A theory of torsion of thin-walled beams of arbitrary open sections with influence of shear

Abstract

A novel theory of torsion of thin walled beams (“shear deformable beams”) of arbitrary open cross-sections with influence of shear (TTTS) is presented. The theory is based on the classical Vlasov’s theory of thin-walled beams of open cross-section, as well on the Timoshenko’s beam bending theory. The theory is valid for general thin-walled open cross-section shapes, for distributed and concentrated transverse torsion loads and for isotropic materials. Four parameters due to shear warping are introduced. Closed-form analytical solutions for three-dimensional expressions of the normal and shear stresses are obtained. Under general transverse loads, reduced to moments of torsion with respect to the cross-section principal pole (by Vlasov’s theory), for arbitrary cross-sections, the beam will be subjected to torsion with influence of shear and in addition to bending due to shear in the beam principal planes and to tension/compression due to shear. The theory is tested by comparing it to the classical Vlasov’s thin-walled beam theory and to the finite element method using shell elements, as well as to some results in literatures.

Keywords:

• Torsion
• shear
• thin-walled beams
• arbitrary open sections
• general torsion loads
• analytic solution comparisons with FEM