Torsional analysis of open thin-walled doubly symmetric beams under torsion and bimoment

Abstract

The present paper investigated the static analysis for the coupled torsional-warping response of open thin-walled doubly symmetric beams subjected to various twisting moments and bimoments. The static equilibrium torsional-warping coupling differential equations and associated boundary conditions for the thin-walled beams are derived using total potential energy variational principle. The exact closed-form solutions for the beams having a cantilever, simply-supported, fixed-fixed and fixed-fork boundary conditions and under various torsional and warping moments are determined. The present solution is shown to successfully capture the coupled torsional-warping static response of the thin-walled beams with various boundary conditions and by excluding and including axial static force effects. The validity and the accuracy of the numerical results based on the present solution are accomplished throughout the numerical examples presented and compared with well-established ABAQUS finite beam model solution and other exact solution available in the literature.