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Title: Some Mooted Questions in Reinforced Concrete Design - American Society of Civil Engineers, Transactions, Paper - No. 1169, Volume LXX, Dec. 1910
Author: Godfrey, Edward
Language: English
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Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

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AMERICAN SOCIETY OF CIVIL ENGINEERS INSTITUTED 1852

TRANSACTIONS

Paper No. 1169

SOME MOOTED QUESTIONS IN REINFORCED CONCRETE DESIGN.[A]

BY EDWARD GODFREY, M. AM. SOC. C. E.

WITH DISCUSSION BY MESSRS. JOSEPH WRIGHT, S. BENT RUSSELL, J.R.
WORCESTER, L.J. MENSCH, WALTER W. CLIFFORD, J.C. MEEM, GEORGE H. MYERS,
EDWIN THACHER, C.A.P. TURNER, PAUL CHAPMAN, E.P. GOODRICH, ALBIN H.
BEYER, JOHN C. OSTRUP, HARRY F. PORTER, JOHN STEPHEN SEWELL, SANFORD E.
THOMPSON, AND EDWARD GODFREY.


Not many years ago physicians had certain rules and practices by which
they were guided as to when and where to bleed a patient in order to
relieve or cure him. What of those rules and practices to-day? If they
were logical, why have they been abandoned?

It is the purpose of this paper to show that reinforced concrete
engineers have certain rules and practices which are no more logical
than those governing the blood-letting of former days. If the writer
fails in this, by reason of the more weighty arguments on the other side
of the questions he propounds, he will at least have brought out good
reasons which will stand the test of logic for the rules and practices
which he proposes to condemn, and which, at the present time, are quite
lacking in the voluminous literature on this comparatively new subject.

Destructive criticism has recently been decried in an editorial in an
engineering journal. Some kinds of destructive criticism are of the
highest benefit; when it succeeds in destroying error, it is
reconstructive. No reform was ever accomplished without it, and no
reformer ever existed who was not a destructive critic. If showing up
errors and faults is destructive criticism, we cannot have too much of
it; in fact, we cannot advance without it. If engineering practice is to
be purged of its inconsistencies and absurdities, it will never be done
by dwelling on its excellencies.

Reinforced concrete engineering has fairly leaped into prominence and
apparently into full growth, but it still wears some of its
swaddling-bands. Some of the garments which it borrowed from sister
forms of construction in its short infancy still cling to it, and, while
these were, perhaps, the best makeshifts under the circumstances, they
fit badly and should be discarded. It is some of these misfits and
absurdities which the writer would like to bring prominently before the
Engineering Profession.

[Illustration: FIG. 1.]

The first point to which attention is called, is illustrated in Fig. 1.
It concerns sharp bends in reinforcing rods in concrete. Fig. 1 shows a
reinforced concrete design, one held out, in nearly all books on the
subject, as a model. The reinforcing rod is bent up at a sharp angle,
and then may or may not be bent again and run parallel with the top of
the beam. At the bend is a condition which resembles that of a hog-chain
or truss-rod around a queen-post. The reinforcing rod is the hog-chain
or the truss-rod. Where is the queen-post? Suppose this rod has a
section of 1 sq. in. and an inclination of 60° with the horizontal, and
that its unit stress is 16,000 lb. per sq. in. The forces, _a_ and _b_,
are then 16,000 lb. The force, _c_, must be also 16000 lb. What is to
take this force, _c_, of 16,000 lb.? There is nothing but concrete. At
500 lb. per sq. in., this force would require an area of 32 sq. in. Will
some advocate of this type of design please state where this area can be
found? It must, of necessity, be in contact with the rod, and, for
structural reasons, because of the lack of stiffness in the rod, it
would have to be close to the point of bend. If analogy to the
queen-post fails so completely, because of the almost complete absence
of the post, why should not this borrowed garment be discarded?

If this same rod be given a gentle curve of a radius twenty or thirty
times the diameter of the rod, the side unit pressure will be from
one-twentieth to one-thirtieth of the unit stress on the steel. This
being the case, and being a simple principle of mechanics which ought to
be thoroughly understood, it is astounding that engineers should
perpetrate the gross error of making a sharp bend in a reinforcing rod
under stress.

The second point to which attention is called may also be illustrated by
Fig. 1. The rod marked 3 is also like the truss-rod of a queen-post
truss in appearance, because it ends over the support and has the same
shape. But the analogy ends with appearance, for the function of a
truss-rod in a queen-post truss is not performed by such a reinforcing
rod in concrete, for other reasons than the absence of a post. The
truss-rod receives its stress by a suitable connection at the end of the
rod and over the support of the beam. The reinforcing rod, in this
standard beam, ends abruptly at the very point where it is due to
receive an important element of strength, an element which would add
enormously to the strength and safety of many a beam, if it could be
introduced.

Of course a reinforcing rod in a concrete beam receives its stress by
increments imparted by the grip of the concrete; but these increments
can only be imparted where the tendency of the concrete is to stretch.
This tendency is greatest near the bottom of the beam, and when the rod
is bent up to the top of the beam, it is taken out of the region where
the concrete has the greatest tendency to stretch. The function of this
rod, as reinforcement of the bottom flange of the beam, is interfered
with by bending it up in this manner, as the beam is left without
bottom-flange reinforcement, as far as that rod is concerned, from the
point of bend to the support.

It is true that there is a shear or a diagonal tension in the beam, and
the diagonal portion of the rod is apparently in a position to take this
tension. This is just such a force as the truss-rod in a queen-post
truss must take. Is this reinforcing rod equipped to perform this
office? The beam is apt to fail in the line, _A B_. In fact, it is apt
to crack from shrinkage on this or almost any other line, and to leave
the strength dependent on the reinforcing steel. Suppose such a crack
should occur. The entire strength of the beam would be dependent on the
grip of the short end of Rod 3 to the right of the line, _A B_. The grip
of this short piece of rod is so small and precarious, considering the
important duty it has to perform, that it is astounding that designers,
having any care for the permanence of their structures, should consider
for an instant such features of design, much less incorporate them in a
building in which life and property depend on them.

The third point to which attention is called, is the feature of design
just mentioned in connection with the bent-up rod. It concerns the
anchorage of rods by the embedment of a few inches of their length in
concrete. This most flagrant violation of common sense has its most
conspicuous example in large engineering works, where of all places
better judgment should prevail. Many retaining walls have been built,
and described in engineering journals, in papers before engineering
societies of the highest order, and in books enjoying the greatest
reputation, which have, as an essential feature, a great number of rods
which cannot possibly develop their strength, and might as well be of
much smaller dimensions. These rods are the vertical and horizontal rods
in the counterfort of the retaining wall shown at _a_, in Fig. 2. This
retaining wall consists of a front curtain wall and a horizontal slab
joined at intervals by ribs or counterforts. The manifest and only
function of the rib or counterfort is to tie together the curtain wall
and the horizontal slab. That it is or should be of concrete is because
the steel rods which it contains, need protection. It is clear that
failure of the retaining wall could occur by rupture through the Section
_A B_, or through _B C_. It is also clear that, apart from the cracking
of the concrete of the rib, the only thing which would produce this
rupture is the pulling out of the short ends of these reinforcing rods.
Writers treat the triangle, _A B C_, as a beam, but there is absolutely
no analogy between this triangle and a beam. Designers seem to think
that these rods take the place of so-called shear rods in a beam, and
that the inclined rods are equivalent to the rods in a tension flange of
a beam. It is hard to understand by what process of reasoning such
results can be attained. Any clear analysis leading to these conclusions
would certainly be a valuable contribution to the literature on the
subject. It is scarcely possible, however, that such analysis will be
brought forward, for it is the apparent policy of the reinforced
concrete analyst to jump into the middle of his proposition without the
encumbrance of a premise.

There is positively no evading the fact that this wall could fail, as
stated, by rupture along either _A B_ or _B C_. It can be stated just as
positively that a set of rods running from the front wall to the
horizontal slab, and anchored into each in such a manner as would be
adopted were these slabs suspended on the rods, is the only rational and
the only efficient design possible. This design is illustrated at _b_ in
Fig. 2.

[Illustration: FIG. 2.]

The fourth point concerns shear in steel rods embedded in concrete. For
decades, specifications for steel bridges have gravely given a unit
shear to be allowed on bridge pins, and every bridge engineer knows or
ought to know that, if a bridge pin is properly proportioned for bending
and bearing, there is no possibility of its being weak from shear. The
centers of bearings cannot be brought close enough together to reduce
the size of the pin to where its shear need be considered, because of
the width required for bearing on the parts. Concrete is about
one-thirtieth as strong as steel in bearing. There is, therefore,
somewhat less than one-thirtieth of a reason for specifying any shear on
steel rods embedded in concrete.

The gravity of the situation is not so much the serious manner in which
this unit of shear in steel is written in specifications and building
codes for reinforced concrete work (it does not mean anything in
specifications for steelwork, because it is ignored), but it is apparent
when designers soberly use these absurd units, and proportion shear rods
accordingly.

Many designers actually proportion shear rods for shear, shear in the
steel at units of 10,000 or 12,000 lb. per sq. in.; and the blame for
this dangerous practice can be laid directly to the literature on
reinforced concrete. Shear rods are given as standard features in the
design of reinforced concrete beams. In the Joint Report of the
Committee of the various engineering societies, a method for
proportioning shear members is given. The stress, or shear per shear
member, is the longitudinal shear which would occur in the space from
member to member. No hint is given as to whether these bars are in shear
or tension; in fact, either would be absurd and impossible without
greatly overstressing some other part. This is just a sample of the
state of the literature on this important subject. Shear bars will be
taken up more fully in subsequent paragraphs.

The fifth point concerns vertical stirrups in a beam. These stirrups are
conspicuous features in the designs of reinforcing concrete beams.
Explanations of how they act are conspicuous in the literature on
reinforced concrete by its total absence. By stirrups are meant the
so-called shear rods strung along a reinforcing rod. They are usually
U-shaped and looped around the rod.

It is a common practice to count these stirrups in the shear, taking the
horizontal shear in a beam. In a plate girder, the rivets connecting the
flange to the web take the horizontal shear or the increment to the
flange stress. Compare two 3/4-in. rivets tightly driven into holes in a
steel angle, with a loose vertical rod, 3/4 in. in diameter, looped
around a reinforcing rod in a concrete beam, and a correct comparison of
methods of design in steel and reinforced concrete, as they are commonly
practiced, is obtained.

These stirrups can take but little hold on the reinforcing rods--and
this must be through the medium of the concrete--and they can take but
little shear. Some writers, however, hold the opinion that the stirrups
are in tension and not in shear, and some are bold enough to compare
them with the vertical tension members of a Howe truss. Imagine a Howe
truss with the vertical tension members looped around the bottom chord
and run up to the top chord without any connection, or hooked over the
top chord; then compare such a truss with one in which the end of the
rod is upset and receives a nut and large washer bearing solidly against
the chord. This gives a comparison of methods of design in wood and
reinforced concrete, as they are commonly practiced.

Anchorage or grip in the concrete is all that can be counted on, in any
event, to take up the tension of these stirrups, but it requires an
embedment of from 30 to 50 diameters of a rod to develop its full
strength. Take 30 to 50 diameters from the floating end of these shear
members, and, in some cases, nothing or less than nothing will be left.
In any case the point at which the shear member, or stirrup, is good for
its full value, is far short of the centroid of compression of the beam,
where it should be; in most cases it will be nearer the bottom of the
beam. In a Howe truss, the vertical tension members having their end
connections near the bottom chord, would be equivalent to these shear
members.

The sixth point concerns the division of stress into shear members.
Briefly stated, the common method is to assume each shear member as
taking the horizontal shear occurring in the space from member to
member. As already stated, this is absurd. If stirrups could take shear,
this method would give the shear per stirrup, but even advocates of this
method acknowledge that they can not. To apply the common analogy of a
truss: each shear member would represent a tension web member in the
truss, and each would have to take all the shear occurring in a section
through it.

If, for example, shear members were spaced half the depth of a beam
apart, each would take half the shear by the common method. If shear
members take vertical shear, or if they take tension, what is between
the two members to take the other half of the shear? There is nothing in
the beam but concrete and the tension rod between the two shear members.
If the concrete can take the shear, why use steel members? It is not
conceivable that an engineer should seriously consider a tension rod in
a reinforced concrete beam as carrying the shear from stirrup to
stirrup.

The logical deduction from the proposition that shear rods take tension
is that the tension rods must take shear, and that they must take the
full shear of the beam, and not only a part of it. For these shear rods
are looped around or attached to the tension rods, and since tension in
the shear rods would logically be imparted through the medium of this
attachment, there is no escaping the conclusion that a large vertical
force (the shear of the beam) must pass through the tension rod. If the
shear member really relieves the concrete of the shear, it must take it
all. If, as would be allowable, the shear rods take but a part of the
shear, leaving the concrete to take the remainder, that carried by the
rods should not be divided again, as is recommended by the common
method.

Bulletin No. 29 of the University of Illinois Experiment Station shows
by numerous experiments, and reiterates again and again, that shear rods
do not act until the beam has cracked and partly failed. This being the
case, a shear rod is an illogical element of design. Any element of a
structure, which cannot act until failure has started, is not a proper
element of design. In a steel structure a bent plate which would
straighten out under a small stress and then resist final rupture, would
be a menace to the rigidity and stability of the structure. This is
exactly analogous to shear rods which cannot act until failure has
begun.

When the man who tears down by criticism fails to point out the way to
build up, he is a destructive critic. If, under the circumstances,
designing with shear rods had the virtue of being the best thing to do
with the steel and concrete disposed in a beam, as far as experience and
logic in their present state could decide, nothing would be gained by
simply criticising this method of design. But logic and tests have shown
a far simpler, more effective, and more economical means of disposing of
the steel in a reinforced concrete beam.

In shallow beams there is little need of provision for taking shear by
any other means than the concrete itself. The writer has seen a
reinforced slab support a very heavy load by simple friction, for the
slab was cracked close to the supports. In slabs, shear is seldom
provided for in the steel reinforcement. It is only when beams begin to
have a depth approximating one-tenth of the span that the shear in the
concrete becomes excessive and provision is necessary in the steel
reinforcement. Years ago, the writer recommended that, in such beams,
some of the rods be curved up toward the ends of the span and anchored
over the support. Such reinforcement completely relieves the concrete
of all shearing stress, for the stress in the rod will have a vertical
component equal to the shear. The concrete will rest in the rod as a
saddle, and the rod will be like the cable of a suspension span. The
concrete could be in separate blocks with vertical joints, and still the
load would be carried safely.

By end anchorage is not meant an inch or two of embedment in concrete,
for an iron vise would not hold a rod for its full value by such means.
Neither does it mean a hook on the end of the rod. A threaded end with a
bearing washer, and a nut and a lock-nut to hold the washer in place, is
about the only effective means, and it is simple and cheap. Nothing is
as good for this purpose as plain round rods, for no other shape affords
the same simple and effective means of end connection. In a line of
beams, end to end, the rods may be extended into the next beam, and
there act to take the top-flange tension, while at the same time finding
anchorage for the principal beam stress.

The simplicity of this design is shown still further by the absence of a
large number of little pieces in a beam box, as these must be held in
their proper places, and as they interfere with the pouring of the
concrete.

It is surprising that this simple and unpatented method of design has
not met with more favor and has scarcely been used, even in tests. Some
time ago the writer was asked, by the head of an engineering department
of a college, for some ideas for the students to work up for theses, and
suggested that they test beams of this sort. He was met by the
astounding and fatuous reply that such would not be reinforced concrete
beams. They would certainly be concrete beams, and just as certainly be
reinforced.

Bulletin 29 of the University of Illinois Experiment Station contains a
record of tests of reinforced concrete beams of this sort. They failed
by the crushing of the concrete or by failure in the steel rods, and
nearly all the cracks were in the middle third of the beams, whereas
beams rich in shear rods cracked principally in the end thirds, that is,
in the neighborhood of the shear rods. The former failures are ideal,
and are easier to provide against. A crack in a beam near the middle of
the span is of little consequence, whereas one near the support is a
menace to safety.

The seventh point of common practice to which attention is called, is
the manner in which bending moments in so-called continuous beams are
juggled to reduce them to what the designer would like to have them.
This has come to be almost a matter of taste, and is done with as much
precision or reason as geologists guess at the age of a fossil in
millions of years.

If a line of continuous beams be loaded uniformly, the maximum moments
are negative and are over the supports. Who ever heard of a line of
beams in which the reinforcement over the supports was double that at
mid-spans? The end support of such a line of beams cannot be said to be
fixed, but is simply supported, hence the end beam would have a negative
bending moment over next to the last support equal to that of a simple
span. Who ever heard of a beam being reinforced for this? The common
practice is to make a reduction in the bending moment, at the middle of
the span, to about that of a line of continuous beams, regardless of the
fact that they may not be continuous or even contiguous, and in spite of
the fact that the loading of only one gives quite different results, and
may give results approaching those of a simple beam.

If the beams be designed as simple beams--taking the clear distance
between supports as the span and not the centers of bearings or the
centers of supports--and if a reasonable top reinforcement be used over
these supports to prevent cracks, every requirement of good engineering
is met. Under extreme conditions such construction might be heavily
stressed in the steel over the supports. It might even be overstressed
in this steel, but what could happen? Not failure, for the beams are
capable of carrying their load individually, and even if the rods over
the supports were severed--a thing impossible because they cannot
stretch out sufficiently--the beams would stand.

Continuous beam calculations have no place whatever in designing
stringers of a steel bridge, though the end connections will often take
a very large moment, and, if calculated as continuous, will be found to
be strained to a very much larger moment. Who ever heard of a failure
because of continuous beam action in the stringers of a bridge? Why
cannot reinforced concrete engineering be placed on the same sound
footing as structural steel engineering?

The eighth point concerns the spacing of rods in a reinforced concrete
beam. It is common to see rods bunched in the bottom of such a beam with
no regard whatever for the ability of the concrete to grip the steel, or
to carry the horizontal shear incident to their stress, to the upper
part of the beam. As an illustration of the logic and analysis applied
in discussing the subject of reinforced concrete, one well-known
authority, on the premise that the unit of adhesion to rod and of shear
are equal, derives a rule for the spacing of rods. His reasoning is so
false, and his rule is so far from being correct, that two-thirds would
have to be added to the width of beam in order to make it correct. An
error of 66% may seem trifling to some minds, where reinforced concrete
is considered, but errors of one-tenth this amount in steel design would
be cause for serious concern. It is reasoning of the most elementary
kind, which shows that if shear and adhesion are equal, the width of a
reinforced concrete beam should be equal to the sum of the peripheries
of all reinforcing rods gripped by the concrete. The width of the beam
is the measure of the shearing area above the rods, taking the
horizontal shear to the top of the beam, and the peripheries of the rods
are the measure of the gripping or adhesion area.

Analysis which examines a beam to determine whether or not there is
sufficient concrete to grip the steel and to carry the shear, is about
at the vanishing point in nearly all books on the subject. Such
misleading analysis as that just cited is worse than nothing.

The ninth point concerns the T-beam. Excessively elaborate formulas are
worked out for the T-beam, and haphazard guesses are made as to how much
of the floor slab may be considered in the compression flange. If a
fraction of this mental energy were directed toward a logical analysis
of the shear and gripping value of the stem of the T-beam, it would be
found that, when the stem is given its proper width, little, if any, of
the floor slab will have to be counted in the compression flange, for
the width of concrete which will grip the rods properly will take the
compression incident to their stress.

The tenth point concerns elaborate theories and formulas for beams and
slabs. Formulas are commonly given with 25 or 30 constants and variables
to be estimated and guessed at, and are based on assumptions which are
inaccurate and untrue. One of these assumptions is that the concrete is
initially unstressed. This is quite out of reason, for the shrinkage of
the concrete on hardening puts stress in both concrete and steel. One of
the coefficients of the formulas is that of the elasticity of the
concrete. No more variable property of concrete is known than its
coefficient of elasticity, which may vary from 1,000,000 to 5,000,000
or 6,000,000; it varies with the intensity of stress, with the kind of
aggregate used, with the amount of water used in mixing, and with the
atmospheric condition during setting. The unknown coefficient of
elasticity of concrete and the non-existent condition of no initial
stress, vitiate entirely formulas supported by these two props.

Here again destructive criticism would be vicious if these mathematical
gymnasts were giving the best or only solution which present knowledge
could produce, or if the critic did not point out a substitute. The
substitute is so simple of application, in such agreement with
experiments, and so logical in its derivation, that it is surprising
that it has not been generally adopted. The neutral axis of reinforced
concrete beams under safe loads is near the middle of the depth of the
beams. If, in all cases, it be taken at the middle of the depth of the
concrete beam, and if variation of intensity of stress in the concrete
be taken as uniform from this neutral axis up, the formula for the
resisting moment of a reinforced concrete beam becomes extremely simple
and no more complex than that for a rectangular wooden beam.

The eleventh point concerns complex formulas for chimneys. It is a
simple matter to find the tensile stress in that part of a plain
concrete chimney between two radii on the windward side. If in this
space there is inserted a rod which is capable of taking that tension at
a proper unit, the safety of the chimney is assured, as far as that
tensile stress is concerned. Why should frightfully complex formulas be
proposed, which bring in the unknowable modulus of elasticity of
concrete and can only be solved by stages or dependence on the
calculations of some one else?

The twelfth point concerns deflection calculations. As is well known,
deflection does not play much of a part in the design of beams.
Sometimes, however, the passing requirement of a certain floor
construction is the amount of deflection under a given load. Professor
Gaetano Lanza has given some data on recorded deflections of reinforced
concrete beams.[B] He has also worked out the theoretical deflections on
various assumptions. An attempt to reconcile the observed deflections
with one of several methods of calculating stresses led him to the
conclusion that:

     "The observations made thus far are not sufficient to furnish the
     means for determining the actual distribution of the stresses, and
     hence for the deduction of reliable formulæ for the computation of
     the direct stresses, shearing stresses, diagonal stresses,
     deflections, position of the neutral axis, etc., under a given
     load."

Professor Lanza might have gone further and said that the observations
made thus far are sufficient to show the hopelessness of deriving a
formula that will predict accurately the deflection of a reinforced
concrete beam. The wide variation shown by two beam tests cited by him,
in which the beams were identical, is, in itself, proof of this.

Taking the data of these tests, and working out the modulus of
elasticity from the recorded deflections, as though the beams were of
plain concrete, values are found for this modulus which are not out of
agreement with the value of that variable modulus as determined by other
means. Therefore, if the beams be considered as plain concrete beams,
and an average value be assumed for the modulus or coefficient of
elasticity, a deflection may be found by a simple calculation which is
an average of that which may be expected. Here again, simple theory is
better than complex, because of the ease with which it may be applied,
and because it gives results which are just as reliable.

The thirteenth point concerns the elastic theory as applied to a
reinforced concrete arch. This theory treats a reinforced concrete arch
as a spring. In order to justify its use, the arch or spring is
considered as having fixed ends. The results obtained by the intricate
methods of the elastic theory and the simple method of the equilibrium
polygon, are too nearly identical to justify the former when the arch is
taken as hinged at the ends.

The assumption of fixed ends in an arch is a most extravagant one,
because it means that the abutments must be rigid, that is, capable of
taking bending moments. Rigidity in an abutment is only effected by a
large increase in bulk, whereas strength in an arch ring is greatly
augmented by the addition of a few inches to its thickness. By the
elastic theory, the arch ring does not appear to need as much strength
as by the other method, but additional stability is needed in the
abutments in order to take the bending moments. This latter feature is
not dwelt on by the elastic theorists.

In the ordinary arch, the criterion by which the size of abutment is
gauged, is the location of the line of pressure. It is difficult and
expensive to obtain depth enough in the base of the abutment to keep
this line within the middle third, when only the thrust of the arch is
considered. If, in addition to the thrust, there is a bending moment
which, for many conditions of loading, further displaces the line of
pressure toward the critical edge, the difficulty and expense are
increased. It cannot be gainsaid that a few cubic yards of concrete
added to the ring of an arch will go much further toward strengthening
the arch than the same amount of concrete added to the two abutments.

In reinforced concrete there are ample grounds for the contention that
the carrying out of a nice theory, based on nice assumptions and the
exact determination of ideal stresses, is of far less importance than
the building of a structure which is, in every way, capable of
performing its function. There are more than ample grounds for the
contention that the ideal stresses worked out for a reinforced concrete
structure are far from realization in this far from ideal material.

Apart from the objection that the elastic theory, instead of showing
economy by cutting down the thickness of the arch ring, would show the
very opposite if fully carried out, there are objections of greater
weight, objections which strike at the very foundation of the theory as
applied to reinforced concrete. In the elastic theory, as in the
intricate beam theory commonly used, there is the assumption of an
initial unstressed condition of the materials. This is not true of a
beam and is still further from the truth in the case of an arch. Besides
shrinkage of the concrete, which always produces unknown initial
stresses, there is a still more potent cause of initial stress, namely,
the settlement of the arch when the forms are removed. If the initial
stresses are unknown, ideal determinations of stresses can have little
meaning.

The elastic theory stands or falls according as one is able or unable to
calculate accurately the deflection of a reinforced concrete beam; and
it is an impossibility to calculate this deflection even approximately.
The tests cited by Professor Lanza show the utter disagreement in the
matter of deflections. Of those tested, two beams which were identical,
showed results almost 100% apart. A theory grounded on such a shifting
foundation does not deserve serious consideration. Professor Lanza's
conclusions, quoted under the twelfth point, have special meaning and
force when applied to a reinforced concrete arch; the actual
distribution of the stresses cannot possibly be determined, and complex
cloaks of arithmetic cannot cover this fact. The elastic theory, far
from being a reliable formula, is false and misleading in the extreme.

The fourteenth point refers to temperature calculations in a reinforced
concrete arch. These calculations have no meaning whatever. To give the
grounds for this assertion would be to reiterate much of what has been
said under the subject of the elastic arch. If the unstressed shape of
an arch cannot be determined because of the unknown effect of shrinkage
and settlement, it is a waste of time to work out a slightly different
unstressed shape due to temperature variation, and it is a further waste
of time to work out the supposed stresses resulting from deflecting that
arch back to its actual shape.

If no other method of finding the approximate stresses in an arch
existed, the elastic theory might be classed as the best available; but
this is not the case. There is a method which is both simple and
reliable. Accuracy is not claimed for it, and hence it is in accord with
the more or less uncertain materials dealt with. Complete safety,
however, is assured, for it treats the arch as a series of blocks, and
the cementing of these blocks into one mass cannot weaken the arch.
Reinforcement can be proportioned in the same manner as for chimneys, by
finding the tension exerted to pull these blocks apart and then
providing steel to take that tension.

The fifteenth point concerns steel in compression in reinforced concrete
columns or beams. It is common practice--and it is recommended in the
most pretentious works on the subject--to include in the strength of a
concrete column slender longitudinal rods embedded in the concrete. To
quote from one of these works:

     "The compressive resistance of a hooped member exceeds the sum of
     the following three elements: (1) The compressive resistance of the
     concrete without reinforcement. (2) The compressive resistance of
     the longitudinal rods stressed to their elastic limit. (3) The
     compressive resistance which would have been produced by the
     imaginary longitudinals at the elastic limit of the hooping metal,
     the volume of the imaginary longitudinals being taken as 2.4 times
     that of the hooping metal."

This does not stand the test, either of theory or practice; in fact, it
is far from being true. Its departure from the truth is great enough
and of serious enough moment to explain some of the worst accidents in
the history of reinforced concrete.

It is a nice theoretical conception that the steel and the concrete act
together to take the compression, and that each is accommodating enough
to take just as much of the load as will stress it to just the right
unit. Here again, initial stress plays an important part. The shrinkage
of the concrete tends to put the rods in compression, the load adds more
compression on the slender rods and they buckle, because of the lack of
any adequate stiffening, long before the theorists' ultimate load is
reached.

There is no theoretical or practical consideration which would bring in
the strength of the hoops after the strength of the concrete between
them has been counted. All the compression of a column must, of
necessity, go through the disk of concrete between the two hoops (and
the longitudinal steel). No additional strength in the hoops can affect
the strength of this disk, with a given spacing of the hoops. It is true
that shorter disks will have more strength, but this is a matter of the
spacing of the hoops and not of their sectional area, as the above
quotation would make it appear.

Besides being false theoretically, this method of investing phantom
columns with real strength is wofully lacking in practical foundation.
Even the assumption of reinforcing value to the longitudinal steel rods
is not at all borne out in tests. Designers add enormously to the
calculated strength of concrete columns when they insert some
longitudinal rods. It appears to be the rule that real columns are
weakened by the very means which these designers invest with reinforcing
properties. Whether or not it is the rule, the mere fact that many tests
have shown these so-called reinforced concrete columns to be weaker than
similar plain concrete columns is amply sufficient to condemn the
practice of assuming strength which may not exist. Of all parts of a
building, the columns are the most vital. The failure of one column
will, in all probability, carry with it many others stronger than
itself, whereas a weak and failing slab or beam does not put an extra
load and shock on the neighboring parts of a structure.

In Bulletin No. 10 of the University of Illinois Experiment Station,[C]
a plain concrete column, 9 by 9 in. by 12 ft., stood an ultimate
crushing load of 2,004 lb. per sq. in. Column 2, identical in size, and
having four 5/8-in. rods embedded in the concrete, stood 1,557 lb. per
sq. in. So much for longitudinal rods without hoops. This is not an
isolated case, but appears to be the rule; and yet, in reading the
literature on the subject, one would be led to believe that longitudinal
steel rods in a plain concrete column add greatly to the strength of the
column.

A paper, by Mr. M.O. Withey, before the American Society for Testing
Materials, in 1909, gave the results of some tests on concrete-steel and
plain concrete columns. (The term, concrete-steel, is used because this
particular combination is not "reinforced" concrete.) One group of
columns, namely, _W1_ to _W3_, 10-1/2 in. in diameter, 102 in. long, and
circular in shape, stood an average ultimate load of 2,600 lb. per sq.
in. These columns were of plain concrete. Another group, namely, _E1_ to
_E3_, were octagonal in shape, with a short diameter (12 in.), their
length being 120 in. These columns contained nine longitudinal rods, 5/8
in. in diameter, and 1/4-in. steel rings every foot. They stood an
ultimate load averaging 2,438 lb. per sq. in. This is less than the
column with no steel and with practically the same ratio of slenderness.

