고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.2-7

6.2-7 A beam with a guided support and 4 m span supports a distributed load of intensity \( q = 4\text{ kN/m} \) over its first half (see figure part a) and a moment \( M_0 = 5\text{ kN}\cdot\text{m} \) at joint \( B \). The beam consists of a wood member (actual dimensions \( 97\text{ mm} \times 295\text{ mm} \) in cross section, as shown in the figure part b) that is reinforced by 7-mm thick steel plates on top and bottom. The moduli of elasticity for the steel and wood are \( E_s = 210\text{ GPa} \) and \( E_w = 10\text{ GPa} \), respectively. (a) Calculate the maximum bending stresses \( \sigma_s \) in the steel plates and \( \sigma_w \) in the wood member due to the applied loads. (b) If the allowable bending stress in the steel plates is \( \sigma_{as} = 100\text{ MPa} \) and that in the wood is \( \sigma_{aw} = 6.5\text{ MPa} \), find \( q_{max} \). (Assume that the moment at \( B \), \( M_0 \), remains at \( 5\text{ kN}\cdot\text{m} \).) (c) If \( q = 4\text{ kN/m} \) and allowable stress values in part (b) apply, what is \( M_{0,max} \) at \( B \)?