JOSEPH WRIGHT, M. AM. SOC. C. E. (by letter).--If, as is expected, Mr.
Godfrey's paper serves to attract attention to the glaring
inconsistencies commonly practiced in reinforced concrete designs, and
particularly to the careless detailing of such structures, he will have
accomplished a valuable purpose, and will deserve the gratitude of the
Profession.
No engineer would expect a steel bridge to stand up if the detailing
were left to the judgment or convenience of the mechanics of the shop,
yet in many reinforced concrete designs but little more thought is given
to the connections and continuity of the steel than if it were an
unimportant element of the structure. Such examples, as illustrated by
the retaining wall in Fig. 2, are common, the reinforcing bars of the
counterfort being simply hooked by a 4-in. U-bend around those of the
floor and wall slabs, and penetrating the latter only from 8 to 12 in.
The writer can cite an example which is still worse--that of a T-wall,
16 ft. high, in which the vertical reinforcement of the wall slab
consisted of 3/4-in. bars, spaced 6 in. apart. The wall slab was 8 in.
thick at the top and only 10 in. at the bottom, yet the 3/4-in. vertical
bars penetrated the floor slab only 8 in., and were simply hooked around
its lower horizontal bars by 4-in. U-bends. Amazing as it may appear,
this structure was designed by an engineer who is well versed in the
theories of reinforced concrete design. These are only two examples from
a long list which might be cited to illustrate the carelessness often
exhibited by engineers in detailing reinforced concrete structures.
In reinforced concrete work the detailer has often felt the need of some
simple and efficient means of attaching one bar to another, but, in its
absence, it is inexcusable that he should resort to such makeshifts as
are commonly used. A simple U-hook on the end of a bar will develop only
a small part of the strength of the bar, and, of course, should not be
relied on where the depth of penetration is inadequate; and, because of
the necessity of efficient anchorage of the reinforcing bars where one
member of a structure unites with another, it is believed that in some
instances economy might be subserved by the use of shop shapes and shop
connections in steel, instead of the ordinary reinforcing bars. Such
cases are comparatively few, however, for the material in common use is
readily adapted to the design, in the ordinary engineering structure,
and only requires that its limitations be observed, and that the
designer be as conscientious and consistent in detailing as though he
were designing in steel.
This paper deserves attention, and it is hoped that each point therein
will receive full and free discussion, but its main purport is a plea
for simplicity, consistency, and conservatism in design, with which the
writer is heartily in accord.
S. BENT RUSSELL, M. AM. SOC. C. E. (by letter).--The author has given
expression in a forcible way to feelings possessed no doubt by many
careful designers in the field in question. The paper will serve a
useful purpose in making somewhat clearer the limitations of reinforced
concrete, and may tend to bring about a more economical use of
reinforcing material.
It is safe to say that in steel bridges, as they were designed in the
beginning, weakness was to be found in the connections and details,
rather than in the principal members. In the modern advanced practice of
bridge design the details will be found to have some excess of strength
over the principal members. It is probable that the design of reinforced
concrete structures will take the same general course, and that progress
will be made toward safety in minor details and economy in principal
bars.
Many of the author's points appear to be well taken, especially the
first, the third, and the eighth.
In regard to shear bars, if it is assumed that vertical or inclined bars
add materially to the strength of short deep beams, it can only be
explained by viewing the beam as a framed structure or truss in which
the compression members are of concrete and the tension members of
steel. It is evident that, as generally built, the truss will be found
to be weak in the connections, more particularly, in some cases, in the
connections between the tension and compression members, as mentioned in
the author's first point.
It appears to the writer that this fault may be aggravated in the case
of beams with top reinforcement for compression; this is scarcely
touched on by the author. In such a case the top and bottom chords are
of steel, with a weakly connected web system which, in practice, is
usually composed of stirrup rods looped around the principal bars and
held in position by the concrete which they are supposed to strengthen.
While on this phase of the subject, it may be proper to call attention
to the fact that the Progress Report of the Special Committee on
Concrete and Reinforced Concrete[E] may well be criticised for its scant
attention to the case of beams reinforced on the compression side. No
limitations are specified for the guidance of the designer, but approval
is given to loading the steel with its full share of top-chord
stress.[F]
In certain systems of reinforcement now in use, such as the Kahn and
Cummings systems, the need for connections between the web system and
the chord member is met to some degree, as is generally known. On the
other hand, however, these systems do not provide for such intensity of
pressure on the concrete at the points of connection as must occur by
the author's demonstration in his first point. The author's criticisms
on some other points would also apply to such systems, and it is not
necessary to state that one weak detail will limit the strength of the
truss.
