Gere & Goodno — Applications of Plane Stress: Problem 8.4-5

8.4-5 A beam with a width $b = 150 \text{ mm}$ and depth $h = 200 \text{ mm}$ is simply supported at $A$ and $B$. The beam has a length $L = 3 \text{ m}$ and is subjected to a linearly varying distributed load with peak intensity $q_0 = 22 \text{ kN/m}$ at $B$ and $0$ at $A$. Calculate the state of plane stress at point $C$ located $75 \text{ mm}$ below the top of the beam and $30 \text{ mm}$ to the left of point $B$. Also find the principal stresses on element $C$. Neglect the weight of the beam.