Topic: Strength of Materials
Strain energy U, in the case of axially loaded bar is expressed as (where P is axial load, L is bar length, A is cross-section area of the bar, E is Young's Modulus of the bar, $\sigma$ is axial stress, $\delta L$ is elongation due to axial load)
- A. $\frac{P^{2}L^{2}}{2AE(\delta L)}$
- B. Area under stress versus strain diagram of axially loaded bar
- C. $\frac{\sigma}{2}\frac{(\delta L)}{L}$
- D. $\frac{P^{2}L}{2AE}$
Answer: D. $\frac{P^{2}L}{2AE}$
Explanation: The strain energy ($U$) stored in an axially loaded bar is given by the formula $U = \frac{1}{2} \times \text{Force} \times \text{deflection}$. Substituting the applied load $P$ for Force and the elongation $\frac{PL}{AE}$ for deflection gives $U = \frac{1}{2} \times P \times \frac{PL}{AE}$. This simplifies to the standard expression $\frac{P^{2}L}{2AE}$.