The author has only condemnation for the use of longitudinal rods in
concrete columns (Point 15). It would seem that if the longitudinal bars
are to carry a part of the load they must be supported laterally by the
concrete, and, as before, in the beam, it may be likened to a framed
structure in which the web system is formed of concrete alone, or of a
framework of poorly connected members, and the concrete and steel must
give mutual support in a way not easy to analyze. It is scarcely
surprising that the strength of such a structure is sometimes less than
that shown by concrete alone.
In the Minneapolis tests, quoted by the author, there are certain points
which should be noted, in fairness to columns reinforced longitudinally.
Only four columns thus reinforced failed below the strength shown by
concrete alone, and these were from 52 to 63 days old only, while the
plain concrete was 98 days old. There was nothing to hold the rods in
place in these four columns except the concrete and the circular hoops
surrounding them. On the other hand, all the columns in which the
hooping was hooked around the individual rods showed materially greater
strength than the plain concrete, although perhaps one should be
excepted, as it was 158 days old and showed a strength of only 2,250 lb.
per sq. in., or 12% more than the plain concrete.[G]
In considering a column reinforced with longitudinal rods and hoops, it
is proper to remark that the concrete not confined by the steel ought
not to be counted as aiding the latter in any way, and that,
consequently, the bond of the outside bars is greatly weakened.
In view of these considerations, it may be found economical to give the
steel reinforcement of columns some stiffness of its own by sufficiently
connected lateral bracing. The writer would suggest, further, that in
beams where rods are used in compression a system of web members
sufficiently connected should be provided, so that the strength of the
combined structure would be determinate.
To sum up briefly, columns and short deep beams, especially when the
latter are doubly reinforced, should be designed as framed structures,
and web members should be provided with stronger connections than have
been customary.
J.R. WORCESTER, M. AM. SOC. C. E. (by letter).--This paper is of value
in calling attention to many of the bad practices to be found in
reinforced concrete work, and also in that it gives an opportunity for
discussing certain features of design, about which engineers do not
agree. A free discussion of these features will tend to unify methods.
Several of the author's indictments, however, hit at practices which
were discarded long ago by most designers, and are not recommended by
any good authorities; the implication that they are in general use is
unwarranted.
The first criticism, that of bending rods at a sharp angle, may be said
to be of this nature. Drawings may be made without indicating the curve,
but in practice metal is seldom bent to a sharp angle. It is undoubtedly
true that in every instance a gradual curve is preferable.
The author's second point, that a suitable anchorage is not provided for
bent-up rods at the ends of a beam, may also be said to be a practice
which is not recommended or used in the best designs.
The third point, in reference to the counterforts of retaining walls, is
certainly aimed at a very reprehensible practice which should not be
countenanced by any engineer.
The fourth, fifth, and sixth items bring out the fact that undoubtedly
there has been some confusion in the minds of designers and authors on
the subject of shear in the steel. The author is wholly justified in
criticising the use of the shearing stress in the steel ever being
brought into play in reinforced concrete. Referring to the report of the
Special Committee on Concrete and Reinforced Concrete, on this point, it
seems as if it might have made the intention of the Committee somewhat
clearer had the word, tensile, been inserted in connection with the
stress in the shear reinforcing rods. In considering a beam of
reinforced concrete in which the shearing stresses are really diagonal,
there is compression in one case and tension in another; and, assuming
that the metal must be inserted to resist the tensile portion of this
stress, it is not essential that it should necessarily be wholly
parallel to the tensile stress. Vertical tensile members can prevent the
cracking of the beam by diagonal tension, just as in a Howe truss all
the tensile stresses due to shear are taken in a vertical direction,
while the compressive stresses are carried in the diagonal direction by
the wooden struts. The author seems to overlook the fact, however, that
the reinforced concrete beam differs from the Howe truss in that the
concrete forms a multiple system of diagonal compression members. It is
not necessary that a stirrup at one point should carry all the vertical
tension, as this vertical tension is distributed by the concrete. There
is no doubt about the necessity of providing a suitable anchorage for
the vertical stirrups, and such is definitely required in the
recommendations of the Special Committee.
The cracks which the author refers to as being necessary before the
reinforcing material is brought into action, are just as likely to occur
in the case of the bent-up rods with anchors at the end, advocated by
him. While his method may be a safe one, there is also no question that
a suitable arrangement of vertical reinforcement may be all that is
necessary to make substantial construction.
With reference to the seventh point, namely, methods of calculating
moments, it might be said that it is not generally considered good
practice to reduce the positive moments at the center of a span to the
amount allowable in a beam fully fixed at the end, and if provision is
made for a negative moment over supports sufficient to develop the
stresses involved in complete continuity, there is usually a
considerable margin of safety, from the fact of the lack of possible
fixedness of the beams at the supports. The criticism is evidently aimed
at practice not to be recommended.
