diff options
Diffstat (limited to '17137.txt')
| -rw-r--r-- | 17137.txt | 5685 |
1 files changed, 5685 insertions, 0 deletions
diff --git a/17137.txt b/17137.txt new file mode 100644 index 0000000..021d0e1 --- /dev/null +++ b/17137.txt @@ -0,0 +1,5685 @@ +The Project Gutenberg EBook of Some Mooted Questions in Reinforced +Concrete Design, by Edward Godfrey + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Some Mooted Questions in Reinforced Concrete Design + American Society of Civil Engineers, Transactions, Paper + No. 1169, Volume LXX, Dec. 1910 + +Author: Edward Godfrey + +Release Date: November 23, 2005 [EBook #17137] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK REINFORCED CONCRETE DESIGN *** + + + + +Produced by Juliet Sutherland, Taavi Kalju and the Online +Distributed Proofreading Team at https://www.pgdp.net + + + + + + + + + + +AMERICAN SOCIETY OF CIVIL ENGINEERS INSTITUTED 1852 + +TRANSACTIONS + +Paper No. 1169 + +SOME MOOTED QUESTIONS IN REINFORCED CONCRETE DESIGN.[A] + +BY EDWARD GODFREY, M. AM. SOC. C. E. + +WITH DISCUSSION BY MESSRS. JOSEPH WRIGHT, S. BENT RUSSELL, J.R. +WORCESTER, L.J. MENSCH, WALTER W. CLIFFORD, J.C. MEEM, GEORGE H. MYERS, +EDWIN THACHER, C.A.P. TURNER, PAUL CHAPMAN, E.P. GOODRICH, ALBIN H. +BEYER, JOHN C. OSTRUP, HARRY F. PORTER, JOHN STEPHEN SEWELL, SANFORD E. +THOMPSON, AND EDWARD GODFREY. + + +Not many years ago physicians had certain rules and practices by which +they were guided as to when and where to bleed a patient in order to +relieve or cure him. What of those rules and practices to-day? If they +were logical, why have they been abandoned? + +It is the purpose of this paper to show that reinforced concrete +engineers have certain rules and practices which are no more logical +than those governing the blood-letting of former days. If the writer +fails in this, by reason of the more weighty arguments on the other side +of the questions he propounds, he will at least have brought out good +reasons which will stand the test of logic for the rules and practices +which he proposes to condemn, and which, at the present time, are quite +lacking in the voluminous literature on this comparatively new subject. + +Destructive criticism has recently been decried in an editorial in an +engineering journal. Some kinds of destructive criticism are of the +highest benefit; when it succeeds in destroying error, it is +reconstructive. No reform was ever accomplished without it, and no +reformer ever existed who was not a destructive critic. If showing up +errors and faults is destructive criticism, we cannot have too much of +it; in fact, we cannot advance without it. If engineering practice is to +be purged of its inconsistencies and absurdities, it will never be done +by dwelling on its excellencies. + +Reinforced concrete engineering has fairly leaped into prominence and +apparently into full growth, but it still wears some of its +swaddling-bands. Some of the garments which it borrowed from sister +forms of construction in its short infancy still cling to it, and, while +these were, perhaps, the best makeshifts under the circumstances, they +fit badly and should be discarded. It is some of these misfits and +absurdities which the writer would like to bring prominently before the +Engineering Profession. + +[Illustration: FIG. 1.] + +The first point to which attention is called, is illustrated in Fig. 1. +It concerns sharp bends in reinforcing rods in concrete. Fig. 1 shows a +reinforced concrete design, one held out, in nearly all books on the +subject, as a model. The reinforcing rod is bent up at a sharp angle, +and then may or may not be bent again and run parallel with the top of +the beam. At the bend is a condition which resembles that of a hog-chain +or truss-rod around a queen-post. The reinforcing rod is the hog-chain +or the truss-rod. Where is the queen-post? Suppose this rod has a +section of 1 sq. in. and an inclination of 60 deg. with the horizontal, and +that its unit stress is 16,000 lb. per sq. in. The forces, _a_ and _b_, +are then 16,000 lb. The force, _c_, must be also 16000 lb. What is to +take this force, _c_, of 16,000 lb.? There is nothing but concrete. At +500 lb. per sq. in., this force would require an area of 32 sq. in. Will +some advocate of this type of design please state where this area can be +found? It must, of necessity, be in contact with the rod, and, for +structural reasons, because of the lack of stiffness in the rod, it +would have to be close to the point of bend. If analogy to the +queen-post fails so completely, because of the almost complete absence +of the post, why should not this borrowed garment be discarded? + +If this same rod be given a gentle curve of a radius twenty or thirty +times the diameter of the rod, the side unit pressure will be from +one-twentieth to one-thirtieth of the unit stress on the steel. This +being the case, and being a simple principle of mechanics which ought to +be thoroughly understood, it is astounding that engineers should +perpetrate the gross error of making a sharp bend in a reinforcing rod +under stress. + +The second point to which attention is called may also be illustrated by +Fig. 1. The rod marked 3 is also like the truss-rod of a queen-post +truss in appearance, because it ends over the support and has the same +shape. But the analogy ends with appearance, for the function of a +truss-rod in a queen-post truss is not performed by such a reinforcing +rod in concrete, for other reasons than the absence of a post. The +truss-rod receives its stress by a suitable connection at the end of the +rod and over the support of the beam. The reinforcing rod, in this +standard beam, ends abruptly at the very point where it is due to +receive an important element of strength, an element which would add +enormously to the strength and safety of many a beam, if it could be +introduced. + +Of course a reinforcing rod in a concrete beam receives its stress by +increments imparted by the grip of the concrete; but these increments +can only be imparted where the tendency of the concrete is to stretch. +This tendency is greatest near the bottom of the beam, and when the rod +is bent up to the top of the beam, it is taken out of the region where +the concrete has the greatest tendency to stretch. The function of this +rod, as reinforcement of the bottom flange of the beam, is interfered +with by bending it up in this manner, as the beam is left without +bottom-flange reinforcement, as far as that rod is concerned, from the +point of bend to the support. + +It is true that there is a shear or a diagonal tension in the beam, and +the diagonal portion of the rod is apparently in a position to take this +tension. This is just such a force as the truss-rod in a queen-post +truss must take. Is this reinforcing rod equipped to perform this +office? The beam is apt to fail in the line, _A B_. In fact, it is apt +to crack from shrinkage on this or almost any other line, and to leave +the strength dependent on the reinforcing steel. Suppose such a crack +should occur. The entire strength of the beam would be dependent on the +grip of the short end of Rod 3 to the right of the line, _A B_. The grip +of this short piece of rod is so small and precarious, considering the +important duty it has to perform, that it is astounding that designers, +having any care for the permanence of their structures, should consider +for an instant such features of design, much less incorporate them in a +building in which life and property depend on them. + +The third point to which attention is called, is the feature of design +just mentioned in connection with the bent-up rod. It concerns the +anchorage of rods by the embedment of a few inches of their length in +concrete. This most flagrant violation of common sense has its most +conspicuous example in large engineering works, where of all places +better judgment should prevail. Many retaining walls have been built, +and described in engineering journals, in papers before engineering +societies of the highest order, and in books enjoying the greatest +reputation, which have, as an essential feature, a great number of rods +which cannot possibly develop their strength, and might as well be of +much smaller dimensions. These rods are the vertical and horizontal rods +in the counterfort of the retaining wall shown at _a_, in Fig. 2. This +retaining wall consists of a front curtain wall and a horizontal slab +joined at intervals by ribs or counterforts. The manifest and only +function of the rib or counterfort is to tie together the curtain wall +and the horizontal slab. That it is or should be of concrete is because +the steel rods which it contains, need protection. It is clear that +failure of the retaining wall could occur by rupture through the Section +_A B_, or through _B C_. It is also clear that, apart from the cracking +of the concrete of the rib, the only thing which would produce this +rupture is the pulling out of the short ends of these reinforcing rods. +Writers treat the triangle, _A B C_, as a beam, but there is absolutely +no analogy between this triangle and a beam. Designers seem to think +that these rods take the place of so-called shear rods in a beam, and +that the inclined rods are equivalent to the rods in a tension flange of +a beam. It is hard to understand by what process of reasoning such +results can be attained. Any clear analysis leading to these conclusions +would certainly be a valuable contribution to the literature on the +subject. It is scarcely possible, however, that such analysis will be +brought forward, for it is the apparent policy of the reinforced +concrete analyst to jump into the middle of his proposition without the +encumbrance of a premise. + +There is positively no evading the fact that this wall could fail, as +stated, by rupture along either _A B_ or _B C_. It can be stated just as +positively that a set of rods running from the front wall to the +horizontal slab, and anchored into each in such a manner as would be +adopted were these slabs suspended on the rods, is the only rational and +the only efficient design possible. This design is illustrated at _b_ in +Fig. 2. + +[Illustration: FIG. 2.] + +The fourth point concerns shear in steel rods embedded in concrete. For +decades, specifications for steel bridges have gravely given a unit +shear to be allowed on bridge pins, and every bridge engineer knows or +ought to know that, if a bridge pin is properly proportioned for bending +and bearing, there is no possibility of its being weak from shear. The +centers of bearings cannot be brought close enough together to reduce +the size of the pin to where its shear need be considered, because of +the width required for bearing on the parts. Concrete is about +one-thirtieth as strong as steel in bearing. There is, therefore, +somewhat less than one-thirtieth of a reason for specifying any shear on +steel rods embedded in concrete. + +The gravity of the situation is not so much the serious manner in which +this unit of shear in steel is written in specifications and building +codes for reinforced concrete work (it does not mean anything in +specifications for steelwork, because it is ignored), but it is apparent +when designers soberly use these absurd units, and proportion shear rods +accordingly. + +Many designers actually proportion shear rods for shear, shear in the +steel at units of 10,000 or 12,000 lb. per sq. in.; and the blame for +this dangerous practice can be laid directly to the literature on +reinforced concrete. Shear rods are given as standard features in the +design of reinforced concrete beams. In the Joint Report of the +Committee of the various engineering societies, a method for +proportioning shear members is given. The stress, or shear per shear +member, is the longitudinal shear which would occur in the space from +member to member. No hint is given as to whether these bars are in shear +or tension; in fact, either would be absurd and impossible without +greatly overstressing some other part. This is just a sample of the +state of the literature on this important subject. Shear bars will be +taken up more fully in subsequent paragraphs. + +The fifth point concerns vertical stirrups in a beam. These stirrups are +conspicuous features in the designs of reinforcing concrete beams. +Explanations of how they act are conspicuous in the literature on +reinforced concrete by its total absence. By stirrups are meant the +so-called shear rods strung along a reinforcing rod. They are usually +U-shaped and looped around the rod. + +It is a common practice to count these stirrups in the shear, taking the +horizontal shear in a beam. In a plate girder, the rivets connecting the +flange to the web take the horizontal shear or the increment to the +flange stress. Compare two 3/4-in. rivets tightly driven into holes in a +steel angle, with a loose vertical rod, 3/4 in. in diameter, looped +around a reinforcing rod in a concrete beam, and a correct comparison of +methods of design in steel and reinforced concrete, as they are commonly +practiced, is obtained. + +These stirrups can take but little hold on the reinforcing rods--and +this must be through the medium of the concrete--and they can take but +little shear. Some writers, however, hold the opinion that the stirrups +are in tension and not in shear, and some are bold enough to compare +them with the vertical tension members of a Howe truss. Imagine a Howe +truss with the vertical tension members looped around the bottom chord +and run up to the top chord without any connection, or hooked over the +top chord; then compare such a truss with one in which the end of the +rod is upset and receives a nut and large washer bearing solidly against +the chord. This gives a comparison of methods of design in wood and +reinforced concrete, as they are commonly practiced. + +Anchorage or grip in the concrete is all that can be counted on, in any +event, to take up the tension of these stirrups, but it requires an +embedment of from 30 to 50 diameters of a rod to develop its full +strength. Take 30 to 50 diameters from the floating end of these shear +members, and, in some cases, nothing or less than nothing will be left. +In any case the point at which the shear member, or stirrup, is good for +its full value, is far short of the centroid of compression of the beam, +where it should be; in most cases it will be nearer the bottom of the +beam. In a Howe truss, the vertical tension members having their end +connections near the bottom chord, would be equivalent to these shear +members. + +The sixth point concerns the division of stress into shear members. +Briefly stated, the common method is to assume each shear member as +taking the horizontal shear occurring in the space from member to +member. As already stated, this is absurd. If stirrups could take shear, +this method would give the shear per stirrup, but even advocates of this +method acknowledge that they can not. To apply the common analogy of a +truss: each shear member would represent a tension web member in the +truss, and each would have to take all the shear occurring in a section +through it. + +If, for example, shear members were spaced half the depth of a beam +apart, each would take half the shear by the common method. If shear +members take vertical shear, or if they take tension, what is between +the two members to take the other half of the shear? There is nothing in +the beam but concrete and the tension rod between the two shear members. +If the concrete can take the shear, why use steel members? It is not +conceivable that an engineer should seriously consider a tension rod in +a reinforced concrete beam as carrying the shear from stirrup to +stirrup. + +The logical deduction from the proposition that shear rods take tension +is that the tension rods must take shear, and that they must take the +full shear of the beam, and not only a part of it. For these shear rods +are looped around or attached to the tension rods, and since tension in +the shear rods would logically be imparted through the medium of this +attachment, there is no escaping the conclusion that a large vertical +force (the shear of the beam) must pass through the tension rod. If the +shear member really relieves the concrete of the shear, it must take it +all. If, as would be allowable, the shear rods take but a part of the +shear, leaving the concrete to take the remainder, that carried by the +rods should not be divided again, as is recommended by the common +method. + +Bulletin No. 29 of the University of Illinois Experiment Station shows +by numerous experiments, and reiterates again and again, that shear rods +do not act until the beam has cracked and partly failed. This being the +case, a shear rod is an illogical element of design. Any element of a +structure, which cannot act until failure has started, is not a proper +element of design. In a steel structure a bent plate which would +straighten out under a small stress and then resist final rupture, would +be a menace to the rigidity and stability of the structure. This is +exactly analogous to shear rods which cannot act until failure has +begun. + +When the man who tears down by criticism fails to point out the way to +build up, he is a destructive critic. If, under the circumstances, +designing with shear rods had the virtue of being the best thing to do +with the steel and concrete disposed in a beam, as far as experience and +logic in their present state could decide, nothing would be gained by +simply criticising this method of design. But logic and tests have shown +a far simpler, more effective, and more economical means of disposing of +the steel in a reinforced concrete beam. + +In shallow beams there is little need of provision for taking shear by +any other means than the concrete itself. The writer has seen a +reinforced slab support a very heavy load by simple friction, for the +slab was cracked close to the supports. In slabs, shear is seldom +provided for in the steel reinforcement. It is only when beams begin to +have a depth approximating one-tenth of the span that the shear in the +concrete becomes excessive and provision is necessary in the steel +reinforcement. Years ago, the writer recommended that, in such beams, +some of the rods be curved up toward the ends of the span and anchored +over the support. Such reinforcement completely relieves the concrete +of all shearing stress, for the stress in the rod will have a vertical +component equal to the shear. The concrete will rest in the rod as a +saddle, and the rod will be like the cable of a suspension span. The +concrete could be in separate blocks with vertical joints, and still the +load would be carried safely. + +By end anchorage is not meant an inch or two of embedment in concrete, +for an iron vise would not hold a rod for its full value by such means. +Neither does it mean a hook on the end of the rod. A threaded end with a +bearing washer, and a nut and a lock-nut to hold the washer in place, is +about the only effective means, and it is simple and cheap. Nothing is +as good for this purpose as plain round rods, for no other shape affords +the same simple and effective means of end connection. In a line of +beams, end to end, the rods may be extended into the next beam, and +there act to take the top-flange tension, while at the same time finding +anchorage for the principal beam stress. + +The simplicity of this design is shown still further by the absence of a +large number of little pieces in a beam box, as these must be held in +their proper places, and as they interfere with the pouring of the +concrete. + +It is surprising that this simple and unpatented method of design has +not met with more favor and has scarcely been used, even in tests. Some +time ago the writer was asked, by the head of an engineering department +of a college, for some ideas for the students to work up for theses, and +suggested that they test beams of this sort. He was met by the +astounding and fatuous reply that such would not be reinforced concrete +beams. They would certainly be concrete beams, and just as certainly be +reinforced. + +Bulletin 29 of the University of Illinois Experiment Station contains a +record of tests of reinforced concrete beams of this sort. They failed +by the crushing of the concrete or by failure in the steel rods, and +nearly all the cracks were in the middle third of the beams, whereas +beams rich in shear rods cracked principally in the end thirds, that is, +in the neighborhood of the shear rods. The former failures are ideal, +and are easier to provide against. A crack in a beam near the middle of +the span is of little consequence, whereas one near the support is a +menace to safety. + +The seventh point of common practice to which attention is called, is +the manner in which bending moments in so-called continuous beams are +juggled to reduce them to what the designer would like to have them. +This has come to be almost a matter of taste, and is done with as much +precision or reason as geologists guess at the age of a fossil in +millions of years. + +If a line of continuous beams be loaded uniformly, the maximum moments +are negative and are over the supports. Who ever heard of a line of +beams in which the reinforcement over the supports was double that at +mid-spans? The end support of such a line of beams cannot be said to be +fixed, but is simply supported, hence the end beam would have a negative +bending moment over next to the last support equal to that of a simple +span. Who ever heard of a beam being reinforced for this? The common +practice is to make a reduction in the bending moment, at the middle of +the span, to about that of a line of continuous beams, regardless of the +fact that they may not be continuous or even contiguous, and in spite of +the fact that the loading of only one gives quite different results, and +may give results approaching those of a simple beam. + +If the beams be designed as simple beams--taking the clear distance +between supports as the span and not the centers of bearings or the +centers of supports--and if a reasonable top reinforcement be used over +these supports to prevent cracks, every requirement of good engineering +is met. Under extreme conditions such construction might be heavily +stressed in the steel over the supports. It might even be overstressed +in this steel, but what could happen? Not failure, for the beams are +capable of carrying their load individually, and even if the rods over +the supports were severed--a thing impossible because they cannot +stretch out sufficiently--the beams would stand. + +Continuous beam calculations have no place whatever in designing +stringers of a steel bridge, though the end connections will often take +a very large moment, and, if calculated as continuous, will be found to +be strained to a very much larger moment. Who ever heard of a failure +because of continuous beam action in the stringers of a bridge? Why +cannot reinforced concrete engineering be placed on the same sound +footing as structural steel engineering? + +The eighth point concerns the spacing of rods in a reinforced concrete +beam. It is common to see rods bunched in the bottom of such a beam with +no regard whatever for the ability of the concrete to grip the steel, or +to carry the horizontal shear incident to their stress, to the upper +part of the beam. As an illustration of the logic and analysis applied +in discussing the subject of reinforced concrete, one well-known +authority, on the premise that the unit of adhesion to rod and of shear +are equal, derives a rule for the spacing of rods. His reasoning is so +false, and his rule is so far from being correct, that two-thirds would +have to be added to the width of beam in order to make it correct. An +error of 66% may seem trifling to some minds, where reinforced concrete +is considered, but errors of one-tenth this amount in steel design would +be cause for serious concern. It is reasoning of the most elementary +kind, which shows that if shear and adhesion are equal, the width of a +reinforced concrete beam should be equal to the sum of the peripheries +of all reinforcing rods gripped by the concrete. The width of the beam +is the measure of the shearing area above the rods, taking the +horizontal shear to the top of the beam, and the peripheries of the rods +are the measure of the gripping or adhesion area. + +Analysis which examines a beam to determine whether or not there is +sufficient concrete to grip the steel and to carry the shear, is about +at the vanishing point in nearly all books on the subject. Such +misleading analysis as that just cited is worse than nothing. + +The ninth point concerns the T-beam. Excessively elaborate formulas are +worked out for the T-beam, and haphazard guesses are made as to how much +of the floor slab may be considered in the compression flange. If a +fraction of this mental energy were directed toward a logical analysis +of the shear and gripping value of the stem of the T-beam, it would be +found that, when the stem is given its proper width, little, if any, of +the floor slab will have to be counted in the compression flange, for +the width of concrete which will grip the rods properly will take the +compression incident to their stress. + +The tenth point concerns elaborate theories and formulas for beams and +slabs. Formulas are commonly given with 25 or 30 constants and variables +to be estimated and guessed at, and are based on assumptions which are +inaccurate and untrue. One of these assumptions is that the concrete is +initially unstressed. This is quite out of reason, for the shrinkage of +the concrete on hardening puts stress in both concrete and steel. One of +the coefficients of the formulas is that of the elasticity of the +concrete. No more variable property of concrete is known than its +coefficient of elasticity, which may vary from 1,000,000 to 5,000,000 +or 6,000,000; it varies with the intensity of stress, with the kind of +aggregate used, with the amount of water used in mixing, and with the +atmospheric condition during setting. The unknown coefficient of +elasticity of concrete and the non-existent condition of no initial +stress, vitiate entirely formulas supported by these two props. + +Here again destructive criticism would be vicious if these mathematical +gymnasts were giving the best or only solution which present knowledge +could produce, or if the critic did not point out a substitute. The +substitute is so simple of application, in such agreement with +experiments, and so logical in its derivation, that it is surprising +that it has not been generally adopted. The neutral axis of reinforced +concrete beams under safe loads is near the middle of the depth of the +beams. If, in all cases, it be taken at the middle of the depth of the +concrete beam, and if variation of intensity of stress in the concrete +be taken as uniform from this neutral axis up, the formula for the +resisting moment of a reinforced concrete beam becomes extremely simple +and no more complex than that for a rectangular wooden beam. + +The eleventh point concerns complex formulas for chimneys. It is a +simple matter to find the tensile stress in that part of a plain +concrete chimney between two radii on the windward side. If in this +space there is inserted a rod which is capable of taking that tension at +a proper unit, the safety of the chimney is assured, as far as that +tensile stress is concerned. Why should frightfully complex formulas be +proposed, which bring in the unknowable modulus of elasticity of +concrete and can only be solved by stages or dependence on the +calculations of some one else? + +The twelfth point concerns deflection calculations. As is well known, +deflection does not play much of a part in the design of beams. +Sometimes, however, the passing requirement of a certain floor +construction is the amount of deflection under a given load. Professor +Gaetano Lanza has given some data on recorded deflections of reinforced +concrete beams.