Part 8 (1/2)
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.