고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-3

5.6-3 The cross section of a narrow-gage railway bridge is shown in part a of the figure. The bridge is constructed with longitudinal steel girders that support the wood cross ties. The girders are restrained against lateral buckling by diagonal bracing, as indicated by the dashed lines. The spacing of the girders is \(s_1 = 0.8 \text{ m}\) and the spacing of the rails is \(s_2 = 0.6 \text{ m}\). The load transmitted by each rail to a single tie is \(P = 16 \text{ kN}\). The cross section of a tie, shown in part b of the figure, has a width \(b = 120 \text{ mm}\) and depth \(d\). Determine the minimum value of \(d\) based upon an allowable bending stress of \(8 \text{ MPa}\) in the wood tie. (Disregard the weight of the tie itself.)