Analyses of thin-walled sections under localised loading for general end boundary conditions – Part 1: Pre-buckling

Abstract The Finite Strip Method (FSM) for pre-buckling analysis of thin-walled sections under localised loading has been developed for general end boundary conditions. For different boundary conditions at supports and locations of applied loads, different displacement functions are required for both flexural and membrane displacements. As the stresses are not uniform along the member due to localised loading, the pre-buckling analysis also requires multiple series terms with orthogonal functions. This paper briefly summaries the displacement functions used for different boundary conditions. In addition, the theory of the FSM for pre-buckling analysis of thin-walled sections under localised loading with general end boundary conditions is developed. The analysis is subsequently benchmarked against the Finite Element Method (FEM) using software package ABAQUS/Standard. The results from this pre-buckling analysis are deflections (pre-buckling modes) and membrane stresses which are used for the buckling analysis described in Part 2 - Buckling in the companion paper.