고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-12

8.4-12 A cantilever wood beam with a width $b = 100 \text{ mm}$ and depth $h = 150 \text{ mm}$ has a length $L = 2 \text{ m}$ and is subjected to point load $P$ at mid-span and uniform load $q = 15 \text{ N/m}$. (a) If the normal stress $\sigma_x = 0$ at point $C$, located $120 \text{ mm}$ below the top of the beam at the fixed support $A$, calculate the point load $P$. Also show the complete state of plane stress on the element at point $C$. (b) Repeat Part a if $\sigma_x = 220 \text{ kPa}$. Assume that element $C$ is a sufficient distance from support $A$ so that stress concentration effects are negligible.