole bored in the first pile; the second pile is then fitted on the
first one. The sides of the piles are then flattened, and four 2- by 4-
inch planks, 4 to 6 feet long, are securely spiked on the flattened
sides of the piles. Such a joint is weak at its best, and the power of
lateral resistance of a joint pile is less than would be expected from a
single stick of equal length. Nevertheless, such an arrangement is
in some cases the only solution.

Pile Caps. One practical trouble in driving piles, especially
those made of soft wood, is that the end of the pile will become
crushed or broomed by the action of the heavy hammer. Unless this
crushed material is trimmed off the head of the pile, the effect of the
hammer is largely lost in striking this cushioned head. This crushed
portion of the top of a pile should always be cut off just before the
test blows are made to determine the resistance of the pile, since
the resistance of a pile indicated by blows upon it, if its end is
broomed, will apparently be far greater than the actual resistance of
the pile.

The steam pile driver does not produce such an amount of
brooming as is caused by the ordinary pile driver and this is another
advantage in its favor. Whenever the hammer bounces off the

148

MASONRY AND REINFORCED CONCRETE 137

head of the pile, it shows either that the fall is too great or that the
pile has already been driven to its limit. Whenever the pile refuses
to penetrate appreciably for each blow, it is useless to drive it any
farther, since added blows can only have the effect of crushing the
pile and rendering it useless. It has frequently been discovered
that piles which have been hammered after they had been driven
to their limit have become broken and crushed, perhaps several
feet underground. In such cases, their supporting power is very
much reduced.

Usually about two inches of the head is chamfered off to prevent
this bruising and splitting in driving the pile. A steel band, 2 to 3
inches wide and \ to 1 inch thick, is often hooped over the head of
the pile to assist in keeping it from splitting. These devices have
led to the use of a cast-iron cap for the protection of the head of the
pile. The cap is made with two tapering recesses, one to fit on the
chamfered head of the pile, while in the other is placed a piece of
hard wood, on which the hammer falls.

Sawing Off the Piles. When the piles have been driven, they
are sawed off to bring the tops of them to the same elevation, that
they may have an even bearing surface. When the tops of the piles
are above water, this sawing is usually done by hand; and when
under water, by machinery. The usual method of cutting piles off
under water is by means of a circular saw on a vertical shaft, which is
supported on a special frame, the saw being operated by the engine
used in driving the piles.

Finishing the Foundations. A pile supports a load coming on
an area of the foundation which is approximately proportional to
the spacing between the piles. This area, of course, is several times
the area of the top of the pile. It is therefore necessary to cap at
least a group of the piles with a platform or grillage which not only
will support any portion of the load located between the piles, but
which also will tend to prevent a concentration of load on one pile.
When the heads of the piles are above water, a layer of concrete is
usually placed over them, the concrete resting on the ground between
the piles, as well as on the piles themselves. It is necessary to use a
thick plate of concrete, so that a concentrated load will be distributed
over a number of piles, Fig. 55. A concrete grillage is usually
laid with its lower surface 8 to 12 inches below the tops of the piles.

149

138 MASONRY AND REINFORCED CONCRETE

The piles are thus firmly anchored together at their tops. When
reinforced-concrete structures are supported on piles or other con-
centrated points of support, the heads of the piles are usually con-
nected by reinforced-concrete beams, which will be described in
Part III. Sometimes a platform of heavy timbers is constructed
on top of the piles, to assist in distributing the load; and in this case
the concrete is placed on the platform, as shown in Fig. 56.

When the heads of the piles are under water, it is always neces-
sary to construct a grillage of heavy timber and float it into place,
unless a cofferdam is constructed and the water pumped out, in
which case the foundation can be completed as already described.
The timbers used to cap the piles in constructing a grillage are usually

fc&ff A ^3? i £ <? ; *v£' ^ 'V ^ ' :-
'^fei

. is ^ />."

Fig. 55. Concrete Foundation on Wood Piles Fig. 56. Timber Foundation on Wood Piles

about 12 by 12 inches, and are fastened to the head of each pile by a
driftbolt — a plain bar of steel. A hole is bored in the cap and into
the head of the pile, in which the driftbolt is driven. The section of
the driftbolt is always larger than the hole into which it is to be
driven; that is, if a 1-inch round driftbolt is to be used, a f-inch
auger would be used to bore the hole. The transverse timbers of
the grillage are driftbolted to the caps.

Advantage of Concrete and Reinforced=Concrete Piles. A re-
inforced-concrete pile foundation does not materially differ in con-
struction from a timber pile foundation. The piles are driven and
capped, in the usual manner, with concrete ready for the super-
structure. In comparing this type of piles with timber piles, they
have the advantage of being equally durable in a wet or dry soil,

150

MASONRY AND REINFORCED CONCRETE 139

and the disadvantage of being more expensive in first cost. Some-
times their use will effect a saving in the total cost of the foundation
by obviating the necessity of cutting the piles off below the water
line. The depth of the excavation and the volume of masonry may
be greatly reduced, as shown in Fig. 57. In this figure is shown a
comparison of the relative amount of excavation which would be
necessary, and also of the concrete which would be required for the
piles, thus indicating the economy which is possible in the items of
excavation and concrete. There is also shown a possible economy
in the number of piles required, since concrete piles can readily be

SURFACED

Fig. 57. Comparison of Wood and Concrete Piles

made of any desired diameter, while there is a practical limitation to
the diameter of wood piles. Therefore a less number of concrete
piles will furnish the same resistance as a larger number of wood
piles. In Fig. 57 it is assumed that the three concrete piles not only
take the place of the four wood piles in the width of the foundation,
but there will also be a corresponding reduction in the number of
piles in a direction perpendicular to the section shown. The extent
of these advantages depends very greatly on the level of the ground-
water^ line. When this level is considerably below the surface of
the ground, the excavation and the amount of concrete required, in
order that the timber grillage and the 'tops of the piles shall be

151

140 MASONRY AND REINFORCED CONCRETE

always below the water line, will be correspondingly great, and the
possible economy of concrete piles will also be correspondingly
great.

The pile and cap being of the same material, they readily bond
together and form a monolithic structure. The capping should be
thoroughly reinforced with steel. Reinforced-concrete piles can be
driven in almost any soil that a timber pile can penetrate, and they
are driven in the same manner as the timber piles. A combination
of the hammer and water jet has been found to be the most success-
ful manner of driving them. The
hammer should be heavy and
drop a short distance writh rapid
blows, rather than a light ham-
mer dropping a greater distance.
For protection while being driven,
a hollow cast-iron cap filled with
sand is placed on the head of the
pile. The cap shown in Fig. 58
has been used successfully in
driving concrete piles. A ham-
mer weighing 2,500 pounds wras
dropped 25 feet, 20 to 30 times
per minute, without injury to the
head.

Loading for Piles. The spac-
ing for wood piles is generally 30
inches on centers. The loading
of wood piles, with 12-inch
butts, driven through wet, loose
soil to a good bearing, is taken usually at 10 to 12 tons per pile.
When driven through a firm soil the loading may be increased to
15 to 20 tons. Under the same conditions of soil, concrete piles
1C inches in diameter at the top and tapering to 8 or 10 inches at
the bottom support loads of 25 to 30 tons.

Cost. In comparing the cost of timber piles and concrete or
reinforced-concrete piles, the former are found to be much cheaper
per linear foot than the latter. As already stated, however, there
are many cases where the economy of the concrete pile as compared

*~e' JET PIPE

EL £ VA TION 3EC T10N

Fig. 58. Cushion Head for Driving Piles

152

MASONRY AND REINFORCED CONCRETE 141

with the wood pile is worth considering. In general, the require-
ments of the work to be done should be carefully noted before the
type of pile is selected.

The cost of wood piles varies, depending on the size and length
of the piles, and on the section of the country in which the piles are
bought. Usually piles can be bought of lumber dealers at 10 to
20 cents per linear foot for all ordinary lengths; but very long piles
will cost more. The cost of driving piles is variable, ranging from
2 or 3 cents to 12 or 15 cents per linear foot. A great many piles
have been driven for wrhich the contract price ranged from 20 cents
to 30 cents per linear foot of pile driven. The length of the pile
driven is the full length of the pile left in the work after cutting it
off at the level desired for the cap.

The contract price for concrete piles about 16 inches in diameter
and 25 to 30 feet long is approximately $1.00 per linear foot. When
a price of $1 .00 per linear foot is given for a pile of this size and length,
the price will generally be somewhat reduced for a longer pile of the
same diameter. Concrete piles have been driven for 70 cents per
linear foot, and perhaps less; and again, they have cost much more
than the approximate price of $1.00 per linear foot.

Piles for the Charles River Dam. The first piles driven for the
Cambridge, Massachusetts, conduit of the Charles River dam were
on the Cambridge shore. On January 1, 1907, 9,969 piles had been
driven in the Boston and Cambridge cofferdams, amounting to
297,000 linear feet. Under the lock, the average length of the piles,
after being cut off, was 29 feet; and under the sluices, 31 feet 4 inches.
The specifications called for piles to be winter-cut from straight, live
trees, not less than 10 inches in diameter at the butt when cut off in
the work, and not less than 6 inches in diameter at the small end.
The safe load assumed for the lock foundations was 12 tons per pile,
and for the sluices 7 tons per pile.

The Engineering News formula was used in determining the
bearing power of the piles. The piles under the lock wralls were
driven ^ery close together; and, as a result, many of them rose dur-
ing the driving of adjacent piles, and it was necessary to re-drive
these piles.*

*From Engineering-Contracting.

153

142 MASONRY AND REINFORCED CONCRETE

Pile Foundation for Sea Wall at Annapolis. The piles for
constructing the new sea wall, Fig. 59, at Annapolis, Maryland,
ranged in length from 70 to 110 feet. On the outer end of the
breakwater, piles 70 to 85 feet were used. These piles were in one
length, single sticks. Toward the inner end of the breakwater,
lengths of 100 to 110 feet were required. Single sticks of this
length could not be secured, and it was therefore necessary to resort
to splicing. After a trial of several methods, it was found that a
splice made by means of a 10-inch wrought-iron pipe was most

satisfactory. When the top
of the first pile had been
driven to within three feet
of the water, it was trimmed
down to 10 inches in diam-
eter. On this end was
placed a piece of 10-inch
wrought-iron pipe 10 inches
long. The lower end of the
top pile was trimmed the
same as the top of the first
pile, and, when raised by
the leads, was fitted into
the pipe and driven until
the required penetration

was reached. The piles were cut off 4| feet below the surface of
the water, by a circular saw mounted on a vertical shaft.*

COFFERDAMS, CRIBS, AND CAISSONS
Cofferdams. Foundations are frequently constructed through
shallow bodies of water by means of cofferdams. These are essen-
tially walls of clay confined between wood frames, the walls being
sufficiently impervious to water so that all water and mud within
the walled space may be pumped out and the soil excavated to the
desired depth. It is seldom expected that a cofferdam can be con-
structed which will be so impervious to water that no pumping will
be required to keep it clear; but when a cofferdam can be kept clear
with a moderate amount of pumping, the advantages are so great

*Proceedings of the Engineers' Club of Philadelphia, Vol. XXIII, No. 3.

Fig. 59. Section of New Sea Wall, Annapolis, Maryland

154

MASONRY AND REINFORCED CONCRETE 143

that its use becomes advisable. A dry cofferdam is most easily
obtained when there is a firm soil, preferably of clay, at a moderate
depth, say 5 to 10 feet, into which sheet piling may be driven.
The sheet piles are driven as closely together as possible. The
bottom of each pile, when made of wood, is beveled so as to form a
wedge which tends to force it against the pile previously driven,
Fig. 50. In this way a fairly tight joint between adjacent piles
is obtained. Larger piles, a, Fig. 60, made of squared timber, are
first driven to act as guide piles.
These are connected by waling
strips, b, Fig. 60, which are bolted
to the guide piles and which serve
as guides for the sheet piling, c,
Fig. 60. The space between the
two rows of sheet piling is filled
with puddle, which ordinarily con-
sists chiefly of clay. It is found
that if the puddling material con-
tains some gravel, there is less
danger that a serious leak will
form and enlarge. Numerous cross
braces or tie-rods, d, Fig. 60, must
be used to prevent the walls of
sheet piling from spreading when
the puddle is being packed between
them. The width of the puddle
wall is usually made to vary
between three feet and ten feet,
depending upon the depth of the
water. When the sheet piling
obtains a firm footing in the subsoil, it is comparatively easy to
make the cofferdam water-tight; but when the soil is very porous
so that^tfee water soaks up from under the lower edge of the coffer-
dam, or when, on the other hand, the cofferdam is to be placed on
a bare ledge of rock, or when the rock has only a thin layer of soil
over it, it becomes exceedingly difficult to obtain a water-tight joint
at the bottom of the dam. Excessive leakage is sometimes reduced
by a layer of canvas or tarpaulin which is placed around the outside

Fig. 60. Plan and Cross Section of
Cofferdam

155

144 MASONRY AND REINFORCED CONCRETE

of the base of the cofferdam, and which is held in place by stones
laid on top of it. Brush, straw, and similar fibrous materials are
used in connection with earth for stopping the cracks on the outside
of the dam, and are usually effective, provided they are not washed
away by a swift current.

Although cofferdams can readily be used at depths of 10 feet,
and have been used in some cases at considerably greater depth,
the difficulty of preventing leakage, on account of the great water
pressure at the greater depths, usually renders some other method
preferable when the depth is much, if any, greater than 10 feet.

Cribs. A crib is essentially a framework (called a bird-cage by
the English) which is made of timber, and which is filled with stone
to weight it down. Such a construction is used only when the
entire timber work will be perpetually under water. The timber
framework must, of course, be so designed that it will safely support
the entire weight of the structure placed upon it. The use of such a
crib necessarily implies that the subsoil on which the crib is to rest
is sufficiently dense and firm to withstand the pressure of the crib
and its load without perceptible yielding. It is also necessary for
the subsoil to be leveled off so that the crib itself shall be not only
level but also shall be so uniformly supported that it is not sub-
jected to transverse stresses which might cripple it. This is some-
times done by dredging the site until the subsoil is level and suffi-
ciently firm. Some of this dredging may be avoided through leveling
up low spots by depositing loose stones which will imbed themselves
in the soil and furnish a fairly firm subsoil. Although such methods
may be tolerated when the maximum unit loading is not great —
as for a breakwater or a wharf — it is seldom that a satisfactory
foundation can be thus obtained for heavy bridge piers and similar
structures.

Caissons. Open Type. A caisson is literally a box; and an open
caisson is virtually a huge box which is built on shore and launched
in very much the same way as a vessel, and which is sunk on tlje site
of the proposed pier, Fig. 61. The box is made somewhat larger
than the proposed pier, which is started on the bottom of the box.
The sinking of the box is usually accomplished by the building of
the pier inside of the box, the weight of the pier lowering it until it
reaches the bed prepared for it on the subsoil. The preparation of

156

MASONRY AND REINFORCED CONCRETE 145

this bed involves the same difficulties and the same objections as
those already referred to in the adoption of cribs. The bottom of
the box is essentially a large platform made of heavy timbers and
planking. The sides of the caissons have sometimes been made so
that they are merely tied to the bottom by means of numerous tie-
rods extending from the top down to the extended platform at the
bottom, where they are hooked into large iron rings. When the pier
is complete above the water line so that the caisson is no longer
needed, the tie-rods may be loosened by unscrewing nuts at the top.

Fig. 61. Section of Open Caisson

The rods may then be unhooked, and nearly all the timber in the
sides of the caisson will be loosened and may be recovered.

Hollow-Crib Type. The foundation for a pier is sometimes
made in the form of a box with walls several feet in thickness, but
with a large opening or well through the center. Such piers may be
sunk in situations where there is a soft soil of considerable depth
through which the pier must pass before it can reach the firm sub-
soil. In such a case, the crib or caisson, which is usually made of
timber, may be built on shore and towed to the site of the proposed
pier. The^masonry work may be immediately started; and as the
pier sinks into the mud, the masonry work is added so that it is
always considerably above the water line, Fig. 62. The deeper the
pier sinks, the greater will be the resistance of the subsoil, until,
finally, the weight of the uncompleted pier is of itself insufficient to
cause it to sink further. At this stage, or even earlier, dredging
may be commenced by means of a clam-shell or orange-peel dredging

157

146 MASONRY AND REINFORCED CONCRETE

OPEN

WELL

OPEN
WELL

Fig. 62. Hollow Crib Material

bucket, through the interior
well. The removal of the
earth from the center of the
subsoil on which the pier is
resting will cause the mud
and soft soil to flow toward
the center, where it is within
reach of the dredge. The
pressure of the pier accom-
plishes this. The deeper the
pier sinks, the greater is its
weight and the greater its
pressure on the subsoil,
although this is somewhat
counteracted by the con-
stantly increasing friction
of the soil around the out-
side of the pier. Finally,
the pier will reach such a
depth, and the subsoil will
be so firm, that even the
pressure of the pier is not
sufficient to force any more
loose soil toward the central
well. The interior well may
then be filled solidly with
concrete, and thus the entire
area of the base of the pier
is resting on the subsoil,
and the unit pressure is
probably reduced to a safe
figure for the subsoil at that
depth.

This principle was adopt-
ed in the Hawkesbury bridge
in Australia, which was sunk
to a depth of 185 feet below
high water- a depth which

158

MASONRY AND REINFORCED CONCRETE 147

would have been impracticable for the pneumatic caisson method
described later. In this case, the caissons were made of iron, ellip-
tical in shape, and about 48 feet by 20 feet. There were three tubes
8 feet in diameter through each caisson. At the bottom, these
tubes flared out in bell-shaped extensions which formed sharp cutting
edges with the outside line of the caisson. These bell-mouthed
extensions thus forced the soil toward the center of the wells until
the material was within reach of the dredging buckets.

This method of dredging through an opening is very readily
applicable to the sinking of a comparatively small iron cylinder. As
it sinks, new sections of the cylinder can be added ; while the dredge,
working through the cylinder, readily removes the earth until the
subsoil becomes so firm that the dredge will not readily excavate it.
Under such conditions the subsoil is firm enough for a foundation,
and it is then only necessary to fill the cylinder with concrete to
obtain a solid pier on a good and firm foundation.

One practical difficulty which applies to all of these methods of
sinking cribs and caissons is the fact that the action of a heavy
current in a river, or the meeting of some large obstruction, such as
a boulder or large sunken log, may deflect the pier somewhat out of
its intended position. When such a deflection takes place, it is
difficult, if not impossible, to force the pier back to its intended
position. It therefore becomes necessary to make the pier some-
what larger than the strict requirements of the superstructure would
demand, in order that the superstructure may have its intended
alignment, even though the pier is six inches or even a foot out
of its intended position.

Pneumatic Type. A pneumatic caisson is essentially a large
inverted box on which a pier is built, and inside of which work may
be done because the water is forced out of the box by compressed
air. If an inverted tumbler is forced down into a bowl of water,
the large airspace within the tumbler gives some idea of the possi-
bilities of working within the caisson. If the tumbler is forced to
the bottom of the bowl, the possibilities of working on a river bottom
are somewhat exemplified. It is, of course, necessary to have a
means of communication between this working chamber and the
surface; and it is likewise necessary to have an air lock through
which workmen and perhaps materials may pass.

159

148 MASONRY AND REINFORCED CONCRETE

The process of sinking resembles, in many points, that described
for the previous type. The caisson is built on shore, is launched,
and is towed to its position. Sometimes, for the sake of economy,
provided timber is cheap, that portion of the pier from the top of
the working chamber to within a few feet below the low-water line
may be built as a timber crib and filled with loose stone or gravel
merely to weight it down. This method is usually cheaper than
masonry; and the timber, being always under water, is durable. As
in the previous instance, the caisson sinks as the material is removed

-SAND
PIPES

ftlR
LOCK

TRUSSES

Fig. 63. Outline of Pneumatic Caisson

from the base, the sinking being assisted by the additional weight
on the top. The only essential difference between the two processes
consists in the method of removing the material from under the
caisson. The greatest depth to which such a caisson has ever been
sunk is about 110 feet below the water line. This depth was reached
in sinking one of the piers for the St. Louis bridge. At such depths
the air pressure per square inch is about 48 pounds, which is between
three and four times the normal atmospheric pressure. Elaborate
precautions are necessary to prevent leakage of air at such a pressure.
Only men with strong constitutions and in perfect health can work

160

MASONRY AND REINFORCED CONCRETE 149

in such an air pressure, and even then four hours' work per day, in
two shifts of two hours each, is considered a good day's work at these
depths. The workmen are liable to a form of paralysis which is
called caisson disease, and which, especially in those of weak con-
stitution or intemperate habits, will result in partial or permanent
disablement and even death.

In Fig. 63 is shown an outline, with but few details, of the
pneumatic caisson used for a large bridge over the Missouri River
near Blair, Nebraska. The caisson was constructed entirely of
timber, which was framed in a fashion somewhat similar to that
shown in greater detail in Fig. 62. The soil was very soft, consisting
chiefly of sand and mud, which was raised to the surface by the
operation of mud pumps that would force a stream of liquid mud
and sand through the smaller pipes, which are shown passing through
the pier. The larger pipes near each side of the pier were kept
closed during the process of sinking the caisson and were opened
only after the pier had been sunk to the bottom and the working
chamber was being filled with concrete, as described below. These
extra openings facilitated the fill-
ing of the working chamber with
concrete. Near the center of the
pier is an air lock with the shafts
extending down to the working
chamber and up to the surface.
The structure of the caisson was
considerably stiffened by the use
of three trusses in order to resist
any tendency of the caisson to
collapse.

Fig. 64. Combination of Pneumatic Caisson
and Open-Well Methods

A caisson ^necessarily constructed in a very rigid manner, the
timbers being generally 12- by 12-inch and laid crosswise in alternate
layers, which are thoroughly interlocked. An irregularity in the
settling may often be counteracted by increasing the rate of excava-
tion under one side or the other of the caisson, so that the caisson
will be guided in its descent in that direction.

A great economy in the operation of the compressed-air locks is
afforded by combining the pneumatic process with the open-well
process, already described, by maintaining a pit in the center of the

161

150 MASONRY AND REINFORCED CONCRETE

caisson. A draft tube which is as low as the cutting edge of the
caisson prevents a blow-out of air into the central well. The mate-
rial dug by the workmen in the caisson is thrown loosely into the
central well or sump, from which it is promptly raised by the dredg-
ing machinery, Fig. 64. By the adoption of this plan, the air lock
needs to be used only for the entrance and exit of the workmen to
and from the working chamber.

When the caisson has sunk to a satisfactory subsoil, and the
bottom has been satisfactorily cleaned and leveled off, the working
chamber is at once filled with concrete. As soon as sufficient con-
crete has been placed to seal the chamber effectively against the
entrance of water, the air locks may be removed, and then the com-
pletion of the filling of the chamber and of the central shaft is merely
open-air work.

RETAINING WALLS

A retaining wall is a wall built to sustain the lateral pressure of
earth. The pressure that will be exerted on the wall will depend
on the kind of material to be supported, the manner of placing it,
and the amount of moisture that it contains. Earth and most
other granular masses possess some frictional stability. Loose soil
or a hydraulic pressure will exert a full pressure; but a compacted
earth, such as clay, may exert only a small pressure due to the
cohesion in the materials. This cohesion cannot be depended upon
to relieve the pressure against a wall, for the cohesion may be
destroyed by vibration due to moving loads or to saturation. In
designing a wall the pressure due to a granular mass or a semifluid
without cohesion must always be considered.

Causes of Failure of Walls. There are three ways in which
a masonry wall may fail: (1) by sliding along a horizontal plane;
(2) by overturning or rotating; (3) by crushing of the masonry or
its footing. These are the three points that must be considered in
order to design a wall that will be successful in resisting an embank-
ment. A wall, therefore, must be of sufficient size and weight to
prevent the occurrence of sliding, rotation, or crushing.

Stability of Wall Against Sliding. Stability against sliding is
secured by making the structure of sufficient weight so that there
will be no danger of a movement at the base. In Fig. 65 let E be
the horizontal pressure and W the weight of all materials above the

162

MASONRY AND REINFORCED CONCRETE 151

joint. A movement will occur when E equals fW, where/ is the coeffi-
cient of friction. Let n be a number greater than unity, the factor
of safety, then in order that there be no movement n must be suffi-
ciently large so that nE equals fW. A common value for n is 2,
but sometimes it is taken as low as \\. Substituting 2 for n,

(6)

Average values of the coefficients of friction of masonry on
masonry is 0.65; for masonry on dry clay, 0.50; for masonry on wet
clay, 0.33; masonry on gravel, 0.60; masonry on wood, 0.50.

Stability Against Rotation. The stability against rotation of a
wall is secured by making the wall of such dimension and weight
that the resultant R of the external forces
will pass through the base and well within
the base, as shown in Fig. 65. Generally,
in designing, the resultant is made to come
within or at the edge of the middle third.
The nearer the center of the base the
resultant comes, the more evenly the pres-
sure will be distributed over the foundation
for the wall. When R passes through A,
Fig. 65, the wall will fail by rotation. Meth-
ods for finding R will be demonstrated in
another paragraph.

Stability Against Crushing. The compressive unit stresses in
walls must not be^greater than the unit stresses permitted for safe
working loads of masonry (see pages 13, 54, Part I), when the wall is
built on a stone foundation; but when it is built on clay, sand, or gravel
the allowable pressure for such foundations must not be exceeded.

Foundations. The foundations for a retaining wall must be
below the frost line, which is about three feet below the surface in
a temperate climate, and deeper in a cold climate. The foundation
should be of such a character that it will safely support the wall.
If necessary, the soil should be tested to determine if it will safely
support the wall.

The foundation should always be well drained. Many failures
of walls have occurred owing to the lack of drainage. Water behind

Fig. 65. Section of Retain-
ing Wall

163

152 MASONRY AND REINFORCED CONCRETE

a wall greatly increases the stresses in the wall. When water freezes
behind a wall it usually causes it to bulge out, which is the first step
in the failure of the wall. On a clay foundation the friction is greatly
reduced by the clay becoming thoroughly soaked with water. On
page 151 it is shown that the difference of the coefficients of friction
of masonry on dry clay and wet clay is 0.17. There are different
ways of draining a fill behind a retaining wall. The method shown
in Fig. 38 for drainage often can be used. Pipes two to four inches
in diameter are often built in the wall, as shown in Fig. 65.

DESIGN OF WALL

In designing a retaining wall the dimensions of the section of a
wall are generally assumed and then the section investigated graph-
ically to see if it is right for the conditions assumed. There are
theoretical formulas for designing walls which will be given. In
designing a wall, the student is advised to first make the section
according to the formulas and investigate it graphically.

Fill Behind Wall. The fills behind the walls are sometimes
made horizontal with the top of the wall; at other times the fill
is sloped back from the top of the wall, as shown in Fig. 65. When
there is a "slope to be supported, the wall is said to be surcharged,
and the load to be supported is greater than for a horizontal fill.

Faces of Wall. The front or face of retaining walls is usually
built with a batter. This batter often varies from less than an inch
per foot in height to more than an inch per foot. The rear face may
be built either straight, with a batter, or stepped up. A wall should
never be less than 2| feet to 3 feet in width on top, unless the wall
is a very small one. In that case, probably a width of 12 to 18
inches would be sufficient for the top.

Width of Base. The following values for the width of the
base of a wall are taken from Trautwine's Handbook, and are based
on the fill behind the wall being placed loosely, as is usually the
case.

Wall of cut stone or of first-class large-ranged rubble, in mortar

.35 of its entire vertical height
Wall of good common mortar rubble or brick

.4 of its entire vertical height
Wall of well-laid dry rubble

.5 of its entire vertical height

164

MASONRY AND REINFORCED CONCRETE 153

In recent years concrete has come into extensive use in building
retaining walls. A wall built of a 1:3:6 concrete should be equal in
strength to a wall built of cut stone or large-ranged rubble. In heavy
walls large stones, twenty-five to fifty per cent in volume, are often
placed in the concrete. This, usually, greatly reduces the cost of
the wall and does not weaken the wall if the stones are properly placed.

Value of Study of Existing Walls. When designing a retaining
wall, all existing walls in that vicinity should be examined to deter-
mine their dimensions and to discover if they have been successfully
designed. Often, existing walls will give more information to an
engineer than he will obtain by a theoretical or graphical study.

Pressure Behind Wall. The development of the formulas for
finding the pressure behind a wall is a long, complicated theory, and
the demonstration will not be given here. The formulas given are
those usually found in textbooks. They are based on the Rankine
theory, which considers that the earth is a granular mass with an
assumed angle of repose of 1.5 to 1, which in degrees is 33° 42'.
In applying this method it is immaterial whether the forces repre-
senting the earth pressure are considered as acting directly upon
the back of the wall, or are considered as acting on a vertical plane
passing through the extreme back of the footing. In the latter
case, the force representing the lateral earth pressure must be
combined with (1) the vertical force representing the weight of the
earth prism between the back of the] wall and the vertical plane
considered; and (2) .combined with the vertical force representing
the weight of the wall itself.

In the formulas for determining pressures behind a wall let E
equal total pressure against rear face of wall on a unit length of
wall; W equal weight of a unit volume of the earth; h equal height
of wall; and <$> equal angle of repose.

When the upper surface of the earth is horizontal, the equation is

(7)

Since the angle of repose for the earth behind the wall has been
taken as 33° 42', Equation (7) may be reduced to the following form
by substituting the value of the tangent of the angle in the equation

£=.286^ <7a)

165

154 MASONRY AND REINFORCED CONCRETE

When a wall must sustain a surcharge at the slope of 1.5 to 1, the
equation is

E = %cos<f>Wh2 (7b)

£ = .833^! (7c)

The force E is applied at one-third the height of the wall, meas-
ured from the bottom, but for surcharged wall it is applied at one-
third of the height of a plane that passes just behind the wall. This
is clearly shown in the different figures illustrating retaining walls.

The direction of the center of pressure E is assumed as being
parallel to the top of the earth back of the wall. The angle of the
surcharge is generally made 1.5 to 1.

Fig. 66. Diagrams Showing Pressures on Foundations

Example. What is the pressure per foot of length of a wall 18 feet high,
earth weighing 100 pounds per cubic foot, if the fill is level with the top of the
wall.

Solution. Substituting in equation (7a),
WhJ

E = .286

= .286

100 X 182

= 4633 pounds

Pressure on Foundation. The formulas for determining the
pressure on the foundation, recommended to the American Railway

166

MASONRY AND REINFORCED CONCRETE 155

Engineering Association by a committee appointed by that Society
to investigate the subject of retaining walls, are as follows, see
Fig. 66:

NOTE: When P equals the vertical component of the resultant pressure
on the base, B is the full width of the base in feet, and Q is the distance from
the toe to where the force P cuts the base.

When Q is equal to or greater than —

Pressure at the toe

Pressure at the heel= (6Q-25) ^

When Q is less than —
o

Pressure at the toe = — (7f )

Example. Design a retaining
wall to support an embankment 20 feet
high, the top of the fill being level with
the top of the wall; the face of the wall
to be vertical, the back to slope.

Solution. Draw an outline of the
proposed section, Fig. 67, and then
investigate the section to see if it has
sufficient strength to suppott^the em-
bankment. Make the base .45 of the
height of the wall.

Width of base = 20 feet X .45
= 9.0 feet

Assume the width at the top at 3
feet, and find the pressure E at the 6330
back, substituting in equation (7a), and ,-/

apply that pressure at — .

«* Fig. 67. Design Diagram for Retain-

ing Wall

9-i

fng'wa

E =

Wh2

2
100 X 20Z

= .286

= 5,720

P is found by dividing the wall into a rectangle and a triangle and finding
the weights and the center of gravity of each, and also that of the triangle of

167

156 MASONRY AND REINFORCED CONCRETE

earth back of the wall, and then finding the combined weights and the center
of gravity of the wall and earth. Assume that the weight of the masonry is
140 pounds per foot and the earth 100 pounds per cubic foot, and consider
the section of wall as being one foot in length. The center of gravity of the
wall may be obtained thus:

SECTION

AREA

MOMENT

(Arm)

MOMENT

(Area)

AEC D

60.0

1.5

90.0

EEC

60.0

5.0

300.0

120.0

390.0

Distance from A to center of gravity = 390 -^ 120 = 3.25 feet

Weight of wall per lineal foot = 120 X 140 = 16,800 pounds

.'. Static moment about A = 16,800 X 3.25 = 54,600 foot-pounds

Center of gravity of the earth is at one-third of the distance from the back of the
triangle, or 7 . 0 feet from the face of the wall.

Weight of earth per lineal foot, 6 *20 X 100

6,000 pounds

/. Static moment about A = 6,000 X 7 = 42,000 foot-pounds

The position of the resultant is determined by dividing the sum of the static
moments by the sum of the weights:

54,600 + 42,000
16,800 + 6,000

96,600
22,800

4. 24 feet

Produce the line E to meet the vertical line passing through the combined
center of gravity. On this vertical line lay off the value of P, which is 22,800,
to any convenient scale. At the lower end of P draw a line parallel to line E
and on this line lay off the value of E, which is 5,720. Draw line a b, which
is the resultant of the two forces. This line cuts the base at a scaled distance
of 2 . 6 feet from the toe, which is a point without the middle third of the base,

therefore, Q is less than — .
o

Substituting in equation (7f ) for the condition when Q is less than — we have

Pressure at toe =

2 X 22,800
3 X 2.6

6,330 pounds

Lay off A d, at any convenient scale, equal to 6,330 pounds and on the base
lay off a distance equal to 3Q = 7.8 feet. Through this point draw de and scale
the force shown from e to the base line, which is 1,000 pounds.

The examination of this section of wall shows that the pressure of the toe
is not excessive for an ordinary foundation, such as clay. At the heel there is
an uplift of 1,000 pounds. This 'uplift would be overcome by the friction of
the materials in the fill. This section would probably support an embankment

MASONRY AND REINFORCED CONCRETE 157

20 feet high, although the resultant does not come in the middle third of the
base. The weight of the material in this problem was taken as 140 pounds
per cubic foot. This is the weight of 1:3:6 concrete. If closely laid stone
were used, the weight of the masonry
per cubic foot would be increased to
160 pounds at least. This increased
weight would bring the resultant within
the middle third.

The wall will next be investigated
for stability against sliding on its base.
Suppose that the wall is to be built
on dry clay. The horizontal thrust E
is 5,720 pounds, the total weight is
22,800 pounds, and the coefficient of
friction of masonry on dry clay is .50.

Substituting in equation (6),

22,800 = —

11,400 = 11,440 Kg gg Retaining Wall with Curved

The approximate equality of the equa-
tion shows that there is a factor of two

against sliding on such a base. On a base of wet clay the factor against sliding
would be less than one and a quarter and it would be necessary to secure the wall
against sliding in some way.

Types of Walls. In Fig. 68 is shown a type of wall that has
sometimes been used. The tendency to slide outward at the bot-
tom, and even the tend-
ency to overturn, is resisted
by making the lower course
with the joints inclined
towards the rear. This
method of construction
makes the joints nearer
perpendicular to the line of
pressure than in a vertical
wall. The weakness of
this type of wall is that
water running down the
face of it will enter the

Retaining Wall for Railroad Embankment

joints and produce an additional pressure to that of the earth.
There is also the danger of this water freezing behind the wall and
causing the wall to bulge out.

169

158 MASONRY AND REINFORCED CONCRETE

A type of wall often used in railroad work is shown in Fig. 69.
It should be noted that the width of the base is nearly one-half the
height but that this width is only carried up a short distance. The
back is stepped, therefore it receives the assistance of the maximum
vertical pressure of the earth on the horizontal steps. The wall
is anchored to the foundation by a projection below the base of
the wall.

BRIDGE PIERS AND ABUTMENTS
PIERS

Location. The outline design of a long bridge which requires
several spans involves many considerations:

(1) If the river is navigable, at least one deep and wide channel
must be left for navigation. The placing of piers, the clear height
of the spans above high water, and the general plans of all bridges
over navigable rivers are subject to the approval of the United
States Government.

(2) A long bridge always requires a solution of the general
question of few piers and long spans, or more piers and shorter spans.
No ge'neral solution of the question is possible, since it depends on the
required clear height of the spans above the water, on the required
depth below the water for a suitable foundation, and on several other
conditions (such as swift current, etc.) which would influence the
relative cost of additional piers or longer spans. Each case must be
decided according to its particular circumstances.

(3) Even the general location of the line of the bridge is often
determined by a careful comparison, not only of several plans for
a given crossing, but even a comparison of the plans for several
locations.

Sizes and Shapes. The requirements for the bridge seats for
the ends of the two spans resting on a pier are usually such that a
pier with a top as large as thus required, and with a proper batter
to the faces, will have all the strength necessary for the external
forces acting on the pier. For example, the channel pier of one of
the large railroad bridges crossing the Mississippi River was capped
by a course of stonework 14 feet wide and 29, feet long, besides two
semicircles with a radius- of 7 feet. The footing of this pier was
30 feet wide by 70 feet long, and the total height from subsoil to

170

o s

O g

^ cS

MASONRY AND REINFORCED CONCRETE 159

top was about 170 feet. This pier, of course, was unusually large.
For trusses of shorter span, the bridge seats are correspondingly
smaller. The elements which affect stability are so easily computed
that it is always proper, as a matter of precaution, to test every pier
designed to fulfil the other usual requirements, to see whether it is
certainly safe against certain possible methods of failure. This is
especially true when the piers are unusually high.

The requirements for supporting the truss are, fortunately, just
such as give the pier the most favorable formation so that it offers
the least obstruction to the flow of the current in the river. In other
words, since the normal condition is for a bridge to cross a river at
right angles, the bridge piers are always comparatively long, in the
direction of the river, and narrow in a direction perpendicular to the
flow of the current. The rectangular shape, however, is modified
by making both the upper and the lower ends pointed. The pointing
of the upper end serves the double purpose of deflecting the current,
and thus offers less resistance to the flow of the water; and it also
deflects the floating ice and timber, so that there is less danger of the
formation of a jam during a freshet. The lower end should also be
pointed in order to reduce the resistance to the flow of the water
The ends of the piers are sometimes made semicircular, but a better
plan is to make them in the form of two arcs of circles which intersect
at a point.

Causes of Failure. The forces tending to cause a bridge pier
to fait in a direction perpendicular to the line of the bridge include
the action of wind on the pier itself, on the trusses, and on a train
which may be crossing the bridge. They will also include the max-
imum possible effect of floating ice in the river and of the current
due to a freshet. It is not at all improbable that all of these causes
may combine to act together simultaneously. The least favorable
condition for resisting such an effect is that produced by the weight
of the bridge, together with that of a train of empty cars, and the
weight of the masonry of the pier above any j.oint whose stability
is in question. The effects of wind, ice, and current will tend to
make the masonry slide on the horizontal joints. They will also
increase the pressure on the subsoil on the downstream end of the
foundation of a pier. They will tend to crush the masonry on the
downstream side, causing the pier to tip over.

171

1GO MASONRY AND REINFORCED CONCRETE

Another possible eause of failure of a bridge pier arises from
forces parallel with the length of the bridge. The stress produced
on a bridge by the sudden stoppage of a train thereon, combined
with a wind pressure parallel with the length of the bridge, will tend
to cause the pier to fail in that direction, Fig. 70. Although these
forces are never so great as the other external forces, yet the resisting
power of the pier in this direction is so very much less than that in
the other direction, that the factor of safety against failure is prob-
ably less, even if there is no actual danger under any reasonable

values for these external forces.

Abutment Piers. A pier is
usually built comparatively thin
in the direction of the line of the
bridge, because the f >rces tending
to produce overturning in that
direction are usually very small.
When a series of stone arches are
placed on piers, the thrusts of the
two arches on each side of a
pier nearly balance each other, and
it is only necessary for the pier to
be sufficiently rigid to withstand
the effect of an eccentric loading on
the arches; but if, by any accident
or failure, one arch is destroyed,
the thrust on such a pier is unbalanced and the pier will probably
be overturned by the unbalanced thrust of the adjoining arch.
The failure of that arch would similarly cause the failure of the
succeeding pier and arch. On this account a very long series of
arches usually includes an abutment pier for every fourth or fifth
pier. An abutment pier is one which has sufficient thickness to
withstand the thrust of an arch, even though it is not balanced
by the thrust of an arch on the other side of the pier. Abutment
piers are chiefly for arch bridges; but all piers should have sufficient
rigidity in the direction of the line of the bridge so that any possible
thrust which may come from the action of a truss of the bridge may
be resisted, even if there is no counterbalancing thrust from an
adjoining truss.

Fig. 70. Bridge Pier

172

MASONRY AND REINFORCED CONCRETE 161

ABUTMENTS

Requirements of Design. The term abutment usually implies
not only a support for the bridge, but also what is virtually a retain-
ing wall for the bank behind it. In the case of an arch bridge, the
thrust of the arch is invariably
so great that there is never
any chance that the pressure of
the earth behind the abutment
will throw the abutment over,
and therefore the abutment
never needs to be designed as
a retaining wall in this case;
but when the abutment sup-
ports a truss bridge which
does not transmit any horizontal

Fig.

Typical Abutmen

Wing Walls

with Flaring

thrust through the bridge, the
abutment must be designed as a retaining wall. The conditions
of stability for such structures have already been discussed. This
principle of the retaining wall
is especially applicable\ if the
abutment consists of a perfectly
straight wall. There are other
forms of abutments which tend
to prevent failure as a retaining
wall, on account of their design.
Abutments with Flaring
Wing Walls. These are con-
structed substantially as shown
in Fig. 71. The wing walls
make an angle of about 30° to
45° with the face of the abut-
ment, and the height decreases
at such a rate that it will just
catch the embankment formed

Fig. 72. U-Shaped Abutment

behind it, the slopes of the em-
bankment probably being at the rate of 1.5 : 1. If the bonding of
the wing walls, and especially the bonding at the junction of the
wing walls with the face of the abutment, are properly done, the

173

102 MASONRY AND REINFORCED CONCRETE

wing walls will act virtually as counterforts and will materially
assist in resisting the overturning tendency of the earth. The
assistance given by these wing walls will be much greater as the
angle between the wing walls and the face becomes larger.

U=Shaped Abutments. These consist of a head wall and two
wralls which run back perpendicular to the head wall, Fig. 72.
This form of wall is occasionally used, but the occasions are rare
when such a shape is necessary or desirable.

T=Shaped Abutments. As the name implies, these consist of
a head wall which has a core wall extending perpendicularly back
from the center. The core wall serves to tie the head wall and
prevent its overturning. Of course such an effect can be produced
only by the adoption of great care in the construction of the wall, so
that the bonding is very perfect and so that the wall has very con-
siderable tensile strength ; otherwise the core wall could not resist
the overturning tendency of the earth pressure against the rear
face of the abutment.

CULVERTS

The term culvert is usually applied to a small waterway which
passes under an embankment of a railroad or a highway. The term
is confined to waterways which are so small that standard plans are
prepared which depend only on the assumed area of waterway that
is required. Although the term is sometimes applied to arches
having a span of 10 or 15 feet, or even more, the fact that the struc-
tures are built according to standard plans justifies the use of the
term culvert as distinguished from a structure crossing some peren-
nial stream where a special design for the location is made. The
term culvert, therefore, includes the drainage openings which may be
needed to drain the hollow on one side of an embankment, even
though the culvert is normally dry.

Types of Culverts. Culverts are variously made of cast iron,
wrought iron, and tile pipe, wood, stone blocks with large cover
plates of stone slabs, stone arches, and plain and reinforced con-
crete; still another variety is made by building two side walls of
stone and making a cover plate of old rails.

Culverts made of wood should be considered as temporary, on
account of the inevitable decay of the wood in the course of a few

174

MASONRY AND REINFORCED CONCRETE 163

years. When wood is used, the area of the opening should be made
much larger than that actually required, so that a more permanent
culvert of sufficient size may be constructed inside of the wood
culvert before it has decayed. For present purposes, the discussion
of the subject of Culverts will be limited to those built of stone and
concrete.

Stone Box Culverts. The choice of stone as a material for cul-
verts should depend on the possibility of obtaining a good quality
of building stone in the immediate neighborhood. Frequently
temporary trestles are used when good stone is unobtainable, with
the idea that after the railroad is completed, it will be possible to
transport a suitable quality of building stone from a distance and
build the culvert under the trestle. The engineer should avoid the
mistake of using a poor quality of building stone for the construction
of even a culvert, simply because such a stone is readily obtainable.
Since a culvert always implies a stream of water which will have a
scouring action during floods, it is essential that the side walls of
culverts should have an ample foundation, which is sunk to such a
depth that there is no danger that it will be undermined. There are
cases where a bed of quicksand has been encountered, and where the
cost of excavating to a firmer soil would be very large. In such a
case, it is generally possible to obtain a sufficient foundation by con-
structing a platform or grillage of timber, which underlies the entire
culvert, beneath the floor of the culvert. Of course, timber should
not be used for the foundation, except in cases where it will always be,
underneath the level of the ground water and will therefore always
be wet. If the soil has a character such that it will be easily scoured,
the floor of the culvert between the side walls should be paved with
large pebbles, so as to protect it from scouring action. At both ends
of the culvert, there should always be built a vertical wall, which
should run from the floor of the culvert down to a depth that will
certainly be below any possible scouring influence, in order that
the side walls and the flooring of the culvert cannot possibly be
undermined.

The above specifications apply to all forms of stone culverts, and
even to arch culverts, and in the cases of the larger arch cul-
verts the precautions in these respects should be correspondingly
observed. When stone culverts are built with vertical side walls

175

164 MASONRY AND REINFORCED CONCRETE

which are from 2 to 4 feet apart, they are sometimes capped with
large flagstones covering the span between the walls. The thickness
of the cover stone is sometimes determined by an assumption as to
the transverse strength of the stone, and by applying the ordinary
theory of flexure. The application of this theory depends on the
assumption that the neutral axis for a rectangular section is at the
center of depth of the stone, and that the modulus of elasticity for
tension and compression is the same. Although these assumptions
are practically true for steel and even wood, they are far from being
true for stone. It is therefore improper to apply the theory of
flexure to stone slabs, except on the basis of moduli of rupture which
have been experimentally determined from specimens having sub-
stantially the same thickness as the thickness proposed. Also, on
account of the variability of the actual strength of stones, though
nominally of the same quality, a very large factor of safety over
the supposed ultimate strength of the stone should be used.

The maximum moment at the center of a slab one foot wide
equals J Wl, in which W equals the total load on the width of one foot
of the slab, and I equals the span of the slab, in feet; but by the prin-
ciples of mechanics, this moment equals g R A2, in which R equals the
modulus of transverse strength, in pounds per square foot; and h
equals the thickness of the stone, in feet. Placing these two expres-
sions equal to each other, and solving for h, we find :

(8)

h =

Example. Assume that a culvert is covered with 6 feet of earth weigh-
ing 100 pounds per cubie foot. Assume a live load on top of the embankment
equivalent to 500 pounds per square foot, in addition; or that the total load
on top of the slab is equivalent to 1,100 pounds per square foot of slab. Assume
that the slab is to have a span I of 4 feet. Then the total load W on a, section
of the slab one foot wide will be 1,100 X 4 or 4,400 pounds. Assume that
the stone is sandstone with an average ultimate modulus of 525 pounds per
per square inch (see Table XVI), and that the safe value R is 55 pounds per
square inch, or 144 X 55 pounds per square foot. Substituting these values
in the above equation for h, we find that h equals 1.29 feet, or 15.5 inches.

The above problem has been worked out on the basis of the live
load which would be found on a railroad. For highways, this could

176

MASONRY AND REINFORCED CONCRETE 165

be correspondingly decreased. It should be noted that in the above
formula the thickness of the stone h varies as the square root of the
span ; therefore, for a span of 3 feet (other things being the same as

I 3

above), the thickness of the stone h equals 15.5 X\l — or 13.4 inches.

\ 4

For a span of 2 feet, the thickness should be 15.5 X \l — °r H-0 inches.

* 4

Owing to the uncertainty of the true transverse strength of
building stone, as has already been discussed in the design of offsets
for footings (see pages 117, 118), no precise calculation is possible;
and therefore many box culverts are made according to empirical

fi/l/V Of HEAD WALLS

HIM

1 1

Fig. 73. Detail Dhgrams for a Double Box Culvert

rules, which dictate that the thickness shall be 10 inches for a 2-foot
span, 13 inches for a 3-foot span, and 15 inches for a 4-foot span.
These values are slightly less than those computed above.

Although a good quality of granite, and especially of bluestone
flagging, will stand higher transverse stresses than those given above
for sandstone, the rough rules just quoted are more often used, and
are, of course, safer. When it is desired to test the safety of stone
already cut into slabs of a given thickness, their strength may be
computed from Equation (8) , using the values for transverse stresses
as already given in Table XVI.

Double Box Culverts. A box culvert with a stone top is gen-
erally limited by practice to a soan of 4 feet, although it would, of

177

166 MASONRY AND REINFORCED CONCRETE

course, be possible to obtain thicker stones which would safely
carry the load over a considerably greater span. Therefore, when
the required culvert area demands a greater width of opening than 4
feet, and when this type of culvert is to be used, the culvert may be
made as illustrated in Fig. 73, by constructing an intermediate wall
which supports the ends of the two sets of cover stones forming the
top. A section and elevation of a double box culvert of 3 feet span
and a net height of 3 feet is shown in Fig. 73. The details of the
wing walls and end walls are also shown. The double box culvert
illustrated in Fig. 74 has two spans, each of 4 feet. The stone used

Fig. 74. Double Box Culvert. Openings 4 by 3 Feet

was a good quality of limestone. The cover stones were made 15
inches thick.

Box culverts are sometimes constructed as dry masonry — that is,
without the use of mortar. This should never be done, except for
very small culverts and when the stones are so large and regular that
they form close, solid walls with comparatively small joints. A dry
wall made up of irregular stones cannot withstand the thrusts which
are usually exerted by the subsequent expansion of the earth embank-
ment above it.

Plain Concrete Culverts.^ Culverts may be made of plain con-
crete, either in the box form or of an arched type, and having very

178

MASONRY AND REINFORCED CONCRETE 167

much the same general dimen-
sions as those already given
for stone box culverts. They
have a great advantage over
stone culverts in that they are
essentially monoliths. If the
side walls and top are formed
in one single operation, the
joint between the side walls
and top becomes a source of
additional strength, and the
culverts are therefore much
better than similar culverts
made of stone. The formula
developed above, Equation (8),
for the thickness of the con-
crete slab on top of a bos cul-
vert may be used, together
with the modulus of trans-
verse strength as given for
concrete in Table XVI. This
formula will apply, even
though the slab for the cover
of the culvert is laid after the
side walls are built, and the
slab is considered as merely
resting on the side walls. If
the side walls and top are
constructed in one operation
so that the whole structure is
actually a monolith, it may be
considered that there is that
much additional strength in the
structure; but it would hardly
be wise to reduce the thickness
of the concrete slab by depend-
ing upon the continuity be-
tween the top and the sides.

Fig. 75, Stone Arch Culvert. See Fig. 76 for
Photographic View

179

168 MASONRY AND REINFORCED CONCRETE

Arch Culverts. Stone arches are frequently used for culverts
in cases where the span is not great, and in which the design of the
culvert, except for some small details regarding the wing walls,
depends only on the span of the culvert. The design of some arch
culverts used on the Atchison, Topeka & Santa Fe Railway, Figs. 73
arid 75, is copied from a paper presented to the American Society of
Civil Engineers by A. G. Allan, Assoc. M. Am. Soc. C. E. The
span of these arches is 14 feet, and the thickness at the crown is 18
inches. A photograph of one of these arch culverts, which shows
also many other details, is reproduced in Fig. 76.

Fig. 76. Double Arch Culvert. Openings, 14 by 51A Feet

End Walls. The ends of a culvert are usually expanded into
end walls for the retention of the embankment. For the larger
culverts, this may develop into two wing walls which act as retaining
walls to prevent the embankment from falling over into the bed of the
stream. An end wall is especially necessary on the upstream end of
the culvert, so as to avoid the danger that the stream will scour the
bank and wrork its way behind the culvert walls. The end wall is
also carried up above the height of the top of the culvert, in order to
guard still further against the washing of earth from the embank-
ment over the end of the culvert into the stream below. All of these
details are illustrated in the figures shown.

180

MASONRY AND REINFORCED CONCRETE 169

CONCRETE WALKS

Drainage of Foundations. The excavation should be made to
a sufficient depth, so as to get below the frost line. The ground
should be tamped thoroughly, and the excavation filled with cin-
ders, broken stone, gravel, or brickbat, to within four inches (or
whatever thickness of slab is to be used) of the top of the grade. The
foundation should be thoroughly rammed, and by using gravel or
cinders to make this foundation, a very firm surface can be secured.

Side drains should be put in at convenient intervals where
outlets can be secured. The foundation is sometimes omitted, even
in cold climates, if the soil is porous. Walks laid on the natural soils
have proven, in many cases, to be very satisfactory.

At the Convention of the National Cement Users' Association,
held at Buffalo, New York, in 1908, the Committee on Sidewalks,
Streets, and Floors presented the following specifications for side-
walk foundations :

The ground base shall be made as solid and permanent as possible. Where
excavations or fills are made, afll wood or other materials which will decompose
shall be removed, and replaced Vith earth or other filling like the rest of the
foundation. Fills of clay or other material which will settle after heavy rains
or deep frost should be tamped, and laid in layers not more than six inches
in thickness, so as to insure a solid embankment which will remain firm after
the walk is laid. Embankments should not be less than 2| feet wider than the
walk which is to be laid. When porous materials, such as coal ashes, gran-
ulated slag, or gravel, are used, underdrains of tile should be laid to the curb
drains or gutters, so as to prevent water accumulating and freezing under the
walk and breaking the block.

Concrete Base. The concrete for the base of walks is usually
composed of 1 part Portland cement, 3 parts sand, and 5 parts stone
or gravel. Sometimes, however, a richer mix-
ture is used, consisting of 1 part cement, 2 parts
sand, and 4 parts broken stone; but this mix-
ture seems to be richer than what is generally
required. The concrete should be thoroughly
mixed and rammed, Fig. 77, and cut into uni-
form blocks. The size of the broken stone or
gravel should not be larger than one inch, varv-

f . . , * II • • If £ ^

ing in size down to [f inch, and free from fine
screenings or soft stone, All stone or gravel under \ inch is con-
sidered sand,

181

170 MASONRY AND REINFORCED CONCRETE

The thickness of the concrete base will depend upon the loca-
tion, the amount of travel, or the danger of being broken by frost.
The usual thickness in residence districts is 3 inches, with a wearing
thickness of 1 inch, making a total of 4 inches, Fig. 78. In business
sections, the walks vary from 4 to 6 inches in total thickness, in
which the finishing coat should not be less than 1 J inches thick. The
concrete base is cut into uniform blocks.

The lines and grades given for walks by the Engineer should be
carefully followed. The mold strips should be firmly blocked and
kept perfectly straight to the height of the grade given. The walks
usually are laid with a slope of \ inch to the foot toward the curb.

The blocks are usually from 4 to 6 feet square, but sometimes
they are made much larger than these dimensions. The joints made

S CINDERS, (fRf( VEL OK BKOKEH SrM

Fig. 78. Concrete Sidewalk and Curb

by cutting the concrete should be filled with dry sand, and the exact
location of these joints should be marked on the forms. The cleaver
or spud that is used in making the joints. should not be less than g
of an inch or over \ of an inch in thickness.

Top Surface. The wearing surface usually consists of 1 part
Portland cement and 2 parts crushed stone or good, coarse sand — all
of which will pass through a |-inch mesh screen — thoroughly mixed
so that a uniform color will be secured. This mixture is then spread
over the concrete base to a thickness of one inch, this being done
before the concrete of the base has set or become covered with dust.
The mortar is leveled off with a straightedge, and smoothed down
with a float or trowel after the surface water has been absorbed.
The exact time at which the surface should be floated depends upon
the setting of the cement, and must be determined by the workmen ;
but the final floating is not usually performed until the mortar has

182

MASONRY AND REINFORCED CONCRETE 171

been in place from two to five hours and is partially set. This final
floating is done first with a wood float, and afterwards with a
metal float or trowel. The top
surface is then cut directly over
the cuts made in the base, care
being taken to cut entirely through
the top and base all around each
block. The joint is then finished
with a jointer, Fig. 79, and all
edges rounded or beveled. Care
should be taken, in the final float-
ing or finishing, not to overdo it,
as too much working will draw
the cement to the surface, leaving
a thin layer of neat cement, which
is likely to peel off. Just before the floating, a very thin layer of
dryer, consisting of dry cehjent and sand mixed in the proportion
of one to one, or even richer, is frequently spread over the surface;

Fig. 79. Jointers

Fig. 80. Brass Dot Roller

Fig. 81.

ra->3 Line Roller

but this is generally undesirable, as it tends to make a glossy walk.
A dot roller or line roller, Figs. 80 and 81, may be employed to
relieve the smoothness.

At the meeting of the National Cement Users' Association

183

172 MASONRY AND REINFORCED CONCRETE

already referred to, the Committee on Sidewalks, Floors, and Streets
recommended the following specifications for the top coat:

Throe parts high-grade Portland cement and five parts clean, sharp sand,
mixed dry and screened through a No. 4 sieve. In the top coat, the amount
of water used should be just enough so that the surface of the walk can be tamped,
struck off, floated, and finished within 20 minutes after it is spread on the bot-
tom coat; and when finished, it should be solid and not quaky.

In the January, 1907, number of Cement, Mr. Albert Moyer,
Assoc. M. Am. Soc. C. E., in discussing the subject of cement side-
walk pavements, gives specifications for monolithic slab for paving
purposes. For an example of this construction, he gives the pave-
ment around the Astor Hotel, New York:

As an alternative, and instead of using a top coat, make one slab of selected
aggregates for base and wearing surface, filling in between the frames concrete
flush with established grade. Concrete to be of selected aggregates, all of which
will pass through a f-inch mesh sieve; hard, tough stones or pebbles, graded
in size; proportions to be 1 part cement, 2£ parts crushed hard stone screenings
or coarse sand, all passing a J-inch mesh, and all collected on a j-inch mesh.
Tamped to an even surface, prove surface with straightedge, smooth down
with float or trowel, and in addition a natural finish can be obtained by scrub-
bing with a wire brush and water while concrete is "green", but after final set.

Seasoning. The wearing surface must be protected from the
rays of the sun by a covering which is raised a few inches above the
pavement so as not to come in contact with the surface. After the
pavement has set hard, sprinkle freely two or three times a day for a
week or more.

Cost. The cost of concrete sidewalks is variable. The con-
struction at each location usually requires only a few days' work;
and the time and expense of transporting the men, tools, and mate-
rials make an important item. One of the skilled workmen should
be in charge of the men, so that the expense of a foreman will not be
necessary. The amount of walk laid per day is limited by the
amount of surface that can be floated and troweled in a day. If the
surfacers do not work overtime, it will be necessary to stop concret-
ing in the middle of the afternoon, so that the last concrete placed
will be in condition to finish during the regular working hours. The
work of concreting may be continued considerably later in the after-
noon if a drier concrete is used in mixing the top coat, and only
enough water is used so that the surface can be floated and finished

184

MASONRY AND REINFORCED CONCRETE

173

soon after being placed. The men who have been mixing, placing,
and ramming concrete can complete their day's work by preparing
and ramming the foundations for the next day's work.

The contract price for a well-constructed sidewalk 4 to 5 inches
in thickness, with a granolithic finish, will vary from 15 cents to 30
cents per square foot.

CONCRETE CURB

The curb is usually built just in advance of the sidewalk. The
foundation is prepared similarly to that of walks. The curb is
divided into lengths similar to
that of the walk; and the joints
between the blocks, and also
between the wralk and the curb,
are made similar to the joints
between the blocks of the walk.
The concrete is generally com-
posed of 1 part Portland cement,
3 parts sand, and 5 parts stone,
although a richer mixture is
sometimes used. A facing of mortar or granolithic finish on the part
exposed to wear will improve the wearing qualities of the curb.

Types of Curbing. There are two general types of curb used —
a curb rectangular in section, and a combined curb and gutter; both
types are shown in Fig. 82. The foundation for either type is con-
structed in the same manner. Both these types of curb are made
in place or molded and set in place like stone curb, but the former
method is preferable. A metal corner is sometimes laid in the
exposed edge of the curb to protect it from wrear.

Construction. The construction of the rectangular section is a
simple process, but requires care to secure a good job. This is
usually about 7 inches wide and from 20 to 30 inches deep. After
the foundation has been properly prepared, the forms are set in place.
Fig. 83 shows the section of a curb 7 inches wide and 24 inches deep,
and the forms as they are often used. The forms for the front and
back each consist of three planks 1| inches thick and 8 inches wide,
and are surfaced on the side next the concrete. They are held in
place at the bottom by the two 2- by 4-inch stakes, and at the top the

Fig. 82. Typical Curb Sections

185

174 MASONRY AND REINFORCED CONCRETE

stakes are kept from spreading by a clamp. A sheet-iron plate
1 inch thick is inserted every 6 feet, or at whatever distance the
joints are made. After the concrete has
been placed and rammed, and has set hard
enough to support itself, the plate and front
forms are removed, and the surface and top
are finished smooth with a trowel, and with
other tools such as shown in Figs. 84, 85,
and 86. The joint is usually plastered
over, and acts as an expansion joint. The
forms on the back are not removed until

Fig. 83. Forms for Construct-
ing Curb

Fig. 84. Curb Edger

the concrete is well set. If a mortar or granolithic finish is used, a
piece of sheet iron is placed in the form one inch from the facing, and
mortar is placed between the sheet iron and the front form, and the
coarser concrete is placed back of the sheet iron, Fig. 87. The sheet
iron is then withdrawn and the two concretes thoroughly tamped.

Fig. 87 shows the section of a combined curb and gutter, and
the forms that are necessary for its construction. This combination
is often laid on a porous soil without any special foundation, with fair

186

MASONRY AND REINFORCED CONCRETE 175

results. A IJ-inch plank 12 inches wide is used for the back form,
and is held in place at the bottom by pegs. The front form consists
of a plank 1| by 6 inches, and is held in place by pegs. Before the
concrete is placed, two sheet-iron plates, cut as shown in the figure,
are placed in the forms, six feet to eight feet apart. After the con-
crete for the gutter and the lower part of the curb is placed and
rammed, a If -inch plank is placed against these plates and held in
place by screw clamps, Fig. 87. The upper part of the curb is then
molded. When the concrete is set enough to stay in place, the front
forms and plates are removed, and the surface is treated in the same
manner as described for the other type of curb.

Fig. 87. Forma for Curb and Gutter

Cost. The cost of concrete curb will depend upon the condi-
tions under which it is made. Under ordinary circumstances, the
contract price for rectangular curbing 6 inches wide and 24 inches
deep will be about 60 cents per linear foot; or 80 cents per linear foot
for curb 8 inches wide and 24 inches deep. Under favorable condi-
tions on large jobs, 6-inch curbing can be constructed for 40 cents or
45 cents per linear foot. These prices include the excavation that is
required below the street grade.

The cost of the combined curb and gutter is about 10 to 20 per
cent more than that of the rectangular curbing. In addition to hav-
ing a larger surface to finish, the combined curb and gutter requires
more material, and therefore more work, to construct it.

187

«1

MASONRY AND REINFORCED
CONCRETE

PART III

REINFORCED CONCRETE BEAM DESIGN

GENERAL THEORY OF FLEXURE

Introduction. The theory of flexure in reinforced concrete is
exceptionally complicated. A multitude of simple rules, formulas,
and tables for designing reinforced-concrete work have been pro-
posed, some of which are sufficiently accurate and applicable under
certain conditions. But the effect of these various conditions should
be thoroughly understood. Reinforced concrete should not be
designed by "rule-of-thumb" engineers. It is hardly too strong a
statement to say that a man is criminally careless and negligent
when he attempts to design a structure, on which the safety and
lives of people will depend, without thoroughly understanding the
theory on which any formula he may use is based. The applica-
bility of all formulas is so dependent on the quality of both the steel
and the concrete, as well as on many of the details of the design,
that a blind application of a formula is very unsafe. Although the
greatest pains will be taken to make the following demonstration as
clear and plain as possible, it will be necessary to employ symbols,
and to work out several algebraic formulas on which the rules for
designing will be based. The full significance of many of the follow-
ing terms may not be fully understood until several subsequent
paragraphs have been studied:

SYMBOLS DEFINED
6 = Breadth of concrete beam

d = Depth from compression face to center of gravity of the steel
A = Area of the steel

p = Ratio of area of steel to area of concrete above the center of gravity
of the steel, generally referred to as percentage of reinforcement,

A
= bd

189

178 MASONRY AND REINFORCED CONCRETE

Ea = Modulus of elasticity of steel

Ec = Initial modulus of elasticity of concrete

n = -rr- = Patio of the moduli

s = Tensile stress per unit of area in steel

c = Compressive stress per unit of area in concrete at the outer fiber of

the beam

€s = Deformation per unit of length in the steel
fc = Deformation per unit of length in outer fiber of concrete
A; = Ratio of dimension from neutral axis to center of compressive stresses

to the total effective depth d
j = Ratio of dimension from steel to center of compressive stresses to

the total effective depth d

x = Distance from compressive face to center of compressing stresses
S X = Summation of horizontal compressive stresses
M = Resisting moment of a section

Statics of Plain Homogeneous Beams. As a preliminary to the
theory of the use of reinforced concrete in beams, a very brief dis-
cussion will be given of the statics of an ordinary homogeneous

beam, made of a material
whose moduli of elasticity in
tension and compression are
equal. Let AB, Fig. 88,

T represent a beam carrying a

T * uniformly distributed load

Fig. 88. Diagram of Beam Carrying Uniformly JF • then the beam is Sub-

Distributed Load

jected to transverse stresses.

Let us imagine that one-half of the beam is a "free body" in space
and is acted on by exactly the same external forces; let us also
assume forces C and T (acting on the exposed section), which are
just such forces as are required to keep that half of the beam in
equilibrium. These forces and their direction are represented in
the lower diagram by arrows. The load W is represented by the
series of small, equal, and equally spaced vertical arrows pointing
downward. The reaction of the abutment against the beam is an
upward force, shown at the left. The forces acting on a section at
the center are the equivalent of the two equal forces C and T.

The force C, acting at the top of the section, must act toward
the left, and there is therefore compression in that part of the sec-
tion. Similarly, the force T is a force acting toward the right, and
the fibers of the lower part of the beam are in tension. For our
present purpose we may consider that the forces C and T are in each

190

MASONRY AND REINFORCED CONCRETE 179

Fig. 89. Diagram Showing Posi-
tion of Neutral Axis in Beam

case the resultant of the forces acting on a very large number of
"fibers". The stress in the outer fibers is, of course, greatest. At
the center of the height, there is neither tension nor compression.
This is called the neutral axis, Fig. 89.

