Question

The strain energy stored in the bar subjected to loads as shown in figure will be:

(AE is constant)

• A. $\frac{13P^{2}L}{3AE}$
• B. $\frac{13P^{2}L}{6AE}$
• C. $\frac{17P^{2}L}{6AE}$
• D. $\frac{17P^{2}L}{3AE}$

Answer 1

The correct option is B $\frac{13P^{2}L}{6AE}$


$\begin{array}{cccc}\text{Member}& \text{Axial force}& \text{Length}& \text{Strain energy}\left(U_i\right)=\frac{P_i^2{L}_i}{2AE}\\ AB& 0& L/3& 0\\ BC& 2P& L/3& \frac{4P^2}{2AE}\times \frac{L}{3}=\frac{2P^{2}L}{3AE}\\ CD& 3P& L/3& \frac{9P^2}{2AE}\times \frac{L}{3}=\frac{3P^{2}L}{2AE}\end{array}$
Strain energy $=\sum U_i$
$=\frac{2}{3}\frac{P^{2}L}{AE}+\frac{3}{2}\frac{P^{2}L}{AE}$
$=\frac{13P^{2}L}{6AE}$