As to the eighth point, the necessary width of a beam in order to
transfer, by horizontal shear, the stress delivered to the concrete from
the rods, it might be well worth while for the author to take into
consideration the fact that while the bonding stress is developed to its
full extent near the ends of the beam, it very frequently happens that
only a portion of the total number of rods are left at the bottom, the
others having been bent upward. It may be that the width of a beam would
not be sufficient to carry the maximum bonding stress on the total
number of rods near its center, and yet it may have ample shearing
strength on the horizontal planes. The customary method of determining
the width of the beams so that the maximum horizontal shearing stress
will not be excessive, seems to be a more rational method than that
suggested by Mr. Godfrey.
Referring to the tenth and fourteenth points, it would be interesting to
know whether the author proportions his steel to take the remaining
tension without regard to the elongation possible at the point where it
is located, considering the neutral axis of the section under the
combined stress. Take, for instance, a chimney: If the section is first
considered to be homogeneous material which will carry tension and
compression equally well, and the neutral axis is found under the
combined stresses, the extreme tensile fiber stress on the concrete will
generally be a matter of 100 or 200 lb. Evidently, if steel is inserted
to replace the concrete in tension, the corresponding stress in the
steel cannot be more than from 1,500 to 3,000 lb. per sq. in. If
sufficient steel is provided to keep the unit stress down to the proper
figure, there can be little criticism of the method, but if it is worked
to, say, 16,000 lb. per sq. in., it is evident that the result will be a
different position for the neutral axis, invalidating the calculation
and resulting in a greater stress in compression on the concrete.
L.J. MENSCH, M. AM. SOC. C. E. (by letter).--Much of the poor practice
in reinforced concrete design to which Mr. Godfrey calls attention is
due, in the writer's opinion, to inexperience on the part of the
designer.
It is true, however, that men of high standing, who derided reinforced
concrete only a few years ago, now pose as reinforced concrete experts,
and probably the author has the mistakes of these men in mind.
The questions which he propounds were settled long ago by a great many
tests, made in various countries, by reliable authorities, although the
theoretical side is not as easily answered; but it must be borne in mind
that the stresses involved are mostly secondary, and, even in steel
construction, these are difficult of solution. The stresses in the web
of a deep steel girder are not known, and the web is strengthened by a
liberal number of stiffening angles, which no expert can figure out to a
nicety. The ultimate strength of built-up steel columns is not known,
frequently not even within 30%; still less is known of the strength of
columns consisting of thin steel casings, or of the types used in the
Quebec Bridge. It seems to be impossible to solve the problem
theoretically for the simplest case, but had the designer of that bridge
known of the tests made by Hodgkinson more than 40 years ago, that
accident probably would not have happened.
Practice is always ahead of theory, and the writer claims that, with the
great number of thoroughly reliable tests made in the last 20 years, the
man who is really informed on this subject will not see any reason for
questioning the points brought out by Mr. Godfrey.
The author is right in condemning sharp bends in reinforcing rods.
Experienced men would not think of using them, if only for the reason
that such sharp bends are very expensive, and that there is great
likelihood of breaking the rods, or at least weakening them. Such sharp
bends invite cracks.
Neither is there any question in regard to the advantage of continuing
the bent-up rods over the supports. The author is manifestly wrong in
stating that the reinforcing rods can only receive their increments of
stress when the concrete is in tension. Generally, the contrary happens.
In the ordinary adhesion test, the block of concrete is held by the jaws
of the machine and the rod is pulled out; the concrete is clearly in
compression.
The underside of continuous beams is in compression near the supports,
yet no one will say that steel rods cannot take any stress there. It is
quite surprising to learn that there are engineers who still doubt the
advisability of using bent-up bars in reinforced concrete beams.
Disregarding the very thorough tests made during the last 18 years in
Europe, attention is called to the valuable tests on thirty beams made
by J.J. Harding, M. Am. Soc. C. E., for the Chicago, Milwaukee and St.
Paul Railroad.[H] All the beams were reinforced with about 3/4% of
steel. Those with only straight rods, whether they were plain or
patented bars, gave an average shearing strength of 150 lb. per sq. in.
Those which had one-third of the bars bent up gave an average shearing
strength of 200 lb. per sq. in., and those which had nearly one-half of
the rods bent up gave an average shearing strength of 225 lb. per sq.
in. Where the bent bars were continued over the supports, higher
ultimate values were obtained than where some of the rods were stopped
off near the supports; but in every case bent-up bars showed a greater
carrying capacity than straight rods. The writer knows also of a number
of tests with rods fastened to anchor-plates at the end, but the tests
showed that they had only a slight increase of strength over straight
rods, and certainly made a poorer showing than bent-up bars. The use of
such threaded bars would increase materially the cost of construction,
as well as the time of erection.
