32. A thin-walled cylindrical pressure vessel with closed ends is subjected to an internal pressure p = 100 psi and also a torque T around its axis of symmetry. Determine T that will cause yield¬

ing according to von Mises' yield criterion. The design requires a safety factor of 2. The nominal diameter D of the pressure vessel = 20 inches, wall thickness t = 0.1 inch, and yield strength of the material = 30ksi. (1 ksi = lOOOpsi). Stresses in a thin-walled cylinder are longitudinal stress 07, hoop stress 07,, and shear stress r due to torsion. They are given by pD pD 2T ar'-~4t> ah ~~ hi' T~~^t