Hoop Stress
Engineering fundamentals for pipeline design
1. Thin-Wall Cylinder Theory
Internal pressure in a pipe creates circumferential (hoop) stress in the pipe wall. This stress acts perpendicular to the pipe axis and is the primary design consideration for pressure containment.
π Hoop Stress in Pipe Cross-Section
Cross-sectional view of pipe showing: Internal pressure P acting radially outward on inner wall, hoop stress Ο_h acting circumferentially within the pipe wall (shown as tensile arrows in wall thickness), dimensions labeled (D = outside diameter, t = wall thickness). Include force balance diagram showing pressure force balanced by wall tension.
Thin-Wall Assumption
The simplified Barlow formula applies when:
- D/t > 20 (diameter-to-thickness ratio)
- Stress is assumed uniform through wall thickness
- Most pipelines satisfy this criterion
Why hoop stress dominates: Hoop stress is exactly 2Γ the longitudinal stress in a closed cylinder. Pipeline design focuses on hoop stress because it's always the limiting factor.
Stress Components
| Stress Type |
Formula |
Ratio |
| Hoop (circumferential) |
Ο_h = PD / 2t |
1.0 |
| Longitudinal (axial) |
Ο_L = PD / 4t |
0.5 |
| Radial |
Ο_r β -P (inner) to 0 (outer) |
Negligible |
2. Barlow's Formula
The fundamental equation for hoop stress in thin-walled cylinders:
Barlow's Formula:
S = (P Γ D) / (2 Γ t)
Where:
S = Hoop stress (psi)
P = Internal pressure (psig)
D = Outside diameter (inches)
t = Wall thickness (inches)
Rearranged Forms
| Solve For |
Formula |
Use Case |
| Wall thickness |
t = PD / 2S |
Minimum wall for given pressure |
| Pressure |
P = 2St / D |
MAOP calculation |
| Stress |
S = PD / 2t |
Verify existing pipe |
Example Calculation
Given: 16" OD pipe, 0.375" wall, 1000 psig operating pressure
S = (1000 Γ 16) / (2 Γ 0.375)
S = 16,000 / 0.75
S = 21,333 psi
3. Design Factors
Pipeline codes limit allowable stress to a fraction of the pipe's Specified Minimum Yield Strength (SMYS). The design factor accounts for safety margins based on location and service.
Design Pressure Formula (49 CFR 192.105):
P = (2 Γ S Γ t Γ F Γ E Γ T) / D
Where:
S = SMYS (psi)
F = Design factor (0.40 β 0.72)
E = Longitudinal joint factor (0.60 β 1.00)
T = Temperature derating factor (1.00 for T β€ 250Β°F)
Design Factors by Location Class
| Class |
Description |
Factor (F) |
%SMYS |
| Class 1 |
Rural (β€10 buildings) |
0.72 |
72% |
| Class 2 |
Fringe areas (11β46 buildings) |
0.60 |
60% |
| Class 3 |
Suburban (>46 buildings) |
0.50 |
50% |
| Class 4 |
High-density/multi-story |
0.40 |
40% |
πΊοΈ Location Class Determination
Diagram showing pipeline centerline with 1-mile sliding window and 220-yard corridor on each side. Illustrate building count method within the rectangle. Show example with scattered buildings representing Class 1 (rural) vs. clustered buildings representing Class 3 (suburban). Label dimensions: 1 mile length, 440 yards total width (220 each side).
Common SMYS Values
| Grade |
SMYS (psi) |
Specification |
| B |
35,000 |
API 5L / ASTM A106 |
| X42 |
42,000 |
API 5L |
| X52 |
52,000 |
API 5L |
| X60 |
60,000 |
API 5L |
| X65 |
65,000 |
API 5L |
| X70 |
70,000 |
API 5L |
4. Applications
Pipeline Design
- New construction: Select wall thickness for design pressure + location class
- Uprating: Verify existing pipe can handle increased pressure
- Class change: Evaluate if pipe meets new class requirements
- Anomaly assessment: Calculate remaining strength with corrosion/defects
Design Example
Problem: Select wall thickness for 20" pipeline, 1000 psig MAOP, Class 1, X52 pipe
Given: D = 20", P = 1000 psig, S = 52,000 psi, F = 0.72, E = 1.0, T = 1.0
t = PD / (2 Γ S Γ F Γ E Γ T)
t = (1000 Γ 20) / (2 Γ 52,000 Γ 0.72 Γ 1.0 Γ 1.0)
t = 20,000 / 74,880
t = 0.267" β Select 0.312" (5/16") nominal
Wall thickness selection: Always round up to next standard wall thickness. Account for corrosion allowance and manufacturing tolerance (typically -12.5% on wall per API 5L).
5. Code Requirements
Applicable Codes
| Code |
Application |
| 49 CFR 192 |
Gas transmission & distribution (DOT/PHMSA) |
| 49 CFR 195 |
Hazardous liquids pipelines |
| ASME B31.8 |
Gas transmission & distribution (design code) |
| ASME B31.4 |
Liquid petroleum pipelines |
| API 5L |
Line pipe specification |
β Federal vs. Industry: 49 CFR 192/195 are federal regulations (mandatory). ASME B31.8/B31.4 are industry codes often referenced by regulations. When conflicts exist, federal regulations take precedence.
Key Requirements
- Maximum design factor: 72% SMYS (Class 1 gas)
- Hydrostatic test: Minimum 1.25Γ MAOP for 8 hours
- Manufacturing tolerance: -12.5% on wall thickness (API 5L)
- Corrosion allowance: Add to minimum calculated thickness
References
- 49 CFR Part 192 β Transportation of Natural Gas
- 49 CFR Part 195 β Transportation of Hazardous Liquids
- ASME B31.8 β Gas Transmission and Distribution Piping Systems
- API 5L β Line Pipe Specification
- ASME B31G β Manual for Determining Remaining Strength of Corroded Pipelines