Question

In a system, two connected rigid bars AC and BC are of identical length L with pin supports at A and B. The bar are interconnected at C by a frictionless hinge is restrained by rotational spring of stiffness k. The system initially assumes a straight line configuration ACB. Assuming both the bars as weightless, rotation at support A and B due to transverse load P applied at C is

• A. $\frac{PL}{4K}$
• B. $\frac{PL}{2K}$
• C. $\frac{P}{4K}$
• D. $\frac{PK}{4L}$

Answer 1

The correct option is A $\frac{PL}{4K}$


External work $\frac{1}{2}\times P\times L\theta$
Strain energy stored in spring
$=\frac{1}{2}\left(K\right(2\theta \left)\right(2\theta \left)\right)$
$\frac{PL\theta }{2}=\frac{4K{\theta }^2}{2}$
$\Rightarrow \theta =\frac{PL}{4k}$