Calculate the damped and undamped pipe natural vibration frequency (simply supported, fixed, and cantilever).
For lateral vibration, the buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). The buckling load is dependent on the end type, and is used for mode 1 vibration only. Added mass should be included for submerged or wet beams. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one. The axial load is calculated from temperature and pressure.
For longitudinal and torsional vibration, the natural frequency is independent of the cross section, and the general beam calculators can be used.
The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration. For multi layer pipes the bending stiffness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which affect the pipe stiffness.
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CALCULATOR : Beam Lateral Natural Vibration Frequency (Circular Pipe) [PLUS] ±
Calculate beam damped and undamped lateral natural vibration frequency for single layer pipes (no axial load). Beam unit mass and EI are calculated for a single layer circular beam with no coatings or internal liners. Beam unit mass can be calculated for full and empty beams. Added mass should be included for submerged or wet beams. The added mass coefficient is calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. 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). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Select the end type, and vibration mode number (modes 1 to 5). Use the Result Table option to display the natural frequency versus either mode number, end type, or line pipe wall thickness. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website) 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
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- sectype : Section Properties Type
- mmtype : Added Mass Type
- ρe : External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Unit Mass Type
- mu : User Defined Unit Mass
- endtype : End Type
- MN : Vibration Mode Number
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- ρi : Internal Fluid Density
- Lo : Nominal Length
Tool Output- ρp : Line Pipe Density
- E : Elastic Modulus
- EI : E x I
- ID : Inside Diameter
- Le : Effective Length
- OD : Outside Diameter
- cm : Added Mass Coefficient
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Mass Per Length
- ma : Added Unit Mass
- mc : Contents Unit Mass
- md : Displaced Unit Mass
- mp : Line Pipe Unit Mass
- tn : Wall Thickness
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CALCULATOR : Beam Lateral Natural Vibration Frequency (Multi Layer Pipe) [PLUS] ±
Calculate beam damped and undamped lateral natural vibration frequency for multi layer pipes (no axial load). Beam unit mass and EI are calculated for a circular beam with coatings and or internal liners. 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. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. 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). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. 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 EI. Select the end type, and vibration mode number (modes 1 to 5). Use the Result Table option to display the natural frequency versus either mode number, end type, or line pipe wall thickness. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. 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 : E x I Type
- Kcu : User Defined Coating Factor
- CSFu : User Defined Concrete Stiffness Factor
- EIu : User Defined Pipe E x I
- mmtype : Mass Type
- ρe : User Defined External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Mass Type
- mu : User Defined Beam Unit Mass
- endtype : End Type
- MN : Mode Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- WTi : Pipe Liner Wall Thickness
- ρi : Pipe And Liner Density
- Ei : Pipe And Liner Elastic Modulus
- WTo : Pipe Coating Wall Thickness
- ρo : Pipe Coating Density
- Eo : Pipe Coating Elastic Modulus
- ρf : Internal Fluid Density
- Lo : Nominal Length
Tool Output- CSF : Concrete Stiffness factor
- Cm : Added Mass Coefficient
- EI : Effective E x I
- EIc : Concrete E x I
- EIp : Pipe E x I
- IID : Pipe Inside Diameter Including Liner
- Kc : Coating Factor
- Le : Effective Length
- OD : Line Pipe Diameter
- OOD : Pipe Outer Diameter Including Coatings
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Nominal Mass Per Unit Length
- md : Displaced Unit Mass
- mla : Added Unit Mass
- mlc : Contents Unit Mass
- mlp : Pipe Unit Mass Including Liner And Coating
- tn : Line Pipe Thickness
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CALCULATOR : Beam Lateral Natural Vibration Frequency With Axial Load (Circular Pipe) [PLUS] ±
Calculate beam damped and undamped lateral natural vibration frequency with axial load for single layer pipes. For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases. The axial load can either be calculated from temperature and pressure, or user defined. Beam unit mass and EI are calculated for a single layer circular beam with no coatings or internal liners. Beam unit mass can be calculated for full and empty beams. Added mass should be included for submerged or wet beams. The added mass coefficient is calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. 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). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Select the end type, and vibration mode number (mode 1 only). Use the Result Table option to display the natural frequency versus either mode number, end type, or line pipe wall thickness. Use the Result Plot option to display the natural frequency versus axial load and end type, or beam length and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website) 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
- syutype : Line Pipe Stress Type
- mattype : Material Type
