On the shear deformation modes in the framework of Generalized Beam Theory

This paper extends previous work concerning the determination of cross-section deformation modes in thin-walled members with arbitrary polygonal cross-section, in the framework of Generalized Beam Theory (Gonçalves et al., 2010 [1]). In particular, the paper addresses the so-called “natural shear deformation modes” (i.e. the deformation modes that involve non-null membrane shear strains and are independent of the cross-section discretization employed), which are relevant for capturing the behaviour of thin-walled members with complex multi-cell cross-sections undergoing torsion and/or distortion. The contributions of the paper are (i) the derivation of fundamental properties of the shear modes, (ii) the proposal of an efficient mode extraction procedure and (iii) the development of analytical results for several particular cases. In order to illustrate the application of the proposed mode extraction procedure and demonstrate the validity of the derived properties, several cross-sections are analyzed, including complex multi-cell tubes.