고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-22

5.6-22 A steel beam ABC is simply supported at A and B and has an overhang BC of length L = 150 mm (see figure). The beam supports a uniform load of intensity q = 4.0 kN/m over its entire span AB and 1.5q over BC. The cross section of the beam is rectangular with width b and height 2b. The allowable bending stress in the steel is \(\sigma_{\text{allow}} = 60 \text{ MPa}\), and its weight density is \(\gamma = 77.0 \text{ kN/m}^3\). (a) Disregarding the weight of the beam, calculate the required width b of the rectangular cross section. (b) Taking into account the weight of the beam, calculate the required width b.