Strain in physics and engineering refers to the deformation or displacement of material that results from an applied stress. It's a measure of how much an object is stretched or compressed. Strain is dimensionless, as it represents the ratio of change in length to the original length. There are different types of strain, such as tensile strain (stretching), compressive strain (compressing), and shear strain (distortion). Understanding strain is crucial for assessing material properties and behaviour under various forces.
In this article, we will learn what strain is and solve some problems based on strain.
What is Strain?
Strain is a measure of deformation representing the displacement between particles in the material body. It is a dimensionless quantity. Strain can be classified as normal strain and shear strain. Here we focus on the derivation of the normal strain formula.
Normal Strain (ε)
Normal strain is defined as the change in length of a material per unit original length when subjected to a load. It measures the relative deformation of the material.
Strain Formula
The Greek symbol epsilon (ε) represents the strain equation. The formula to calculate the strain is added below:
ε = Δx/x
Where,
- Δx is Change in Dimension
- x is Original Dimension
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Examples of Strain Formula
Example 1: Calculate the strain if the body's original length is 10 cm and the length after stretching is 10.2 cm.
Solution
Here, original length is L = 10 cm
ΔL = 10.2 - 10 = 0.2 cm
Now, strain formula is given as follows:
εL = (Change in Length) / (Original Length)
= ΔL / L
Substituting the values we get,
εL= 0.2 / 10
= 0.02 cm
Therefore, the strain is 0.02 cm.
Example 2: If the Body Strain is 0.0125 and the Original Length is 8 cm, then Calculate the Body's Change in Length.
Solution
Here, strain is εL= 0.0125
Original length is L = 8 cm
εL = (Change in Length) / (Original Length)
= ΔL / L
Substituting the values we get,
0.0125 = ΔL / 8
0.0125 x 8 = ΔL
ΔL = 0.1 cm
Therefore, the change in length of the body is 0.1 cm
Example 3: Calculate the body's original length if the strain is 0.015 and the length change is 0.3 cm.
Solution
Here the longitudinal strain is εL= 0.015.
Change in length is ΔL = 0.3 cm
εL = (Change in Length) / (Original Length)
= ΔL/L
Substituting the values we get
0.015 = 0.3/ L
L = 0.3 / 0.015
L = 20 cm
Therefore, the original length of the body is 20 cm.
Example 4: A force pulls a string with an original length of 100 cm. The chord length changes by 2 mm. Identify the strain
Solution
Original length (L) = 100 cm = 1 m
Change in length (ΔL) = 2 mm = 0.002 m
εL = (Change in Length) / (Original Length)
= ΔL/L
= 0.002/1
= 0.002 m
Worksheet: Strain Formula
Problem 1: A metal rod with an original length of 2 meters is stretched to 2.01 meters. Calculate the strain.
Problem 2: A cylindrical rod with a diameter of 10 mm and a length of 50 mm is compressed along its length by 0.5 mm. Determine the compressive strain.
Problem 3: A rubber band is originally 0.1 m long. When a force is applied, its length increases to 0.12 m. Calculate the tensile strain.
Problem 4: A steel beam undergoes a shear deformation of 2 mm across a section length of 1 m. Calculate the shear strain.
Problem 5: A plastic ruler bends such that a point on its edge moves 5 mm from its original position, while the length of the ruler remains 30 cm. Determine the bending strain.
Problem 6: A wooden beam with a length of 1.5 m is compressed longitudinally by 3 mm. Find the compressive strain.
Problem 7: A bar of aluminum alloy is subjected to a tensile force, resulting in an elongation of 0.4 mm. The original length of the bar is 0.8 m. Calculate the tensile strain.
Problem 8: A plastic rod 1 m long is heated and expands by 2 cm. Calculate the thermal strain.
Problem 9: A wire of initial length 1.2 m is stretched to a length of 1.22 m. Find the tensile strain.
Problem 10: A concrete column shortens by 1 mm under a load. If the initial height of the column is 3 m, determine the compressive strain.