Question

A rigid beam ABCD is hinged at D and supported by two springs at A and B as shown in the given figure. The beam carries a vertical load P at C. The stiffness of spring at A is 2k and that of B is k.

The ratio of forces of spring at A and that of spring at B is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

The rigid beam will rotate about point D, due to the load at C.


From similar triangle,

$\frac{{\delta }_B}{2a}=\frac{{\delta }_A}{3a}$ $or\frac{{\delta }_A}{{\delta }_B}=\frac{3}{2}$

$\frac{\text{Force in spring A}}{\text{Force in spring B}}=\frac{P_A}{P_B}$

$=\frac{k_A{\delta }_A}{k_B{\delta }_B}=\frac{2k}{k}\times \frac{3}{2}=3$