Notes : Stress and Strain: Types, Formulas, Units & Dimensions | Class 11 Physics for IIT JEE , NEET

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Stress and Strain are important concepts used to explain the deformation of solids when external forces act on them. When a body is subjected to a deforming force, its length, shape, or volume may change. The study of stress and strain helps us understand the elastic behaviour of materials.

What is Stress?

When an external deforming force acts on a body, internal restoring forces develop within the body to oppose the deformation. The restoring force acting per unit area is called Stress.

Definition of Stress

Stress is defined as the restoring force acting per unit area inside a body when an external deforming force acts on it.

Symbol of Stress

$ \sigma $

Formula of Stress

$ \sigma = \frac{F}{A} $

Where:

$ F $ = Restoring Force

$ A $ = Area of Cross-section

SI Unit of Stress

Pascal (Pa) or N m-2

Dimensional Formula of Stress

$ [ML^{-1}T^{-2}] $

Types of Stress

1. Longitudinal Stress

When the deforming force acts perpendicular (normal) to the cross-sectional area of a body, the stress produced is called Longitudinal Stress.

Longitudinal stress changes the length of the body.

Tensile Stress

When equal and opposite forces stretch a body and increase its length, the stress produced is called Tensile Stress.

Example: Stretching a wire by hanging a weight.

Symbol: $ \sigma_t $

Formula: $ \sigma_t = \frac{F}{A} $

Compressive Stress

When equal and opposite forces compress a body and decrease its length, the stress produced is called Compressive Stress.

Example: Compressing a spring.

Symbol: $ \sigma_c $

Formula: $ \sigma_c = \frac{F}{A} $

2. Shearing or Tangential Stress

When equal and opposite forces act parallel to the surface of a body, the stress produced is called Shearing Stress or Tangential Stress.

It changes the shape of the body without significantly changing its volume.

Example: Pushing the top cover of a thick book sideways while keeping the bottom fixed.

Symbol: $ \tau $

Formula: $ \tau = \frac{F_t}{A} $

Where $ F_t $ is the tangential force.

3. Hydraulic Stress

When a body is subjected to equal pressure from all directions, the stress developed is called Hydraulic Stress.

Hydraulic stress changes the volume of a body while its shape remains unchanged.

Example: A rubber ball immersed deep inside water.

Symbol: $ P $

Formula: $ P = \frac{F}{A} $

or

$ \sigma_h = P $

What is Strain?

The ratio of deformation produced in a body to its original dimension is called Strain.

Definition of Strain

Strain is the fractional change in the dimensions of a body produced by an external force.

Symbol of Strain

$ \varepsilon $

Formula of Strain

$ \varepsilon = \frac{\text{Change in Dimension}}{\text{Original Dimension}} $

Important Points

• Strain has no unit.

• Strain is a dimensionless quantity.

• Strain has no dimensional formula.

Types of Strain

1. Longitudinal Strain (Linear Strain)

When the length of a body changes due to tensile or compressive stress, the strain produced is called Longitudinal Strain.

Symbol: $ \varepsilon_l $

Formula:

$ \varepsilon_l = \frac{\Delta L}{L} $

Where:

$ \Delta L $ = Change in Length

$ L $ = Original Length

Example: Stretching a wire by hanging a weight.

2. Shearing Strain (Angular Strain)

When a tangential force changes the shape of a body, the strain produced is called Shearing Strain.

Symbol: $ \gamma $

Formula:

$ \gamma = \frac{\Delta x}{L} $

For small angular deformation:

$ \gamma = \tan\theta \approx \theta $

Where:

$ \Delta x $ = Lateral Displacement

$ L $ = Height of the Body

$ \theta $ = Angle of Shear

Example: Pushing the top cover of a book sideways.

3. Volume Strain (Cubical Strain)

When the volume of a body changes due to hydraulic pressure, the strain produced is called Volume Strain.

Symbol: $ \varepsilon_v $

Formula:

$ \varepsilon_v = \frac{\Delta V}{V} $

Where:

$ \Delta V $ = Change in Volume

$ V $ = Original Volume

Example: A rubber ball placed deep inside water.

Comparison of Stress and Strain

Stress: Restoring force per unit area.

Strain: Change in dimension per unit original dimension.

Stress: Has unit Pascal (Pa).

Strain: Has no unit.

Stress: Cause of deformation.

Strain: Measure of deformation.

Summary of Symbols

$ \sigma $ = Stress

$ \sigma_t $ = Tensile Stress

$ \sigma_c $ = Compressive Stress

$ \tau $ = Shearing Stress

$ P $ = Hydraulic Stress

$ \varepsilon $ = Strain

$ \varepsilon_l $ = Longitudinal Strain

$ \gamma $ = Shearing Strain

$ \varepsilon_v $ = Volume Strain

Very Short Answer Questions

1. What is stress?

Stress is the restoring force per unit area developed inside a body.

2. What is strain?

Strain is the ratio of deformation to the original dimension.

3. What is the SI unit of stress?

Pascal (Pa).

4. Why is strain dimensionless?

Because it is the ratio of two quantities having the same dimensions.

5. Name the three types of stress.

Longitudinal Stress, Shearing Stress and Hydraulic Stress.

Fill in the Blanks

1. Stress is restoring force per unit Area.

2. The SI unit of stress is Pascal.

3. Strain is a Dimensionless quantity.

4. Hydraulic stress changes the Volume of a body.

5. Shearing stress changes the Shape of a body.

True or False

1. Stress is dimensionless. False

2. Strain has no unit. True

3. Volume strain is equal to $ \frac{\Delta V}{V} $. True

4. Stress is measured in Pascal. True

5. Shearing stress changes shape. True

MCQs

1. Stress is defined as:

A. Force × Area

B. Force per unit area

C. Area per unit force

D. Change in volume

Answer: B. Force per unit area

2. The SI unit of stress is:

A. Joule

B. Newton

C. Pascal

D. Watt

Answer: C. Pascal

3. Which stress changes the shape of a body?

A. Longitudinal Stress

B. Hydraulic Stress

C. Shearing Stress

D. Tensile Stress

Answer: C. Shearing Stress

Conclusion

Stress and Strain explain how solids respond to external forces. Longitudinal stress and strain are associated with changes in length, shearing stress and strain with changes in shape, and hydraulic stress and volume strain with changes in volume. These concepts form the foundation of elasticity and are important for Class 11 Physics, JEE and NEET examinations.

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