Question

A rigid beam CBDA is hinged at A and supported by two springs at C and B with a vertical load 'P' at point D as shown in the given figure. The ratio of stiffness $\left(k_2/k_1\right)$ of springs at B and C is 2. The ratio of forces in spring at C to that at B is

• A. $3/4$
• B. $1$
• C. $4/3$
• D. $2$

Answer 1

The correct option is A $3/4$

Let the deformation in spring at B be ${\delta }_B$ and the deformation in spring at $C$ be ${\delta }_C$
$\frac{{\delta }_B}{{\delta }_C}=\frac{2}{3}$
$\frac{F_C}{F_B}=\left(\frac{k_1}{k_2}\right)\frac{{\delta }_C}{{\delta }_B}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}$