Restrained Torsion of Thin-Walled Beams

Abstract

A first-order torsion formulation for closed thin-walled (CTW) beam subjected to restrained torsion is developed to consider the warping deformation and restrained shear stresses on cross section and their effect on the behavior of thin-walled (TW) beam. The total torque on closed cross section in the current formulation consists of four component torques. The expressions of various torques and corresponding shear stresses are given. To account for the distribution of true restrained shear stress due to restrained shear rotation in TW cross section, torsion shear coefficient is proposed for CTW beam. Like the transverse shear coefficient in Timoshenko beam theory, the torsion shear coefficient lies at the heart of the first-order torsion theory. The new governing equations of restrained torsion of CTW beam are obtained, which have obvious physical meaning and is easy to be used in engineering and can also be used to solve the torsion problem of open thin-walled beam. The initial parameter method is developed so as to obtain the analytical solution effectively. To demonstrate the accuracy and applicability of the present theory, numerical and closed-form results are compared with those of some other available method. The effects of restrained shear stress on the behavior of open and CTW beams are investigated and verified.