Calculate beam buckling load for pipe beams.
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).
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. Buckling will generally occur about the axis with the lowest EI, depending on constraints.
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).
Concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The concrete stiffness factor is calculated from the ratio of concrete EI over beam EI in accordance with DNVGL RP F105. The method is suitable for circular beams and pipes. For other profile shapes engineering judgement is required.
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CALCULATOR : Beam Cross Section Properties (Circular Pipe) [PLUS] ±
Calculate circular beam cross section properties for vibration. Unit mass can be calculated with or without added mass. Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient is calculated in accordance with DNVGL RP F105. EAα is required for beams with axial load. Use the Result Table option to display the cross section properties versus wall thickness. Refer to the help pages for more details. Tool Input- schdtype : Schedule Type
- diamtype : Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- zstype : Pipe Section Modulus Type
- mmtype : Added Mass Type
- ρe : External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Unit Mass Type
- L : Length
- ρi : Internal Fluid Density
Tool Output- α : Thermal Expansion Coefficient
- ρp : Line Pipe Density
- AX : Line Pipe Cross Section Area
- E : Elastic Modulus
- EA : Pipe And Liner E x A
- EAα : Pipe And Liner E x A x alpha
- EI : E x I
- I : Pipe Moment Of Inertia
- ID : Nominal Inside Diameter
- Ip : Pipe Polar Moment Of Inertia
- J : Pipe Mass Moment Of Inertia
- L/r : Slenderness Ratio
- M : Total Mass
- Mc : Contents Mass
- Mp : Line Pipe Mass
- OD : Nominal Outside Diameter
- SG : Pipe Specific Gravity (Including Contents)
- Zs : Pipe Section Modulus
- cm : Added Mass Coefficient
- m : Mass Per Unit Length (Including Contents)
- ma : Added Unit Mass
- mc : Contents Unit Mass
- md : Displaced Fluid Unit Mass
- mp : Line Pipe Unit Mass
- r : Radius Of Gyration
- tn : Nominal Wall Thickness
- w : Weight Per Unit Length (Including Contents And Buoyancy)
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CALCULATOR : Beam Cross Section Properties (Multi Layer Pipe) [PLUS] ±
Calculate multi layer circular beam cross section properties for vibration. Unit mass can be calculated with or without added mass. Added mass is included in the unit mass for submerged beams to account for the fluid which is displaced by the beam. The added mass coefficient is calculated in accordance with DNVGL RP F105. EAα is required for beams with axial load. The bending stifness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which will contribute to either ExA or EI. ExA and EAα are calculated for the inside layers only. Use the Result Table option to display the cross section properties versus wall thickness. Refer to the help pages for more details. Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website) 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 : Axial Stiffness Modulus Type
- Kcu : User Defined Coating Factor
- CSFu : User Defined Concrete Stiffness Factor
- zstype : Pipe Section Modulus Type
- mmtype : Mass Type
- ρe : User Defined External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Mass Type
- WTi : Pipe Liner Wall Thickness
- ρi : Pipe And Liner Density
- 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
- ρo : Pipe Coating Density
- Eo : Pipe Coating Elastic Modulus
- L : Length
- ρf : Internal Fluid Density
Tool Output- ν : Effective Poisson Ratio
- CSF : Concrete Stiffness factor
- Cm : Added Mass Coefficient
- EA : Axial Stiffness Modulus (E x A)
- EAα : Thermal Expansion Modulus (E x A x alpha)
- EI : Effective Axial Stiffness Modulus (E x I)
- EIc : Concrete E x I
- EIp : Pipe E x I
- I : Pipe Moment Of Inertia
- IID : Pipe Inside Diameter Including Liners
- Ip : Pipe Polar Moment Of Inertia
- J : Pipe Mass Moment Of Inertia
- Kc : Coating Factor
- L/r : Slenderness Ratio
- M : Total Mass
- Mc : Contents Mass
- Mp : Pipe Mass Including Layers
- OD : Line Pipe Diameter
- OOD : Pipe Outer Diameter Including Coatings
- SG : Pipe Specific Gravity (Including Contents)
- Zs : Pipe Section Modulus
- m : Mass Per Unit Length (Including Contents)
- md : Displaced Fluid Unit Mass
- mla : Added Unit Mass
- mlc : Contents Unit Mass
- mlp : Pipe Unit Mass Including Liner And Coating
- r : Radius Of Gyration
- tn : Line Pipe Thickness
- w : Weight Per Unit Length (Including Contents And Buoyancy)
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CALCULATOR : Beam Buckling Load (Circular Pipe) [PLUS] ±
Calculate beam buckling load from beam effective length for 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 : Schedule Type
- diamtype : Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
