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Pipeng Free Online Software : Hobbs Global Buckling Calculators
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Pipeng : Hobbs Global Lateral and Upheaval Buckling Calculation Module

Hobbs Global Buckling Calculators

Description : Hobbs global lateral and upheaval buckling calculators

Discussion : The Hobbs method includes four lateral or snaking buckling modes, and one upheaval or vertical buckling mode. The Hobbs method is only suitable for unburied pipelines. Do not use these tools for buried pipelines.

Global buckling occurs because of restrained axial expansion due to temperature and pressure. The compressed pipeline is unstable but restrained by lateral forces (soil friction and or its self weight). At a critical load determined by the initial out of straightness amplitude Δ, and the lateral forces, the pipeline will snap and form a buckle. The initial out of straightness can occur because of seabed undulations, seabed debris, lay barge movement during laying, construction or remedial activities and plastic deformation of the pipeline over the stinger which causes the pipe to roll as it is laid. A typical out of straightness will have an amplitude Δ and a length L (refer to figures).

For lateral or snaking buckles, the buckle will generally localise on a short section of the initial out of straightness so that the effective initial amplitude Δeff is smaller than the amplitude Δ, and the effective length Leff is shorter than the length L. Use an estimate of the effective amplitude Δeff as the initial buckle amplitude (find Δeff so that Leff matches the calculated buckle length). The mode is partly determined by the shape of the initial out of straightness. It is difficult to predict which mode will form so the mode with the lowest initiation temperature should be assumed.

Two lateral friction coefficent values are required for the lateral bucklng analysis. The initial lateral friction coefficient should take account of pipeline embedment, and that the pipe is intially stationary. The post buckling friction coefficient is generally lower because the pipeline is moving and there is no embedment.

Upheaval buckling generally occurs when the pipe is laid over an obstacle and is restrained by self weight only. The Hobbs model is not suitable for buried pipeilnes.

Two different formula are included for the reduction in axial load due to the hoop stress poisson effect. The thin wall formula is based on Barlows formula, and ignores radial stress. The thick wall formula is based on Lames equation and includes the effect of radial stress. The thick wall formula is more accurate and is recommended. If you are using a finite element package some simple beam elements use the thin wall formula. For compatibility it may be preferable to use the thin wall formula.

Use the calculated maximum bending moment and pipe wall axial force to evaluate the stresses in the buckle.

The force convention used: The global restrained axial load, the buckle load and the pipe wall axial load are positive in compression and negative in tension (the opposite of the usual sign convention). The installation forces follow the normal sign convention and are positive in tension and negative in compression.

The standard pipeline tool is for a single layer pipeline with a single coating layer. For non standard pipeline sections for example metallurgically lined pipe or pipes with multiple outer coating layers, use the custom temperature tool. For arbitrary sections (including non pipeline sections) use the custom axial load tool.

Figures :

References :

Calculator Tools In This Module:

CALC : Buckling : Deflection 001 : Hobbs Global Buckling Model : Pipeline Temperature From Buckling Deflection : Calculator
CALC : Buckling : Deflection 002 : Hobbs Global Buckling Model : Temperature From Buckling Deflection For Custom Pipeline Section : Calculator
CALC : Buckling : Deflection 003 : Hobbs Global Buckling Model : Axial Load From Buckling Deflection For Custom Section : Calculator


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Module List

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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CALC : Buckling : Deflection 002 : Hobbs Global Buckling Model : Temperature From Buckling Deflection For Custom Pipeline Section : Calculator

Description : Calculate the Hobbs global lateral or upheaval buckling temperature from buckle amplitude for a pipeline with custom user defined section properties.

Discussion : For non standard pipeline sections such as CRA lined pipelines. Define custom values for the pipeline weight, internal diameter ID, bending stiffness EI, axial stiffness EA and thermal expansion force coefficient EAα. Calculate the post buckle loads and temperature from the initial out of straightness amplitude and the post buckle amplitude. The post buckle temperature is the temperature required to form a buckle of that amplitude. Iterate the post buckle amplitude to determine the amplitude at the design temperature.

