Question

Two elastic rods AB and BC are hinged at B. The joint A is a hinged one, joint C is over a roller and the joint B is supported on a spring having its stiffness as k.

A load P acts at mid-point of the rod BC. The downward deflection of joint B is:

• A.
  $P/k$
• B.
  
  $2P/k$
  
• C.
  
  $P/2k$
  
• D.
  $0$

Answer 1

The correct option is C


$P/2k$


$\sum M_A=0,$
$R_c\times 2L+R\times L-P\times \frac{3L}{2}=0$ ...(1)

$\sum M_C=0,$
$R_A\times 2L+R\times L-P\times \frac{L}{2}=0$ ...(2)

$\sum M_B=0,R_A\times L=0$
$R_A=0$
$\Rightarrow$ $R=\frac{P}{2}$

Downward deflection of spring is-
$\delta =\frac{R}{K}=\frac{P}{2K}$