1. A shaft wit a channel section shown in fig. 3.40 is subjected to a torque T. Assume that neither end is constrained. Find the warping distribution on the cross-section, the maximum warp, and the location of the maximum warp.
2. Consider the shaft of the channel section shown in fig. 3.40. If one end of the shaft is built in and the other end is free, find the effective torsional rigidity as a function of the distance from the built-in end. Assume that the length L of the shaft is sufficiently large so that near the free end the Saint-Venant torsion assumptions are valid. Compare the total twist angle with that for a free-free shaft for L=2m (Fig. 3.40 is in the attached file)