Strain Energy Formula

What is Strain Energy?

Strain energy is the energy in a material that occurs during deformation because of an applied load. The strain of a material happens in the form of tension, compression, and bending. For a material to behave elastically, it will return to its original state when the load is removed. Thus, the energy accompanying such deformation is known as strain energy.

Formulas 

The strain energy formula is given as, 

U = Fδ / 2

Where,

• δ = compression

• F = force applied

When stress σ is proportional to strain ϵ, the strain energy formula is given by,

Where,

• σ = stress

• = stress

• V = volume of body

As stated above concerning Young's modulus E the strain energy formula is given as,

U = σ2 / 2E × V.

Where,

• σ = stress,

• E = Young's modulus,

• V = volume of body.

Solved Examples

Example 1: If a force of 1000 N is applied to a body, it compresses by 1.2 mm. Determine the strain energy.

Solution:

Given,

Force F = 1000 N,

Compression δ = 1.2 mm

The strain energy formula is given by,

U = Fδ / 2

U = 1000 ×1.2×10−3 / 2

U = 0.6 J.

Example 2: A bar with an area of 90 mm2 is stretched up to a length of 3 m. Calculate the strain energy if the stress of 300 MPa is applied when stretched. Young's modulus is given as 200 GPa.

Solution:

Given,

Area A = 90 mm2

Length l = 3m

Stress σ = 300 MPa

Young's modulus E = 200 GPa

Volume V is calculated by using the relation

V = arealength

   = (90 × 10−6) × 3

V = 270 x 10−6 m3

The strain energy formula is given as,

U = σ2 / 2E× V

U = (300×106)2 / 2 x 200×109 x 270 x 10-6

U =83.3 x 106 J

Thus, the strain energy of the rod is 83.3 x 106 J