Marks on column--none.
Reinforcement--eight 7/8-in. bars vertically.
Hoops spaced 10 in. vertically.
Outside diameter of hoops--14-1/2 in.
Wire spiral as before.
Load at failure--1,100,000 lb.
Ultimate load--1,130,000 lb.
Remarks.--The main point of failure in this, as in all other columns,
was within 2 ft. of the top, although this column showed some scaling
off at the lower end.
In these tests it will be noted that the concrete outside of the hooped
area seems to have had very little value in determining the ultimate
strength; that, figuring the compression on the core area and deducting
the probable value of the vertical steel, these columns exhibited from
5,000 to 7,000 lb. per sq. in. as the ultimate strength of the hooped
area, not considering the vertical steel. Some of them run over 8,000
lb.
The concrete mixture was 1 part Alpena Portland cement, 1 part sand,
1-1/2 parts buckwheat gravel and 3-1/2 parts gravel ranging from 1/4 to
3/4 in. in size.
The columns were cast in the early part of December, and tested in
April. The conditions under which they hardened were not particularly
favorable, owing to the season of the year.
The bands used were 1-3/4 by 1/4 in., except in the light column, where
they were 1-3/4 by 3/16 in.
In his remarks regarding the tests at Minneapolis, Minn., Mr. Godfrey
has failed to note that these tests, faulty as they undoubtedly were,
both in the execution of the work, and in the placing of the
reinforcement, as well as in the character of the hooping used, were
sufficient to satisfy the Department of Buildings that rational design
took into consideration the amount of hooping and the amount of
vertical steel, and on a basis not far from that which the writer
considers reasonable practice.
Again, Mr. Godfrey seems to misunderstand the influence of Poisson's
ratio in multiple-way reinforcement. If Mr. Godfrey's ideas are correct,
it will be found that a slab supported on two sides, and reinforced with
rods running directly from support to support, is stronger than a
similar slab reinforced with similar rods crossing it diagonally in
pairs. Tests of these two kinds of slabs show that those with the
diagonal reinforcement develop much greater strength than those
reinforced directly from support to support. Records of small test slabs
of this kind will be found in the library of the Society.
Mr. Godfrey makes the good point that the accuracy of an elastic theory
must be determined by the elastic deportment of the construction under
load, and it seems to the writer that if authors of textbooks would pay
some attention to this question and show by calculation that the elastic
deportment of slabs is in keeping with their method of figuring, the
gross errors in the theoretical treatment of slabs in the majority of
works on reinforced concrete would be remedied.
Although he makes the excellent point noted, Mr. Godfrey very
inconsistently fails to do this in connection with his theory of slabs,
otherwise he would have perceived the absurdity of any method of
calculating a multiple-way reinforcement by endeavoring to separate the
construction into elementary beam strips. This old-fashioned method was
discarded by the practical constructor many years ago, because he was
forced to guarantee deflections of actual construction under severe
tests. Almost every building department contains some regulation
limiting the deflection of concrete floors under test, and yet no
commissioner of buildings seems to know anything about calculating
deflections.
In the course of his practice the writer has been required to give
surety bonds of from $50,000 to $100,000 at a time, to guarantee under
test both the strength and the deflection of large slabs reinforced in
multiple directions, and has been able to do so with accuracy by methods
which are equivalent to considering Poisson's ratio, and which are given
in his book on concrete steel construction.
Until the engineer pays more attention to checking his complicated
theories with facts as determined by tests of actual construction, the
view, now quite general among the workers in reinforced concrete
regarding him will continue to grow stronger, and their respect for him
correspondingly less, until such time as he demonstrates the
applicability of his theories to ordinary every-day problems.
PAUL CHAPMAN, ASSOC. M. AM. SOC. C. E. (by letter).--Mr. Godfrey has
pointed out, in a forcible manner, several bad features of text-book
design of reinforced concrete beams and retaining walls. The practical
engineer, however, has never used such methods of construction. Mr.
