Gere & Goodno — Stresses in Beams (Advanced Topics): Problem 6.2-10

6.2-10 The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core is shown in the figure. The width $b$ of the beam is $50 \text{ mm}$, the thickness $t$ of the faces is $4 \text{ mm}$, and the height $h_c$ of the core is $92 \text{ mm}$ (total height $h = 100 \text{ mm}$). The moduli of elasticity are $75 \text{ GPa}$ for the fiberglass and $1.2 \text{ GPa}$ for the plastic. A bending moment $M = 275 \text{ N}\cdot\text{m}$ acts about the $z$ axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams and (b) the approximate theory for sandwich beams.