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Thus, since the initial modulus of elasticity found for this same
concrete ranged from 5.86 (10)^ to 4.8 (10)*' in standard cylindrical
specimens, it must be apparent that straight-line stress was practically
obtained on these three beams. In fact, comparing Beam No. 342 with
its particular collateral specimen, the beam developed 5.05 (10)^ for a
stress of 1 640 lb. per sq. in., or 31-|% (ultimate) for cylinders, and the
cylinder 5.22 (lO)*' at initial stress.

Now, this being the status, for the concrete in compression, it is at
once apparent that in the three beams there were stresses of 46 000,
43 300, and 49 500 lb. per sq. in. in the reinforcement, if Assumption
c4 of the report is correct; and then the modulus of elasticity of the


Mr. embedded steel should equal this vmit stress divided by the unit deforma-
tion recorded in the "log" for the particular condition of loading under

Beam Beam Beam

No. 342. No. 343. No. 344.

' consideration, and would be. . . . 52.6(10)" Tl.2(10)« 44.5(10)«

and not 30 (10)^, as laid down
by the Committee.

Then, again (and this is par-
ticularly interesting), the
breaking loads on these
beams, in pounds, would be. 6 280 5 800 6 800

and these exceed that at less than
yield point (so-called in the
paper) by 5% only 6% only 5% only

In other words, it is folmd that the modulus of elasticity of the
embedded steel in these beams ranges from 71 (10)* to 44^ (10)" when
they are within 6% of their ultimate strength.

Then, again, take the average
reading for the three beams
at the following applied
loads (in pounds) 2 000 4 000 5 500

Deformations, upper fiber, in
millionths of an inch per
inch 76 146 293

Deformations, steel fiber, in
millionths of an inch per
inch 67 154 650

Neutral axis, distances from top

fiber 0.5Sd 0A85d O.SlOd

Bending moments, in inch-
pounds divided by hd- 84.4 144.4 189.4

From which the stresses on the
upper fiber, in pounds per
square inch, are 387 710 1 360

and these are the following per-
centages of the average ulti-
mate unit load per square
inch on the twenty-one col-
lateral specimens 7.4% 13.6% 26%

for which the moduli of elas-
ticity are 5.1(10)« 4.85(10)" 4.65(10)"

On the basis of Assumption c4 of
the report, the stresses on the
steel, in pounds per square
inch, are 20 700 35 200 43 000


Beam Beam Beam Mr

No. 342. No. 343. No. 344. Scott.

310(10)" 230(10)« G0(10)«

32% 64% 87%

10 times 7 times 2 times

and these stresses divided by the
unit deformation (modulus
of elasticity) are

and, as 6 290 lb. is the mean
maximum applied load for
the three beams, it is found
that for loads at the fol-
lowing percentages of maxi-

the moduli of elasticity of em-
bedded steel are

that laid down by the Committee.

The concrete of these beams was very rich in cement, but exactly
similar results can be shown with concrete beams which are poor in

The writer has developed his own figures from the data in the
'"Log" of the paper mentioned, and they produce entirely different
results from those given in the "Summary of Tests", both in the Bureau
of Standards paper.

The two curves on Fig. 9 are based on a general analysis of two
groups only, namely two-rod beams and eight-rod beams.

Carl Gayler,* M. Am. See. C. E. (by letter). — The writer gladly Mr.
acknowledges the great merits of the work of the Committee, and has
no doubt that the report will be for a long time an aid to the concrete
engineer as a book of reference, guiding him in his work and correct-
ing or sustaining him in his judgment. Aside from a few objections
which can be raised, it will probably be accepted as a standard by the
Profession. Still, in the writer's opinion, there are such objections,
and he begs to state them.

It is to be regretted that so little prominence is given to the im-
portant problem of eliminating the dangers from laitance. Every
engineer, active in reinforced concrete work, has been aware of this
danger for years; many engineers (among them the writer) have come
to its realization only after bitter experience; but few have had a clear
conception of the magnitude of the problem before reading the classic
paper "Water the Chief Factor in the Making of Good Concrete", by
Nathan C. Jolmson, Assoc. M. Am. Soc. C. E.f

jSIow, in the Keport, Chapter II, Section 2, laitance is not men-
tioned as one of the causes through which reinforced concrete struc-
tures fail, nor is there — and this is more important — any cautioning

* St. Louis, Mo.

t The Engineering Record, December 30th, 1916.