Godfrey proposes certain rules for the calculation of stresses, but
there are no data of experiments, or theoretical demonstrations, to
justify their use.
It is also of the utmost importance to consider the elastic behavior of
structures, whether of steel or concrete. To illustrate this, the writer
will cite a case which recently came to his attention. A roof was
supported by a horizontal 18-in. I-beam, 33 ft. long, the flanges of
which were coped at both ends, and two 6 by 4-in. angles, 15 ft. long,
supporting the same, were securely riveted to the web, thereby forming a
frame to resist lateral wind pressure. Although the 18-in. I-beam was
not loaded to its full capacity, its deflection caused an outward
flexure of 3/4 in. and consequent dangerous stresses in the 6 by 4-in.
angle struts. The frame should have been designed as a structure fixed
at the base of the struts. The importance of the elastic behavior of a
structure is forcibly illustrated by comparing the contract drawings for
a great cantilever bridge which spans the East River with the expert
reports on the same. Due to the neglect of the elastic behavior of the
structure in the contract drawings, and another cause, the average error
in the stresses of 290 members was 18-1/2%, with a maximum of 94 per
cent.
Mr. Godfrey calls attention to the fact that stringers in railroad
bridges are considered as simple beams; this is theoretically proper
because the angle knees at their ends can transfer practically no flange
stress. It is also to be noted that when stringers are in the plane of a
tension chord, they are milled to exact lengths, and when in the plane
of a compression chord, they are given a slight clearance in order to
prevent arch action.
[Illustration: FIG. 3.]
The action of shearing stresses in concrete beams may be illustrated by
reference to the diagrams in Fig. 3, where the beams are loaded with a
weight, _W_. The portion of _W_ traveling to the left support, moves in
diagonal lines, varying from many sets of almost vertical lines to a
single diagonal. The maximum intensity of stress probably would be in
planes inclined about 45°, since, considered independently, they produce
the least deflection. While the load, _W_, remains relatively small,
producing but moderate stresses in the steel in the bottom flange, the
concrete will carry a considerable portion of the bottom flange tension;
when the load _W_ is largely increased, the coefficient of elasticity of
the concrete in tension becomes small, or zero, if small fissures
appear, and the concrete is unable to transfer the tension in diagonal
planes, and failure results. For a beam loaded with a single load, _W_,
the failure would probably be in a diagonal line near the point of
application, while in a uniformly loaded beam, it would probably occur
in a diagonal line near the support, where the shear is greatest.
It is evident that the introduction of vertical stirrups, as at _b_, or
the more rational inclined stirrups, as at _c_, influences the action of
the shearing forces as indicated, the intensity of stress at the point
of connection of the stirrups being high. It is advisable to space the
stirrups moderately close, in order to reduce this intensity to
reasonable limits. If the assumption is made that the diagonal
compression in the concrete acts in a plane inclined at 45°, then the
tension in the vertical stirrups will be the vertical shear times the
horizontal spacing of the stirrups divided by the distance, center to
center, of the top and bottom flanges of the beam. If the stirrups are
inclined at 45°, the stress in them would be 0.7 the stress in vertical
stirrups with the same spacing. Bending up bottom rods sharply, in order
to dispense with suspenders, is bad practice; the writer has observed
diagonal cracks in the beams of a well-known building in New York City,
which are due to this cause.
[Illustration: FIG. 4.]
In several structures which the writer has recently designed, he has
been able to dispense with stirrups, and, at the same time, effect a
saving in concrete, by bending some of the bottom reinforcing rods and
placing a bar between them and those which remain horizontal. A typical
detail is shown in Fig. 4. The bend occurs at a point where the vertical
component of the stress in the bent bars equals the vertical shear, and
sufficient bearing is provided by the short cross-bar. The bars which
remain horizontal throughout the beam, are deflected at the center of
the beam in order to obtain the maximum effective depth. There being no
shear at the center, the bars are spaced as closely as possible, and
still provide sufficient room for the concrete to flow to the soffit of
the beam. Two or more adjacent beams are readily made continuous by
extending the bars bent up from each span, a distance along the top
flanges. By this system of construction one avoids stopping a bar where
the live load unit stress in adjoining bars is high, as their continual
lengthening and shortening under stress would cause severe shearing
stresses in the concrete surrounding the end of the short bar.
