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