1. Overview
When piping systems operate at temperatures different from installation conditions, thermal expansion creates stresses and forces that must be accommodated. Expansion loops are the most reliable and maintenance-free method of providing piping flexibility.
Above-Ground Pipelines
Expansion Loops
U-loops, Z-bends, and L-bends absorb thermal growth without mechanical joints.
Process Piping
B31.3 Flexibility
ASME B31.3 requires flexibility analysis for all process piping subject to thermal cycling.
Gas Transmission
B31.8 Requirements
Gas pipelines must accommodate expansion at compressor stations, meter runs, and river crossings.
Anchor Design
Force & Moment
Anchors must resist thermal forces that can exceed 100 tons for large-diameter pipe.
2. Thermal Expansion Theory
Thermal expansion is the tendency of materials to change length in response to temperature changes. The expansion is governed by the material's coefficient of linear thermal expansion.
Expansion Coefficients by Material
| Material | α (×10²&sup6; /°F) | Expansion per 100 ft per 100°F | E at 200°F (×10&sup6; psi) |
|---|---|---|---|
| Carbon Steel (A106-B) | 6.33 | 0.76 in | 29.0 |
| Stainless Steel 304 | 9.00 | 1.08 in | 27.6 |
| Stainless Steel 316 | 8.85 | 1.06 in | 27.4 |
| Chrome-Moly (P11) | 5.97 | 0.72 in | 29.5 |
Example Calculation
Thermal Stress When Restrained
If a pipe is fully restrained (both ends anchored rigidly with no flexibility), the thermal expansion creates compressive stress:
3. ASME B31.3 Flexibility Criteria
ASME B31.3 paragraph 319.4.1 provides both simplified screening criteria and detailed analysis requirements for piping flexibility.
Simplified Flexibility Criterion
Allowable Stress Range
Stress Range Reduction Factor (f)
| Number of Cycles (N) | f Factor | Application |
|---|---|---|
| ≤ 7,000 | 1.0 | Most pipelines (1 cycle/day for 20 years) |
| 7,000 – 14,000 | 0.9 | Frequent cycling systems |
| 14,000 – 22,000 | 0.8 | Daily cycling for 40+ years |
| 22,000 – 45,000 | 0.7 | Multiple daily cycles |
| 45,000 – 100,000 | 0.6 | High-frequency thermal cycling |
| > 100,000 | 0.5 | Requires fatigue analysis |
4. Guided Cantilever Method
The guided cantilever method is a classical approximation for sizing expansion loop legs. It models each offset leg as a cantilever beam deflected by the thermal expansion, and calculates the minimum leg length to keep bending stress within the allowable range.
Derivation
The guided cantilever model treats the expansion loop leg as a beam fixed at one end (anchor) and guided at the other end (where it connects to the straight run). The deflection equals the thermal expansion, and the maximum bending stress must not exceed the allowable stress range.
Anchor Forces and Moments
Example: 8" CS Pipeline at 250°F
5. Loop Type Selection
The choice of expansion loop configuration depends on available space, thermal movement magnitude, pipe size, and routing constraints.
U-Loop (Full Expansion Loop)
The most common configuration for pipelines and process piping. Provides maximum flexibility per unit of developed pipe length. The loop extends perpendicular to the pipe run, absorbing axial thermal growth through bending of the offset legs.
Z-Bend (Offset Routing)
Uses two direction changes to create offset legs that absorb expansion. Each offset leg acts as a cantilever. Useful when the pipe route naturally includes offsets.
L-Bend (Direction Change)
Uses a single natural direction change (90-degree turn) to absorb expansion from one run into perpendicular movement. Limited flexibility but requires no additional pipe routing.
Lyre Loop (Circular Loop)
A circular loop that wraps the pipe around itself. Used in low-pressure systems and where vertical space is limited. Less common in midstream applications.
Configuration Comparison
| Loop Type | Flexibility | Space Required | Typical Application |
|---|---|---|---|
| U-Loop | Highest | Moderate to large | Above-ground pipelines, process piping |
| Z-Bend | Moderate | Uses existing routing offsets | Pipe racks, interconnecting piping |
| L-Bend | Low | Minimal (uses direction change) | Short runs, small-diameter piping |
| Lyre Loop | Moderate | Compact lateral, more vertical | Utility piping, low-pressure lines |
6. Stress Range Concepts
Understanding the distinction between sustained loads and displacement (thermal) loads is fundamental to piping flexibility analysis.
Primary vs. Secondary Stress
| Characteristic | Primary (Sustained) | Secondary (Displacement) |
|---|---|---|
| Source | Pressure, weight, external loads | Thermal expansion, anchor settlement |
| Nature | Load-controlled (force-driven) | Displacement-controlled (strain-driven) |
| Failure mode | Gross deformation or rupture | Fatigue (cyclic yielding) |
| Self-limiting? | No — continues until rupture | Yes — yielding redistributes stress |
| Allowable | S_h (basic allowable at temp) | S_A = f(1.25S_c + 0.25S_h) |
Shakedown Concept
When a piping system first heats up, thermal stresses may exceed the material yield strength at localized points (elbows, branch connections). This causes plastic deformation that creates residual stresses. On subsequent cycles, the system operates within an elastic range equal to twice the yield strength. This process is called "shakedown."
Stress Ratio Interpretation
| Stress Ratio (σ/Sa) | Status | Action Required |
|---|---|---|
| < 0.50 | Very flexible | Consider reducing loop size to save material/space |
| 0.50 – 0.80 | Good design range | Optimal balance of flexibility and economy |
| 0.80 – 1.00 | Near limit | Acceptable but verify with detailed analysis |
| > 1.00 | Overstressed | Increase loop size, add expansion joints, or reduce anchor spacing |
7. Practical Considerations
Installation Temperature
The temperature at which the piping is assembled and welded into final position determines the "zero-stress" reference point. All thermal expansion is measured from this temperature.
Support Spacing and Types
| Support Type | Function | Location |
|---|---|---|
| Anchor | Fixed point preventing all movement | At equipment nozzles, segment boundaries |
| Guide | Allows axial movement, prevents lateral | Along straight runs between anchors |
| Slide support | Supports weight, allows all horizontal movement | At expansion loop legs |
| Spring hanger | Supports weight while allowing vertical movement | Where vertical thermal movement is significant |
Guide Spacing Near Expansion Loops
When Guided Cantilever Is Not Sufficient
The guided cantilever method should be used for preliminary sizing only. Detailed computer analysis (CAESAR II, AutoPIPE, or equivalent) is required for:
- Multi-branch piping systems with complex routing
- Systems with multiple temperature zones
- Equipment nozzle load compliance (API 610, API 617)
- Systems with large-diameter thin-wall pipe (D/t > 100)
- Piping connected to rotating equipment (pumps, compressors, turbines)
- Cyclic service where fatigue life must be evaluated
- Stress ratio > 0.8 from guided cantilever screening
Expansion Joint Alternatives
When space constraints prevent adequate expansion loops, mechanical expansion joints may be considered. However, they have significant drawbacks compared to loops.
| Factor | Expansion Loop | Bellows Expansion Joint |
|---|---|---|
| Maintenance | None | Periodic inspection required |
| Service life | Indefinite (same as pipe) | Limited (fatigue life of bellows) |
| Leak potential | None (all-welded) | Bellows can fatigue-crack |
| Space | Large (loop legs extend laterally) | Compact (inline) |
| Anchoring | Standard pipe anchors | Requires main anchors and guides |
| Cost | Pipe and fittings only | Expensive specialty item |
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