Let us consider for simplicity a very
narrow portion of the beam, having the
full length and depth but so narrow that
it includes only one set of fibers, one
above the other, as shown in Fig. 90.
In the case of a plain rectangular ho-
mogeneous beam, the elasticity being
assumed equal for tension and compression, the stresses in the fibers
would be as given in Fig. 89; the neutral axis would be at the center
of the height, and the stress \t the bottom and the top would be
equal but opposite. If the section were at the center of the beam,
with a uniformly distributed load, as indicated in Fig. 88, the shear
would be zero.

A beam may be constructed of plain concrete; but its strength
will be very small, since the tensile strength of concrete is compara-
tively insignificant. Reinforced concrete utilizes the great tensile
strength of steel in combination with the compressive strength of
concrete. It should be realized that two of the most essential
qualities are compression and tension, and that, other things being
equal, the cheapest method of obtaining the necessary compression
and tension is the most economical.

Economy of Concrete for Compression. The ultimate com-
pressive strength of concrete is generally 2,000 pounds, or over, per
square inch. With a factor of safety of 4, a
working stress of 500 pounds per square inch
may be considered allowable. We may esti-
mate that the concrete costs 20 cents per
cubic foot, or $5.40 per cubic yard. On the
other hand, we may estimate that the steel,
placed in the work, costs about 3 cents per
pound.

foot; therefore, the steel costs $14.40 per cubic
foot, or 72 times as much as an equal volume of concrete or an equal
cross section per unit of length. But the steel can safely withstand a

It will weigh 480 pounds per cubic Fig-^:g PoM^vt^t^

191

180 MASONRY AND REINFORCED CONCRETE

compressive stress of 16,000 pounds per square inch, which is 32
times the safe working load on concrete. Since, however, a given
volume of steel costs 72 times an equal volume of concrete, the cost
of a given compressive resistance in steel is ] |, or 2.25, times the cost
of that resistance in concrete. Of course, the above assumed unit
prices of concrete and steel will vary with circumstances. The
advantage of concrete over steel for compression may be somewhat
greater or less than the ratio given above, but the advantage is almost
invariably with the concrete. There are many other advantages
which will be discussed later.

Economy of Steel for Tension. The ultimate tensile strength
of ordinary concrete is rarely more than 200 pounds per square inch.
With a factor of safety of 4, this would allow a working stress of only
50 pounds per square inch. This is gen-
erally too small for practical use and cer-
tainly too small for economical use. On
the other hand, steel may be used with a
working stress of 16,000 pounds per square
inch, which is 320 times that allowable
for concrete. Using the same unit values
for the cost of steel and concrete as given
in the previous paragraph, even if steel
costs 72 times as much as an equal vol-
ume of concrete, its real tensile value economically is V/? or
4.44, times as great. Any reasonable variation from the above unit
values cannot alter the essential truths of the economy of steel for
tension and of concrete for compression. In a reinforced-concrete
beam, the steel is placed in the tension side of the beam. Usually
it is placed 1 to 2 inches from the outer face, with the double purpose
of protecting the steel from corrosion or fire, and also to better insure
the union of the concrete and the steel. But the concrete below
the steel is not considered in the numerical calculations. The con-
crete between the steel and the neutral axis performs the very
necessary function of transmitting the tension in the steel to the
concrete. This stress is called shear and is discussed on page 207.
Although the concrete in the lower part of the beam is, theoretically,
subject to the tension of transverse stress and does actually con-
tribute its share of the tension when the stresses in the beam are

Fig. 91. Diagram Showing Tran

mission of Tension in Steel lo

Concrete

192

MASONRY AND REINFORCED CONCRETE 181

small, the proportion of the necessary tension which the concrete
can furnish when the beam is heavily loaded is so very small that it is
usually ignored, especially since such a policy is on the side of safety,
and also since it greatly simplifies the theoretical calculations and
yet makes very little difference in the final result. We may, there-
fore, consider that in a unit section of the beam, Fig. 91, the con-
crete above the neutral axis is subject to compression, and that the
tension is furnished entirely by the steel.

Elasticity of Concrete in Compression. In computing the trans-
verse stresses in a wood beam or steel I-beam, it is assumed that
the modulus of elasticity is uniform for all stresses within the elastic
limit. Experimental tests have shown this to be so nearly true
that it is accepted as a mechanical law. This means that if a force
of 1,000 pounds is required to stretch a bar .001 of an inch, it will
require 2,000 pounds to stretch it, .002 of an inch. Similar tests
have been made with concrete, to determine the law of its elasticity.
Unfortunately, concrete is not so uniform in its behavior as steel.
The results of tests are somewhat erratic. Many engineers have
argued that the elasticity is so nearly uniform that it may be con-
sidered to be such within the limits of practical use. But all experi-
menters, who have tested concrete by measuring the proportional
compression produced by various pressures, agree that the addi-
tional shortening produced by an additional pressure is greater at
higher pressures than at low pressures.

A test of this sort may be made substantially as follows: A
square or circular column of concrete at least one foot long is placed
in a testing machine. A very delicate micrometer mechanism is
fastened to the concrete by pointed screws of hardened steel. These
points are originally at a known distance apart — say 8 inches.
When the concrete is compressed, the distance between these
points will be slightly less. A very delicate mechanism will permit
this distance to be measured as closely as the ten-thousandth part

of an inch, or to about 77^77^; of the length. Suppose that the

various pressures per square inch, and the proportionate com-
pressions, are as given in the following tabular form, which gives
figures which are fairly representative of the behavior of ordinary
concrete.

193

182 MASONRY AND REINFORCED CONCRETE

PRESSURE PER
SQUARE INCH

200 pounds

400 pounds

600 pounds

800 pounds

1,000 pounds

1,200 pounds

1,400 pounds

1,600 pounds

PROPORTIONATE
COMPRESSION

.00010 of total length
.00020 of total length
.00032 of total length
.00045 of total length
.00058 of total length
.00062 of total length
.00090 of total length
.00112 of total length

We may plot these pressures and compressions, Fig. 92, using any
convenient scale for each. For example, for a pressure of 800
pounds per square inch, select the vertical line which is at the
horizontal distance from the origin 0 of 800, according to the scale
adopted. Scaling off on this vertical line the ordinate .00045,
^ according to the scale

adopted for compres-
sions, we have the posi-
tion of one point of the
curve. The other points
are obtained similarly.
Although the points thus
obtained from the test-
ing of a single block of
concrete would not be
considered sufficient to
establish the law of the
elasticity of concrete in
compression, a study of the curves, which may be drawn through
the series of points obtained for each of a large number of blocks,
shows that these curves will average very closely to parabolas
that are tangent to the initial modulus of elasticity, which is here
represented in the diagram by a straight line running diagonally
across the figure.

It was formerly quite common to base the computation of
formulas on the assumption that the curve of compression is a
parabola. The development of the theory is correspondingly
complex, but it may be noted from Fig. 92 that for a compression
of 600 or even 800 pounds per square inch, the parabolic curve is
not very different from a straight line. A comparison of the results
based on the strict parabolic theory with those based on the more

Deformation of Concrete per unit
\ ^ I

</_

—

1000 2000 3000

Compression in concrete -pounds,
Fig. 92. Curve of Pressure and Compressions :

194

MASONRY AND REINFORCED CONCRETE 183

simple straight-line formulas shows that the difference is small and
often not greater than the uncertainty as to the true strength of the
concrete. The straight-line theory will, therefore, be used exclu-
sively in the demonstrations which follow.

Theoretical Assumptions. The theory of reinforced-concrete
beams is based on the usual assumptions that:

(1) The loads are applied at right angles to the axis of the beam. The
usual vertical gravity loads supported by a horizontal beam fulfill this condition.

(2) There is no resistance
to free horizontal motion. This
condition is seldom, if ever, exactly
fulfilled in practice. The more
rigidly the beam is held at the
ends, the greater will be its strength
above that computed by the simple \, _
theory. Under ordinary conditions

the added strength is quite inde-
terminate; and is not allowed for,
except in the appreciation that it
adds indefinitely to the safety.

(3) The concrete and steel
stretch together without breaking
the bond between them. This is
absolutely essential.

(4) Any section of the beam which is plane before bending is plane after
bending.

In Fig. 93 io shown, in a very exaggerated form, the essential
meaning of assumption (4). The section abed
in the unstrained condition, is changed to the
plane a'b'd'c' when the load is applied. The
compression at the top equals a a' equals bb'.
The neutral axis is unchanged. The concrete at
the bottom is stretched an amount equal to cc'
equals dd', while the stretch in the steel equals
gg' '. The compression in the concrete between
the neutral axis and the top is proportional to
the distance from the neutral axis.

In Fig. 94 is given a side view of the beam,
with special reference to the deformation of the
fibers. Since the fibers between the neutral axis
and the compressive face are compressed proportionally, then,
if a a' represents the linear compression of the outer fiber, the

Fig. 93. Exaggerated Diagram Showing Plane
Section of Beam Before and After Bending

f-Vf

Fig. 94. Diagram
Showing Side View of
Beam with Reference
to Deformation of
Fibers

195

184 MASONRY AND REINFORCED CONCRETE

shaded lines represent, at the same scale, the compression of the
intermediate fibers.

Summation of Compressive Forces. The summation of com-
pressive forces evidently equals the sum of all the compressions,
varying from zero to the maximum compressive stress c at the
extreme upper fiber, where the linear compression is ec. The
average unit compressive stress is, therefore, \c. Since k is the
ratio of the distance from the, neutral axis to the upper fiber to the
total effective depth d, that distance equals kd; the breadth of the
beam is b. Therefore

2X = %cbkd (9)

Center of Gravity of Compressive Forces. The center of grav-
ity of compressive forces is sometimes called the centroid of com-
pression. It here coincides with the center of gravity of the tri-
angle, which is at one-third the height of the triangle from the upper
face. Therefore

x = $kd (10)

The ratio of the dimension from the steel to the center of the
compressive stress to the dimension d equals j and, therefore, the
dimension between the centroids of the tensile and the compressive
forces equals jd, which equals (d — x).

Position of the Neutral Axis. According to one of the funda-
mental laws of mechanics, the sum of the horizontal tensile forces
must be equal and opposite to the sum of the compressive forces.
Ignoring the very small amount of tension furnished by the con-
crete below the neutral axis, the tension in the steel equals As
equals pbds equals the total compression in the concrete which as
stated in Equation (9) equals %cbkd. Therefore

pbds—^cbkd
or

ps = \ck (11)

The position of the neutral axis is determined by the value of
k, which is a function of the steel ratio p and the ratio of the moduli
of elasticities n. We must also eliminate s and c. By definition,
c equals ec Ec and s equals es Es and n equals Ea-^-Ec. Substitut-
ing in Equation (11), we have

pesEs = $ccEck (12)

196

MASONRY AND REINFORCED CONCRETE 185

TABLE XVII

Value of k for Various Values of n and p
(Straight-Line Formulas)

.020

.018

.016

.014

.012

.010

.008

.006

.004

.003

.464

.446

.427

.407

.385

.358

.328

.292

.246

.216

.493

.476

.457

.436

.412

.385

.353

.314

.266

.235

.531

.513

.493

.471

.446

.418

.384

.343

.291

.258

.562

.544

.524

.501

.476

.446

.412

.369

.315

.279

.580

.562

.542

.519

v.493

.463

.428

.384

.328

.292

.618

.600

.580

.557

N531

.500

.463

.418

.358

.319

.649

.631

.611

.588

.562

.531

.493

.446

.384

.344

.698

.679

.659

.637

.611

.579

.542

.493

.428

.384

From the two proportional triangles in Fig. 94, we may write the
proportion

e1=_c£_
kd d-kd

or ec =

Substituting in Equation (12) for the ratio ~ its value n, and for

ec the value just obtained, we have

pn =

Solving this quadratic for k, we have

(13)

pn (14)

Values of Ratio of Moduli of Elasticity. The various values for
the ratio of the moduli of elasticity n are discussed in the succeeding
paragraphs. The values of k for various values of n and p, have
been computed in Table XVII. Eight values have been chosen
for n, in conjunction with ten values of p, varying by 0.2 per cent
and covering the entire practicable range of p, on the basis of
which values k has been worked out in the tabular form. Usually
the value of k can be determined directly from Table XVII. By
interpolating between two values in Table XVII, any required
value within the limits of ordinary practice can be determined
with all necessary accuracy.

197

186 MASONRY AND REINFORCED CONCRETE

TABLE XVIII

Value of j for Various Values of n and p
(Straight-Line Formulas)

.020

.018

.016

.014

.012

.010

.008

.006

.004

.003

.845

.851

.858

.864

.872

.881

.891

.903

.918

.928

.836

.841

.848

.855

.863

.872

.882

.895

.911

.922

.823

.829

.836

.843

.851

.861

.872

.886

.903

.914

.813

.819

.825

.833

.841

.851

.863

.877

.895

.907

.807

.813

.819

.827

.836

.846

.857

.872

.891

.903

.794

.800

.807

.814

.823

.833

.846

.861

.881

.894

.784

.790

.796

.804

.813

.823

.836

.851

.872

.885

.767

.774

.780

.788

.796

.807

.819

.836

.857

.872

The dimension jd from the center of the steel to the centroid of
the compression in the concrete equals (d — x). Therefore

.= d-x_d-j_kd
J d " d

-1 L i-
-1--L

(15)

The corresponding values for j have been computed for the
several values of p and n, as shown in Table XVIII.

These several values for k and j which correspond to the various
values for p and n are shown in Fig. 95, which is especially useful
when the required values of k and j must be obtained by inter-
polation.

Examples. 1. Assume n = 15 and p = .01; how much are k and j?

Solution. Follow up the vertical line on the diagram for the steel ratio, p
= .010, to the point where it intersects the A; curve for n = 15; the intersection
point is i9o of one of the smallest divisions above the .40 line, as shown on the
scale at the left; each small division is .020, and, therefore, the reading is
AX. 020 = .018 plus .400 or .418, the value of k. Similarly the .010 p line
intersects the j curve for n = 15 at a point slightly above the .860 line or at .861.

2. Assume n = 16 and p = .0082; how much are k and jf

Solution. One must imagine a vertical line (or perhaps draw one) at f of a
space between the .0080 and .0085 vertical lines for p. This line would inter-
sect the line for n = 15 at about .388; and the line for n = 18 at about .416; one-
third of the difference (.028) or .009, added to .388 gives .397, the interpolated
value. Although this is sufficiently close for practical purposes, the precise
value (.398) may be computed from Equation (27). Similarly the value of j
may be interpolated as .867. Although the values of these ratios have been
computed to three significant figures (thousandths), the uncertainties as to the
actual character and strength of 'the concrete used will make it useless to obtain
these ratios closer than th'e nearest hundredth.

198

MASONRY AND REINFORCED CONCRETE 187

Theoretically, there are an indefinite number of values of n, the
ratio of the moduli of elasticity of the steel and the concrete. The
modulus for steel is fairly constant at about 29,000,000 or 30,000,000.
The value of the initial modulus for stone concrete varies, according
to the quality of the concrete, from 1,500,000 to 3,000,000. An

Ya/ves of k t/J for
various t^s/ues ofpvn
fSfr&iyhf line formulae)

.005

Fig. 95. Curves Giving Values of k and j for Various Values of p and n.

Values used for these curves will be found in

Tables XVII and XVIII

average value for 1:2:4 cinder concrete is about 1,200,000. Some
experimental values for stone concrete have fallen somewhat lower
than 1,500,000, while others have reached 4,000,000 and even more.
We may use the values in Table XIX with the constant value of
30,000,000 for the steel.

199

188

MASONRY AND REINFORCED CONCRETE

TABLE XIX
Modulus of Elasticity of Some Grades of Concrete

KIND OK CONCRETE

AGE
(Days)

MIXTURE

•

Cinder

1:2:4

1,200,000

Broken stone

1:3:6

2,000,000

Broken stone

1:2:4

2,000,000

Broken stone

1:2:4

2,500,000

Percentage of Steel. The previous calculations have been
made as if the percentage of the steel might be varied almost indefi-
nitely. While there is considerable freedom of choice, there are
limitations beyond which it is useless to pass; and there is always a
most economical percentage, depending on the conditions. We
must, therefore, determine p in terms of c, s, and n. Substituting
in Equation (11) the value of k in Equation (14), we have

which mav be reduced to

(16)

The above equation shows that we cannot select the percentage
of steel at random, since it evidently depends on the selected stresses
for the steel and concrete and also on the ratio of their moduli. For
example, consider a high-grade concrete — 1:2:4 — whose modulus of
elasticity is considered to be 2,500,000, and which has a working
compressive stress c of 600 pounds, which we may consider in con-
junction with a tensile stress of 16,000 pounds in the steel. The
values of c, *, and n are therefore 600, 16,000, and 12, respectively.
Substituting these values in Equation (16), we compute p equals
.0058.

The "theoretical" percentage is not, necessarily, the most
economical or the most desirable percentage to use. For a beam of
given size, some increase of strength may be obtained by using a
higher percentage of steel; or for a given strength, or load capacity,
the depth may be somewhat decreased by using a higher percentage
of steel. The decrease in height, making possible a decrease in the
total height of the building for a given clear headroom between

200

MASONRY AND REINFORCED CONCRETE 189

floors, way justify the increase in the percentage of steel, but that
is a matter of economics.

Evample. What is the theoretical percentage of steel for ordinary stone
concrete when n = 15, c = 650, and s = 18,000? Ans. .0063 per cent

Resisting Moment. The moment which resists the action of
the external forces is evidently measured by the product of the
distance from the center of gravity of the steel to the centroid of
compression of the concrete, times the total compression of the con-
crete, or times the tension in the steel. As the compression in the
concrete and the tension in the ste^l are equal, it is only a matter
of convenience to express this product in terms of the tension in the
steel. Therefore, adopting the notation already mentioned, we
have the formula

M = As(jd) (17)

But since the computations are frequently made in terms of the
dimensions of the concrete and of the percentage of the reinforcing
steel, it may be more convenient to write the equation

M=(pbds}jd (18)

From Equation (9) we have the total compression in the concrete.
Multiplying this by the distance from the steel to the centroid of
compression j d, we have another equation for the moment

M=±(cbkd)jd (19)

When the percentage of steel used agrees with that computed
from Equation (13), then Equations (18) and (19) will give identi-
cally the same results; but when the percentage of steel is selected
arbitrarily, as is frequently done, then the proposed section should
be tested by both equations. When the percentage of steel is
larger than that required by Equation (13), the concrete will be
compressed more than is intended before the steel attains its normal
tension. On the other hand, a lower percentage of steel will require
a higher unit tension in the steel before the concrete attains its
normal compression. Wlien the discrepancy between the percent-
age of steel assumed and the true economical value is very great,
the stress in the steel, or the concrete, may become dangerously high
when the stress in the other element, on which the computation
may have been made, is only normal.

201

190

MASONRY AND REINFORCED CONCRETE

TABLE XX
Value of p for Various Values of (s-r-e) and n

Formula

: p = — X — I T -I, in which R=(s-7
2 n\R+n/

= (*-*-<•)

(s • c)

.0250

.0273

.0300

.0321

.0333

.0357

.0375

.0400

12.5

.0178

.0196

.0218

.0236

.0246

.0267

.0282

.0304

.0133

.0148

.0167

.0182

.0190

.0208

.0222

.0242

17.5

.0104

.0116

.0132

.0145

.0152

.0168

.0180

.0199

.0083

.0094

.0107

.0118

.0125

.0139

.0150

.0167

.0057

.0065

.0075

.0084

.0089

.0100

.0109

.0123

.0042

.0048

.0056

.0062

.0067

.0076

.0083

.0095

.0025

.0029

.0034

.0039

.0042

.0048

.0054

.0062

50 .0017

.0019

.0023

.0026

.0029

.0033

.0037

.0044

Working Values for the Ratio of the Steel Tension to the Concrete
Compression, It is often more convenient to obtain working values
from tables or diagrams rather than to compute them each time
from equations.

Solving Equation (16) for several combinations of values of
(,9-f-r) and n, the values are tabulated in Table XX. These values
are also shown in Fig. 96. For other combinations than those used
in Table XX, the values of p may be obtained with great accuracy
provided that (s-j-c) corresponds with some curve already on the
diagram. If it is necessary to interpolate for some value of (*-J-c) of
which the curve has not been drawn, it must be recognized that the
space between the curves increases rapidly as (s-s-c) is smaller.
For example, to interpolate for (s + c) equals 32, the point must be
below the 30 curve by considerably more than 0.2 of the interval
between the 30 and the 40 curve.

The relative elasticities (n) of various grades of concrete and
steel are usually roughly proportional to the relative working values,
as expressed by (s + c). In other words, if n is large, (*-5-c) is corre-
spondingly large unless the working value for s or for c is for some
reason made abnormally low. Therefore, there will be little if any
use for the values given in the lower left-hand and upper right-hand
corners of Table XX.

MASONRY AND REINFORCED CONCRETE 191

203

192 MASONRY AND REINFORCED CONCRETE

Determination of Values for Frequent Use. The moment of
resistance of a beam equals the total tension in the steel, or the
total compression in the concrete (which are equal), times jd. There-
fore, we have the choice of twro values, as given in Equations (17)
to (19).

If the theoretical percentage p has already been determined
from Equation (16), then either equation may be used, as most
convenient, since they will give identical results. If the percentage
has been arbitrarily chosen, then the least value must be determined,
as was described on page 189. For any given steel ratio and any
one grade of concrete, the factors %ckj or psj are constant and
Equation (20) may be written

Mc=Rcbd*

Ms
or, in general,

when the theoretical percentage of steel is used. Diagrams for
quickly determining R are given in Figs. 99 and 100.

For 1:2:4 concrete, using n equals 15, and with a working value
for c equals 600, and s equals 16,000, we find from Equation (16)
that the percentage of steel equals

^X 6°0 x 600X15 =
P 2 16,000 600X15+16,000 '

From Table XVII we find by interpolation that, for n equals 15
and p equals .00675, k equals .360. Then (from Equation (10),

x=—kd=.12Qd and j = . 880

Substituting these values in either formula of Equation (20), we have

The percentage of steel computed from Equation (16) has been
called the theoretical percentage, because it is the percentage which will
develop the maximum allowed stress in the concrete and the steel
at the same time, or by the loading of the beam to some definite
maximum loading. The real meaning of this is best illustrated by

204

MASONRY AND REINFORCED CONCRETE 193

a numerical example using another percentage. Assume that the
percentage of steel is exactly doubled, or that p equals 2 X. 00675
equals .0135. From Table XVII for n equals 15, and p equals
.0135, we find k equals .465; x equals 155 d; and j equals .845. Sub-
stituting these values in both forms of Equation (20), we have

The interpretation of these two equations, and also of the equation
found above (If = 956 d2), is as follows: Assume a beam of definite
dimensions b and d, and made of concrete whose modulus of elas-
ticity is j-g that of the modulus of elasticity of the reinforcing steel;
assume that it is reinforced with steel having a cross-sectional area
equal to .00675 bd. Then, when it is loaded with a load which will
develop a moment of 95 b d2, the tension in the steel will equal
16,000 pounds per square inch, and the compression in the concrete
will equal 600 pounds per square inch at the outer fiber. Assume
that the area of the steel is exactly doubled. One effect of this is
to lower the neutral axis — k is increased from .360 to .465 — and
more of the concrete is available for compression. The load may
be increased about 24 per cent, or until the moment equals 118 bd2,
before the compression in the concrete reaches 600 pounds per square
inch. Under these conditions the steel has a tension of about 10,340
pounds per square inch, and its full strength is not utilized. If the
load were increased until the moment was 183 bd2, then the steel
would be stressed to 16,000 pounds per square inch, but the con-
crete would be compressed to about 930 pounds, which would, of
course, be unsafe with such a grade of concrete. If the compression
in the concrete is to be limited to 600 pounds per square inch, then
the load must be limited to that which will give a moment of 118
b dz. Even for this the steel is doubled in order to increase the load
24 per cent. Whether this is justifiable, depends on several circum-
stances — the relative cost of steel and concrete, the possible neces-
sity for keeping the dimensions of the beam within certain limits,
etc. Usually a much larger ratio of steel than 0.675 per cent is
used; 1.0 per cent is far more common; but when such is used, it
means that the strength of the steel cannot be fully utilized unless
the concrete can stand high compression. A larger value of n will

205

194 MASONRY AND REINFORCED CONCRETE

indicate higher values of k, which will indicate higher moments; but
n cannot be selected at pleasure. It depends on the character of
the concrete used; and, with E8 constant, a large value of n means
a small value for Ec, which also means a small value for c, the per-
missible compression stress. Whenever the percentage of steel is
greater than the theoretical percentage, as is usual, then the upper
of the two formulas of Equation (20) should be used. When in
doubt, both should be tested, and that one giving the lower moment
should be used.

When p equals .0075, n equals 15, c equals 600, and s equals
16,000, as before, wre have k equals .374, x equals. 125 d and j equals
.875. Then, since p is greater than the theoretical value, we use
the upper formula of Equation (20) and have

Examples. 1. What, is the working moment for a slab with 5-inch thick-
ness to the steel, the concrete having the properties described above?

Solution. Let 6 = 12 inches, M = 98X12X25 = 29,400 inch-pounds, the
permissible moment on a section 12 inches wide.

2. A slab having a span of 8 feet is to support a load of 150 pounds per
square foot. The concrete is to be as described above, and the percentage of
steel is to be 0.75. What is the required thickness d to the steel?

Solution. Allowing 70 pounds per square foot as the estimated weight of
the slab itself, the total load is 220 pounds per square foot. A strip 12 inches
wide has an area of 8 square feet, and the total load is 1,760 pounds. Assuming
the slab as free-ended, the moment is £ W Z = iXl,760X96 = 21,120 inch-pounds.
For a strip 12 inches wide, 6 = 12 inches and M = 98Xl2Xd2 = l,176 d2 = 21,120;
from which d- = 17.96, and d = 4.24 inches. Then, allowing one inch of concrete
below the steel, the total thickness of the slab would be 5j inches and its weight,
allowing 12 pounds per square foot per inch of depth, would be about 63 pounds
per square foot, thus agreeing safely with the estimated allowance for dead load.
If the computed thickness and weight had proved to be materially more than
the original allowance, another calculation would be necessary, assuming a
somewhat greater dead load. This increase of dead load would of itself produce
a somewhat greater moment, but the increased thickness would develop a greater
resisting moment. A little experience will enable one to make the preliminary
estimate so close to the final that not more than one trial calculation should be
necessary.

PRACTICAL CALCULATION AND DESIGN OF BEAMS
AND SLABS

Tables for Slab Computations. The necessity of very fre-
quently computing the required thickness of slabs renders very
useful the data given in Table XXI, which has been worked out on

206

MASONRY AND REINFORCED CONCRETE 195

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207

196 MASONRY AND REINFORCED CONCRETE

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MASONRY AND REINFORCED CONCRETE W7

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209

198 MASONRY AND REINFORCED CONCRETE

the basis of several combinations of values of c and s. Municipal
building laws frequently specify the unit values which must be used
and even the moment formula. For example, slabs are usually
continuous over beams and even the wall ends of slabs are so
restrained at the wall that the working moment is considerably less
than JF/-7-8and, therefore, the formula JF/-f-10 is specifically per-
mitted in many municipal regulations. Table XXI is computed
on that basis, but the tabulated unit loads may be very easily
changed to the basis of Wl + 8 or TH-f-12. It must be noted that
the unit loads given in Table XXI include the slab weight, which
must, therefore, be subtracted before the net live load is known.
In the last column are shown the unit weights of various slab thick-
nesses on the basis of 108 pounds per cubic foot for cinder concrete
and 144 pounds per cubic foot for stone concrete. These subtractive
weights may need to be altered if a concrete of different weight is
used, or if an extra top coat of concrete, which cannot be consid-
ered to be structurally a part of the slab, is laid on afterward.
The "thickness of concrete below steel" is such as is -approved
by good practice, but in case municipal regulations or other rea-
sons should require other thicknesses of concrete below the steel,
Table XXI may still be used by considering the effective thickness d
and by varying, as need be, the subtractive weight of the slab to deter-
mine the net load. The blanks in the upper right-hand corner of each
section of the table indicate that for those spans and slab thicknesses
the slabs cannot safely carry their own weight and that even the
weights nearest the blanks are so small that, after subtracting the
slab weights, the remainders are too small for practical working
floor loads, or even roof loads. The blanks in the lower left-hand
corner of each section of the table indicate that for these combina-
tions of span, load, and slab thickness, the shearing strength would
be insufficient for the load which its transverse strength would
enable it to carry and, therefore, although those slabs would carry
a great load, those combinations of span and slab thickness are
uneconomical and should not be used.

Examples. 1. Using stone concrete such that c = 600, w = 15, and s =
16,000, and with a required working load of 200 pounds per square foot, what
span may be chosen?

Solution. This requires Section 3 of Table XXI. We note that an 8-inch
slab on a span of 12 feet will carry 300 pounds per square foot gross, or 204

210

MASONRY AND REINFORCED CONCRETE 199

pounds net, which is substantially what is required. Another combination
would be a 7-inch slab with a span between 10 and 11 feet. To interpolate,
subtract 84, the unit slab weight, from 314 and from 259, giving 230 and 175.
It should be noted that the difference 388—314, or 74, is greater than the differ-
ence 314—259, or 55, which in turn is greater than the difference 259—218,
or 41. From this we may know, without precise calculations, that the value
for the span 10 feet 6 inches must be such that the difference between 230 (net
value) and the net value for 10 feet 6 inches must be greater than the difference
between this net value and 175, the net value for an 11-foot span. 230— 200 = 30
and 200 — 175 = 25. Therefore, a span of 10 feet 6 inches is very close to the
theoretical value — close enough for practical purposes. Whether an 8-inch
slab with 12-foot span or a 7-inch slab with 10-foot\6-inch span is most economical
or desirable depends on other conditions, one of which is the span of the beams.
This will be considered later.

2. Find the span, assuming the same data as above, except that muni-
cipal regulations require at least 1| inches of concrete below the steel and also
require using the formula Wl + 8.

Solution. An 8-inch slab with 1£ inches of concrete under the steel
will be 8j inches thick and will weigh 99 pounds per square foot. On the 11-foot
span the total load, after subtracting 20 per cent, will be 286 pounds and, after
subtracting 99, will leave 187 pounds net. Similarly, the net load on the 10-foot
span is 247 pounds. 200-187 = 13, and 247-187 = 60; 13 is nearly one-fourth
of 60 and, therefore, the interpolated span is about one-fourth of the interval
from 11 feet back to 10 feet, or 10 feet 9 inches. The net effect of adding the
extra concrete below the steel and using Wl + 8 instead of Wl + 10, therefore,
reduces the span of the 8-inch slab from 12 feet to 10 feet 9 inches. A similar
computation could be made for a 7-inch slab — actual thickness 1\ inches.

3. Assume a slab made of 1:2^:5 concrete; the span has been determined
already as 6 feet; the floor is to be covered with 2 inches of cinder-concrete fill
between the wood sleepers and a wood floor, weighing 23 pounds per square foot;
the live load is to be 150 pounds per square foot; required the slab thickness.

Solution. For such concrete, use Section 2, Table XXI. 150+23 = 173,
and adding a trial figure of 50 pounds for the unit weight of the slab, we have 223
as the total load. Under 6 feet span we find 192 for a 4-inch slab and 261 for a
4£ inch slab; 4 inches is too thin and 4 5 somewhat needlessly thick. Since 223
is nearer to 192 than to 261, we may economize by cutting the thickness to 4|
inches. The detail of the interpolation, elaborated in Example 2, shows this
to be justifiable. The required area of steel for the 4j-inch slab is found by
interpolation, between .223 and .260, or .242 square inch — the area of steel in
12 inches of width of slab. This is .020 square inch per inch of width; a |-inch
square bar has an area of .1406 square inch; therefore, such bars spaced 7 inches
apart will fulfill the requirements.

Practical Methods of Spacing Slab Bars. It is too much to
expect of workmen that bars will be accurately spaced when their
distance apart is expressed in fractions of an inch. But it is a
comparatively simple matter to require the workmen to space the
bars evenly, provided it is accurately computed how many bars

211

200 MASONRY AND REINFORCED CONCRETE

X «
X «-

5 5

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to«~

SCO O
— I -

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rH i-l N CO

i r>- 1^. t^. •

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t^ 1^ O Tf i-H O 1-H •

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i lO CO t^ 00 O5 O I-H (M CO •

S -2

212

MASONRY AND REINFORCED CONCRETE 201

should be laid in a given width of slab. As an illustration, in Exam-
ple 3 above, a panel of the flooring, which is, say 20 feet wide, should
have a definite number of bars. As 20 feet equals 240 inches and
240-7-7 equals 34.3, we shall call this 34, and instruct the workmen
to distribute 34 bars equally in the panel 20 feet wide. The work-
men can do this without even using a foot-rule, and can adjust the
bars to an even spacing with sufficient accuracy for the purpose.

A regulation of the New York City building code is that the
spacing of slab bars shall be not greater than 2| times the thickness
of the slab. In the above case the margin is ample; 2^ times 4|
equals 10.6 inches; the designed spacing is 7 inches.

Table for Computation of Simple Beams. In Table XXII has
been computed, for convenience, the working total load (including
the weight of the beam) on rectangular beams one inch wide and of
various depths and spans. For other widths of beams, multiply
the tabular load by the width of the beam in inches. Table XXII
is based on a grade of concrete such that M equals 1006d2; for
any other grade of concrete, determine the corresponding factor of
bd2, or, in other words, Equation (20), compute the value of %ckj,
or of psj, whichever is least. Multiply the tabular load by the
percentage of that factor to 100. The concrete of Section 5, Table
XXI, has the factor 100 and if such concrete is used, no percentage
multiplication is necessary. The blanks in the upper right-hand
corner of Table XXII are similar to the corresponding blankn of
the other sections of Table XXI; the beams cannot safely carry
their own weight. And, as before, the values immediately adjacent
to the blanks are of little or no use, since the possible load, after
deducting the weight of the beam, would be too small for practical
use. The values in the lower left-hand corner should be used with
great caution. Many of the beams of such relative span and depth
would fail from diagonal shear long before the tabulated loads were
reached. But, since the liability to failure from diagonal shear is
dependent on the nature of the web reinforcement, the line of demar-
cation is not easily drawn, as was done in Table XXII.

Examples. 1. Assume the concrete described in Section 3, Table XXI,
which has the factor 95; how much load will be carried by a beam of such
concrete, when the beam is 8 inches wide, 16 inches effective depth, and 18 feet

213

202 MASONRY AND REINFORCED CONCRETE

Solution. From Table XXII, under 18 feet span and opposite 16 inches
effective depth, we find 948, the load for a beam one inch wide. An 8-inch
beam will carry 8X948, or 7,584 pounds. 95 per cent of 7,584 is 7,205 pounds,
the load for that particular grade of concrete. The weight of the concrete,

Q I O

assuming a total depth of 18 inches, 53^X^X18X144 = 2,592. Deducting

this from 7,205, we have the net load as 4,613 pounds.

2. Assume that c = 500, s = 16,000, n = 12, and p = .006; how much load
will be carried by a beam 6 inches wide, 12 inches effective depth, and 14 feet
span?

Solution. From the percentage diagram on page 191, we seethatfors-f-c =
32 and n = 12, p = .0043; and since this is less than the chosen steel ratio .006,
we must use the first part of Equation (20). For n = 12 and p = . 006, k = .3 14
and j = . 895. Then £cfc./ = 250X.314X.895 = 70, the factor of 6cP. The load
on a beam one inch wide, 12 inches effective depth, and 14 feet span is 685 pounds.
For 6 inches wide it would be 4,110 pounds. 70 per cent of this is 2,877 pounds.

6 14
The weight, allowing 2 inches below the steel, is — XT~ X 14X144, or 1,176

pounds. The net load is, therefore, 4,110-1,176, or 2,934 pounds.

BONDING STEEL AND CONCRETE

Resistance to the Slipping of the Steel in the Concrete. The

previous discussion has considered merely the tension and compres-
sion in the upper and lower sides of the beam. A plain, simple beam
resting freely on two end supports has neither tension nor compres-
sion in the fibers at the ends of the beam. The horizontal tension
and compression, found at or near the center of the beam, entirely
disappear by the time the end of the beam is reached. This is done
by transferring the tensile stress in the steel at the bottom of the
beam to the compression fibers in the top of the beam, by means of
the intermediate concrete. This is, in fact, the main use of the
concrete in the lower part of the beam.

It is, therefore, necessary that the bond between the concrete
and the steel shall be sufficiently great to withstand the tendency to
slip. The required strength of this bond is evidently equal to the
difference in the tension in the steel per unit of length. For example,
suppose that we are considering a bar 1 inch square in the middle of
the length of a beam. Let the bar be under an actual tension of
15,000 pounds per square inch. Since the bar is 1 inch square, the
actual total tension is 15,000 pounds. Suppose that, at a point 1
inch beyond, the moment in the beam is so reduced that the tension
in the bar is 14,900 pounds instead of 15,000 pounds. This means

214

MASONRY AND REINFORCED CONCRETE 203

that the difference of pull (100 pounds) has been taken up by the
concrete. The surface of the bar for that length of one inch is four
square inches. This will require an average adhesion of 25 pounds
per square inch between the steel and the concrete in order to take
up this difference of tension. The adhesion between concrete and
plain bars is usually considerably greater than this, and there is,
therefore, but little question about the bond in the center of the
beam. But near the ends of the beam, the change in tension in the
bar is far more rapid, and it then becomes questionable whether the
bond is sufficient.

Virtue of "Deformed" Bars. The fact that the adhesion of the
concrete to the steel is a critical feature under some conditions,
called attention to the desirability of using "deformed" bars, which
furnish a mechanical bond. Microscopical examination of the
surface of steel, and of concrete wrhich has been molded around the
steel, shows that the adhesion depends chiefly on the roughness of
the steel, and that the cement actually enters into the microscopical
indentations in the surface of the metal. Since a stress in the metal
even within the elastic limit necessarily reduces its cross section
somewhat, the so-called adhesion will be more and more reduced as
the stress in the metal becomes greater. This view of the case has
been verified by recent experiments by Professor Talbot, who used
bars made of tool steel in many of his tests. These bars were excep-
tionally smooth; and concrete beams reinforced with these bars
failed generally on account of the slipping of the bars. Special tests
to determine the bond resistance showed that it wras far lower than
the bond resistance of ordinary plain bars. The designing of the
various deformed bars, described on pages 81-83, is only a develop-
ment of this same principle. The accidental roughness of rolled
bars is purposely magnified and the resistance is correspondingly
increased. The deformed bars have a variety of shapes; and since
they are not prismatic, it is evident that, apart from adhesion, they
cannot be drawn through the concrete without splitting or crushing
the concrete immediately around the bars. The choice of form is
chiefly a matter of designing a form which will furnish the greatest
resistance, and which at the same time is not unduly expensive to
manufacture. Non-partisan tests have shown that, even under con-
ditions which are most favorable to the plain bars, the deformed

215

204 MASONRY AND REINFORCED CONCRETE

TABLE XXIII
Bond Adhesion of Plain and Deformed Bars per Inch of Length

=. i 75 Ib. adhesion per square inch for plain bars
°'S\125 Ib. adhesion per square inch for deformed bars
For any other unit basis, multiply surface (column 2 or 3) by unit

BOND ADHESION PEB LINEAL INCH

SURFACE;

SIZE OF BAR

(Square Inches
per Lineal Inch)

Plain Bars at 75

Deformed Bars at 125

. INCHES

Square

Round

Square

Round

Square

Round

1.00

0.785

125

1.25
1.50

0.982
1.178

94
112

74
88

156
187

123

147

1.75

1.375

131

103

219

172

2.00
2.50

1.571
1.964

150

187

118
147

250
312

196
245

3.00

2.356

225

177

375

294

3.50

2.749

262

206

437

344

4.00

3.142

300

236

500

393

4.50

3.534

337

265

562

442

5.00

3.927

375

324

625

491

bars have an actual hold in the concrete which is from 50 to 100 per
cent greater than that of plain bars. It is unquestionable that age
will increase rather than dimmish the relative inferiority of plain
bars.

The specifications of the American Railway Engineering Asso-
ciation, adopted in 1910, allow 80 pounds per square inch of surface
for plain bars, 40 for drawn wire, and from 100 to 150 for
deformed bars "depending upon form". Municipal regulations fre-
quently limit the adhesion to 75 pounds, without any mention of
deformed bars or of any extra allowable adhesion if such are used.
The adhesion is of special importance in short but deep, heavily
loaded beams. It is frequently difficult to obtain the necessary
adhesion with an allowance of only 75 pounds per square inch. For
convenience, Table XXIII is given.

Computation of the Bond Required in Bars. From theoretical
mechanics, we learn that the total shear at any section equals the
difference in moment for a section of infinitesimal length. This
may be seen from Fig. 97 where T is tension in steel at left end of
section, and toward the center of the beam; T' is tension in steel at

216

MASONRY AND REINFORCED CONCRETE 205

right end of section; then T— T is the difference in tension, which
ig the amount of tension taken up by the concrete in the length x.
Then (T-T')jd is the difference of moment in the unit distance x.
But by taking moments about a, we have

Vx = (T-T')jd
from which

NCUTRfIL

If x is considered to be the unit length
— say one inch — then the bond adhesion on .•—
all the bars will be V+jd. If we call v the
unit horizontal shear, and the width of the
beam fe, then

H—V^-hirl 01} FiK- 97- Diagram for Calcu-

V • °Ja \*'L) lating Moments of Inertia

Illustrative Example. Assume an 8-foot

beam, uniformly loaded to its capacity, with an effective depth d= 16
inches, width 6 = 8 inches, c = 600, 5 = 16,000, and n=15. Then
p = . 00675, k = .360, j = .880, and A = 16 X 8 X. 0067 = 0.86 square
inch. This area may be obtained from three f-inch round bars,
each of which will have a cross-sectional area of .30 square inch
and circumference of 1.96 inches, which means an adhesion area of
5.88 square inches per inch of length of the three bars. M equals
95 fed2 or 194,560 inch-pounds equals WI-&8. Since Z = 96 inches,
W= 16,213, and V, the maximum total shear, is one-half of this or
8,107 pounds. At a point one foot from the center the shear will be
one-fourth of the maximum shear, or 2,027 pounds, and dividing this
by jd, or .880X16, we have .144 pounds, the required bond adhesion
at that point. Dividing this by the area, 5.88, we have 24 pounds
per square inch, the adhesion stress, which is amply safe.

At the abutment the shear is 8,107 pounds; dividing this by
jd, or .880X16; we have 575 pounds, the required total adhesion.
575 -r-5.88 is 98, the required unit adhesion. This is greater than the
permissible unit adhesion of plain bars, and greater than the uni-
form figure (75) given in so many municipal building codes, although
not greater than that which deformed bars can safely carry. An-
other possible solution of the problem, although at some loss of
economy, would be to use four ^-inch square bars, whose total cross-
sectional area would be one square inch (instead of 0.86) and whose

217

206 MASONRY AND REINFORCED CONCRETE

superficial area per inch of length would be 8 square inches.
578-:- 8 = 72 pounds per square inch. This is within the speci-
fied limit for plain bars. Strictly speaking, this would not be the
precise figure, since the added percentage of steel would slightly
decrease j and therefore slightly increase the required adhesion, but
the effect in this case is very slight, about one pound per square inch.
Since the variation of j is very little for the usual variations in
percentage of steel and quality of concrete, it is a common practice
to consider that, as applied to this equation, j has the uniform value
of .875 or |. This would reduce Equation (21) to

which means that v, the maximum unit horizontal or vertical shear
in a section, is about \ more than the average shear, found by divid-
ing the total shear by the effective section of the beam.

VERTICAL SHEAR AND DIAGONAL TENSION

Distribution of Vertical Shears. Beams which are tested to
destruction frequently fail at the ends of the beams, long before the
transverse strength at the center has been
fully developed. Even if the bond between
the steel and the concrete is amply strong
for the requirements, the beam may fail on
account of the shearing or diagonal stresses
in the concrete between the steel and the
neutral axis. The student must accept with-
out proof some of the following statements
regarding the distribution of the shear.

The intensity of the shear of various
points in the height of the beam may be rep-
resented by the diagram in Fig. 98. If we
ignore the tension in the concrete due to
transverse bending, the shear will be uniform between the steel and
the neutral axis. Above the neutral axis, the shear will diminish
toward the top of the beam, the curve being parabolic.

The maximum diagonal tensile stress t at any point in a homo-
geneous beam may be represented by the equation

Fig. 98. Diagram Showing In-
tensity of Shear in Various
Points in Height of Beam

218

MASONRY AND REINFORCED CONCRETE 207

in which / is the unit horizontal tensile stress and v the unit vertical
or horizontal shearing stress. The direction of this maximum
tensile stress is given by the formula

tan 20 = 20 -=-/

in which 6 is the angle of the maximum tension with the horizontal.

The application of these equations to reinforced concrete beams
is uncertain and unreliable, since it depends W assumptions which
are themselves uncertain. If there were absolutely no tension in
the concrete,/ would equal 0, t would equal v, and 6 would equal 45°.
But there is always some tension in the concrete and this increases t.
If there is no web reinforcement, or if all the bars run straight
through the beam for their entire length, the equations might be
used, provided we could know how much tension is actually taken
up by the concrete and how much by the steel. According to the
best information on the subject, derived from actual tests, t varies
from once to twice v, and since v is readily computed from Equation
(20), this value may be used as an approximate measure of the
probable value of t.

Methods of Guarding against Failure by Shear or Diagonal
Tension. The failure of a beam by actual shear is almost unknown.
The failures usually ascribed to shear are generally caused by diag-
onal tension. A solution of the very simple Equation (21) will
indicate the intensity of the vertical shear. If a beam is so reinforced
that it will safely stand <the tests for moment, diagonal shear, and
bond adhesion, there is almost no question of its ability to resist
vertical shear.

Resistance to Diagonal -Tension by Bending Bars or Use of
Stirrups. Resistance to diagonal tension is furnished by bending up
the main reinforcing bars, and also by the use of "stirrups". Unfor-
tunately, it seems impossible to devise any simple, practicable
rules (like those for resisting moment) for the precise design of
reinforcement to resist diagonal tension.

Professor Talbot (Bulletin No. 29, University of Illinois)
suggests that the working stress P in a stirrup may be computed
from the formula

P=Va+jd (22)

in which a is the spacing between stirrups, the other symbols being

219

208 MASONRY AND REINFORCED CONCRETE

those previously used. At the same time, he admits that the stress
in the stirrup cannot be developed until incipient failure by diagonal
tension has already commenced. The rule seems to have the advan-
tage of being amply safe, and since the cost of stirrups is propor-
tionally small, the very slight additional cost of a possible excess in
strength is justifiable. Applying the rule to the problem on page 205,
the shear at the abutment is 8,107; for a stirrup spacing a = 6 inches

P = (8,107 X 6) 4- (.881X16) = 3,454 Ib.

Each bar of the stirrup would hold 1,727 pounds, which at 16,000
pounds per square inch would require .11 square inch, which is
exactly the area of a f -inch round bar. But it would be impossible
to develop even this tension in the stirrup bars unless they were
looped at the top, since they are never long enough to develop a
bond adhesion equal to the tensile strength. If the beam is capped
by a slab, the stirrup should bend over and extend some distance
into the slab.

Resistance to diagonal tension is most efficiently provided by
bending up the bars diagonally as fast as they can be spared from
their primary work of resisting transverse moment. Diagonal ten-
sion tends to produce diagonal cracks which start at the bottom of
the beam and develop upward and toward the center. If some of
the bars are bent up from the bottom near the ends of the beam,
those bars will be nearly normal to these cracks and will resist such
tension. From this standpoint alone, it would be preferable to use
a large number of small bars, so that a pair of them could be turned
up at intervals not greater than the depth of the beam and still have
left at least one pair of bars to extend straight through to the end
of the beam. But the use and the bending up of a very large number
of small bars adds considerably to the cost of small beams, although
a large number of bars is sometimes necessary with very large beams.
Therefore, although one or two pairs of bars are usually turned up
diagonally near the ends of each beam, where the diagonal shear is
the greatest, stirrups are depended on to resist diagonal tension.

Example. Assume a plain beam with a span of 18 feet, which is carrying
a total load of 1,800 pounds per running foot or 32,400 pounds. Find the
reinforcing bars necessary to take care of the diagonal tension and shear.

Solution. The moment may be computed thus:

= (32,400X216) -8 = 874,800 in.-lb.

220

MASONRY AND REINFORCED CONCRETE 209

Assuming the data of Section 3, Table XXI, M = 956 <P = 874,800.
Then 6d2 = 9,208. If 6 = 12, d2 = 767.3 and d = 27.7. Then A = .00675X
12X27.7 = 2.24 square inches. This area will be provided by four f-inch
square bars.

Shear. The total equivalent load" is 32,400; the maximum shear is one-
half, or 16,200. Applying Equation (21), the horizontal shear below the neutral
axis equals v = V+bjd or 16,200 ^ (12 X-880X 27.7) =55 pounds per square
iach, which is safe as a unit stress for true shear, but since the diagonal tension
may be double this, the beam should be reinforced againsjt diagonal shear. Since
there are only four main reinforcing bars and since two should be extended
straight through without bending up, it leaves only one pair which may be
bent up, the bends commencing about two feet from the support at each end.

Stirrups. Transposing Equation (22), we have a=*Pj d+V. Talbot's
experiments showed that a considerable shearing stress must be developed
before the stirrups will begin to take up any stress. Assume that a safe unit
shearing stress v = 30 pounds is developed in the concrete. Then, by inversion
of Equation (21), there will be developed a shear of
V = vbjd

= 30 X 12 X. 88X27.7
= 8,775 Ib.

16,200-8,775=7,425, the shear which should be provided for to be taken
up by the first stirrup. Assume that the first stirrup is a pair of f-inch round
bars. The area of the bar is 0.11 square inch and at 16,000 pounds per square
inch, a pair of the bars can sustain 3,520 pounds, whick is one value for P. Then
a = (3,520X.88X27.7)^-7,425 = 11.6 inches, the rate of spacing for the stir-
rups at the support. Practically, this means that we should place a stirrup
about six inches from the support and the next with a spacing of about 12 inches.
At the quarter point, the shear is one-half of 16,200 or 8,100 pounds; but since
this is less than 8,775 pounds, the available shearing strength of the concrete,
there is no need, on the basis assumed, for stirrups even at the quarter points,
nor throughout the middle hah" of the beam. The accuracy of these calculations
depends upon uncertain assumptions and the work illustrates the uselessness
of precise computations, especially in view of the fact that the very great resist-
ance to diagonal tension provided by the main bent-up bars has been numerically
disregarded. The chief use of this method of stirrup calculation is that it indi-
cates a limit beyond which it is useless to pass. Therefore, if we place stirrups
made of f-inch round steel at either end, the first at 6 inches from the support,
the others at successively added intervals of 12, 15, 18, and 24 inches, the fourth
stirrup will be 6 feet 3 inches from the support. We may feel sure that such
stirrups, especially with the added but uncertain aid furnished by the bending-
up of the main reinforcing bars, will fully resist all diagonal tension produced
by the assumed load.

Although the above method shows how to calculate all the
diagonal tension and shear which can be definitely computed, it is
becoming common practice to place stirrups along the entire length
of the beam. These serve the purpose of furnishing a skeleton to
which the other bars may be wired and thus fixed in place, and

221

210 MASONRY AND REINFORCED CONCRETE

also bind the top and bottom of the beam together. This adds
a positive but non-computable amount to the strength of the
beam.

Calculations by Diagrams of Related Factors. A very large
proportion of concrete work is done with a grade of concrete such
that we may call the ratio n of the moduli of the steel and the con-
crete either 12 or 15. The working values of the stresses in the
steel and the concrete, s and c, are determined either by public
regulation or by the engineer's estimate of the proper values to be
used. The diagrams, Figs. 99 and 100, fully cover the whole range
of practicable values for steel and for stone concrete. In the pre-
vious problems all values have been calculated on the basis of
formulas. By means of these diagrams all needed values, on the
basis of the other factors, may be read from the diagram with suffi-
cient accuracy for practical work. In addition, the diagrams
enable one to note readily the effect of any proposed change in one
or more factors.

Illustrative Examples. 1. If a beam, made of concrete such
that n = 15, is to be so loaded that when the stress in the steel (s) is
16,000, the stress in the concrete (c) shall simultaneously be 600, the
steel ratio (p) must be .00675. This is found on the diagram, Fig.
99, for n= 15, by following the line s = 16,000 to its intersection with
the line c = 600. The intersection point, measured on the steel ratio
scale at the bottom of the diagram, reads .00675. Also, running
horizontally from the intersection point to the scale at the left, we
read R = 95, which is the factor for bd2 in the moment equation,
Equation (20). Incidentally, the corresponding values of k andj for
this steel ratio may be obtained, with greater convenience, from
this diagram, although they are also obtainable from the more
general diagram, Fig. 95.

2. Assume that, for reasons discussed on page 188, it is decided
to increase the steel ratio to 1.2 per cent. Following the vertical
line for steel ratio equal to .012, we find it intersects the line c = 600 at
a point where /? = 114, but the point is about halfway between the
lines s = 10,000 and s = 12,000, indicating that, using that steel ratio,
the stress in the steel for a proper stress in the concrete is far less
than the usual working stress, and that it would be about 11,000.
If the load were increased so that s equals 16,000, we can see by

222

MASONRY AND REINFORCED CONCRETE 211

estimation that c would probably be over 800, which is far greater
than a proper working value.

3. Assume p = .004, c = 600, and n=15; how much are R
and s? R equals 79 and s equals 22,000, which is impracticably

STEEL ftfJTIO-p

Fig. 99. Curves Showing Values of Moment Factor R for n =15

high. The diagram, Fig, 100, shows plainly that for low steel ratios
the values of s are abnormally high for ordinary values of c; on the
other hand, for high steel ratios, the ordinary values of c cannot
utilize the full working strength of the steel.

212 MASONRY AND REINFORCED CONCRETE

Slabs on I=Beams. The skeleton framework of buildings,
especially if very high, is frequently made of steel, even when the
floors are made of concrete girders, beams, and slabs. But some-

/60

RfJTIO-p

Fig. 100. Curves Showing Values of Moment Factor R for n =12

times even the girders and beams are made of steel and only the slab
is made of concrete, using steel I-beams for floor girders and beams,
and then connecting the beams with concrete floor slabs, Fig. 101.
These are usually computed on the basis of transverse beams which

MASONRY AND REINFORCED CONCRETE 213

are free at the ends, instead of considering them as continuous
beams, which will add about 50 per cent to their strength. Since it
would be necessary to move the reinforcing steel from the lower part
to the upper part of the slab when passing over the floor beams, in
order to develop the additional strength which is theoretically possi-
ble with continuous beams, and since this is not usually done, it is
by far the safest practice to consider all floor slabs as being "free-
ended". The additional strength, which they undoubtedly have to
some extent because they are continuous over the beams, merely
adds indefinitely to the factor of safety. Usually, the requirement
that the I-beams shall be fireproof ed by surrounding the beam
itself with a layer of concrete such that the outer surface is at least
2 inches from the nearest point of the steel beam results in having
a shoulder of concrete under the end of each slab, which quite mate-

BflRS TO PREVENT
SHRINKAGE CftftCKS

EXPfl/VDFD METfJL —
or WIRE L/TTH

Fig. 101. Diagram Showing Method of Placing Concrete Floor Slabs on I-Beam Girders

rially adds to its structural strength. This justifies the frequent
practice of using the moment formula M = Wl+W, which is a com-
promise between Wl-s-$ and Wl+12. Even this should only be
done when the bars are run into tke adjoining span far enough so
that the bond adhesion, computed at a safe working value, will not
exceed the tension in the steel, and also when the steel is raised to
a point near the top of the slab over the supports. The fireproofing
around the beam must usually be kept in place by wrapping a small
sheet of expanded metal or wire lath around the lower part of the
beam before the concrete is placed.

Slabs Reinforced in Both Directions. When the floor beams of
a floor are spaced about equally in both directions, so that they
form, between the beams, panels which are nearly square, a material
saving can be made in the thickness of the slab by reinforcing it with
bars running in both directions. The theoretical computation of the

214 MASONRY AND REINFORCED CONCRETE

strength of such slabs is exceedingly complicated. The usual
method is to estimate that the total load is divided into two parts
such that if I equals the length of a rectangular panel and b equals
the breadth (I being greater than, or equal to 6), then the ratio of the
load carried by the "6" bars is given by the proportion Z4-r- (/4+64).
If the value of this proportion is worked out for several values of
the ratio / : 6, we have the figures given by the tabular form :

RATIO I : b

1.0

1.1

i •>

1.3

1.4

1.5

Proportion of load
carried by "b"
bars

50%

59%

67%

74%

80%

83%

When I and b are equal, each set of bars takes half the load.
When I is only 50 per cent greater than b, the shorter bars take 83
per cent of the load and it is uneconomical to use bars for transverse
moment in the longer direction. The lack of economy begins at
about 25 per cent excess length, and therefore panels in which the
proportion of length to breadth is greater than 125 per cent should
be reinforced in the shorter direction only. Strictly speaking, the
slab should be thicker by the thickness of one set of reinforcing bars.

Reinforcement against Temperature Cracks. The modulus of
elasticity of ordinary concrete is approximately 2,400,000 pounds
per square inch, while its ultimate tensional strength is about 200
pounds per square inch. Therefore, a pull of about TW<T7-of the
length would nearly, if not quite, rupture the concrete. The coeffi-
cient of expansion of concrete has been found to be almost identical
with that of steel, or .0000065 for each degree Fahrenheit. There-
fore, if a block of concrete were held at the ends with absolute rigid-
ity, while its temperature was lowered about 12 degrees, the stress
developed in the concrete wrould be very nearly, if not quite, at the
rupture point. Fortunately, the ends will not usually be held with
such rigidity; but, nevertheless, it does generally happen that, unless
the entire mass of concrete is permitted to expand and contract
freely so that the temperature stresses are small, the stresses will
usually localize themselves at the weak point of the cross section,
wherever it may be, and will there develop a crack, provided the
concrete is not reinforced with steel. If, however, steel is well
distributed throughout the cross section of the concrete, it will

22(3

MASONRY AND REINFORCED CONCRETE 215

prevent the concentration of the stresses at local points, and will
distribute it uniformly throughout the mass.

Reinforced-concrete structures are usually provided with bars
running in all directions, so that temperature cracks are prevented
by the presence of such bars, and it is generally unnecessary to make
any special provision against such cracks. The most common excep-
tion to this statement occurs in floor slabs, which structurally require
bars in only one direction. It is found that cracks parallel with the
bars which reinforce the slab will be prevented, if a few bars are laid
perpendicularly to the direction of the main reinforcing bars. Usually,
^-inch or f -inch bars, spaced about 2 feet apart, will be sufficient to
prevent such cracks.

Retaining walls, the balustrades of bridges, and other similar
structures, which may not need any bars for purely structural
reasons, should be provided with such bars in order to prevent
temperature cracks. A theoretical determination of the amount of
such reinforcing steel is practically impossible, since it depends on
assumptions which are themselves very doubtful. It is usually con-
ceded that if there is placed in the concrete an amount of steel whose
cross-sectional area equals about £ of 1 per cent of the area of the
concrete, the structure will be proof against such cracks. Fortu-
nately, this amount of steel is so small that any great refinement in
its determination is of little importance. Also, since such bars have
a value in tying the structure together, and thus adding somewhat
to its strength and ability to resist disintegration owing to vibra-
tions, the bars are usually worth what they cost.

T-BEAM CONSTRUCTION

When concrete beams are laid in conjunction with overlying
floor slabs, the concrete for both the beams and the slabs being laid
in one operation, the strength of such beams is very much greater
than their strength considered merely as plain beams, even though
we compute the depth of the beams to be equal to the total depth
from the bottom of the beam to the top of the slab. An explanation
of this added strength may be made as follows:

If we were to construct a very wide beam as shown by the com-
plete rectangle in Fig. 102, there is no hesitation about calculating
such strength as that of a plain beam whose width is b, and whose

227

216 MASONRY AND REINFORCED CONCRETE

effective depth to the reinforcement is d. Our previous study in
plain beams has shown us that the steel in the bottom of the beam
takes care of practically all the tension; that the neutral axis of the
beam is somewhat above the center of its height; that the only work
of the concrete below the neutral axis is to transfer the stress in the
steel to the concrete in the top of the beam; and that even in this
work it must be assisted somewhat by stirrups or by bending up the
steel bars. If, therefore, we cut out from the lower corners of the
beam two rectangles, as shown by the unshaded areas, we are saving
a very large part of the concrete, with very little loss in the strength
of the beam, provided we can fulfil certain conditions. The steel,
instead of being distributed uniformly throughout the bottom of
the wide beam, is concentrated into
the comparatively narrow portion
which we shall hereafter call the rib
of the beam. The concentrated ten-
sion in the bottom of this rib must
be transferred to the compression area
at the top of the beam. We must
also design the beam so that the shear-
ing stresses in the plane mn imme-

Fig. 102. Diagram of T-Beam in diately below the slab shall not CX-
Cross Section .

ceed the allowable shearing stress in

the concrete. We must also provide that failure shall not occur
on account of shearing in the vertical planes mr and ns between
the sides of the beam and the flanges.

Resisting Moments of T=Beams. The resisting moments of
T-beams will be computed in accordance with straight-line formulas.
There are three possible cases, according as the neutral axis is: (1)
below the bottom of the slab (which is the most common case, and
which is illustrated in Fig. 103); (2) at the bottom of the slab; or
(3) above it. All possible effect of tension in the concrete is ignored.
For Case I, even the compression furnished by the concrete between
the neutral axis and the under side of the slab is ignored. Such
compression is, of course, zero at the neutral axis; its maximum
value at the bottom of the slab is small ; the summation of its com-
pression is evidently small ; the lever arm is certainly not more than
§ y; therefore, the moment due to such compression is insignificant

MASONRY AND REINFORCED CONCRETE 217

compared with the resisting moment due to the slab. The com-
putations are much more complicated if it is included; the resulting
error is a very small percentage of the true figure, and the error is on
the side of safety.

Case I. If c is the maximum compression at the top of the slab,
and the stress-strain diagram is rectilinear, as in Fig. 103, then the

compression at the bottom of the slab is c . The average com-

pression equals \ (c + c ) = — (k d —

/c d fc cL

The total compression

equals the average compression multiplied by the area b't; or

C = As = b't-^(kd-$t) (23)

The center of gravity of the compressive stresses is evidently at the

*' A

NEUTRfJL fJXfS

Fig. 103. Compression Stress Diagram for T-Beam

center of gravity of the trapezoid of pressures. The distance x of
this center of gravity from the top of the beam is given by the
formula

t 3kd-2t /0/1N

*=i>x^rt (24)

It has already been shown on page 185 that
ec _cn_ kd
es s d—kd

Combining this equation with Equation (23), we may eliminate —
and obtain a value for kd

,,_

(25)

229

218 MASONRY AND REINFORCED CONCRETE

If the percentage of steel is chosen at random, the beam will probably
be over-reinforced or under-reinforced. In general it will therefore
be necessary to compute the moment with reference to the steel and
also with reference to the concrete, and, as before with plain beams
(Equation 20), we shall have a pair of equations

c , ,
kd ' (26)

Ms = As(d — x)=pb'ds(d — x)

Case II. If wre place kd = t in the equation just above Equation
(25), and solve for d, we have a relation between d, c, s, n, and t,
which holds when the neutral axis is just at the bottom of the slab.
The equation becomes

dJ(£H±£) (27)

A combination of dimensions and stresses which would place the
neutral axis exactly in this position is improbable, although readily
possible; but Equation (27) is very useful to determine whether a
given numerical problem belongs to Case I or Case III. When the
stresses s and c in the steel and concrete, the ratio n of the elasticities,
and the thickness t of the slab are all determined, then the solution
of Equation (27) will give a value of d which would bring the neutral
axis at the bottom of the slab. But it should not be forgotten that
the compression in the concrete (c) and the tension in the steel
will not simultaneously have certain definite values, say c = 500
and 5=16,000, unless the percentage of steel has been so chosen
as to give those simultaneous values. When, as is usual, some
other percentage of steel is used, the equation is not strictly applica-
ble, and it therefore should not be used to determine a value of d
which will place the neutral axis at the bottom of the slab and thus
simplify somewhat the numerical calculations. For example,
for c = 500, 5 = 16,000, ?i=12, and t = 4 inches, d will equal 14.67
inches. Of course this particular depth may not satisfy the require-
ments of the problem. If the proper value for d is less than that
indicated by Equation (27), the problem belongs to Case III; if it is
more, the problem belongs to Case I.

Case III. The diagram of pressure is very similar to that in Fig.
103, except that it is a triangle instead of a trapezoid, the triangle

230

MASONRY AND REINFORCED CONCRETE 219

having a base c and a height kd which is less than t. The center of
compression is at £ the height from the base, or x equals £ kd. Equa-
tions (17) to (20) are applicable to this case as well as to Case II, which
may be considered merely as the limiting case to Case III. But it
should be remembered that 6' refers to the width of the flange or
slab, and not to the width of the stem or rib.

Width of Flange. The width b' of the flange is usually con-
sidered to be equal to the width between adjacent beams, or that
it extends from the middle of one panel to the middle of the next.
The chief danger in such an assumption lies in the fact that if the
beams are very far apart, they must have corresponding strength
to carry such a floor load, and the shearing stresses between the rib
and the slab will be very great. The method of calculating such
shear will be given later. It sometimes happens (as illustrated on
page 227), that the width of slab on each side of the rib is almost
indefinite. In such a case we must arbitrarily assume some limit.
Since the unit shear is greater for short beams than for long beams,
the slab thickness should bear some relation to the span of the beam.
The building code specifications for New York City limit the width
on each side of the beam to not greater than one-sixth of the beam
span, and not greater than six times the slab thickness. If the
width of the rib is twice the slab thickness, this rule permits the
width of flange b' to be fourteen times the slab thickness, and some-
thing over one-third of the beam span, whichever is least. If the
compression is computed for two cases, both of which have the same
size of rib, same steel, same thickness of slab, but different slab
widths, it is found, as might be expected, that for the narrower slab
width the unit compression is greater, the neutral axis is very slightly
lower, and even the unit tension in the steel is slightly greater.
No demonstration has ever been made to determine any limitation
of width of slab beyond which no compression would be developed by
the transverse stress in a T-beam rib under it. It is probably safe to
assume that it extends for six times the thickness of the slab on each
side of the rib. If the beam as a whole is safe on this basis, then it
is still safer for any additional width to which the compression may
extend.

