Question

Two identical weightless rods are hinged to each other and to a horizontal beam (Fig. 13). The rigidity of each rod is k₀, and the angle between them is 2α. Determine the rigidity k of the system of rods relative to the vertical displacement

of a hinge A under the action of a certain force F, assuming that displacements are small in comparison with the length of the rods.

Answer 1

Let the hinge be displaced downwards by a small distance Δx as a result of application of the force F, and let the rods be elongated by Δl

(Fig. 147). Then the rigidity k of the system of rods can be determined from the equation kΔx = 2k₀ Δl cos a', where 2α' is the angle between the rods after the displacement. Since the displacement is small