Pipeline Anchor Length Calculations

Virtual Anchor Calculations

Prepared By Shahid

Pipeline Virtual Anchor Length Calculations Variables: Pipe Properties Do = Outside Diameter of Pipe Di = Inside Diameter of Pipe D = Mean Diameter of Pipe TNom = Nominal Wall Thickness of Pipe TAc = Actual Thickness of Pipe v α ρP CA E ρF L

= = = = = = =

A

=

Or A

=

WP

=

=

Do - TNom

=

TNom − C A

=

(D =π

=

π ⋅ D ⋅ TNom

Poisson’s Ratio Coefficient of Thermal Expansion Pipe Density Corrosion Allowance Modulus of Elasticity of Pipe Pipe Fluid Density Length of Pipe Cross Section Area of pipe

2 O

− DI2 4

)

Full Weight Pipe and its fluid.

Design & Other Conditions P = Design Pressure = Design Temperature TD TI = Installation Temperature ∆T = TD - TI Soil µ ρS H

= = =

Others Sh = Sa = e = FEx = FEx(T) = FEx(P) = FP = FF =

Coefficient of Friction between Pipe & Soil Soil Density Depth of Burial

Hoop Stress Axial Stress Strain Total Force Due to Expansion Expansion Force Due to Temperature Change Expansion Force Due to Pressure Force due to Pressure Frictional Force

C:\Stresses\Pipeline Anchor Length Calculations.doc

Page 1 of 3

Virtual Anchor Calculations Required La =

Prepared By Shahid

Anchor Length

Solution: Theoretically, there will be pipe movement from entry point due to thermal expansion. Also an expansion will be there due to the pressure. Opposing these two is the frictional force between pipe and soil. Let us find these factors first: Expansion Force due to Temperature Change: Expansion Force due to Change in Temperature will be: FEx(T) = E ⋅ A ⋅ α ⋅ ∆T ………………………………..(1) Expansion Force due to Pressure: Pressure force will be found out as below: Hoop Stress in the pipe (Sh)

=

P⋅D 2 ⋅ T Ac

Axial Stress in the pipe (Sa)

=

P⋅D 4 ⋅ T Ac

Expansion due to Axial Stress (∆ L1)

=

L ⋅ Sa E

Contraction Due to Hoop Stress (∆ L2) =

L ⋅ν ⋅ S h E

Total Pressure Expansion

=

∆L1 − ∆L2

Total Pressure Expansion

=

L ⋅ [S a − (ν ⋅ S h )] E Sh = Sa 2

As So Total Pressure Expansion

=

 L  S h  ⋅   − (ν ⋅ S h ) E  2  

C:\Stresses\Pipeline Anchor Length Calculations.doc

Page 2 of 3

Virtual Anchor Calculations

Prepared By Shahid

Total Pressure Expansion

=

 L ⋅ Sh  1   ⋅ ( 2 −ν )  E 

Pressure Exp. Force

=

E ⋅ A⋅

FEx(P)

=

A ⋅ S h ⋅ (0.5 − ν ) …………………………….…(2)

=

(E ⋅ A ⋅ α ⋅ ∆T ) + ( A ⋅ S h ⋅ (0.5 − ν )) ……………(3)

Weight of soil over pipe

=

(D ⋅ H ⋅ La ).ρ S

Weight of Pipe along this length

=

A ⋅ ρ P ⋅ La

=

 DI2   π  ⋅ ρ F ⋅ La  4 

Total Pipe Weight (WP)

=

 DI2   ⋅ ρ F ⋅ La A ⋅ ρ P ⋅ La +  π 4  

The Frictional Force (FF)

=

µ ⋅ [(2 ⋅ ρ S ⋅ D ⋅ H ⋅ La ) + WP ] ………………...(4)

∆L L

So Adding (1) and (2) we get: FEx Friction Force at Soil/Pipe interface:

Weight of Fluid Inside Pipe

At virtual anchor this force must be equal to the force due to expansion. So equating (3) & (4) we get,

(E ⋅ A ⋅ α ⋅ ∆T ) + ( A ⋅ S h ⋅ (0.5 − ν ))

=

µ ⋅ [(2 ⋅ ρ S ⋅ D ⋅ H ⋅ La ) + WP ]

So rearranging we get the length of Virtual Anchor from point of entry:

La =

(E ⋅ A ⋅ α ⋅ ∆T ) + ( A ⋅ S h ⋅ (0.5 − ν )) 

 π ⋅ DI2  4

µ ⋅ (2 ⋅ ρ S ⋅ D ⋅ H ) + ( A ⋅ ρ P ) +  

C:\Stresses\Pipeline Anchor Length Calculations.doc

    ⋅ ρ F     

Page 3 of 3