Width of Rib. Since it is assumed that all of the compression
occurs in the slab, the only work done by the concrete in the rib is

231

220 MASONRY AND REINFORCED CONCRETE

to transfer the tension in the steel to the slab, to resist the shearing
and web stresses, and to keep the bars in their proper place. The
width of the rib is somewhat determined by the amount of reinforcing
steel which must be placed in the rib, and whether it is desirable to
use two or more rows of bars instead of merely one row. As indi-
cated in Fig. 102, the amount of steel required in the base of a
T-beam is frequently so great that two rows of bars are necessary in
order that the bars may have a sufficient spacing between them so
that the concrete will not split apart between the bars. Although
it would be difficult to develop any rule for the proper spacing
between bars without making assumptions which are perhaps doubt-
ful, the following empirical rule is frequently adopted by designers:
The minimum spacing betwreen bars, center to center, should be
two-and-a-quarter times the diameter of the bars. Fire insurance
and municipal specifications usually require that there shall be one-
and-a-half to two inches clear outside of the steel. This means that
the beam shall be three or four inches wider than the net width
from out to out of the extreme bars. The data given in Table XXIV
will therefore be found very convenient, since, when it is desired to
use a certain number of bars of given size, a glance at the table will
show immediately whether it is possible to space them in one row;
and, if this is not possible, the necessary arrangement can be very
readily designed. For example, assume that six |-inch bars are to
be used in a beam. The table shows immediately that, following the
rule, the required width of the beam will be 14.72 inches; but if,
for any reason, a beam 11 inches wide is considered preferable, the
table shows that four |-inch bars may be placed side by side, leaving
two bars to be placed in an upper row. Following the same rule
regarding the spacing of the bars in vertical rows, the distance
from center to center of the two rows should be 2. 25 X. 875, or 1.97
inches, showing that the rows should be, say two inches apart center
to center. It should also be noted that the plane of the center of
gravity of this steel is at two-fifths of the distance between the bars
above the lower row, or that it is .8 inch above the center of the
lower row.

Examples. 1. Assume that a 5-inch slab is supporting a load on beams
spaced 5 feet apart, the beams having a span of 20 feet. Assume that the moment
of the beam has been computed as 900,000 inch-pounds. What will be the

MASONRY AND REINFORCED CONCRETE 221

TABLE XXIV

Required Width of Beam, Allowing 2l/4Xd, for Spacing, Center to
Center, and 2 Inches Clear on Each Side

n = number of bars; d= diameter
Formula: Width = (n-l) 2.25d+d+4 = 2.25 n<2-1.25d+4

No. OF
BARS

fetf.

BAR

I-IN.

BAB

1-IN.

BAR

S-IN.

BAR

1-IN.

BAR

It-IN

BAR

li-IN.

BAR

Inches

5.62

6.03

6.44

6.84

7.25

7.66

8.06

6.75

7.44

8.13

8.81

9.50

8.19

10.87

7.87

8.84

9.81

10.78

11.75

12.72

13.68

9.00

10.25

11.50

12.75

14.00

15.25

16.50

10.12

11.65

13.19

14.72

16.25

17.78

19.31

11.25

13.06

14.87

16.68

18.50

20.31

22.12

12.37

14.46

16.56

18.65

20.75

22.84

24.94

13.50

15.87

18.25

20.62

23.00

25.37

27.75

14.62

17.28

19.94

22.59

25.25

27.90

30.56

NOTE. For side protection of only one and one-half inches, deduct one inch from above
figures.

dimensions of the beam if the concrete is not to have a compression greater
than 600 pounds per square inch and the tension of the steel is not to be greater
than 16,000 pounds per square inch?

Solution. There are an indefinite number of solutions to this problem.
There are several terms in Equation (26) which are mutually dependent; it is
therefore impracticable to obtain directly the depth of the beam on the basis
of assuming the other quantities; therefore, it is only possible to assume figures
which experience shows will give approximately accurate results, and then test
these figures to see whether all the conditions are satisfied. Within limitations,
we may assume the amount of steel to be used, and determine the depth of
beam which will satisfy the other conditions, together with that of the assumed
area of steel. For example, we shall assume that six f-inch square bars having
an area of 4.59 square inches will be a suitable reinforcement for this beam.
We shall also assume as a trial figure that x equals 1.5. Substituting these
values in the second formula of Equation (26), we may write the second formula

900,000 = 4.59 Xl6,000(d- 1.5)

Solving for d, we find that d equals 13.75. If we test this value by means of
Equation (27), we shall find that, substituting the values of t, c, n, and s in
Equation (27), the resulting value of d equals 16.11. This shows that if we
make the depth of the beam only 13.75, the neutral axis will be within the slab,
and the problem comes under Case III, to which we must apply Equation (20).
Dividing the area of the steel 4.59 by (6'Xd), we have the value of p equals
.00556. Interpolating with this value of p in Table XVII, we find that when
n equals 12, fc = .303; /bd = 4.17; z = 1.39; and jd = 12.36. Substituting these
values in Equation (20), we find that the moment 900,000 equals 1.545c, or that
c equals 582 pounds per square inch. This shows that the unit compression of
the concrete is safely within the required figure. Substituting the known values

222 MASONRY AND REINFORCED CONCRETE

in the second part of Equation (20), we find that the stress in the steel s equals
about 15,860 pounds per square inch.

2. Assume that a floor is loaded so that the total weight of live and dead
load is 200 pounds per square foot; assume that the T-beams are to be 5 feet
apart, and that the slab is to be 4 inches thick; assume that the span of the
T-beams is 30 feet. Find the dimensions of the beams.

Solution. We have an area of 150 square feet to be supported by each
beam, which gives a total load of 30,000 pounds on each. The moment at the
center of such a beam will equal the total load times one-eighth of the span (in
inches), or 1,350,000 inch-pounds. As a trial value, we shall assume that the
beam is to be reinforced with six f-inch square bars, which have an area of 3.375
square inches. Substituting this value of the area in the second part of Equation
(26), and assuming that s equals 16,000 pounds per square inch, we find as an
approximate value for d-x, that it will equal 25 inches. This is very much
greater than the value of d that would be found from substituting the proper values
in Equation (27), so that we know at once that the problem must be solved
by the methods of Case I. For a 4-inch slab, the value of x must be somewhere
between 1.33 and 2.0. As a trial value, we may call it 1.5, and this means that
d will equal 26.5. Assuming that this slab is to be made of concrete using a
value for n equal to 12, we know all the values in Equation (25), and may solve
for kd, which we find to equal 5.54 inches. As a check on the approximations
made above, we may substitute this value of k d, and also the value of t in Equa-
tion (24), and obtain a more precise value of x, which we find to equal 1.62.
Substituting the value of the moment and the other known quantities in the
upper formula of Equation (26), we may solve for the value of c, and obtain
the value of 352 pounds per square inch. This value for c is so very moderate
that it would probably be economy to assume a lower value for the area of
the steel, and increase the unit compression in the concrete; but this solution
will not be worked out here.

Calculations by Approximate Formulas. A great deal of
T-beam computation is done on the basis that the center of pressure
of the concrete is at the middle of the slab and, therefore, that the
lever arm of the steel equals d— \i. From these assumptions we
may write the approximate formula

Ms*=As(d-\t] (28)

If the values of M8 and s are known or assumed, we may assume a
reasonable value for either A or d — \t and calculate the correspond-
ing value of the other. On the assumption that the slab takes all
the compression, the distance between the steel and the center of
compression of the concrete varies between d—\t and d— .142,
which is the approximate value when the beam becomes so small that
it merges into the slab. The smaller value d—\t is the absolute
limit which is never reached. Therefore the lever arm is always

234

MASONRY AND REINFORCED CONCRETE 223

larger than d—\t. Therefore, if we use Equation (28) to compute
the area of steel A for a definite moment Ms and unit steel tension s,
the resulting value of A for an assumed depth d, or the resulting
value of d for an assumed area A, will be larger than necessary. In
either case the result is safe, but not economically so.

As an illustration, using the values in Example 2, above of
Ms=l,350,000; 5 = 16,000; (d-^) = 26.5-2 or 24.5, the resulting
value of A equals 3.44 square inches, which is larger than the more
precise value previously computed.

Equation (28) is particularly applicable when the neutral axis is
in the rib. Under this condition, the average pressure on the con-
crete of the slab is always greater than \c, or at least it is never less
than |c. As before explained, the average pressure just equals \v
when the neutral axis is at the bottom of the slab. We may, there-
fore, say that the total pressure on the slab is always greater than
\c\)'t. We therefore write the approximate equation

Mc = ±cb't(d-W (29)

As before, the values obtained from this equation are safe, but are
unnecessarily so. Applying them to Example 2, by substituting
Mc = 1,350,000, 6' = 60, < = 4, and d-^ = 24.5, we compute c = 459.
But we know that this approximate value of c is greater than the
true value ; and if this value is safe, then the true value is certainly
safe. The more accurate value of c, computed in the example
cited, is 352: If the value of c in Equation (29) is assumed, and
the value of d is computed, the result is a depth of beam unnec-
essarily great.

If the beam is so shallow that we may know, even without the
test of Equation (27), that the neutral axis is certainly within the
slab, then we may know that the center of pressure is certainly less
than J t from the top of the slab, and that the lever arm is certainly
less than d — \t; and we may therefore modify Equation (28) to read

M. = As(d-W (30)

Applying this to Example 1, and substituting Ms = 900,000,
s = 16,000, d-$t = (13.75 -1.67) = 12.08, we find that ^4=4.65,
instead of the 4.59 previously computed. This again illustrates
that the formula gives an excessively safe value, although in this
case the difference is small.

235

224 MASONRY AND REINFORCED CONCRETE

Equations (28) and (29) should be considered as a pair which are
applied according as the steel or the concrete is the determining
feature. When the percentage of steel is assumed (as is usual), both
equations should be used to test whether the unit stresses in both
the steel and the concrete are safe. It is impracticable to form a
simple approximate equation corresponding to Equation (30), which
will express the moment as a function of the compression in the con-
crete. Fortunately it is unnecessary, since, when the neutral axis
is within the slab, there is always an abundance of compressive
strength.

Shearing Stresses between Beam and Slab. Every solution
for T-beam construction should be tested at least to the extent of
knowing that there is no danger of failure on account of the shear
between the beam and the slab, either on the horizontal plane at the

iuummuuul ,,

Fig. 104. Diagram Showing Analysis of St

lower edge of the slab, or in the two vertical planes along the two
sides of the beam. Let us consider a T-beam such as is illustrated
in Fig. 104. In the lower part of the figure is represented one-half of
the length of the flange, which is considered to have been separated
from the rib. Following the usual method of considering this as a
free body in space, acted on by external forces and by such internal
forces as are necessary to produce equilibrium, we find that it is acted
on at the left end by the abutment reaction, which is a vertical force,
and also by a vertical load on top. We may consider P' to represent
the summation of all compressive forces acting on the flanges at the
center of the beam. In order to produce equilibrium, there must be
a shearing force acting on the under side of the flange. We represent
this force by Sh. Since these two forces are the only horizontal
forces, or forces with horizontal components, which are acting on
this free body in space, P' must equal Sh. Let us consider z to

236

MASONRY AND REINFORCED CONCRETE 225

represent the shearing force per unit of area. We know from the
laws of mechanics that, with a uniformly distributed load on'the beam,
the shearing force is maximum at the ends of the beam, and dimin-
ishes uniformly towards the center, where it is zero. Therefore the
average value of the unit shear for the half length of the beam "must
equal \z. As before, we represent the width of the rib by 6. For
convenience in future computations, we shall consider L to repre-
sent the length of the beam, measured in feet. All other dimensions
are measured in inches. Therefore the total shearing force along
the lower side of the flange will be

(31)

There is also a possibility that a beam may fail in case the flange,
or the slab, is too thin; but the slab is always reinforced by bars
which are transverse to the beam, and the slab will be placed on both
sides of the beam, giving two shearing surfaces.

Numerical Illustration. It is required to test the beam which
was computed in Example 1. Here the total compressive stress
in the flange equals %cb'kd = %X582X 60X4. 17 = 72,808 pounds.
But this compressive stress measures the shearing stress Sh
between the flange and the rib. This beam requires six f-inch
bars for the reinforcement. We shall assume that the rib is to
be 11 inches wide, and that four of the bars are placed in the
bottom row, and two bars about 2 inches above them. The effect
of this will be to deepen the beam slightly, since d measures the
depth of the beam to the center of the reinforcement, and, as already
computed numerically on page 220, the center of gravity of this
combination will be T\ of an inch above the center of gravity of the
lower row of bars. Substituting in Equation (31) the values
Sh = 72,808, 6=11, and Z=20, we find for the unit value of z 110
pounds per square inch. This shows that the assumed dimensions
of the beam are satisfactory in this respect, since the true shearing
stress permissible in concrete is higher than this.

But the beam must be tested also for its ability to withstand
shear in vertical planes along the sides of the rib. Since the slab in
this case is 5 inches thick and we can count on both surfaces to with-
stand the shear, we have a width of 10 inches to withstand the shear
as compared with the 11 inches on the underside of the slab. The

237

220 MASONRY AND REINFORCED CONCRETE

unit shear would, therefore, be ] J of the unit shear on the underside
of the slab, or 121 pounds per square inch. This is at or beyond
the limit, 120 pounds, but danger of failure in this respect is
avoided by the fact that the slab contains bars which are inserted
to reinforce it, and which have such an area that they will
effectively prevent any shearing in this way.

Testing Example 2 similarly, we may find the total compression
C from Equation (23), which equals ;4 5 = 3.375X16,000 = 54,000
pounds. The steel reinforcement is six f-inch bars, and from
Table XXIV we find that if placed side by side, the beam must be
13.19 inches in width, or, in round numbers, 13| inches. Sh = 54,000,
6 = 13.25, I/ = 30; therefore, from Equation (31), 2 = 45 pounds per
square inch. Such a value is of course perfectly safe. The shear
along the sides of the beam will be considerably greater, since the
slab is only four inches thick, and twice the thickness is but 8 inches ;
therefore, the maximum unit shear along the sides will equal 45
times the ratio of 13.25 to 8, or 75 pounds per square inch. Even
this would be perfectly safe, to say nothing of the additional shearing
strength afforded by the slab bars.

Shear in a T=Beam. The shear here referred to is the shear of
the beam as a whole on any vertical section. It does not refer to
the shearing stresses between the slab and the rib.

The theoretical computation of the shear of a T-beam is a very
complicated problem. Fortunately, it is unnecessary to attempt
to solve it exactly. The shearing resistance is certainly far greater
in the case of a T-beam than in the case of a plain beam of the same
width and total depth and loaded with the same total load. There-
fore, if the shearing strength is sufficient, according to the rule, for
a plain beam, it is certainly sufficient for the T-beam. In Example
1, page 220, the total load on the beam is 30,000 pounds; therefore,
the maximum shear V at the end of the beam is 15,000 pounds.
In this particular case, jd equals 12.36. For this beam, d equals
13.75 inches and b equals 11 inches. Substituting these values in
Equation (22), we have

15,000

= 113 Ib. per sq. in.

b(jd) 11X12.36
Although this is probably a very safe stress for direct shearing, it is

238

MASONRY AND REINFORCED CONCRETE 227

more than double the allowable direct tension, 40, due to the diag-
onal stresses and, therefore, ample reinforcement must be provided.
If only two of the f -inch bars are turned at an angle of 45° at the
end, these two bars will have an area of 1.54 square inches, and will
have a working tensile strength (at the unit stress of 16,000 pounds)
of 24,640 pounds. This is more than the total vertical shear at the
ends of the beam, and a pair of turned-up bars would therefore take
care of the shear at that point. But considering that stirrups
would be used on a beam of 20-foot span, it will be very easy to design
these stirrups to provide for this shear, as was explained on page 207.

Numerical Illustration of Slab, Beam, and Girder Construction.
Assume a floor construction as outlined in skeleton form in Fig. 105.
The columns are spaced 16 feet by 20 feet. Girders which support
the alternate rows of beams connect the columns in the 16-foot
direction. The live load on the floor is 150 pounds per square foot.
The concrete is to be 1:2:4 mixture, with n = l2 and c = 600.
Required the proper dimensions for the girders, beams, and slab.

Slab. The load on the girders may be computed in either one of
two ways, both of which give the same results. We must consider
that each beam supports an area of 8 feet by 20 feet. We may there-
fore consider that girder d supports the load of b (on a floor area 8 feet
by 20 feet) as a concentrated load in the center. Or, we may consider
that, ignoring the beams, the girder supports a uniformly distributed
load on an area 16 feet by 20 feet. The moment in either case is the
same. Assume that we shall use a 1 per cent reinforcement in the
slab. Then, from Table XVIII, -with n=l2 and p = .01, we find
that k = . 385; then x = A2Sd, orjd=.872d. As a trial, we estimate
that a 5-inch slab (or d=4) will carry the load. This will weigh 60
pounds per square foot, and make a total live and dead load of 210
pounds per square foot. A strip one foot wide and 8 feet long
will carry a total load of 1,680 pounds, and its moment wrill be JX
1,680X96 = 20,160 inch-pounds. Using the first half of Equa-
tion (20), we can substitute the known values and say that

20,160 =— X600xl2X.385rfX.872d

= l,209d2
d2 = 16.67
d = 4.08

228 MASONRY AND REINFORCED CONCRETE

In this case the span of the slab is considered as the distance from
center to center of the beams. This is evidently more exact than to
use the net span — which equals 8 feet, less the still unknown width
of beam — since the true span is the distance between the centers of
pressure on the two beams. It is probable that the true span (really
indeterminable) will be somewhat less than 8 feet, which would
probably justify using the round value of d = 4 inches and the slab
thickness as 5 inches, as first assumed. The area of the steel per
inch of width of slab equals pbd=. 01X1X4.08 = .0408 square inch.
Using f-inch round bars whose area equals .1963 square inch, the

required spacing of the bars will
be . 1963 H- .0408 = 4.81 inches. As
shown later, the girder will be
11 inches wide and the net width
of the slab is 240 inches - 11
inches = 229 inches. 229-4-4.81
= 47.6; call it 48, the number
of bars to be spaced equally in
one panel. (See page 199.)

Beam. The load on a beam
is that on an area of 8 feet by 20
feet, and equals 8X20X210, or

33,600 pounds for live and dead load. As a rough trial value, we
shall assume that the beam will be 12 inches wide and 15 inches
deep below the slab, or a volume of 1X1.25X20, or 25 cubic feet,
which will weigh 3,600 pounds. Adding this, we have 37,200
pounds as the total live and dead load carried by each beam. The
load is uniformly distributed and the moment is

J/ = 4-X37,2(X)X240 = 1,116,000 in.-lb.

We shall assume that the beam is to have a depth d to the reinforce-
ment of 22 inches, and shall utilize Equation (30) to obtain an
approximate value for the area. Substituting the known quantities
in Equation (30), wre have

1,116,000 = A X 16,000 X (22- 1.67)
^1=3.43 sq. in.

For T-beams with very wide slabs and great depth of beam, the

(

N BE flM a (

(GIRDER d QlRDEKey

* 4

3£AM b

~\ ££AM C (

j
J[

J , „ V

•^ £0'0 fc>

Fig. 105. Skeleton Outline of Floor Panel
Showing Slab, Beam, and Girder Con-

240

MASONRY AND REINFORCED CONCRETE 229

percentage of steel is always very small. In this case, p = '3A3 +
(96X22) = .00162. Such a value is beyond the range of those given
in Table XVII, and therefore we must compute the value of k from
Equation (14), and we find fc = .I80 and &<£ = 3.96, which shows
that the neutral axis is within the slab; x = $kd = 1.32, and there-
fore jd = 20.68. Assume that b' equals fourteen times the slab
thickness, or 70 inches; see page 219. Substituting these values in
the upper part of Equation (20) in order to find the value of c, we
find that c = 390 pounds per square inch. Substituting the known
values in the second half of Equation (20), in order to obtain a more
precise value of s, we find that s = 15,734 pounds per square inch.

The required area (3.43 square inches) of the bars will be afforded
by six f-inch round bars (6 X. 60 = 3.60) with considerable to spare.
From Table XXIV we find that six f-inch bars, either square or
round, if placed in one row, would require a beam 14.72 inches
wide. This is undesirably wride, and so we shall use two rows, three
in each row, and make the beam 9 inches wide. This will add an
inch to the depth, and the total depth will be 22+3, or 25 inches.
The concrete below the slab is therefore 9 inches wide by 20 inches
deep, instead of 12 inches wide by 15 inches deep, as assumed when
computing the dead load, but the weight is the same. It should
also be noted that the span of these beams was considered as 20
feet, which is the distance from center to center of the columns (or
of the girders). This is certainly more nearly correct than to use the
net span between the columns — or girders — which is yet unknown,
since neither the columns nor the girders are yet designed. There
is probably some margin of safety in using the span as 20 feet.

Girder. The load on one beam is computed above as 37,200
pounds. The load on the girder is, therefore, the equivalent of this
load concentrated at the center, or of double the load (74,400 pounds)
uniformly distributed. Assuming for a trial value that the girder
will be 12 inches by 22 inches below the slab, its weight for sixteen
feet will be 4,224 pounds. This gives a total of 78,624 pounds as
the equivalent total live load and dead load uniformly distributed
over the girder. Its moment in the center, therefore, equals
| X 78,624X192 = 1,886,976 inch-pounds.

The width of the slab in this case is almost indefinite, being
20 feet, or forty-eight times the thickness of the slab. We shall

241

230 MASONRY AND REINFORCED CONCRETE

therefore assume that the compression is confined to a width of
fourteen times the slab thickness, or that b' = 70 inches. Assume for
a trial value that d = 25 inches; then from Equation (30), if s=* 16,000,
we find that ^4=5.05 square inches. Then p = . 00288; and, from
Equation (14), & = .231 and kd = 5.775. This shows that the
neutral axis is below the slab, and that it belongs to Case I, page
217. Checking the computation of kd from Equation (25), we
compute kd = 5.82, which is probably the more correct value because
computed more directly. The discrepancy is due to the dropping
of decimals during the computations. From Equation (24), we
compute that a: = 1.87, then (d-x) =23.13. Substituting the value
of the moment and of the dimensions in the upper part of Equation
(26), we compute c to be 409 pounds per square inch. Similarly,
making substitutions in the lower part of Equation (26), using the
more precise value of d — x for the lever arm of the steel, we find
* = 16,052 pounds per square inch. The student should verify in
detail all these computations.

The total required area of 5.08 square inches may be divided
into, say 8 round bars | inch in diameter. These would have an
area of 4.81 square inches. The discrepancy is about five per cent.
Using the eight round |-inch bars, the unit stress would be nearly
17,000 pounds. If this is considered undesirable, a more exact area
may be obtained by using six f-inch round bars and two 1-inch
round bars. The area wrould be 5.18 square inches, somewhat in
excess of that required. These bars, placed in two rows, would
require that the beam should be at least 10.78 inches wide. We
shall call it 11 inches. The total depth of the beam will be 3
inches greater than d, or 28 inches. This means 23 inches below
the slab, and the area of concrete below the slab is, therefore, 11 X23,
or 253 square inches, rather than 12x22, or 264 square inches, as
assumed for trial.

Shear. The shearing stresses between the rib and slab of the
girder are of special importance in this case. The quantity Sh, page
224, equals the total compression in the concrete, which equals the
total tension in the steel, which equals, in this case, 16,052X5.08, or
81,544 pounds. This equals 3bzL, in which b equals 1 1, L equals 16
(feet), and z is to be determined.

2 = 81,544^ (3X11X16) = 154 Ib. per sq. in.

242

MASONRY AND REINFORCED CONCRETE 231

This measures the maximum shearing stress under the slab and is
almost safe, even without the assistance furnished by the stirrups and
the bars, which would come up diagonally through the ends of the
beam — where this maximum shear occurs — nearly to the top of the
slab. The vertical planes on each side of the rib have a combined
width of 10 inches, and therefore the unit stress is 1^X154, or 169
pounds per square inch. This is a case of true shear, though it is
somewhat larger than the permissible working shear. But there are
still other shearing stresses in these vertical planes. Considering a strip
of the slab, say one foot wide, which is reinforced by slab bars that
are parallel to the girder, the elasticity of such a strip (if disconnected
from the girder) would cause it to sag in the center. This must be
prevented by the shearing strength of the concrete in the vertical
plane along each edge of the girder rib. On account of the combined
shearing stresses along these planes, it is usual to specify that when
girders are parallel with the slab bars, bars shall be placed across
the girder and through the top of the slab for the special purpose of
resisting these shearing stresses. Some of the stresses are indefinite,
and therefore no precise rules can be computed for the amount of
the reinforcement. But since the amount required is evidently very
small, no great percentage of accuracy is important. Specifications
on this point usually require f-inch bars, 5 feet long, spaced 12
inches apart.

The shear of the girder, taken as a whole, should be computed
as for simple beams, as already discussed on page 226; and stirrups
should be used, as described on page 207.

Another special form of shear must be considered in this prob-
lem. Where the beams enter the girders there is a tendency for
the beams to tear their way out through the girder. The total load
on the girder by the two beams on each side is of course equal to the
total load on one beam, and equals 37,200 pounds. Some of the
reinforcing bars of the beam will be bent up diagonally so that they
enter the girder near its top, and therefore the beam could not tear
out without shearing through the girder from near its top or for a
depth of, say 22 inches (3 inches less than d). If there were no
reinforcing steel in the girder and enough load were placed on the
beam to actually tear it out, the fracture would evidently be in the
form of an inverted V. The resistance to such tearing out would

243

232 MASONRY AND REINFORCED CONCRETE

be chiefly that of the tensile strength of the concrete. Assuming the
width of the fracture, or its horizontal projection, to be 44 inches,
and the other dimension, which is the
width of the girder rib, 1 1 inches, there
is an area of 484 square inches, and at 40
pounds working tension, it could safely
carry a load of 19,360 pounds. But the
total load, as shown above, is 37,200
pounds. The steel reinforcement of the
girder is, therefore, essential to safety.
Although the main reinforcing bars of the
girder would have to be torn out before

complete failure could take place, the resistance to a small displace-
ment, perpendicular to the bars, is comparatively small, and there-
fore these bars should not be depended on to resist this stress. But

Fig. 106. Details of Reinforce-
ment at Junction of Beam and
Girder

'••-,-•••

--TP r' ;!i;^ - ! !:'l !• 111 I [OT

J— "US-'T lij :j,ir r- --HI K'-1J ^-i

jL__.$i:3 |j

Fig. 107. Detail of Complete Floor Panel

a pair of ordinary vertical stirrups bb, Fig. 106, passing under
the main girder bars can easily be made of such size as to take any
desired portion, or all, of that load. The stirrups should be bent at

244

MASONRY AND REINFORCED CONCRETE 233

the upper end so that the strength of the bars may be developed
without dependence upon bond adhesion. Although precise numer-
ical calculations are impossible without making assumptions which
are themselves uncertain, the following calculation is probably
safe. 37,200-19,360=17,840; for s equals 16,000, the required
area would be 1.115 square inches. Two pairs of stirrups would
give four bar areas which could each be 0.28 square inch, provided
by f-inch round bars. Fig. 107 shows assembled details.

FLAT=SLAB CONSTRUCTION*

Outline of Method. The so-called "flat-slab method" has the
advantages that (a) there is a very considerable saving in the required
height (and cost) of the building on the basis of a given net clear
height between floors; (6) the architectural appearance is improved
by having a flat ceiling surface rather than visible beams and gird-
ers; (c) there is a saving in the cost of forms, not only in surface
area and amount of lumber required but also in simplicity of con-
struction, although this saving is offset by an increase in total vol-
ume of concrete used; (d) there are no deep ceiling beams to cast
shadows and it is possible to extend the windows up to the ceiling,
which are important items in the lighting of a factory building.
Almost the only disadvantage is the difficulty in making perfectly
definite and exact computations of the stresses, as may be done for
simple beams and slabs. But methods of computation have been
devised which, although admittedly approximate, will produce
designs for economical construction, and structures so designed
have endured, without distress, test loads considerably greater than
the designed working loads.

Consider, first, a simple beam, as in Fig. 108-a, the beam being
continuous over the supports and uniformly loaded for the distance
I between the supports with a load amounting to W. Then the
maximum moment is located just over the supports and equals
Wl+12. Another local maximum, equal to Wl+24, is found at
the center. Points of inflection are at .21 ll from each column.

Assume that a uniformly loaded plate of indefinite extent is
supported on four columns, A, B, C, and D, Fig. 108-6, the exten-

* A Supreme Court decision in June, 1915, sustained the Noreross patent as basic on all flat
slab construction. The largest and most responsible flat-slab builders of the country now operate
under a Norcrosa license.

245

234 MASONRY AND REINFORCED CONCRETE

sions beyond the columns being such that planes tangent to the
plate just over the columns will be horizontal. Then the fol-
lowing conditions may be ob-
served :

( 1 ) The plate will be convex
upward over the columns;

(2) the plate will be con-
cave upward at the point 0 in
the center;

(3) there will be curves of
inflection, approximately as
shown by the dotted curves
sketched in around the columns ;
from the analogy of the simple
beam, given above, we may as-
sume that the curves of inflection
are approximately at 21 per cent
of the span in every direction
from the columns.

The columns at the top are
made with enlarged sections so
as to form a "column head"-
which is generally in the form of
a frustum of an inverted pyra-
mid or cone, the base being a
circle, a square, or a regular
polygon.

This device shortens the clear
span and decreases the moment.
It also increases the size of the
hole which the column tends to
punch through the plate and
hence increases the surface area
which resists this punching shear,
and thus decreases the unit
shear. The diameter of the col-
umn head should be about 25, per cent of the span between column
centers.

Fig. 108. Diagrams Showing Details of "Flat-
Slab" Method of Floor Construction

246

MASONRY AND REINFORCED CONCRETE 235

Placing Reinforcing Bars. Various systems of placing the rein-
forcing bars have been devised, and some of them patented. The
methods may be classified as follows: (1) "Four-way" method, in
which the bars run not only in lines parallel to the sides of the
rectangles joining the column heads, but also parallel to the diag-
onals; (2) "two-way" method, in which there are no diagonal
bars; and (3) designs which have, in addition to the bands of
straight bars from column to column, spirals or a series of rings
around the column heads for the specific purpose of providing for
the "circumferential tension, or moment". This circumferential
tension unquestionably exists, but those who use the first two
methods claim that the gridiron of bars formed over the column by
the two-way method, and still more so by the four- way method,
develops plate action, and that the circumferential stress is amply
provided for.

It is a simple matter of geometry to prove that if bands
of bars of width b, Fig. 108-6, are placed across columns which
form square panels with span I, the width b must equal .414 1,
if the bands exactly cover the space without leaving either
gaps or overlaps at ra, n, o, and p. The bands may be a little
narrower than this, say b equals Al, provided the gaps are not
much, if any, greater than the spacing of the bars. On the other
hand, the bands should not be wider than twice the diameter of
the column head. Fig. 108-c shows that, using the four-way system
and with b equal to .414/, every part of the slab has at least one
layer of bars, some parts have two, some three, and that there are
four layers of bars over each column. This is where the moment is
maximum.

Method of Calculation. One of the simplest methods of calcu-
lation, which probably gives a considerable but undeterminate
excess of strength, is to consider the bands as so many simple con-
tinuous beams, which are wide but shallow. Consider a direct band
of width b, equal to Al, the word direct being used in contradistinc-
tion to diagonal. If w is the unit dead and live load per square foot,
and s the net span between column heads, then the total load on the
band is Awls. Computed as a simple continuous beam, the
moment in the center would be (Awls)s-i- 24, and that over the
columns would be (Awls) s + 12. By prolonging the steel bars of

247

236 MASONRY AND REINFORCED CONCRETE

adjoining bands sufficiently over a column head so that the bond
adhesion is sufficient to develop the full tension over the column
head, the total effective area of steel in that band over the column
head is double what it is in the center. Practically, this means that
the steel should extend to the point of inflection beyond the column
head or that its length should be 42 per cent longer than the distance
between column centers. Then, on the principle of T-beam flanges,
it is assumed that the concrete above the neutral axis for a width
of (b+5f) may be computed as taking the compression. For the
diagonal bands, the load is wX- 4lXl .414s = .5G5wls, and then,
considering that a considerable part of the area of the diagonal
bands includes that already covered by the direct bands, and also
that the diagonal bands both support a square in the center which
is one-half of the area lying inside of the direct bands, the moment
for the central area is divided between the two diagonal bands and
that for each is considered to be (.565w^X 1.414s) -^48 = .0166wZs2.
As before, the moment over the columns for these bands is twice
as much, but the steel for the double moment may be obtained,
as before, by lapping the bars of adjoining diagonal bands over the
columns. The area of a panel, outside of the column heads, which
are here assumed to be square, is I2 — (/ — s)2. When the column
head is 25 per cent of /, then (7— s) = \ I and the area of the panel is
HI2, or .9375 12; and the total effective load causing moment on a
panel is JF=.9375u'/2. If we eliminate s and w from the above
moment equations, we have

A/r (Awls') s Awl3& 3.6 7,

Moment at center, direct band = - — —-*— = — — - — = r.wl

100

Moment over cap, direct band = (double the above) = H'/-i-50
Moment at center, diagonal band = .0166w/s2 = JF/-MOO
Moment over cap, diagonal band = (double the above) = Wl ^-50

Illustrative Example. Assume a live load of 200 pounds per
square foot on a square panel 22 feet between column centers. A
working rule is that the thickness of the slab should be at least ^V of
the span ; 7V of 22 feet, or 264 inches, is 8.8 inches. We will therefore
assume the slab thickness as 10 inches, which will weigh 120 pounds

248

MASONRY AND REINFORCED CONCRETE 237

per square foot. Therefore, w = 320 and IF = if w I* = $ X 320 X 222 =
145,200. Then the moment at the center of a direct band equals
W Z •*- 100 = (145,200 X 264) -5- 100 = 383,328 inch-pounds, and the
moment for that band over the column is 766,656 inch-pounds.
The width of each band b is .4 1 = .4x264 =105.6 inches. Assume
that the steel for one of the bands is placed at 8.5 inches from
the compression face, or that d equals 8.5; estimate j equals .91;
then

M=pbdsjd

= pXl05.6X8.5Xl6,OOOX. 91X8.5

= 383,328
from which

p=. 00345

From Table XVIII, we may note that for n equals 15 and p equals
.00345, j would be about .91. This checks the assumed value.
Then

^=^ = .00345X105.6X8.5 = 3.10 Sq. in.

This may be amply provided by 13 bars ^ inch square. 105.6 -j- 12,
or about 9 inches, gives the spacing of the bars. Although
doubling p changes the value of j and will not exactly double
the moment, yet it will be sufficiently exact to say that double
the moment will be obtained over the cap by prolonging the
13 bars of each of the two direct bands in the same line over
the columns as far as the circle of inflection, thus doubling the
area of the steel. The student should work this out as an exer-
cise. Double p and find the corresponding value of j from Table
XVIII; use the actual area of the 26 bars for the value of A,
and compute M from Asjd. On account of the slight excess in
the area of the 26 bars here used, the moment is a little more
than necessary.

Location of Bars. There are four layers of bars over the column
head and it is evident that they cannot all lie in the same plane or
be at the same distance from the compression face. For the layer
of bars considered above, d was assumed at 8.5, the maximum per-
missible with a 10-inch slab. For the next row deduct \ inch, the
thickness of the bars, and let d equal 8.0. Since the moment is

249

23S MASONRY AND REINFORCED CONCRETE

the same, and d is reduced, then p must be increased and j will be
less. Assume j equals .90; then

M = pbdsjd

= pXl05.6X8Xl6,OOOX.9XS
= 383,328
from which

p = . 00394

This is a little more than for the other band, as was expected. Then
A=pbd = 3.33 square inches, provided by 14 bars \ inch square.
Similarly, it may be shown that reducing d another half-inch for the
next layer will add another bar, making 15 bars for the third layer
and 10 bars for the fourth layer. Since the computed moments for
the direct and diagonal bands is the same for the center of the band,
and since the diagonal bands are the longer, there will be some
economy in giving them the advantageous position in the slab
(larger values of d) and using 13 and 14 bars for the diagonal bands
and 15 and 16 bars for the direct bands. The above variation in
the number of bars with the change in d indicates the importance of
placing the steel exactly as called for by the plans. The design
might be made a little more symmetrical, and more foolproof dur-
ing construction by using 14 bars in each of the diagonal bands
and 16 bars in each of the direct bands, and then being sure that
the direct bands are under the diagonal bands where they pass over
the column heads.

Unit Compression. The unit compression may be computed
from the equation

For the concrete compression, we may call V = 105.6+5£ = 105.6+
50= 155.6. The critical place is over the column. Here, where the
moment is double,

p = A + b'd = Q.5+ (155.6X8.5) = .00724
Then M = 766,656; A: = .369; andj = .88.
Substituting these values, we find that

c = 420 pounds per sq. in.
But this is a more favorable case than the compression computed for

250

MASONRY AND REINFORCED CONCRETE 239

the band whose d is only 7 inches. In this case, p = A + bd = 8-t-
(155.6X7) = .00734, which makes £ = .371 and j=.88.
Substituting these values, we find that

c = 616 pounds per sq. in.

This is amply safe, especially in view of the fact that a cube sub-
jected to compression on all six faces, as it is in this case, can stand
a far higher unit compression than it can when the compression is
only on two faces.

Shear. The cap is a square 66 inches on a side and its perim-
eter is 264 inches. V in this case equals W and is 145,200 pounds.
For this calculation let j equal .88 and d equal 8.5; then

V 145,200

6J264X.88X8.5
Since this is a punching shear rather than diagonal tension, this
working value is allowable. The usual allowed unit value is 80.
At any section farther away from the column head, the total shear
is less, and the perimeter, and hence the shearing area, is greater,
and therefore the unit shear becomes less and less. The zone around
the column head is the critical section and, since it is where the
moment is also maximum, no main reinforcing bars can be spared to
resist this shear, as is done at the ends of simple beams. A ring
of stirrups around each column head is the only practicable method
of resisting such shear, if it is excessive.

Wall Panels. The above calculations are virtually for interior
panels, or for those where the loads are balanced over the columns.
When panels are next to a wall, the bands perpendicular to the wall,
and even the diagonal bands, must be anchored by bending them
down into the columns. The extra steel is just as necessary, in
order to develop the moment at the column head, as if the bands
were extended into an adjoining panel. The band along the wall
between the wall columns may have part of the usual width cut
off. In addition to the floor load, the weight of the wall makes an
additional load. This may be most efficiently supported by a
"spandrel beam", which is a narrow but deep beam extending up
from the floor to the window sill, and which virtually forms that
part of the wall, although there may be an outside facing. Some-
times the exterior columns are set in from the building line so as

251

240 MASONRY AND REINFORCED CONCRETE

to partially, if not entirely, balance the load on the other side of the
columns.

General Constructive Details. The column head should have a
considerable thickness at its edge, immediately under the slab, to
enable it to withstand shear, as shown in Fig. WS-d. If, as is some-
times done, the sloping sides of the head are continued to the slab
surface, a considerable deduction should be made in estimating the
effective diameter of the head, which means an increase in the net
span between columns. The four points marked i, Fig. WS-d, are
at about 20 per cent of the net span between column heads
and are the computed points of inflection where there is no
moment. The bars should be in about the middle of the slab
at these points. They should be at the minimum permissible
distance above the bottom of the slab at 0 and similarly near
the top of the slab at the edges and across the column heads.
There should not be abrupt bends at these points, but the bars
should have easy curves through the required positions at 0
and the points of inflection and then, reversing curvature so that
it will be concave downward, should again reach a horizontal
direction just over the edge of the column head. While no great
precision is essential in locating the bars between these specified
points, care must be taken to fasten the bars in exact position
at the critical points so that they cannot be disturbed. There
should always be at least one inch of concrete below the bars in the
center of the slab.

Rectangular Panels. The flat-slab method of construction is
most economically used when the panels are nearly, if not quite,
square, and also when the column spacing can be made about 23
feet. The ratio of length to breadth for rectangular panels should
not exceed 4:3. The two pairs of direct bands must then be com-
puted independently and separately. The diagonal bands must be
computed according to their actual dimensions, which means that
the moment equations given above will not apply, and other
equations, computed in the same general manner, must be
derived. The quantity 6 may be considered as 0.4 of the mean of
the two column spans. The economy of the flat-slab method is
chiefly applicable to heavy floor loadings, such as are required for
factories, warehouses, etc.

MASONRY AND REINFORCED CONCRETE 241

REINFORCED=CONCRETE COLUMNS
AND WALLS

FLEXURE AND DIRECT STRESS

General Principles. In all of the previous work, the forces
acting on a beam are assumed to be perpendicular to the beam; the
forces acting on a column are assumed to coincide with the axis of
the column. There are many cases in designing in which the
resultant of the forces is oblique to the axis of the beam — or column
— and, therefore, develops both flexural and direct stress. This is
particularly the case in elastic arches. Usually, in concrete work
the combination is that of a compressive thrust and flexure, although
tension combined with flexure is not impossible. The following
demonstration will be made on the basis of the direct stress being
exclusively compression.

Columns have reinforcement near two (or four) faces. If the
load is eccentric, and especially if it is variable in position, direction,
and magnitude, the steel in either face may be alternately in tension
and in compression. In the case of arches, steel is placed near the
extrados, or upper surface of the arch, and also near the intrados, or
lower surface, and variations in the live load may cause the stress in
either set of bars to be alternately tension or compression. The
reinforcement is, therefore, in compression as well as in tension.
And since, for practical reasons, the reinforcement is made uniform
throughout the length of the column (beam or arch) and usually the
same on both faces, the stresses in the steel are sometimes compres-
sion, sometimes tension, sometimes zero, and in general will average
far less than the possible safe working value. It is economically
impracticable to vary the cross section of the steel to be everywhere
at the lowest safe limit of unit stress, especially when the stresses at
any section are variable for different loadings. It is, therefore,
necessary to use a design which shall be safe for the worst section
under the worst condition, although the strength will be excessive at
all other sections.

Moment of Inertia of Any Section. In the perfectly general
case, the steel near one face is not the same as that near the other.
If the steel were replaced by two external "wings" of concrete, each
of which is as far from the center as the steel and each of which has

253

242 MASONRY AND REINFORCED CONCRETE

an area n times the area of the steel (n = Es-t-Ec), we would have a
section such as is indicated in Fig. 109. 0 is the "centroid" of that
figure, but it is net necessarily in the middle of the height.
Let Ic = moment of inertia of the concrete rectangle with respect to

the axis through 0

Is = moment of inertia of the areas of steel about the same axis
Then

nls = moment of inertia of the concrete wings about the same axis;
/ = moment of inertia of the "transformed section" — the rec-

tangle and wings
Then

/=/c+n/s (32)

Let p = steel ratio on tension side (assumed here as lower side)

p' = steel ratio on compression side

Then, taking moments about the
upper edge of the concrete,

u_bh(%h)+nA'd'+nAd
bh+nA'+nA

But Af = p'bh and A=pbh.
Then

^bhfih+np'd'+npd)

Fig. 109. Diagram Showing Method of Cal-
culating Moment of Inertia of any Section

bh(\+np'+np)
\h-\-npd-\-np'd'
1+np+np'

(33)
(34)

IS=A (d-u)*+A' (u-d'Y

When, as is frequently the case, A equals A', and the whole section
is, therefore, symmetrical, u equals | h, and the two equations (34)
reduce to

(35)

It is a common practice to make d' = TV h, which would make

I, = 2A (Ahy
Then

(36)

254

MASONRY AND REINFORCED CONCRETE 243

Effect of Oblique Force Acting on a Section. A force which is
oblique to an axis can always be transformed into two components,
one of them parallel with, and the other perpendicular to, the axis
of the column, or the tangent to the arch rib. The perpendicular
component produces shear, and, although it should be tested on
general principles to be sure that the section can stand it, it is
generally true that the obliquity of the force is so small that the
shearing component does not produce a dangerous shearing stress
even for plain concrete. The component parallel to the axis is
called the thrust. Its effect on the section depends on its eccentricity,
or its distance e from the cen-
ter of gravity of the section.
There are three general cases :

First, when e is so small
that there is compression over
the entire section. When e is
0, the compression is uniform;
for very small values of e the

Compression Varies about as FiS- no- Diagram Showing Effect of Oblique

Force Acting on a Section

shown in Fig. 110, the great-
est unit compression being on the side of the eccentric force.

Second, for some special value of e (called e0) ; in this case the
compression at one face becomes just zero.

Third, for still larger values of e; in this case the stress on
the side away from the force T becomes tension. When this tension
is still small and less than the unit tension which may safely be
sustained by concrete, certain formulas apply. When the eccentric-
ity, and the consequent tension, becomes too great and the tension
must all be taken by the steel, other formulas must be used. For
simplicity, all of the following demonstrations on this subject will be
based on the two very common conditions that the section is rectan-
gular and that the steel reinforcement is the same on both sides.

These cases may now be considered in greater detail under four
heads, the first one being divided into two, when e = 0 and when
e>Q but still small.

Case I. e = 0 . Then the unit compression in the concrete equals

1 l (37)

255

244 MASONRY AND REINFORCED CONCRETE
and the unit compression in the steel equals

s = —(- "\ (38)

bh \(l+2?ip)/

Case II. e>Q, but is so small that there is compression over
the entire section. Then the maximum unit compression in the
concrete is

= __

' bh

and the maximum unit compression in the steel

= nT f _ 1_ 12gg ,-ft.

' bh +2*

In this case the force T may be considered as replaced by the series
of forces shown in Fig. 110 — two concentrated forces carried by the
steel near top and bottom and a graded series of compressions on
the concrete. The minimum unit values of the compression are of
little practical importance.

Case III. e = e0, the special value of e, determined later,
which will make the compression in the concrete at one face just
zero. The maximum unit compression in the concrete equals
2T

-6*

which is just twice the value found in Equation (37), which was to
be expected. Since Equation (39) is applicable to all values of e
between 0 and e0, we may place the two values of c from Equations
(39) and (41) equal and find the value of e, which is the special
value e0

_h2+24npa2 ' /A~

'°~oT(T+2M

Using this value of e0 for the e of Equation (40), the unit steel com-
pression is

O+T)

As before, the minimum unit stresses are of no practical importance.
Illustrative Example. Assume a concrete section bh equal to 12
inches by 18 inches, with J-inch square bars, spaced 6 inches, at top
and bottom. The distance d(, Fig. 1 10, is as usual TV h; therefore a is
equal to 7.2 inches. Assume that a force having a component parallel

256

MASONRY AND REINFORCED CONCRETE 245

with the axis of 62,500 pounds is applied 3 inches (e) from the
center; required the maximum unit stresses in the concrete and
in the steel. Then, since p = A -f- b h,
2 X. 7656

0 „

From Equation (42), if n= 15,

_324+(24xl5X.007x51.84)

6X18 (1+30X.007)

This being greater than e = 3 inches, it shows that the stress is
wholly compressive. For this case, and for all cases when n equals
15 and a equals Ah, we may simplify Equations (39) and (40) to the
following:

T f 1 e 6

(45)

Then

c =

62,500 /I , 3 / 6

per sq- m-

and

3/4.8

Case IV. As e is so great there is tension on one face. When
e is but little more than e0, the tension is not greater than the con-
crete can withstand without rup-
ture and the stresses in both con-
crete and steel may be deter-
mined by equations similar to
those given above. But when
the tension is evidently so great
that the concrete will be ruptured
on the tension side, the steel
must be considered as carrying all the tension and then other
formulas must be used, as developed below.

In Fig. Ill the triangle of forces may be considered as repre-
senting, proportionately, the deformation in the concrete and also in
the steel. But since it requires n times as much force to produce a

Eccentricity « is Large

257

246 MASONRY AND REINFORCED CONCRETE

certain deformation in steel as would be required with concrete, we
may consider that the triangle represents the proportionate stresses
in the concrete at the several points in the section and also that the
stress in the steel is represented at the same scale by n times the ordi-
nate at the position of the steel, or that the actual ordinate represents
s-^n. From proportionate triangles we can write

s' fkh-d'

or
also

The algebraic sum of all the forces acting on the section must equal
the thrust T. Therefore

T=s'pbh+±cbkh-spbh (48)

Substituting the above values for s' and s, we have, after reducing,
T_cbhfk*+4pnk-2pn\

But the moment M on this section about the gravity axis evidently
equals Te. We may also say that the moment M equals the sum of
the moments of the separate forces about the gravity axis. The
compressive forces have their center of gravity at one-third the
height of the triangle and its distance from the gravity axis is
%h— $kh, and the summation of the compressive moments of the
concrete equals \ c b k h (% h - J kh) . The entire moment equals

Placing this equal to the above value for T in Equation (49), multi
plied by e, we have, after reduction,

-+ 12 pnki

258

MASONRY AND REINFORCED CONCRETE 247

V/fLUESof(e+h}for UPPER CURVES

as 0.4- 0.3 o.z a/_

VflLUES offe*h) for LOWEf? CUtfYES

Fig. 112. Curves Showing Relations of k, p, and (e-rh) for Flexure and Direct Stress

259

248 MASONRY AND REINFORCED CONCRETE

This equation is general for all values of n, p, and a, which is the dis-
tance from the center to the reinforcement. For the common
values of a = .4 h and n = 15, the equation becomes

(52)

O.O6

Fig. 113. Relations of k, p, and B for Flexure and Direct Stress

The direct solution of this cubic equation is not easy, but the desired
relation between k, p, and (e-^-Ji) may be obtained by assuming all
pairs of values for k and p within any desired range, computing the

260

MASONRY AND REINFORCED CONCRETE 249

corresponding values of (e + K) and plotting the results in curves as
shown in the diagram, Fig. 112. Then, for any selected values of
p and (e-i-h), the value of k may be read from the diagram with
practicable accuracy.

The practical application of Equation (50) usually consists in
the numerical determination of c, on the basis of a beam of given
dimensions (6 Ji) and with other known characteristics (k, n, p, and
a), which is acted on by a known moment M. The value of k is
determined from Equation (51) or (52), or by the use of the diagram.
But the work can be still further simplified by using another dia-
gram, Fig. 113, for the determination of the value of the parenthesis

(— ---- 1 — r~, — - I, which we will call equal to B. Then we have
4 6 kh2 J

As before, using the special values of n=15 and a = Ah, we have

Numerical examples of this will be given under "Arches", Part V.

FOOTINGS

Simple Footings. When a definite load, such as a weight carried
by a column or wall, is to be supported on a subsoil whose bearing
power has been estimated at some definite figure, the required area
of the footing becomes a perfectly definite quantity, regardless of the
method of construction of the footing. But with the area of the
footing once determined, it is possible to effect considerable economy
in the construction of the footing by the use of reinforced concrete.
An ordinary footing of masonry is usually made in a pyramidal form,
although the sides will be stepped off, instead of being made sloping.
It may be approximately stated that the depth of the footing below
the base of the column or wall, when ordinary masonry is used,
must be practically equal to the width of the footing. The offsets
in the masonry cannot ordinarily be made any greater than the
heights of the various steps. Such a plan requires an excessive
amount of masonry.

Wall Footing. Assume that a 24-inch wall, with a total load
of 42,000 pounds per running foot, is to rest on a soil which can

261

250 MASONRY AND REINFORCED CONCRETE

safely bear a load of 7,000 pounds per square foot. The required
width of footing is 6 feet. The footing will project 2 feet on either
side of the wall. For each lineal foot of the wall and on each side,
there is an inverted cantilever, with an area 2 feetXl foot, and
carrying a load of 14,000 pounds. The center of pressure is 12
inches from the wrall; the moment about a section through the
face of the wall is 12x14,000, or 168,000 inch-pounds. Using a
grade of concrete such that M equals 95 &d2, p equals. 00675, and
j equals .88, then with b equal to 12, we have

rf2 = J/-^956 = 168,000 4-1, 140 = 147.4
d = 12.15

Using this value, the amount of steel required per inch of width
will equal .00675X12.15, or .082 square inch, which may be sup-
plied by f-inch bars spaced about 7 inches on centers. A total
thickness of 15 inches will, therefore, fulfil the requirements.
Theoretically, this thickness could be reduced to 8 or even 6 inches
at the outer edge, since there the moment and the shear both reduce
to zero. But when concrete is used very wet and soft, it cannot
be laid with an upper surface of even moderate slope without using
forms, which would cost more than the saving in concrete.

Shear. The shear (V] on a vertical section directly under
the face of the wall, and 12 inches long, is 14,000 pounds. Applying
Equation (21)

v=V+bjd

= 14,000 -J- (12 X. 88X12.15)

= 109 Ib. per sq. in.

This is far greater than a safe working stress and the slab might fail
from diagonal tension. When a loaded beam is supported freely
at each end, the maximum shear is found at the ends where the
moment is minimum, and some of the bars which are not needed there
for moment may be bent up so as to resist the shear. Unfortunately,
in the case of a cantilever, the maximum moment and maximum
shear are found at the same beam section — in this case, at the face
of the wall. Therefore, if the concrete itself cannot carry the shear,
additional steel must be used to do that work. Bars which are
inclined about 45° serve the purpose most economically, provided
they are secured against slipping and can develop their full strength.

262

MASONRY AND REINFORCED CONCRETE 251

This may be done by having them extend through the column and
by bending the free ends. Assume that the concrete alone takes
up 40 pounds of the 109 pounds shear, found above, or 37 per cent.
This leaves 63 per cent to be taken by the steel reinforcement.
14,000 X. 63 = 8,820 pounds per foot, or 735 pounds per lineal inch.
The only practicable arrangement is to alternate these bars with the
moment bars and therefore space them 7 inches apart. Then each
bar must take up 7 X 735, or 5, 145 pounds of shear. A & -inch square
bar will safely sustain that stress. Such a bar has a perimeter of 2.25
inches. At 75 pounds per square
inch for bond adhesion (plain bars),
each lineal inch of the bar would
have a working adhesion of 169
pounds. 5, 145 H- 169 = 30 inches,
which is the required length of
bar beyond any point where the
stress is as much as 5,145 pounds.
Since there is not that length of
bar available, bond adhesion can-
not be relied on and the bars must
be bent, as shown in Fig. 114.
Even a deformed bar, although
a good type may be used with
working adhesion about double
that of a plain bar, would need
to be longer than space permits, if
straight, and it should be hooked.

Bond Adhesion in Moment Bars. The steel per inch of width
is .082 square inch and in 7 inches, .574 square inch. Since the
design calls for a unit tension of 16,000 pounds in the steel, the actual
tension in the bar will be 16,000 X. 574 = 9, 184 pounds. A f-inch
square bar has a perimeter of 3 inches and, at 75 pounds per square
inch, can furnish a working bond adhesion of 225 pounds per lineal
inch of bar. But this would require 9, 184 -5- 225, or 41 inches, the
required length beyond the face of the wall. Allowing 150 per
square inch bond adhesion, for a good type of deformed bar, the
required length, computed similarly, would be a little over 20 inches,
and as this is less than the 24-inch cantilever, straight deformed

k-*^

— 2'0"^

-t^

WALL

ON S)

C x^ /. )

Fig. 114. Diagram of Footing for a Wall

252 MASONRY AND REINFORCED CONCRETE

bars will do. The designer, therefore, has the choice of using a hook
on each end of plain bars, as illustrated in Fig. 114, or using straight
deformed bars, which would be cheaper at the usual relative prices.
Column Footing. The most common method of reinforcing a
simple column footing is shown in Fig. 115. Two sets of the rein-
forcing bars are at a-a and b-b, and are placed only under the column.
To develop the strength of the corners of the footings, bars are
placed diagonally across the footing, as at c-c and d-d. In designing

this footing, the projections of
the footing beyond the column
are treated as free cantilever
beams, or by the method dis-
cussed above. The maximum
shear occurs near the center;
and therefore, if it is necessary
to take care of this shear by
means of reinforcement, it
should be provided by using
stirrups or bent bars.

Example. Assume that a load
of 300,000 pounds is to be carried by
a column 28 inches square, on a soil
that will safely carry a load of 6,000
pounds per square foot. What should
be the dimensions of the footing and
the size and spacing of the reinforcing
bars? The bars are to be placed
diagonally as well as directly across
the footing, as illustrated in Fig. 115.
Also investigate the shear.

Solution. The load of 303,000 pounds will evidently require an area of
50 square feet. The sides of the square footing will evidently be 7.07 feet, or
say 85 inches; and the offset on each side of the 28-inch column is 28.5 inches.
The area of each cantilever wing which is straight out from the column is 28.5 X
28, or 798 square inches. The load is, therefore, (798 -i-1 44) X 6,000, or 33,250
pounds. Its lever arm is one-half of 28.5 inches, or 14.25 inches. The moment
is therefore 473,812 inch-pounds. Adopting the straight-line formula, M = 95 6 d2,
on the basis that p = .00675, we may write the equation

473,812 = 95X28Xr/2,
from which d- = 178

d =13.3

Therefore, A =pbd = . 00675X28X13.3

= 2.51 sq. in.

n n n i") n

Fig.

Diagram of Footing fo

264

MASONRY AND REINFORCED CONCRETE 253

This area of metal may be furnished by six f-inch round bars, and therefore
there should be six f-inch round bars spaced about 4.5 inches apart under the
column in both directions, a-a and b-b.

Corner Sections. The mechanics of the reinforcements of the corner
sections, which are each 28.5 inches square, is exceedingly complicated in
its precise theory. The following approximation is probably sufficiently
exact. The area of each corner section is the square of 28.5 inches, or 812.25
square inches. At 6,000 pounds per square foot, the pressure on such a section
will be 33,844 pounds, and the center of gravity of this section is of course at the
center of the square, which is 14. 25X1.414, or 20.15 inches from the corner of
the column. A bar immediately under this diagonal line would have a lever
arm of 20.15 inches. A bar parallel to it would have the same lever arm from
the middle of the bar to the point where it passes under the column. Therefore,
if we consider that this entire pressure of 33,844 pounds has an average lever
arm of 20.15 inches, we have a moment of 681,957 inch-pounds. Using, as
before, the moment equation M =956d2, we may transpose this equation to read

, M
b "953*
Then

, , M , M
A = pbd=P95d>d = P95d

681»957
95X14.5
= 3.34 sq. in.

This area of steel will be furnished by six f-inch round bars. The diagonal rein-
forcement will therefore consist of six f-inch round bars running diagonally in both
directions. These bars should be spaced about 5 inches apart. Those that
are nearly under the diagonal lines of the square should be about 9 feet 8 inches
long; those parallel to them will each be 10 inches shorter than the next bar.

Bond Adhesion. The total tension in the steel of the a and 6 bars is 16,000 X
2.51 =40,160 pounds, or 6,693 pounds per bar, which is found at a point imme-
diately under the column face. There wrill be 28.5 inches length of steel in each
bar from the column face to the edge of the slab, and this will require a bond
adhesion of 6,693 + 28.5 = 235 pounds per lineal inch. From Table XXIII, we see
that this unit value is greater than a proper working value for f-inch plain round
bars but is safe for f-inch deformed round bars. Making a similar calculation for
the diagonal bars, the stress in each one is (16,000X3.34) -=-6 = 8,907 pounds. The
length, practically uniform for each, beyond the face of the column is 40 inches,
which will require a bond adhesion of 223 pounds per lineal inch. This is just
within the limit for f-inch plain square bars.

It should be noted from the solution of this and the previous
problem that, on account of the combination of heavy load and
small cantilever projection, the bond adhesion of footings is always
a critical matter and its investigation should never be neglected.
It frequently happens, as above illustrated, that the greater bond
resistance of deformed bars will permit the use of a certain bar which

265

254 MASONRY AND REINFORCED CONCRETE

is safe for the moment resistance when the same size of plain bar
cannot be used. Since smaller bars have a greater surface and
a greater adhesion per unit both of area and of strength than larger
bars, the requisite adhesion may sometimes be obtained by using a
proportionately larger number of smaller bars. When neither
method will produce the required adhesion, the bars should be bent
into a hook, which should be a full semicircle with a diameter about
8 to 12 times the diameter of the bar.

Shear. The "punching shear" on the slab is measured by the
upward pressure on that part of the slab which is outside of the
column area. This equals 852 — 282 = 6441 square inches, or 44.73
square feet. Multiplying by 6,000 we have 268,380 pounds. The
resisting area equals the perimeter of the column times jd, which
here equals 4X28X.88X13.3, or 1,311 square inches. Dividing
this into 268,380, we have 204 pounds per square inch. If the
column and slab were made of plain concrete, this figure would be
considered too high for working stress, 120 being usually allowed.
In this case, an actual punching of the slab would require that 48
sections of f -inch round bars should be sheared off. Allowing that
the concrete actually takes an average of 120 pounds per square inch
on 1,311 square inches of surface, the concrete would take up 157,320
pounds, leaving 111,060 pounds for the 48 bars, or 2,314 pounds for
each bar. Dividing by the bar area, we have a shearing stress of
5,237 pounds per square inch of bar section, which is insignificant
for the steel and is amply safe, provided that any such shearing
stress as 2,314 pounds per bar could be developed before the con-
crete itself were crushed by the bars. Considering the various
forces resisting the punching action, and also that even the 204
pounds per square inch is far short of the ultimate value of true
shear, the design is probably safe, although the factor of safety is
probably low. If further reinforcement were considered necessary,
it could be added in the form of bent bars, as in the previous
problem.

It is impracticable to develop a true rational formula for the
computation of the diagonal tension in slabs which support columns,
but the results of a series of elaborate tests by Prof. Talbot (Bulletin
No. 67, Univ. of Illinois) show that the following method gives
results which are reasonably consistent and also comparable with

MASONRY AND REINFORCED CONCRETE 255

the corresponding results for ordinary beams. Consider a section
through the slab all the way around the column and at a distance d

•wr

from the face of the column, and. apply Equation (21), v = .

bjd

In this case the section would be a square (2 X13.3) +28 = 54.6 inches
on a side. The area is 2,981 square inches. The area of the whole
footing is 85 2, or 7,225 square inches and the area outside this
square is 7,225—2,981=4,244 square inches, or 29.5 square feet.
29.5 X6,000 = 177,000 pounds = V; the perimeter of the square is b and
equals 4X54.6, or 218.4; jd equals .88X13.3, or 11.7. Then v equals
69. Since this is higher than 40, the usual permissible working stress
when taken as a measure of non-reinforced diagonal tension, it shows
that bent bars or stirrups must be used, but in either case the rein-
forcement need carry only the extra 29 pounds per square inch.
Multiplying this by jd, we have 29X11.7 = 339, the required
assistance in pounds per lineal inch. If a bar is placed every 4.5
inches (corresponding with the main reinforcing bars), the stress per
bar will be 1,525 pounds, which at 16,000 pounds unit stress will
require .095 square inches, or a & -inch square bar. Perhaps the
most convenient form of reinforcement in this case would be a series
of stirrups made by a continuous bar ^ inch square, which zigzags
up and down with an amplitude equal to jd, or 11.7 inches, and so
that there is a bar up or down each 4.5 inches. This should be
located at the "critical section" at a distance d equal to 13.3 inches
from the column face. It will require a bar about 16 feet 6 inches
long to make the continuous stirrup for each side of the square.
Each bar must be bent with about eleven semicircular bends, as
shown in Fig. 115, and so placed that each downward loop shall pass
under one of the main reinforcing bars. The loops at the top will
preclude all possibility of bond failure.

Since the shear decreases to zero at the edge of the slab, and the
distance from the stirrup to the edge of the slab is only a little more
than the thickness of the slab, it is apparent without calculation that
no further shear reinforcement is needed.

Continuous Beams. Continuous beams are sometimes used to
save the expense of underpinning an adjacent foundation or wall.
These footings are designed as simple beams, but the steel is placed
in the top of the beams.

267

256 MASONRY AND REINFORCED CONCRETE

Illustrative Example. Assume that the columns on one side of
a building are to be supported by a continuous footing; that the
columns are 22 inches square, spaced 12 feet on center; and that
they support a load of 195,000 pounds each. If the soil will safely
support 6,000 pounds per square foot, the area required for a footing
will be 195,000-7-6,000, or 32.5 square feet. Since the columns are
spaced 12 feet apart, the width of footing will be 32.5^ 12 = 2.71
feet, or 2 feet 9 inches. To find the depth and amount of rein-
forcement necessary for this footing, it is designed as a simple
inverted beam supported at both ends (the columns), and loaded
with an upward pressure of 6,000 pounds per square foot on a beam
2 feet 9 inches wide. In computing the moment of this beam, the

^ continuous-beam principle

•T I il ''J. I !L" ! Jlffi ~T may be utilized on all ex-
cept the end spans, and thus
reduce the moment and,
therefore, the required
dimensions of the beam.

Compound Footing.
When a simple footing sup-
ports a single column, the
center of pressure of the
column must pass vertically
through the center of grav-
ity of the footing, or there
will be dangerous transverse stresses in the column, as discussed later.
But it is sometimes necessary to support a column on the edge of a
property when it is not permissible to extend the foundations beyond
the property line. In such a case, a simple footing is impracticable.
The method of such a solution is indicated in Fig. 116. The nearest
interior column (or even a column on the opposite side of the build-
ing, if the building be not too wide) is selected, and a combined
footing is constructed under both columns. The weight on both
columns is computed. If the weights are equal, the center of gravity
is halfway between them; if unequal, the center of gravity is on the
line joining their centers, and at a distance from them such that
x:y::W<t: W\, Fig. 116. In this case, evidently W2 is the greater
weight. The area abdc must fulfill two conditions:

Fig. 116. Combined Footin
One on Edge of

! for Twc
'roperty

Columns,

268

MASONRY AND REINFORCED CONCRETE 257

(1) The area must equal the total loading (W,+W.J) divided by the
allowable loading per square foot; and,

(2) The center of gravity must be located at O.

An analytical solution for all cases of the relative and absolute
values of ab and cd which will fulfill the .two conditions is very
difficult. Sometimes the only practicable solution is to obtain, by
trial and adjustment, a set of dimensions which will be sufficiently
accurate for practical purposes. It usually happens that an inner
column of a building carries a greater load than an outer column.
This facilitates the solution, for then, as in the example given below,
the footing may be extended beyond the inner column and may be
made approximately rectangular.

Example. A column W ., carrying 400,000 pounds, is to be located on the
edge of a property and another column W2, carrying 600,000 pounds, is located
16 feet from it. Assume that the subsoil can sustain safely 7,000 pounds per
square foot. Required the shape and design of the footing.

Solution. Assume that the footing slab weighs 400 pounds per square
foot of surface; then the net effective upward pressure of the subsoil which will
support the column equals 7,000—400 = 6,600 pounds per square foot. For
simplicity of calculation in the computations involving soil pressures and slab
areas, feet and decimals will generally be used. The change to feet and inches
can be made when the final dimensions have been computed.

The total column load is 1,000,000 pounds; at 6,600 pounds per square
foot the area must be 151.515 square feet. Assume that the W2 column is
2.89 feet'square, and that the Wl column is 2 feetX2.78 feet. This means that
the net average load is 500 pounds per square inch on each column. In Fig. 116,
let a b equal n, and c d equal TO, both still unknown. The smaller column is on
the edge of the property, and the 06 line is made 1.0 foot from the column center.
As a trial solution, assume that the cd line is 4.0 feet beyond the other column
center. Then the total length of the trapezoid is 21.0; then £ (m+ri) 21.0 =
151.515; solving this

(TO +n)= 14.43

600 000
The center of gravity of the two loads is at t QQQ QQQ of 16 feet, or at 9.6 feet from

the smaller column center. This locates 0. To fulfill condition (2), the dimen-
sions m and n must be such that the center of gravity of the trapezoid shall be
at 0. In general, the distance z of the center of gravity of a trapezoid from its
larger base equals one-third of the height h times the quotient of the larger base,
plus twice the smaller base divided by the sum of the bases; or, as an equation

Substituting z equals 10.4, h equals 21.0, m and n still unknown, we have

258 MASONRY AND REINFORCED CONCRETE

Combining this equation with the equation (m+n) = 14.43, we may solve and
find ?M = 7.419 and n = 7.011. By proportion, we find the dimension ef through
O = 7.217 feet.

