The torsional centre position of stocky beams with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties

Abstract

The aim of this study focuses on torsional centre position of the cross section of a complex section stocky beam (CSSB), a new type of model for structural members with arbitrary noncircular cross-sectional shapes and with arbitrary elastic material properties and with length-to-height or length-to-width ratio no more than 3 encountered in modern civil engineering structures. The nodal-line method is utilized to describe the shapes of the out-of-plane warpages of all cross sections of a CSSB under restrained torsional conditions by employing n unknown displacement functions of nodal lines, together with n quadratic interpolation functions inspired and evolved by the shape of Prandtl’ membrane. The governing ordinary differential equations are established by employing the principle of energy in elasticity. Based on the fact that the torsional stiffness of cross section of the same CSSB stays unchangeable with the change of the torque modes exerted to it, and on the computational results of the change rate of torsional angle due to the individual action of each torque corresponding to three torque modes, a formula for calculating two coordinates of the torsional centre position of the cross section is formulated. The computational results of numerical examples are demonstrated to verify the rationality and correctness of the formula.