Some years ago the writer tested a number of slabs in a building, with a load of 250 lb. per sq. ft. These slabs were 3 in. thick and had a clear span of 44 in. between beams. They were totally without reinforcement. Some had cracked from shrinkage, the cracks running through them and practically the full length of the beams. They all carried this load without any apparent distress. If these slabs had been reinforced with some special reinforcement of very small cross-section, the strength which was manifestly in the concrete itself, might have been made to appear to be in the reinforcement. Magic properties could be thus conjured up for some special brand of reinforcement. An energetic proprietor could capitalize tension in concrete in this way and "prove" by tests his claims to the magic properties of his reinforcement.
To say that Poisson's ratio has anything to do with the reinforcement of a slab is to consider the tensile strength of concrete as having a positive value in the bottom of that slab. It means to reinforce for the stretch in the concrete and not for the tensile stress. If the tensile strength of concrete is not accepted as an element in the strength of a slab having one-way reinforcement, why should it be accepted in one having reinforcement in two or more directions? The tensile strength of concrete in a slab of any kind is of course real, when the slab is without cracks; it has a large influence in the deflection; but what about a slab that is cracked from shrinkage or otherwise?
Mr. Turner dodges the issue in the matter of stirrups by stating that they were not correctly placed in the tests made at the University of Illinois. He cites the Hennebique system as a correct sample. This system, as the writer finds it, has some rods bent up toward the support and anchored over it to some extent, or run into the next span. Then stirrups are added. There could be no objection to stirrups if, apart from them, the construction were made adequate, except that expense is added thereby. Mr. Turner cannot deny that stirrups are very commonly used just as they were placed in the tests made at the University of Illinois. It is the common practice and the prevailing logic in the literature of the subject which the writer condemns.
Mr. Thacher says of the first point:
"At the point where the first rod is bent up, the stress in this rod runs out. The other rods are sufficient to take the horizontal stress, and the bent-up portion provides only for the vertical and diagonal shearing stresses in the concrete."
If the stress runs out, by what does that rod, in the bent portion, take shear? Could it be severed at the bend, and still perform its office? The writer can conceive of an inclined rod taking the shear of a beam if it were anchored at each end, or long enough somehow to have a grip in the concrete from the centroid of compression up and from the center of the steel down. This latter is a practical impossibility. A rod curved up from the bottom reinforcement and curved to a horizontal position and run to the support with anchorage, would take the shear of a beam. As to the stress running out of a rod at the point where it is bent up, this will hardly stand the test of analysis in the majority of cases. On account of the parabolic variation of stress in a beam, there should be double the length necessary for the full grip of a rod in the space from the center to the end of a beam. If 50 diameters are needed for this grip, the whole span should then be not less than four times 50, or 200 diameters of the rod. For the same reason the rod between these bends should be at least 200 diameters in length. Often the reinforcing rods are equal to or more than one-two-hundredth of the span in diameter, and therefore need the full length of the span for grip.
Mr. Thacher states that Rod 3 provides for the shear. He fails to answer the argument that this rod is not anchored over the support to take the shear. Would he, in a queen-post truss, attach the hog-rod to the beam some distance out from the support and thus throw the bending and shear back into the very beam which this rod is intended to relieve of bending and shear? Yet this is just what Rod 3 would do, if it were long enough to be anchored for the shear, which it seldom is; hence it cannot even perform this function. If Rod 3 takes the shear, it must give it back to the concrete beam from the point of its full usefulness to the support. Mr. Thacher would not say of a steel truss that the diagonal bars would take the shear, if these bars, in a deck truss, were attached to the top chord several feet away from the support, or if the end connection were good for only a fraction of the stress in the bars. Why does he not apply the same logic to reinforced concrete design?
Answering the third point, Mr. Thacher makes more statements that are characteristic of current logic in reinforced concrete literature, which does not bother with premises. He says, "In a beam, the shear rods run through the compression parts of the concrete and have sufficient anchorage." If the rods have sufficient anchorage, what is the nature of that anchorage? It ought to be possible to analyze it, and it is due to the seeker after truth to produce some sort of analysis. What mysterious thing is there to anchor these rods? The writer has shown by analysis that they are not anchored sufficiently. In many cases they are not long enough to receive full anchorage. Mr. Thacher merely makes the dogmatic statement that they are anchored. There is a faint hint of a reason in his statement that they run into the compression part of the concrete. Does he mean that the compression part of the concrete will grip the rod like a vise? How does this comport with his contention farther on that the beams are continuous? This would mean tension in the upper part of the beam. In any beam the compression near the support, where the shear is greatest, is small; so even this hint of an argument has no force or meaning.
In this same paragraph Mr. Thacher states, concerning the third point and the case of the retaining wall that is given as an example, "In a counterfort, the inclined rods are sufficient to take the overturning stress." Mr. Thacher does not make clear what he means by "overturning stress." He seems to mean the force tending to pull the counterfort loose from the horizontal slab. The weight of the earth fill over this slab is the force against which the vertical and inclined rods of [Fig. 2], at a, must act. Does Mr. Thacher mean to state seriously that it is sufficient to hang this slab, with its heavy load of earth fill, on the short projecting ends of a few rods? Would he hang a floor slab on a few rods which project from the bottom of a girder? He says, "The proposed method is no more effective." The proposed method is [Fig. 2], at b, where an angle is provided as a shelf on which this slab rests. The angle is supported, with thread and nut, on rods which reach up to the front slab, from which a horizontal force, acting about the toe of the wall as a fulcrum, results in the lifting force on the slab. There is positively no way in which this wall could fail (as far as the counterfort is concerned) but by the pulling apart of the rods or the tearing out of this anchoring angle. Compare this method of failure with the mere pulling out of a few ends of rods, in the design which Mr. Thacher says is just as effective. This is another example of the kind of logic that is brought into requisition in order to justify absurd systems of design.
Mr. Thacher states that shear would govern in a bridge pin where there is a wide bar or bolster or a similar condition. The writer takes issue with him in this. While in such a case the center of bearing need not be taken to find the bending moment, shear would not be the correct governing element. There is no reason why a wide bar or a wide bolster should take a smaller pin than a narrow one, simply because the rule that uses the center of bearing would give too large a pin. Bending can be taken in this, as in other cases, with a reasonable assumption for a proper bearing depth in the wide bar or bolster. The rest of Mr. Thacher's comment on the fourth point avoids the issue. What does he mean by "stress" in a shear rod? Is it shear or tension? Mr. Thacher's statement, that the "stress" in the shear rods is less than that in the bottom bars, comes close to saying that it is shear, as the shearing unit in steel is less than the tensile unit. This vague way of referring to the "stress" in a shear member, without specifically stating whether this "stress" is shear or tension, as was done in the Joint Committee Report, is, in itself, a confession of the impossibility of analyzing the "stress" in these members. It gives the designer the option of using tension or shear, both of which are absurd in the ordinary method of design. Writers of books are not bold enough, as a rule, to state that these rods are in shear, and yet their writings are so indefinite as to allow this very interpretation.