- SMYSu : User Defined Specified Minimum Yield Stress
- modptype : Material Property Type
- αu : User Defined Thermal Expansion Coefficient
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- νpu : User Defined Poisson Ratio
- sectype : Section Properties Type
- EIu : User Defined E x I
- EAαu : User Defined E x A x alpha
- mmtype : Added Mass Type
- ρe : External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Unit Mass Type
- mu : User Defined Unit Mass
- loadtype : Axial Load Type
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- ρi : Internal Fluid Density
- Lo : Nominal Length
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Load
Tool Output- α : Thermal Expansion Coefficient
- ν : Poisson Ratio
- ρp : Density
- 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
- ID : Inside Diameter
- Le : Effective Length
- Lt : Transition Length (Short to Long Beam)
- OD : Outside Diameter
- SMYS : Yield Stress
- cm : Added Mass Coefficient
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Mass Per Length
- ma : Added Unit Mass
- mc : Contents Unit Mass
- md : Displaced Unit Mass
- mp : Line Pipe Unit Mass
- tn : Wall Thickness
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CALCULATOR : Beam Lateral Natural Vibration Frequency With Axial Load (Multi Layer Pipe) [PLUS] ±
Calculate beam damped and undamped lateral natural vibration frequency with axial load for multi layer pipes. For compressive axial loads, the natural frequency tends to zero as the axial load tends to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). For tension loads, the natural frequency increases with increasing tension. The axial load can either be calculated from temperature and pressure, or user defined. Beam unit mass and EI are calculated for a circular beam with coatings and or internal liners. 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. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. 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). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. 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 EI. Select the end type, and vibration mode number (mode 1 only). Use the Result Table option to display the natural frequency versus either mode number, end type, or line pipe wall thickness. Use the Result Plot option to display the natural frequency versus axial load and end type, or beam length and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. 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
- syutype : Line Pipe Stress Type
- mattype : Material Type
- SMYSu : User Defined Specified Minimum 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
- mmtype : Mass Type
- ρe : User Defined External Fluid Density
- Cmu : User Defined Added Mass Coefficient
- G : Gap Height
- mltype : Mass Type
- mu : User Defined Beam Unit Mass
- loadtype : Axial Load Type
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : End Type
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- 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
- ρf : Internal Fluid Density
- Lo : Nominal Length
- Pi : Internal Pressure
- Td : Design Temperature
- Tin : Installation Temperature
- Fin : Installation Force
Tool Output- ν : Effective Poisson Ratio
- AX : Effective Cross Section Area
- CSF : Concrete Stiffness factor
- Cm : Added Mass Coefficient
- 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
- 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
- SMYS : Yield Stress
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
- m : Nominal Mass Per Unit Length
- md : Displaced Unit Mass
- mla : Added Unit Mass
- mlc : Contents Unit Mass
- mlp : Pipe Unit Mass Including Liner And Coating
- tn : Line Pipe Thickness
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CALCULATOR : Beam Longitudinal Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped longitudinal natural vibration frequency from beam elastic modulus, density and length. The longitudinal natural frequency is independent of the cross section profile. Select the end type, and vibration mode number (modes 1 to 8). The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. Tool Input- modptype : Material Property Type
- Eu : User Defined Elastic Modulus
- ρpu : User Defined Density
- endtype : End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output- ρ : Density
- E : Elastic Modulus
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Torsional Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped torsional natural vibration frequency from beam shear modulus, density and length. The torsional natural frequency is independent of the cross section profile. Select the end type, and vibration mode number (modes 1 to 8). The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, or beam length and end type. Tool Input- modptype : Material Property Type
- Gu : User Defined Shear Modulus
- ρpu : User Defined Density
- endtype : End Type
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output- ρ : Density
- G : Shear Modulous
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Torsional Natural Vibration Frequency With End Mass (Circular Pipe) [PLUS] ±
Calculate beam damped and undamped torsional natural vibration frequency for a circular beam with an end mass. The system is modelled as a beam fixed at one end, with a mass at the other (free) end. The circular beam mass moment of inertia is calculated from the beam inside diameter, outside diameter, length and density. The mass moment of inertia of the end mass is calculated for either a soid circular mass, or a hollow circular mass. The natural frequency is calculated from the mass moment of inertia ratio of the beam and the end mass for modes 1 to 8. The ᵞ factor is calculated so that ᵞ tan(ᵞ) equals the inertia ratio. The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. Use the Result Table option to display the natural frequency versus either the mode number, or wall thickness type. Use the Result Plot option to display the natural frequency versus beam length and mode number, natural frequency versus inertia ratio, or ᵞ versus inertia ratio. Tool Input- schdtype : Line Pipe Schedule Type
