Elastic flexural buckling of non-uniform members: Closed-form expression and equivalent load approach

Experienced structural engineers have an intuitive understanding of the buckling behavior of uniform members subjected to compressive loads. The Euler critical load and the concept of buckling length are extensively used in this context. Unfortunately, the extension of this intuitive approach to cases with non-uniform load or non-uniform members is not straightforward. Based on an extensive numerical parametric study, the paper first presents a closed-form expression for the buckling load of constant cross-section members with non-uniform axial loading. Consequently, an equivalent load approach for non-uniform members subjected to non-uniform axial load distribution is proposed and validated. The combination of both procedures has the power of transforming the general complex case of a non-uniform member under non-uniform load into an equivalent simple case of a uniform member subjected to uniform load. The new methodology is simple and direct, and produces more than acceptable approximate results.