Post on 31-Oct-2015
description
Virtual Anchor Calculations Prepared By Shahid
C:\Stresses\Pipeline Anchor Length Calculations.doc Page 1 of 3
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