# Difference Between Stress and Strain

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.

### Stress Formula

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.

Ïƒ = F/A

Where,

• Ïƒ = 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.

### Strain Formula

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.

Ïµ = (Lf – Li)/Li = Î´L/Li

Where,

Ïµ  = Strain
Li = Initial Length
Lf = Final Length
Î´L = 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: Ïƒ = F/A

The formula for strain is: Ïµ =  Î´l/L

It is denoted by Ïƒ

It is denoted by Ïµ

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 as two Related but Distinct Concepts

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.

1. 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.
2. 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.
3. 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.

## 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

= 0.002/2

= 0.001 m

To Find: Stress

Area (A)= Ï€r2

= (3.14)(0.001)2

Area (A)= 3.14 Ã—10-6m2

Stress(Ïƒ)= F/A

= 100 N/3.14Ã—10-6m2

= 31.5Ã—106 N/m2

So, the stress is 31.5Ã—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(Î´l)= 2 mm= 0.002 m

To Find: Strain

Strain(Ïµ)= Change in length(Î´l)/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(Ïƒ) = F/A

= 300000 N/ 3 m3

= 1Ã—105 N/m2

So, the stress is 1Ã—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( Î´l) = 5 mm = 0.005 m

To Find: Strain

Strain(Ïµ) = Change in length(Î´l)/ 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(Î´l) = 2.02 m – 2m = 0.02 m

Diameter(d) = 4 mm = 0.004 m

= 0.004/2

= 0.002 m

Area(A) = Ï€r2

= (3.14)(0.002)2

= 12.56Ã—10-6 m2

To Find: Stress and Strain

Stress(Ïƒ) = F/A

= 200 N/12.56Ã—10-6 m2

= 15.92Ã—106 N/m2

Strain(Ïµ) = Change in length(Î´l)/Original Length(L)

= 0.02 m/2m

= 0.01

So, the stress is 15.92Ã—106 N/m2 and the strain is 0.01.

## FAQs on Difference between Stress and Strain

### Q1: What is Stress?

Stress is the force acting per unit area of the object.

### Q2: What is the Formula of Stress?

The formula of stress is Ïƒ = F/A

Where,

Ïƒ = Stress
F = Force applied
A = Area of the surface

### Q3: What is Unit of Stress?

The unit of stress is N/m2 or Pascal(Pa).

### Q4: What are the different types of Stress?

The different types of stress are Normal Stress, Longitudinal Stress which includes Tensile Stress and Compression Stress, Bulk Stress, Shear Stress, etc.

### Q5: What is Strain?

Strain is the measure of deformation achieved by applying stress on an object. It is given as the ratio change in dimension to the original dimension of the object.

### Q6: What is the Formula of Strain?

The formula for strain is given by Ïµ = (Lf – Li)/Li = Î´L/Li

Where,

Ïµ  = Strain
Li = Initial Length
Lf = Final Length
Î´L = Change in length
L= Original length

### Q7: What are the differences between Stress and Strain in Physics?

Stress is the force acting per unit area of the object while strain is the ratio of the change in dimension of the object to the original dimension of the object. Stress is equivalent to Pressure in physical terms and its unit is Pascal while strain is a ratio of change in dimension to the original dimension, hence it has no units.

### Q8: What is the difference between Plane Stress and Plain Strain?

Plane Stress is a situation when the value of normal stress is zero and the component of shear stress perpendicular to the direction of the applied load is assumed to be zero. Plane Stress is an approximation based on assumption. Plane Strain refers to the distortion in the object perpendicular to the plane of the object. Unlike Plane Stress which is an approximation, Plane Stress provides accurate solutions.

### Q9: What is the difference between Shear Stress and Shear Strain?

Shear stress is the stress applied parallel to the plane of the object that causes lateral distortion in the object while shear strain is the measurement of lateral strain in terms of tanÎ¸. Shear Strain is given as tanÎ¸ = Lateral Distortion/Perpendicular height.

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