Developments on the GBT-based stability analysis of thin-walled members and structural systems

This chapter addresses the use of Generalized Beam Theory (GBT) to analyze the local, distortional, and global linear stability (or bifurcation, or buckling) behavior of thin-walled steel members and structural systems. After presenting a brief historical perspective of the GBT developments, the main concepts and procedures involved in performing buckling analyses are summarized in a systematic fashion - particular attention is paid to a recently developed cross-section analysis procedure that provides automatically “hierarchically ordered” deformation mode families (the GBT “trademark”). Then, the chapter addresses the most recent GBT formulations and applications developed to assess the buckling behavior of thin-walled members, frames, and trusses exhibiting arbitrary flat-walled or circular cross sections and a wide range of loading and support conditions-a detailed list of the key references on the various topics involved is also included. To illustrate the application and show the potential, stemming from its unique modal features, of the GBT approach to perform buckling analysis, numerical results involving several problems of practical interest are presented and discussed. These numerical results concern isolated members with various cross-section shapes and different loading/support conditions, space building frames, and plane roof-supporting trusses. For validation purposes, most of these results are compared with values yielded by shell finite element analyses, performed in the code Ansys. Finally, the chapter closes with a few concluding remarks.