[B] He has also worked out the theoretical deflections on +various assumptions. An attempt to reconcile the observed deflections +with one of several methods of calculating stresses led him to the +conclusion that: + + "The observations made thus far are not sufficient to furnish the + means for determining the actual distribution of the stresses, and + hence for the deduction of reliable formulae for the computation of + the direct stresses, shearing stresses, diagonal stresses, + deflections, position of the neutral axis, etc., under a given + load." + +Professor Lanza might have gone further and said that the observations +made thus far are sufficient to show the hopelessness of deriving a +formula that will predict accurately the deflection of a reinforced +concrete beam. The wide variation shown by two beam tests cited by him, +in which the beams were identical, is, in itself, proof of this. + +Taking the data of these tests, and working out the modulus of +elasticity from the recorded deflections, as though the beams were of +plain concrete, values are found for this modulus which are not out of +agreement with the value of that variable modulus as determined by other +means. Therefore, if the beams be considered as plain concrete beams, +and an average value be assumed for the modulus or coefficient of +elasticity, a deflection may be found by a simple calculation which is +an average of that which may be expected. Here again, simple theory is +better than complex, because of the ease with which it may be applied, +and because it gives results which are just as reliable. + +The thirteenth point concerns the elastic theory as applied to a +reinforced concrete arch. This theory treats a reinforced concrete arch +as a spring. In order to justify its use, the arch or spring is +considered as having fixed ends. The results obtained by the intricate +methods of the elastic theory and the simple method of the equilibrium +polygon, are too nearly identical to justify the former when the arch is +taken as hinged at the ends. + +The assumption of fixed ends in an arch is a most extravagant one, +because it means that the abutments must be rigid, that is, capable of +taking bending moments. Rigidity in an abutment is only effected by a +large increase in bulk, whereas strength in an arch ring is greatly +augmented by the addition of a few inches to its thickness. By the +elastic theory, the arch ring does not appear to need as much strength +as by the other method, but additional stability is needed in the +abutments in order to take the bending moments. This latter feature is +not dwelt on by the elastic theorists. + +In the ordinary arch, the criterion by which the size of abutment is +gauged, is the location of the line of pressure. It is difficult and +expensive to obtain depth enough in the base of the abutment to keep +this line within the middle third, when only the thrust of the arch is +considered. If, in addition to the thrust, there is a bending moment +which, for many conditions of loading, further displaces the line of +pressure toward the critical edge, the difficulty and expense are +increased. It cannot be gainsaid that a few cubic yards of concrete +added to the ring of an arch will go much further toward strengthening +the arch than the same amount of concrete added to the two abutments. + +In reinforced concrete there are ample grounds for the contention that +the carrying out of a nice theory, based on nice assumptions and the +exact determination of ideal stresses, is of far less importance than +the building of a structure which is, in every way, capable of +performing its function. There are more than ample grounds for the +contention that the ideal stresses worked out for a reinforced concrete +structure are far from realization in this far from ideal material. + +Apart from the objection that the elastic theory, instead of showing +economy by cutting down the thickness of the arch ring, would show the +very opposite if fully carried out, there are objections of greater +weight, objections which strike at the very foundation of the theory as +applied to reinforced concrete. In the elastic theory, as in the +intricate beam theory commonly used, there is the assumption of an +initial unstressed condition of the materials. This is not true of a +beam and is still further from the truth in the case of an arch. Besides +shrinkage of the concrete, which always produces unknown initial +stresses, there is a still more potent cause of initial stress, namely, +the settlement of the arch when the forms are removed. If the initial +stresses are unknown, ideal determinations of stresses can have little +meaning. + +The elastic theory stands or falls according as one is able or unable to +calculate accurately the deflection of a reinforced concrete beam; and +it is an impossibility to calculate this deflection even approximately. +The tests cited by Professor Lanza show the utter disagreement in the +matter of deflections. Of those tested, two beams which were identical, +showed results almost 100% apart. A theory grounded on such a shifting +foundation does not deserve serious consideration. Professor Lanza's +conclusions, quoted under the twelfth point, have special meaning and +force when applied to a reinforced concrete arch; the actual +distribution of the stresses cannot possibly be determined, and complex +cloaks of arithmetic cannot cover this fact. The elastic theory, far +from being a reliable formula, is false and misleading in the extreme. + +The fourteenth point refers to temperature calculations in a reinforced +concrete arch. These calculations have no meaning whatever. To give the +grounds for this assertion would be to reiterate much of what has been +said under the subject of the elastic arch. If the unstressed shape of +an arch cannot be determined because of the unknown effect of shrinkage +and settlement, it is a waste of time to work out a slightly different +unstressed shape due to temperature variation, and it is a further waste +of time to work out the supposed stresses resulting from deflecting that +arch back to its actual shape. + +If no other method of finding the approximate stresses in an arch +existed, the elastic theory might be classed as the best available; but +this is not the case. There is a method which is both simple and +reliable. Accuracy is not claimed for it, and hence it is in accord with +the more or less uncertain materials dealt with. Complete safety, +however, is assured, for it treats the arch as a series of blocks, and +the cementing of these blocks into one mass cannot weaken the arch. +Reinforcement can be proportioned in the same manner as for chimneys, by +finding the tension exerted to pull these blocks apart and then +providing steel to take that tension. + +The fifteenth point concerns steel in compression in reinforced concrete +columns or beams. It is common practice--and it is recommended in the +most pretentious works on the subject--to include in the strength of a +concrete column slender longitudinal rods embedded in the concrete. To +quote from one of these works: + + "The compressive resistance of a hooped member exceeds the sum of + the following three elements: (1) The compressive resistance of the + concrete without reinforcement. (2) The compressive resistance of + the longitudinal rods stressed to their elastic limit. (3) The + compressive resistance which would have been produced by the + imaginary longitudinals at the elastic limit of the hooping metal, + the volume of the imaginary longitudinals being taken as 2.4 times + that of the hooping metal." + +This does not stand the test, either of theory or practice; in fact, it +is far from being true. Its departure from the truth is great enough +and of serious enough moment to explain some of the worst accidents in +the history of reinforced concrete. + +It is a nice theoretical conception that the steel and the concrete act +together to take the compression, and that each is accommodating enough +to take just as much of the load as will stress it to just the right +unit. Here again, initial stress plays an important part. The shrinkage +of the concrete tends to put the rods in compression, the load adds more +compression on the slender rods and they buckle, because of the lack of +any adequate stiffening, long before the theorists' ultimate load is +reached. + +There is no theoretical or practical consideration which would bring in +the strength of the hoops after the strength of the concrete between +them has been counted. All the compression of a column must, of +necessity, go through the disk of concrete between the two hoops (and +the longitudinal steel). No additional strength in the hoops can affect +the strength of this disk, with a given spacing of the hoops. It is true +that shorter disks will have more strength, but this is a matter of the +spacing of the hoops and not of their sectional area, as the above +quotation would make it appear. + +Besides being false theoretically, this method of investing phantom +columns with real strength is wofully lacking in practical foundation. +Even the assumption of reinforcing value to the longitudinal steel rods +is not at all borne out in tests. Designers add enormously to the +calculated strength of concrete columns when they insert some +longitudinal rods. It appears to be the rule that real columns are +weakened by the very means which these designers invest with reinforcing +properties. Whether or not it is the rule, the mere fact that many tests +have shown these so-called reinforced concrete columns to be weaker than +similar plain concrete columns is amply sufficient to condemn the +practice of assuming strength which may not exist. Of all parts of a +building, the columns are the most vital. The failure of one column +will, in all probability, carry with it many others stronger than +itself, whereas a weak and failing slab or beam does not put an extra +load and shock on the neighboring parts of a structure. + +In Bulletin No. 10 of the University of Illinois Experiment Station,[C] +a plain concrete column, 9 by 9 in. by 12 ft., stood an ultimate +crushing load of 2,004 lb. per sq. in. Column 2, identical in size, and +having four 5/8-in. rods embedded in the concrete, stood 1,557 lb. per +sq. in. So much for longitudinal rods without hoops. This is not an +isolated case, but appears to be the rule; and yet, in reading the +literature on the subject, one would be led to believe that longitudinal +steel rods in a plain concrete column add greatly to the strength of the +column. + +A paper, by Mr. M.O. Withey, before the American Society for Testing +Materials, in 1909, gave the results of some tests on concrete-steel and +plain concrete columns. (The term, concrete-steel, is used because this +particular combination is not "reinforced" concrete.) One group of +columns, namely, _W1_ to _W3_, 10-1/2 in. in diameter, 102 in. long, and +circular in shape, stood an average ultimate load of 2,600 lb. per sq. +in. These columns were of plain concrete. Another group, namely, _E1_ to +_E3_, were octagonal in shape, with a short diameter (12 in.), their +length being 120 in. These columns contained nine longitudinal rods, 5/8 +in. in diameter, and 1/4-in. steel rings every foot. They stood an +ultimate load averaging 2,438 lb. per sq. in. This is less than the +column with no steel and with practically the same ratio of slenderness. + +In some tests on columns made by the Department of Buildings, of +Minneapolis, Minn.[D], Test _A_ was a 9 by 9-in. column, 9 ft. 6 in. +long, with ten longitudinal, round rods, 1/2 in. in diameter, and +1-1/2-in. by 3/16-in. circular bands (having two 1/2-in. rivets in the +splice), spaced 4 in. apart, the circles being 7 in. in diameter. It +carried an ultimate load of 130,000 lb., which is much less than half +"the compressive resistance of a hooped member," worked out according to +the authoritative quotation before given. Another similar column stood a +little more than half that "compressive resistance." Five of the +seventeen tests on the concrete-steel columns, made at Minneapolis, +stood less than the plain concrete columns. So much for the longitudinal +rods, and for hoops which are not close enough to stiffen the rods; and +yet, in reading the literature on the subject, any one would be led to +believe that longitudinal rods and hoops add enormously to the strength +of a concrete column. + +The sixteenth indictment against common practice is in reference to flat +slabs supported on four sides. Grashof's formula for flat plates has no +application to reinforced concrete slabs, because it is derived for a +material strong in all directions and equally stressed. The strength of +concrete in tension is almost nil, at least, it should be so considered. +Poisson's ratio, so prominent in Grashof's formula, has no meaning +whatever in steel reinforcement for a slab, because each rod must take +tension only; and instead of a material equally stressed in all +directions, there are generally sets of independent rods in only two +directions. In a solution of the problem given by a high English +authority, the slab is assumed to have a bending moment of equal +intensity along its diagonal. It is quite absurd to assume an intensity +of bending clear into the corner of a slab, and on the very support +equal to that at its center. A method published by the writer some years +ago has not been challenged. By this method strips are taken across the +slab and the moment in them is found, considering the limitations of the +several strips in deflection imposed by those running at right angles +therewith. This method shows (as tests demonstrate) that when the slab +is oblong, reinforcement in the long direction rapidly diminishes in +usefulness. When the ratio is 1:1-1/2, reinforcement in the long +direction is needless, since that in the short direction is required to +take its full amount. In this way French and other regulations give +false results, and fail to work out. + +If the writer is wrong in any or all of the foregoing points, it should +be easy to disprove his assertions. It would be better to do this than +to ridicule or ignore them, and it would even be better than to issue +reports, signed by authorities, which commend the practices herein +condemned. + + +FOOTNOTES: + +[Footnote A: Presented at the meeting of March 16th, 1910.] + +[Footnote B: "Stresses in Reinforced Concrete Beams," _Journal_, Am. +Soc. Mech. Engrs., Mid-October, 1909.] + +[Footnote C: Page 14, column 8.] + +[Footnote D: _Engineering News_, December 3d, 1908.] + + + + +DISCUSSION + + +JOSEPH WRIGHT, M. AM. SOC. C. E. (by letter).--If, as is expected, Mr. +Godfrey's paper serves to attract attention to the glaring +inconsistencies commonly practiced in reinforced concrete designs, and +particularly to the careless detailing of such structures, he will have +accomplished a valuable purpose, and will deserve the gratitude of the +Profession. + +No engineer would expect a steel bridge to stand up if the detailing +were left to the judgment or convenience of the mechanics of the shop, +yet in many reinforced concrete designs but little more thought is given +to the connections and continuity of the steel than if it were an +unimportant element of the structure. Such examples, as illustrated by +the retaining wall in Fig. 2, are common, the reinforcing bars of the +counterfort being simply hooked by a 4-in. U-bend around those of the +floor and wall slabs, and penetrating the latter only from 8 to 12 in. +The writer can cite an example which is still worse--that of a T-wall, +16 ft. high, in which the vertical reinforcement of the wall slab +consisted of 3/4-in. bars, spaced 6 in. apart. The wall slab was 8 in. +thick at the top and only 10 in. at the bottom, yet the 3/4-in. vertical +bars penetrated the floor slab only 8 in., and were simply hooked around +its lower horizontal bars by 4-in. U-bends. Amazing as it may appear, +this structure was designed by an engineer who is well versed in the +theories of reinforced concrete design. These are only two examples from +a long list which might be cited to illustrate the carelessness often +exhibited by engineers in detailing reinforced concrete structures. + +In reinforced concrete work the detailer has often felt the need of some +simple and efficient means of attaching one bar to another, but, in its +absence, it is inexcusable that he should resort to such makeshifts as +are commonly used. A simple U-hook on the end of a bar will develop only +a small part of the strength of the bar, and, of course, should not be +relied on where the depth of penetration is inadequate; and, because of +the necessity of efficient anchorage of the reinforcing bars where one +member of a structure unites with another, it is believed that in some +instances economy might be subserved by the use of shop shapes and shop +connections in steel, instead of the ordinary reinforcing bars. Such +cases are comparatively few, however, for the material in common use is +readily adapted to the design, in the ordinary engineering structure, +and only requires that its limitations be observed, and that the +designer be as conscientious and consistent in detailing as though he +were designing in steel. + +This paper deserves attention, and it is hoped that each point therein +will receive full and free discussion, but its main purport is a plea +for simplicity, consistency, and conservatism in design, with which the +writer is heartily in accord. + + +S. BENT RUSSELL, M. AM. SOC. C. E. (by letter).--The author has given +expression in a forcible way to feelings possessed no doubt by many +careful designers in the field in question. The paper will serve a +useful purpose in making somewhat clearer the limitations of reinforced +concrete, and may tend to bring about a more economical use of +reinforcing material. + +It is safe to say that in steel bridges, as they were designed in the +beginning, weakness was to be found in the connections and details, +rather than in the principal members. In the modern advanced practice of +bridge design the details will be found to have some excess of strength +over the principal members. It is probable that the design of reinforced +concrete structures will take the same general course, and that progress +will be made toward safety in minor details and economy in principal +bars. + +Many of the author's points appear to be well taken, especially the +first, the third, and the eighth. + +In regard to shear bars, if it is assumed that vertical or inclined bars +add materially to the strength of short deep beams, it can only be +explained by viewing the beam as a framed structure or truss in which +the compression members are of concrete and the tension members of +steel. It is evident that, as generally built, the truss will be found +to be weak in the connections, more particularly, in some cases, in the +connections between the tension and compression members, as mentioned in +the author's first point. + +It appears to the writer that this fault may be aggravated in the case +of beams with top reinforcement for compression; this is scarcely +touched on by the author. In such a case the top and bottom chords are +of steel, with a weakly connected web system which, in practice, is +usually composed of stirrup rods looped around the principal bars and +held in position by the concrete which they are supposed to strengthen. + +While on this phase of the subject, it may be proper to call attention +to the fact that the Progress Report of the Special Committee on +Concrete and Reinforced Concrete[E] may well be criticised for its scant +attention to the case of beams reinforced on the compression side. No +limitations are specified for the guidance of the designer, but approval +is given to loading the steel with its full share of top-chord +stress.[F] + +In certain systems of reinforcement now in use, such as the Kahn and +Cummings systems, the need for connections between the web system and +the chord member is met to some degree, as is generally known. On the +other hand, however, these systems do not provide for such intensity of +pressure on the concrete at the points of connection as must occur by +the author's demonstration in his first point. The author's criticisms +on some other points would also apply to such systems, and it is not +necessary to state that one weak detail will limit the strength of the +truss. + +The author has only condemnation for the use of longitudinal rods in +concrete columns (Point 15). It would seem that if the longitudinal bars +are to carry a part of the load they must be supported laterally by the +concrete, and, as before, in the beam, it may be likened to a framed +structure in which the web system is formed of concrete alone, or of a +framework of poorly connected members, and the concrete and steel must +give mutual support in a way not easy to analyze. It is scarcely +surprising that the strength of such a structure is sometimes less than +that shown by concrete alone. + +In the Minneapolis tests, quoted by the author, there are certain points +which should be noted, in fairness to columns reinforced longitudinally. +Only four columns thus reinforced failed below the strength shown by +concrete alone, and these were from 52 to 63 days old only, while the +plain concrete was 98 days old. There was nothing to hold the rods in +place in these four columns except the concrete and the circular hoops +surrounding them. On the other hand, all the columns in which the +hooping was hooked around the individual rods showed materially greater +strength than the plain concrete, although perhaps one should be +excepted, as it was 158 days old and showed a strength of only 2,250 lb. +per sq. in., or 12% more than the plain concrete.[G] + +In considering a column reinforced with longitudinal rods and hoops, it +is proper to remark that the concrete not confined by the steel ought +not to be counted as aiding the latter in any way, and that, +consequently, the bond of the outside bars is greatly weakened. + +In view of these considerations, it may be found economical to give the +steel reinforcement of columns some stiffness of its own by sufficiently +connected lateral bracing. The writer would suggest, further, that in +beams where rods are used in compression a system of web members +sufficiently connected should be provided, so that the strength of the +combined structure would be determinate. + +To sum up briefly, columns and short deep beams, especially when the +latter are doubly reinforced, should be designed as framed structures, +and web members should be provided with stronger connections than have +been customary. + + +J.R. WORCESTER, M. AM. SOC. C. E. (by letter).--This paper is of value +in calling attention to many of the bad practices to be found in +reinforced concrete work, and also in that it gives an opportunity for +discussing certain features of design, about which engineers do not +agree. A free discussion of these features will tend to unify methods. +Several of the author's indictments, however, hit at practices which +were discarded long ago by most designers, and are not recommended by +any good authorities; the implication that they are in general use is +unwarranted. + +The first criticism, that of bending rods at a sharp angle, may be said +to be of this nature. Drawings may be made without indicating the curve, +but in practice metal is seldom bent to a sharp angle. It is undoubtedly +true that in every instance a gradual curve is preferable. + +The author's second point, that a suitable anchorage is not provided for +bent-up rods at the ends of a beam, may also be said to be a practice +which is not recommended or used in the best designs. + +The third point, in reference to the counterforts of retaining walls, is +certainly aimed at a very reprehensible practice which should not be +countenanced by any engineer. + +The fourth, fifth, and sixth items bring out the fact that undoubtedly +there has been some confusion in the minds of designers and authors on +the subject of shear in the steel. The author is wholly justified in +criticising the use of the shearing stress in the steel ever being +brought into play in reinforced concrete. Referring to the report of the +Special Committee on Concrete and Reinforced Concrete, on this point, it +seems as if it might have made the intention of the Committee somewhat +clearer had the word, tensile, been inserted in connection with the +stress in the shear reinforcing rods. In considering a beam of +reinforced concrete in which the shearing stresses are really diagonal, +there is compression in one case and tension in another; and, assuming +that the metal must be inserted to resist the tensile portion of this +stress, it is not essential that it should necessarily be wholly +parallel to the tensile stress. Vertical tensile members can prevent the +cracking of the beam by diagonal tension, just as in a Howe truss all +the tensile stresses due to shear are taken in a vertical direction, +while the compressive stresses are carried in the diagonal direction by +the wooden struts. The author seems to overlook the fact, however, that +the reinforced concrete beam differs from the Howe truss in that the +concrete forms a multiple system of diagonal compression members. It is +not necessary that a stirrup at one point should carry all the vertical +tension, as this vertical tension is distributed by the concrete. There +is no doubt about the necessity of providing a suitable anchorage for +the vertical stirrups, and such is definitely required in the +recommendations of the Special Committee. + +The cracks which the author refers to as being necessary before the +reinforcing material is brought into action, are just as likely to occur +in the case of the bent-up rods with anchors at the end, advocated by +him. While his method may be a safe one, there is also no question that +a suitable arrangement of vertical reinforcement may be all that is +necessary to make substantial construction. + +With reference to the seventh point, namely, methods of calculating +moments, it might be said that it is not generally considered good +practice to reduce the positive moments at the center of a span to the +amount allowable in a beam fully fixed at the end, and if provision is +made for a negative moment over supports sufficient to develop the +stresses involved in complete continuity, there is usually a +considerable margin of safety, from the fact of the lack of possible +fixedness of the beams at the supports. The criticism is evidently aimed +at practice not to be recommended. + +As to the eighth point, the necessary width of a beam in order to +transfer, by horizontal shear, the stress delivered to the concrete from +the rods, it might be well worth while for the author to take into +consideration the fact that while the bonding stress is developed to its +full extent near the ends of the beam, it very frequently happens that +only a portion of the total number of rods are left at the bottom, the +others having been bent upward. It may be that the width of a beam would +not be sufficient to carry the maximum bonding stress on the total +number of rods near its center, and yet it may have ample shearing +strength on the horizontal planes. The customary method of determining +the width of the beams so that the maximum horizontal shearing stress +will not be excessive, seems to be a more rational method than that +suggested by Mr. Godfrey. + +Referring to the tenth and fourteenth points, it would be interesting to +know whether the author proportions his steel to take the remaining +tension without regard to the elongation possible at the point where it +is located, considering the neutral axis of the section under the +combined stress. Take, for instance, a chimney: If the section is first +considered to be homogeneous material which will carry tension and +compression equally well, and the neutral axis is found under the +combined stresses, the extreme tensile fiber stress on the concrete will +generally be a matter of 100 or 200 lb. Evidently, if steel is inserted +to replace the concrete in tension, the corresponding stress in the +steel cannot be more than from 1,500 to 3,000 lb. per sq. in. If +sufficient steel is provided to keep the unit stress down to the proper +figure, there can be little criticism of the method, but if it is worked +to, say, 16,000 lb. per sq. in., it is evident that the result will be a +different position for the neutral axis, invalidating the calculation +and resulting in a greater stress in compression on the concrete. + + +L.J. MENSCH, M. AM. SOC. C. E. (by letter).--Much of the poor practice +in reinforced concrete design to which Mr. Godfrey calls attention is +due, in the writer's opinion, to inexperience on the part of the +designer. + +It is true, however, that men of high standing, who derided reinforced +concrete only a few years ago, now pose as reinforced concrete experts, +and probably the author has the mistakes of these men in mind. + +The questions which he propounds were settled long ago by a great many +tests, made in various countries, by reliable authorities, although the +theoretical side is not as easily answered; but it must be borne in mind +that the stresses involved are mostly secondary, and, even in steel +construction, these are difficult of solution. The stresses in the web +of a deep steel girder are not known, and the web is strengthened by a +liberal number of stiffening angles, which no expert can figure out to a +nicety. The ultimate strength of built-up steel columns is not known, +frequently not even within 30%; still less is known of the strength of +columns consisting of thin steel casings, or of the types used in the +Quebec Bridge. It seems to be impossible to solve the problem +theoretically for the simplest case, but had the designer of that bridge +known of the tests made by Hodgkinson more than 40 years ago, that +accident probably would not have happened. + +Practice is always ahead of theory, and the writer claims that, with the +great number of thoroughly reliable tests made in the last 20 years, the +man who is really informed on this subject will not see any reason for +questioning the points brought out by Mr. Godfrey. + +The author is right in condemning sharp bends in reinforcing rods. +Experienced men would not think of using them, if only for the reason +that such sharp bends are very expensive, and that there is great +likelihood of breaking the rods, or at least weakening them. Such sharp +bends invite cracks. + +Neither is there any question in regard to the advantage of continuing +the bent-up rods over the supports. The author is manifestly wrong in +stating that the reinforcing rods can only receive their increments of +stress when the concrete is in tension. Generally, the contrary happens. +In the ordinary adhesion test, the block of concrete is held by the jaws +of the machine and the rod is pulled out; the concrete is clearly in +compression. + +The underside of continuous beams is in compression near the supports, +yet no one will say that steel rods cannot take any stress there. It is +quite surprising to learn that there are engineers who still doubt the +advisability of using bent-up bars in reinforced concrete beams. +Disregarding the very thorough tests made during the last 18 years in +Europe, attention is called to the valuable tests on thirty beams made +by J.J. Harding, M. Am. Soc. C. E., for the Chicago, Milwaukee and St. +Paul Railroad.