고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.10-16

6.10-16 Solve the preceding problem for a box beam with dimensions \(h = 400\text{ mm}\), \(h_1 = 360\text{ mm}\), \(b = 200\text{ mm}\), and \(b_1 = 160\text{ mm}\), and with yield stress \(\sigma_Y = 220\text{ MPa}\). (Problem 6.10-15 reference: The hollow box beam shown in the figure is subjected to a bending moment \(M\) of such magnitude that the flanges yield but the webs remain linearly elastic. (a) Calculate the magnitude of the moment \(M\) if the dimensions of the cross section are \(h = 350\text{ mm}\), \(h_1 = 310\text{ mm}\), \(b = 200\text{ mm}\), and \(b_1 = 175\text{ mm}\). Also, the yield stress is \(\sigma_Y = 220\text{ MPa}\). (b) What percent of the moment \(M\) is produced by the elastic core?)