11 Torsion and Bending of Prismatic Rods
In this chapter we present the Saint-Venant’s theory of torsion and bending of prismatic rods. We first consider torsion of the prismatic rod by two concentrated torques at its ends, and then analyze bending of a cantilever beam by a concentrated transverse force at its end.
11.1 Torsion of Prismatic Rods
We consider here the torsional deformation of prismatic rods subject to a torque or imposed angle of twist per unit length along the rod. The coordinate system, as illustrated in Fig. 11.1, has the z axis along the rod and the rod’s cross section in the x-y plane. The rod is deformed such that adjacent cross-sectional planes are rotated with respect to each other about the z axis; the angle of rotation ...