Bending Stress and Deflection – Gas

Introduction

This application is related bending stresses and deflection on a uniformly loaded span. The weight of the pipe and product.

If there is more than one loading, superimposing individual solutions will be required. To account for unknown stresses multiply the longitudinal stress by 1.1.

Fixed End Supports:

y=\frac{7.6WL^4}{E(D^4-d^4)}\~\S=\frac{10.2WL^2}{(D^4-d^4)}

y=\frac{7.6WL^4}{E(D^4-d^4)}\\~\\S=\frac{10.2WL^2}{(D^4-d^4)}

Where:
𝑦 − Maximum Deflection (ft)
𝑆 − Maximum Bending Stress (psi)
𝑊 − Unit Weight (lbf)
𝐿 − Length (ft)
𝐸 − Modulus of Elasticity (psi)
(𝑆𝑡𝑒𝑒𝑙 = 30,000,000, 𝑝𝑙𝑎𝑠𝑡𝑖𝑐 (𝑑𝑢𝑝𝑜𝑛𝑡) = 100,000, 𝑝𝑙𝑎𝑠𝑡𝑖𝑐 (𝑝𝑙𝑒𝑥𝑐𝑜) = 125,000, 𝑐𝑎𝑠𝑡 𝑖𝑟𝑜𝑛 = 15,000,000, 𝑐𝑜𝑝𝑝𝑒𝑟 = 15,000,000)
𝐷 − Outside Diameter (in)
𝑑 − Inside Diameter (in)

Simple Supports:

𝑦 = 5 times 𝑦 for fixed ends
𝑆 = 1.5 times 𝑆 for fixed ends

Cantilever Supports:

𝑦 = 48 times 𝑦 for fixed ends
𝑆 = 6 times 𝑆 for fixed ends
𝑆 and 𝑦 on the schematics indicate the points of MAXIMUM stress deflection.

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 Length (ft)
• Youngs Modulus of Elasticity (psi)

Part 2: Outputs/Reports

Results

• Fixed End Supports/ Simple Supports/Cantilever Supports
  • Maximum Bending Stress (psi)
  • Maximum Deflection (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