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.