[Illustration: FIG. 5.]
The beam shown in Fig. 5 illustrates the principles stated in the
foregoing, as applied to a heavier beam. The duty of the short
cross-bars in this case is performed by wires wrapped around the
longitudinal rods and then continued up in order to support the bars
during erection. This beam, which supports a roof and partitions, etc.,
has supported about 80% of the load for which it was calculated, and no
hair cracks or noticeable deflection have appeared. If the method of
calculation suggested by Mr. Godfrey were a correct criterion of the
actual stresses, this particular beam (and many others) would have shown
many cracks and noticeable deflection. The writer maintains that where
the concrete is poured continuously, or proper bond is provided, the
influence of the slab as a compression flange is an actual condition,
and the stresses should be calculated accordingly.
In the calculation of continuous T-beams, it is necessary to consider
the fact that the moment of inertia for negative moments is small
because of the lack of sufficient compressive area in the stem or web.
If Mr. Godfrey will make proper provision for this point, in studying
the designs of practical engineers, he will find due provision made for
negative moments. It is very easy to obtain the proper amount of steel
for the negative moment in a slab by bending up the bars and letting
them project into adjoining spans, as shown in Figs. 4 and 5 (taken from
actual construction). The practical engineer does not find, as Mr.
Godfrey states, that the negative moment is double the positive moment,
because he considers the live load either on one span only, or on
alternate spans.
[Illustration: FIG. 6.]
In Fig. 6 a beam is shown which has many rods in the bottom flange, a
practice which Mr. Godfrey condemns. As the structure, which has about
twenty similar beams, is now being built, the writer would be thankful
for his criticism. Mr. Godfrey states that longitudinal steel in columns
is worthless, but until definite tests are made, with the same
ingredients, proportions, and age, on both plain concrete and reinforced
concrete columns properly designed, the writer will accept the data of
other experiments, and proportion steel in accordance with recognized
formulas.
[Illustration: FIG. 7.]
Mr. Godfrey states that the "elastic theory" is worthless for the design
of reinforced concrete arches, basing his objections on the shrinkage of
concrete in setting, the unreliability of deflection formulas for beams,
and the lack of rigidity of the abutments. The writer, noting that
concrete setting in air shrinks, whereas concrete setting in water
expands, believes that if the arch be properly wetted until the setting
up of the concrete has progressed sufficiently, the effect of shrinkage,
on drying out, may be minimized. If the settlement of the forms
themselves be guarded against during the construction of an arch, the
settlement of the arch ring, on removing the forms, far from being an
uncertain element, should be a check on the accuracy of the calculations
and the workmanship, since the weight of the arch ring should produce
theoretically a certain deflection. The unreliability of deflection
formulas for beams is due mainly to the fact that the neutral axis of
the beam does not lie in a horizontal plane throughout, and that the
shearing stresses are neglected therein. While there is necessarily
bending in an arch ring due to temperature, loads, etc., the extreme
flanges sometimes being in tension, even in a properly designed arch,
the compression exceeds the tension to such an extent that comparison to
a beam does not hold true. An arch should not be used where the
abutments are unstable, any more than a suspension bridge should be
built where a suitable anchorage cannot be obtained.