Moment. The maximum moment is found where the shear is zero, and
this must be at the right-hand end of a portion of the slab on which the net
upward pressure equals 600,000 pounds. That portion must have an area of
(600,000 -T- 6,600) =90.909 square feet. Similarly, the remaining area is com-
puted to be 60.606 square feet. Let p equal the length of this section (qs in the
figure) and h equal its distance from cd. We may write the two equations

1(7.419 +p) h = 90.909
and

J(p+7.011)(21-A)=60.606

Solving these two equations for p and h, we have p = 7.178 and h = 12.456. It
should be noted that this section of maximum moment (on the line qs) is not
on the line of center of gravity of the whole footing, but is in this case about two
feet to the right. The center of gravity of the trapezoid cdqs, calculated as
above, is at a point 6.262 feet from qs and the net upward pressure on this section
is 600,000 pounds. Therefore, taking moments about qs, we have

M = 600,000 (8.456-6.262) = 1,316,400 ft.-lb. = 15,796,800 in.-lb.
In this case, b = 7.178 feet = 86.136 inches; call it even 86. Then for M = 95 bd2,
we have

95 b rf2 = 8170 d'2 = 15,796,800; then d1 = 1,934 and d = 44.0
Then

A = .00675X86X44 = 25.54 sq. in.
which may be provided by 20 bars, 1 £ inches square.

That portion of the slab between x and z is subject to transverse stress,
the parts near x and z tending to bend upward. Although the stresses are not
computable with perfect definiteness, being comparable to those in a simple
footing (see page 249), we may consider them as approximately measured by
the moment of the quadrilateral between the face of the column and x about
the face of the column, xz equals 7.34; subtracting the column width and
dividing by 2, we have 2.225 feet, or 26.7 inches; the area of the quadrilateral is
approximately f (8 '+2.89)2.225, or 12.11 square feet. The effective upward
pressure equals 12.11X6,600 = 79,926 pounds. The lever arm is approximately
& of the distance from the face, or 0.6X26.7 = 16 inches. M = 79,926X16 =
1,278,816 =95 bd1. Here d is about one inch less than for the main slab, or
say 43 inches. Solving, fc = 7.3 and A =pbd = . 00675X43X7.3, or 2.12 square
inches, which may be supplied by 4 bars f-inch square. This calculation
shows that a relatively small amount of reinforcement, which should run
under the column from x to z, will resist this stress. Increasing the number of
bars to 5 or 6 will certainly cover all uncertainties in this part of the calculation.
The stresses under the other column are somewhat less and therefore the same
reinforcement will be even more safe.

Shear. The shear around the larger column can be calculated as "punch-
ing" shear, b for this case is the perimeter of the column, and equals 4X2.89
= 11.56 feet, or 138.72 inches; jd equals .88X44 = 38.72; V equals 600,000-
(2.892 X 6,600) = 600,000 - 55;110 = 544,890. v equals V + bj d = 544,890 -*-

270

MASONRY AND REINFORCED CONCRETE 259

(138.72X38.72) = 102. Since this is a case of true shear, when a working stress
of 120 pounds per square inch is allowable, no added reinforcement is necessary.
The other column may be considered similarly, except that it is supported only
on three sides. 6 = 81 inches, and &j<Z = 3,136; 7 = 300,000-36,667 = 263,333;
then v equals 84. Since this is only 70 per cent of the allowable stress for true
shear, it is probably safe. In addition, the bending down of the main reinforc-
ing bars under each column, as shown in the figure, will add a very large factor
of safety.

Case Where Heavier Column Is Next to the Property Line. It is far more
difficult, in case the heavier column is next to the property line, to obtain, by
the analytical method given above, a trapezoid which will fulfill the two funda-
mental requirements there given. If the wall column has twice (or more than
twice) the load carried by the inner column, no trapezoid is obtainable. In
such a case, a figure shaped somewhat like a shovel, the blade being under the
heavy column and the handle being a beam which transfers the load of the lighter
column to the broad base, may be used, the dimensions and exact shape of which
can only be determined by successive trials.

REINFORCED CONCRETE RETAINING WALLS

Forms of Walls. Reinforced concrete walls are usually made
in such shape that advantage is taken of the weight of part of the
material supported to increase the stability
of the wall against overturning. Fig. 117
shows the outline of such a wall. It consists
of a vertical wall CD, attached to a floor plate
A B. To prevent the wall from overturning,
the moment of downward forces about the
outer edge of the base M = Wili-\- WJv must be
greater than that of the overturning moment
Mz = Ek. Mi should be from one and one-
half to twice I/a, which would be the factor
of safety. In addition to this factor of safety
there would be the shearing of the earth along
the line a b.

Owing to the skeleton form of these walls they are usually more
economical to construct than solid walls of masonry. The cost per
cubic yard of reinforced concrete in the wall will be more than the
cost per cubic yard of plain concrete or stone, in a gravity retaining
wall, but the quantity of material required will be reduced by 30
to 50 per cent in most cases. There are two forms of these walls.
The outline in Fig. 117 shown in solid lines is the simplest to con-

Fig. 117. Outline of Rein-
forced Concrete Wall

271

2GO MASONRY AND REINFORCED CONCRETE

struct and is the more economical of the two types of reinforced
concrete walls, up to a height of 18 feet. For higher walls the form
shown by the solid lines and heavy dotted line be is used. Exam-
ples of both types will be worked out in detail.

Illustrative Example. Design a retaining wall 14 feet high
to support an earth face with a surcharge at a slope of 1| to 1.

The width of the base for reinforced concrete walls is usually
made from TV to T6<r of the height. For this wall, with a surcharge,
the base will be made one-half of the height, or 14X^ = 7 feet.

Fig. 118.

ng Wall

Assume the weight of the earth at 100 pounds per cubic foot and the
reinforced concrete at 150 pounds per cubic foot. Then substituting
in Equation (7c), we have

Wh2

.833

100X142

= .833X-
= 8,163 Ib.

This force is applied on the plane cm, Fig. 118, and at a point
one-third of the height above the base.

272

MASONRY AND REINFORCED CONCRETE 261

It will be necessary to determine the thickness of the vertical
wall and the base plate before the stability of the wall can be de-
termined. Assume the base plate to be 18 inches thick; then the
vertical slab will be 12 feet 6 inches high and the pressure against
this slab will be

6,508 Ib.

The horizontal component of this pressure is 6, 508 X cos 33°
42', or 5,421 pounds, as shown diagrammatically in Fig. 118.

12 ^

The bending moment will be M = 5,421 X — — X 12 = 271,272

inch-pounds. Placing this equal to M = 95 bd2 (see page 192) with
b equals 12, d2 equals 238, and d equals 15.4 inches. Adding 2.6
inches for protecting this steel, the total thickness will be 18
inches. The area of the reinforcing steel will be .00675X15.4,
or .104 square inch of steel per inch of length of wall. Bars
1| inches round (.99 -i-. 10 = 9.9) spaced 10 inches apart, will be
required. The bending moment rapidly decreases from the bottom
of the slab upwards, and, therefore, it will not be necessary to keep
the thickness of 18 inches to the top of the slab or to have all the
bars the full length. Make the top 9 inches thick, drop off one-third
of the bars at one-third of the height of the slab and one-third at
two-thirds of the height. The shear at the bottom of the slab is

— — — —j=29 pounds per square inch; therefore, as this does not
12 X 15.4

exceed the working stress, no stirrups are needed. It is very im-
portant in a wall of this type not to exceed the bonding stress.

The vertical bars must be well anchored in the base plate or
they will be of no great value. The bars are 1J inches in diameter,
the circumference then is 3.53 inches. Allowing a bonding stress of
75 pounds per square inch, the total bonding per inch of length of
bar is 3.53X75, or 265 pounds. The lever arm is 15.4. Since the
bars are spaced 10 inches on centers, the stress to be resisted is f
of 271,272, or 226,060 inch-pounds. Let a: be length of anchorage
required, then

M = 265 X 1 5.4 X x = 226,060
x = 55 inches

273

262 MASONRY AND REINFORCED CONCRETE

That is, the vertical 1 J-inch round bars must extend into the footing
55 inches or be anchored in such a way that their strength will be
developed.

In designing the footing of a reinforced concrete retaining wall
the resultant force should intersect the base within the middle third
the same as in a masonry wall. The forces acting on the footing
are the earth pressure on the plane me, the weight of the earth fill,
and the weight of the concrete. The distance from the toe a to
the point where the resultant acts is obtained as follows: The
centers of gravity of the concrete and the earth are found, also the
weight of each. The weights are multiplied by the distances from
a, respectively, which gives the static moment. The sum of the
static moments divided by the sum of the weights equals the dis-
tance from the toe to the line at which the resultant acts. The
detail figures for the problem are given below.

Center of Gravity of Wall

SECTION

AREA

Sq. Ft.

MOMENT
ARM

MOMENT
Area

abed
efig
fih

10.50
9.38
4.69

3.50

1.88
2.50

36.75
17.63
11.73

24.57

66.11

Distance from a to center of gravity is ' =2.69 ft.

24.57

Weight per lineal foot is 24.57 X 150 = 3,686 = WC
Static moment about a is 3,686X2.69 = 9,915 ft.-lb.

Center of Gravity of Earth

SECTION

AREA

Sq. Ft.

MOMENT

Arm

MOMENT

fkh'

hblk
flm

4.69
50.00
7.50

2.75
5.00
5.42

12.90
250.00
40.65

62.19

303.55

303 55
Distance from a to center of gravity is — — — = 4.88 ft.

Weight per lineal foot is 62. 19 X 100 = 6,219 = We

274

MASONRY AND REINFORCED CONCRETE 263

Static moment about a is 6,219X4.88 = 30,355 ft.-lb.
The distance from a to the combined center of gravity of the
concrete and the earth fill is

9,915+30,355^40,270 .
3,686+ 6,219 9,905

To find where the resultant R cuts the base, produce E to meet
the combined center of gravity of the concrete and earth. From
their intersection lay off on the vertical line, at any convenient
scale, the combined weight 9,905 pounds. At the end of this dis-
tance draw a line parallel to the line E and lay off the value of E
which is 8,163 pounds. Draw R, which is the resultant and in this
case cuts the base at the edge of the middle third, so that the wall
will not fall by overturning.

The pressure produced on the foundation is next to be inves-
tigated. Since the resultant comes at the edge of the middle third,
Equations (7d) and (7e) are used.

Pressure at the toe = (45-6Q) -

=4,242 pounds
Pressure at the heel = (6Q - 25) -

= 0

The pressure on the foundation of 4,242 pounds at the toe is
permissible on most soils.

The stability of a wall of this type must be carefully investi-
gated. Suppose this wall is to be located on a wet clay soil.
The coefficient of friction between concrete and wet clay is .33;
the horizontal force is 6,800 pounds; and the weight of the concrete
and earth acting in a downward direction is 9,915 pounds. With
a coefficient of .33, or ^, the resistance to sliding is 9,915 Xi, or 3,305
pounds, which is less than one-half of the horizontal pressure 6,800.
The resistance should be about twice the pressure in order to make
the wall safe against sliding, which would require that the weight

275

264 MASONRY AND REINFORCED CONCRETE

should be about four times as much in order that mere friction
should surely prevent sliding. This shows that it will be necessary
to construct a projection in the base, as shown in Fig. 118.

The thickness of the base is always made greater than the
moment requirements just behind the vertical slab (or at K) would
demand. If the wall were actually on the point of tipping over,
there would cease to be any upward pressure on the base. But
there would be a downward pressure on the right cantilever equal
to the weight of the earth above it, and the moment in the base at
the point h would be that produced by that earth pressure and by
the weight of the concrete from h to b. Since the above calcula-
tions for the stability of the wall show that the computed lateral
pressure cannot produce actual tipping about the toe, no such
moment can actually be developed, but the calculation of the
required thickness to resist such a moment gives a dimension which
is certainly more than safe and which, for other reasons, is sometimes
made still greater. The weight of the earth is 6,229 pounds and
the weight of the concrete is 4X1^X150 = 900 pounds. Then
6,229+900 = 7,129 pounds. Therefore

M = 7,129 XI. 86X12 = 158,977 in.-lb.

Placing this moment equal to M = 95 bd2 and solving for d, we find
that d equals 11.7. Adding 2.5 inches for protecting the steel, the
total thickness would be 14.2 inches. To properly anchor the bars
in the vertical slab, the thickness of base plate is seldom made less
than the vertical slab. Therefore, we will make d=l5 inches,
6 = 12, and solve for the moment factor R.

M = 12 xl52X/? = 158,977

7? = 58.8

Fig. 99 shows that when R = 59, C = 400 and S = 12,000 and that
the percentage of steel required is practically .006. Therefore, the
steel required equals 12 X 15 X. 006 = 1.08 square inches. Bars If
inches in diameter, spaced 10 inches, will be required. The moment
in this part of the base plate is negative, therefore the steel must
be placed in the top of the concrete.

7 129

The vertical shear is ' " or 39 pounds per square inch, which
12X 15

is less than the working value allowed in concrete.

276

MASONRY AND REINFORCED CONCRETE 265

The left cantilever or toe has an upward pressure. At the
extreme end it is 4,240 pounds and at the face of the vertical wall it
is 3,200— scaled from Fig. 118. The average pressure is (4,240+
3,200) -r- 2 = 3,720 pounds. The moment is, therefore,

M = 3,720 X— X 12 = 33,480 in.-lb.
Let d=15, 6 = 12, and solve for R

# = 33,480
R = 12.4

This value of 12.4 for R is smaller than is found in Fig. 99. Since
the bars in the vertical slab are bent in such a shape as to supply
this tension, no further consideration of this stress is necessary
in this problem.

Some longitudinal bars must be placed in the wall to prevent
temperature cracks, and also to tie the concrete together. About
.003 per cent of the area above the ground is often used. In
this case f-inch round bars spaced 18 inches on centers will be
used.

Reinforced Concrete Retaining Walls with Counterforts. In this
type of wall the vertical slab is supported by the counterforts,
the principal steel being horizontal. The counterforts act as
cantilever beams, being supported by the footing.

Illustrative Example. Design a reinforced-concrete wall with
counterforts, the wall to be 20 feet high and the fill to be level with
the top of the wall.

The spacing of the counterforts is first determined. The
economical spacing will vary from 8 feet to 12 feet or more, depend-
ing on the height of the wall. A spacing of 9 feet on centers will be
used for the counterforts in this case, Fig. 119. The maximum
load on the slab is on the bottom unit and decreases uniformly to
zero at the top, when the earth is horizontal with the top of the wall,
as in this case. Assume that the base plate will be 18 inches in
thickness, then the center of the bottom foot of slab will be 18 feet
from the top of the wall. Then pressure to be sustained by the
lower foot of the slab will be

277

266

MASONRY AND REINFORCED CONCRETE

in which P is the intensity of the horizontal pressure at any depth
h, and w is the weight per cubic foot of the earth.

P = -1X100X18

= 600 pounds per square foot

Multiplying this value of P by the distance between the centers of
the counterforts— 600X9 = 5,400— the full load is obtained.
5,400X9X12

M =

72,900 in.-lb.

Fig. 119. Design Diagrams for Retaining Wall with Counterforts

Placing this value of M equal to 95bd2 in which &
solving for d, we have

95 X 12 d* = 72,900

12, and

d=S

Adding 2 inches to this — 8+2 = 10 — for protecting the steel, the total
thickness of the wall will be 10 inches. For convenience of con-
struction the slab will be made uniform in thickness. The steel
for the bottom inch will be .00675x18 = .054 square inch. .60 -^
.054 = 11 inches. That is, |-inch round bars may be spaced 11
inches on centers. Use this size of bars and spacing for one-fourth
the height of the wall. The next quarter will be reduced twenty-

278

MASONRY AND REINFORCED CONCRETE 267

five per cent, and f-inch round bars, spaced 11 inches, will be used.
In the third quarter, the required area will be one-half of that
required for the first quarter. .054 -5- 2 = .027 square inch, or
.44-r-.027 = 16, that is, f-inch round bars spaced 16 inches on
centers should be used. In the upper part of the wall use f-inch
round bars, 18 inches on centers.

To determine the requirements of the counterforts it will be
necessary to determine the horizontal pressure against a section of
the wall nine feet long. Referring to page 153, Part II, we see that
Equation (7) is stated thus:

Substituting in the modified form of Equation (7a) and multiplying

£= 286xioox(M>°x9

= 44,048 Ib.

This load is applied at one-third of the height of the wall, which
is 6.5 feet above the base. The moment in the counterfort is

M = 44,048X6iXl2
= 3,435,744 in.-lb.

The width of counterfort must be sufficient to insure rigidity,
to resist any unequal pressures, and to thoroughly embed the rein-
forcing steel. The width is made by judgment and in this case
will be made 12 inches wide. The counterfort and vertical slab
together form a T-beam with a depth at the bottom of 84 inches.
Allow 4 inches to the center of the steel, then d = 80 inches; jd
= . 87 d=. 87X80 = 69.6 inches.

M = AsXJdX 16,000
3,435,744 = As X 69.6 X 16,000
in.

Four one-inch round bars will give this area. Two of these bars
will extend to the top of the wall and two may be dropped off at
half the height.

Now that these dimensions have been determined, the wall will

279

268 MASONRY AND REINFORCED CONCRETE

be investigated for stability against overturning. Substituting in
Equation (7a)

Wtf

2
.100X20"

.286

= .286X-

= 5,720

To find the center of gravity of the wall, it will be necessary to
take a section 9 feet long, that is, center to center of counterforts.

Center of Gravity of Concrete

Moments taken about A

SECTION

VOLUME
Cu. Ft.

MOMENT
ARM

VOLUME
MOMENT

a b c d
efhg
hfb

135.0
138.8
57.0

5.0
2.92
5.538

675.0
405.3
306.7

330.8

1,387.0

Distance from a to center of gravity

1,387.0
330.8

= 4.19 ft.

Weight of 9 feet of wall = 330.8X150 = 49,620 Ib.
Static moment about a for section 9 feet long, 49,620X4.19 :
207,908 ft.-lb.

Center of Gravity of Earth

Moments about A

SECTION

VOLUME
Cu. Ft.

MOMENT
ARM

VOLUME
MOMENT

fb lh
blh

987.0
66.4

6.66

7.77

6,573.4
515.9

1,053.4

7,089.3

Distance from a to center of gravity

7,089.3

: 6.73 ft.

1,053.4

Weight of earth per 9 feet of wall 1,053.4X100 = 105,340 Ib.
Static moment about a, for section 9 feet long equals 105,340
X6.73 = 708,930 ft.-lb.

Distance from a to the resultant of the concrete and earth
207,908+708,930 916,838

49,620+1-05,340 154,960

= 5.92 ft.

280

MASONRY AND REINFORCED CONCRETE 269

Draw tlie line We+We at a distance 5.92 feet from A and
produce the line E to meet it. From the intersection of these two
lines lay off the sum of the weight of the concrete plus the weight of
the earth at any convenient scale. At the end of this distance draw
a line parallel to E and lay off on it the value found for E. Draw the
resultant R. This line produced on to the base falls within the middle
third, and therefore, the wall should be safe against overturning.

Since the resultant cuts the base within the middle third, Q is
greater than one-third of the width of the base and Equations (7d)
and (7e) will be applied in finding the pressure on the base. Sub-
stituting in Equation (7d)

Pressure at the toe = (4 B -6Q) —

= (4X10-6X3.73)^4^

= 27,304 Ib.

Dividing 27,304 by 9 we have 3,034 pounds, which is the weight per
foot in length of the wall on the toe.

The pressure at the heel is found by substituting in Equation

(7e)

p
Pressure at the heel = (6Q-25) —

= 3,688 Ib.

Dividing 3,688 by 9 gives 410 pounds, which is the weight per lineal
foot at the heel.

In designing the toe (left cantilever) there is the average pres-
sure, (3,034 + 2,378) -^ 2 = 2,706, for which steel must be provided.

2,706X2.5 = 6,765

9 ^

Jf = 6,765X^X12 = 101,475

With 6 = 12 and d=l5 (the total thickness allowed was 18 inches),
and solving for R, we have

M = R bd2 = 101,475
= 101,475

281

270 MASONRY AND REINFORCED CONCRETE

Therefore C = 300 and 5 = 12,000, approximately, and p =
.0035.

12 X 15 X .0035 = .63 square inches of steel per lineal foot of wall,
which is equal to |-inch round bars spaced 11 inches on centers.
As a precaution against the load being concentrated under the
counterforts, three extra bars should be placed in the toe at these
places.

The rear portion of the footing is designed as a simple beam
between the counterforts. It must have sufficient strength to sup-
port the earth above it and also its own weight, although, as
explained previously for the L-shaped wall, such a stress cannot be
developed unless the wall were just at the point of overturning, and
the investigation for stability shows that this cannot happen. The
following calculation therefore introduces an additional factor of
safety in the design of the base slab of perhaps 2, in addition to
the usual working factor of about 4.

Weight of earth = 105,340
Weight of base = 13,500

1 18,840 Ib.

With 6 = 80 and d= 15, solve for R

# = 1,604,340

From Fig. 99 we find, with steel stressed to 16,000 pounds, the
concrete would be stressed to about 575 pounds per square inch and
the required percentage of steel of .0062 will be required.

.0062X80X15 = 7.44 sq. in.

Nine bars 1 inch round, spaced 8 inches apart, will be required.

In addition to the steel that has been required to satisfy the
different equations, the bars in the vertical slab and those in the
rear portion of the footing must be tied to the counterforts. (See
Fig. 1 19.) A few bars should also be placed in the top of the footing,
but no definite calculation can be made for them. The vertical
slab should be reinforced for temperature stresses. In this wall
|-inch round bars spaced 18 inches on centers will be used.

SPREADING CONCRETE OVER REINFORCING STEEL BY MEANS OF TOWER AND
DISTRIBUTING CHUTE

Courtesy of Leonard Construction Company, General Contractors, Chicago

MASONRY AND REINFORCED CONCRETE 271

Coping and Anchorages. Retaining walls generally have a
coping at the top. This can be made to suit the conditions or the
designer. When reinforced concrete walls are not stable against
sliding, they can be anchored by making a projection of the bottom
into the foundation. This is shown in Figs. 118 and 119.

VERTICAL WALLS

Curtain Walls. Vertical walls which are not intended to carry
any weight are sometimes made of reinforced concrete. They are
then called curtain walls, and are designed merely to fill in the
panels between the posts and girders which form the skeleton frame
of the building. When these walls are interior walls, there is no
definite stress which can be assigned to them, except by making
assumptions that may be more or less unwarranted. When such
walls are used for exterior walls of buildings, they must be designed
to withstand wind pressure. This wind pressure will usually be
exerted as a pressure from the outside, tending to force the wall
inward; but if the wind is in the contrary direction, it may cause a
lower atmospheric pressure on the outside, while the higher pressure
of the air within the building will tend to force the wall outward.
It is improbable, however, that such a pressure would ever be as
great as that tending to force the wall inward. Such walls may be
designed as slabs carrying a uniformly distributed load and sup-
ported on all four sides. If the panels are approximately square,
they should have bars in both directions and should be designed by
the same method as "slabs reinforced in both directions", as has
previously been explained. If the vertical posts are much -closer
together than the height of the floor, as sometimes occurs, the prin-
cipal reinforcing bars should be horizontal, and the walls should be
designed as slabs having a span equal to the distance between the
posts. Some small bars spaced about 2 feet apart should be placed
vertically to prevent shrinkage. The pressure of the wind, corre-
sponding to the loading of the slab, is usually considered to be 30
pounds per square foot, although the actual wind pressure will very
largely depend on local conditions, such as the protection which the
building receives from surrounding buildings. A pressure of thirty
pounds per square foot is usually sufficient; and a slab designed on
this basis will usually be so thin, perhaps only 4 inches, that it is not

283

272 MASONRY AND REINFORCED CONCRETE

desirable to make it any thinner. Since designing such walls is
such an obvious application of the equations and problems already
solved in detail, no numerical illustration will here be given.

CULVERTS

A flat slab design is generally used for spans up to 20 feet for both
highway and railroad culverts. In highway construction, it is some-

60 TON CAR — -|

~-l4'-0"FOR 40 TON CflR -J „

*«•- SJ0 — H

Fig. 120. Load Diagram for 60-Ton and 40-Ton Electric Cars

times found more economical to use the girder bridge for spans as short
as 14 or 16 feet. This discussion will be confined to box culverts for
highway use. Concrete, and particularly reinforced concrete, is

now much used for culverts and
bridges. Its permanence and free-
dom from maintenance charges,
compared with wood and with steel
structures, is much in its favor.
Classification by Loadings.
Highway structures are usually
divided into three classes, as
follows :

Class No. 1. Light high way
structures for ordinary country
use where the heaviest load may
be taken as a 12-ton road roller.
The uniform live load 100 pounds
per square foot.

Fig. 121. Load Diagram for Road Roller ClaSS No.2. Heavy highway

structures for use where 20-ton

road rollers and electric cars of a minimum weight of 40 tons must be
provided for. The uniform distributed load 125 pounds per square foot.

284

MASONRY AND REINFORCED CONCRETE 273

Class No. 3. City highway structures for heavy concentrated
loads, such as large interurban cars, weighing 60 tons. The uni-
form distributed load 150 pounds per square foot.

Load Diagrams. Diagrams representing the loadings for 40-
and 60-ton cars and for road rollers are shown in Figs. 120 and 121,
respectively. Since short-span structures are being considered,
only one truck of a car will be on the culvert at one time. The truck
of a car will be considered as distributing the load over an area 2
feet longer than the center to center of the wheels, and of a width
equal to the length of the ties,
which is usually 8 feet. The
fill will further distribute this
load on a slope of \ to 1 . The
fill over a culvert should never
be less than 1 foot. For
fast-moving cars the bending
moment for the live load
should be increased 35 per
cent for impact when the fill
is less than 5 feet.

Example. Design a flat-
slab culvert with a span of 15 feet
to support a fill of 4 feet under the
ties, a macadam roadway, and a
40-ton car.

Solution. The top will be considered first and a width of 1 foot will be
taken. The fill at 100 pounds per cubic foot will equal 100X4X15 = 6,000
pounds. The macadam would have a thickness of the rail plus the tie, which
will be about 12 inches. Phis material at 125 pounds per cubic foot would equal
125X1X15 = 1,875 pounds for a strip 1 foot wide. The maximum bending
moment for the live load will occur when one of the trucks of a car is at the
middle of the span. The load, 20 tons, will be distributed over an area, as shown
in Fig. 122, 9 feet by 10 feet = 90 square feet. A strip 1 foot wide then must
support 20X2,000-^10 = 4,000 pounds. The formula for this bending moment
would be

Fig. 122. Design Diagram for Flat-Slab Culvert
with 15- Foot Span

Substituting in this formula, we have

^(iMOXlS.iSOOX?) ^^

Add 30 per cent for impact 37,800

163,800

Total moment for live load

285

274 MASONRY AND REINFORCED CONCRETE

Assume that the slab will be 22 inches thick, then a strip 1 foot wide
weighs 1|X 15X150 = 4, 125 pounds. The total weight of the fill, macadam and
concrete, is 12,000 pounds. The moment for this load is

Moment for live load 163,800 in.-lb.

Total moment 433,800

Placing this moment equal to 95 bd2, where b = 12, we have
433,800 = 95 X 12 Xd2
</2 = 380

d =19.5 inches

Add 2 1 inches for protecting the steel, then the total thickness will be 22

inches. The steel required equals .00675 X 12 X 19.5 = 1.58 square inches. Round

bars 1 inch in diameter, spaced 6 inches on centers, will satisfy this requirement.

The shear at the point of supports will equal one-half the sum of the live

and dead loads divided by the area of the section.

8,000 8,000

t) = T/T = 12X.87X19.

which is much less than the permissible working load. Even in this case one-

third of the bars should be turned up at about 3 feet from the end of the span.

The horizontal pressure on the side walls of the culvert produced by the

earth will vary with the depth below the surface. The center of the top foot

of the side walls is 7.5 feet and the center of tha bottom foot is 12.5 feet below

the surface of the roadway. Substituting in Equation (7)

At the top P™= 12?><ZI = 25o ib. per sq. ft.

o o

At the bottom P = 100^12*=416 Ib. per sq. ft.

The average pressure equals (250 +416) -^2 = 333 pounds. This is not
strictly accurate but sufficiently so for the side walls. The live load is 4, 000 •£• 9
= 444 per square foot. It will be assumed that the horizontal pressure from the
live load equals 444 -4-3 = 148 pounds per square foot, this load being independent
of the depth of the fill. The total live and dead load is, therefore, 333 + 148 = 481
pounds per square foot.

^481XfX12 =25,974 in.-lb.
o

A slab with a thickness of 7 inches would satisfy this equation. Since the
side walls must support the top slab as well as the side pressures, they should
not be much less in thickness than the top. Make the walls 15 inches thick
and reinforce them as shown in Fig. 122.

The bottom is sometimes made the same as the top. This is
not necessary unless the foundation is very soft and the load must
be distributed over the whole area. In this case it will be made the
same as the side walls and reinforced as shown.

MASONRY AND REINFORCED CONCRETE 275

In designing the culvert, the student will note that while some
of the calculations are definite other dimensions must be assumed.
The fillets in the corners will assist 'in ^4-^

stiffening the structure. Wing walls must
be provided at the ends. Longitudinal
reinforcement also must be provided. \^ I ^/

Exam pie. Design a box culvert 5 feet square
to support a road roller weighing 12 tons (Class
No. 1), fill 2 feet deep.

Solution. The maximum load will occur
when the rear wheel is at the center of the span,
which is two-thirds of 12 tons, or 8 tons, Fig. 123.
This will be distributed over an area of 1 foot by
9 feet 6 inches. The live load is, therefore,
8X2,000-5-9.5 = 1,664 pounds for a strip 1 foot
wide. The dead load will be 100 X 2 = 200 pounds
per square foot for fill and, assuming that the top
slab will be 8 inches thick, 12.5X8 = 100 pounds
per square foot.

The moments will be as follows:

Fig. 123.
Box Culvert 5 Feet Square

Diagram for

Live load M=

= 24,960 in.-lb.

Add 35 per cent for impact = 24,960 X. 35= 8,736 in.-lb.
Dead load = M = — ^- X 12

44,946 in.-lb.
Placing this equal to 95 b dz where 6 = 12

95 X 12 Xd2 = 44,946.

<Z2 = 39.43
d = 6.28

Make the total thickness 8 inches. The steel required equals .00675 X
6.28 = .04239 square inch per inch of width, f-inch round bars spaced 10 inches
on centers will fulfill the requirements.

The earth pressure on the sides is as follows :

Wh 100X3.2
3

At the top

At the bottom

Average pressure
Pressure for live load
Total pressure

YV II 1UUA0..4 , _„ .,

-5-= 5 =106 Ib. per sq. ft.

100X7.2 „„-,.
= g = 240 Ib. per sq. ft.

(106+240) -=-2 = 173 Ib. per sq. ft.
P = 1,664 -5-3 =555 Ib. per sq. ft.
173 +555 = 728 pounds

The bending moment for this load is

X 12 =27,300 in.-lb.

287

276 MASONRY AND REINFORCED CONCRETE

A slab 7 inches thick will more than satisfy this equation, but the sides for
a culvert of this size should not be made less than the thickness of the top to
insure stiffness. Use f-inch round bars, spaced 9 inches on centers, Fig. 123.
The bottom will be made 8 inches thick, also, and reinforced with 1-inch round
bars, spaced 10 inches on centers. Temperature bars must also be provided.

GIRDER BRIDGES

Method of Design. Girder bridges are being extensively used
for country highways for spans from 20 to 40 feet. They are
sometimes used for spans up to 60 feet and often for spans
as short as 16 feet. Fig. 124 shows the section of one-half the

Fig. 124. Design Diagram for Girder Bridge

width of such a bridge. The slab of such a bridge must always
be paved or macadamized so that no wheels will come direct on
the concrete.

Illustrative Example. Design a girder bridge with a clear span
of 26 feet; width of roadway 16 feet; and two sidewalks each 4 feet
6 inches wide. The loading for this bridge to be as specified for
Class No. 2, the car line being in the center of the bridge, a fill of
six inches to be placed under the ties with a macadam-surfaced
roadway.

The slab for such a structure should never be less than 5
inches thick on account of concentrated loads and shear due to road
rollers and other such loads. The slab will be designed for a live

288

MASONRY AND REINFORCED CONCRETE 277

load of 500 pounds per square foot. The slab load and moment,
therefore, would be as follows:

Live load 4 X 1 X 500 = 2,000

Slab, 5 inches TV X 1 50 X 4 = 250

Fill, 20 inches If X 125X4= 833

3,083

95 X 12 Xd2 = 18,600
<22 = 16.3
d = 4

The steel area equals .00675X4X12, or .32 square inches per
foot of width, which requires f-inch round bars, spaced 4 inches on
centers.

The outside girder G\ supports one-half of the sidewalk load,
which is as follows:

Live load 125 125X2^X26 = 7,313 Ib.

Walk 4 in. thick 50X2|X26 = 2,925 Ib.

Cinderfill 15 in. 60X11X21X26 = 4,388 Ib.

Slab 5 in. . 60X2^X26 = 3,510 Ib.

Girder 12X54 in. 150X4^X26X1 = 17,550 Ib.

35,686 Ib.

,, 35,686X26X12 , oni _.. . „
M=— - =1,391,754 m.-lb.

This moment placed equal to 95 b d2, when 6 = 12, would only
require a depth of 35 inches to the center of the steel, while the total
depth of the beam is 54 inches. Therefore, make 6 = 12 and d = 51,
and solve for the moment factor R.

12 X512X R = 1,505,400
# = 48

Referring to the diagram, Fig. 99, it is at once to be seen that
when R = 4:8, the compression in the concrete will be low and
that a percentage of steel of .005 is more than actually will be
required. However, that amount will be used. 12 X 51 X .005 = 3.1
square inches. Four 1-inch round bars will be used, 2 -bars to be

289

278 MASONRY AND REINFORCED CONCRETE

straight and 2 turned up near the ends. The shear per square
inch is small, but stirrups should be used.

Girder G$ will next be designed. For this beam there are three
live loads to be considered and the girder will be designed to support
the maximum one combined with the dead load. The three live

H-/,-7V -H

(*)

Fig. 125. Diagrams for Loadings for Road Roller and Electric Car

loads are: the uniform load of 125 pounds per square foot,
20-ton road roller, and a 40-ton electric car.

The dead load and moment for this load will be as follows :
Macadam and fill If X 125X5X26 = 27,084 Ib.

Slab AX150X5X26= 8,125 Ib.

Beaml2"X24" 1X2X150X26= 7,800 Ib.

(assumed)

43,000X26X12

-8

43,009 Ib.
1,677,000 in.-lb.

290

MASONRY AND REINFORCED CONCRETE 279

The moment for a uniform live load of 125 pounds per square
foot would be 125X5X26 = 16,250 pounds.

Since the fill is so small the weight of a road roller or car cannot
be distributed to any great extent by this means, it will not be
considered in the calculations. Each of these beams may be re-
quired to support the whole weight of the front wheel and half the
weight of the rear wheel. This moment will be a maximum when
one wheel is one-fourth of the distance between the center of wheels
from the center of the span of the bridge.

The maximum reaction is at the right and is

^13,333X4.75 | 13,333 X 15.75 = 1Q 17g

Then

M = 10,478 X 10.25 X 12 = 1,288,794 in.-lb.

The maximum load produced on girders Gs by an electric car
takes place when one of the trucks is at the center of the span. Each
of these girders at that time would be supporting one-fourth of the
total weight of 40 tons, which is 10 tons, see Fig. 125.

The moment is, therefore

M_ (20,OOOX26_20,OOOX7j 12 = 1)350j000

Add 35 per cent for impact 472,500

1,822,500

The electric car produces a greater bending moment than either
of the other live loads and, therefore, will be used together with the
dead load. That is, 1,822,500+1,677,000 = 3,499,500. Let d equal
25.5, then 25.5 X. 88 = 22.4 inches. The required amount of steel
then is 3,499,500 ^ 22.4 X 16,000 = 9.8 square inches. Eight bars 1J
inches in diameter will be used, one-half of which will be turned up
in pairs at different points near the ends of the girder.

The shear in this girder will be £(20,000 + 43,000) = 31,500
pounds.

T/ 31,500

12X23 Per Sq> m*

Therefore stirrups must be used. They should be f of an inch

291

280 MASONRY AND REINFORCED CONCRETE

in diameter, used throughout the length of the girder, and spaced
not over 6 inches apart near the ends of the girders.

The bending moment for girder Gz will be taken as the mean
of girders Gi and G3, plus the dead load, which will be as follows:

<?i = l, 505,400 in.-lb.

G'3 = 3,499,500 in.-lb.

1,505,400 +3,499,500 = 5,004,900 in.-lb.

G2 = 5,004,900 -f- 2 = 2,502,450 in.-lb.

The steel required equals 2,502,450-^22.4x16,000 = 7 square
inches. Seven bars 1J inches in diameter will be used, f of which
will be turned up near the ends of the girders. Use f -inch shear bars.

In designing girder bridges the designer must always investigate
the shear in the girders and the compression in the T-beams very
carefully and see that these stresses are satisfied.

Arch Culverts. Arch culverts come under the head of arches
and as the general subject of arches, and especially the application
of reinforced concrete to arch construction, is taken up in Part V,
this subject will not be further discussed here.

COLUMNS

Methods of Reinforcement. The laws of mechanics, as well as
experimental testing on full-sized columns of various structural
materials, show that very short columns, or even those whose length
is ten times their smallest diameter, will fail by crushing or shearing
of the material, assuming that the line of pressure is practically coin-
cident with the axis of the column. If the columns are very long,
say twenty or more times their smallest diameter, they will prob-
ably fail by bending, which will produce an actual tension on the
convex side of the column. The line of division between long and
short columns is, practically, very uncertain, owing to the fact that
the center line of pressure of a column is frequently more or less
eccentric because of irregularity of the bearing surface at top or
bottom. Such an eccentric action will cause buckling of the column,
even when its length is not very great. On this account, it is always
wise, especially for long columns, to place reinforcing bars within
the column. The reinforcing bars consist of longitudinal bars
(usually four, and sometimes more with the larger columns), and

292

MASONRY AND REINFORCED CONCRETE 281

bands of small bars spaced from 6 to 18 inches apart vertically,
which bind together the longitudinal bars. The longitudinal bars
are used for the purpose of providing the necessary transverse
strength to prevent buckling of the column. As it is practically
impossible to develop a satisfactory theory on which to compute the
required tensional strength in the convex side of a column of given
length, without making assumptions which are themselves of doubt-
ful accuracy, no exact rules for the sizes of the longitudinal bars
required to resist buckling in a column will be given. The bars
ordinarily used vary from f inch square to 1 inch square; and the
number is usually four, unless the column is very large — 400 square
inches or larger — or is rectangular rather than square. It has been
claimed by many, that longitudinal bars in a column may actually
be a source of danger, since the buckling of the bars outward may
tend to disintegrate the column. This buckling can be avoided, and
the bars made mutually self-supporting, by means of the bands
which are placed around the column. These bands are usually
J-inch or f-inch round or square bars. The specifications of the
Prussian Public Works for 1904 require that these horizontal bars
shall be spaced a distance not more than 30 times their diameter,
which would be 1\ inches for £-inch bars, and \\\ inches for f-inch
bars. The bands in the column are likewise useful to resist the
bursting tendency of the column, especially when it is short. They
will also reinforce the column against the tendency to shear, which
is the method by which failure usually takes place. The angle
between this plane of rupture and a plane perpendicular to the line
of stress is stated to be 60°. If, therefore, the bands are placed at
a distance apart equal to the smallest diameter of the column, any
probable plane of rupture will intersect one of the bands, even if the
angle of rupture is somewhat smaller than 60°.

The following specifications are from the code for Greater New
York (1912):

27. Axial compression in columns without hoops, bands, or spirals, and
with not less than \ nor more than 4 per cent of vertical reinforcement secured
against lateral displacement by steel ties placed not farther apart than 15 diam-
eters of the rods nor more than 12 in., shall not exceed 500 Ib. per sq. in. on
the concrete nor 6,000 Ib. per sq. in. on the vertical reinforcement.

28. Axial compression in columns with not less than 1 per cent of hoops
or spirals spaced not farther apart than £ of the diameter of enclosed column

293

282 MASONRY AND REINFORCED CONCRETE

and in no case more than three inches, and with not less than 1 nor more than
4 oer cent of vertical reinforcement, shall not exceed 725 Ib. per sq. in. on the
concrete within the hoops or spirals nor 8,700 Ib. per sq. in. on the vertical
reinforcement.

Design of Columns. It may be demonstrated by theoretical
mechanics, that if a load is jointly supported by two kinds of material
with dissimilar elasticities, the proportion of the loading borne by
each will be in a ratio depending on their relative areas and moduli
of elasticity. The formula for this may be developed as follows:

C = Total unit compression upon concrete and steel in pounds per square
inch = total load divided by the combined area of the concrete and
the steel

c = Unit compression in the concrete, in pounds per square inch

s = Unit compression in the steel, in pounds per square inch

p = Ratio of area of steel to total area of column

n=-=p- = ratio of the moduli of elasticity

tic

€s = Deformation per unit of length in the steel

€ = Deformation per unit of length in the concrete
^4s = Area of steel
Ac = Area of concrete

The total compressive force in the concrete equals AcXc; and
that in the steel equals AsXs.

The sum of these compressions equal the total compression ; and
therefore

The actual lineal compression of the concrete equals that of the
steel; therefore

From this equation, since n = -^, we may write the equation nc = s

-L/C

Solving the above equation for C, we obtain

r,_Acc+Ass
" AC+AS

Substituting the value of s = nc, we have

r- (Ae+A.n\_ (A.+A,-A.+A.n
-° AC+A.

294

MASONRY AND REINFORCED CONCRETE 283

If p equals the ratio of cross section of steel to the total cross sec-
tion of the column, we have

Substituting this value of — — 8—r in the above equation, we have

Ac-rA8

C=c(\-p+pri)
Solving this equation for p, we obtain

Examples. 1. A column is designed to carry a load of 160,000 pounds.
If the column is made 16 inches square, and the load per square inch to be
carried by the concrete is limited to 500 pounds, what must be the ratio of the
steel and how much steel would be required?

Solution. A column 16 inches square has an area of 256 square inches.
Dividing 160,000 by 256, we have 625 pounds per square inch as the total unit
compression upon the concrete and the steel, which is C in the above formula.
Assume that the concrete is 1:2:4 concrete, and that the ratio of the moduli of
elasticity n is, therefore, 15. Substituting these values in Equation (55), we have
625-500

Multiplying this ratio by the total area of the column — 256 square inches — we
have 4.57 square inches of steel required in the column. This would be amply
provided by 4 bars If inches square. The bands, if made of 5-inch bars,
should be spaced not more than 7| inches (15 diameters) apart.

2. A column 16 inches square is subjected to a load of 126,000 pounds
and is reinforced by four f-inch square bars besides the bands. What is the
actual compressive stress in the concrete per square inch, assuming the same
grade of concrete as above?

Solution. Dividing the total stress, 126,000, by the area, 256, we have
the combined unit stress C = 492 pounds per square inch. By inverting one of
the equations above, we have

C = - - : -

1-p+np

In the above case, the four |-inch bars have an area of 3.06 square inches; and
therefore

1-w--012 «=15

Substituting these values in the above equations, we have
492 492

l-.012 + (. 012X15) 68

The net area of the concrete in the above problem is 252.94 square
inches. Multiplying this by 421, we have the total load carried by

284 MASONRY AND REINFORCED CONCRETE

the concrete, which is 100,488 pounds. Subtracting this from
126,000 pounds, the total load, we have 19,512 pounds as the com-
pressive stress carried by the steel. Dividing this by 3.00, the area
of the steel, we have 6,376 pounds as the unit compressive stress in
the steel. This is practically fifteen times the unit compression in
the concrete, which is an illustration of the fact that if the compres-
sion is shared by the two materials in the ratio of their moduli of
elasticity, the unit stresses in the materials will be in the same ratio.
This unit stress in the steel is about four-tenths of the working stress
which may properly be placed on the steel. It shows that we cannot
economically use the steel in order to reduce the area of the concrete,
and that the chief object in using steel in the columns is in order to
protect the columns against buckling, and also to increase their
strength by the use of bands.

It sometimes happens that in a building designed to be struc-
turally of reinforced concrete, the column loads in the columns of the
lower story may be so very great that concrete columns of sufficient
size wrould take up more space than it is desirable to spare for such
a purpose. For example, it might be required to support a load of
320,000 pounds on a column 15 inches square. If the concrete
(1:2:4) is limited to a compressive stress of 500 pounds per square
inch, we may solve for the area of steel required, precisely as was
done in Example 1. We should find that the required percentage of
steel was 13.17 per cent, and that the required area of the steel was,
therefore, 29.6 square inches. But such an area of steel could carry
the entire load of 320,000 pounds without the aid of the concrete,
and would have a compressive unit stress of only 10,800 pounds.
In such a case, it would be more economical to design a steel column
to carry the entire load, and then to surround the column with
sufficient concrete to fireproof it thoroughly. Since the stress in
the steel and the concrete are divided in proportion to their relative
moduli of elasticity, which is usually about 12 to 15, we cannot
develop a working stress of say 16,000 pounds per square inch in
the steel without at the same time developing a compressive stress
of 1,100 to 1,300 pounds in the concrete, which is objectionably high
as a working stress.

Hooped Columns. It has been found that the strength of a
column is very greatly increased and even multiplied by surrounding

MASONRY AND REINFORCED CONCRETE 285

the column by numerous hoops or bands or by a spiral of steel. The
basic principle of this strength can best be appreciated by considering
a section of stovepipe filled with sand and acting as a column. The
sand alone, considered as a column, would not be able to maintain
its form, much less to support a load, especially if it were dry. But
when it is confined in the pipe, the columnar strength is very con-
siderable. Concrete not only has great crushing strength, even when
plain, but can also be greatly strengthened against failure by
the tensile strength of bands which confine it. The theory of the
amount of this added resistance is very complex, and will not be
given here. The general conclusions, in which experimental results
support the theory, are as follows :

1. The deformation of a hooped column is practically the same as that
of a plain concrete column of equal size for loads up to the maximum for a plain
column.

2. Further loading of a hooped column still further increases the shorten-
ing and swelling of the column, the bands stretching out, but without causing
any apparent failure of the column.

3. Ultimate failure occurs when the bands break, or, having passed their
elastic limit, stretch excessively.

Hooped columns may thus be trusted to carry a far greater unit
load than plain columns, or even columns with longitudinal rods and
a few bands. There is one characteristic that is especially useful for
a column which is at all liable to be loaded with a greater load than
its nominal loading. A hooped column will shorten and swell very
perceptibly before it is in danger of sudden failure, and will thus give
ample warning of an overload.

Considere has developed an empirical formula based on actual
tests, for the strength of hooped columns, as follows :

Ultimate strength = c'A +2As'pA (56)

where c' is ultimate strength of the concrete; s! is elastic limit of the
steel; p is ratio of area of the steel to the whole area; and A is whole
area of the column. This formula is applicable only for reinforce-
ment of mild steel. Applying this formula to a hooped column
tested to destruction by Professor Talbot, in which the ultimate
strength c' of similar concrete was 1,380 pounds per square inch,
the elastic limit sf of the steel was 48,000 pounds per square inch;
the ratio p of reinforcement wras .0212; and the area A was 104
square inches; and substituting these quantities in Equation (56), we

297

286 MASONRY AND REINFORCED CONCRETE

have, for the computed ultimate strength, 409,900 pounds. The
actual ultimate by Talbot's test was 351,000 pounds, or about 86
per cent.

Talbot has suggested the following formulas for the ultimate
strength of hooped columns per square inch :

Ultimate strength = 1,600+ 65,000 p (for mild steel) (57)
Ultimate strength = 1,600+100,000 p (for high steel) (58)

In these formulas p applies only to the area of concrete within
the hooping; and this is unquestionably the correct principle, as the
concrete outside of the hooping should be considered merely as fire
protection and ignored in the numerical calculations, just as the con-
crete below the reinforcing steel of a beam is ignored in calculating
the strength of the beam. The ratio of the area of the steel is com-
puted by computing the area of an equivalent thin cylinder of steel
which would contain as much steel as that actually used in the bands
or spirals. For example, suppose that the spiral reinforcement con-
sisted of a |-inch round rod, the spiral having a pitch of 3 inches.
A ^-inch round rod has an area of .196 square inch. That area for 3
inches in height would be the equivalent of a solid band .0653 inch
thick. If the spiral had a diameter of, say, 11 inches, its circum-
ference would be 34.56 inches, and the area of metal in a horizontal
section, would be 34.56 X. 0653, or 2.257 square inches. The area
of the concrete within the spiral is 95.0 square inches. The value of
p is therefore 2.257-^95.0 = .0237. If the Hnch bar were made of
high-carbon steel, the ultimate strength per square inch of the column
would be 1,600+ (100,000 X. 0237) = 1,600+2,370, or 3,970. The
unit strength is considerably more than doubled. The ultimate
strength of the whole column is, therefore, 95X3,970, or 377,150
pounds. Such a column could be safely loaded with about 94,300
pounds, provided its length were not so great that there was danger
of buckling. In such a case, the unit stress should be reduced accord-
ing to the usual ratios for long columns, or the column should be
liberally reinforced with longitudinal rods, which would increase its
transverse strength.

Effect of Eccentric Loading of Columns. It is well known that
if a load on a column is eccentric, its strength is considerably less
than when the resultant line of pressure passes through the axis

298

MASONRY AND REINFORCED CONCRETE 287

of the column. The theoretical demonstration of the amount of
this eccentricity depends on assumptions which may or may not be
found in practice. The following formula is given without proof or
demonstration, in Taylor and Thompson's treatise on Concrete:

/'=/d +y) (59)

in which e is eccentricity of load; 6 is breadth of column; / is average
unit pressure ; /' is total unit pressure of outer fiber nearest to line of
vertical pressure.

As an illustration of this formula, if the eccentricity on a 12-inch
column were 2 inches, we should have b equals 12, and e equals 2.
Substituting these values in Equation (59) , we should have /' equals
2/, which means that the maximum pressure would equal twice the
average pressure. In the extreme case, where the line of pressure
came to the outside of the column, or when e equals \b, we should
have a maximum pressure on the edge of the column equal to four
times the average pressure.

Any refinements in such a calculation, however, are frequently
overshadowed by the uncertainty of the actual location of the center
of pressure. A column which supports two equally loaded beams
on each side is probably loaded more symmetrically than a column
which supports merely the end of a beam on one side of it. The
best that can be done is arbitrarily to lower the unit stress on a
column that is probably loaded somewhat eccentrically.

TANKS

Design. The extreme durability of reinforced-concrete tanks
and their immunity from deterioration by rust, which so quickly
destroys steel tanks, have resulted in the construction of a large
and increasing number of tanks in reinforced concrete. Such tanks
must be designed to withstand the bursting pressure of the water.
If they are very high compared with their diameter, it is even possi-
ble that failure might result from excessive wind pressure. The
method of designing one of these tanks may best be considered
from an example.

Illustrative Example. Suppose that it is required to design a
reinforced-concrete tank with an inside diameter of 18 feet and with

2SS MASONRY AND REINFORCED CONCRETE

a capacity of 50,000 gallons. At 7.48 gallons per cubic foot, a
capacity of 50,000 gallons will require 6,084 cubic feet. If the inside
diameter of the tank is to be 18 feet, then the 18-foot circle will con-
tain an area of 254.5 square feet. The depth of the water in the
tank will, therefore, be 20.26 feet. The lowest foot of the tank will
therefore be subjected to a bursting pressure due to 25.26 vertical
feet of water. Since the water pressure per square foot increases 62^
pounds for each foot of depth, wTe shall have a total pressure
of 1,610 pounds per square foot on the lowest foot of the tank.
Since the diameter is 18 feet, the bursting pressure it must resist
on each side is \ (18X1,610), or 14,490 pounds. If we allow
a working stress of 15,000 pounds per square inch, this will
require .966 square inch of metal in the lower foot. Since the
bursting pressure is strictly proportional to the depth of the water,
we need only divide this number proportionally to the depth to obtain
the bursting pressure at other depths. For example, the ring one foot
high, at one-half the depth of the tank, should have .483 square inch
of metal ; and that at one-third of the depth should have .322 square
inch of metal. The actual bars required for the lowest foot may be
figured as follows : .966 square inch per foot equals .0805 square inch
per inch; f-inch square bars, having an area .5625 square inch, will
furnish the required strength wThen spaced 7 inches apart. At one-
half the height, the required metal per lineal inch of height is half
of the above, or .040. This could be provided by using f-inch bars
spaced 14 inches apart; but this is not so good a distribution of
metal as to use f-inch square bars having an area of .39 square inch,
and to space the bars nearly 10 inches apart. It would give a still
better distribution of metal to use ^-inch bars spaced 6 inches apart
at this point, although the ^-inch bars are a little more expensive per
pound, and, if they are spaced very closely, will add slightly to the
cost of placing the steel. The size and spacing of bars for other
points in the height can be similarly determined.

A circle 18 feet in diameter has a circumference of somewhat
over 56 feet. Assuming, as a preliminary figure, that the tank is
to be 10 inches thick at the bottom, the mean diameter of the base
ring would be 18.83 feet, which would give a circumference of over
59 feet. Allowing a lap of 3 feet on the bars, this would require
that the bars should be about 62 feet long. Although it is possible

300

MASONRY AND REINFORCED CONCRETE 289

to have bars rolled of this length, they are very difficult to handle,
and require to be transported on the railroads on two flat cars. It is
therefore preferable to use bars of somewhat more than half this
length, say 32 feet 6 inches, and to make two joints in each band.

The bands wrhich are used for ordinary wooden tanks are usually
fastened at the ends by screw bolts. Some form of joint, which is
as strong as the bar, should be used. It has been found that if
deformed bars are overlapped from 1$ inches to 3 feet, according
to their size, and are-then wired together tightly so that their lugs
interlock, it will require a greater force than the strength of the bar
to pull the joints apart after they are once thoroughly incased in
the concrete and the concrete has hardened.

Test for Overturning. Since the computed depth of the water
is over 26 feet, we must calculate that the tank will be, say 28
feet high. Its outer diameter will be approximately 20 feet. The
total area exposed to the surface of the wind will be 560 square feet.
We may assume that the wrind has an average pressure of 50 pounds
per square foot; but, owing to the circular form of the tank, we shall
assume that its effective pressure is only one-half of this; and there-
fore, we may figure that the total overturning pressure of the wind
equals 560X25, or 14,000 pounds. If this is considered to be applied
at a point 14 feet above the ground, we have an overturning moment
of 196,000 foot-pounds, or 2,352,000 inch-pounds.

Although it is not strictly accurate to consider the moment of
inertia of this circular section of the tank as it would be done if it
were a strictly homogeneous material, since the neutral axis, instead
of being at the center of the section will be nearer to the compression
side of the section, our simplest method of making such a calculation
is to assume that the simple theory applies, and then to use a generous
factor of safety. The effect of shifting the neutral axis from the
center toward the compression side will be to increase the unit com-
pression on the concrete and reduce the unit tension in the steel; but,
as will be seen, it is generally necessary to make the concrete so thick
that its unit compressive stress is at a very safe figure, wrhile the
reduction of the unit tension in the steel is merely on the side of safety.

Applying the usual theory, we have, for the moment of inertia of
a ring section, .049 (rfi4 — d4). Let us assume as a preliminary
figure, that the wall of the tank is 10 inches thick at the bottom.

301

290 MASONRY AND REINFORCED CONCRETE

Its outside diameter is, therefore, 18+ (2X10), or 236 inehes. The
moment of inertia / equals .049 (2364-2164) =45,337,842 biquadratic
inches. Calling c the unit compression, we have, as the ultimate
moment due to wind pressure

in which |rfi = 118 inches.

Solving the above equation for c, we have c equals a fraction
less than 6 pounds per square inch. This pressure is so utterly
insignificant, that, even if we double or treble it to allow for the
shifting of the neutral axis from the center, and also double or treble
the allowance made for wind pressure, although the pressure chosen is
usually considered ample, we shall still find that there is practically
no danger that the tank will fail owing to a crushing of the concrete
due to wind pressure.

The above method of computation has its value in estimating
the amount of steel required for vertical reinforcement. On the basis
of 6 pounds per square inch, a sector with an average width of 1 inch
and a diametral thickness of 10 inches would sustain a compression
of about 60 pounds. Since we have been figuring working stresses,
we shall figure a working tension of, say 16,000 pounds per square

inch in the steel. This tension would therefore require — - ,or

16,000

.0037 square inch of metal per inch of width. Even if f-inch bars
were used for the vertical reinforcement, they would need to be
spaced only about 17 inches apart. This, however, is on the basis
that the neutral axis is at the center of the section, which is known to
be inaccurate.

A theoretical demonstration of the position of the neutral axis
for such a section is so exceedingly complicated that it will not be
considered here. The theoretical amount of steel required is always
less than that computed by the above approximate method ; but the
necessity for preventing cracks, which would cause leakage, would
demand more vertical reinforcement than would be required by wind
pressure alone.

Practical Details of Above Design. It was assumed as an
approximate figure, that the thickness of the concrete side wall at

MASONRY AND REINFORCED CONCRETE 291

the base of the tank should be 10 inches. The calculations have
shown that, so far as wind pressure is concerned, such a thickness is
very much greater than is required for 'this purpose; but it will not
do to reduce the thickness in accordance with the apparent require-
ments for wind pressure. Although the thickness at the bottom
might be reduced below 10 inches, it probably would not be wise to
make such reduction. It may, however, be tapered slightly towards
the top, so that at the top the thickness will not be greater than
6 inches, or perhaps even 5 inches. The vertical bars in the lower
part of the side wall must be bent so as to run into the base slab of
tank. This will bind the side wall to the bottom. The necessity
for reinforcement in the bottom of the tank depends very largely
upon the nature of the foundation, and also, to some extent, on the
necessity for providing against temperature cracks, as has been
discussed on preceding pages. Even if the tank is placed on a firm
and absolutely unyielding foundation, some reinforcement should be
used in the bottom in order to prevent cracks which might produce
leakage. These bars should run from a point near the center and
be bent upward at least 2 or 3 feet into the vertical wall. Sometimes
a gridiron of bars running in both directions is used for this purpose.
This method is really preferable to the radial method.

S 5

MASONRY AND REINFORCED
CONCRETE

PART IV

CONCRETE CONSTRUCTION WORK

MACHINERY FOR CONCRETE WORK

Concrete Plant. No general rule can be given for laying out a
plant for concrete work. Every job is, generally, a problem by
itself, and usually requires a careful analysis to secure the most
economical results. Since it is much easier and cheaper .to handle the
cement, sand, and stone before they are mixed, the mixing should
be done as near the point of installation as possible. All facilities for
handling these materials, charging the mixer, and distributing the
concrete after it is mixed must be secured and maintained. The
charging and distributing are often done by wheelbarrows or carts;
and economy of operation depends largely upon system and regu-
larity of operation. Simple cycles of operations, the maintenance
of proper runways, together with clocklike regularity, are necessary
for economy. To shorten the distance of wheeling the concrete, it is
very often found, on large buildings, that it is more economical to
have two medium-sized plants located some distance apart, than
to have one large plant. In city work, where it is usually impossible
to locate the hoist outside of the building, it is constructed in the
elevator shaft or light well. In purchasing a new plant, care must
be exercised in selecting machinery that will not only be satisfactory
for the first job, but that will fulfill the general needs of the purchaser
on other work. All parts of the plant, as well as all parts of any one
machine, should be easy to duplicate from stock, so that there will
not be any great delay from breakdowns or from the use of worn-
out parts.

The design of a plant for handling the material and concrete,
and the selection of a mixer, depend upon local conditions, the

305

294 MASONRY AND REINFORCED CONCRETE

amount of concrete to be mixed per day, and the total amount
required on the contract. It is very evident that on large jobs it
pays to invest a large sum in machinery to reduce the number of men
and horses; but, if not over 50 cubic yards are to be deposited per
day, the cost of the machinery is a big item, and hand labor is gen-
erally cheaper. The interest on the plant must be charged against the
number of cubic yards of concrete; that is, the interest on the plant
for a year must be charged to the number of cubic yards of concrete
laid in a year. The depreciation of the plant is found by taking the
cost of the entire plant when new, and then appraising it after the
contract is finished, and dividing the difference by the total cubic
yards of concrete laid. This will give the depreciation per cubic
yard of concrete manufactured.

CONCRETE MIXERS

Characteristics. The best concrete mixer is the one that turns
out the maximum of thoroughly mixed concrete at the minimum
of cost for power, interest, and maintenance. The type of mixer with
a complicated motion gives better and quicker results than one with
a simpler motion. There are two general classes of concrete mixers —
continuous mixers and batch mixers. A continuous mixer is one into
which the materials are fed constantly, and from which the concrete
is discharged constantly. Batch mixers are constructed to receive
the cement with its proportionate amount of sand and stone, all at
one charge, and, when mixed, discharge it in a mass. No very distinct
line can be drawn between these two classes, for many of these mixers
are adapted to either continuous or batch mixing. Usually, batch
mixers are preferred, as it is a very difficult matter to feed the mixers
uniformly unless the materials are mechanically measured.

Continuous mixers usually consist of a long screw or pug mill
that pushes the materials along a drum until they are discharged in a
continuous stream of concrete. Where the mixers are fed with auto-
matic measuring devices, the concrete is not regular, as there is no
reciprocating motion of the materials. In a paper read before the
Association of American Portland Cement Manufacturers, S. B.
Newberry says:

For the preparation of concrete for blocks in which thorough mixing and
use of an exact and uniform proportion of water are necessary, continuous
mixing machines are unsuitable; and batch mixers, in which a measured batch

306

MASONRY AND REINFORCED CONCRETE 295

of the material is mixed the required time, and then discharged, are the only
type which will be found effective.

Concrete mixers use one of three different methods of combining
the ingredients: the gravity, the rotary, or the paddle principle.

Gravity Mixers. Gravity mixers are the oldest type of concrete
mixers. They require no power, the materials being mixed by
striking obstructions which throw them together in their descent
through the machine. These mixers are of simple construction
comprising a steel trough or chute in which are contained the mixing
members, consisting of pins or
blades. The mixer is portable,
and requires no skilled labor to
operate it. There is nothing to
get out of order or cause delays.
It is adapted for both large and
small jobs. In the former case,
it is usually fed by measure, and
by this method will produce con-
crete as fast as the materials
can be fed to their respective
bins and the mixed concrete
can be taken from the dis-
charge end of the mixer. On
very small jobs, the best way
to operate is to measure the
batch in layers of stone, sand, and cement, respectively, men with
shovels feeding them to the mixer.

There are two spray pipes placed on the mixer: for feeding by
hand, one spray, only, would be used; the other spray is intended
for use only when operating with the measure and feeder, and a large
amount of water is required. These sprays are operated by handles
which control two gate valves and regulate the quantity of water
flowing from the spray pipes.

These mixers are made in two styles, sectional and non-sectional.
The sectional can be made either 4, 6, or 8 feet long. The non-sec-
tional are in one length of 6, 8, or 10 feet. Both are constructed of
|-inch steel. To operate this mixer, the materials must be raised to a
platform, as shown in Fig. 126.

Fig. 126. Operation of Portable Gravity
Mixer

307

296 MASONRY AND REINFORCED CONCRETE

Rotary Mixers. Cube Type. The cube mixer shown in Fig.
127 consists of a cubical box of steel, at diagonally opposite corners
of which hollow trunnions are provided which ride on rollers and
support the drum. These trunnions are made large enough to serve
as openings for charging and discharging the mixer. To rotate the
cube, a circumferential rack is fastened around the drum, at right-
angles to, and midway between, the hollow trunnions. This rack is

Fig. 127. Austin Improved Concrete Mixer
Courtesy of Municipal Engineering and Contracting Company, Chicago, Illinois

in mesh with a pinion shaft which is driven by the engine or motor.
To discharge the mixer, an automatic dumping device is manipu-
lated by the engine operator. At the charging end the usual form
of hopper is provided. There are no paddles or blades of any kind
to assist in the mixing, the stirring and kneeding of the cement
being brought about by the tumbling action of the rotating cube.

Smith Type. Rotating mixers which contain reflectors or blades,
Fig. 128, are usually mounted on a suitable frame by the manufac-

308

MASONRY AND REINFORCED CONCRETE 297

Fig. 128. Smith Mixer on Skids with Driving Pulley
Courtesy of T. L. Smith Company, Milwaukee, Wisconsin

Fig. 129. Interior of Smith Mixer Drum
Courtesy of T. L. Smith Company, Milwaukee, Wisconsin

309

298 MASONRY AND REINFORCED CONCRETE

turers. The rotating of the drum tumbles the material, and it is
thrown against the mixing blades, which cut it and throw it from side
to side. Many of these machines can be filled and dumped while
running, either by tilting or by their chutes. Fig. 128 illustrates the
Smith mixer, and Fig. 129 gives a sectional view of the drum, and
shows the arrangement of the blades. This mixer is furnished on
skids with driving pulley. The concrete is discharged by tilting the
drum, which is done by power.

Fig. 130. Ransome Gasoline-Driven Concrete Mixing Outfit with Fixed Batch Hopper.

Discharge Chute in Position for Mixing
Courtesy of Ransome Concrete Machinery Company, Chicago, Illinois

Ransome Type. Fig. 130 represents a Ransome mixer, which is a
batch mixer. The concrete is discharged after it is mixed, without
tilting the body of the mixer. It revolves continuously even while the
concrete is being discharged. Riveted to the inside of the drum are
a number of steel scoops or blades. These scoops pick up the material
in the bottom of the mixer, and, as the mixer revolves, carry the
material upward until it slides out of the scoops, which, therefore,
assist in mixing the materials.

310

MASONRY AND REINFORCED CONCRETE

299

Smith-Chicago Type. The Smith-Chicago mixer, like the Ran-
some, does not tilt its drum when discharging the concrete. Dis-
charge is accomplished by placing the chute in the position shown
in Fig. 131. The outfit shown consists of the mixer, steam engine,
boiler, power charger, and water tank mounted on a steel truck.

Paddle Mixers. Paddle mixers may be either continuous or of
the batch type. Mixing paddles, on two shafts, revolve in opposite

Fig. 131. Smith-Chicago Concrete Mixer on Steel Truck with Steam Engine and Boiler.

