A solid steel bar of diameter d1 = 1.50 in. is enclosed by a steel tube of

Question:

A solid steel bar of diameter d1 = 1.50 in. is enclosed by a steel tube of outer diameter d3 = 2.25 in. and inner diameter d2 = 1.75 in. (see figure). Both bar and tube are held rigidly by a support at end A and joined securely to a rigid plate at end B. The composite bar, which has length L = 30.0 in., is twisted by a torque T = 5000 lb-in. acting on the end plate.

(b) Determine the angle of rotation ( (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.6 ( 106 psi.
(c) Determine the torsional stiffness kT of the composite bar. (Use Eqs. 3-44 a and b to find the torques in the bar and tube.)