# Strain Energy Formula

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape. It is usually denoted by U.

**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,**

**U = **1 / 2** V **σ ϵ

Where,

σ = stress,

ϵ = strain,

**V** = volume of body

**Regarding young’s modulus E, the strain energy formula is given as,**

**U = **σ^{2} / 2E ×** V.**

Where,

σ = stress,

**E** = young’s modulus,

**V** = volume of body.

**Example 1**

When a force of 1000 N is applied on a body, it gets compressed by 1.2 mm. Determine the strain energy.

**Solution:**

Given:

Force F = 1000 N,

Compression δ = 1.2 mm

Strain energy formula is given by,

U = Fδ / 2

= 1000 ×1.2×10^{−3} / 2

Therefore, U = 0.6 J.

**Example 2**

A rod of area 90 mm^{2} has a length of 3 m. Determine the strain energy if a stress of 300 MPa is applied when stretched. Young’s modulus is given as 200 GPa.

**Solution:**

Given:

Area A = 90 mm^{2},

Length l = 3m,

Stress σ = 300 MPa,

Young’s modulus E = 200 GPa.

Volume V is given by the formula,

V = AL

= (90 × 10^{−6}) × 3

V = 27 x10^{−6} m^{3}

The strain energy formula is given as,

U = σ^{2 }/ 2E× V

= (300×10^{6})^{2} / 2 x 200×10^{9} x 27 x 10^{-6}

Therefore, U = 12.15 J.

Therefore, the strain energy of rod is **12.15 J.**