Some Mooted Questions in Reinforced Concrete Design Part 8

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 a.s.sume 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 anch.o.r.ed there by bending it down at about the same angle as it is bent up on the approach, and then hooking the ends.

[Ill.u.s.tration: 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 pa.s.sed 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, furnis.h.i.+ng 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 anch.o.r.ed, 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 a.n.a.lysis of the stresses incurred in the different parts of this beam, although it might be interesting and instructive.

[Ill.u.s.tration: FIG. 14.]

The concrete, with the reinforcement disposed as described, may be regarded as reposing on the steel as a saddle, furnis.h.i.+ng 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 bas.e.m.e.nt, the beams giving way abruptly over the supports. Had an adequate tie of steel been provided across the supports, the collapse, undoubtedly, would have stopped at the fourth floor. So many faults were apparent in this structure, that, although only half of it had fallen, it was ordered to be entirely demolished and reconstructed.

The cracks in the beams, due to the action of the dead weight alone, were most interesting, and illuminative of the action which takes place in a concrete beam. They were in every case on the diagonal, at an angle of approximately 45, and extended upward and outward from the edge of the support to the bottom side of the slab. Never was the necessity for diagonal steel, crossing this plane of weakness, more emphatically demonstrated. To the writer--an eye-witness--the following line of thought was suggested:

Should not the concrete in the region above the supports and for a distance on either side, as encompa.s.sed by the opposed 45 lines (Fig.

14), be regarded as abundantly able, of and by itself, and without reinforcing, to convey all its load into the column, leaving only the bending to be considered in the truncated portion intersected? Not even the bending should be considered, except in the case of relatively shallow members, but simply the tendency on the part of the wedge-shaped section to slip out on the 45 planes, thereby requiring sufficient reinforcement at the crossing of these planes of princ.i.p.al weakness to take the component of the load on this portion, tending to shove it out.

This reinforcement, of course, should be anch.o.r.ed 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 a.s.sumed to a.s.sist partly or not at all.

This would seem to be a fair a.s.sumption. In all events, beams designed in this manner and checked by comparison with the usual methods of calculation, allowing continuity of action, are found to agree fairly well. Hence, the following statement seems to be warranted: If enough steel is provided, crossing normally or nearly so the 45 planes from the edge of the support upward and outward, to care for the component of the load on the portion included within a pair of these planes, tending to produce sliding along the same, and this steel is adequately anch.o.r.ed 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 a.s.sist 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 diminis.h.i.+ng 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 sc.r.a.ps of iron or bits of expanded metal with the concrete, thereby greatly increasing its resistance. The experiments made by the Department of Bridges of the City of New York, on the value of nails in concrete, in which results as high as 18,000 lb. per sq. in. were obtained, indicate the availability of this device; the writer has not used it, nor does he know that it has been used, but it seems to be entirely rational, and to offer possibilities.

Another practical test, which indicates the value of proper reinforcement, may be mentioned. In a storage warehouse in Canada, the floor was designed, according to the building laws of the town, for a live load of 150 lb. per sq. ft., but the restrictions being more severe than the standard American practice, limiting the lever arm of the steel to 75% of the effective depth, this was about equivalent to a 200-lb.

load in the United States. The structure was to be loaded up to 400 or 500 lb. per sq. ft. steadily, but the writer felt so confident of the excess strength provided by his method of reinforcing that he was willing to guarantee the structure, designed for 150 lb., according to the Canadian laws, to be good for the actual working load. Plain, round, medium-steel bars were used. A 10-ft. panel, with a beam of 14-ft. span, and a slab 6 in. thick (not including the top coat), with 1/2-in. round bars, 4 in. on centers, was loaded to 900 lb. per sq. ft., at which load no measurable deflection was apparent. The writer wished to test it still further, but there was not enough cement--the material used for loading. The load, however, was left on for 48 hours, after which, no sign of deflection appearing, not even an incipient crack, it was removed. The total area of loading was 14 by 20 ft. The beam was continuous at one end only, and the slab only on one side. In other parts of the structure conditions were better, square panels being possible, with reinforcement both ways, and with continuity, both of beams and slabs, virtually in every direction, end spans being compensated by shortening. The method of reinforcing was as before indicated. The enormous strength of the structure, as proved by this test, and as further demonstrated by its use for nearly two years, can only be explained on the basis of the continuity of action developed and the great stiffness secured by liberal stirruping. Steel was provided in the middle section according to the rule, (_w_ _l_)/8, the span being taken as the clear distance between the supports; two-thirds of the steel was bent up and carried across the supports, in the case of the beams, and three-fourths of the slab steel was elevated; this, with the lap, really gave, on the average, four-thirds as much steel over the supports as in the center, which, of course, was excessive, but usually an excess has to be tolerated in order to allow for adequate anchorage.

