The resilience in simple tension or compression is (where σ is tensile or compressive stress, A is area of cross-section and E is modulus of elasticity.)
- Aσ²/2ECorrect
- Bσ²/2A
- Cσ²/2AE
- D2σ²/AE
Solution
Concept
Strain energy per unit volume (modulus of resilience)
Formula
u = σ² / 2E; total U = (σ² / 2E) × V
Step-by-step solution
1. Strain energy stored per unit volume = ½ σ ε = ½ σ (σ/E) = σ²/2E. 2. This is the resilience (per unit volume); the total resilience is this value multiplied by the volume.
Explanation
Resilience is the strain energy stored in a body when it is stressed within the elastic limit. Per unit volume it equals σ²/2E.
Why the other options are wrong
The other expressions do not have the correct dimensions of energy per unit volume (σ²/2AE and 2σ²/AE contain an extra area, σ²/2A does not contain E).
Shortcut
u = σ²/2E.
Common mistake
Dividing by area A.
Correct answer: A) σ²/2E