Thermal Expansion Strain Calculator
Calculate the thermal strain and length change in a material due to a temperature difference.
Thermal Strain (epsilon)
0.001200
Thermal Strain (epsilon) vs Coefficient of Thermal Expansion (alpha)
Formule
## Thermal Expansion and Strain Materials expand or contract when their temperature changes. The thermal strain is proportional to the temperature change and the coefficient of thermal expansion (CTE). ### Formula **epsilon_thermal = alpha × delta_T** **delta_L = alpha × delta_T × L** where alpha is the CTE, delta_T is the temperature change, and L is the original length. If the component is constrained from expanding, a thermal stress develops: sigma = E × alpha × delta_T.
Exemple Résolu
A 1000 mm steel bar (alpha = 12 × 10⁻⁶/°C) heated by 100°C.
- 01epsilon = 12 × 10⁻⁶ × 100 = 0.0012 (0.12%)
- 02delta_L = 0.0012 × 1000 = 1.2 mm
- 03If constrained: sigma = 200000 × 0.0012 = 240 MPa
Questions Fréquentes
What are typical CTE values?
Steel: 11-13 × 10⁻⁶/°C, aluminum: 23 × 10⁻⁶/°C, copper: 17 × 10⁻⁶/°C, concrete: 10-12 × 10⁻⁶/°C, Invar alloy: 1.2 × 10⁻⁶/°C (designed for low expansion).
Why do expansion joints exist on bridges?
Bridges can be hundreds of meters long. Even small thermal strains create centimeters of movement. Expansion joints accommodate this movement; without them, thermal stresses would damage the structure.
Can thermal expansion cause yielding?
Yes. If a component is fully restrained, the thermal stress can exceed yield strength. For steel with yield at 250 MPa and alpha=12e-6, yielding starts at delta_T = 250000/(12×200000) ≈ 104°C.
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