Buckling and Vibration Analysis of Cold-Formed Steel CHS Members and Frames Using Generalized Beam Theory

This paper reports the results of an investigation on the use of Generalized Beam Theory (GBT) to assess the buckling and vibration behaviors of thin-walled members and frames built from cold-formed steel circular hollow section (CHS) profiles. Initially, the concepts and procedures involved in performing GBT buckling and vibration analyses are presented, paying particular attention to the derivation of the mass tensors that account for the influence of the inertia forces. Then, the formulation, numerical implementation and validation of a GBT-based beam finite element for isolated members are described. Next, the determination of the frame linear stiffness, geometric stiffness and mass matrices, which incorporate the influence of the frame joints, is addressed. Finally, in order to illustrate the application and capabilities of the proposed GBT finite element formulation, numerical results are presented and discussed — they concern the buckling and vibration behaviors of an "L-shaped" frame. For validation purposes, most GBT-based results are compared with values yielded by shell finite element analyses carried out in the code ANSYS.