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LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

Class



CONCRETE



BY

JOHN C. TRAUTWINE, JR.

'/ AND

JOHN C. TRAUTWINE, SD.

CIVIL ENGINEERS



FIRST EDITION, FIRST THOUSAND



REPRINTED FROM

TRAUTWINE'S
CIVIL ENGINEER'S POCKET-BOOK

19xH EDITION, lOOrn THOUSAND, 1909




NEW YORK

JOHN WILEY & SONS

LONDON : CHAPMAN & HALL, LIMITED

1909






8ENEHAL



Copyright 1909 by
JOHN C. TRAUTWINE, JR.

AND

JOHN C. TRAUTWINE, 3n.



WM. F. FELL COMPANY MURPHY-PARKER CO.

ELECTROTYPERS AND PRINTERS BINDERS

PHILADELPHIA PHILADELPHIA




PREFACE.



In the nineteenth (1909) edition, 100th thousand, of our Civil
Engineer's Pocket-Book, the most notable of the new features is the
series of articles on Concrete (plain and reinforced), including
Cement, Sand and Mortar. Practically all of this matter (occupy-
ing about 200 pages), altho by no means original, is entirely new,
so far as our publications are concerned. In compiling it, our
object has been to present, in convenient and condensed form, the
essentials of existing knowledge and opinion in regard to these
subjects.

Special attention has therefore been given to the rules and results
of modern practice in concrete construction ; a feature which is
reflected thruout the text and especially in the "Selected Results
of Experiment and Practice," pp 1135, etc., and in the "Digest of
Specifications," pp 1184, etc. These contain, we believe, a more
complete and more conveniently classified presentation of modern
practice in concrete than is to be found elsewhere in equal space.
To attain this, great care has been taken so to arrange the material
as to give maximum density in the resulting text, and maximum
convenience for reference.

In the selection of "results of experiment and practice," we have
had in mind not only the weight and standing of the authorities
quoted, but also the importance of covering, as nearly as possible,
the entire field of practice, with its very numerous and diversified
problems.

For reasons explained on p 1140, it was found impracticable to
arrange these results in satisfactory logical order, and they are
therefore furnished with a special and very complete table of
contents, or "Directory," pp 1135-1139, arranged in practically
the same order as are the articles on cement, etc., pp 930, etc., and
on concrete, etc., pp 1084-1134. It is believed that, in connection
with this "Directory," the "selected results" will be found a
very useful feature.

Similarly, the concrete specifications have been selected from
different lines of work, including not only U. S. Government

iii



192880



IV PREFACE.

operations and the building codes of the larger cities, but the care-
fully prepared rules of consulting engineers and experts in concrete.
As in the case of our digests of specifications for trusses and build-
ings, etc., prepared for our 18th Edition (1902), these digests are
"by no means mere quotations from the originals ; but, as their
name implies, the result of careful digesting of the contents of the
specifications selected for the purpose ; their several provisions
being carefully studied, in nearly all cases re- worded or reduced to
figures, and tabulated in form convenient for reference, the whole
being arranged in such logical order as to facilitate reference."

The specifications include those for concrete blocks and for
concrete sidewalks, adopted by the National Association of Cement
Users at Philadelphia, January, 1908.

With these exceptions, and those of beams and columns, we
refrain from extended discussion of special works (such as arches,
dams, etc. ) in concrete ; confining ourselves, for the present, to the
material itself and its constituent parts.

Under Cement, the Committee Report of the American Society
of Civil Engineers, submitted in 1885, has been replaced by that of
the later Committee, submitted in 1903 and amended in 1904 and
in 1908. The recommendations of the Board of U. S. Engineer
Officers, 1901, are retained ; and those of the American Society for
Testing Materials (1904, amended 1908) and of the Engineering
Standards Committee of Great Britain (1904) are added.

Owing to the nature of the materials involved, the theory of
concrete design and construction is less firmly established and less
capable of satisfactory demonstration than that of other branches
of engineering. We have therefore avoided useless refinement and
expenditure of space upon this branch of the subject, devoting
ourselves chiefly to its practical side ; but we have nevertheless
endeavored to state, clearly, succinctly, and in form convenient for
reference and use, the commonly accepted theories, as they affect
the principal features of practice.

In the article on Cost of Concrete, pp 1207-1210, we have aimed
to give merely the ranges of cost to be expected in different features
of concrete work, keeping in mind those differences of condition
which so largely affect the several items of cost.