- syutype : Line Pipe Stress Type
- mattype : Material Type
- Syu : User Defined Yield Stress
- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- νpu : User Defined Poisson Ratio
- sectype : Section Properties Type
- EIu : User Defined E x I
- EAαu : User Defined E x A x alpha
- 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
- Lo : Nominal Length
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Load
Tool Output- α : Thermal Expansion Coefficient
- ν : Poisson Ratio
- AX : Cross Section Area
- E : Elastic Modulus
- EAα : E x A x alpha
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (< 1)
- Fb : Buckling Load
- I : Moment Of Inertia
- ID : Inside Diameter
- Le : Effective Length
- Lt : Transition Length (Short to Long Beam)
- OD : Outside Diameter
- Pe : External Pressure
- Sy : Yield Stress
- tn : Wall Thickness
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CALCULATOR : Beam Buckling Load (Multi Layer Pipe) [PLUS] ±
Calculate beam 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
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CALCULATOR : Beam Buckling Load (General Beam) [FREE] ±
Calculate beam buckling load from beam effective length for general beams (user defined properties). 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- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- eitype : E x I Type
- Iu : User Defined Section Modulus
- ru : User Defined Radius Of Gyration
- EIu : User Defined E x I
- eaatype : E x A x alpha Type
- EAαu : User Defined E x A x alpha
- loadtype : Axial Load Type
- Td : User Defined Operating Temperature
- Tin : User Defined Installation Temperature
- Fin : User Defined Preload
- 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
- AX : Cross Section Area
- Lo : Nominal Length
- Sy : Yield Stress
Tool Output- α : Thermal Expansion Coefficient
- E : Elastic Modulus
- EAα : E x A x alpha (E x AX x α)
- EI : E x I
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (< 1)
- Fb : Buckling Load
- I : Moment Of Inertia
- Le : Effective Length
- Le/r : Slenderness Ratio
- Lt : Transition Length (Short to Long Beam)
- r : Radius Of Gyration
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CALCULATOR : Beam Buckling Concrete Stiffness Factor (General Beam) [FREE] ±
Calculate beam concrete stiffness factor and effective EI from the concrete beam 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 beam 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
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CALCULATOR : Beam Buckling Line Pipe Schedule [FREE] ±
Calculate beam buckling line pipe schedule outside diameter inside diameter and wall thickness. Select the pipe schedule (NPS or ISO etc), pipe diameter and wall thickness, or use the user defined option. Use the Result Table option to display the pipe schedule for the selected diameter. Tool Input- schdtype : Line Pipe Schedule Type
- diamtype : Line Pipe Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
Tool Output- ID : Nominal Inside Diameter
- OD : Nominal Outside Diameter
- OD/tn : Diameter Over Wall Thickness Ratio
- tn : Nominal Wall Thickness
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CALCULATOR : Beam Buckling Yield Stress [FREE] ±
Calculate beam buckling yield stress (SMYS) and tensile stress (SMTS). Select one of the API, ASME or DNV stress table options. Use the Result Table option to display the stress values for the selected stress table. Tool Input- syutype : Stress Table Type
- mattype : Material Type
- SMYSu : User Defined Specified Minimum Yield Stress
- SMTSu : User Defined Specified Minimum Tensile Stress
Tool Output- SMTS : Specified Minimum Tensile Stress
- SMTS/SMYS : Tensile Stress Over Yield Stress Ratio
- SMYS : Specified Minimum Yield Stress
- SMYS/SMTS : Yield Stress Over Tensile Stress Ratio
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CALCULATOR : Beam Buckling Material Property [FREE] ±
Calculate beam buckling elastic modulus, shear modulus, bulk modulus, density, and thermal expansion coefficient. 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
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CALCULATOR : Beam Buckling Axial Load From Temperature And Pressure (Circular Pipe) [PLUS] ±
Calculate pipeline restrained and unrestrained global or external axial load and wall load from temperature and pressure for single layer pipelines. The external pressure is assumed to be constant during installation and operation (submerged pipeline). The internal pressure is assumed to be zero during installation. Pipeline section properties are either calculated or user defined. The axial load is calculated using the thick wall formula (API RP 1111 and DNVGL ST F101). Loads are positive in tension, and negative in compression. The axial load can be calculated for either the nominal wall thickness, or the corroded wall thickness (nominal wall thickness minus corrosion allowance). Tool Input- pletype : External Pressure Type