[H] All the beams were reinforced with about 3/4% of +steel. Those with only straight rods, whether they were plain or +patented bars, gave an average shearing strength of 150 lb. per sq. in. +Those which had one-third of the bars bent up gave an average shearing +strength of 200 lb. per sq. in., and those which had nearly one-half of +the rods bent up gave an average shearing strength of 225 lb. per sq. +in. Where the bent bars were continued over the supports, higher +ultimate values were obtained than where some of the rods were stopped +off near the supports; but in every case bent-up bars showed a greater +carrying capacity than straight rods. The writer knows also of a number +of tests with rods fastened to anchor-plates at the end, but the tests +showed that they had only a slight increase of strength over straight +rods, and certainly made a poorer showing than bent-up bars. The use of +such threaded bars would increase materially the cost of construction, +as well as the time of erection. + +The writer confesses that he never saw or heard of such poor practices +as mentioned in the author's third point. On the other hand, the +proposed design of counterforts in retaining walls would not only be +very expensive and difficult to install, but would also be a decided +step backward in mechanics. This proposition recalls the trusses used +before the introduction of the Fink truss, in which the load from the +upper chord was transmitted by separate members directly to the +abutments, the inventor probably going on the principle that the +shortest way is the best. There are in the United States many hundreds +of rectangular water tanks. Are these held by any such devices? And as +they are not thus held, and inasmuch as there is no doubt that they must +carry the stress when filled with water, it is clear that, as long as +the rods from the sides are strong enough to carry the tension and are +bent with a liberal radius into the front wall and extended far enough +to form a good anchorage, the connection will not be broken. The same +applies to retaining walls. It would take up too much time to prove that +the counterfort acts really as a beam, although the forces acting on it +are not as easily found as those in a common beam. + +The writer does not quite understand the author's reference to shear +rods. Possibly he means the longitudinal reinforcement, which it seems +is sometimes calculated to carry 10,000 lb. per sq. in. in shear. The +writer never heard of such a practice. + +In regard to stirrups, Mr. Godfrey seems to be in doubt. They certainly +do not act as the rivets of a plate girder, nor as the vertical rods of +a Howe truss. They are best compared with the dowel pins and bolts of a +compound wooden beam. The writer has seen tests made on compound +concrete beams separated by copper plates and connected only by +stirrups, and the strength of the combination was nearly the same as +that of beams made in one piece. + +Stirrups do not add much to the strength of the beams where bent bars +are used, but the majority of tests show a great increase of strength +where only straight reinforcing bars are used. Stirrups are safeguards +against poor concrete and poor workmanship, and form a good connection +where concreting is interrupted through inclemency of weather or other +causes. They absolutely prevent shrinkage cracks between the stem and +the flange of T-beams, and the separation of the stem and slab in case +of serious fires. For the latter reason, the writer condemns the use of +simple U-bars, and arranges all his stirrups so that they extend from +6 to 12 in. into the slabs. Engineers are warned not to follow the +author's advice with regard to the omission of stirrups, but to use +plenty of them in their designs, or sooner or later they will thoroughly +repent it. + +In regard to bending moments in continuous beams, the writer wishes to +call attention to the fact that at least 99% of all reinforced +structures are calculated with a reduction of 25% of the bending moment +in the center, which requires only 20% of the ordinary bending moment of +a freely supported beam at the supports. There may be some engineers who +calculate a reduction of 33%; there are still some ultra-confident men, +of little experience, who compute a reduction of 50%; but, inasmuch as +most designers calculate with a reduction of only 25%, too great a +factor of safety does not result, nor have any failures been observed on +that account. + +In the case of slabs which are uniformly loaded by earth or water +pressure, the bending moments are regularly taken as (_w_ _l^{2}_)/24 in +the center and (_w_ _l^{2}_)/12 at the supports. The writer never +observed any failure of continuous beams over the supports, although he +has often noticed failures in the supporting columns directly under the +beams, where these columns are light in comparison with the beams. +Failure of slabs over the supports is common, and therefore the writer +always places extra rods over the supports near the top surface. + +The width of the beams which Mr. Godfrey derives from his simple rule, +that is, the width equals the sum of the peripheries of the reinforcing +rods, is not upheld by theory or practice. In the first place, this +width would depend on the kind of rods used. If a beam is reinforced by +three 7/8-in. round bars, the width, according to his formula, would be +8.2 in. If the beam is reinforced by six 5/8-in. bars which have the +same sectional area as the three 7/8-in. bars, then the width should be +12 in., which is ridiculous and does not correspond with tests, which +would show rather a better behavior for the six bars than for the three +larger bars in a beam of the same width. + +It is surprising to learn that there are engineers who still advocate +such a width of the stem of T-beams that the favorable influence of the +slab may be dispensed with, although there were many who did this 10 or +12 years ago. + +It certainly can be laid down as an axiom that the man who uses +complicated formulas has never had much opportunity to design or build +in reinforced concrete, as the design alone might be more expensive than +the difference in cost between concrete and structural steel work. + +The author attacks the application of the elastic theory to reinforced +concrete arches. He evidently has not made very many designs in which he +used the elastic theory, or he would have found that the abutments need +be only from three to four times thicker than the crown of the arch +(and, therefore, their moments of inertia from 27 to 64 times greater), +when the deformation of the abutments becomes negligible in the elastic +equations. Certainly, the elastic theory gives a better guess in regard +to the location of the line of pressure than any guess made without its +use. The elastic theory was fully proved for arches by the remarkable +tests, made in 1897 by the Austrian Society of Engineers and Architects, +on full-sized arches of 70-ft. span, and the observed deflections and +lateral deformations agreed exactly with the figured deformation. + +Tests on full-sized arches also showed that the deformations caused by +temperature changes agree with the elastic theory, but are not as great +for the whole mass of the arch as is commonly assumed. The elastic +theory enables one to calculate arches much more quickly than any +graphical or guess method yet proposed. + +Hooped columns are a patented construction which no one has the right to +use without license or instructions from M. Considere, 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 deg. 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 deg. 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 deg. 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 deg. 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 ( ----- - _x_ ) x _S_ , + 12 2 II II + +where + + _a_ = the area of steel per linear foot, + _x_{II}_ = the distance from the center of the steel to the outer + fiber, and + _S_{II}_ = the strength of the steel in tension. + +Then for a beam, 12 in. wide, + + 2 _d_ + _d_ _S_ = _a_ _S_ ( ----- - _x_ ) , + II 2 II + +or + + 2 + _d_ _S_ + _a_ = --------------------- . + _d_ + _S_ ( ----- - _x_ ) + II 2 II + +Carrying this to its conclusion, we have, for example, in a beam 12 in. +deep and 12 in. wide, + + _S_ = 500, + _S_{II}_ = 15,000, + _x_{II}_ = 2-1/2 in. + _a_ = 1.37 sq. in. per ft. + +The writer has used this formula very extensively, in calculating new +work and also in checking other designs built or to be built, and he +believes its results are absolutely safe. There is the further fact to +its credit, that its simplicity bars very largely the possibility of +error from its use. He sees no reason to introduce further complications +into such a formula, when actual tests will show results varying more +widely than is shown by a comparison between this simple formula and +many more complicated ones. + + +GEORGE H. MYERS, JUN. AM. SOC. C. E. (by letter).--This paper brings out +a number of interesting points, but that which strikes the writer most +forcibly is the tenth, in regard to elaborate theories and complicated +formulas for beams and slabs. The author's stand for simplicity in this +regard is well taken. A formula for the design of beams and slabs need +not be long or complicated in any respect. It can easily be obtained +from the well-known fact that the moment at any point divided by the +distance between the center of compression and the center of tension at +that point gives the tension (or compression) in the beam. + +The writer would place the neutral axis from 0.42 to 0.45 of the +effective depth of the beam from the compression side rather than at the +center, as Mr. Godfrey suggests. This higher position of the neutral +axis is the one more generally shown by tests of beams. It gives the +formula _M_ = 0.86 _d_ _As_ _f_, or _M_ = 0.85 _d_ _As_ _f_, which the +writer believes is more accurate than _M_ = 5/6 _d_ _As_ _f_, or +0.83-1/3 _d_ _As_ _f_, which would result if the neutral axis were taken +at the center of the beam. + + _d_ = depth of the beam from the compression side to the center + of the steel; + _As_ = the area of the steel; +and _f_ = the allowable stress per square inch in the steel. + +The difference, however, is very slight, the results from the two +formulas being proportional to the two factors, 83-1/3 and 85 or 86. +This formula gives the area of steel required for the moment. The +percentage of steel to be used can easily be obtained from the allowable +stresses in the concrete and the steel, and the dimensions of the beam +can be obtained in the simplest manner. This formula is used with great +success by one of the largest firms manufacturing reinforcing materials +and designing concrete structures. It is well-known to the Profession, +and the reason for using any other method, involving the Greek alphabet +and many assumptions, is unknown to the writer. The only thing to +assume--if it can be called assuming when there are so many tests to +locate it--is the position of the neutral axis. A slight difference in +this assumption affects the resulting design very little, and is +inappreciable, from a practical point of view. It can be safely said +that the neutral axis is at, or a little above, the center of the beam. + +Further, it would seem that the criticism to the effect that the initial +stress in the concrete is neglected is devoid of weight. As far as the +designer is concerned, the initial stress is allowed for. The values for +the stresses used in design are obtained from tests on blocks of +concrete which have gone through the process of setting. Whatever +initial stress exists in concrete due to this process of setting exists +also in these blocks when they are tested. The value of the breaking +load on concrete given by any outside measuring device used in these +tests, is the value of that stress over and above this initial stress. +It is this value with which we work. It would seem that, if the initial +stress is neglected in arriving at a safe working load, it would be safe +to neglect it in the formula for design. + + +EDWIN THACHER, M. AM. SOC. C. E. (by letter).--The writer will discuss +this paper under the several "points" mentioned by the author. + +_First Point._--At the point where the first rod is bent up, the stress +in this rod runs out. The other rods are sufficient to take the +horizontal stress, and the bent-up portion provides only for the +vertical and diagonal shearing stresses in the concrete. + +_Second Point._--The remarks on the first point are also applicable to +the second one. Rod 3 provides for the shear. + +_Third Point._--In a beam, the shear rods run through the compression +parts of the concrete and have sufficient anchorage. In a counterfort, +the inclined rods are sufficient to take the overturning stress. The +horizontal rods support the front wall and provide for shrinkage. The +vertical rods also provide for shrinkage, and assist the diagonal rods +against overturning. The anchorage is sufficient in all cases, and the +proposed method is no more effective. + +_Fourth Point._--In bridge pins, bending and bearing usually govern, +but, in case a wide bar pulled on a pin between the supports close to +the bar, as happens in bolsters and post-caps of combination bridges and +in other locations, shear would govern. Shear rods in concrete-steel +beams are proportioned to take the vertical and diagonal shearing +stresses. If proportioned for less stress per square inch than is used +in the bottom bars, this cannot be considered dangerous practice. + +_Fifth Point._--Vertical stirrups are designed to act like the vertical +rods in a Howe truss. Special literature is not required on the subject; +it is known that the method used gives good results, and that is +sufficient. + +_Sixth Point._--The common method is not "to assume each shear member as +taking the horizontal shear occurring in the space from member to +member," but to take all the shear from the center of the beam up to the +bar in question. + +Cracks do not necessarily endanger the safety of a beam. Any device that +will prevent the cracks from opening wide enough to destroy the beam, is +logical. By numerous experiments, Mr. Thaddeus Hyatt found that nuts and +washers at the ends of reinforcing bars were worse than useless, and +added nothing to the strength of the beams. + +_Seventh Point._--Beams can be designed, supported at the ends, fully +continuous, or continuous to a greater or less extent, as desired. The +common practice is to design slabs to take a negative moment over the +supports equal to one-half the positive moment at the center, or to bend +up the alternate rods. This is simple and good practice, for no beam can +fail as long as a method is provided by which to take care of all the +stresses without overstraining any part. + +_Eighth Point._--Bars in the bottom of a reinforced concrete beam are +often placed too close to one another. The rule of spacing the bars not +less than three diameters apart, is believed to be good practice. + +_Ninth Point._--To disregard the theory of T-beams, and work by +rule-of-thumb, can hardly be considered good engineering. + +_Tenth Point._--The author appears to consider theories for reinforced +concrete beams and slabs as useless refinements, but as long as theory +and experiment agree so wonderfully well, theories will undoubtedly +continue to be used. + +_Eleventh Point._--Calculations for chimneys are somewhat complex, but +are better and safer than rule-of-thumb methods. + +_Twelfth Point._--Deflection is not very important. + +_Thirteenth Point._--The conclusion of the Austrian Society of Engineers +and Architects, after numerous experiments, was that the elastic theory +of the arch is the only true theory. No arch designed by the elastic +theory was ever known to fail, unless on account of insecure +foundations, therefore engineers can continue to use it with confidence +and safety. + +_Fourteenth Point._--Calculations for temperature stresses, as per +theory, are undoubtedly correct for the variations in temperature +assumed. Similar calculations can also be made for shrinkage stresses, +if desired. This will give a much better idea of the stresses to be +provided for, than no calculations at all. + +_Fifteenth Point._--Experiments show that slender longitudinal rods, +poorly supported, and embedded in a concrete column, add little or +nothing to its strength; but stiff steel angles, securely latticed +together, and embedded in the concrete column, will greatly increase its +strength, and this construction is considered the most desirable when +the size of the column has to be reduced to a minimum. + +_Sixteenth Point._--The commonly accepted theory of slabs supported on +four sides can be correctly applied to reinforced concrete slabs, as it +is only a question of providing for certain moments in the slab. This +theory shows that unless the slab is square, or nearly so, nothing is to +be gained by such construction. + + +C.A.P. TURNER, M. AM. SOC. C. E. (by letter).--Mr. Godfrey has expressed +his opinion on many questions in regard to concrete construction, but he +has adduced no clean-cut statement of fact or tests, in support of his +views, which will give them any weight whatever with the practical +matter-of-fact builder. + +The usual rules of criticism place the burden of proof on the critic. +Mr. Godfrey states that if his personal opinions are in error, it should +be easy to prove them to be so, and seems to expect that the busy +practical constructor will take sufficient interest in them to spend the +time to write a treatise on the subject in order to place him right in +the matter. + +The writer will confine his discussion to only a few points of the many +on which he disagrees with Mr. Godfrey. + +First, regarding stirrups: These may be placed in the beam so as to be +of little practical value. They were so placed in the majority of the +tests made at the University of Illinois. Such stirrups differ widely in +value from those used by Hennebique and other first-class constructors. + +Mr. Godfrey's idea is that the entire pull of the main reinforcing rod +should be taken up apparently at the end. When one frequently sees slabs +tested, in which the steel breaks at the center, with no end anchorage +whatever for the rods, the soundness of Mr. Godfrey's position may be +questioned. + +Again, concrete is a material which shows to the best advantage as a +monolith, and, as such, the simple beam seems to be decidedly out of +date to the experienced constructor. + +Mr. Godfrey appears to consider that the hooping and vertical +reinforcement of columns is of little value. He, however, presents for +consideration nothing but his opinion of the matter, which appears to be +based on an almost total lack of familiarity with such construction. + +The writer will state a few facts regarding work which he has executed. +Among such work have been columns in a number of buildings, with an +18-in. core, and carrying more than 500 tons; also columns in one +building, which carry something like 1100 tons on a 27-in. core. In each +case there is about 1-1/2 in. of concrete outside the core for a +protective coating. The working stress on the core, if it takes the +load, is approximately equal to the ultimate strength of the concrete in +cubes, to say nothing of the strength of cylinders fifteen times their +diameter in height. These values have been used with entire confidence +after testing full-sized columns designed with the proper proportions of +vertical steel and hooping, and are regarded by the writer as having at +least double the factor of safety used in ordinary designs of structural +steel. + +An advantage which the designer in concrete has over his fellow-engineer +in the structural steel line, lies in the fact that, with a given type +of reinforcement, his members are similar in form, and when the work is +executed with ordinary care, there is less doubt as to the distribution +of stress through a concrete column, than there is with the ordinary +structural steel column, since the core is solid and the conditions are +similar in all cases. + +Tests of five columns are submitted herewith. The columns varied little +in size, but somewhat in the amount of hooping, with slight differences +in the vertical steel. The difference between Columns 1 and 3 is nearly +50%, due principally to the increase in hooping, and to a small addition +in the amount of vertical steel. As to the efficiency of hooping and +vertical reinforcement, the question may be asked Mr. Godfrey, and those +who share his views, whether a column without reinforcement can be cast, +which will equal the strength of those, the tests of which are +submitted. + + +TEST NO. 1.[I] + +Marks on column--none. + +Reinforcement--eight 1-1/8-in. round bars vertically. + +Band spacing--- 9 in. vertically. + +Hooped with seven 32-in. wire spirals about 2-in. raise. + +Outside diameter of hoops--14-1/2 in. + +Total load at failure--1,360,000 lb. + +Remarks.--Point of failure was about 22 in. from the top. Little +indication of failure until ultimate load was reached. + +Some slight breaking off of concrete near the top cap, due possibly to +the cap not being well seated in the column itself. + + +TEST NO. 2. + +Marks on column--Box 4. + +Reinforcement--eight 1-1/8-in. round bars vertically. + +Band spacing about 13 in. vertically. + +Wire spiral about 3-in. pitch. + +Point of failure about 18 in. from top. + +Top of cast-iron cap cracked at four corners. + +Ultimate load--1,260,000 lb. + +Remarks.--Both caps apparently well seated, as was the case with all the +subsequent tests. + + +TEST NO. 3. + +Marks on column--4-B. + +Reinforcement--eight 7/8-in. round bars vertically. + +Hoops--1-3/4 in. x 3/16 in. x 14 in. outside diameter. + +Band spacing--13 in. vertically. + +Ultimate load--900,000 lb. + +Point of failure about 2 ft. from top. + +Remarks.--Concrete, at failure, considerably disintegrated, probably due +to continuance of movement of machine after failure. + + +TEST NO. 4. + +Marks on column--Box 4. + +Reinforcement--eight 1-in. round bars vertically. + +Hoops spaced 8 in. vertically. + +Wire spirals as on other columns. + +Total load at failure--1,260,000 lb. + +Remarks.--First indications of failure were nearest the bottom end of +the column, but the total failure was, as in all other columns, within 2 +ft. of the top. Large cracks in the shell of the column extended from +both ends to very near the middle. This was the most satisfactory +showing of all the columns, as the failure was extended over nearly the +full length of the column. + + +TEST NO. 5. + +Marks on column--none. + +Reinforcement--eight 7/8-in. bars vertically. + +Hoops spaced 10 in. vertically. + +Outside diameter of hoops--14-1/2 in. + +Wire spiral as before. + +Load at failure--1,100,000 lb. + +Ultimate load--1,130,000 lb. + +Remarks.--The main point of failure in this, as in all other columns, +was within 2 ft. of the top, although this column showed some scaling +off at the lower end. + +In these tests it will be noted that the concrete outside of the hooped +area seems to have had very little value in determining the ultimate +strength; that, figuring the compression on the core area and deducting +the probable value of the vertical steel, these columns exhibited from +5,000 to 7,000 lb. per sq. in. as the ultimate strength of the hooped +area, not considering the vertical steel. Some of them run over 8,000 +lb. + +The concrete mixture was 1 part Alpena Portland cement, 1 part sand, +1-1/2 parts buckwheat gravel and 3-1/2 parts gravel ranging from 1/4 to +3/4 in. in size. + +The columns were cast in the early part of December, and tested in +April. The conditions under which they hardened were not particularly +favorable, owing to the season of the year. + +The bands used were 1-3/4 by 1/4 in., except in the light column, where +they were 1-3/4 by 3/16 in. + +In his remarks regarding the tests at Minneapolis, Minn., Mr. Godfrey +has failed to note that these tests, faulty as they undoubtedly were, +both in the execution of the work, and in the placing of the +reinforcement, as well as in the character of the hooping used, were +sufficient to satisfy the Department of Buildings that rational design +took into consideration the amount of hooping and the amount of +vertical steel, and on a basis not far from that which the writer +considers reasonable practice. + +Again, Mr. Godfrey seems to misunderstand the influence of Poisson's +ratio in multiple-way reinforcement. If Mr. Godfrey's ideas are correct, +it will be found that a slab supported on two sides, and reinforced with +rods running directly from support to support, is stronger than a +similar slab reinforced with similar rods crossing it diagonally in +pairs. Tests of these two kinds of slabs show that those with the +diagonal reinforcement develop much greater strength than those +reinforced directly from support to support. Records of small test slabs +of this kind will be found in the library of the Society. + +Mr. Godfrey makes the good point that the accuracy of an elastic theory +must be determined by the elastic deportment of the construction under +load, and it seems to the writer that if authors of textbooks would pay +some attention to this question and show by calculation that the elastic +deportment of slabs is in keeping with their method of figuring, the +gross errors in the theoretical treatment of slabs in the majority of +works on reinforced concrete would be remedied. + +Although he makes the excellent point noted, Mr. Godfrey very +inconsistently fails to do this in connection with his theory of slabs, +otherwise he would have perceived the absurdity of any method of +calculating a multiple-way reinforcement by endeavoring to separate the +construction into elementary beam strips. This old-fashioned method was +discarded by the practical constructor many years ago, because he was +forced to guarantee deflections of actual construction under severe +tests. Almost every building department contains some regulation +limiting the deflection of concrete floors under test, and yet no +commissioner of buildings seems to know anything about calculating +deflections. + +In the course of his practice the writer has been required to give +surety bonds of from $50,000 to $100,000 at a time, to guarantee under +test both the strength and the deflection of large slabs reinforced in +multiple directions, and has been able to do so with accuracy by methods +which are equivalent to considering Poisson's ratio, and which are given +in his book on concrete steel construction. + +Until the engineer pays more attention to checking his complicated +theories with facts as determined by tests of actual construction, the +view, now quite general among the workers in reinforced concrete +regarding him will continue to grow stronger, and their respect for him +correspondingly less, until such time as he demonstrates the +applicability of his theories to ordinary every-day problems. + + +PAUL CHAPMAN, ASSOC. M. AM. SOC. C. E. (by letter).--Mr. Godfrey has +pointed out, in a forcible manner, several bad features of text-book +design of reinforced concrete beams and retaining walls. The practical +engineer, however, has never used such methods of construction. Mr. +Godfrey proposes certain rules for the calculation of stresses, but +there are no data of experiments, or theoretical demonstrations, to +justify their use. + +It is also of the utmost importance to consider the elastic behavior of +structures, whether of steel or concrete. To illustrate this, the writer +will cite a case which recently came to his attention. A roof was +supported by a horizontal 18-in. I-beam, 33 ft. long, the flanges of +which were coped at both ends, and two 6 by 4-in. angles, 15 ft. long, +supporting the same, were securely riveted to the web, thereby forming a +frame to resist lateral wind pressure. Although the 18-in. I-beam was +not loaded to its full capacity, its deflection caused an outward +flexure of 3/4 in. and consequent dangerous stresses in the 6 by 4-in. +angle struts. The frame should have been designed as a structure fixed +at the base of the struts. The importance of the elastic behavior of a +structure is forcibly illustrated by comparing the contract drawings for +a great cantilever bridge which spans the East River with the expert +reports on the same. Due to the neglect of the elastic behavior of the +structure in the contract drawings, and another cause, the average error +in the stresses of 290 members was 18-1/2%, with a maximum of 94 per +cent. + +Mr. Godfrey calls attention to the fact that stringers in railroad +bridges are considered as simple beams; this is theoretically proper +because the angle knees at their ends can transfer practically no flange +stress. It is also to be noted that when stringers are in the plane of a +tension chord, they are milled to exact lengths, and when in the plane +of a compression chord, they are given a slight clearance in order to +prevent arch action. + +[Illustration: FIG. 3.] + +The action of shearing stresses in concrete beams may be illustrated by +reference to the diagrams in Fig. 3, where the beams are loaded with a +weight, _W_. The portion of _W_ traveling to the left support, moves in +diagonal lines, varying from many sets of almost vertical lines to a +single diagonal. The maximum intensity of stress probably would be in +planes inclined about 45 deg., 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 deg., 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 deg., 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 Moersch, 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 Moersch, 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. Moersch, 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 +Moersch, 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 Considere, the speaker understands +that to be the inventor's view as well. + +The speaker makes use of the scheme mentioned by the author in regard to +the design of flat slabs supported on more than two sides (noted in the +sixteenth point), namely, that of dividing the area into strips, the +moments of which are determined so as to produce computed deflections +which are equal in the two strips running at right angles at each point +of intersection. This method, however, requires a large amount of +analytical work for any special case, and the speaker is mildly +surprised that the author cannot recommend some simpler method so as to +carry out his general scheme of extreme simplification of methods and +design. + +If use is to be made at all of deflection observations, theories, and +formulas, account should certainly be taken of the actual settlements +and other deflections which invariably occur in Nature at points of +support. These changes of level, or slope, or both, actually alter very +considerably the stresses as usually computed, and, in all rigorous +design work, should be considered. + +On the whole, the speaker believes that the author has put himself in +the class with most iconoclasts, in that he has overshot his mark. There +seems to be a very important point, however, on which he has touched, +namely, the lack of care exercised by most designers with regard to +those items which most nearly correspond with the so-called "details" of +structural steel work, and are fully as important in reinforced +concrete as in steel. It is comparatively a small matter to proportion a +simple reinforced concrete beam at its intersection to resist a given +moment, but the carrying out of that item of the work is only a start on +the long road which should lead through the consideration of every +detail, not the least important of which are such items as most of the +sixteen points raised by the author. + +The author has done the profession a great service by raising these +questions, and, while full concurrence is not had with him in all +points, still the speaker desires to express his hearty thanks for +starting what is hoped will be a complete discussion of the really vital +matter of detailing reinforced concrete design work. + + +ALBIN H. BEYER, ESQ.