고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.3-7

6.3-7 The cross section of a beam made of thin strips of aluminum separated by a lightweight plastic is shown in the figure. The beam has width $b = 75 \text{ mm}$, the aluminum strips have thickness $t = 2.5 \text{ mm}$, and the plastic segments have heights $d = 30 \text{ mm}$ and $3d = 90 \text{ mm}$. The total height of the beam is $h = 160 \text{ mm}$. The moduli of elasticity for the aluminum and plastic are $E_{Al} = 75 \text{ GPa}$ and $E_p = 3 \text{ GPa}$, respectively. Determine the maximum stresses $\sigma_{Al}$ and $\sigma_p$ in the aluminum and plastic, respectively, due to a bending moment of $1.2 \text{ kN}\cdot\text{m}$.