On the cross-section deformation modes in the framework of GBT

Many structural systems involve thin-walled beams that must operate in a complex loading environment where axial, bending, shearing, and torsional loads are present. Accordingly, a significant amount of research has been conducted toward the development of computational tools which combine an easy usage and good predictive capabilities for analyzing the structural behavior of such systems. The contributions can be subdivided in two main categories: one towards an effective three-dimensional ”shell” modeling [1], and the other towards the formulation and development of mono-dimensional finite elements based on beam models with enriched cross-section kinematics. In the second category we find the model early proposed by Capurso in the 60s [2], which generalizes the Vlasov beam by enriching the warping description, up to the recent improvements of the Generalized Beam Theory - GBT, originally proposed by Schardt in the 80s [3], characterized by an enriched cross-section kinematics capable to capture phenomena of cross-section distortion. Several contributions have been devoted to improve the GBT theory both in linear and nonlinear context [4]. Recently, the application of the GBT to analyze cold-formed roof systems has been presented in [5]. In this work, a critical review of the so called cross-section analysis procedure [3] is presented with special attention to the shear deformation modes. In particular, an improved cross-section analysis procedure capable to separate the shear deformation modes coherently with the flexural modes and capable to recover the typical deformation modes of a classical shear deformable beam is presented. In this way, cross-section rotations can be easily identified so permitting a direct implementation of corotational formulations [6] to perform geometrically non linear analyses. Some test cases enlighten the effectiveness and reliability of the approach.