We have of course drawn freely upon the existing literature of
concrete. In giving credit for material so used, we have aimed to
err upon the side of liberality, not only as a matter of justice
to the authorities quoted, but also for the convenience of those of



PREFACE. V

our readers who may wish to study the sources of our information
in further detail. With the same object in view, we give these
references with full detail as to volume, page, date, etc. ; and it is
therefore hoped that these articles, together with the references
under " Bibliography, " may serve, to some extent, as an "Index
to Current Literature" on the subject of concrete.

For convenience of reference we reprint here also, from The Civil
Engineer's Pocket-Book, pp 454 to 461, remarks on the general
principles of the strength of materials, and, pp 494 a to 494 h, on
diagonal stresses in beams.

For economy of space we not only (as heretofore) use such obvious
abbreviations as cen, diag, hor, vert, cem, agg, cone, etc., but we
frequently drop certain letters which (like "ugh" in "though")
are as useless as the "k " which our forefathers considered essential
in "musick," or the "u" which our English cousins still like to
use in ' ' honour. ' 7

The same consideration of space has led also to the liberal
use of symbols, such as D for "square," Q" for "square inch,"
/ for "per," > < > and < for "more than," "less than," "not
more than" (equal to, or less than), "not less than " (equal to,
or more than), respectively.

In connection with the theory of reinforced concrete we have
been forced to the extensive use of letters with subscripts, as/,, E c ,
etc., etc. We have made special arrangements to secure the great-
est possible legibility for these characters, as well as in connection
with the symbols, mentioned above.

In this reprint, the paging is that of the Pocket- Book ; and the
matter is here accompanied by the appropriate portions of the
Table of Contents, Price List, Business Directory, Bibliography
and Index of that work.



Our acknowledgments are made to many who have assisted us
in our labors, notably to Professors A. W. French and L. J. Johnson,
and to Messrs. J. Y. Wheatley and Wm. H. Balch.

JOHN C. TRAUTWINE, JR.,
JOHN C. TRAUTWINE, 3D.
PHILADELPHIA, September, 1909.



CONTENTS.



In this reprint, the paging is that of
The Civil Engineer's Pocket-Book.

See Index.



STRENGTH OF MATE-
RIALS.


PAGE

Mortar.

Constituents . 947d


PAGE


Amount Required in Masonry . 947d
Cement. . 947d


Stress and Stretch . . .454


Sand 947e


Elastic Modulus 456




Elastic Limit 459


Consistency 947/


Yield Point 460


Setting and Hardening 947/


Resilience 460


Strength 947 i


Suddenly Applied Loads 461


Finish 947?




Behavior in Water 947/c


Transverse Strength.

Diagonal Stresses 494a
Horizontal and Vertical Shear 494c
Maximum Unit Stresses 494e


CONCRETE.

Aggregates 1084
Size . 1084




Density 1084
Cyclopean.... 1085


CEMESf T MORT VR


Constituents 1086




Advantages 1086


Cement


Proportions 1086


Materials 930


Materials Required 1087


Manufacture 931
Natural and Portland 931


Density 1089


Puzzolana 932


Consistency 1090


Silica Cement 932
Other Cements 933


Handling and Mixing : . . . 1090
Handling Ingredients 1090
Mixing 1092


Composition 933


Mixers 1092


Packages . . 935


Placing. 1093


Age 935


Forms 1094


Testing 936




Specifications


Strength. 1098


Requirements


Details 1098


U S Engr Officers 937


Adhesion 1099


Am Soc Test Materials . . . 940
Engng Standds Comm of


Removal 1099
Joints 1099


Gt Brit 940
Tests
Am Soc Civ Engrs 942


Ramming . 1100
Placing under Water .1100




Properties . . 1 103


Sand.


Weight.. 1103
Permeability 1103


Composition 946


Elastic Modulus . 1106


Sizes of Grains. ... ' 946


Strength 1106


Density 947a
Other Properties. . . . .947c


Setting 1106
Effects of Heat and Cold. .1107



VI



CONTENTS.



vii



PAGE

Protection 1107

Expansion 1 108

Chemical Effects 1108

Tests in Place... ..1109



Reinforced Concrete.

Expansion, Contraction, etc . . .1110

Adhesion 1111

Columns 1112

Hooped 1113

Beams 1115

Theory 1115

Tee Sections 1122

Shear 1123

Reinforcement 1124

Unit 1125

Diagonal Stresses 1125

Adhesion 1126

Continuous Beams 1126

Methods 1127

Bar 1128

Web 1132

Trussed 1133

With Structural Shapes 1133

Column... ..1134



Experiments.

Directory 1135

Results 1140

Specifications.