Chute Shown in Discharging Position
Courtesy of T. L. Smith Company, Milwaukee, Wisconsin

directions, and the concrete falls through a trapdoor in the bottom of
the machine. In the continuous type, the materials should be put in
at the upper end so as to be partially mixed while dry. The water is
supplied near the middle of the mixer. Fig. 132 represents a type of
the paddle mixer.

Automatic Measurers for Concrete Materials. Mechanical
measuring machines for concrete materials have not been very

311

300 MASONRY AND REINFORCED CONCRETE

extensively developed. One difficulty is that they require the con-
stant attention of an attendant, unless the materials are perfectly
uniform. If the machine-is adjusted for sand with a certain percen-
tage of moisture, and then is suddenly supplied with sand having
greater or less moisture, the adjustment must be changed or the
mixture will not be uniform. If the attendant does not watch
the condition of the materials very closely, the proportions of the
ingredients will vary greatly from what they should.

Fig. 132. Paddle Mixer

SOURCES OF POWER

General Considerations. In each case the source of power for
operating the mixer, conveyors, hoists, derricks, or cableways must
be considered. If it is possible to run the machinery by electricity, it
is generally economical to do so. But this will depend a great deal
upon the local price of electricity. When all the machinery can be
supplied with steam from one centrally located boiler, this arrange-
ment will be found perhaps more efficient.

In the construction of some reinforced-concrete buildings, a part
of the machinery wras operated by steam and a part by electricity. In
constructing the Ingalls Building, Cincinnati, the machinery was
operated by a gas engine, an electric motor, and a steam engine. The
mixer wras generally run by a motor; but by shifting the belt, it could
be run by the gas engine. - The hoisting was done by a 20-horsepower

312

MASONRY AND REINFORCED CONCRETE 301

TABLE XXV
Dimensions for Ransome Steam Engines

No. OF MIXER

2 .

3 1 4

^- ""- 1

SIZE OF BATCH

10 cu. ft.

20 cu. ft.

30 cu. ft.

40 cu. ft.

CAPACITY PER HOUR (Cu. Yds.)

20 30

HORSEPOWER
REQUIRED

'Engine
Rated

GbyG
7h.p.

7 by 7
10 h.p.

8 by 8
14 h.p.

9 by 9
20 h.p.

Boiler
Rated

30 by 72
lOh.p.

36 by 78
15 h.p.

36 by 96
20 h'.p.

42 by 102
30 h.p.

SPEED OF DRUM

14|

(Rev. per min.)

SPEED OP DRIVING SHAFT

116

122

(Rev. per min.)

Lidgerwood engine. This engine
was also connected up to a boom
derrick, to hoist lumber and steel.
The practice of operating the
machinery of one plant by power
from different sources is to be
questioned; but the practice of
operating the mixer by steam and
the hoist by electricity seems to
be very common in the construc-
tion of buildings. A contractor,
before purchasing machinery for
concrete work, should carefully
investigate the different sources
of power for operating the ma-
chinery, not forgetting to con-
sider the local conditions as well
as general conditions.

Power for Mixing Concrete.
A vertical steam engine is gen-
erally used to operate the mixer.
The smaller sizes of engines and

Fig. 133. Typical Steam Engine for

Hunting Purposes

Courtesy of Ransome Concrete Machinery
Company, Chicago

313

302 MASONRY AND REINFORCED CONCRETE

mixers are mounted on the same frame; but, on account of the
weight, it is necessary to mount the larger sizes on separate frames.
Fig. 133 shows a Ransome disk crank, , vertical engine, and Table
XXV is taken from a Ransome catalogue on concrete machinery.
These engines are well built, heavy in construction, and will stand
hard wTork and high speed.

Gasoline Engines. Gasoline engines are used to some extent
to operate concrete mixers. Their use, so far, has been limited

chiefly to portable plants,
such as are used for street
work. The fuel for the
gasoline engine is much
easier moved from place
to place than the fuel for
a steam engine. Another
advantage that the gaso-
line engine has over the
steam engine is that it
does not require the con-
stant attention of an en-
gineer.

There are two types
of engines — the hori&mtal
and the vertical. The
vertical engines occupy
much less floor space for
a given horsepower than
the horizontal. While
each type has its advan-
tages and disadvantages,
there does not really
appear to be any very great advantages of one type over the other.
Both types of engines are what are commonly known as four-cycle
engines. In the operation of a 4-cycle engine, 4 strokes of the piston
are required to draw in a charge of fuel, compress and ignite it,
and discharge the exhaust gases. Fig. 134 shows a vertical gasoline
engine made by the International Harvester Company.

The quantity of gasoline consumed in 10 hours, on an average, is

ig. 131. Typical Single-Cylinder Gasoline Engine ii

Hoisting Purposes
Courtesy of Fairbanks. Morse & Company, Chicago

314

MASONRY AND REINFORCED CONCRETE 303

about 1 gallon for each rated horsepower for any given size of engine.
At 15 cents per gallon for gasoline, the hourly expense per horse-
power will be 1.5 cents.

HOISTING AND TRANSPORTING EQUIPMENT

General Types of Units. When the concrete requires hoisting,
it is done sometimes by the same engine that is used in mixing the
concrete. It is generally considered better practice on large buildings
to have a separate engine to do the hoisting. If it is possible to use a
standard hoist, it is usually economical to do so. These hoists are
equipped with automatic dump buckets.

Typical Hoisting Engine. Fig. 135 shows a standard double-
cylinder, double-friction-drum hoisting engine of the Lambert type.

Fig. 135. Lambert Hoisting Engine

This type of engine is designed to fulfill the requirements of a general
contractor for all classes of derrick work and hoisting. Steam can be
applied by a single boiler, or from a boiler that supplies various
engines with steam. The double-friction drums are independent of
each other; therefore one or two derricks can be handled at the same
time, if desired. This hoist is fitted with ratchets and pawls, and
winch heads attached to the end of each drum shaft. The winch

3i5

304 MASONRY AND REINFORCED CONCRETE

TABLE XXVI
Sizes of Lambert Hoisting Engines

HORSE-
POWER
USUALLY
RATED

CYLINDERS

DRUMS

WEIGHT
HOISTED
SINGLE LINE
(Pounds)

WEIGHT FOR
PILE-DRIVING
HAMMER

FOR

QUICK WORK

Diameter

Stroke

Diameter

Length
between

(Inche.s)

(Inches)

Flanges

(Pounds)

(Inches)

2,500

1,600

6£

3,000

2,000

5,000

3,000

6,500

4,000

30 8^

8,000

5,000

35 9

9,000

5,000

40 9£

10,000

6,000

heads can be used for any hoisting or hauling desired, independent of
the drums. These engines are also geared with reversible link motion.

Fig. 13b. Single Drum, Cone-Friction Belt Hoist
Courtesy of Ransome Concrete Machinery Company, Chicago

The standard sizes and dimensions of Lambert hoisting engines are
given in Table XXVI.

Cone=Friction Belt Hoist. A single drum cone-friction hoist of
the Ransome type is illustrated in Fig. 136. The same engine that

316

MASONRY AND REINFORCED CONCRETE 305

drives the mixer can be used to operate the crab hoist. By means
of a belt this hoist can be connected up to any engine and, when so
connected, is ready for hoisting purposes. The hoisting drum is
controlled by one lever. This hoist can be run by an electric motor,
if desired.

Fig. 137. Type "K" Hoisting Motor Showing Fields Parted

Courtesy of Westinghouse Electric and Manufacturing Company,

East Pittsburgh. Pennsylvania

Electric Motors. Very often the cycle of operation of a hoist
is of an intermittent character. The power required is at a maximum
only a part of the time, even though the hoist may be operated
practically continuously. From an economical point of view, these
conditions give the electric-motor-driven hoist special advantages, in
that the electric hoist would always be ready, but using power only
when in actual operation, and then only in proportion to the load

317

306 MASONRY AND REINFORCED CONCRETE

handled. The ease with which a motor is moved, and the simplicity
of the connection to the service supply — requiring only two wires to
be connected — are also in favor of the electric motor.

Fig. 137 shows a motor made by the Westinghouse Electric and
Manufacturing Company, which is designed for the operation of
cranes and hoists, or for intermittent service in which heavy starting
torques and a wide speed variation are required. The frames are
enclosed, to guard against dirt and moisture, but are so designed that
the working parts may be exposed for inspection or adjustment
without dismantling. These motors are series-wound, and are
designed for operating on direct-cur-
rent circuits. The motor frames are
of cast steel, nearly square in section
and very compact. The frame is
built in two parts, and so divided
that the upper half of the field can be
removed without disturbing the gear
or shaft, making it easy to take out a
pole piece and field coils, or to remove
the armature. Fig. 138 shows the
controller for this type of motor.
These controllers, when used for
crane service, may be placed directly
in the crane cage and operated by
hand, or mounted on the resistance
frames outside the cage, and operated

Fig. las. westinKhouse Regulating *>y bel1 cranks and levers, so that the
attendant may stand closer to the

operating handles and away from the contacts and resistance.
Polyphase induction motors are being used to some extent for
general hoisting and derrick work. These motors may be of the
two-phase or three-phase type; but the latter are slightly more
efficient. These motors are provided with resistances in the motor
circuit, and with external contacts for varying the same. Two
capacities of resistance can be furnished : (a) intermittent service,
zero to full load ; and (b) intermittent service, zero to half-speed ; and
continuous service, half-speed to full speed. The controllers are of
the drum type, similar to those used on street cars.

318

MASONRY AND REINFORCED CONCRETE 307

Hoisting Lumber and Steel.

In constructing large reinforced-
concrete buildings, usually a sepa-
rate hoist is used to elevate the steel
and lumber for the forms. It may
be equipped with either an electric
motor or an engine, depending upon
the general arrangement of the
plant. These hoists are usually of
the single-drum type.

Hoisting Buckets. In building
construction, concrete is usually
hoisted in automatic dumping buck-
ets. The bucket is designed to
slide up and down a light framework
of timber, as shown in Fig. 139, and
to dump automatically when it
reaches the proper place to dump.
The dumping of the buckets is ac-
complished by the bucket pitching !
forward at the point where the front
guide in the hoisting tower is cut
off. The bucket rights itself auto-
matically as soon as it begins to
descend. These buckets are often
used for hoisting sand and stone as
well as concrete. The capacity of
the buckets varies from 10 cubic
feet to 40 cubic feet. Fig. 140
shows a Ransome bucket which has
been satisfactorily used for this pur-
pose.

Methods of Charging Mixers.
The mixers are usually charged by
means of wheelbarrows, although
other means are sometimes used.
Fig. 141 shows the type of wheel- SECT/ON fJ-/7

barrOW Customarily USed for this Fig- 139. Details of Hoisting Tower with

Automatic Dumping Bucket

319

308 MASONRY AND REINFORCED CONCRETE

work. The capacity varies from 2 cubic feet to 4 cubic feet, the
former size being generally used, though with good runways, a man

can handle 4 cubic feet of stone
or sand in a well-constructed
wheelbarrow.

In ordinary massive concrete
construction, as foundations,
piers, etc., where it is not neces-
sary to hoist the concrete after it
is mixed, the mixer is usually ele-
vated so that the concrete can be
discharged directly into wheel-
barrows, carts, cars, or a chute
from which the wheelbarrows or
carts are filled. It is much bet-
ter to discharge the concrete into
a receiving chute than to dis-
charge it directly into the conveyor. The chute can be emptied while
the mixer is being charged and rotated; while, if the concrete is dis-
charged directly into wheelbarrows or carts, there must be enough

Fig. 140. liar

Hoist Buckets for

Courtesy of Ransome Concrete Machinery
Company, Chicago

Fig. 141. Typical Concrete Barrow
Courtesy of Ransome Concrete Machinery Company, Chicago

wheelbarrows or carts waiting to receive the discharge, or the man
charging the mixer will be idle while the mixer is being discharged.
A greater objection is, that if the man in charge of the mixer finds

320

MASONRY AND REINFORCED CONCRETE 309

Fig. 143. Smith Concrete Mixer on Truck with Gasoline Engine, Power

Charger, and Water Tank
Courtesy of T. L. Smith Company, Milwaukee, Wisconsin

321

310 MASONRY AND REINFORCED CONCRETE

that the charging men or conveying men are waiting, he is very

apt to discharge the concrete before it is thoroughly mixed, in an

effort to keep all the men
busy. A platform is built
at the elevation of the
top of the hopper, through
which the materials are
fed to the mixer, Fig. 142.
This is a rather expensive
operation for mixing con-
crete, and should always
be avoided wrhen possible.
In Fig. 143 is shown
a charging elevator man-
ufactured by the T. L.
Smith Company of Mil-
waukee, Wisconsin. The
bucket is raised and low-
ered by the same engine
by which the concrete is
mixed, and it is operated

by the same man. The capacity of the charging bucket is the same

as that of the mixer.

In Fig. 144 is shown
an automatic loading
bucket which has been
devised by the Koehring
Machine Company for
charging the mixers made
by them. The bucket is
operated by a friction
clutch, and is provided
with an automatic stop.
In using either make of
these charging buckets,
it is necessary to use

wheelbarrows to charge the buckets, unless the materials are close to

the mixer.

Fig. 144. Koehring Stcam-Driven Concrete Mixer with

Side Loader and Water Measuring Tank

Courtesy of Koehring Machine Company,

Milwaukee, Wisconsin

Fig. 145. Typical Concrete Cart

Courtesy of Ransome Concrete Machinery Company,

Chicago

322

MASONRY AND REINFORCED CONCRETE 311

Transporting Mixed Concrete. Concrete is usually transported
by wheelbarrows, carts, cars, or derricks, although other means are
frequently used. It is essential, in handling or transporting concrete,
that care be taken to prevent the separation of the stone from the
mortar. With a wet mixture, there is not so much danger of the stone
separating. Owing to the difference in the time of setting of Portland
cement and natural cement, the former can be conveyed much farther
and with less danger of the initial setting taking place before the
concrete is deposited. When concrete is mixed by hand, wheelbarrows
are generally used to transport the concrete ; and they are very often
used, also, for transporting
machine-mixed concrete.
The wheelbarrows used are of
the type shown in Fig. 141.
About 1^ cubic feet of wet
concrete is the average load
for a man to handle in a wheel-
barrow.

Fig. 145 shows a cart of
the Ilansome make, for trans-
porting concrete. The capa-
city of these carts is 6 cubic
feet, and one man can push or
pull them over a plank run-
way. The runways are made
of two planks, and in width
are at least a foot wider than
the distance between the
wheels. These planks are fastened together on the back with 2- by
6-inch cross pieces, and made in sections so that they can be handled
by four men.

When it is necessary to convey concrete a longer distance than is
economical by means of wheelbarrows or carts, a dumping car, run on
a track, is often used. Fig. 146 shows a steel car for this purpose. The
capacity of these cars is from 10 to 40 cubic feet, and the track gage
is from 18 to 36 inches. Both end- and side-dumping cars are made.

If a large amount of concrete is to be deposited near where it is
mixed, derricks are frequently used to convey the concrete. A corn-

Fig. 146. Typical Rotary Dump Car

Courtesy of Ransome Concrete Machinery Company,

Chicago

323

312 MASONRY AND REINFORCED CONCRETE

bination of car and derrick work is easily made by using flat cars with
derrick buckets.

Boilers. Upright tubular boilers are generally used to supply
steam for concrete mixers and hoists operated by steam engines, when
they are isolated. For the smaller sizes of mixers, the boilers are on
the same frame as the engine and mixer. Fig. 131 shows a Smith-
Chicago mixer, engine, and boiler mounted on the same frame. In
a similar manner the boiler is often fastened to the same frame as the
hoisting engine. This arrangement cannot be used for the larger sizes
of mixers and hoists, as they are too heavy to be handled conveniently.

When it is possible, the mixer and hoists should be supplied with
steam from one centrally located boiler. A portable boiler is then
generally used.

SPECIFICATIONS FOR CONSTRUCTION PLANTS
Woodworking Plant. A portable woodworking plant can very
often be used to advantage in shaping the lumber for the forms, when
a large building is to be erected. The plant can be set near the site of
the building to be erected, and the woodworking done there. The
machinery for such a plant should consist of a planer adapted for
surfacing lumber on three sides, a ripsa\v, and a crosscut circular
saw; in some cases, a band saw can be used to advantage. Usually,
the difference in cost between surfaced and unsurfaced lumber is so
slight that the lumber could not be surfaced in a plant of this kind,
for the difference in cost; but perhaps it would be more uniform in
thickness. In such a plant the ripsaw and the crosscut saw would be
found to be the most useful; and, if reasonable care is taken, this
machinery will soon pay for itself. It is often difficult to get work
done at a planing mill when it is wanted; and if a contractor has his
own woodworking machinery, he will be independent of any planing
mill. A plant of this kind can be operated by a steam or gasoline
engine or by an electric motor.

Plant for Ten=Story Building. The plant used by Cramp and
Company in constructing a reinforced-concrete building in Phila-
delphia will be described to show the arrangement of the plant rather
than the make of the machinery used. The building is 80 feet by 120
feet, and is ten stories high; also, there is a mezzanine floor between
the first and second floors. This building is, structurally, of rein-

324

MASONRY AND REINFORCED CONCRETE 313

forced concrete, except that the interior columns in the lower floors
were constructed of angles and plates and fireproofed with concrete.
The power plant for the building is located at a level of about seven
feet below the basement floor. The hoisting shaft is built in the
elevator shaft located in the rear of the building. The hoisting tower

Basement
Floor

Platform

Fig. 147. Concrete Plant for Ten-Story Building

is constructed of four 4- by 4-inch corner-posts, and well braced with
2- by 6-inch plank. Two guides are placed on opposite sides; also one
on the front, Fig. 147. The front guide was made in lengths equal to
the height of different floors of the building. Fig. 147 shows the
location of the machinery, all of which is of the Ransome make. The
concrete was discharged directly from the mixer into the bucket,

314 MASONRY AND REINFORCED CONCRETE

which rested at the bottom of the elevator shaft. At the elevation
where it was desirable to dump the concrete, the front slide was taken
out, and the concrete was dumped automatically, by the bucket tip-
ping forward, the bucket righting itself as soon as it began to descend.

The capacity of the mixer and hoisting bucket, per batch, was 20
cubic feet. A 9- by 9-inch, 20-horsepower vertical engine was used to
mix and hoist the concrete, steel, structural steel for columns, and lum-
ber for the forms. A 30-horsepower boiler was used to supply the steam ;
this boiler was located several feet from the engine, and is not shown in
the plan view of the plant. A Ransome friction crab hoist was used to
hoist the concrete, and was connected to the engine by a sprocket wheel
and chain. The steel and lumber were hoisted by means of a rope,
wrapped three or four times around a winch head which was on the
same shaft as the mixer. The rope extended vertically up from the
pulley, through a small hole in each floor, to a small pulley at the height
required to hoist the lumber or steel; it then extended horizontally
to another pulley at the place where the material was to be hoisted,
the rope descending over the pulley to the ground. A man was sta-
tioned at the engine to operate the rope. There were two rope haulages
operated from the pulley on the engine shaft, one being used at a
time. On being given the signal, the operator wrapped the rope
around the winch head three or four times, kept it in place, and took
care of the rope that ran off the pulley as material was being hoisted.

Wheelbarrows were used in charging the mixer, and handcarts
were used in distributing the concrete. The runways were made by
securely fastening two 2- by 10-inch planks together in sections of
12 to 16 feet, which were handled by two men. By keeping the run-
way in good condition, two men were usually able to distribute
the concrete, except on the lower floors, and when it was to be
transported the full length of the building. The capacity of the
carts was 6 cubic feet each. Concrete for the ninth floor was
hoisted and placed at the rate of 15 cubic yards per hour.

Plant for the Locust Realty Company Building. The plant used
for constructing a five-story reinforced-concrete building, 117 feet
by 200 feet, for the Locust Realty Company, by Moore and Com-
pany, is a good example of a centrally located plant. Near the center
of the building is an elevator shaft, in which was constructed the
framework for hoisting the concrete. Fig. 148 shows the arrange-

326

HOPPER

HOISTING SHfTFT

HOISTING

Fig. 148. Diagrammatic Layout
for Typical Concrete Plant

MASONRY AND REINFORCED CONCRETE 315

ment of the plant, which is located in the basement and near the
center of the building. The mixer is located so that the concrete can
be dumped directly into the hoisting bucket. The chute for receiving
the materials being about 18 inches above the basement floor, it was
necessary to wheel the materials up an incline. An excavation was
made below the level of the basement
floor for the hoisting bucket. The mix-
ing was done by a steam engine located on
the same frame as the mixer. The con-
crete was hoisted by a hoisting engine
which was located about twenty feet from
the shaft. A small hoisting engine was
also used for hoisting the steel and lum-
ber used for forms; as this engine was
located some distance from the rest of the
plant, it is not shown in Fig. 148. The
three engines are supplied with steam from a portable boiler which is
located as shown in the figure. The efficiency of this plant was
shown in the mixing and hoisting of the concrete for the second
floor, when 240 cubic yards were mixed and hoisted in 16 hours, or
at an average rate of 1 cubic yard in 4 minutes.

All materials were delivered at the front of the building; it was
necessary, therefore, to transport the cement, sand, and stone about
100 feet to the mixer. This was done by means of wheelbarrows
of 4 cubic feet capacity, which were especially designed and made for
the Moore Company. A 1 : 2 : 4 concrete was used, mixed in batches of
14 cubic feet. The materials for a batch, therefore, consisted of 2
bags of cement, 1 wyheelbarrow of sand, and 2 wheelbarrows of stone.

The lumber for the forms was lj-inch plank, except the support
and braces. Details of the forms will be given and discussed under
the heading of "Forms".

Concrete Plant for Street Work. A self-propelling mixing and
spreading machine has been found very desirable for laying concrete
base for street pavements. Fig. 149 illustrates a plant of this kind,
devised by the Municipal Engineering and Contracting Company.

The mixer is of the improved cube type, mounted on a heavy
truck frame. The concrete is discharged into a specially designed
bucket, which receives the whole batch and travels to the rear on a

327

310 MASONRY AND REINFORCED CONCRETE

truck which is about 25 feet long. The head of the truck is supported
by guys, and also by a pair of small wheels near the middle of the

truck, which rest on the graded surface of the street. The truck or
boom is pivoted at the end' connected to the main truck, and has a

328

MASONRY AND REINFORCED CONCRETE 317

horizontal swing of about 170 degrees, so that a street 50 feet wide is
covered. An inclined track is also constructed, on which a bucket
is operated for elevating and charging the mixer. The bucket is
loaded while resting on the ground, with the proper ingredients for a
batch, from the materials that have been distributed in piles along
the street. The bucket is then pulled up the incline, and the contents
dumped into the mixer. An automatic water-measuring supply tank,
mounted on the upper part of the frame, insures a uniform amount
of water for each batch mixed. The power for hoisting, mixing, and
distributing the concrete, and propelling the machine was furnished
by a 16-horsepower gasoline engine of the automobile type. The
machine can be moved backward as well as forward, and is supplied
with complete steering gear.

MISCELLANEOUS OPERATIONS

Concrete=Block Machines. There are two general types of
hollow-concrete-block machines on the market — those with a vertical

Fig. 150. "Hercules" Cement Stone Machine
Courtesy of Century Cement Company, Rochester, New York

face and those with a horizontal face. In making blocks with the
vertical-faced machine, the face of the block is in a vertical position
when molded, and is simply lifted from the machine on its base
plate. The horizontal-faced type of block is made with the face
down, the face plate forming the bottom of the mold. The cores are
withdrawn horizontally, or the mold is turned over and the core is
taken out vertically; the block is then ready for removal. The
principal difference in the twro types of machine is that, if it is desired

318

MASONRY AND REINFORCED CONCRETE

to put a special facing on the block, it is more convenient to do it with
a horizontal-faced machine. With the vertical-faced machine, the
special facing is put on by the use of a parting plate. When the part-
ing plate is removed, the two mixtures of concrete are bonded together
by tamping the coarser material into the facing mixture.

Fig. 150 shows a Hercules machine. The foundation parts can
be attached for making any length of block up to (> feet. The illus-
tration shows two molds of different lengths attached. These machines
are constructed of iron and steel, except that the pallets (the plates on

Fig. 151. Group of Blocks made on "Hercules" Machine

which the blocks are taken from the machine) may be either wood or
steel. This type of machine is the horizontal or face-down machine.

In Fig. 151 are shown a group of the various forms which may be
made. The figure also illustrates the facility writh which concrete
may be utilized for ornamental as wrell as structural purposes.

Another machine of the face-down type is shown in Fig. 152.
This machine, the Ideal, is simple in construction and operation,
and, being portable, it is convenient to operate. In making blocks
with this machine, the cores are removed by means of a lever, while
the block is in the position in which it was made. The mold and
block are then turned over, and the face plates and end plates are

330

MASONRY AND REINFORCED CONCRETE 319

Fig. 152. "Ideal" Concrete Block Machine
Courtesy Ideal Concrete Machinery Company,
Cincinnati, Ohio

released, and the block removed in the pallet. Fig. 153 shows an

Ideal block machine being operated under the Ideal Automatic

Tamper. This device increases

the capacity of the block machine

and gives a better block.

In Fig. 154 is shown a Hobbs

face-down, wet-process block ma-
chine. The front and sides of the

machine can be let down, thus

facilitating the removal of the

blocks. The cores are shown

withdrawn in the figure.

Cement=Brick Machines.

Fig. 155 shows a machine for

making cement brick. Ten

bricks, 2| by 3| by 8 inches, are

made at one operation. By using

a machine in which the
bricks are made on the
side, a wetter mixture of
concrete can be used than
if they are made on the
edge. The concrete
usually consists of a mix-
ture of 1 part Portland
cement and 4 parts sand.
The curing of these bricks
is the same as that for
concrete blocks. In mak-
ing these bricks, a num-
ber of wood pallets are
required, as the brick
should not be removed
from the pallet until the

Fig. 153

per

with Block Machine

Courtesy of Ideal Concrete Machinery Company,
Cincinnati, Ohio

Sand Washing. It

sometimes becomes nec-
essary to wash dirty sand, which can easily be obtained, while clean

331

320 MASONRY AND REINFORCED CONCRETE

sand can be secured only at a high cost. If only a small quantity is
to be washed, it may be done with a hose. A trough should be built

about 8 feet wide and 15 feet
long, the bottom having a
slope of about 19 inches in its
entire length. The sides
should be about 8 inches
high at the lower end, and
increase gradually to a height
of about 36 inches at the
upper end. In the lower end
of the trough should be a gate
about 6 inches high, sliding
in guides so that it can be
easily removed. The sand is
placed in the upper end of the
trough, and a stream of water
is played on it. The sand and
water flow down the trough,
and the dirt passes over the
gate with the overflow water. With a trough of the above dimen-
sions, and a stream of water from a f-inch hose, three cubic yards
of sand should be washed in an hour.

Concrete mixers are often
used for washing sand. The sand
is dumped into the mixer in the
usual manner and the water is
turned on. When the mixer is
filled with water so that it over-
flows at the discharge end, the
mixer is started. By revolving
the mixer, the water is able to
separate the dirt from the sand,
and it is carried off by the overflow of water. When the water
runs clear, the washing is complete, and the sand is dumped in the
usual way.

When large quantities of sand require washing, special machin-
ery for that purpose should be employed.

Fig. 154. Hobbs Face-Down, Wet-Process Con-
crete Block Machine

Courtesy of Hobbs Concrete Machinery Company,
Detroit, Michigan

Fig. 155. "Century" Cement Brick Machine

332

MASONRY AND REINFORCED CONCRETE 321

FORMS
BUILDING FORMS

General Requirements. In actual construction work, the cost
of forms is a large item of expense and offers the best field for the
exercise of ingenuity. For economical work, the design should consist
of a repetition of identical units; and the forms should be so devised
that it will require a minimum of nailing to hold them, and of labor
to make and handle them. Forms are constructed of the cheaper
grades of lumber. To secure a smooth surface, the planks are planed
on the side on which the concrete will be placed. Green lumber is
preferable to dry, as it is less affected by wet concrete. If the surface
of the planks that is placed next to the concrete is well oiled, the
planks can be taken down much easier, and, if kept from the sun,
they can be used several times.

Crude oil is an excellent and cheap material for greasing forms,
and can be applied with a whitewash brush. The oil should be
applied every time the forms are used. The object is to fill the
pores of the wood, rather than
to cover it with a film of grease.
Thin soft soap, or a paste made

frr»m «mnr» anr\ wafpr i<* fllio Fig. 156. Typical Form of Construction

irom SOap ana \Vater, IS aiSO * Showing Tongued-and-Grooved

Sometimes USed. and Beveled-Edge Boards

In constructing a factory building of two or three stories, usually
the same set of forms is used for the different floors; but when the
building is more than four stories high, two or more sets of forms are
specified, so as always to have one set of forms ready to move.

The forms should be so tight as to prevent the water and thin
mortar from running through and thus carrying off the cement.
This is accomplished by means of tongued-and-grooved or beveled-
edge boards, Fig. 156; but it is often possible to use square lumber
if it is wet thoroughly, so as to swell it before the concrete is placed.
The beveled-edge boards are often preferred to tongued-and-grooved
boards, as the edges tend to crush as the boards swell, and beveling
prevents buckling.

Lumber for forms may be made of 1-inch, l|-inch, or 2-inch
plank. The spacing of studs depends in part upon the thickness of
concrete to be supported, and upon the thickness of the boards on
which the concrete is placed. The size of the studding depends upon

322

MASONRY AND REINFORCED CONCRETE

the height of the wall and the amount of bracing used. Exeept in
very heavy or high walls, 2- by 4-ineh or 2- by 6-inch studs are used.
For ordinary floors with 1-inch plank, the supports should be placed
about 2 feet apart; with l|-inch plank, about 3 feet apart; and with
2-inch plank, 4 feet apart.

The length of time required for concrete to set depends upon the
weather, the consistency of the concrete, and the strain which is
to come on it. In good drying weather, and for very light work,
it is often possible to remove the forms in 12 to 24 hours after

placing the concrete, if there
is no load placed on it. The
setting of concrete is greatly
retarded by cold or wet
weather. Forms for con-
crete arches and beams must
be left in place longer than
in wall work, because of the
tendency to fail by rupture
across the arch or beam. In
small, circular arches, like
sewers, the forms may be
removed in 18 to 24 hours,
if the concrete is mixed dry ;
but if wet concrete is used,
in 24 to 48 hours. Forms
for large arch culverts and
arch bridges are seldom
taken down in less than 28
days. The minimum time
for the removal of forms
should be :

For bottom of slabs and sidos of beams and girders, 7 days
For bottom of beams and girders, 14 days
For columns, 4 days
For walls, not loaded, 1 to 2 days
For bridge arches, 28 days

The concrete should be thoroughly examined before any forms
are removed. Forms must be taken down in such a way as not to
deface the structure or to-disturb the remaining supports.

V'V

~^<f

rV V

lii

•v>

Fig. 157. Forms for Columns, (a) Common Method
of Construction; (b) Method in Con-
structing Harvard Stadium

334

MASONRY AND REINFORCED CONCRETE 323

vvATVI

Forms for Columns. In constructing columns, the forms
are usually erected complete, the full height of the columns, and con-
crete is dumped in at the top. The concrete must
be mixed very wet, as it cannot be rammed very
thoroughly at the bottom, and care must be taken
not to displace the steel. Sometimes the forms
are constructed in short sections, and the concrete
is placed and rammed as the forms are built. The
ends of the bottom of the forms for the girders
and beams are usually supported by the column
forms. To give a beveled edge to the corner of
the columns, a triangular strip is fastened in the
corner of the forms.

Fig. 157-.1 shows the common way, or some
modification of it, of constructing forms for col-
umns. The plank may be 1 inch, 1^ inches, or 2
inches thick; and the cleats are usually 1 by 4
inches and 2 by 4 inches. The spacing of
the cleats depends on the size of the columns
and the thickness of the vertical plank.

Fig. 157-5

Fig. 158. Forms for
Square Columns

shows column

forms similar to those used in con-
structing the Harvard stadium.
The planks forming each side of
the column are fastened together
by cleats, and then the four sides
are fastened together by slotted
cleats and steel tie-rods. These
forms can be quickly and easily
removed.

Fig. 158 shows a column form
in which concrete is placed and
rammed as the form is con-
structed. Three sides are erected
to the full height, and the steel

is then placed. The fourth side is built up with horizontal boards

as the concrete is placed and rammed.

Round columns are often desirable for the interior columns of

Fig. 1">9. Forms for Round Columns

335

;]2l MASONRY AND REINFORCED CONCRETE

buildings. Fig. 159 shows a form that has been used for this type
of column. The columns for which these forms were used were 20
inches in diameter, and had a star-shaped core made of structural
steel. The forms for each column were made in two parts and bolted
together. The sides were made of 2- by 3-inch plank surfaced on all
four sides, beveled on two, and held in place by steel bands, f by 2|

Fig. KiO. F

inches, spaced about 2| feet apart. One screw in the outer plank of
both parts of each band, together with a few intermediate screws,
held the planks in place. The building for which these forms were
made was ten stories in height. Enough forms were provided for
two stories, which was sufficient, as they could be removed when the
concrete had been in place one week. Later, these same forms were
used in constructing the interior columns of a six-story building.
Some difficulty was experienced in removing these forms, owing to

7 8*X6"

Fig. 161. Forms for Reinforced Concrete Slab Supported by I-Beam3

the concrete sticking to the plank. But had the forms been made in
four sections, instead of two, and well oiled, it is thought that this
trouble would have been avoided. Columns constructed with forms
as shown in Fig. 159 will not have a round surface, but will consist
of many flat surfaces, 2| inches wide. If a perfectly round column
is desired, it will be necessary to cut the surface of the plank next to

336

MASONRY AND REINFORCED CONCRETE 325

the concrete to the desired radius. Forms for octagonal columns can
be made in a manner somewhat similar to these just described.

Forms for Beams and Slabs.
A very common style of form for
beam and slab construction is
shown in Fig. 160. The size of
the different members of the
forms depends upon the size of
the beams, the thickness of the
slabs, and the relative spacing
of some of the members. If the beam is 10 by 20 inches, and the
slab is 4 inches thick, then 1-inch plank supported by 2- by 6-inch
timbers spaced 2 feet apart will r-
support the slab. The sides and p
bottom of the beams are enclosed £
by l£-inch °r 2-inch plank sup- \
ported by 3- by 4-inch posts
spaced 4 feet apart.

Fig. 162. Forms for Reinforced Concrete Slab
between I-Beama

Fig. 163. Forms for Floor-Slab on I-Beama

In Fig. 101 are shown the forms for a reinfo reed-concrete slab,
with I-beam construction. These forms are constructed similarly
to those just described.

A slab construction sup-
ported on I-beams, the bottom
of which is not covered with con-
crete, may have forms con-
structed as shown in Fig. 162.
This method of constructing
forms was designed by Mr. Wil-
liam F. Kearns (Taylor and
Thompson, "Plain and Rein-
forced Concrete").

The construction of forms
for a slab that is supported on the
top of I-beams is a compara-
tively simple process, as shown in
Fig. 163. In any form of I-beam and slab construction, the forms
can be constructed to <;arry the combined weight of the concrete
and forms. When the bottom of the I-beam is to be covered with

164. Beam and Slab Forms for Locust
Realty Company Building

337

326 MASONRY AND REINFORCED CONCRETE

concrete, it is not so easily done as when the haunch rests on the

bottom flange, as shown in Fig. 162, or when it is a flat plate, as

shown in Fig. 163.

Forms for Locust Realty Company Building. The forms used

in constructing the building for the Locust Realty Company (the

mixing plant has already been
described), present one rather un-
usual feature. The lumber for
the slabs, beams, girders, and col-
umns was all the same thickness,
\\ inches. Fig. 164 shows the
details of the forms for the beams
and slabs. The beams are spaced
about 6 feet apart, and are 8 by
16 inches; the slab is 4 inches
thick. A notch is cut into the 1 \-
by 6-inch strip on the side of the
beams, to support the 2- by 4-
inch strip under the plank which
supports the concrete for the slab.
The posts supporting the forms
are 3|- by 3|-inch, and are braced
by two 1- by 6-inch boards which
are spaced about 3 feet apart
and extend in the direction of
the beams.

Fig. 165 shows the forms for
the columns. The planks for each
side of the column are held to-
gether by the 1- by 4-inch strip,

^/WKArV

Fig. 105. Column Forms for Locust Realty
Company Building

and, when erected in place, are
clamped by the 2- by 4-inch strip.
A large opening is always left at

the bottom of the form for each column, so that all shavings and

sawdust can be removed. This opening is closed just before the

concrete is deposited.

Cost of Forms for Buildings. An analysis of the cost of forms

for an eight-story building is given by R. E. Lamb in Concrete Engi-

338

MASONRY AND REINFORCED CONCRETE 327

neering. The basis of his estimate is made on using f -inch by 6-inch
tongued-and-grooved lumber for slab forms; If -inch dressed plank
for the sides and bottom of the beams and girders; and posts 4- by
4-inch, spaced 6 feet center to center. He makes the further
assumption that it cost $20.00 per thousand feet of lumber to make
and set one floor of forms; that it cost $15.00 per thousand feet of
lumber to strip the forms and reset them on the next floor; and
that it cost about $8.00 per thousand feet to strip the forms and
lower them to the ground.

With the size of the beams and girders as shown in Fig. 166,
Mr. Lamb states that it will take an average of 4 feet, board measure,
to erect each square foot of floor area. The basis of his estimate is
as follows: That 1.5 board feet of lumber per square foot of floor is
required for the slab; that for every square foot of beam surface,
including the bottom, 3.2 board feet per square foot is required;
and that for each square foot of girder, including the bottom, 3.6
board feet of lumber is required.
Taking these figures, for the
panel shown, the slab will require
1.5 board feet per square foot;
the beams, which are 8- by 18-
inch, will have 3 feet 8 inches of
surface per lineal foot; and mul-
tiplying this by 3.2 board feet
per square foot, and .dividing by
7.5 feet, the distance center to
center of beams, we find that
1.56 board feet per square foot
of floor surface is required. Tak-
ing the girder in the same way, with 4 feet 8 inches of surface,
multiplied by 3.6 board feet, and divided by 18 feet, the distance
center to center of girders, we find that .94 board foot per square
foot of floor is required. The total of the lumber required, then, is
1.5 board feet for the slab, 1.56 board feet for the beam, and .94
board foot for the girders — a total of 4 board feet per square foot of
floor area.

In this estimate for an eight-story building, three sets of forms
were used:

» //

L J

8X/8

ix.

Li,

8"xl8" rJ-

~ ^ ^p1

ig. 166. Diagram of Forms

339

328 MASONRY AND REINFORCED CONCRETE

Roof. Stripping the sixth floor, resetting, altering to form valleys, and
finally stripping roof and lowering forms to ground, 4 board feet
at 2. 6 cents $0.104

Eighth Floor. Stripping the fifth floor, resetting, and finally stripping

and lowering forms to ground, 4 board feet at 2.3 cents .092

Seventh Floor. Stripping the fourth floor, resetting, and finally strip-
ping and lowering forms to ground, 4 board feet at 2.3 cents .092
Sixth Floor. Cost, same as for the fourth floor .060
Fifth Floor. Cost, same as for the fourth floor .060
Fourth Floor. Stripping the first floor, and resetting, 4 board feet at

1.5 cents .060

Third Floor. Cost, the same as for the first floor . 184

Second Floor. Cost, same as for the first floor . 184

First Floor. Making and setting forms, 4 board feet at

2 cents $0.080

Material, 4 board feet at 2 . (> cents .104 .184

0)1.020
Average cost per square foot of surface $0.113

To this average cost of 11.3 cents, 10 per cent should be added for
waste, breakage, nails, etc.; and if two sets of forms are used, the
third floor would cost 6 cents per square foot, and the seventh floor
6 cents, giving an average of 9.6 cents per square foot.

In estimating the cost of the forms for the columns, it is assumed
that making and placing the forms for the basement columns will cost
about $26.00 per thousand; the cost of stripping and resetting,
$16.00 per thousand; and 3.1 square feet of lumber is required for
each square foot of column surface.

Eighth Story. Stripping sixth story, resetting and altering, finally strip-
ping eighth story and lowering to ground, 3 . 1 board feet at 2 . 2 cent s $0 . 068
Seventh Story. Stripping fifth story, resetting, and finally stripping

and lowering to ground, 3.1 board feet at 1.9 cents .059

Sixth Story. Cost, same as second story .050

Fifth Story. Cost, same as second story .050

Fourth Story. Cost, same as second story .050

Third. Story. Cost, same as second story .050
Second Story. Stripping basement columns and resetting, 3 . 1 board

feet at 1.6 cents .050

First Story. Cost, same as for the basement columns . 162
Basement. Material, 3 . 1 board feet at 2 . 6 cents $0 . 081
Making and setting, 3 . 1 board feet at 2 . 6 cents .081

$0.162 .162

9)0.701

Average cost per square foot of surface $0 . 077

To this average cost of 7.7 cents per square foot of column surface,
should be added 10 per cent for bolts, nails, waste, etc. If three sets

340

MASONRY AND REINFORCED CONCRETE 329

of forms are required, the second-story cost would be 16.2 cents, and
the sixth 5.9 cents, giving an average cost per square foot of 9.1 cents.
The student should remember that this lumber has a value
after it has been removed from the building, and that this value
should be deducted from the total to find the actual cost of the forms.
Cost of Forms for Garage. Some interesting cost data are
given by Mr. Reygondeau de Gratresse, Assoc. M. Am. Soc. C. E.
in Engineering-Contracting, on the cost of forms used in erecting a
reinforced-concrete garage in Philadelphia. The building was 53
feet wide, 200 feet long, and four stories high; also, there was a mezza-
nine floor. Tongued-and-grooved lumber f inch thick was used for
the slab forms, and 1 f -inch plank for the beams and girders. The
area of the 1,740 cubic yards of concrete covered by forms was:

Sq. Ft.

Footings 4,000

Columns 20,000

Floors and Girders 70,000

. Total 94,000

For this work, 1 70,000 feet, board measure, of new lumber, and
50,000 feet, board measure, of old lumber was used, the cost being :

50,000 ft. B. M. at $13 $ 650

170,000 ft. B. M. at $26 4,420

220,000 ft. B. M. at $23 $5,070

Since 220,000 feet, board measure, were used for the 1,740 cubic
yards, there were 126 feet, board measure, per cubic yard of concrete.

New forms were made for each floor, except the sides of the
girders, which were used over for each floor, where the sizes would
admit of this being done. The props under the girders were allowed
to remain in place throughout the building until the entire job was
completed. The forms for the roof were made entirely of the material
used on the floors below. The area of concrete covered by the new
lumber was approximately 80,000 square feet. This gives a cost for
lumber of 6.4 cents per square foot.

A force of fifteen carpenters, working under one foreman, framed,
erected, and tore down all forms. All the lumber for the carpenters
was handled by the laborers excepting when they were at work
mixing and placing concrete. The foreman was paid $35 per week,
while the carpenters were paid an average of $4.40 for an 8-hour day.
Laborers were paid 17 cents per hour, and worked a 10-hour day;

341

330

MASONRY AND REINFORCED CONCRETE

over them was a foreman who received the same wages as the
boss carpenter. The forms for a floor were erected in from 8 to 10
days. For the framing, erecting, and tearing down of the forms, the
labor cost was about $3,480, which gives a cost of $2 per cubic yard.
For the carrying and handling of the lumber, the cost was about
$1,914, which gives a cost of $1.10 per cubic yard. This gives a total
cost per cubic yard of forms as follows :

Lumber, 126 ft. B. M.

Framing, erecting, and tearing down

Handling lumber

Total

Per Cu. Yd.
$2.90
2.00
1.10

$6.00

Tlu's cost is high, owing to the fact that so little of the lumber
was used a second time, there being only from 16 to 20 per cent so

Fig. 167. Typical Adjustable Clamp

Ij STOF'PIN

used. For the 220,000 feet, board measure, of lumber used on the job,
the average cost per thousand for the forms was

Lumber

Framing, erecting, and tearing down

Handling lumber

Total

Per M.
$23.00
15.67
8.70

$47.37

The cost per square foot of concrete for the area covered was
Lumber $0.064

Labor .057

Total $0.121

The cost per cubic yard for lumber and labor was

Lumber
Labor on forms

$2.90

Total $6.00

It should be remembered that the lumber used in the forms had
a salvage value, for which no allowance is made in the above $2.90.

342

MASONRY AND REINFORCED CONCRETE 331

Adjustable Clamps. Fig. 167 illustrates an adjustable clamp
for holding forms together. It is commonly used to hold the plank
forming the sides of a beam or girder in place, and also in clamping
opposite sides of columns. It is forged from a l|-inch by f-inch
steel bar, and is held in place by the slotted forging, 1 inch square.

FORMS FOR SEWERS AND WALLS

Forms for Conduits and Sewers. Forms for conduits and
sewers must be strong enough not to give way, or to become deformed,
while the concrete is being placed and rammed; and must be rigid
enough not to warp from being alternately wet and dry. They must
be constructed so that they can readily be put up and taken down,
and can be used several times on the same job. The forms must
give a smooth finish to the interior of the sewer. This has usually
been done by covering the forms with light-weight sheet iron.

These forms are usually built in lengths of 16 feet, with one
center at each end, and with three to five — depending on the size of
the sewer or conduit — intermediate centers in the lengths of 15 feet.
The segmental ribs are bolted together. The plank for these forms
are made of 2- by 4-inch material, surfaced on the outer side, with the
edge beveled to the radius of the conduit. The segmental ribs are
bolted together, and are held in place by wood ties 2 by 4 inches
or 2 by 6 inches.

Forms of Torresdale Filters. In constructing the Torresdale
filters for supplying Philadelphia with water, several large sewers and
conduits were built of concrete and reinforced with expanded metal.
In section, the sewers were round and the conduits were horseshoe-
shaped, with a comparatively flat bottom. The sewers were 6 feet and
8 feet 6 inches, respectively, in diameter, and the forms were con-
structed similarly to the forms shown in Fig. 168, except that at the
bottom the lower side ribs were connected to the bottom rib by a
horizontal joint, and the spacing of the ribs was 2 feet 6 inches,
center to center. Fig. 169 shows the form for the 7-foot 6-inch con-
duit. The centering for the 9-foot and 10-foot conduits was con-
structed similarly to the 7-foot 6-inch conduit, except that the ribs
were divided into 7 parts instead of 5 parts as shown in Fig. 169. The
spacing of the braces depended on the thickness of the lagging. For
lagging I inch by 2£ inches, the braces were spaced 18 inches, center

343

332 MASONRY AND REINFORCED CONCRETE

to center; and for 2- by 3-inch lagging, the spacing of the bracing
was 2 feet 0 inches.

These forms were constructed in lengths of 8 feet. The lagging

Fig. 108. Center for Round Scwc

Fig. 10'J. Form for Construction of Horseshoe-
Shaped Conduit

for the smaller sizes of the conduits was 1 inch by 2\ inches, and
for the larger sizes 2 by 3 inches; all of this was made of dressed
lumber and covered with No. 27 galvanized sheet iron. The bracing

'ig. 170. niaw Collapsible Steel Ft

of the forms was arranged to permit the centering to be taken apart
and brought forward through the sections set in front of it. Three
sets of these forms were required for each conduit. The specifications

MASONRY AND REINFORCED CONCRETE 333

required that the centering be left in place for at least GO hours after
the concrete had been placed. It was also required that this work
should be constructed in monolithic sections1 — that is, the contractor
could build as long a section as he could finish in a day — and that
the sections should be securely keyed together.

Blaw Steel Forms. The Blaw collapsible steel forms, Fig. 170,
appear to be the only successful steel forms, so far, in general use.
There have been many attempts to devise
steel centering for column, girder, and slab
construction, but no available system has
yet been invented. The main trouble with
those used is their liability to leak, tendency
to rust, and susceptibility to injury by dents
in removing.

The Blaw collapsible steel centering is
in general use for sewer and conduit con-
struction. This centering consists of one
or more steel plates about f inch thick and
bent to the shape required by the interior of
the sewer to be constructed. The steel
plates are held in shape by angle irons.
When set in position, the sections are held
rigid by means of turnbuckles, which also
facilitate the collapsing of the sections. The
adjacent sections are held together by staples
and wedges, the former being riveted to the
plates as seen in Fig. 170. The sections are
usually made five feet long, and in any de-
sired shape or size required for sewer or
conduit work. When these forms are used

•I

Fig. 171. Typical Forms
for Wall

to construct concrete sewers or conduits, the surface of the forms
must be well coated with grease or soap, to prevent the concrete from
adhering to the steel.

Forms for Walls. The forms for concrete walls should be built
strong enough to make sure they will retain their correct position
while the concrete is being placed and rammed. In high, thin walls,
a great deal of care is required to keep the forms in place so that the
wall will be true and straight.

345

334 MASONRY AND REINFORCED CONCRETE

Fig. 171 shows a very common method of constructing these
forms. The plank against which the concrete is placed is seldom
less than 1^ inches thick, and is usually 2 inches thick. One-inch
plank is sometimes used for* very thin walls; but even then, the
supports must be placed close. The planks are generally surfaced
on the side against which the concrete is placed. The vertical
timbers that hold the plank in place will vary in size from 2 inches
by 4 inches to 4 inches by 6 inches, or even larger, depending on the
thickness of the wall, spacing of these vertical timbers, etc. The
vertical timbers are always placed in pairs, and are usually held in
place by means of bolts, except for thin walls, when heavy wire is
often used. If the bolts are greased before the concrete is placed,
there is ordinarily not much trouble experienced in removing them.
Some contractors place the bolts in short pieces of pipe, the diameter
of the pipe being about | inch greater than that of the bolt, and the
length equal to the thickness of the wall. When the bolts are removed
the holes are filled with mortar.

FORMS FOR CENTER OF ARCHES

General Specifications. The centers for stone, plain concrete,
and reinforced-concrete arches are constructed in a similar manner.
A reinforced-concrete arch of the same span and designed for the same
loading will not be so heavy as a plain concrete or stone arch, and the
centers need not be constructed so strong as for the other types of
arches. One essential difference in the centering for stone arches and
that for concrete or reinforced-concrete arches is that centering for the
latter types of arches serves as a mold for shaping the soffit of the
arch ring, the face of the arch ring, and the spandrel walls.

The successful construction of arches depends nearly as much
on the centers and their supports as it does on the design of the arch.
The centers should be as well constructed and the supports as unyield-
ing as it is possible to make them. When it is necessary to use piles,
they should be as well driven as permanent foundation piles, and
the load, in most cases, should not be heavier than that on per-
manent piles.

Classes of Centers. There are two general classes of centers —
those which act as a truss; and those in wrhich the support, at the
intersection of braces, rests on a pile or footing. Trusses are used

346

MASONRY AND REINFORCED CONCRETE 335

when it is necessary to span a stream or roadway. Sometimes the
length of the span for the centering is very short, or there are a series
of short spans, or the span may be equal to that of the arch. The
trusses must be carefully designed, in order that the deflection and
deformation due to the changes in the loading will be reduced to a
minimum. By placing a temporary load on the centers at the crown,
the deformation during construction may be very greatly reduced.
This load is removed as the weight of the arches comes on the centers.
For the design of trusses, the reader is referred to the Instruction
Papers, or other treatises, on Bridge Engineering and Roof Trusses.

The lagging for concrete arches usually consists of 2- by 3-inch
or 2- by 4-inch plank, either set on edge or laid flat, depending on the
thickness of the arch and the spacing of
the supports. The surface on which the
concrete is laid is usually surfaced on the
side on which the concrete is to be placed. 7 T

The lagging is very often supported on

ribs constructed of 2- by 12-inch plank,

on the back of which is placed a 2-inch

plank cut to a curve parallel with the in-

trados. These 2- by 12-inch planks are

set on the timber used to cap the piles,

and are usually spaced about 2 feet apart. /^ .)

All the supports should be well braced.

The centers should be constructed to give Fig- 172and

a camber to the arch about equal to the

deflection of the arch when under full load. It is, therefore, necessary to

make an allowance for the settlement of centering, for the deflection of

the arch after the removal of the centering, and for permanent camber.

The centers should be constructed so that they can easily be
taken down. To facilitate the striking of centers, the practice is to
support them on folding wedges or sand boxes. When the latter
method is used, the sand should be fine, clean, and perfectly dry, and
the boxes should be sealed around the plunger with cement mortar.
Striking forms by means of wedges is the commoner method. The
type of wedges generally used is shown in Fig. 172-a, although some-
times three wedges are used, as shown by Fig. 172-6. They are from
1 to 2 feet long, 6 to 8 inches wide, and have a slope of from 1:6

347

336 MASONRY AND REINFORCED CONCRETE

TABLE XXVII*

Safe Load in Pounds Uniformly Distributed for Rectangular Beams,
One Inch Thick, Long-Leaf Yellow Pine

Allowable fiber stress, 1,200 pounds per square inch; factor of safety, G; modulus of rupture,

7,200 pounds per square inch
Safe loads for other factors of safety may be obtained as follows:

New safe load =Safe load from table Xr; 7

SPAN-

DEPT

a OF BE

A.M IN IN

CHE8

DEFLEC-

FEET

EFFICIENT

533

833

1,200

1,633

2,133

3,333

4,800

6,533

.38

427

667

960

1,307

1,707

2,667

3,840

5,227

.60

356

556

800

1,089

1,422

2,222

3,200

4,356

.86

305

476

686

933

1,219

1,905

2,743

3,733

1.18

267

417

600

817

1,067

1,667

2,400

3,267

1.54

237

370

533

726

948

1,481

2,133

2,904

3,793

1.94

213

333

480

653

853

1,333

1,920

2,613

3,413

2.40

178

278

400

544

711

1,111

1,600

2,178

2,844

3.46

152

238

343

467

610

952

1,371

1,867

2,438

4.70

133

208

300

408

533

833

1,200

1,633

2,133

6.14

119

185

267

363

474

741

1,067

,452

1,896

7.78

107

167

240

327

427

667

960

,307

,707

9.60

152

218

297

388

606

873

,188

,552

11.62

139

200

272

356

556

800

,089

,422

13.82

128

185

251

328

513

738

1,005

,313

16.22

119

171

233

305

476

686

933

,219

18.82

111

160

218

284

444

640

871

1,138

21.60

To find the safe load for beams of hemlock from Table XXVII, the above values must
be divided by 2; for beams of short-leaf yellow pine and white oak, the values must be divided
by 1.2; for white pine, spruce, eastern fir, and chestnut, the values must be divided by 1.71.

to 1 : 10. The centering is lowered by driving back the wedges; and
to do this slowly, it is necessary that the wedges have a very slight
taper. All wedges should be driven equally when the centering is
being lowered. The wedges should be made of hardwood, and are
placed on top of the vertical supports or on timbers which rest on the
supports. The wedges are placed at about the same elevation as the
springing line of the arch.

Tables XXVII and XXVIII can be used to assist in the design
of the different members of the centers for arches.

Safe Stresses in Lumber for Wood Forms. In Table XXVII
are given the safe loads which may be placed on beams of long-leaf
yellow pine, of various depths, on various spans.

The values given in Table XXVII are the safe loads in pounds

*From Handbook of the Cambria Steal Company.

MASONRY AND REINFORCED CONCRETE 337

TABLE XXVIII*
Strength of Solid Wood Columns of Different Kinds of Timber

RED PINE (NORWAY

PINE), SPRUCE (EAST-

WHITE OAK, SOUTHERN

DOUGLAS FIB

ERN FIR), HEMLOCK

WHITE PINE

LONG-LEAP PINE

SHORT-LEAP PINE

CYPRESS, CHESTNUT

CEDAR

CALIFORNIA REDWOOD.

CALIFORNIA SPRUCE

5,000

4,500

4,000

3,500

4,897

4,407

3,918

3,428

4,782

4,304

3,826

3,347

4,638

4,174

3,710

3,247

4,474

4,026

3,579

• 3,132

4,297

3,867

3,438

3,008

4,114

3,703

3,291

2,880

3,930

3,537

3,144

2,751

3,748

3,373

2,998

2,624

3,571

3,214

2,857

2,500

3,402

3,061

2,721

2,381

3,086

2,777

2,469

2,160

2,805

2,524

2,244

1,963

2,445

2,200

1,956

1,711

2,241

2,017

1,793

1,569

1,835

1,652

1,468

1,285

To find the load that a wood column will support per square inch of sectional area,
from Table XXVIII, the length of the column in inches is divided by the least diameter of the
column, and the result is the ratio of length to diameter of the column. From this ratio is found
the ultimate strength per square inch of section of a column of any kind of wood given in Table
XXVIII. A factor of safety of 5 should be used in finding the size of column required; that is,
the working load should not be greater than one-fifth of the values given.

uniformly distributed, exclusive of the weight of the beam itself, for
rectangular beams one inch thick. The safe load for a beam of any
thickness may be found by multiplying the values given in the tables
by the thickness of the beam ir inches. From the last column, the
deflection may be obtained, corresponding to the given span and
safe load, by dividing the coefficient by the depth of the beam in
inches, which will give approximately the deflection in inches.

Example. If a beam is required to support a uniformly distributed load
of 4,000 pounds on a span of 10 feet, what would be the dimensions of the beam
of long-leaf yellow pine, and what would be the deflection?

Solution. Following the line for beams of 10-foot span, it is found that a
beam 8 inches deep and 5 inches wide (853X5=4,265) would support the load
of 4,000 pounds, and the deflection would be 2. 40-5-8 =.30 inch. A second

* From Handbook of the Cambria Steel Company.

349

338 MASONRY AND REINFORCED CONCRETE

solution would be to use a beam 12 inches deep and 2 inches wide (1,920X2 =
3,840); but according to Table XXVII this beam would not be quite strong
enough, as it would only support a load of 3,840 pounds.

Safe Loads on Wood Columns. The values given in Table
XXIX are based on the formula:

700+15c

700+15c+c2

where P is the ultimate strength of timber in pounds per square inch ;
F is the ultimate crushing strength of timber; / is the length of column,

in inches; d is the least diameter in inches; and c equals —r.

Example. If a column 10 feet long is required to support a load of 20,000
pounds, what would be the size of the column required if California redwood
were used?

Solution. Dividing the length of the beam in inches by the assumed least
diameter, 6 inches, we have 120 -f- 6 = 20, which gives the ratio of the length
to the diameter. By Table XXVIII it is shown that 2,857 pounds is the ultimate
strength for a column of California redwood, when l+d = 2Q. Assuming a
factor of safety of 5, and dividing 2,857 by 5, the working load is found to be
571 pounds per square inch. Dividing 20,000 by 571, it is found that a column
whose area is 35 square inches is required to support the load. The square
root of 35 is 5.9. Therefore a column of California redwood 6 inches square
will support the load.

Form for Arch at 175th Street, New York City. In constructing
the 175th Street Arch in New York City, the forms were so built
that they could be easily moved. The arch is elliptical and is built
of hard-burned brick and faced with granite. The span of the arch
is 66 feet; the rise is 20 feet; the thickness of the arch ring is 40 inches
and 48 inches, at the crown and the springing line, respectively; and
the arch is built on a 9-degree skew. The total length of this arch is
800 feet.

The arch is constructed in sections, the centering being sup-
ported on 1 1 trusses placed perpendicular to the axis of the arch and
having the form and dimensions shown in Fig. 173. The trusses
are placed 5 feet on centers, and are supported at the ends and middle
by three lines of 12- by 12-inch yellow pine caps. The caps are
supported by 12- by 12-inch posts, spaced five feet center to center,
and rest on timber sills on concrete foundations. The upper and
lower chord members of the trusses are of long-leaf yellow pine, but
the diagonals and verticals are of short-leaf yellow pine. The lagging

350

MASONRY AND REINFORCED CONCRETE 339

is 2f - by 6-inch, long-leaf yellow pine plank. The connections of the
timbers are made by means of f-inch steel plates and f-inch bolts,
arranged as shown in the illustration. As it' was absolutely necessary

Fig. 173. Typical Arch Form Used at 175th Street, New York City

to have the forms alike, to enable them to be moved along the arch
and at all times fit the brickwork, they were built on the ground from
the same pattern, and hoisted to their places by two guyed derricks
with 70-foot booms.

Fig. 174. Centers for Bridge at Canal Dover, Ohio

On the 12- by 12-inch cap was a 3- by 8-inch timber, on which the
double wedges were placed. When it was necessary to move the
forms, the wedges were removed, the forms rested on the rollers, and

351

340 MASONRY AND REINFORCED CONCRETE

there was then a clearance of about 2j inches between the brick-
work and the lagging. The timber on which the rollers ran was faced
with a steel plate \ inch by 4 inches in dimensions. The forms were
moved forward by means of the derricks. The settlement of the forms
under the first section constructed was | inch; and the settlement of
the arch ring of that section, after the removal of forms, was j inch.*
Forms for Bridge at Canal Dover, Ohio.* The details of the
centering used in erecting one of the 106-foot 8-inch spans of a
reinforced-concrete bridge over the Tuscarawas River at Canal
Dover, Ohio, are shown in Figs. 174 and 175. Besides this span,
the bridge consisted of two other spans of 106 feet 8 inches each, and a

W Ml

Fig. 175. Centers for Bridge at Canal Dover, Ohio

canal span of 70 feet. The centering for the canal span was built
in 6 bents, each bent having 7 piles. A clear waterway of 18 feet was
required in the canal span by the State Canal Commissioner, and
this passage was arranged under the center of the arch. The piles
were driven by means of a scow. The cap for the piles was a 3- by
12-inch timber. Planks 2 inches thick were sawed to the correct
curvature, and nailed to the 2- by 12-inch joists, which were spaced
about 12 inches apart. The lagging was one inch thick, and was
nailed to the curved plank. The wedges were made and used as shown.
The centering wras constantly checked; this was found important
after a strong wind. The centering for the other two of the main
arches was constructed similarly to that of the arch shown.

*Engineering Record

352

MASONRY AND REINFORCED CONCRETE 341

After some difficulty had been experienced in keeping the forms
in place during the concreting of the first arch, the concrete for the
other arches was placed in the order shown in Fig. 176, and no diffi-
culty was encountered. Sections 1 and 1 were first placed, then 2 and
2, etc., finishing with section 6.

The concreting on the canal span was begun in the late fall, and

Fig. 170

Showing Order of Placing Concrete
iridge at Canal Dover, Ohio

finished in 12 days; the forms were lowered by means of the wedges
five weeks later. The deflection at the crown was 0.5 inch, and after
the spandrel walls were built and the fill made, there was an additional
deflection of 0.4 inch. In building the forms, an allowance of -gfa part
of the span was made, to allow for this deflection. The deflections
at the crown of the other three arches were 0.6 inch, 1.45 inches, and
1.34 inches, respectively.

BENDING OR TRUSSING BARS

Bending Details. Drawings showing all the bending details of
the bars, for all reinforced-concrete work, should be made before the
steel is ordered. The designing engineer should detail a few of the

\3r

SECTlOtfflf?
Fig. 177. Details of Beam Construction

typical beams and girders to show, in a general way, what length of
bars will be required, the number of turned-up bars, the number,
size, and spacing of stirrups required, and the dimensions of the
concrete. These details will then be a guide for the construction
engineer to make up the details required to properly construct the
work. Fig. 177 shows the manner in which the designing engineer

353

342 MASONRY AND REINFORCED CONCRETE

should detail a typical beam so that the constructing engineer can
develop these details as shown in Fig. 178.

Tables for Bending Bars. A simple outfit for bending the bars
cold consists of a strong table, the top of which is constructed as shown
in Fig. 179. The outline to which the bar is to be bent is laid out on

A7A.

%*ZL

IV? o/ Bars
in each Beam

Shape

Stirrups

16'- 0"

Straight

'^lf

SO- 8"

~^y. „ £^P

Fig. 178. Bending Details for Beams

the table, and holes are bored at the point where the bends are to be
made. Steel plugs 5 inches to 6 inches long are then placed in these
holes. Short pieces of boards are nailed to the table where necessary,
to hold the bar in place while being bent. The bar is then placed in

; |

\ l"X6"Plank \ \

•"' t"f ^°c

! \L^

\ \

Fig. 179. Plan of Bendi'ng Table

the position A-B, Fig. 176, and bent around the plugs C and D, and
then around the plugs E and F, until the ends EH and FG are
parallel to AB. When bends with a short radius are required, the
bars are placed in the vise, near the point where the bend is wanted,

Fig. 180. Type of Lever Bender

and the end of the bar is pulled around until the required angle is
secured. The vise is usually fastened to the table. The lever shown
in Fig. 180 is also used in making bends of short radii. This is done
by placing the bar between the prongs and pulling the end of the lever
around until the required shape is secured.

354

MASONRY AND REINFORCED CONCRETE 343

Bars with Hooked Ends. When plain bars are used for rein-
forced concrete, architects and engineers very often require that the

Fig. 181. Bars with Hooked Ends

ends of all the bars in the beams and girders shall be hooked as shown
in Fig. 181. This is done to prevent the bars from slipping before
their tensile strength is fully
developed.

Slab Bars. To secure the
advantage of a continuous slab,
it is very often required that a
percentage of the slab bars, usu- Fig' 182' Slab Bars

ally one-half, shall be turned up over each beam. Construction com-
panies have different methods of bending and holding these bars in
place; but the method shown in Fig. 182 will insure good results, as

Fig. 183. Diagram Showing Bent Bars for Slabs

the slab bars are well supported by the two longitudinal bars which
are wired to the tops of the stirrups. Fig. 183 shows the bending
details of slab bars, the beams being spaced six feet, center to center.
When slabs are designed as

simple beams I — I none of

V8' *

(a)

Fig. 184. Diagram Showing Bending Bars
for Stirrup

the slab bars are bent.

Stirrups. Fig. 184 shows
the bending of the bars for
stirrups. The ends of the
stirrups rest on the forms and
support the beam bars, which assist in keeping these bars in place.
The ends of the stirrups never show on the bottom of the slab of the
finished floor, although the cut ends of the stirrups rest directly on
the slab forms. Sufficient mortar seems to get under the ends of the

355

344 MASONRY AND REINFORCED CONCRETE

stirrups to cover them. The type of stirrup shown in Fig. 184-a is
much more extensively used than that in Fig. 184-6. The latter type
is most frequently used when a large amount of steel is required for
stirrups, or if the stirrups are made of
very small bars.

Column Bands. In Fig. 185 two
types of column bands are shown. Fig.
185-a shows bands for a square or a round
column; and Fig. 185-6, bands fora rec-
tangular column. The bar which forms the
band is bent close around each vertical
bar in the columns, and therefore assists
in holding these bars in place. The bands for the rectangular column
b are made up of two separate bands of the same size and shape.

