Strain Formula

What is the Formula of Strain?

Strain is a deformation measurement that represents the displacement of particles in the body in relation to a reference length. Strain is defined as a change in the shape or size of a body caused by a deforming force.

The strain equation is represented by the Greek letter epsilon (ε). 

ε = \[\frac{\text{Change in dimension}}{Original dimension}\] = \[\frac{\Delta x}{x}\]

Since strain is a ratio of two similar quantities, it is dimensionless. 


Strain Example:

When a body is subjected to a tension force along its length then there develops stress due to which the body experiences a longitudinal strain along the length. Similarly when the same body is subjected to loading in all directions then the body will experience a volumetric strain. If the body is loaded parallel to the axis then shearing occurs which results in shearing strain.


Types of Strain

There are three types of strain:

  • Longitudinal strain

  • Volumetric strain

  • Shearing strain

Longitudinal Strain

The strain produced by a deforming force that only changes length is known as longitudinal strain. The ratio of the change in length to the initial length is used to calculate the longitudinal strain formula.

The longitudinal strain formula physics is given as follows:

ε\[_{L}\] = \[\frac{\text{Change in length}}{Original length}\] = \[\frac{\Delta L}{L}\]


Volumetric Strain

The strain is called volume strain when the deforming force changes volume. The ratio of change in volume to the original volume is used to calculate the volumetric strain formula.

The volumetric strain formula physics is given as follows:

ε\[_{v}\] = \[\frac{\text{Change in volume}}{Original volume}\] = \[\frac{\Delta v}{v}\]


Shearing Strain

Shearing strain occurs when a deforming force causes a change in the shape of the body. It's calculated as the difference between the original location and the displacement of the surface in direct contact with the applied shear stress. Shear strain is represented by the lowercase Greek letter gamma (ℽ) or Greek letter epsilon (ε).

The shear strain formula physics is given as follows:

γ = ε\[_{s}\] = \[\frac{\text{Change in volume}}{Original volume}\] = \[\frac{\Delta v}{v}\]


Solved Examples on Strain Formula

1) Calculate the Longitudinal Strain if the Original Length of the Body is 10cm and After Stretching the Length of the Body Is 10.2 Cm. 

Ans: Here the original length is L = 10cm.

To calculate the change in length, we have to subtract the final length from the original length. So the change in length is, 

\[\Delta\]L = 10.2 - 10 = 0.2 cm

Now the longitudinal strain formula is given as follows:

ε\[_{L}\] = \[\frac{\text{Change in length}}{Original length}\] = \[\frac{\Delta L}{L}\]

Substituting the values we get,

ε\[_{L}\] = \[\frac{0.2}{10}\] = 0.02 cm

Therefore, the longitudinal strain is 0.02 cm.


2) If the Longitudinal Strain of the Body is 0.0125 and the Original Length is 8 Cm. Calculate the Change in Length of the Body.

Ans: Here the longitudinal strain is ε\[_{L}\] = 0.0125.

The original length is L = 8 cm.

To calculate the change in length we will use the longitudinal strain equation

ε\[_{L}\] = \[\frac{\text{Change in length}}{Original length}\] = \[\frac{\Delta L}{L}\]

Substituting the values we get,

0.0125 = \[\frac{\Delta L}{8}\]

0.0125 x 8 = \[\Delta\]L

\[\Delta\]L = 0.1 cm

Therefore, the change in length of the body is 0.1 cm.


3) Calculate the Original Length of the Body if the Longitudinal Strain is 0.015 and the Change in Length is 0.3 Cm.

Ans: Here the longitudinal strain is ε\[_{L}\] = 0.015.

Change in length is \[\Delta\]L = 0.3 cm

To calculate the original length we will use the longitudinal strain equation

ε\[_{L}\] = \[\frac{\text{Change in length}}{Original length}\] = \[\frac{\Delta L}{L}\]

Substituting the values we get

0.015 = \[\frac{0.3}{L}\]

L = \[\frac{0.3}{0.015}\]

L = 20 cm.

Therefore, the original length of the body is 20 cm.


Conclusion

Strain is a word used to describe deformation in terms of relative particle displacement in the body, excluding rigid-body motions. External loads, body forces such as gravity or electromagnetic forces, changes in temperature, moisture content, or chemical reactions, among other things, can induce deformation. A deformation field occurs in a continuous body as a result of a stress field caused by applied forces or as a result of changes in the temperature field inside the body. Constitutive equations represent the relationship between stresses and induced strains and are used to solve a variety of structural problems.

FAQs (Frequently Asked Questions)

Q1: What is a Strain?

Ans: Strain is a term used to describe the result of stress. The strain is a measurement of how much the body has distorted in comparison to its original shape as a result of the force's action. The strain is represented by the Greek letter epsilon (ε).

Q2: What is the Strain Equation?

Ans: Strain is defined as a change in the shape or size of a body caused by a deforming force.

It is given by the formula 

ε = Change in dimension/Original dimension = Δx/x

Q3: What are the Types of Strain?

Ans: There are three types of strain:


Longitudinal Strain

εL = Change in length/Original length = ΔL/L 


Volumetric Strain

εV = Change in volume/Original volume = Δv/v


Shearing Strain

γ = εs = Change in volume/Original volume = Δv/v