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Pipeline Ovality And Ovalisation Modules

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CALCULATOR MODULE : Pipe Beam Natural Vibration Frequency   ±

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.

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

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CALCULATOR MODULE : Beam Lateral Vibration Frequency   ±

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

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 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

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CALCULATOR MODULE : 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

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CALCULATOR MODULE : Beam Torsional Vibration Frequency With End Mass   ±

Calculate beam torsional vibration frequency for a beam with an end mass for modes 1 to 8.

The torsional natural vibration frequency for a beam with an end mass can be calculated by

`fn = β / (2 π L) √(G / ρ) `
`β tan(β) = (Jb)/(Jm) `

where :

fn = natural frequency [Hz]
β = mode factor
L = beam length
G = beam shear modulus
ρ = beam density
Jb = beam mass moment of inertia
Jm = end mass mass moment of inertia

The mode factor (β) can be solved iteratively for each mode (modes 1 to 8). The system is modelled as a beam fixed at one end, with a mass at the other (free) end.

Use the Result Table and Result Plot options to display tables and plots. Refer to the 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

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CALCULATOR MODULE : Beam Vibration Added Mass   ±

Calculate submerged beam added mass coefficient and added mass from gap height.

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 can be calculated in accordance with DNVGL RP F105. The equation is suitable for undamped vibration of circular beams in a still fluid. For other beam profiles use the beam width. The method may not be valid for other profiles (engineering judgment is required). The gap height is measured along the axis of vibration and is assumed to be perpendicular to the adjacent surface.

Use the Result Table and Result Plot options to display tables and plots. Refer to the 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

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CALCULATOR MODULE : Beam Cross Section   ±

Calculate beam cross section properties for circular pipes: cross section area, moment of inertia, polar moment of inertia, mass moment of inertia, section modulus, EI, EA, EAα, unit mass, total mass, unit weight and specific gravity.

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 can be calculated in accordance with DNVGL RP F105. For multi layer pipes 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. Use the Result Table option to display the cross section properties versus wall thickness. Refer to the help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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Related Modules :

CALCULATOR MODULE : Beam Cross Section Parallel Axis Theorem   ±

Calculate beam moment of inertia using the parallel axis theorem.

The moment of inertia about an offset can be calculated by

`Ix = Il + Y AX^2 `
`Iy = Im + X AX^2 ::Hxy = Hlm + X Y AX^2 `

where :

Ix = moment of inertia about X axis
Iy = moment of inertia about Y axis
Il = moment of inertia about L axis
Im = moment of inertia about M axis
Hxy = product of inertia about offset
Hlm = product of inertia about the centroid
X = offset length from Y axis to centroid
Y = offset length from X axis to centroid
AX = cross section area

X and Y are perpendicular axes passing through the offset. L and M are perpendicular axes passing through the centroid and parallel to X and Y. The X and Y axes pass through the offset point.

For principal axes the product of inertia equals zero. Axes which are an axis of symmetry are principal axes. If the moment of inertia for a principal axis is equal to the moment of inertia of any other axis, all moments of inertia through that point are equal.

For rotated axes, the rotation is calculated relative to either the X axis or the L axis (anti clockwise is positive). Use the Result Plot option to plot the rotated moments of inertia and product of inertia versus the rotation angle.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Pipe Beam Bending   ±

Calculate beam bending shear force, bending moment, slope and deflection for pipe beams using the Euler Bernoulli beam equation.

The Euler Bernoulli beam equation is suitable for slender beams (it does not include the effect of shear), and for small angles (θ < 0.5 rad). The calculations are not valid past the beam end points. For combined loads, the shear force, bending moment, slope and deflection are assumed to be additive. 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.

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.

Combined loads include axial loads, point loads, distributed loads, weight loads, concentrated moments, angular displacements, lateral displacements, and uniform temperature gradient.

For beams with compressive axial loads the bending moment, slope and deflection tend to infinity as the axial load tends to the buckling load. For tension loads, the bending moment, slope and deflection decrease with increasing tension. 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 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).

For multi layer beams the concrete stiffness can be included in EI by multiplying EI by a factor (1 + CSF). The bending stress at the field joint should also be multiplied by the factor (1 + CSF) to account for stress localisation (select the pipe joint option for bending stiffness) . 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.

The stress check includes longitudinal stress, Tresca combined stress, and von Mises equivalent stress. The bending stress is calculated at the pipe mid wall. The hoop stress is calculated using the Barlow mid wall equation with the nominal wall thickness.

:

`Sh = (P - Pe) (OD - tn) / (2 tn) `

where :

Sh = hoop stress
P = internal pressure
Pe = external pressure
OD = pipe outside diameter
tn = pipe nominal thickness

Use the Result Plot option to plot the bending moment, shear force, slope, deflection and stress versus position x. Refer to the figures and help pages for more details.

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : Pipe Beam Buckling Load   ±

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.

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

Reference : Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill

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CALCULATOR MODULE : ASME B31G Pipe Corrosion Defect   ±

Calculate ASME B31G piping level 0 corrosion defect assessment for blunt defects (corrosion defects or other defects).

