Gere & Goodno — Torsion: Problem 3.3-18

3.3-18 A vertical pole of solid, circular cross section is twisted by horizontal forces \( P = 5 \text{ kN} \) 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 \( c = 125 \text{ mm} \) (see figure part b) and the pole height \( L = 350 \text{ mm} \). (a) If the allowable shear stress in the pole is \( 30 \text{ MPa} \), what is the minimum required diameter \( d_{\text{min}} \) of the pole? (b) What is the torsional stiffness of the pole (\( \text{kN}\cdot\text{m/rad} \))? Assume that \( G = 28 \text{ GPa} \).