고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.2-13

6.2-13 A simply supported wooden I-beam with a 3.6 m span supports a distributed load of intensity \( q = 1.3 \text{ kN/m} \) over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web, as shown in the figure part b. The plywood is 10 mm thick; the flanges are \( 50 \text{ mm} \times 50 \text{ mm} \) (actual size). The modulus of elasticity for the plywood is \( 11 \text{ GPa} \) and for the pine is \( 8.3 \text{ GPa} \). (a) Calculate the maximum bending stresses in the pine flanges and in the plywood web. (b) What is \( q_{\text{max}} \) if allowable stresses are \( 11 \text{ MPa} \) in the flanges and \( 8 \text{ MPa} \) in the web?