Nonlinear instability of angle section beams under uniformly distributed loads

Abstract

This paper presents a study on the flattening behavior of angle-section beams of finite length subjected to uniformly distributed transverse loads. Analytical solutions for static instabilities of angle-section beams when they are bent about their weak axis are derived using energy methods. The basic assumptions used in the present study are that the total strain energy of an angle-section beam subjected to a uniformly distributed load can be simplified into a two-stage process. One is the bending response of the two legs behaving as the plate; the other is the bending response as a beam with flattened section. The nonlinear instability is derived by applying the minimum potential energy principle and the corresponding static critical moments associated with the section flattening-induced buckling are determined. To validate the analytical solution developed, nonlinear finite element analyses are also conducted. Good agreement between the present solution and the FEA results is demonstrated.