Mr. of the inspectors on this point in Section 3 of the same chapter. The
'^^' '^''' "Destructive Agencies'' mentioned are: "Corrosion of Metal Rein-
forcement", "Electrolysis", "Sea Water", "Acids", "Oils", and "Alka-
lies", but not one word of "Laitance."

The short references in Chapter IV, Section 3, to the removal
of laitance can hardly be considered as emphasizing the subject suf-
ficiently, nor is mention made of the chief agency of the trouble,
that is, excess of water.

The field covered by reinforced concrete work has grown to such
astonishing dimensions that an engineer, no matter what his specialty,
to be competent, must have a general knowledge of the principles and
requirements of such work. Whether he is engaged in hydraulic works,
power stations, bridge or irrigation work, it confronts him in the shape
of foundations, conduits, reservoirs, retaining walls, or viaducts. Now,
of this immense field, many features of which are still in the midst of
evolution, and for which the iDractising engineer expected enlighten-
ment from the report, not so much on detailed features as through
broad, general rules, very little is to be found, with the exception of
the indoor slab.

It will be objected that the different types of structures just men-'
tioned do not come within the scope of a report on concrete and rein-
forced concrete (and, in fact, the Committee makes this claim in the
introduction to the report), that such a report is complete after full
presentation of the qualities of the materials and of the principles
underlying their wise and economical use. Even granting the force of
this objection, it is thought that by allowing one-tenth of the space
allotted to the flat slab, with its dropped panel, column capital, wall
girders, etc., to a few other types of structures of general interest, the
value of the report would have been much increased. Some expression
of opinion, for instance, on the problems of skeleton retaining walls,
on the advantages of the hinged arch, slabs of bridge floors (very dif-
ferent, indeed, with their delicate problems of drainage and shrinkage,
from the indoor slab), etc., in the form of concise resumes of the
experience of the eminent engineers to whom we owe this report, would
have been of great value to the Profession.

Reinforced concrete structures are, essentially, heavy structures.
Their success and appearance depend on unyielding support during
conrstruction. In many important cases the designing of falsework and
centers requires as careful study as the planning of the superstructure;
and their maintenance, until the full completion of the work, as much
attention as the depositing of the concrete. A reference in the report
to this siibject, perhaps with the addition of permissible stresses in
the materials used, might have been expected. The case is entirely
different from the additional types referred to previously. Ealsework
and centers may be said to form, during construction, an integral part


of the superstructure, and it seems that a general report on concrete Mr.
and reinforced concrete is not complete if this subject is omitted. '*^ ^^'

There is one other point on which the writer takes exception to the
report, that is, the exclusion of high-grade steel. The Committee has
been careful in the wording: it merely recommends the structural
grade, but the unit stresses, adopted in the report, practically eliminate
the Tise of high-carbon steel.

High-carbon steel is in general use for reinforced concrete work.
It is specified, on even terms, with structural steel, in the standard
specifications of the American Society for Testing Materials, of the
American Railway Engineering Association, in the building codes of
our larger cities, and in the specifications for highway bridge work; and
railroad and municipal engineers, as well as engineers in private prac-
tice, use it.

As no explanation is given in the report, of the Committee's pref-
erence for the milder grade, it may be assumed that the question of
greater brittleness of the harder steel has been the deciding one. On
this point it is found that Taylor and Thompson, in their treatise on
"Concrete, Plain and Reinforced", in a lengthy and clear discussion
(p. 414) on the advisability of using hard steel, in which due stress
is laid on the difference in the use of steel for bridge work and for
reinforced concrete work, and in which careful inspection at the mills
is insisted on as an efficient means of obviating dangers from brittle-
ness, end the paragraph with the following (as it seems to the writer)
unanswerable argument :

"Steel which can be employed with safety for all locomotive and
car wheels of the country certainly cannot be discarded as unsafe for
concrete, provided similar precautions are taken in its purchase.''

