# Strain Energy Formula

## Strain Energy Formula

Understanding the Strain Energy Formula can be difficult for some students. This does not imply that the formula will remain difficult indefinitely. A student must learn several formulas during their educational journey. One of them is the Strain Energy Formula. Students must be aware of all aspects of the topic as well as related topics. This means they must apply the Strain Energy Formula. It may appear unfamiliar and intimidating at first, but students experience a number of hiccups while learning. The textbooks are the main source of learning and information for students, but they also have limited information. This information about the Strain Energy Formula is good for the examinations, but might not be enough for other competitive examinations. Students need to rely on other sources, learning to have an entire idea of any topic like Strain Energy Formula.

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### Definition of Strain Energy

Strain energy is a type of potential energy stored in a structural member due to elastic deformation. When a member is deformed from its unstressed state, the external work done on it is transformed into (and considered equal to) the strain energy stored in it. When a beam supported at both ends is subjected to a bending moment caused by a load suspended in the canter, the beam is said to be deflected from its unstressed state, and strain energy is stored in it.

The integration for strain energy can only be used over a length of beam with a continuous expression. This usually means that each section between two concentrated loads or reactions must be integrated separately.

When we apply force to an object made of a deformable material, it changes shape. Sometimes there is a significant difference, such as when we stretch out a rubber band. It’s also difficult to see, as when a load is applied to a steel support beam. The object will continue to stretch as we apply more and more force. The amount of force applied divided by the object’s cross-sectional area equals stress.

### Formula for Strain Energy

As a result, strain energy is the energy stored in a body as a result of its deformation. As a result, we call this strain energy per unit volume strain energy density. In addition, the area under the stress-strain curve closest to the point of deformation. When the applied force is released, the entire system returns to its original shape.

1] The strain energy formula is: U=Fδ2

U Strain Energy

δ Compression

F Force applied

2] When stress σ is proportional to strain \epsilon, the strain energy formula is: U=12Vσϵ

U Strain Energy

σ Strain

V Volume of body

3] Regarding young’s modulus E, the strain energy formula is : U=σ22E×V.

U Strain Energy

σ Strain

V Volume of body

E young’s modulus,

### Solved Examples for Strain Energy Formula

Q.1: A rod of area 90 square mm has a length of 3 m. Then find out the strain energy if the stress of 300 MPa is applied when stretched. Young’s modulus is 200 GPa.

Solution: Given parameters are,

Area A = 90 square mm,

Length, l = 3m,

Stress, σ=300MPa=300×106Pa

Young’s modulus, E=200GPa.=200×109Pa

Volume V is: V = AL

=(90×10−6)×3

V=27×10−6cubicm

The strain energy formula is:

U=σ22E×V.

=300×10622×200×109×27×10−6.

= 12.15 J

Therefore, the strain energy of the rod will be 12.15 J.