Length change from heating or cooling, with material coefficients and restrained stress.
Overrides the material above.
Positive for heating, negative for cooling.
Adds the stress if the part cannot move.
With I, adds a buckling check for a member held at both ends.
Use the weak axis.
1 for pinned ends, 0.5 for ends fully fixed against rotation. Leave empty for 1.
This is a screening figure, not a pipe-stress analysis. Pressure piping needs a stress check to its code. A long member held at both ends can buckle at a small fraction of its yield stress, so a yield check alone is not enough.
Example Result
Your result will appear here
The calculated result will appear here after you press Calculate.
Most materials grow when heated and shrink when cooled. Choose a material or enter its coefficient, then the length and the temperature change, to get the change in length. Add Young's modulus to see the stress if the part cannot move at all, and its yield strength to compare. Use a negative temperature change for cooling.
Choose metric or US units.
Pick a material, or enter a coefficient in the same temperature unit.
Enter the length and the temperature change, negative for cooling.
Add Young's modulus and yield strength to check a part that cannot move.
For a long member held at both ends, add its area and I to check buckling as well.
By O.E. — Partner, chairman of the board and CEO of a metal products manufacturer for 21 years; the company exports to 45 countries.
Drafted with AI assistance; calculations checked against primary sources and tested with the site's own code. About FlowUtil
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ΔL = α × L₀ × ΔT
α is the coefficient of linear expansion, L₀ the starting length and ΔT the temperature change. The answer takes the unit of L₀. For the idea behind it, see what thermal expansion is.
Match α to your temperature unit. A value per °C is 1.8 times a value per °F, so steel at 12 × 10⁻⁶/°C is 6.67 × 10⁻⁶/°F. Mixing them overstates growth by 80%. The thermal expansion converter switches between the two.
| Material | α (10⁻⁶/°C) | α (10⁻⁶/°F, ÷ 1.8) |
|---|---|---|
| Invar | 1.5 | 0.8 |
| Gray cast iron | 10.8 | 6.0 |
| Carbon steel | 10.8–12.5 | 6.0–6.9 |
| Concrete | 13–14 (varies, see below) | 7.2–7.8 |
| Copper | 16–16.7 | 8.9–9.3 |
| 304 stainless steel | 17.3 | 9.6 |
| Brass | 18–19 | 10–10.6 |
| Aluminium | 23 | 12.8 |
| PVC | 54–110 | 30–61 |
These are mean values near room temperature, and α rises with temperature. For concrete, the coarse aggregate sets the value, so use a measured figure on a project that depends on it.
α = 12 × 10⁻⁶/°C, L = 30 m, ΔT = 100 °C.
ΔL = 12 × 10⁻⁶ × 30,000 mm × 100 = 36 mm
The same run in other materials:
| Material | α | Growth over 30 m, 100 °C |
|---|---|---|
| Carbon steel, low end | 11 | 33 mm |
| Carbon steel | 12 | 36 mm |
| Carbon steel, high end | 13 | 39 mm |
| 304 stainless | 17.3 | 52 mm |
| Aluminium | 23 | 69 mm |
An alloy uncertainty of ±1 unit moves the result ±8%. The choice of material matters far more.
α = 6.67 × 10⁻⁶/°F, L = 1,200 in, ΔT = 100 °F.
ΔL = 6.67 × 10⁻⁶ × 1,200 × 100 = 0.80 in, or about 20.3 mm.
If both ends are fixed, the growth turns into stress:
σ = E × α × ΔT
For steel with E = 200 GPa and α = 12 × 10⁻⁶/°C:
| ΔT | Restrained stress |
|---|---|
| 25 °C | 60 MPa |
| 50 °C | 120 MPa |
| 100 °C | 240 MPa |
Mild steel of 235 MPa yield reaches yield at about 98 °C of restrained heating, whatever its length. Heating puts the part in compression, so a long slender member may buckle well before that. Cooling puts it in tension, and welds and bolts take the load. The stress does not depend on length, and full restraint is the worst case. Check E with the Young's modulus calculator. The strain itself is α × ΔT, which you can compare in the strain calculator.
This is a screening figure, not a pipe-stress analysis. Pressure piping needs a stress check to its code.
Compression has a second failure mode. A restrained bar reaches its Euler load when:
ΔT = π² × I ÷ (α × A × (K × L)²)
E cancels out. A 12 m steel bar with A = 2,000 mm² and I = 1,000,000 mm⁴, pinned at both ends, gets there after a 2.9 °C rise, at 6.9 MPa, far below a 355 MPa yield strength. Enter A and I above to run this check, and use the buckling load calculator for the load itself. Real supports give a little, and real bars start slightly bent, so treat the figure as a guide.
Different materials move apart. An aluminium hub on a 50 mm steel shaft gains (23 − 12) × 10⁻⁶ × 50 × 50 = 0.028 mm of clearance for a 50 °C rise, which can use up a tight fit from the ISO fits and tolerances chart.
For volume, ΔV ÷ V ≈ 3 × α × ΔT. That applies to solids that expand equally in every direction. Liquids have their own volumetric coefficient, so do not use 3α for oil or water.
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