Generalised beam theory (GBT) formulation to analyse the vibration behaviour of thin-walled steel frames

This paper reports the results of an investigation on the use of Generalised Beam Theory (GBT) to analyse the vibration behaviour of thin-walled steel frames. After an overview of the main concepts and procedures involved in performing a GBT vibration analysis, the formulation and implementation of a GBT-based beam finite element are presented, namely the determination of the finite element and frame linear stiffness and mass matrices (incorporating the influence frame joint configurations). Finally, in order to illustrate the application and capabilities of the proposed GBT-based finite element formulation, numerical results concerning the local, distortional and global vibration behaviour of (i) a symmetric portal frame and (ii) an “L-shaped” frame exhibiting four commonly used joint configurations are presented and discussed. For validation purposes, some GBT results (frequency values and vibration mode shapes) are compared with values yielded by Ansys shell finite element analyses.