Torsion in Shafts

Shafts that transmit torsional loads are common in engineering applications. A robot driven by a motor, automobile wheels driven by an engine, a milling machine in a factory, a jet engine, all have shafts of various types, shapes, and materials. Uniform shafts of circular cross-section are common in these applications, and they often carry purely torsional loads. Even when they are subjected to other types of loads as well (e.g., axial forces, lateral/transverse support forces, bending moments, etc.), one can simultaneously analyze the torsional loading separately and then add to the effects of other types of loading by using the principle of superposition (assuming linear behavior). It follows that circular shafts subjected to purely torsional loads are a topic of much importance in Mechanics of Materials. Their analysis is the subject of the present chapter. The main contents of the chapter are the following: Analysis of uniform shafts of circular cross-section, Assumptions in the analysis, Sign convention for the analysis, Linear elastic case, Sketching the internal torque distribution, Determination of the angle of twist, Definition and use of the polar moment of area, Analysis of statically indeterminate torsion members, and Torsion of members with non-circular cross-section.