Strain Energy due to Axial Deformation:

When a body is subjected to axial deformation, it undergoes a change in its dimensions. This change in dimensions is accompanied by a change in the internal energy of the body. The internal energy stored in the body due to the deformation is called strain energy.

Formula:

The strain energy due to axial deformation is given by the formula:

U = 1/2 * P * delta

Where,
U = Strain energy
P = Axial load
delta = Deformation

Explanation:

The strain energy is directly proportional to the square of the deformation. This means that if the deformation is doubled, the strain energy will increase four times. Similarly, if the deformation is halved, the strain energy will decrease to one-fourth of its original value.

The strain energy is also directly proportional to the square of the load applied. This means that if the load is doubled, the strain energy will increase four times. Similarly, if the load is halved, the strain energy will decrease to one-fourth of its original value.

The strain energy is inversely proportional to the modulus of elasticity. This means that if the modulus of elasticity is doubled, the strain energy will decrease to half of its original value. Similarly, if the modulus of elasticity is halved, the strain energy will increase two times.

Conclusion:

The formula for strain energy due to axial deformation is U = 1/2 * P * delta, where U is the strain energy, P is the axial load, and delta is the deformation. The strain energy is directly proportional to the square of the deformation and load applied, and inversely proportional to the modulus of elasticity.