**Strain Energy** usually denoted by U is basically the energy stored in a body **due to deformation**.

It is a type of potential energy that is stored in a structure as a result of elastic deformation. For example, if a bar is bent by applying force on it then, then the bar is said to be deformed from its unstressed state, and the amount of strain energy stored in it is equal to the work done on the bar by that force.

It is calculated as the area under the stress-strain curve towards the *point of deformation*.

Index

**Strain Energy Formul**a

Strain energy is denoted by \(U\).

\(U = \frac{F \delta}{2}\)

Where,

\(\delta\) – Compression

\(F\) – Force Applied

If stress \(\sigma\) is proportional to strain \(\epsilon\), the formula can also be given by,

\(U = \frac{1}{2}V \sigma \epsilon\)

Where,

\(V\) – Volume of the body

**Strain energy formula using Young’s Modulus**,

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

**Solved Examples**

**Question 1.** When a force of 100 N is applied to an object, it is compressed by 1.5 mm. Calculate the strain energy.

**Solution.** Given,

Force, \(F = 100 N\)

Compression, \(\delta = 1.5 mm\)

\(U = \frac{F \delta}{2} = \frac{100*1.5*10^{-3}}{2}\)

∴ \(U = 0.075 J\)

**Question 2.** A rod of area 100 mm^{2} has a length of 5 m. Determine the strain energy if the stress of 500 MPa is applied when stretched. Young’s Modulus is taken to be 200 GPa.

**Solution.** Given,

Area, \(A = 100 {mm}^2\)

Length, \(l = 5m\)

Stress, \(\delta = 500 MPa = 500 * 10^6 Pa\)

Young’s Modulus, \(E = 200 GPa = 200 * 10^9 Pa\)

As we know, Volume = Area x Length

V = (100 x 10^{-6}) x 3

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

\(U = \frac{(500 * 10^6 )^2}{2 * 200 * 10^9} (100 * 10^{-6}) * 3\)

∴ \(U = 18.75 J\)

**FAQs**

**What is the strain energy of a material?**It is defined as the energy stored in an object due to a temporary deformation.

**How do you calculate the strain energy?**It is calculated using the following formula:

\(U = \frac{F \delta}{2}\)

Where,

\(\delta\) – Compression

\(F\) – Force Applied

**What is strain?**

Strain is simply the measure of how much an object is stretched or deformed. It occurs when force is applied to an object. Strain deals mostly with the change in length of the object.

If the original length of the body L_{0} changes by ΔL, then stress can be expressed as

\(\text{Strain}=\frac{\Delta L}{L}=\frac{\text{Change in Length}}{\text{Original Length}}\)