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An Ordinary Meeting of the Institution of Structural Engineers was held at 11, Upper Belgrave Street, London, S.W.1, on Thursday, March 2nd, 1944.
It is thought that the following data, which can be used as an alternative to the more usual tabulated method of analysis for the solution of this class of frame, might be of interest, particularly to the junior member. The simple form of integration used will be explained in detail, therefore, knowledge of the calculus is not required. Certain assumptions are made, and these will be noted. The example chosen to illustrate the method is shown in Fig. 1. Principals of portal frame design will be taken as read. The thod is applicable to frames generally of the type indicated which have members of constant moment of inertia. In the frame under discussion, one equation of elasticity is required to find the magnitude of true horizontal thrusts. The equation, which is quite well known, will be repeated for reference. It is:-
". . . as to the knowledge that they (i.e. relaxation methods) presume, the answer is that we have regarded no problem as solved until, for the actual computations, no more than the first four rules of arithmetic is required. What is of greater importance, even though a computer may not comprehend the theoretical basis of his calculations he will have, throughout, a mental picture of what he is doing; he will see his task as that of bringing unaccounted or 'residual' quantities within a specified margin of uncertainty. Whether regarded philosophically or practically, this is the essential feature by which the new mathematics differs from the old; it is 'mathematics with a fringe.'"
PROFESSOR R. V. SOUTHWELL (Ref. 7)