Energy Equation for Beam Lateral Buckling

Abstract

This paper presents a derivation of the classical energy equation for the lateral buckling of doubly symmetric thin‐walled beams. This is based on the use of second‐order rotation components to obtain the nonlinear relationship between the longitudinal normal strain and the member deformations. The classical energy equation is compared with an alternative energy equation, and found to be significantly different in terms used to represent the work done by centroidal loads during buckling. The difference is attributed to the omission of some nonlinear components from the longitudinal displacements used for the alternative equation. Comparisons of finite element predictions based on the two energy equations demonstrate some substantial differences with the predictions by the alternative energy equation being higher for simply supported and continuous beams, and lower for cantilevers. Comparisons show that the available experimental evidence agrees well with the classical predictions, and they provide independent evidence that the alternative energy equation is incorrect.