The writer confesses that he never saw or heard of such poor practices
as mentioned in the author's third point. On the other hand, the
proposed design of counterforts in retaining walls would not only be
very expensive and difficult to install, but would also be a decided
step backward in mechanics. This proposition recalls the trusses used
before the introduction of the Fink truss, in which the load from the
upper chord was transmitted by separate members directly to the
abutments, the inventor probably going on the principle that the
shortest way is the best. There are in the United States many hundreds
of rectangular water tanks. Are these held by any such devices? And as
they are not thus held, and inasmuch as there is no doubt that they must
carry the stress when filled with water, it is clear that, as long as
the rods from the sides are strong enough to carry the tension and are
bent with a liberal radius into the front wall and extended far enough
to form a good anchorage, the connection will not be broken. The same
applies to retaining walls. It would take up too much time to prove that
the counterfort acts really as a beam, although the forces acting on it
are not as easily found as those in a common beam.
The writer does not quite understand the author's reference to shear
rods. Possibly he means the longitudinal reinforcement, which it seems
is sometimes calculated to carry 10,000 lb. per sq. in. in shear. The
writer never heard of such a practice.
In regard to stirrups, Mr. Godfrey seems to be in doubt. They certainly
do not act as the rivets of a plate girder, nor as the vertical rods of
a Howe truss. They are best compared with the dowel pins and bolts of a
compound wooden beam. The writer has seen tests made on compound
concrete beams separated by copper plates and connected only by
stirrups, and the strength of the combination was nearly the same as
that of beams made in one piece.
Stirrups do not add much to the strength of the beams where bent bars
are used, but the majority of tests show a great increase of strength
where only straight reinforcing bars are used. Stirrups are safeguards
against poor concrete and poor workmanship, and form a good connection
where concreting is interrupted through inclemency of weather or other
causes. They absolutely prevent shrinkage cracks between the stem and
the flange of T-beams, and the separation of the stem and slab in case
of serious fires. For the latter reason, the writer condemns the use of
simple U-bars, and arranges all his stirrups so that they extend from
6 to 12 in. into the slabs. Engineers are warned not to follow the
author's advice with regard to the omission of stirrups, but to use
plenty of them in their designs, or sooner or later they will thoroughly
repent it.
In regard to bending moments in continuous beams, the writer wishes to
call attention to the fact that at least 99% of all reinforced
structures are calculated with a reduction of 25% of the bending moment
in the center, which requires only 20% of the ordinary bending moment of
a freely supported beam at the supports. There may be some engineers who
calculate a reduction of 33%; there are still some ultra-confident men,
of little experience, who compute a reduction of 50%; but, inasmuch as
most designers calculate with a reduction of only 25%, too great a
factor of safety does not result, nor have any failures been observed on
that account.
In the case of slabs which are uniformly loaded by earth or water
pressure, the bending moments are regularly taken as (_w_ _l^{2}_)/24 in
the center and (_w_ _l^{2}_)/12 at the supports. The writer never
observed any failure of continuous beams over the supports, although he
has often noticed failures in the supporting columns directly under the
beams, where these columns are light in comparison with the beams.
Failure of slabs over the supports is common, and therefore the writer
always places extra rods over the supports near the top surface.
The width of the beams which Mr. Godfrey derives from his simple rule,
that is, the width equals the sum of the peripheries of the reinforcing
rods, is not upheld by theory or practice. In the first place, this
width would depend on the kind of rods used. If a beam is reinforced by
three 7/8-in. round bars, the width, according to his formula, would be
8.2 in. If the beam is reinforced by six 5/8-in. bars which have the
same sectional area as the three 7/8-in. bars, then the width should be
12 in., which is ridiculous and does not correspond with tests, which
would show rather a better behavior for the six bars than for the three
larger bars in a beam of the same width.
It is surprising to learn that there are engineers who still advocate
such a width of the stem of T-beams that the favorable influence of the
slab may be dispensed with, although there were many who did this 10 or
12 years ago.
It certainly can be laid down as an axiom that the man who uses
complicated formulas has never had much opportunity to design or build
in reinforced concrete, as the design alone might be more expensive than
the difference in cost between concrete and structural steel work.
The author attacks the application of the elastic theory to reinforced
concrete arches. He evidently has not made very many designs in which he
used the elastic theory, or he would have found that the abutments need
be only from three to four times thicker than the crown of the arch
(and, therefore, their moments of inertia from 27 to 64 times greater),
when the deformation of the abutments becomes negligible in the elastic
equations. Certainly, the elastic theory gives a better guess in regard
to the location of the line of pressure than any guess made without its
use. The elastic theory was fully proved for arches by the remarkable
tests, made in 1897 by the Austrian Society of Engineers and Architects,
on full-sized arches of 70-ft. span, and the observed deflections and
lateral deformations agreed exactly with the figured deformation.
