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Thermal stress

A bar that is heated wants to expand, but if it is fixed at both ends, the expansion is prevented. This creates stress even with no external load. The more the material "wants" to expand ( $\alpha$ ) and the stiffer it is ( $E$ ), the larger the stress.

\sigma = E\alpha\Delta T

stress from prevented thermal expansion

Symbols

$\alpha$	coefficient of thermal expansion	1/K
$\Delta T$	temperature change	K
$E$	modulus of elasticity	Pa

Example

A steel bar ( $E = 210$ GPa, $\alpha = 12\cdot10^{-6}$ /K) heated by 40 K:

$\sigma = 210\,000\cdot 12\cdot10^{-6}\cdot 40 \approx 100.8$ MPa.

Sign: heating a fixed bar gives compressive stress, cooling gives tensile stress.

Practise stress and strain for free →

← Poisson's ratio · Stress concentration →

Part of Strength of Materials: Stress and strain.