In some tests on columns made by the Department of Buildings, of
Minneapolis, Minn.[D], Test _A_ was a 9 by 9-in. column, 9 ft. 6 in.
long, with ten longitudinal, round rods, 1/2 in. in diameter, and
1-1/2-in. by 3/16-in. circular bands (having two 1/2-in. rivets in the
splice), spaced 4 in. apart, the circles being 7 in. in diameter. It
carried an ultimate load of 130,000 lb., which is much less than half
"the compressive resistance of a hooped member," worked out according to
the authoritative quotation before given. Another similar column stood a
little more than half that "compressive resistance." Five of the
seventeen tests on the concrete-steel columns, made at Minneapolis,
stood less than the plain concrete columns. So much for the longitudinal
rods, and for hoops which are not close enough to stiffen the rods; and
yet, in reading the literature on the subject, any one would be led to
believe that longitudinal rods and hoops add enormously to the strength
of a concrete column.

The sixteenth indictment against common practice is in reference to flat
slabs supported on four sides. Grashof's formula for flat plates has no
application to reinforced concrete slabs, because it is derived for a
material strong in all directions and equally stressed. The strength of
concrete in tension is almost nil, at least, it should be so considered.
Poisson's ratio, so prominent in Grashof's formula, has no meaning
whatever in steel reinforcement for a slab, because each rod must take
tension only; and instead of a material equally stressed in all
directions, there are generally sets of independent rods in only two
directions. In a solution of the problem given by a high English
authority, the slab is assumed to have a bending moment of equal
intensity along its diagonal. It is quite absurd to assume an intensity
of bending clear into the corner of a slab, and on the very support
equal to that at its center. A method published by the writer some years
ago has not been challenged. By this method strips are taken across the
slab and the moment in them is found, considering the limitations of the
several strips in deflection imposed by those running at right angles
therewith. This method shows (as tests demonstrate) that when the slab
is oblong, reinforcement in the long direction rapidly diminishes in
usefulness. When the ratio is 1:1-1/2, reinforcement in the long
direction is needless, since that in the short direction is required to
take its full amount. In this way French and other regulations give
false results, and fail to work out.

If the writer is wrong in any or all of the foregoing points, it should
be easy to disprove his assertions. It would be better to do this than
to ridicule or ignore them, and it would even be better than to issue
reports, signed by authorities, which commend the practices herein
condemned.


FOOTNOTES:

[Footnote A: Presented at the meeting of March 16th, 1910.]

[Footnote B: "Stresses in Reinforced Concrete Beams," _Journal_, Am.
Soc. Mech. Engrs., Mid-October, 1909.]

[Footnote C: Page 14, column 8.]

[Footnote D: _Engineering News_, December 3d, 1908.]



DISCUSSION


JOSEPH WRIGHT, M. AM. SOC. C. E. (by letter).--If, as is expected, Mr.
Godfrey's paper serves to attract attention to the glaring
inconsistencies commonly practiced in reinforced concrete designs, and
particularly to the careless detailing of such structures, he will have
accomplished a valuable purpose, and will deserve the gratitude of the
Profession.

No engineer would expect a steel bridge to stand up if the detailing
were left to the judgment or convenience of the mechanics of the shop,
yet in many reinforced concrete designs but little more thought is given
to the connections and continuity of the steel than if it were an
unimportant element of the structure. Such examples, as illustrated by
the retaining wall in Fig. 2, are common, the reinforcing bars of the
counterfort being simply hooked by a 4-in. U-bend around those of the
floor and wall slabs, and penetrating the latter only from 8 to 12 in.
The writer can cite an example which is still worse--that of a T-wall,
16 ft. high, in which the vertical reinforcement of the wall slab
consisted of 3/4-in. bars, spaced 6 in. apart. The wall slab was 8 in.
thick at the top and only 10 in. at the bottom, yet the 3/4-in. vertical
bars penetrated the floor slab only 8 in., and were simply hooked around
its lower horizontal bars by 4-in. U-bends. Amazing as it may appear,
this structure was designed by an engineer who is well versed in the
theories of reinforced concrete design. These are only two examples from
a long list which might be cited to illustrate the carelessness often
exhibited by engineers in detailing reinforced concrete structures.

In reinforced concrete work the detailer has often felt the need of some
simple and efficient means of attaching one bar to another, but, in its
absence, it is inexcusable that he should resort to such makeshifts as
are commonly used. A simple U-hook on the end of a bar will develop only
a small part of the strength of the bar, and, of course, should not be
relied on where the depth of penetration is inadequate; and, because of
the necessity of efficient anchorage of the reinforcing bars where one
member of a structure unites with another, it is believed that in some
instances economy might be subserved by the use of shop shapes and shop
connections in steel, instead of the ordinary reinforcing bars. Such
cases are comparatively few, however, for the material in common use is
readily adapted to the design, in the ordinary engineering structure,
and only requires that its limitations be observed, and that the
designer be as conscientious and consistent in detailing as though he
were designing in steel.

This paper deserves attention, and it is hoped that each point therein
will receive full and free discussion, but its main purport is a plea
for simplicity, consistency, and conservatism in design, with which the
writer is heartily in accord.


S. BENT RUSSELL, M. AM. SOC. C. E. (by letter).--The author has given
expression in a forcible way to feelings possessed no doubt by many
careful designers in the field in question. The paper will serve a
useful purpose in making somewhat clearer the limitations of reinforced
concrete, and may tend to bring about a more economical use of
reinforcing material.

It is safe to say that in steel bridges, as they were designed in the
beginning, weakness was to be found in the connections and details,
rather than in the principal members. In the modern advanced practice of
bridge design the details will be found to have some excess of strength
over the principal members. It is probable that the design of reinforced
concrete structures will take the same general course, and that progress
will be made toward safety in minor details and economy in principal
bars.

Many of the author's points appear to be well taken, especially the
first, the third, and the eighth.

In regard to shear bars, if it is assumed that vertical or inclined bars
add materially to the strength of short deep beams, it can only be
explained by viewing the beam as a framed structure or truss in which
the compression members are of concrete and the tension members of
steel. It is evident that, as generally built, the truss will be found
to be weak in the connections, more particularly, in some cases, in the
connections between the tension and compression members, as mentioned in
the author's first point.

It appears to the writer that this fault may be aggravated in the case
of beams with top reinforcement for compression; this is scarcely
touched on by the author. In such a case the top and bottom chords are
of steel, with a weakly connected web system which, in practice, is
usually composed of stirrup rods looped around the principal bars and
held in position by the concrete which they are supposed to strengthen.

While on this phase of the subject, it may be proper to call attention
to the fact that the Progress Report of the Special Committee on
Concrete and Reinforced Concrete[E] may well be criticised for its scant
attention to the case of beams reinforced on the compression side. No
limitations are specified for the guidance of the designer, but approval
is given to loading the steel with its full share of top-chord
stress.[F]

In certain systems of reinforcement now in use, such as the Kahn and
Cummings systems, the need for connections between the web system and
the chord member is met to some degree, as is generally known. On the
other hand, however, these systems do not provide for such intensity of
pressure on the concrete at the points of connection as must occur by
the author's demonstration in his first point. The author's criticisms
on some other points would also apply to such systems, and it is not
necessary to state that one weak detail will limit the strength of the
truss.

The author has only condemnation for the use of longitudinal rods in
concrete columns (Point 15). It would seem that if the longitudinal bars
are to carry a part of the load they must be supported laterally by the
concrete, and, as before, in the beam, it may be likened to a framed
structure in which the web system is formed of concrete alone, or of a
framework of poorly connected members, and the concrete and steel must
give mutual support in a way not easy to analyze. It is scarcely
surprising that the strength of such a structure is sometimes less than
that shown by concrete alone.

In the Minneapolis tests, quoted by the author, there are certain points
which should be noted, in fairness to columns reinforced longitudinally.
Only four columns thus reinforced failed below the strength shown by
concrete alone, and these were from 52 to 63 days old only, while the
plain concrete was 98 days old. There was nothing to hold the rods in
place in these four columns except the concrete and the circular hoops
surrounding them. On the other hand, all the columns in which the
hooping was hooked around the individual rods showed materially greater
strength than the plain concrete, although perhaps one should be
excepted, as it was 158 days old and showed a strength of only 2,250 lb.
per sq. in., or 12% more than the plain concrete.[G]

In considering a column reinforced with longitudinal rods and hoops, it
is proper to remark that the concrete not confined by the steel ought
not to be counted as aiding the latter in any way, and that,
consequently, the bond of the outside bars is greatly weakened.

In view of these considerations, it may be found economical to give the
steel reinforcement of columns some stiffness of its own by sufficiently
connected lateral bracing. The writer would suggest, further, that in
beams where rods are used in compression a system of web members
sufficiently connected should be provided, so that the strength of the
combined structure would be determinate.

To sum up briefly, columns and short deep beams, especially when the
latter are doubly reinforced, should be designed as framed structures,
and web members should be provided with stronger connections than have
been customary.


J.R. WORCESTER, M. AM. SOC. C. E. (by letter).--This paper is of value
in calling attention to many of the bad practices to be found in
reinforced concrete work, and also in that it gives an opportunity for
discussing certain features of design, about which engineers do not
agree. A free discussion of these features will tend to unify methods.
Several of the author's indictments, however, hit at practices which
were discarded long ago by most designers, and are not recommended by
any good authorities; the implication that they are in general use is
unwarranted.

The first criticism, that of bending rods at a sharp angle, may be said
to be of this nature. Drawings may be made without indicating the curve,
but in practice metal is seldom bent to a sharp angle. It is undoubtedly
true that in every instance a gradual curve is preferable.

The author's second point, that a suitable anchorage is not provided for
bent-up rods at the ends of a beam, may also be said to be a practice
which is not recommended or used in the best designs.

The third point, in reference to the counterforts of retaining walls, is
certainly aimed at a very reprehensible practice which should not be
countenanced by any engineer.

The fourth, fifth, and sixth items bring out the fact that undoubtedly
there has been some confusion in the minds of designers and authors on
the subject of shear in the steel. The author is wholly justified in
criticising the use of the shearing stress in the steel ever being
brought into play in reinforced concrete. Referring to the report of the
Special Committee on Concrete and Reinforced Concrete, on this point, it
seems as if it might have made the intention of the Committee somewhat
clearer had the word, tensile, been inserted in connection with the
stress in the shear reinforcing rods. In considering a beam of
reinforced concrete in which the shearing stresses are really diagonal,
there is compression in one case and tension in another; and, assuming
that the metal must be inserted to resist the tensile portion of this
stress, it is not essential that it should necessarily be wholly
parallel to the tensile stress. Vertical tensile members can prevent the
cracking of the beam by diagonal tension, just as in a Howe truss all
the tensile stresses due to shear are taken in a vertical direction,
while the compressive stresses are carried in the diagonal direction by
the wooden struts. The author seems to overlook the fact, however, that
the reinforced concrete beam differs from the Howe truss in that the
concrete forms a multiple system of diagonal compression members. It is
not necessary that a stirrup at one point should carry all the vertical
tension, as this vertical tension is distributed by the concrete. There
is no doubt about the necessity of providing a suitable anchorage for
the vertical stirrups, and such is definitely required in the
recommendations of the Special Committee.

The cracks which the author refers to as being necessary before the
reinforcing material is brought into action, are just as likely to occur
in the case of the bent-up rods with anchors at the end, advocated by
him. While his method may be a safe one, there is also no question that
a suitable arrangement of vertical reinforcement may be all that is
necessary to make substantial construction.

With reference to the seventh point, namely, methods of calculating
moments, it might be said that it is not generally considered good
practice to reduce the positive moments at the center of a span to the
amount allowable in a beam fully fixed at the end, and if provision is
made for a negative moment over supports sufficient to develop the
stresses involved in complete continuity, there is usually a
considerable margin of safety, from the fact of the lack of possible
fixedness of the beams at the supports. The criticism is evidently aimed
at practice not to be recommended.

As to the eighth point, the necessary width of a beam in order to
transfer, by horizontal shear, the stress delivered to the concrete from
the rods, it might be well worth while for the author to take into
consideration the fact that while the bonding stress is developed to its
full extent near the ends of the beam, it very frequently happens that
only a portion of the total number of rods are left at the bottom, the
others having been bent upward. It may be that the width of a beam would
not be sufficient to carry the maximum bonding stress on the total
number of rods near its center, and yet it may have ample shearing
strength on the horizontal planes. The customary method of determining
the width of the beams so that the maximum horizontal shearing stress
will not be excessive, seems to be a more rational method than that
suggested by Mr. Godfrey.

Referring to the tenth and fourteenth points, it would be interesting to
know whether the author proportions his steel to take the remaining
tension without regard to the elongation possible at the point where it
is located, considering the neutral axis of the section under the
combined stress. Take, for instance, a chimney: If the section is first
considered to be homogeneous material which will carry tension and
compression equally well, and the neutral axis is found under the
combined stresses, the extreme tensile fiber stress on the concrete will
generally be a matter of 100 or 200 lb. Evidently, if steel is inserted
to replace the concrete in tension, the corresponding stress in the
steel cannot be more than from 1,500 to 3,000 lb. per sq. in. If
sufficient steel is provided to keep the unit stress down to the proper
figure, there can be little criticism of the method, but if it is worked
to, say, 16,000 lb. per sq. in., it is evident that the result will be a
different position for the neutral axis, invalidating the calculation
and resulting in a greater stress in compression on the concrete.


L.J. MENSCH, M. AM. SOC. C. E. (by letter).--Much of the poor practice
in reinforced concrete design to which Mr. Godfrey calls attention is
due, in the writer's opinion, to inexperience on the part of the
designer.

It is true, however, that men of high standing, who derided reinforced
concrete only a few years ago, now pose as reinforced concrete experts,
and probably the author has the mistakes of these men in mind.

The questions which he propounds were settled long ago by a great many
tests, made in various countries, by reliable authorities, although the
theoretical side is not as easily answered; but it must be borne in mind
that the stresses involved are mostly secondary, and, even in steel
construction, these are difficult of solution. The stresses in the web
of a deep steel girder are not known, and the web is strengthened by a
liberal number of stiffening angles, which no expert can figure out to a
nicety. The ultimate strength of built-up steel columns is not known,
frequently not even within 30%; still less is known of the strength of
columns consisting of thin steel casings, or of the types used in the
Quebec Bridge. It seems to be impossible to solve the problem
theoretically for the simplest case, but had the designer of that bridge
known of the tests made by Hodgkinson more than 40 years ago, that
accident probably would not have happened.

Practice is always ahead of theory, and the writer claims that, with the
great number of thoroughly reliable tests made in the last 20 years, the
man who is really informed on this subject will not see any reason for
questioning the points brought out by Mr. Godfrey.

The author is right in condemning sharp bends in reinforcing rods.
Experienced men would not think of using them, if only for the reason
that such sharp bends are very expensive, and that there is great
likelihood of breaking the rods, or at least weakening them. Such sharp
bends invite cracks.

Neither is there any question in regard to the advantage of continuing
the bent-up rods over the supports. The author is manifestly wrong in
stating that the reinforcing rods can only receive their increments of
stress when the concrete is in tension. Generally, the contrary happens.
In the ordinary adhesion test, the block of concrete is held by the jaws
of the machine and the rod is pulled out; the concrete is clearly in
compression.

The underside of continuous beams is in compression near the supports,
yet no one will say that steel rods cannot take any stress there. It is
quite surprising to learn that there are engineers who still doubt the
advisability of using bent-up bars in reinforced concrete beams.
Disregarding the very thorough tests made during the last 18 years in
Europe, attention is called to the valuable tests on thirty beams made
by J.J. Harding, M. Am. Soc. C. E., for the Chicago, Milwaukee and St.
Paul Railroad.[H] All the beams were reinforced with about 3/4% of
steel. Those with only straight rods, whether they were plain or
patented bars, gave an average shearing strength of 150 lb. per sq. in.
Those which had one-third of the bars bent up gave an average shearing
strength of 200 lb. per sq. in., and those which had nearly one-half of
the rods bent up gave an average shearing strength of 225 lb. per sq.
in. Where the bent bars were continued over the supports, higher
ultimate values were obtained than where some of the rods were stopped
off near the supports; but in every case bent-up bars showed a greater
carrying capacity than straight rods. The writer knows also of a number
of tests with rods fastened to anchor-plates at the end, but the tests
showed that they had only a slight increase of strength over straight
rods, and certainly made a poorer showing than bent-up bars. The use of
such threaded bars would increase materially the cost of construction,
as well as the time of erection.

The writer confesses that he never saw or heard of such poor practices
as mentioned in the author's third point. On the other hand, the
proposed design of counterforts in retaining walls would not only be
very expensive and difficult to install, but would also be a decided
step backward in mechanics. This proposition recalls the trusses used
before the introduction of the Fink truss, in which the load from the
upper chord was transmitted by separate members directly to the
abutments, the inventor probably going on the principle that the
shortest way is the best. There are in the United States many hundreds
of rectangular water tanks. Are these held by any such devices? And as
they are not thus held, and inasmuch as there is no doubt that they must
carry the stress when filled with water, it is clear that, as long as
the rods from the sides are strong enough to carry the tension and are
bent with a liberal radius into the front wall and extended far enough
to form a good anchorage, the connection will not be broken. The same
applies to retaining walls. It would take up too much time to prove that
the counterfort acts really as a beam, although the forces acting on it
are not as easily found as those in a common beam.

The writer does not quite understand the author's reference to shear
rods. Possibly he means the longitudinal reinforcement, which it seems
is sometimes calculated to carry 10,000 lb. per sq. in. in shear. The
writer never heard of such a practice.

In regard to stirrups, Mr. Godfrey seems to be in doubt. They certainly
do not act as the rivets of a plate girder, nor as the vertical rods of
a Howe truss. They are best compared with the dowel pins and bolts of a
compound wooden beam. The writer has seen tests made on compound
concrete beams separated by copper plates and connected only by
stirrups, and the strength of the combination was nearly the same as
that of beams made in one piece.

Stirrups do not add much to the strength of the beams where bent bars
are used, but the majority of tests show a great increase of strength
where only straight reinforcing bars are used. Stirrups are safeguards
against poor concrete and poor workmanship, and form a good connection
where concreting is interrupted through inclemency of weather or other
causes. They absolutely prevent shrinkage cracks between the stem and
the flange of T-beams, and the separation of the stem and slab in case
of serious fires. For the latter reason, the writer condemns the use of
simple U-bars, and arranges all his stirrups so that they extend from
6 to 12 in. into the slabs. Engineers are warned not to follow the
author's advice with regard to the omission of stirrups, but to use
plenty of them in their designs, or sooner or later they will thoroughly
repent it.

In regard to bending moments in continuous beams, the writer wishes to
call attention to the fact that at least 99% of all reinforced
structures are calculated with a reduction of 25% of the bending moment
in the center, which requires only 20% of the ordinary bending moment of
a freely supported beam at the supports. There may be some engineers who
calculate a reduction of 33%; there are still some ultra-confident men,
of little experience, who compute a reduction of 50%; but, inasmuch as
most designers calculate with a reduction of only 25%, too great a
factor of safety does not result, nor have any failures been observed on
that account.

In the case of slabs which are uniformly loaded by earth or water
pressure, the bending moments are regularly taken as (_w_ _l^{2}_)/24 in
the center and (_w_ _l^{2}_)/12 at the supports. The writer never
observed any failure of continuous beams over the supports, although he
has often noticed failures in the supporting columns directly under the
beams, where these columns are light in comparison with the beams.
Failure of slabs over the supports is common, and therefore the writer
always places extra rods over the supports near the top surface.

The width of the beams which Mr. Godfrey derives from his simple rule,
that is, the width equals the sum of the peripheries of the reinforcing
rods, is not upheld by theory or practice. In the first place, this
width would depend on the kind of rods used. If a beam is reinforced by
three 7/8-in. round bars, the width, according to his formula, would be
8.2 in. If the beam is reinforced by six 5/8-in. bars which have the
same sectional area as the three 7/8-in. bars, then the width should be
12 in., which is ridiculous and does not correspond with tests, which
would show rather a better behavior for the six bars than for the three
larger bars in a beam of the same width.

It is surprising to learn that there are engineers who still advocate
such a width of the stem of T-beams that the favorable influence of the
slab may be dispensed with, although there were many who did this 10 or
12 years ago.

It certainly can be laid down as an axiom that the man who uses
complicated formulas has never had much opportunity to design or build
in reinforced concrete, as the design alone might be more expensive than
the difference in cost between concrete and structural steel work.

The author attacks the application of the elastic theory to reinforced
concrete arches. He evidently has not made very many designs in which he
used the elastic theory, or he would have found that the abutments need
be only from three to four times thicker than the crown of the arch
(and, therefore, their moments of inertia from 27 to 64 times greater),
when the deformation of the abutments becomes negligible in the elastic
equations. Certainly, the elastic theory gives a better guess in regard
to the location of the line of pressure than any guess made without its
use. The elastic theory was fully proved for arches by the remarkable
tests, made in 1897 by the Austrian Society of Engineers and Architects,
on full-sized arches of 70-ft. span, and the observed deflections and
lateral deformations agreed exactly with the figured deformation.

Tests on full-sized arches also showed that the deformations caused by
temperature changes agree with the elastic theory, but are not as great
for the whole mass of the arch as is commonly assumed. The elastic
theory enables one to calculate arches much more quickly than any
graphical or guess method yet proposed.

Hooped columns are a patented construction which no one has the right to
use without license or instructions from M. Considère, who clearly
states that his formulas are correct only for rich concrete and for
proper percentages of helical and longitudinal reinforcement, which
latter must have a small spacing, in order to prevent the deformation of
the core between the hoops. With these limitations his formulas are
correct.

Mr. Godfrey brings up some erratic column tests, and seems to have no
confidence in reinforced concrete columns. The majority of column tests,
however, show an increase of strength by longitudinal reinforcement. In
good concrete the longitudinal reinforcement may not be very effective
or very economical, but it safeguards the strength in poorly made
concrete, and is absolutely necessary on account of the bending stresses
set up in such columns, due to the monolithic character of reinforced
concrete work.

Mr. Godfrey does not seem to be familiar with the tests made by good
authorities on square slabs of reinforced concrete and of cast iron,
which latter material is also deficient in tensile strength. These tests
prove quite conclusively that the maximum bending moment per linear foot
may be calculated by the formulas, (_w_ _l^{2}_)/32 or (_w_ _l^{2}_)/20,
according to the degree of fixture of the slabs at the four sides.
Inasmuch as fixed ends are rarely obtained in practice, the formula,
(_w_ _l^{2}_)/24, is generally adopted, and the writer cannot see any
reason to confuse the subject by the introduction of a new method of
calculation.


WALTER W. CLIFFORD, JUN. AM. SOC. C. E. (by letter).--Some of Mr.
Godfrey's criticisms of reinforced concrete practice do not seem to be
well taken, and the writer begs to call attention to a few points which
seem to be weak. In Fig. 1, the author objects to the use of diagonal
bars for the reason that, if the diagonal reinforcement is stressed to
the allowable limit, these bars bring the bearing on the concrete, at
the point where the diagonal joins the longitudinal reinforcement, above
a safe value. The concrete at the point of juncture must give, to some
extent, and this would distribute the bearing over a considerable length
of rod. In some forms of patented reinforcement an additional safeguard
is furnished by making the diagonals of flat straps. The stress in the
rods at this point, moreover, is not generally the maximum allowable
stress, for considerable is taken out of the rod by adhesion between the
point of maximum stress and that of juncture.

Mr. Godfrey wishes to remedy this by replacing the diagonals by rods
curved to a radius of from twenty to thirty times their diameter. In
common cases this radius will be about equal to the depth of the beam.
Let this be assumed to be true. It cannot be assumed that these rods
take any appreciable vertical shear until their slope is 30° from the
horizontal, for before this the tension in the rod would be more than
twice the shear which causes it. Therefore, these curved rods, assuming
them to be of sufficient size to take, as a vertical component, the
shear on any vertical plane between the point where it slopes 30° and
its point of maximum slope, would need to be spaced at, approximately,
one-half the depth of the beam. Straight rods of equivalent strength, at
45° with the axis of the beam, at this same spacing (which would be
ample), would be 10% less in length.

Mr. Godfrey states:

     "Of course a reinforcing rod in a concrete beam receives its stress
     by increments imparted by the grip of the concrete; but these
     increments can only be imparted where the tendency of the concrete
     is to stretch."

He then overlooks the fact that at the end of a beam, such as he has
shown, the maximum tension is diagonal, and at the neutral axis, not at
the bottom; and the rod is in the best position to resist failure on the
plane, _AB_, if its end is sufficiently well anchored. That this rod
should be anchored is, as he states, undoubtedly so, but his implied
objection to a bent end, as opposed to a nut, seems to the writer to be
unfounded. In some recent tests, on rods bent at right angles, at a
point 5 diameters distant from the end, and with a concrete backing,
stress was developed equal to the bond stress on a straight rod embedded
for a length of about 30 diameters, and approximately equal to the
elastic limit of the rod, which, for reinforcing purposes, is its
ultimate stress.

Concerning the vertical stirrups to which Mr. Godfrey refers, there is
no doubt that they strengthen beams against failure by diagonal tension
or, as more commonly known, shear failures. That they are not effective
in the beam as built is plain, for, if one considers a vertical plane
between the stirrups, the concrete must resist the shear on this plane,
unless dependence is placed on that in the longitudinal reinforcement.
This, the author states, is often done, but the practice is unknown to
the writer, who does not consider it of any value; certainly the
stirrups cannot aid.

Suppose, however, that the diagonal tension is above the ultimate stress
for the concrete, failure of the concrete will then occur on planes
perpendicular to the line of maximum tension, approximately 45° at the
end of the beam. If the stirrups are spaced close enough, however, and
are of sufficient strength so that these planes of failure all cut
enough steel to take as tension the vertical shear on the plane, then
these cracks will be very minute and will be distributed, as is the case
in the center of the lower part of the beam. These stirrups will then
take as tension the vertical shear on any plane, and hold the beam
together, so that the friction on these planes will keep up the strength
of the concrete in horizontal shear. The concrete at the end of a simple
beam is better able to take horizontal shear than vertical, because the
compression on a horizontal plane is greater than that on a vertical
plane. This idea concerning the action of stirrups falls under the ban
of Mr. Godfrey's statement, that any member which "cannot act until
failure has started, is not a proper element of design," but this is not
necessarily true. For example, Mr. Godfrey says "the steel in the
tension side of the beam should be considered as taking all the
tension." This is undoubtedly true, but it cannot take place until the
concrete has failed in tension at this point. If used, vertical tension
members should be considered as taking all the vertical shear, and, as
Mr. Godfrey states, they should certainly have their ends anchored so as
to develop the strength for which they have been calculated.

The writer considers diagonal reinforcement to be the best for shear,
and it should be used, especially in all cases of "unit" reinforcement;
but, in some cases, stirrups can and do answer in the manner suggested;
and, for reasons of practical construction, are sometimes best with
"loose rod" reinforcement.


J.C. MEEM, M. AM. SOC. C. E. (by letter).--The writer believes that
there are some very interesting points in the author's somewhat
iconoclastic paper which are worthy of careful study, and, if it be
shown that he is right in most of, or even in any of, his assumptions, a
further expression of approval is due to him. Few engineers have the
time to show fully, by a process of _reductio ad absurdum_, that all the
author's points are, or are not, well considered or well founded, but
the writer desires to say that he has read this paper carefully, and
believes that its fundamental principles are well grounded. Further, he
believes that intricate mathematical formulas have no place in practice.
This is particularly true where these elaborate mathematical
calculations are founded on assumptions which are never found in
practice or experiment, and which, even in theory, are extremely
doubtful, and certainly are not possible within those limits of safety
wherein the engineer is compelled to work.

The writer disagrees with the author in one essential point, however,
and that is in the wholesale indictment of special reinforcement, such
as stirrups, shear rods, etc. In the ordinary way in which these rods
are used, they have no practical value, and their theoretical value is
found only when the structure is stressed beyond its safe limits;
nevertheless, occasions may arise when they have a definite practical
value, if properly designed and placed, and, therefore, they should not
be discriminated against absolutely.

Quoting the author, that "destructive criticism is of no value unless it
offers something in its place," and in connection with the author's
tenth point, the writer offers the following formula which he has always
used in conjunction with the design of reinforced concrete slabs and
beams. It is based on the formula for rectangular wooden beams, and
assumes that the beam is designed on the principle that concrete in
tension is as strong as that in compression, with the understanding that
sufficient steel shall be placed on the tension side to make this true,
thus fixing the neutral axis, as the author suggests, in the middle of
the depth, that is, _M_ = (1/6)_b d_^{2} _S_, _M_, of course, being the
bending moment, and _b_ and _d_, the breadth and depth, in inches. _S_
is usually taken at from 400 to 600 lb., according to the conditions. In
order to obtain the steel necessary to give the proper tensile strength
to correspond with the compression side, the compression and tension
areas of the beam are equated, that is

   1        2                _d_
 ---- _b_ _d_ _S_ = _a_ × ( ----- - _x_   ) × _S_  ,
  12                          2       II        II

where

 _a_      = the area of steel per linear foot,
 _x_{II}_ = the distance from the center of the steel to the outer
            fiber, and
 _S_{II}_ = the strength of the steel in tension.

Then for a beam, 12 in. wide,

   2                   _d_
 _d_ _S_ = _a_ _S_  ( ----- - _x_ ) ,
                 II     2       II

or

                 2
               _d_ _S_
 _a_ = --------------------- .
               _d_
        _S_ ( ----- - _x_ )
          II    2       II

Carrying this to its conclusion, we have, for example, in a beam 12 in.
deep and 12 in. wide,

 _S_      = 500,
 _S_{II}_ = 15,000,
 _x_{II}_ = 2-1/2 in.
 _a_      = 1.37 sq. in. per ft.

