Unrestrained Pipeline Stress Analysis B31.4 – Liquid

Introduction

Unrestrained pipes are unburied or spans where the pipe is bedded or supported beam. These could be designed or mother nature exposing the pipe due to flooding or other natural causes.

Allowable expansion stresses sustained and occasional loads that are greater than 80% stress. Thermal expansion greater than 75% of SMYS.

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=0.5S_H

S_p=0.5S_H

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

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 0.75ST
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
• Longitudinal Joint Type
• 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)
• Bending Moment (lbf-in)
• Axial Force (lbf)
• Is the Pipe Straight (Yes/No)
• i -In Plane Intensification Factor
• Nominal Bending Stress (psi) (Offline Calculation or Estimated Bending Stress)
• Stress due to Axial Load (psi) (Offline Calculation or Estimated Bending Stress)

Part 2: Outputs/Reports

Results

• Hoop Stress (psi)
• Allowable Hoop Stress (psi)
• Net Longitudinal Stress (psi)
• Allowable Net Longitudinal 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
• MMS Regulations
• USDA-SCS Modified (Permissible Velocity of Water and Soil Erodibility)
• FHWA-HEC
• Pipeline Rules of Thumb Handbook

FAQ