The proper design of concrete slabs supported on four sides is a complex
and interesting study. The writer has recently designed a floor
construction, slabs, and beams, supported on four corners, which is
simple and economical. In Fig. 7 is shown a portion of a proposed
twelve-story building, 90 by 100 ft., having floors with a live-load
capacity of 250 lb. per sq. ft. For the maximum positive bending in any
panel the full load on that panel was considered, there being no live
load on adjoining panels. For the maximum negative bending moment all
panels were considered as loaded, and in a single line. "Checker-board"
loading was considered too improbable for consideration. The flexure
curves for beams at right angles to each other were similar (except in
length), the tension rods in the longer beams being placed underneath
those in the shorter beams. Under full load, therefore, approximately
one-half of the load went to the long-span girder and the other half to
the short-span girder. The girders were the same depth as the beams. For
its depth the writer found this system to be the strongest and most
economical of those investigated.
E.P. GOODRICH, M. AM. SOC. C. E.--The speaker heartily concurs with the
author as to the large number of makeshifts constantly used by a
majority of engineers and other practitioners who design and construct
work in reinforced concrete. It is exceedingly difficult for the human
mind to grasp new ideas without associating them with others in past
experience, but this association is apt to clothe the new idea (as the
author suggests) in garments which are often worse than
"swaddling-bands," and often go far toward strangling proper growth.
While the speaker cannot concur with equal ardor with regard to all the
author's points, still in many, he is believed to be well grounded in
his criticism. Such is the case with regard to the first point
mentioned--that of the use of bends of large radius where the main
tension rods are bent so as to assist in the resistance of diagonal
tensile stresses.
As to the second point, provided proper anchorage is secured in the top
concrete for the rod marked 3 in Fig. 1, the speaker cannot see why the
concrete beneath such anchorage over the support does not act exactly
like the end post of a queen-post truss. Nor can he understand the
author's statement that:
"A reinforcing rod in a concrete beam receives its stress by
increments imparted by the grip of the concrete; but these
increments can only be imparted where the tendency of the concrete
is to stretch."
The latter part of this quotation has reference to the point questioned
by the speaker. In fact, the remainder of the paragraph from which this
quotation is taken seems to be open to grave question, no reason being
evident for not carrying out the analogy of the queen-post truss to the
extreme. Along this line, it is a well-known fact that the bottom chords
in queen-post trusses are useless, as far as resistance to tension is
concerned. The speaker concurs, however, in the author's criticism as to
the lack of anchorage usually found in most reinforcing rods,
particularly those of the type mentioned in the author's second point.
This matter of end anchorage is also referred to in the third point, and
is fully concurred in by the speaker, who also concurs in the criticism
of the arrangement of the reinforcing rods in the counterforts found in
many retaining walls. The statement that "there is absolutely no analogy
between this triangle [the counterfort] and a beam" is very strong
language, and it seems risky, even for the best engineer, to make such a
statement as does the author when he characterizes his own design
(Diagram _b_ of Fig. 2) as "the only rational and the only efficient
design possible." Several assumptions can be made on which to base the
arrangement of reinforcement in the counterfort of a retaining wall,
each of which can be worked out with equal logic and with results which
will prevent failure, as has been amply demonstrated by actual
experience.
The speaker heartily concurs in the author's fourth point, with regard
to the impossibility of developing anything like actual shear in the
steel reinforcing rods of a concrete beam; but he demurs when the author
affirms, as to the possibility of so-called shear bars being stressed in
"shear or tension," that "either would be absurd and impossible without
greatly overstressing some other part."
As to the fifth point, reference can be given to more than one place in
concrete literature where explanations of the action of vertical
stirrups may be found, all of which must have been overlooked by the
author. However, the speaker heartily concurs with the author's
criticism as to the lack of proper connection which almost invariably
exists between vertical "web" members and the top and bottom chords of
the imaginary Howe truss, which holds the nearest analogy to the
conditions existing in a reinforced concrete beam with vertical "web"
reinforcement.
The author's reasoning as to the sixth point must be considered as
almost wholly facetious. He seems to be unaware of the fact that
concrete is relatively very strong in pure shear. Large numbers of tests
seem to demonstrate that, where it is possible to arrange the
reinforcing members so as to carry largely all tensile stresses
developed through shearing action, at points where such tensile stresses
cannot be carried by the concrete, reinforced concrete beams can be
designed of ample strength and be quite within the logical processes
developed by the author, as the speaker interprets them.
