Forces or moments that tend to twist a member are called torisonal loads. In shafts, the stresses and corresponding strains induced by these loads depend on both the shape and size of the cross section.
Suppose that a circular shaft is fixed at one end and a twisting couple, or torque, is applied at the other end (Fig. 3.21a). When the angle of twist is small, the circular cross section remains circular during twist. Also, the distance between any two sections remains the same, indicating that there is no longitudinal stress along the length of the member.
Figure 3.21b shows a cylindrical section with length dx isolated from the shaft. The lower cross section has rotated with respect to its top section through an angle d@, where @ is the
The factor GJ/L represents the stiffness of the member in resisting twisting loads. It gives the magnitude of a torque needed to produce a unit rotation.
Noncircular shafts behave differently under torsion from the way circular shafts do. In noncircular shafts, cross sections do not remain plane, and radial lines through the centroid do not remain straight. Hence the direction of the shear stress is not normal to the radius, and the distribution of shear stress is not linear. If the end sections of the shaft are free to warp, however, Eq. (3.55) may be applied generally when relating an applied torque T to the corresponding member deformation . Table 3.1 lists values of J and maximum shear stress for various types of sections.
(Torsional Analysis of Steel Members, American Institute of Steel Construction; F. Arbabi, Structural Analysis and Behavior, McGraw-Hill, Inc., New York.)