Question

The rotation at point C in the frame shown below is $\frac{1}{k}\frac{ML}{EI}$. The value of k will be____

• A. 4
• B. 8
• C. 16
• D. 32

Answer 1

The correct option is C 16

$\begin{array}{ccccc}\text{Joint}& \text{Member}& k& \sum k& D.F.\\ & OA& \frac{4EI}{2L}& & 1/4\\ O& OB& \frac{3EI}{L}& \frac{8EI}{L}& 3/8\\ & OC& \frac{3EI}{L}& & 3/8\end{array}$
$\therefore M_{OC}=\frac{3}{8}M$
$\therefore$ Rotation at joint $C,{\theta }_C=\frac{M_{OC}L}{6EI}=\left(\frac{3M}{8}\right)\left(\frac{L}{6EI}\right)$
$\Rightarrow {\theta }_C=\frac{ML}{16EI}$