Some Mooted Questions in Reinforced Concrete Design | Page 7

that tensile stress is

concerned. Why should frightfully complex formulas be proposed,
which bring in the unknowable modulus of elasticity of concrete and
can only be solved by stages or dependence on the calculations of some
one else?
The twelfth point concerns deflection calculations. As is well known,
deflection does not play much of a part in the design of beams.
Sometimes, however, the passing requirement of a certain floor
construction is the amount of deflection under a given load. Professor
Gaetano Lanza has given some data on recorded deflections of
reinforced concrete beams.[B] He has also worked out the theoretical
deflections on various assumptions. An attempt to reconcile the
observed deflections with one of several methods of calculating stresses
led him to the conclusion that:
"The observations made thus far are not sufficient to furnish the means
for determining the actual distribution of the stresses, and hence for the
deduction of reliable formulæ for the computation of the direct stresses,
shearing stresses, diagonal stresses, deflections, position of the neutral
axis, etc., under a given load."
Professor Lanza might have gone further and said that the observations
made thus far are sufficient to show the hopelessness of deriving a
formula that will predict accurately the deflection of a reinforced
concrete beam. The wide variation shown by two beam tests cited by
him, in which the beams were identical, is, in itself, proof of this.
Taking the data of these tests, and working out the modulus of
elasticity from the recorded deflections, as though the beams were of
plain concrete, values are found for this modulus which are not out of
agreement with the value of that variable modulus as determined by
other means. Therefore, if the beams be considered as plain concrete
beams, and an average value be assumed for the modulus or coefficient
of elasticity, a deflection may be found by a simple calculation which is
an average of that which may be expected. Here again, simple theory is
better than complex, because of the ease with which it may be applied,
and because it gives results which are just as reliable.

The thirteenth point concerns the elastic theory as applied to a
reinforced concrete 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 theory, as in the intricate
beam theory commonly