crete arch. This theory treats a reinforced concrete arch
as a spring. In order to justify its use, the arch or spring is
considered as having fixed ends. The results obtained by the intricate
methods of the elastic theory and the simple method of the equilibrium
polygon, are too nearly identical to justify the former when the arch is
taken as hinged at the ends.

The assumption of fixed ends in an arch is a most extravagant one,
because it means that the abutments must be rigid, that is, capable of
taking bending moments. Rigidity in an abutment is only effected by a
large increase in bulk, whereas strength in an arch ring is greatly
augmented by the addition of a few inches to its thickness. By the
elastic theory, the arch ring does not appear to need as much strength
as by the other method, but additional stability is needed in the
abutments in order to take the bending moments. This latter feature is
not dwelt on by the elastic theorists.

In the ordinary arch, the criterion by which the size of abutment is
gauged, is the location of the line of pressure. It is difficult and
expensive to obtain depth enough in the base of the abutment to keep
this line within the middle third, when only the thrust of the arch is
considered. If, in addition to the thrust, there is a bending moment
which, for many conditions of loading, further displaces the line of
pressure toward the critical edge, the difficulty and expense are
increased. It cannot be gainsaid that a few cubic yards of concrete
added to the ring of an arch will go much further toward strengthening
the arch than the same amount of concrete added to the two abutments.

In reinforced concrete there are ample grounds for the contention that
the carrying out of a nice theory, based on nice assumptions and the
exact determination of ideal stresses, is of far less importance than
the building of a structure which is, in every way, capable of
performing its function. There are more than ample grounds for the
contention that the ideal stresses worked out for a reinforced concrete
structure are far from realization in this far from ideal material.

Apart from the objection that the elastic theory, instead of showing
economy by cutting down the thickness of the arch ring, would show the
very opposite if fully carried out, there are objections of greater
weight, objections which strike at the very foundation of the theory as
applied to reinforced concrete. In the elastic th