Hot Pipeline Euler Buckling Or Bar Buckling

Calculate typical elastic modulus, shear modulus, bulk modulus, density, and thermal expansion coefficient of a solid.

The table values of Poisson ratio and bulk modulus are calculated from the elastic modulus and shear modulus. Use the Result Table option to display a table of properties versus material type.

Tool Input

• modptype : Material Type
  • Eu : User Defined Elastic Modulus
  • Gu : User Defined Shear Modulus
  • Ku : User Defined Bulk Modulus
  • νu : User Defined Poisson Ratio
  • ρu : User Defined Density
  • αu : User Defined Thermal Expansion Coefficient

Tool Output

• α : Thermal Expansion Coefficient
• ν : Poisson Ratio
• ρ : Density
• E : Elastic Modulus
• G : Shear Modulus
• K : Bulk Modulus

Calculate high temperature pipeline beam buckling or Euler buckling load from beam effective length for multi layer circular pipes.

Beam end types include: free fixed (cantilever), guided fixed, pinned fixed, fixed fixed (built in or fixed), pinned pinned (simply supported), and guided pinned beam ends. The beam end conditions are of the form left end - right end (for example Pin-Fix is left end pinned and right end fixed). All distances are measured from the left end of the beam.

The buckling load can be calculated using either the Euler equation (suitable for long beams), the Johnson equation (suitable for short beams), or the buckling load equation can be determined from the transition length. The buckling load is positive. The axial load is negative in compression.

The effective length factor should be used for beams on a soft foundation such as soil, where the beam ends are poorly defined. For defined beam ends, such as structures, the effective length factor should be set to one (fe = 1).

Use the Result Plot option to plot the buckling load versus nominal length. Use the Result Table option to display the buckling load versus end type. Refer to the figures and help pages for more details.

Tool Input

• pletype : External Pressure Type
  • Peu : User Defined External Pressure
• schdtype : Line Pipe Schedule Type
• diamtype : Line Pipe Diameter Type
  • ODu : User Defined Outside Diameter
  • IDu : User Defined Inside Diameter
• wtntype : Line Pipe Wall Thickness Type
  • tnu : User Defined Wall Thickness
• syutype : Line Pipe Stress Type
• mattype : Material Type
  • Syu : User Defined Yield Stress
• sectype : Section Properties Type
  • EAαu : User Defined E x A x alpha
  • νu : User Defined Pipe Poisson's Ratio
• eitype : E x I Type
  • Kcu : User Defined Coating Factor
  • CSFu : User Defined Concrete Stiffness Factor
  • EIu : User Defined Pipe E x I
• loadtype : Axial Load Type
  • Fau : User Defined Axial Load
• fbtype : Buckling Load Type
  • Fbu : User Defined Buckling Load
• endtype : End Type
• leftype : Effective Length Type
  • feu : User Defined Effective Length Factor
• WTi : Pipe Liner Wall Thickness
• Ei : Pipe And Liner Elastic Modulus
• αi : Pipe And Liner Thermal Expansion Coefficient
• νi : Pipe And Liner Poisson's Ratio
• WTo : Pipe Coating Wall Thickness
• Eo : Pipe Coating Elastic Modulus
• Lo : Nominal Length
• Pi : Internal Pressure
• Td : Design Temperature
• Tin : Installation Temperature
• Fin : Installation Load

Tool Output

• α : Effective Thermal Expansion Coefficient
• ν : Effective Poisson Ratio
• AX : Effective Cross Section Area
• CSF : Concrete Stiffness factor
• EAα : E x A x alpha
• EI : Effective E x I
• EIc : Concrete E x I
• EIp : Pipe E x I
• Fa : Axial Load
• Fa/Fb : Axial Load Over Buckling Load Ratio (< 1)
• Fb : Buckling Load
• I : Moment Of Inertia
• IID : Pipe Inside Diameter Including Liner
• Kc : Coating Factor
• Le : Effective Length
• Lt : Transition Length (Short to Long Beam)
• OD : Line Pipe Diameter
• OOD : Pipe Outer Diameter Including Coatings
• Pe : External Pressure
• Sy : Yield Stress
• tn : Line Pipe Thickness

Calculate high temperature pipeline EI (ExI), unit mass and unit weight for multi layer pipelines.

The concrete stiffness factor is used to account for the effect of the concrete layer. The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Only include the Young's modulus value for the layers which will contribute to EI. The unit weight can be calculated for dry empty, dry full, wet empty and wet full pipe.

Tool Input

• schdtype : Line Pipe Schedule Type
• diamtype : Line Pipe Diameter Type
  • ODu : User Defined Outside Diameter
  • IDu : User Defined Inside Diameter
• wtntype : Line Pipe Wall Thickness Type
  • tnu : User Defined Wall Thickness
• eitype : E x I Type
  • Kcu : User Defined Coating Factor
  • CSFu : User Defined Concrete Stiffness Factor
• wltype : Pipe Weight Type
• WTi : Pipe Liner Wall Thickness
• Ei : Pipe And Liner Elastic Modulus
• ρi : Pipe And Liner Density
• WTo : Pipe Coating Wall Thickness
• Eo : Pipe Coating Elastic Modulus
• ρo : Pipe Coating Density
• ρf : Contents Fluid Density
• ρb : Displaced Fluid Density

Tool Output

• CSF : Concrete Stiffness Factor (DNVGL)
• EIi : Inside Layers E x I
• EIo : Outside Layers E x I
• EIp : Total E x I
• IID : Pipe Inner Diameter Including Liners
• Kc : Coating Factor (DNVGL)
• OD : Line Pipe Nominal Diameter
• OOD : Pipe Outer Diameter Including Coatings
• SG : Pipe Specific Gravity Relative To Displaced Fluid
• mb : Displaced Fluid Mass Per Length
• mc : Contents Fluid Mass Per Length
• mi : Inner Layers Total Unit Mass
• mo : Outer Layers Total Unit Mass
• mp : Pipe Mass Per Length Including Liner And Coating
• tn : Line Pipe Nominal Wall Thickness
• w : Pipe Total Weight Per Length Including Contents and Buoyancy

Calculate high temperature pipeline concrete stiffness factor and effective EI from the concrete pipe EI ratio for a general pipeline.

The concrete stiffness factor is used to account for the effect of the concrete layer on the bending modulus EI and the natural frequency. The concrete stiffness factor is calculated from the ratio of concrete EI over pipe EI.

`CSF= A ((EIc) / (EIp))^0.75 `
`EI = EIp (1 + CSF) `

where :

CSF = concrete stiffness factor
EIc = concrete EI
EIp = pipe EI
EI = effective EI
A = 0.33 for asphalt coating and 0.25 for PP/PE coating

The concrete stiffness factor is calculated in accordance with DNVGL RP F105. The method is suitable for circular pipes. Use the Result Plot option to plot the concrete stiffness factor (CSF) versus EI ratio and CSF type, or effective EI versus EI ratio and CSF type. Refer to the help pages for more details.

Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website)

Tool Input

• coptype : Cross Section Type
  • EIcu : User Defined Concrete E x I
  • EIC/EIPu : User Defined E x I Ratio
• csftype : Concrete Stiffness Factor Type
  • Kcu : User Defined Coating Factor
  • CSFu : User Defined Concrete Stiffness Factor
• EIp : Beam E x I

Tool Output

• CSF : Concrete Stiffness Factor
• EI : Effective E x I
• EIC/EIP : E x I Ratio