Anylisis of a branched cross-section through the Generalized Beam Theory

Abstract

This volume contains the memory of the ‘Final project's analysis of a branched crosssection through the Generalized Beam Theory’. The study, as it is indicated in the title, focuses on the analysis of a profile of branched opened section with thin walls, similar to those made with the cold rolling processes. The analysis is done using the Generalized Beam Theory (GBT). The GBT can unify the classical theories for prismatic profiles in a single expression. Classical theories include, independently, four main modes of deformation: the axial, bending according to the two principal axes and torsion. In these four modes, section behaves as an undeformable rigid section without displaying any distortion. Using the GBT, it is possible to recover enriched kinematics that include section distortion. This volume begins with a presentation of the cold formed elements and the GBT. Following a brief description of the conventional Generalized Beam Theory, the necessary modifications to conventional GBT in order to deal with open branched sections are explained. According to this indications and modifications, we analyze a specific beam with a branched cross section and also a method to calculate its displacement is developed. A Matlab program is implemented to calculate all modal displacements of the studied profile and some features, such as geometry or material properties are taken as variables. Finally a validation of the obtained results is carried out.