Chapter 11

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.