Tests on full-sized arches also showed that the deformations caused by
temperature changes agree with the elastic theory, but are not as great
for the whole mass of the arch as is commonly assumed. The elastic
theory enables one to calculate arches much more quickly than any
graphical or guess method yet proposed.
Hooped columns are a patented construction which no one has the right to
use without license or instructions from M. Considère, who clearly
states that his formulas are correct only for rich concrete and for
proper percentages of helical and longitudinal reinforcement, which
latter must have a small spacing, in order to prevent the deformation of
the core between the hoops. With these limitations his formulas are
correct.
Mr. Godfrey brings up some erratic column tests, and seems to have no
confidence in reinforced concrete columns. The majority of column tests,
however, show an increase of strength by longitudinal reinforcement. In
good concrete the longitudinal reinforcement may not be very effective
or very economical, but it safeguards the strength in poorly made
concrete, and is absolutely necessary on account of the bending stresses
set up in such columns, due to the monolithic character of reinforced
concrete work.
Mr. Godfrey does not seem to be familiar with the tests made by good
authorities on square slabs of reinforced concrete and of cast iron,
which latter material is also deficient in tensile strength. These tests
prove quite conclusively that the maximum bending moment per linear foot
may be calculated by the formulas, (_w_ _l^{2}_)/32 or (_w_ _l^{2}_)/20,
according to the degree of fixture of the slabs at the four sides.
Inasmuch as fixed ends are rarely obtained in practice, the formula,
(_w_ _l^{2}_)/24, is generally adopted, and the writer cannot see any
reason to confuse the subject by the introduction of a new method of
calculation.
WALTER W. CLIFFORD, JUN. AM. SOC. C. E. (by letter).--Some of Mr.
Godfrey's criticisms of reinforced concrete practice do not seem to be
well taken, and the writer begs to call attention to a few points which
seem to be weak. In Fig. 1, the author objects to the use of diagonal
bars for the reason that, if the diagonal reinforcement is stressed to
the allowable limit, these bars bring the bearing on the concrete, at
the point where the diagonal joins the longitudinal reinforcement, above
a safe value. The concrete at the point of juncture must give, to some
extent, and this would distribute the bearing over a considerable length
of rod. In some forms of patented reinforcement an additional safeguard
is furnished by making the diagonals of flat straps. The stress in the
rods at this point, moreover, is not generally the maximum allowable
stress, for considerable is taken out of the rod by adhesion between the
point of maximum stress and that of juncture.
Mr. Godfrey wishes to remedy this by replacing the diagonals by rods
curved to a radius of from twenty to thirty times their diameter. In
common cases this radius will be about equal to the depth of the beam.
Let this be assumed to be true. It cannot be assumed that these rods
take any appreciable vertical shear until their slope is 30° from the
horizontal, for before this the tension in the rod would be more than
twice the shear which causes it. Therefore, these curved rods, assuming
them to be of sufficient size to take, as a vertical component, the
shear on any vertical plane between the point where it slopes 30° and
its point of maximum slope, would need to be spaced at, approximately,
one-half the depth of the beam. Straight rods of equivalent strength, at
45° with the axis of the beam, at this same spacing (which would be
ample), would be 10% less in length.
Mr. Godfrey states:
"Of course a reinforcing rod in a concrete beam receives its stress
by increments imparted by the grip of the concrete; but these
increments can only be imparted where the tendency of the concrete
is to stretch."
He then overlooks the fact that at the end of a beam, such as he has
shown, the maximum tension is diagonal, and at the neutral axis, not at
the bottom; and the rod is in the best position to resist failure on the
plane, _AB_, if its end is sufficiently well anchored. That this rod
should be anchored is, as he states, undoubtedly so, but his implied
objection to a bent end, as opposed to a nut, seems to the writer to be
unfounded. In some recent tests, on rods bent at right angles, at a
point 5 diameters distant from the end, and with a concrete backing,
stress was developed equal to the bond stress on a straight rod embedded
for a length of about 30 diameters, and approximately equal to the
elastic limit of the rod, which, for reinforcing purposes, is its
ultimate stress.
Concerning the vertical stirrups to which Mr. Godfrey refers, there is
no doubt that they strengthen beams against failure by diagonal tension
or, as more commonly known, shear failures. That they are not effective
in the beam as built is plain, for, if one considers a vertical plane
between the stirrups, the concrete must resist the shear on this plane,
unless dependence is placed on that in the longitudinal reinforcement.
This, the author states, is often done, but the practice is unknown to
the writer, who does not consider it of any value; certainly the
stirrups cannot aid.