From his own experience, the writer considers high-carbon steel for
reinforced concrete work a thoroughly safe material. With proper care
and judgment used, where any bending is to be done, no undue risks
are run.

Assuming now the safe use of hard steel to be granted (its general
use cannot be denied), we reach the important question whether steel
with a higher percentage of carbon should be proportioned for the
same low unit stress as milder steel (always assuming that the condi-
tions imposed by the bond stress are fulfilled). As far as general
practice goes, the answer has been, almost universally, in the negative.

The difl'erence in the unit stresses allowed for high steel over struc-
tural steel may be stated, approximately, to be as follows : In railroad
work from 2 000 to 3 000 lb. ; highway bridge work from 2 000 to 4 000
lb. ; and city building laws from 4 000 to 6 000 lb. (the building laws of
the City of St. Louis, for instance, specify 14 000 lb. for medium steel
and 20 000 lb. for high elastic limit steel).



Mr. Considering that, in the report, not less than fifteen different unit

*^ ^"^^ stresses are specified for stone or gravel concretes, according to the
nature of the aggregates and the ratio of the mixtures, it seems strange
to find the single line "the tensile or compressive stress in steel should
not exceed 16 000 lb. per sq. in.", covering the whole subject of propor-
tioning steel, whether the elastic limit is 30 000, 40 000, or 50 000 lb.,
or the ultimate strength 50 000, 70 000, or 80 000 lb. per sq. in.

Taking into consideration that this question of permissible unit
stresses in the steel affects the universal practice in concrete work all
over the country, and for every class of such work, there must have
been strong reasons for the action of the Committee, and engineers
hope to find them stated in the concluding answer to the different dis-
cussions on the report.

H. V. Hinckley,* M. Am. Soc. C. E. (by letter). — Three points
pertaining to "coarse aggregate" occur to the writer as being possibly
worthy of mention, namely, large aggregate, glassy aggregate, and
strong aggregate.

That "a large aggregate produces a stronger concrete than a fine
one" will not be questioned by any competent engineer. It is for-
tunate, however, that the point has been brought out, because public
officials are apt to look on coarse aggregate as a shirking of duty
on the part of the rock crusher rather than the exercise of good judg-
ment by the engineer.

The following substitute clause is offered as a suggestion : "The
Committee does not feel warranted in recommending the use of blast-
furnace slag," flint, or other aggregates which produce smooth, glassy
faces, especially for reinforced concrete in which high strains are
to be developed.

It is fully as important that the coarse aggregate shall be of
tough, strong rock, as it is that "fine aggregate should always be tested
for strength." Of two classes of rock (other conditions being equal),
the class that, as a beam, will support the heavier load will make, if
crushed for coarse aggregate, the stronger concrete. When concrete
fails under compression, it fails in tension, and, in failing, it generally
splits through the coarse aggregate rather than around it, and as the
rock thus broken makes up the greater portion of the section of failure,
the strength of the concrete is largely dependent on the strength of
the stone. The writer recently statedf :

"Every engineer of experience should know that, under any ordinary
concrete specifications, he can build two slabs side by side, using
the same sand, the same cement, the same proportion, the same time
of mix in the same machine, and at the end of 90 days have one
slab at least twice as strong as the other."

* Oklahoma, Okla.

t Transactions, Oklahoma Soc. of Engrs., Vol. III.


If the writer had to build a reinforced concrete structure, in which Mr.
high strains were to be developed, he would pay as much attention to "'"'^''^''y-
the modulus of rupture of the rock to be used as he would to the
tests of the fine aggregate. It is time for the Society to get away from
the idea that any old stone will make good concrete. A "clean, hard,
and durable" stone may be brittle and weak, and it might not be
out of place to add, at least, the word "strong."

Since writing the foregoing, the writer's attention has been called
to Professor George A. Hool's "Eeinforced Concrete Construction",
in which is found the only corroboration of the foregoing views which
he has ever noticed. Professor Hool says : "Any stone is suitable
which is clean and durable, and has sufficient strength to prevent the
strength of the concrete from being limited by the strength of the
stone," and this means that the stone must be as strong as the mortar.