Brackets were not used, but extra horizontal reinforcement, in addition to the regular horizontal steel, was laid in the bottom across the supports, which, seemingly, was satisfactory. The columns, it should be added, were calculated for a very low value, something like 350 lb. per sq. in., in order to compensate for the excess of actual live load over and above the calculated load.

This piece of work was done during the winter, with the temperature almost constantly at +10 and dropping below zero over night. The precautions observed were to heat the sand and water, thaw out the concrete with live steam, if it froze in transporting or before it was settled in place, and as soon as it was placed, it was decked over and salamanders were started underneath. Thus, a job equal in every respect to warm-weather installation was obtained, it being possible to remove the forms in a fortnight.

[Ill.u.s.tration: 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.]

[Ill.u.s.tration: PLATE IV, FIG. 2.--REINFORCEMENT IN PLACE OVER ONE COMPLETE FLOOR OF STORAGE WAREHOUSE. SLABS, 14 FT. SQUARE. REINFORCED TWO WAYS. NOTE CONTINUITY OF REINFORCEMENT AND ELEVATION OVER SUPPORTS.

FLOOR DESIGNED FOR 150 LB. PER SQ. FT. LIVE LOAD. TESTED TO 900 LB. PER SQ. FT.]

In another part of this job (the factory annex) where, owing to the open nature of the structure, it was impossible to house it in as well as the warehouse which had bearing walls to curtain off the sides, less fortunate results were obtained. A temperature drop over night of nearly 50, followed by a spell of alternate freezing and thawing, effected the ruin of at least the upper 2 in. of a 6-in. slab spanning 12 ft. (which was reinforced with 1/2-in. round bars, 4 in. on centers), and the remaining 4 in. was by no means of the best quality. It was thought that this particular bay would have to be replaced. Before deciding, however, a test was arranged, supports being provided underneath to prevent absolute failure. But as the load was piled up, to the extent of nearly 400 lb. per sq. ft., there was no sign of giving (over this span) other than an insignificant deflection of less than 1/4 in., which disappeared on removing the load. This slab still performs its share of the duty, without visible defect, hence it must be safe. The question naturally arises: if 4 in. of inferior concrete could make this showing, what must have been the value of the 6 in. of good concrete in the other slabs?

The reinforcing in the slab, it should be stated, was continuous over several supports, was proportioned for (_w_ _l_)/8 for the clear span (about 11 ft.), and three-fourths of it was raised over the supports.

This shows the value of the continuous method of reinforcing, and the enormous excess of strength in concrete structures, as proportioned by existing methods, when the reverse stresses are provided for fully and properly, though building codes may make no concession therefor.

Another point may be raised, although the author has not mentioned it, namely, the absurdity of the stresses commonly considered as occurring in tensile steel, 16,000 lb. per sq. in. for medium steel being used almost everywhere, while some zealots, using steel with a high elastic limit, are advocating stresses up to 22,000 lb. and more; even the National a.s.sociation 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, a.s.soc. 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 a.s.sistance 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 a.s.suming stresses which have no real existence?

The point made by Mr. G.o.dfrey 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 s.p.a.cing of bars in the same. As to elastic arches, the writer is not sufficiently versed in designs of this cla.s.s 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 a.n.a.lyzed otherwise. His point about chimneys, however, is not as clear.

As to columns, the writer agrees with Mr. G.o.dfrey 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 a.s.sumed 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 a.s.sumed 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. G.o.dfrey 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. G.o.dfrey states that, in his opinion, the lamina of concrete between each hoop is not a.s.sisted; but, as a matter of fact, practically regarded, it is, the coa.r.s.e 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 const.i.tuted 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 ma.s.s here and there throughout, thus creating a condition of h.o.m.ogeneity 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. G.o.dfrey's sixteenth point, as to the action in square panels, seems also to the writer to be well taken; he recollects a.n.a.lyzing Mr.