--Mr. Goodrich has brought out very clearly the +efficiency of vertical stirrups. As Mr. Godfrey states that explanations +of how stirrups act are conspicuous in the literature of reinforced +concrete by their absence, the speaker will try to explain their action +in a reinforced concrete beam. + +It is well known that the internal static conditions in reinforced +concrete beams change to some extent with the intensity of the direct or +normal stresses in the steel and concrete. In order to bring out his +point, the speaker will trace, in such a beam, the changes in the +internal static conditions due to increasing vertical loads. + +[Illustration: FIG. 8.] + +Let Fig. 8 represent a beam reinforced by horizontal steel rods of such +diameter that there is no possibility of failure from lack of adhesion +of the concrete to the steel. The beam is subjected to the vertical +loads, [Sigma] _P_. For low unit stresses in the concrete, the neutral +surface, _n n_, is approximately in the middle of the beam. Gradually +increase the loads, [Sigma] _P_, until the steel reaches an elongation +of from 0.01 to 0.02 of 1%, corresponding to tensile stresses in the +steel of from 3,000 to 6,000 lb. per sq. in. At this stage plain +concrete would have reached its ultimate elongation. It is known, +however, that reinforced concrete, when well made, can sustain without +rupture much greater elongations; tests have shown that its ultimate +elongation may be as high as 0.1 of 1%, corresponding to tensions in +steel of 30,000 lb. per sq. in. + +Reinforced concrete structures ordinarily show tensile cracks at very +much lower unit stresses in the steel. The main cause of these cracks is +as follows: Reinforced concrete setting in dry air undergoes +considerable shrinkage during the first few days, when it has very +little resistance. This tendency to shrink being opposed by the +reinforcement at a time when the concrete does not possess the necessary +strength or ductility, causes invisible cracks or planes of weakness in +the concrete. These cracks open and become visible at very low unit +stresses in the steel. + +Increase the vertical loads, [Sigma] _P_, and the neutral surface will +rise and small tensile cracks will appear in the concrete below the +neutral surface (Fig. 8). These cracks are most numerous in the central +part of the span, where they are nearly vertical. They decrease in +number at the ends of the span, where they curve slightly away from the +perpendicular toward the center of the span. The formation of these +tensile cracks in the concrete relieves it at once of its highly +stressed condition. + +It is impossible to predict the unit tension in the steel at which these +cracks begin to form. They can be detected, though not often visible, +when the unit tensions in the steel are as low as from 10,000 to 16,000 +lb. per sq. in. As soon as the tensile cracks form, though invisible, +the neutral surface approaches the position in the beam assigned to it +by the common theory of flexure, with the tension in the concrete +neglected. The internal static conditions in the beam are now modified +to the extent that the concrete below the neutral surface is no longer +continuous. The common theory of flexure can no longer be used to +calculate the web stresses. + +To analyze the internal static conditions developed, the speaker will +treat as a free body the shaded portion of the beam shown in Fig. 8, +which lies between two tensile cracks. + +[Illustration: FIG. 9.] + +In Fig. 9 are shown all the forces which act on this free body, _C b b' +C'_. + +At any section, let + + _C_ or _C'_ represent the total concrete compression; + _T_ or _T'_ represent the total steel tension; + _J_ or _J'_ represent the total vertical shear; + _P_ represent the total vertical load for the length, _b_ - _b'_; + +and let [Delta] _T_ = _T'_ - _T_ = _C'_ - _C_ represent the total +transverse shear for the length, _b_ - _b'_. + +Assuming that the tension cracks extend to the neutral surface, _n n_, +that portion of the beam _C b b' C'_, acts as a cantilever fixed at _a +b_ and _a' b'_, and subjected to the unbalanced steel tension, [Delta] +_T_. The vertical shear, _J_, is carried mainly by the concrete above +the neutral surface, very little of it being carried by the steel +reinforcement. In the case of plain webs, the tension cracks are the +forerunners of the sudden so-called diagonal tension failures produced +by the snapping off, below the neutral surface, of the concrete +cantilevers. The logical method of reinforcing these cantilevers is by +inserting vertical steel in the tension side. The vertical +reinforcement, to be efficient, must be well anchored, both in the top +and in the bottom of the beam. Experience has solved the problem of +doing this by the use of vertical steel in the form of stirrups, that +is, U-shaped rods. The horizontal reinforcement rests in the bottom of +the U. + +Sufficient attention has not been paid to the proper anchorage of the +upper ends of the stirrups. They should extend well into the compression +area of the beam, where they should be properly anchored. They should +not be too near the surface of the beam. They must not be too far apart, +and they must be of sufficient cross-section to develop the necessary +tensile forces at not excessive unit stresses. A working tension in the +stirrups which is too high, will produce a local disintegration of the +cantilevers, and give the beam the appearance of failure due to diagonal +tension. Their distribution should follow closely that of the vertical +or horizontal shear in the beam. Practice must rely on experiment for +data as to the size and distribution of stirrups for maximum efficiency. + +The maximum shearing stress in a concrete beam is commonly computed by +the equation: + + _V_ + _v_ = ------------- (1) + 7 + --- _b_ _d_ + 8 + +Where _d_ is the distance from the center of the reinforcing bars to the +surface of the beam in compression: + + _b_ = the width of the flange, and + _V_ = the total vertical shear at the section. + +This equation gives very erratic results, because it is based on a +continuous web. For a non-continuous web, it should be modified to + + _V_ +_v_ = ------------- (2) + _K_ _b_ _d_ + +In this equation _K b d_ represents the concrete area in compression. +The value of _K_ is approximately equal to 0.4. + +Three large concrete beams with web reinforcement, tested at the +University of Illinois[K], developed an average maximum shearing +resistance of 215 lb. per sq. in., computed by Equation 1. Equation 2 +would give 470 lb. per sq. in. + +Three T-beams, having 32 by 3-1/4-in. flanges and 8-in. webs, tested at +the University of Illinois, had maximum shearing resistances of 585, +605, and 370 lb. per. sq. in., respectively.[L] They did not fail in +shear, although they appeared to develop maximum shearing stresses which +were almost three times as high as those in the rectangular beams +mentioned. The concrete and web reinforcement being identical, the +discrepancy must be somewhere else. Based on a non-continuous concrete +web, the shearing resistances become 385, 400, and 244 lb. per sq. in., +respectively. As none of these failed in shear, the ultimate shearing +resistance of concrete must be considerably higher than any of the +values given. + +About thirteen years ago, Professor A. Vierendeel[M] developed the +theory of open-web girder construction. By an open-web girder, the +speaker means a girder which has a lower and upper chord connected by +verticals. Several girders of this type, far exceeding solid girders in +length, have been built. The theory of the open-web girder, assuming the +verticals to be hinged at their lower ends, applies to the concrete beam +reinforced with stirrups. Assuming that the spaces between the verticals +of the girder become continually narrower, they become the tension +cracks of the concrete beam.[N] + + +JOHN C. OSTRUP, M. AM. SOC. C. E.--The author has rendered a great +service to the Profession in presenting this paper. In his first point +he mentions two designs of reinforced concrete beams and, inferentially, +he condemns a third design to which the speaker will refer later. The +designs mentioned are, first, that of a reinforced concrete beam +arranged in the shape of a rod, with separate concrete blocks placed on +top of it without being connected--such a beam has its strength only in +the rod. It is purely a suspension, or "hog-chain" affair, and the +blocks serve no purpose, but simply increase the load on the rod and its +stresses. + +The author's second design is an invention of his own, which the +Profession at large is invited to adopt. This is really the same system +as the first, except that the blocks are continuous and, presumably, +fixed at the ends. When they are so fixed, the concrete will take +compressive stresses and a certain portion of the shear, the remaining +shear being transmitted to the rod from the concrete above it, but only +through friction. Now, the frictional resistance between a steel rod and +a concrete beam is not such as should be depended on in modern +engineering designs. + +The third method is that which is used by nearly all competent +designers, and it seems to the speaker that, in condemning the general +practice of current reinforced designs in sixteen points, the author +could have saved himself some time and labor by condemning them all in +one point. + +What appears to be the underlying principle of reinforced concrete +design is the adhesion, or bond, between the steel and the concrete, and +it is that which tends to make the two materials act in unison. This is +a point which has not been touched on sufficiently, and one which it was +expected that Mr. Beyer would have brought out, when he illustrated +certain internal static conditions. This principle, in the main, will +cover the author's fifth point, wherein stirrups are mentioned, and +again in the first point, wherein he asks: "Will some advocate of this +type of design please state where this area can be found?" + +To understand clearly how concrete acts in conjunction with steel, it is +necessary to analyze the following question: When a steel rod is +embedded in a solid block of concrete, and that rod is put in tension, +what will be the stresses in the rod and the surrounding concrete? + +The answer will be illustrated by reference to Fig. 10. It must be +understood that the unit stresses should be selected so that both the +concrete and the steel may be stressed in the same relative ratio. +Assuming the tensile stress in the steel to be 16,000 lb. per sq. in., +and the bonding value 80 lb., a simple formula will show that the length +of embedment, or that part of the rod which will act, must be equal to +50 diameters of the rod. + +[Illustration: FIG. 10.] + +When the rod is put in tension, as indicated in Fig. 10, what will be +the stresses in the surrounding concrete? The greatest stress will come +on the rod at the point where it leaves the concrete, where it is a +maximum, and it will decrease from that point inward until the total +stress in the steel has been distributed to the surrounding concrete. At +that point the rod will only be stressed back for a distance equal in +length to 50 diameters, no matter how far beyond that length the rod may +extend. + +The distribution of the stress from the steel rod to the concrete can be +represented by a cone, the base of which is at the outer face of the +block, as the stresses will be zero at a point 50 diameters back, and +will increase in a certain ratio out toward the face of the block, and +will also, at all intermediate points, decrease radially outward from +the rod. + +The intensity of the maximum stress exerted on the concrete is +represented by the shaded area in Fig. 10, the ordinates, measured +perpendicularly to the rod, indicating the maximum resistance offered by +the concrete at any point. + +If the concrete had a constant modulus of elasticity under varying +stress, and if the two materials had the same modulus, the stress +triangle would be bounded by straight lines (shown as dotted lines in +Fig. 10); but as this is not true, the variable moduli will modify the +stress triangle in a manner which will tend to make the boundary lines +resemble parabolic curves. + +A triangle thus constructed will represent by scale the intensity of the +stress in the concrete, and if the ordinates indicate stresses greater +than that which the concrete will stand, a portion will be destroyed, +broken off, and nothing more serious will happen than that this stress +triangle will adjust itself, and grip the rod farther back. This process +keeps on until the end of the rod has been reached, when the triangle +will assume a much greater maximum depth as it shortens; or, in other +words, the disintegration of the concrete will take place here very +rapidly, and the rod will be pulled out. + +In the author's fourth point he belittles the use of shear rods, and +states: "No hint is given as to whether these bars are in shear or in +tension." As a matter of fact, they are neither in shear nor wholly in +tension, they are simply in bending between the centers of the +compressive resultants, as indicated in Fig. 12, and are, besides, +stressed slightly in tension between these two points. + +[Illustration: FIG. 11.] + +In Fig. 10 the stress triangle indicates the distribution and the +intensity of the resistance in the concrete to a force acting parallel +to the rod. A similar triangle may be drawn, Fig. 11, showing the +resistance of the rod and the resultant distribution in the concrete to +a force perpendicular to the rod. Here the original force would cause +plain shear in the rod, were the latter fixed in position. Since this +cannot be the case, the force will be resolved into two components, one +of which will cause a tensile stress in the rod and the other will pass +through the centroid of the compressive stress area. This is indicated +in Fig. 11, which, otherwise, is self-explanatory. + +[Illustration: FIG. 12.] + +Rods are not very often placed in such a position, but where it is +unavoidable, as in construction joints in the middle of slabs or beams, +they serve a very good purpose; but, to obtain the best effect from +them, they should be placed near the center of the slab, as in Fig. 12, +and not near the top, as advocated by some writers. + +If the concrete be overstressed at the points where the rod tends to +bend, that is, if the rods are spaced too far apart, disintegration will +follow; and, for this reason, they should be long enough to have more +than 50 diameters gripped by the concrete. + +This leads up to the author's seventh point, as to the overstressing of +the concrete at the junction of the diagonal tension rods, or stirrups, +and the bottom reinforcement. + +[Illustration: FIG. 13.] + +Analogous with the foregoing, it is easy to lay off the stress triangles +and to find the intensity of stress at the maximum points, in fact at +any point, along the tension rods and the bottom chord. This is +indicated in Fig. 13. These stress triangles will start on the rod 50 +diameters back from the point in question and, although the author has +indicated in Fig. 1 that only two of the three rods are stressed, there +must of necessity also be some stress in the bottom rod to the left of +the junction, on account of the deformation which takes place in any +beam due to bending. Therefore, all three rods at the point where they +are joined, are under stress, and the triangles can be laid off +accordingly. + +It will be noticed that the concrete will resist the compressive +components, not at any specific point, but all along the various rods, +and with the intensities shown by the stress triangles; also, that some +of these triangles will overlap, and, hence, a certain readjustment, or +superimposition, of stresses takes place. + +The portion which is laid off below the bottom rods will probably not +act unless there is sufficient concrete below the reinforcing bars and +on the sides, and, as that is not the case in ordinary construction, it +is very probable, as Mr. Goodrich has pointed out, that the concrete +below the rods plays an unimportant part, and that the triangle which is +now shown below the rod should be partially omitted. + +The triangles in Fig. 13 show the intensity of stress in the concrete at +any point, or at any section where it is wanted. They show conclusively +where the components are located in the concrete, their relation to the +tensile stresses in the rods, and, furthermore, that they act only in a +general way at right angles to one another. This is in accordance with +the theory of beams, that at any point in the web there are tensile and +compressive stresses of equal intensity, and at right angles to one +another, although in a non-homogeneous web the distribution is somewhat +different. + +After having found at the point of junction the intensity of stress, it +is possible to tell whether or not a bond between the stirrups and the +bottom rods is necessary, and it would not seem to be where the stirrups +are vertical. + +It would also seem possible to tell in what direction, if any, the bend +in the inclined stirrups should be made. It is to be assumed, although +not expressly stated, that the bends should curve from the center up +toward the end of the beam, but an inspection of the stress triangles, +Fig. 13, will show that the intensity of stress is just as great on the +opposite side, and it is probable that, if any bends were required to +reduce the maximum stress in the concrete, they should as likely be made +on the side nearest the abutment. + +From the stress triangles it may also be shown that, if the stirrups +were vertical instead of inclined, the stress in the concrete on both +sides would be practically equal, and that, in consequence, vertical +stirrups are preferable. + +The next issue raised by the author is covered in his seventh point, and +relates to bending moments. He states: "* * * bending moments in +so-called continuous beams are juggled to reduce them to what the +designer would like to have them. This has come to be almost a matter of +taste, * * *." + +The author seems to imply that such juggling is wrong. As a matter of +fact, it is perfectly allowable and legitimate in every instance of beam +or truss design, that is, from the standpoint of stress distribution, +although this "juggling" is limited in practice by economical +considerations. + +In a series of beams supported at the ends, bending moments range from +(_w_ _l^{2}_)/8 at the center of each span to zero at the supports, and, +in a series of cantilevers, from zero at the center of the span to (_w_ +_l^{2}_)/8 at the supports. Between these two extremes, the designer can +divide, adjust, or juggle them to his heart's content, provided that in +his design he makes the proper provision for the corresponding shifting +of the points of contra-flexure. If that were not the case, how could +ordinary bridge trusses, which have their maximum bending at the center, +compare with those which, like arches, are assumed to have no bending at +that point? + +In his tenth point, the author proposes a method of simple designing by +doing away with the complicated formulas which take account of the +actual co-operation of the two materials. He states that an ideal +design can be obtained in the same manner, that is, with the same +formulas, as for ordinary rectangular beams; but, when he does so, he +evidently fails to remember that the neutral axis is not near the center +of a reinforced concrete beam under stress; in fact, with the percentage +of reinforcement ordinarily used in designing--varying between +three-fourths of 1% to 1-1/2%--the neutral axis, when the beam is +loaded, is shifted from 26 to 10% of the beam depth above the center. +Hence, a low percentage of steel reinforcement will produce a great +shifting of the neutral axis, so that a design based on the formulas +advocated by the author would contain either a waste of materials, an +overstress of the concrete, or an understress of the steel; in fact, an +error in the design of from 10 to 26 per cent. Such errors, indeed, are +not to be recommended by good engineers. + +The last point which the speaker will discuss is that of the elastic +arch. The theory of the elastic arch is now so well understood, and it +offers such a simple and, it might be said, elegant and self-checking +solution of the arch design, that it has a great many advantages, and +practically none of the disadvantages of other methods. + +The author's statement that the segments of an arch could be made up of +loose blocks and afterward cemented together, cannot be endorsed by the +speaker, for, upon such cementing together, a shifting of the lines of +resistance will take place when the load is applied. The speaker does +not claim that arches are maintained by the cement or mortar joining the +voussoirs together, but that the lines of pressure will be materially +changed, and the same calculations are not applicable to both the +unloaded and the loaded arch. + +It is quite true, as the author states, that a few cubic yards of +concrete placed in the ring will strengthen the arch more than a like +amount added to the abutments, provided, however, that this material be +placed properly. No good can result from an attempt to strengthen a +structure by placing the reinforcing material promiscuously. This has +been tried by amateurs in bridge construction, and, in such cases, the +material either increased the distance from the neutral axis to the +extreme fibers, thereby reducing the original section modulus, or caused +a shifting of the neutral axis followed by a large bending moment; +either method weakening the members it had tried to reinforce. In other +words, the mere addition of material does not always strengthen a +structure, unless it is placed in the proper position, and, if so +placed, it should be placed all over commensurately with the stresses, +that is, the unit stresses should be reduced. + +The author has criticized reinforced concrete construction on the ground +that the formulas and theories concerning it are not as yet fully +developed. This is quite true, for the simple reason that there are so +many uncertain elements which form their basis: First, the variable +quantity of the modulus of elasticity, which, in the concrete, varies +inversely as the stress; and, second, the fact that the neutral axis in +a reinforced concrete beam under changing stress is migratory. There are +also many other elements of evaluation, which, though of importance, are +uncertain. + +Because the formulas are established on certain assumptions is no reason +for condemning them. There are, the speaker might add, few formulas in +the subject of theoretical mechanics which are not based on some +assumption, and as long as the variations are such that their range is +known, perfectly reliable formulas can be deduced and perfectly safe +structures can be built from them. + +There are a great many theorists who have recently complained about the +design of reinforced concrete. It seems to the speaker that such +complaints can serve no useful purpose. Reinforced concrete structures +are being built in steadily increasing numbers; they are filling a long +needed place; they are at present rendering great service to mankind; +and they are destined to cover a field of still greater usefulness. +Reinforced concrete will undoubtedly show in the future that the +confidence which most engineers and others now place in it is fully +merited. + + +HARRY F. PORTER, JUN. AM. SOC. C. E. (by letter).--Mr. Godfrey has +brought forward some interesting and pertinent points, which, in the +main, are well taken; but, in his zealousness, he has fallen into the +error of overpersuading himself of the gravity of some of the points he +would make; on the other hand, he fails to go deeply enough into others, +and some fallacies he leaves untouched. Incidentally, he seems somewhat +unfair to the Profession in general, in which many earnest, able men are +at work on this problem, men who are not mere theorists, but have been +reared in the hard school of practical experience, where refinements of +theory count for little, but common sense in design counts for much--not +to mention those self-sacrificing devotees to the advancement of the +art, the collegiate and laboratory investigators. + +Engineers will all agree with Mr. Godfrey that there is much in the +average current practice that is erroneous, much in textbooks that is +misleading if not fallacious, and that there are still many designers +who are unable to think in terms of the new material apart from the +vestures of timber and structural steel, and whose designs, therefore, +are cumbersome and impractical. The writer, however, cannot agree with +the author that the practice is as radically wrong as he seems to think. +Nor is he entirely in accord with Mr. Godfrey in his "constructive +criticism" of those practices in which he concurs, that they are +erroneous. + +That Mr. Godfrey can see no use in vertical stirrups or U-bars is +surprising in a practical engineer. One is prompted to ask: "Can the +holder of this opinion ever have gone through the experience of placing +steel in a job, or at least have watched the operation?" If so, he must +have found some use for those little members which he professes to +ignore utterly. + +As a matter of fact, U-bars perform the following very useful and +indispensable services: + +(_1_).--If properly made and placed, they serve as a saddle in which to +rest the horizontal steel, thereby insuring the correct placing of the +latter during the operation of concreting, not a mean function in a type +of construction so essentially practical. To serve this purpose, +stirrups should be made as shown in Plate III. They should be restrained +in some manner from moving when the concrete strikes them. A very good +way of accomplishing this is to string them on a longitudinal rod, +nested in the bend at the upper end. Mr. Godfrey, in his advocacy of +bowstring bars anchored with washers and nuts at the ends, fails to +indicate how they shall be placed. The writer, from experience in +placing steel, thinks that it would be very difficult, if not +impractical, to place them in this manner; but let a saddle of U-bars be +provided, and the problem is easy. + +(_2_).