Suppose, however, that the diagonal tension is above the ultimate stress
for the concrete, failure of the concrete will then occur on planes
perpendicular to the line of maximum tension, approximately 45° at the
end of the beam. If the stirrups are spaced close enough, however, and
are of sufficient strength so that these planes of failure all cut
enough steel to take as tension the vertical shear on the plane, then
these cracks will be very minute and will be distributed, as is the case
in the center of the lower part of the beam. These stirrups will then
take as tension the vertical shear on any plane, and hold the beam
together, so that the friction on these planes will keep up the strength
of the concrete in horizontal shear. The concrete at the end of a simple
beam is better able to take horizontal shear than vertical, because the
compression on a horizontal plane is greater than that on a vertical
plane. This idea concerning the action of stirrups falls under the ban
of Mr. Godfrey's statement, that any member which "cannot act until
failure has started, is not a proper element of design," but this is not
necessarily true. For example, Mr. Godfrey says "the steel in the
tension side of the beam should be considered as taking all the
tension." This is undoubtedly true, but it cannot take place until the
concrete has failed in tension at this point. If used, vertical tension
members should be considered as taking all the vertical shear, and, as
Mr. Godfrey states, they should certainly have their ends anchored so as
to develop the strength for which they have been calculated.
The writer considers diagonal reinforcement to be the best for shear,
and it should be used, especially in all cases of "unit" reinforcement;
but, in some cases, stirrups can and do answer in the manner suggested;
and, for reasons of practical construction, are sometimes best with
"loose rod" reinforcement.
J.C. MEEM, M. AM. SOC. C. E. (by letter).--The writer believes that
there are some very interesting points in the author's somewhat
iconoclastic paper which are worthy of careful study, and, if it be
shown that he is right in most of, or even in any of, his assumptions, a
further expression of approval is due to him. Few engineers have the
time to show fully, by a process of _reductio ad absurdum_, that all the
author's points are, or are not, well considered or well founded, but
the writer desires to say that he has read this paper carefully, and
believes that its fundamental principles are well grounded. Further, he
believes that intricate mathematical formulas have no place in practice.
This is particularly true where these elaborate mathematical
calculations are founded on assumptions which are never found in
practice or experiment, and which, even in theory, are extremely
doubtful, and certainly are not possible within those limits of safety
wherein the engineer is compelled to work.
The writer disagrees with the author in one essential point, however,
and that is in the wholesale indictment of special reinforcement, such
as stirrups, shear rods, etc. In the ordinary way in which these rods
are used, they have no practical value, and their theoretical value is
found only when the structure is stressed beyond its safe limits;
nevertheless, occasions may arise when they have a definite practical
value, if properly designed and placed, and, therefore, they should not
be discriminated against absolutely.
Quoting the author, that "destructive criticism is of no value unless it
offers something in its place," and in connection with the author's
tenth point, the writer offers the following formula which he has always
used in conjunction with the design of reinforced concrete slabs and
beams. It is based on the formula for rectangular wooden beams, and
assumes that the beam is designed on the principle that concrete in
tension is as strong as that in compression, with the understanding that
sufficient steel shall be placed on the tension side to make this true,
thus fixing the neutral axis, as the author suggests, in the middle of
the depth, that is, _M_ = (1/6)_b d_^{2} _S_, _M_, of course, being the
bending moment, and _b_ and _d_, the breadth and depth, in inches. _S_
is usually taken at from 400 to 600 lb., according to the conditions. In
order to obtain the steel necessary to give the proper tensile strength
to correspond with the compression side, the compression and tension
areas of the beam are equated, that is
1 2 _d_
---- _b_ _d_ _S_ = _a_ × ( ----- - _x_ ) × _S_ ,
12 2 II II
where
_a_ = the area of steel per linear foot,
_x_{II}_ = the distance from the center of the steel to the outer
fiber, and
_S_{II}_ = the strength of the steel in tension.
Then for a beam, 12 in. wide,
2 _d_
_d_ _S_ = _a_ _S_ ( ----- - _x_ ) ,
II 2 II
or
2
_d_ _S_
_a_ = --------------------- .
_d_
_S_ ( ----- - _x_ )
II 2 II
Carrying this to its conclusion, we have, for example, in a beam 12 in.
deep and 12 in. wide,
_S_ = 500,
_S_{II}_ = 15,000,
_x_{II}_ = 2-1/2 in.
_a_ = 1.37 sq. in. per ft.
The writer has used this formula very extensively, in calculating new
work and also in checking other designs built or to be built, and he
believes its results are absolutely safe. There is the further fact to
its credit, that its simplicity bars very largely the possibility of
error from its use. He sees no reason to introduce further complications
into such a formula, when actual tests will show results varying more
widely than is shown by a comparison between this simple formula and
many more complicated ones.
