Restrained Pipeline Stress Analysis – Gas

Introduction

Restrained pipes are typically buried with proper bedding. However, when settlement or subsidence occurs the longitudinal and combined stresses may be replaced with a strain limit of 2% in ASME B31.4

Yielding that does not impair the serviceability of the pipe. Local stresses caused by periodic or repetitive load resulting in fatigue. Unanticipated earthquakes vibration and thermal expansion.

Hoop Stress

S_H=\frac{PD}{2t}

S_H=\frac{PD}{2t}

Where:
𝑆_𝐻 − Hoop stress (psi)
𝑃 − Pipe internal pressure (psi)
𝐷 − Pipe outside diameter (in)
𝑡 − Pipe wall thickness (in)

Longitudinal Stress due to Internal Pressure

S_p=0.3S_H

S_p=0.3S_H

Where:
𝑆_𝑃 − Longitudinal stress due to internal pressure (psi)
𝑆_𝐻 − Hoop stress (psi)

Longitudinal Stress due to Thermal Expansion

S_T=E\alpha(T_1-T_2)

S_T=E\alpha(T_1-T_2)

Where:
𝑆_𝑇 − Longitudinal stress due to thermal expansion (psi)
𝛼 − Coefficient of thermal expansion (1/℉)
𝐸 − Elastic modulus of ambient temperature (psi)
𝑇₁ − Pipe Temperature at the time of installation (℉)
𝑇₂ − The warmest or coldest pipe operating temperature (℉)

Nominal Bending Stress

S_B=\frac{M}{Z}

S_B=\frac{M}{Z}

Where:
𝑆_𝐵 − Nominal bending stress (lb/in)
𝑀 − Calculated bending moment
𝑍 − Pipe section modulus (in³)

Stress due to Axial Loading

S_X=\frac{R}{A}

S_X=\frac{R}{A}

Where:
𝑆_𝑋 − Axial loading stress (lb/in)
𝑅 − External for axial component (lb)
𝐴 − Pipe metal cross sectional area (in²)

Net Longitudinal Stresses

S_L=S_P+S_T+S_B+S_X

S_L=S_P+S_T+S_B+S_X

Where:
𝑆_𝐿 − Net longitudinal stress in restrained pipe(psi)
Note: The maximum permitted value for 𝑆_𝐿 is 0.9ST
𝑆 − Specified minimum yield strength (psi)
𝑇 − Temperature derating factor

Combined Biaxial Stress

S_C=\sqrt{ S_L^2-S_LS_H+S_H^2 }

S_C=\sqrt{  S_L^2-S_LS_H+S_H^2   }

Where:
𝑆_𝐶 − Combined biaxial stress (psi)
Note: The maximum permitted value of 𝑆_𝐶 is 𝑘𝑆𝑇
𝑘 ≤ 0.9 − For load of long duration
𝐾 = 1.0 − For occasional nonperiodic loads of short duration
𝑆 − Specified minimum yield strength (psi)
𝑇 − Temperature derating factor

Case Guide

Part 1: Create Case

Input Parameters

• Nominal Pipe Size (in): (0.625” – 48”)
• Wall Thickness (in): (0.068”- >2”)
• Pipe grade: (24000psi-80000psi) (if unknown use Grade A 24000)
• Pipe Operating Temperature: (-70°F – 160°F)
• Pipe Internal Pressure
• Young’s Modulus of Elasticity: (29000000psi – 30000000psi)
• Poisson’s Ratio: (0.0 – 0.5)
• Thermal Expansion Coefficient (1/°F) : (0.0000022in/inF – 0.000012in/inF)
• T – Temperature Derating Factor
• Pipe Installation Temperature: (-70°F – 160°F)
• Nominal Bending Stress (psi) (Offline Calculation or Estimated Bending Stress)
• Stress due to Axial Load (psi) (Offline Calculation or Estimated Bending Stress)
• k – Load Factor: (1000psi @ 10’-1500psi @ 15’)

Part 2: Outputs/Reports

Results

• Hoop Stress (psi)
• Longitudinal Stress due to Internal Pressure (psi)
• Longitudinal Stress due to Thermal Expansion (psi)
• Net Longitudinal Stress (psi)
• Maximum Permitted Longitudinal Stress (psi)
• Combined Biaxial Stress (psi)
• Maximum Permitted Combined Biaxial Stress (psi)

References

• ASME B31.8 – Gas Transmission and Distribution Piping Systems
• API 5L, API 5LS and API 5LX – Specification of Pipe Grade
• ASTM – Various – Weld Joint Factor
• CFR Code Part 192
• USDA-SCS Modified (Permissible Velocity of Water and Soil Erodibility)
• FHWA-HEC
• Pipeline Rules of Thumb Handbook
• Timoshenko, S – Theory of Elasticity Anchor Force

FAQ