고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.10-4

6.10-4 A steel beam of rectangular cross section is 40 mm wide and 80 mm high (see figure). The yield stress of the steel is 210 MPa. (a) What percent of the cross-sectional area is occupied by the elastic core if the beam is subjected to a bending moment of \(12.0 \text{ kN} \cdot \text{m}\) acting about the \(z\) axis? (b) What is the magnitude of the bending moment that will cause 50% of the cross section to yield?