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📏 Pipe Thermal Expansion & Loop Sizing

Compute piping linear thermal expansion, design thermal stresses, anchor forces, and size L-bend, Z-bend, or U-loop expansion flexibilities per ASME B31.3.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
Pipe Thermal Expansion & Loop Sizing Tools
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📅 Released Jun 2026
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📝 Configuration

🔧 Pipe & Material
🌡️ Temperatures & Boundary
Key Equations:
ΔL = α·L·ΔT
σ = E·α·ΔT (fixed)
SA = f·(1.25·Sc + 0.25·Sh)
L_loop = √(3·E·OD·ΔL/SA)

📊 Results

Configure inputs and click Compute.

📘 Methodology

Thermal Expansion

Free expansion ΔL = α·L·ΔT, where α is the material's coefficient of thermal expansion. For constrained pipes (both ends anchored), the restrained thermal stress is σ = E·α·ΔT.

ASME B31.3 Allowable

The allowable displacement stress range SA = f·(1.25·Sc + 0.25·Sh), where Sc and Sh are basic allowable stresses at cold and hot temperatures, and f is the stress range reduction factor for cyclic conditions.

Expansion Loops

When σ exceeds SA, an expansion loop or expansion joint is required. The approximate loop leg length is L_loop = √(3·E·D·ΔL/SA). For critical applications, formal flexibility analysis per B31.3 Appendix D is recommended.

📘 Calculation Methodology: Thermal Pipe Expansion & U-Loop Sizing

Mathematical Model & Theory

Piping networks expand and contract under operating temperature variations. Unconstrained thermal growth is calculated via linear expansion coefficient $\alpha$, sized for flexible U-loops:

$$\Delta L = \alpha \cdot L \cdot (T_{op} - T_{install}), \quad L_{loop} = C \sqrt{D_{od} \cdot \Delta L} \quad (\text{Kellogg Method})$$
$$\text{Anchor Force: } F_{anchor} \le F_{allowable}$$

Assumptions

  • Uniform pipe metal temperature throughout system.
  • ASME B31.1 / B31.3 allowable displacement stress range criteria.

Academic References

  1. ASME B31.3-2020: Process Piping Design Code.
  2. Kellogg, M. W.: Design of Piping Systems, John Wiley & Sons.

Worked Engineering Example

Problem Statement:
A 100 m long carbon steel steam line ($\alpha = 12.5 \times 10^{-6}\text{ m/m}\cdot\text{K}$) is installed at $20^\circ\text{C}$ and operates at $220^\circ\text{C}$. Calculate total thermal expansion growth.

Step-by-step Solution:
1. Temperature delta $\Delta T = 220 - 20 = 200\text{ K}$.
2. $\Delta L = 12.5 \times 10^{-6} \times 100\text{ m} \times 200 = 0.250\text{ m} = 250.0\text{ mm}$.
Final Result:
Total linear thermal expansion is $\Delta L = \mathbf{250.0\text{ mm}}$ (requires expansion loops or bellows joints).