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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: S = ΔxX
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]
M = Mass
L = Length
T = Time
Therefore, one can derive the following formula of strain from the above formula or equation:
[M0L0T0] = M0L1T0×[M0L1T0]−1
Now from the above, one can derive the dimensional formula of length = [M0L1T0]
Finally, the formula of strain is = changeindimensionoriginalvalueofdimension
Types of Strain
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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.