--Stirrups serve also as a tie, to knit the stem of the beam to +its flange--the superimposed slab. The latter, at best, is not too well +attached to the stem by the adhesion of the concrete alone, unassisted +by the steel. T-beams are used very generally, because their +construction has the sanction of common sense, it being impossible to +cast stem and slab so that there will be the same strength in the plane +at the junction of the two as elsewhere, on account of the certainty of +unevenness in settlement, due to the disproportion in their depth. There +is also the likelihood that, in spite of specifications to the contrary, +there will be a time interval between the pouring of the two parts, and +thus a plane of weakness, where, unfortunately, the forces tending to +produce sliding of the upper part of the beam on the lower (horizontal +shear) are a maximum. To offset this tendency, therefore, it is +necessary to have a certain amount of vertical steel, disposed so as to +pass around and under the main reinforcing members and reach well up +into the flange (the slab), thus getting a grip therein of no mean +security. The hooking of the U-bars, as shown in Plate III, affords a +very effective grip in the concrete of the slab, and this is still +further enhanced by the distributing or anchoring effect of the +longitudinal stringing rods. Thus these longitudinals, besides serving +to hold the U-bars in position, also increase their effectiveness. They +serve a still further purpose as a most convenient support for the slab +bars, compelling them to take the correct position over the supports, +thus automatically ensuring full and proper provision for reversed +stresses. More than that, they act in compression within the middle +half, and assist in tension toward the ends of the span. + +Thus, by using U-bars of the type indicated, in combination with +longitudinal bars as described, tying together thoroughly the component +parts of the beam in a vertical plane, a marked increase in stiffness, +if not strength, is secured. This being the case, who can gainsay the +utility of the U-bar? + +Of course, near the ends, in case continuity of action is realized, +whereupon the stresses are reversed, the U-bars need to be inverted, +although frequently inversion is not imperative with the type of U-bar +described, the simple hooking of the upper ends over the upper +horizontal steel being sufficient. + +As to whether or not the U-bars act with the horizontal and diagonal +steel to form truss systems is relatively unessential; in all +probability there is some such action, which contributes somewhat to the +total strength, but at most it is of minor importance. Mr. Godfrey's +points as to fallacy of truss action seem to be well taken, but his +conclusions in consequence--that U-bars serve no purpose--are +impractical. + +The number of U-bars needed is also largely a matter of practice, +although subject to calculation. Practice indicates that they should be +spaced no farther apart than the effective depth of the member, and +spaced closer or made heavier toward the ends, in order to keep pace +with cumulating shear. They need this close spacing in order to serve as +an adequate saddle for the main bars, as well as to furnish, with the +lighter "stringing" rods, an adequate support to the slab bars. They +should have the requisite stiffness in the bends to carry their burden +without appreciable sagging; it will be found that 5/16 in. is about the +minimum practical size, and that 1/2 in. is as large as will be +necessary, even for very deep beams with heavy reinforcement. + +If the size and number of U-bars were to be assigned by theory, there +should be enough of them to care for fully 75% of the horizontal shear, +the adhesion of the concrete being assumed as adequate for the +remainder. + +Near the ends, of course, the inclined steel, resulting from bending up +some of the horizontal bars, if it is carried well across the support to +secure an adequate anchorage, or other equivalent anchorage is provided, +assists in taking the horizontal shear. + +The embedment, too, of large stone in the body of the beam, straddling, +as it were, the neutral plane, and thus forming a lock between the +flange and the stem, may be considered as assisting materially in taking +horizontal shear, thus relieving the U-bars. This is a factor in the +strength of actual work which theory does not take into account, and by +the author, no doubt, it would be regarded as insignificant; +nevertheless it is being done every day, with excellent results. + +The action of these various agencies--the U-bars, diagonal steel, and +embedded stone--in a concrete beam, is analogous to that of bolts or +keys in the case of deepened timber beams. A concrete beam may be +assumed, for the purposes of illustration, to be composed of a series of +superimposed layers; in this case the function of the rigid material +crossing these several layers normally, and being well anchored above +and below, as a unifier of the member, is obvious--it acts as so many +bolts joining superimposed planks forming a beam. Of course, no such +lamination actually exists, although there are always incipient forces +tending to produce it; these may and do manifest themselves on occasion +as an actual separation in a horizontal plane at the junction of slab +and stem, ordinarily the plane of greatest weakness--owing to the method +of casting--as well as of maximum horizontal shear. Beams tested to +destruction almost invariably develop cracks in this region. The +question then naturally arises: If U-bars serve no purpose, what will +counteract these horizontal cleaving forces? On the contrary, T-beams, +adequately reinforced with U-bars, seem to be safeguarded in this +respect; consequently, the U-bars, while perhaps adding little to the +strength, as estimated by the ultimate carrying capacity, actually must +be of considerable assistance, within the limit of working loads, by +enhancing the stiffness and ensuring against incipient cracking along +the plane of weakness, such as impact or vibratory loads might induce. +Therefore, U-bars, far from being superfluous or fallacious, are, +practically, if not theoretically, indispensable. + +At present there seems to be considerable diversity of opinion as to the +exact nature of the stress action in a reinforced concrete beam. +Unquestionably, the action in the monolithic members of a concrete +structure is different from that in the simple-acting, unrestrained +parts of timber or structural steel construction; because in monolithic +members, by the law of continuity, reverse stresses must come into play. +To offset these stresses reinforcement must be provided, or cracking +will ensue where they occur, to the detriment of the structure in +appearance, if not in utility. Monolithic concrete construction should +be tied together so well across the supports as to make cracking under +working loads impossible, and, when tested to destruction, failure +should occur by the gradual sagging of the member, like the sagging of +an old basket. Then, and then only, can the structure be said to be +adequately reinforced. + +In his advocacy of placing steel to simulate a catenary curve, with end +anchorage, the author is more nearly correct than in other issues he +makes. Undoubtedly, an attempt should be made in every concrete +structure to approximate this alignment. In slabs it may be secured +simply by elevating the bars over the supports, when, if pliable enough, +they will assume a natural droop which is practically ideal; or, if too +stiff, they may be bent to conform approximately to this position. In +slabs, too, the reinforcement may be made practically continuous, by +using lengths covering several spans, and, where ends occur, by +generous lapping. In beams the problem is somewhat more complicated, +as it is impossible, except rarely, to bow the steel and to extend it +continuously over several supports; but all or part of the horizontal +steel can be bent up at about the quarter point, carried across the +supports into the adjacent spans, and anchored there by bending it down +at about the same angle as it is bent up on the approach, and then +hooking the ends. + +[Illustration: PLATE III.--JUNCTION OF BEAM AND WALL COLUMN. +REINFORCEMENT IN PLACE IN BEAM, LINTEL, AND SLAB UP TO BEAM. NOTE END +ANCHORAGE OF BEAM BARS.] + +It is seldom necessary to adopt the scheme proposed by the author, +namely, a threaded end with a bearing washer and a nut to hold the +washer in place, although it is sometimes expedient, but not absolutely +necessary, in end spans, where prolongation into an adjacent span is out +of the question. In end spans it is ordinarily sufficient to give the +bars a double reverse bend, as shown in Plate III, and possibly to clasp +hooks with the horizontal steel. If steel be placed in this manner, the +catenary curve will be practically approximated, the steel will be +fairly developed throughout its length of embedment, and the structure +will be proof against cracking. In this case, also, there is much less +dependence on the integrity of the bond; in fact, if there were no bond, +the structure would still develop most of its strength, although the +deflection under heavy loading might be relatively greater. + +The writer once had an experience which sustains this point. On peeling +off the forms from a beam reinforced according to the method indicated, +it was found that, because of the crowding together of the bars in the +bottom, coupled with a little too stiff a mixture, the beam had hardly +any concrete on the underside to grip the steel in the portion between +the points of bending up, or for about the middle half of the member; +consequently, it was decided to test this beam. The actual working load +was first applied and no deflection, cracking, or slippage of the bars +was apparent; but, as the loading was continued, deflection set in and +increased rapidly for small increments of loading, a number of fine +cracks opened up near the mid-section, which extended to the neutral +plane, and the steel slipped just enough, when drawn taut, to destroy +what bond there was originally, owing to the contact of the concrete +above. At three times the live load, or 450 lb. per sq. ft., the +deflection apparently reached a maximum, being about 5/16 in. for a +clear distance, between the supports, of 20 ft.; and, as the load was +increased to 600 lb. per sq. ft., there was no appreciable increase +either in deflection or cracking; whereupon, the owner being satisfied, +the loading was discontinued. The load was reduced in amount to three +times the working load (450 lb.) and left on over night; the next +morning, there being no detectable change, the beam was declared to be +sound. When the load was removed the beam recovered all but about 1/8 +in. of its deflection, and then repairs were made by attaching light +expanded metal to the exposed bars and plastering up to form. Although +nearly three years have elapsed, there have been no unfavorable +indications, and the owner, no doubt, has eased his mind entirely in +regard to the matter. This truly remarkable showing can only be +explained by the catenary action of the main steel, and some truss +action by the steel which was horizontal, in conjunction with the +U-bars, of which there were plenty. As before noted, the clear span +was 20 ft., the width of the bay, 8 ft., and the size under the slab +(which was 5 in. thick) 8 by 18 in. The reinforcement consisted of three +1-1/8-in. round medium-steel bars, with 3/8-in. U-bars placed the +effective depth of the member apart and closer toward the supports, the +first two or three being 6 in. apart, the next two or three, 9 in., the +next, 12 in., etc., up to a maximum, throughout the mid-section, of 15 +in. Each U-bar was provided with a hook at its upper end, as shown in +Plate III, and engaged the slab reinforcement, which in this case was +expanded metal. Two of the 1-1/8-in. bars were bent up and carried +across the support. At the point of bending up, where they passed the +single horizontal bar, which was superimposed, a lock-bar was inserted, +by which the pressure of the bent-up steel against the concrete, in the +region of the bend, was taken up and distributed along the horizontal +bar. This feature is also shown in Fig. 14. The bars, after being +carried across the support, were inclined into the adjacent span and +provided with a liberal, well-rounded hook, furnishing efficient +anchorage and provision for reverse stresses. This was at one end only, +for--to make matters worse--the other end was a wall bearing; +consequently, the benefit of continuity was denied. The bent-up bars +were given a double reverse bend, as already described, carrying them +around, down, in, and up, and ending finally by clasping them in the +hook of the horizontal bar. This apparently stiffened up the free end, +for, under the test load, its action was similar to that of the +completely restrained end, thus attesting the value of this method of +end-fixing. + +The writer has consistently followed this method of reinforcement, with +unvaryingly good results, and believes that, in some measure, it +approximates the truth of the situation. Moreover, it is economical, for +with the bars bent up over the supports in this manner, and positively +anchored, plenty of U-bars being provided, it is possible to remove +the forms with entire safety much sooner than with the ordinary methods +which are not as well stirruped and only partially tied across the +supports. It is also possible to put the structure into use at an +earlier date. Failure, too, by the premature removal of the centers, is +almost impossible with this method. These considerations more than +compensate for the trouble and expense involved in connection with such +reinforcement. The writer will not attempt here a theoretical analysis +of the stresses incurred in the different parts of this beam, although +it might be interesting and instructive. + +[Illustration: FIG. 14.] + +The concrete, with the reinforcement disposed as described, may be +regarded as reposing on the steel as a saddle, furnishing it with a +rigid jacket in which to work, and itself acting only as a stiff floor +and a protecting envelope. Bond, in this case, while, of course, an +adjunct, is by no means vitally important, as is generally the case with +beams unrestrained in any way and in which the reinforcement is not +provided with adequate end anchorage, in which case a continuous bond is +apparently--at any rate, theoretically--indispensable. + +An example of the opposite extreme in reinforced concrete design, where +provision for reverse stresses was almost wholly lacking, is shown in +the Bridgeman Brothers' Building, in Philadelphia, which collapsed while +the operation of casting the roof was in progress, in the summer of +1907. The engineering world is fairly familiar with the details of this +disaster, as they were noted both in the lay and technical press. In +this structure, not only were U-bars almost entirely absent, but the +few main bars which were bent up, were stopped short over the support. +The result was that the ties between the rib and the slab, and also +across the support, being lacking, some of the beams, the forms of which +had been removed prematurely, cracked of their own dead weight, and, +later, when the roof collapsed, owing to the deficient bracing of the +centers, it carried with it each of the four floors to the basement, the +beams giving way abruptly over the supports. Had an adequate tie of +steel been provided across the supports, the collapse, undoubtedly, +would have stopped at the fourth floor. So many faults were apparent in +this structure, that, although only half of it had fallen, it was +ordered to be entirely demolished and reconstructed. + +The cracks in the beams, due to the action of the dead weight alone, +were most interesting, and illuminative of the action which takes place +in a concrete beam. They were in every case on the diagonal, at an angle +of approximately 45 deg., 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 deg. 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 deg. 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 deg. 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 deg. 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 deg., 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 deg., 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 deg. 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 deg., or even 45 deg., 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. Considere in testing small +specimens cannot be depended on in practice, but that the reinforcement +is of great value, nevertheless. The writer believes that when +load-carrying capacity, stresses due to eccentricity, and fire-resisting +qualities are all given due consideration, a type of column with close +hooping and longitudinal reinforcement provided with shear members, will +finally be developed, which will more than justify itself. + +_Point 16_.--The writer has not gone as deeply into this question, from +a theoretical point of view, as he would like; but he has had one +experience that is pertinent. Some years ago, he built a plain slab +floor supported by brick walls. The span was about 16 ft. The dimensions +of the slab at right angles to the reinforcement was 100 ft. or more. +Plain round bars, 1/2 in. in diameter, were run at right angles to the +reinforcement about 2 ft. on centers, the object being to lessen cracks. +The reinforcement consisted of Kahn bars, reaching from wall to wall. +The rounds were laid on top of the Kahn bars. The concrete was frozen +and undeniably damaged, but the floors stood up, without noticeable +deflection, after the removal of the forms. The concrete was so soft, +however, that a test was decided on. An area about 4 ft. wide, and +extending to within about 1 ft. of each bearing wall, was loaded with +bricks piled in small piers not in contact with each other, so as to +constitute practically a uniformly distributed load. When the total load +amounted to much less than the desired working load for the 4-ft. strip, +considerable deflection had developed. As the load increased, the +deflection increased, and extended for probably 15 or 20 ft. on either +side of the loaded area. Finally, under about three-fourths of the +desired breaking load for the 4-ft. strip, it became evident that +collapse would soon occur. The load was left undisturbed and, in 3 or 4 +min., an area about 16 ft. square tore loose from the remainder of the +floor and fell. The first noticeable deflection in the above test +extended for 8 or 10 ft. on either side of the loaded strip. It would +seem that this test indicated considerable distributing power in the +round rods, although they were not counted as reinforcement for +load-carrying purposes at all. The concrete was extremely poor, and none +of the steel was stressed beyond the elastic limit. While this test may +not justify the designer in using lighter reinforcement for the short +way of the slab, it at least indicates a very real value for some +reinforcement in the other direction. It would seem to indicate, also, +that light steel members in a concrete slab might resist a small amount +of shear. The slab in this case was about 6 in. thick. + + +SANFORD E. THOMPSON, M. AM. SOC. C. E. (by letter).--Mr. Godfrey's +sweeping condemnation of reinforced concrete columns, referred to in his +fifteenth point, should not be passed over without serious criticism. +The columns in a building, as he states, are the most vital portion of +the structure, and for this very reason their design should be governed +by theoretical and practical considerations based on the most +comprehensive tests available. + +The quotation by Mr. Godfrey from a writer on hooped columns is +certainly more radical than is endorsed by conservative engineers, but +the best practice in column reinforcement, as recommended by the Joint +Committee on Concrete and Reinforced Concrete, which assumes that the +longitudinal bars assist in taking stress in accordance with the ratio +of elasticity of steel to concrete, and that the hooping serves to +increase the toughness of the column, is founded on the most substantial +basis of theory and test. + +In preparing the second edition of "Concrete, Plain and Reinforced," the +writer examined critically the various tests of concrete columns in +order to establish a definite basis for his conclusions. Referring more +particularly to columns reinforced with vertical steel bars, an +examination of all the tests of full-sized columns made in the United +States appears to bear out the fact very clearly that longitudinal steel +bars embedded in concrete increase the strength of the column, and, +further, to confirm the theory by which the strength of the combination +of steel and concrete may be computed and is computed in practice. + +Tests of large columns have been made at the Watertown Arsenal, the +Massachusetts Institute of Technology, the University of Illinois, by +the City of Minneapolis, and at the University of Wisconsin. The results +of these various tests were recently summarized by the writer in a paper +presented at the January, 1910, meeting of the National Association of +Cement Users[O]. Reference may be made to this paper for fuller +particulars, but the averages of the tests of each series are worth +repeating here. + +In comparing the averages of reinforced columns, specimens with spiral +or other hooping designed to increase the strength, or with horizontal +reinforcement placed so closely together as to prevent proper placing of +the concrete, are omitted. For the Watertown Arsenal tests the averages +given are made up from fair representative tests on selected proportions +of concrete, given in detail in the paper referred to, while in other +cases all the corresponding specimens of the two types are averaged. The +results are given in Table 1. + +The comparison of these tests must be made, of course, independently in +each series, because the materials and proportions of the concrete and +the amounts of reinforcement are different in the different series. The +averages are given simply to bring out the point, very definitely and +distinctly, that longitudinally reinforced columns are stronger than +columns of plain concrete. + +A more careful analysis of the tests shows that the reinforced columns +are not only stronger, but that the increase in strength due to the +reinforcement averages greater than the ordinary theory, using a ratio +of elasticity of 15, would predicate. + +Certain of the results given are diametrically opposed to Mr. Godfrey's +conclusions from the same sets of tests. Reference is made by him, for +example (page 69), to a plain column tested at the University of +Illinois, which crushed at 2,001 lb. per sq. in., while a reinforced +column of similar size crushed at 1,557 lb. per sq. in.,[P] and the +author suggests that "This is not an isolated case, but appears to be +the rule." Examination of this series of tests shows that it is somewhat +more erratic than most of those made at the University of Illinois, but, +even from the table referred to by Mr. Godfrey, pursuing his method of +reasoning, the reverse conclusion might be reached, for if, instead of +selecting, as he has done, the weakest reinforced column in the entire +lot and the strongest plain column, a reverse selection had been made, +the strength of the plain column would have been stated as 1,079 lb. per +sq. in. and that of the reinforced column as 3,335 lb. per sq. in. If +extremes are to be selected at all, the weakest reinforced column should +be compared with the weakest plain column, and the strongest reinforced +column with the strongest plain column; and the results would show that +while an occasional reinforced column may be low in strength, an +occasional plain column will be still lower, so that the reinforcement, +even by this comparison, is of marked advantage in increasing strength. +In such cases, however, comparisons should be made by averages. The +average strength of the reinforced columns, even in this series, as +given in Table 1, is considerably higher than that of the plain columns. + + TABLE 1.--AVERAGE RESULTS OF TESTS OF PLAIN _vs._ + LONGITUDINALLY REINFORCED COLUMNS. + +--------------+--------+--------------+--------------------------------- + | | Average | + |Average | strength of | + Location |strength|longitudinally| Reference. + of test. |of plain| reinforced | + |columns.| columns. | +--------------+--------+--------------+--------------------------------- + Watertown | 1,781 | 2,992 |Taylor and Thompson's + Arsenal. | | |"Concrete, Plain and Reinforced" + | | |(2nd edition), p. 493. +--------------+--------+--------------+--------------------------------- + Massachusetts| 1,750 | 2,370 |_Transactions_, + Institute of | | |Am. Soc. C. E., Vol. L, p. 487. + Technology. | | | +--------------+--------+--------------+--------------------------------- + University of| 1,550 | 1,750 |_Bulletin No. 10._ + Illinois. | | |University of Illinois, 1907. +--------------+--------+--------------+--------------------------------- + City of | 2,020 | 2,300 |_Engineering News_, + Minneapolis.| | |Dec. 3d, 1908, p. 608. +--------------+--------+--------------+--------------------------------- + University of| 2,033 | 2,438 |_Proceedings_, + Wisconsin. | | |Am. Soc. for Testing Materials, + | | |Vol. IX, 1909, p. 477. +--------------+--------+--------------+--------------------------------- + +In referring, in the next paragraph, to Mr. Withey's tests at the +University of Wisconsin, Mr. Godfrey selects for his comparison two +groups of concrete which are not comparable. Mr. Withey, in the paper +describing the tests, refers to two groups of plain concrete columns, +_A1_ to _A4_, and _W1_ to _W3_. He speaks of the uniformity in the tests +of the former group, the maximum variation in the four specimens being +only 2%, but states, with reference to columns, _W1_ to _W3_, that: + + "As these 3 columns were made of a concrete much superior to that + in any of the other columns made from 1:2:4 or 1:2:3-1/2 mix, they + cannot satisfactorily be compared with them. Failures of all plain + columns were sudden and without any warning." + +Now, Mr. Godfrey, instead of taking columns _A1_ to _A3_, selects for +his comparison _W1_ to _W3_, made, as Mr. Withey distinctly states, with +an especially superior concrete. Taking columns, _A1_ to _A3_, for +comparison with the reinforced columns, _E1_ to _E3_, the result shows +an average of 2,033 for the plain columns and 2,438 for the reinforced +columns. + +Again, taking the third series of tests referred to by Mr. Godfrey, +those at Minneapolis, Minn., it is to be noticed that he selects for his +criticism a column which has this note as to the manner of failure: +"Bending at center (bad batch of concrete at this point)." Furthermore, +the column is only 9 by 9 in., and square, and the stress referred to is +calculated on the full section of the column instead of on the strength +within the hooping, although the latter method is the general practice +in a hooped column. The inaccuracy of this is shown by the fact that, +with this small size of square column, more than half the area is +outside the hooping and never taken into account in theoretical +computations. A fair comparison, as far as longitudinal reinforcement is +concerned, is always between the two plain columns and the six columns, +_E_, _D_, and _F_. The results are so instructive that a letter[Q] by +the writer is quoted in full as follows: + + "SIR:-- + + "In view of the fact that the column tests at Minneapolis, as + reported in your paper of December 3, 1908, p. 608, are liable + because of the small size of the specimens to lead to divergent + conclusions, a few remarks with reference to them may not be out of + place at this time. + + "1. It is evident that the columns were all smaller, being only 9 + in. square, than is considered good practice in practical + construction, because of the difficulty of properly placing the + concrete around the reinforcement. + + "2. The tests of columns with flat bands, _A_, _B_, and _C_, in + comparison with the columns _E_, _D_ and _F_, indicate that the + wide bands affected the placing of the concrete, separating the + internal core from the outside shell so that it would have been + nearly as accurate to base the strength upon the material within + the bands, that is, upon a section of 38 sq. in., instead of upon + the total area of 81 sq. in. This set of tests, _A_, _B_ and _C_, + is therefore inconclusive except as showing the practical + difficulty in the use of bands in small columns, and the necessity + for disregarding all concrete outside of the bands when computing + the strength. + + "3. The six columns _E_, _D_ and _F_, each of which contained eight + 5/8-in. rods, are the only ones which are a fair test of columns + longitudinally reinforced, since they are the only specimens except + the plain columns in which the small sectional area was not cut by + bands or hoops. Taking these columns, we find an average strength + 38% in excess of the plain columns, whereas, with the percentage of + reinforcement used, the ordinary formula for vertical steel (using + a ratio of elasticity of steel to concrete of 15) gives 34% as the + increase which might be expected. In other words, the actual + strength of this set of columns was in excess of the theoretical + strength. The wire bands on these columns could not be considered + even by the advocates of hooped columns as appreciably adding to + the strength, because they were square instead of circular. It may + be noted further in connection with these longitudinally reinforced + columns that the results were very uniform and, further, that the + strength of _every specimen_ was much greater than the strength of + the plain columns, being in every case except one at least 40% + greater. In these columns the rods buckled between the bands, but + they evidently did not do so until their elastic limit was passed, + at which time of course they would be expected to fail. + + "4. With reference to columns, _A_, _B_, _C_ and _L_, which were + essentially hooped columns, the failure appears to have been caused + by the greater deformation which is always found in hooped columns, + and which in the earlier stages of the loading is apparently due to + lack of homogeneity caused by the difficulty in placing the + concrete around the hooping, and in the later stage of the loading + to the excessive expansion of the concrete. This greater + deformation in a hooped column causes any vertical steel to pass + its elastic limit at an earlier stage than in a column where the + deformation is less, and therefore produces the buckling between + the bands which is noted in these two sets of columns. This + excessive deformation is a strong argument against the use of high + working stresses in hooped columns. + + "In conclusion, then, it may be said that the columns reinforced + with vertical round rods showed all the strength that would be + expected of them by theoretical computation. The hooped columns, on + the other hand, that is, the columns reinforced with circular bands + and hoops, gave in all cases comparatively low results, but no + conclusions can be drawn from them because the unit-strength would + have been greatly increased if the columns had been larger so that + the relative area of the internal core to the total area of the + column had been greater." + +From this letter, it will be seen that every one of Mr. Godfrey's +comparisons of plain _versus_ reinforced columns requires explanations +which decidedly reduce, if they do not entirely destroy, the force of +his criticism. + +This discussion can scarcely be considered complete without brief +reference to the theory of longitudinal steel reinforcement for columns. +The principle[R] is comparatively simple. When a load is placed on a +column of any material it is shortened in proportion, within working +limits, to the load placed upon it; that is, with a column of +homogeneous material, if the load is doubled, the amount of shortening +or deformation is also doubled. If vertical steel bars are embedded in +concrete, they must shorten when the load is applied, and consequently +relieve the concrete of a portion of its load. It is therefore +physically impossible to prevent such vertical steel from taking a +portion of the load unless the steel slips or buckles. + +As to the possible danger of the bars in the concrete slipping or +buckling, to which Mr. Godfrey also refers, again must tests be cited. +If the ends are securely held--and this is always the case when bars are +properly butted or are lapped for a sufficient length--they cannot slip. +With reference to buckling, tests have proved conclusively that vertical +bars such as are used in columns, when embedded in concrete, will not +buckle until the elastic limit of the steel is reached, or until the +concrete actually crushes. Beyond these points, of course, neither steel +nor concrete nor any other material is expected to do service. + +As proof of this statement, it will be seen, by reference to tests at +the Watertown Arsenal, as recorded in "Tests of Metals," that many of +the columns were made with vertical bar reinforcement having absolutely +no hoops or horizontal steel placed around them. That is, the bars, 8 +ft. long, were placed in the four corners of the column--in some tests +only 2 in. from the surface--and held in place simply by the concrete +itself.[S] There was no sign whatever of buckling until the compression +was so great that the elastic limit of the steel was passed, when, of +course, no further strength could be expected from it. + +To recapitulate the conclusions reached as a result of a study of the +tests: It is evident that, not only does theory permit the use of +longitudinal bar reinforcement for increasing the strength of concrete +columns, whenever such reinforcement is considered advisable, but that +all the important series of column tests made in the United States to +date show a decisive increase in strength of columns reinforced with +longitudinal steel bars over those which are not reinforced. +Furthermore, as has already been mentioned, without treating the details +of the proof, it can be shown that the tests bear out conclusively the +conservatism of computing the value of the vertical steel bars in +compression by the ordinary formulas based on the ratio of the moduli of +elasticity of steel to concrete. + + +EDWARD GODFREY, M. AM. SOC. C. E. (by letter).