The writer has used this formula very extensively, in calculating new
work and also in checking other designs built or to be built, and he
believes its results are absolutely safe. There is the further fact to
its credit, that its simplicity bars very largely the possibility of
error from its use. He sees no reason to introduce further complications
into such a formula, when actual tests will show results varying more
widely than is shown by a comparison between this simple formula and
many more complicated ones.


GEORGE H. MYERS, JUN. AM. SOC. C. E. (by letter).--This paper brings out
a number of interesting points, but that which strikes the writer most
forcibly is the tenth, in regard to elaborate theories and complicated
formulas for beams and slabs. The author's stand for simplicity in this
regard is well taken. A formula for the design of beams and slabs need
not be long or complicated in any respect. It can easily be obtained
from the well-known fact that the moment at any point divided by the
distance between the center of compression and the center of tension at
that point gives the tension (or compression) in the beam.

The writer would place the neutral axis from 0.42 to 0.45 of the
effective depth of the beam from the compression side rather than at the
center, as Mr. Godfrey suggests. This higher position of the neutral
axis is the one more generally shown by tests of beams. It gives the
formula _M_ = 0.86 _d_ _As_ _f_, or _M_ = 0.85 _d_ _As_ _f_, which the
writer believes is more accurate than _M_ = 5/6 _d_ _As_ _f_, or
0.83-1/3 _d_ _As_ _f_, which would result if the neutral axis were taken
at the center of the beam.

    _d_  = depth of the beam from the compression side to the center
           of the steel;
    _As_ = the area of the steel;
and _f_  = the allowable stress per square inch in the steel.

The difference, however, is very slight, the results from the two
formulas being proportional to the two factors, 83-1/3 and 85 or 86.
This formula gives the area of steel required for the moment. The
percentage of steel to be used can easily be obtained from the allowable
stresses in the concrete and the steel, and the dimensions of the beam
can be obtained in the simplest manner. This formula is used with great
success by one of the largest firms manufacturing reinforcing materials
and designing concrete structures. It is well-known to the Profession,
and the reason for using any other method, involving the Greek alphabet
and many assumptions, is unknown to the writer. The only thing to
assume--if it can be called assuming when there are so many tests to
locate it--is the position of the neutral axis. A slight difference in
this assumption affects the resulting design very little, and is
inappreciable, from a practical point of view. It can be safely said
that the neutral axis is at, or a little above, the center of the beam.

Further, it would seem that the criticism to the effect that the initial
stress in the concrete is neglected is devoid of weight. As far as the
designer is concerned, the initial stress is allowed for. The values for
the stresses used in design are obtained from tests on blocks of
concrete which have gone through the process of setting. Whatever
initial stress exists in concrete due to this process of setting exists
also in these blocks when they are tested. The value of the breaking
load on concrete given by any outside measuring device used in these
tests, is the value of that stress over and above this initial stress.
It is this value with which we work. It would seem that, if the initial
stress is neglected in arriving at a safe working load, it would be safe
to neglect it in the formula for design.


EDWIN THACHER, M. AM. SOC. C. E. (by letter).--The writer will discuss
this paper under the several "points" mentioned by the author.

_First Point._--At the point where the first rod is bent up, the stress
in this rod runs out. The other rods are sufficient to take the
horizontal stress, and the bent-up portion provides only for the
vertical and diagonal shearing stresses in the concrete.

_Second Point._--The remarks on the first point are also applicable to
the second one. Rod 3 provides for the shear.

_Third Point._--In a beam, the shear rods run through the compression
parts of the concrete and have sufficient anchorage. In a counterfort,
the inclined rods are sufficient to take the overturning stress. The
horizontal rods support the front wall and provide for shrinkage. The
vertical rods also provide for shrinkage, and assist the diagonal rods
against overturning. The anchorage is sufficient in all cases, and the
proposed method is no more effective.

_Fourth Point._--In bridge pins, bending and bearing usually govern,
but, in case a wide bar pulled on a pin between the supports close to
the bar, as happens in bolsters and post-caps of combination bridges and
in other locations, shear would govern. Shear rods in concrete-steel
beams are proportioned to take the vertical and diagonal shearing
stresses. If proportioned for less stress per square inch than is used
in the bottom bars, this cannot be considered dangerous practice.

_Fifth Point._--Vertical stirrups are designed to act like the vertical
rods in a Howe truss. Special literature is not required on the subject;
it is known that the method used gives good results, and that is
sufficient.

_Sixth Point._--The common method is not "to assume each shear member as
taking the horizontal shear occurring in the space from member to
member," but to take all the shear from the center of the beam up to the
bar in question.

Cracks do not necessarily endanger the safety of a beam. Any device that
will prevent the cracks from opening wide enough to destroy the beam, is
logical. By numerous experiments, Mr. Thaddeus Hyatt found that nuts and
washers at the ends of reinforcing bars were worse than useless, and
added nothing to the strength of the beams.

_Seventh Point._--Beams can be designed, supported at the ends, fully
continuous, or continuous to a greater or less extent, as desired. The
common practice is to design slabs to take a negative moment over the
supports equal to one-half the positive moment at the center, or to bend
up the alternate rods. This is simple and good practice, for no beam can
fail as long as a method is provided by which to take care of all the
stresses without overstraining any part.

_Eighth Point._--Bars in the bottom of a reinforced concrete beam are
often placed too close to one another. The rule of spacing the bars not
less than three diameters apart, is believed to be good practice.

_Ninth Point._--To disregard the theory of T-beams, and work by
rule-of-thumb, can hardly be considered good engineering.

_Tenth Point._--The author appears to consider theories for reinforced
concrete beams and slabs as useless refinements, but as long as theory
and experiment agree so wonderfully well, theories will undoubtedly
continue to be used.

_Eleventh Point._--Calculations for chimneys are somewhat complex, but
are better and safer than rule-of-thumb methods.

_Twelfth Point._--Deflection is not very important.

_Thirteenth Point._--The conclusion of the Austrian Society of Engineers
and Architects, after numerous experiments, was that the elastic theory
of the arch is the only true theory. No arch designed by the elastic
theory was ever known to fail, unless on account of insecure
foundations, therefore engineers can continue to use it with confidence
and safety.

_Fourteenth Point._--Calculations for temperature stresses, as per
theory, are undoubtedly correct for the variations in temperature
assumed. Similar calculations can also be made for shrinkage stresses,
if desired. This will give a much better idea of the stresses to be
provided for, than no calculations at all.

_Fifteenth Point._--Experiments show that slender longitudinal rods,
poorly supported, and embedded in a concrete column, add little or
nothing to its strength; but stiff steel angles, securely latticed
together, and embedded in the concrete column, will greatly increase its
strength, and this construction is considered the most desirable when
the size of the column has to be reduced to a minimum.

_Sixteenth Point._--The commonly accepted theory of slabs supported on
four sides can be correctly applied to reinforced concrete slabs, as it
is only a question of providing for certain moments in the slab. This
theory shows that unless the slab is square, or nearly so, nothing is to
be gained by such construction.


C.A.P. TURNER, M. AM. SOC. C. E. (by letter).--Mr. Godfrey has expressed
his opinion on many questions in regard to concrete construction, but he
has adduced no clean-cut statement of fact or tests, in support of his
views, which will give them any weight whatever with the practical
matter-of-fact builder.

The usual rules of criticism place the burden of proof on the critic.
Mr. Godfrey states that if his personal opinions are in error, it should
be easy to prove them to be so, and seems to expect that the busy
practical constructor will take sufficient interest in them to spend the
time to write a treatise on the subject in order to place him right in
the matter.

The writer will confine his discussion to only a few points of the many
on which he disagrees with Mr. Godfrey.

First, regarding stirrups: These may be placed in the beam so as to be
of little practical value. They were so placed in the majority of the
tests made at the University of Illinois. Such stirrups differ widely in
value from those used by Hennebique and other first-class constructors.

Mr. Godfrey's idea is that the entire pull of the main reinforcing rod
should be taken up apparently at the end. When one frequently sees slabs
tested, in which the steel breaks at the center, with no end anchorage
whatever for the rods, the soundness of Mr. Godfrey's position may be
questioned.

Again, concrete is a material which shows to the best advantage as a
monolith, and, as such, the simple beam seems to be decidedly out of
date to the experienced constructor.

Mr. Godfrey appears to consider that the hooping and vertical
reinforcement of columns is of little value. He, however, presents for
consideration nothing but his opinion of the matter, which appears to be
based on an almost total lack of familiarity with such construction.

The writer will state a few facts regarding work which he has executed.
Among such work have been columns in a number of buildings, with an
18-in. core, and carrying more than 500 tons; also columns in one
building, which carry something like 1100 tons on a 27-in. core. In each
case there is about 1-1/2 in. of concrete outside the core for a
protective coating. The working stress on the core, if it takes the
load, is approximately equal to the ultimate strength of the concrete in
cubes, to say nothing of the strength of cylinders fifteen times their
diameter in height. These values have been used with entire confidence
after testing full-sized columns designed with the proper proportions of
vertical steel and hooping, and are regarded by the writer as having at
least double the factor of safety used in ordinary designs of structural
steel.

An advantage which the designer in concrete has over his fellow-engineer
in the structural steel line, lies in the fact that, with a given type
of reinforcement, his members are similar in form, and when the work is
executed with ordinary care, there is less doubt as to the distribution
of stress through a concrete column, than there is with the ordinary
structural steel column, since the core is solid and the conditions are
similar in all cases.

Tests of five columns are submitted herewith. The columns varied little
in size, but somewhat in the amount of hooping, with slight differences
in the vertical steel. The difference between Columns 1 and 3 is nearly
50%, due principally to the increase in hooping, and to a small addition
in the amount of vertical steel. As to the efficiency of hooping and
vertical reinforcement, the question may be asked Mr. Godfrey, and those
who share his views, whether a column without reinforcement can be cast,
which will equal the strength of those, the tests of which are
submitted.


TEST NO. 1.[I]

Marks on column--none.

Reinforcement--eight 1-1/8-in. round bars vertically.

Band spacing--- 9 in. vertically.

Hooped with seven 32-in. wire spirals about 2-in. raise.

Outside diameter of hoops--14-1/2 in.

Total load at failure--1,360,000 lb.

Remarks.--Point of failure was about 22 in. from the top. Little
indication of failure until ultimate load was reached.

Some slight breaking off of concrete near the top cap, due possibly to
the cap not being well seated in the column itself.


TEST NO. 2.

Marks on column--Box 4.

Reinforcement--eight 1-1/8-in. round bars vertically.

Band spacing about 13 in. vertically.

Wire spiral about 3-in. pitch.

Point of failure about 18 in. from top.

Top of cast-iron cap cracked at four corners.

Ultimate load--1,260,000 lb.

Remarks.--Both caps apparently well seated, as was the case with all the
subsequent tests.


TEST NO. 3.

Marks on column--4-B.

Reinforcement--eight 7/8-in. round bars vertically.

Hoops--1-3/4 in. × 3/16 in. × 14 in. outside diameter.

Band spacing--13 in. vertically.

Ultimate load--900,000 lb.

Point of failure about 2 ft. from top.

Remarks.--Concrete, at failure, considerably disintegrated, probably due
to continuance of movement of machine after failure.


TEST NO. 4.

Marks on column--Box 4.

Reinforcement--eight 1-in. round bars vertically.

Hoops spaced 8 in. vertically.

Wire spirals as on other columns.

Total load at failure--1,260,000 lb.

Remarks.--First indications of failure were nearest the bottom end of
the column, but the total failure was, as in all other columns, within 2
ft. of the top. Large cracks in the shell of the column extended from
both ends to very near the middle. This was the most satisfactory
showing of all the columns, as the failure was extended over nearly the
full length of the column.


TEST NO. 5.

Marks on column--none.

Reinforcement--eight 7/8-in. bars vertically.

Hoops spaced 10 in. vertically.

Outside diameter of hoops--14-1/2 in.

Wire spiral as before.

Load at failure--1,100,000 lb.

Ultimate load--1,130,000 lb.

Remarks.--The main point of failure in this, as in all other columns,
was within 2 ft. of the top, although this column showed some scaling
off at the lower end.

In these tests it will be noted that the concrete outside of the hooped
area seems to have had very little value in determining the ultimate
strength; that, figuring the compression on the core area and deducting
the probable value of the vertical steel, these columns exhibited from
5,000 to 7,000 lb. per sq. in. as the ultimate strength of the hooped
area, not considering the vertical steel. Some of them run over 8,000
lb.

The concrete mixture was 1 part Alpena Portland cement, 1 part sand,
1-1/2 parts buckwheat gravel and 3-1/2 parts gravel ranging from 1/4 to
3/4 in. in size.

The columns were cast in the early part of December, and tested in
April. The conditions under which they hardened were not particularly
favorable, owing to the season of the year.

The bands used were 1-3/4 by 1/4 in., except in the light column, where
they were 1-3/4 by 3/16 in.

In his remarks regarding the tests at Minneapolis, Minn., Mr. Godfrey
has failed to note that these tests, faulty as they undoubtedly were,
both in the execution of the work, and in the placing of the
reinforcement, as well as in the character of the hooping used, were
sufficient to satisfy the Department of Buildings that rational design
took into consideration the amount of hooping and the amount of
vertical steel, and on a basis not far from that which the writer
considers reasonable practice.

Again, Mr. Godfrey seems to misunderstand the influence of Poisson's
ratio in multiple-way reinforcement. If Mr. Godfrey's ideas are correct,
it will be found that a slab supported on two sides, and reinforced with
rods running directly from support to support, is stronger than a
similar slab reinforced with similar rods crossing it diagonally in
pairs. Tests of these two kinds of slabs show that those with the
diagonal reinforcement develop much greater strength than those
reinforced directly from support to support. Records of small test slabs
of this kind will be found in the library of the Society.

Mr. Godfrey makes the good point that the accuracy of an elastic theory
must be determined by the elastic deportment of the construction under
load, and it seems to the writer that if authors of textbooks would pay
some attention to this question and show by calculation that the elastic
deportment of slabs is in keeping with their method of figuring, the
gross errors in the theoretical treatment of slabs in the majority of
works on reinforced concrete would be remedied.

Although he makes the excellent point noted, Mr. Godfrey very
inconsistently fails to do this in connection with his theory of slabs,
otherwise he would have perceived the absurdity of any method of
calculating a multiple-way reinforcement by endeavoring to separate the
construction into elementary beam strips. This old-fashioned method was
discarded by the practical constructor many years ago, because he was
forced to guarantee deflections of actual construction under severe
tests. Almost every building department contains some regulation
limiting the deflection of concrete floors under test, and yet no
commissioner of buildings seems to know anything about calculating
deflections.

In the course of his practice the writer has been required to give
surety bonds of from $50,000 to $100,000 at a time, to guarantee under
test both the strength and the deflection of large slabs reinforced in
multiple directions, and has been able to do so with accuracy by methods
which are equivalent to considering Poisson's ratio, and which are given
in his book on concrete steel construction.

Until the engineer pays more attention to checking his complicated
theories with facts as determined by tests of actual construction, the
view, now quite general among the workers in reinforced concrete
regarding him will continue to grow stronger, and their respect for him
correspondingly less, until such time as he demonstrates the
applicability of his theories to ordinary every-day problems.


PAUL CHAPMAN, ASSOC. M. AM. SOC. C. E. (by letter).--Mr. Godfrey has
pointed out, in a forcible manner, several bad features of text-book
design of reinforced concrete beams and retaining walls. The practical
engineer, however, has never used such methods of construction. Mr.
Godfrey proposes certain rules for the calculation of stresses, but
there are no data of experiments, or theoretical demonstrations, to
justify their use.

It is also of the utmost importance to consider the elastic behavior of
structures, whether of steel or concrete. To illustrate this, the writer
will cite a case which recently came to his attention. A roof was
supported by a horizontal 18-in. I-beam, 33 ft. long, the flanges of
which were coped at both ends, and two 6 by 4-in. angles, 15 ft. long,
supporting the same, were securely riveted to the web, thereby forming a
frame to resist lateral wind pressure. Although the 18-in. I-beam was
not loaded to its full capacity, its deflection caused an outward
flexure of 3/4 in. and consequent dangerous stresses in the 6 by 4-in.
angle struts. The frame should have been designed as a structure fixed
at the base of the struts. The importance of the elastic behavior of a
structure is forcibly illustrated by comparing the contract drawings for
a great cantilever bridge which spans the East River with the expert
reports on the same. Due to the neglect of the elastic behavior of the
structure in the contract drawings, and another cause, the average error
in the stresses of 290 members was 18-1/2%, with a maximum of 94 per
cent.

Mr. Godfrey calls attention to the fact that stringers in railroad
bridges are considered as simple beams; this is theoretically proper
because the angle knees at their ends can transfer practically no flange
stress. It is also to be noted that when stringers are in the plane of a
tension chord, they are milled to exact lengths, and when in the plane
of a compression chord, they are given a slight clearance in order to
prevent arch action.

[Illustration: FIG. 3.]

The action of shearing stresses in concrete beams may be illustrated by
reference to the diagrams in Fig. 3, where the beams are loaded with a
weight, _W_. The portion of _W_ traveling to the left support, moves in
diagonal lines, varying from many sets of almost vertical lines to a
single diagonal. The maximum intensity of stress probably would be in
planes inclined about 45°, since, considered independently, they produce
the least deflection. While the load, _W_, remains relatively small,
producing but moderate stresses in the steel in the bottom flange, the
concrete will carry a considerable portion of the bottom flange tension;
when the load _W_ is largely increased, the coefficient of elasticity of
the concrete in tension becomes small, or zero, if small fissures
appear, and the concrete is unable to transfer the tension in diagonal
planes, and failure results. For a beam loaded with a single load, _W_,
the failure would probably be in a diagonal line near the point of
application, while in a uniformly loaded beam, it would probably occur
in a diagonal line near the support, where the shear is greatest.

It is evident that the introduction of vertical stirrups, as at _b_, or
the more rational inclined stirrups, as at _c_, influences the action of
the shearing forces as indicated, the intensity of stress at the point
of connection of the stirrups being high. It is advisable to space the
stirrups moderately close, in order to reduce this intensity to
reasonable limits. If the assumption is made that the diagonal
compression in the concrete acts in a plane inclined at 45°, then the
tension in the vertical stirrups will be the vertical shear times the
horizontal spacing of the stirrups divided by the distance, center to
center, of the top and bottom flanges of the beam. If the stirrups are
inclined at 45°, the stress in them would be 0.7 the stress in vertical
stirrups with the same spacing. Bending up bottom rods sharply, in order
to dispense with suspenders, is bad practice; the writer has observed
diagonal cracks in the beams of a well-known building in New York City,
which are due to this cause.

[Illustration: FIG. 4.]

In several structures which the writer has recently designed, he has
been able to dispense with stirrups, and, at the same time, effect a
saving in concrete, by bending some of the bottom reinforcing rods and
placing a bar between them and those which remain horizontal. A typical
detail is shown in Fig. 4. The bend occurs at a point where the vertical
component of the stress in the bent bars equals the vertical shear, and
sufficient bearing is provided by the short cross-bar. The bars which
remain horizontal throughout the beam, are deflected at the center of
the beam in order to obtain the maximum effective depth. There being no
shear at the center, the bars are spaced as closely as possible, and
still provide sufficient room for the concrete to flow to the soffit of
the beam. Two or more adjacent beams are readily made continuous by
extending the bars bent up from each span, a distance along the top
flanges. By this system of construction one avoids stopping a bar where
the live load unit stress in adjoining bars is high, as their continual
lengthening and shortening under stress would cause severe shearing
stresses in the concrete surrounding the end of the short bar.

[Illustration: FIG. 5.]

The beam shown in Fig. 5 illustrates the principles stated in the
foregoing, as applied to a heavier beam. The duty of the short
cross-bars in this case is performed by wires wrapped around the
longitudinal rods and then continued up in order to support the bars
during erection. This beam, which supports a roof and partitions, etc.,
has supported about 80% of the load for which it was calculated, and no
hair cracks or noticeable deflection have appeared. If the method of
calculation suggested by Mr. Godfrey were a correct criterion of the
actual stresses, this particular beam (and many others) would have shown
many cracks and noticeable deflection. The writer maintains that where
the concrete is poured continuously, or proper bond is provided, the
influence of the slab as a compression flange is an actual condition,
and the stresses should be calculated accordingly.

In the calculation of continuous T-beams, it is necessary to consider
the fact that the moment of inertia for negative moments is small
because of the lack of sufficient compressive area in the stem or web.
If Mr. Godfrey will make proper provision for this point, in studying
the designs of practical engineers, he will find due provision made for
negative moments. It is very easy to obtain the proper amount of steel
for the negative moment in a slab by bending up the bars and letting
them project into adjoining spans, as shown in Figs. 4 and 5 (taken from
actual construction). The practical engineer does not find, as Mr.
Godfrey states, that the negative moment is double the positive moment,
because he considers the live load either on one span only, or on
alternate spans.

[Illustration: FIG. 6.]

In Fig. 6 a beam is shown which has many rods in the bottom flange, a
practice which Mr. Godfrey condemns. As the structure, which has about
twenty similar beams, is now being built, the writer would be thankful
for his criticism. Mr. Godfrey states that longitudinal steel in columns
is worthless, but until definite tests are made, with the same
ingredients, proportions, and age, on both plain concrete and reinforced
concrete columns properly designed, the writer will accept the data of
other experiments, and proportion steel in accordance with recognized
formulas.

[Illustration: FIG. 7.]

Mr. Godfrey states that the "elastic theory" is worthless for the design
of reinforced concrete arches, basing his objections on the shrinkage of
concrete in setting, the unreliability of deflection formulas for beams,
and the lack of rigidity of the abutments. The writer, noting that
concrete setting in air shrinks, whereas concrete setting in water
expands, believes that if the arch be properly wetted until the setting
up of the concrete has progressed sufficiently, the effect of shrinkage,
on drying out, may be minimized. If the settlement of the forms
themselves be guarded against during the construction of an arch, the
settlement of the arch ring, on removing the forms, far from being an
uncertain element, should be a check on the accuracy of the calculations
and the workmanship, since the weight of the arch ring should produce
theoretically a certain deflection. The unreliability of deflection
formulas for beams is due mainly to the fact that the neutral axis of
the beam does not lie in a horizontal plane throughout, and that the
shearing stresses are neglected therein. While there is necessarily
bending in an arch ring due to temperature, loads, etc., the extreme
flanges sometimes being in tension, even in a properly designed arch,
the compression exceeds the tension to such an extent that comparison to
a beam does not hold true. An arch should not be used where the
abutments are unstable, any more than a suspension bridge should be
built where a suitable anchorage cannot be obtained.

The proper design of concrete slabs supported on four sides is a complex
and interesting study. The writer has recently designed a floor
construction, slabs, and beams, supported on four corners, which is
simple and economical. In Fig. 7 is shown a portion of a proposed
twelve-story building, 90 by 100 ft., having floors with a live-load
capacity of 250 lb. per sq. ft. For the maximum positive bending in any
panel the full load on that panel was considered, there being no live
load on adjoining panels. For the maximum negative bending moment all
panels were considered as loaded, and in a single line. "Checker-board"
loading was considered too improbable for consideration. The flexure
curves for beams at right angles to each other were similar (except in
length), the tension rods in the longer beams being placed underneath
those in the shorter beams. Under full load, therefore, approximately
one-half of the load went to the long-span girder and the other half to
the short-span girder. The girders were the same depth as the beams. For
its depth the writer found this system to be the strongest and most
economical of those investigated.


E.P. GOODRICH, M. AM. SOC. C. E.--The speaker heartily concurs with the
author as to the large number of makeshifts constantly used by a
majority of engineers and other practitioners who design and construct
work in reinforced concrete. It is exceedingly difficult for the human
mind to grasp new ideas without associating them with others in past
experience, but this association is apt to clothe the new idea (as the
author suggests) in garments which are often worse than
"swaddling-bands," and often go far toward strangling proper growth.

While the speaker cannot concur with equal ardor with regard to all the
author's points, still in many, he is believed to be well grounded in
his criticism. Such is the case with regard to the first point
mentioned--that of the use of bends of large radius where the main
tension rods are bent so as to assist in the resistance of diagonal
tensile stresses.

As to the second point, provided proper anchorage is secured in the top
concrete for the rod marked 3 in Fig. 1, the speaker cannot see why the
concrete beneath such anchorage over the support does not act exactly
like the end post of a queen-post truss. Nor can he understand the
author's statement that:

     "A reinforcing rod in a concrete beam receives its stress by
     increments imparted by the grip of the concrete; but these
     increments can only be imparted where the tendency of the concrete
     is to stretch."

The latter part of this quotation has reference to the point questioned
by the speaker. In fact, the remainder of the paragraph from which this
quotation is taken seems to be open to grave question, no reason being
evident for not carrying out the analogy of the queen-post truss to the
extreme. Along this line, it is a well-known fact that the bottom chords
in queen-post trusses are useless, as far as resistance to tension is
concerned. The speaker concurs, however, in the author's criticism as to
the lack of anchorage usually found in most reinforcing rods,
particularly those of the type mentioned in the author's second point.

This matter of end anchorage is also referred to in the third point, and
is fully concurred in by the speaker, who also concurs in the criticism
of the arrangement of the reinforcing rods in the counterforts found in
many retaining walls. The statement that "there is absolutely no analogy
between this triangle [the counterfort] and a beam" is very strong
language, and it seems risky, even for the best engineer, to make such a
statement as does the author when he characterizes his own design
(Diagram _b_ of Fig. 2) as "the only rational and the only efficient
design possible." Several assumptions can be made on which to base the
arrangement of reinforcement in the counterfort of a retaining wall,
each of which can be worked out with equal logic and with results which
will prevent failure, as has been amply demonstrated by actual
experience.

The speaker heartily concurs in the author's fourth point, with regard
to the impossibility of developing anything like actual shear in the
steel reinforcing rods of a concrete beam; but he demurs when the author
affirms, as to the possibility of so-called shear bars being stressed in
"shear or tension," that "either would be absurd and impossible without
greatly overstressing some other part."

As to the fifth point, reference can be given to more than one place in
concrete literature where explanations of the action of vertical
stirrups may be found, all of which must have been overlooked by the
author. However, the speaker heartily concurs with the author's
criticism as to the lack of proper connection which almost invariably
exists between vertical "web" members and the top and bottom chords of
the imaginary Howe truss, which holds the nearest analogy to the
conditions existing in a reinforced concrete beam with vertical "web"
reinforcement.

The author's reasoning as to the sixth point must be considered as
almost wholly facetious. He seems to be unaware of the fact that
concrete is relatively very strong in pure shear. Large numbers of tests
seem to demonstrate that, where it is possible to arrange the
reinforcing members so as to carry largely all tensile stresses
developed through shearing action, at points where such tensile stresses
cannot be carried by the concrete, reinforced concrete beams can be
designed of ample strength and be quite within the logical processes
developed by the author, as the speaker interprets them.

The author's characterization of the results secured at the University
of Illinois Experiment Station, and described in its Bulletin No. 29, is
somewhat misleading. It is true that the wording of the original
reference states in two places that "stirrups do not come into action,
at least not to any great extent, until a diagonal crack has formed,"
but, in connection with this statement, the following quotations must be
read:

     "The tests were planned with a view of determining the amount of
     stress (tension and bond) developed in the stirrups. However, for
     various reasons, the results are of less value than was expected.
     The beams were not all made according to the plans. In the 1907
     tests, the stirrups in a few of the beams were poorly placed and
     even left exposed at the face of the beam, and a variation in the
     temperature conditions of the laboratory also affected the results.
     It is evident from the results that the stresses developed in the
     stirrups are less than they were calculated to be, and hence the
     layout was not well planned to settle the points at issue. The
     tests, however, give considerable information on the effectiveness
     of stirrups in providing web resistance."

     "A feature of the tests of beams with stirrups is slow failure, the
     load holding well up to the maximum under increased deflection and
     giving warning of its condition."

     "Not enough information was obtained to determine the actual final
     occasion of failure in these tests. In a number of cases the
     stirrups slipped, in others it seemed that the steel in the
     stirrups was stretched beyond its elastic limit, and in some cases
     the stirrups broke."

     "As already stated, slip of stirrups and insufficient bond
     resistance were in many cases the immediate cause of diagonal
     tension failures, and therefore bond resistance of stirrups may be
     considered a critical stress."

These quotations seem to indicate much more effectiveness in the action
of vertical stirrups than the author would lead one to infer from his
criticisms. It is rather surprising that he advocates so strongly the
use of a suspension system of reinforcement. That variety has been used
abroad for many years, and numerous German experiments have proved with
practical conclusiveness that the suspension system is not as efficient
as the one in which vertical stirrups are used with a proper
arrangement. An example is the conclusion arrived at by Mörsch, in
"Eisenbetonbau," from a series of tests carried out by him near the end
of 1906:

     "It follows that with uniform loads, the suspended system of
     reinforcement does not give any increase of safety against the
     appearance of diagonal tension cracks, or the final failure
     produced by them, as compared with straight rods without stirrups,
     and that stirrups are so much the more necessary."

Again, with regard to tests made with two concentrated loads, he writes:

     "The stirrups, supplied on one end, through their tensile strength,
     hindered the formation of diagonal cracks and showed themselves
     essential and indispensable elements in the * * * [suspension]
     system. The limit of their effect is, however, not disclosed by
     these experiments. * * * In any case, from the results of the
     second group of experiments can be deduced the facts that the
     bending of the reinforcement according to the theory concerning the
     diagonal tensile stress * * * is much more effective than according
     to the suspension theory, in this case the ultimate loads being in
     the proportion of 34: 23.4: 25.6."

It is the speaker's opinion that the majority of the failures described
in Bulletin No. 29 of the University of Illinois Experiment Station,
which are ascribed to diagonal tension, were actually due to deficient
anchorage of the upper ends of the stirrups.

Some years ago the speaker demonstrated to his own satisfaction, the
practical value of vertical stirrups. Several beams were built identical
in every respect except in the size of wire used for web reinforcement.
The latter varied from nothing to 3/8-in. round by five steps. The beams
were similarly tested to destruction, and the ultimate load and type of
failure varied in a very definite ratio to the area of vertical steel.