The author's characterization of the results secured at the University
of Illinois Experiment Station, and described in its Bulletin No. 29, is
somewhat misleading. It is true that the wording of the original
reference states in two places that "stirrups do not come into action,
at least not to any great extent, until a diagonal crack has formed,"
but, in connection with this statement, the following quotations must be
read:
"The tests were planned with a view of determining the amount of
stress (tension and bond) developed in the stirrups. However, for
various reasons, the results are of less value than was expected.
The beams were not all made according to the plans. In the 1907
tests, the stirrups in a few of the beams were poorly placed and
even left exposed at the face of the beam, and a variation in the
temperature conditions of the laboratory also affected the results.
It is evident from the results that the stresses developed in the
stirrups are less than they were calculated to be, and hence the
layout was not well planned to settle the points at issue. The
tests, however, give considerable information on the effectiveness
of stirrups in providing web resistance."
"A feature of the tests of beams with stirrups is slow failure, the
load holding well up to the maximum under increased deflection and
giving warning of its condition."
"Not enough information was obtained to determine the actual final
occasion of failure in these tests. In a number of cases the
stirrups slipped, in others it seemed that the steel in the
stirrups was stretched beyond its elastic limit, and in some cases
the stirrups broke."
"As already stated, slip of stirrups and insufficient bond
resistance were in many cases the immediate cause of diagonal
tension failures, and therefore bond resistance of stirrups may be
considered a critical stress."
These quotations seem to indicate much more effectiveness in the action
of vertical stirrups than the author would lead one to infer from his
criticisms. It is rather surprising that he advocates so strongly the
use of a suspension system of reinforcement. That variety has been used
abroad for many years, and numerous German experiments have proved with
practical conclusiveness that the suspension system is not as efficient
as the one in which vertical stirrups are used with a proper
arrangement. An example is the conclusion arrived at by Mörsch, in
"Eisenbetonbau," from a series of tests carried out by him near the end
of 1906:
"It follows that with uniform loads, the suspended system of
reinforcement does not give any increase of safety against the
appearance of diagonal tension cracks, or the final failure
produced by them, as compared with straight rods without stirrups,
and that stirrups are so much the more necessary."
Again, with regard to tests made with two concentrated loads, he writes:
"The stirrups, supplied on one end, through their tensile strength,
hindered the formation of diagonal cracks and showed themselves
essential and indispensable elements in the * * * [suspension]
system. The limit of their effect is, however, not disclosed by
these experiments. * * * In any case, from the results of the
second group of experiments can be deduced the facts that the
bending of the reinforcement according to the theory concerning the
diagonal tensile stress * * * is much more effective than according
to the suspension theory, in this case the ultimate loads being in
the proportion of 34: 23.4: 25.6."
It is the speaker's opinion that the majority of the failures described
in Bulletin No. 29 of the University of Illinois Experiment Station,
which are ascribed to diagonal tension, were actually due to deficient
anchorage of the upper ends of the stirrups.
Some years ago the speaker demonstrated to his own satisfaction, the
practical value of vertical stirrups. Several beams were built identical
in every respect except in the size of wire used for web reinforcement.
The latter varied from nothing to 3/8-in. round by five steps. The beams
were similarly tested to destruction, and the ultimate load and type of
failure varied in a very definite ratio to the area of vertical steel.
