Theories of Torsion

Abstract

The engineer’s theory of torsion (e.t.t.) relates the shear stress τ and angular twist θ (rad), that are produced in a solid circular shaft or tube under an externally applied axial torque T. Let the shaft length be L, the material’s rigidity modulus G, the section’s radius r and the polar second moment of area J. Consider the cylindrical core element in Fig. 7.1a of radius r lying within a solid shaft of outer radius R (Fig. 7.lb) when one end is fixed and the other end is free.