GBT buckling analysis of generally loaded thin-walled members with arbitrary flat-walled cross-sections

Abstract

This paper deals with extending the domain of applicability of a recently developed Generalised Beam Theory (GBT) formulation intended to perform elastic linear buckling analyses of thin-walled members (i) exhibiting arbitrary flat-walled cross-sections (including those combining closed cells and open branches), and (ii) acted by general loadings. These loadings, which include transverse forces acting away from the member shear centre axis, are termed “general” in the sense that they may involve the presence of pre-buckling stress distributions associated with any possible combination of all the stress tensor membrane components (σxx, σss and τxs, for a plane stress state), including cell shear flows – therefore, all the relevant geometrically non-linear effects need to be taken into consideration. After briefly presenting the main concepts and procedures involved in the development and implementation of the above GBT formulation, this same formulation is employed to analyse the buckling behaviour of beams with different types of cross-section geometry (containing closed cells) and exhibiting different loading and support conditions. In particular, they consist of (i) a RHS cantilever acted by two tip point loads, (ii) a closed-flange I-section simply supported beam subjected to a uniformly distributed load and (iii) a two-cell RHS section cantilever acted by tip transverse forces and couples. In all cases, the loads are applied both along the shear centre axis and also along axes parallel to it and located at the beam top and bottom surfaces. The results presented and discussed, which consist of pre-buckling stress fields, buckling curves and buckling mode shapes, are obtained by means of the newly released code GBTul 2.0 and validated by means of the comparison with shell finite element values obtained with the code Ansys.