CHAPTER 6 - ELEMENTARY THEORY OF TORSION

Abstract

This chapter focuses on the elementary theory of torsion. It describes the elastic torsion of various thin-walled closed and open sections, in addition to the shaft of solid circular cross section. In a thin-walled circular tube, the cross section at one end rotates through an angle θ with respect to the other end. The longitudinal and transverse symmetry of the tube leads to the conclusion that out-of-plane distortion of an initially plane cross section cannot occur. Hence, deformation takes the form of rotation of one plane relative to the next and so on, the planes remaining normal to the axis of the tube. The magnitude of the shear stress may be found in terms of the applied torque by considering the equilibrium of the tube. Owing to the variation of shear stress around the circumference of the tube, it is not possible to predict the deformations and, hence, the angle of twist in the simple manner used for the circular shaft or tube. The angle of twist (θ) can be determined, however, from the strain energy stored in the tube.