Alphabetical List 1 184

Classified List 1185

Contents 1185

Cement 1186

Sand 1186

Aggregate 1 186

Consistency 1187

Mixing 1188

Forms 1189



PAGE

Placing, etc 1189

Joints 1190

Under Water 1190

Rain 1191

Frost 1191

Moistening 1191

Removal of Forms 1191

Finish, Waterproofing, etc 1192

Artificial Stone 1193

.1193
.1193
.1194
.1194
.1194
.1196



Strength.

Permissible Loads. . . .

Elastic Modulus

Safety Factors

Reinforcement

Permit

Clearance 1196

Columns 1197

Beams 1198

Slabs 1199

Continuity 1200

Tests 1200

Sidewalks 1201

Blocks 1203



Cost

Materials 1207

Transportation 1208

Storage 1208

Mixing and Placing 1208

Forms 1209

Miscellaneous 1210

Total ..1210



PRICE LIST.
BUSINESS DIRECTORY.
BIBLIOGRAPHY.
INDEX.



NOTICE.

The following pages are selected
from those of The Civil Engineer's
Pocket-Book, and they are numbered
similarly with the corresponding
pages in that book.



454



STRENGTH OP MATERIALS.



STEENGTH OF MATERIALS,



<; I;M:IJ A i, PRIJTCTPMS.

Stress.

1. Stress occurs when forces act upon a body in such a way that its
particles tend to move simultaneously with different velocities or in differ-
ent directions; to do which, the particles must change their relative posi-
tions. This occurs, for instance, when a body is so placed as to oppose the
relative motion of two other bodies; as when a block is placed between a
weight and a'hor table. Here the two bodies (the wt and the table) tend to
come closer together; but they cannot do so without distortion of the in-
tervening block; and such distortion is resisted by internal forces, act-
ing betw the particles of the block and tending to keep those particles in
their original relative positions. The action of these internal forces is called
stress.*

2. Similarly, if a body be suspended by a long chord, and if we push or
pull the body to one side, the particles, on the side acted upon, will first
tend to move, and the transmission of this tendency to the remaining par-
ticles causes stress within the body.

3. For internal equilibrium, the internal stresses must balance
the external forces. Hence, it is not unusual to apply the term,

indifferently to either.



4. Let the two forces, a and 6, Figs A, B, acting upon the body, o, meet
at an angle, a o b. Then the two equal and opposite components, a" o
and b" o, cause compressive or tensile stress in the body, o, as in t 1; while
the other two components, a' o and b' o, unite to form the resultant, c o,
which, unless balanced by other forces, moves the body, o, in its own direc-
tion, causing, as in ^ 2, another comp stress, Fig A, or tensile stress, Fig B.




c
Fig. A.

5. Upon any plane within a body, a force may act (1) normally,
(2) tangeiitially, or (8) obliquely. If it act obliquely, it may be
resolved into two components (see Statics, If 65, p 372), one acting normally
and the other tangentially, upon the plane.

6. Consider the two portions into which the body is divided by such a
plane, Then (1) forces, acting normally upon the plane, produce ten-
sion (or compression) in the plane, tending to separate the two por-
tions (or to push them closer together); and (2) forces, acting tangentially
upon the plane, produce shear (or torsion) in the plane, tending to
slide the two portions one past the other in a straight line (or with a twisting
motion). Torsion occurs in planes betw and parallel to two con-
trary couples, as in cross sections of a hand-brake axle when the brake
is applied.

7. Thus, if an iron bar be pulled (or pushed) lengthwise, its cross sections
sustain normal tension (or compression). If it be sheared across (or'twisted),
the cross sections, between and parallel to the two shearing (or twisting)
forces, sustain shearing (or torsional) stress.

8. At any point, in the circular path of a torsional stress, we may consider
the tangents to the path as representing shearing forces. Torsion is



* In every-day language, and often in the writings of engineers, this action
of the internal forces, or the external force causing it, is called "strain";
but scientists apply the word " strain " to the deformation occurring under
See "stretch," U* 11 etc.



GENERAL PRINCIPLES.



455



therefore merely a shearing 1 stress in which the direction changes at each
point.

9. Transverse stress. In Fig 124, p 438, the two equal and parallel
forces, W and R, in opposite directions, cause a tangential or shearing stress,
= W = R, in the vertical planes lying between their lines of action; but
W and R, as a couple, have a moment, which, for equilibrium, must be re-
sisted by the equal and opposite moment of another couple, as C and T;
and the opposition of these two couples causes normal (comp and tensile)
stresses in the same vert planes parallel to and betw W and R.

