Validation of Bredt\u2019s formulas for beams with hollow cross sections by the method of asymptotic splitting for pure torsion and their extension to shear force bending

Abstract

The equations governing pure torsion of prismatic beams with thin-walled closed cross sections, known as Bredt’s formulas, are verified using the method of asymptotic splitting. In particular, the strong formulation of the Saint-Venant problem of a straight beam is expanded asymptotically. We begin by validating well-known technical assumptions for the shear stress distribution. Furthermore, the influence of a transverse force acting on the beam is considered. This shear force causes a deformation of the cross section, and therefore an adaption of Bredt’s formulas is needed. Two distinct formulations of the shear center, called the kinematic and the energetic shear center, are obtained. The latter is verified in numerical experiments.