A framework ABC consists of two rigid bars AB and BC, each having length b (see the first part of the figure). 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 α to the hoizontal.

When a vertical load P is applied at joint B (see the second part of the figure) the roller support C moves to the right, the spring is stretched, and the angle of the bars decreases from α to the angle θ.
Determine the angle and the increase θ in the distance between points A and C. (Use the following data; b = 8.0 in., k = 16 lb/in., α = 45°, and P = 10 lb.)

2 b2 2 2 PB