Topic 7.210 min read
Deformation, Stress and Strain
An external force deforms a solid. Stress is force per unit area, while strain is the dimensionless fractional deformation in length, shape or volume.
Choose Your Level
Beginner Level
A force can stretch, compress, twist or squeeze a solid. Stress tells how strongly the force acts over an area, while strain tells how much the solid changes compared with its original size.
Recommended for Class 11
Deformation, Stress and Strain
Overview
An external force can change the shape, length or volume of a solid. Stress measures the force intensity producing deformation, while strain measures the resulting fractional deformation.
Learning Outcomes
- Define deformation, stress and strain.
- Calculate normal stress.
- Distinguish tensile, shear and volume stress.
- Calculate tensile, shear and volume strain.
- State SI units and dimensions.
- Relate microscopic slip and twinning to deformation.
Intermediate Level
Deformation in Solids
A solid has definite shape and volume because its particles are closely packed. When an external force changes its shape, length or volume, the solid is deformed. A spring stretches under tension, a rubber ball changes shape when squeezed, and a crystal may deform by slip of one plane over another or by twinning.
Stress
Stress is the internal resistance developed per unit cross-sectional area against deformation. In elementary calculations its magnitude equals the applied force divided by the area over which it acts.
- σ
- stress (Pa)
- F
- applied force (N)
- A
- cross-sectional area (m²)
The SI unit is newton per square metre, N m⁻², called the pascal (Pa).
Types of Stress
| Type | Direction of force | Main deformation | Example |
|---|---|---|---|
| Tensile or compressive stress | perpendicular to area | change in length | pulling or pressing a rod |
| Shear stress | tangential to area | change in shape | pushing the top face sideways |
| Volume stress | normal from all directions | change in volume | uniform fluid pressure on a body |
Strain
Strain is the quantitative measure of deformation: the change in a dimension divided by its original value. It is a ratio of like quantities, so it has no unit and no dimensions.
Tensile Strain
- ΔL
- change in length (m)
- L
- original length (m)
Shear Strain
A tangential force displaces one face relative to a fixed face. For small deformation, shear strain equals lateral displacement divided by the perpendicular separation of the faces.
- ΔX
- sideways displacement (m)
- Y
- distance from fixed face (m)
Volume Strain
- ΔV
- change in volume (m³)
- V
- original volume (m³)
Stress versus Strain
| Feature | Stress | Strain |
|---|---|---|
| Meaning | force per unit area | fractional deformation |
| Cause or response | cause/intensity | response |
| Unit | Pa | none |
| Dimensions | ML⁻¹T⁻² | dimensionless |
| Typical symbol | σ | ε |
Solved Examples
Example 1: Tensile Stress
A 600 N force pulls a wire of cross-sectional area 2.0 × 10⁻⁶ m². Find the tensile stress.
- F = 600 N
- A = 2.0 × 10⁻⁶ m²
σ = FA
σ = 6002.0 × 10⁻⁶
Final answer: σ = 3.0 × 10⁸ Pa
Example 2: Tensile Strain
A 2.0 m wire extends by 1.5 mm. Find tensile strain.
- L = 2.0 m
- ΔL = 1.5 mm = 1.5 × 10⁻³ m
ε = ΔL/L
ε = 1.5 × 10⁻³2.0
Final answer: ε = 7.5 × 10⁻⁴
Example 3: Volume Strain
A solid of volume 4.0 × 10⁻³ m³ decreases in volume by 2.0 × 10⁻⁶ m³. Find the magnitude of volume strain.
- V = 4.0 × 10⁻³ m³
- |ΔV| = 2.0 × 10⁻⁶ m³
|εV| = |ΔV|/V
|εV| = 2.0 × 10⁻⁶4.0 × 10⁻³
Final answer: |εV| = 5.0 × 10⁻⁴
Applications
- Designing cables, columns and beams.
- Testing construction materials.
- Estimating deformation of machine parts.
- Understanding crystal slip and twinning.
- Selecting materials for safe loads.
Common Mistakes
- Using total surface area instead of the loaded cross-sectional area.
- Failing to convert mm² or cm² to m².
- Giving strain a unit.
- Confusing shear displacement ΔX with separation Y.
- Using final length instead of original length in ΔL/L.
- Ignoring whether a question asks for signed strain or magnitude.
Short-Question Preparation
Q. Define deformation.
A. A change in shape, length or volume caused by an external force.
Q. Define stress and state its SI unit.
A. Stress is force per unit area, σ = FA; its unit is pascal.
Q. Why is strain dimensionless?
A. It is the ratio of a change in a dimension to the original same dimension.
Q. Name the three principal stress types.
A. Tensile or normal stress, shear stress and volume stress.
Q. Differentiate stress and strain.
A. Stress measures force intensity; strain measures fractional deformation.
Long-Question Preparation
Q. Explain stress and strain and their types.
A. 1. Define deformation. 2. Define stress as FA, with unit Pa and dimensions ML⁻¹T⁻². 3. Explain tensile, shear and volume stress. 4. Define strain as fractional deformation. 5. Write εL = ΔL/L, εs = ΔXY and εV = ΔV/V. 6. State that all strains are dimensionless. 7. Compare stress and strain and give examples.
Sticky Notes
- Stress = force/area.
- Stress unit = Pa.
- Strain = fractional change.
- Strain has no unit.
- Tensile: ΔL/L.
- Shear: ΔXY.
- Volume: ΔV/V.
60-Second Revision
Summary
Deformation is a force-produced change in a solid. Stress quantifies force per area, while strain quantifies the corresponding fractional change in length, shape or volume.
Ask-the-Tutor Modes
- Explain deformation simply.
- Compare stress and strain.
- Identify a stress type.
- Solve a stress numerical.
- Solve a strain numerical.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Definitions
- Stress types
- Strain types
- Units and dimensions
Important formulas
- σ = FA
- εL = ΔL/L
- εs = ΔXY
- εV = ΔV/V
Common exam traps
- Giving strain a unit
- Wrong area
Long question structure
Deformation → stress → stress types → strain → strain types → comparison.
Common Mistakes
Common Mistakes
- Mistake
Stress has units; strain does not.
- Mistake
Use the loaded cross-sectional area.
- Mistake
Convert all values to SI units.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
σ = FA
εL = ΔL/L
εs = ΔXY
εV = ΔV/V
Stress is force per area; strain is fractional deformation.
σ = FA; ε = change/original
- Definition
- Stress is force per area; strain is fractional deformation.
- Formula
- σ = FA; ε = change/original
- Example
- A thin wire experiences greater stress than a thick wire under the same force.
- Critical warning
- Do not give strain a unit.
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Exam Practice
Important Short Question
Q1. Define stress and strain.
Important Short Question
Q2. Name and explain types of stress.
Numerical Preparation
Q3. Calculate tensile stress and strain for a loaded wire.
Long Question Preparation
Q4. Explain stress, strain and their types.