- Peu : User Defined External Pressure
- syutype : Stress Table Type
- mattype : Yield Stress Type
- SMYSu : User Defined Specified Minimum Yield Stress
- schdtype : Pipe Schedule Type
- diamtype : Pipe Diameter Type
- ODu : User Defined Outside Diameter
- IDu : User Defined Inside Diameter
- wtntype : Wall Thickness Type
- tnu : User Defined Wall Thickness
- corrtype : Pipe Wall Corrosion Type
- modptype : Pipe Material Type
- νu : User Defined Pipe Poisson's Ratio
- αu : User Defined Pipe Thermal Expansion Coefficient
- Eu : User Defined Pipe Elastic Modulus
- sectype : Pipe Section Properties Type
- Asu : User Defined Steel Cross Section Area
- EAαu : User Defined Pipe E x A x alpha
- loadtype : Axial Load Type
- Fgu : User Defined Global Axial Load
- Fwu : User Defined Pipe Wall Axial Load
- tc : Corrosion Allowance
- Fd : Design Factor
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Load
Tool Output- α : Pipe Thermal Expansion Coefficient
- ν : Pipe Poisson's Ratio
- Ax : Pipe Cross Section Area
- E : Pipe Elastic Modulus
- EAα : Pipe E x A x alpha
- Fg : Global Or External Axial Load
- Fw : Pipe Wall Axial Load
- ID : Pipe Inside Diameter
- OD : Pipe Outside Diameter
- OD/tn : Pipe Diameter Over Wall Thickness Ratio
- PΔ : Pressure Difference
- Pe : External Pressure
- SMYS : Specified Minimum Yield Stress
- Sd : Allowable Stress
- Sw : Pipe Wall Axial Stress
- Sw/Sd : Axial Stress Over Allowable Stress Ratio
- t : Stress Check Wall Thickness
- tn : Pipe Nominal Wall Thickness
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CALCULATOR : Beam Buckling Axial Load From Temperature And Pressure (Multi Layer Pipe) [PLUS] ±
Calculate pipeline restrained and unrestrained external or global axial load and wall load from temperature and pressure for multi layer pipelines. The internal pressure is assumed to be zero during installation. The external pressure is assumed to be constant during installation and operation (submerged pipeline). The first inside layer is the pipe wall. Select the pipe wall thickness and diameter from the pipe schedule. Enter all inside layers. The Young's modulus should be set to zero for inside layers which do not contribute to the axial load. Change the number of layers on the setup page. The axial load is calculated using the thick wall formula (API RP 1111 and DNVGL ST F101). Loads are positive in tension, and negative in compression. Nominal pipe diameter and wall thickness should normally be used for axial load calculations. Pipe wall stress is calculated for the line pipe layer. Tool Input- pletype : External Pressure Type
- Peu : User Defined External Pressure
- syutype : Stress Table Type
- mattype : Yield Stress Type
- SMYSu : User Defined Specified Minimum Yield Stress
- 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
- sectype : Pipe Section Properties Type
- EAu : User Defined Pipe E x A
- EAαu : User Defined Pipe E x A x alpha
- νu : User Defined Pipe Poisson's Ratio
- loadtype : Axial Load Type
- Fgu : User Defined Global Axial Load
- Fwu : User Defined Pipe Wall Axial Load
- 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
- Fd : Design Factor
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Load
Tool Output- εw : Pipe Wall Axial Strain
- ν : Pipe Poisson's Ratio
- EA : E x A
- EAα : Pipe E x A x alpha
- Fg : Global Or External Axial Load
- Fw : Pipe Wall Axial Load
- IID : Pipe Inside Diameter Including Liner
- OD : Pipe Outside Diameter
- OD/tn : Pipe Diameter Over Wall Thickness Ratio
- Pe : External Pressure
- SMYS : Specified Minimum Yield Stress
- Sd : Allowable Stress
- Sw : Pipe Wall Axial Stress
- Sw/Sd : Axial Stress Over Allowable Stress Ratio
- tn : Line Pipe Thickness
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CALCULATOR : Beam Buckling Axial Load From Temperature And Pressure (General Pipe) [FREE] ±
Calculate pipeline restrained and unrestrained global or external axial load and wall load from temperature and pressure for single layer pipelines. The external pressure is assumed to be constant during installation and operation (submerged pipeline). The internal pressure is assumed to be zero during installation. The axial load is calculated using the thick wall formula (API RP 1111 and DNVGL ST F101). Loads are positive in tension, and negative in compression. Tool Input- pletype : External Pressure Type
- Peu : User Defined External Pressure
- loadtype : Axial Load Type
- Fgu : User Defined Global Axial Load
- Fwu : User Defined Pipe Wall Axial Load
- OD : Pipe Outside Diameter
- tn : Pipe Wall Thickness
- ν : Poisson Ratio
- α : Thermal Expansin Coefficient
- E : Elastic Modulus
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Load
Tool Output- EAα : Pipe E x A x alpha
- Fg : Global Or External Axial Load
- Fw : Pipe Wall Axial Load
- Pe : External Pressure
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