고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-22

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. 8.4-22 Solve the preceding problem using the numerical data: $b = 90\text{ mm}$, $h = 280\text{ mm}$, $d = 210\text{ mm}$, $q = 14\text{ kN/m}$, and $L = 1.2\text{ m}$.