Question

The equivalent spring constant for the set up shown in the below figure, where EI = unity throughout is

• A. 30 units
• B. 36 units
• C. 40 units
• D. 48 units

Answer 1

The correct option is A 30 units

Let ${\Delta }_1,{\Delta }_{2}and{\Delta }_3$ is deflection of beam AB, compression of spring and deflection of beam CD respectively.


${\Delta }_2={\Delta }_1-{\Delta }_3$

$\Rightarrow \frac{R}{48}=\frac{(P-R)(2{)}^3}{48\times 1}-\frac{R(1{)}^3}{48\times 1}$

$\Rightarrow R=\frac{4}{5}P$

$N0ow,{\Delta }_1=\frac{P}{30}$

$k_{eq}=\frac{P}{deflectioninthedirectionofP}$

$=\frac{P}{{\Delta }_1}=30units$