With regard to the author's seventh point, the speaker concurs heartily
as far as it has to do with a criticism of the usual design of
continuous beams, but his experience with beams designed as suggested by
the author is that failure will take place eventually by vertical cracks
starting from the top of the beams close to the supports and working
downward so as to endanger very seriously the strength of the structures
involved. This type of failure was prophesied by the speaker a number of
years ago, and almost every examination which he has lately made of
concrete buildings, erected for five years or longer and designed
practically in accord with the author's suggestion, have disclosed such
dangerous features, traceable directly to the ideas described in the
paper. These ideas are held by many other engineers, as well as being
advocated by the author. The only conditions under which the speaker
would permit of the design of a continuous series of beams as simple
members would be when they are entirely separated from each other over
the supports, as by the introduction of artificial joints produced by a
double thickness of sheet metal or building paper. Even under these
conditions, the speaker's experience with separately moulded members,
manufactured in a shop and subsequently erected, has shown that similar
top cracking may take place under certain circumstances, due to the
vertical pressures caused by the reactions at the supports. It is very
doubtful whether the action described by the author, as to the type of
failure which would probably take place with his method of design, would
be as described by him, but the beams would be likely to crack as
described above, in accordance with the speaker's experience, so that
the whole load supported by the beam would be carried by the reinforcing
rods which extend from the beam into the supports and are almost
invariably entirely horizontal at such points. The load would thus be
carried more nearly by the shearing strength of the steel than is
otherwise possible to develop that type of stress. In every instance the
latter is a dangerous element.

This effect of vertical abutment action on a reinforced beam was very
marked in the beam built of bricks and tested by the speaker, as
described in the discussion[J] of the paper by John S. Sewell, M. Am,
Soc. S. E., on "The Economical Design of Reinforced Concrete Floor
Systems for Fire-Resisting Structures." That experiment also went far
toward showing the efficacy of vertical stirrups.

The same discussion also contains a description of a pair of beams
tested for comparative purposes, in one of which adhesion between the
concrete and the main reinforcing rods was possible only on the upper
half of the exterior surfaces of the latter rods except for short
distances near the ends. Stirrups were used, however. The fact that the
beam, which was theoretically very deficient in adhesion, failed in
compression, while the similar beam without stirrups, but with the most
perfect adhesion, and anchorage obtainable through the use of large end
hooks, failed in bond, has led the speaker to believe that, in affording
adhesive resistance, the upper half of a bar is much more effective than
the lower half. This seems to be demonstrated further by comparisons
between simple adhesion experiments and those obtained with beams.

The speaker heartily concurs with the author's criticism of the amount
of time usually given by designing engineers to the determination of the
adhesive stresses developed in concrete beams, but, according to the
speaker's recollection, these matters are not so poorly treated in some
books as might be inferred by the author's language. For example, both
Bulletin No. 29, of the University of Illinois, and Mörsch, in
"Eisenbetonbau," give them considerable attention.

The ninth point raised by the author is well taken. Too great emphasis
cannot be laid on the inadequacy of design disclosed by an examination
of many T-beams.

Such ready concurrence, however, is not lent to the author's tenth
point. While it is true that, under all usual assumptions, except those
made by the author, an extremely simple formula for the resisting moment
of a reinforced concrete beam cannot be obtained, still his formula
falls so far short of fitting even with approximate correctness the
large number of well-known experiments which have been published, that a
little more mathematical gymnastic ability on the part of the author and
of other advocates of extreme simplicity would seem very necessary, and
will produce structures which are far more economical and amply safe
structurally, compared with those which would be produced in accordance
with his recommendations.

As to the eleventh point, in regard to the complex nature of the
formulas for chimneys and other structures of a more or less complex
beam nature, the graphical methods developed by numerous German and
Italian writers are recommended, as they are fully as simple as the
rather crude method advocated by the author, and are in almost identical
accord with the most exacting analytical methods.

With regard to the author's twelfth point, concerning deflection
calculations, it would seem that they play such a small part in
reinforced concrete design, and are required so rarely, that any
engineer who finds it necessary to make analytical investigations of
possible deflections would better use the most precise analysis at his
command, rather than fall back on simpler but much more approximate
devices such as the one advocated by the author.

Much of the criticism contained in the author's thirteenth point,
concerning the application of the elastic theory to the design of
concrete arches, is justified, because designing engineers do not carry
the theory to its logical conclusion nor take into account the actual
stresses which may be expected from slight changes of span, settlements
of abutments, and unexpected amounts of shrinkage in the arch ring or
ribs. Where conditions indicate that such changes are likely to take
place, as is almost invariably the case unless the foundations are upon
good rock and the arch ring has been concreted in relatively short
sections, with ample time and device to allow for initial shrinkage; or
unless the design is arranged and the structure erected so that hinges
are provided at the abutments to act during the striking of the
falsework, which hinges are afterward wedged or grouted so as to produce
fixation of the arch ends--unless all these points are carefully
considered in the design and erection, it is the speaker's opinion that
the elastic theory is rarely properly applicable, and the use of the
equilibrium polygon recommended by the author is much preferable and
actually more accurate. But there must be consistency in its use, as
well, that is, consistency between methods of design and erection.

The author's fourteenth point--the determination of temperature stresses
in a reinforced concrete arch--is to be considered in the same light as
that described under the foregoing points, but it seems a little amusing
that the author should finally advocate a design of concrete arch which
actually has no hinges, namely, one consisting of practically rigid
blocks, after he has condemned so heartily the use of the elastic
theory.

A careful analysis of the data already available with regard to the heat
conductivity of concrete, applied to reinforced concrete structures like
arches, dams, retaining walls, etc., in accordance with the well-known
but somewhat intricate mathematical formulas covering the laws of heat
conductivity and radiation so clearly enunciated by Fourier, has
convinced the speaker that it is well within the bounds of engineering
practice to predict and care for the stresses which will be produced in
structures of the simplest forms, at least as far as they are affected
by temperature changes.

The speaker concurs with the author in his criticism, contained in the
fifteenth point, with regard to the design of the steel reinforcement in
columns and other compression members. While there may be some question
as to the falsity or truth of the theory underlying certain types of
design, it is unquestioned that some schemes of arrangement undoubtedly
produce designs with dangerous properties. The speaker has several
times called attention to this point, in papers and discussions, and
invariably in his own practice requires that the spacing of spirals,
hoops, or ties be many times less than that usually required by building
regulations and found in almost every concrete structure. Mörsch, in his
"Eisenbetonbau," calls attention to the fact that very definite limits
should be placed on the maximum size of longitudinal rods as well as on
their minimum diameters, and on the maximum spacing of ties, where
columns are reinforced largely by longitudinal members. He goes so far
as to state that:

     "It is seen from * * * [the results obtained] that an increase in
     the area of longitudinal reinforcement does not produce an increase
     in the breaking strength to the extent which would be indicated by
     the formula. * * * In inexperienced hands this formula may give
     rise to constructions which are not sufficiently safe."

Again, with regard to the spacing of spirals and the combination with
them of longitudinal rods, in connection with some tests carried out by
Mörsch, the conclusion is as follows:

     "On the whole, the tests seem to prove that when the spirals are
     increased in strength, their pitch must be decreased, and the
     cross-section or number of the longitudinal rods must be
     increased."

In the majority of cases, the spiral or band spacing is altogether too
large, and, from conversations with Considère, the speaker understands
that to be the inventor's view as well.

The speaker makes use of the scheme mentioned by the author in regard to
the design of flat slabs supported on more than two sides (noted in the
sixteenth point), namely, that of dividing the area into strips, the
moments of which are determined so as to produce computed deflections
which are equal in the two strips running at right angles at each point
of intersection. This method, however, requires a large amount of
analytical work for any special case, and the speaker is mildly
surprised that the author cannot recommend some simpler method so as to
carry out his general scheme of extreme simplification of methods and
design.

If use is to be made at all of deflection observations, theories, and
formulas, account should certainly be taken of the actual settlements
and other deflections which invariably occur in Nature at points of
support. These changes of level, or slope, or both, actually alter very
considerably the stresses as usually computed, and, in all rigorous
design work, should be considered.

On the whole, the speaker believes that the author has put himself in
the class with most iconoclasts, in that he has overshot his mark. There
seems to be a very important point, however, on which he has touched,
namely, the lack of care exercised by most designers with regard to
those items which most nearly correspond with the so-called "details" of
structural steel work, and are fully as important in reinforced
concrete as in steel. It is comparatively a small matter to proportion a
simple reinforced concrete beam at its intersection to resist a given
moment, but the carrying out of that item of the work is only a start on
the long road which should lead through the consideration of every
detail, not the least important of which are such items as most of the
sixteen points raised by the author.

The author has done the profession a great service by raising these
questions, and, while full concurrence is not had with him in all
points, still the speaker desires to express his hearty thanks for
starting what is hoped will be a complete discussion of the really vital
matter of detailing reinforced concrete design work.


ALBIN H. BEYER, ESQ.--Mr. Goodrich has brought out very clearly the
efficiency of vertical stirrups. As Mr. Godfrey states that explanations
of how stirrups act are conspicuous in the literature of reinforced
concrete by their absence, the speaker will try to explain their action
in a reinforced concrete beam.

It is well known that the internal static conditions in reinforced
concrete beams change to some extent with the intensity of the direct or
normal stresses in the steel and concrete. In order to bring out his
point, the speaker will trace, in such a beam, the changes in the
internal static conditions due to increasing vertical loads.

[Illustration: FIG. 8.]

Let Fig. 8 represent a beam reinforced by horizontal steel rods of such
diameter that there is no possibility of failure from lack of adhesion
of the concrete to the steel. The beam is subjected to the vertical
loads, [Sigma] _P_. For low unit stresses in the concrete, the neutral
surface, _n n_, is approximately in the middle of the beam. Gradually
increase the loads, [Sigma] _P_, until the steel reaches an elongation
of from 0.01 to 0.02 of 1%, corresponding to tensile stresses in the
steel of from 3,000 to 6,000 lb. per sq. in. At this stage plain
concrete would have reached its ultimate elongation. It is known,
however, that reinforced concrete, when well made, can sustain without
rupture much greater elongations; tests have shown that its ultimate
elongation may be as high as 0.1 of 1%, corresponding to tensions in
steel of 30,000 lb. per sq. in.

Reinforced concrete structures ordinarily show tensile cracks at very
much lower unit stresses in the steel. The main cause of these cracks is
as follows: Reinforced concrete setting in dry air undergoes
considerable shrinkage during the first few days, when it has very
little resistance. This tendency to shrink being opposed by the
reinforcement at a time when the concrete does not possess the necessary
strength or ductility, causes invisible cracks or planes of weakness in
the concrete. These cracks open and become visible at very low unit
stresses in the steel.

Increase the vertical loads, [Sigma] _P_, and the neutral surface will
rise and small tensile cracks will appear in the concrete below the
neutral surface (Fig. 8). These cracks are most numerous in the central
part of the span, where they are nearly vertical. They decrease in
number at the ends of the span, where they curve slightly away from the
perpendicular toward the center of the span. The formation of these
tensile cracks in the concrete relieves it at once of its highly
stressed condition.

It is impossible to predict the unit tension in the steel at which these
cracks begin to form. They can be detected, though not often visible,
when the unit tensions in the steel are as low as from 10,000 to 16,000
lb. per sq. in. As soon as the tensile cracks form, though invisible,
the neutral surface approaches the position in the beam assigned to it
by the common theory of flexure, with the tension in the concrete
neglected. The internal static conditions in the beam are now modified
to the extent that the concrete below the neutral surface is no longer
continuous. The common theory of flexure can no longer be used to
calculate the web stresses.

To analyze the internal static conditions developed, the speaker will
treat as a free body the shaded portion of the beam shown in Fig. 8,
which lies between two tensile cracks.

[Illustration: FIG. 9.]

In Fig. 9 are shown all the forces which act on this free body, _C b b'
C'_.

At any section, let

 _C_ or _C'_ represent the total concrete compression;
 _T_ or _T'_ represent the total steel tension;
 _J_ or _J'_ represent the total vertical shear;
 _P_         represent the total vertical load for the length, _b_ - _b'_;

and let [Delta] _T_ = _T'_ - _T_ = _C'_ - _C_ represent the total
transverse shear for the length, _b_ - _b'_.

Assuming that the tension cracks extend to the neutral surface, _n n_,
that portion of the beam _C b b' C'_, acts as a cantilever fixed at _a
b_ and _a' b'_, and subjected to the unbalanced steel tension, [Delta]
_T_. The vertical shear, _J_, is carried mainly by the concrete above
the neutral surface, very little of it being carried by the steel
reinforcement. In the case of plain webs, the tension cracks are the
forerunners of the sudden so-called diagonal tension failures produced
by the snapping off, below the neutral surface, of the concrete
cantilevers. The logical method of reinforcing these cantilevers is by
inserting vertical steel in the tension side. The vertical
reinforcement, to be efficient, must be well anchored, both in the top
and in the bottom of the beam. Experience has solved the problem of
doing this by the use of vertical steel in the form of stirrups, that
is, U-shaped rods. The horizontal reinforcement rests in the bottom of
the U.

Sufficient attention has not been paid to the proper anchorage of the
upper ends of the stirrups. They should extend well into the compression
area of the beam, where they should be properly anchored. They should
not be too near the surface of the beam. They must not be too far apart,
and they must be of sufficient cross-section to develop the necessary
tensile forces at not excessive unit stresses. A working tension in the
stirrups which is too high, will produce a local disintegration of the
cantilevers, and give the beam the appearance of failure due to diagonal
tension. Their distribution should follow closely that of the vertical
or horizontal shear in the beam. Practice must rely on experiment for
data as to the size and distribution of stirrups for maximum efficiency.

The maximum shearing stress in a concrete beam is commonly computed by
the equation:

            _V_
 _v_ = -------------                    (1)
         7
        --- _b_ _d_
         8

Where _d_ is the distance from the center of the reinforcing bars to the
surface of the beam in compression:

 _b_ = the width of the flange, and
 _V_ = the total vertical shear at the section.

This equation gives very erratic results, because it is based on a
continuous web. For a non-continuous web, it should be modified to

           _V_
_v_ = -------------                     (2)
       _K_ _b_ _d_

In this equation _K b d_ represents the concrete area in compression.
The value of _K_ is approximately equal to 0.4.

Three large concrete beams with web reinforcement, tested at the
University of Illinois[K], developed an average maximum shearing
resistance of 215 lb. per sq. in., computed by Equation 1. Equation 2
would give 470 lb. per sq. in.

Three T-beams, having 32 by 3-1/4-in. flanges and 8-in. webs, tested at
the University of Illinois, had maximum shearing resistances of 585,
605, and 370 lb. per. sq. in., respectively.[L] They did not fail in
shear, although they appeared to develop maximum shearing stresses which
were almost three times as high as those in the rectangular beams
mentioned. The concrete and web reinforcement being identical, the
discrepancy must be somewhere else. Based on a non-continuous concrete
web, the shearing resistances become 385, 400, and 244 lb. per sq. in.,
respectively. As none of these failed in shear, the ultimate shearing
resistance of concrete must be considerably higher than any of the
values given.

About thirteen years ago, Professor A. Vierendeel[M] developed the
theory of open-web girder construction. By an open-web girder, the
speaker means a girder which has a lower and upper chord connected by
verticals. Several girders of this type, far exceeding solid girders in
length, have been built. The theory of the open-web girder, assuming the
verticals to be hinged at their lower ends, applies to the concrete beam
reinforced with stirrups. Assuming that the spaces between the verticals
of the girder become continually narrower, they become the tension
cracks of the concrete beam.[N]


JOHN C. OSTRUP, M. AM. SOC. C. E.--The author has rendered a great
service to the Profession in presenting this paper. In his first point
he mentions two designs of reinforced concrete beams and, inferentially,
he condemns a third design to which the speaker will refer later. The
designs mentioned are, first, that of a reinforced concrete beam
arranged in the shape of a rod, with separate concrete blocks placed on
top of it without being connected--such a beam has its strength only in
the rod. It is purely a suspension, or "hog-chain" affair, and the
blocks serve no purpose, but simply increase the load on the rod and its
stresses.

The author's second design is an invention of his own, which the
Profession at large is invited to adopt. This is really the same system
as the first, except that the blocks are continuous and, presumably,
fixed at the ends. When they are so fixed, the concrete will take
compressive stresses and a certain portion of the shear, the remaining
shear being transmitted to the rod from the concrete above it, but only
through friction. Now, the frictional resistance between a steel rod and
a concrete beam is not such as should be depended on in modern
engineering designs.

The third method is that which is used by nearly all competent
designers, and it seems to the speaker that, in condemning the general
practice of current reinforced designs in sixteen points, the author
could have saved himself some time and labor by condemning them all in
one point.

What appears to be the underlying principle of reinforced concrete
design is the adhesion, or bond, between the steel and the concrete, and
it is that which tends to make the two materials act in unison. This is
a point which has not been touched on sufficiently, and one which it was
expected that Mr. Beyer would have brought out, when he illustrated
certain internal static conditions. This principle, in the main, will
cover the author's fifth point, wherein stirrups are mentioned, and
again in the first point, wherein he asks: "Will some advocate of this
type of design please state where this area can be found?"

To understand clearly how concrete acts in conjunction with steel, it is
necessary to analyze the following question: When a steel rod is
embedded in a solid block of concrete, and that rod is put in tension,
what will be the stresses in the rod and the surrounding concrete?

The answer will be illustrated by reference to Fig. 10. It must be
understood that the unit stresses should be selected so that both the
concrete and the steel may be stressed in the same relative ratio.
Assuming the tensile stress in the steel to be 16,000 lb. per sq. in.,
and the bonding value 80 lb., a simple formula will show that the length
of embedment, or that part of the rod which will act, must be equal to
50 diameters of the rod.

[Illustration: FIG. 10.]

When the rod is put in tension, as indicated in Fig. 10, what will be
the stresses in the surrounding concrete? The greatest stress will come
on the rod at the point where it leaves the concrete, where it is a
maximum, and it will decrease from that point inward until the total
stress in the steel has been distributed to the surrounding concrete. At
that point the rod will only be stressed back for a distance equal in
length to 50 diameters, no matter how far beyond that length the rod may
extend.

The distribution of the stress from the steel rod to the concrete can be
represented by a cone, the base of which is at the outer face of the
block, as the stresses will be zero at a point 50 diameters back, and
will increase in a certain ratio out toward the face of the block, and
will also, at all intermediate points, decrease radially outward from
the rod.

The intensity of the maximum stress exerted on the concrete is
represented by the shaded area in Fig. 10, the ordinates, measured
perpendicularly to the rod, indicating the maximum resistance offered by
the concrete at any point.

If the concrete had a constant modulus of elasticity under varying
stress, and if the two materials had the same modulus, the stress
triangle would be bounded by straight lines (shown as dotted lines in
Fig. 10); but as this is not true, the variable moduli will modify the
stress triangle in a manner which will tend to make the boundary lines
resemble parabolic curves.

A triangle thus constructed will represent by scale the intensity of the
stress in the concrete, and if the ordinates indicate stresses greater
than that which the concrete will stand, a portion will be destroyed,
broken off, and nothing more serious will happen than that this stress
triangle will adjust itself, and grip the rod farther back. This process
keeps on until the end of the rod has been reached, when the triangle
will assume a much greater maximum depth as it shortens; or, in other
words, the disintegration of the concrete will take place here very
rapidly, and the rod will be pulled out.

In the author's fourth point he belittles the use of shear rods, and
states: "No hint is given as to whether these bars are in shear or in
tension." As a matter of fact, they are neither in shear nor wholly in
tension, they are simply in bending between the centers of the
compressive resultants, as indicated in Fig. 12, and are, besides,
stressed slightly in tension between these two points.

[Illustration: FIG. 11.]

In Fig. 10 the stress triangle indicates the distribution and the
intensity of the resistance in the concrete to a force acting parallel
to the rod. A similar triangle may be drawn, Fig. 11, showing the
resistance of the rod and the resultant distribution in the concrete to
a force perpendicular to the rod. Here the original force would cause
plain shear in the rod, were the latter fixed in position. Since this
cannot be the case, the force will be resolved into two components, one
of which will cause a tensile stress in the rod and the other will pass
through the centroid of the compressive stress area. This is indicated
in Fig. 11, which, otherwise, is self-explanatory.

[Illustration: FIG. 12.]

Rods are not very often placed in such a position, but where it is
unavoidable, as in construction joints in the middle of slabs or beams,
they serve a very good purpose; but, to obtain the best effect from
them, they should be placed near the center of the slab, as in Fig. 12,
and not near the top, as advocated by some writers.

If the concrete be overstressed at the points where the rod tends to
bend, that is, if the rods are spaced too far apart, disintegration will
follow; and, for this reason, they should be long enough to have more
than 50 diameters gripped by the concrete.

This leads up to the author's seventh point, as to the overstressing of
the concrete at the junction of the diagonal tension rods, or stirrups,
and the bottom reinforcement.

[Illustration: FIG. 13.]

Analogous with the foregoing, it is easy to lay off the stress triangles
and to find the intensity of stress at the maximum points, in fact at
any point, along the tension rods and the bottom chord. This is
indicated in Fig. 13. These stress triangles will start on the rod 50
diameters back from the point in question and, although the author has
indicated in Fig. 1 that only two of the three rods are stressed, there
must of necessity also be some stress in the bottom rod to the left of
the junction, on account of the deformation which takes place in any
beam due to bending. Therefore, all three rods at the point where they
are joined, are under stress, and the triangles can be laid off
accordingly.

It will be noticed that the concrete will resist the compressive
components, not at any specific point, but all along the various rods,
and with the intensities shown by the stress triangles; also, that some
of these triangles will overlap, and, hence, a certain readjustment, or
superimposition, of stresses takes place.

The portion which is laid off below the bottom rods will probably not
act unless there is sufficient concrete below the reinforcing bars and
on the sides, and, as that is not the case in ordinary construction, it
is very probable, as Mr. Goodrich has pointed out, that the concrete
below the rods plays an unimportant part, and that the triangle which is
now shown below the rod should be partially omitted.

The triangles in Fig. 13 show the intensity of stress in the concrete at
any point, or at any section where it is wanted. They show conclusively
where the components are located in the concrete, their relation to the
tensile stresses in the rods, and, furthermore, that they act only in a
general way at right angles to one another. This is in accordance with
the theory of beams, that at any point in the web there are tensile and
compressive stresses of equal intensity, and at right angles to one
another, although in a non-homogeneous web the distribution is somewhat
different.

After having found at the point of junction the intensity of stress, it
is possible to tell whether or not a bond between the stirrups and the
bottom rods is necessary, and it would not seem to be where the stirrups
are vertical.

It would also seem possible to tell in what direction, if any, the bend
in the inclined stirrups should be made. It is to be assumed, although
not expressly stated, that the bends should curve from the center up
toward the end of the beam, but an inspection of the stress triangles,
Fig. 13, will show that the intensity of stress is just as great on the
opposite side, and it is probable that, if any bends were required to
reduce the maximum stress in the concrete, they should as likely be made
on the side nearest the abutment.

From the stress triangles it may also be shown that, if the stirrups
were vertical instead of inclined, the stress in the concrete on both
sides would be practically equal, and that, in consequence, vertical
stirrups are preferable.

The next issue raised by the author is covered in his seventh point, and
relates to bending moments. He states: "* * * bending moments in
so-called continuous beams are juggled to reduce them to what the
designer would like to have them. This has come to be almost a matter of
taste, * * *."

The author seems to imply that such juggling is wrong. As a matter of
fact, it is perfectly allowable and legitimate in every instance of beam
or truss design, that is, from the standpoint of stress distribution,
although this "juggling" is limited in practice by economical
considerations.

In a series of beams supported at the ends, bending moments range from
(_w_ _l^{2}_)/8 at the center of each span to zero at the supports, and,
in a series of cantilevers, from zero at the center of the span to (_w_
_l^{2}_)/8 at the supports. Between these two extremes, the designer can
divide, adjust, or juggle them to his heart's content, provided that in
his design he makes the proper provision for the corresponding shifting
of the points of contra-flexure. If that were not the case, how could
ordinary bridge trusses, which have their maximum bending at the center,
compare with those which, like arches, are assumed to have no bending at
that point?

In his tenth point, the author proposes a method of simple designing by
doing away with the complicated formulas which take account of the
actual co-operation of the two materials. He states that an ideal
design can be obtained in the same manner, that is, with the same
formulas, as for ordinary rectangular beams; but, when he does so, he
evidently fails to remember that the neutral axis is not near the center
of a reinforced concrete beam under stress; in fact, with the percentage
of reinforcement ordinarily used in designing--varying between
three-fourths of 1% to 1-1/2%--the neutral axis, when the beam is
loaded, is shifted from 26 to 10% of the beam depth above the center.
Hence, a low percentage of steel reinforcement will produce a great
shifting of the neutral axis, so that a design based on the formulas
advocated by the author would contain either a waste of materials, an
overstress of the concrete, or an understress of the steel; in fact, an
error in the design of from 10 to 26 per cent. Such errors, indeed, are
not to be recommended by good engineers.

The last point which the speaker will discuss is that of the elastic
arch. The theory of the elastic arch is now so well understood, and it
offers such a simple and, it might be said, elegant and self-checking
solution of the arch design, that it has a great many advantages, and
practically none of the disadvantages of other methods.

The author's statement that the segments of an arch could be made up of
loose blocks and afterward cemented together, cannot be endorsed by the
speaker, for, upon such cementing together, a shifting of the lines of
resistance will take place when the load is applied. The speaker does
not claim that arches are maintained by the cement or mortar joining the
voussoirs together, but that the lines of pressure will be materially
changed, and the same calculations are not applicable to both the
unloaded and the loaded arch.

It is quite true, as the author states, that a few cubic yards of
concrete placed in the ring will strengthen the arch more than a like
amount added to the abutments, provided, however, that this material be
placed properly. No good can result from an attempt to strengthen a
structure by placing the reinforcing material promiscuously. This has
been tried by amateurs in bridge construction, and, in such cases, the
material either increased the distance from the neutral axis to the
extreme fibers, thereby reducing the original section modulus, or caused
a shifting of the neutral axis followed by a large bending moment;
either method weakening the members it had tried to reinforce. In other
words, the mere addition of material does not always strengthen a
structure, unless it is placed in the proper position, and, if so
placed, it should be placed all over commensurately with the stresses,
that is, the unit stresses should be reduced.

The author has criticized reinforced concrete construction on the ground
that the formulas and theories concerning it are not as yet fully
developed. This is quite true, for the simple reason that there are so
many uncertain elements which form their basis: First, the variable
quantity of the modulus of elasticity, which, in the concrete, varies
inversely as the stress; and, second, the fact that the neutral axis in
a reinforced concrete beam under changing stress is migratory. There are
also many other elements of evaluation, which, though of importance, are
uncertain.

Because the formulas are established on certain assumptions is no reason
for condemning them. There are, the speaker might add, few formulas in
the subject of theoretical mechanics which are not based on some
assumption, and as long as the variations are such that their range is
known, perfectly reliable formulas can be deduced and perfectly safe
structures can be built from them.

There are a great many theorists who have recently complained about the
design of reinforced concrete. It seems to the speaker that such
complaints can serve no useful purpose. Reinforced concrete structures
are being built in steadily increasing numbers; they are filling a long
needed place; they are at present rendering great service to mankind;
and they are destined to cover a field of still greater usefulness.
Reinforced concrete will undoubtedly show in the future that the
confidence which most engineers and others now place in it is fully
merited.


HARRY F. PORTER, JUN. AM. SOC. C. E. (by letter).--Mr. Godfrey has
brought forward some interesting and pertinent points, which, in the
main, are well taken; but, in his zealousness, he has fallen into the
error of overpersuading himself of the gravity of some of the points he
would make; on the other hand, he fails to go deeply enough into others,
and some fallacies he leaves untouched. Incidentally, he seems somewhat
unfair to the Profession in general, in which many earnest, able men are
at work on this problem, men who are not mere theorists, but have been
reared in the hard school of practical experience, where refinements of
theory count for little, but common sense in design counts for much--not
to mention those self-sacrificing devotees to the advancement of the
art, the collegiate and laboratory investigators.

Engineers will all agree with Mr. Godfrey that there is much in the
average current practice that is erroneous, much in textbooks that is
misleading if not fallacious, and that there are still many designers
who are unable to think in terms of the new material apart from the
vestures of timber and structural steel, and whose designs, therefore,
are cumbersome and impractical. The writer, however, cannot agree with
the author that the practice is as radically wrong as he seems to think.
Nor is he entirely in accord with Mr. Godfrey in his "constructive
criticism" of those practices in which he concurs, that they are
erroneous.

That Mr. Godfrey can see no use in vertical stirrups or U-bars is
surprising in a practical engineer. One is prompted to ask: "Can the
holder of this opinion ever have gone through the experience of placing
steel in a job, or at least have watched the operation?" If so, he must
have found some use for those little members which he professes to
ignore utterly.

As a matter of fact, U-bars perform the following very useful and
indispensable services:

(_1_).--If properly made and placed, they serve as a saddle in which to
rest the horizontal steel, thereby insuring the correct placing of the
latter during the operation of concreting, not a mean function in a type
of construction so essentially practical. To serve this purpose,
stirrups should be made as shown in Plate III. They should be restrained
in some manner from moving when the concrete strikes them. A very good
way of accomplishing this is to string them on a longitudinal rod,
nested in the bend at the upper end. Mr. Godfrey, in his advocacy of
bowstring bars anchored with washers and nuts at the ends, fails to
indicate how they shall be placed. The writer, from experience in
placing steel, thinks that it would be very difficult, if not
impractical, to place them in this manner; but let a saddle of U-bars be
provided, and the problem is easy.

