Difference Between Stress and Strain
Last Updated : 22 Apr, 2025
Stress and Strain is an important concept in the field of Material Science and Metallurgy to get into insights about the strength of the material. When a material is put under pressure or has a load applied to it, it develops stress is developed. When a solid is put under stress, it has the ability to deform. This deformation is called Strain. The stress is the pressure per unit area of the material, and the resulting strain is the deformation that occurs as a result of this stress. Strain and stress are strongly intertwined because strain occurs solely as a result of stress.
Stress Definition
Stress is defined as the force per unit area generated within materials as a result of externally applied forces, unequal heating, or persistent deformation. The measure of stress and its impact on a material allows us to interpret its elastic, plastic, or fluidic behaviour. The unit for stress is Nm-2. The dimension of stress is ML-1T-2. Stress is a scalar quantity.
In physical terms, stress is given as the ratio of applied force and the area onto which stress is applied. Physically we can say that it is equivalent to pressure, however, there exist some differences between stress and pressure.
σ = F/A
Where,
- σ = Stress
- F = Force applied
- A = Area of the surface
Unit of Stress: The unit of stress is N/m2 or Pascal(Pa). The larger units are Megapascal (MPa) and Gigapascal (GPa).
Dimensional Formula of Stress: The Dimensional Formula of Stress is M1L-1T-2
Now we will briefly look into types of stress
Types of Stress
Stress is classified majorly into two types in the manner they are applied.
- Normal Stress
- Shear Stress
Normal Stress
Normal Stress as the name suggests acts perpendicular to the cross-sectional area of the surface of the material. It can be classified into two categories
- Longitudinal Stress
- Bulk Stress
Longitudinal Stress
The stress that acts along only one axis of the body of the material is called Longitudinal Stress. It is further classified into the following two types:
- Tensile Stress
- Compression Stress
Tensile Stress: When a body is extended from two sides along a line of the axis that results in the elongation of the object then it is called Tensile Stress. It is analogous to the stretching of a material.
Compression Stress: When a body is compressed from two sides along a line of the axis that results in the shortening of the object then the stress acting on the body is called Compression Stress.
Bulk Stress
The stress acts along the axis of the body such that there is deformation in the shape of the body in all directions, then it is called Bulk Stress.
Shear Stress
The stress that acts parallel to the surface of an object, then it is called Shear Stress. Shear Stress causes tangential deformation in the shape of the object.
Now, we will learn briefly about Strain and its types.
Strain Definition
Strain is defined as the amount of distortion experienced by the body in the direction of force compared to the original dimension of the object. It gives an idea that how much deformation a material can undergo on applying stress. Strain defines the relative change in the shape of an object.
In mathematical terms, the strain developed in a body is given by the ratio of change in the dimension of the object to the original dimension of the object.
ϵ = (Lf - Li)/Li = δL/Li
Where,
ϵ = Strain
Li = Initial Length
Lf = Final Length
δL = Change in length
Unit of Strain: Strain has no unit as it is the ratio of the same physical quantities.
Dimensional Formula of Strain: Since strain has no unit, thus it has no dimensional formula.
Types of Strain
Strain is basically of three types:
- Longitudinal Strain
- Volumetric Strain
- Shear Strain
Longitudinal Strain
The ratio of deformation in the length of the object due to tensile or compressive stress is called Longitudinal Strain. If the strain is negative then the strain is compressive and if the strain is positive then the strain is tensile in nature.
Volumetric Strain
The ratio of change in volume to the original volume of the object is called volumetric strain. It is caused due to bulk stress.
Shear Strain
It is given as the ratio of perpendicular length to the lateral displacement of the surface of the object.
Now, we will learn the difference between Stress and Strain in a tabular form.
