Strain
The fractional change in dimension of a body due to deforming forces.
What is Strain?
The fractional change in dimension (length, volume, or shape) of a body due to deforming forces. It is a dimensionless quantity.
Key formula / rule: Longitudinal Strain
Key points
- Define strain and its three main types: longitudinal, volumetric, and shear strain.
- Calculate longitudinal, volumetric, and shear strain given appropriate parameters.
- Understand the dimensionless nature of strain and its implications.
- Differentiate clearly between stress and strain.
Common exam trap
Confusing strain with stress; stress is force per unit area, while strain is fractional deformation.
Definitions
- Term
Strain
- Meaning
The fractional change in dimension (length, volume, or shape) of a body due to deforming forces. It is a dimensionless quantity.
- Term
Longitudinal Strain
- Meaning
The ratio of the change in length (ΔL) to the original length (L₀) of a body when subjected to a deforming force along its length.
- Term
Volumetric Strain
- Meaning
The ratio of the change in volume (ΔV) to the original volume (V₀) of a body when subjected to a uniform deforming force (pressure) over its entire surface.
- Term
Shear Strain
- Meaning
The ratio of the relative displacement (Δx) of any layer to its perpendicular distance (L) from the fixed layer, or the angle (θ) through which a plane perpendicular to the fixed surface is turned, when a tangential deforming force is applied.
Learning objectives
Define strain and its three main types: longitudinal, volumetric, and shear strain.
Calculate longitudinal, volumetric, and shear strain given appropriate parameters.
Understand the dimensionless nature of strain and its implications.
Differentiate clearly between stress and strain.
Relate the concept of strain to the physical deformation of materials.
Formulae
- Name
Longitudinal Strain
- Note
ΔL is the change in length, L₀ is the original length.
- Expression
ε = ΔL / L₀
- Name
Volumetric Strain
- Note
ΔV is the change in volume, V₀ is the original volume.
- Expression
εᵥ = ΔV / V₀
- Name
Shear Strain
- Note
Δx is the relative displacement, L is the perpendicular distance from the fixed layer. θ is the angle of shear in radians (for small angles, tanθ ≈ θ).
- Expression
γ = Δx / L ≈ θ
Prerequisites
Basic understanding of force and pressure.
Concept of elasticity and deformation.
Understanding of stress (normal and tangential).
Knowledge of units and dimensions.
Basic geometry, especially angles.
Common mistakes
Confusing strain with stress; stress is force per unit area, while strain is fractional deformation.
Forgetting that strain is dimensionless and unitless.
Not converting angles to radians when calculating shear strain.
Incorrectly applying the formulas for different types of strain (e.g., using length change for volumetric strain).
Using inconsistent units for change in dimension and original dimension in calculations.
Keywords
Elasticity
Deformation
Longitudinal Strain
Volumetric Strain
Shear Strain
Dimensionless
Stress
Hooke's Law
Modulus of Elasticity
Practice preview
A metal rod of length 10 cm and diameter 1 cm is stretched by a force such that its length increases by 0.1 mm. What is the percentage strain?…
medium
Consider a wire of length 2 m and cross-sectional area 1 mm². When a load of 1 kg is suspended from it, the length increases by 0.5 mm. What is the longitudinal strain?…
medium
Which of the following is a dimensionless quantity?…
easy