TABLE OF CONTENTS The formulas in this section are based on the following assumptions: (1) The bar is straight, of uniform circular section (solid or concentrically hollow), and of homogeneous isotropic material; (2) the bar is loaded only by equal and opposite twisting couples, which are applied at its ends in planes normal to its axis; and (3) the bar is not stressed beyond the elastic limit.
Behavior . The bar twists, each section rotating about the longitudinal axis. Plane sections remain plane, and radii remain straight. There is at any point a shear stress ? on the plane of the section; the magnitude of this stress is proportional to the distance from the center of the section, and its direction is perpendicular to the radius drawn through the point. Accompanying this shear stress there is an equal longitudinal shear stress on a radial plane and equal tensile and compressive stresses ? t and ? c at 45 (see Sec. 7.5). The deformation and stresses described are represented in Fig. 10.1.
In addition to these deformations and stresses, there is some longitudinal strain and stress. A solid circular cylinder wants to lengthen under twist, as shown experimentally by Poynting (Ref. 26). In any event, for elastic loading of metallic circular bars, neither longitudinal deformation nor stress is likely to be large enough to have engineering significance.
Formulas . Let T = twisting moment, l = length...
