Free Engineering Tool
Pipe Thermal Expansion & Flexibility Calculator
Calculate thermal expansion, required expansion loop dimensions, and thermal stress for piping systems using the guided-cantilever approximation — a simplified screening method; full flexibility analysis per EN 13480 / ASME B31.3 requires pipe stress software.
Results
Thermal Expansion
The total thermal expansion of a pipe run is:
- α — coefficient of thermal expansion (µm/m/°C)
- L — pipe length (m)
- ΔT — temperature change (°C)
Expansion Loop Sizing
The required expansion loop leg length to absorb the expansion without exceeding allowable stress:
- E — elastic modulus (MPa)
- D — pipe outside diameter (mm)
- Δ — thermal expansion to be absorbed (mm)
- Sa — allowable stress range (MPa)
This is the guided-cantilever approximation (bending stress σ = 3·E·D·Δ/L² set equal to Sa), assuming one loop leg absorbs the full expansion. It is conservative for screening; it is not a full code flexibility analysis.
Guided Cantilever Method
The thermal stress if the pipe is rigidly fixed at both ends (fully restrained):
CTE Reference Table
| Material | α (µm/m/°C) | E (GPa) |
|---|---|---|
| Carbon Steel | 12.0 | 200 |
| SS 304 | 17.3 | 193 |
| SS 316 | 16.0 | 193 |
| Copper | 16.5 | 117 |
| Inconel 625 | 12.8 | 207 |
| Titanium Gr.2 | 8.6 | 105 |
Given: L = 30 m, CS (α = 12.0, E = 200 GPa = 200,000 MPa), ΔT = 180°C, OD = 168.3 mm, Sa = 138 MPa
Δ = 12.0 × 30 × 180 / 1000 = 64.8 mm
Lloop = √(3 × 200,000 × 168.3 × 64.8 / 138) = √(4.74 × 10⁷) ≈ 6,886 mm ≈ 6.9 m
⚠️ Note: This is a simplified guided cantilever calculation. Actual piping flexibility analysis requires considering branch connections, multiple directional changes, support locations, and should be performed with pipe stress analysis software for critical systems.
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Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
