고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.5-10

6.5-10 A built-up beam supporting a condominium balcony is made up of a structural T for the top flange and web and two angles for the bottom flange and web, as shown. The beam is subjected to a bending moment $M$ having its vector at an angle $\theta$ to the $z$ axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress $\sigma_t$ and maximum compressive stress $\sigma_c$ in the beam. Assume that $\theta = 30^\circ$ and $M = 10 \text{ kN}\cdot\text{m}$. Use the numerical properties: $c_1 = 4.111 \text{ mm}$, $c_2 = 4.169 \text{ mm}$, $b_f = 134 \text{ mm}$, $L_s = 76 \text{ mm}$, $A = 4144 \text{ mm}^2$, $I_y = 3.88 \times 10^6 \text{ mm}^4$, and $I_z = 34.18 \times 10^6 \text{ mm}^4$.