(_2_).--Stirrups serve also as a tie, to knit the stem of the beam to
its flange--the superimposed slab. The latter, at best, is not too well
attached to the stem by the adhesion of the concrete alone, unassisted
by the steel. T-beams are used very generally, because their
construction has the sanction of common sense, it being impossible to
cast stem and slab so that there will be the same strength in the plane
at the junction of the two as elsewhere, on account of the certainty of
unevenness in settlement, due to the disproportion in their depth. There
is also the likelihood that, in spite of specifications to the contrary,
there will be a time interval between the pouring of the two parts, and
thus a plane of weakness, where, unfortunately, the forces tending to
produce sliding of the upper part of the beam on the lower (horizontal
shear) are a maximum. To offset this tendency, therefore, it is
necessary to have a certain amount of vertical steel, disposed so as to
pass around and under the main reinforcing members and reach well up
into the flange (the slab), thus getting a grip therein of no mean
security. The hooking of the U-bars, as shown in Plate III, affords a
very effective grip in the concrete of the slab, and this is still
further enhanced by the distributing or anchoring effect of the
longitudinal stringing rods. Thus these longitudinals, besides serving
to hold the U-bars in position, also increase their effectiveness. They
serve a still further purpose as a most convenient support for the slab
bars, compelling them to take the correct position over the supports,
thus automatically ensuring full and proper provision for reversed
stresses. More than that, they act in compression within the middle
half, and assist in tension toward the ends of the span.

Thus, by using U-bars of the type indicated, in combination with
longitudinal bars as described, tying together thoroughly the component
parts of the beam in a vertical plane, a marked increase in stiffness,
if not strength, is secured. This being the case, who can gainsay the
utility of the U-bar?

Of course, near the ends, in case continuity of action is realized,
whereupon the stresses are reversed, the U-bars need to be inverted,
although frequently inversion is not imperative with the type of U-bar
described, the simple hooking of the upper ends over the upper
horizontal steel being sufficient.

As to whether or not the U-bars act with the horizontal and diagonal
steel to form truss systems is relatively unessential; in all
probability there is some such action, which contributes somewhat to the
total strength, but at most it is of minor importance. Mr. Godfrey's
points as to fallacy of truss action seem to be well taken, but his
conclusions in consequence--that U-bars serve no purpose--are
impractical.

The number of U-bars needed is also largely a matter of practice,
although subject to calculation. Practice indicates that they should be
spaced no farther apart than the effective depth of the member, and
spaced closer or made heavier toward the ends, in order to keep pace
with cumulating shear. They need this close spacing in order to serve as
an adequate saddle for the main bars, as well as to furnish, with the
lighter "stringing" rods, an adequate support to the slab bars. They
should have the requisite stiffness in the bends to carry their burden
without appreciable sagging; it will be found that 5/16 in. is about the
minimum practical size, and that 1/2 in. is as large as will be
necessary, even for very deep beams with heavy reinforcement.

If the size and number of U-bars were to be assigned by theory, there
should be enough of them to care for fully 75% of the horizontal shear,
the adhesion of the concrete being assumed as adequate for the
remainder.

Near the ends, of course, the inclined steel, resulting from bending up
some of the horizontal bars, if it is carried well across the support to
secure an adequate anchorage, or other equivalent anchorage is provided,
assists in taking the horizontal shear.

The embedment, too, of large stone in the body of the beam, straddling,
as it were, the neutral plane, and thus forming a lock between the
flange and the stem, may be considered as assisting materially in taking
horizontal shear, thus relieving the U-bars. This is a factor in the
strength of actual work which theory does not take into account, and by
the author, no doubt, it would be regarded as insignificant;
nevertheless it is being done every day, with excellent results.

The action of these various agencies--the U-bars, diagonal steel, and
embedded stone--in a concrete beam, is analogous to that of bolts or
keys in the case of deepened timber beams. A concrete beam may be
assumed, for the purposes of illustration, to be composed of a series of
superimposed layers; in this case the function of the rigid material
crossing these several layers normally, and being well anchored above
and below, as a unifier of the member, is obvious--it acts as so many
bolts joining superimposed planks forming a beam. Of course, no such
lamination actually exists, although there are always incipient forces
tending to produce it; these may and do manifest themselves on occasion
as an actual separation in a horizontal plane at the junction of slab
and stem, ordinarily the plane of greatest weakness--owing to the method
of casting--as well as of maximum horizontal shear. Beams tested to
destruction almost invariably develop cracks in this region. The
question then naturally arises: If U-bars serve no purpose, what will
counteract these horizontal cleaving forces? On the contrary, T-beams,
adequately reinforced with U-bars, seem to be safeguarded in this
respect; consequently, the U-bars, while perhaps adding little to the
strength, as estimated by the ultimate carrying capacity, actually must
be of considerable assistance, within the limit of working loads, by
enhancing the stiffness and ensuring against incipient cracking along
the plane of weakness, such as impact or vibratory loads might induce.
Therefore, U-bars, far from being superfluous or fallacious, are,
practically, if not theoretically, indispensable.

At present there seems to be considerable diversity of opinion as to the
exact nature of the stress action in a reinforced concrete beam.
Unquestionably, the action in the monolithic members of a concrete
structure is different from that in the simple-acting, unrestrained
parts of timber or structural steel construction; because in monolithic
members, by the law of continuity, reverse stresses must come into play.
To offset these stresses reinforcement must be provided, or cracking
will ensue where they occur, to the detriment of the structure in
appearance, if not in utility. Monolithic concrete construction should
be tied together so well across the supports as to make cracking under
working loads impossible, and, when tested to destruction, failure
should occur by the gradual sagging of the member, like the sagging of
an old basket. Then, and then only, can the structure be said to be
adequately reinforced.

In his advocacy of placing steel to simulate a catenary curve, with end
anchorage, the author is more nearly correct than in other issues he
makes. Undoubtedly, an attempt should be made in every concrete
structure to approximate this alignment. In slabs it may be secured
simply by elevating the bars over the supports, when, if pliable enough,
they will assume a natural droop which is practically ideal; or, if too
stiff, they may be bent to conform approximately to this position. In
slabs, too, the reinforcement may be made practically continuous, by
using lengths covering several spans, and, where ends occur, by
generous lapping. In beams the problem is somewhat more complicated,
as it is impossible, except rarely, to bow the steel and to extend it
continuously over several supports; but all or part of the horizontal
steel can be bent up at about the quarter point, carried across the
supports into the adjacent spans, and anchored there by bending it down
at about the same angle as it is bent up on the approach, and then
hooking the ends.

[Illustration: PLATE III.--JUNCTION OF BEAM AND WALL COLUMN.
REINFORCEMENT IN PLACE IN BEAM, LINTEL, AND SLAB UP TO BEAM. NOTE END
ANCHORAGE OF BEAM BARS.]

It is seldom necessary to adopt the scheme proposed by the author,
namely, a threaded end with a bearing washer and a nut to hold the
washer in place, although it is sometimes expedient, but not absolutely
necessary, in end spans, where prolongation into an adjacent span is out
of the question. In end spans it is ordinarily sufficient to give the
bars a double reverse bend, as shown in Plate III, and possibly to clasp
hooks with the horizontal steel. If steel be placed in this manner, the
catenary curve will be practically approximated, the steel will be
fairly developed throughout its length of embedment, and the structure
will be proof against cracking. In this case, also, there is much less
dependence on the integrity of the bond; in fact, if there were no bond,
the structure would still develop most of its strength, although the
deflection under heavy loading might be relatively greater.

The writer once had an experience which sustains this point. On peeling
off the forms from a beam reinforced according to the method indicated,
it was found that, because of the crowding together of the bars in the
bottom, coupled with a little too stiff a mixture, the beam had hardly
any concrete on the underside to grip the steel in the portion between
the points of bending up, or for about the middle half of the member;
consequently, it was decided to test this beam. The actual working load
was first applied and no deflection, cracking, or slippage of the bars
was apparent; but, as the loading was continued, deflection set in and
increased rapidly for small increments of loading, a number of fine
cracks opened up near the mid-section, which extended to the neutral
plane, and the steel slipped just enough, when drawn taut, to destroy
what bond there was originally, owing to the contact of the concrete
above. At three times the live load, or 450 lb. per sq. ft., the
deflection apparently reached a maximum, being about 5/16 in. for a
clear distance, between the supports, of 20 ft.; and, as the load was
increased to 600 lb. per sq. ft., there was no appreciable increase
either in deflection or cracking; whereupon, the owner being satisfied,
the loading was discontinued. The load was reduced in amount to three
times the working load (450 lb.) and left on over night; the next
morning, there being no detectable change, the beam was declared to be
sound. When the load was removed the beam recovered all but about 1/8
in. of its deflection, and then repairs were made by attaching light
expanded metal to the exposed bars and plastering up to form. Although
nearly three years have elapsed, there have been no unfavorable
indications, and the owner, no doubt, has eased his mind entirely in
regard to the matter. This truly remarkable showing can only be
explained by the catenary action of the main steel, and some truss
action by the steel which was horizontal, in conjunction with the
U-bars, of which there were plenty. As before noted, the clear span
was 20 ft., the width of the bay, 8 ft., and the size under the slab
(which was 5 in. thick) 8 by 18 in. The reinforcement consisted of three
1-1/8-in. round medium-steel bars, with 3/8-in. U-bars placed the
effective depth of the member apart and closer toward the supports, the
first two or three being 6 in. apart, the next two or three, 9 in., the
next, 12 in., etc., up to a maximum, throughout the mid-section, of 15
in. Each U-bar was provided with a hook at its upper end, as shown in
Plate III, and engaged the slab reinforcement, which in this case was
expanded metal. Two of the 1-1/8-in. bars were bent up and carried
across the support. At the point of bending up, where they passed the
single horizontal bar, which was superimposed, a lock-bar was inserted,
by which the pressure of the bent-up steel against the concrete, in the
region of the bend, was taken up and distributed along the horizontal
bar. This feature is also shown in Fig. 14. The bars, after being
carried across the support, were inclined into the adjacent span and
provided with a liberal, well-rounded hook, furnishing efficient
anchorage and provision for reverse stresses. This was at one end only,
for--to make matters worse--the other end was a wall bearing;
consequently, the benefit of continuity was denied. The bent-up bars
were given a double reverse bend, as already described, carrying them
around, down, in, and up, and ending finally by clasping them in the
hook of the horizontal bar. This apparently stiffened up the free end,
for, under the test load, its action was similar to that of the
completely restrained end, thus attesting the value of this method of
end-fixing.

The writer has consistently followed this method of reinforcement, with
unvaryingly good results, and believes that, in some measure, it
approximates the truth of the situation. Moreover, it is economical, for
with the bars bent up over the supports in this manner, and positively
anchored, plenty of U-bars being provided, it is possible to remove
the forms with entire safety much sooner than with the ordinary methods
which are not as well stirruped and only partially tied across the
supports. It is also possible to put the structure into use at an
earlier date. Failure, too, by the premature removal of the centers, is
almost impossible with this method. These considerations more than
compensate for the trouble and expense involved in connection with such
reinforcement. The writer will not attempt here a theoretical analysis
of the stresses incurred in the different parts of this beam, although
it might be interesting and instructive.

[Illustration: FIG. 14.]

The concrete, with the reinforcement disposed as described, may be
regarded as reposing on the steel as a saddle, furnishing it with a
rigid jacket in which to work, and itself acting only as a stiff floor
and a protecting envelope. Bond, in this case, while, of course, an
adjunct, is by no means vitally important, as is generally the case with
beams unrestrained in any way and in which the reinforcement is not
provided with adequate end anchorage, in which case a continuous bond is
apparently--at any rate, theoretically--indispensable.

An example of the opposite extreme in reinforced concrete design, where
provision for reverse stresses was almost wholly lacking, is shown in
the Bridgeman Brothers' Building, in Philadelphia, which collapsed while
the operation of casting the roof was in progress, in the summer of
1907. The engineering world is fairly familiar with the details of this
disaster, as they were noted both in the lay and technical press. In
this structure, not only were U-bars almost entirely absent, but the
few main bars which were bent up, were stopped short over the support.
The result was that the ties between the rib and the slab, and also
across the support, being lacking, some of the beams, the forms of which
had been removed prematurely, cracked of their own dead weight, and,
later, when the roof collapsed, owing to the deficient bracing of the
centers, it carried with it each of the four floors to the basement, the
beams giving way abruptly over the supports. Had an adequate tie of
steel been provided across the supports, the collapse, undoubtedly,
would have stopped at the fourth floor. So many faults were apparent in
this structure, that, although only half of it had fallen, it was
ordered to be entirely demolished and reconstructed.

The cracks in the beams, due to the action of the dead weight alone,
were most interesting, and illuminative of the action which takes place
in a concrete beam. They were in every case on the diagonal, at an angle
of approximately 45°, and extended upward and outward from the edge of
the support to the bottom side of the slab. Never was the necessity for
diagonal steel, crossing this plane of weakness, more emphatically
demonstrated. To the writer--an eye-witness--the following line of
thought was suggested:

Should not the concrete in the region above the supports and for a
distance on either side, as encompassed by the opposed 45° lines (Fig.
14), be regarded as abundantly able, of and by itself, and without
reinforcing, to convey all its load into the column, leaving only the
bending to be considered in the truncated portion intersected? Not even
the bending should be considered, except in the case of relatively
shallow members, but simply the tendency on the part of the wedge-shaped
section to slip out on the 45° planes, thereby requiring sufficient
reinforcement at the crossing of these planes of principal weakness to
take the component of the load on this portion, tending to shove it out.
This reinforcement, of course, should be anchored securely both ways; in
mid-span by extending it clear through, forming a suspensory, and, in
the other direction, by prolonging it past the supports, the concrete,
in this case, along these planes, being assumed to assist partly or not
at all.

This would seem to be a fair assumption. In all events, beams designed
in this manner and checked by comparison with the usual methods of
calculation, allowing continuity of action, are found to agree fairly
well. Hence, the following statement seems to be warranted: If enough
steel is provided, crossing normally or nearly so the 45° planes from
the edge of the support upward and outward, to care for the component of
the load on the portion included within a pair of these planes, tending
to produce sliding along the same, and this steel is adequately anchored
both ways, there will be enough reinforcement for every other purpose.
In addition, U-bars should be provided for practical reasons.

The weak point of beams, and slabs also, fully reinforced for continuity
of action, is on the under side adjacent to the edge of the support,
where the concrete is in compression. Here, too, the amount of concrete
available is small, having no slab to assist it, as is the case within
the middle section, where the compression is in the top. Over the
supports, for the width of the column, there is abundant strength, for
here the steel has a leverage equal to the depth of the column; but at
the very edge and for at least one-tenth of the span out, conditions are
serious. The usual method of strengthening this region is to subpose
brackets, suitably proportioned, to increase the available compressive
area to a safe figure, as well as the leverage of the steel, at the same
time diminishing the intensity of compression. Brackets, however, are
frequently objectionable, and are therefore very generally omitted by
careless or ignorant designers, no especial compensation being made for
their absence. In Europe, especially in Germany, engineers are much more
careful in this respect, brackets being nearly always included. True, if
brackets are omitted, some compensation is provided by the strengthening
which horizontal bars may give by extending through this region, but
sufficient additional compressive resistance is rarely afforded thereby.
Perhaps the best way to overcome the difficulty, without resorting to
brackets, is to increase the compressive resistance of the concrete, in
addition to extending horizontal steel through it. This may be done by
hooping or by intermingling scraps of iron or bits of expanded metal
with the concrete, thereby greatly increasing its resistance. The
experiments made by the Department of Bridges of the City of New York,
on the value of nails in concrete, in which results as high as 18,000
lb. per sq. in. were obtained, indicate the availability of this device;
the writer has not used it, nor does he know that it has been used, but
it seems to be entirely rational, and to offer possibilities.

Another practical test, which indicates the value of proper
reinforcement, may be mentioned. In a storage warehouse in Canada, the
floor was designed, according to the building laws of the town, for a
live load of 150 lb. per sq. ft., but the restrictions being more severe
than the standard American practice, limiting the lever arm of the steel
to 75% of the effective depth, this was about equivalent to a 200-lb.
load in the United States. The structure was to be loaded up to 400 or
500 lb. per sq. ft. steadily, but the writer felt so confident of the
excess strength provided by his method of reinforcing that he was
willing to guarantee the structure, designed for 150 lb., according to
the Canadian laws, to be good for the actual working load. Plain, round,
medium-steel bars were used. A 10-ft. panel, with a beam of 14-ft. span,
and a slab 6 in. thick (not including the top coat), with 1/2-in. round
bars, 4 in. on centers, was loaded to 900 lb. per sq. ft., at which load
no measurable deflection was apparent. The writer wished to test it
still further, but there was not enough cement--the material used for
loading. The load, however, was left on for 48 hours, after which, no
sign of deflection appearing, not even an incipient crack, it was
removed. The total area of loading was 14 by 20 ft. The beam was
continuous at one end only, and the slab only on one side. In other
parts of the structure conditions were better, square panels being
possible, with reinforcement both ways, and with continuity, both of
beams and slabs, virtually in every direction, end spans being
compensated by shortening. The method of reinforcing was as before
indicated. The enormous strength of the structure, as proved by this
test, and as further demonstrated by its use for nearly two years, can
only be explained on the basis of the continuity of action developed and
the great stiffness secured by liberal stirruping. Steel was provided in
the middle section according to the rule, (_w_ _l_)/8, the span being
taken as the clear distance between the supports; two-thirds of the
steel was bent up and carried across the supports, in the case of the
beams, and three-fourths of the slab steel was elevated; this, with the
lap, really gave, on the average, four-thirds as much steel over the
supports as in the center, which, of course, was excessive, but usually
an excess has to be tolerated in order to allow for adequate anchorage.
Brackets were not used, but extra horizontal reinforcement, in addition
to the regular horizontal steel, was laid in the bottom across the
supports, which, seemingly, was satisfactory. The columns, it should be
added, were calculated for a very low value, something like 350 lb. per
sq. in., in order to compensate for the excess of actual live load over
and above the calculated load.

This piece of work was done during the winter, with the temperature
almost constantly at +10° and dropping below zero over night. The
precautions observed were to heat the sand and water, thaw out the
concrete with live steam, if it froze in transporting or before it
was settled in place, and as soon as it was placed, it was decked
over and salamanders were started underneath. Thus, a job equal in every
respect to warm-weather installation was obtained, it being possible to
remove the forms in a fortnight.

[Illustration: PLATE IV, FIG. 1.--SLAB AND BEAM REINFORCEMENT
CONTINUOUS OVER SUPPORTS. SPAN OF BEAMS = 14 FT. SPAN OF SLABS = 12 FT.
SLAB, 6 IN. THICK.]

[Illustration: PLATE IV, FIG. 2.--REINFORCEMENT IN PLACE OVER ONE
COMPLETE FLOOR OF STORAGE WAREHOUSE. SLABS, 14 FT. SQUARE. REINFORCED
TWO WAYS. NOTE CONTINUITY OF REINFORCEMENT AND ELEVATION OVER SUPPORTS.
FLOOR DESIGNED FOR 150 LB. PER SQ. FT. LIVE LOAD. TESTED TO 900 LB. PER
SQ. FT.]

In another part of this job (the factory annex) where, owing to the open
nature of the structure, it was impossible to house it in as well as the
warehouse which had bearing walls to curtain off the sides, less
fortunate results were obtained. A temperature drop over night of nearly
50°, followed by a spell of alternate freezing and thawing, effected the
ruin of at least the upper 2 in. of a 6-in. slab spanning 12 ft. (which
was reinforced with 1/2-in. round bars, 4 in. on centers), and the
remaining 4 in. was by no means of the best quality. It was thought that
this particular bay would have to be replaced. Before deciding, however,
a test was arranged, supports being provided underneath to prevent
absolute failure. But as the load was piled up, to the extent of nearly
400 lb. per sq. ft., there was no sign of giving (over this span) other
than an insignificant deflection of less than 1/4 in., which disappeared
on removing the load. This slab still performs its share of the duty,
without visible defect, hence it must be safe. The question naturally
arises: if 4 in. of inferior concrete could make this showing, what must
have been the value of the 6 in. of good concrete in the other slabs?
The reinforcing in the slab, it should be stated, was continuous over
several supports, was proportioned for (_w_ _l_)/8 for the clear span
(about 11 ft.), and three-fourths of it was raised over the supports.
This shows the value of the continuous method of reinforcing, and the
enormous excess of strength in concrete structures, as proportioned by
existing methods, when the reverse stresses are provided for fully and
properly, though building codes may make no concession therefor.

Another point may be raised, although the author has not mentioned it,
namely, the absurdity of the stresses commonly considered as occurring
in tensile steel, 16,000 lb. per sq. in. for medium steel being used
almost everywhere, while some zealots, using steel with a high elastic
limit, are advocating stresses up to 22,000 lb. and more; even the
National Association of Cement Users has adopted a report of the
Committee on Reinforced Concrete, which includes a clause recommending
the use of 20,000 lb. on high steel. As theory indicates, and as F.E.
Turneaure, Assoc. M. Am. Soc. C. E., of the University of Wisconsin, has
proven by experiment, failure of the concrete encircling the steel under
tension occurs when the stress in the steel is about 5,000 lb. per sq.
in. It is evident, therefore, that if a stress of even 16,000 lb. were
actually developed, not to speak of 20,000 lb. or more, the concrete
would be so replete with minute cracks on the tension side as to expose
the embedded metal in innumerable places. Such cracks do not occur in
work because, under ordinary working loads, the concrete is able to
carry the load so well, by arch and dome action, as to require very
little assistance from the steel, which, consequently, is never stressed
to a point where cracking of the concrete will be induced. This being
the case, why not recognize it, modify methods of design, and not go on
assuming stresses which have no real existence?

The point made by Mr. Godfrey in regard to the fallacy of sharp bends is
patent, and must meet with the agreement of all who pause to think of
the action really occurring. This is also true of his points as to the
width of the stem of T-beams, and the spacing of bars in the same. As to
elastic arches, the writer is not sufficiently versed in designs of this
class to express an opinion, but he agrees entirely with the author in
his criticism of retaining-wall design. What the author proposes is
rational, and it is hard to see how the problem could logically be
analyzed otherwise. His point about chimneys, however, is not as clear.

As to columns, the writer agrees with Mr. Godfrey in many, but not in
all, of his points. Certainly, the fallacy of counting on vertical steel
to carry load, in addition to the concrete, has been abundantly shown.
The writer believes that the sole legitimate function of vertical steel,
as ordinarily used, is to reinforce the member against flexure, and that
its very presence in the column, unless well tied across by loops of
steel at frequent intervals, so far from increasing the direct carrying
capacity, is a source of weakness. However, the case is different when a
large amount of rigid vertical steel is used; then the steel may be
assumed to carry all the load, at the value customary in structural
steel practice, the concrete being considered only in the light of
fire-proofing and as affording lateral support to the steel, increasing
its effective radius of gyration and thus its safe carrying capacity. In
any event the load should be assumed to be carried either by the
concrete or by the steel, and, if by the former, the longitudinal and
transverse steel which is introduced should be regarded as auxiliary
only. Vertical steel, if not counted in the strength, however, may on
occasion serve a very useful practical purpose; for instance, the writer
once had a job where, owing to the collection of ice and snow on a
floor, which melted when the salamanders were started, the lower ends of
several of the superimposed columns were eaten away, with the result
that when the forms were withdrawn, these columns were found to be
standing on stilts. Only four 1-in. bars were present, looped at
intervals of about 1 ft., in a column 12 ft. in length and having a
girth of 14 in., yet they were adequate to carry both the load of the
floor above and the load incidental to construction. If no such
reinforcement had been provided, however, failure would have been
inevitable. Thus, again, it is shown that, where theory and experiment
may fail to justify certain practices, actual experience does, and
emphatically.

Mr. Godfrey is absolutely right in his indictment of hooping as usually
done, for hoops can serve no purpose until the concrete contained
therein is stressed to incipient rupture; then they will begin to act,
to furnish restraint which will postpone ultimate failure. Mr. Godfrey
states that, in his opinion, the lamina of concrete between each hoop is
not assisted; but, as a matter of fact, practically regarded, it is, the
coarse particles of the aggregate bridging across from hoop to hoop; and
if--as is the practice of some--considerable longitudinal steel is also
used, and the hoops are very heavy, so that when the bridging action of
the concrete is taken into account, there is in effect a very
considerable restraining of the concrete core, and the safe carrying
capacity of the column is undoubtedly increased. However, in the latter
case, it would be more logical to consider that the vertical steel
carried all the load, and that the concrete core, with the hoops, simply
constituted its rigidity and the medium of getting the load into the
same, ignoring, in this event, the direct resistance of the concrete.

What seems to the writer to be the most logical method of reinforcing
concrete columns remains to be developed; it follows along the lines of
supplying tensile resistance to the mass here and there throughout, thus
creating a condition of homogeneity of strength. It is precisely the
method indicated by the experiments already noted, made by the
Department of Bridges of the City of New York, whereby the compressive
resistance of concrete was enormously increased by intermingling wire
nails with it. Of course, it is manifestly out of the question,
practically and economically, to reinforce column concrete in this
manner, but no doubt a practical and an economical method will be
developed which will serve the same purpose. The writer knows of one
prominent reinforced concrete engineer, of acknowledged judgment, who
has applied for a patent in which expanded metal is used to effect this
very purpose; how well this method will succeed remains to be seen. At
any rate, reinforcement of this description seems to be entirely
rational, which is more than can be said for most of the current
standard types.

Mr. Godfrey's sixteenth point, as to the action in square panels, seems
also to the writer to be well taken; he recollects analyzing Mr.
Godfrey's narrow-strip method at the time it appeared in print, and
found it rational, and he has since had the pleasure of observing actual
tests which sustained this view. Reinforcement can only be efficient in
two ways, if the span both ways is the same or nearly so; a very little
difference tends to throw the bulk of the load the short way, for
stresses know only one law, namely, to follow the shortest line. In
square panels the maximum bending comes on the mid-strips; those
adjacent to the margin beams have very little bending parallel to the
beam, practically all the action being the other way; and there are all
gradations between. The reinforcing, therefore, should be spaced the
minimum distance only in the mid-region, and from there on constantly
widened, until, at about the quarter point, practically none is
necessary, the slab arching across on the diagonal from beam to beam.
The practice of spacing the bars at the minimum distance throughout is
common, extending the bars to the very edge of the beams. In this case
about half the steel is simply wasted.

In conclusion, the writer wishes to thank Mr. Godfrey for his very able
paper, which to him has been exceedingly illuminative and fully
appreciated, even though he has been obliged to differ from its
contentions in some respects. On the other hand, perhaps, the writer is
wrong and Mr. Godfrey right; in any event, if, through the medium of
this contribution to the discussion, the writer has assisted in
emphasizing a few of the fundamental truths; or if, in his points of
non-concordance, he is in coincidence with the views of a sufficient
number of engineers to convince Mr. Godfrey of any mistaken stands; or,
finally, if he has added anything new to the discussion which may help
along the solution, he will feel amply repaid for his time and labor.
The least that can be said is that reform all along the line, in matters
of reinforced concrete design, is insistent.


JOHN STEPHEN SEWELL, M. AM. SOC. C. E. (by letter).--The author is
rather severe on the state of the art of designing reinforced concrete.
It appears to the writer that, to a part of the indictment, at least, a
plea of not guilty may properly be entered; and that some of the other
charges may not be crimes, after all. There is still room for a wide
difference of opinion on many points involved in the design of
reinforced concrete, and too much zeal for conviction, combined with
such skill in special pleading as this paper exhibits, may possibly
serve to obscure the truth, rather than to bring it out clearly.

_Point 1._--This is one to which the proper plea is "not guilty." The
writer does not remember ever to have seen just the type of construction
shown in Fig. 1, either used or recommended. The angle at which the bars
are bent up is rarely as great as 45°, much less 60 degrees. The writer
has never heard of "sharp bends" being insisted on, and has never seen
them used; it is simply recommended or required that some of the bars be
bent up and, in practice, the bend is always a gentle one. The stress to
be carried by the concrete as a queen-post is never as great as that
assumed by the author, and, in practice, the queen-post has a much
greater bearing on the bars than is indicated in Fig. 1.

_Point 2._--The writer, in a rather extensive experience, has never seen
this point exemplified.

_Point 3._--It is probable that as far as Point 3 relates to retaining
walls, it touches a weak spot sometimes seen in actual practice, but
necessity for adequate anchorage is discussed at great length in
accepted literature, and the fault should be charged to the individual
designer, for correct information has been within his reach for at least
ten years.

_Point 4._--In this case it would seem that the author has put a wrong
interpretation on what is generally meant by shear. However, it is
undoubtedly true that actual shear in reinforcing steel is sometimes
figured and relied on. Under some conditions it is good practice, and
under others it is not. Transverse rods, properly placed, can surely act
in transmitting stress from the stem to the flange of a T-beam, and
could properly be so used. There are other conditions under which the
concrete may hold the rods so rigidly that their shearing strength may
be utilized; where such conditions do not obtain, it is not ordinarily
necessary to count on the shearing strength of the rods.

_Point 5._--Even if vertical stirrups do not act until the concrete has
cracked, they are still desirable, as insuring a gradual failure and,
generally, greater ultimate carrying capacity. It would seem that the
point where their full strength should be developed is rather at the
neutral axis than at the centroid of compression stresses. As they are
usually quite light, this generally enables them to secure the requisite
anchorage in the compressed part of the concrete. Applied to a riveted
truss, the author's reasoning would require that all the rivets by which
web members are attached to the top chord should be above the center of
gravity of the chord section.

_Point 6._--There are many engineers who, accepting the common theory of
diagonal tension and compression in a solid beam, believe that, in a
reinforced concrete beam with stirrups, the concrete can carry the
diagonal compression, and the stirrups the tension. If these web
stresses are adequately cared for, shear can be neglected.

The writer cannot escape the conclusion that tests which have been made
support the above belief. He believes that stirrups should be inclined
at an angle of 45° or less, and that they should be fastened rigidly to
the horizontal bars; but that is merely the most efficient way to use
them--not the only way to secure the desired action, at least, in some
degree.

The author's proposed method of bending up some of the main bars is
good, but he should not overlook the fact that he is taking them away
from the bottom of the beam just as surely as in the case of a sharp
bend, and this is one of his objections to the ordinary method of
bending them up. Moreover, with long spans and varying distances of the
load, the curve which he adopts for his bars cannot possibly be always
the true equilibrium curve. His concrete must then act as a stiffening
truss, and will almost inevitably crack before his cable can come into
action as such.

