Part 12

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."