Spacers. Spacers for holding the bars in place in beams and
girders have been successfully used. These spacers, Fig. 186, are

made of heavy sheet iron. They
are fastened to the stirrups by
means of the loops in the spacers.
The ends of the spacers which

o A,

J C
•> Vs

j r

^ C

f*; (b)

Fig. 185. Column Bands

Typical Spacer for Reinforcing Bar

project out to the forms of the
sides of the beams should be made
blunt or rounded. This will pre-
vent the ends of the spacers being driven into the forms when the
concrete is being tamped. The number of these spacers required
will depend on the lengths of the beams; usually 2 to 4 spacers are
used in each beam.

Several devices have been manufactured for holding slab bars
in place while the concrete is being poured. Fig. 187- shows a spacer,

patented and manufactured by

the Concrete Steel Company,
that has been in use for several

Fig. 187. Spacer for S.ab Bars *™™ aild hftS be6n f°Und

satisfactory.

Unit Frames. Companies making a specialty of supplying
reinforcing steel generally have their own method of making the bars
for a beam into a unit. This is accomplished in different ways. The
frames are made up at a shop, where there is machinery for doing the

MASONRY AND REINFORCED CONCRETE 345

357

346 MASONRY AND REINFORCED CONCRETE

work, and shipped to the job as a unit. Fig. 188 shows a unit made
by the Corrugated Bar Company, in which the shear bars are laced
around the tension bars. These units can be closed up for shipment.
Fig. 189 shows a collapsible frame made by the Concrete
Steel Company. The frame is made up of four small bars, usually
j inch around, and the stirrups that are required for the beam are
fastened to these bars by clips that will permit the frame to be
folded up for shipment. When the frame is received on the job it is
unfolded, placed in the beam for which it is designed, and then the
tension bars are put in the frame and held in place by two or more
spacers.

BONDING OLD AND NEW CONCRETE

The place and manner of making breaks or joints in floor con-
struction at the end of a day's work is a subject that has been much
discussed by engineers and construction companies. But there has
not yet been any general agreement as to the best method and place
of constructing these joints. Wherever joints are made, great care
should be exercised to secure a bond between the new and the old
concrete.

Methods of Making Bonds. First Method. Fig. 190 shows a
sectional view of one method of making a break at the end of the day's
work; this method has been used very
extensively and successfully. The stir-
rups and slab bars form the main bond
between the old and the new work, if the
break is left more than a few hours. Short
bars in the top of the slab will also assist
in making a good bond; an additional
number of stirrups should also be used
where the break is to be made in the beam.
Before the new concrete is placed, the old
concrete should be well scraped, thoroughly soaked with clean water,
and given a thin coat of neat cement grout. An objection to this
method of forming a joint is that the shrinkage in the concrete may
cause a separation of the concrete placed at the two different times,
and that water will thus find a passage. The top coat that is generally
placed later will greatly assist in overcoming this objection.

B/1K3 -4-0"

Fig. 190. Method of Bonding
and New Concrete in Slab

35b

Fig. 191. Method of Bonding Old
and New Concrete in Beam

MASONRY AND REINFORCED CONCRETE 347

Second Method. Another method of forming stopping places is
by dividing the beam vertically — that is, making two L-beams
instead of one T-beam, Fig. 191. Theo-
retically, this is a very good method, but
practically, it is found difficult to con-
struct the forms dividing the beam, as the
steel is greatly in the way.

Third Method. The method of stop-
ping the work at the center of the span
of the beams and parallel to the girders
is the method in general use. Fig. 192 illustrates this method. Theo-
retically, the slab is not weakened; and' as the maximum bending
moment occurs at this point, the shear is zero, and, therefore, the
beams are not supposed to be weakened, except for the loss of con-
crete in tension, and this
is not considered in the
calculation. The bottoms
of the beams are tied
together by the steel that
is placed in the beams to
take the tensile stresses;
and there should be some

.!*!_

BEffM

Ifel

'3i

VMSB/iR3 Ifcl

Fig. 192. Method of Bonding Break in Center of Span

short bars placed in the

top of these beams, as

well as in the top of the

slab, to tie them together.

The objection made in the description of the first method — in that

any shrinkage in the concrete at the joint will permit water to pass

through — is greater in the second and third methods than in the first.

FINISHING SURFACES OF CONCRETE

Imperfections. To give a satisfactory finish.to exposed surfaces
of concrete is a rather difficult problem. In many instances, when
the forms are taken down, the surface of the concrete shows the joints,
knots, and grain of the wood ; it has more the appearance of a piece of
rough carpentry work than that of finished masonry. Also, failure
to tamp or flat-spade the surfaces next to the forms will result in
rough places or stone pockets. Lack of homogeneity in the concrete

359

348 MASONRY AND REINFORCED CONCRETE

will cause a variation in the surface texture of the concrete. Varia-
tion of color, or discoloration, is one of the most common imperfec-
tions. Old concrete adhering to the forms will leave pits in the
surface; or the pulling-off of the concrete in spots, as a result
of its adhering to the forms when they are removed, will cause a
roughness.

To guard against these imperfections, the forms must be well
constructed of dressed lumber, and the pores should be well filled
with soap or paraffine. The concrete should be thoroughly mixed,
and, when placed, care should be taken to compact the concrete
thoroughly, next to the forms. The variation in color is usually
due to the leaching-out of lime, which is deposited in the form of an
efflorescence on the surface; or to the use of different cements in
adjacent parts of the same wrork. The latter cause can almost always
be avoided by using the same brand of cement on the entire work,
and the former will be treated under the heading of "Efflorescence".

Plastering. Plastering is not usually satisfactory, although
there are cases where a mixture of equal parts of cement and sand
has, apparently, been successful; and, when finished rough, it did not
show any cracks. It is generally considered impossible to apply
mortar in thin layers to a concrete surface, and make it adhere for any
length of time. When the plastering begins to scale off, it looks
worse than the unfinished surface. This paragraph is intended more
as a warning against this manner of finishing concrete surfaces than
as a description of it as an approved method of finish.

Mortar Facing. The following method has been adopted by the
New York Central Railroad for giving a good finish to exposed con-
crete surfaces :

The forms of 2-inch tongued-and-grooved pine were coated with
soft soap, all openings in the joints of the forms being filled with hard
soap. The concrete was then deposited, and, as it progressed, was
drawn back from the face with a square-pointed shovel, and 1 : 2
mortar poured in along the forms. When the forms wrere removed,
and while the concrete wras green, the surface was rubbed, with a
circular motion, with pieces of wThite fire brick, or brick composed of
one part cement and one part sand. The surface was then dampened
and painted with a 1 : 1 grout, rubbed in, and finished with a wood
float, leaving a smooth and hard surface when dry.

MASONRY AND REINFORCED CONCRETE 349

A method of placing mortar facing that has been found very
satisfactory, and has been adopted very extensively in the last
few years, is as follows: A sheet-iron plate, '6 or 8 inches wide and
about 5 or 6 feet long, has riveted across it on one side, angles of
f -inch size, or such other size as may be necessary to give the desired

Fig. 193. Sheet-Iron Plate for Giving Finish Surface to Concrete

thickness of mortar facing, these angles being spaced about two feet
apart, Fig. 193. In operation, the ribs of the angles are placed
against the forms; and the space between the plate and forms is filled
with mortar, which is mixed in small batches, and thoroughly tamped.
The concrete back filling is then placed; the mold is withdrawn; and
the facing and back filling are rammed together. The mortar facing
is mixed in the proportion of one part cement, to 1, 2, or 3 parts sand;
usually a 1 : 2 mixture is employed, mixed wet and in small batches
as it is needed for use. As mortar facing shows the roughness of the
forms more readily than concrete does, care is required, in construct-
ing, to secure a smooth finish. When the forms are removed, the face
may be treated either in the manner already described, or according
to the following method taken from the Proceedings of the American
Railway Engineering Association : r/v///////////////////?//////////////?/////*.

After the forms are removed, any
small cavities or openings in the con-
crete shall be filled with mortar, if nec-
essary. Any ridges due to cracks or
joints in the lumber shall be rubbed
down; the entire face shall be washed
with a thin grout of the consistency of
whitewash, mixed in the proportion of
1 part cement to 2 parts of sand. The
wash shall be applied with a brush.

Masonry Facing. Concrete surfaces may be finished to repre-
sent ashlar masonry. The process is similar to stone dressing; and
any of the forms of finish employed for cut stone can be used for
concrete. Very often, when the surface is finished to represent ashlar

Fig. 194. Diagram Showing Method of gi\
Masonry Facing to Concrete

361

350 MASONRY AND REINFORCED CONCRETE

masonry, vertical and horizontal three-sided pieces of wood are
fastened to the forms to make V-shaped depressions in the concrete,
as shown in Fig. 194.

Stone or Brick Facing. A facing of stone or brick is frequently
used for reinforced concrete, and is a very satisfactory solution of
the problem of finish. The same care is required with a stone or
brick facing as if the entire structure were stone or brick. The Ingalls
Building at Cincinnati, Ohio, 16 stories, is veneered on the outside
with marble to a height of three stories, and with brick and terra
cotta above the third story. Exclusive of the facing, the wall is
8 inches thick.

In constructing the Harvard University Stadium, care was
taken, after the concrete was placed in the forms, to force the stones
back from the face and permit the mortar to cover every stone. When

the forms were removed, the sur-
face was picked with the tool
shown in Fig. 195. A pneumatic
tool has also been adopted for this
purpose.

The number of square feet to
be picked per day depends on the
hardness of the concrete. If the
picking is performed by hand, it is
done by a common laborer; and he is expected to cover, on an average,
about 50 square feet per day of 10 hours. With a pneumatic tool,
a man would cover from 400 to 500 square feet per day.

Recently a motor-driven hand tool, Fig. 196, has been invented.
This works dry, and it leaves the surface slightly porous, so that it
provides an excellent base for the application of a float or a coat of
paint. The machine is driven through a flexible shaft by a motor
carried by the operator. The whole apparatus, motor included,
weighs only 20 pounds. The motor may take its actuating current
from an ordinary electric light socket.

The method of chipping the concrete surface is very ingenious.
Mounted in a disk are twenty-four cutter wheels arranged in pairs,
each wheel having from twenty-four to twenty-eight cutting teeth.
As the disk revolves at high speed, the cutter wheels are made to
roll over the concrete surface, each tooth acting as a tiny hammer

Fig. 195. Typical Facing Hammer

362

MASONRY AND REINFORCED CONCRETE 351

to strike the concrete. The cutter wheels look like small spur gears,
but instead of being radial, the teeth are eccentrically directed so
that their edges are brought into contact absolutely square with the
surface, and deal a direct blow to the material that is to be cut.
The disk revolves at the rate of about 2,000 revolutions a minute,
so that the number of blows per minute delivered by the cutter
wheels runs up into the mil-
lions. The cutting tool is
of such a form that it may
be conveniently grasped and
guided by the operator, and
on it is a small switch by
means of which the power
may be readily turned on
and off. The average work
per day of this tool is from
700 to 900 square feet. It
may be used, as well, for
surfacing stone and imita-
tion stone, and for bringing
out the aggregate in con-
crete, when that is desired.
Granolithic Finish.
Several concrete bridges in
Philadelphia have been fin-
ished according to the fol-
lowing specifications and
their appearance is very
satisfactory:

Fig. 196. Pow

Driven Hand Tool for Surfacing

Concrete
Courtesy of "Scientific American"

Granolithic surfacing, where
required, shall be composed of 1
part cement, 2 parts coarse sand
or gravel, and 2 parts grano-
lithic grit, made into a stiff

mortar. Granolithic grit shall be granite or trap rock, crushed to pass a |-inch
sieve, and screened of dust. For vertical surfaces, the mixture shall be deposited
against the face forms to a minimum thickness of 1 inch, by skilled workmen,
as the placing of the concrete proceeds; and it thus forms a part of the body of
the work. Care must be taken to prevent the occurrence of air space or voids
in the surface. The face shall be removed as soon as the concrete has sufficiently

352 MASONRY AND REINFORCED CONCRETE

hardened; and any voids that may appear shall be filled with the mixture.
The surface shall then be immediately washed with water until the grit is exposed
and rinsed clean, and shall be protected from the sun and kept moist for three
days. For bridge-seat courses and other horizontal surfaces, the granolithic
mixture shall be deposited on the concrete to a thickness of at least l£ inches,
immediately after the concrete has been tamped and before it has set, and shall
be troweled to an even surface, and, after it has set sufficiently hard, shall be
washed until the grit is exposed.

The success of this method depends greatly on the removal of
the forms at the proper time. In general, the washing is done the day
following that on which the concrete is deposited. The fresh con-
crete is scrubbed with an ordinary scrubbing brush, removing the
film, and the impressions of the forms, and exposing the sand and
stone of the concrete. If this is done when the material is at the

Fig. 197. Quimby's Finish on Concrete Surfaces. Left — Aggregate -ft Inch
White Pebbles; Right— Aggregate f Inch Screened Stone

proper degree of hardness, merely a few rubs of an ordinary house
scrubbing brush, with a free flow of water to cut and to rinse clean,
constitutes all the work and apparatus required. The cost of scrub-
bing is small if done at the right time. A laborer will wash 100 square
feet in an hour; but if that same area is permitted to get hard, it may
require two men a day, with wire brushes, to secure the desired
results. The practicability of removing the forms at the proper time
for such treatment depends upon the character of the structure and
the conditions under which the work must be done. This method
is applicable to vertical walls, but it would not be applicable to the
soffit of an arch, Fig. 197.

The Acid Treatment. This treatment consists in washing the
surface of the concrete with diluted acid, then with an alkaline
solution. The diluted acid is applied first, to remove the cement and

364

MASONRY AND REINFORCED CONCRETE 353

expose the sand and stone; the alkaline solution is then applied to
remove all of the free acid; and, finally, the surface is washed with
clear water. The treatment may be applied at any time after the
forms are removed; it is simple and effective. Limestone cannot be
used in the concrete for any surfaces that are to have this treatment,
as the limestone would be affected by the acid. This process has been
used very successfully.

Dry Mortar Finish. The dry mortar method consists of a dry,
rich mixture, with finely crushed stone. The concrete is usually
composed of 1 part cement, 3 parts sand, and 3 parts crushed
stone, known as the |-inch size, and mixed dry so that no mortar will
flush to the surface, when well rammed in the forms. When placed,
the concrete is not spaded next to the forms and, being dry, there is
no smooth mortar surface, but there should be an even-grained,
rough surface. With the dry mixture, the imprint of joints of the
forms is hardly noticed, and the grain of the wood is not seen at all.
This, style of finish has been extensively used in the South Park
system of Chicago, and there has been no efflorescence apparent on
the surface, which is explained by "the dryness of the mix and the
porosity of the surface".

Cast Slab Veneer. Cast-concrete-slab veneer can be made of
any desired thickness or size. It is set in place like stone veneer,
with the remainder of the concrete forming the backing. It is usually
cast in wood molds, face down. A layer of mortar, 1 part cement,
1 part sand, and 2 or 3 parts fine stone or coarse sand is placed in the
mold to a depth of about 1 inch, and then the mold is filled up with
a 1:2:4 concrete. Any steel reinforcement that is desired may be
placed in the concrete. Usually, cast-concrete-slab veneer is cheaper
than concrete facing cast in place, and a better surface finish is
secured by its use.

Moldings and Ornamental Shapes. Concrete is now in demand
in ornamental shapes for buildings and bridges. The shapes may be
either constructed in place, or molded in sections and placed the
same as cut stone. Plain cornices or panels are usually constructed
in place, but complicated molding or balusters, Fig. 198, are frequently
made in sections and erected in separate pieces.

The molds may be constructed of wood, metal, or plaster of
Paris, or molded in sand. The operation of casting concrete in sand

354

MASONRY AND REINFORCED CONCRETE

TABLE XXIX*

Colors Given to Portland Cement Mortars Containing Two Parts
River Sand to One Part Cement

WEIGHT OF DRY COLORING MATTER TO 100 LB. OF CEMENT

COST OF

DRY

COLORING

MATERIAL

MATTER PER

USED

i Pound

1 Pound

2 Pound-)

4 Pounds

POUND

Lampblack

Light Slate

Light Gray

Blue-Gray

Dark Blue

15 cents

Slate

Prussian

Light Green

Light Blue

Blue Slate

Bright Blue

50 cents

Blue

Slate

Ultramarine

Light Blue

Blue Slate

Bright Blue

20 cents

Blue

Slate

Yellow

Light Green

Light Buff

3 cents

Ocher

Burnt
Umber

Light Pink-
ish Slate

Pinkish
Slate

Dull Laven-
der-Pink

Chocolate

10 cents

Venetian

Slate, Pink

Bright Pink-

Light Dull

Dull Pink

1\ cents

Red

Tinge

ish Slate

Pink

Red Iron

Pinkish

Dull Pink

Terra Gotta

Light Brick

2| cents

Ore

Slate

Red

Fig. 198. Typical Molded
Concrete Baluster

is similar to that of casting iron. The pattern
is made of wood the exact size required. It
is then molded in flasks exactly as is done in
casting iron. The ingredients for concrete
consist of cement and sand or fine crushed
stone; the mixture, with a consistency about
that of cream, is poured into the mold with
the aid of a funnel and a T-pipe. Generally,
the casting is left in the sand for three or
four days, and, after being taken out of the
sand, should harden in the air a week or ten
days before being placed. Balusters are very
often made in this manner.

Colors for Concrete Finish. Coloring
matter has not been used very extensively in
concrete work, except in ornamental work.
It has not been very definitely determined
what coloring matters are detrimental to con-
crete. Lampblack (boneblack) has been used
more extensively than any other coloring mat-
ter. It gives different shades of gray, depend-

*Sabin'a "Cement and Concrete". •

366

MASONRY AND REINFORCED CONCRETE 355

ing on the amount used. Common lampblack and Venetian red
should not be used, as they are apt to run or fade. Dry mineral
colors, mixed in proportions of 2 to 10 per cent of the cement, give
shades approaching the color used. Red lead should never be used;
even one per cent is injurious to the concrete. Variations in the color
of cement and in the character of the sand used will affect the results
obtained in using coloring matter as shown in Table XXIX.

Painting Concrete Surfaces. Special paints are made for
painting concrete surfaces. Ordinary paints, as a rule, are not
satisfactory. Before the paint is applied, the surface of the wall
should be washed with dilute sulphuric acid, 1 part acid to 100
parts water.

Finish for Floors. Floors in manufacturing buildings are often
finished with a 1-inch coat of cement and sand, mixed in the propor-
tions of 1 part cement to 1 part sand; or 1 part cement to 2 parts

r£p-*< T°

/.> i

'•'-.Cinder Fill :-V. . ' .' :;>.:•;: '•^^^^.•y:.::'-.''--.;-:- :'•.•.:•:•;•.•-••

±j££±^3£i:±i'}

'V.^ Concrete * -*\+. 'V. ».*«'. *.'•'* •«: J".*:^';'^*' "d V* C'"4-.'

Fig. 199. Diagram Showing Typical Cinder Fill between Stringers

sand. This finishing coat must be put on before the concrete base
sets, or it will break up and shell off, unless it is made very thick,
1| to 2 inches. A more satisfactory method of finishing such floors
is to put 2 inches of cinder concrete on the concrete base, and then
put the finishing coat on the cinder concrete. The finish coat and
cinder concrete bond together, making a thickness of 3 inches.
The cinder concrete may consist of a mixture of 1 part cement, 2 parts
sand, and 6 parts cinders, and may be put down at any time; that is,
this method of finishing a floor can be used as satisfactorily on an old
concrete floor as on one just constructed.

In office buildings, and generally in factory buildings, a wood
floor is laid over the concrete. Wood stringers are first laid on
the concrete, about 1 to 1| feet apart. The stringers are 2 inches
thick and 3 inches wide on top, with sloping edges. The space
between the string-ers is filled with cinder concrete, as shown in

367

356 MASONRY AND REINFORCED CONCRETE

Fig. 199; as a rule this is mixed 1:4:8. When the concrete has set,
the flooring is nailed to the stringers. Usually a layer of waterproof
paper or saturated felt is spread between the concrete and the flooring
to prevent the floor from warping.

Efflorescence. The white deposit found on the surface of
concrete, brick, and stone masonry is called efflorescence. It is
caused by the leaching of certain lime compounds, which are deposited
on the surface by the evaporation of the water. This is believed to
be due, primarily, to the variation in the amount of water used in
mixing the mortar. An excess of water will cause a segregation of
the coarse and fine materials, resulting in a difference of color. In a
very wet mixture, more lime will be set free from the cement and
brought to the surface. When great care is used as to the amount of
water, and care is taken to prevent the separation of the stone from
the mortar when deposited, the concrete will present a fairly uniform
color wrhen the forms are removed. There is greater danger of the
efflorescence at joints than at any other point, unless special care is
taken. If the work is to be continued within 24 hours, and care is
taken to scrape and remove the laitance, and then, before the next
layer is deposited, if the scraped surface is coated with a thin cement
mortar, the joint should be impervious to moisture, and no trouble
with efflorescence should be experienced.

A very successful method of removing efflorescence from a con-
crete surface consists in applying a wash of diluted hydrochloric
acid. The wash consists of 1 part acid to 5 parts water, and is
applied with scrubbing brushes. Water is kept constantly played on
the work, by means of a hose, to prevent the penetration of the acid.
The cleaning is very satisfactory, and for plain surfaces costs about
20 cents per square yard.

Laitance. Laitance is whitish, spongy material that is washed
out of the concrete when it is deposited in water. Before settling
on the concrete, it gives the wrater a milky appearance. It is a semi-
fluid mass, composed of a very fine, flocculent matter in the cement;
generally contains hydrate of lime; stays in a semifluid state for a
long time; and acquires very little hardness at its best. Laitance
interferes with the bonding of the layers of concrete, and should
always be thoroughly cleaned from the surface before another layer
of concrete is placed.

MASONRY AND REINFORCED CONCRETE 357

-M--4-

Fig. 200. Typical Structural Floor Plan of Buck Building, Philadelphia, Pennsylvania

369

358

MASONRY AND REINFORCED CONCRETE

REPRESENTATIVE EXAMPLES OF REINFORCED-

CONCRETE WORK

Buck Building. Fig. 200 shows the typical structural floor-plan,
above the first floor, of a building constructed for J. C. Buck at
Fifth and Appletree Streets, Philadelphia. The architects were
Ballinger and Perrot, and the building was constructed by Cramp and
Company, Philadelphia. The building has a frontage of 90 feet on
Fifth Street, and a depth of (51 feet on Appletree Street, and is seven
stories high. The building is constructed, structurally, of reinforced

concrete, excepting the first floor
and the columns in the lower
floor. The floors are all designed
to carry 200 pounds per square
foot. The side walls are con-
structed of light-colored brick,
and trimmed writh terra cotta.
The first floor, being constructed
especially to suit the requirements
of a chemical company that
would occupy the building for
several years, was planned with
a view to the probable necessity
of reconstructing the floor if this
company should leave the build-
ing at the expiration of its lease,

PLAN

• io'-o —

Fig. 201. Interior Column Footing for
Buck Building, Philadelphia

and hence was constructed of
structural steel, since it is much
easier to remodel a floor of steel than one constructed of reinforced
concrete.

Footings. The footings for each of the interior columns were
designed as single footings. They are 10 feet square, 30 inches thick,
and are reinforced as shown in Fig. 201.

Columns. The columns in the basement, first, and second floors
are of structural steel, and fireproofed with concrete. The wall
columns are either square or rectangular in shape; and the interior
columns are round, being twenty inches in diameter. The stress
allowed in the structural steel of these columns is 16,000 pounds per
square inch of the steel section; but no allowance is made for the four

370

MASONRY AND REINFORCED CONCRETE 359

small bars placed in the column. These steel cores are provided with
angle brackets to support the beams, and with spread bases to trans-
mit the stress in the steel to the foundation.
The cores are composed of angles and plates,
and are riveted together in the usual man-
The columns are built in sections of

ner.

a length equal to the height of two stories.
This requires very little extra metal and saves
the expense of half the joints required if
a change of section is made at each floor.

The general outline and details of these
steel cores are illustrated in Fig. 202. In the
exterior columns, the steel cores are used in
the basement and the first, second, and third
floors, where necessary; in the interior col-
umns, they are used also in the fourth story,
and in two columns the structural steel is
extended to the sixth floor line. The exte-
rior columns above the structural steel, and
also the columns in which structural steel is
not required, are in general reinforced with
8 bars 1 inch square in the lower floors;
and this amount of steel is gradually reduced
to 4 bars 1 inch square, in the seventh story.
In the interior columns, the reinforcement
above the steel cores consists of 8 bars f
inch square, in the floor just above the struc-
tural steel; and the number of these bars is
gradually reduced to 4 in the seventh floor.

Floor Slabs. The floor slabs are 5 inches
thick and reinforced with f -inch square bars
spaced 6 inches on centers, and ^-inch bars,
spaced 24 inches on centers, the latter being
placed at right angles to the former. The
roof slab is designed to carry a live load of
40 pounds per square foot, and is 3? inches
thick. The reinforcement consists of &-inch bars spaced 6 inches,
and the same sized bars spaced 24 inches at right angles.

Fig. 202. Steel Column Core
for Buck Building, Phila-
delphia, Pennsylvania

371

360

MASONRY AND REINFORCED CONCRETE

Floor Beams. The floor beams are, in general, 8 inches wide,
and the depth below the slab is 18 inches. The amount of reinforce-
ment in the beams varies, depending on the length of the beams. Most
of the beams are reinforced with 2 bars 1 inch square, and 1 bar 1 1
inches square. The l|-inch bar is turned up or trussed at the ends,
and the 1-inch bars are straight. The roof beams are 6- by 12-inch
below the slab, and are reinforced with 2 bars f inch square, except
in the longest beams, in which 2 bars 1 inch square are required.
A f-inch bar, 5 feet long, is placed in the top of all floor and roof

Fig. 203. Details of Beams and Girders for Buck Building, Philadelphia, Pennsylvania

beams, where they are framed into a girder. The ends of these bars
are turned down. The stirrups are made of §-inch round bars, and
are spaced as shown in the detail of the beam, Fig. 203.

Floor Girders. The floor girders are 12- by 24-inch below the
slab. The span of the girders varies from about 18 feet to about
20 feet; and they are all reinforced with 6 bars 1 inch square, three of
the bars being turned up at the ends. Two f-inch square bars are
placed in the top of the girders over the supports, these bars being
5 feet long, and hooked at the ends. Bars f inch square, 5 feet long,

372

MASONRY AND REINFORCED CONCRETE 361

are placed in the slab near the top, at
right angles to the girders. The bars are
12 inches, center to center, and are placed
over the center of the girders.

Lintels. The wall beams or lintels
on the Fifth Street and Appletree Street
sides of the building are shown in section
in Fig. 204. They are 9 inches by 24
inches, and are reinforced with 2 bars 1
inch square. The wall girders in the side
of the building opposite Appletree Street
are 14 inches by 24 inches, and are rein-
forced with 6 bars 1 inch square.

Stairs. The stairs are constructed as
shown in Fig. 205. The structural con-
crete slab is 6 inches thick, and is rein-
forced with f-inch bars. Safety treads 5^
inches in width, and 12 inches shorter
than the width of the stairs, are set in
each step.

Concrete Mixture. The concrete for
the beams, girders, slabs, and footings is
a 1:2^:5 mixture ; and for the columns, a

Fig. 205. Section of Stairs for Buck Building, Philadelphia

Fig. 204. Details of Wall Beams,
Buck Building, Philadelphia

1:2:4 mixture is required.
The stone used in this
concrete is trap rock. The
concrete was mixed in a
batch mixer, the consist-
ency being what is com-
monly known as a wet
mixture. Square twisted
bars are used as the rein-
forcing steel.

Floors. The first,
second, and third floors
are finished with lj-inch
maple flooring. The
stringers, 2 inches by 3

373

362 MASONRY AND REINFORCED CONCRETE

inches, are spaced 16 inches apart, and the space between the
stringers is filled with cinder concrete. The other floors are finished
with a one-inch coat of cement finish. A cinder fill 2 inches thick is
laid on the concrete floor slab, on which was laid the cement finish.
The cinder concrete consists of 1 part Portland cement, 3 parts sand,
and 7 parts cinders. The cement finish is composed of 1 part Port-
land cement, 1 part sand, and 1 part £-inch crushed granite.

ffx/0"

e-i'f

In Top of Slab
Fig. 206. Plan of Two Bays of a Floor in Allman Building, Philadelphia, Pennsylvania

Allman Building. The seven-story office building, 24 feet 9?
inches by 122 feet 2\ inches, was constructed for Herbert D. Allman,
at Seventeenth and Walnut Streets, Philadelphia. Baker and Dallett
are the architects for this work. The building is constructed of
reinforced concrete, except that steel-core columns are carried up to
the sixth floor. Fig. 206 shows the plans of two bays of a floor, the
bay windows occurring in alternate bays. The floors are designed for
120 pounds per square foot, live load. The sizes of the different
members are given on the plan. The tensile stress in the reinforcing

374

MASONRY AND REINFORCED CONCRETE 363

steel is 16,000 pounds per square inch. Direct compression in the
concrete is 500 pounds per square inch and the transverse stress in
compression 600 pounds per square inch, while the shearing stress is
75 pounds per square inch. In designing the columns in which the
steel cores occur, the radius of gyration is taken for the whole column;

•$"'

\+-POrfy Li

Street Line-

Fig. 207. Footing of Allman Building, Philadelphia, Pennsylvania

this reduces the working load to 14,000 pounds per square inch for
the steel, nothing being allowed for the concrete except the increased
radius of gyration. The concrete is a 1:2:4 mixture. The footings
used for this building are shown in Fig. 207.

Erben=Harding Company Building. The exterior and interior
of a factory building, designed and constructed by Wm. Steele and
Sons Company for the Erben-Harding Company, Philadelphia, are
shown in Figs. 208 and 209. This building is 100 feet by 153 feet,
and is constructed structurally of reinforced concrete, except that
structural steel is used in the columns. The floors and columns are
designed to support safely a live load of 120 pounds per square foot.

Floor Panels. The floor panels are about 12 feet by 25 feet, the
girders having a span of about 12 feet, and the beams a span of 25
feet. One intermediate beam is placed in each panel, as shown in the
interior view. The girders are 12 inches wide and 20 inches deep
below the slab, and are reinforced with 4 bars 1& inches in diameter.
The beams are 12- by 18-inch, and are reinforced with 4 bars 1 \ inches
in diameter. The floor slab is 4 inches thick, and is reinforced with
3-inch mesh, No. 10 gage, expanded metal.

Columns. The columns are all 18- by 18-inch; but the structural
steel in the columns is designed to support the entire load on the
columns. Four f-inch bars are placed in the columns and wrapped
with expanded metal. The exterior columns are exposed to view on
both the exterior and the interior of the building. The entire width

375

364 MASONRY AND REINFORCED CONCRETE

376

MASONRY AND REINFORCED CONCRETE 365

377

366 MASONRY AND REINFORCED CONCRETE

between the wall columns is filled by triple windows. The wall
beams are constructed flush with the exterior surface of the wall
columns, as shown in Fig. 208. The space between the bottom of the
windows and the wall beams is filled with white brick. The two fire
towers, located at the corners of the building, are also constructed
of white brick.

Floor Finish. The floor finish of this building is somewhat
unusual. Sills 2 by 4 inches are laid on the structural floor slab of
concrete, and the space between these sills is filled with cinder con-
crete. On these sills is laid a covering of 2-inch tongued-and-grooved
plank; and on these planks is laid a floor of f-inch maple, the latter
being laid perpendicular to the 2-inch plank.

Swarthmore Shop Building. In constructing the shop building
at Swarthmore College, Swarthmore, Pennsylvania, concrete blocks

1 1

1 —

1 — i

1
1

) ".!L

^ '
* i

--t

"t"

1
1

-I

• -

>•

~ •

._.

.._

.-<

i--

•-

•H

H-

-HJHH

-f

-I

--1

_ . .

kid

•LI

ite

Fig. 210. Plan of Shop Building, Swarthmore College, Swarthmore, Pennsylvania

were used for the side wTalls, and the floors were constructed of rein-
forced concrete. This building is 49 feet 8 inches by 112 feet, ftnd is
3 stories high. The floors are designed to carry a live load of 150
pounds per square foot. A factor of safety of 4 was used in all the
reinforced-concrete construction.

The columns are located as shown in Fig. 210. The span of the
girders is 20 feet, except for the three middle bays, in which the span
is only 10 feet. The 20-foot girders are 14 inches wide, and the depth
below the slab is 23 inches. The reinforcement consists of 8 bars
f inch square. The beams are spaced 5 feet center to center. The
span of these beams is about 16 feet, the width 8 inches, and the

378

1^
S-5.S

gal

MASONRY AND REINFORCED CONCRETE 367

depth 12 inches below the slab; and the reinforcement consists of 5
bars | inch square. The slab is 4 inches thick, including the top coat

Fig. 211. Stairway Details in Shop Building, Swarthmore College,
Swarthmore, Pennsylvania

of 1 inch, which is composed of
1 part Portland cement and 1
part sand. This finishing coat
was put on before the other con-
crete had set, and was figured as
part of the structural slab. The
slab reinforcement consists of \-
inch bars spaced 4 inches on cen-
ters, and j-inch bars spaced 24
inches at right angles to the bars
spaced 4 inches. The columns
range in size from 10- by 10-inch
to 18- by 18-inch, and are rein-
forced by placing a bar in each
corner of the column, which bars
are tied together by j-inch bars
spaced 12 inches. The amount of
this steel is about one per cent of
the total area of the column.

Fig. 211 shows the plans of
molded on the ground, and placed

Fig 212. Floor Construction in Shop Building
of Swarthmore (Pa.) College Showing Con-
nection of Girder Beams with Column

the stairway. The lintels were
when the side walls had been built

379

368 MASONRY AND REINFORCED CONCRETE

to the proper height. The size of the lintels varies on the different
floors to conform with the architectural features of the building. The
width of the lintels is made the same as the thickness of the walls, and
therefore both sides of the lintels are exposed to view. They are
reinforced with 3 bars ^ inch square.

The concrete was composed of 1 part Portland cement, 3 parts
sand, and 5 parts stone. The stone was graded in size from £ inch to
1 inch. Johnson corrugated bars were used as the reinforcing steel.
A panel, 16 by 20 feet, of one of the floors, was tested by placing a
load of 300 pounds per square foot over this area. The deflection was
so slight that it could not be conveniently measured. In Fig. 212 is
given a view of the under side of a floor, showing the connection of
the girder and beams with the column.

Tile and Joist System. The tile and joist system of construct-
ing fireproof floors is found economical for a certain class of work. It

is probably used for apartment houses oftener than anywhere else.
The advantage secured by this construction is that a flat ceiling is
secured. The structural frame of the building may be either steel
or reinforced concrete. The columns are connected by girders and
the space between the girders is filled in with tile and joists. When
reinforced-concrete girders are used between the columns, a slab of
concrete of sufficient width and thickness to take the compression
must be constructed.

Fig. 213 shows a section of a tile and joist floor. The terra cotta
tile is always 12 inches in width and from 4 inches to 15 inches in
depth. The tile is simply a filler between the joists and is so much
dead weight to be carried by the joists. The joists are usually 4
inches in width and are designed as T-beams. The slab is usually
2 to 3 inches in thickness. "The reinforcing steel in the beam consists

380

MASONRY AND REINFORCED CONCRETE 369

381

370 MASONRY AND REINFORCED CONCRETE

of one bar of sufficient area for the tensile stress. The slab should
be reinforced with j-inch bars, 24 inches center to center each way.
Heinz Warehouse. A good example of a ceiling of the flat-slab
system is given in Fig. 214. This shows an interior view of a ware-
house designed by the Condron Company of Chicago, Illinois, for
the H. T. Heinz Company, Chicago. The panels are 18 feet 6 inches
square and are designed for a live load of 300 pounds per square foot.
Steel Cores. It is often necessary, in reinforced-concrete build-
ings, to construct columns of some other material than concrete on
account of the large space that would be occupied by the columns.
In such cases steel-core columns are often used. Fig. 215 shows two
types of the steel cores. Type a is used for round columns and the

steel consists of four angles,
but, when necessary, plates
are inserted between the an-
gles to make up the full sec-
tion. Type b is used for
square columns. In figuring
the strength of these col-
umns, the Bureau of Building
Inspection of Philadelphia
will permit the steel to be figured as having a radius of gyration equal
to that of the concrete section, which for ordinary story heights makes
the permissible loading about 14,000 pounds per square inch, but
additional loading is not permitted on the concrete. The steel must
be surrounded by at least 2 inches of concrete, in which there must be
placed 4 small vertical bars, usually f inch, banded by j-inch bars, 12
inches on centers. The loads are transmitted from the beams and
girders to the steel by means of large steel brackets which are riveted
to the columns. The work is riveted up in the usual manner for
structural steel.

The McNulty Building.* The columns used in the construction
of the McXulty Building, New York City, are a very interesting
feature in this building. The building is 50 feet by 96 feet, and is
10 stories high. The- plan of all the floors is the same. A single row
of interior columns is placed in the center of the building, about 22
feet center to center.

* Engineering Record.

Fig. 215. Typical Sections of Steel Core

MASONRY AND REINFORCED CONCRETE 371

The columns are of the hooped type, and are designed from the
formula approved by the building laws, of New York City. The
formula used was

P = l,600r2+ (160,000 J^P)Xr+6,000 As

in which P is the total working load, r is the radius of the helix, A s is
the total area of the vertical steel, Ah is the sectional area of the
hooping wire, and P is the pitch of the helix.

The interior columns are cylindrical in form, except those sup-
porting the roof, which are 12- by 12-inch and are reinforced with 4
bars f inch in diameter. In all the other stories except the ninth, they
are 27 inches in diameter. Below the fifth floor the reinforcement in
each of these columns consists of 2-inch round vertical bars, ranging
in number from 7 in the fifth floor to 30 in the basement, and banded
by a 24-inch helix of ^-inch wire, with a pitch of 1^ inches. The
vertical bars were omitted between the sixth and tenth floors; and
the diameter of the helix was gradually decreased, while the pitch
was increased. In the ninth floor the otiameter was reduced to 21
inches.

The wall columns are, in general, 26 by 30 inches, and support
loads from 48,000 pounds in the tenth floor to 719,750 pounds in the
basement. In the sixth story, the reinforcement in these columns
consists of 3 round, vertical bars 2 inches in diameter; and in each of
the floors below, the number of bars in these columns was increased,
there being 24 in the basement columns. These are spirally wound
with ^-inch steel wire forming a helix 23 inches in diameter, with a
pitch of 2| inches. Above the seventh floor, the columns are rein-
forced with 4 bars f inch in diameter, and tied together by ^-inch
wire spaced 18 inches apart. The columns rest on cast-iron shoes,
which are bedded on solid rock about 2| feet below the basement floor.

The main-floor girders extend transversely across the building,
and have a clear span of 21 feet. The floor beams are spaced about
6 feet apart, and have a span of about 20 feet 6 inches. The sides of
the beams slope, the width at .the bottom being two inches less than
the width at the under surface of the slab. The reinforcement con-
sists of plain round bars. The bars for the girders and beams were
bent and made into a truss — the Unit System — at the shops of the
contractor, and were shipped to the work ready to be put in place.

383

372 MASONRY AND REINFORCED CONCRETE

The stirrups were hot-shrunk on the longitudinal bars. The helixes
for the columns were wound and attached to some of the vertical rods
at the shop, to preserve the pitch. The vertical rods in each column
project 6 inches above the floor line, and are connected to the bar
placed on it by a piece of pipe 12 inches long.

The concrete was a 1 :2:4 mixture. Giant Portland cement was
used, and f-inch trap rock.

The McGraw Building. The McGraw Building, New York
City, is a good example of a reinforced-concrete building. The
building has a frontage of 126 feet and a depth of 90 feet, and is 11

SECTION BB
Fig. 216. Stair Detaila for the Fridenbcrg Building

stories in height. The height of the roof is about 150 feet above the
street level. The building was designed to resist the vibration of
heavy printing machinery. The first and second floors were designed
for a live load of 250 pounds per square foot; for the third floor, 150
pounds per square foot; for the fourth floor and all floors above the
fourth floor, 125 pounds per square foot.

All beams and girders were designed as continuous beams, even
where supported on the outside beams. There is twice as much steel
over the supports as in the center of the spans. The Building Code
of New York City requires that the moment for continuous

beams be taken as — — - at the center of the span, and as — — over the

384

MASONRY AND REINFORCED CONCRETE 373

support. These values are more than twice the theoretical value as
computed for continuous beams.

One very interesting feature of this building is that it was con-
structed during the winter. The first concrete was laid during Sep-
tember, and the concrete work was completed in April. During
freezing weather, the windows of the floors below the floor that was
being constructed were closed with canvas; and salamanders (open
stoves) were distributed over the completed floor, and kept in con-
stant operation. Coke was used as the
fuel for the salamanders. The concrete
was mixed with hot water, and the sand
and the stone were also heated. After
two or three stories had been erected,
and the construction force was fully
organized, a floor was completed in
about 12 days. Three complete sets of
forms were provided and used. They
were usually left in place nearly three
weeks.

Fridenberg Building. In Fig. 216
are showrn the plans of stairs constructed
in the Fridenberg building at 908 Chest-
nut Street, Philadelphia. This building
is 24 feet by 60 feet, and is seven stories
high. Structurally, the building is con-
structed of reinforced concrete. The
stair and elevator tower is located in the
rear of the main building.

The plans of the stairs are interest-
ing on account of the long-span (about
16 feet) slab construction. The stairs
are designed to carry safely a live load
of 100 pounds per square foot; and in the
theoretical calculations the slab was treated as a flat slab with a clear
span of 16 feet. The shear bars are made and spaced as shown in
the details. The calculations showed a low shearing value in the
concrete, but stirrups were used to secure a good bond between
the steel and concrete.

Fig. 217. Details of Special Type
of Lintel

385

374 MASONRY AND REINFORCED CONCRETE

The concrete was a 1:2:4 mixture, and was mixed wet. The
reinforcing steel consisted of square deformed bars, except the
stirrups, which were made of £-inch plain round steel.

Special Type of Lintel. An interesting feature of a large rein-
forced-concrete building constructed for the General Electric Com-
pany at Fort Wayne, Indiana, is the design of the lintels. As shown
in Fig. 217, the bottom of the lintel is at the same^elevation as the
bottom of the slab. The total space between the colusains is filled

with double windows; an4 the
space from the top of these win-
dows to the bottom of those
above, is filled with a beam which
also serves as a wall.

Water=Basin and Circular
Tanks. Figs. 218 and 219 illus-
trate sections of the walls of the
pure water basin and the 50-foot
circular tanks which have been
partly described in Part I, page
69, under the heading of "Water-
proofing".

The pure water basin is 100
feet by 200 feet, and 14 feet
deep, giving a capacity of over
1 ,500,000 gallons. The counter-
forts are spaced 12 feet 6 inches,
center to center, and are 12
inches thick, except every fourth
one, which was made 18 inches
thick . The 1 8-inch counterforts were constructed as two counterforts
each 9 inches thick, as the vertical joints in the walls were made at this
point; that is, the concrete between the centers of two of the 18-inch
counterforts was placed in one day. On the two ends and one side
of the basin the counterforts were constructed on the exterior of the
basin to support about 10 feet of earth. But on one side it would
have been necessary to remove rock 6 to 8 feet in thickness to make
room for the counterforts, had they been constructed on the exterior
of the basin. Therefore, they were constructed inside of the basin.

Fig. 218. Typical Section of Water-
Basin Wall

MASONRY AND REINFORCED CONCRETE 375

If both faces of the vertical wall had been reinforced, the same as the
one shown, then the wall would have been able to resist an outward
or an inward pressure, and the "piers" would act as counterforts or
buttresses, depending on whether they were in tension or in com-
pression.

The concrete used consisted of 1 part Portland cement, 3 parts
sand, and 5 parts crushed stone. The stone was graded in size from
j inch as the minimum to f inch as the maximum size. Square-
sectioned deformed bars were used as the steel reinforcement. The
forms were constructed in units so that they
could be put up and taken down quickly. ^

The size and spacing of the bars in the
walls of the circular tanks are shown in Fig.
219. The framework of the forms to which
the lagging was fastened was cut to the desired
curve at a planing mill. This framing was
cut from 2- by 12-inch lumber. The lagging
was | inch thick, and surfaced on one side. ••

Main Intercepting Sewer. In the devel-
opment of sewage purification work at Water-
bury, Connecticut, the construction of a main
intercepting sewer was a necessity. This
sewer is three miles long. It is of horseshoe
shape, 4 feet 6 inches by 4 feet 5 inches, and
is constructed of reinforced concrete. The
details are illustrated in Fig. 220.

The trench excavations were principally
through water-bearing gravel, the gravel rang- Fig. 219^ J1^^1 Sec"
ing from coarse to fine. Some rock was encoun-
tered in the trench excavations. It was a granite gneiss of irregular
fracture, and cost, with labor at 17^ cents per hour, about $2.00 per
cubic yard to remove it. Much of the trench work varied in depth
from 20 to 26 feet. Owing to the varying conditions, it was necessary
to vary the sewer section somewhat. Frequently, the footing course
was extended. However, the section shown in the figure is the normal
section.

The concrete was mixed very wet, and poured into practically
water-tight forms. The proportions used were 1 part Atlas Portland

387*

376 MASONRY AND REINFORCED CONCRETE

cement to 7£ parts of aggregate, graded to secure a dense concrete.
Care was used in placing the concrete, and very smooth surfaces were
secured. Plastering of the surfaces was avoided. Any voids were
grouted or pointed, and smoothed with a wood float. Expanded
metal and square-twisted bars were used in different parts of
the work. In Fig. 220, the size and spacing of the bars are shown.
The bars were bent to their required shape before they were lowered
into the excavation.

The forms in general were constructed as shown in the figure.
The inverted section was built as the first operation; and after the

-Strap Iron

Fig. 220. Section of Intercepting Sewer at Waterbury, Connecticut

surface was thoroughly troweled, the section was allowed to set 36
to 48 hours before the concreting of the arch section was begun. The
lagging was f inch thick, with tongue-and-groove radial joints, and
toenailed to the 2-inch plank ribs. The exterior curve was planed
and scraped to a true surface. The vertical sides of the inner form
are readily removable, and the semicircular arch above is hinged at
the soffit and is collapsible. The first cost of these forms has averaged
$18.00 for 10 feet of length; and the cost of the forms per foot of
sewer built, including first cost and maintenance, averaged 10 cents.
Petrolene, a crude petroleum, was found very effective in preventing
the concrete from adhering to the forms.

388

MASONRY AND REINFORCED CONCRETE 377

Cost records kept under the several contracts and assembled into
a composite form show what is considered to be the normal cost of
this section, under the local conditions. Common labor averaged \1\
cents, sub-foremen 30 cents, and general foremen 50 cents per hour.

Normal Cost per Lineal Foot of 53- by 54=Inch Reinforced-
Concrete Sewer

Steel reinforcement, 17g Ib $0 . 43

Making and placing reinforcement cages 14

Wood interior forms, cost, maintenance, and depreciation 12

Wood exterior forms, cost, maintenance, and depreciation 05

Operation of forms 16

Coating oil 01

Mixing concrete 30

Placing concrete 27

Screeding and finishing invert 08

Storage, handling, and cartage of cement 08

0 . 482 bbl. cement at $1 . 53. . . . 74

0.17 cu. yd. sand at $0.50 v

0 . 435 cu. yd. broken stone at $1.10

Finishing interior surface

Sprinkling and wetting completed work

.09

.47
.01
.02

$2 . 97

Total cost per lineal foot

This is equivalent to a cost of $9.02 per cubic yard.

Bronx Sewer, New York. In Fig. 221 is shown a section of one
of the branch sewers constructed in the Borough of the Bronx, New
York City. A large part of
this sewer is located in a salt
marsh where wrater and un-
stable soil made construction
work very difficult. The gen-
eral elevation of the marsh
is 1.5 feet above mean high
water. In constructing this
sewer in the marsh, it was
necessary to construct a pile
foundation to support the
sewer. The foundation was
capped with reinforced con-
crete; and then the sewer, as shown in the section, was constructed on
the pile foundation. The concrete for this work is composed of 1
part Portland cement, 2^ parts sand, and 5 parts trap rock. The

Fig. 221.

389

378 MASONRY AND REINFORCED CONCRETE

rock was crushed to pass a f-inch screen. Twisted bars were used
for the reinforcement in the work.

Girder Bridge. The reinforced-concrete bridge shown in Fig.
222 was constructed near Allentown, Pennsylvania. This type of
bridge has been found to be economical for short spans. Worn-out
wood and steel highway bridges are in general being replaced with
reinforced-concrete bridges, and usually at a cost less than that of
a steel bridge of the same strength. Steel bridges should be painted
every year; and plank floors, as commonly used in highway bridges,
require almost constant attention, and must be entirely renewed
several times during the life of a bridge. A reinforced-concrete

Fig. 222. Details of Girder Bridge near Allentown, Pennsylvania

bridge, however, is entirely free of these expenses, and its life should
at least be equal to that of a stone arch. From an architectural
standpoint, a well-finished concrete bridge compares very favorably
with a cut-stone arch.

The bridge shown in Fig. 222 is 16 feet wide, and has a clear
span of 30 feet. It is designed to carry a uniformly distributed
load of 150 pounds per square foot, or a steel road roller weighing 15
tons, the road roller having the following dimensions: The width
of the front roller is 4 feet, and of each rear roller, 20 inches; the dis-
tance apart of the two rear rollers is 5 feet, center to center; and
the distance between front and rear rollers is 11 feet, center to center;

390

MASONRY AND REINFORCED CONCRETE 379

the weight on the front roller is 6 tons, with 4.5 tons weight on each
of the rear rollers.

In designing this bridge, the slab was designed to carry a live
load of 4.5 tons on a width of 20 inches, when placed at the middle of
the span, together with the dead load consisting of the weight of the
macadam and the slab. The load considered in designing the cross-
beams consisted of the dead load — weight of the macadam, slab, and
beam — and a live load of 6 tons placed at the center of the span of the
beam, which was designed as a T-beam. In designing each of the
longitudinal girders, the live load was taken as a uniformly distributed
load of 150 pounds per square foot over one-half of the floor area of
the bridge. The live load was increased 20 per cent over the live
load given above, to allow for impact.

In a bridge of this type, longitudinal girders act as a parapet, as
well as the main members of the bridge. The concrete for this work
was composed of 1 part Portland cement, 2 parts sand, and 4 parts
1-inch stone. Corrugated bars were used as the reinforcing steel.

When there is sufficient headroom, all the beams can be con-
structed in the longitudinal direction of the bridge, and are under the
slab. The parapet may be constructed of concrete; or a cheaper
method is to construct a handrailing with l|-inch or 2-inch pipe.

391

MASONRY AND REINFORCED
CONCRETE

PART V

CONCRETE ARCH DESIGN AND
CONSTRUCTION

Definitions of Terms Pertaining to Arch Masonry. The follow-
ing are definitions of technical terms frequently used in connection
with the subject of arch masonry (see Fig. 223) :

Abutment. An abutment is the masonry which supports an
arch at either end, and which is so designed that it can resist the
lateral thrust of the arch.

Arch Sheeting. Arch sheeting is that portion of an arch which
lies between the ring stones.

Backing. Backing is the masonry which is placed outside of or
above the extrados, with the sole purpose of furnishing additional
weight on that portion of the arch; it is always made of an inferior
quality of masonry and with the joints approximately horizontal.

Coursing Joint. A coursing joint is a mortar joint which
runs continuously from one face of the arch to the other.

Crown. The crown is the vertex or highest part of an arch ring.

Extrados. The extrados is the upper, or outer, surface of the
voussoirs which compose the arch ring.

Haunch. That portion of an arch which is between the crown
and the skewback is called the haunch; although there is no definite
limitation, the term applies, generally, to that portion of the arch
ring which is approximately halfway between the crown and the
skewback.

Heading Joint. A heading joint is a joint between two consecu-
tive stones in the same string course. In order that the arch shall
be properly bonded together, such joints are purposely made not
continuous.

393

382 MASONRY AND REINFORCED CONCRETE

Intrados. The intrados is the inner or lower surface of an arch.
The term is frequently restricted to the line which is the intersection
of the inner surface by a plane that is perpendicular to the axis of the
arch.

Keystone. The keystone is the voussoir which is placed at the
crown of an arch.

Parapet. The wall which is usually built above the spandrel
walls and above the level of the roadway is termed the parapet.

Ring Stones. Ring stones are the voussoirs which form the
arch ring at each end of the arch.

Rise. The rise is the vertical height of the bottom of the key-
stone above the plane of the skewrbacks.

Fig. 223. Diagram Showing Parts of a Typical A

Skewback. Skewback is the term applied to the top course of
stones on the abutments. The upper surfaces of the stones are cut
at such an angle that "the surfaces are approximately perpendicular
to the direction of the thrust of the arch.

Soffit. The inner or lower surface of an arch is known as the
soffit.

Span. The span is the perpendicular distance between the two
springing lines of an arch.

Spandrel. The space between the extrados of an arch and the
roadway is designated as the spandrel. The walls above the ring
stones at the ends of the arch are called spandrel walls. The mate-
rial deposited between the spandrel walls and in this spandrel space
is called the spandrel filling . "

394

MASONRY AND REINFORCED CONCRETE 383

Springer. Springer is, loosely, the point from which an arch
seems to spring; or specifically, the first arch stone above a skew-
back.

Springing Line. The springing line is the upper (and inner)
edge of the line of skewbacks on an abutment.

String Course. A string course is a course of voussoirs of the
same width — perpendicular to the axis of the arch — which extends
from one arch face to the other.

Voussoirs. Voussoirs are the separate stones forming an arch
ring.

Classification of Arches. Arches are variously described
according to the shape of the intrados, and also according to the
form of the soffit :

Basket-Handle Arch. A basket-handle arch is one whose
intrados consists of a series of circular arcs tangent to each other.
They are usually three-centered OT five-centered.

Catenarian Arch. A catenarian arch is an arch whose
intrados is a mathematical curve known as the catenary. This
is the natural curve assumed by a chain which is hung loosely
from two points.

Circular Arch. Circular arches are those in which the intrados
is the arc of a circle.

Elliptical Arch. An elliptical arch is an arch whose intrados is
a portion of an ellipse.

Hydrostatic Arch. A hydrostatic arch is one whose intrados is
of such a form that the equilibrium of the arch is dependent upon
such a loading as would be made by water.

Pointed Arch. A pointed arch is one whose intrados consists of
two similar curves which meet at a point at the top of the arch.

Relieving Arch. An arch which is built above a lintel, and
which relieves the lintel of the greater portion of its load, is called a
relieving arch.

Right Arch. A right arch is an arch whose soffit is a cylinder,
and whose ends are perpendicular to the axis of the arch.

Segmental Arch. A segmental arch is one whose intrados is a
circular arc which is less than a semicircle.

Semicircular Arch. A semicircular arch is one whose intrados
is a full semicircle. Such an arch is also called a full-centered arch.

395

384 MASONRY AND REINFORCED CONCRETE

Skew Arch. A skew arch is an arch whose soffit may or may
not be cylindrical, but whose ends are not perpendicular to the axis
of the arch. They are also called oblique arches.

THEORY OF ARCHES

General Statement. The mechanics of the arch are almost
invariably solved by a graphical method, or by a combination of
the graphical method with numerical calculations. This is done,
not only because it simplifies the work, but also because, although
the accuracy of the graphical method is somewhat limited, yet, with
careful work, it may easily be made even more accurate than is
necessary, considering the uncertainty as to the true ultimate
strength of the masonry used. The development of this graphical

method must necessarily follow
the same lines as in Statics. It
is here assumed that the student
has a knowledge of Statics, and
that he already understands the
graphical method of representing
tne magnitude, direction, and
line of application of a force.
Several of the theorems or gen-
eral laws regarding the compo-

Fig. 224. Diagram of Resultant of Two Forces ^j^ an(j resolutionof forces>

will be briefly reviewed as a preliminary to the proof of those laws
of graphical statics which are especially applied in computing the
stresses in an arch.

Resultant of Two Non=Parallel Forces. The resultant of two
forces, A and B, which are not parallel, whose lines of action are as
shown in Fig. 224-a, and which are measured by the lengths of the
lines A and B, Fig. 224-b, is readily found by producing the lines of
action to their intersection at c. The two known forces are drawn in
Fig. 224-b, so that their direction is parallel to the known directions
of the forces, and so that the point of one force is at the butt end of
the other. Then the line R joining the points m and n, Fig. 224-b,
gives the direction of the resultant; and a line through c parallel to
that direction gives the actual line of that resultant. The line mn
also measures the amount of the resultant. Note that Fig. 224-b, is

MASONRY AND REINFORCED CONCRETE 385

a closed figure. If an arrow is marked on R so that it points upward,
the arrows on the forces would run continuously around the figure.
If R were acting upward, it would represent the force which would
just hold A and B in equilibrium; pointing downward, it is the
resultant or combined effect of the two forces. We may thus define
the resultant of two — or more — forces as the force which is the equal
and opposite of that force which will just hold that combination of
forces in equilibrium.

Resultant of Three or More Forces. This may be solved by an
extension of the method previously given as shown in Fig. 224.
The resultant of B and C, Fig. 225, is R'; and this is readily com-
bined with A, giving R" as the resultant of all three forces. The
same principle may be ex-
tended to any number of
non-parallel forces acting in
a plane. The resultant of
four non-parallel forces is
best determined by finding,
first, the resultant of each
pair of the forces taken two
and two. Then the result-
ant of the two resultant Fig'225' Diagram Showing Resultant °f Three Force3
forces is found, just as if each resultant were a single force.

Resultant of Two or More Parallel Forces. When the forces
are all parallel, the direction of the resultant is parallel to the com-
ponent forces; the amount is equal to the sum of the component
forces; but the line of action of the resultant is not determinable as
in the above cases, since the forces do not intersect. It is a principle
of Statics which is easily appreciated, that it does not alter the statics
of any combination of forces to assume that two equal and opposite
forces are applied along any line of action. From Fig. 226-b, we see
that the forces F and G will hold A in equilibrium; that G and //
will hold B in equilibrium; and that // and K will hold C in equilib-
rium. But the force G required to hold A in equilibrium is the
equal and opposite of the force G required to hold B in equilibrium ;
and similarly the force // for B is equal and opposite to the force //
for C. We thus find that the forces A, B, and C can be held in equi-
librium by an unbalanced force F, two equal and opposite forces G,

397

386 MASONRY AND REINFORCED CONCRETE

two equal and opposite forces //, and the unbalanced force K, The
net result, therefore, is that A, B, and C are held in equilibrium by
the two forces F and A'. The resultant R is the sum of A, B, and C;
and therefore the combined-load line represents the resultant R.
The external lines of Fig. 226-b show that F, K, and R form a closed
figure with the arrows running continuously around the figure; and
that F and K are two forces which hold R, the resultant of A, B, and
C, in equilibrium. By producing the lines representing the forces
F and K in Fig. 226-a until they intersect at x, we may draw a
vertical line through it which gives the desired line of action of 7?.
This is in accordance with the principles given in the previous
article.

Fig. 226. Equilibrium Polygon with Oblique Closing Line

Nothing was said as to how F, G, II, and K were drawn in
Fig. 226-a and Fig. 226-b. These forces simply represent one of an
infinite number of combinations of forces which would produce the
same result. The point o is chosen at random, and lines, called
rays, are drawn to the extremities of all the forces. The lines of
force (A, B, and C) in Fig. 226-b — which is called the force diagram
—are together called the load line. The line of forces (F, G, II,
and K) in Fig. 226-a, together with the closing line y z, is called an
equilibrium polygon.

Statics of a Linear Arch. We shall assume that the lines in
Fig. 226 by which we have represented forces F, G, II, and K repre-
sent struts which are hinged at their intersections with the forces
A, B, and C, which represent loads; and that the two end struts F

MASONRY AND REINFORCED CONCRETE 387

and K are hinged at two abutments located at y and z. Then all of
the struts will be in compression, and the rays of the force diagram
will represent, at the same scale as that employed to represent
forces or loads A, B, and C, the compression in each of the struts.
In the force diagram, draw a line from o, parallel with the line y z.
It intersects the load line in the point n. Considering the triangle
op n as a force diagram, op represents the force F, while pn and on
may represent the direction and amount of two forces which will
hold F in equilibrium. Therefore pn would represent the amount
and direction of the vertical component of the abutment reaction at
y, and on would represent the component in the direction of yz.
Similarly, we may consider the triangle onq as a force diagram; that
nq represents the vertical component R", and that on represents
the component in the direction zy. Since on is common to both of
these force triangles, they neutralize each other, and the net result-
ant of the two forces F and K is the two vertical forces R and R";
but since the resultant R is the resultant of F and K, we may say
that R' and R" are two vertical forces whose combined effect is the
equal and opposite of the force R. Although an indefinite number
of combinations of forces could begin and end at the points y and 2,
and could produce equilibrium with the forces A, B, and C, the
forces R' and R" are independent of that particular combination of
struts, F, G, II, and K.

Graphical Demonstration of Laws of Statics by Student. The
student should test all this work in Statics by drawing figures, very
carefully and on a large scale, in accordance with the general instruc-
tions as described in the text, and should purposely make some
variation in the relative positions and amounts of the forces, from
those indicated by the figures. By this means the student will be
able to obtain a virtual demonstration of the accuracy of the laws
of Statics as formulated. The student should also remember that
the laws are theoretically perfect; and when it is stated, for example,
that certain lines should be parallel, or that a certain line drawn in
a certain way should intersect some certain point, the mathematical
laws involved are perfect; and if the drawing does not result in the
expected way, it either proves that a blunder has been made, or it
may mean that the general method is correct, but that the drawing
is more or less inaccurate.

388 MASONRY AND REINFORCED CONCRETE

Equilibrium Polygon with Horizontal Closing Lines. In Fig.
227, the same forces A, B, and C have been drawn, having the same
relative positions as in Fig. 226. The lines of action of the two
vertical forces 7?' and R" have also been drawn in the same relative
position as in Fig. 226. The point n has also been located on the
load line in the same position as in Fig. 226. Thus far the lines are
a repetition of those already drawn in Fig. 226, the remainder of the
figure being omitted, for simplicity. Since the point n in Fig. 226 is
the end of the line from the trial pole o, which is parallel to the closing
line yz, and since the point n is a definitely fixed point and determines
the abutment reactions regardless of the position of the trial pole o,
we may draw from n an indefinite horizontal line, such as no', and

Fig. 227. Equilibrium Polygon with Horizontal Closing Line

wre know that the pole of any force diagram must be on this line if
the closing line of the corresponding equilibrium polygon is to be a
horizontal line. For example, we shall select a point o' on this line,
at random. From </ we shall draw rays to the points p, s, r, and q.
From the point y, we shall draw a line parallel to o'p. Where this
line intersects the force A, draw a line parallel to the ray o's. Where
this intersects the force B, draw a line parallel to the ray o'r. Where
this intersects the force C, draw a line parallel to the ray o'q. This
line must intersect the point z', which is on a horizontal line from y.
The student should make some such drawing as here described, and
should demonstrate for himself the accuracy of this law. This
equilibrium polygon is merely one of an infinite number which, if
acting as struts, would hold these forces in equilibrium, but it com-

400

MASONRY AND REINFORCED CONCRETE 389

bines the special condition that it shall pass through the points y and
z'. There are also an infinite number of equilibrium polygons which
will hold these forces in equilibrium arid which will pass through the
points y and z'.

We may also impose another condition, which is that the first
line of the equilibrium polygon shall have some definite direction, such
as y I. In this case the ray from the point p of the force diagram must
be parallel to yl; and where this line intersects the horizontal line no'
(produced in this case) is the required position for the pole o".
Draw rays from o" to s, r, and q, continuing the equilibrium polygon
by lines which are respectively parallel to these rays. As a check on
the work, the last line of the equilibrium polygon which is parallel to
o"q should intersect the point z'. The triangles yk h and o'pn have
their sides respectively parallel to each other, and the triangles are
therefore similar. Their corresponding sides are therefore propor-
tional, and we may write the equation

o'n : yh :: pn : kh
Also, from the triangles ylh and o"pn, we may write the proportion

o"n : yh :: pn : Ih

From these two proportions we may derive the proportion
o'n:o"n::lh:kh

but o'n and o"n are the pole distances of their respective force dia-
grams, wrhile k h and I h are intercepts by a vertical line through the
corresponding equilibrium polygons. The proportion is therefore a
proof, in at least a special case, of the general law that "the perpen-
dicular distances from the poles to the load lines of any two force
diagrams are inversely proportional to any two intercepts in the
corresponding equilibrium polygons". The above proportions prove
the theorem for the intercepts hk and hi. A similar combination
of proportions would prove it for any vertical intercept between y
and h. The proof of this general theorem for intercepts which pass
through other lines of the equilibrium polygon is more complicated
and tedious, but it is equally conclusive. Therefore, if we draw
any vertical intercept, such as tvw, we may write out the general
proportion

o"n : o'n ::tw:vw (60)

401

390 MASONRY AND REINFORCED CONCRETE

In this proportion, if o"n were an unknown quantity, or the position
of o" were unknown, it could be readily obtained by drawing two
random lines as shown in Fig. 227-c, and laying off on one of them
the distance no' , and on the other line the distances vw and tw.
By joining v and o' in Fig. 227-c, and drawing a line from t par-
allel to vo', it will intersect the line no' produced, in the point
o". As a check, this distance to o" should equal the distance no" in
Fig. 227-b. A practical application of this case, and one that is
extensively employed in arch work, is the requirement that the
equilibrium polygon shall be drawn so that it shall pass through
three points, of which the abutments are two, and some other point
(such as fl) is the third. After obtaining a trial equilibrium polygon
whose closing line passes through the points y and z', the proper
position for the pole o" which shall give the equilibrium polygon that
will pass through the point v may be easily determined by the method
described above.

The process of obtaining an equilibrium polygon for parallel
forces which shall pass through two given abutment points and a
third intermediate point may be still further simplified by the appli-
cation of another property, and without drawing two trial equilib-
rium polygons before we can draw the required equilibrium polygon.
It may be demonstrated that if the pole distance from the pole to the
load line is unchanged, all the vertical intercepts of any two equilib-
rium polygons drawn with these same pole distances are equal. For
example, in Fig. 226, a line is drawn vertically upward from o, until
it intersects the horizontal line drawn through n in the point o". This
point is the pole of another equilibrium polygon whose closing line
will be horizontal, because the pole lies on a horizontal line from the
previously determined point n in the load line. Any vertical inter-
cept of this equilibrium polygon will be equal to the corresponding
intercept on the first trial equilibrium polygon. Therefore, in order
to draw a special equilibrium polygon for a given set of vertical loads,
the polygon to pass through two horizontal abutment points and a
definite third point between them, we need only draw, first, a trial
equilibrium polygon, the rays in the force diagram being drawn
through any point chosen as a pole. Then if we draw a line
from the trial pole parallel with the closing line of this trial equilib-
rium polygon, the line will intersect the load line in the point n.

