Introduction
The following analysis determines stresses and deflections in pipelines at the transition from below ground (restrained) to above ground (unrestrained) to determine if an anchor is required for above ground pig traps or other piping facilities.
Internal pressure, temperature change, flexibility of to absorb a degree of lateral anchor movement is not considered in this calculation.
Tensile stress due to Poisson effect:
S_{poisson}=\vartheta S_H[psi]\,\,\,\,\,S_H=\frac{Pd}{2t}[psi]
S_{poisson}=\vartheta S_H[psi]\,\,\,\,\,S_H=\frac{Pd}{2t}[psi]Where:
𝜗 − Poisson′s Ratio = 0.3
𝑃 − Design Pressure (psig)
𝑑 − Inside pipe diameter (in)
𝑡 − Pipe wall thickness (in)
Compressive stress due to temperature change:
S_{Temp}=E\alpha\triangle T\,[psi]
S_{Temp}=E\alpha\triangle T\,[psi]Where:
𝐸 − Young′s Mosulus of Elasticity 𝐸 = 29×106
𝛼 − Coefficient of Thermal Expansion for steel α = 6.5×10−6 (in/in℉)
Δ𝑇 = 𝑇𝑜 − 𝑇𝑖
𝑇𝑜 − Operating Temperature (℉)
𝑇𝑖 − Installation Temperature (℉)
Net longitudinal stress at beginning point (A) of the transition:
S_A=S_{Poisson}-S_{Temp} [psi]\,The\,strain\,will\,be\,\varepsilon=0,\,fully\,restrained
S_A=S_{Poisson}-S_{Temp} [psi]\,The\,strain\,will\,be\,\varepsilon=0,\,fully\,restrainedNet longitudinal stress at end point (B) of the transition:
S_B=\frac{S_H}{2}\,[psi]
S_B=\frac{S_H}{2}\,[psi]Net strain at point (B), will be:
\varepsilon_B=\alpha\triangle T+\frac{S_H}{E}(\frac{1}{2}-\vartheta).[in/in]
\varepsilon_B=\alpha\triangle T+\frac{S_H}{E}(\frac{1}{2}-\vartheta)\.[in/in]Soil resistance force based on Wilbur’s formula for average soil:
F_S=80(\frac{D}{12})\,[lbf/ft],\,where
F_S=80(\frac{D}{12})\,[lbf/ft],\,where𝐷 − Outside pipe diameter (in)
Length of transition zone:
L=\frac{A(S_B-S_A)}{F_S}\,[ft].\,where \~\A=\pi(D-t)t
L=\frac{A(S_B-S_A)}{F_S}\,[ft].\,where \\~\\A=\pi(D-t)t𝐴 − Pipe metal area (in2)
Total pipe movement at point (B) will be:
\delta=\frac{\varepsilon_B}{2}12L\,[in]
\delta=\frac{\varepsilon_B}{2}12L\,[in]Anchor force:
F=(S_B-S_A)A\,\,\,[lbf]
F=(S_B-S_A)A\,\,\,[lbf]
Case Guide
Part 1: Create Case
- Select the Pipe Anchor Force Analysis application from the Design & Stress Analysis Module
- To create a new case, click the “Add Case” button
- Enter Case Name, Location, Date and any necessary notes.
- Fill out all required Parameters.
- Make sure the values you are inputting are in the correct units.
- Click the CALCULATE button to overview results.
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)
- Design Pressure (psig)
- Operating Temperature: (-70°F – 160°F)
- 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)
- Installation Temperature: (-70°F – 160°F)
Part 2: Outputs/Reports
- If you need to modify an input parameter, click the CALCULATE button after the change.
- To SAVE, fill out all required case details then click the SAVE button.
- To rename an existing file, click the SAVE As button. Provide all case info then click SAVE.
- To generate a REPORT, click the REPORT button.
- The user may export the Case/Report by clicking the Export to Excel icon.
- To delete a case, click the DELETE icon near the top of the widget.
Results
- Hoop Stress (psi)
- Compressive Stress Due to Temperature Change (psi)
- Net Longitudinal Stress at Point A (psi)
- Net Longitudinal Stress at Point B (psi)
- Net Longitudinal Stress at Point B (in/in)
- Soil Resistance (lbf/ft)
- Length of the Transition Zone A-B (ft)
- Total Pipe Moment at Point B (in)
- Anchor Force (lbs)
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
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Restrained versus Unrestrained Pipe (Difference in Gas vs. Liquid)?
ASME B31.4 liquid and B31.8 gas codes include calculations for the net longitudinal compressive stress that must be applied only for a restrained line that equates to a low (less than 2%) longitudinal strain. This stress status is characteristic to underground pipelines located some distance away from above ground piping facilities.
Unrestrained lines means those above ground sections of piping without axial restraint as with buried pipe with soil. In others words the soil exerts substantial axial restraint, but not fully restrained. Check Out
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What is the Maximum Span Length of rev1?
Regarding span factors with and without water are based on bending stress and deflection. Larger diameter pipe spans require saddles for stability. Many standards that require pipes to be filled with water are based on bending and shear stresses not to exceed 1,500 psi and a deflection between supports not exceed 0.1 inches. Check Out
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What is the model used for Thrust at Blow-Off?