| CALC : Buckling : Deflection 001 : Hobbs Global Buckling Model : Pipeline Temperature From Buckling Deflection : Calculator
Description : Calculate the Hobbs global lateral or upheaval buckling temperature from buckle amplitude for a single layer pipeline with a single coating layer.
Discussion : Calculate the buckle initiation load and temperature from the initial out of straightness amplitude, and the post buckle load and temperature from the post buckle amplitude. The post buckle temperature is the pipeline temperature required to form the buckle. Iterate the post buckle amplitude to calculate the maximum buckle deflection for the design temperature.
Calculation Steps :
- Pipeline weight and section properties
- Buckle initiation load and temperature from the initial buckle amplitude
- Post buckle load from the post buckle amplitude
- Pressure load
- Fully restrained pipeline load and the pipeline temperature from the post buckle amplitude.
Options :
- Pressure load: thin wall and thick wall formula.
- Buckling mode shapes: lateral buckling modes 1, 2, 3 and 4, and an upheaval buckling mode.
Input Variables :
- μA = Axial Friction Coefficient
- μLi = Initiation Lateral Friction Coefficient
- μLp = Post Buckle Lateral Friction Coefficient
- Δi = Initial Buckle Amplitude
- Δp = Post Buckle Amplitude
- α = Pipe Thermal Expansion Coefficient
- ν = Poisson's Ratio
- ρc = Fluid Density
- ρd = External Fluid Density
- ρe = Pipe External Coating Density
- ρw = Pipe Wall Density
- D = Pipe Nominal Diameter
- E = Pipeline Youngs Modulus E
- Fi = Pipeline Installation Force
- M = Lateral Buckling Mode
- NP = Axial Load Model
- Pd = Pipeline Design Gauge Pressure
- Pi = Pipeline Installation Gauge Pressure
- Ti = Installation Temperature
- g = Standard Gravity Acceleration At Sea Level
- t = Pipe Nominal Wall Thickness
- te = Coating Nominal Thickness
Output Variables :
- Ax = Pipe Wall Nominal Cross Section Area
- BM = Pipeline Bending Moment
- EI = Pipeline Nominal EI Modulus
- Fai = Buckling Initiation Force
- Fao = Restrained Axial Force
- Fap = Post Buckling Force
- Faw = Pipeline Wall Axial Force
- Fpc = Pipeline Pressure End Cap Force
- Fpp = Pipeline Pressure Poisson Force
- Fri = Initiation Feed In Force Reduction
- Frp = Post Buckle Feed In Force Reduction
- ID = Pipe Nominal Inside Diameter
- Lbi = Buckle Initiation Length
- Lbp = Post Buckle Length
- Mc = Fluid Contents Mass Per Unit Length
- Md = Displaced Fluid or Buoyancy Mass Per Unit Length
- Me = Pipe Coating Mass Per Unit Length
- Mp = Pipe Nominal Mass Per Unit Length - Including Layers
- OD = Pipe Outer Diameter Including Layers
