A direct approach for the evaluation of the conventional modes within the GBT formulation

• New one-step approach for derivation of conventional deformation modes for GBT analysis.
• Approach based on a new quadratic functional.
• Procedure applicable to open, partially-closed and closed sections.

This paper proposes a new approach for the evaluation of the conventional modes, i.e. rigid, distortional, local and Bredt shear-modes, to be used in the framework of the Generalised Beam Theory (GBT) for the analysis of thin-walled members. The new method identifies a set of conventional modes in a single step cross-sectional analysis and for any type of cross-section, i.e. open, closed and partially-closed ones. 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 method is based on a definition of a new quadratic functional, whose steady condition leads to an eigenvalue problem, and directly generates the sought orthogonal basis, here found using a finite-element approach. The accuracy of the proposed method is validated by means of two numerical examples, one dealing with a lipped C-section and one with a partially-closed profile. It is shown that the conventional modes derived with the proposed approach are identical to those determined with the classical two-step procedure, thus limiting the computational effort required in their identification.