Formulation of a GBT-Based Finite Element to Analyse the Global Buckling Behaviour of Plane and Spatial Thin-Walled Frames

Abstract

This paper deals with the use of Generalised Beam Theory (GBT) to analyse the global buckling behaviour of plane and spatial thin-walled frames. After a brief presentation of the main concepts and procedures involved in the performance of a GBT buckling analysis, one presents in detail the formulation and numerical implementation of a GBT-based beam finite element that includes only the four rigid-body deformation modes namely, one describes the determination of the elementary and frame linear and geometric stiffness matrices (the latter incorporate the influence of the frame joints and boundary conditions). Particular attention is paid to issues concerning (i) the quantification of the warping transmission at the frame joints, (ii) effects stemming from the non-coincidence of the member centroidal and shear centre axes (cross-sections without double symmetry), and (iii) the definition of joint elements that relate the connected member GBT degrees of freedom to the joint generalised displacements. Next, one addresses kinematical models to simulate the warping transmission at frame joints connecting two or more non-aligned U and I-section members and exhibiting two different configurations (diagonal-stiffened and box-stiffened). Finally, in order to illustrate the application and capabilities of the proposed GBT-based finite element formulation, one presents and discusses numerical results concerning the global buckling behaviour of (i) an “L-shaped” frame (see Fig. 1), (ii) a pitched-roof plane frame (in-plane and spatial behaviours) and (iii) a three-bar simple spatial frame, acted by loadings that cause only member compression. Both diagonal-stiffened and box-stiffened joints are considered and, for validation purposes, most of the GBT-based results are compared with values yielded by beam finite element analyses carried out in the commercial code ANSYS. An excellent correlation, involving both the frame critical buckling loads and mode shapes, was found in all cases. Open image in new window Figure 1 “L-shaped” plane frame global buckling: deformed configurations of the member mid-span cross-sections.