Question

The strain energy stored in a body, when the load is gradually applied, is :
(where σ = Stress in the material of the body, V = Volume of the body, and E = Modulus of elasticity of the material)
1. σE/V 
2. σ2E/2V
3. σ²V/2E 
4. σV/E

Answer 1

Correct Answer - Option 3 : σ²V/2E 

Concept:

• When a body is loaded within the elastic limit, it changes its dimensions and on the removal of the load, it regains its original dimensions.
• So long as it remains loaded, it has stored energy in itself.
• On removing the load, the energy stored is given off as in the case of a spring.
• This energy, which is absorbed in a body when strained within the elastic limit, is known as strain energy.
• The strain energy stored in a body due to external loading, within the elastic limit, is known as resilience and the maximum energy which can be stored in a body up to the elastic limit is called proof resilience.
• Strain energy stored in a body due to tensile or compressive load or resilience:

\(U = \frac{{{\sigma ^2}V}}{{2E}}\)

• Modulus of resilience: The proof resilience per unit volume of a material is known as modulus of resilience.

\(U = \frac{{{\sigma ^2}}}{{2E}}\)