Gere & Goodno — Axially Loaded Members: Problem 2.2-13

2.2-13 Two rigid bars are connected to each other by two linearly elastic springs. Before loads are applied, the lengths of the springs are such that the bars are parallel and the springs are without stress. (a) Derive a formula for the displacement \(\delta_4\) at point 4 when the load \(P\) is applied at joint 3 and moment \(PL\) is applied at joint 1, as shown in the figure part a. (Assume that the bars rotate through very small angles under the action of load \(P\).) (b) Repeat part (a) if a rotational spring, \(k_r = kL^2\), is now added at joint 6. What is the ratio of the deflection \(\delta_4\) in the figure part a to that in the figure part b?