Direct procedure for the determination of conventional modes within the GBT approach

This paper presents a procedure for the determination of the conventional modes to be used in the framework of the Generalised Beam Theory (GBT) for the analysis of thin-walled members. These deformation modes consist of the rigid, distortional, local and Bredt shear modes and, with the proposed approach, are evaluated in a single step cross-sectional analysis. This procedure is applicable to any type of cross-section, i.e. open, closed and partially-closed one. The algorithm differs from that of the classical GBT, which requires a two-step evaluation procedure, consisting of an initial choice of the vector basis and its successive orthogonalization. The procedure is based on the definition of a quadratic functional, whose steady condition leads to an eigenvalue problem, and directly generates the sought orthogonal basis, here found using a finite element analysis. The accuracy of the proposed method is validated by means of a numerical example carried out with a partially-closed section. It is shown that the conventional modes derived with the proposed approach are identical to those determined with the classical two-step procedure.