402

MASONRY AND REINFORCED CONCRETE 391

Drawing a horizontal line from the point n in the load line, we
have the locus of the pole of the desired special equilibrium polygon.
We next draw a vertical through the point through which the
special equilibrium polygon is to pass. The vertical distance of
this point above the line joining the abutments is the required inter-
cept of the true equilibrium polygon. The intersection of that
vertical with the upper line and the closing line of the trial equilib-
rium polygon is the intercept of the trial polygon. The pole dis-
tance of the true equilibrium polygon is then obtained by the appli-
cation of Equation (60), by which the pole distances are declared
inversely proportional to any two corresponding intercepts of the
equilibrium polygons.

Another useful property, which will be utilized later, and which
may be readily verified from Figs. 226 and 227, is that, no matter
what equilibrium polygon may be drawn, the two extreme lines of the
equilibrium polygon, if produced, intersect in the resultant R; there-
fore, when it is desired to draw an equilibrium polygon which shall
pass through any two abutment rpoints, such as yz or yz', we may
draw, from these two abutment points, two lines which shall inter-
sect at any point on the resultant R. We may then draw two lines
which will be respectively parallel to these lines from the extremities
p and q of the load lines, their intersection giving the pole of the
corresponding force diagram.

Equilibrium Polygon for Non=Vertical Forces. The above
method is rendered especially simple, owing to the fact that the
forces are all vertical. When the forces are not vertical, the method
becomes more complicated. The principle will first be illustrated
by the problem of drawing an equilibrium polygon which shall pass
through the points y, z, and v in Fig. 228. We shall first draw
the two non-vertical forces in the force diagram. The resultant R
of the forces A and B is obtained as shown in Fig. 224. Utilizing
the property referred to above, we may at once draw two lines
through y and z w^hich intersect at some assumed point e on the
resultant R. Drawing lines from p and q parallel respectively to
ez and ey, we determine the point o' as the trial pole for our force
diagram. As a check on the drawing, the line joining the inter-
sections 6 and c should be parallel to the ray o'*, thus again verifying
one of the laws of Statics. If the line b c is produced until it inter-

403

392 MASONRY AND REINFORCED CONCRETE

sects the line yz produced, and a line is drawn from the intersection x
through the required point v, it will intersect the forces A and B in
the points d and g. Then d g will be one of the lines of the required
equilibrium polygon. By drawing lines from q and p parallel to yd
and zg, we find their intersection o", which is the pole of the required
force diagram. There are two checks on this result: (1) the line
so" is parallel to dg; and (2) the line o'o" is horizontal.

If the line be is horizontal or nearly so, the intersection (,r) of
b c and y z produced is at an infinite distance away, or is at least oft'
the drawing. If b c is actually horizontal, the line dg will also be a
horizontal line passing through i\ When be is not horizontal, but is

Fig. 228. Equilibrium Polygon through Three Chosen Points

so nearly so that it will not intersect yz at a convenient point, the
line dg may be determined as is indicated by the dotted lines in the
figure. Select any point on the line yz, such as the point o.
Through the given point v, draw a vertical line which intersects the
known line be in the point k. From some point in the line be (such
as the point 6), draw the horizontal line bh and the vertical line bn.
The line from o through k intersects the horizontal line from 6 in the
point h. From the point h, drop a vertical; this intersects the line
ov produced, in the point ra. From ra, draw a horizontal line which
intersects the vertical line from b. This intersection is at the point
n. The line vn forms part of the required line dg. As a check on
the work, the lines zg and yd should intersect at some point/ on

404

MASONRY AND REINFORCED CONCRETE 393

the force R. Another check on the work, which the student should
make, both as a demonstration of the law and as a proof of the
accuracy of his work, is to select some other point on the line yz
than the point o, and likewise some other point on the line be than
the point 6, and make another independent solution of the problem.
It will be found that when the drawing is accurate, the new position
for the point n will also be on the line dg.

In applying the above principle to the mechanics of an arch,
the force A represents the resultant of all the forces acting on the
arch on one side of the point v through which the desired equilibrium
polygon is required to pass; and the force B is the resultant of all the
forces on the other side of that point. A practical illustration of this
method will be given later.

VOUSSOIR ARCHES

Definition. A voussoir arch is an arch composed of separate
stones, called voussoirs, which are so shaped and designed that the
line of pressures between the stones is approximately perpendicular
to the joints between the stones. So far as it affects the mechanics
of the problem, it is assumed that the mortar in the joints between
the voussoirs acts merely as a cushion, and that the mortar has no
tensile strength whatever, even if the pressure at any joint should
be such as to develop tensile action. It is this feature which
constitutes the distinction between a voussoir arch and an elastic
arch, which is assumed to be an arch of such material that tensile or
transverse stresses may be developed.

Distribution of Pressure between Two Voussoirs. The unit
pressure on any joint is assumed to vary in accordance with the
location of the center of pressure, as is illustrated in Fig. 229. In
the first case, where the center of pressure is over the center of the
face of the joint and is perpendicular to it, the pressure will be
uniformly distributed, and may be represented, as in Fig. 229-a, by
a series of arrows which are all made equal, thus representing equal
unit pressures. As the center of pressure varies from the center of
the joint, the unit pressure on one side increases and the unit pressure
on the other side decreases, as shown in Fig. 229-b. The trapezoid in
this diagram has the same area as the rectangle of the first diagram
(a), and the center of pressure passes through the center of gravity

405

394 MASONRY AND REINFORCED CONCRETE

of the trapezoid. As the center of pressure continues to move away
from the center of the joint, the unit pressure on one side becomes
greater, and on the other side less, until the center of pressure is at a
point { of the width of the joint away from the center. In this case
(c), the center of pressure is at the extreme edge of the middle third of
the joint. The group of pressures illustrated in Fig. 229-c becomes
a triangle, which means that the pressure at one side of the joint has
become just equal to zero, and that the maximum pressure at the
other side of the joint is twice the average pressure. If the line of
pressure varies still further from the center of the joint, the diagram

of pressures will always be a tri-
angle wrhose base is always three
times the distance of the center
of pressure from the nearest edge
of the joint. If the total pressure
on that joint remains constant,
then the intensity of pressure on
one side of the joint becomes ex-
treme, and may be sufficient to
crush the stone. Also, since the
elasticity of the stone — or of the
mortar between the stones — will
cause the stone (or mortar) to
yield, the yielding being propor-
tional to the pressure, the joint
will open at the other side,
where there is no pressure. In
accordance with this principle of the distribution of pressure, it is
always specified that a design for an arch cannot be considered sa^e
unless it is possible to dra\v a line of pressure — an equilibrium poly-
gon— which shall at every joint pass through the middle third of that
joint. If the line of pressure at any joint does not pass through the
middle third, it means that such a joint will inevitably open, and
make a bad appearance, even though the unit pressure on the other
end of that joint is not so great that the masonry is actually crushed.
Factor of Safety. Since the actual crushing strength of stone is
a rather uncertain and variable quantity, a larger factor of safety is
usually employed with stone than with other materials of construe-

Fig. 229. Diagram Showing Distribu-
tion of Pressure

406

MASONRY AND REINFORCED CONCRETE 395

tion. This factor is usually made ten; and therefore, whenever the
line of pressures passes through the edge of the middle third, the
average unit pressure on the joint should not be greater than ^V of
the crushing strength of the stone.

Quality of Stone. Ultimate values for crushing strength have been
given in Table I, Part I, page 6. They vary from about 3,000
pounds per square inch, for a sandstone found in Colorado, up to
28,000 pounds per square inch for a granite found in Minnesota.
The weaker stone would hardly be selected for any important work.
Usually, a stone whose ultimate strength is 10,000 pounds per square
inch or more would be selected for a stone arch. Such a stone
could be used with a working pressure of 500 pounds per square inch
at any joint, assuming that the line of pressure does not pass outside
of the middle third at any joint.

External Forces Acting on an Arch. There is always some
uncertainty regarding the actual external forces acting on ordinary
arches. The ordinary stone arch
consists of a series of voussoirs,
which are usually overlaid with a
mass of earth or cinders having a
depth of perhaps several feet, on

top of which may be the pavement Fig 23o. Diagram Showing Method of
of a roadway. The spandrel walls

over the ends of the arch, especially when made of squared-stone
masonry, also develop an arch action of their own which materially
modifies the loading on the arch rings. As this, however, invariably
assists the arch, rather than weakens it, no modification of plan is
essential on this account. The actual pressure of the earth filling,
together with that caused by the live load passing over the arch, on
any one stone, is uncertain in very much the same way as the pressure
on a retaining wall is uncertain, as previously explained.

The simplest plan is to consider that each voussoir is carrying a
load of earth equal to that indicated by lines from the joints in the
voussoir vertically upward to the surface. The development of the
graphical method makes it more convenient to draw what is called
a reduced load line on top of the arch, in which the depth of earth
above the arch is reduced in the ratio of the relative weights per
cubic foot of the earth filling and of the stone of which the arch is

407

396 MASONRY AND REINFORCED CONCRETE

made, Fig. 230. Even the live load on the arch is represented in
the same manner, by an additional area on top of the reduced line
for the earth pressure, the depth of that area being made in propor-
tion to the intensity of the live load compared with the unit weight
of stone. For example, if the earth filling weighs 100 pounds per
cubic foot, and the stone of the arch weighs 160 pounds per cubic
foot, then each ordinate for the earth load would be JH of the
actual depth of the earth. Likewise, if the live load per square

foot on the arch equals 120 pounds,
then the area representing the live
load would be -\ £ §• of a foot, ac-
cording to the scale adopted for
the arch. The weight of the pav-
ing, if there is any, should be sim-
ilarly allowed for. If we draw
from the upper end of each joint
a vertical line extending to the top
of the reduced load line, then the
area between these two verticals
and between the arch and the load
line represents the weight at the
scale adopted for the drawing, and
at the unit value for the weight
per cubic foot — 160 pounds per
cubic foot, as suggested above —
actually pressing on that particular
voussoir. A line through the cen-
ter of gravity of the stone itself
gives the line of action of the force
of gravity on the voussoir. An approximation to the position of
this center of gravity, which is usually amply accurate, is the point
which is midway between the two joints, and which is also on the
arch curve that lies in the middle of the depth of each voussoir. The
center of gravity of the load on the voussoir is approximately in the
center of its width. The resultant of two parallel forces, such as V
and L, Fig. 231, equals in amount their sum R, and its line of action
is between them and at distances from them such that
ac:bc::L:V

Fig. 231. Graphical Determina
Circular Arch; Span and Ri
Being Known

408

MASONRY AND REINFORCED CONCRETE 397

Usually, the horizontal space between the forces V and L is so
very small that the position of their resultant R can be drawn by
estimation as closely as the possible accuracy of drawing will permit,
without recourse to the theoretically accurate method just given.
The amount of the resultant is determined by measuring the areas,
and multiplying the sum of the two areas by the weight per cubic
foot of the stone. This gives the weight of a section of the
arch ring one foot thick — parallel with the axis of the arch. The
area of the voussoir practically equals the length (between the
joints of that section) of the middle curve, times the thickness
of the arch ring. The area of the load trapezoid equals the hori-
zontal width between the vertical sides, times its middle height.
The student should notice that several of the above statements
regarding areas, etc., are not theoretically accurate; but, with the
usual proportions of the dimensions of the voussoirs to the span
of the arch, the errors involved by the approximations are harmless,
while the additional labor necessary for a more accurate solution
would not be justified by the inappreciable difference in the final
results.

Depth of Keystone. The proper depth of keystone for an arch
should, theoretically, depend on the total pressure on the keystone
of the arch as developed from the force diagram; and the depth
should be such that the unit pressure shall not be greater than a safe
working load on that stone. But since we cannot compute the
stresses in the arch until we know, at least approximately, the
dimensions of the arch and its thickness, from which we may com-
pute the dead weight of the arch, it is necessary to make at least a
trial determination of the thickness. The mechanics of such an
arch may then be computed, and a correction may subsequently be
made, if necessary. Usually, the only correction which would be
made wrould be to increase the thickness of the arch, in case it was
found that the unit pressure on any voussoir wrould become danger-
ously high. Trautwine's Handbook quotes a rule which he declares
to be based on a very large number of cases that were actually
worked out by himself, the cases including a very large range of
spans and of ratios of span to rise. The rule is easily applied, and
is sufficiently accurate to obtain a trial depth of the keystone. It
will probably be seldom, if ever, that the depth of the keystone, as

409

398 MASONRY AND REINFORCED CONCRETE

determined by this rule, would need to be altered. The rule is as
follows :

Vrad. + half-span , //-<\

Depth of keystone, in feet = — -^— - +0.2 ft. (61)

For architectural reasons, the actual keystone of an arch is
usually made considerably deeper than the voussoirs on each side of
it, as illustrated in Fig. 223. When computing the maximum per-
missible pressure at the crown, the actual depth of the voussoirs on
each side of the keystone is used as the depth of the keystone; or,
perhaps it would be more accurate to say that the extrados is drawn
as a regular curve over the keystone, as illustrated in Fig. 233, and
then any extra depth which may subsequently be given to the key-
stone should be considered as mere ornamentation and as not affect-
ing the mechanics of the problem.

ILLUSTRATIVE PROBLEM

Design of Arch with Twenty=Foot Span. The above principles
will be applied to the case of an arch having a span of 20 feet
and a rise of 3 feet. If this arch is to be a circular arch or a seg-
mental arch, the radius which will fulfill
these conditions may be computed as
illustrated in Fig. 232. We may draw a
horizontal line, at some scale, which will
represent the span of 20 feet. At the
center of this line we may erect a perpen-
dicular which shall be 3 feet long, at the
same scale. Joining the points a and c,
Diagram of stresses in and bisecting do at d, we may draw a line
TT^ oHginaThDrae^n0gdated f rom the bisecting point, which is perpen-
dicular to ac, and this must pass through

the center of the required arc. A vertical line through c will also pass
through the center of the required arc, and their intersection will give
the point o. As a graphical check on the work, a circle drawn about o
as a center, and with o c as a radius, should also pass through the
points a and 6. Since some prefer a numerical solution to determine
the radius for a given span and rise, the radius for this case may be
computed as follows: The line ac equals the square root of the
sum of the squares of the half-span and the rise, which equals

410

Reduced

1,2.3

Fig. 233. Diagram Showinli

Loadinq 3

/, ic- to Top of Pavament -^^

£) /Scale of force diagrams
3000 pounds per inc/i

Loading z Loading i

at Vertical Pressure

MASONRY AND REINFORCED CONCRETE 403

"^ac'+ce2; but the angle cae equals angle aod, and, from similar
triangles, we may write the proportion

ao : ad :: ac : ce

adXac_lac _ 1 ae+ce2_ 1 half-span2 + rise2
ce 2ce 2 ce 2 rise

This equals numerically, in the above case, 109-^6 = 18.17.

Applying the above rule for the depth of the keystone, we would
find for this case that the depth should be

= 1.33+0.2
= 1.53 ft.

Since the total pressure on the voussoirs is always greater at the abut-
ment than at the crown, the depth of the stones near the end of the
arch should be somewhat greater than the depth of the keystone.
We shall therefore adopt, in this case, the dimensions of 18 inches
for the depth of the keystone, and 2 feet for the depth at the skew-
back.

Plotting Reduced Load Line. Characteristics of Three Load-
ings. We shall assume that the earth or cinder fill on top of the
arch has a thickness of one foot at the crown, and that it is level
on top. We shall also assume that the arch ring is composed of stones
which weigh 160 pounds per cubic foot and we shall therefore con-
sider 160 pounds per cubic foot as the unit weight in determining
the reduced load line. From the extremities of the extrados, draw
verticals until they intersect the upper line of the earth fill. For
convenience we shall divide the horizontal distance between these
verticals into 1 1 equal parts, each to be about 2 feet wide, Fig. 233.
Draw verticals through these points of division down to the extrados;
then draw radial lines from the extrados to the intrados. These
lines are drawn radially from a point approximately halfway
between the center of the extrados and the center of the intrados.
This means that the joints, instead of being exactly perpendicular to
either the extrados or intrados, have a direction which is a com-

411

404 MASONRY AND REINFORCED CONCRETE

promise between the two. The discrepancy is greatest at the abut-
ments, and approaches zero at the crown. This will divide the arch
ring into 11 voussoirs, together with a keystone at the center or
crown. Assuming that the earth fill weighs 100 pounds per cubic
foot, the lines of division between the 11 sections of the earth fill
should each be reduced to liU or f of its actual depth. If we further
assume that the pavement is a little over six inches thick, and that
its weight is equivalent to six inches of solid stone, we may add a
uniform ordinate equal to six inches in thickness (according to the
scale adopted), and this gives the total dead load on the arch. We
shall assume further a live load amounting to 200 pounds per square
foot over the whole bridge. This is equivalent to f £ £ of a foot, or 1
foot 3 inches of solid masonry over the whole arch. This gives the
reduced load line for the condition of loading where the entire arch
is loaded with its maximum load.

As another condition of loading, we shall assume that the above
load extends only across one-half of the arch. We shall probably
find that, owing to the eccentricity of this form of loading, the sta-
bility of the arch is in much greater danger than when the entire
arch is loaded with a maximum load.

We shall also consider the condition which would be found by
running a twenty-ton road roller over the arch. A complete test of
all the possible stresses which might be produced under this condition
would be long and tedious; but we may make a first trial of it by
finding the stresses which would be produced by placing the road
roller at one of the quarter-points of the arch — a position which would
test the arch almost, if not quite, as severely as any other possible
position. Owing to the very considerable thickness of earth fill, as
well as the effect of the pavement, the load of the roller is distributed
in a very much unknown and very uncertain fashion over a con-
siderable area of the haunch of the arch. The extreme width of such
a roller is eight feet; the weight on each of the rear wheels is approxi-
mately 12,000 pounds. We shall assume that the weight of each
rear wheel is distributed over a width of three feet and a length of four
feet, so that the load on the top of the arch under one of the wheels
may be considered at the rate of 1,000 pounds per square foot over
an area of 12 square feet. For the unit section of the arch one foot
wide, this means a load of 4,000 pounds loaded on two voussoirs

412

MASONRY AND REINFORCED CONCRETE 405

which are four feet in total length. The front roller of the road roller
comes between the two rear rollers, and therefore would affect but
little, if any, the particular arch ring which we are testing. Not only
is it improbable that there would be a full loading of the arch simul-
taneously with that of a road roller, but it is also true that a full
loading would add to the stability of the arch. Yet, in order to make
the worst possible condition, we shall assume that the part of the arch
which has the road roller is also loaded for the remainder of its length
with a maximum load of 200 pounds per square foot; this item alone
will take care of the effect of the front roller. A load of 1,000 pounds
per square foot is the equivalent of a loading of 6 feet 3 inches of
stone; and therefore, if we draw over voussoirs Nos. 3 and 4 a paral-
lelogram having a vertical height above the dead-load line equal to 6
feet 3 inches of stone, and consider a reduced live-load line 15 inches
deep (f g £ equal to 1.25, or 1 foot 3 inches) over the remainder of that
half-span, we have the reduced load line for the third condition of
loading.

The loads on each voussoir are scaled from the reduced load line
according to the various conditions of loading. The area between
the two verticals over each voussoir is measured with all necessary
accuracy by multiplying the horizontal wddth between the verticals
by the scaled length of the perpendicular which is midway between
the verticals. The weight of the voussoir itself may be computed
as accurately as necessary, by multiplying the radial thickness by
the length between the joints as measured on the curve lying half-
way between the intrados and the extrados.

For example, the load for full loading of the arch which is over
voussoir No. 1 is measured as follows: The width between the per-
pendiculars is 2.0 feet; the height measured on the middle vertical is
4.05 feet; the area is therefore 8.10 feet, which, multiplied by 160,
equals 1,296 pounds, which is the load on this voussoir for every foot
of width of the arch parallel with the axis. The radial thickness of
voussoir No. 1 is 1.90 feet, and the length is 2.15 feet; this gives an
area of 4.085 feet, which, multiplied by 160, equals 653.6 pounds.
The weight of the voussoir is, therefore, almost exactly one-half that
of the live and dead loads above it; therefore, the resultant of these
two weights will be almost precisely one-third of the distance between
the center of this stone and the vertical through the center of the

413

406 MASONRY AND REINFORCED CONCRETE

TABLE XXX
First Condition of Loading

VOUSSOIR No.

LOAD

WEIGHT OF VOUSSOIR

TOTAL

1 and 11

1,296

654

1,950

2 and 10

1,135

£92

1,727

3 and 9

1,010

528

1,538

4 and 8

927

483

1,410

5 and 7

880

456

1,336

867

1,322

Second Condition of Loading Third Condition of Loading

VOUSSOIR No.

TOTAL LOAD

VOUSSOIR No.

TOTAL LOAD

1,950

1,727 '

1,727

,538

3,138

1,410

3,010

1,336

,336

1,122

,122

936

1,010

,010

,138

1,327

,327

1,550

,550

loading. By drawing this line, we have the line of action of the
resultant of these two forces, and this value is the sum of 1 ,296 and
654, or 1,950 pounds.

In order to simplify the figure, the arrows representing the lines
of force of the loading on the voussoir and the weight of the voussoir
have been omitted from the figure, and only their resultant is drawn
in. It was of course necessary to draw in these forces in pencil and
obtain the position of the resultant, as explained in Fig. 231; and
then, for simplicity, only the resultant was inked in.

The loads on the other voussoirs are computed similarly. The
numerical values for the loads on the various voussoirs— including
the weights of the voussoirs — are given in Table XXX.

For this first condition of loading, the total loads for voussoirs
Nos. 7, 8, 9, 10, and 11 will be the same as those for voussoirs 5, 4,
3, 2, and 1, respectively.

The loads for the second condition of loading are found by using
the same load on the first five voussoirs, but with only half of the live
load on voussoir No. 6, which means that the load for the first con-

414

MASONRY AND REINFORCED CONCRETE 407

dition of loading (1,322 pounds) is reduced by 200 pounds, making it
1,122 pounds. Voussoirs Nos. 7 to 1 1 are each reduced by 400 pounds.

The loads for the third condition of loading are found by using
the same loads as were employed for the second condition, except
that for voussoirs Nos. 3 and 4, 1,600 pounds should be added to
each load.

Fig. 233 was originally drawn at the scale of \ inch equal to 1
foot, and with the force diagram at the scale of 1,500 pounds per inch.
The photographic reproduction has, of course, changed these scales
somewhat. The student should redraw the figure at these scales,
and should obtain substantially the same final results.

Drawing the Load Line for the First Condition of Loading. When
the load is uniformly distributed over the entire arch, the load is
symmetrical, and we need to consider only one-half of the arch. The
sections of the load line for the force diagram corresponding to this
condition of loading must be drawn as explained in detail on page
386. Since the arch is quite flat, the loading is considered to be
entirely vertical. Since the load is symmetrical and the abutments
are at the same elevation, we need only draw a horizontal line from
the lower end of the half-load line, and select on it a trial position
(GI) for the pole, drawing the rays as previously explained; the trial
equilibrium polygon passes through the center vertical at the point
a'. Drawing a horizontal line from a' until it intersects the first
line (produced) of the trial equilibrium polygon, and drawing through
it a vertical line, we have the line of action of the resultant (R\) of
all the forces on that half of the arch. If we draw through a, the
center of the keystone, a horizontal line, its intersection with RI
gives a point in the first line (produced) of the true equilibrium
polygon. A line from the upper end of the load line parallel to this
first section of the true equilibrium polygon intersects the horizontal
line through the middle of the load line at o\, which is the position
of the true pole. Drawing the rays from the true pole to the load
line, and drawing the segments of the true equilibrium polygon
parallel to these rays, we may at once test whether the true equilib-
rium polygon always passes through the middle third of each joint.
As is almost invariably the case, it is found that for full loading, the
true equilibrium polygon passes within the middle third at every
joint.

415

408 MASONRY AND REINFORCED CONCRETE

The student should carefully check over all these calculations,
drawing the arch at the scale of one-half inch to the foot, and the
load line of the force diagram at the scale of 1,500 pounds per inch;
then the rays of the true equilibrium polygon will represent at that
scale the pressure at the joints. Dividing the total depth of any
joint by the pressure found at that joint gives the average pressure.
In the case of the joint at the crown, the total pressure at the joint
is 13,900 pounds. The depth of the joint is 1.5 feet, and the area of
the joint is 216 square inches; therefore the average unit pressure is
64 pounds per square inch; if it is assumed that the line of pressure
passes through either edge of the middle third, then the pressure at
the edge of the joint is twice the average, or is 128 pounds per
square inch. This is a very low pressure for any good quality of
building stone.

Similarly, the maximum pressure at the skewback is scaled from
the force diagram as 16,350 pounds; but since the arch is here two
feet thick, and the area is 288 square inches, it gives an average
pressure of 57 pounds per square inch. Since this equilibrium poly-
gon is supposed to start from the center of this joint, it represents
the actual pressure.

Usually, it is only a matter of form to make the test for uniform
full loading. Eccentric loading nearly always tests an arch more
severely than uniform loading. The ability to carry a full uniform
load is no indication of ability to carry a partial eccentric loading,
except that if the arch appeared to be only just able to carry the uni-
form load, it might be predicted that it would probably fail under
the eccentric load. On the other hand, if an arch will safely carry a
heavy eccentric load, it will certainly carry a load of the same inten-
sity uniformly distributed over it.

Test for the Second Condition, or Loading of Maximum Load over
One- Half of the Arch. Since the arch has a dead load over the entire
arch, and a live load over only one-half of the arch, the load line for
the entire arch must be drawn. The load line for the loaded half of
the arch will be identical with that already drawn for the previous
case. The load line for the remainder of the arch may be similarly
drawn. This case is worked out by precisely the same general
method as that already employed in the similar case given in detail
on page 407. As in that instance, we select a trial pole which in

416

MASONRY AND REINFORCED CONCRETE 409

general will give an oblique closing line for the equilibrium polygon.
This closing line must be brought down to the horizontal by the
method already explained on page 388; then a second trial must be
made, in order to shift the polygon so that it shall pass through the
middle third at the crown joint. This line should pass through
the middle of the crown joint; the real test is then to determine how
it passes through the haunches of the arch. As in the previous case,
the total pressure at any joint will be determined by the correspond-
ing lines in the force diagram, and the unit pressure at the joint may
be determined from the area of the joint and the position of the line
of force with respect to the center of the joint. Even though a line
of force passed slightly outside of the middle third, it would not
necessarily mean that the arch will fail, provided that the maximum
intensity of pressure, determined according to the principles enunci-
ated on page 393, does not exceed the safe unit pressure for the kind
of stone used.

An inspection of the force diagram with the pole at o2' shows
that the rays are all shorter than those of the force diagram for the
first condition of loading — with pole at o/. This means that the
actual pressure at any joint is less than for the first case; but since
the true equilibrium polygon for this case does not pass so near the
center of the joints as it does for the first condition of loading, the
intensity of pressure at the edges of the joints may be higher than in
the first case. However, since the equilibrium polygon for this
second case is always well within the middle third at every joint, and
since even twice the average joint pressure for the first case is well
within the safe allowable pressure on any good building stone, we
may know that the second condition of loading will be safe, even
without exactly measuring and computing the maximum intensity of
pressure produced by this loading.

Test for the Third Condition, Involving Concentrated Load. The
method of making this test is exactly similar to that previously given;
but, on account of a load eccentrically placed, the force diagram will
be more distorted than in either of the cases previously given, and
there is greater danger that the arch will prove to be unstable on
such a test. An inspection of the equilibrium polygon for this case
shows that the critical point is the joint between voussoirs Nos. 3
and 4. This is what might be expected, since it is the joint under

417

410 MASONRY AND REINFORCED CONCRETE

the heavy concentrated load. The ray in the force diagram which
is parallel to the section of the equilibrium polygon passing through
this joint is the ray which reaches the load line between loads 3 and
4. This ray, measured at the scale of 1,500 pounds per square inch,
indicates a pressure of 15,625 pounds on the joint. The line of
pressure is 4| inches from the upper edge of the joint; it is outside
of the middle third; and therefore the joint will probably open some-
where under this loading. According to the theory of the distribu-
tion of pressure over a stone joint, the pressure will be maximum on
the upper edge of this joint, and will be zero at three times 4f inches,
or 14.25 inches, from the upper edge. The area of pressure for a
joint 12 inches wide will be 14.25X12, or 171 square inches. Divid-
ing 171 into 15,625, we have an average pressure of 91 pounds, or a
maximum pressure of twice this, or 182 pounds, per square inch at
the edge of the joint. But this is so safe a wrorking pressure for such
a class of masonry as cut-stone voussoirs, that the arch certainly
would not fail, even though the elasticity of the stone caused the
joint to open slightly at the intrados during the passage of the steam
roller.

Correcting a Design. The above general method of testing an
arch consists of first designing the arch, and then testing it to see
whether it will satisfy all the required conditions. In case some
condition of loading is found which will cause the line of pressure to
pass outside of the middle third or to introduce an excessive unit
pressure in the stones, it is theoretically necessary to begin anew
with another design, and to make all the tests again on the basis of a
new design; but it is usually possible to determine with sufficient
closeness just what alterations should be made in the design so that
the modified design will certainly satisfy the required conditions.
For example, if the line of pressure passes on the upper side of the
middle third at the haunches of the arch, a thickening of the arch at
that point, until the line of pressure is within the middle third
of the revised thickness, will usually solve the difficulty. The
effect of the added weight on the haunch of the arch will be to
make the line of pressure move upward slightly; but the added
thickness can allow for this. As another illustration, the unit pres-
sure, as determined for the crown of the arch, might be considerably
in excess of a safe pressure for the arch, and it might indicate a

418

MASONRY AND REINFORCED CONCRETE 411

necessity to thicken the arch, not only at the center, but also
throughout its entire length.

For example, in the above numerical case, although it is prob-
ably not really necessary to alter the design, the arch might be
thickened on the haunches, say, 3 inches. This would add to the
weight on the haunches one-fourth of the difference of the weights
per cubic foot of stone and earth, or | (160 — 100), or 15 pounds per
square foot. This is so utterly insignificant compared with the
actual total load of about 750 pounds per square foot, that its effect
on the line of pressure is practically inappreciable, although it should
be remembered that the effect, slight as it is, will be to raise the line
of pressure. A thickening of 3 inches will leave the line of pressure
nearly 7f inches — or, say, 1\ inches, to allow generously for the
slight raising of the line of pressure — from the extrados, while the
thickness of the arch is increased from 19 inches to 22 inches. But
the line of pressure would now be within the middle third.

Location of True Equilibrium Polygon. In the above demon-
stration, it is assumed that the true equilibrium polygon will pass
through the center of each abutment, and also through the center
of the keystone; and the test then consists in determining whether
the equilibrium polygon which is drawn through these three points
will pass within the middle third at every joint, or at least whether
it will pass through the joints in such a way that the maximum
intensity of pressure at either edge of the joint shall not be greater
than a safe working pressure. With any system of forces acting on
an arch, it is possible to draw an infinite number of equilibrium
polygons; and then the question arises, which polygon, among the
infinite number that can be drawn, represents the true equilibrium
polygon and will represent the actual line of pressure passing through
the joints. On the general principle that forces always act along the
line of least resistance, the pressure acting through any voussoir
would tend to pass as nearly as possible through the center of the
voussoir; but since the forces of an equilibrium polygon, which rep-
resent a combination of lines of pressure, must all act simultaneously,
it is evident that the line of pressure will pass through the voussoirs
by a course which will make the summation of the intensity of pres-
sures at the various joints a minimum. It is not only possible, but
probable, that the true equilibrium polygon does not pass through the

419

412 MASONRY AND REINFORCED CONCRETE

center of the keystone, but at some point a little above or below,
through which a polygon may be drawn which will give a less sum-
mation of pressures than those for a polygon which does pass through
the point a. The value and safety of the method given above lie
in the fact that the true equilibrium polygon always passes through
the voussoirs in such a way that the summation of the intensities of
the pressures is the least possible combination of pressures; and,
therefore, any polygon which can be drawn through the voussoirs in
such a way that the pressures at all the joints are safe merely indi-
cates that the arch will be safe, since the true combination of pressures
is something less than that determined. In other words, the true
system of pressures is never greater, and is probably less, than the
system as determined by the equilibrium polygon, which is assumed
to be the true polygon.

When an equilibrium polygon for eccentric loading passes
through the arch at some distance from the center of the joint at one
part of the arch, and very near the center of the joint in all other
sections, it can be safely counted on, that the true polygon passes a
little nearer the center at the most unfavorable portion, and a little
farther away from the center at some other joints where there is a
larger margin of safety. For example, the true equilibrium polygon
for the third condition of loading, Fig. 233, probably passes a little
nearer the center on the left-hand haunch, and a little farther away
from the center on the right-hand haunch, where there is a larger
margin; in other words, the whole equilibrium polygon is slightly
lowered throughout the arch. No definite reliance should be placed
on this allowance of safety; but it is advantageous to know that
the margin exists, even though that margin is very small. The
margin, of course, would reduce to zero in case the equilibrium poly-
gon chosen actually represented the true equilibrium polygon.
While it would be convenient and very satisfactory to be able to
obtain always the true equilibrium polygon, it is sufficient for the
purpose to obtain a polygon which indicates a safe condition when
we know that the true polygon is still safer.

Design of Abutments. Pressure Diagram. The force diagram
of Fig. 233, which shows the pressures between the voussoirs of the
arch, also gives, for any condition of loading, the pressure of the last
voussoir against the abutment. A glance at the diagram shows that

420

MASONRY AND REINFORCED CONCRETE 413

the maximum pressure against the abutment comes against the left-
hand abutment under the third condition of loading, when the con-
centrated load is on the left-hand side of the arch. Although the
first condition of loading does not create so great a pressure against
the left-hand abutment, yet the angle of the line of pressure is some-
what flatter, and this causes the resultant pressure on the base of
the abutment to be slightly nearer the rear toe of the abutment. It
is therefore necessary to consider this case, as well as that of the
third condition of loading.

Failure of Abutments. An abutment may fail in three ways: (1)
by sliding on its foundations; (2) by tipping over; and (3) by crush-
ing the masonry. The possibility of failure by crushing the masonry
at the skewback may be promptly dismissed, provided the quality of
the masonry is reasonably good, since the abutment is always made
somewhat larger than the arch ring, and the unit pressure is there-
fore less. The possibility of failure by the crushing of the masonry
at the base, owing to an intensity of pressure near the rear toe of the
abutment, will be discussed below. The possibility that the abut-
ment may slide on its foundations is usually so remote that it hardly
need be considered. The resultant pressure of the abutment on its
subsoil is usually nearer to the perpendicular than is the angle of
friction; and in such a case, there will be no danger of sliding, even if
there is no backing of earth behind the abutment, such as is almost
invariably found.

The test for possible tipping over or crushing of the masonry,
due to an intensity of pressure near the rear toe, must be investi-
gated by determining the resultant pressure on the subsoil of the
abutment. This is done graphically by the method illustrated in
Fig. 234. This is an extension of the arch problem already consid-
ered. The line be gives the angle of the skewback at the abutment,
while the lines of force for the pressures induced by the first and third
conditions of loading have been drawn at their proper angle. In
common with the general method used in designing an arch, it is
necessary to design first an abutment which is assumed to fulfill the
conditions, and then to test the design to see whether it is actually
suitable. The cross section abcde has been assumed as the cross
section of solid masonry for the abutment. The problem, therefore,
consists in finding the amount and line of action of the force repre-

421

414 MASONRY AND REINFORCED CONCRETE

senting the weight of the abutment. It will be proved that this
force passes through the point o5, and it therefore intersects the
pressure on the abutment for the first condition of loading, at the
point k. The weight of a section of the abutment one foot thick —
parallel with the axis of the arch — is computed, as detailed below, to
weigh 19,500 pounds, while the pressure of the arch is scaled from
Fig. 233 as 16,350 pounds. Laying off these forces on these two lines
at the scale of 5,000 pounds per inch, we have the resultant, which

Fig. 234. Diagram of Forces Acting on Abutments

intersects the base at the point ra, and which scales 31,350 pounds.
Similarly, the resultant of the weight of the abutment and the line
of pressure for the third condition of loading intersects the base at
the point n, and scales 33,600 pounds. These pressures on the base
will be discussed later.

Line of Action. The line of action and the amount of the
weight of a unit section of the abutment are determined as follows:
The center of gravity of the pentagon abcde is determined by
dividing the pentagon into three elementary triangles, abe, bee,
and cde. We may consider be as a base which is common to the

422

MASONRY AND REINFORCED CONCRETE 415

triangles abe and bee. By bisecting the base be and drawing lines
to the vertices a and c, and trisecting these lines to the vertices, we
determine the points o\ and o2, which are the centers of gravity,
respectively, of the two triangles. The center of gravity of the
combination of the two triangles must lie on the line joining 01 and
o2, and must be located on the line at distances from each end which
are inversely proportional to the areas of the triangles. Since the
triangles have a common base be, their areas are proportional to
their altitudes af and g c. In the diagram at the side, we may lay
off in succession, on the horizontal line, the distances gc and af.
On the vertical line, we lay off a distance equal to Oi02. By joining
the lower end of this line with the right-hand end of the line af, and
then drawing a parallel line from the point between gc and af, we
have divided the distance Oi02 into two parts which are proportional
to the two altitudes af and gc. Laying off the shorter of these
distances toward the triangle abe (since its greater altitude shows
that it has the greater area), we have the position of o3, which is the
center of gravity of the two triangles combined. The area abce is
measured by one-half the product of eb and the sum of af and gc.
The triangle cde is measured by one-half the product of the base
ed by the altitude ch. If we lay off b e as a vertical line in the side
diagram, and also the line ed as a vertical line, and join the lower
end of ed with the line which represents the sum of gc and af, and
then draw a line from the lower end of be, parallel with this other
line, we have two similar triangles from which we may write the
proportion

ed : (gc+af) :: be : a'f'g'c'

Since the product of the means equals the product of the extremes,
we find that (gc+af)Xbe = edXa'f'g'c'; but | (gc+af)Xbe equals
the combined area of the two triangles, and therefore the line a'f'g'c'
is the height of an equivalent triangle whose base equals ed; there-
fore the area of these two combined triangles is to the" area of the
triangle cde as the equivalent altitude a'f'g'c' is to the altitude ch
of the triangle cde. By bisecting the base ed, and drawing a line
from the bisecting point to the point c, and trisecting this line in the
point o4, we have the center of gravity of the triangle cde. The
center of gravity of the entire area, therefore, lies on the line o3o4,
and at a distance from o4 which is inversely proportional to the

423

416 MASONRY AND REINFORCED CONCRETE

areas of the two combined triangles and. the triangle cde. These
areas are proportional to the altitudes as determined above; there-
fore, by laying off in the side diagram the line o3o4, and drawing a
line from its lower extremity to the right-hand extremity of the line
ch, and then drawing a parallel line from the point between a'f'g'c'
and ch, we divide the line o3o4 into two parts which are proportional
to these altitudes. The line ch is the greater altitude, and the tri-
angle cde has the greater area; therefore, the point 05 is nearer to
the point o4 than it is to the point 03, and the shorter of these two
sections is laid off from the point o4. This gives the point o5, which
is the center of gravity of the entire area of the abutment.

Weight of Unit Section. The actually computed weight of a
unit section of the abutment is determined by multiplying the sum
of a'f'g'c' and ch by the base ed. Since this masonry is assumed to
weigh 160 pounds per cubic foot, the product of these scaled dis-
tances, measured at the scale of | inch equal to one foot, which was
the scale adopted for the original drawing, shows that the section
one foot thick has a weight of 19,500 pounds. Laying off this weight
from the point k, and laying off the pressure for the first condition of
loading, 16,350 pounds, at the scale of 5,000 pounds per inch, and
forming a parallelogram on these two lines, we have the resultant
of 31,350 pounds as the pressure on the base of the abutment, that
pressure passing through the point m.

Line of Pressure. The intersection of the weight of the abut-
ment with the line of pressure for the third condition of loading is a
little below the point k; and we similarly form a parallelogram which
shows a resulting pressure of 33,600 pounds, passing through the
base at the point n. It is usually required that such a line of pres-
sure shall pass through the middle third of the abutment; but there
are other conditions which may justify the design, even when the
line of pressure passes a little outside of the middle third.

The point n is 2.85 feet from the point e. According to the
theory of pressures enunciated on page 393, it may be considered that
the pressure is maximum at the point e, and that it extends backward
toward the point d for a distance of three times en, or a distance of
8.55 feet. This would give an average pressure of 3,930 pounds per
square foot, or, since the pressure at the toe is twice the average
pressure, 7,860 pounds per square foot on the toe. Such a pressure

424

MASONRY AND REINFORCED CONCRETE 417

might or might not be greater than the subsoil could endure without
yielding. Since this pressure is equivalent to about 55 pounds per
square inch, there should be no danger that the masonry itself would
fail; and, if the subsoil is rock or even a hard, firm clay, there will be
no danger in trusting such a pressure on it.

Effect of Back Pressure. Another very large item of safety
which has been utterly ignored, but which would unquestionably be
present, is the pressure of the earth back of the abutment. The
effect of the back pressure of the earth would be to make the line
which represents the resultant pressure on the subsoil more nearly
vertical, and to make it pass much more nearly through the center
of the base ed. This would very much reduce the intensity of
pressure near the point e, and would reduce very materially the unit
pressure on the subsoil. Cases, of course, are conceivable, in which
there might be no back pressure of earth against the rear of the
abutment. In such cases, the ability of the subsoil to withstand
the unit pressure at the rear toe of the abutment — near the point e —
must be more carefully considered. In order that the investigation
shall be complete, it should be numerically determined whether the
lower pressure, 31,350 pounds, passing through the point ra, might
produce a greater intensity of pressure at the point e than the larger
pressure passing through the point n.

Various Forms of Abutments. The abutment described above
is the general form which is adopted very frequently. The front
face cd is made with a batter of one in twelve. The line b a slopes
backward from the arch on an angle which is practically the continu-
ation of the extrados of the arch. The total thickness of the abut-
ment de must be such that the line of pressure will come nearly, if
not quite, within the middle third. The line ea generally has a con-
siderable slope, as is illustrated. When the subsoil is very soft, so
that the area of the base is necessarily very great, the abutment is
sometimes made hollow, with the idea of having an abutment with a
very large area of base, but one which does not require the full weight
of so much masonry to hold it down; and therefore economy is sought
in the reduction of the amount of masonry. As such a hollow
abutment would require a better class of masonry than could be used
for a solid block of masonry, it is seldom that there is any economy in
such methods. Since the abutment of an arch invariably must

425

418 MASONRY AND REINFORCED CONCRETE

withstand a very great lateral thrust from the arch, there is never
any danger that the resultant pressure of the abutment on the sub-
soil will approach the front toe of the arch, as is the case in the
abutment of a steel bridge, which has little or no lateral pressure
from the bridge, but which is usually subjected to the pressure 'of
the earth behind it. These questions have already been taken up
under the subject of abutments for truss bridges, in Part II.

VOUSSOIR ARCHES SUBJECTED TO OBLIQUE FORCES
Determination of Load on a Voussoir. The previous determin-
ations have been confined to arches which are assumed to be acted
on solely by vertical forces. For flat seg-
mental arches, or even for elliptical arches
where the arch is very much thickened at
each end so that the virtual abutment of
the arch is at a considerable distance above
the nominal springing line, such a method
is sufficiently accurate, and it has the ad-
vantage of simplicity of computation; but
where the arch has a very considerable
rise in comparison with its span, the
pressure on the extrados, which is pre-
sumably perpendicular to the surface of
the extrados, has such a large horizontal
component that the horizontal forces can-
not be ignored. The method of determin-
ing the amount and direction of the force
acting on each voussoir is illustrated in
Fig. 235. The reduced load line, found
as previously described, is indicated in
the figure. A trapezoid represents the
loading resting on the voussoir a c. The
line c?/ represents, at some scale, the
amount of this vertical loading. Drawing
the line de perpendicular to the extrados ac, we may complete the
rectangle on the line df, and obtain the horizontal component, while
the equivalent normal pressure on the voussoir is represented by de.
This method, although simple, is inaccurate because it disregards the

Fig. 235. Diagram of Result
Oblique Pressures

426

MASONRY AND REINFORCED CONCRETE 419

effect of the friction of the earth on the voussoir, which will invari-
ably reduce the horizontal component by some uncertain amount.
The actual horizontal component is ah indeterminate quantity
except on the basis of assumptions which are perhaps unwar-
ranted.

Drawing a vertical line through the center of gravity of the vous-
soir, and producing it, if necessary, until it intersects ed in the point
v, we may lay off vw to represent, at the same scale, the weight of the
voussoir. Making vs equal to de, we find vt as the resultant of the
forces; and it therefore measures, according to the scale chosen, the
amount and direction of the resultant of the forces acting on that
voussoir. Although the figure apparently shows the line de as
though it passed through the center of gravity of the voussoir, and
although it generally will do so very nearly, it should be remembered
that de does not necessarily pass through the center of gravity of
the voussoir.

A practical graphical method of laying off the line xt to represent
the actual resultant force is as follows: The reduced load line,
drawn as previously described, gives the line for a loading of solid
stone, which would be the equivalent of the actual load line. If this
loading has a unit value of, say, 160 pounds per cubic foot, and if
the horizontal distance a 6 is made 2 feet for the load over each
voussoir, then each foot of height (at the same scale at which a 6
represents 2 feet) of the line gd represents 320 pounds of loading.
If the voussoir were actually a rectangle, then its area would be
equal to that of the dotted parallelogram vertically under ac, and
its area would equal abxdk; and in such a case dk would represent
the weight of that voussoir, and the force vw could be scaled directly
equal to dk, without further computation. The accuracy of this
method, of course, depends on the equality of the dotted triangle
below c and that below a. For voussoirs which are near the crown
of the arch, the error involved by this method is probably within the
general accuracy of other determinations of weight; but near the
abutment of a full-centered arch, the inaccuracy would be too great
to be tolerated, and the area of the voussoir should be actually
computed. Dividing the area by 2 (or the width a&), we have the
equivalent height in the same terms at which gd represents the
external load, and its equivalent height would be laid off as vw.

427

420 MASONRY AND REINFORCED CONCRETE

ILLUSTRATIVE PROBLEM

Application to Full=Centered Arch. Assumed Dimensions. We
shall assume for this case a full-centered circular arch whose intrados
has a radius of 15 feet. The depth of the keystone computed
according to the rule given in Equation (61), would be 1.57 feet,
which is practically 19 inches. By drawing first the intrados of the
arch as a full semicircle, as in Fig. 236, and then laying off the crown
thickness of 19 inches, we find by trial that a radius of 20 feet for the
extrados will make the arch increase to a thickness of about 1\ feet
at a point 45 degrees from the center, which is usually a critical point
in such arches. We shall therefore draw the extrados with a radius
of 20 feet, the center point being determined by measuring 20 feet
down from the top of the keystone. We shall likewise assume that
this arch is one of a series resting on piers which are 4 feet thick at
the springing line.

By drawing a portion of the adjoining arch, we find that its
extrados intersects the extrados of the arch considered, at a point
about 7 feet 6 inches above the pier. By drawing a line from this
point toward the center for joints, lying about midway between the
center for the extrados and the center for the intrados, we have the
line for the joint which is virtually the skewback joint and the abut-
ment of the arch.

Assumed Earth and Track Loads. The center of the pier is
precisely 17 feet from the center of the arch. We shall assume that
the arch is overlaid with a filling of earth or cinders which is 18
inches thick at the crown, and that it is level. Drawing a hori-
zontal line to represent the top of this earth filling, we may divide
this line into sections which are 2 feet wide, commencing at the ver-
tical line through the center of the pier. Extending this similarly to
the other side of the arch, we have eight sections of loading on each
side of the keystone section. Drawing lines from the points where
these verticals between the sections intersect the extrados, toward
the center for joints, previously determined, we have the various
joints of the voussoirs. Assuming, as in the previous numerical
problem, that the cinder fill weighs 100 pounds per cubic foot, and
that the stone weighs 160 pounds per cubic foot, we determine the
reduced load line for the top of the earth fill over the entire arch.

We shall assume that the arch carries a railroad track and a

423

Reduced Load Line, for Locomotive ^

Fig. 236. Diagram of Resultant Forces Acting

90 500 0

1000 2000 3000 -4-000 5000 6000

Scale, of Forces -I706pounfo per inch.

"PT?
i I

issoirs of a Full-Centered Arch. Scale & Inch = 1 Foot

MASONRY AND REINFORCED CONCRETE 425

heavy class of traffic. The weight of roadbed and track may be
computed as follows: The ties are to be 8 feet long; the weight of
the roadbed and track (and also the live load) is assumed to be dis-
tributed over an area 8 feet wide.

Two rails at 100 pounds per yd. will weigh, per sq. ft. of surface 8.4 Ib.

Oak ties, weighing 150 pounds per tie, will weigh, per sq. ft. of surface. . 9 . 4 Ib.
Weight of ballast, at 100 pounds per cu. ft.; average depth 9 in 75.0 Ib.

Total weight 92.8 Ib.

This is the equivalent of 0.58 foot depth of stone, and we therefore
add this uniform depth to the reduced load line for the earth.

Assumed Live Load. A 50-ton freight-car, fully loaded, will
weigh 134,000 pounds; with a length between bumpers of 37 feet,
this will exert a pressure of about 450 pounds per square foot on a
strip 8 feet wide. This is equivalent to 2.8 feet of masonry. We
shall therefore consider this as a requirement for uniform loading
over the whole arch.

Summary of Conditions of Loading. It would be more precise
to consider the actual wheel loads for the end trucks of two such cars
which are immediately following each other; but since the effect of
this would be even less than that of the calculation for a locomotive,
which will be given later, and since the deep cushion of earth filling
will largely obliterate the effect of concentrated loads, the method of
considering the loading as uniformly distributed will be used. We
therefore add the uniform ordinate equal to 2.8 feet over the whole
arch. We shall call this the first condition of loading.

We shall assume for the concentrated loading, a consolidation
locomotive with 40,000 pounds on each of the four driving axles,
spaced 5 feet apart. This means a wiieel base 15 feet long; and we
shall assume that this extends over voussoirs 1 to 8 inclusive, while
the loading of 450 pounds per square foot is on the other portion of
the arch. A weight of 40,000 pounds on an axle, which is supposed
to be distributed over an area 5 feet long and 8 feet wide, gives a
pressure of 1,000 pounds per square foot, or it would add an ordinate
of 6.33 feet of stone; these ordinates are added above the load line
representing the load of the roadbed and track. We shall call this
the second condition of loading.

Method of Computing Loads. The load for each voussoir is
determined by the method given on page 418. The direction of the

429

426 MASONRY AND REINFORCED CONCRETE

pressure on the voussoir is determined by drawing a line toward the
extrados center from the intersection of the vertical through the
trapezoid of loading with the extrados. The length of that vertical
is laid off below that point of intersection; then a horizontal line
drawn from the lower end of the vertical intersects the line of force
at a point which measures the amount of that pressure on the vous-
soir. The area of the voussoir is determined as described on page
418; and the resultant of the loading and the weight of the voussoir
is obtained. This is indicated as force No. 1 in Fig. 236. In this
case, it includes the locomotive loading on the left-hand side of the
arch. The forces acting on voussoirs Nos. 2, 3, 4, 5, 6, 7, and 8 are
similarly determined. The forces on voussoirs Nos. 9 to 17, inclu-
sive, on the basis of the uniformly distributed load equal to 450
pounds per square foot, are also similarly determined. The loads on
voussoirs Nos. 10 to 17, inclusive, will be considered to measure the
loads on voussoirs Nos. 8 to 1, inclusive, for the first condition of
loading. The loading with the locomotive over voussoirs Nos. 1 to
8, and cars over voussoirs Nos. 9 to 17, constitutes the second condi-
tion of loading.

As described above, the arrows representing the forces in Fig.
236 are drawn at a scale such that each f of an inch represents 2
cubic feet of masonry, or 320 pounds; therefore every inch will
represent the quotient of 320 divided by f , or 853 pounds per lineal
inch. The practical method of making a scale for this use is illus-
trated in the diagram in the upper right-hand corner of Fig. 236.
We may draw a horizontal line as a scale line, and lay off on it, with
a decimal scale, a length ca which represents, at some convenient
scale, a length of 800. Drawing the line a b at any convenient angle,
we lay off from the point c the length cb to represent 853 at the
same scale as that used for ca. The line cd is then laid off to repre-
sent 7,000 units at the scale of 800 units per inch. By drawing a line
from d parallel to b a, we have the distance ce, which represents
7,000 units at the scale of 853 units per inch. By trial, a pair of
dividers may be so spaced that it steps off precisely seven equal
parts for the distance ce; or the line ce may also be divided into
equal parts by laying off on cd to the decimal scale, the seven equal
parts of 1,000, each of which is at the scale of 800 units per inch;
and then lines may be drawn from these points parallel to b a and de.

430

Special zyuil polygon for second
condition of loading

Fig. 237. Diagram of Pressures on Voussoin

v first condition of loading

•**

Jcale offeree diagram
8000 pounds per inch

W-i'-o*

'nil-Centered Arch. Scale A Inch = 1 Foot

MASONRY AND REINFORCED CONCRETE 431

The last division may be similarly divided into 10 equal parts, which
will represent 100 pounds each. Using dividers, the resultant force
on each voussoir from No. 1 to No. 17 may be scaled off as follows:

7,825

3,170

2,400

5,970

3,040

2,905

4,940

1,880

3,570

4,190

1,910

4,420

3,725

2,040

6,005

3,380

2,200

Graphical Check. Note the three dotted curves in the lower
part of Fig. 236, which have been drawn through the extremities
of the forces. The object in drawing these three curves is merely
to note the uniformity with which the ends of these arrows form a
regular curve. If it were found that one of the forces did not pass
through this curve, it would probably imply a blunder in the method
of determining that particular force. Even if such curves are not
actually drawn in, it is well to observe that the points do come on a
regular curve, as this constitutes one of the checks on the graphical
solution of problems.

Fig. 236 is merely the beginning of the problem of determining
the stresses in the arch. In order to save the complication of the
figure, the arch itself and the resultant forces (1 to 17) are repeated
in Fig. 237, the direction, intensity, and point of application of these
forces being copied from one figure to the other.

Pressure Diagram for Both Conditions of Loading. Forces Nos.
1 to 17 are drawn in the force diagram of Fig. 237 at the scale of
4,000 pounds per inch. Forces 1 to 8, inclusive, have a resultant
whose direction is given by the line marked R\ which joins the
extremities of forces 1 to 8. Similarly, the direction of the resultant
(R\ or jR2') of forces 9 to 17, inclusive, is given by the line which
joins the extremities of this group. The direction of the resultant
of all the forces, Nos. 1 to 17, is given by the line joining the extremi-
ties of these forces in the force diagram, this resultant being marked
7?2. By choosing a pole at random (the point o2' in the force dia-
gram), drawing rays to the forces, and beginning at the left-hand
abutment, we may draw the trial equilibrium polygon, which passes
through the point a on force No. 17. The line through a, parallel to

431

432 MASONRY AND REINFORCED CONCRETE

the last ray, has the direction a b. Producing the section of the
polygon which is between forces 8 and 9 — and which is parallel to
the ray which reaches the load line between forces 8 and 9 — it inter-
sects the first and last lines of the trial equilibrium polygon at the
points b and d. The point b is, therefore, a point on the resultant /?/
of forces Nos. 9 to 17, inclusive; and by drawing a line parallel to the
force RI' in the force diagram, we have the actual line of action of the
resultant.

Similarly, the line of action of the force R2" is determined by
drawing from the point d a line parallel to RJ' in the force diagram.
Their intersection at the point e gives a point in the line of action of
the resultant of the whole system of forces, J??2; and by drawing from
the point e a line parallel to 7?2 of the force diagram, we have the line
of action of 7?2. We select a point / at random on the resultant R%,
and join the point/ with the center of each abutment. By drawing
lines from the extremities of the load line parallel to these two lines
from/, they intersect at the point o2". A horizontal line through o2"
is therefore the locus of the pole of the true equilibrium polygon
passing through the center of both abutments. The line fn inter-
sects Rz in the point g, and the line fm intersects the force Rz" in
the point h. The intersection of gh with the vertical through the
center — the point i — is the trial point which must be raised up to
the point c, which is done by the method illustrated on page 390.
The application of this method gives the line kl, passing through c;
and the line In is therefore the first line of the special equilibrium
polygon for the complete system of forces from No. 1 to No. 17; and
the line k m is similarly the last line of that polygon. By drawing lines
from the extremities of the load line, parallel to In and km, we find
that they intersect at the point o2'", which is the pole of the special
equilibrium polygon passing through n, c, and m, for the complete
system of forces Nos. 1 to 17.

As a check on the work, the intersection of these lines from the
ends of the load line, parallel to In and km, must be on the hori-
zontal line passing through o2". By drawing rays from the new pole
o2"' to the load line, and completing the special equilibrium polygon,
we should find, as a double check on the work, that both of these
partial polygons starting from m and n should pass through the point
c; and also that the section of the polygon between forces Nos. 8

432

MASONRY AND REINFORCED CONCRETE 433

and 9 lies on the line kl. This gives the special equilibrium polygon
for the system of forces Nos. 1 to 17, which corresponds with the
second condition of loading, as specified above.

The first condition of loading is given by duplicating about the
center, in the force diagram, the system of forces from No. 17 to No.
9, inclusive. Since this system of forces is symmetrical about the
center, we know that its resultant RI passes through the center of
the arch, and that it must be a vertical force. We may draw from
the middle of force No. 9 a horizontal line, and also draw a vertical
from the lower end of the load line. Their intersection is evidently
at the center of the resultant RI, which is, therefore, carried above
this horizontal line for an equal amount. Joining the upper end of
RI with the upper end of force No. 9, we have the direction and
amount of the force RI". The intersection of n g with the force R\
at the point j, gives a point which, when joined with the point ra,
gives one line of a trial equilibrium polygon passing through the
required points m and n, but which does not pass through the required
point c. The intersection of jra with the force Rf at the point p,
gives us the line pg, which is the same kind of line for this trial
polygon as the line hg was for the other.

By a similar method to that used before and as described in
detail on page 391, we obtain the line qr passing through c, which
gives us also the section of our true equilibrium polygon between
forces Nos. 8 and 9. The line rn also gives us that portion of the
true equilibrium polygon for this system of loading, from the point
n up to the force No. 17.

By drawing a line from the lower end of the load line, parallel to
n r, until it intersects the horizontal line through the middle of force
No. 9 at the point o/, we have the pole of the special equilibrium
polygon for this system of loading, which is the first condition of
loading. The rays are drawn from o\ only to the forces from No. 9
to No. 17, inclusive, and the special equilibrium polygon is completed
between n and c by drawing them parallel to these rays.

On account of the symmetry of loading, we know that the
equilibrium polygon would be exactly similar on the left-hand side of
the arch. In discussing these equilibrium polygons, we must there-
fore remember that of the two equilibrium polygons lying between the
extrados and intrados on the right-hand side of the arch, the upper

433

434 MASONRY AND REINFORCED CONCRETE

line represents the line of pressure for a uniform loading over the
whole arch — the first condition of loading — while the lower line on
the right-hand side, and also the one equilibrium polygon which is
shown on the left-hand side of the arch, represent the special equilib-
rium polygon for the second condition of loading.

Intensity of Pressures on the Voussoirs of the Arch. An inspec-
tion of the equilibrium polygon for the first condition of loading
shows that it passes everywhere within the middle third. The maxi-
mum total pressure on a joint, of course, occurs at the abutment,
where the pressure equals 24,750 pounds. Since the joint is here
about 42 inches thick, and a section one foot wide has an area of 504
square inches, the pressure on the joint is at the rate of 49 pounds per
square inch. At the keystone, the actual pressure is 19,750 pounds;
and since the keystone has an area of 228 square inches, the pressure
is at the rate of 87 pounds per square inch.

At the joint between forces Nos. 13 and 14, the line of force passes
just inside the edge of the middle third. The ray from the pole o/
to the joint between voussoirs Nos. 13 and 14 of the force diagram
has a scaled length of 20,250 pounds. The joint has a total thickness
of about 24 inches, and therefore an area of 288 square inches. This
gives an average pressure of 70 pounds per square inch ; but since the
line of pressure passes near the edge of the middle third, we may
double it, and say that the maximum pressure at the upper edge of
the joint is 140 pounds per square inch. All of these pressures for
the first condition of loading are so small a proportion of the crushing
strength of any stone such as would be used for an arch, or even of
the good quality of mortar which would, of course, be used in such a
structure, that we may consider the arch, as designed, to be perfectly
safe for the first condition of loading.

The special equilibrium polygon for the second condition of
loading shows that the stability of the arch is far more questionable
under this condition, since the special equilibrium polygon passes out-
side the middle third, especially on the left-hand haunch of the arch.
The critical joint appears to be between voussoirs Nos. 4 and 5. The
pressure at this joint, as determined by scaling the distance from the
point o2'" to the load line between forces Nos. 4 and 5, is approxi-
mately 24,500 pounds. The section of the equilibrium polygon
parallel to this ray passes through the joint at a distance of a little

434

MASONRY AND REINFORCED CONCRETE 435

over three inches from the edge. On the basis of the distribution of
pressure at a joint, the compression at this joint would be confined to
a width of 9 inches from the upper edge, the pressure being zero at a
distance of 9 inches from the edge. This gives an area of pressure
of 108 square inches, and an average pressure of 227 pounds per
square inch. At the upper edge of the joint, there would, therefore,
be a pressure of double this, or 454 pounds per square inch. This
pressure approaches the extreme limit of intensity of pressure which
should be used in arch work; and even this should not be used unless
the voussoirs were cut and dressed in a strictly first-class manner,
and the joints were laid with a first-class quality of mortar.

The propriety of leaving the dimensions as first assumed for trial
figures, depends, therefore, on the following considerations :

First. The loading assumed above for the uniformly distributed
load is as great a loading as that produced by ordinary locomotives
such as are used on the majority of railroads; while the locomotive
requirements as assumed above are excessive, and are used on only
a comparatively few railroads.

Second. If an equilibrium polygon had been started from a
point nearer the intrados than the point ra — using the same pole o2'"
— it would have passed a little below the point c, and likewise a little
nearer the intrados than the point n. Although this would have
brought the equilibrium polygon a little nearer to the intrados on the
right-hand haunch of the arch, it would likewise have drawn it away
from the extrados on the left-hand haunch. Although it is uncertain
just which equilibrium polygon, among the infinite number which
may mathematically be drawn, will actually represent the true equi-
librium polygon, there is reason to believe that the true equilibrium
polygon is the one of which the summation of the intensity of pres-
sures at the various joints is a minimum; and it is evident from mere
inspection, that an equilibrium polygon drawn a little nearer the
center, as described above, will have a slightly less summation of
intensity of pressure, although the intensity of pressure on the
joints on the right-hand haunch will rapidly increase as the polygon
approaches the intrados. It is therefore quite possible that the true
equilibrium polygon would have a less intensity of pressure at the
joint between voussoirs Nos. 4 and 5.

If it is still desired to increase the thickness of the arch so that

435

436 MASONRY AND REINFORCED CONCRETE

the line of pressure will pass further from the extrados, it may be
done, approximately as indicated for a similar problem on page 411.
Evidently, the keystone is sufficiently thick, and the voussoirs at the
abutments also have ample thickness. The extrados must evidently
be changed from an arc of a circle to some form of curve which shall
pass through the same three points at the crown and the two abut-
ments. This may be either an ellipse or a three-centered or five-
centered curve. Although it will cause an extra loading on the
haunches of the arch to increase the thickness of the arch on the
haunches, and although this will cause the equilibrium polygon to
rise somewhat, the rise of the equilibrium polygon will not be nearly
so rapid as the increase in the thickness of the arch ; and therefore the
added thickness will add very nearly that same amount to the
distance from the extrados to the equilibrium polygon. For example,
by adding a little over three inches to the thickness of the arch at
voussoirs Nos. 4 and 5, the distance from the equilibrium polygon to
the extrados would be increased from three inches to six inches, and
the maximum intensity of pressure on the joint would be approxi-
mately half of the previous figure. To be perfectly sure of the
results, of course, the problem should be again worked out on the
basis of the new dimensions for the arch.

The required radii for a multicentered arch which should have
this required extrados, or the axes of an arc of an ellipse which should
pass through the required points, are best determined by trial. The
effect of the added thickness on the load line for the right-hand side
of the arch will be to bring the load line nearer to the center of the
voussoirs and, therefore, will actually improve the conditions on that
side of the arch. Of course, when the concentrated load is over the
right-hand side of the arch instead of the left, the form of the equilib-
rium polygon will be exactly reversed. It is quite probable that,
for mere considerations of architectural effect, the revised extrados
would be made the same kind of a curve as the intrados. This would
practically be done by selecting a radius which would leave the same
thickness at the crown, allow the required thickness on the haunches,
and let the thickness come what it will at the abutments, even though
it is needlessly thick.

Stability of Pier between Arches. The stability of the pier
on the right-hand side of the arch in Fig. 237 is determined on

436

MASONRY AND REINFORCED CONCRETE 437

the assumption of the concentrated locomotive loading on the left-
hand end of the next arch which is at the right of the given arch,
and the uniform loading over the right-hand end of the given arch.
We therefore draw through the point m' a line of force parallel to
mk, and also produce the line In until it intersects the other line
of force in the point s. A line from s parallel to RZ, therefore, gives
the line of action of the resultant of the forces passing down the pier,
for this system of loading. Since this system of loading will give
the most unfavorable condition, or the condition whicji will give a
resultant with the greatest variation from the perpendicular, we shall
consider this as the criterion for the stability of the pier. The piers
were drawn with a batter of 1 in 12, and it should be noted that the
resultant R2 is practically parallel to the batter line. If the slope of
RZ were greater than it is, the batter should then be increased. The
value of RZ is scaled from the force diagram as 55,650 pounds. The
force RZ is about 14 inches from the face of the pier, and this would
indicate a maximum intensity of pressure of 221 pounds per square
inch. This is a safe pressure for a good class of masonry work. The
actual pressure on the top of the pier is somewhat in excess of this,
on account of the weight of that portion of the arch between the
virtual abutment at n and the top of the pier; and the total pressure
at any lower horizontal section, of course, gradually increases; but,
on the other hand, the weight of the pier combines with the resultant
thrust of the two arches to form a resultant wrhich is more nearly
vertical than R2, and the center of pressure, therefore, approaches
more nearly to the axis of the pier. The effect of this is to reduce
the intensity of pressure on the outer edge of the pier; and since the
numerical result obtained aboye is a safe value, the actual maximum
intensity of pressure is certainly safe.

