Interactively Induced Localization in Thin-walled I-section Struts Buckling About the Strong Axis

Abstract

A variational model describing the behaviour of a thin-walled I-section strut suffering from local–global buckling mode interaction is presented where global (Euler) buckling about the strong axis is the critical mode. A system of differential and integral equations is derived that describe the equilibrium states from variational principles and are solved numerically using the continuation and bifurcation software Auto-07p for the perfect case. Initially stress relieved out-of-straightness imperfections are subsequently introduced and the nonlinear response is modelled. The modelled interaction is between the critical global buckling mode about the strong axis and local buckling in the flange and web simultaneously, where the flange–web joint is assumed to be free to rotate as a rigid body. The initial eigenmode is shown to be destabilized at a secondary bifurcation where interactive buckling is triggered. A progressive change in the buckling mode is then observed, initially with local buckling localizing at the mid-span of the compression flange, which also triggers sympathetic local buckling in the web. The results from the analytical model have been validated using the commercial finite element (FE) software Abaqus with good comparisons presented for the initial post-buckling behaviour. The strut also exhibits sensitivity to initial out-of-straightness imperfections, with a notable decrease in the ultimate load as the imperfection size increases. The ultimate loads for a range of imperfection amplitudes are found using both analytical models and FE analysis, with very good correlation observed.