Equivalent Systems for Inelastic Analysis of Prismatic and Nonprismatic Members

Abstract

This paper deals with the analysis of prismatic and nonprismatic members of any arbitrary variation in moment of inertia, and where the material is permitted to be stressed well beyond its elastic limit, thus causing the modulus of elasticity to vary along their length. The stress and deflection characteristics of such members are determined by the method of the equivalent systems, which permits to replace the original member of variable stiffness with one of uniform stiffness, whose elastic line is identical to the one of the original variable stiffness member. It is proven mathematically that the inelastic analysis of members with continuously varying moment of inertia and modulus of elasticity can be carried out by using equivalent linear systems of constant stiffness and applying known handbook formulas or methods of linear elementary mechanics. The member can be analyzed for both elastic and inelastic ranges, all the way to failure, thus permitting observation of progressive deterioration of the member's ability to resist stress and deformation, and establish useful, practical critical limits.