1 (a) Figure 1 shows a rigid bar ABC pin-jointed to a support at A and connected to two springs of equal stiffness k at B. The other ends of the springs are roller supported at D and E. The portions AB and BC are of lengths 2L and L, respectively. The free length of each spring is equal to l?. The horizontal distance between point A and D is a (as shown). Under the action of horizontal force P applied at C, the springs are in stretched condition and the bar is inclined at an angle ? as shown. Ignore the weights of all components and any friction at the joints and contacts. Using the principle of virtual work (?W = ?U), obtain an expression for P in terms of ? and possibly other parameters such as L, k and a.
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Since the bar is rigid, the virtual work done by P is zero. Show more…
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Adi S.
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 $P L$ 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 $\operatorname{load} P .)$ (b) Repeat part (a) if a rotational spring, $k_{r}=k L^{2}$ 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?
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