고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.2-12

6.2-12 A simply supported composite beam 3 m long carries a uniformly distributed load of intensity \(q = 3.0 \text{ kN/m}\) (see figure). The beam is constructed of a wood member, 100 mm wide by 150 mm deep, and is reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide. (a) Find the maximum bending stresses \(\sigma_w\) and \(\sigma_s\) in the wood and steel, respectively, due to the uniform load if the moduli of elasticity are \(E_w = 10 \text{ GPa}\) for the wood and \(E_s = 210 \text{ GPa}\) for the steel. (b) Find the required thickness of the steel plate so that the steel plate and wood reach their allowable stress values, \(\sigma_{as} = 100 \text{ MPa}\) and \(\sigma_{aw} = 8.5 \text{ MPa}\), simultaneously under the maximum moment.