고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-5

6.3-5 A simple beam that is 5.5 m long supports a uniform load of intensity \( q \). The beam is constructed of two UPN 200 sections on either side of a 97 mm × 195 mm (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel (\( E_s = 210 \text{ GPa} \)) is 20 times that of the wood (\( E_w \)). (a) If the allowable stresses in the steel and wood are 110 MPa and 8.2 MPa, respectively, what is the allowable load \( q_{\text{allow}} \)? Note: Disregard the weight of the beam, and see Table F-3 of Appendix F for the dimensions and properties of the UPN-shape beam. (b) If the beam is rotated 90° to bend about its \( y \) axis (see figure part b) and uniform load \( q = 3.6 \text{ kN/m} \) is applied, find the maximum stresses \( \sigma_s \) and \( \sigma_w \) in the steel and wood, respectively. Include the weight of the beam. (Assume weight densities of \( 5.5 \text{ kN/m}^3 \) and \( 77 \text{ kN/m}^3 \) for the wood and steel, respectively.)