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Strain and modulus of elasticity

In the linear elastic range, stress and strain are proportional. The slope in the $\sigma$ – $\varepsilon$ diagram is the modulus of elasticity $E$ , a material property showing how stiff the material is. Steel has a much higher $E$ than aluminum or plastic.

\varepsilon = \sigma/E

strain from Hooke's law

Symbols

$\varepsilon$	strain
$\sigma$	stress	Pa
$E$	modulus of elasticity	Pa

Example

Steel, $E = 210$ GPa, $\sigma = 210$ MPa:

$\varepsilon = 210/210\,000 = 0.001 = 1$ ‰.

E

is a material constant and does not depend on the shape or size of the cross-section.

Practise stress and sizing for free →

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Part of Machine Design: Stress and sizing.