_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?"