A wood pole with a solid circular cross section $(d=\text { diameter })$ is subjected to a triangular distributed horizontal force of peak intensity $q_{0}=20 \mathrm{lb} / \mathrm{in}$ (see figure). The length of the pole is $L=6 \mathrm{ft}$, and the allowable stresses in the wood are 1900 psi in bending and 120 psi in shear. Determine the minimum required diameter of the pole based upon (a) the allowable bending stress, and
(b) the allowable shear stress.