고체역학 (Gere) — Torsion: Problem 3.4-6

3.4-6 A shaft with a solid, circular cross section consisting of two segments is shown in part a of the figure. The left-hand segment has a diameter of 80 mm and length of 1.2 m; the right-hand segment has a diameter of 60 mm and length of 0.9 m. Shown in part b of the figure is a hollow shaft made of the same material and having the same length. The thickness \( t \) of the hollow shaft is \( d/10 \), where \( d \) is the outer diameter. Both shafts are subjected to the same torque. (a) If the hollow shaft is to have the same torsional stiffness as the solid shaft, what should be its outer diameter \( d \)? (b) If torque \( T \) is applied at either end of both shafts and the hollow shaft is to have the same maximum shear stress as the solid shaft, what should be its outer diameter \( d \)?