Calculation Steps :

  • 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
  • ν = Poisson's Ratio
  • D = Pipe Nominal Diameter
  • EA = Pipeline EA Modulus
  • EAα = Pipeline Thermal Expansion Force Coefficient
  • EI = Pipeline Nominal EI Modulus
  • Fi = Pipeline Installation Force
  • ID = Pipe Nominal Inside Diameter
  • M = Lateral Buckling Mode
  • NP = Axial Load Model
  • Pd = Pipeline Design Gauge Pressure
  • Pi = Pipeline Installation Gauge Pressure
  • Ti = Installation Temperature
  • W = Total Weight Per Unit Length - Pipeline Contents Buoyancy

Output Variables :

  • BM = Pipeline Bending Moment
  • 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
  • Lbi = Buckle Initiation Length
  • Lbp = Post Buckle Length
  • Tdi = Buckle Initiation Temperature
  • Tdo = Design Temperature
  • t = Pipe Nominal Wall Thickness

Calculation :

 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 0.5 μA W Lbp ( √( 1 + ( 6.391e-5 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.0 μA W Lbp ( √( 1 + ( 1.743e-4 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.294 μA W Lbp ( √( 1 + ( 1.668e-4 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.608 μA W Lbp ( √( 1 + ( 2.144e-4 1 EA 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 1 EA W μA Lbi 5 - 0.25 ( μA EI ) 2 )
  Frp = ( W Lbp ) / EI √( 1.597e-5 1 EA W μA Lbp 5 - 0.25 ( μA EI ) 2 )
  BM = 0.06938 Lbp 2 W
 End of If Block
t = ( D - ID ) / 2
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 ) / EAα + Ti
Tdo = ( Fao - Fpc + Fpp + Fi ) / EAα + Ti

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CALC : Buckling : Deflection 003 : Hobbs Global Buckling Model : Axial Load From Buckling Deflection For Custom Section : Calculator

Description : Calculate the Hobbs global lateral or upheaval buckling load from buckle amplitude for a custom user defined section.

Discussion : For arbitrary sections including non pipeline sections. Define custom values for the pipeline weight W, axial stiffness EA and bending stiffness EI. Calculate the maximum axial load for the out of straightness or buckle amplitude.

Calculation Steps :

  • Buckle initiation load and temperature from the initial buckle amplitude
  • Post buckle load from the post buckle amplitude
  • Fully restrained pipeline load from the post buckle amplitude.

Options :

  • 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
  • EA = Pipeline EA Modulus
  • EI = Pipeline Nominal EI Modulus
  • M = Lateral Buckling Mode
  • W = Total Weight Per Unit Length - Pipeline Contents Buoyancy

Output Variables :

  • BM = Pipeline Bending Moment
  • Fai = Buckling Initiation Force
  • Fao = Restrained Axial Force
  • Fap = Post Buckling Force
  • Fri = Initiation Feed In Force Reduction
  • Frp = Post Buckle Feed In Force Reduction
  • Lbi = Buckle Initiation Length
  • Lbp = Post Buckle Length

Calculation :

 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 0.5 μA W Lbp ( √( 1 + ( 6.391e-5 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.0 μA W Lbp ( √( 1 + ( 1.743e-4 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.294 μA W Lbp ( √( 1 + ( 1.668e-4 1 EA 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 1 EA W μLi 2 Lbi 5 ) / ( μA EI 2 ) ) - 1 )
  Frp = 1.608 μA W Lbp ( √( 1 + ( 2.144e-4 1 EA 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 1 EA W μA Lbi 5 - 0.25 ( μA EI ) 2 )
  Frp = ( W Lbp ) / EI √( 1.597e-5 1 EA W μA Lbp 5 - 0.25 ( μA EI ) 2 )
  BM = 0.06938 Lbp 2 W
 End of If Block
Fao = Fap + Frp - Fri

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