Maximum Allowable Pipe Span Length – Gas

Introduction

API 1117 Movement of In-Service Pipelines using the free span between pipe supports. PLTB predicts stresses due to pipe movement of in-service and out of service lines as well as operating pipelines having unintended free spans.

This calculation is based on a four-span loaded beam. Because there are many variables during the construction movement of the pipe to the new lowered bedding position, this puts limits on the stresses that can be calculated.

Step 1. Variable Definition

Where:
𝐷 − Pipe Outside Diameter (in)
𝑊 − Weight (lb/ft), includes water weight if hydrostatic testing is specified
MAOP − Maximum Allowable Operating Pressure (psi)

MOP – Maximum Operating Pressure [psi],
SMYS − Specified Minimum Yield Strength or Grade of Steel (psi)
OP − Operating Pressure (psi)
𝑡 − Pipe Wall Thickness (in)
𝑆 − Section Modulus (in³)
𝐼 − Moment of Inertia (in⁴)
𝑒 − Modulus of Elasticity (29000 ksi)
𝐻 − Hoop Stress (psi)
𝐵 − Bending Stress (psi)
𝑀 − Bending Moment (ft−lb)
𝐿 − Span Length (ft)
𝑑 − Deflection (in)

MAOP=\frac{2St}{D}FET

MAOP=\frac{2*SMYS*t}{D}F.E.T

𝐹 − Design Factor
𝐸 − Longitudinal Joint Factor
𝑇 − Temperature Derating Factor

Important Notes:
Maximum Operating Pressure (MOP) must be less than Maximum Allowable Operating Pressure (MAOP)

Step 2: Calculate Hoop Stress

H=\frac{PD}{2t}

H=\frac{PD}{2t}

Where:
𝑃 = MOP

Step 3: Calculate Maximum Allowable Bending Stress

Solve Von Mises Equation through Quadratic Equation, and than solve for
Bending Stress B

B=\frac{-H^2-4H^2-(SF)^2}{2}

Von Mises Stress = percentSMYS = \sqrt{(H^2+HB+B^2)}

B^2 +BH+H^2+(percentSMYS)^2 = 0

Step 4: Calculate Maximum Allowable Bending Moment

I=\frac{\pi}{4}(\frac{D}{2})^2-(\frac{D}{2t})^4\~\ B=\frac{M_c}{I},\,where\,S=\frac{I}{c},\,therefore\,B=\frac{M}{S},\,and\,M=BS

I=\frac{\pi}{4}(\frac{D}{2})^2-(\frac{D}{2t})^4\\~\\ B=\frac{M_c}{I},\,where\,S=\frac{I}{c},\,therefore\,B=\frac{M}{S},\,and\,M=BS

Step 5: Calculate Maximum Span Length L, Due to Bending

M=\frac{WL^2}{8}\~\L=\sqrt{\frac{8M}{W}}

M=\frac{WL^2}{8}\\~\\L=\sqrt{\frac{8M}{W}}

Step 6: Calculate Maximum Span Length L, Due to Deflection

d=\frac{5WL^4}{384EI},\,Maximum \,deflection\, must\, be \~\ d<\frac{L}{360}

d=\frac{5WL^4}{384EI},\,\\~\\Maximum \,deflection\, must\, be \ d<\frac{L}{360}

Case Guide

Part 1: Create Case

Input Parameters

• Nominal Pipe Size
• Outside Diameter (in)
• Wall Thickness (in.)
• Pipe Grade
• Internal Diameter (in)
• SMYS (psi)
• Pipe Class
• Operating Pressure (psi)
• Joint Type (Dropdown)
• Longitudinal Joint Factor
• Youngs Modulus of Steel (psi)
• Poisson’s Ratio for Steel
• Temperature (°F)
• Temperature Derating Factor
• Average Unit Weight of Steel (Calculated)
• Pipe installed after November 11, 1970 (Y/N)
• Additional Uniform Load on Pipe
• Maximum Test Pressure (psi)
• Maximum Allowable % of SMYS for Testing (%)

Part 2: Outputs/Reports

Results

• MAOP – Maximum Allowable Operating Pressure (psig)
• Hoop/Barlow Stress (psi)
• Maximum Allowable Bending Stress (psi)
• Moment of Inertia (in⁴)
• Sections Modulus (in³)
• Bending Moment (lbf-ft)
• Maximum Pipe Span Length due to Bending (ft)
• Deflection (in)
• Maximum Pipe Span Length due to Deflection (ft)
• Maximum Allowable Pipe Span Length (ft)

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