Deflection and Slope of Beams with Varying I

This paper formulates a numerical procedure for calculating deflections and slopes of flexural members subject to loads acting in their longitudinal plane of symmetry. The integration of the Maxwell-Mohr strain-energy function is performed beforehand, and limits consistent with the position of the loads and step-wise variation of the moment of inertia are introduced. The tedium of recurring integration and algebraic manipulation is thus reduced to a simple summation of finite differences. A table of differences of both the cubes and the squares of integers ranging from 1 to 50 is provided to simplify the numerical work and to increase the reliability of results. Slope may be computed independently of deflection calculations, or it may be rapidly determined from known deflection values, and vice versa