고체역학 (Beer) — Analysis and Design of Beams for Bending: Problem 5.139

5.139 A cantilever beam AB consisting of a steel plate of uniform depth \(h\) and variable width \(b\) is to support the distributed load \(w\) along its centerline AB. (a) Knowing that the beam is to be of constant strength, express \(b\) in terms of \(x\), \(L\), and \(b_0\). (b) Determine the maximum allowable value of \(w\) if \(L = 15\text{ in.}\), \(b_0 = 8\text{ in.}\), \(h = 0.75\text{ in.}\), and \(\sigma_{\text{all}} = 24\text{ ksi}\).