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After the solid shaft of Prob. 3.116 has been loaded and unloaded as described in that problem, a torque T1 of sense opposite to the original torque T is applied to the shaft. Assuming no change in the value of ϕY, determine the angle of twist ϕ1 for which yield is initiated in this second loading and compare it with the angle ϕY for which the shaft started to yield in the original loading.
3.116 The solid shaft shown is made of a steel that is assumed to be elastoplastic with τY= 145 MPa and G = 77.2 GPa. The torque is increased in magnitude until the shaft has been twisted through 6°; the torque is then removed. Determine (a) the magnitude and location of the maximum residual shearing stress, (b) the permanent angle of twist.
Fig .P3.116
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