GEORGE H. MYERS, JUN. AM. SOC. C. E. (by letter).--This paper brings out
a number of interesting points, but that which strikes the writer most
forcibly is the tenth, in regard to elaborate theories and complicated
formulas for beams and slabs. The author's stand for simplicity in this
regard is well taken. A formula for the design of beams and slabs need
not be long or complicated in any respect. It can easily be obtained
from the well-known fact that the moment at any point divided by the
distance between the center of compression and the center of tension at
that point gives the tension (or compression) in the beam.
The writer would place the neutral axis from 0.42 to 0.45 of the
effective depth of the beam from the compression side rather than at the
center, as Mr. Godfrey suggests. This higher position of the neutral
axis is the one more generally shown by tests of beams. It gives the
formula _M_ = 0.86 _d_ _As_ _f_, or _M_ = 0.85 _d_ _As_ _f_, which the
writer believes is more accurate than _M_ = 5/6 _d_ _As_ _f_, or
0.83-1/3 _d_ _As_ _f_, which would result if the neutral axis were taken
at the center of the beam.
_d_ = depth of the beam from the compression side to the center
of the steel;
_As_ = the area of the steel;
and _f_ = the allowable stress per square inch in the steel.
The difference, however, is very slight, the results from the two
formulas being proportional to the two factors, 83-1/3 and 85 or 86.
This formula gives the area of steel required for the moment. The
percentage of steel to be used can easily be obtained from the allowable
stresses in the concrete and the steel, and the dimensions of the beam
can be obtained in the simplest manner. This formula is used with great
success by one of the largest firms manufacturing reinforcing materials
and designing concrete structures. It is well-known to the Profession,
and the reason for using any other method, involving the Greek alphabet
and many assumptions, is unknown to the writer. The only thing to
assume--if it can be called assuming when there are so many tests to
locate it--is the position of the neutral axis. A slight difference in
this assumption affects the resulting design very little, and is
inappreciable, from a practical point of view. It can be safely said
that the neutral axis is at, or a little above, the center of the beam.
Further, it would seem that the criticism to the effect that the initial
stress in the concrete is neglected is devoid of weight. As far as the
designer is concerned, the initial stress is allowed for. The values for
the stresses used in design are obtained from tests on blocks of
concrete which have gone through the process of setting. Whatever
initial stress exists in concrete due to this process of setting exists
also in these blocks when they are tested. The value of the breaking
load on concrete given by any outside measuring device used in these
tests, is the value of that stress over and above this initial stress.
It is this value with which we work. It would seem that, if the initial
stress is neglected in arriving at a safe working load, it would be safe
to neglect it in the formula for design.
EDWIN THACHER, M. AM. SOC. C. E. (by letter).--The writer will discuss
this paper under the several "points" mentioned by the author.
_First Point._--At the point where the first rod is bent up, the stress
in this rod runs out. The other rods are sufficient to take the
horizontal stress, and the bent-up portion provides only for the
vertical and diagonal shearing stresses in the concrete.
_Second Point._--The remarks on the first point are also applicable to
the second one. Rod 3 provides for the shear.
_Third Point._--In a beam, the shear rods run through the compression
parts of the concrete and have sufficient anchorage. In a counterfort,
the inclined rods are sufficient to take the overturning stress. The
horizontal rods support the front wall and provide for shrinkage. The
vertical rods also provide for shrinkage, and assist the diagonal rods
against overturning. The anchorage is sufficient in all cases, and the
proposed method is no more effective.
_Fourth Point._--In bridge pins, bending and bearing usually govern,
but, in case a wide bar pulled on a pin between the supports close to
the bar, as happens in bolsters and post-caps of combination bridges and
in other locations, shear would govern. Shear rods in concrete-steel
beams are proportioned to take the vertical and diagonal shearing
stresses. If proportioned for less stress per square inch than is used
in the bottom bars, this cannot be considered dangerous practice.
_Fifth Point._--Vertical stirrups are designed to act like the vertical
rods in a Howe truss. Special literature is not required on the subject;
it is known that the method used gives good results, and that is
sufficient.
_Sixth Point._--The common method is not "to assume each shear member as
taking the horizontal shear occurring in the space from member to
member," but to take all the shear from the center of the beam up to the
bar in question.
Cracks do not necessarily endanger the safety of a beam. Any device that
will prevent the cracks from opening wide enough to destroy the beam, is
logical. By numerous experiments, Mr. Thaddeus Hyatt found that nuts and
washers at the ends of reinforcing bars were worse than useless, and
added nothing to the strength of the beams.
_Seventh Point._--Beams can be designed, supported at the ends, fully
continuous, or continuous to a greater or less extent, as desired. The
common practice is to design slabs to take a negative moment over the
supports equal to one-half the positive moment at the center, or to bend
up the alternate rods. This is simple and good practice, for no beam can
fail as long as a method is provided by which to take care of all the
stresses without overstraining any part.
