고체역학 (Gere) — Axially Loaded Members: Problem 2.5-20

2.2-20 A framework $ABC$ consists of two rigid bars $AB$ and $BC$, each having a length $b$ (see the first part of the figure part a). The bars have pin connections at $A$, $B$, and $C$ and are joined by a spring of stiffness $k$. The spring is attached at the midpoints of the bars. The framework has a pin support at $A$ and a roller support at $C$, and the bars are at an angle $\alpha$ to the horizontal. When a vertical load $P$ is applied at joint $B$ (see the second part of the figure part a) the roller support $C$ moves to the right, the spring is stretched, and the angle of the bars decreases from $\alpha$ to the angle $\theta$. (a) Determine the angle $\theta$ and the increase $\delta$ in the distance between points $A$ and $C$. Also find reactions at $A$ and $C$. (Use the following data: $b = 200\text{ mm}$, $k = 3.2\text{ kN/m}$, $\alpha = 45^\circ$, and $P = 50\text{ N}$.) (b) Repeat part (a) if a translational spring $k_1 = k/2$ is added at $C$ and a rotational spring $k_r = kb^2/2$ is added at $A$ (see figure part b).