고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.2-4

6.2-4 A wood beam with cross-sectional dimensions 200 mm × 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are \(E_s = 190 \text{ GPa}\) and \(E_w = 11 \text{ GPa}\), respectively. Also, the corresponding allowable stresses are \(\sigma_s = 110 \text{ MPa}\) and \(\sigma_w = 7.5 \text{ MPa}\). (a) Calculate the maximum permissible bending moment \(M_{\text{max}}\) when the beam is bent about the z axis. (b) Repeat part (a) if the beam is now bent about its y axis. (c) Find the required thickness of the steel plates on the beam bent about the y axis so that \(M_{\text{max}}\) is the same for both beam orientations.