The grass withers, the flower fades, but the word of the Lord stands forever. Isiah 40:8
Pipeng Free Online Software : Restrained Axial Load Calculators
Home Up Level Site Map My Pipeng Help? Contact
List Detail Email Instructions Bookmark
Pipeng : Restrained Axial Load From Temperature And Pressure Calculation Module

Restrained Axial Load Calculators

Description : Pipeline restrained axial load due to temperature and pressure calculators.

Discussion : Pipelines expand during operation because of the difference between the operating temperature and pressure, and the installation temperature and pressure. For long pipelines axial expansion due to temperature and pressure is restrained by soil friction. For a fully restrained pipeline the total or global restrained axial force includes the end cap force (the force required to constrain the pressurised fluid column inside the pipeline), the hoop stress poisson force (which reduces the axial force), temperature expansion force (the force required to restrain the thermal expansion), and external installation forces. The installation pressure is normally taken as zero (gauge pressure). The installation forces generally are due to lay tension. The global force drives global upheaval and lateral buckling.

The axial load in the pipe wall does not include the end cap pressure force. Depending on the operating pressure and temperature, it is possible for the global force to be compressive, while the pipeline wall is in tension. The force in the pipe wall drives local buckling of the pipe wall.

Two different formula are included for the hoop stress poisson load: thin wall formula and thick wall formula. 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.

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

The standard pipeline tools are for single layer pipelines. For non standard pipeline sections for example metallurgically lined pipe or non pipeline sections, use the custom user defined section tools.

Calculator Tools In This Module:

CALC : Buckling : Load 001 : Pipeline Restrained Axial Load From Pressure And Temperature : Calculator
CALC : Buckling : Load 002 : Pipeline Temperature From Restrained Axial Load And Pressure : Calculator
CALC : Buckling : Load 003 : Pipeline Restrained Axial Load From Temperature and Pressure For Custom Pipeline Section : Calculator
CALC : Buckling : Load 004 : Pipeline Temperature From Restrained Axial Load and Pressure For Custom Pipeline Section : Calculator


Link

Module List

CALC : Buckling : Load 001 : Pipeline Restrained Axial Load From Pressure And Temperature : Calculator

Description : Calculate pipeline restrained axial load from temperature and pressure for a single layer pipeline.

Discussion : The global axial load generated in a pipeline due to restrained axial expansion as a result of temperature and pressure.

Calculation Steps :

  • Pipeline ID and cross section area
  • Temperature load
  • Pressure load
  • Global restrained axial load
  • Pipe wall load, stress and strain

Options :

  • Pressure load: thin wall and thick wall formula.

Input Variables :

  • α = Pipe Thermal Expansion Coefficient
  • ν = Poisson's Ratio
  • D = Pipe Nominal Diameter
  • E = Pipeline Youngs Modulus E
  • Fi = Pipeline Installation Force
  • NP = Axial Load Model
  • Pd = Pipeline Design Gauge Pressure
  • Pi = Pipeline Installation Gauge Pressure
  • Td = Design Temperature
  • Ti = Installation Temperature
  • t = Pipe Nominal Wall Thickness

Output Variables :

  • Ax = Pipe Wall Nominal Cross Section Area
  • Fag = Restrained Axial Force
  • Faw = Pipeline Axial Strain
  • Fpc = Pipeline Pressure End Cap Force
  • Fpp = Pipeline Pressure Poisson Force
  • Ft = Pipeline Temperature Force
  • ID = Pipe Nominal Inside Diameter
  • Saw = Pipeline Axial Stress

Calculation :

ID = D - 2 t
Ax = π / 4 ( D 2 - ID 2 )
Ft = E Ax α ( Td - Ti )
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
Fag = Ft + Fpc - Fpp - Fi
Faw = Ft - Fpp - Fi
Saw = - Faw / Ax
Faw = Saw / E

Back To Top

CALC : Buckling : Load 002 : Pipeline Temperature From Restrained Axial Load And Pressure : Calculator

Description : Calculate pipeline temperature from restrained axial load and pressure for a single layer pipeline.

Discussion : The pipeline temperature required to generate the restrained global axial load.

Calculation Steps :

  • Pipeline ID and cross section area
  • Pressure load or force
  • Temperature load and temperature
  • Pipe wall load, stress and strain

Options :

  • Pressure load: thin wall and thick wall formula.

