고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-6

6.3-6 The composite beam shown in the figure is simply supported and carries a total uniform load of \(40 \text{ kN/m}\) on a span length of \(4.0 \text{ m}\). The beam is built of a southern pine wood member having cross-sectional dimensions of \(150 \text{ mm} \times 250 \text{ mm}\) and two brass plates of cross-sectional dimensions \(30 \text{ mm} \times 150 \text{ mm}\). (a) Determine the maximum stresses \(\sigma_B\) and \(\sigma_w\) in the brass and wood, respectively, if the moduli of elasticity are \(E_B = 96 \text{ GPa}\) and \(E_w = 14 \text{ GPa}\). (Disregard the weight of the beam.) (b) Find the required thickness of the brass plates so that the plate and wood reach their allowable stress values of \(\sigma_{aB} = 70 \text{ MPa}\) and \(\sigma_{aw} = 8.5 \text{ MPa}\) simultaneously under the maximum moment. What is the maximum moment?