Pipeng Toolbox : Beam Vibration With Axial Load Calculators Blank User
Short Cuts
GO
Main ±
Beams ±
References ±
Fluid Flow ±
Fluid Properties ±
Maths ±
Materials ±
Pipelines ±
Soils ±
Subsea ±
Demo

Beam Lateral Vibration Frequency With Axial Load

Calculate the damped and undamped beam natural vibration frequency for lateral vibration with axial load (simply supported, fixed, and cantilever beams).

For beams with axial load the axis with minimum stiffness (I1 or I2) should be used unless the beam is constrained to deflect on an alternative axis (buckling normally occurs on the minimum stiffness axis). Use the general beam calculators for cases where vibration and buckling are not parallel. 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. For pipes the axial load is calculated from temperature and pressure. For general beams the axial load is user defined.

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.

Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.

References :

Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

Change Module :

[FREE] tools are free in basic mode with no login (no plots, tables, goal seek etc). Login or Open a free account to use the tools in plus mode (with plots, tables, goal seek etc).
[PLUS] tools are free in basic CHECK mode with Login or Open a free account (CHECK values no plots, tables, goal seek etc). Buy a Subscription to use the tools in plus mode (with plots, tables, goal seek etc).
Try plus mode using the Plus Mode Demo tools with no login.   Help Using The Pipeng Toolbox (opens in the popup workbook)

Links : ±
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

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

CALCULATOR : Beam Lateral Natural Vibration Frequency With Axial Load (General Beam) [FREE]   ±

Calculate beam damped and undamped lateral natural vibration frequency with axial load for general beams (user defined properties). Beam unit mass bending stiffness modulus and axial load are user defined.

Select the end type: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, mode 1 only. 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)
  • 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)
  • AX : Cross Section Area
  • m : Unit Mass
  • Lo : Nominal Length
  • SY : Yield Stress
  • Fa : Axial Load

Tool Output

  • EIb : Buckling Bending Modulus (E x I)
  • EIv : Vibration Bending Modulus (E x I)
  • 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
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
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
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
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
pipeng.com 2025 (524 μs : 5 ms : 0.746 MB) Pengu CMS ©