ELASTIC ARCHES

Technical Meaning. All of the previous demonstrations in
arches have been made on the basis that the arch is made up of
voussoirs, which are acted on only by compressive forces. The
demonstration would still remain the same, even if the arches were
monolithic rather than composed of voussoirs; but in the case of an
arch composed of voussoirs, it is essential that the line of pressure
shall pass within the middle third of each joint, in order to avoid a

437

438 MASONRY AND REINFORCED CONCRETE

tendency for the joint to open. If the line of pressure passes very far
outside of the middle third of the joint, the arch will certainly col-
lapse. An elastic arch is one which is capable of withstanding
tension, and this practically means that the line of pressure may pass
outside of the middle third and even outside of the arch rib itself.
In stTch a case, transverse stresses will be developed in the arch at
such a section, and the stability of the arch will depend upon the
ability of the arch rib to withstand the transverse stresses developed
at that sectjpn. A voussoir arch is, of course, incapable of with-
standing any such stresses. A monolithic arch of plain concrete
could withstand a considerable variation of the line of pressure from
the middle third of an arch rib; but since its tensile strength is com-
paratively low, this variation is very small compared with the
variation that would be possible with a steel arch rib. A reinforced-
concrete arch rib can be designed to stand a very considerable vari-
ation of the line of pressure from the center of the arch rib.

Advantages and Economy. The durability of concrete, and
the perfect protection that it affords to the reinforcing steel which
is buried in it, give a great advantage to these materials in the con-
struction of arch ribs. Although the theoretical economy is not so
great as might be expected, there are some very practical features
which render the method ecbnomical. It is always found that,
before any considerable transverse stresses can be developed in a
reinforced-concrete arch bridge, the concrete will be compressed to
the maximum safe limit while the unit stress in the steel is still com-
paratively low. Since a variation in the live load often changes the
line of pressure from one side of the arch rib to the other, and thus
changes the direction of the transverse bending, it becomes neces-
sary to place steel near both faces of the arch rib, in order to with-
stand the tension which will be alternately on either side of the rib.
Of course the steel which is — for the moment — on the compressive
side of the rib will assist the concrete in withstanding compression,
but this is not an economical use of the steel. There is, however,
the practical economy and advantage, that the reinforcement of the
concrete makes it far more reliable, even from the compression stand-
point. It prevents cracks in the concrete, and it also permits the
use of a much higher unit pressure than would be considered good
practice in the use of plain concrete. This advantage becomes

438

MASONRY AND REINFORCED CONCRETE 439

especially great in the construction of arches of long span, since in
such a case the dead load is generally several times as great as the
live load. Therefore, the maximum variation in the line of pressure
produced by any possible change in loading is not very great; and
any method which will permit the use of a higher unit pressure in
the concrete is fully justified by the use of such an amount of steel
as is required in this case.

Mathematical Principles. A complete and logical demonstra-
tion of the theory of elastic arches requires the use of Integral Calcu-
lus. The theory is too long and too complicated for insertion here.
The student will be asked to accept as demonstrable, several equa-
tions derived by calculus methods. Numerical problems will be pro-
posed and the application of the data of the problems to these equa-
tions will be fully illustrated. In the practical numerical application
of Integral Calculus to these problems, it is necessary to make a
summation of a series of quantities. Theoretically, the number of
the quantities should be infinitely great' and the quantities them-
selves infinitesimally small. It is found -that sufficiently accurate
solutions can be obtained with a comparatively small number of
quantities, twenty, ten, or even five; but the greater the number the
more accurate will be the results. The center line of the arch rib
between the abutments must be divided into five (ten or twenty)
divisions on each side of the center, but each division must be of
such length that the length ds divided by its moment of inertia / is
a constant. If the rib were of constant depth h throughout, then the
moment of inertia would be constant and each length ds would be
the same. But an arch rib is generally made deeper at the abut-
ment than at the crown. If the arch consists of plain concrete or
other homogeneous material, ds varies as h3. Equation (36) shows
that, when the concrete is reinforced, even though the sections are
symmetrical, / varies as a function of h3 and hz, and in the more
general cases the function is still more complicated. There is no
direct and exact method of dividing the half-span length into a
given number of variable lengths, each one of which shall be propor-
tional to the mean value of the moment of inertia of that section.
The problem can only be solved either by a series of trials and
approximations or else by making, at the outset, an approximation
which permits a direct solution and yet such that the effect of the

440 MASONRY AND REINFORCED CONCRETE

approximation on the final result is demonstrably small and perhaps
within the uncertainties of the construction work. An illustration
of this approximation will be given in the numerical problem which
will now be worked out.

ILLUSTRATIVE PROBLEM

Segmental Arch of Sixty-Foot Span. Assume a segmental arch
having a net span of 60 feet and a net rise to the intrados of 15 feet.
The only practicable method of solution is to assume trial dimen-
sions which previous experience has suggested to be approximately
right, and then test the strength of such a design. To find the
radius for the intrados which will fulfill these conditions, we may
note from Fig. 238 that the angle A'B'C' is measured by one-half
of the arc A'C', and therefore A'B'C' is one-half a, but its natural
tangent equals 15-:- 30, or 0.5. The angle whose tangent is 0.5 is
26° 34'. Therefore a equals 53° 8'. To find the radius, we must
divide the half-span (30) by the sine of 53° 8', which makes the
radius 37.50 feet.

Depth of Arch Rkig. For the depth of the keystone, we can
employ only empirical rules. The depth as computed from Equa-
tion (61) would call for a keystone depth of about 27 inches, which
would be proper for an ordinary masonry arch; but considering the
accumulated successful practice in reinforced-concrete arches, and
the far greater reliability and higher permissible unit stresses which
may be adopted, we may select about two-thirds of this — or, say,
18 inches — as the depth of the arch ring at the crown. We will also
assume that the variable lengths ds have the ratios 1.00, 1.10, 1.21,
1.33, 1.46, 1.61, 1.77, 1.95, 2.14, 2.36, in which the several values
are those of a geometrical progression of 1.1. We will now assume,
as a first approximation, that the moments of inertia, instead of
varying according to the comparatively simple relation shown in
Equation (42) vary directly as h3. Then h, the mean height for the
abutment section, will equal ^/2.36Xl83 = 23.96, which we may call
24 inches at the skewback line. The first value of 7, 7,387, given in
Table XXXI is computed from Equation (36), by calling 6 = 12,
h = 18, n= 15, and A = 1.00, it being assumed that the reinforcement
consists of 1-inch square bars, spaced 12 inches on centers, in both
intrados and extrados. The other values of I are obtained by

440

Pavement- 80 -

Fig. 23S. Force Diagram for Arch Ri

ixed Ends. Scale J Inch = 1 Foot

MASONRY AND REINFORCED CONCRETE 445

TABLE XXXI

Data for Segmental Arch, 60-Foot Span

(Illustrative Problem, page 440)

POINT

d a RATIO

d s FEET

1.00

7,387

2.231

1.11

0.02

.10

8,126

2.454

3.45

0.15

.21

8,938

2.699

6.01

0.47

.33

9,825

2.967

8.79

1.01

.46

10,785

3.257

11.80

1.84

.61

11,893

3.591

15.01

3.02

1.77

13,075

3.948

18.40

4.65

1.95

14,405

4.350

21.94

6.82

2.14

15,808

4.774

25.53

9.62

2.36

17,433

5.264

29.09

13.17

15.93

35.535

30.75

15.20

multiplying 7,387 by the several values of the ds ratios. The
approximation error, referred to above, will be greatest at the skew-
back section. If we compute the / for the skewback section accord-
ing to Equation (36), calling h equal to 23.96, we get /equals 16,511,
about 5 per cent less than the tabular value, 17,433. Ic = ^bh3 =
13,755, when h = 23.96 and by subtracting 13,755 from 17,433 we
have 3,678, which we may place equal to nls = 2n A (%h—d')z, see
Equation (35). Solving for d', we find that d' equals 0.91, or that
by placing the bars 0.91 inch from the extrados and intrados, instead
of 2.4 inches, the inertia requirement would be exactly satisfied. A
very slight increase of thickness will not only cover the bars suffici-
ently but will also so increase the moment of inertia of the plain
concrete that the inertia requirement will be exactly satisfied.
Assume that h is increased only one-half inch, making it 24.46 inches;
the moment of inertia becomes 17,506, which more than makes up
the deficiency. Since the placing of the concrete might not be closer
than this, our approximation is justified in this case and we may use
the column of values for I and the corresponding ratio values of ds as
they stand. It is thus practicable to assume, at least after one or
two trials, a law of increase of ds which, by numerical test, will
prove to be sufficiently close to the actual increase in the value of I
and yet give a suitable increase in the depth of the arch ring — in
this case an increase from 18 inches at the crown to 24 inches at the
abutment.

441

446 MASONRY AND REINFORCED CONCRETE

Arch Rib Curve. The center line of the rib ACS must be 9
inches above the intrados at C and 12 inches at A and B, and is,
approximately, an arc of a circle of somewhat larger radius than the
radius of the intrados. The curve of the extrados has a still greater
radius. The skewback lines A A' and B B' should be approxi-
mately perpendicular to both the intrados and extrados and for that
reason we average it by making them perpendicular to the middle
curve ACS. A and B are therefore located 12 inches from A' and
B' and on lines through A' and B' from a center which must be first
approximated and which is determined graphically by finding the
center of a circle which will pass through C, A, and B, and whose
radii will pass through A A' and B B'. Such a circle has a radius
38.7 and the scaled height of C above A B is 15.2 feet. This 15.2
is the versed sine of the angle A OC having a radius 38.7, from
which AOC equals 52° 37'. Then the arc A C equals 52.61°X38.7
X arc 1° = 35.535 feet. Multiplying this half-span length by the
ratio of each d s to 15.93 (the sum of the ds ratios) we have the values
in the fourth column of Table XXXI. As a check, the sum of these
computed values equals 35.535.

Strictly speaking, the intrados being an arc of a circle, the arch
rib line, ACB, and the extrados line are probably not exact circles,
but the approximation is here too small to be of importance. It
would have been more simple to have assumed the span and rise of
the arch rib line ACB, making it a true circle or some other definite
curve, and laying off the half depth of the arch at each point to
obtain the intrados and extrados curves. But this would not have
permitted an exact preliminary requirement as to the precise form
of the intrados, and the problem can only be solved this way by
assuming an extra allowance which will prove to be sufficiently
exact for the purpose. For example, in the above case, we might
have chosen a span of 61.50 and a rise of 15.2 after making an approx-
imate calculation that the result would give a net span of 60 and a
net rise of 15. In fact, the arch rib curve is usually the one which
is chosen. The other method was worked out to show how it might
be done when for any reason the form of the intrados is strictly
limited in its dimensions.

Loads on Arch. The dead load of a masonry arch is usually
very large compared with the live load. But the weight of the dead

442

/ 1 1. '•. m «:

VIEW OF APPROACH FOR NEW HELL GATE BRIDGE, SHOWING R2INFORCED
CONCRETE PIER CONSTRUCTION

MASONRY AND REINFORCED CONCRETE 447

load may be reduced by supporting the roadbed and the live load on
columns or small piers extending from the deck down to the arch
rib, which gives virtually the effect of concentrated loads at those
points. The weight of the arch rib between these points may be
considered as concentrated at these several points. The numerical
problem considered indicates ten points on each side of the center.
A solution can hardly be considered precise without having at least
this number, but the numerical work involved is very great and
very tedious. Therefore, in order to abbreviate somewhat, a solu-
tion will first be worked out in detail as if there were only three
forces acting on the arch on each side of the center. Afterward, the
solution for ten forces on each side of the center will be indicated as
being worked out by the same method and the results will be given,
but the details, which would require many pages, will be omitted.
We will therefore assume that equal and symmetrical forces are
applied at the points 2, 5, and 8 on each side of the center. Also,
in order to cover another complication of the general problem, we
will assume that while the forces at 2 are vertical, and equal 2,400,
the forces at 5 and 8 are inclined and have horizontal and vertical
components, those for 5 being 4,200 and 500 and those for 8 being
6,000 and 900. On pages 395, 403, and 420 are given in detail meth-
ods of computing, from the actual conditions of dead and live load,
the amounts of the horizontal and vertical components of the forces
at any point in the arch ring. The following numerical calculation,
while much more condensed than would be proper for the complete
investigation of an arch rib, even as small as that proposed above,
will contain the complete method of work, and the more complete
solution will only differ from it by having a far greater number of
quantities and much more numerical work.

Forces at Any Section of Arch. The principles of graphical
statics show that all the external forces lying in the plane of the
arch rib and acting on any assumed section of the rib may be resolved
into a force tangent to the rib curve, which we will call the thrust,
T ; also a force normal to the curve, which we will call the shear, S;
and also a couple which produces a moment, M, about that point of
the arch rib. The problem of the elastic arch is the determination
of these forces at any section so that the sectional strength of the
rib may be designed accordingly. By the application of Integral

443

448 MASONRY AND REINFORCED CONCRETE

Calculus to the mechanical theory of the elastic arch, the following
general equations are derived, which the student must accept as
demonstrable:

- f,~

S(raB-raL):r

Mc=

Z 7/1+27^0

(63)
(64)

in which jTc, Sc, and M c are the thrust, shear, and moment, respectively,
at the crown of the arch, m is the moment at any point, of all the

loads between that point
and the crown of the
arch. The symbol S
signifies the summation
of a series of similar but
variable quantities. 2 y
signifies the summation
of all the values of y;
(Zy)2 equals the square
of the sum of all the y's;
2y2 is the sum of the
squares of each value of
y. Note the distinction.
2, my is the sum of the
products of each value of
m times its corresponding

-TC-

s^^\ I ; sc\

]*| |*l

[>* i*| ^

value of y.

Assume a section
made at the crown, and
that equal and opposite
forces (Te, Sc, and Mc)
are applied which will keep the two halves of the arch in equilibrium
with the several external forces W and the abutment forces which
are still unknown. When the moment forces at the crown are as
shown in Fig. 239, there will be tension at the intrados and com-
pression at the extrados. When the moment at the crown is in the
direction indicated, it is called positive. Considering, now, the left

(t)

Fig. 239. Diagram of Forces in Segmental Arch

444

MASONRY AND REINFORCED CONCRETE 449

TABLE XXXII

Values of Quantities Used in Equations (62), (63), Etc.

POINT

2m y

(m m,)x

2
5

3.45

11.80
21.94

0.15

1.84
6.82

11.90
139.24
481.36

- .02
3.39
46.51

0
2,004
89,454

7,375
1,220,153

0
0
0

8.81

632.50

49.92

91,458

1,227,528

Abut.

30.75

15.20

224,072

half of the arch, Fig. 239, as a cantilever, and taking moments about
the point 8 of all the external forces, which in this case are W2 and
W5, we will have

m (for point 8) =4,200 (21. 94 -11. 80) +2,400 (21.94-3.45)
+500(6.82-1.84)

The moment is taken about each point in turn, as above. These
moments are in each case in the contrary direction to the assumed
(3/c) moment at the crown — whether for the left-hand or right-hand
half of the arch — and are therefore considered as negative. Since
each point of the left-hand side of the arch has the same y as the
corresponding point on the right-hand side, 2wi/ = 2(mIj+mB)i/.
2 TO =2(7/^+7/0. 2(mB— rnjz equals the sum of the products of
the (TOB— 7/O for each pair of points, each multiplied by the common
value of x for that pair. Having determined, after proper substitu-
tion of the numerical values in Equations (62), (63), and (64), the
numerical values of Tc, Sc, and Mc at the crown, the value of M for
any point, Q, may be determined from the equation

M = m+Mc+Tcy±Scx (65)

The negative sign is used with the last term when considering the
right-hand half of the arch.

We will now apply these principles to the forces (named on
page 447), which are applied at the points 2, 5, and 8. The several
quantities needed for the solution of Equations (62), (63), and (64),
and also some later equations, are given in Table XXXII.

The moment m for point 2 is zero (in this case) since there
is no force between point 2 and the crown. For point 5, m = 2,400
fo-a*) =2,400 (11. 80 -3.45) =2,400X8.35 = 2,004. For point 8,
m = 2,400(a-8-z2) + 4,200 (z8-z5)+ 500 (z/8-7/5) =2,400X18.49+4,200
X 10.14+500X4.98 = 89,454. Although not used immediately, the

445

450 MASONRY AND REINFORCED CONCRETE

moments for the abutment points are calculated similarly and placed
below. The student should verify this calculation for practice.
These moments (wj are all negative, as stated above. Since, in
this case, we have assumed the loads to be symmetrical, the moments
raR equal those of mu each to each. I, my is found by adding the mL
and niR for each point and multiplying by the corresponding value of
y, thus obtaining the next column. The loads being symmetrical,
(mR— 7HL)=0 for each point, which gives a line of zeros for the last
column, which means that the shear Sc in Equation (63) equals zero.
This is only what might have been predicted — that there would be
no shear at the crown when the loading is symmetrical. By sub-
stituting these values in Equation (62) and (64), we obtain numerical
values for the crown thrust and moment as follows :
n equals 10; Smy equals -1,227,528; SraSy equals (-91,458-
91,458) X8.81 = - 182,916X8.81; (S?/)2 equals 8.812 = 77.616; and
n 2 y2 equals 10X49.92 = 499.2. Then

T =10 (-1,227,528) -(-182,916X8.81) ^-12,275,280+ 1,61 1,490
2(77.62-499.2) -843.16

_!^™.+IW7

As stated above, Sc = 0.

,, = -182,916+2x12,647x8.81 = . „

This moment being negative, it indicates that there is compression
at the intrados and tension at the extrados and that there is a ten-
dency for the crown to rise, w'hich is the invariable effect of heavy
loads on the haunches and little or nothing on the crown.

It should be clearly understood that this very simple numerical
solution only gives the stresses produced on the arch by the forces
assumed. These forces do not allow for the weight of the arch.
They are the stresses which would be produced if they were the only
forces and the arch itself weighed nothing.

The moment at the abutment is found from Equation (65), in
which m equals -224,072, and Sc equals 0. Then

3/A= -224,072+(-l,996) + 12,646Xl5.20+0= -33,849 ft.-lb.
The moment at point 5 is

M,= -2,004+(-l,996) + 12,646Xl.84+0=+19,269 ft.-lb.

446

MASONRY AND REINFORCED CONCRETE 451

Comparing the moments produced by these three forces at the crown,
the abutment, and at point 5, they are negative at the crown and at
the abutment but positive at point 5, showing that these forces
create a tendency for the extrados to open (because of tension) at the
crown and at the abutment, but there is tension in the intrados at
point 5. This also means that there are two points on each side of
the center, one between point 5 and the abutment and one between
point 5 and the crown, where the moment changes sign and is
zero.

Laying Off Load Line. We shall assume that the arch car-
ries a filling of earth or cinders weighing 100 pounds per cubic
foot, that the top of this filling is level, and that it has a thickness of
one foot above the crown. Since concrete weighs about 150 pounds
per cubic foot, we shall assume this weight of 150 pounds as the unit
of measurement, and therefore reduce the ordinates of earthwork to
the load line for the top of the earth. We shall assume, as an addi-
tional dead load, a pavement weighing 80 pounds per square foot,
and shall therefore lay off an ordinate of iVV of a foot above the
ordinates for the earth-filling load. For this particular problem,
we shall only investigate a live load of 200 pounds per square foot,
extending over one-half of the span from the abutment to the center.
From our previous work in arches, we know that such a loading will
test the arch more severely than a similar unit live load extending
over the entire arch; and therefore, if the arch proves safe for this
eccentric load, we may certainly assume that it wrill be safe for a full
load. The detail of the following calculation is worked out by
precisely the same method as given in the previous article, but has
been omitted here to save space. Although the calculations are
long and tedious, the student will find that the surest method of
grasping these principles is to work out and verify all the calcula-
tions of which the results only are given here. The horizontal pro-
jection of each ds, multiplied by the load-line ordinate in the line of
each point, times 150, equals the vertical load on each joint. These
loads are given in Table XXXIII. The horizontal component of
each force is computed on the methods previously described for
voussoir arches, the results being given in Table XXXIII.

Thrust, Shear, and Moment. Substituting in Equation (62),
w=10; S my = S(mL + mB)?/= - 16,403,641; SwSy = [-779,435 +

447

452 MASONRY AND REINFORCED CONCRETE

TABLE XXXIII
Load Data for Segmental Arch Problem

LEFT HALF or ARCH

RIGHT HALF OF ARCH

BM.

Hor.

Reduced

LOAD

of da

Load

Line
Ordin.

Vert.
Comp.

Hor.
Comp.

Line
Ordin.

Vert.
Comp.

Hor.
Comp.

2.23

410

910

1.11

0.02

1.23

0.00

610

1,360

2.44

440

1,070

3.45

0.15

11.90

0.02

640

1,560

2.68

470

1,260

6.01

0.47

36.12

0.22

670

1,800

2.90

530

1,540

8.79

1.01

77.26

1.02

730

2,120

3.11

630

1,960

11.80

1.84

139.24

3.39

830

2,580

3.31

750

2,480

15.01

3.02

225.30

9.12

950

3,140

3.48

930

3,230

18.40

4.65

338.56

21.62

1,130

3,930

3.58

1,175

4,200

350

21.94

6.82

481.36

46.51

1,375

4,920

410

3.57

1,470

5,240

1,070

25.53

9.62

651.78

92.54

1,670

5,960

1,220

3.45

1,890

6,520

2,240

29.09

13.17

846.23

173.45

2,090

7,200

2,470

30.75

40.77

2,808.98

347.89

(-1,082,880)] 40.77 =(-1,862,315) 40.77= -75,926,583; (27/)2 =
(40.77)2 = 1,662.2; and S(*/2) =347.89. Then

-164,036,410- (-75,926,583) -88,109,827

+24,250 Ib.

2 [1,662.2- 10X347.89] -3,633.4

The unit thrust at the crown under this condition of loading is only
24,250-^216 = 112 Ib. per sq. in. Then by Equation (63)

-7,082,939 -7,082,939

-1,261 Ib.

• 2X2,808.98 5,618
which is an insignificant shearing stress per square inch on 216
square inches. Then from Equation (64)

(-1,862,315)+2X24,250X40.77

= -5,751 ft.-lb.

2X10

The moment at any point is found from Equation (65). For exam-
ple, for point 5 on the left-hand side we use the values of m = —30,595
and Scx=+(- 1,261) 11.80= -14,880. Then
jl/L5=_ 30,595+ (- 5,751) + (24,250 xl.84) + (- 14,880)

= -6,606
MU7=-83,490+(-5,751) + (24,250X4.65) + (- 1,261X18.40)

= +1,320

At the left-hand abutment, the moment is

MLA=-325,850+(-5,751) + (24,250xl5.20) + (-l,26lX30.75)
= -1,777

448

MASONRY AND REINFORCED CONCRETE 453

TABLE XXXIII— (Continued)
Load Data for Segmental Arch Problem

SEC.

(m^+m^y

(n^-mjx

-2,130

-3,180

-797

-3,622

-7,200

-10,650

-8,390

-20,735

-16,200

-23,770

-40,370

-66,540

-30,595

-44,370

-137,936

-162,545

-52,230

-74,600

-383,027

-335,774

-83,490

-117,170

-933,069

-619,712

-127,990

-175,350

-2,068,779

-1,039,078

-188,320

-253,560

-4,250,886

-1,665,577

-271,280

-380,230

-8,580,387

-3,169,356

-779,435

-1,082,880 -16,403,641

-7,082,939

Abut.

-325,850

-422,390 |

At the right-hand abutment, the moment is

l/KA=-422,390+(- 5,751) + (24,250X15.20) -(-1,261X30.75)

= - 20,765 ft.-lb.
At the point 5, on the right-hand side

MK =- 44,370 - 5,751 + (24,250 X 1 .84) -(- 1,261 X 1 1 .80)

= +9,379 ft.-lb.
At the point 7, on the right-hand side, the moment is

MB7=-117,170-5,751+(24,250X4.65)-(-l,261Xl8.40)

= +23,044 ft.-lb.

The moment at the right-hand abutment (20,765 ft.-lb., or
249,180 in.-lb.) is evidently the maximum produced by this system
of loading. Some of the work is simplified and is more easily under-
stood by utilizing some of the principles of graphics. In Fig. 238 we
lay off a load line, at some convenient scale, showing the loads given
in Table XXXIII. The shear at the center, 8e, equal to -1,261,
is laid off downward (being negative) from the dividing point 0
of the load line. Then the true pole distance (call it Tc) equal to
24,250 is laid off horizontally, giving the position of the pole, P,
as shown in Fig. 238. Mc+ 7> (-5,751) 4- (24,250) = -0.24, the
eccentric distance of the thrust at the crown. Laying off this
distance below the crown center, and drawing a line parallel to PO.
we have one section of the true equilibrium polygon. The remainder
is drawn by the method previously explained for voussoir arches.
Although the numerical computations are far more accurate than

449

454 MASONRY AND REINFORCED CONCRETE

those scaled from the drawing, it is found that one checks the other
closely. The moment at any point equals the force, as shown by
the proper ray of the force diagram, times the distance of the corre-
sponding side of the equilibrium polygon from the rib center. The
moment is negative at the crown and at both abutments, but posi-
tive on both haunches, only 1,320 at L7 but 23,044 at R7. The
thrust at any point is given by that component of the corresponding
ray of the force diagram which is parallel to the tangent at that
point. Usually, the tangent component is so nearly parallel with
the ray itself that they are substantially equal and the thrust is
considered as measured by the ray itself. The thrust is, of course,
maximum at the abutments, the ray parallel to the thrust at the
right abutment scaling 38,900. The eccentricity equals the moment
divided by the thrust and, for the right abutment, equals 20,765 -5-
38,900 = .534 ft. or 6.4 inches. Referring to page 241 and following,
Part III on flexure and direct stress, the 6.4 equals e, while the h
equals 24 inches. Then e + h = .266; p = 1 + (24 X 12) = .00347. Then,
according to the diagram, Fig. 1 12, k equals .785. Substituting in
Equation (50) the values M = 249,180 in.-lb., 6 = 12, h = 24, k = .785,
7i = 15, p = . 00347, and a = .4 h or 9.6, we may solve for c. Then

c = 249,180^ri2x576

= 249,180 -5- [6,912 (.1962-.1027+.0212)]

= 314 Ib. per sq. in.
Then from Equation (47), since kh = 18.84,

=4,710X.146

= 688 Ib. per sq. in.

Temperature Stresses. The provision which should be made
for temperature stresses in a concrete arch is often a very serious
matter, for the double reason that the stresses are sometimes very
great, and that the wrhole subject is frequently neglected. It will be
shown later that the stresses due to certain assumed changes of tem-
perature may be greater than those due to loading. There is much
uncertainty regarding the actual temperature which will be assumed
by a large mass of concrete. The practice which is common and

450

MASONRY AND REINFORCED CONCRETE 455

proper with metal structures is not applicable to masonry arches.
A steel bridge, with its high thermal conductivity, will readily absorb
or discharge heat; and it is usually assumed that it will readily
acquire the temperature of the surrounding air. On the other hand,
concrete is relatively a nonconductor. No matter what changes of
temperature may take place in the outer air, the interior of the con-
crete will change its temperature very slowly. One test bearing on
this subject was conducted by burying some electrically recording
thermometers in the interior of a large mass of concrete, and record-
ing the temperatures as they varied for a period of ten months, which
included a winter season. It was found that the total variation of
temperature was but a few degrees.

It is probably safe to assume that even during the coldest of
winter weather the temperature of the interior of a large mass of
concrete will not fall below that of the mean temperature for the
month. Since the Weather Bureau records for temperate climates
show that the mean temperature for a month, even during the winter
months, is but little if any below freezing, it may usually be assumed
that for concrete a fall of 30 degrees below the temperature of con-
struction— say 60° — will be a sufficient allowance. A rise of tem-
perature to 90° F. is probably much greater than would ever be found
in an arch of concrete. The earth and pavement covering protect
the arch from the direct action of the sun. Even in the hottest day,
the space under a masonry arch seems cool, and the real temperature
of the masonry probably does not exceed 70°, even if the outer air
registers 95°. Therefore, if we calculate the stress produced by a
change of temperature of 30 degrees from the temperature of con-
struction, we are probably exceeding the real stresses produced.
Even if this extreme limit should be sometimes exceeded, it simply
lowers, temporarily, the factor of safety by a small amount.

Let Tt be the thrust at the crown due to the assumed change in
temperature; Mt, the moment at the crown due to the assumed
change in temperature; E, the modulus of elasticity, which is here
taken as that of the concrete, since the moment of inertia is that
of the "transformed" section, or the equivalent concrete section;
and 7, the moment of inertia of the equivalent concrete section,
which is variable but proportional to ds so that ds+I is con-
stant. Since the foot unit has been used for all dimensions, we

451

456 MASONRY AND REINFORCED CONCRETE

must find a numerical value for ds + I, by expressing 7 in biquad-
ratic feet. Taking the first combination, since they are all equal,
7,387 biquadratic inches equals (7,387 -f- 124) = 7,387 + 20,736 = 0.3562
biquadratic feet. The value of d s corresponding to I equals 7,387
is 2.231 feet. Therefore, ds+ 1 equals 2.231 ^0.3562 or 6.262. e is
coefficient of expansion with temperature or .0000065 for both steel
and concrete.

Analytical Mechanics and Calculus gives us the temperature
equation

_EI Lne(t-Q , .

(67)

The summations refer to one-half of the arch only.
Also

n
The bending moment at any point due to temperature is

M = Mt+Tty (68)

= Tty-^

=4-?)

The equilibrium polygon for these temperature stresses is a hori-

y i,

zontal line which is at a distance below the crown equal to — -.

Where this line intersects the arch rib, there is no moment due to
temperature, no matter how much change of temperature there may
be. Above and below this line, the temperature moments have
opposite signs.

Note that the denominator of the main term in Equation (66)
is the same, but with opposite sign, as that in Equation (62). We
can therefore use the same numerical value. Substituting, E equals
2,000,000 pounds per square inch, or 288,000,000 pounds per
square foot; L equals 61.60; n equals 10; e equals .0000065; (t-t0)
equals +30° F.; (ds + I) equals 6.262; and 2 [n2y2-(2yy] equals
+3,633.4, as previously determined.

452

Then

MASONRY AND REINFORCED CONCRETE 457

„, 288,000,000 X 61. 60 X .10 X. 0000065X30

Tt= 6.262X (+3,633.4) =1,520 Ib.

It should be noted that this moment, produced by a rise of tempera-
ture of 30° above the temperature of construction is more than the
moment produced at the center by the load over the half-span.
Also that the algebraic sign is negative, showing that the moment
produces compression at the intrados and that the arch tends to
rise, due to this force. This is what we might expect when the
temperature rises and expands the arch. Also note that for a fall of
temperature of (t— 10) below the temperature of construction, (t—t0]
would be negative, which would change the algebraic sign of the
moment, and this is what we would expect.

Substituting in Equation (69), we have at either abutment

40 77
M = 1,520 (15.20-——) = +16,906 ft.-lb.

Again it should be noted that this is nearly as much as the moment
produced at the right-hand abutment by the load above considered.
Also that for a rise of temperature, as in midsummer, these two
moments at the right abutment are opposite in sign and relieve each
other, the net moment being the algebraic sum or numerical differ-
ence. For a fall in temperature, the moments have the same sign
and their numerical sum must be taken as the measure of stress.

The horizontal component of the thrust at each section is the
same and equals the thrust at the crown — in this case, 1,520 pounds.
At any other point it equals the thrust at the crown times the cosine
of the angle of that point from the center. For the abutment, it
equals 1,520 X cos 52° 37', or 923 pounds. For other points the thrust
may be more easily obtained by a graphical method, i.e., draw a line
representing the crown temperature thrust, at some scale. Let that
line be the hypothenuse of a right-angled triangle ; the other two
lines being parallel to the tangent, and to the normal to the arch
curve at the desired point. The lengths of these other two sides
represent the thrust and shear at that point, respectively, meas-
ured at that same scale.

453

458 MASONRY AND REINFORCED CONCRETE

Stresses Due to Rib Shortening. The thrust in a rib results in
shortening the arch very slightly and this produces precisely the
same effect in altering the moment as an equivalent fall in tempera-
ture. Since the thrust is variable along the arch, we must consider
the average thrust. A thrust of c pounds per square foot on a span
of L feet would produce a shortening of cL-f- E, which would also be
produced by a fall of temperature of —(t—t0) degrees, whose effect
would be —eL(t — t0). Therefore, we may substitute — cL-^-E for
eL (t — tg) in Equation (66) and obtain

Applying this equation to our numerical problem, we will assume an
average thrust of 150 pounds per square inch or 21,600 pounds per
square foot equals c. The other quantities will be the same as those
used on page 456 and following.

T 1 21,600X61.60X10

Ts=~QM2X 3,633,4

This is less than 40 per cent of the stress due to a change of 30
degrees in temperature. For a rise in temperature, these stresses
tend to neutralize each other; for a fall in temperature, they combine
to produce a greater stress.

Combined Stresses for Above Loading. The worst combi-
nation of stresses on an arch occur in winter when the temperature
is below normal. For a temperature 30 degrees below normal, and
for the above described loading on the half-span, we would have at
the right abutment, Mu equals —20,765; M (for temperature stress
at right abutment) equals —16,906; M (for rib shortening at right

COC

abutment) equals - -——X 16,906= -6,504; which totals 44,175
1,520

foot-pounds, or 530,100 inch-pounds. The thrust due to live and
dead load is 38,900; that due to a fall of temperature is a tension
(hence negative) and equals —923; that due to rib shortening is

copr

= -355. The combined thrust is 38,900-923-355

= 37,622. Dividing 530,100 by 37,622 we have 14.09 inches, which
is the eccentricity for this combination of stresses. e-s-h = 14.09-7-24
= .587. Using the diagram, Fig. 112, for e-r^ = .587 and p =

454

MASONRY AND REINFORCED CONCRETE 459

.00347, £ = .632. Using Equation (50), making substitutions and
solving for c, we have

0 = 530,100+ ri2x576(.158-.06-+15X-00347X2X92-16)l
L V .632X576 /J

= 530,100^(6,912 (.158 -.067 +.026)]
= 530,100^-808.7
= 655

Since A- A = .632X24 = 15.2, then according to Equation (47)
5 = 15X655 21'"15'2 = 4>037 Ib- Per sq- in- tension

(ic 2 — 9 4\
' ' 1 = 8,074 Ib. per sq. in. compressive

stress in the steel near the intrados.

It should be noted that the compressive stress in the concrete
for this combination of loading and stresses is practically at the
limit and that the steel serves a very useful purpose in assisting the
compression. Also, that the steel on the tension side has a very low
unit stress, but the percentage of reinforcement is not too high,
since a lower percentage would increase very materially the unit
compression in the concrete, which is now at its limit. The com-
bined stresses at other points can be worked up similarly, with com-
paratively little additional computations, and this should be done
for a complete investigation of the problem, but it is probably true
that the above conditions represent the worst conditions and that
the design, as approximated, is probably safe.

Although the investigation of another form of loading, such as
a maximum load over the whole arch, will require another complete
set of calculations and the drawing of another equilibrium polygon
and force diagram, some of the work already done may be utilized
so that the effort need not be altogether doubled.

Testing Arch for Other Loading. A live load of 200 pounds
per square foot over the entire arch would unquestionably increase
the thrust over the entire arch, especially at the abutments. The
stress due to shortening will, of course, be increased in proportion to
the increase in the thrust. The stress due to moment cannot be
accurately predicted. Of course, such an examination and test for
full loading should be made in the case of any arch to be constructed,

455

460 MASONRY AND REINFORCED CONCRETE

and should be worked out precisely on the same principles and, in
general, by identically the same method as was used above.

To test the arch for a concentrated loading, such as would be
produced by the passage of a road roller, or, in the case of a railroad
bridge, by an especially heavy locomotive, the test must be made by
assuming the position of that concentrated load which will test the
arch most severely. Ordinarily, this will be found wyhen the concen-
trated load is at or near one of the quarter points of the arch. The
only modification of this test over that given above in detail is in the
drawing of the load line, but the general method is identical.

HINGED ARCH RIBS

General Principles. The construction of hinged arches of
reinforced concrete is very rare, but is not unknown. We may con-
sider that, structurally, they consist of curved ribs which have
hinges at each abutment, and which may or may not have a hinge
at the center of the arch. The advantage of the three-hinged arch
lies in the fact that it is not subject to temperature stresses. The
two-hinged arch is partially subject to temperature stresses, but not
to the same extent as the fixed arch, since the arch rib is not held
rigid at the abutments as in the case of the fixed arch. Practically
the hinges are made by having at each hinge a pair of large cast-
iron plates which are a little larger than the size of the rib, and which
have at their centers a bearing for a pin of due proportionate size.
The bearings are so made that one may turn, with respect to the
other, about the axis of the pin through an angle of a very few degrees.

Arches have been made writh a single hinge at the center. This
eliminates all moment at the center. If one abutment settles \vith
respect to the other, the center hinge might relieve the stress some-
what, especially if the settlement happened to be in the arc of a
circle about the hinge. The two-hinged arch is less subject to the
effect of settlement, and the effect would be zero, provided that the
net distance between the hinges remained unchanged. The three-
hinged arch is practically independent of both settlement stresses
and temperature stresses, excepting those developed by the friction
of the pins in their bearings. Theoretically, the three-hinged type
has very great advantages, particularly if the foundations are not
firm, and some settlement or yielding seems to be inevitable. But

456

MASONRY AND REINFORCED CONCRETE 461

457

462 MASONRY AND REINFORCED CONCRETE

the hinges are, necessarily, very expensive features. The stresses
produced in a fixed arch by arch settling may become indefinitely
great and enough to produce complete failure. In spite of this fact
and the immunity of the three-hinged type from such risk, com-
paratively few such arches have been built.

Description of Two Reinforced=Concrete Arches. Berkley
Bridge. In Figs. 240 and 241 are shown the details and sections of
two reinforced-concrete arches having fixed abutments. The first
bridge, Fig. 240, has a nominal span of 60 feet between the two

Fig. 241. Reinforced-Concrete Oblique Arch of Graver's Lane Bridge,
Philadelphia, Pennsylvania

faces of the abutments. On account of the great thickening of the
arch rib near the abutment, the virtual abutments are practically at
points which are approximately 26 feet on each side of the center.
The method of reinforcing the spandrel and parapet walls is clearly
shown in the figure. The side view also gives an indication of some
buttresses which were used on the inside of the retaining walls above
the abutments in order to reinforce them against a tendency to burst
outward.

Graver's Lane Bridge. Fig. 241 shows a bridge which is slightly
oblique, and which spans a double-track railroad. The perpendicu-
lar span between the abutments is 34 feet, but the span measured on

458

MASONRY AND REINFORCED CONCRETE 463

the oblique face walls is 35 feet 8 inches. In this case, similarly, the
arch is very rapidly thickened near the abutment, so that the virtual
abutment on each side is at some little distance out from the vertical
face of the abutment wall. In both of these cases, the arch rib was
made of a better quality of concrete than the abutments.

The arch of Fig. 240 was designed for the loading of a country
highway bridge; that of Fig. 241 was designed for the traffic of a city
street, including that of heavy electric cars.

Stone Arch. In Fig. 242 is shown a stone arch on the New
York, New Haven and Hartford Railroad at Pelhamville, New York.
This arch was constructed over a highway, and the length of its axis
is sufficient for four overhead tracks. The span is 40 feet, and the

Fig. 242. Stone Arch on Line of New York, New Haven and Hartford Railroad

rise is 10 feet above the springing line, the latter being 7 feet 6 inches
above the roadway. The length of the barrel of the arch is 76 feet.

The arch is a five-centered arch, the intrados corresponding
closely to an ellipse, the greatest variation from a true ellipse being
1 inch. The theoretical line of pressure is well within the middle
third, with the full dead load and partial live load, until the short
radius is reached, where it passes to the outer edge of the ring stone,
and thence down through the abutment. There is a joint at the
points where the radii change, to simplify the construction.

The stone is a gneiss found near Yonkers, New York, except the
keystone, which is Connecticut granite, and the coping, which is
bluestone from Palatine Bridge, New York.

459

REVIEW QUESTIONS

461

REVIEW QUESTIONS

ON THE SUBJECT OF

MASONRY AND REINFORCED CONCRETE

PART I

1. Describe the tests that should be applied to determine the
qualities of a building stone.

2. Describe the distinguishing characteristics of limestone,
sandstone, and granite; and the uses for which these characteristics
make them especially suitable.

3. Discuss the crushing strength of various kinds of brick.

4. Describe briefly the characteristics and method of manu-
facture of sand-lime brick.

5. Describe the essential features in the manufacture of
concrete building blocks.

6. Describe the various changes that take place in trans-
forming the original limestone into lime, and from that into the
hardened mortar.

7. What is the essential characteristic of hydraulic lime?

8. What is the essential characteristic of slag cement, and
for what kind pf use is it especially suited?

9. What is the essential difference between natural cement
and Portland cement?

10. If a certain brand of cement requires 30 per cent of
water to produce a paste of standard consistency, how much
water should be used in a 1 : 3 mortar?

11. What is "initial set"? How soon should it develop, and
what is the standard test for the time?

12. How much tensile strength should be developed by
briquettes of neat natural cement, and also by those of neat Port-
land cement, in 7 days? Also in 28 days?

13. What are the desirable characteristics of sand for use in
mortar?

14. Why does sand with grains of variable size produce a
stronger concrete?

463

MASONRY AND REINFORCED CONCRETE

15. What are the characteristics of various kinds of broken
stone and gravel which have an influence on their value in concrete?

16. What practical method should be adopted to mix a large
amount of lime mortar in the proper proportions?

17. Assume that the voids in the sand are measured to be
approximately 40 per cent, and that the voids in the stone are
approximately 45 per cent. Using barrels containing 3.8 cubic
feet of cement, how much cement, sand, and stone will be required
for 100 cubic yards of 1:3:6 concrete?

18. With cement at $1.25 per barrel, sand at $1.00 per cubic
yard, and broken stone at $1.40 per cubic yard, the cost including
delivery on the site of the work, what will be the cost on the mixing
board, per cubic yard of 1:3:6 concrete?

19. Under what conditions is it proper to use dry concrete?

20. What is the danger in the excessive ramming of very
wet concrete?

21. Why is there any practical difficulty in bonding old and
new concrete?

22. What is the effect of the freezing of concrete before it is
set? How can concrete be safely placed in freezing weather?

23. Describe in detail how you would make concrete water-
tight by varying the proportions or by the use of cement grout.

24. Describe the method of waterproofing by the use of felt
and asphalt, or by the use of asphalt alone.

25. What form of bitumen should be used for waterproofing
purposes?

26. Discuss the effectiveness of concrete in preserving
imbedded steel from corrosion.

27. Discuss the protection afforded to imbedded steel by the
concrete, against fire.

28. What precautions should be taken to insure that hand-
mixed concrete is properly mixed?

29. Discuss the relative strength of machine-mixed and
hand-mixed concrete.

30. What requirements should a high-carbon steel satisfy in
order to be suitable for reinforcing concrete?

31. What is the effect of using lime in cement mortar?

32. Describe the principles underlying the mixing of con-
crete so as to obtain the best possible product.

464

REVIEW QUESTIONS

ON THE SUBJECT OF

MASONRY AND REINFORCED CONCRETE

PART II

1. Define the different classes of masonry with respect to the
dressing of the stones.

2. Give an outline of the method of dressing a stone which
shall have a warped surface.

3. What is the purpose of bonding? Describe several ways
in which it is accomplished.

4. A square pier in a building is to carry a load of 420,000
pounds; the pier is to be made of squared-stone masonry. What
are the proper dimensions of the pier?

5. What are the elements affecting the cost of stone
masonry?

6. Describe the various kinds of bonds used in brick masonry.

7. What tools are used", and how are they employed in the
operation of quarrying and dressing stone for ashlar masonry?

8. Describe the various methods used in measuring brick-
work.

9. A brick pier is 20 feet high; it is required to carry a load of
400,000 pounds, and is to be laid in a 1 to 2 natural cement mortar.
Assume that the pier is to be square, what should be its cross-
sectional dimensions?

10. Assuming that two-man stone is to be used in making
rubble concrete, what will be the proper proportions of cement,
sand, small broken stone, and rubble in such a concrete?

11. Describe the method of depositing concrete under water,
using buckets.

12. What precautions must be taken when depositing con-
crete under water through a tube?

13. Describe the tests for determining the suitability of clay
for use as clay puddle.

465,

MASONRY AND REINFORCED CONCRETE

14. How would you test the bearing power of a soft soil?

15. Discuss the bearing power of various kinds of soil.

16. Describe some of the methods of improving a compress-
ible soil.

17. Describe some of the methods of preparing the bed for
foundations on various kinds of soil.

18. What is the purpose of a footing?

19. The wall of a building has a thickness of 2 feet; the total
load on the wall has been computed as 16,000 pounds per running
foot of the wall; the soil is estimated to carry safely a load of 3,000
pounds per square foot. What should be the thickness and width
of limestone footings to support this wall on such a soil?

20. Classify the various kinds of piles, describing their uses.

21. Under what conditions do timber piles rapidly decay?

22. What are the most necessary specifications for timber
piles?

23. A wall having a weight of 15,000 pounds per running foot
is to be built on two lines of piles placed 1\ feet apart transversely.
It is found that piles driven 20 feet into such a soil have an average
penetration for the last five blows of 1.5 inches, when a 2,500-pound
hammer is dropped 24 feet. What is the bearing power of such
piles, and how far apart must they be placed longitudinally in order
to carry that wall?

24. Discuss the advantages and disadvantages of drop-
hammer and steam-hammer pile drivers, and the use of the
water jet.

25. What are the relative advantages and disadvantages of
concrete piles compared with wood piles?

26. What is a grillage, and what is its purpose?

27. What combination of circumstances justifies the use of a
cofferdam?

28. What is the essential disadvantage nvolved in the use of
a crib as a foundation for a pier?

29. What general constructive principle is involved in the
sinking of a hollow crib through a soft soil?

466

REVIEW QUESTIONS

ON THE SUBJECT OF

MASONRY AND REINFORCED CONCRETE

PART III

1 . Why is there but little, if any, structural value to a beam
made of plain concrete?

2. Develop a series of equations (similar to Equation 23) on
the basis of 1:2|:5 concrete whose modulus of elasticity (Ec) is
assumed at 2,650,000, and whose ultimate crushing strength (c') is
assumed at 2,200 pounds.

3. Using a factor of 2 for dead load and a factor of 4 for live
load, what is the maximum permissible live load which may be
carried on a slab of 1 :2|:5 concrete with a total actual thickness of
6 inches and a span of 8 feet?

4. If a roof slab is to be made of 1:3:5 concrete and designed
to carry a live load of 40 pounds per square foot on a span of 10
feet, what should be the thickness of the slab, and the spacing of
f-inch square bars?

5. A beam having a span of 18 feet is required to carry a live
load of 12,000 pounds uniformly distributed. Using 1:3:5 concrete
and a factor of 4, what should be the dimensions of the beam whose
depth is approximately twice its width?

6. What will be the intensity per square inch of the maxi-
mum vertical shear in the above beam?

7. What are the two general methods of providing for
diagonal shear near the ends of the beam?

8. Make a drawing of the beam designed in Question 11,
showing especially the reinforcement and the method of providing
for the diagonal shear.

9. Make a design for a slab of 1:3:5 concrete, reinforced in
both directions, which is laid on I-beams spaced 10 feet apart in
each direction.

467

MASONRY AND REINFORCED CONCRETE

10. What is the general structural principle which makes
T-beams more economical and efficient than plain rectangular
beams having the same volume of concrete?

11. What assumption is made regarding the distribution of
compressive stress in a T-beam?

12. How is the width of the flange of a T-beam usually
determined?

13. What principles govern the determination of the proper
width of the rib of a T-beam?

14. Make complete drawings of the reinforcement of the
floor slabs and beams (Question 20), making due provision for
shear, and making all necessary checks on the design as called for
by the theory?

15. What will be the bursting stress per inch of height at the
bottom of a concrete tank having an inside diameter of 10 feet,
designed to hold water with a depth of 40 feet? What size and
spacing of bars will furnish such a reinforcement?

16. With a nominal wind pressure of 50 pounds per square
foot, on a flat surface, what will be the intensity of the compression
on the leeward side of the tank, allowing also for the weight of the
concrete, and assuming a thickness of 12 inches?

17. On the basis of the approximate theory given in the text,
what would be the required steel vertical reinforcement for the
above described tank?

18. Design a retaining wall to hold up an embankment 30 feet
high, making a cross-sectional drawing and plan drawing similar to
Fig. 113, assuming that the buttresses are to be 12 feet apart.

19. Compute the required detail dimensions and the rein-
forcement for the box culvert illustrated in Fig. 119, on the basis
that the culvert is to be 10 feet wide, 12 feet high, supporting an
embankment 15 feet deep, and also a railroad loading of 1,500
pounds per square foot.

20. A column is to be supported on a soil on which the safe
load is estimated at 6,000 pounds per square foot; the column
carries a total load of 210,000 pounds; the column is 22 inches
square; what should be the dimensions of the footing, and how
should it be reinforced?

468

REVIEW QUESTIONS

ON THE SUBJECT OF

MASONRY AND REINFORCED CONCRETE

PART IV

1. What are the difficulties encountered in obtaining a
satisfactory outer surface of concrete?

2. Describe two successful methods of obtaining a good
outer surface.

3. When and how can acid be properly used in treating a
concrete surface?

4. What pigments should (and should not) be used for color-
ing concrete?

5. Describe the various methods of finishing concrete floors.

6. How may efflorescence be removed from masonry sur-
faces?

7. What are the practical difficulties and disadvantages of
measuring the materials of concrete in the operation of automatic
measuring machines?

8. Make a sketch and plan for the concrete plant for a
6-story building, 40 feet by 100 feet; or, describe, with comments
and sketch, the plant of some similar building actually being erected.

9. What precautions are taken to prevent the lumber in the
forms from swelling or buckling?

10. Describe various devices for holding column forms
together.

11. How are I-beams utilized to support the forms for con-
crete slabs laid on them?

12. Make a sketch design for the forms for a vertical wall ten
feet high, six inches thick, and twenty feet long.

13. Describe the methods of lowering the centering under
arches.

14. What should be the dimensions of a column of hemlock
12 feet high, to support safely a load of 15,000 pounds?

15. What are the several methods of bonding old and new
concrete in floor construction?

469

REVIEW QUESTIONS

ON THE SUBJECT OF

MASONRY AND REINFORCED CONCRETE

PART V

1. Draw the intrados for a segmental arch with a span of 40
feet and a rise of 10 feet. Compute the proper depth of keystone;
make the thickness at the abutment £ greater, and draw the
extrados. Use scale of \ inch as equal to 1 foot.

2. On the basis of Question 8, draw the load line, allowing
for a level cinder fill, a 7-inch pavement, and a live load of 200
pounds per square foot.

3. Assuming 15 voussoirs in the above arch, compute the
vertical loads on each voussoir, and draw a half load line for full
loading over the whole arch. Use scale of 3,000 pounds per inch
for load line.

4. Determine the special equilibrium polygon for the above
loading, and the maximum unit-intensity of pressure at any joint.

5. Determine the load line for a concentrated load of 20,000
pounds on an area of 25 square feet at the quarter-point of the arch,
and a load of 200 pounds per square foot over the remainder of the
half -span.

6. Draw the special equilibrium polygon for the loading of
Question 12, and determine the maximum unit-intensity of pressure
at any joint.

7. Design an abutment for the above arch which shall be
stable under either of the above conditions of loading.

8. Draw the load line for the above arch on the basis of the
loading of Question 12, but on the assumption that the pressures on
the arch are perpendicular to the extrados.

9. Redraw the extrados and intrados of Fig. 230 on the
scale of \ inch equals 1 foot; and then, by scaling the various thick-
nesses at every two-foot section, for 26 feet on each side of the cen-
ter, compute the moment of inertia for each section.

10. On the basis that Fig. 230 is virtually a segmental arch
with abutments 26 feet each side of the center, determine the posi-
tion of vm on the drawing- made for Question 20.

470

INDEX

471

INDEX

The page numbers of this volume will be found at the bottom of the pages;
the numbers at the top refer only to the section.

Page

Belt course

100

Abutments

173, 393

Bonding

100

design

173

brick masonry

113

flaring wing walls, with

173

old and new concrete 73, 358

T-shaped

174

steel and concrete

214

U-shaped

174

bond required in bars

216

Arch design and construction,

con-

slipping of steel in concrete

, '

crete

393

resistance to

214

Arch masonry, terms of

393

Brick

Arch ribs, hinged

456

absorptive power

Berkley bridge

458

common

Graver's Lane bridge

458

color

principles, general

456

crushing strength

stone arch

459

definition and characteristics

Arch sheeting

393

fire

Arches

requisites

elastic

437

sand-lime

kinds

395

size and weight

theory

396

Brick masonry

112

voussoir

405

bonding

113

Arris

constructive features

114

Ashlar

cost of

115

Ax or peen hammer

efflorescence

115

impermeability

115

measuring

115

Backing

99, 393

piers

116

Bars, bending or trussing

353

strength

114

bands, column

356

Broken stone

bars, slab

355

classification

details

353

size and uniformity

frames, unit

356

Bushhammering

100

spacers

356

Buttress (see Counterfort)

100

stirrups, for

355

tables

354

Basket-handle arch

395

Batter

Caissons

156

Bearing block

100

hollow-crib

157

Bed joint (see Joint) •

100

open

156

Note. — For page numbers see foot of pag

es.

473

INDEX

Page

Caissons (continued)

Concrete (continued)

pneumatic

159

fire protective qualities of

Cast-iron piles

136

Baltimore fire, results shown 86

Catenarian arch

395

cinder vs. stone

Cavil

100

high resistance

Cement materials

theory

common lime

thickness of concrete requi

red 84

hydraulic lime

mixing and laying

natural

bonding

Pozzuolana or slag

freezing, effect of

Portland

proportioning, methods of

Cement testing

ramming

details of

transporting and dopos

it-

form of test pieces

ing

molds

wetness of

selection of samples

mixing, methods of

storage of test pieces

by hand

machines

by machinery

standard tests

machine vs. hand

chemical analysis

preservation of steel in

compressive strength

cinder vs. stone

constancy of volume

tests by Professor Norton

fineness

tests, short time

mixing

waterproofing

molding

alum and soap

normal consistency

asphalt

specific gravity

felt laid with asphalt

specifications, standard

hydrated lime

standard sand

linseed oil

tensile strength

plastering

time of setting

Sylvester process

Chisel

100

Concrete building blocks

Cinder concrete

cost

Circular arch

395

curing

Clay puddle

120

facing, mixture for

puddling

121

materials

quality of clay

120

mixing and tamping

Cofferdams

154

size

Concrete

61 .

types

characteristics and properties

Concrete construction work

305

compressive strength

bars, bending or trussing

353

cost

bonding

358

modulus of elasticity

examples of

370

shearing strength

forms

333

tensile strength

machinery for

305

weight

representative examples

370

fire protective qualities of

surfaces, finishing

359

Note. — For page numbers see foot of pages.

474

INDEX

Page

Concrete curb

185

Concrete work, machinery for

305

construction

185

block

329

cost

187

cement-brick

331

types

185

Construction plants

324

Concrete, hoisting and transporting

buildings

324, 326

equipment for

315

hoisting

315

boilers

324

measurers

311

charging mixers

319

mixers

306

hoist, cone-friction belt

316

mixing concrete, power for

312

hoisting buckets

319

sand washing

331

hoisting engine

315

street work

327

hoisting lumber and steel

319

transporting

323

hoists, electric motor

317

Conglomerates

transporting mixed concrete

323

Coping

101

Concrete masonry

116

Corbel

101

methods for under-water work

118

Counterfort (see Buttress)

101

bags

119

Course

101

buckets

119

Coursed masonry (cf. Random)

101

tubes

119

Coursed rubble (see Rubble)

101

rubble

117

Coursing joint

393

advantages over ordinary

Cramp

101

concrete

117

Crandall

101

materials, quantities of
stone, proportion and size of
uses of 117,

118
117
118

Crandalling
Cribs

101
156

Concrete walks

181

Crown

393

base

181

Culverts

174, 284

cost

184

arch

180, 292

drainage of foundations

181

classification by loadings

284

seasoning

184

double box

177

top surface

182

end walls

180

Concrete work, finishing surfaces of

359

plain concrete

178

acid

364

stone box

175

cast-concrete-slab

365

Curing concrete blocks

colors for

366

air

dry mortar

365

steam

efflorescence

368

Gushing pile foundation

143

floors, for

367

granolithic

363

imperfections

359

Dimension stone

102

laitance

368

Disk piles

136

masonry

361

Dolomite

mortar

360

Dowel

102

painting

367

Draft

102

plastering

360

Drop-hammer pile driver

147

stone or brick

362

Dry-stone masonry

102

Note. — For page numbers see foot of pages.

475

INDEX

Elastic arches

advantages and economy
illustrative example
mathematical principles

Elliptical arch

Extrados (cf. Intrados)

Face

Face hammer

Feathers (see Plugs)

Flat-slab construction
bars, location of
calculation, method of
constructive details
outline of method
panels, rectangular
reinforcing bars, placing

Flexure of concrete beam design

Page

437
438
440
439
395
102, 393

102
102

245
249
247
252
245
252
247
189

compressive forces, center of

gravity of 196
compressive forces, summation

of 196
economy of concrete for com-
pression 191
economy of steel for tension 192
elasticity of concrete in com-
pression 193
moduli of elasticity, values of

ratio of 197

neutral axis, position of 196

resisting moment 201
statics of plain homogeneous

beams 190

steel, percentage of 200

theoretical assumptions 195

Footing 102

beams, continuous 267

compound 268

simple 261

Forms, building

Blaw collapsible steel 345

clamp for holding, adjustable 342
cost for

8-story building 338

garage 341

Note. — For page numbers see foot of pages-.

Page

Forms, building (continued)
design for

arches, center of 346

classes of centers 346

illustrative examples

3.30, 352
safe loads on wood

columns 350

safe stresses in lumber

for wood forms 348
beams and slabs 337

columns 335

conduits and sewers 343

Locust Realty Building 338

Torresdale filters 343

walls 345

requirements of 333

Foundations 121

bridge piers and abutments 170

cofferdams, cribs, and caissons 154
concrete curb 185

concrete walks 181

culverts 174

piles 135

preliminary work 121

footings 128

beam 131

calculation of 129

pier 133

requirements of 128

preparing bed 126

on firm earth 127

on rock 126

on wet ground 127

soil, character of 122

bearing power 124

compressible, improving 125
compressive value, test-
ing 123
examination of, with

auger 123

subsoils, classification of 122

retaining walls 162

Granite
Grout

13
102

476

INDEX 5
Page Page

Masonry, types of (continued)

Haunch

393 clay puddle

120

Header

102 concrete

116

Heading joint

393 stone

107

Hydraulic lime

29 Mixers, concrete

306

Hydrostatic arch

395 gravity

307

paddle

311

rotary

308

Intrados (cf. Extrados) /03, 394 M°*^da of

57
57

common lime

natural cement

Jamb

Portland cement

Joint

materials for

cement mortar

Keystone

lime mortar
re-gaging or re-mixing, effect of

61
59

lime paste

Lime, common
in cement mortar

2g natural cement
en Portland cement

60
60

Limestone

Lintel

103 N

Natural bed

103

Natural cement

Marble

12 Natural stone

Masonry and reinforced concrete

11 appearance of

arch design and construction,

conglomerates

concrete

393 cost

beam design, reinforced-concrete

189 dolomite

columns and walls, reinforced-

durability

concrete

253 granite

concrete construction work

305 limestone

foundations

121 marble

masonry materials

1 1 sandstone

masonry, types of

99 seasoning

Masonry materials

11 strength

brick

20 tests

broken stone

54 trap rock

cement

27 Q

concrete
concrete building blocks

^ One-man stone

103

mortar

57 P

natural stone

11 Parapet

394

sand

51 Pick

103

steel for reinforcing concrete

89 Piers

170

Masonry, types of

99 abutment

172

brick

112 failures, causes of

171

Note. — For page numbers see foot of pages.

477

INDEX

Page
Piers (continued)

location 170
sizes and shapes 170
Piles 135
Annapolis, foundations for sea-
wall at 154
Charles River Dam, for 153
types 136
cast-iron 136
concrete and reinforccd-con-

crete 140

Cushing 143

Raymond 141

simplex 141

steel-shelled 142

disk 136

screw 136

sheet 138

wood bearing 137

construction factors 144

bearing power 144

caps 148

concrete and reinforced-con-

crete, advantage of 150

cost 152

foundations, finishing 149

loading for 152

methods of driving 146

sawing 149

splicing 148

Pile driving, methods of 146

drop-hammer 147

steam-hammer 147

water jet 147

Pitch face masonry 103

Pitching chisel 104

Plinth (see Water-table) 104

Plug 104

Point 104

Pointed arch 395

Pointing 104

Portland cement 30

Pozzuolana or slag cement 29

Puddling 121

Quarry-faced stone 105

Quoin 105
Note. — For page numbers see foot of pages.

Page

Random (cf. Coursed masonry) 105

Range 105

Raymond concrete pile 141

Reinforced-concrete beam design 189
flat-slab construction 245

flexure 189

practical calculation and design of 206
T-beams 227

Reinforced-concrete beams and slabs,
calculation and design
of 206

bonding steel and concrete 214

I-beams, slabs on 224

simple beams, table for compu-
tation of 213
slabs reinforced in both directions 225
slab bars, spacing 211
slab computations, tables for 206
temperature cracks, reinforce-
ment against 226
vertical shear and diagonal ten-
sion 218
Reinforced-concrete columns and

walls 253

columns 292

design 294

eccentric loading 298

hooped 296

reinforcement, methods of 292
culverts 284

flexure and direct stress 253

footings 261

girder bridges 288

retaining walls 271

tanks 299

vertical walls 283

Reinforced-concrete work, representa-
tive examples of 370
Allman building 374
Bronx sewer 389
Buck building 370
Erben-Harding building 375
Fridenberg building 385
General Electric Company at

Ft. Wayne, lintels of 386

478

INDEX

Reinforced-concrete work, representa-
tive examples of (con-
tinued)

girder bridge, Allentown, Pa. 390
Heinz warehouse 382

McGraw building 384

McNulty building 382

sewer, Waterbury, Conn. 387

Swarthmore Shop building 378

tile and joist system in apart-
ments 380
water-basin and circular tanks 386
Relieving arch 395
Retaining walls 162, 271
causes of failure 162
design 164
base, width of 164
existing walls, value of study

of 165

faces 164

fill behind wall 164

pressure behind wall 165

pressure on foundation 166

foundations 163

types 169

Right arch 395

Ring stones 394

Riprap 105

Rise 394

Rough-pointing 105

Rubble 105

Rubble concrete 63, 117

Sand 51

character, geological 52

52
52

qualities 51

sharpness 52

use 51

voids, percentage of 53

Sandstone 12

Segmental arch 395

Semicircular arch 395

Shear, of reinforced concrete beams 218
diagrams of related factors, cal-
culations by 222

Note. — For page numbers see foot of pages.

Page
Shear, of reinforced concrete beams

(continued)

distribution of 218

guarding against failure by 219

in T-beam 236

Sheet piling 138

Simplex concrete pile 141

Skew arch 396

Skewback 394

Slope-wall masonry 105

Soffit 394

Spalls 106

Span 394

Spandrel 394

Springer 395

Springing line 395

Squared-stone masonry 106

Steam-hammer pile-drivers 147

Steel bars 90

deformed 91

corrugated 91

expanded metal 93

Havemeyer 92

Kahn 92

square twisted 91

steel wire fabric 93

reinforcing bars, specifications for 94

determinations, chemical 94

elongation, modification in 95

finish 96

manufacture, process of 94

properties, chemical and

physical 94

specimens, form of 94

tests, number of 95

twists, number of 96

weight, variation in 96

yield point 94

structural 91

Steel for reinforcing concrete 89

bars, types of 90

quality of 89

reinforcing bars, specifications for 94

Steel-core columns

Steel-shelled concrete piles

Stone masonry 107

cost of 112

479

INDEX

Page
Stone masonry (continued)

features, constructive 110

bonding 110

mortar, amount of 111

pressures, allowable unit 111

stone, cutting and dressing 107

blocks, economical size of 109

blocks, rectangular 108

cost of 110

surface, cylindrical 108

surface, warped 109

stones, classification of dressed 107

Stone tests 17

absorption 18

chemical test 19

physical tests 19

quarry examinations 20

test for frost 18

Stretcher 106

Stringcourse (see Beltcourse) 106, 395

Tables

barrels of Portland cement per

cubic yard of mortar 69, 70

bond adhesion of plain and de-
formed bars per inch of
length 216

chemical and physical properties

of reinforcing bars 95

compressive strength of concrete 64

compressive tests of concrete 64

gross load on rectangular beam

one inch wide 212

ingredients in one cubic yard of

concrete 70

Lambert hoisting engines, sizes of 316

load data for segmental arch

problem 448, .449

modulus of elasticity of some

grades of concrete 200

mortar per cubic yard of masonry 111

percentage of water for standard

mortars 38

physical properties of some build-
ing stones 16

Note. — For page numbers sef fool of pages.

Page
Tables (continued)

Portland cement mortars contain-
ing two parts river sand
to one part cement, col-
ors given to 366

proportions of cement, sand, and
stone in actual struc-
tures 67

quantities of brick and mortar 114

Ransome steam engines, dimen-
sions for 313

ratio of offset to thickness for
footings of various kinds
of masonry 130

required width of beam, allowing
2iXd, for spacing, cen-
ter to center, and 2
inches clear on each side 233

segmental arch, 60-foot span,

data for 441

solid wood columns of differ-
ent kinds of timber,
strength of 349

standard sizes of expanded metal 93

tensile tests of concrete 89

value of j for various values of n
and p (straight-line for-
mulas) 198

value of k for various values of n
and p (straight-line for-
mulas) 197

value of p for various values of

(s-i-c)andn 202

values of quantities used in

equations (62), (63), etc. 445

voussoir arches, first, second,
and third condition of
loading for 414

weights and areas of square and

round bars 94

working loads on floor slabs, M =

Wl + 10 207-209

T-beam construction 227

approximate formulas 234

flange, width of 231

resisting moments of 228

rib, width of 231

480

INDEX

Page
T-beam construction (continued)

shear in 238

shearing stresses between beam

and slab 236

Blab, beam, and girder construc-
tion, numerical illus-
tration of 239
testing, numerical illustration 237

Tanks

design

overturning, test for
Template

Tile and joist system
Trap rock
Two-man stone

Voussoir
Voussoir arches

Note. — For page numbers see fo

299

299, 302
301
106
380
13
106

106
405

Voussoir arches (continued)

abutments, various forms of

definition

depth of keystone

design, correcting a

Page

425
405
409

418

distribution of pressure between

two voussoirs 405

external forces acting on 407

voussoir, determination of load

on a 426

Water basin
Water- jet pile-driving
Water table
Wood bearing piles
Wood brick

147
106
137
106

481

THE LIBRARY

UNIVERSITY OF CALIFORNIA LIBRARY

Los Angeles
This book is DUE on the last date stamped below.

JAN

93*

Form L9-10m-3,'48(A7920)444

K \

000 688 1 64 3

145

C99

1916

v.6

.4
-^4

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