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.