고체역학 (Gere) — Torsion: Problem 3.3-17

3.3-17 A vertical pole of solid, circular cross section is twisted by horizontal forces \( P = 12 \text{ kN} \) acting at the ends of a rigid horizontal arm \( AB \) (see figure part a). The distance from the outside of the pole to the line of action of each force is \( c = 212 \text{ mm} \) (see figure part b) and the pole height is \( L = 425 \text{ mm} \). (a) If the allowable shear stress in the pole is \( 32 \text{ MPa} \), what is the minimum required diameter \( d_{\min} \) of the pole? (b) Find the torsional stiffness of the pole (\(\text{kN}\cdot\text{m/rad}\)). Assume that \( G = 28 \text{ GPa} \). (c) If two translational springs, each with stiffness \( k = 2700 \text{ kN/m} \), are added at \( 2c/5 \) from \( A \) and \( B \) (see figure part c), repeat part (a) to find \( d_{\min} \). Hint: Consider the pole and pair of springs as “springs in parallel.”