GBT-based local, distortional and global buckling analysis of thin-walled steel frames

This paper reports research work concerning the use of Generalised Beam Theory (GBT) to analyse the local, distortional and global buckling behaviour of thin-walled steel frames. After a brief review of the main concepts and procedures involved in performing a GBT buckling analysis, one addresses the formulation and implementation of a GBT-based beam finite element that incorporates local, distortional and global deformation modes – in particular, one describes (i) the definition of joint elements, which involves providing a relation between the connected member GBT degrees of freedom and the joint generalised displacements, and (ii) the kinematical models adopted to simulate the torsion warping transmission. Next, one uses evidence gathered from shell finite element analyses to establish kinematical constraint conditions that ensure cross-section warping and in-plane displacement compatibility at the frame joints connecting two non-aligned plain or lipped channel members. Finally, one presents and discusses numerical results that make it possible to illustrate the application and show the capabilities of the above GBT-based finite element formulation and implementation. For validation purposes, some GBT-based results (critical buckling loads and mode shapes) are compared with values yielded by shell finite element analyses carried out in the code ANSYS.