--As was to be expected, +this paper has brought out discussion, some of which is favorable and +flattering; some is in the nature of dust-throwing to obscure the force +of the points made; some would attempt to belittle the importance of +these points; and some simply brings out the old and over-worked +argument which can be paraphrased about as follows: "The structures +stand up and perform their duty, is this not enough?" + +The last-mentioned argument is as old as Engineering; it is the +"practical man's" mainstay, his "unanswerable argument." The so-called +practical man will construct a building, and test it either with loads +or by practical use. Then he will modify the design somewhere, and the +resulting construction will be tested. If it passes through this +modifying process and still does service, he has something which, in his +mind, is unassailable. Imagine the freaks which would be erected in the +iron bridge line, if the capacity to stand up were all the designer had +to guide him, analysis of stresses being unknown. Tests are essential, +but analysis is just as essential. The fact that a structure carries the +bare load for which it is computed, is in no sense a test of its correct +design; it is not even a test of its safety. In Pittsburg, some years +ago, a plate-girder span collapsed under the weight of a locomotive +which it had carried many times. This bridge was, perhaps, thirty years +old. Some reinforced concrete bridges have failed under loads which they +have carried many times. Others have fallen under no extraneous load, +and after being in service many months. If a large number of the columns +of a structure fall shortly after the forms are removed, what is the +factor of safety of the remainder, which are identical, but have not +quite reached their limit of strength? Or what is the factor of safety +of columns in other buildings in which the concrete was a little better +or the forms have been left in a little longer, both sets of columns +being similarly designed? + +There are highway bridges of moderately long spans standing and doing +service, which have 2-in. chord pins; laterals attached to swinging +floor-beams in such a way that they could not possibly receive their +full stress; eye-bars with welded-on heads; and many other equally +absurd and foolish details, some of which were no doubt patented in +their day. Would any engineer with any knowledge whatever of bridge +design accept such details? They often stand the test of actual service +for years; in pins, particularly, the calculated stress is sometimes +very great. These details do not stand the test of analysis and of +common sense, and, therefore, no reputable engineer would accept them. + +Mr. Turner, in the first and second paragraphs of his discussion, would +convey the impression that the writer was in doubt as to his "personal +opinions" and wanted some free advice. He intimates that he is too busy +to go fully into a treatise in order to set them right. He further tries +to throw discredit on the paper by saying that the writer has adduced no +clean-cut statement of fact or tests in support of his views. If Mr. +Turner had read the paper carefully, he would not have had the idea that +in it the hooped column is condemned. As to this more will be said +later. The paper is simply and solely a collection of statements of +facts and tests, whereas his discussion teems with his "personal +opinion," and such statements as "These values * * * are regarded by the +writer as having at least double the factor of safety used in ordinary +designs of structural steel"; "On a basis not far from that which the +writer considers reasonable practice." Do these sound like clean-cut +statements of fact, or are they personal opinions? It is a fact, pure +and simple, that a sharp bend in a reinforcing rod in concrete violates +the simplest principles of mechanics; also that the queen-post and Pratt +and Howe truss analogies applied to reinforcing steel in concrete are +fallacies; that a few inches of embedment will not anchor a rod for its +value; that concrete shrinks in setting in air and puts initial stress +in both the concrete and the steel, making assumed unstressed initial +conditions non-existent. It is a fact that longitudinal rods alone +cannot be relied on to reinforce a concrete column. Contrary to Mr. +Turner's statement, tests have been adduced to demonstrate this fact. +Further, it is a fact that the faults and errors in reinforced concrete +design to which attention is called, are very common in current design, +and are held up as models in nearly all books on the subject. + +The writer has not asked any one to believe a single thing because he +thinks it is so, or to change a single feature of design because in his +judgment that feature is faulty. The facts given are exemplifications of +elementary mechanical principles overlooked by other writers, just as +early bridge designers and writers on bridge design overlooked the +importance of calculating bridge pins and other details which would +carry the stress of the members. + +A careful reading of the paper will show that the writer does not accept +the opinions of others, when they are not backed by sound reason, and +does not urge his own opinion. + +Instead of being a statement of personal opinion for which confirmation +is desired, the paper is a simple statement of facts and tests which +demonstrate the error of practices exhibited in a large majority of +reinforced concrete work and held up in the literature on the subject as +examples to follow. Mr. Turner has made no attempt to deny or refute any +one of these facts, but he speaks of the burden of proof resting on the +writer. Further, he makes statements which show that he fails entirely +to understand the facts given or to grasp their meaning. He says that +the writer's idea is "that the entire pull of the main reinforcing rod +should be taken up apparently at the end." He adds that the soundness of +this position may be questioned, because, in slabs, the steel frequently +breaks at the center. Compare this with the writer's statement, as +follows: + + "In shallow beams there is little need of provision for taking + shear by any other means than the concrete itself. The writer has + seen a reinforced slab support a very heavy load by simple + friction, for the slab was cracked close to the supports. In slabs, + shear is seldom provided for in the steel reinforcement. It is only + when beams begin to have a depth approximating one-tenth of the + span that the shear in the concrete becomes excessive and provision + is necessary in the steel reinforcement. Years ago, the writer + recommended that, in such beams, some of the rods be curved up + toward the ends of the span and anchored over the support." + +It is solely in providing for shear that the steel reinforcement should +be anchored for its full value over the support. The shear must +ultimately reach the support, and that part which the concrete is not +capable of carrying should be taken to it solely by the steel, as far as +tensile and shear stresses are concerned. It should not be thrown back +on the concrete again, as a system of stirrups must necessarily do. + +The following is another loose assertion by Mr. Turner: + + "Mr. Godfrey appears to consider that the hooping and vertical + reinforcement of columns is of little value. He, however, presents + for consideration nothing but his opinion of the matter, which + appears to be based on an almost total lack of familiarity with + such construction." + +There is no excuse for statements like this. If Mr. Turner did not read +the paper, he should not have attempted to criticize it. What the writer +presented for consideration was more than his opinion of the matter. In +fact, no opinion at all was presented. What was presented was tests +which prove absolutely that longitudinal rods without hoops may actually +reduce the strength of a column, and that a column containing +longitudinal rods and "hoops which are not close enough to stiffen the +rods" may be of less strength than a plain concrete column. A properly +hooped column was not mentioned, except by inference, in the quotation +given in the foregoing sentence. The column tests which Mr. Turner +presents have no bearing whatever on the paper, for they relate to +columns with bands and close spirals. Columns are sometimes built like +these, but there is a vast amount of work in which hooping and bands are +omitted or are reduced to a practical nullity by being spaced a foot or +so apart. + +A steel column made up of several pieces latticed together derives a +large part of its stiffness and ability to carry compressive stresses +from the latticing, which should be of a strength commensurate with the +size of the column. If it were weak, the column would suffer in +strength. The latticing might be very much stronger than necessary, but +it would not add anything to the strength of the column to resist +compression. A formula for the compressive strength of a column could +not include an element varying with the size of the lattice. If the +lattice is weak, the column is simply deficient; so a formula for a +hooped column is incorrect if it shows that the strength of the column +varies with the section of the hoops, and, on this account, the common +formula is incorrect. The hoops might be ever so strong, beyond a +certain limit, and yet not an iota would be added to the compressive +strength of the column, for the concrete between the hoops might crush +long before their full strength was brought into play. Also, the hoops +might be too far apart to be of much or any benefit, just as the lattice +in a steel column might be too widely spaced. There is no element of +personal opinion in these matters. They are simply incontrovertible +facts. The strength of a hooped column, disregarding for the time the +longitudinal steel, is dependent on the fact that thin discs of concrete +are capable of carrying much more load than shafts or cubes. The hoops +divide the column into thin discs, if they are closely spaced; widely +spaced hoops do not effect this. Thin joints of lime mortar are known to +be many times stronger than the same mortar in cubes. Why, in the many +books on the subject of reinforced concrete, is there no mention of this +simple principle? Why do writers on this subject practically ignore the +importance of toughness or tensile strength in columns? The trouble +seems to be in the tendency to interpret concrete in terms of steel. +Steel at failure in short blocks will begin to spread and flow, and a +short column has nearly the same unit strength as a short block. The +action of concrete under compression is quite different, because of the +weakness of concrete in tension. The concrete spalls off or cracks apart +and does not flow under compression, and the unit strength of a shaft of +concrete under compression has little relation to that of a flat block. +Some years ago the writer pointed out that the weakness of cast-iron +columns in compression is due to the lack of tensile strength or +toughness in cast iron. Compare 7,600 lb. per sq. in. as the base of a +column formula for cast iron with 100,000 lb. per sq. in. as the +compressive strength of short blocks of cast iron. Then compare 750 lb. +per sq. in., sometimes used in concrete columns, with 2,000 lb. per sq. +in., the ultimate strength in blocks. A material one-fiftieth as strong +in compression and one-hundredth as strong in tension with a "safe" unit +one-tenth as great! The greater tensile strength of rich mixtures of +concrete accounts fully for the greater showing in compression in tests +of columns of such mixtures. A few weeks ago, an investigator in this +line remarked, in a discussion at a meeting of engineers, that "the +failure of concrete in compression may in cases be due to lack of +tensile strength." This remark was considered of sufficient novelty and +importance by an engineering periodical to make a special news item of +it. This is a good illustration of the state of knowledge of the +elementary principles in this branch of engineering. + +Mr. Turner states, "Again, concrete is a material which shows to the +best advantage as a monolith, and, as such, the simple beam seems to be +decidedly out of date to the experienced constructor." Similar things +could be said of steelwork, and with more force. Riveted trusses are +preferable to articulated ones for rigidity. The stringers of a bridge +could readily be made continuous; in fact, the very riveting of the ends +to a floor-beam gives them a large capacity to carry reverse moments. +This strength is frequently taken advantage of at the end floor-beam, +where a tie is made to rest on a bracket having the same riveted +connection as the stringer. A small splice-plate across the top flanges +of the stringers would greatly increase this strength to resist reverse +moments. A steel truss span is ideally conditioned for continuity in the +stringers, since the various supports are practically relatively +immovable. This is not true in a reinforced concrete building where each +support may settle independently and entirely vitiate calculated +continuous stresses. Bridge engineers ignore continuity absolutely in +calculating the stringers; they do not argue that a simple beam is out +of date. Reinforced concrete engineers would do vastly better work if +they would do likewise, adding top reinforcement over supports to +forestall cracking only. Failure could not occur in a system of beams +properly designed as simple spans, even if the negative moments over the +supports exceeded those for which the steel reinforcement was provided, +for the reason that the deflection or curving over the supports can only +be a small amount, and the simple-beam reinforcement will immediately +come into play. + +Mr. Turner speaks of the absurdity of any method of calculating a +multiple-way reinforcement in slabs by endeavoring to separate the +construction into elementary beam strips, referring, of course, to the +writer's method. This is misleading. The writer does not endeavor to +"separate the construction into elementary beam strips" in the sense of +disregarding the effect of cross-strips. The "separation" is analogous +to that of considering the tension and compression portions of a beam +separately in proportioning their size or reinforcement, but unitedly in +calculating their moment. As stated in the paper, "strips are taken +across the slab and the moment in them is found, considering the +limitations of the several strips in deflection imposed by those running +at right angles therewith." It is a sound and rational assumption that +each strip, 1 ft. wide through the middle of the slab, carries its half +of the middle square foot of the slab load. It is a necessary limitation +that the other strips which intersect one of these critical strips +across the middle of the slab, cannot carry half of the intercepted +square foot, because the deflection of these other strips must diminish +to zero as they approach the side of the rectangle. Thus, the nearer the +support a strip parallel to that support is located, the less load it +can take, for the reason that it cannot deflect as much as the middle +strip. In the oblong slab the condition imposed is equal deflection of +two strips of unequal span intersecting at the middle of the slab, as +well as diminished deflection of the parallel strips. + +In this method of treating the rectangular slab, the concrete in tension +is not considered to be of any value, as is the case in all accepted +methods. + +Some years ago the writer tested a number of slabs in a building, with a +load of 250 lb. per sq. ft. These slabs were 3 in. thick and had a clear +span of 44 in. between beams. They were totally without reinforcement. +Some had cracked from shrinkage, the cracks running through them and +practically the full length of the beams. They all carried this load +without any apparent distress. If these slabs had been reinforced with +some special reinforcement of very small cross-section, the strength +which was manifestly in the concrete itself, might have been made to +appear to be in the reinforcement. Magic properties could be thus +conjured up for some special brand of reinforcement. An energetic +proprietor could capitalize tension in concrete in this way and "prove" +by tests his claims to the magic properties of his reinforcement. + +To say that Poisson's ratio has anything to do with the reinforcement of +a slab is to consider the tensile strength of concrete as having a +positive value in the bottom of that slab. It means to reinforce for the +stretch in the concrete and not for the tensile stress. If the tensile +strength of concrete is not accepted as an element in the strength of a +slab having one-way reinforcement, why should it be accepted in one +having reinforcement in two or more directions? The tensile strength of +concrete in a slab of any kind is of course real, when the slab is +without cracks; it has a large influence in the deflection; but what +about a slab that is cracked from shrinkage or otherwise? + +Mr. Turner dodges the issue in the matter of stirrups by stating that +they were not correctly placed in the tests made at the University of +Illinois. He cites the Hennebique system as a correct sample. This +system, as the writer finds it, has some rods bent up toward the support +and anchored over it to some extent, or run into the next span. Then +stirrups are added. There could be no objection to stirrups if, apart +from them, the construction were made adequate, except that expense is +added thereby. Mr. Turner cannot deny that stirrups are very commonly +used just as they were placed in the tests made at the University of +Illinois. It is the common practice and the prevailing logic in the +literature of the subject which the writer condemns. + +Mr. Thacher says of the first point: + + "At the point where the first rod is bent up, the stress in this + rod runs out. The other rods are sufficient to take the horizontal + stress, and the bent-up portion provides only for the vertical and + diagonal shearing stresses in the concrete." + +If the stress runs out, by what does that rod, in the bent portion, take +shear? Could it be severed at the bend, and still perform its office? +The writer can conceive of an inclined rod taking the shear of a beam if +it were anchored at each end, or long enough somehow to have a grip in +the concrete from the centroid of compression up and from the center of +the steel down. This latter is a practical impossibility. A rod curved +up from the bottom reinforcement and curved to a horizontal position and +run to the support with anchorage, would take the shear of a beam. As to +the stress running out of a rod at the point where it is bent up, this +will hardly stand the test of analysis in the majority of cases. On +account of the parabolic variation of stress in a beam, there should be +double the length necessary for the full grip of a rod in the space from +the center to the end of a beam. If 50 diameters are needed for this +grip, the whole span should then be not less than four times 50, or 200 +diameters of the rod. For the same reason the rod between these bends +should be at least 200 diameters in length. Often the reinforcing rods +are equal to or more than one-two-hundredth of the span in diameter, and +therefore need the full length of the span for grip. + +Mr. Thacher states that Rod 3 provides for the shear. He fails to answer +the argument that this rod is not anchored over the support to take the +shear. Would he, in a queen-post truss, attach the hog-rod to the beam +some distance out from the support and thus throw the bending and shear +back into the very beam which this rod is intended to relieve of bending +and shear? Yet this is just what Rod 3 would do, if it were long enough +to be anchored for the shear, which it seldom is; hence it cannot even +perform this function. If Rod 3 takes the shear, it must give it back to +the concrete beam from the point of its full usefulness to the support. +Mr. Thacher would not say of a steel truss that the diagonal bars would +take the shear, if these bars, in a deck truss, were attached to the top +chord several feet away from the support, or if the end connection were +good for only a fraction of the stress in the bars. Why does he not +apply the same logic to reinforced concrete design? + +Answering the third point, Mr. Thacher makes more statements that are +characteristic of current logic in reinforced concrete literature, which +does not bother with premises. He says, "In a beam, the shear rods run +through the compression parts of the concrete and have sufficient +anchorage." If the rods have sufficient anchorage, what is the nature of +that anchorage? It ought to be possible to analyze it, and it is due to +the seeker after truth to produce some sort of analysis. What mysterious +thing is there to anchor these rods? The writer has shown by analysis +that they are not anchored sufficiently. In many cases they are not long +enough to receive full anchorage. Mr. Thacher merely makes the dogmatic +statement that they are anchored. There is a faint hint of a reason in +his statement that they run into the compression part of the concrete. +Does he mean that the compression part of the concrete will grip the rod +like a vise? How does this comport with his contention farther on that +the beams are continuous? This would mean tension in the upper part of +the beam. In any beam the compression near the support, where the shear +is greatest, is small; so even this hint of an argument has no force or +meaning. + +In this same paragraph Mr. Thacher states, concerning the third point +and the case of the retaining wall that is given as an example, "In a +counterfort, the inclined rods are sufficient to take the overturning +stress." Mr. Thacher does not make clear what he means by "overturning +stress." He seems to mean the force tending to pull the counterfort +loose from the horizontal slab. The weight of the earth fill over this +slab is the force against which the vertical and inclined rods of Fig. +2, at _a_, must act. Does Mr. Thacher mean to state seriously that it is +sufficient to hang this slab, with its heavy load of earth fill, on the +short projecting ends of a few rods? Would he hang a floor slab on a few +rods which project from the bottom of a girder? He says, "The proposed +method is no more effective." The proposed method is Fig. 2, at _b_, +where an angle is provided as a shelf on which this slab rests. The +angle is supported, with thread and nut, on rods which reach up to the +front slab, from which a horizontal force, acting about the toe of the +wall as a fulcrum, results in the lifting force on the slab. There is +positively no way in which this wall could fail (as far as the +counterfort is concerned) but by the pulling apart of the rods or the +tearing out of this anchoring angle. Compare this method of failure with +the mere pulling out of a few ends of rods, in the design which Mr. +Thacher says is just as effective. This is another example of the kind +of logic that is brought into requisition in order to justify absurd +systems of design. + +Mr. Thacher states that shear would govern in a bridge pin where there +is a wide bar or bolster or a similar condition. The writer takes issue +with him in this. While in such a case the center of bearing need not be +taken to find the bending moment, shear would not be the correct +governing element. There is no reason why a wide bar or a wide bolster +should take a smaller pin than a narrow one, simply because the rule +that uses the center of bearing would give too large a pin. Bending can +be taken in this, as in other cases, with a reasonable assumption for a +proper bearing depth in the wide bar or bolster. The rest of Mr. +Thacher's comment on the fourth point avoids the issue. What does he +mean by "stress" in a shear rod? Is it shear or tension? Mr. Thacher's +statement, that the "stress" in the shear rods is less than that in the +bottom bars, comes close to saying that it is shear, as the shearing +unit in steel is less than the tensile unit. This vague way of referring +to the "stress" in a shear member, without specifically stating whether +this "stress" is shear or tension, as was done in the Joint Committee +Report, is, in itself, a confession of the impossibility of analyzing +the "stress" in these members. It gives the designer the option of using +tension or shear, both of which are absurd in the ordinary method of +design. Writers of books are not bold enough, as a rule, to state that +these rods are in shear, and yet their writings are so indefinite as to +allow this very interpretation. + +Mr. Thacher criticises the fifth point as follows: + + "Vertical stirrups are designed to act like the vertical rods in a + Howe truss. Special literature is not required on the subject; it + is known that the method used gives good results, and that is + sufficient." + +This is another example of the logic applied to reinforced concrete +design--another dogmatic statement. If these stirrups act like the +verticals in a Howe truss, why is it not possible by analysis to show +that they do? Of course there is no need of special literature on the +subject, if it is the intention to perpetuate this senseless method of +design. No amount of literature can prove that these stirrups act as the +verticals of a Howe truss, for the simple reason that it can be easily +proven that they do not. + +Mr. Thacher's criticism of the sixth point is not clear. "All the shear +from the center of the beam up to the bar in question," is what he says +each shear member is designed to take in the common method. The shear of +a beam usually means the sum of the vertical forces in a vertical +section. If he means that the amount of this shear is the load from the +center of the beam to the bar in question, and that shear members are +designed to take this amount of shear, it would be interesting to know +by what interpretation the common method can be made to mean this. The +method referred to is that given in several standard works and in the +Joint Committee Report. The formula in that report for vertical +reinforcement is: + + _V_ _s_ + _P_ = --------- , + _j_ _d_ + +in which _P_ = the stress in a single reinforcing member, _V_ = the +proportion of total shear assumed as carried by the reinforcement, _s_ = +the horizontal spacing of the reinforcing members, and _j d_ = the +effective depth. + +Suppose the spacing of shear members is one-half or one-third of the +effective depth, the stress in each member is one-half or one-third of +the "shear assumed to be carried by the reinforcement." Can Mr. Thacher +make anything else out of it? If, as he says, vertical stirrups are +designed to act like the vertical rods in a Howe truss, why are they not +given the stress of the verticals of a Howe truss instead of one-half or +one-third or a less proportion of that stress? + +Without meaning to criticize the tests made by Mr. Thaddeus Hyatt on +curved-up rods with nuts and washers, it is true that the results of +many early tests on reinforced concrete are uncertain, because of the +mealy character of the concrete made in the days when "a minimum amount +of water" was the rule. Reinforcement slips in such concrete when it +would be firmly gripped in wet concrete. The writer has been unable to +find any record of the tests to which Mr. Thacher refers. The tests +made at the University of Illinois, far from showing reinforcement of +this type to be "worse than useless," showed most excellent results by +its use. + +That which is condemned in the seventh point is not so much the +calculating of reinforced concrete beams as continuous, and reinforcing +them properly for these moments, but the common practice of lopping off +arbitrarily a large fraction of the simple beam moment on reinforced +concrete beams of all kinds. This is commonly justified by some virtue +which lies in the term monolith. If a beam rests in a wall, it is "fixed +ended"; if it comes into the side of a girder, it is "fixed ended"; and +if it comes into the side of a column, it is the same. This is used to +reduce the moment at mid-span, but reinforcement which will make the +beam fixed ended or continuous is rare. + +There is not much room for objection to Mr. Thacher's rule of spacing +rods three diameters apart. The rule to which the writer referred as +being 66% in error on the very premise on which it was derived, namely, +shear equal to adhesion, was worked out by F.P. McKibben, M. Am. Soc. C. +E. It was used, with due credit, by Messrs. Taylor and Thompson in their +book, and, without credit, by Professors Maurer and Turneaure in their +book. Thus five authorities perpetrate an error in the solution of one +of the simplest problems imaginable. If one author of an arithmetic had +said two twos are five, and four others had repeated the same thing, +would it not show that both revision and care were badly needed? + +Ernest McCullough, M. Am. Soc. C. E., in a paper read at the Armour +Institute, in November, 1908, says, "If the slab is not less than +one-fifth of the total depth of the beam assumed, we can make a +T-section of it by having the narrow stem just wide enough to contain +the steel." This partly answers Mr. Thacher's criticism of the ninth +point. In the next paragraph, Mr. McCullough mentions some very nice +formulas for T-beams by a certain authority. Of course it would be +better to use these nice formulas than to pay attention to such +"rule-of-thumb" methods as would require more width in the stem of the T +than enough to squeeze the steel in. + +If these complex formulas for T-beams (which disregard utterly the +simple and essential requirement that there must be concrete enough in +the stem of the T to grip the steel) are the only proper +exemplifications of the "theory of T-beams," it is time