Restrained torsion theory of open thin-walled beams and its application

Based on Vlasov's thin-walled beam theory, a first-ordertorsion theory of restrained torsion of open thin-walled beam is developedin consideration with the effects of shear deformation. It is assumed thatthe total rotation of a cross section is divided into a free warpingrotation and a restrained shear rotation. In the restrained torsion, St.Venant torque is only related to the free warping rotation and theexpression of St. Venant torque is derived by using a semi-inverse method.The torsion shear coefficient is derived by using the energy method. Thegoverning equation of the restrained torsion theory is derived by using thededuced formulae. In order to solve the governing equation efficiently, thecorresponding initial method is presented, and the influence function isobtained. When the St. Venant constant is negligible, an approximateanalytical approach is obtained, and there exists an analogy between it andTimoshenko beam theory. To validate the new approach, an example isillustrated, and the results obtained from the current theory are comparedwith those of the existing theory, which demonstrate the efficiency of thecurrent theory.