With regard to the author's seventh point, the speaker concurs heartily
as far as it has to do with a criticism of the usual design of
continuous beams, but his experience with beams designed as suggested by
the author is that failure will take place eventually by vertical cracks
starting from the top of the beams close to the supports and working
downward so as to endanger very seriously the strength of the structures
involved. This type of failure was prophesied by the speaker a number of
years ago, and almost every examination which he has lately made of
concrete buildings, erected for five years or longer and designed
practically in accord with the author's suggestion, have disclosed such
dangerous features, traceable directly to the ideas described in the
paper. These ideas are held by many other engineers, as well as being
advocated by the author. The only conditions under which the speaker
would permit of the design of a continuous series of beams as simple
members would be when they are entirely separated from each other over
the supports, as by the introduction of artificial joints produced by a
double thickness of sheet metal or building paper. Even under these
conditions, the speaker's experience with separately moulded members,
manufactured in a shop and subsequently erected, has shown that similar
top cracking may take place under certain circumstances, due to the
vertical pressures caused by the reactions at the supports. It is very
doubtful whether the action described by the author, as to the type of
failure which would probably take place with his method of design, would
be as described by him, but the beams would be likely to crack as
described above, in accordance with the speaker's experience, so that
the whole load supported by the beam would be carried by the reinforcing
rods which extend from the beam into the supports and are almost
invariably entirely horizontal at such points. The load would thus be
carried more nearly by the shearing strength of the steel than is
otherwise possible to develop that type of stress. In every instance the
latter is a dangerous element.
This effect of vertical abutment action on a reinforced beam was very
marked in the beam built of bricks and tested by the speaker, as
described in the discussion[J] of the paper by John S. Sewell, M. Am,
Soc. S. E., on "The Economical Design of Reinforced Concrete Floor
Systems for Fire-Resisting Structures." That experiment also went far
toward showing the efficacy of vertical stirrups.
The same discussion also contains a description of a pair of beams
tested for comparative purposes, in one of which adhesion between the
concrete and the main reinforcing rods was possible only on the upper
half of the exterior surfaces of the latter rods except for short
distances near the ends. Stirrups were used, however. The fact that the
beam, which was theoretically very deficient in adhesion, failed in
compression, while the similar beam without stirrups, but with the most
perfect adhesion, and anchorage obtainable through the use of large end
hooks, failed in bond, has led the speaker to believe that, in affording
adhesive resistance, the upper half of a bar is much more effective than
the lower half. This seems to be demonstrated further by comparisons
between simple adhesion experiments and those obtained with beams.
The speaker heartily concurs with the author's criticism of the amount
of time usually given by designing engineers to the determination of the
adhesive stresses developed in concrete beams, but, according to the
speaker's recollection, these matters are not so poorly treated in some
books as might be inferred by the author's language. For example, both
Bulletin No. 29, of the University of Illinois, and Mörsch, in
"Eisenbetonbau," give them considerable attention.
The ninth point raised by the author is well taken. Too great emphasis
cannot be laid on the inadequacy of design disclosed by an examination
of many T-beams.
Such ready concurrence, however, is not lent to the author's tenth
point. While it is true that, under all usual assumptions, except those
made by the author, an extremely simple formula for the resisting moment
of a reinforced concrete beam cannot be obtained, still his formula
falls so far short of fitting even with approximate correctness the
large number of well-known experiments which have been published, that a
little more mathematical gymnastic ability on the part of the author and
of other advocates of extreme simplicity would seem very necessary, and
will produce structures which are far more economical and amply safe
structurally, compared with those which would be produced in accordance
with his recommendations.
As to the eleventh point, in regard to the complex nature of the
formulas for chimneys and other structures of a more or less complex
beam nature, the graphical methods developed by numerous German and
Italian writers are recommended, as they are fully as simple as the
rather crude method advocated by the author, and are in almost identical
accord with the most exacting analytical methods.
With regard to the author's twelfth point, concerning deflection
calculations, it would seem that they play such a small part in
reinforced concrete design, and are required so rarely, that any
engineer who finds it necessary to make analytical investigations of
possible deflections would better use the most precise analysis at his
command, rather than fall back on simpler but much more approximate
devices such as the one advocated by the author.