for engineers to +ignore theory and resort to rule-of-thumb. It is not theory, however, +which is condemned in the paper, it is complex theory; theory totally +out of harmony with the materials dealt with; theory based on false +assumptions; theory which ignores essentials and magnifies trifles; +theory which, applied to structures which have failed from their own +weight, shows them to be perfectly safe and correct in design; +half-baked theories which arrogate to themselves a monopoly on +rationality. + +To return to the spacing of rods in the bottom of a T-beam; the report +of the Joint Committee advocates a horizontal spacing of two and +one-half diameters and a side spacing of two diameters to the surface. +The same report advocates a "clear spacing between two layers of bars of +not less than 1/2 in." Take a T-beam, 11-1/2 in. wide, with two layers +of rods 1 in. square, 4 in each layer. The upper surface of the upper +layer would be 3-1/2 in. above the bottom of the beam. Below this +surface there would be 32 sq. in. of concrete to grip 8 sq. in. of +steel. Does any one seriously contend that this trifling amount of +concrete will grip this large steel area? This is not an extreme case; +it is all too common; and it satisfies the requirements of the Joint +Committee, which includes in its make-up a large number of the +best-known authorities in the United States. + +Mr. Thacher says that the writer appears to consider theories for +reinforced concrete beams and slabs as useless refinements. This is not +what the writer intended to show. He meant rather that facts and tests +demonstrate that refinement in reinforced concrete theories is utterly +meaningless. Of course a wonderful agreement between the double-refined +theory and test can generally be effected by "hunching" the modulus of +elasticity to suit. It works both ways, the modulus of elasticity of +concrete being elastic enough to be shifted again to suit the designer's +notion in selecting his reinforcement. All of which is very beautiful, +but it renders standard design impossible. + +Mr. Thacher characterizes the writer's method of calculating reinforced +concrete chimneys as rule-of-thumb. This is surprising after what he +says of the methods of designing stirrups. The writer's method would +provide rods to take all the tensile stresses shown to exist by any +analysis; it would give these rods unassailable end anchorages; every +detail would be amply cared for. If loose methods are good enough for +proportioning loose stirrups, and no literature is needed to show why or +how they can be, why analyze a chimney so accurately and apply +assumptions which cannot possibly be realized anywhere but on paper and +in books? + +It is not rule-of-thumb to find the tension in plain concrete and then +embed steel in that concrete to take that tension. Moreover, it is safer +than the so-called rational formula, which allows compression on slender +rods in concrete. + +Mr. Thacher says, "No arch designed by the elastic theory was ever known +to fail, unless on account of insecure foundations." Is this the correct +way to reach correct methods of design? Should engineers use a certain +method until failures show that something is wrong? It is doubtful if +any one on earth has statistics sufficient to state with any authority +what is quoted in the opening sentence of this paragraph. Many arches +are failures by reason of cracks, and these cracks are not always due to +insecure foundations. If Mr. Thacher means by insecure foundations, +those which settle, his assertion, assuming it to be true, has but +little weight. It is not always possible to found an arch on rock. Some +settlement may be anticipated in almost every foundation. As commonly +applied, the elastic theory is based on the absolute fixity of the +abutments, and the arch ring is made more slender because of this +fixity. The ordinary "row-of-blocks" method gives a stiffer arch ring +and, consequently, greater security against settlement of foundations. + +In 1904, two arches failed in Germany. They were three-hinged masonry +arches with metal hinges. They appear to have gone down under the weight +of theory. If they had been made of stone blocks in the old-fashioned +way, and had been calculated in the old-fashioned row-of-blocks method, +a large amount of money would have been saved. There is no good reason +why an arch cannot be calculated as hinged ended and built with the arch +ring anchored into the abutments. The method of the equilibrium polygon +is a safe, sane, and sound way to calculate an arch. The monolithic +method is a safe, sane, and sound way to build one. People who spend +money for arches do not care whether or not the fancy and fancied +stresses of the mathematician are realized; they want a safe and lasting +structure. + +Of course, calculations can be made for shrinkage stresses and for +temperature stresses. They have about as much real meaning as +calculations for earth pressures behind a retaining wall. The danger +does not lie in making the calculations, but in the confidence which the +very making of them begets in their correctness. Based on such +confidence, factors of safety are sometimes worked out to the hundredth +of a unit. + +Mr. Thacher is quite right in his assertion that stiff steel angles, +securely latticed together, and embedded in the concrete column, will +greatly increase its strength. + +The theory of slabs supported on four sides is commonly accepted for +about the same reason as some other things. One author gives it, then +another copies it; then when several books have it, it becomes +authoritative. The theory found in most books and reports has no correct +basis. That worked out by Professor W.C. Unwin, to which the writer +referred, was shown by him to be wrong.[T] An important English report +gave publicity and much space to this erroneous solution. Messrs. Marsh +and Dunn, in their book on reinforced concrete, give several pages to +it. + +In referring to the effect of initial stress, Mr. Myers cites the case +of blocks and says, "Whatever initial stress exists in the concrete due +to this process of setting exists also in these blocks when they are +tested." However, the presence of steel in beams and columns puts +internal stresses in reinforced concrete, which do not exist in an +isolated block of plain concrete. + +Mr. Meem, while he states that he disagrees with the writer in one +essential point, says of that point, "In the ordinary way in which these +rods are used, they have no practical value." The paper is meant to be a +criticism of the ordinary way in which reinforced concrete is used. + +While Mr. Meem's formula for a reinforced concrete beam is simple and +much like that which the writer would use, he errs in making the moment +of the stress in the steel about the neutral axis equal to the moment of +that in the concrete about the same axis. The actual amount of the +tension in the steel should equal the compression in the concrete, but +there is no principle of mechanics that requires equality of the moments +about the neutral axis. The moment in the beam is, therefore, the +product of the stress in steel or concrete and the effective depth of +the beam, the latter being the depth from the steel up to a point +one-sixth of the depth of the concrete beam from the top. This is the +method given by the writer. It would standardize design as methods using +the coefficient of elasticity cannot do. + +Professor Clifford, in commenting on the first point, says, "The +concrete at the point of juncture must give, to some extent, and this +would distribute the bearing over a considerable length of rod." It is +just this local "giving" in reinforced concrete which results in cracks +that endanger its safety and spoil its appearance; they also discredit +it as a permanent form of construction. + +Professor Clifford has informed the writer that the tests on bent rods +to which he refers were made on 3/4-in. rounds, embedded for 12 in. in +concrete and bent sharply, the bent portion being 4 in. long. The 12-in. +portion was greased. The average maximum load necessary to pull the rods +out was 16,000 lb. It seems quite probable that there would be some +slipping or crushing of the concrete before a very large part of this +load was applied. The load at slipping would be a more useful +determination than the ultimate, for the reason that repeated +application of such loads will wear out a structure. In this connection +three sets of tests described in Bulletin No. 29 of the University of +Illinois, are instructive. They were made on beams of the same size, and +reinforced with the same percentage of steel. The results were as +follows: + +Beams 511.1, 511.2, 512.1, 512.2: The bars were bent up at third points. +Average breaking load, 18,600 lb. All failed by slipping of the bars. + +Beams 513.1, 513.2: The bars were bent up at third points and given a +sharp right-angle turn over the supports. Average breaking load, 16,500 +lb. The beams failed by cracking alongside the bar toward the end. + +Beams 514.2, 514.3: The bars were bent up at third points and had +anchoring nuts and washers at the ends over the supports. Average +breaking load, 22,800 lb. These failed by tension in the steel. + +By these tests it is seen that, in a beam, bars without hooks were +stronger in their hold on the concrete by an average of 13% than those +with hooks. Each test of the group of straight bars showed that they +were stronger than either of those with hooked bars. Bars anchored over +the support in the manner recommended in the paper were nearly 40% +stronger than hooked bars and 20% stronger than straight bars. These +percentages, furthermore, do not represent all the advantages of +anchored bars. The method of failure is of greatest significance. A +failure by tension in the steel is an ideal failure, because it is +easiest to provide against. Failures by slipping of bars, and by +cracking and disintegrating of the concrete beam near the support, as +exhibited by the other tests, indicate danger, and demand much larger +factors of safety. + +Professor Clifford, in criticizing the statement that a member which +cannot act until failure has started is not a proper element of design, +refers to another statement by the writer, namely, "The steel in the +tension side of the beam should be considered as taking all the +tension." He states that this cannot take place until the concrete has +failed in tension at this point. The tension side of a beam will stretch +out a measurable amount under load. The stretching out of the beam +vertically, alongside of a stirrup, would be exceedingly minute, if no +cracks occurred in the beam. + +Mr. Mensch says that "the stresses involved are mostly secondary." He +compares them to web stresses in a plate girder, which can scarcely be +called secondary. Furthermore, those stresses are carefully worked out +and abundantly provided for in any good design. To give an example of +how a plate girder might be designed: Many plate girders have rivets in +the flanges, spaced 6 in. apart near the supports, that is, girders +designed with no regard to good practice. These girders, perhaps, need +twice as many rivets near the ends, according to good and acceptable +practice, which is also rational practice. The girders stand up and +perform their office. It is doubtful whether they would fail in these +rivet lines in a test to destruction; but a reasonable analysis shows +that these rivets are needed, and no good engineer would ignore this +rule of design or claim that it should be discarded because the girders +do their work anyway. There are many things about structures, as every +engineer who has examined many of those erected without engineering +supervision can testify, which are bad, but not quite bad enough to be +cause for condemnation. Not many years ago the writer ordered +reinforcement in a structure designed by one of the best structural +engineers in the United States, because the floor-beams had sharp bends +in the flange angles. This is not a secondary matter, and sharp bends in +reinforcing rods are not a secondary matter. No amount of analysis can +show that these rods or flange angles will perform their full duty. +Something else must be overstressed, and herein is a violation of the +principles of sound engineering. + +Mr. Mensch mentions the failure of the Quebec Bridge as an example of +the unknown strength of steel compression members, and states that, if +the designer of that bridge had known of certain tests made 40 years +ago, that accident probably would not have happened. It has never been +proven that the designer of that bridge was responsible for the accident +or for anything more than a bridge which would have been weak in +service. The testimony of the Royal Commission, concerning the chords, +is, "We have no evidence to show that they would have actually failed +under working conditions had they been axially loaded and not subject to +transverse stresses arising from weak end details and loose +connections." Diagonal bracing in the big erection gantry would have +saved the bridge, for every feature of the wreck shows that the lateral +collapse of that gantry caused the failure. Here are some more simple +principles of sound engineering which were ignored. + +It is when practice runs "ahead of theory" that it needs to be brought +up with a sharp turn. It is the general practice to design dams for the +horizontal pressure of the water only, ignoring that which works into +horizontal seams and below the foundation, and exerts a heavy uplift. +Dams also fail occasionally, because of this uplifting force which is +proven to exist by theory. + +Mr. Mensch says: + + "The author is manifestly wrong in stating that the reinforcing + rods can only receive their increments of stress when the concrete + is in tension. Generally, the contrary happens. In the ordinary + adhesion test, the block of concrete is held by the jaws of the + machine and the rod is pulled out; the concrete is clearly in + compression." + +This is not a case of increments at all, as the rod has the full stress +given to it by the grips of the testing machine. Furthermore, it is not +a beam. Also, Mr. Mensch is not accurate in conveying the writer's +meaning. To quote from the paper: + + "A reinforcing rod in a concrete beam receives its stress by + increments imparted by the grip of the concrete, but these + increments can only be imparted where the tendency of the concrete + is to stretch." + +This has no reference to an adhesion test. + +Mr. Mensch's next paragraph does not show a careful perusal of the +paper. The writer does not "doubt the advisability of using bent-up bars +in reinforced concrete beams." What he does condemn is bending up the +bars with a sharp bend and ending them nowhere. When they are curved up, +run to the support, and are anchored over the support or run into the +next span, they are excellent. In the tests mentioned by Mr. Mensch, the +beams which had the rods bent up and "continued over the supports" gave +the highest "ultimate values." This is exactly the construction which +is pointed out as being the most rational, if the rods do not have the +sharp bends which Mr. Mensch himself condemns. + +Regarding the tests mentioned by him, in which the rods were fastened to +anchor-plates at the end and had "slight increase of strength over +straight rods, and certainly made a poorer showing than bent-up bars," +the writer asked Mr. Mensch by letter whether these bars were curved up +toward the supports. He has not answered the communication, so the +writer cannot comment on the tests. It is not necessary to use threaded +bars, except in the end beams, as the curved-up bars can be run into the +next beam and act as top reinforcement while at the same time receiving +full anchorage. + +Mr. Mensch's statement regarding the retaining wall reinforced as shown +at _a_, Fig. 2, is astounding. He "confesses that he never saw or heard +of such poor practices." If he will examine almost any volume of an +engineering periodical of recent years, he will have no trouble at all +in finding several examples of these identical practices. In the books +by Messrs. Reid, Maurer and Turneaure, and Taylor and Thompson, he will +find retaining walls illustrated, which are almost identical with Fig. 2 +at _a_. Mr. Mensch says that the proposed design of a retaining wall +would be difficult and expensive to install. The harp-like reinforcement +could be put together on the ground, and raised to place and held with a +couple of braces. Compare this with the difficulty, expense and +uncertainty of placing and holding in place 20 or 30 separate rods. The +Fink truss analogy given by Mr. Mensch is a weak one. If he were making +a cantilever bracket to support a slab by tension from the top, the +bracket to be tied into a wall, would he use an indiscriminate lot of +little vertical and horizontal rods, or would he tie the slab directly +into the wall by diagonal ties? This is exactly the case of this +retaining wall, the horizontal slab has a load of earth, and the +counterfort is a bracket in tension; the vertical wall resists that +tension and derives its ability to resist from the horizontal pressure +of the earth. + +Mr. Mensch states that "it would take up too much time to prove that the +counterfort acts really as a beam." The writer proposes to show in a +very short time that it is not a beam. A beam is a part of a structure +subject to bending strains caused by transverse loading. This will do as +a working definition. The concrete of the counterfort shown at _b_, Fig. +2, could be entirely eliminated if the rods were simply made to run +straight into the anchoring angle and were connected with little cast +skewbacks through slotted holes. There would be absolutely no bending in +the rods and no transverse load. Add the concrete to protect the rods; +the function of the rods is not changed in the least. M.S. Ketchum, M. +Am. Soc. C. E.,[U] calculates the counterfort as a beam, and the six +1-in. square bars which he uses diagonally do not even run into the +front slab. He states that the vertical and horizontal rods are to "take +the horizontal and vertical shear." + +Mr. Mensch says of rectangular water tanks that they are not held +(presumably at the corners) by any such devices, and that there is no +doubt that they must carry the stress when filled with water. A water +tank,[V] designed by the writer in 1905, was held by just such devices. +In a tank[W] not held by any such devices, the corner broke, and it is +now held by reinforcing devices not shown in the original plans. + +Mr. Mensch states that he "does not quite understand the author's +reference to shear rods. Possibly he means the longitudinal +reinforcement, which it seems is sometimes calculated to carry 10,000 +lb. per sq. in. in shear;" and that he "never heard of such a practice." +His next paragraph gives the most pointed out-and-out statement +regarding shear in shear rods which this voluminous discussion contains. +He says that stirrups "are best compared with the dowel pins and bolts +of a compound wooden beam." This is the kernel of the whole matter in +the design of stirrups, and is just how the ordinary designer considers +stirrups, though the books and reports dodge the matter by saying +"stress" and attempting no analysis. Put this stirrup in shear at 10,000 +lb. per sq. in., and we have a shearing unit only equalled in the +cheapest structural work on tight-fitting rivets through steel. In the +light of this confession, the force of the writer's comparison, between +a U-stirrup, 3/4-in. in diameter, and two 3/4-in. rivets tightly driven +into holes in a steel angle, is made more evident, Bolts in a wooden +beam built up of horizontal boards would be tightly drawn up, and the +friction would play an important part in taking up the horizontal shear. +Dowels without head or nut would be much less efficient; they would be +more like the stirrups in a reinforced concrete beam. Furthermore, wood +is much stronger in bearing than concrete, and it is tough, so that it +would admit of shifting to a firm bearing against the bolt. Separate +slabs of concrete with bolts or dowels through them would not make a +reliable beam. The bolts or dowels would be good for only a part of the +safe shearing strength of the steel, because the bearing on the concrete +would be too great for its compressive strength. + +Mr. Mensch states that at least 99% of all reinforced structures are +calculated with a reduction of 25% of the bending moment in the center. +He also says "there may be some engineers who calculate a reduction of +33 per cent." These are broad statements in view of the fact that the +report of the Joint Committee recommends a reduction of 33% both in +slabs and beams. + +Mr. Mensch's remarks regarding the width of beams omit from +consideration the element of span and the length needed to develop the +grip of a rod. There is no need of making a rod any less in diameter +than one-two-hundredth of the span. If this rule is observed, the beam +with three 7/8-in. round rods will be of longer span than the one with +the six 5/8-in. rods. The horizontal shear of the two beams will be +equal to the total amount of that shear, but the shorter beam will have +to develop that shear in a shorter distance, hence the need of a wider +beam where the smaller rods are used. + +It is not that the writer advocates a wide stem in the T-beam, in order +to dispense with the aid of the slab. What he desires to point out is +that a full analysis of a T-beam shows that such a width is needed in +the stem. + +Regarding the elastic theory, Mr. Mensch, in his discussion, shows that +he does not understand the writer's meaning in pointing out the +objections to the elastic theory applied to arches. The moment of +inertia of the abutment will, of course, be many times that of the arch +ring; but of what use is this large moment of inertia when the abutment +suddenly stops at its foundation? The abutment cannot be anchored for +bending into the rock; it is simply a block of concrete resting on a +support. The great bending moment at the end of the arch, which is found +by the elastic theory (on paper), has merely to overturn this block of +concrete, and it is aided very materially in this by the thrust of the +arch. The deformation of the abutment, due to deficiency in its moment +of inertia, is a theoretical trifle which might very aptly be minutely +considered by the elastic arch theorist. He appears to have settled all +fears on that score among his votaries. The settlement of the abutment +both vertically and horizontally, a thing of tremendously more magnitude +and importance, he has totally ignored. + +Most soils are more or less compressible. The resultant thrust on an +arch abutment is usually in a direction cutting about the edge of the +middle third. The effect of this force is to tend to cause more +settlement of the abutment at the outer, than at the inner, edge, or, in +other words, it would cause the abutment to rotate. In addition to this +the same force tends to spread the abutments apart. Both these efforts +put an initial bending moment in the arch ring at the springing; a +moment not calculated, and impossible to calculate. + +Messrs. Taylor and Thompson, in their book, give much space to the +elastic theory of the reinforced concrete arch. Little of that space, +however, is taken up with the abutment, and the case they give has +abutments in solid rock with a slope about normal to the thrust of the +arch ring. They recommend that the thrust be made to strike as near the +middle of the base of the abutment as possible. + +Malverd A. Howe, M. Am. Soc. C. E., in a recent issue of _Engineering +News_, shows how to find the stresses and moments in an elastic arch; +but he does not say anything about how to take care of the large bending +moments which he finds at the springing. + +Specialists in arch construction state that when the centering is +struck, every arch increases in span by settlement. Is this one fact not +enough to make the elastic theory a nullity, for that theory assumes +immovable abutments? + +Professor Howe made some recent tests on checking up the elastic +behavior of arches. He reports[X] that "a very slight change at the +support does seriously affect the values of _H_ and _M_." The arch +tested was of 20-ft. span, and built between two heavy stone walls out +of all proportion to the magnitude of the arch, as measured by +comparison with an ordinary arch and its abutment. To make the arch +fixed ended, a large heavily reinforced head was firmly bolted to the +stone wall. Practical fixed endedness could be attained, of course, by +means such as these, but the value of such tests is only theoretical. + +Mr. Mensch says: + + "The elastic theory was fully proved for arches by the remarkable + tests, made in 1897 by the Austrian Society of Engineers and + Architects, on full-sized arches of 70-ft. span, and the observed + deflections and lateral deformations agreed exactly with the + figured deformation." + +The writer does not know of the tests made in 1897, but reference is +often made to some tests reported in 1896. These tests are everywhere +quoted as the unanswerable argument for the elastic theory. Let us +examine a few features of those tests, and see something of the strength +of the claim. In the first place, as to the exact agreement between the +calculated and the observed deformations, this exact agreement was +retroactive. The average modulus of elasticity, as found by specimen +tests of the concrete, did not agree at all with the value which it was +necessary to use in the arch calculations in order to make the +deflections come out right. + +As found by tests on blocks, the average modulus was about 2,700,000; +the "practical" value, as determined from analysis of a plain concrete +arch, was 1,430,000, a little matter of nearly 100 per cent. Mansfield +Merriman, M. Am. Soc. C. E., gives a digest of these famous Austrian +tests.