Gere & Goodno — Stresses in Beams (Basic Topics): Problem 5.9-1

5.9-1 A wood pole with a solid circular cross section (\(d\) = diameter) is subjected to a triangular distributed horizontal force of peak intensity \(q_0 = 3.75 \text{ kN/m}\) (see figure). The length of the pole is \(L = 2 \text{ m}\), and the allowable stresses in the wood are \(13 \text{ MPa}\) in bending and \(820 \text{ kPa}\) in shear. Determine the minimum required diameter of the pole based upon (a) the allowable bending stress, and (b) the allowable shear stress.