GBT AND cFSM: TWO MODAL APPROACHES TO THE BUCKLING ANALYSIS OF UNBRANCHED THIN-WALLED MEMBERS

The objective of this paper is to provide (i) the fundamental derivation details and (ii) a comparison between Generalised Beam Theory (GBT) and the constrained Finite Strip Method (cFSM), two alternative modal approaches to analyse the elastic buckling behaviour of unbranched thin-walled members.Thin-walled members may generally buckle in three families (or types) of modes: global, distortional and local (or local-plate) modes.The distinguishing feature of the GBT and cFSM methodologies to obtain buckling solutions is that they can formally separate these three types of buckling modes.An overall comparison of the two methods is provided, including practical aspects, such as the different notations, and theoretical points related to how the displacement fields are either constructed or decomposed into deformation modes akin to the above families.Specific derivation details are provided for both GBT and cFSM, along with numerical examples concerning the buckling behaviour of cold-formed steel lipped channel members under compression and bending.The numerical examples (i) show the power of both GBT and cFSM to separate general stability solutions into pure solutions related to the buckling mode types, (ii) illustrate the use of the identified deformation fields to examine the modal contributions to a buckling solution, and (iii) demonstrate that, in spite of their quite distinct developments, GBT and cFSM modal approaches provide essentially the same extended capabilities for examining and understanding thin-walled member stability.Moreover, considerable attention is also paid to the different handling of the membrane deformations by the two methods, which is responsible for the minor (but fully explainable) discrepancies existing between the results yielded by the two methods.