Applies To
Product(s):	AutoPIPE
Version(s):	ALL;
Area:	Calculation
Date Logged & Current Version	May 2023 23.00.00.230

Problem:

How does AutoPIPE Calculate internal pressure effects for CSA-Z662 -2007?

Solution:

Code combinations: Internal Pressure stresses and Equivalent Stress verifications

Reference: CSA-Z662-07

Notes:
1. No corrosion or Mill tolerance to keep calculations simple
2. All weld factors are set to 1.0 - no effect on stresses or allowables
3. Specific gravity is set to 0.0, and density of pipe is also set to 0.0
4. Y factor = 0.0, Temper. derating factor = 1.0, Range reduction factor = 1.0, Design pressure
factor = 1.0
5. SIF values assumed to be 1.0 for all calculations

Pipe Properties:

Actual O.D: Do (in)

Wall thickness: t (in)

Minimum Yield: Sy (psi)

Cold Modulus: Ec (psi)

Poisson's ratio: ν

Inside Dia. (in)

Area cross sectional: (in²)

Area inside pipe: (in²)

Section modulus: (in³)

Pressure & Temperature:

Pressure: P (psi)

Temperature: T (Deg F)

Expansion (α*ΔT): (in / 100 Ft)

Thermal Expansion Stress Equivalence:

Intended Verification: For this part of verification, we will verify that axial force due to thermal
case in a fully restrained pipe (Segment A in this case, which is restrained with anchors at
both ends and restrained in the transverse direction with very stiff soil) result in an equivalent
stress as calculated by code formulas E*alpha*dT

Axial Thermal Force from AutoPIPE: F_TA01(Lbf)

Stress due to Thermal Force: (psi)

Stress calculation per code formula: (psi)

Conclusion:

AutoPIPE results compare well with code formula in case of thermal expansion stress for a fully restrained pipe. The results calculated from code formula match well with results calculated from AutoPIPE forces result. Note that α*ΔT = Expansion value in AutoPIPE.

Longitudinal Pressure Stress Equivalence:

Intended Verification: For this part of verification, we will try to verify that axial force due to pressure extension combined with post processing calculation of adding longitudinal stress results in an equivalent stress as calculated by code formulas v*S_H

Axial Pressure Force at point from AutoPIPE: F_PA01(lbf)

Stress due to Pressure: (psi)

Longitudinal Pressure Stress (Pressure Area formula): (psi)

Longitudinal Pressure Stress (PD/4t formula): (psi)

Hoop Stress: σH: (psi)

Longitudinal effect of Hoop Stress: σLH = ν * σH (psi)

Net Longitudinal Stress (Pressure area formula): σ_L1 = σ_lpA - σ_PA01 (psi)

Net Longitudinal Stress(PD/4t formula): σ_L2 = σ_lpP - σ_PA01 (psi)

Conclusion:

We can see that the net longitudinal stress σL1 and σL2 (which is what is calculated by AutoPIPE) is close to the longitudinal effect of Hoop Stress v.Sh as required by the code. AutoPIPE, in this case, matches exact code formula requirements. The results from pressure analysis, when combined with the post processing calculations, gives the code intended results
and also takes in to consideration the actual restraint conditions of the pipe.

It is imperative to include pressure extension analysis for the results to be meaningful. Also, depending on the actual restraint conditions, the pressure forces will vary, which gives more realistic results for actual condition.

Equivalent Stress Equivalence:

Intended Verification: For this part of verification, we will try to verify that Equivalent Stress calculated by AutoPIPE for CSA-Z662-07 is actually very similar to what is intended by the code equations. AutoPIPE may actually calculate the stress using a slightly different approach of incorporating analysis results and post processing, but the final results match the code formula results.

Combined Axial force from Gravity, Pressure & Temperature: Faxl (lbf)

Axial stress due to force: (psi)