고체역학 (Gere) — Torsion: Problem 3.3-8

3.3-8 An aluminum bar of solid circular cross section is twisted by torques \(T\) acting at the ends (see figure). The dimensions and shear modulus of elasticity are \(L = 1.4 \text{ m}\), \(d = 32 \text{ mm}\), and \(G = 28 \text{ GPa}\). (a) Determine the torsional stiffness of the bar. (b) If the angle of twist of the bar is \(5^\circ\), what is the maximum shear stress? What is the maximum shear strain (in radians)? (c) If a hole of diameter \(d/2\) is drilled longitudinally through the bar, what is the ratio of the torsional stiffnesses of the hollow and solid bars? What is the ratio of their maximum shear stresses if both are acted on by the same torque? (d) If the hole diameter remains at \(d/2\), what new outside diameter \(d_2\) will result in equal stiffnesses of the hollow and solid bars?