Question

A rigid beam is hinged at one end and supported on linear elasitc spring (both having a stiffness of 'k') at points '1' and'2', and an inclined load acts at '2', as shown in figure




If the load P equals 100 kN, which of the follwoing options represents forces $R_{1}and{R}_2$ in springs at points 1 and 2?

• A. $R_1=20kNand{R}_2=40kN$
• B. $R_1=50kNand{R}_2=50kN$
• C. $R_1=30kNand{R}_2=60kN$
• D. $R_1=40kNand{R}_2=80kN$

Answer 1

The correct option is D $R_1=40kNand{R}_2=80kN$

Given,
P=100 kN
$R_1=k\delta$
$=k.\frac{2P}{5k}$
$=\frac{2P}{5}$
$=\frac{2\times 100}{5}=40kN$
$R_2=2k\delta$
$=80kN$