Thermal expansion calculator
Materials expand roughly linearly with temperature, and the area and volume coefficients follow from the linear one.
K
per K
Steel 12e-6; aluminium 23e-6; concrete 12e-6; glass 9e-6; PVC 52e-6.
Change in length
0.0048mm
- New length
- 10.0048
- Strain
- 0.000 48
- Change in area
- 0.096 %
- Change in volume
- 0.144 %
- Stress if fully restrained, steel
- 96.00 MPa
Show the working
- Original length = 10
- Temperature change = 40
- Linear expansion coefficient = 0.000 012
- Change in length = 10 * 0.000 012 * 40 = 0.0048
- New length = 10 + 0.0048 = 10.0048
- Strain = 0.000 012 * 40 = 0.000 48
- Change in area = 2 * 0.000 012 * 40 * 100 = 0.096
- Change in volume = 3 * 0.000 012 * 40 * 100 = 0.144
- Stress if fully restrained, steel = 0.000 012 * 40 * 200e9 / 1e6 = 96
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- delta L = L alpha delta T
- area coefficient is about 2 alpha, volume about 3 alpha
- restrained stress = E alpha delta T
Ten metres of steel over a 40 K swing moves nearly 5 mm. Restrain it and you get 96 MPa of stress instead, which is why rails and bridges need expansion joints.