고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-16

5.6-16 A small balcony constructed of wood is supported by three identical cantilever beams (see figure). Each beam has length \(L_1 = 2.1 \text{ m}\), width \(b\), and height \(h = 4b/3\). The dimensions of the balcony floor are \(L_1 \times L_2\), where \(L_2 = 2.5 \text{ m}\). The design load is \(5.5 \text{ kPa}\) acting over the entire floor area. (This load accounts for all loads except the weights of the cantilever beams, which have a weight density \(\gamma = 5.5 \text{ kN/m}^3\).) The allowable bending stress in the cantilevers is \(15 \text{ MPa}\). Assuming that the middle cantilever supports \(50\%\) of the load and each outer cantilever supports \(25\%\) of the load, determine the required dimensions \(b\) and \(h\).