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Stress and strain

Stress is force per area, and strain is the relative change in length. Hooke's law states that the two are proportional for an elastic material, with the modulus of elasticity $E$ as the ratio. This is the basis of almost all sizing calculations.

\sigma = F/A

normal stress

\varepsilon = \Delta L/L

strain

\sigma = E\varepsilon

Hooke's law

Symbols

$\sigma$	normal stress	Pa
$F$	axial force	N
$A$	cross-sectional area	m²
$E$	modulus of elasticity	Pa

Example

A bar with $A = 100$ mm², $F = 10$ kN in tension:

$\sigma = 10\,000/100 = 100$ N/mm² $= 100$ MPa.

Hooke's law only holds below the yield point – beyond that the relation is no longer linear.

Practise stress and strain for free →

Poisson's ratio →

Part of Strength of Materials: Stress and strain.