1. A cylindrical metal tube of mean radius r = 5 in., length L = 14 ft, and shear modulus G = 11 × 106 psi carries the torque T = 320 kip in. Determine the smallest allowable constant wall thickness t if the shear stress is limited to 12 ksi and the angle of twist is not to exceed 2°.
2. A cylindrical tube of constant wall thickness t and inside radius r = 10t carries a torque T. Find the expression for the maximum shear stress in the tube using
(a) the torsion formula for a hollow shaft in Eq. (3.5d); and
(b) the thin-walled tube formula in Eq. (3.8b). What is the percentage error in the thin-walled tube approximation?
