# Strain Formula

## Strain Formula

Strain is defined as the deformation or change in length of a body caused by stress. Strain occurs when stress is applied to a body that is in an equilibrium condition. Strain applied to a body might result in either reduction or extension. Strain is defined as a fractional change in either volume, length, or geometry. Hence, it is a dimensionless number. There are three sorts of strains:

• Longitudinal Strain
• Shearing Strain
• Volumetric strain

### What is Strain?

Strain is the amount of deformation that an object experiences as a result of the application of stress. Simply put, stress refers to the internal force, whereas strain refers to the physical effect of that force on the object. Strain is a measure of the amount of deformation that occurs on an object as a result of force. Longitudinal strain, shearing strain, and volumetric strain are the three major types of strain.

Strain is a quantity that has no units. This is due to the fact that the values in the numerator and denominator are always in the same units. Furthermore, strain is a deformation description in terms of the relative displacement of particles in a specific body.

This description, however, excludes rigid body motions. Different equivalent choices for the expression of a strain field are certainly possible. Furthermore, this is dependent on whether it is defined with respect to the body’s final or initial configuration.

### Strain Formula and Derivation

The strain formula is:

Strain = Δx/x

Here,

S = strain (it is unitless)

Δx = change in dimension

X = original dimension

An important thing to consider is the dimensional representation of strain which takes place as [M0L0T0]

Here,

M = Mass

L = Length

T = Time

Therefore, one can derive the following formula of strain from the above formula or equation:

Strain = Δ x/x

= L/L

= M0 L1 T0 / M0 L1 T0

= M0 L0 T0

Types of Strain

### Solved Example on Strain Formula

Q1 Heating results in the expansion of metals. A hot liquid enters through a copper pipe 10.00 m long. This causes an increase in length to 10.17 m. Calculate the longitudinal strain?

A1 The longitudinal strain refers to the change in length divided by the original length. The change in length refers to the difference between the final length (l2) and the length which is initial(l1). Now one can find the strain:

S = ΔxX

S = Δll1

S = l2−l1l1

S = 10.17–1010

S = 0.1710

S = 0.017

Hence, the longitudinal strain is 0.01.