Buckling Analysis of Unbranched Thin-Walled Members: Generalised Beam Theory and Constrained Finite Strip Method

Abstract

The load-carrying capacity of thin-walled members is often governed by buckling phenomena. Usually, three main families of buckling phenomena/modes are considered: (i) global buckling, in which the member axis deforms (e.g., flexural or lateral-torsional buckling), (ii) local-plate buckling, involving only plate (wall) bending, and (iii) distortional buckling, combining wall bending with crosssection distortion the last two phenomena are sometimes jointly described as “local buckling”. Although there exist several numerical and/or analytical methods to determine the buckling load/moment values and the associated buckling mode shapes, it is fair to state that only generalised beam theory (GBT) and the constrained finite strip method (cFSM) are able to perform this task for isolated (“pure”) or arbitrarily combined (“coupled”) modes. Although both methods lead to very similar solutions, (i) GBT is a generalisation of classical beam theories that includes additional degrees of freedom to allow for cross-section deformation, whilst (ii) cFSM is a specialisation of the classical plate theory that carefully selects constraints in order to force the member to deform (buckle) according to pre-defined configurations. This paper provides an in-depth comparison between the fundamentals of the two above approaches (GBT / cFSM), focusing on (i) their mechanical assumptions and domains of application, and (ii) the procedures adopted. This will contribute to a better understanding of both methods and the phenomena that they aim to uncover, thus paving the way to the development of more efficient tools for the analysis and design of thin-walled members. In order to illustrate the GBT / cFSM comparison, the local, distortional and global buckling behaviours of lipped channel columns (see Figure 1) and beams are analysed in detail. As one would expect, there is a virtually perfect coincidence between the two sets of buckling results. Open image in new window Figure 1 Variation of the buckling load P b with the column length L