Input Variables :

  • α = Pipe Thermal Expansion Coefficient
  • ν = Poisson's Ratio
  • D = Pipe Nominal Diameter
  • E = Pipeline Youngs Modulus E
  • Fag = Restrained Axial Force
  • Fi = Pipeline Installation Force
  • NP = Axial Load Model
  • Pd = Pipeline Design Gauge Pressure
  • Pi = Pipeline Installation Gauge Pressure
  • Ti = Installation Temperature
  • t = Pipe Nominal Wall Thickness

Output Variables :

  • Ax = Pipe Wall Nominal Cross Section Area
  • Faw = Pipeline Axial Strain
  • Fpc = Pipeline Pressure End Cap Force
  • Fpp = Pipeline Pressure Poisson Force
  • Ft = Pipeline Temperature Force
  • ID = Pipe Nominal Inside Diameter
  • Saw = Pipeline Axial Stress
  • Td = Design Temperature

Calculation :

ID = D - 2 t
Ax = π / 4 ( D 2 - 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
Ft = Fag - Fpc + Fpp + Fi
Td = Ft / ( E Ax α ) + Ti
Faw = Ft - Fpp - Fi
Saw = - Faw / Ax
Faw = Saw / E

Back To Top

CALC : Buckling : Load 003 : Pipeline Restrained Axial Load From Temperature and Pressure For Custom Pipeline Section : Calculator

Description : Calculate pipeline global restrained axial load from temperature and pressure for a pipeline with custom user defined section properties.

Discussion : For non standard pipeline sections such as CRA lined pipelines or for non pipeline sections. Define the internal diameter and thermal expansion force coefficent for the pipeline.

Calculation Steps :

  • Temperature load
  • Pressure load
  • Global restrained axial load
  • Pipe wall load, stress and strain

Options :

  • Pressure load: thin wall and thick wall formula.

Input Variables :

  • ν = Poisson's Ratio
  • D = Pipe Nominal Diameter
  • EAα = Pipeline Thermal Expansion Force Coefficient
  • Fi = Pipeline Installation Force
  • ID = Pipe Nominal Inside Diameter
  • NP = Axial Load Model
  • Pd = Pipeline Design Gauge Pressure
  • Pi = Pipeline Installation Gauge Pressure
  • Td = Design Temperature
  • Ti = Installation Temperature

Output Variables :

  • Fag = Restrained Axial Force
  • Fpc = Pipeline Pressure End Cap Force
  • Fpp = Pipeline Pressure Poisson Force
  • Ft = Pipeline Temperature Force
  • t = Pipe Nominal Wall Thickness

Calculation :

t = ( D - ID ) / 2
Ft = EAα ( Td - Ti )
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
Fag = Ft + Fpc - Fpp - Fi

Back To Top

CALC : Buckling : Load 004 : Pipeline Temperature From Restrained Axial Load and Pressure For Custom Pipeline Section : Calculator

Description : Calculate pipeline temperature from restrained axial load and pressure for a pipeline with custom user defined section properties.

Discussion : For non standard pipeline sections such as CRA lined pipelines or for non pipeline sections. Define the internal diameter and thermal expansion force coefficent for the pipeline.

Calculation Steps :

  • Pressure load or force
  • Temperature load and temperature
  • Pipe wall load, stress and strain

Options :

  • Pressure load: thin wall and thick wall formula.

Input Variables :

  • ν = Poisson's Ratio
  • D = Pipe Nominal Diameter
  • EAα = Pipeline Thermal Expansion Force Coefficient
  • Fag = Restrained Axial Force
  • Fi = Pipeline Installation Force
  • ID = Pipe Nominal Inside Diameter
  • NP = Axial Load Model
  • Pd = Pipeline Design Gauge Pressure
  • Pi = Pipeline Installation Gauge Pressure
  • Ti = Installation Temperature

Output Variables :

  • Fpc = Pipeline Pressure End Cap Force
  • Fpp = Pipeline Pressure Poisson Force
  • Ft = Pipeline Temperature Force
  • Td = Design Temperature
  • t = Pipe Nominal Wall Thickness

Calculation :

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
Ft = Fag - Fpc + Fpp + Fi
Td = Ft / EAα + Ti

Back To Top

4 rows selected

Back To Top

Copyright © Pipeng Ltd 2010 : EULA
List Detail Email Instructions Bookmark
Home Up Level Site Map My Pipeng Help? Contact
pipeng.com (190 μs : 18 ms : 1.245 MB)