Gere & Goodno — Stresses in Beams (Basic Topics): Problem 5.8-8

5.8-8 A beam of rectangular cross section (width \(b\) and height \(h\)) supports a uniformly distributed load along its entire length \(L\). The allowable stresses in bending and shear are \(\sigma_{\text{allow}}\) and \(\tau_{\text{allow}}\), respectively. (a) If the beam is simply supported, what is the span length \(L_0\) below which the shear stress governs the allowable load and above which the bending stress governs? (b) If the beam is supported as a cantilever, what is the length \(L_0\) below which the shear stress governs the allowable load and above which the bending stress governs?