Validation of Bredt's formulas by the method of asymptotic splitting

Abstract

The equations describing torsion of prismatic bars 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. At first, well-known technical assumptions of the shear stress distribution are validated. Further, 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. Two distinct formulations of the shear center, called the kinematic and the energetic shear center, are obtained. The latter are verified in numerical experiments.This is an open access article under the terms of the Creative Commons Attribution-Non-Commercial-NoDerivs Licence 4.0, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.