- Tdi = Buckle Initiation Temperature
- Tdo = Design Temperature
- W = Total Weight Per Unit Length - Pipeline Contents Buoyancy
Calculation :
ID = D - 2 t
Ax = π / 4 ( D 2 - ID 2 )
OD = D + 2 te
EI = E π / 64 ( D 4 - ID 4 )
Mp = π / 4 ( D 2 - ID 2 ) ρw
Me = π / 4 ( OD 2 - D 2 ) ρe
Mc = π / 4 ID 2 ρc
Md = π / 4 OD 2 ρd
W = ( Mp + Mc + Me - Md ) g
If M = 1 : Hobbs Lateral Mode 1
Lbi = ( ( Δi EI ) / ( 2.407e-3 μLi W ) ) 0.25
Lbp = ( ( Δp EI ) / ( 2.407e-3 μLp W ) ) 0.25
Fai = ( 80.76 EI ) / Lbi 2
Fap = ( 80.76 EI ) / Lbp 2
Fri = 0.5 μA W Lbi ( √( 1 + ( 6.391e-5 E Ax W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
Frp = 0.5 μA W Lbp ( √( 1 + ( 6.391e-5 E Ax W μLp 2 Lbp 5 ) / ( μA EI 2 ) ) - 1 )
BM = 0.06938 Lbp 2 μLp W
Otherwise If M = 2 : Hobbs Lateral Mode 2
Lbi = ( ( Δi EI ) / ( 5.532e-3 μLi W ) ) 0.25
Lbp = ( ( Δp EI ) / ( 5.532e-3 μLp W ) ) 0.25
Fai = ( 4 π 2 EI ) / Lbi 2
Fap = ( 4 π 2 EI ) / Lbp 2
Fri = 1.0 μA W Lbi ( √( 1 + ( 1.743e-4 E Ax W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
Frp = 1.0 μA W Lbp ( √( 1 + ( 1.743e-4 E Ax W μLp 2 Lbp 5 ) / ( μA EI 2 ) ) - 1 )
BM = 0.1088 Lbp 2 μLp W
Otherwise If M = 3 : Hobbs Lateral Mode 3
Lbi = ( ( Δi EI ) / ( 1.032e-2 μLi W ) ) 0.25
Lbp = ( ( Δp EI ) / ( 1.032e-2 μLp W ) ) 0.25
Fai = ( 34.06 EI ) / Lbi 2
Fap = ( 34.06 EI ) / Lbp 2
Fri = 1.294 μA W Lbi ( √( 1 + ( 1.668e-4 E Ax W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
Frp = 1.294 μA W Lbp ( √( 1 + ( 1.668e-4 E Ax W μLp 2 Lbp 5 ) / ( μA EI 2 ) ) - 1 )
BM = 0.1434 Lbp 2 μLp W
Otherwise If M = 4 : Hobbs Lateral Mode 4
Lbi = ( ( Δi EI ) / ( 1.047e-2 μLi W ) ) 0.25
Lbp = ( ( Δp EI ) / ( 1.047e-2 μLp W ) ) 0.25
Fai = ( 28.20 EI ) / Lbi 2
Fap = ( 28.20 EI ) / Lbp 2
Fri = 1.608 μA W Lbi ( √( 1 + ( 2.144e-4 E Ax W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
Frp = 1.608 μA W Lbp ( √( 1 + ( 2.144e-4 E Ax W μLp 2 Lbp 5 ) / ( μA EI 2 ) ) - 1 )
BM = 0.1483 Lbp 2 μLp W
Otherwise If M = 5 : Hobbs Upheaval Mode
Lbi = ( ( Δi EI ) / ( 2.408e-3 W ) ) 0.25
Lbp = ( ( Δp EI ) / ( 2.408e-3 W ) ) 0.25
Fai = ( 80.76 EI ) / Lbi 2
Fap = ( 80.76 EI ) / Lbp 2
Fri = ( W Lbi ) / EI √( 1.597e-5 E Ax W μA Lbi 5 - 0.25 ( μA EI ) 2 )
Frp = ( W Lbp ) / EI √( 1.597e-5 E Ax W μA Lbp 5 - 0.25 ( μA EI ) 2 )
BM = 0.06938 Lbp 2 W
End of If Block
Fpc = π / 4 ( Pd - Pi ) ID 2
If NP = 1 : Thin Wall
Fpp = ( Pd - Pi ) π / 2 ID ( ID + t ) ν
Otherwise If NP = 2 : Thick Wall
Fpp = π / 2 ( Pd - Pi ) ID 2 ν
End of If Block
Faw = Fap - Fpc
Fao = Fap + Frp - Fri
Tdi = ( Fai - Fpc + Fpp + Fi ) / ( E Ax α ) + Ti
Tdo = ( Fao - Fpc + Fpp + Fi ) / ( E Ax α ) + Ti
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