Stress vs Strain Explained Simply (Strength of Materials)

 

Introduction

In mechanical engineering, Strength of Materials (SOM) is one of the most important core subjects. Among all its topics, stress and strain form the foundation. Almost every concept in mechanical engineering—such as elasticity, deformation, bending, torsion, and failure of materials—starts with understanding stress and strain.

Many students get confused between stress and strain because both are related to force and deformation. But once you understand their definitions, formulas, and differences clearly, the topic becomes very easy.

In this article, we will explain stress vs strain in a simple and beginner-friendly way, covering:

• Definitions

• Types

• Formulas

• Units

• Stress-strain curve

• Real-life examples

This guide is perfect for mechanical engineering students, especially for exams, interviews, and concept clarity.

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What Is Stress?

Stress is defined as the internal resisting force per unit area developed inside a material when an external force is applied.

Simple Definition

Stress is the force applied on a material divided by its cross-sectional area.

Formula of Stress

$$\text{Stress} (\sigma) = \frac{\text{Force (F)}}{\text{Area (A)}}$$

Unit of Stress

• SI Unit: Pascal (Pa)

• Commonly used: N/mm² or MPa

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Real-Life Example of Stress

When you pull a rubber band with your hands:

• Your hands apply force

• The rubber band resists that force internally
  That internal resistance is called stress.

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Types of Stress

Stress is classified based on how the force acts on the material.

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1. Tensile Stress

• Occurs when a material is pulled

• Causes elongation

Example:
Stretching a steel rod

Formula:

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

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2. Compressive Stress

• Occurs when a material is pushed

• Causes shortening

Example:
Column supporting a building

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3. Shear Stress

• Occurs when force acts parallel to the surface

Example:
Cutting a paper using scissors

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4. Bending Stress

• Occurs when a material bends under load

Example:
Beam carrying a load

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5. Torsional Stress

• Occurs when a material is twisted

Example:
Shaft transmitting power

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What Is Strain?

Strain is defined as the ratio of change in dimension to the original dimension of a material due to applied stress.

Simple Definition

Strain measures how much a material deforms when stress is applied.

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Formula of Strain

$$\text{Strain} (\varepsilon) = \frac{\text{Change in length}}{\text{Original length}}$$

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Unit of Strain

• No unit (dimensionless)

• Sometimes expressed as percentage (%)

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Real-Life Example of Strain

If a wire of length 1 m stretches by 1 mm:

• That change in length represents strain

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Types of Strain

Just like stress, strain also has different types.

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1. Tensile Strain

• Occurs due to tensile stress

• Increase in length

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2. Compressive Strain

• Occurs due to compressive stress

• Decrease in length

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3. Shear Strain

• Occurs due to shear stress

• Angular deformation

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4. Volumetric Strain

• Change in volume divided by original volume

Example:
Compression of a solid cube

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Difference Between Stress and Strain

This is a very important exam question.

Feature	Stress	Strain
Definition	Force per unit area	Deformation per unit length
Symbol	σ (Sigma)	ε (Epsilon)
Formula	F/A	ΔL/L
Unit	Pascal (Pa)	No unit
Depends on	Applied force	Material deformation

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Relationship Between Stress and Strain

Stress and strain are directly related up to a certain limit.

Hooke’s Law

Within the elastic limit, stress is directly proportional to strain.

$$\sigma \propto \varepsilon$$ $$\sigma = E \varepsilon$$

Where:

• E = Young’s Modulus

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Young’s Modulus

Young’s Modulus is the ratio of stress to strain within the elastic limit.

Formula

$$E = \frac{\text{Stress}}{\text{Strain}}$$

Unit

• Pascal (Pa)

Significance

• Measures stiffness of a material

• Higher value → stiffer material

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Stress-Strain Curve

The stress-strain curve is a graphical representation of stress vs strain.

Important Points on Stress-Strain Curve

1. Proportional Limit – Hooke’s law valid

2. Elastic Limit – Material returns to original shape

3. Yield Point – Permanent deformation begins

4. Ultimate Stress – Maximum stress

5. Breaking Point – Material failure

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Ductile vs Brittle Materials

• Ductile materials: Mild steel, copper

• Brittle materials: Glass, cast iron

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Elastic and Plastic Deformation

Elastic Deformation

• Temporary deformation

• Material returns to original shape

Plastic Deformation

• Permanent deformation

• Material does not return to original shape

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Factors Affecting Stress and Strain

• Type of material

• Magnitude of force

• Temperature

• Cross-sectional area

• Length of the material

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Applications of Stress and Strain

• Design of machine components

• Construction of buildings and bridges

• Automotive and aerospace industries

• Manufacturing and material testing

• Structural analysis

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Common Mistakes Students Make

• Confusing stress with strain

• Forgetting units

• Ignoring elastic limit

• Incorrect formula usage

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Numerical Example

A rod of cross-sectional area 100 mm² is subjected to a tensile force of 10 kN.

$$\sigma = \frac{10,000}{100} = 100 \text{ N/mm}^2$$

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FAQs on Stress and Strain

Is stress a force?

No. Stress is force per unit area.

Does strain have a unit?

No. Strain is dimensionless.

Why is stress important?

Stress helps determine whether a material can withstand applied loads.

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Importance of Stress and Strain in Exams

• Frequently asked in SOM, GATE, and university exams

• Forms base for bending, torsion, and columns

• Numerical problems are common

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Conclusion

Understanding stress vs strain is essential for mastering Strength of Materials. These concepts help engineers design safe, efficient, and reliable structures and machine components.

Once you clearly understand stress, strain, their types, and their relationship, advanced SOM topics become much easier.