- diamtype : Diameter Type
- ODpu : User Defined Pipe Outside Diameter
- IDpu : User Defined Pipe Inside Diameter
- wtntype : Wall Thickness Type
- tnpu : User Defined Pipe Wall Thickness
- modptypea : Pipe Material Property Type
- Gpu : User Defined Pipe Shear Modulus
- ρpu : User Defined Pipe Density
- jptype : Pipe Mass Moment Of Inertia Type
- Jpu : User Defined Pipe Mass Moment Of Inertia
- modptypeb : End Mass Material Property Type
- Gmu : User Defined End Mass Shear Modulus
- ρmu : User Defined End Mass Density
- jmtype : End Mass Moment Of Inertia Type
- ODmu : User Defined End Mass Outside Diameter
- IDmu : User Defined End Mass Inside Diameter
- Lmu : User Defined End Mass Length
- Jmu : User Defined End Mass Mass Moment Of Inertia
- jojtype : Mass Moment Of Inertia Type
- Jb/Jmu : User Defined Mass Moment Of Inertia Ratio
- MN : Vibration Mode Number
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- L : Length
Tool Output- β : Vibration β Value
- ρm : End Mass Density
- ρp : Pipe Density
- CVG : Convergence Check (≥ 1)
- Gm : End Mass Shear Modulus
- Gp : Pipe Shear Modulous
- Jm : End Mass Moment Of Intertia
- Jp : Pipe Mass Moment Of Intertia
- Jp/Jm : Mass Moment Of Inertia Ratio
- ODp : Pipe Outside Diameter
- fd : Damping Factor
- fn : Natural Frequency
- idp : Pipe Inside Diameter
- tnp : Pipe Wall Thickness
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CALCULATOR : Beam Added Mass Coefficient (General Beam) [FREE] ±
Calculate general beam added mass coefficient and added mass from gap height and characteristic length. 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. The equation is suitable for undamped vibration of circular pipes in still fluid. For circular pipes the diameter should be used as the characteristic length. For other profile shapes the width can be used as the characteristic length. The method may not be valid for other profile shapes (engineering judgement is required). Refer to the help pages for more details. Reference : DNVGL RP F105 Free Spanning Pipelines (Download From DNVGL website) Tool Input- cmtype : Added Mass Coefficient Type
- Cmu : User Defined Added Mass Coefficient
- mb : Beam Mass Per Unit Length
- ρe : External Fluid Density
- W : Beam Characteristic Length
- G : Gap Height
- AX : Beam Cross Section Area
Tool Output- Cm : Added Mass Coefficient
- G/W : Gap Over Characteristic Length Ratio
- m : Total Mass Per Unit Length
- ma : Added Mass Per Unit Length
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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 Lateral Natural Vibration Frequency (General Beam) [FREE] ±
Calculate beam damped and undamped lateral natural vibration frequency for general beams (user defined properties - with axial load or no axial load). Beam unit mass bending stiffness modulus and axial load are user defined. Select the load type, end type, and vibration mode number (modes 1 to 5 for beams with no axial load, or mode 1 for beams with axial load. The end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, also pinned free ends, and free ends (unsupported beams). For beams with axial load the natural frequency equals zero for compressive axial loads greater than or equal to the buckling load. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). Buckling normally occurs on the axis with lowest stiffness modulus. The buckling stiffness modulus and the vibration stiffness modulus can be defined independently for cases where vibration is not parallel to buckling. 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). The damping factor = 0 for undamped vibration, and 1 for critically damped vibration. The natural frequency equals zero for critical damping. Use the Result Table option to display the natural frequency versus either mode number, or end type. Use the Result Plot option to display the natural frequency versus beam length and mode number, beam length and end type, or axial load and end type. The Fix-Fix and Free-Free modes have the same natural frequencies, but different mode shapes. Refer to the figures and help pages for more details. Tool Input- eitype : Bending Modulus Type
- EIvu : User Defined Vibration Bending Modulus (E x I)
- EIbu : User Defined Buckling Bending Modulus (E x I)
- loadtype : Axial Load Type
- Fau : User Defined Axial Load
- fbtype : Buckling Load Type
- endtype : End Type
- MN : Mode Number
- leftype : Effective Length Type
- feu : User Defined Effective Length Factor
- fdtype : Damping Factor Type (0 = Undamped 1 = Critical Damping)
- fdu : User Defined Damping Factor (0 ≤ fd ≤ 1)
- AX : Cross Section Area
- m : Unit Mass
- Lo : Nominal Length
- SY : Yield Stress
Tool Output- EIb : Buckling Bending Modulus (E x I)
- EIv : Vibration Bending Modulus (E x I)
- Fa : Axial Load
- Fa/Fb : Axial Load Over Buckling Load Ratio (> -1)
- Fb : Buckling Load
- Le : Effective Length
- Lt : Transition Length (Short to Long Beam)
- fd : Damping Factor
- fn : Natural Frequency
- k : Natural Frequency K Factor
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CALCULATOR : Beam Vibration Line Pipe Schedule [FREE] ±
Calculate 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 Vibration Yield Stress [FREE] ±
Calculate beam 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 Vibration Material Property [FREE] ±
Calculate beam 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 Vibration 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 Vibration 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 Vibration 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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