Strain Energy Stored in a Body

Formula:
The strain energy stored in a body of volume V subjected to uniform stress σ is given by the formula:
\[ U = \frac{σ^2V}{2E} \]

Explanation:
- The formula for strain energy stored in a body relates the stress applied to the body (σ), the volume of the body (V), and the modulus of elasticity of the material (E).
- The formula shows that the strain energy stored is directly proportional to the square of the stress applied (σ^2).
- The strain energy stored is also directly proportional to the volume of the body (V).
- The strain energy stored is inversely proportional to the modulus of elasticity (E) of the material. This means that materials with higher modulus of elasticity will store less strain energy for the same stress and volume.

Significance:
- Understanding the strain energy stored in a body is important in engineering applications where materials are subjected to stress and deformation.
- Calculating the strain energy helps in analyzing the behavior of materials under different loading conditions.
- The formula helps in designing structures and components to ensure they can withstand the expected stress without failing.
In conclusion, the formula for strain energy stored in a body subjected to uniform stress σ provides a way to quantify the energy stored in a material due to deformation. It is an essential concept in material science and engineering.