Bulletin No. 29 of the University of Illinois contains nothing to
indicate that the bars bent up in the tests reported were bent up in any
other than the ordinary way; certainly they could not be considered as
equivalent to the cables of a suspension bridge. These beams behaved
pretty well, but the loads were applied so as to make them practically
queen-post trusses, symmetrically loaded. While the bends in the bars
were apparently not very sharp, and the angle of inclination was much
less than 60°, or even 45°, it is not easy to find adequate bearings for
the concrete posts on theoretical grounds, yet it is evident that the
bearing was there just the same. The last four beams of the series,
521-1, 521-2, 521-5, 521-6, were about as nearly like Fig. 1 as anything
the writer has ever seen in actual practice, yet they seem to have been
the best of all. To be sure, the ends of the bent-up bars had a rather
better anchorage, but they seem to have managed the shear question
pretty much according to the expectation of their designer, and it is
almost certain that the latter's assumptions would come under some part
of the author's general indictment. These beams would seem to justify
the art in certain practices condemned by the author. Perhaps he
overlooked them.

_Point 7._--The writer does not believe that the "general" practice as
to continuity is on the basis charged. In fact, the general practice
seems to him to be rather in the reverse direction. Personally, the
writer believes in accepting continuity and designing for it, with
moments at both center and supports equal to two-thirds of the center
movement for a single span, uniformly loaded. He believes that the
design of reinforced concrete should not be placed on the same footing
as that of structural steel, because there is a fundamental difference,
calling for different treatment. The basis should be sound, in both
cases; but what is sound for one is not necessarily so for the other. In
the author's plan for a series of spans designed as simple beams, with a
reasonable amount of top reinforcement, he might get excessive stress
and cracks in the concrete entirely outside of the supports. The shear
would then become a serious matter, but no doubt the direct
reinforcement would come into play as a suspension bridge, with further
cracking of the concrete as a necessary preliminary.

Unfortunately, the writer is unable to refer to records, but he is quite
sure that, in the early days, the rivets and bolts in the upper part of
steel and iron bridge stringer connections gave some trouble by failing
in tension due to continuous action, where the stringers were of
moderate depth compared to the span. Possibly some members of the
Society may know of such instances. The writer's instructors in
structural design warned him against shallow stringers on that account,
and told him that such things had happened.

Is it certain that structural steel design is on such a sound basis
after all? Recent experiences seem to cast some doubt on it, and we may
yet discover that we have escaped trouble, especially in buildings,
because we almost invariably provide for loads much greater than are
ever actually applied, and not because our knowledge and practice are
especially exact.

_Point 8._--The writer believes that this point is well taken, as to a
great deal of current practice; but, if the author's ideas are carried
out, reinforced concrete will be limited to a narrow field of
usefulness, because of weight and cost. With attached web members, the
writer believes that steel can be concentrated in heavy members in a way
that is not safe with plain bars, and that, in this way, much greater
latitude of design may be safely allowed.

_Point 9._--The writer is largely in accord with the author's ideas on
the subject of T-beams, but thinks he must have overlooked a very
careful and able analysis of this kind of member, made by A.L. Johnson,
M. Am. Soc. C. E., a number of years ago. While too much of the floor
slab is still counted on for flange duty, it seems to the writer that,
within the last few years, practice has greatly improved in this
respect.

_Point 10._--The author's statement regarding the beam and slab formulas
in common use is well grounded. The modulus of elasticity of concrete is
so variable that any formulas containing it and pretending to determine
the stress in the concrete are unreliable, but the author's proposed
method is equally so. We can determine by experiment limiting
percentages of steel which a concrete of given quality can safely carry
as reinforcement, and then use empirical formulas based on the stress in
the steel and an assumed percentage of its depth in the concrete as a
lever arm with more ease and just as much accuracy. The common methods
result in designs which are safe enough, but they pretend to determine
the stress in concrete; the writer does not believe that that is
possible within 30% of the truth, and can see no profit in making
laborious calculations leading to such unreliable results.

_Point 11._--The writer has never designed a reinforced concrete
chimney, but if he ever has to do so, he will surely not use any formula
that is dependent on the modulus of elasticity of concrete.

_Points 12, 13, and 14._--The writer has never had to consider these
points to any extent in his own work, and will leave discussion to those
better qualified.

_Point 15._--There is much questionable practice in regard to reinforced
concrete columns; but the matter is hardly disposed of as easily as
indicated by the author. Other engineers draw different conclusions from
the tests cited by the author, and from some to which he does not refer.
To the writer it appears that here is a problem still awaiting solution
on a really satisfactory basis. It seems incredible that the author
would use plain concrete in columns, yet that seems to be the inference.
The tests seem to indicate that there is much merit in both hooping and
longitudinal reinforcement, if properly designed; that the
fire-resisting covering should not be integral with the columns proper;
that the high results obtained by M. Considère in testing small
specimens cannot be depended on in practice, but that the reinforcement
is of great value, nevertheless. The writer believes that when
load-carrying capacity, stresses due to eccentricity, and fire-resisting
qualities are all given due consideration, a type of column with close
hooping and longitudinal reinforcement provided with shear members, will
finally be developed, which will more than justify itself.

_Point 16_.--The writer has not gone as deeply into this question, from
a theoretical point of view, as he would like; but he has had one
experience that is pertinent. Some years ago, he built a plain slab
floor supported by brick walls. The span was about 16 ft. The dimensions
of the slab at right angles to the reinforcement was 100 ft. or more.
Plain round bars, 1/2 in. in diameter, were run at right angles to the
reinforcement about 2 ft. on centers, the object being to lessen cracks.
The reinforcement consisted of Kahn bars, reaching from wall to wall.
The rounds were laid on top of the Kahn bars. The concrete was frozen
and undeniably damaged, but the floors stood up, without noticeable
deflection, after the removal of the forms. The concrete was so soft,
however, that a test was decided on. An area about 4 ft. wide, and
extending to within about 1 ft. of each bearing wall, was loaded with
bricks piled in small piers not in contact with each other, so as to
constitute practically a uniformly distributed load. When the total load
amounted to much less than the desired working load for the 4-ft. strip,
considerable deflection had developed. As the load increased, the
deflection increased, and extended for probably 15 or 20 ft. on either
side of the loaded area. Finally, under about three-fourths of the
desired breaking load for the 4-ft. strip, it became evident that
collapse would soon occur. The load was left undisturbed and, in 3 or 4
min., an area about 16 ft. square tore loose from the remainder of the
floor and fell. The first noticeable deflection in the above test
extended for 8 or 10 ft. on either side of the loaded strip. It would
seem that this test indicated considerable distributing power in the
round rods, although they were not counted as reinforcement for
load-carrying purposes at all. The concrete was extremely poor, and none
of the steel was stressed beyond the elastic limit. While this test may
not justify the designer in using lighter reinforcement for the short
way of the slab, it at least indicates a very real value for some
reinforcement in the other direction. It would seem to indicate, also,
that light steel members in a concrete slab might resist a small amount
of shear. The slab in this case was about 6 in. thick.


SANFORD E. THOMPSON, M. AM. SOC. C. E. (by letter).--Mr. Godfrey's
sweeping condemnation of reinforced concrete columns, referred to in his
fifteenth point, should not be passed over without serious criticism.
The columns in a building, as he states, are the most vital portion of
the structure, and for this very reason their design should be governed
by theoretical and practical considerations based on the most
comprehensive tests available.

The quotation by Mr. Godfrey from a writer on hooped columns is
certainly more radical than is endorsed by conservative engineers, but
the best practice in column reinforcement, as recommended by the Joint
Committee on Concrete and Reinforced Concrete, which assumes that the
longitudinal bars assist in taking stress in accordance with the ratio
of elasticity of steel to concrete, and that the hooping serves to
increase the toughness of the column, is founded on the most substantial
basis of theory and test.

In preparing the second edition of "Concrete, Plain and Reinforced," the
writer examined critically the various tests of concrete columns in
order to establish a definite basis for his conclusions. Referring more
particularly to columns reinforced with vertical steel bars, an
examination of all the tests of full-sized columns made in the United
States appears to bear out the fact very clearly that longitudinal steel
bars embedded in concrete increase the strength of the column, and,
further, to confirm the theory by which the strength of the combination
of steel and concrete may be computed and is computed in practice.

Tests of large columns have been made at the Watertown Arsenal, the
Massachusetts Institute of Technology, the University of Illinois, by
the City of Minneapolis, and at the University of Wisconsin. The results
of these various tests were recently summarized by the writer in a paper
presented at the January, 1910, meeting of the National Association of
Cement Users[O]. Reference may be made to this paper for fuller
particulars, but the averages of the tests of each series are worth
repeating here.

In comparing the averages of reinforced columns, specimens with spiral
or other hooping designed to increase the strength, or with horizontal
reinforcement placed so closely together as to prevent proper placing of
the concrete, are omitted. For the Watertown Arsenal tests the averages
given are made up from fair representative tests on selected proportions
of concrete, given in detail in the paper referred to, while in other
cases all the corresponding specimens of the two types are averaged. The
results are given in Table 1.

The comparison of these tests must be made, of course, independently in
each series, because the materials and proportions of the concrete and
the amounts of reinforcement are different in the different series. The
averages are given simply to bring out the point, very definitely and
distinctly, that longitudinally reinforced columns are stronger than
columns of plain concrete.

A more careful analysis of the tests shows that the reinforced columns
are not only stronger, but that the increase in strength due to the
reinforcement averages greater than the ordinary theory, using a ratio
of elasticity of 15, would predicate.

Certain of the results given are diametrically opposed to Mr. Godfrey's
conclusions from the same sets of tests. Reference is made by him, for
example (page 69), to a plain column tested at the University of
Illinois, which crushed at 2,001 lb. per sq. in., while a reinforced
column of similar size crushed at 1,557 lb. per sq. in.,[P] and the
author suggests that "This is not an isolated case, but appears to be
the rule." Examination of this series of tests shows that it is somewhat
more erratic than most of those made at the University of Illinois, but,
even from the table referred to by Mr. Godfrey, pursuing his method of
reasoning, the reverse conclusion might be reached, for if, instead of
selecting, as he has done, the weakest reinforced column in the entire
lot and the strongest plain column, a reverse selection had been made,
the strength of the plain column would have been stated as 1,079 lb. per
sq. in. and that of the reinforced column as 3,335 lb. per sq. in. If
extremes are to be selected at all, the weakest reinforced column should
be compared with the weakest plain column, and the strongest reinforced
column with the strongest plain column; and the results would show that
while an occasional reinforced column may be low in strength, an
occasional plain column will be still lower, so that the reinforcement,
even by this comparison, is of marked advantage in increasing strength.
In such cases, however, comparisons should be made by averages. The
average strength of the reinforced columns, even in this series, as
given in Table 1, is considerably higher than that of the plain columns.

      TABLE 1.--AVERAGE RESULTS OF TESTS OF PLAIN _vs._
             LONGITUDINALLY REINFORCED COLUMNS.

--------------+--------+--------------+---------------------------------
              |        |   Average    |
              |Average | strength of  |
   Location   |strength|longitudinally|           Reference.
   of test.   |of plain|  reinforced  |
              |columns.|   columns.   |
--------------+--------+--------------+---------------------------------
   Watertown  | 1,781  |    2,992     |Taylor and Thompson's
   Arsenal.   |        |              |"Concrete, Plain and Reinforced"
              |        |              |(2nd edition), p. 493.
--------------+--------+--------------+---------------------------------
 Massachusetts| 1,750  |    2,370     |_Transactions_,
 Institute of |        |              |Am. Soc. C. E., Vol. L, p. 487.
  Technology. |        |              |
--------------+--------+--------------+---------------------------------
 University of| 1,550  |    1,750     |_Bulletin No. 10._
   Illinois.  |        |              |University of Illinois, 1907.
--------------+--------+--------------+---------------------------------
    City of   | 2,020  |    2,300     |_Engineering News_,
  Minneapolis.|        |              |Dec. 3d, 1908, p. 608.
--------------+--------+--------------+---------------------------------
 University of| 2,033  |    2,438     |_Proceedings_,
  Wisconsin.  |        |              |Am. Soc. for Testing Materials,
              |        |              |Vol. IX, 1909, p. 477.
--------------+--------+--------------+---------------------------------

In referring, in the next paragraph, to Mr. Withey's tests at the
University of Wisconsin, Mr. Godfrey selects for his comparison two
groups of concrete which are not comparable. Mr. Withey, in the paper
describing the tests, refers to two groups of plain concrete columns,
_A1_ to _A4_, and _W1_ to _W3_. He speaks of the uniformity in the tests
of the former group, the maximum variation in the four specimens being
only 2%, but states, with reference to columns, _W1_ to _W3_, that:

     "As these 3 columns were made of a concrete much superior to that
     in any of the other columns made from 1:2:4 or 1:2:3-1/2 mix, they
     cannot satisfactorily be compared with them. Failures of all plain
     columns were sudden and without any warning."

Now, Mr. Godfrey, instead of taking columns _A1_ to _A3_, selects for
his comparison _W1_ to _W3_, made, as Mr. Withey distinctly states, with
an especially superior concrete. Taking columns, _A1_ to _A3_, for
comparison with the reinforced columns, _E1_ to _E3_, the result shows
an average of 2,033 for the plain columns and 2,438 for the reinforced
columns.

Again, taking the third series of tests referred to by Mr. Godfrey,
those at Minneapolis, Minn., it is to be noticed that he selects for his
criticism a column which has this note as to the manner of failure:
"Bending at center (bad batch of concrete at this point)." Furthermore,
the column is only 9 by 9 in., and square, and the stress referred to is
calculated on the full section of the column instead of on the strength
within the hooping, although the latter method is the general practice
in a hooped column. The inaccuracy of this is shown by the fact that,
with this small size of square column, more than half the area is
outside the hooping and never taken into account in theoretical
computations. A fair comparison, as far as longitudinal reinforcement is
concerned, is always between the two plain columns and the six columns,
_E_, _D_, and _F_. The results are so instructive that a letter[Q] by
the writer is quoted in full as follows:

     "SIR:--

     "In view of the fact that the column tests at Minneapolis, as
     reported in your paper of December 3, 1908, p. 608, are liable
     because of the small size of the specimens to lead to divergent
     conclusions, a few remarks with reference to them may not be out of
     place at this time.

     "1. It is evident that the columns were all smaller, being only 9
     in. square, than is considered good practice in practical
     construction, because of the difficulty of properly placing the
     concrete around the reinforcement.

     "2. The tests of columns with flat bands, _A_, _B_, and _C_, in
     comparison with the columns _E_, _D_ and _F_, indicate that the
     wide bands affected the placing of the concrete, separating the
     internal core from the outside shell so that it would have been
     nearly as accurate to base the strength upon the material within
     the bands, that is, upon a section of 38 sq. in., instead of upon
     the total area of 81 sq. in. This set of tests, _A_, _B_ and _C_,
     is therefore inconclusive except as showing the practical
     difficulty in the use of bands in small columns, and the necessity
     for disregarding all concrete outside of the bands when computing
     the strength.

     "3. The six columns _E_, _D_ and _F_, each of which contained eight
     5/8-in. rods, are the only ones which are a fair test of columns
     longitudinally reinforced, since they are the only specimens except
     the plain columns in which the small sectional area was not cut by
     bands or hoops. Taking these columns, we find an average strength
     38% in excess of the plain columns, whereas, with the percentage of
     reinforcement used, the ordinary formula for vertical steel (using
     a ratio of elasticity of steel to concrete of 15) gives 34% as the
     increase which might be expected. In other words, the actual
     strength of this set of columns was in excess of the theoretical
     strength. The wire bands on these columns could not be considered
     even by the advocates of hooped columns as appreciably adding to
     the strength, because they were square instead of circular. It may
     be noted further in connection with these longitudinally reinforced
     columns that the results were very uniform and, further, that the
     strength of _every specimen_ was much greater than the strength of
     the plain columns, being in every case except one at least 40%
     greater. In these columns the rods buckled between the bands, but
     they evidently did not do so until their elastic limit was passed,
     at which time of course they would be expected to fail.

     "4. With reference to columns, _A_, _B_, _C_ and _L_, which were
     essentially hooped columns, the failure appears to have been caused
     by the greater deformation which is always found in hooped columns,
     and which in the earlier stages of the loading is apparently due to
     lack of homogeneity caused by the difficulty in placing the
     concrete around the hooping, and in the later stage of the loading
     to the excessive expansion of the concrete. This greater
     deformation in a hooped column causes any vertical steel to pass
     its elastic limit at an earlier stage than in a column where the
     deformation is less, and therefore produces the buckling between
     the bands which is noted in these two sets of columns. This
     excessive deformation is a strong argument against the use of high
     working stresses in hooped columns.

     "In conclusion, then, it may be said that the columns reinforced
     with vertical round rods showed all the strength that would be
     expected of them by theoretical computation. The hooped columns, on
     the other hand, that is, the columns reinforced with circular bands
     and hoops, gave in all cases comparatively low results, but no
     conclusions can be drawn from them because the unit-strength would
     have been greatly increased if the columns had been larger so that
     the relative area of the internal core to the total area of the
     column had been greater."

From this letter, it will be seen that every one of Mr. Godfrey's
comparisons of plain _versus_ reinforced columns requires explanations
which decidedly reduce, if they do not entirely destroy, the force of
his criticism.

This discussion can scarcely be considered complete without brief
reference to the theory of longitudinal steel reinforcement for columns.
The principle[R] is comparatively simple. When a load is placed on a
column of any material it is shortened in proportion, within working
limits, to the load placed upon it; that is, with a column of
homogeneous material, if the load is doubled, the amount of shortening
or deformation is also doubled. If vertical steel bars are embedded in
concrete, they must shorten when the load is applied, and consequently
relieve the concrete of a portion of its load. It is therefore
physically impossible to prevent such vertical steel from taking a
portion of the load unless the steel slips or buckles.

As to the possible danger of the bars in the concrete slipping or
buckling, to which Mr. Godfrey also refers, again must tests be cited.
If the ends are securely held--and this is always the case when bars are
properly butted or are lapped for a sufficient length--they cannot slip.
With reference to buckling, tests have proved conclusively that vertical
bars such as are used in columns, when embedded in concrete, will not
buckle until the elastic limit of the steel is reached, or until the
concrete actually crushes. Beyond these points, of course, neither steel
nor concrete nor any other material is expected to do service.

As proof of this statement, it will be seen, by reference to tests at
the Watertown Arsenal, as recorded in "Tests of Metals," that many of
the columns were made with vertical bar reinforcement having absolutely
no hoops or horizontal steel placed around them. That is, the bars, 8
ft. long, were placed in the four corners of the column--in some tests
only 2 in. from the surface--and held in place simply by the concrete
itself.[S] There was no sign whatever of buckling until the compression
was so great that the elastic limit of the steel was passed, when, of
course, no further strength could be expected from it.

To recapitulate the conclusions reached as a result of a study of the
tests: It is evident that, not only does theory permit the use of
longitudinal bar reinforcement for increasing the strength of concrete
columns, whenever such reinforcement is considered advisable, but that
all the important series of column tests made in the United States to
date show a decisive increase in strength of columns reinforced with
longitudinal steel bars over those which are not reinforced.
Furthermore, as has already been mentioned, without treating the details
of the proof, it can be shown that the tests bear out conclusively the
conservatism of computing the value of the vertical steel bars in
compression by the ordinary formulas based on the ratio of the moduli of
elasticity of steel to concrete.


EDWARD GODFREY, M. AM. SOC. C. E. (by letter).--As was to be expected,
this paper has brought out discussion, some of which is favorable and
flattering; some is in the nature of dust-throwing to obscure the force
of the points made; some would attempt to belittle the importance of
these points; and some simply brings out the old and over-worked
argument which can be paraphrased about as follows: "The structures
stand up and perform their duty, is this not enough?"

The last-mentioned argument is as old as Engineering; it is the
"practical man's" mainstay, his "unanswerable argument." The so-called
practical man will construct a building, and test it either with loads
or by practical use. Then he will modify the design somewhere, and the
resulting construction will be tested. If it passes through this
modifying process and still does service, he has something which, in his
mind, is unassailable. Imagine the freaks which would be erected in the
iron bridge line, if the capacity to stand up were all the designer had
to guide him, analysis of stresses being unknown. Tests are essential,
but analysis is just as essential. The fact that a structure carries the
bare load for which it is computed, is in no sense a test of its correct
design; it is not even a test of its safety. In Pittsburg, some years
ago, a plate-girder span collapsed under the weight of a locomotive
which it had carried many times. This bridge was, perhaps, thirty years
old. Some reinforced concrete bridges have failed under loads which they
have carried many times. Others have fallen under no extraneous load,
and after being in service many months. If a large number of the columns
of a structure fall shortly after the forms are removed, what is the
factor of safety of the remainder, which are identical, but have not
quite reached their limit of strength? Or what is the factor of safety
of columns in other buildings in which the concrete was a little better
or the forms have been left in a little longer, both sets of columns
being similarly designed?

There are highway bridges of moderately long spans standing and doing
service, which have 2-in. chord pins; laterals attached to swinging
floor-beams in such a way that they could not possibly receive their
full stress; eye-bars with welded-on heads; and many other equally
absurd and foolish details, some of which were no doubt patented in
their day. Would any engineer with any knowledge whatever of bridge
design accept such details? They often stand the test of actual service
for years; in pins, particularly, the calculated stress is sometimes
very great. These details do not stand the test of analysis and of
common sense, and, therefore, no reputable engineer would accept them.

Mr. Turner, in the first and second paragraphs of his discussion, would
convey the impression that the writer was in doubt as to his "personal
opinions" and wanted some free advice. He intimates that he is too busy
to go fully into a treatise in order to set them right. He further tries
to throw discredit on the paper by saying that the writer has adduced no
clean-cut statement of fact or tests in support of his views. If Mr.
Turner had read the paper carefully, he would not have had the idea that
in it the hooped column is condemned. As to this more will be said
later. The paper is simply and solely a collection of statements of
facts and tests, whereas his discussion teems with his "personal
opinion," and such statements as "These values * * * are regarded by the
writer as having at least double the factor of safety used in ordinary
designs of structural steel"; "On a basis not far from that which the
writer considers reasonable practice." Do these sound like clean-cut
statements of fact, or are they personal opinions? It is a fact, pure
and simple, that a sharp bend in a reinforcing rod in concrete violates
the simplest principles of mechanics; also that the queen-post and Pratt
and Howe truss analogies applied to reinforcing steel in concrete are
fallacies; that a few inches of embedment will not anchor a rod for its
value; that concrete shrinks in setting in air and puts initial stress
in both the concrete and the steel, making assumed unstressed initial
conditions non-existent. It is a fact that longitudinal rods alone
cannot be relied on to reinforce a concrete column. Contrary to Mr.
Turner's statement, tests have been adduced to demonstrate this fact.
Further, it is a fact that the faults and errors in reinforced concrete
design to which attention is called, are very common in current design,
and are held up as models in nearly all books on the subject.

The writer has not asked any one to believe a single thing because he
thinks it is so, or to change a single feature of design because in his
judgment that feature is faulty. The facts given are exemplifications of
elementary mechanical principles overlooked by other writers, just as
early bridge designers and writers on bridge design overlooked the
importance of calculating bridge pins and other details which would
carry the stress of the members.

A careful reading of the paper will show that the writer does not accept
the opinions of others, when they are not backed by sound reason, and
does not urge his own opinion.

Instead of being a statement of personal opinion for which confirmation
is desired, the paper is a simple statement of facts and tests which
demonstrate the error of practices exhibited in a large majority of
reinforced concrete work and held up in the literature on the subject as
examples to follow. Mr. Turner has made no attempt to deny or refute any
one of these facts, but he speaks of the burden of proof resting on the
writer. Further, he makes statements which show that he fails entirely
to understand the facts given or to grasp their meaning. He says that
the writer's idea is "that the entire pull of the main reinforcing rod
should be taken up apparently at the end." He adds that the soundness of
this position may be questioned, because, in slabs, the steel frequently
breaks at the center. Compare this with the writer's statement, as
follows:

     "In shallow beams there is little need of provision for taking
     shear by any other means than the concrete itself. The writer has
     seen a reinforced slab support a very heavy load by simple
     friction, for the slab was cracked close to the supports. In slabs,
     shear is seldom provided for in the steel reinforcement. It is only
     when beams begin to have a depth approximating one-tenth of the
     span that the shear in the concrete becomes excessive and provision
     is necessary in the steel reinforcement. Years ago, the writer
     recommended that, in such beams, some of the rods be curved up
     toward the ends of the span and anchored over the support."

It is solely in providing for shear that the steel reinforcement should
be anchored for its full value over the support. The shear must
ultimately reach the support, and that part which the concrete is not
capable of carrying should be taken to it solely by the steel, as far as
tensile and shear stresses are concerned. It should not be thrown back
on the concrete again, as a system of stirrups must necessarily do.

The following is another loose assertion by Mr. Turner:

     "Mr. Godfrey appears to consider that the hooping and vertical
     reinforcement of columns is of little value. He, however, presents
     for consideration nothing but his opinion of the matter, which
     appears to be based on an almost total lack of familiarity with
     such construction."

There is no excuse for statements like this. If Mr. Turner did not read
the paper, he should not have attempted to criticize it. What the writer
presented for consideration was more than his opinion of the matter. In
fact, no opinion at all was presented. What was presented was tests
which prove absolutely that longitudinal rods without hoops may actually
reduce the strength of a column, and that a column containing
longitudinal rods and "hoops which are not close enough to stiffen the
rods" may be of less strength than a plain concrete column. A properly
hooped column was not mentioned, except by inference, in the quotation
given in the foregoing sentence. The column tests which Mr. Turner
presents have no bearing whatever on the paper, for they relate to
columns with bands and close spirals. Columns are sometimes built like
these, but there is a vast amount of work in which hooping and bands are
omitted or are reduced to a practical nullity by being spaced a foot or
so apart.

A steel column made up of several pieces latticed together derives a
large part of its stiffness and ability to carry compressive stresses
from the latticing, which should be of a strength commensurate with the
size of the column. If it were weak, the column would suffer in
strength. The latticing might be very much stronger than necessary, but
it would not add anything to the strength of the column to resist
compression. A formula for the compressive strength of a column could
not include an element varying with the size of the lattice. If the
lattice is weak, the column is simply deficient; so a formula for a
hooped column is incorrect if it shows that the strength of the column
varies with the section of the hoops, and, on this account, the common
formula is incorrect. The hoops might be ever so strong, beyond a
certain limit, and yet not an iota would be added to the compressive
strength of the column, for the concrete between the hoops might crush
long before their full strength was brought into play. Also, the hoops
might be too far apart to be of much or any benefit, just as the lattice
in a steel column might be too widely spaced. There is no element of
personal opinion in these matters. They are simply incontrovertible
facts. The strength of a hooped column, disregarding for the time the
longitudinal steel, is dependent on the fact that thin discs of concrete
are capable of carrying much more load than shafts or cubes. The hoops
divide the column into thin discs, if they are closely spaced; widely
spaced hoops do not effect this. Thin joints of lime mortar are known to
be many times stronger than the same mortar in cubes. Why, in the many
books on the subject of reinforced concrete, is there no mention of this
simple principle? Why do writers on this subject practically ignore the
importance of toughness or tensile strength in columns? The trouble
seems to be in the tendency to interpret concrete in terms of steel.
Steel at failure in short blocks will begin to spread and flow, and a
short column has nearly the same unit strength as a short block. The
action of concrete under compression is quite different, because of the
weakness of concrete in tension. The concrete spalls off or cracks apart
and does not flow under compression, and the unit strength of a shaft of
concrete under compression has little relation to that of a flat block.
Some years ago the writer pointed out that the weakness of cast-iron
columns in compression is due to the lack of tensile strength or
toughness in cast iron. Compare 7,600 lb. per sq. in. as the base of a
column formula for cast iron with 100,000 lb. per sq. in. as the
compressive strength of short blocks of cast iron. Then compare 750 lb.
per sq. in., sometimes used in concrete columns, with 2,000 lb. per sq.
in., the ultimate strength in blocks. A material one-fiftieth as strong
in compression and one-hundredth as strong in tension with a "safe" unit
one-tenth as great! The greater tensile strength of rich mixtures of
concrete accounts fully for the greater showing in compression in tests
of columns of such mixtures. A few weeks ago, an investigator in this
line remarked, in a discussion at a meeting of engineers, that "the
failure of concrete in compression may in cases be due to lack of
tensile strength." This remark was considered of sufficient novelty and
importance by an engineering periodical to make a special news item of
it. This is a good illustration of the state of knowledge of the
elementary principles in this branch of engineering.

Mr. Turner states, "Again, concrete is a material which shows to the
best advantage as a monolith, and, as such, the simple beam seems to be
decidedly out of date to the experienced constructor." Similar things
could be said of steelwork, and with more force. Riveted trusses are
preferable to articulated ones for rigidity. The stringers of a bridge
could readily be made continuous; in fact, the very riveting of the ends
to a floor-beam gives them a large capacity to carry reverse moments.
This strength is frequently taken advantage of at the end floor-beam,
where a tie is made to rest on a bracket having the same riveted
connection as the stringer. A small splice-plate across the top flanges
of the stringers would greatly increase this strength to resist reverse
moments. A steel truss span is ideally conditioned for continuity in the
stringers, since the various supports are practically relatively
immovable. This is not true in a reinforced concrete building where each
support may settle independently and entirely vitiate calculated
continuous stresses. Bridge engineers ignore continuity absolutely in
calculating the stringers; they do not argue that a simple beam is out
of date. Reinforced concrete engineers would do vastly better work if
they would do likewise, adding top reinforcement over supports to
forestall cracking only. Failure could not occur in a system of beams
properly designed as simple spans, even if the negative moments over the
supports exceeded those for which the steel reinforcement was provided,
for the reason that the deflection or curving over the supports can only
be a small amount, and the simple-beam reinforcement will immediately
come into play.

