Pipe Thermal Expansion and Restrained Force Calculator
Pipe changes length when its temperature changes. This tool shows the free growth in millimetres and, if the pipe cannot move, the axial stress and the force it pushes on anchors and equipment nozzles.
Your numbers
About 200 GPa for carbon steel, 193 GPa for 304, 190 GPa for duplex.
Your results
Simplified straight run values. Real systems have bends and supports that absorb growth. Use a full flexibility analysis for design. Coefficients are mean values and vary by alloy and temperature range.
Free growth (mm) vs operating temperature
Sweeps Operating temperature from -20 to 400, holding your other inputs fixed.
Keep design movement data with the assembly
Optional review of how to hold engineering notes against assemblies and routings in your ERP.
Optional. The tool and every export work without this. No spam.
How to use it
Enter the length of the straight run, the installation temperature and the operating temperature. Choose the material to set the mean coefficient of thermal expansion, then adjust the elastic modulus if needed. Give the pipe outside diameter and wall so the calculator can turn stress into force. The free growth tells you how much movement the system must absorb with loops, expansion joints or flexible routing. The restrained force shows the worst case if the pipe is anchored at both ends with no flexibility.
Formulas
Free expansion is dL = alpha x L x dT. Restrained thermal stress is sigma = E x alpha x dT, independent of length. Force is stress times metal area, where area = pi/4 x (OD squared - ID squared). For carbon steel, alpha near 12 x 10^-6 per degree C gives about 1.2 mm per metre per 100 C. Stainless steel grows about 40 percent more than carbon steel for the same temperature rise.
- Stress does not depend on length, but the movement does.
- Friction on supports reduces the movement but adds load.
- Cold springing can balance part of the growth at assembly.
Worked example
A 100 m carbon steel run heated from 20 C to 150 C grows 0.000012 x 100 x 1000 x 130 = 156 mm. If anchored fully, the stress would be 200,000 x 0.000012 x 130 = 312 MPa, higher than the allowable stress, and the force on a pipe of 219.1 mm OD with 8.18 mm wall is about 1,690 kN, roughly 170 tonnes. Any real design must absorb the 156 mm with bends or a loop.
Common mistakes
Applying a single coefficient across a very wide temperature span is an approximation, and design codes use tabulated expansion from the install temperature. Confusing the cold install temperature with 20 C is common on outdoor jobs. Do not assume supports are anchors: sliding shoes still add friction. For manufactured skids, record the design growth and movement limits on the drawing and in the ERP item notes so installation crews do not weld in an extra anchor.
Frequently Asked Questions
How much does steel pipe expand?
Carbon steel grows about 1.2 mm per metre for each 100 C of temperature rise. A 100 m run heated by 130 C grows roughly 156 mm. Stainless steel grows about 1.7 mm per metre per 100 C.
Why is restrained stress independent of length?
Because stress depends on strain, and strain is only the fractional length change from temperature. Length cancels. Length matters only for how much movement must be absorbed if the pipe is free.
Does the force exceed what anchors can take?
Fully restrained forces are usually very large, often well over a hundred tonnes for large pipe, which is why designers use flexibility, loops or expansion joints. The tool shows the extreme upper bound.
Which temperature should I use for installation?
Use the metal temperature at the moment the line is closed and restrained, not the average yearly temperature. For outdoor hot sites this can be 40 C or more, which reduces the net temperature rise.
If your skids and spools carry engineering notes in several systems, we can help you pull key design values into one ERP record per assembly.
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