Stress & Strain
Stress & Strain
- Extension alone cannot compare materials fairly. A long wire usually extends more than a short wire, and a thin wire is affected more than a thick wire.
- Stress corrects for cross-sectional area. Strain corrects for original length.
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Stress: force spread over area
The same force is more concentrated in a thinner wire. Stress measures the tensile force per unit cross-sectional area.
Definition
1 markWhat is meant by tensile stress?
Model answer: The tensile force per unit cross-sectional area.
Symbols
- = tensile stress (Pa)
- = tensile force (N)
- = cross-sectional area perpendicular to the force (m²)
- With force fixed, a smaller area gives a larger stress.
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- For a circular wire, measure its diameter and use.
Strain: extension compared with original length
An extension of 1 mm is a much larger change for a 10 mm sample than for a 2 m wire. Strain measures the fractional increase in length.
Definition
1 markWhat is meant by tensile strain?
Model answer: The extension divided by the original length.
Symbols
- = tensile strain (no unit)
- = extension (m)
- = original length (m)
Strain has no unit because it is a length divided by a length. Both lengths must use the same unit before division.
Worked example
Calculate stress and strain separately
A wire has area and original length 4.0 m. A force of 18 N produces an extension of 1.4 mm.
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- Convert the extension: 1.4 mm = 1.4 × 10⁻³ m.
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Define strain. Then calculate the stress and strain for a 2.0 m wire of area when a 60 N force produces an extension of 1.0 mm. (9702/21/M/J/24 Q4(a))
Show worked answer
Strain is the extension divided by the original length.
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Common mistake