The Design of Structural Design Norms

Abstract

This paper deals with the analysis of prismatic and nonprismatic members with axial restraints, where their material is permitted to be stressed well beyond its elastic limit. This loading on the members causes the modulus of elasticity of the material to vary along their length. The mathematical formulation of this problem, as well as its analysis, is based on the method of equivalent systems that was developed by the first author. This method permits replacement of the original nonlinear member of variable stiffness E^xI^x, with one of uniform stiffness E¹I^l, that has the same length, boundary conditions, and elastic line as the original variable stiffness member. It is proven mathematically that this equivalency exists and that the solution of the equivalent system using linear analysis yields the same results as the solution of the original nonlinear variable stiffness member. Deflections and rotations may be easily obtained using equivalent systems, and the member can be analyzed in both elastic and inelastic ranges, all the way to failure, thus permitting observation of progressive deterioration of the ability of the member to resist load, stress, and de-formation. In this manner, practical critical limits regarding these modes of behavior can be established.