Circular Bars under Distributed Torques

Circular bars under distributed torque are formulated based on the linear theory of elasticity, and analysis is presented for bars under a single Fourier term of distributed torque. As the motivation of the study is to examine the extent of adequacy of the conventional technical torsion theory to bars under distributed torques, stress distribution in solid bars is first investigated. Stress distribution for hollow bars under three different loading conditions is then analyzed. Results indicate that the conventional theory is adequate when the region of distributed torque is large. In small regions, the conventional theory may substantially be in error resulting in underestimating the maximum shear stress and misidentifying the location of maximum shearing stress.