Mr. Turner speaks of the absurdity of any method of calculating a
multiple-way reinforcement in slabs by endeavoring to separate the
construction into elementary beam strips, referring, of course, to the
writer's method. This is misleading. The writer does not endeavor to
"separate the construction into elementary beam strips" in the sense of
disregarding the effect of cross-strips. The "separation" is analogous
to that of considering the tension and compression portions of a beam
separately in proportioning their size or reinforcement, but unitedly in
calculating their moment. As stated in the paper, "strips are taken
across the slab and the moment in them is found, considering the
limitations of the several strips in deflection imposed by those running
at right angles therewith." It is a sound and rational assumption that
each strip, 1 ft. wide through the middle of the slab, carries its half
of the middle square foot of the slab load. It is a necessary limitation
that the other strips which intersect one of these critical strips
across the middle of the slab, cannot carry half of the intercepted
square foot, because the deflection of these other strips must diminish
to zero as they approach the side of the rectangle. Thus, the nearer the
support a strip parallel to that support is located, the less load it
can take, for the reason that it cannot deflect as much as the middle
strip. In the oblong slab the condition imposed is equal deflection of
two strips of unequal span intersecting at the middle of the slab, as
well as diminished deflection of the parallel strips.

In this method of treating the rectangular slab, the concrete in tension
is not considered to be of any value, as is the case in all accepted
methods.

Some years ago the writer tested a number of slabs in a building, with a
load of 250 lb. per sq. ft. These slabs were 3 in. thick and had a clear
span of 44 in. between beams. They were totally without reinforcement.
Some had cracked from shrinkage, the cracks running through them and
practically the full length of the beams. They all carried this load
without any apparent distress. If these slabs had been reinforced with
some special reinforcement of very small cross-section, the strength
which was manifestly in the concrete itself, might have been made to
appear to be in the reinforcement. Magic properties could be thus
conjured up for some special brand of reinforcement. An energetic
proprietor could capitalize tension in concrete in this way and "prove"
by tests his claims to the magic properties of his reinforcement.

To say that Poisson's ratio has anything to do with the reinforcement of
a slab is to consider the tensile strength of concrete as having a
positive value in the bottom of that slab. It means to reinforce for the
stretch in the concrete and not for the tensile stress. If the tensile
strength of concrete is not accepted as an element in the strength of a
slab having one-way reinforcement, why should it be accepted in one
having reinforcement in two or more directions? The tensile strength of
concrete in a slab of any kind is of course real, when the slab is
without cracks; it has a large influence in the deflection; but what
about a slab that is cracked from shrinkage or otherwise?

Mr. Turner dodges the issue in the matter of stirrups by stating that
they were not correctly placed in the tests made at the University of
Illinois. He cites the Hennebique system as a correct sample. This
system, as the writer finds it, has some rods bent up toward the support
and anchored over it to some extent, or run into the next span. Then
stirrups are added. There could be no objection to stirrups if, apart
from them, the construction were made adequate, except that expense is
added thereby. Mr. Turner cannot deny that stirrups are very commonly
used just as they were placed in the tests made at the University of
Illinois. It is the common practice and the prevailing logic in the
literature of the subject which the writer condemns.

Mr. Thacher says of the first point:

     "At the point where the first rod is bent up, the stress in this
     rod runs out. The other rods are sufficient to take the horizontal
     stress, and the bent-up portion provides only for the vertical and
     diagonal shearing stresses in the concrete."

If the stress runs out, by what does that rod, in the bent portion, take
shear? Could it be severed at the bend, and still perform its office?
The writer can conceive of an inclined rod taking the shear of a beam if
it were anchored at each end, or long enough somehow to have a grip in
the concrete from the centroid of compression up and from the center of
the steel down. This latter is a practical impossibility. A rod curved
up from the bottom reinforcement and curved to a horizontal position and
run to the support with anchorage, would take the shear of a beam. As to
the stress running out of a rod at the point where it is bent up, this
will hardly stand the test of analysis in the majority of cases. On
account of the parabolic variation of stress in a beam, there should be
double the length necessary for the full grip of a rod in the space from
the center to the end of a beam. If 50 diameters are needed for this
grip, the whole span should then be not less than four times 50, or 200
diameters of the rod. For the same reason the rod between these bends
should be at least 200 diameters in length. Often the reinforcing rods
are equal to or more than one-two-hundredth of the span in diameter, and
therefore need the full length of the span for grip.

Mr. Thacher states that Rod 3 provides for the shear. He fails to answer
the argument that this rod is not anchored over the support to take the
shear. Would he, in a queen-post truss, attach the hog-rod to the beam
some distance out from the support and thus throw the bending and shear
back into the very beam which this rod is intended to relieve of bending
and shear? Yet this is just what Rod 3 would do, if it were long enough
to be anchored for the shear, which it seldom is; hence it cannot even
perform this function. If Rod 3 takes the shear, it must give it back to
the concrete beam from the point of its full usefulness to the support.
Mr. Thacher would not say of a steel truss that the diagonal bars would
take the shear, if these bars, in a deck truss, were attached to the top
chord several feet away from the support, or if the end connection were
good for only a fraction of the stress in the bars. Why does he not
apply the same logic to reinforced concrete design?

Answering the third point, Mr. Thacher makes more statements that are
characteristic of current logic in reinforced concrete literature, which
does not bother with premises. He says, "In a beam, the shear rods run
through the compression parts of the concrete and have sufficient
anchorage." If the rods have sufficient anchorage, what is the nature of
that anchorage? It ought to be possible to analyze it, and it is due to
the seeker after truth to produce some sort of analysis. What mysterious
thing is there to anchor these rods? The writer has shown by analysis
that they are not anchored sufficiently. In many cases they are not long
enough to receive full anchorage. Mr. Thacher merely makes the dogmatic
statement that they are anchored. There is a faint hint of a reason in
his statement that they run into the compression part of the concrete.
Does he mean that the compression part of the concrete will grip the rod
like a vise? How does this comport with his contention farther on that
the beams are continuous? This would mean tension in the upper part of
the beam. In any beam the compression near the support, where the shear
is greatest, is small; so even this hint of an argument has no force or
meaning.

In this same paragraph Mr. Thacher states, concerning the third point
and the case of the retaining wall that is given as an example, "In a
counterfort, the inclined rods are sufficient to take the overturning
stress." Mr. Thacher does not make clear what he means by "overturning
stress." He seems to mean the force tending to pull the counterfort
loose from the horizontal slab. The weight of the earth fill over this
slab is the force against which the vertical and inclined rods of Fig.
2, at _a_, must act. Does Mr. Thacher mean to state seriously that it is
sufficient to hang this slab, with its heavy load of earth fill, on the
short projecting ends of a few rods? Would he hang a floor slab on a few
rods which project from the bottom of a girder? He says, "The proposed
method is no more effective." The proposed method is Fig. 2, at _b_,
where an angle is provided as a shelf on which this slab rests. The
angle is supported, with thread and nut, on rods which reach up to the
front slab, from which a horizontal force, acting about the toe of the
wall as a fulcrum, results in the lifting force on the slab. There is
positively no way in which this wall could fail (as far as the
counterfort is concerned) but by the pulling apart of the rods or the
tearing out of this anchoring angle. Compare this method of failure with
the mere pulling out of a few ends of rods, in the design which Mr.
Thacher says is just as effective. This is another example of the kind
of logic that is brought into requisition in order to justify absurd
systems of design.

Mr. Thacher states that shear would govern in a bridge pin where there
is a wide bar or bolster or a similar condition. The writer takes issue
with him in this. While in such a case the center of bearing need not be
taken to find the bending moment, shear would not be the correct
governing element. There is no reason why a wide bar or a wide bolster
should take a smaller pin than a narrow one, simply because the rule
that uses the center of bearing would give too large a pin. Bending can
be taken in this, as in other cases, with a reasonable assumption for a
proper bearing depth in the wide bar or bolster. The rest of Mr.
Thacher's comment on the fourth point avoids the issue. What does he
mean by "stress" in a shear rod? Is it shear or tension? Mr. Thacher's
statement, that the "stress" in the shear rods is less than that in the
bottom bars, comes close to saying that it is shear, as the shearing
unit in steel is less than the tensile unit. This vague way of referring
to the "stress" in a shear member, without specifically stating whether
this "stress" is shear or tension, as was done in the Joint Committee
Report, is, in itself, a confession of the impossibility of analyzing
the "stress" in these members. It gives the designer the option of using
tension or shear, both of which are absurd in the ordinary method of
design. Writers of books are not bold enough, as a rule, to state that
these rods are in shear, and yet their writings are so indefinite as to
allow this very interpretation.

Mr. Thacher criticises the fifth point as follows:

     "Vertical stirrups are designed to act like the vertical rods in a
     Howe truss. Special literature is not required on the subject; it
     is known that the method used gives good results, and that is
     sufficient."

This is another example of the logic applied to reinforced concrete
design--another dogmatic statement. If these stirrups act like the
verticals in a Howe truss, why is it not possible by analysis to show
that they do? Of course there is no need of special literature on the
subject, if it is the intention to perpetuate this senseless method of
design. No amount of literature can prove that these stirrups act as the
verticals of a Howe truss, for the simple reason that it can be easily
proven that they do not.

Mr. Thacher's criticism of the sixth point is not clear. "All the shear
from the center of the beam up to the bar in question," is what he says
each shear member is designed to take in the common method. The shear of
a beam usually means the sum of the vertical forces in a vertical
section. If he means that the amount of this shear is the load from the
center of the beam to the bar in question, and that shear members are
designed to take this amount of shear, it would be interesting to know
by what interpretation the common method can be made to mean this. The
method referred to is that given in several standard works and in the
Joint Committee Report. The formula in that report for vertical
reinforcement is:

        _V_ _s_
 _P_ = --------- ,
        _j_ _d_

in which _P_ = the stress in a single reinforcing member, _V_ = the
proportion of total shear assumed as carried by the reinforcement, _s_ =
the horizontal spacing of the reinforcing members, and _j d_ = the
effective depth.

Suppose the spacing of shear members is one-half or one-third of the
effective depth, the stress in each member is one-half or one-third of
the "shear assumed to be carried by the reinforcement." Can Mr. Thacher
make anything else out of it? If, as he says, vertical stirrups are
designed to act like the vertical rods in a Howe truss, why are they not
given the stress of the verticals of a Howe truss instead of one-half or
one-third or a less proportion of that stress?

Without meaning to criticize the tests made by Mr. Thaddeus Hyatt on
curved-up rods with nuts and washers, it is true that the results of
many early tests on reinforced concrete are uncertain, because of the
mealy character of the concrete made in the days when "a minimum amount
of water" was the rule. Reinforcement slips in such concrete when it
would be firmly gripped in wet concrete. The writer has been unable to
find any record of the tests to which Mr. Thacher refers. The tests
made at the University of Illinois, far from showing reinforcement of
this type to be "worse than useless," showed most excellent results by
its use.

That which is condemned in the seventh point is not so much the
calculating of reinforced concrete beams as continuous, and reinforcing
them properly for these moments, but the common practice of lopping off
arbitrarily a large fraction of the simple beam moment on reinforced
concrete beams of all kinds. This is commonly justified by some virtue
which lies in the term monolith. If a beam rests in a wall, it is "fixed
ended"; if it comes into the side of a girder, it is "fixed ended"; and
if it comes into the side of a column, it is the same. This is used to
reduce the moment at mid-span, but reinforcement which will make the
beam fixed ended or continuous is rare.

There is not much room for objection to Mr. Thacher's rule of spacing
rods three diameters apart. The rule to which the writer referred as
being 66% in error on the very premise on which it was derived, namely,
shear equal to adhesion, was worked out by F.P. McKibben, M. Am. Soc. C.
E. It was used, with due credit, by Messrs. Taylor and Thompson in their
book, and, without credit, by Professors Maurer and Turneaure in their
book. Thus five authorities perpetrate an error in the solution of one
of the simplest problems imaginable. If one author of an arithmetic had
said two twos are five, and four others had repeated the same thing,
would it not show that both revision and care were badly needed?

Ernest McCullough, M. Am. Soc. C. E., in a paper read at the Armour
Institute, in November, 1908, says, "If the slab is not less than
one-fifth of the total depth of the beam assumed, we can make a
T-section of it by having the narrow stem just wide enough to contain
the steel." This partly answers Mr. Thacher's criticism of the ninth
point. In the next paragraph, Mr. McCullough mentions some very nice
formulas for T-beams by a certain authority. Of course it would be
better to use these nice formulas than to pay attention to such
"rule-of-thumb" methods as would require more width in the stem of the T
than enough to squeeze the steel in.

If these complex formulas for T-beams (which disregard utterly the
simple and essential requirement that there must be concrete enough in
the stem of the T to grip the steel) are the only proper
exemplifications of the "theory of T-beams," it is time for engineers to
ignore theory and resort to rule-of-thumb. It is not theory, however,
which is condemned in the paper, it is complex theory; theory totally
out of harmony with the materials dealt with; theory based on false
assumptions; theory which ignores essentials and magnifies trifles;
theory which, applied to structures which have failed from their own
weight, shows them to be perfectly safe and correct in design;
half-baked theories which arrogate to themselves a monopoly on
rationality.

To return to the spacing of rods in the bottom of a T-beam; the report
of the Joint Committee advocates a horizontal spacing of two and
one-half diameters and a side spacing of two diameters to the surface.
The same report advocates a "clear spacing between two layers of bars of
not less than 1/2 in." Take a T-beam, 11-1/2 in. wide, with two layers
of rods 1 in. square, 4 in each layer. The upper surface of the upper
layer would be 3-1/2 in. above the bottom of the beam. Below this
surface there would be 32 sq. in. of concrete to grip 8 sq. in. of
steel. Does any one seriously contend that this trifling amount of
concrete will grip this large steel area? This is not an extreme case;
it is all too common; and it satisfies the requirements of the Joint
Committee, which includes in its make-up a large number of the
best-known authorities in the United States.

Mr. Thacher says that the writer appears to consider theories for
reinforced concrete beams and slabs as useless refinements. This is not
what the writer intended to show. He meant rather that facts and tests
demonstrate that refinement in reinforced concrete theories is utterly
meaningless. Of course a wonderful agreement between the double-refined
theory and test can generally be effected by "hunching" the modulus of
elasticity to suit. It works both ways, the modulus of elasticity of
concrete being elastic enough to be shifted again to suit the designer's
notion in selecting his reinforcement. All of which is very beautiful,
but it renders standard design impossible.

Mr. Thacher characterizes the writer's method of calculating reinforced
concrete chimneys as rule-of-thumb. This is surprising after what he
says of the methods of designing stirrups. The writer's method would
provide rods to take all the tensile stresses shown to exist by any
analysis; it would give these rods unassailable end anchorages; every
detail would be amply cared for. If loose methods are good enough for
proportioning loose stirrups, and no literature is needed to show why or
how they can be, why analyze a chimney so accurately and apply
assumptions which cannot possibly be realized anywhere but on paper and
in books?

It is not rule-of-thumb to find the tension in plain concrete and then
embed steel in that concrete to take that tension. Moreover, it is safer
than the so-called rational formula, which allows compression on slender
rods in concrete.

Mr. Thacher says, "No arch designed by the elastic theory was ever known
to fail, unless on account of insecure foundations." Is this the correct
way to reach correct methods of design? Should engineers use a certain
method until failures show that something is wrong? It is doubtful if
any one on earth has statistics sufficient to state with any authority
what is quoted in the opening sentence of this paragraph. Many arches
are failures by reason of cracks, and these cracks are not always due to
insecure foundations. If Mr. Thacher means by insecure foundations,
those which settle, his assertion, assuming it to be true, has but
little weight. It is not always possible to found an arch on rock. Some
settlement may be anticipated in almost every foundation. As commonly
applied, the elastic theory is based on the absolute fixity of the
abutments, and the arch ring is made more slender because of this
fixity. The ordinary "row-of-blocks" method gives a stiffer arch ring
and, consequently, greater security against settlement of foundations.

In 1904, two arches failed in Germany. They were three-hinged masonry
arches with metal hinges. They appear to have gone down under the weight
of theory. If they had been made of stone blocks in the old-fashioned
way, and had been calculated in the old-fashioned row-of-blocks method,
a large amount of money would have been saved. There is no good reason
why an arch cannot be calculated as hinged ended and built with the arch
ring anchored into the abutments. The method of the equilibrium polygon
is a safe, sane, and sound way to calculate an arch. The monolithic
method is a safe, sane, and sound way to build one. People who spend
money for arches do not care whether or not the fancy and fancied
stresses of the mathematician are realized; they want a safe and lasting
structure.

Of course, calculations can be made for shrinkage stresses and for
temperature stresses. They have about as much real meaning as
calculations for earth pressures behind a retaining wall. The danger
does not lie in making the calculations, but in the confidence which the
very making of them begets in their correctness. Based on such
confidence, factors of safety are sometimes worked out to the hundredth
of a unit.

Mr. Thacher is quite right in his assertion that stiff steel angles,
securely latticed together, and embedded in the concrete column, will
greatly increase its strength.

The theory of slabs supported on four sides is commonly accepted for
about the same reason as some other things. One author gives it, then
another copies it; then when several books have it, it becomes
authoritative. The theory found in most books and reports has no correct
basis. That worked out by Professor W.C. Unwin, to which the writer
referred, was shown by him to be wrong.[T] An important English report
gave publicity and much space to this erroneous solution. Messrs. Marsh
and Dunn, in their book on reinforced concrete, give several pages to
it.

In referring to the effect of initial stress, Mr. Myers cites the case
of blocks and says, "Whatever initial stress exists in the concrete due
to this process of setting exists also in these blocks when they are
tested." However, the presence of steel in beams and columns puts
internal stresses in reinforced concrete, which do not exist in an
isolated block of plain concrete.

Mr. Meem, while he states that he disagrees with the writer in one
essential point, says of that point, "In the ordinary way in which these
rods are used, they have no practical value." The paper is meant to be a
criticism of the ordinary way in which reinforced concrete is used.

While Mr. Meem's formula for a reinforced concrete beam is simple and
much like that which the writer would use, he errs in making the moment
of the stress in the steel about the neutral axis equal to the moment of
that in the concrete about the same axis. The actual amount of the
tension in the steel should equal the compression in the concrete, but
there is no principle of mechanics that requires equality of the moments
about the neutral axis. The moment in the beam is, therefore, the
product of the stress in steel or concrete and the effective depth of
the beam, the latter being the depth from the steel up to a point
one-sixth of the depth of the concrete beam from the top. This is the
method given by the writer. It would standardize design as methods using
the coefficient of elasticity cannot do.

Professor Clifford, in commenting on the first point, says, "The
concrete at the point of juncture must give, to some extent, and this
would distribute the bearing over a considerable length of rod." It is
just this local "giving" in reinforced concrete which results in cracks
that endanger its safety and spoil its appearance; they also discredit
it as a permanent form of construction.

Professor Clifford has informed the writer that the tests on bent rods
to which he refers were made on 3/4-in. rounds, embedded for 12 in. in
concrete and bent sharply, the bent portion being 4 in. long. The 12-in.
portion was greased. The average maximum load necessary to pull the rods
out was 16,000 lb. It seems quite probable that there would be some
slipping or crushing of the concrete before a very large part of this
load was applied. The load at slipping would be a more useful
determination than the ultimate, for the reason that repeated
application of such loads will wear out a structure. In this connection
three sets of tests described in Bulletin No. 29 of the University of
Illinois, are instructive. They were made on beams of the same size, and
reinforced with the same percentage of steel. The results were as
follows:

Beams 511.1, 511.2, 512.1, 512.2: The bars were bent up at third points.
Average breaking load, 18,600 lb. All failed by slipping of the bars.

Beams 513.1, 513.2: The bars were bent up at third points and given a
sharp right-angle turn over the supports. Average breaking load, 16,500
lb. The beams failed by cracking alongside the bar toward the end.

Beams 514.2, 514.3: The bars were bent up at third points and had
anchoring nuts and washers at the ends over the supports. Average
breaking load, 22,800 lb. These failed by tension in the steel.

By these tests it is seen that, in a beam, bars without hooks were
stronger in their hold on the concrete by an average of 13% than those
with hooks. Each test of the group of straight bars showed that they
were stronger than either of those with hooked bars. Bars anchored over
the support in the manner recommended in the paper were nearly 40%
stronger than hooked bars and 20% stronger than straight bars. These
percentages, furthermore, do not represent all the advantages of
anchored bars. The method of failure is of greatest significance. A
failure by tension in the steel is an ideal failure, because it is
easiest to provide against. Failures by slipping of bars, and by
cracking and disintegrating of the concrete beam near the support, as
exhibited by the other tests, indicate danger, and demand much larger
factors of safety.

Professor Clifford, in criticizing the statement that a member which
cannot act until failure has started is not a proper element of design,
refers to another statement by the writer, namely, "The steel in the
tension side of the beam should be considered as taking all the
tension." He states that this cannot take place until the concrete has
failed in tension at this point. The tension side of a beam will stretch
out a measurable amount under load. The stretching out of the beam
vertically, alongside of a stirrup, would be exceedingly minute, if no
cracks occurred in the beam.

Mr. Mensch says that "the stresses involved are mostly secondary." He
compares them to web stresses in a plate girder, which can scarcely be
called secondary. Furthermore, those stresses are carefully worked out
and abundantly provided for in any good design. To give an example of
how a plate girder might be designed: Many plate girders have rivets in
the flanges, spaced 6 in. apart near the supports, that is, girders
designed with no regard to good practice. These girders, perhaps, need
twice as many rivets near the ends, according to good and acceptable
practice, which is also rational practice. The girders stand up and
perform their office. It is doubtful whether they would fail in these
rivet lines in a test to destruction; but a reasonable analysis shows
that these rivets are needed, and no good engineer would ignore this
rule of design or claim that it should be discarded because the girders
do their work anyway. There are many things about structures, as every
engineer who has examined many of those erected without engineering
supervision can testify, which are bad, but not quite bad enough to be
cause for condemnation. Not many years ago the writer ordered
reinforcement in a structure designed by one of the best structural
engineers in the United States, because the floor-beams had sharp bends
in the flange angles. This is not a secondary matter, and sharp bends in
reinforcing rods are not a secondary matter. No amount of analysis can
show that these rods or flange angles will perform their full duty.
Something else must be overstressed, and herein is a violation of the
principles of sound engineering.

Mr. Mensch mentions the failure of the Quebec Bridge as an example of
the unknown strength of steel compression members, and states that, if
the designer of that bridge had known of certain tests made 40 years
ago, that accident probably would not have happened. It has never been
proven that the designer of that bridge was responsible for the accident
or for anything more than a bridge which would have been weak in
service. The testimony of the Royal Commission, concerning the chords,
is, "We have no evidence to show that they would have actually failed
under working conditions had they been axially loaded and not subject to
transverse stresses arising from weak end details and loose
connections." Diagonal bracing in the big erection gantry would have
saved the bridge, for every feature of the wreck shows that the lateral
collapse of that gantry caused the failure. Here are some more simple
principles of sound engineering which were ignored.

It is when practice runs "ahead of theory" that it needs to be brought
up with a sharp turn. It is the general practice to design dams for the
horizontal pressure of the water only, ignoring that which works into
horizontal seams and below the foundation, and exerts a heavy uplift.
Dams also fail occasionally, because of this uplifting force which is
proven to exist by theory.

Mr. Mensch says:

     "The author is manifestly wrong in stating that the reinforcing
     rods can only receive their increments of stress when the concrete
     is in tension. Generally, the contrary happens. In the ordinary
     adhesion test, the block of concrete is held by the jaws of the
     machine and the rod is pulled out; the concrete is clearly in
     compression."

This is not a case of increments at all, as the rod has the full stress
given to it by the grips of the testing machine. Furthermore, it is not
a beam. Also, Mr. Mensch is not accurate in conveying the writer's
meaning. To quote from the paper:

     "A reinforcing rod in a concrete beam receives its stress by
     increments imparted by the grip of the concrete, but these
     increments can only be imparted where the tendency of the concrete
     is to stretch."

This has no reference to an adhesion test.

Mr. Mensch's next paragraph does not show a careful perusal of the
paper. The writer does not "doubt the advisability of using bent-up bars
in reinforced concrete beams." What he does condemn is bending up the
bars with a sharp bend and ending them nowhere. When they are curved up,
run to the support, and are anchored over the support or run into the
next span, they are excellent. In the tests mentioned by Mr. Mensch, the
beams which had the rods bent up and "continued over the supports" gave
the highest "ultimate values." This is exactly the construction which
is pointed out as being the most rational, if the rods do not have the
sharp bends which Mr. Mensch himself condemns.

Regarding the tests mentioned by him, in which the rods were fastened to
anchor-plates at the end and had "slight increase of strength over
straight rods, and certainly made a poorer showing than bent-up bars,"
the writer asked Mr. Mensch by letter whether these bars were curved up
toward the supports. He has not answered the communication, so the
writer cannot comment on the tests. It is not necessary to use threaded
bars, except in the end beams, as the curved-up bars can be run into the
next beam and act as top reinforcement while at the same time receiving
full anchorage.

Mr. Mensch's statement regarding the retaining wall reinforced as shown
at _a_, Fig. 2, is astounding. He "confesses that he never saw or heard
of such poor practices." If he will examine almost any volume of an
engineering periodical of recent years, he will have no trouble at all
in finding several examples of these identical practices. In the books
by Messrs. Reid, Maurer and Turneaure, and Taylor and Thompson, he will
find retaining walls illustrated, which are almost identical with Fig. 2
at _a_. Mr. Mensch says that the proposed design of a retaining wall
would be difficult and expensive to install. The harp-like reinforcement
could be put together on the ground, and raised to place and held with a
couple of braces. Compare this with the difficulty, expense and
uncertainty of placing and holding in place 20 or 30 separate rods. The
Fink truss analogy given by Mr. Mensch is a weak one. If he were making
a cantilever bracket to support a slab by tension from the top, the
bracket to be tied into a wall, would he use an indiscriminate lot of
little vertical and horizontal rods, or would he tie the slab directly
into the wall by diagonal ties? This is exactly the case of this
retaining wall, the horizontal slab has a load of earth, and the
counterfort is a bracket in tension; the vertical wall resists that
tension and derives its ability to resist from the horizontal pressure
of the earth.

Mr. Mensch states that "it would take up too much time to prove that the
counterfort acts really as a beam." The writer proposes to show in a
very short time that it is not a beam. A beam is a part of a structure
subject to bending strains caused by transverse loading. This will do as
a working definition. The concrete of the counterfort shown at _b_, Fig.
2, could be entirely eliminated if the rods were simply made to run
straight into the anchoring angle and were connected with little cast
skewbacks through slotted holes. There would be absolutely no bending in
the rods and no transverse load. Add the concrete to protect the rods;
the function of the rods is not changed in the least. M.S. Ketchum, M.
Am. Soc. C. E.,[U] calculates the counterfort as a beam, and the six
1-in. square bars which he uses diagonally do not even run into the
front slab. He states that the vertical and horizontal rods are to "take
the horizontal and vertical shear."

Mr. Mensch says of rectangular water tanks that they are not held
(presumably at the corners) by any such devices, and that there is no
doubt that they must carry the stress when filled with water. A water
tank,[V] designed by the writer in 1905, was held by just such devices.
In a tank[W] not held by any such devices, the corner broke, and it is
now held by reinforcing devices not shown in the original plans.

Mr. Mensch states that he "does not quite understand the author's
reference to shear rods. Possibly he means the longitudinal
reinforcement, which it seems is sometimes calculated to carry 10,000
lb. per sq. in. in shear;" and that he "never heard of such a practice."
His next paragraph gives the most pointed out-and-out statement
regarding shear in shear rods which this voluminous discussion contains.
He says that stirrups "are best compared with the dowel pins and bolts
of a compound wooden beam." This is the kernel of the whole matter in
the design of stirrups, and is just how the ordinary designer considers
stirrups, though the books and reports dodge the matter by saying
"stress" and attempting no analysis. Put this stirrup in shear at 10,000
lb. per sq. in., and we have a shearing unit only equalled in the
cheapest structural work on tight-fitting rivets through steel. In the
light of this confession, the force of the writer's comparison, between
a U-stirrup, 3/4-in. in diameter, and two 3/4-in. rivets tightly driven
into holes in a steel angle, is made more evident, Bolts in a wooden
beam built up of horizontal boards would be tightly drawn up, and the
friction would play an important part in taking up the horizontal shear.
Dowels without head or nut would be much less efficient; they would be
more like the stirrups in a reinforced concrete beam. Furthermore, wood
is much stronger in bearing than concrete, and it is tough, so that it
would admit of shifting to a firm bearing against the bolt. Separate
slabs of concrete with bolts or dowels through them would not make a
reliable beam. The bolts or dowels would be good for only a part of the
safe shearing strength of the steel, because the bearing on the concrete
would be too great for its compressive strength.

Mr. Mensch states that at least 99% of all reinforced structures are
calculated with a reduction of 25% of the bending moment in the center.
He also says "there may be some engineers who calculate a reduction of
33 per cent." These are broad statements in view of the fact that the
report of the Joint Committee recommends a reduction of 33% both in
slabs and beams.

Mr. Mensch's remarks regarding the width of beams omit from
consideration the element of span and the length needed to develop the
grip of a rod. There is no need of making a rod any less in diameter
than one-two-hundredth of the span. If this rule is observed, the beam
with three 7/8-in. round rods will be of longer span than the one with
the six 5/8-in. rods. The horizontal shear of the two beams will be
equal to the total amount of that shear, but the shorter beam will have
to develop that shear in a shorter distance, hence the need of a wider
beam where the smaller rods are used.

It is not that the writer advocates a wide stem in the T-beam, in order
to dispense with the aid of the slab. What he desires to point out is
that a full analysis of a T-beam shows that such a width is needed in
the stem.

Regarding the elastic theory, Mr. Mensch, in his discussion, shows that
he does not understand the writer's meaning in pointing out the
objections to the elastic theory applied to arches. The moment of
inertia of the abutment will, of course, be many times that of the arch
ring; but of what use is this large moment of inertia when the abutment
suddenly stops at its foundation? The abutment cannot be anchored for
bending into the rock; it is simply a block of concrete resting on a
support. The great bending moment at the end of the arch, which is found
by the elastic theory (on paper), has merely to overturn this block of
concrete, and it is aided very materially in this by the thrust of the
arch. The deformation of the abutment, due to deficiency in its moment
of inertia, is a theoretical trifle which might very aptly be minutely
considered by the elastic arch theorist. He appears to have settled all
fears on that score among his votaries. The settlement of the abutment
both vertically and horizontally, a thing of tremendously more magnitude
and importance, he has totally ignored.

