The homogeneous, solid cylindrical shaft AB has a length

Chapter 3, Problem 3.C4

(choose chapter or problem)

The homogeneous, solid cylindrical shaft AB has a length L, a diameter d, a modulus of rigidity G, and a yield strength \(\tau_{Y}\). It is subjected to a torque T that is gradually increased from zero until the angle of twist of the shaft has reached a maximum value \(\phi_{m}\) and then decreased back to zero. (a) Write a computer program that, for each of 16 values of \(\phi_{m}\) equally spaced over a range extending from 0 to a value 3 times as large as the angle of twist at the onset of yield, can be used to determine the maximum value \(T_{m}\) of the torque, the radius of the elastic core, the maximum shearing stress, the permanent twist, and the residual shearing stress both at the surface of the shaft and at the interface of the elastic core and the plastic region. (b) Use this program to obtain approximate answers to Probs. 3.114, 3.115, 3.116.