Virtual Anchor Calculations Prepared By Shahid

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Pipeline Virtual Anchor Length Calculations

Variables:

Pipe Properties

Do = Outside Diameter of Pipe

Di = Inside Diameter of Pipe

D = Mean Diameter of Pipe = Do - TNom

TNom = Nominal Wall Thickness of Pipe

TAc = Actual Thickness of Pipe = ANom

CT −

v = Poisson’s Ratio

α = Coefficient of Thermal Expansion

ρP = Pipe Density

CA = Corrosion Allowance

E = Modulus of Elasticity of Pipe

ρF = Pipe Fluid Density

L = Length of Pipe

A = Cross Section Area of pipe = )(

4

22

IODD −

= π

Or

A = = Nom

TD ⋅⋅π

WP = Full Weight Pipe and its fluid.

Design & Other Conditions

P = Design Pressure

TD = Design Temperature

TI = Installation Temperature

∆ T = TD - TI

Soil

µ = Coefficient of Friction between Pipe & Soil

ρS = Soil Density

H = Depth of Burial

Others

Sh = Hoop Stress

Sa = Axial Stress

e = Strain

FEx = Total Force Due to Expansion

FEx(T) = Expansion Force Due to Temperature Change

FEx(P) = Expansion Force Due to Pressure

FP = Force due to Pressure

FF = Frictional Force

Virtual Anchor Calculations Prepared By Shahid

C:\Stresses\Pipeline Anchor Length Calculations.doc Page 2 of 3

Required

La = 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) = TAE ∆⋅⋅⋅ α ………………………………..(1)

Expansion Force due to Pressure:

Pressure force will be found out as below:

Hoop Stress in the pipe (Sh) = Ac

T

DP

⋅

⋅

2

Axial Stress in the pipe (Sa) = Ac

T

DP

⋅

⋅

4

Expansion due to Axial Stress (∆ L1) = a

SE

L⋅

Contraction Due to Hoop Stress (∆ L2) = h

SE

L⋅⋅ν

Total Pressure Expansion =

21 LL ∆−∆

Total Pressure Expansion = ( )[ ]ha

SSE

L⋅−⋅ ν

As a

hS

S=

2

So

Total Pressure Expansion = ( )

⋅−

⋅

h

hS

S

E

Lν

2

Virtual Anchor Calculations Prepared By Shahid

C:\Stresses\Pipeline Anchor Length Calculations.doc Page 3 of 3

Total Pressure Expansion = ( )ν−⋅

⋅2

1

E

SLh

Pressure Exp. Force = L

LAE

∆⋅⋅

FEx(P) = ( )ν−⋅⋅ 5.0h

SA …………………………….…(2)

So Adding (1) and (2) we get:

FEx = ( ) ( )( )να −⋅⋅+∆⋅⋅⋅ 5.0h

SATAE ……………(3)

Friction Force at Soil/Pipe interface:

Weight of soil over pipe = ( )Sa

LHD ρ.⋅⋅

Weight of Pipe along this length = aP

LA ⋅⋅ ρ

Weight of Fluid Inside Pipe = aF

IL

D⋅⋅

ρπ

4

2

Total Pipe Weight (WP) = aP

LA ⋅⋅ ρ + aF

IL

D⋅⋅

ρπ

4

2

The Frictional Force (FF) = ( )[ ]PaS

WLHD +⋅⋅⋅⋅⋅ ρµ 2 ………………...(4)

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

(4) we get,

( ) ( )( )να −⋅⋅+∆⋅⋅⋅ 5.0h

SATAE = ( )[ ]PaS

WLHD +⋅⋅⋅⋅⋅ ρµ 2

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

( ) ( )( )

( ) ( )

⋅

⋅+⋅+⋅⋅⋅⋅

−⋅⋅+∆⋅⋅⋅=

F

I

PS

h

a

DAHD

SATAEL

ρπ

ρρµ

να

42

5.0

2