A small balcony constructed of wood is supported by three identical cantilever beams (see figure). Each beam has length L1= 2.1 m, width b, and height h = 4b/3. The dimensions of the balcony floor are L1 × L2, with L2 = 2.5 m. The design load is 5.5 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 g 5.5 kN/m3.) The allowable bending stress in the cantilevers is 15 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.
