고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.8-14

5.8-14 A wood beam $ABC$ with simple supports at $A$ and $B$ and an overhang $BC$ has height $h = 300\text{ mm}$ (see figure). The length of the main span of the beam is $L = 3.6\text{ m}$ and the length of the overhang is $L/3 = 1.2\text{ m}$. The beam supports a concentrated load $3P = 18\text{ kN}$ at the midpoint of the main span and a moment $PL/2 = 10.8\text{ kN}\cdot\text{m}$ at the free end of the overhang. The wood has a weight density $\gamma = 5.5\text{ kN/m}^3$. (a) Determine the required width $b$ of the beam based upon an allowable bending stress of $8.2\text{ MPa}$. (b) Determine the required width based upon an allowable shear stress of $0.7\text{ MPa}$.