Question

For a cylindrical sample of cross-sectional area $ A $, length $ L $, Young’s modulus $ E $ and axial load $ P $, the strain energy stored is

• A. \( \frac{P^2 L}{2 A E} \)
• B. \( \frac{P L^2}{2 A E} \)
• C. \( \frac{P^2 L}{A E} \)
• D. \( \frac{P^2 L}{A E} \)

Hint:

Strain energy formula for axial load in a cylindrical sample.

Answer 1

The Correct Option is A

Strain energy stored \( U = \frac{1}{2} \times \text{Stress} \times \text{Strain} \times \text{Volume} \) Stress \( = \frac{P}{A} \), Strain \( = \frac{P}{A E} \times L \) Hence, \[ U = \frac{1}{2} \times \frac{P}{A} \times \frac{P L}{A E} \times A L = \frac{P^2 L}{2 A E} \]