_Eighth Point._--Bars in the bottom of a reinforced concrete beam are
often placed too close to one another. The rule of spacing the bars not
less than three diameters apart, is believed to be good practice.
_Ninth Point._--To disregard the theory of T-beams, and work by
rule-of-thumb, can hardly be considered good engineering.
_Tenth Point._--The author appears to consider theories for reinforced
concrete beams and slabs as useless refinements, but as long as theory
and experiment agree so wonderfully well, theories will undoubtedly
continue to be used.
_Eleventh Point._--Calculations for chimneys are somewhat complex, but
are better and safer than rule-of-thumb methods.
_Twelfth Point._--Deflection is not very important.
_Thirteenth Point._--The conclusion of the Austrian Society of Engineers
and Architects, after numerous experiments, was that the elastic theory
of the arch is the only true theory. No arch designed by the elastic
theory was ever known to fail, unless on account of insecure
foundations, therefore engineers can continue to use it with confidence
and safety.
_Fourteenth Point._--Calculations for temperature stresses, as per
theory, are undoubtedly correct for the variations in temperature
assumed. Similar calculations can also be made for shrinkage stresses,
if desired. This will give a much better idea of the stresses to be
provided for, than no calculations at all.
_Fifteenth Point._--Experiments show that slender longitudinal rods,
poorly supported, and embedded in a concrete column, add little or
nothing to its strength; but stiff steel angles, securely latticed
together, and embedded in the concrete column, will greatly increase its
strength, and this construction is considered the most desirable when
the size of the column has to be reduced to a minimum.
_Sixteenth Point._--The commonly accepted theory of slabs supported on
four sides can be correctly applied to reinforced concrete slabs, as it
is only a question of providing for certain moments in the slab. This
theory shows that unless the slab is square, or nearly so, nothing is to
be gained by such construction.
C.A.P. TURNER, M. AM. SOC. C. E. (by letter).--Mr. Godfrey has expressed
his opinion on many questions in regard to concrete construction, but he
has adduced no clean-cut statement of fact or tests, in support of his
views, which will give them any weight whatever with the practical
matter-of-fact builder.
The usual rules of criticism place the burden of proof on the critic.
Mr. Godfrey states that if his personal opinions are in error, it should
be easy to prove them to be so, and seems to expect that the busy
practical constructor will take sufficient interest in them to spend the
time to write a treatise on the subject in order to place him right in
the matter.
The writer will confine his discussion to only a few points of the many
on which he disagrees with Mr. Godfrey.
First, regarding stirrups: These may be placed in the beam so as to be
of little practical value. They were so placed in the majority of the
tests made at the University of Illinois. Such stirrups differ widely in
value from those used by Hennebique and other first-class constructors.
Mr. Godfrey's idea is that the entire pull of the main reinforcing rod
should be taken up apparently at the end. When one frequently sees slabs
tested, in which the steel breaks at the center, with no end anchorage
whatever for the rods, the soundness of Mr. Godfrey's position may be
questioned.
Again, concrete is a material which shows to the best advantage as a
monolith, and, as such, the simple beam seems to be decidedly out of
date to the experienced constructor.
Mr. Godfrey appears to consider that the hooping and vertical
reinforcement of columns is of little value. He, however, presents for
consideration nothing but his opinion of the matter, which appears to be
based on an almost total lack of familiarity with such construction.
The writer will state a few facts regarding work which he has executed.
Among such work have been columns in a number of buildings, with an
18-in. core, and carrying more than 500 tons; also columns in one
building, which carry something like 1100 tons on a 27-in. core. In each
case there is about 1-1/2 in. of concrete outside the core for a
protective coating. The working stress on the core, if it takes the
load, is approximately equal to the ultimate strength of the concrete in
cubes, to say nothing of the strength of cylinders fifteen times their
diameter in height. These values have been used with entire confidence
after testing full-sized columns designed with the proper proportions of
vertical steel and hooping, and are regarded by the writer as having at
least double the factor of safety used in ordinary designs of structural
steel.
An advantage which the designer in concrete has over his fellow-engineer
in the structural steel line, lies in the fact that, with a given type
of reinforcement, his members are similar in form, and when the work is
executed with ordinary care, there is less doubt as to the distribution
of stress through a concrete column, than there is with the ordinary
structural steel column, since the core is solid and the conditions are
similar in all cases.
Tests of five columns are submitted herewith. The columns varied little
in size, but somewhat in the amount of hooping, with slight differences
in the vertical steel. The difference between Columns 1 and 3 is nearly
50%, due principally to the increase in hooping, and to a small addition
in the amount of vertical steel. As to the efficiency of hooping and
vertical reinforcement, the question may be asked Mr. Godfrey, and those
who share his views, whether a column without reinforcement can be cast,
which will equal the strength of those, the tests of which are
submitted.