Much of the criticism contained in the author's thirteenth point,
concerning the application of the elastic theory to the design of
concrete arches, is justified, because designing engineers do not carry
the theory to its logical conclusion nor take into account the actual
stresses which may be expected from slight changes of span, settlements
of abutments, and unexpected amounts of shrinkage in the arch ring or
ribs. Where conditions indicate that such changes are likely to take
place, as is almost invariably the case unless the foundations are upon
good rock and the arch ring has been concreted in relatively short
sections, with ample time and device to allow for initial shrinkage; or
unless the design is arranged and the structure erected so that hinges
are provided at the abutments to act during the striking of the
falsework, which hinges are afterward wedged or grouted so as to produce
fixation of the arch ends--unless all these points are carefully
considered in the design and erection, it is the speaker's opinion that
the elastic theory is rarely properly applicable, and the use of the
equilibrium polygon recommended by the author is much preferable and
actually more accurate. But there must be consistency in its use, as
well, that is, consistency between methods of design and erection.
The author's fourteenth point--the determination of temperature stresses
in a reinforced concrete arch--is to be considered in the same light as
that described under the foregoing points, but it seems a little amusing
that the author should finally advocate a design of concrete arch which
actually has no hinges, namely, one consisting of practically rigid
blocks, after he has condemned so heartily the use of the elastic
theory.
A careful analysis of the data already available with regard to the heat
conductivity of concrete, applied to reinforced concrete structures like
arches, dams, retaining walls, etc., in accordance with the well-known
but somewhat intricate mathematical formulas covering the laws of heat
conductivity and radiation so clearly enunciated by Fourier, has
convinced the speaker that it is well within the bounds of engineering
practice to predict and care for the stresses which will be produced in
structures of the simplest forms, at least as far as they are affected
by temperature changes.
The speaker concurs with the author in his criticism, contained in the
fifteenth point, with regard to the design of the steel reinforcement in
columns and other compression members. While there may be some question
as to the falsity or truth of the theory underlying certain types of
design, it is unquestioned that some schemes of arrangement undoubtedly
produce designs with dangerous properties. The speaker has several
times called attention to this point, in papers and discussions, and
invariably in his own practice requires that the spacing of spirals,
hoops, or ties be many times less than that usually required by building
regulations and found in almost every concrete structure. Mörsch, in his
"Eisenbetonbau," calls attention to the fact that very definite limits
should be placed on the maximum size of longitudinal rods as well as on
their minimum diameters, and on the maximum spacing of ties, where
columns are reinforced largely by longitudinal members. He goes so far
as to state that:
"It is seen from * * * [the results obtained] that an increase in
the area of longitudinal reinforcement does not produce an increase
in the breaking strength to the extent which would be indicated by
the formula. * * * In inexperienced hands this formula may give
rise to constructions which are not sufficiently safe."
Again, with regard to the spacing of spirals and the combination with
them of longitudinal rods, in connection with some tests carried out by
Mörsch, the conclusion is as follows:
"On the whole, the tests seem to prove that when the spirals are
increased in strength, their pitch must be decreased, and the
cross-section or number of the longitudinal rods must be
increased."
In the majority of cases, the spiral or band spacing is altogether too
large, and, from conversations with Considère, the speaker understands
that to be the inventor's view as well.
The speaker makes use of the scheme mentioned by the author in regard to
the design of flat slabs supported on more than two sides (noted in the
sixteenth point), namely, that of dividing the area into strips, the
moments of which are determined so as to produce computed deflections
which are equal in the two strips running at right angles at each point
of intersection. This method, however, requires a large amount of
analytical work for any special case, and the speaker is mildly
surprised that the author cannot recommend some simpler method so as to
carry out his general scheme of extreme simplification of methods and
design.
If use is to be made at all of deflection observations, theories, and
formulas, account should certainly be taken of the actual settlements
and other deflections which invariably occur in Nature at points of
support. These changes of level, or slope, or both, actually alter very
considerably the stresses as usually computed, and, in all rigorous
design work, should be considered.