G.o.dfrey'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 s.p.a.ced 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 s.p.a.cing 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. G.o.dfrey 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. G.o.dfrey right; in any event, if, through the medium of this contribution to the discussion, the writer has a.s.sisted 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. G.o.dfrey of any mistaken stands; or, finally, if he has added anything new to the discussion which may help along the solution, he will feel amply repaid for his time and labor.

The least that can be said is that reform all along the line, in matters of reinforced concrete design, is insistent.

JOHN STEPHEN SEWELL, M. AM. SOC. C. E. (by letter).--The author is rather severe on the state of the art of designing reinforced concrete.

It appears to the writer that, to a part of the indictment, at least, a plea of not guilty may properly be entered; and that some of the other charges may not be crimes, after all. There is still room for a wide difference of opinion on many points involved in the design of reinforced concrete, and too much zeal for conviction, combined with such skill in special pleading as this paper exhibits, may possibly serve to obscure the truth, rather than to bring it out clearly.

_Point 1._--This is one to which the proper plea is "not guilty." The writer does not remember ever to have seen just the type of construction shown in Fig. 1, either used or recommended. The angle at which the bars are bent up is rarely as great as 45, much less 60 degrees. The writer has never heard of "sharp bends" being insisted on, and has never seen them used; it is simply recommended or required that some of the bars be bent up and, in practice, the bend is always a gentle one. The stress to be carried by the concrete as a queen-post is never as great as that a.s.sumed 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 f.l.a.n.g.e of a T-beam, and could properly be so used. There are other conditions under which the concrete may hold the rods so rigidly that their shearing strength may be utilized; where such conditions do not obtain, it is not ordinarily necessary to count on the shearing strength of the rods.

_Point 5._--Even if vertical stirrups do not act until the concrete has cracked, they are still desirable, as insuring a gradual failure and, generally, greater ultimate carrying capacity. It would seem that the point where their full strength should be developed is rather at the neutral axis than at the centroid of compression stresses. As they are usually quite light, this generally enables them to secure the requisite anchorage in the compressed part of the concrete. Applied to a riveted truss, the author's reasoning would require that all the rivets by which web members are attached to the top chord should be above the center of gravity of the chord section.

_Point 6._--There are many engineers who, accepting the common theory of diagonal tension and compression in a solid beam, believe that, in a reinforced concrete beam with stirrups, the concrete can carry the diagonal compression, and the stirrups the tension. If these web stresses are adequately cared for, shear can be neglected.

The writer cannot escape the conclusion that tests which have been made support the above belief. He believes that stirrups should be inclined at an angle of 45 or less, and that they should be fastened rigidly to the horizontal bars; but that is merely the most efficient way to use them--not the only way to secure the desired action, at least, in some degree.

The author's proposed method of bending up some of the main bars is good, but he should not overlook the fact that he is taking them away from the bottom of the beam just as surely as in the case of a sharp bend, and this is one of his objections to the ordinary method of bending them up. Moreover, with long spans and varying distances of the load, the curve which he adopts for his bars cannot possibly be always the true equilibrium curve. His concrete must then act as a stiffening truss, and will almost inevitably crack before his cable can come into action as such.

Bulletin No. 29 of the University of Illinois contains nothing to indicate that the bars bent up in the tests reported were bent up in any other than the ordinary way; certainly they could not be considered as equivalent to the cables of a suspension bridge. These beams behaved pretty well, but the loads were applied so as to make them practically queen-post trusses, symmetrically loaded. While the bends in the bars were apparently not very sharp, and the angle of inclination was much less than 60, or even 45, it is not easy to find adequate bearings for the concrete posts on theoretical grounds, yet it is evident that the bearing was there just the same. The last four beams of the series, 521-1, 521-2, 521-5, 521-6, were about as nearly like Fig. 1 as anything the writer has ever seen in actual practice, yet they seem to have been the best of all. To be sure, the ends of the bent-up bars had a rather better anchorage, but they seem to have managed the shear question pretty much according to the expectation of their designer, and it is almost certain that the latter's a.s.sumptions 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 lat.i.tude 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 a.n.a.lysis 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 f.l.a.n.g.e 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 a.s.sumed 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.