The tenth point concerns elaborate theories and formulas for beams and slabs.  Formulas are commonly given with 25 or 30 constants and variables to be estimated and guessed at, and are based on assumptions which are inaccurate and untrue.  One of these assumptions is that the concrete is initially unstressed.  This is quite out of reason, for the shrinkage of the concrete on hardening puts stress in both concrete and steel.  One of the coefficients of the formulas is that of the elasticity of the concrete.  No more variable property of concrete is known than its coefficient of elasticity, which may vary from 1,000,000 to 5,000,000 or 6,000,000; it varies with the intensity of stress, with the kind of aggregate used, with the amount of water used in mixing, and with the atmospheric condition during setting.  The unknown coefficient of elasticity of concrete and the non-existent condition of no initial stress, vitiate entirely formulas supported by these two props.

Here again destructive criticism would be vicious if these mathematical gymnasts were giving the best or only solution which present knowledge could produce, or if the critic did not point out a substitute.  The substitute is so simple of application, in such agreement with experiments, and so logical in its derivation, that it is surprising that it has not been generally adopted.  The neutral axis of reinforced concrete beams under safe loads is near the middle of the depth of the beams.  If, in all cases, it be taken at the middle of the depth of the concrete beam, and if variation of intensity of stress in the concrete be taken as uniform from this neutral axis up, the formula for the resisting moment of a reinforced concrete beam becomes extremely simple and no more complex than that for a rectangular wooden beam.

The eleventh point concerns complex formulas for chimneys.  It is a simple matter to find the tensile stress in that part of a plain concrete chimney between two radii on the windward side.  If in this space there is inserted a rod which is capable of taking that tension at a proper unit, the safety of the chimney is assured, as far as 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: