Generalized Beam Theory Revisited: From the Kinematical Assumptions To the Deformation Mode Determination

This work is part of an ongoing investigation aimed at comparing the mechanics underlying the application of generalized beam theory (GBT) and the constrained finite strip method (cFSM), two alternative modal approaches to analyze the elastic buckling behavior of open-sectional unbranched thin-walled members. Previous work included an overall comparison between the numerical results yielded by the two approaches for lipped channel columns and beams, which were shown to be essentially identical — the few minor discrepancies were fully explained. The next step consists of revisiting the kinematical assumptions and procedures adopted by GBT to identify and characterize the cross-sectional deformations modes, presenting, explaining, and interpreting them from a novel perspective, deemed more suitable for a true comparison with the displacement field constraints employed in cFSM — the main objective of this paper. The starting point is the derivation of the conventional finite strip method (FSM), intended to show that some of the corresponding matrices also appear in GBT. Indeed, it is demonstrated that the determination of the GBT deformation modes involves a set of particular FSM matrices, termed "cross-sectional matrices." After a brief comparison between the GBT and cFSM assumptions and procedures, an illustrative example is presented and discussed, in order to provide a better grasp of the concepts and procedures involved in the new approach to the GBT deformation mode determination. Finally, the paper closes with a few concluding remarks that also address the work to be carried out in the near future.