[Y] There were no fixed ended arches among them. There was a long +plain concrete arch and a long Monier arch. Professor Merriman says, +"The beton Monier arch is not discussed theoretically, and, indeed, this +would be a difficult task on account of the different materials +combined." And these are the tests which the Engineering Profession +points to whenever the elastic theory is questioned as to its +applicability to reinforced concrete arches. These are the tests that +"fully prove" the elastic theory for arches. These are the tests on the +basis of which fixed ended reinforced concrete arches are confidently +designed. Because a plain concrete bow between solid abutments deflected +in an elastic curve, reinforced concrete arches between settling +abutments are designed with fixed ends. The theorist has departed about +as far as possible from his premise in this case. On an exceedingly +slender thread he has hung an elaborate and important theory of design, +with assumptions which can never be realized outside of the schoolroom +or the designer's office. The most serious feature of such theories is +not merely the approximate and erroneous results which they give, but +the extreme confidence and faith in their certainty which they beget in +their users, enabling them to cut down factors of safety with no regard +whatever for the enormous factor of ignorance which is an essential +accompaniment to the theory itself. + +Mr. Mensch says, "The elastic theory enables one to calculate arches +much more quickly than any graphical or guess method yet proposed." The +method given by the writer[Z] enables one to calculate an arch in about +the time it would take to work out a few of the many coefficients +necessary in the involved method of the elastic theory. It is not a +graphic method, but it is safe and sound, and it does not assume +conditions which have absolutely no existence. + +Mr. Mensch says that the writer brings up some erratic column tests and +seems to have no confidence in reinforced concrete columns. In relation +to this matter Sanford E. Thompson, M. Am. Soc. C. E., in a paper +recently read before the National Association of Cement Users, takes the +same sets of tests referred to in the paper, and attempts to show that +longitudinal reinforcement adds much strength to a concrete column. Mr. +Thompson goes about it by means of averages. It is not safe to average +tests where the differences in individual tests are so great that those +of one class overlap those of the other. He includes the writer's +"erratic" tests and some others which are "erratic" the other way. It is +manifestly impossible for him to prove that longitudinal rods add any +strength to a concrete column if, on one pair of columns, identically +made as far as practicable, the plain concrete column is stronger than +that with longitudinal rods in it, unless the weak column is defective. +It is just as manifest that it is shown by this and other tests that the +supposedly reinforced concrete column may be weaker. + +The averaging of results to show that longitudinal rods add strength, in +the case of the tests reported by Mr. Withey, includes a square plain +concrete column which naturally would show less compressive strength in +concrete than a round column, because of the spalling off at the +corners. This weak test on a square column is one of the slender props +on which is based the conclusion that longitudinal rods add to the +strength of a concrete column; but the weakness of the square concrete +column is due to the inherent weakness of brittle material in +compression when there are sharp corners which may spall off. + +Mr. Worcester says that several of the writer's indictments hit at +practices which were discarded long ago, but from the attitude of their +defenders this does not seem to be true. There are benders to make sharp +bends in rods, and there are builders who say that they must be bent +sharply in order to simplify the work of fitting and measuring them. + +There are examples in engineering periodicals and books, too numerous to +mention, where no anchorage of any kind is provided for bent-up rods, +except what grip they get in the concrete. If they reached beyond their +point of usefulness for this grip, it would be all right, but very often +they do not. + +Mr. Worcester says: "It is not necessary that a stirrup at one point +should carry all the vertical tension, as this vertical tension is +distributed by the concrete." The writer will concede that the stirrups +need not carry all the vertical shear, for, in a properly reinforced +beam, the concrete can take part of it. The shear reinforcement, +however, should carry all the shear apportioned to it after deducting +that part which the concrete is capable of carrying, and it should carry +it without putting the concrete in shear again. The stirrups at one +point should carry all the vertical tension from the portion of shear +assumed to be taken by the stirrups; otherwise the concrete will be +compelled to carry more than its share of the shear. + +Mr. Worcester states that cracks are just as likely to occur from stress +in curved-up and anchored rods as in vertical reinforcement. The fact +that the vertical stretching out of a beam from the top to the bottom, +under its load, is exceedingly minute, has been mentioned. A curved-up +bar, anchored over the support and lying near the bottom of the beam at +mid-span, partakes of the elongation of the tension side of the beam and +crosses the section of greatest diagonal tension in the most +advantageous manner. There is, therefore, a great deal of difference in +the way in which these two elements of construction act. + +Mr. Worcester prefers the "customary method" of determining the width of +beams--so that the maximum horizontal shearing stress will not be +excessive--to that suggested by the writer. He gives as a reason for +this the fact that rods are bent up out of the bottom of a beam, and +that not all of them run to the end. The "customary method" must be +described in literature for private circulation. Mention has been made +of a method which makes the width of beam sufficient to insert the +steel. Considerations of the horizontal shear in a T-beam, and of the +capacity of the concrete to grip the steel, are conspicuous by their +absence in the analyses of beams. If a reinforcing rod is curved up and +anchored over the support, the concrete is relieved of the shear, both +horizontal and vertical, incident to the stress in that rod. If a +reinforcing rod is bent up anywhere, and not carried to the support, and +not anchored over it, as is customary, the shear is all taken by the +concrete; and there is just the same shear in the concrete as though the +rods were straight. + +For proper grip a straight rod should have a diameter of not more than +one two-hundredth of the span. For economy of material, it should not be +much smaller in diameter than this. With this balance in a beam, +assuming shear equal to bond, the rods should be spaced a distance +apart, equal to their perimeters. This is a rational and simple rule, +and its use would go a long way toward the adoption of standards. + +Mr. Worcester is not logical in his criticism of the writer's method of +reinforcing a chimney. It is not necessary to assume that the concrete +is not stressed, in the imaginary plain concrete chimney, beyond that +which plain concrete could take in tension. The assumption of an +imaginary plain concrete chimney and determinations of tensile stresses +in the concrete are merely simplified methods of finding the tensile +stress. The steel can take just as much tensile stress if its amount is +determined in this way as it can if any other method is used. The +shifting of the neutral axis, to which Mr. Worcester refers, is another +of the fancy assumptions which cannot be realized because of initial and +unknown stresses in the concrete and steel. + +Mr. Russell states that the writer scarcely touched on top reinforcement +in beams. This would come in the class of longitudinal rods in columns, +unless the reinforcement were stiff members. Mr. Russell's remarks, to +the effect that columns and short deep beams, doubly reinforced, should +be designed as framed structures, point to the conclusion that +structural beams and columns, protected with concrete, should be used in +such cases. If the ruling motive of designers were uniformly to use what +is most appropriate in each particular location and not to carry out +some system, this is just what would be done in many cases; but some +minds are so constructed that they take pleasure in such boasts as this: +"There is not a pound of structural steel in that building." A +broad-minded engineer will use reinforced concrete where it is most +appropriate, and structural steel or cast iron where these are most +appropriate, instead of using his clients' funds to carry out some +cherished ideas. + +Mr. Wright appreciates the writer's idea, for the paper was not intended +to criticize something which is "good enough" or which "answers the +purpose," but to systematize or standardize reinforced concrete and put +it on a basis of rational analysis and common sense, such a basis as +structural designing has been or is being placed on, by a careful +weeding out of all that is irrational, senseless, and weak. + +Mr. Chapman says that the practical engineer has never used such methods +of construction as those which the writer condemns. The methods are +common enough; whether or not those who use them are practical engineers +is beside the question. + +As to the ability of the end connection of a stringer carrying flange +stress or bending moments, it is not uncommon to see brackets carrying +considerable overhanging loads with no better connection. Even wide +sidewalks of bridges sometimes have tension connections on rivet heads. +While this is not to be commended, it is a demonstration of the ability +to take bending which might be relied on, if structural design were on +as loose a basis as reinforced concrete. + +Mr. Chapman assumes that stirrups are anchored at each end, and Fig. 3 +shows a small hook to effect this anchorage. He does not show how +vertical stirrups can relieve a beam of the shear between two of these +stirrups. + +The criticism the writer would make of Figs. 5 and 6, is that there is +not enough concrete in the stem of the T to grip the amount of steel +used, and the steel must be gripped in that stem, because it does not +run to the support or beyond it for anchorage. Steel members in a bridge +may be designed in violation of many of the requirements of +specifications, such as the maximum spacing of rivets, size of lattice +bars, etc.; the bridge will not necessarily fail or show weakness as +soon as it is put into service, but it is faulty and weak just the same. + +Mr. Chapman says: "The practical engineer does not find * * * that the +negative moment is double the positive moment, because he considers the +live load either on one span only, or on alternate spans." It is just in +such methods that the "practical engineer" is inconsistent. If he is +going to consider the beams as continuous, he should find the full +continuous beam moment and provide for it. It is just this disposition +to take an advantage wherever one can be taken, without giving proper +consideration to the disadvantage entailed, which is condemned in the +paper. The "practical engineer" will reduce his bending moment in the +beam by a large fraction, because of continuity, but he will not +reinforce over the supports for full continuity. Reinforcement for full +continuity was not recommended, but it was intimated that this is the +only consistent method, if advantage is taken of continuity in reducing +the principal bending moment. + +Mr. Chapman says that an arch should not be used where the abutments are +unstable. Unstable is a relative and indefinite word. If he means that +abutments for arches should never be on anything but rock, even such a +foundation is only quite stable when the abutment has a vertical rock +face to take horizontal thrusts. If arches could be built only under +such conditions, few of them would be built. Some settlement is to be +expected in almost any soil, and because of horizontal thrusts there is +also a tendency for arch abutments to rotate. It is this tendency which +opens up cracks in spandrels of arches, and makes the assumption of a +fixed tangent at the springing line, commonly made by the elastic +theorist, absolute foolishness. + +Mr. Beyer has developed a novel explanation of the way stirrups act, but +it is one which is scarcely likely to meet with more serious +consideration than the steel girder to which he refers, which has +neither web plate nor diagonals, but only verticals connecting the top +and bottom flanges. This style of girder has been considered by American +engineers rather as a curiosity, if not a monstrosity. If vertical +stirrups acted to reinforce little vertical cantilevers, there would +have to be a large number of them, so that each little segment of the +beam would be insured reinforcement. + +The writer is utterly at a loss to know what Professor Ostrup means by +his first few paragraphs. He says that in the first point two designs +are mentioned and a third condemned. The second design, whatever it is, +he lays at the writer's door in these words: "The author's second design +is an invention of his own, which the Profession at large is invited to +adopt." In the first point sharp bends in reinforcing rods are condemned +and curves recommended. Absolutely nothing is said of "a reinforced +concrete beam arranged in the shape of a rod, with separate concrete +blocks placed on top of it without being connected." + +In reply to Professor Ostrup, it should be stated that the purpose of +the paper is not to belittle the importance of the adhesion or grip of +concrete on steel, but to point out that the wonderful things this grip +is supposed to do, as exhibited by current design, will not stand the +test of analysis. + +Professor Ostrup has shown a new phase of the stress in shear rods. He +says they are in bending between the centers of compressive resultants. +We have been told in books and reports that these rods are in stress of +some kind, which is measured by the sectional area of the rod. No hint +has been given of designing stirrups for bending. If these rods are not +in shear, as stated by Professor Ostrup, how can they be in bending in +any such fashion as that indicated in Fig. 12? + +Professor Ostrup's analysis, by which he attempts to justify stirrups +and to show that vertical stirrups are preferable, merely treats of +local distribution of stress from short rods into concrete. Apparently, +it would work the same if the stirrups merely touched the tension rod. +His analysis ignores the vital question of what possible aid the stirrup +can be in relieving the concrete between stirrups of the shear of the +beam. + +The juggling of bending moments in beams is not compensating. The +following is a concrete example. Some beams of a span of about 20 ft., +were framed into double girders at the columns. The beams were +calculated as partly continuous, though they were separated at their +ends by about 1-1/2 or 2 ft., the space between the girders. The beams +had 1-1/8-in. tension rods in the bottom. At the supports a short +1/4-in. rod was used near the top of the beam for continuity. Does this +need any comment? It was not the work of a novice or of an inexperienced +builder. + +Professor Ostrup's remarks about the shifting of the neutral axis of a +beam and of the pressure line of an arch are based on theory which is +grounded in impossible assumptions. The materials dealt with do not +justify these assumptions or the hair-splitting theory based thereon. +His platitudes about the danger of misplacing reinforcement in an arch +are hardly warranted. If the depth and reinforcement of an arch ring are +added to, as the inelastic, hinge-end theory would dictate, as against +the elastic theory, it will strengthen the arch just as surely as it +would strengthen a plate girder to thicken the web and flange angles. + +The writer's complaint is not that the theories of reinforced concrete +are not fully developed. They are developed too highly, developed out of +all comparison with the materials dealt with. It is just because +reinforced concrete structures are being built in increasing numbers +that it behooves engineers to inject some rationality (not high-strung +theory) into their designs, and drop the idea that "whatever is is +right." + +Mr. Porter has much to say about U-bars. He states that they are useful +in holding the tension bars in place and in tying the slab to the stem +of a T-beam. These are legitimate functions for little loose rods; but +why call them shear rods and make believe that they take the shear of a +beam? As to stirrups acting as dowel pins, the writer has already +referred to this subject. Answering a query by Mr. Porter, it may be +stated that what would counteract the horizontal cleaving force in a +beam is one or more rods curved up to the upper part of the beam and +anchored at the support or run into the next span. Strangely enough, Mr. +Porter commends this very thing, as advocated in the paper. The +excellent results shown by the test referred to by him can well be +contrasted with some of the writer's tests. This floor was designed for +250 lb. per sq. ft. When that load was placed on it, the deflection was +more than 1 in. in a span of 20 ft. No rods were curved up and run over +the supports. It was a stirrup job. + +Mr. Porter intimates that the correct reinforced concrete column may be +on lines of concrete mixed with nails or wires. There is no doubt but +that such concrete would be strong in compression for the reason that it +is strong in tension, but a column needs some unifying element which is +continuous. A reinforced column needs longitudinal rods, but their +office is to take tension; they should not be considered as taking +compression. + +Mr. Goodrich makes this startling remark: "It is a well-known fact that +the bottom chords in queen-post trusses are useless, as far as +resistance to tension is concerned." The writer cannot think that he +means by this that, for example, a purlin made up of a 3 by 2-in. angle +and a 5/8-in. hog-rod would be just as good with the rod omitted. If +queen-post trusses are useless, some hundreds of thousands of hog-rods +in freight cars could be dispensed with. + +Mr. Goodrich misunderstands the reference to the "only rational and only +efficient design possible." The statement is that a design which would +be adopted, if slabs were suspended on rods, is the only rational and +the only efficient design possible. If the counterfort of a retaining +wall were a bracket on the upper side of a horizontal slab projecting +out from a vertical wall, and all were above ground, the horizontal slab +being heavily loaded, it is doubtful whether any engineer would think of +using any other scheme than diagonal rods running from slab to wall and +anchored into each. This is exactly the condition in this shape of +retaining wall, except that it is underground. + +Mr. Goodrich says that the writer's reasoning as to the sixth point is +almost wholly facetious and that concrete is very strong in pure shear. +The joke, however, is on the experimenters who have reported concrete +very strong in shear. They have failed to point out that, in every case +where great strength in shear is manifested, the concrete is confined +laterally or under heavy compression normal to the sheared plane. +Stirrups do not confine concrete in a direction normal to the sheared +plane, and they do not increase the compression. A large number of +stirrups laid in herring-bone fashion would confine the concrete across +diagonal planes, but such a design would be wasteful, and the common +method of spacing the stirrups would not suggest their office in this +capacity. + +As to the writer's statements regarding the tests in Bulletin No. 29 of +the University of Illinois being misleading, he quotes from that +bulletin as follows: + + "Until the concrete web has failed in diagonal tension and diagonal + cracks have formed there must be little vertical deformation at the + plane of the stirrups, so little that not much stress can have + developed in the stirrups." * * * "It is evident, then, that until + the concrete web fails in diagonal tension little stress is taken + by the stirrups." * * * "It seems evident from the tests that the + stirrups did not take much stress until after the formation of + diagonal cracks." * * * "It seems evident that there is very little + elongation in stirrups until the first diagonal crack forms, and + hence that up to this point the concrete takes practically all the + diagonal tension." * * * "Stirrups do not come into action, at + least not to any great extent, until the diagonal crack has + formed." + +In view of these quotations, the misleading part of the reference to the +tests and their conclusion is not so evident. + +The practical tests on beams with suspension rods in them, referred to +by Mr. Porter, show entirely different results from those mentioned by +Mr. Goodrich as being made by Moersch. Tests on beams of this sort, which +are available in America, seem to show excellent results. + +Mr. Goodrich is somewhat unjust in attributing failures to designs which +are practically in accordance with the suggestions under Point Seven. In +Point Seven the juggling of bending moments is condemned--it is +condemnation of methods of calculating. Point Seven recommends +reinforcing a beam for its simple beam moment. This is the greatest +bending it could possibly receive, and it is inconceivable that failure +could be due to this suggestion. Point Seven recommends a reasonable +reinforcement over the support. This is a matter for the judgment of the +designer or a rule in specifications. Failure could scarcely be +attributed to this. It is the writer's practice to use reinforcement +equal to one-half of the main reinforcement of the beam across the +support; it is also his practice to curve up a part of the beam +reinforcement and run it into the next span in all beams needing +reinforcement for shear; but the paper was not intended to be a treatise +on, nor yet a general discussion of, reinforced concrete design. + +Mr. Goodrich characterizes the writer's method of calculating reinforced +concrete chimneys as crude. It is not any more crude than concrete. The +ultra-theoretic methods are just about as appropriate as calculations of +the area of a circle to hundredths of a square inch from a paced-off +diameter. The same may be said of deflection calculations. + +Mr. Goodrich has also appreciated the writer's spirit in presenting this +paper. Attention to details of construction has placed structural steel +designing on the high plane on which it stands. Reinforced concrete +needs the same careful working out of details before it can claim the +same recognition. It also needs some simplification of formulas. Witness +the intricate column formulas for steelwork which have been buried, and +even now some of the complex beam formulas for reinforced concrete have +passed away. + +Major Sewell, in his discussion of the first point, seems to object +solely to the angle of the bent-up portion of the rod. This angle could +have been much less, without affecting the essence of the writer's +remarks. Of course, the resultant, _b_, would have been less, but this +would not create a queen-post at the sharp bend of the bar. Major Sewell +says that he "does not remember ever to have seen just the type of +construction shown in Fig. 1, either used or recommended." This type of +beam might be called a standard. It is almost the insignia of a +reinforced concrete expert. A little farther on Major Sewell says that +four beams tested at the University of Illinois were about as nearly +like Fig. 1 as anything he has ever seen in actual practice. He is the +only one who has yet accused the writer of inventing this beam. + +If Major Sewell's statement that he has never seen the second point +exemplified simply means that he has never seen an example of the bar +bent up at the identical angle given in the paper, his criticism has not +much weight. + +Major Sewell's comment on the retaining wall begs the question. Specific +references to examples have been given in which the rods of a +counterfort are not anchored into the slabs that they hold by tension, +save by a few inches of embedment; an analysis has also been cited in +which the counterfort is considered as a beam, and ties in the great +weight of the slab with a few "shear rods," ignoring the anchorage of +either horizontal, vertical, or diagonal rods. It is not enough that +books state that rods in tension need anchorage. They should not show +examples of rods that are in pure tension and state that they are merely +thrown in for shear. Transverse rods from the stem to the flange of a +T-beam, tie the whole together; they prevent cracking, and thereby allow +the shearing strength of the concrete to act. It is not necessary to +count the rods in shear. + +Major Sewell's comparison of a stirrup system and a riveted truss is not +logical. The verticals and diagonals of a riveted truss have gusset +plates which connect symmetrically with the top chord. One line of +rivets or a pin in the center line of the top chord could be used as a +connection, and this connection would be complete. To distribute rivets +above and below the center line of the top chord does not alter the +essential fact that the connection of the web members is complete at the +center of the top chord. The case of stirrups is quite different. Above +the centroid of compression there is nothing but a trifling amount of +embedment of the stirrup. If 1/2-in. stirrups were used in an 18-in. +beam, assuming that 30 diameters were enough for anchorage, the centroid +of compression would be, say, 3 in. below the top of the beam, the +middle point of the stirrup's anchorage would be about 8 in., and the +point of full anchorage would be about 16 in. The neutral axis would +come somewhere between. These are not unusual proportions. Analogy with +a riveted truss fails; even the anchorage above the neutral axis is far +from realization. + +Major Sewell refers to shallow bridge stringers and the possibility of +failure at connections by continuity or deflection. Structural engineers +take care of this, not by reinforcement for continuity but by ample +provision for the full bending moment in the stringer and by ample +depth. Provision for both the full bending moment and the ample depth +reduces the possibilities of deflection at the floor-beams. + +Major Sewell seems also to have assumed that the paper was a general +discussion on reinforced concrete design. The idea in pointing out that +a column having longitudinal rods in it may be weaker than a plain +concrete column was not to exalt the plain concrete column but to +degrade the other. A plain concrete column of any slenderness would +manifestly be a gross error. If it can be shown that one having only +longitudinal rods may be as bad, or worse, instead of being greatly +strengthened by these rods, a large amount of life and property may be +saved. + +A partial reply to Mr. Thompson's discussion will be found in the +writer's response to Mr. Mensch. The fault with Mr. Thompson's +conclusions lies in the error of basing them on averages. Average +results of one class are of little meaning or value when there is a wide +variation between the extremes. In the tests of both the concrete-steel +and the plain concrete which Mr. Thompson averages there are wide +variations. In the tests made at the University of Illinois there is a +difference of almost 100% between the minimum and maximum results in +both concrete-steel and plain concrete columns. + +Average results, for a comparison between two classes, can mean little +when there is a large overlap in the individual results, unless there is +a large number of tests. In the seventeen tests made at the University +of Illinois, which Mr. Thompson averages, the overlap is so great that +the maximum of the plain columns is nearly 50% greater than the minimum +of the concrete-steel columns. + +If the two lowest tests in plain concrete and the two highest in +concrete-steel had not been made, the average would be in favor of the +plain concrete by nearly as much as Mr. Thompson's average now favors +the concrete-steel columns. Further, if these four tests be eliminated, +only three of the concrete-steel columns are higher than the plain +concrete. So much for the value of averages and the conclusions drawn +therefrom. + +It is idle to draw any conclusions from such juggling of figures, except +that the addition of longitudinal steel rods is altogether +problematical. It may lessen the compressive strength of a concrete +column. Slender rods in such a column cannot be said to reinforce it, +for the reason that careful tests have been recorded in which columns of +concrete-steel were weaker than those of plain concrete. + +In the averages of the Minneapolis tests Mr. Thompson has compared the +results on two plain concrete columns with the average of tests on an +indiscriminate lot of hooped and banded columns. This method of boosting +the average shows anything but "critical examination" on his part. + +Mr. Thompson, on the subject of Mr. Withey's tests, compares plain +concrete of square cross-section with concrete-steel of octagonal +section. As stated before, this is not a proper comparison. In a fragile +material like concrete the corners spall off under a compressive load, +and the square section will not show up as well as an octagonal or round +one. + +Mr. Thompson's contention, regarding the Minneapolis tests, that the +concrete outside of the hoops should not be considered, is ridiculous. +If longitudinal rods reinforce a concrete column, why is it necessary to +imagine that a large part of the concrete must be assumed to be +non-existent in order to make this reinforcement manifest? An imaginary +core could be assumed in a plain concrete column and any desired results +could be obtained. Furthermore, a properly hooped column does not enter +into this discussion, as the proposition is that slender longitudinal +rods do not reinforce a concrete column; if hoops are recognized, the +column does not come under this proposition. + +Further, the proposition in the writer's fifteenth point does not say +that the steel takes no part of the compression of a column. Mr. +Thompson's laborious explanation of the fact that the steel receives a +share of the load is needless. There is no doubt that the steel receives +a share of the load--in fact, too great a share. This is the secret of +the weakness of a concrete column containing slender rods. The concrete +shrinks, the steel is put under initial compression, the load comes more +heavily on the steel rods than on the concrete, and thus produces a most +absurd element of construction--a column of slender steel rods held +laterally by a weak material--concrete. This is the secret of nearly all +the great wrecks in reinforced concrete: A building in Philadelphia, a +reservoir in Madrid, a factory in Rochester, a hotel in California. All +these had columns with longitudinal rods; all were extensive +failures--probably the worst on record; not one of them could possibly +have failed as it did if the columns had been strong and tough. Why use +a microscope and search through carefully arranged averages of tests on +nursery columns, with exact central loading, to find some advantage in +columns of this class, when actual experience is publishing in bold type +the tremendously important fact that these columns are utterly +untrustworthy? + +It is refreshing to note that not one of the writer's critics attempts +to defend the quoted ultimate strength of a reinforced concrete column. +Even Mr. Thompson acknowledges that it is not right. All of which, in +view of the high authority with whom it originated, and the wide use it +has been put to by the use of the scissors, would indicate that at last +there is some sign of movement toward sound engineering in reinforced +concrete. + +In conclusion it might be pointed out that this discussion has brought +out strong commendation for each of the sixteen indictments. It has also +brought out vigorous defense of each of them. This fact alone would seem +to justify its title. A paper in a similar strain, made up of +indictments against common practices in structural steel design, +published in _Engineering News_ some years ago, did not bring out a +single response. While practice in structural steel may often be faulty, +methods of analysis are well understood, and are accepted with little +question. + +FOOTNOTES: + +[Footnote E: _Transactions_, Am. Soc. C. E., Vol. LXVI, p. 431.] + +[Footnote F: _Loc. cit._, p. 448.] + +[Footnote G: _Engineering News_, Dec. 3d, 1908.] + +[Footnote H: _Journal_ of the Western Society of Engineers, 1905.] + +[Footnote I: Tests made for C.A.P. Turner, by Mason D. Pratt, M. Am. +Soc. C. E.] + +[Footnote J: _Transactions_, Am. Soc. C. E., Vol. LVI, p. 343.] + +[Footnote K: Bulletin No. 28, University of Illinois.] + +[Footnote L: Bulletin No. 12, University of Illinois, Table VI, page +27.] + +[Footnote M: Professeur de Stabilite a l'Universite de Louvain.] + +[Footnote N: A translation of Professor Vierendeel's theory may be found +in _Beton und Eisen_, Vols. X, XI, and XII, 1907.] + +[Footnote O: _Cement_, March, 1910, p. 343; and _Concrete Engineering_, +May, 1910, p. 113.] + +[Footnote P: The correct figures from the _Bulletin_ are 1,577 lb.] + +[Footnote Q: _Engineering News_, January 7th, 1909, p. 20.] + +[Footnote R: For fuller treatment, see the writer's discussion in +_Transactions_, Am. Soc. C. E., Vol. LXI, p. 46.] + +[Footnote S: See "Tests of Metals," U.S.A., 1905, p. 344.] + +[Footnote T: _The Engineering Record_, August 17th, 1907.] + +[Footnote U: "The Design of Walls, Bins and Elevators."] + +[Footnote V: _Engineering News_, September 28th, 1905.] + +[Footnote W: _The Engineering Record_, June 26th, 1909.] + +[Footnote X: _Railroad Age Gazette_, March 26th, 1909.] + +[Footnote Y: _Engineering News_, April 9th, 1896.] + +[Footnote Z: "Structural Engineering: Concrete."] + + + + + +End of the Project Gutenberg EBook of Some Mooted Questions in Reinforced +Concrete Design, by Edward Godfrey + +*** END OF THIS PROJECT GUTENBERG EBOOK REINFORCED CONCRETE DESIGN *** + +***** This file should be named 17137.txt or 17137.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/1/7/1/3/17137/ + +Produced by Juliet Sutherland, Taavi Kalju and the Online +Distributed Proofreading Team at https://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, is critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. |