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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 unrestrained thermal stress if the pipe is rigidly fixed at both ends:
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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