Henkv T. Eddy,* Esq. (by letter). — 1. — The Thichness of Flat Mr.
Slabs. — In the first place the writer desires to consider somewhat ^'
critically the formula recommended in the report for the value of the
minimum total thickness, t, in inches, of a flat slab without dropped
panels, in order to show that it is a formula not suited to give the
minimum thickness, according to accepted principles in reinforced con-
crete design. The formula recommended in the report is :

t = 0.024: I \/w-{-1.5 (1)

in which I = panel length or span between column centers, in feet, and
w = Wq -]- w^, the sum of the live load, w^, and the dead load,
w^ = 12.5 t lb. per sq. ft. Similar formulas have been proposed in the
Chicago Rulingf and in the standard building regulations reported to
the American Concrete Institute.:}:

Equation (1) consists of two parts, the mean effective moment
thickness, d, or the depth of the center of the steel below the compressed
slab surface, and 1.5 in., which last includes half the thickness of the
steel mat of crossed rods plus concrete fire-proofing at least 1 in. thick.
Hence, we have the effective moment thickness

d = 0.024 I V w" (2)

an equation which, together with Equation (1), the writer has reason
to believe is so far from being correct that it should not be recom-
mended or regarded as expressing the minimum value, a conclusion
that follows from considerations that will now be given in detail.

The general expression for the bending moment, due to the applied
forces acting at any panel-wide vertical section of a square panel of

* Professor of Mathematics and Mechanics and Dean Emeritus, University of
Minnesota, Minneapolis, Minn.

t Engineering Neivs, September 24th, 1914.

t Proceedings, Am. Concrete Institute, Vol. XIII, 1917.

1168 DISCUSSION Oisr concrete and reinforced concrete

Mr. span I ft., when loaded with a total uniformly distributed load of w

^ ■ lb. per sq. ft., or a total load of IF = wl~ lb. per panel, may be written

in the form :

I l^
12 W — = 12 w — iu-lb (8)

a a

in which a is a numerical divisor the value of which has frequently
been recommended to be taken at about 24 or 25 for the section at
mid-span and at — 12 or — 15 at the edge of the panel, with inter-
mediate values, positive or negative, at sections situated between these.
These, however, are the two sections which are most frequently taken
into consideration.

Again, the general expression for the resisting moment of the steel
that crosses any vertical cross-section of the panel which has an effec-
tive thickness of d in. and a total effective cross-section of steel of
A = 12 pld sq. in., may be written in the form:

f^Ajd = 12fspljd- in-lb (4)

in which fg, in poiuids, is the unit stress in the steel, jd is the moment
arm, 12Z is the panel length, in inches, and p is the steel ratio of the

It is assumed ordinarily that when the direct tensile resistance of
the concrete acting in parallel with the tensile resistance of the steel
is neglected, the resisting moment must be equal to the applied
moment. The writer, however, has reasons, which he has explained
elsewhere, for believing that the applied moments are more than twice
as large as the actual resisting moments sho^vn by observation. In
case this is the fact, it would only be necessary, in order to make
Equations (3) and (4) equal, to assume, as the numerically correct
value of a, a number which is the same multiple of the value of a,
ordinarily assumed, that the applied moments are of the resisting
moments. However, leaving this question unsettled for the present,
and leaving also the value of a, which will be finally adopted as applica-
ble at mid-span, undetermined, we may nevertheless equate the resist-
ing moment to the applied moment, with the understanding that such
a value of a will finally be adopted as may appear to be required by
the facts. Hence

I JV'^ = "' — •


I w


Now compare Equation (5) for the effective thickness, d, with
Equation (2), which was recommended in the report. In case Equa-
tion (2) is correct, it must be identical with Equation (5). To express


this relation, more concretely, assume that fg = 16 000 lb. per sq. in., jir.
and that ;' = 0.9 at the mid-section. Then, in order that Equations ' '''
(5) and (2) maj be identical, we have

16 000 X 0.9 X (0.024)2pa = 1, or pa = 0.12 (6)