Most soils are more or less compressible. The resultant thrust on an
arch abutment is usually in a direction cutting about the edge of the
middle third. The effect of this force is to tend to cause more
settlement of the abutment at the outer, than at the inner, edge, or, in
other words, it would cause the abutment to rotate. In addition to this
the same force tends to spread the abutments apart. Both these efforts
put an initial bending moment in the arch ring at the springing; a
moment not calculated, and impossible to calculate.

Messrs. Taylor and Thompson, in their book, give much space to the
elastic theory of the reinforced concrete arch. Little of that space,
however, is taken up with the abutment, and the case they give has
abutments in solid rock with a slope about normal to the thrust of the
arch ring. They recommend that the thrust be made to strike as near the
middle of the base of the abutment as possible.

Malverd A. Howe, M. Am. Soc. C. E., in a recent issue of _Engineering
News_, shows how to find the stresses and moments in an elastic arch;
but he does not say anything about how to take care of the large bending
moments which he finds at the springing.

Specialists in arch construction state that when the centering is
struck, every arch increases in span by settlement. Is this one fact not
enough to make the elastic theory a nullity, for that theory assumes
immovable abutments?

Professor Howe made some recent tests on checking up the elastic
behavior of arches. He reports[X] that "a very slight change at the
support does seriously affect the values of _H_ and _M_." The arch
tested was of 20-ft. span, and built between two heavy stone walls out
of all proportion to the magnitude of the arch, as measured by
comparison with an ordinary arch and its abutment. To make the arch
fixed ended, a large heavily reinforced head was firmly bolted to the
stone wall. Practical fixed endedness could be attained, of course, by
means such as these, but the value of such tests is only theoretical.

Mr. Mensch says:

     "The elastic theory was fully proved for arches by the remarkable
     tests, made in 1897 by the Austrian Society of Engineers and
     Architects, on full-sized arches of 70-ft. span, and the observed
     deflections and lateral deformations agreed exactly with the
     figured deformation."

The writer does not know of the tests made in 1897, but reference is
often made to some tests reported in 1896. These tests are everywhere
quoted as the unanswerable argument for the elastic theory. Let us
examine a few features of those tests, and see something of the strength
of the claim. In the first place, as to the exact agreement between the
calculated and the observed deformations, this exact agreement was
retroactive. The average modulus of elasticity, as found by specimen
tests of the concrete, did not agree at all with the value which it was
necessary to use in the arch calculations in order to make the
deflections come out right.

As found by tests on blocks, the average modulus was about 2,700,000;
the "practical" value, as determined from analysis of a plain concrete
arch, was 1,430,000, a little matter of nearly 100 per cent. Mansfield
Merriman, M. Am. Soc. C. E., gives a digest of these famous Austrian
tests.[Y] There were no fixed ended arches among them. There was a long
plain concrete arch and a long Monier arch. Professor Merriman says,
"The beton Monier arch is not discussed theoretically, and, indeed, this
would be a difficult task on account of the different materials
combined." And these are the tests which the Engineering Profession
points to whenever the elastic theory is questioned as to its
applicability to reinforced concrete arches. These are the tests that
"fully prove" the elastic theory for arches. These are the tests on the
basis of which fixed ended reinforced concrete arches are confidently
designed. Because a plain concrete bow between solid abutments deflected
in an elastic curve, reinforced concrete arches between settling
abutments are designed with fixed ends. The theorist has departed about
as far as possible from his premise in this case. On an exceedingly
slender thread he has hung an elaborate and important theory of design,
with assumptions which can never be realized outside of the schoolroom
or the designer's office. The most serious feature of such theories is
not merely the approximate and erroneous results which they give, but
the extreme confidence and faith in their certainty which they beget in
their users, enabling them to cut down factors of safety with no regard
whatever for the enormous factor of ignorance which is an essential
accompaniment to the theory itself.

Mr. Mensch says, "The elastic theory enables one to calculate arches
much more quickly than any graphical or guess method yet proposed." The
method given by the writer[Z] enables one to calculate an arch in about
the time it would take to work out a few of the many coefficients
necessary in the involved method of the elastic theory. It is not a
graphic method, but it is safe and sound, and it does not assume
conditions which have absolutely no existence.

Mr. Mensch says that the writer brings up some erratic column tests and
seems to have no confidence in reinforced concrete columns. In relation
to this matter Sanford E. Thompson, M. Am. Soc. C. E., in a paper
recently read before the National Association of Cement Users, takes the
same sets of tests referred to in the paper, and attempts to show that
longitudinal reinforcement adds much strength to a concrete column. Mr.
Thompson goes about it by means of averages. It is not safe to average
tests where the differences in individual tests are so great that those
of one class overlap those of the other. He includes the writer's
"erratic" tests and some others which are "erratic" the other way. It is
manifestly impossible for him to prove that longitudinal rods add any
strength to a concrete column if, on one pair of columns, identically
made as far as practicable, the plain concrete column is stronger than
that with longitudinal rods in it, unless the weak column is defective.
It is just as manifest that it is shown by this and other tests that the
supposedly reinforced concrete column may be weaker.

The averaging of results to show that longitudinal rods add strength, in
the case of the tests reported by Mr. Withey, includes a square plain
concrete column which naturally would show less compressive strength in
concrete than a round column, because of the spalling off at the
corners. This weak test on a square column is one of the slender props
on which is based the conclusion that longitudinal rods add to the
strength of a concrete column; but the weakness of the square concrete
column is due to the inherent weakness of brittle material in
compression when there are sharp corners which may spall off.

Mr. Worcester says that several of the writer's indictments hit at
practices which were discarded long ago, but from the attitude of their
defenders this does not seem to be true. There are benders to make sharp
bends in rods, and there are builders who say that they must be bent
sharply in order to simplify the work of fitting and measuring them.

There are examples in engineering periodicals and books, too numerous to
mention, where no anchorage of any kind is provided for bent-up rods,
except what grip they get in the concrete. If they reached beyond their
point of usefulness for this grip, it would be all right, but very often
they do not.

Mr. Worcester says: "It is not necessary that a stirrup at one point
should carry all the vertical tension, as this vertical tension is
distributed by the concrete." The writer will concede that the stirrups
need not carry all the vertical shear, for, in a properly reinforced
beam, the concrete can take part of it. The shear reinforcement,
however, should carry all the shear apportioned to it after deducting
that part which the concrete is capable of carrying, and it should carry
it without putting the concrete in shear again. The stirrups at one
point should carry all the vertical tension from the portion of shear
assumed to be taken by the stirrups; otherwise the concrete will be
compelled to carry more than its share of the shear.

Mr. Worcester states that cracks are just as likely to occur from stress
in curved-up and anchored rods as in vertical reinforcement. The fact
that the vertical stretching out of a beam from the top to the bottom,
under its load, is exceedingly minute, has been mentioned. A curved-up
bar, anchored over the support and lying near the bottom of the beam at
mid-span, partakes of the elongation of the tension side of the beam and
crosses the section of greatest diagonal tension in the most
advantageous manner. There is, therefore, a great deal of difference in
the way in which these two elements of construction act.

Mr. Worcester prefers the "customary method" of determining the width of
beams--so that the maximum horizontal shearing stress will not be
excessive--to that suggested by the writer. He gives as a reason for
this the fact that rods are bent up out of the bottom of a beam, and
that not all of them run to the end. The "customary method" must be
described in literature for private circulation. Mention has been made
of a method which makes the width of beam sufficient to insert the
steel. Considerations of the horizontal shear in a T-beam, and of the
capacity of the concrete to grip the steel, are conspicuous by their
absence in the analyses of beams. If a reinforcing rod is curved up and
anchored over the support, the concrete is relieved of the shear, both
horizontal and vertical, incident to the stress in that rod. If a
reinforcing rod is bent up anywhere, and not carried to the support, and
not anchored over it, as is customary, the shear is all taken by the
concrete; and there is just the same shear in the concrete as though the
rods were straight.

For proper grip a straight rod should have a diameter of not more than
one two-hundredth of the span. For economy of material, it should not be
much smaller in diameter than this. With this balance in a beam,
assuming shear equal to bond, the rods should be spaced a distance
apart, equal to their perimeters. This is a rational and simple rule,
and its use would go a long way toward the adoption of standards.

Mr. Worcester is not logical in his criticism of the writer's method of
reinforcing a chimney. It is not necessary to assume that the concrete
is not stressed, in the imaginary plain concrete chimney, beyond that
which plain concrete could take in tension. The assumption of an
imaginary plain concrete chimney and determinations of tensile stresses
in the concrete are merely simplified methods of finding the tensile
stress. The steel can take just as much tensile stress if its amount is
determined in this way as it can if any other method is used. The
shifting of the neutral axis, to which Mr. Worcester refers, is another
of the fancy assumptions which cannot be realized because of initial and
unknown stresses in the concrete and steel.

Mr. Russell states that the writer scarcely touched on top reinforcement
in beams. This would come in the class of longitudinal rods in columns,
unless the reinforcement were stiff members. Mr. Russell's remarks, to
the effect that columns and short deep beams, doubly reinforced, should
be designed as framed structures, point to the conclusion that
structural beams and columns, protected with concrete, should be used in
such cases. If the ruling motive of designers were uniformly to use what
is most appropriate in each particular location and not to carry out
some system, this is just what would be done in many cases; but some
minds are so constructed that they take pleasure in such boasts as this:
"There is not a pound of structural steel in that building." A
broad-minded engineer will use reinforced concrete where it is most
appropriate, and structural steel or cast iron where these are most
appropriate, instead of using his clients' funds to carry out some
cherished ideas.

Mr. Wright appreciates the writer's idea, for the paper was not intended
to criticize something which is "good enough" or which "answers the
purpose," but to systematize or standardize reinforced concrete and put
it on a basis of rational analysis and common sense, such a basis as
structural designing has been or is being placed on, by a careful
weeding out of all that is irrational, senseless, and weak.

Mr. Chapman says that the practical engineer has never used such methods
of construction as those which the writer condemns. The methods are
common enough; whether or not those who use them are practical engineers
is beside the question.

As to the ability of the end connection of a stringer carrying flange
stress or bending moments, it is not uncommon to see brackets carrying
considerable overhanging loads with no better connection. Even wide
sidewalks of bridges sometimes have tension connections on rivet heads.
While this is not to be commended, it is a demonstration of the ability
to take bending which might be relied on, if structural design were on
as loose a basis as reinforced concrete.

Mr. Chapman assumes that stirrups are anchored at each end, and Fig. 3
shows a small hook to effect this anchorage. He does not show how
vertical stirrups can relieve a beam of the shear between two of these
stirrups.

The criticism the writer would make of Figs. 5 and 6, is that there is
not enough concrete in the stem of the T to grip the amount of steel
used, and the steel must be gripped in that stem, because it does not
run to the support or beyond it for anchorage. Steel members in a bridge
may be designed in violation of many of the requirements of
specifications, such as the maximum spacing of rivets, size of lattice
bars, etc.; the bridge will not necessarily fail or show weakness as
soon as it is put into service, but it is faulty and weak just the same.

Mr. Chapman says: "The practical engineer does not find * * * that the
negative moment is double the positive moment, because he considers the
live load either on one span only, or on alternate spans." It is just in
such methods that the "practical engineer" is inconsistent. If he is
going to consider the beams as continuous, he should find the full
continuous beam moment and provide for it. It is just this disposition
to take an advantage wherever one can be taken, without giving proper
consideration to the disadvantage entailed, which is condemned in the
paper. The "practical engineer" will reduce his bending moment in the
beam by a large fraction, because of continuity, but he will not
reinforce over the supports for full continuity. Reinforcement for full
continuity was not recommended, but it was intimated that this is the
only consistent method, if advantage is taken of continuity in reducing
the principal bending moment.

Mr. Chapman says that an arch should not be used where the abutments are
unstable. Unstable is a relative and indefinite word. If he means that
abutments for arches should never be on anything but rock, even such a
foundation is only quite stable when the abutment has a vertical rock
face to take horizontal thrusts. If arches could be built only under
such conditions, few of them would be built. Some settlement is to be
expected in almost any soil, and because of horizontal thrusts there is
also a tendency for arch abutments to rotate. It is this tendency which
opens up cracks in spandrels of arches, and makes the assumption of a
fixed tangent at the springing line, commonly made by the elastic
theorist, absolute foolishness.

Mr. Beyer has developed a novel explanation of the way stirrups act, but
it is one which is scarcely likely to meet with more serious
consideration than the steel girder to which he refers, which has
neither web plate nor diagonals, but only verticals connecting the top
and bottom flanges. This style of girder has been considered by American
engineers rather as a curiosity, if not a monstrosity. If vertical
stirrups acted to reinforce little vertical cantilevers, there would
have to be a large number of them, so that each little segment of the
beam would be insured reinforcement.

The writer is utterly at a loss to know what Professor Ostrup means by
his first few paragraphs. He says that in the first point two designs
are mentioned and a third condemned. The second design, whatever it is,
he lays at the writer's door in these words: "The author's second design
is an invention of his own, which the Profession at large is invited to
adopt." In the first point sharp bends in reinforcing rods are condemned
and curves recommended. Absolutely nothing is said of "a reinforced
concrete beam arranged in the shape of a rod, with separate concrete
blocks placed on top of it without being connected."

In reply to Professor Ostrup, it should be stated that the purpose of
the paper is not to belittle the importance of the adhesion or grip of
concrete on steel, but to point out that the wonderful things this grip
is supposed to do, as exhibited by current design, will not stand the
test of analysis.

Professor Ostrup has shown a new phase of the stress in shear rods. He
says they are in bending between the centers of compressive resultants.
We have been told in books and reports that these rods are in stress of
some kind, which is measured by the sectional area of the rod. No hint
has been given of designing stirrups for bending. If these rods are not
in shear, as stated by Professor Ostrup, how can they be in bending in
any such fashion as that indicated in Fig. 12?

Professor Ostrup's analysis, by which he attempts to justify stirrups
and to show that vertical stirrups are preferable, merely treats of
local distribution of stress from short rods into concrete. Apparently,
it would work the same if the stirrups merely touched the tension rod.
His analysis ignores the vital question of what possible aid the stirrup
can be in relieving the concrete between stirrups of the shear of the
beam.

The juggling of bending moments in beams is not compensating. The
following is a concrete example. Some beams of a span of about 20 ft.,
were framed into double girders at the columns. The beams were
calculated as partly continuous, though they were separated at their
ends by about 1-1/2 or 2 ft., the space between the girders. The beams
had 1-1/8-in. tension rods in the bottom. At the supports a short
1/4-in. rod was used near the top of the beam for continuity. Does this
need any comment? It was not the work of a novice or of an inexperienced
builder.

Professor Ostrup's remarks about the shifting of the neutral axis of a
beam and of the pressure line of an arch are based on theory which is
grounded in impossible assumptions. The materials dealt with do not
justify these assumptions or the hair-splitting theory based thereon.
His platitudes about the danger of misplacing reinforcement in an arch
are hardly warranted. If the depth and reinforcement of an arch ring are
added to, as the inelastic, hinge-end theory would dictate, as against
the elastic theory, it will strengthen the arch just as surely as it
would strengthen a plate girder to thicken the web and flange angles.

The writer's complaint is not that the theories of reinforced concrete
are not fully developed. They are developed too highly, developed out of
all comparison with the materials dealt with. It is just because
reinforced concrete structures are being built in increasing numbers
that it behooves engineers to inject some rationality (not high-strung
theory) into their designs, and drop the idea that "whatever is is
right."

Mr. Porter has much to say about U-bars. He states that they are useful
in holding the tension bars in place and in tying the slab to the stem
of a T-beam. These are legitimate functions for little loose rods; but
why call them shear rods and make believe that they take the shear of a
beam? As to stirrups acting as dowel pins, the writer has already
referred to this subject. Answering a query by Mr. Porter, it may be
stated that what would counteract the horizontal cleaving force in a
beam is one or more rods curved up to the upper part of the beam and
anchored at the support or run into the next span. Strangely enough, Mr.
Porter commends this very thing, as advocated in the paper. The
excellent results shown by the test referred to by him can well be
contrasted with some of the writer's tests. This floor was designed for
250 lb. per sq. ft. When that load was placed on it, the deflection was
more than 1 in. in a span of 20 ft. No rods were curved up and run over
the supports. It was a stirrup job.

Mr. Porter intimates that the correct reinforced concrete column may be
on lines of concrete mixed with nails or wires. There is no doubt but
that such concrete would be strong in compression for the reason that it
is strong in tension, but a column needs some unifying element which is
continuous. A reinforced column needs longitudinal rods, but their
office is to take tension; they should not be considered as taking
compression.

Mr. Goodrich makes this startling remark: "It is a well-known fact that
the bottom chords in queen-post trusses are useless, as far as
resistance to tension is concerned." The writer cannot think that he
means by this that, for example, a purlin made up of a 3 by 2-in. angle
and a 5/8-in. hog-rod would be just as good with the rod omitted. If
queen-post trusses are useless, some hundreds of thousands of hog-rods
in freight cars could be dispensed with.

Mr. Goodrich misunderstands the reference to the "only rational and only
efficient design possible." The statement is that a design which would
be adopted, if slabs were suspended on rods, is the only rational and
the only efficient design possible. If the counterfort of a retaining
wall were a bracket on the upper side of a horizontal slab projecting
out from a vertical wall, and all were above ground, the horizontal slab
being heavily loaded, it is doubtful whether any engineer would think of
using any other scheme than diagonal rods running from slab to wall and
anchored into each. This is exactly the condition in this shape of
retaining wall, except that it is underground.

Mr. Goodrich says that the writer's reasoning as to the sixth point is
almost wholly facetious and that concrete is very strong in pure shear.
The joke, however, is on the experimenters who have reported concrete
very strong in shear. They have failed to point out that, in every case
where great strength in shear is manifested, the concrete is confined
laterally or under heavy compression normal to the sheared plane.
Stirrups do not confine concrete in a direction normal to the sheared
plane, and they do not increase the compression. A large number of
stirrups laid in herring-bone fashion would confine the concrete across
diagonal planes, but such a design would be wasteful, and the common
method of spacing the stirrups would not suggest their office in this
capacity.

As to the writer's statements regarding the tests in Bulletin No. 29 of
the University of Illinois being misleading, he quotes from that
bulletin as follows:

     "Until the concrete web has failed in diagonal tension and diagonal
     cracks have formed there must be little vertical deformation at the
     plane of the stirrups, so little that not much stress can have
     developed in the stirrups." * * * "It is evident, then, that until
     the concrete web fails in diagonal tension little stress is taken
     by the stirrups." * * * "It seems evident from the tests that the
     stirrups did not take much stress until after the formation of
     diagonal cracks." * * * "It seems evident that there is very little
     elongation in stirrups until the first diagonal crack forms, and
     hence that up to this point the concrete takes practically all the
     diagonal tension." * * * "Stirrups do not come into action, at
     least not to any great extent, until the diagonal crack has
     formed."

In view of these quotations, the misleading part of the reference to the
tests and their conclusion is not so evident.

The practical tests on beams with suspension rods in them, referred to
by Mr. Porter, show entirely different results from those mentioned by
Mr. Goodrich as being made by Mörsch. Tests on beams of this sort, which
are available in America, seem to show excellent results.

Mr. Goodrich is somewhat unjust in attributing failures to designs which
are practically in accordance with the suggestions under Point Seven. In
Point Seven the juggling of bending moments is condemned--it is
condemnation of methods of calculating. Point Seven recommends
reinforcing a beam for its simple beam moment. This is the greatest
bending it could possibly receive, and it is inconceivable that failure
could be due to this suggestion. Point Seven recommends a reasonable
reinforcement over the support. This is a matter for the judgment of the
designer or a rule in specifications. Failure could scarcely be
attributed to this. It is the writer's practice to use reinforcement
equal to one-half of the main reinforcement of the beam across the
support; it is also his practice to curve up a part of the beam
reinforcement and run it into the next span in all beams needing
reinforcement for shear; but the paper was not intended to be a treatise
on, nor yet a general discussion of, reinforced concrete design.

Mr. Goodrich characterizes the writer's method of calculating reinforced
concrete chimneys as crude. It is not any more crude than concrete. The
ultra-theoretic methods are just about as appropriate as calculations of
the area of a circle to hundredths of a square inch from a paced-off
diameter. The same may be said of deflection calculations.

Mr. Goodrich has also appreciated the writer's spirit in presenting this
paper. Attention to details of construction has placed structural steel
designing on the high plane on which it stands. Reinforced concrete
needs the same careful working out of details before it can claim the
same recognition. It also needs some simplification of formulas. Witness
the intricate column formulas for steelwork which have been buried, and
even now some of the complex beam formulas for reinforced concrete have
passed away.

Major Sewell, in his discussion of the first point, seems to object
solely to the angle of the bent-up portion of the rod. This angle could
have been much less, without affecting the essence of the writer's
remarks. Of course, the resultant, _b_, would have been less, but this
would not create a queen-post at the sharp bend of the bar. Major Sewell
says that he "does not remember ever to have seen just the type of
construction shown in Fig. 1, either used or recommended." This type of
beam might be called a standard. It is almost the insignia of a
reinforced concrete expert. A little farther on Major Sewell says that
four beams tested at the University of Illinois were about as nearly
like Fig. 1 as anything he has ever seen in actual practice. He is the
only one who has yet accused the writer of inventing this beam.

If Major Sewell's statement that he has never seen the second point
exemplified simply means that he has never seen an example of the bar
bent up at the identical angle given in the paper, his criticism has not
much weight.

Major Sewell's comment on the retaining wall begs the question. Specific
references to examples have been given in which the rods of a
counterfort are not anchored into the slabs that they hold by tension,
save by a few inches of embedment; an analysis has also been cited in
which the counterfort is considered as a beam, and ties in the great
weight of the slab with a few "shear rods," ignoring the anchorage of
either horizontal, vertical, or diagonal rods. It is not enough that
books state that rods in tension need anchorage. They should not show
examples of rods that are in pure tension and state that they are merely
thrown in for shear. Transverse rods from the stem to the flange of a
T-beam, tie the whole together; they prevent cracking, and thereby allow
the shearing strength of the concrete to act. It is not necessary to
count the rods in shear.

Major Sewell's comparison of a stirrup system and a riveted truss is not
logical. The verticals and diagonals of a riveted truss have gusset
plates which connect symmetrically with the top chord. One line of
rivets or a pin in the center line of the top chord could be used as a
connection, and this connection would be complete. To distribute rivets
above and below the center line of the top chord does not alter the
essential fact that the connection of the web members is complete at the
center of the top chord. The case of stirrups is quite different. Above
the centroid of compression there is nothing but a trifling amount of
embedment of the stirrup. If 1/2-in. stirrups were used in an 18-in.
beam, assuming that 30 diameters were enough for anchorage, the centroid
of compression would be, say, 3 in. below the top of the beam, the
middle point of the stirrup's anchorage would be about 8 in., and the
point of full anchorage would be about 16 in. The neutral axis would
come somewhere between. These are not unusual proportions. Analogy with
a riveted truss fails; even the anchorage above the neutral axis is far
from realization.

Major Sewell refers to shallow bridge stringers and the possibility of
failure at connections by continuity or deflection. Structural engineers
take care of this, not by reinforcement for continuity but by ample
provision for the full bending moment in the stringer and by ample
depth. Provision for both the full bending moment and the ample depth
reduces the possibilities of deflection at the floor-beams.

Major Sewell seems also to have assumed that the paper was a general
discussion on reinforced concrete design. The idea in pointing out that
a column having longitudinal rods in it may be weaker than a plain
concrete column was not to exalt the plain concrete column but to
degrade the other. A plain concrete column of any slenderness would
manifestly be a gross error. If it can be shown that one having only
longitudinal rods may be as bad, or worse, instead of being greatly
strengthened by these rods, a large amount of life and property may be
saved.

A partial reply to Mr. Thompson's discussion will be found in the
writer's response to Mr. Mensch. The fault with Mr. Thompson's
conclusions lies in the error of basing them on averages. Average
results of one class are of little meaning or value when there is a wide
variation between the extremes. In the tests of both the concrete-steel
and the plain concrete which Mr. Thompson averages there are wide
variations. In the tests made at the University of Illinois there is a
difference of almost 100% between the minimum and maximum results in
both concrete-steel and plain concrete columns.

Average results, for a comparison between two classes, can mean little
when there is a large overlap in the individual results, unless there is
a large number of tests. In the seventeen tests made at the University
of Illinois, which Mr. Thompson averages, the overlap is so great that
the maximum of the plain columns is nearly 50% greater than the minimum
of the concrete-steel columns.

If the two lowest tests in plain concrete and the two highest in
concrete-steel had not been made, the average would be in favor of the
plain concrete by nearly as much as Mr. Thompson's average now favors
the concrete-steel columns. Further, if these four tests be eliminated,
only three of the concrete-steel columns are higher than the plain
concrete. So much for the value of averages and the conclusions drawn
therefrom.

It is idle to draw any conclusions from such juggling of figures, except
that the addition of longitudinal steel rods is altogether
problematical. It may lessen the compressive strength of a concrete
column. Slender rods in such a column cannot be said to reinforce it,
for the reason that careful tests have been recorded in which columns of
concrete-steel were weaker than those of plain concrete.

In the averages of the Minneapolis tests Mr. Thompson has compared the
results on two plain concrete columns with the average of tests on an
indiscriminate lot of hooped and banded columns. This method of boosting
the average shows anything but "critical examination" on his part.

Mr. Thompson, on the subject of Mr. Withey's tests, compares plain
concrete of square cross-section with concrete-steel of octagonal
section. As stated before, this is not a proper comparison. In a fragile
material like concrete the corners spall off under a compressive load,
and the square section will not show up as well as an octagonal or round
one.

Mr. Thompson's contention, regarding the Minneapolis tests, that the
concrete outside of the hoops should not be considered, is ridiculous.
If longitudinal rods reinforce a concrete column, why is it necessary to
imagine that a large part of the concrete must be assumed to be
non-existent in order to make this reinforcement manifest? An imaginary
core could be assumed in a plain concrete column and any desired results
could be obtained. Furthermore, a properly hooped column does not enter
into this discussion, as the proposition is that slender longitudinal
rods do not reinforce a concrete column; if hoops are recognized, the
column does not come under this proposition.

Further, the proposition in the writer's fifteenth point does not say
that the steel takes no part of the compression of a column. Mr.
Thompson's laborious explanation of the fact that the steel receives a
share of the load is needless. There is no doubt that the steel receives
a share of the load--in fact, too great a share. This is the secret of
the weakness of a concrete column containing slender rods. The concrete
shrinks, the steel is put under initial compression, the load comes more
heavily on the steel rods than on the concrete, and thus produces a most
absurd element of construction--a column of slender steel rods held
laterally by a weak material--concrete. This is the secret of nearly all
the great wrecks in reinforced concrete: A building in Philadelphia, a
reservoir in Madrid, a factory in Rochester, a hotel in California. All
these had columns with longitudinal rods; all were extensive
failures--probably the worst on record; not one of them could possibly
have failed as it did if the columns had been strong and tough. Why use
a microscope and search through carefully arranged averages of tests on
nursery columns, with exact central loading, to find some advantage in
columns of this class, when actual experience is publishing in bold type
the tremendously important fact that these columns are utterly
untrustworthy?

It is refreshing to note that not one of the writer's critics attempts
to defend the quoted ultimate strength of a reinforced concrete column.
Even Mr. Thompson acknowledges that it is not right. All of which, in
view of the high authority with whom it originated, and the wide use it
has been put to by the use of the scissors, would indicate that at last
there is some sign of movement toward sound engineering in reinforced
concrete.

In conclusion it might be pointed out that this discussion has brought
out strong commendation for each of the sixteen indictments. It has also
brought out vigorous defense of each of them. This fact alone would seem
to justify its title. A paper in a similar strain, made up of
indictments against common practices in structural steel design,
published in _Engineering News_ some years ago, did not bring out a
single response. While practice in structural steel may often be faulty,
methods of analysis are well understood, and are accepted with little
question.

FOOTNOTES:

[Footnote E: _Transactions_, Am. Soc. C. E., Vol. LXVI, p. 431.]

[Footnote F: _Loc. cit._, p. 448.]

[Footnote G: _Engineering News_, Dec. 3d, 1908.]

[Footnote H: _Journal_ of the Western Society of Engineers, 1905.]

[Footnote I: Tests made for C.A.P. Turner, by Mason D. Pratt, M. Am.
Soc. C. E.]

[Footnote J: _Transactions_, Am. Soc. C. E., Vol. LVI, p. 343.]

[Footnote K: Bulletin No. 28, University of Illinois.]

[Footnote L: Bulletin No. 12, University of Illinois, Table VI, page
27.]

[Footnote M: Professeur de Stabilité a l'Université de Louvain.]

[Footnote N: A translation of Professor Vierendeel's theory may be found
in _Beton und Eisen_, Vols. X, XI, and XII, 1907.]

[Footnote O: _Cement_, March, 1910, p. 343; and _Concrete Engineering_,
May, 1910, p. 113.]

[Footnote P: The correct figures from the _Bulletin_ are 1,577 lb.]

[Footnote Q: _Engineering News_, January 7th, 1909, p. 20.]

[Footnote R: For fuller treatment, see the writer's discussion in
_Transactions_, Am. Soc. C. E., Vol. LXI, p. 46.]

[Footnote S: See "Tests of Metals," U.S.A., 1905, p. 344.]

[Footnote T: _The Engineering Record_, August 17th, 1907.]

[Footnote U: "The Design of Walls, Bins and Elevators."]

[Footnote V: _Engineering News_, September 28th, 1905.]

[Footnote W: _The Engineering Record_, June 26th, 1909.]

[Footnote X: _Railroad Age Gazette_, March 26th, 1909.]

[Footnote Y: _Engineering News_, April 9th, 1896.]

[Footnote Z: "Structural Engineering: Concrete."]





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