고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-10

6.3-10 The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are \(E_{Al} = 75 \text{ GPa}\) and \(E_s = 200 \text{ GPa}\). (a) Under the action of a bending moment that produces a maximum stress of \(50 \text{ MPa}\) in the aluminum, what is the maximum stress \(\sigma_s\) in the steel? (b) If the height of the beam remains at \(120 \text{ mm}\) and allowable stresses in steel and aluminum are defined as \(94 \text{ MPa}\) and \(40 \text{ MPa}\), respectively, what heights \(h_{Al}\) and \(h_s\) are required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?