10. The ultimate tendency of any opposing external forces is to fracture
the body by incre-asintj the distances between its particles. Even under
compressive stress, rupture can occur only by separation of particles.

Stretch.

11. When the internal stresses and the external forces are in equilibrium,
no distortion takes place; but, at the instant when opposing external
forces are first applied to a body, the internal stresses are not yet developed,
and distortion begins, under the unopposed action of the external forces.
See 11135 etc. But the stresses are brought into action by the distortion,
and they increase with it; and, if the external force is not increased beyond
the elastic limit (If 26) the stresses finally equal the external forces, and
prevent further distortion.



Stretch.

100



WOOe=<tOOOl/L

150 200



250




1.5 2.0

J 000 e = 1000 l/L



1.0 1.5 2.0 . 2.5

Stretch.

Fig. C.

Behavior under Normal Stresses.

12. Fig C represents the behavior of a typical material (mild
steel) under tension. From to A, i.e., under stresses up to the elas-
tic limit (1f 26), say 34,000 Ibs per sq inch, the stretch progresses propor-
tionally with the stress, as indicated by the straight line, A. (The earlier
portions of the process are represented, in the lower diagram, to a scale of
stretch 100 times as great as that of the upper diagram.^ After passing
the point A, the stretch increases faster than the stress; and, betw B and B',
the stretch (in iron and steel) increases with little or no increase of stress, or
even under a slightly diminishing stress.* B is called the yield point.
See If 31. The scale of the lower diagram does not extend to B'. Beyond
B' (upper diagram), the stretch increases much less rapidly than betw B



*See tlf 16, 17



30



456



STRENGTH OF MATERIALS.



and B', and remains, for a time, nearly proportional to the stress* (though
much greater, relatively to stretch, than in A); but the stretch now pro-
ceeds faster and faster, and in increasing ratio with the stress, until the
stress reaches its maximum or ultimate value (say 70,000 Ibs per sq inch)
at C. At C, the stretch is increasing without increase of stress (diagram
horizontal); and, beyond C, the stretch continues increasing altho the stress
is diminishing, until, finally, at D, rupture occurs.

13. If, after passing the elastic limit, the bar is relieved from stress, as
at F, Fig C, lower diagram, its recovery is incomplete, the length remaining
somewhat greater than in its original unstressed condition. The permanent
increase, F', is called the permanent set, or simply the set. The
line F F' is, in general, approx parallel to the line, A, of elastic stretch.
When the same stress is again applied, the stretch is greater than before, by
a small amount represented by F F".

14. When the stress is within the elastic limit (f 26), the
recovery, upon release from stress, is so nearly complete that the per-
manent set cannot be indicated in our Figs. (II 28.)

15. Under tension, the sec area is diminished, and, under compression
increased. In ductile materials, under tension, the reduction of sec area is
very marked, especially along a relatively short portion of the length, usually
near the middle of said length; and fracture occurs normally at the point
of maximum reduction.

16. In Fig C, both diagrams, and, in Fig D, the solid curves, represent
the nominal unit stresses, or those usually stated. These are found
by dividing the total stresses, respectively, by the original section area, as
in If 18.

17. The dotted curves, Fig D, represent the actual unit stresses,
found by dividing the total stresses, respectively, by the actual section area,
as diminished or increased by stress. Under tension, the actual unit stresses
are of course greater, and, under comp, less than the corresponding nominal
unit stresses.



Negative stretch




I




Stretch



t
IS



Fig. .

Elastic Modulus. Fig. C.

18. Let P = the load (one of the two equal and opposite external forces)
acting at one end of a bar and in line with the axis of the bar; and let a =
the original* cross-section area, or section area, of the bar, normal to
its axis. Then, s, = P / a, is the normal stress per unit of area, or stress
intensity, or normal unit stress, in the bar. We assume that, so long as
the external force acts axially, P is uniformly distributed over a, altho this
is seldom strictly the case in practice.

*See 1111 16, 17



GENERAL PRINCIPLES. 457

19. Let L = the original length of the bar, or of some designated portion
of that length, and I = the stretch * which takes place, in the length, L,
under the action of a given- unit stress, s. Then, e, = I / L, is the stretch
per unit of length, or unit stretch,* corresponding to the unit stress, s.

20. In many materials, the unit stress, s, and the unit stretch, e, at first
increase proportionally, the ratio, s/e, or unit stress -=- unit stretch, remain-
ing practically constant. This ratio is called the elastic modulus,
and is designated by E ; or

Elastic modulus = E = s/e = unit stress -=- unit stretch.

