The last point which the speaker will discuss is that of the elastic arch.  The theory of the elastic arch is now so well understood, and it offers such a simple and, it might be said, elegant and self-checking solution of the arch design, that it has a great many advantages, and practically none of the disadvantages of other methods.

The author’s statement that the segments of an arch could be made up of loose blocks and afterward cemented together, cannot be endorsed by the speaker, for, upon such cementing together, a shifting of the lines of resistance will take place when the load is applied.  The speaker does not claim that arches are maintained by the cement or mortar joining the voussoirs together, but that the lines of pressure will be materially changed, and the same calculations are not applicable to both the unloaded and the loaded arch.

It is quite true, as the author states, that a few cubic yards of concrete placed in the ring will strengthen the arch more than a like amount added to the abutments, provided, however, that this material be placed properly.  No good can result from an attempt to strengthen a structure by placing the reinforcing material promiscuously.  This has been tried by amateurs in bridge construction, and, in such cases, the material either increased the distance from the neutral axis to the extreme fibers, thereby reducing the original section modulus, or caused a shifting of the neutral axis followed by a large bending moment; either method weakening the members it had tried to reinforce.  In other words, the mere addition of material does not always strengthen a structure, unless it is placed in the proper position, and, if so placed, it should be placed all over commensurately with the stresses, that is, the unit stresses should be reduced.

The author has criticized reinforced concrete construction on the ground that the formulas and theories concerning it are not as yet fully developed.  This is quite true, for the simple reason that there are so many uncertain elements which form their basis:  First, the variable quantity of the modulus of elasticity, which, in the concrete, varies inversely as the stress; and, second, the fact that the neutral axis in a reinforced concrete beam under changing stress is migratory.  There are also many other elements of evaluation, which, though of importance, are uncertain.

Because the formulas are established on certain assumptions is no reason for condemning them.  There are, the speaker might add, few formulas in the subject of theoretical mechanics which are not based on some assumption, and as long as the variations are such that their range is known, perfectly reliable formulas can be deduced and perfectly safe structures can be built from them.

There are a great many theorists who have recently complained about the design of reinforced concrete.  It seems to the speaker that such complaints can serve no useful purpose.  Reinforced concrete structures are being built in steadily increasing numbers; they are filling a long needed place; they are at present rendering great service to mankind; and they are destined to cover a field of still greater usefulness.  Reinforced concrete will undoubtedly show in the future that the confidence which most engineers and others now place in it is fully merited.