Gere & Goodno — Torsion: Problem 3.5-6

3.5-6 A solid circular bar of diameter \(d = 50 \text{ mm}\) (see figure) is twisted in a testing machine until the applied torque reaches the value \(T = 500 \text{ N}\cdot\text{m}\). At this value of torque, a strain gage oriented at \(45^\circ\) to the axis of the bar gives a reading \(\epsilon = 339 \times 10^{-6}\). What is the shear modulus \(G\) of the material?