2O a. The elastic modulus is thus proportional to the tangent

of the angle, X A , Fig C, the proportion depending upon the scales adopted .

2O b. The elastic modulus, E, increases with the unit stress reqd to pro-
duce a given unit stretch. Hence E is a measure of the stiffness of a body,
i.e., of its ability to resist change of shape. "Stillness modulus"
would have been a better name.

2O c. If equal additions of stress could indefinitely continue producing
equal additional stretches in a bar, beyond as well as within the elastic
limit (H 26), then a stress, equal to the elastic modulus, would double the
length of a bar when applied to it in tension, or would shorten it to zero in
compression.

20 d. For example, within the elastic limit, a one-inch square bar oi
rolled steel will stretch or shorten, on an average, about _ of its length

under each additional load of 1000 Ibs. If it could stretch or shorten in-
definitely at the rate of of its original length for each 1000 Ibs. of

added load, then 30,000 times 1000 Ibs., or 30,000,000 Ibs., (which is about
the average modulus of elasticity for such bars) could either stretch the bar
to double its length or reduce it tp zero.

2O e. If equal infinitesimal stresses, applied to a bar, could indefinitely
produce stretches, each bearing a constant ratio to the increased length of the
bar, if in tension; or to the diminished length, if in compression- then the
same load which would double the original length of the bar, if applied in
tension, would reduce it to half its original length, if applied in compression.

*We regard shortening, under compression, as negative stretch.

V

Of

UNIVERSITY




458 STRENGTH OF MATERIALS.

21. In a prismatic bar, under longitudinal tension or
compression, let

W = the total load ;
a = the cross section area ;

W

s = = the unit stress = the stress per unit of area ;
a

L = the original length ;

I = the stretch * ;

e = l/L = the unit stretch * = the stretch * per unit of original length ;
E = the elastic modulus of the material ;

r = E a = a measure of the resistance of the bar.
Then

Elastic modulus = E = ~ . j = s/e .......................................... (1)

Total load =TF= E a . y = r e ....................................... (2)

LI

Unit stress = s = 5. = E e ............................................... (3)

Total stretch* - I - . -5 ................................................... (4)

a tii



Unit stretch* = e = -~ = ^- = ~ ...................... . ................ (6)

22. In a beam, supported at both ends and loaded at the center, let
L = length of clear span of beam ;

w = weight ;

A = deflection " ;

b = breadth of cross section of beam ;

d = depth l ;

7 = moment of inertia " " " " " .
Then

(W + 5/8 w) L*
48 A /

If the beam is rectangular, I = -j^- (p 469), and

_ 12 (W + 5/8 w) L* _ (W + 5/8 w) L*

48 A b & 4 A & d 3

For beams, see also pp 480-481.

23. Reciprocal of elastic modulus. The]elastic modulus, =

^-, indicates the stress required to produce a certain distortion.
unit stretch
Its reciprocal, = umt stretch ghowg tQ wh&t extent a bar etc of a

unit stress

given material must be distorted in order to produce a given stress. This may
be of great importance, especially in the design of structures of timber, the
elastic modulus of which is low, relatively to that of steel; and in which,
therefore, a relatively great distortion must take place before a given fiber
stress (such as the maximum safe fiber stress) can be brought into action.
Thus, in the case of a wharf, supported by long timber piles, the piles may
submit to so great a lateral deflection as to give the load, resting upon them,
a dangerously great horizontal leverage, and thus a dangerous overturning
moment.

* Compression is regarded as negative stretch.



GENERAL PRINCIPLES. 459

24. Variable elastic modulus. Fig 11, Concrete experiments
81a p 1172, shows an example (in both tension and compressipn) of a
material in which the elastic modulus, E, is constantly changing; the
stretches, from the first, increasing faster than the stresses.

25. Even in the case of ductile materials, the stretches, produced by
stresses within the elastic limit ($ 26), are so small and so irregular that a
satisfactory average value of the elastic modulus can be arrived at only by
comparing the results of many experiments. In the case of brittle materials,
where scarcely any perceptible stretch takes place before rupture, the deter-
mination of the elastic modulus is very uncertain.

Elastic Limit.

26. The stress, A, Fig C, beyond which the stretches in any body
increase perceptibly faster than the stresses, is called its elastic limit,
or limit of elasticity. Owing to the irregularity in the behavior of different
specimens of the same material, and to the extreme smallness of the distor-
tions caused in most materials by moderate loads, and because we often
cannot decide just when the stretch begins to increase faster than the load,
the elastic limit is seldom, if ever, determinable with exactness and certainty.*


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