Post-buckling analysis of thin-walled steel frames using generalised beam theory (GBT)

This paper presents the development and illustrates the application of a beam finite element based on the generalised beam theory (GBT) and intended to analyse the local, distortional and global post-buckling behaviour of thin-walled steel frames. After briefly reviewing the main concepts and procedures required to obtain the GBT system of non-linear equilibrium equations, the paper describes the steps involved in the numerical implementation (incremental-iterative strategy) of a non-linear beam finite element that incorporates the influence of the frame joint behaviour. Next, one uses evidence gathered from shell finite element simulations to establish kinematic constraint conditions ensuring displacement compatibility at frame joints connecting two non-aligned plain/lipped channel members. Finally, the application and capabilities of the proposed GBT-based beam finite element formulation are illustrated by presenting and discussing numerical results concerning the post-buckling behaviour of two “L-shaped” frames and a symmetric portal frame. For validation purposes, most GBT-based results are compared with values yielded by beam and shell finite element analyses carried out in the code Ansys.