Chapter 3, Problem 3.3.21P

A circular tube of inner radius r₁and outer radius r₂is subjected to a torque produced by forces P = 900 lb (see figure part a). The forces have their lines of action at a distance b = 5.5 in. from the outside of the tube.

(a) If the allowable shear stress in the tube is 6300 psi and the inner radius r₁= 1.2 in., what is the minimum permissible outer

radius r₂?

(b) If a torsional spring of stiffness = 450 kip-in./rad is added at the end of the tube (see figure part b), what is the maximum value of forces P lithe allowable shear stress is not to be exceeded? Assume that the tube has a length of L 18 in., outer radius of r₂= 1.45 in. and shear modulus G = 10.800 ksi. Hint: Consider the tube and torsional spring as “springs in parallel.”