고체역학 (Beer) — Torsion: Problem 3.48

3.48 The design of the gear-and-shaft system shown requires that steel shafts of the same diameter be used for both \(AB\) and \(CD\). It is further required that \(\tau_{\text{max}} \le 60 \text{ MPa}\) and that the angle \(\phi_D\) through which end \(D\) of shaft \(CD\) rotates not exceed \(1.5^\circ\). Knowing that \(G = 77.2 \text{ GPa}\), determine the required diameter of the shafts.