Hence, when we

take a^ 12, 15, 20, 24, 30, 40, 50, 60,

we then have p = 0.01, 0.008, 0.006, 0.005, 0.004, 0.003, 0.0024, 0.002,


It thus appears that in case Equation (2) is, in fact, a correct form
of expression for d, then Equation (6) must also hold true; but as a
in Equation (6) is a constant which is fixed by the position where the
section is taken, at mid-span or elsewhere, and, moreover, is inde-
pendent of both I and w, it follows from Equation (0) that p is also
constant so long as a remains constant. If there is anything in the
design of concrete beams, however, that has been indubitably estab-
lished by experience, it is that the steel ratio increases with the relative

thickness, that is, _p increases with —-, and the same principle applies

to slabs also. Hence, Equations (1) and (2) are not, in fact, correct,
and cannot be relied on to fi:s the minimum value of d, because they
require a constant value of p, not in accordance with experience. In
fact, p is found to be nearly twice as large in deep slabs for heavy
loads as it is in shallow slabs for light loads, in case of well-designed
slabs for any given span.

The reason for such increase in the value of p in case of deep beams
is evident from the following considerations. In shallow beams and
slabs the sharpness of the curvature is inversely proportional to d
for a given limiting compression in the concrete at the top surface.
The sharper the curvatures the greater the horizontal shearing dis-
tortions in the concrete at points distant from the sections where maxi-
mum moments occur. Concrete aifords a resistance to shearing dis-
tortion which is small compared with its resistance to compression.
In shallow beams high values of p are futile, for this reason, but, in
deep beams, larger values of p may be used than in shallow beams, on
account of their smaller shearing distortion. In slabs this still further

reason may exist for an increase of j; with — — . that is, the crossed rods

that make up the mat may properly be more numerous and more
closely spaced in a thick slab than in a thin one, thus furnishing
more effective co-action of steel and concrete in thick than in thin

In its present form Equation (2) is not convenient for numerical
calculations, because the value of w itself depends on d. It will be


Mr. more convenient to express d as a function of Wq, the live load. Write
^'^'^^- Equation (2) in the form,

d= 0.024: I V Wq + ^1

by the help of the equation

w; = Wq -f- w^ (7)

and eliminate

w, = 12.5^ = 12.5 (d + 1.5)

by assuming the weight of a cubic foot of concrete to be 150 lb., or
12.5 lb. per in. of thickness per square foot.

J2 = (0.024 I)- («;„ + 12.5 d + 18.75).

Solve this quadratic equation and find,

d = 0.00375 P + 0.024 I \/ {w^ + 18.75 + 0.0225 P) (8)

Table 2 has been computed from Equation (8). Now, if the value
of the divisor in Equation (3) is assumed to be a = 25 at mid-span
of the panel, as recommended in the report, then, by Equation (6),
we find the steel ratio, p = 0.0048, throughout the entire table, regard-
less of — . It is apparent that the thickness found in Table 2 is too

great at the larger spans and loads, so much so as almost to prohibit
the use of flat slabs for the larger loads and spans figured in the table,
but it is evident that this thickness may be reduced by increasing p


somewhat with - — .

The effect of this increase of p with — - will evidently be to produce

a proportionate decrease of the dead load and of the thickness of the
slab at the larger values of w^ over that at the smaller values of Wq.

TABLE 2.— Effective Thickness of Flat Slabs.

d = 0.00375 Z^ 4- 0.024 Z /^ (w^ -f 18.75 + 0.0225 ?) inches;
I = span, in feet; w^ = live load, In pounds per square foot.

in fpet.

Wo = 100













































































With the view of finding a simple approximate expression for d Mr.
that will give values of d more nearly in accordance with the results ^'^'^'^■
of good practice than those obtained from Equation (4) or from Table
2, it is to be observed that, for any given span, I, Equation (8), re-
garded as a quadratic expressing the relation between the variables, d
and Wq, taken as co-ordinates, represents a parabola. The part of the
curve in question ranges from w^ = 100 or less, to Wq = 600 or more.
In Fig. 10 the values of d in this range are plotted for Z = 20 ft. Sim-
ilar curves occur for other values of I.

Suppose that the effective thickness for two different loads as, for
example, at P^ and P^ in Fig 10, were sufficiently well ascertained by
a consensus of good practice to be supposed to be known, then it would
be possible to obtain an equation for a straight line through those two
points that would give values of d for those and other loads, which
might be more nearly in accord with good practice than those given by

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