On the whole, the speaker believes that the author has put himself in
the class with most iconoclasts, in that he has overshot his mark. There
seems to be a very important point, however, on which he has touched,
namely, the lack of care exercised by most designers with regard to
those items which most nearly correspond with the so-called "details" of
structural steel work, and are fully as important in reinforced
concrete as in steel. It is comparatively a small matter to proportion a
simple reinforced concrete beam at its intersection to resist a given
moment, but the carrying out of that item of the work is only a start on
the long road which should lead through the consideration of every
detail, not the least important of which are such items as most of the
sixteen points raised by the author.
The author has done the profession a great service by raising these
questions, and, while full concurrence is not had with him in all
points, still the speaker desires to express his hearty thanks for
starting what is hoped will be a complete discussion of the really vital
matter of detailing reinforced concrete design work.
ALBIN H. BEYER, ESQ.--Mr. Goodrich has brought out very clearly the
efficiency of vertical stirrups. As Mr. Godfrey states that explanations
of how stirrups act are conspicuous in the literature of reinforced
concrete by their absence, the speaker will try to explain their action
in a reinforced concrete beam.
It is well known that the internal static conditions in reinforced
concrete beams change to some extent with the intensity of the direct or
normal stresses in the steel and concrete. In order to bring out his
point, the speaker will trace, in such a beam, the changes in the
internal static conditions due to increasing vertical loads.
[Illustration: FIG. 8.]
Let Fig. 8 represent a beam reinforced by horizontal steel rods of such
diameter that there is no possibility of failure from lack of adhesion
of the concrete to the steel. The beam is subjected to the vertical
loads, [Sigma] _P_. For low unit stresses in the concrete, the neutral
surface, _n n_, is approximately in the middle of the beam. Gradually
increase the loads, [Sigma] _P_, until the steel reaches an elongation
of from 0.01 to 0.02 of 1%, corresponding to tensile stresses in the
steel of from 3,000 to 6,000 lb. per sq. in. At this stage plain
concrete would have reached its ultimate elongation. It is known,
however, that reinforced concrete, when well made, can sustain without
rupture much greater elongations; tests have shown that its ultimate
elongation may be as high as 0.1 of 1%, corresponding to tensions in
steel of 30,000 lb. per sq. in.
Reinforced concrete structures ordinarily show tensile cracks at very
much lower unit stresses in the steel. The main cause of these cracks is
as follows: Reinforced concrete setting in dry air undergoes
considerable shrinkage during the first few days, when it has very
little resistance. This tendency to shrink being opposed by the
reinforcement at a time when the concrete does not possess the necessary
strength or ductility, causes invisible cracks or planes of weakness in
the concrete. These cracks open and become visible at very low unit
stresses in the steel.
Increase the vertical loads, [Sigma] _P_, and the neutral surface will
rise and small tensile cracks will appear in the concrete below the
neutral surface (Fig. 8). These cracks are most numerous in the central
part of the span, where they are nearly vertical. They decrease in
number at the ends of the span, where they curve slightly away from the
perpendicular toward the center of the span. The formation of these
tensile cracks in the concrete relieves it at once of its highly
stressed condition.
It is impossible to predict the unit tension in the steel at which these
cracks begin to form. They can be detected, though not often visible,
when the unit tensions in the steel are as low as from 10,000 to 16,000
lb. per sq. in. As soon as the tensile cracks form, though invisible,
the neutral surface approaches the position in the beam assigned to it
by the common theory of flexure, with the tension in the concrete
neglected. The internal static conditions in the beam are now modified
to the extent that the concrete below the neutral surface is no longer
continuous. The common theory of flexure can no longer be used to
calculate the web stresses.
To analyze the internal static conditions developed, the speaker will
treat as a free body the shaded portion of the beam shown in Fig. 8,
which lies between two tensile cracks.
[Illustration: FIG. 9.]
In Fig. 9 are shown all the forces which act on this free body, _C b b'
C'_.