Difference Between Stress and Strain
The difference between stress and strain is tabulated below:
Stress | Strain |
|---|
The deforming force per unit area of the item is defined as stress. | Strain is defined as the amount of distortion experienced by the body in the direction of force application divided by the body's original dimensions |
The dimension is ML-1T-2 | It has no dimensions. |
The unit for stress is Nm-2 | It has no unit. |
The formula for stress is: σ = F/A | The formula for strain is: ϵ = δl/L |
It is denoted by σ | It is denoted by ϵ |
Longitudinal stress, shear stress, and volumetric stress are the different types of stress. | Longitudinal strain, shear strain, and volumetric strain are the three types of strain. |
Stress can be applied to the object without producing strain. | Without stress, the strain cannot occur. |
Stress and Strain are two related concepts as they go hand in hand in determining the strength of a material. However, they are physically different quantities and we have learned it in above mentioned topics in detail. Let's summarize it in below mentioned points.
- Stress refers to the force per unit area that is applied to a material or structure, and is usually expressed in units of pressure such as pascals (Pa) or pounds per square inch (psi). Stress can be caused by external forces such as weight or pressure, or by internal forces such as tension or compression. Stress can cause deformation or failure of the material or structure if it exceeds the material's yield strength.
- Strain, on the other hand, refers to the measure of deformation or elongation that occurs in a material or structure due to stress. Strain is usually expressed as a dimensionless quantity or percentage, and can be caused by various types of stress such as tension, compression, or shear. Strain can be measured using different techniques such as strain gauges or extensometers.
- In summary, stress and strain are related but distinct concepts that describe different aspects of the mechanical behavior of materials and structures. Stress refers to the force per unit area that is applied to a material, while strain refers to the measure of deformation or elongation that occurs in response to stress.
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Sample Problems on Difference Between Stress and Strain
Problem 1: A 2 mm diameter nylon thread is tugged by a force of 100 N. Determine the level of stress.
Solution:
Given,
Force= 100N
diameter (d)= 2mm= 0.002 m
radius (r)= diameter(d)/2
= 0.002/2
= 0.001 m
To Find: Stress
Area (A)= πr2
= (3.14)(0.001)2
Area (A)= 3.14 ×10-6m2
Stress(σ)= F/A
= 100 N/3.14×10-6m2
= 31.5×106 N/m2
So, the stress is 31.5×106 N/m2
Problem 2: A force pulls a cord with an original length of 100 cm. The cord length has changed by 2 mm. Identify the strain
Solution:
Given,
Original length(L)= 100 cm= 1m
Change in length(δl)= 2 mm= 0.002 m
To Find: Strain
Strain(ϵ)= Change in length(δl)/Original length(L)
= 0.002 m/1 m
= 0.002
So, the stain is 0.002
Problem 3: A concrete slab with a 3 m3 unit area can sustain a mass of 30000 kg. Determine stress. Acceleration due to gravity(g) is 10 m/s2.
Solution:
Given,
Unit Area(A) = 3 m3.
Weight = 30000 kg
Acceleration due to gravity(g) = 10m/s2
Force = mg
= (30000)(10)
= 300000 N
To Find: Stress
Stress(σ) = F/A
= 300000 N/ 3 m3
= 1×105 N/m2
So, the stress is 1×105 N/m2
Problem 4: Original length is 100 cm and the change in length is 5 mm. Determine the strain.
Solution:
Given,
Original length(L) = 100 cm = 1 m
Change in length( δl) = 5 mm = 0.005 m
To Find: Strain
Strain(ϵ) = Change in length(δl)/ Original length(L)
= 0.005 m/1 m
= 0.005
So, the strain is 0.005
Problem 5: The initial length of a 4 mm diameter string was 2 m. A force of 200 N is applied to the string. If the spring's final length is 2.02 m. Determine stress and strain.
Solution:
Given,
Force(F) = 200N
Original length(L) = 2 m
Change in length(δl) = 2.02 m - 2m = 0.02 m
Diameter(d) = 4 mm = 0.004 m
Radius(r) = diameter/ 2
= 0.004/2
= 0.002 m
Area(A) = πr2
= (3.14)(0.002)2
= 12.56×10-6 m2
To Find: Stress and Strain
Stress(σ) = F/A
= 200 N/12.56×10-6 m2
= 15.92×106 N/m2
Strain(ϵ) = Change in length(δl)/Original Length(L)
= 0.02 m/2m
= 0.01
So, the stress is 15.92×106 N/m2 and the strain is 0.01.
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