고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-21

8.4-21 Beam $ABCD$ has a sliding support at $A$, roller supports at $C$ and $D$, and a pin connection at $B$ (see figure). Assume that the beam has a rectangular cross section ($b = 100 \text{ mm}$, $h = 400 \text{ mm}$). Uniform load $q$ acts on $ABC$ and a concentrated moment is applied at $D$. Let load variable $q = 25 \text{ kN/m}$, and assume that dimension variable $L = 1.25 \text{ m}$. First, use statics to confirm the reaction moment at $A$ and the reaction forces at $C$ and $D$, as given in the figure. Then find the ratio of the magnitudes of the principal stresses $(\sigma_1 / \sigma_2)$ just left of support $C$ at a distance $d = 250 \text{ mm}$ up from the bottom.