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In a system, two connected rigid bars AC and BC are of identical length L with pin supports at A and B. The bars are interconnected at C by a friction less hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, k. The system initially assumes a straight line configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to a transverse load, P applied at C is:
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- PL/4k
- PL/2k
- P/4k
- Pk/4L
Correct Option: A
External work = (1/2)P.L θ
Strain energy in spring
=1/2 × k.(2θ)(2θ) = 2 K θ2
External work = strain energy
∴ (1/2)P.L θ = 2 K θ2
∴ θ = PL/4k