The level 0 assessment is useful as a screening check. The allowable defect length is calculated from the maximum defect depth. The calculation is taken from ASME B31G 1999 (original ASME B31G). The level 0 check is suitable for blunt defects of all types, including corrosion, mechanical damage and grinding repairs etc. For crack type defects the NG-18 crack defect calculators are recommended. The RSTRENG method (effective area method) can also be used for blunt type defects. The temperature derating calculation is from ASME B31.8. Material specific test data should be used if it is available.

Defects failing the level 0 check should be checked with a level 1 or level 2 assessment (see module links below). Use the level 1 assessment for simple defects from defect length and depth using either the original ASME B31G equation, or the modified ASME B31G equation. Use the level 2 assessment for complex defects from the defect river bottom profile.

Reference : ANSI/ASME B31G Manual For Determining The Remaining Strength Of Corroded Pipelines (2012)

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CALCULATOR MODULE : DNVGL ST F101 Submarine Pipeline Ovality   ±

Calculate DNVGL-ST-F101 submarine pipeline ovality from the out of roundness tolerance, or measured maximum and minimum diameter. Pipe ovalisation can be calculated from the initial ovality and the bending strain.

Reference : DNVGL-ST-F101 : Submarine Pipeline Systems (Download from the DNVGL website)

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CALCULATOR MODULE : API RP 1111 Pipeline Ovality   ±

Calculate API RP 1111 limit state pipeline out of roundness and ovality from tolerances, or from maximum and minimum diameter.

Out of roundness is equal to the maximum diameter minus the minimum diameter measured at the same cross section. Out of roundness ratio equals the out of roundness divided by either the nominal diameter or the mean diameter. DNV or ISO ovality is equal to the out of roundness ratio. API ovality is equal to half the DNV ovality (DNV or ISO ovality is equal to 2 x API ovality).

`Davg = (Dmax + Dmin) / 2 `
`OOR = (Dmax - Dmin) `
`ro = (OOR) / (Davg) `
`fa = (Dmax - Dmin) / (Dmax + Dmin) = (OOR) / (2.Davg) = (ro) / 2 `
`fd = 2.(Dmax - Dmin) / (Dmax + Dmin) = (OOR) / (Davg) = 2.fa = ro `

where :

OOR = out of roundness
ro = out of roundness ratio
Dmax = maximum diameter
Dmin = minimum diameter
Davg = average or mean diameter
fa = API ovality
fd = DNVGL or ISO ovality

Reference : API RP 1111 : Design, Construction, Operation, and Maintenance of Offshore Hydrocarbon Pipelines (Limit State Design) (2011)

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CALCULATOR MODULE : API 5L Line Pipe Out Of Roundness Tolerance   ±

Calculate API 5L line pipe out of roundness and ovality from diameter and tolerance.

Out of roundness is equal to the maximum diameter minus the minimum diameter measured at the same cross section. Out of roundness ratio equals the out of roundness divided by either the nominal diameter or the mean diameter. DNV or ISO ovality is equal to the out of roundness ratio. API ovality is equal to half the DNV ovality (DNV or ISO ovality is equal to 2 x API ovality).

`Davg = (Dmax + Dmin) / 2 `
`OOR = (Dmax - Dmin) `
`ro = (OOR) / (Davg) `
`fa = (Dmax - Dmin) / (Dmax + Dmin) = (OOR) / (2.Davg) = (ro) / 2 `
`fd = 2.(Dmax - Dmin) / (Dmax + Dmin) = (OOR) / (Davg) = 2.fa = ro `

where :

OOR = out of roundness
ro = out of roundness ratio
Dmax = maximum diameter
Dmin = minimum diameter
Davg = average or mean diameter
fa = API ovality
fd = DNVGL or ISO ovality

Out of roundness can be calculated from API 5L, from user defined out of roundness, or from user defined maximum and minimum diameter. For diameter D ≥ 0.2191 m, the out of roundness can be calculated from the inside diameter. For D < 0.0603 m the out of roundness is included with the diameter tolerance. For D ≥ 1.422 m the out of roundness tolerance is to be agreed with the supplier. All tolerances should be entered as positive (+ve) values.

References :

API 5L : Specification for Line Pipe (2007)
ISO 3183 : Petroleum and Natural Gas Industries - Steel Pipe For Pipeline Transportation Systems (2007)

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Related Modules :

CALCULATOR MODULE : Water Open Channel Or Culvert Flow Rate From The Manning Equation   ±

Calculate flowrate in circular or rectangular water channels using the Manning equation.

`Q = A (rh^2)/3 s^(1/2) / n `
`rh = A/P `

where :

Q = flow rate
A = cross section area
P = wetted perimeter
rh = hydraulic radius
s = channel slope
n = Manning friction factor

The channel is assumed to be either open, or partly full and at ambient pressure. The head loss equals the change in elevation. Channel roughness is accounted for using the Manning friction factor. The hydraulic radius is the ratio of channel cross section area over the wetted perimeter. Valves, tees and other pipe fittings should be included by adding a minor loss equivalent length to the pipeline length.

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CALCULATOR MODULE : Low Pressure Air Pressure Loss From The Moody Diagram   ±

Calculate pressure loss for low pressure air circular and rectangular ducts using the Moody diagram.

The calculators use the Darcy-Weisbach pressure loss equation. For low Reynolds numbers Re < 2000, the fluid flow is laminar and the Darcy friction factor should be calculated using the Hagen-Poiseuille laminar flow equation. For high Reynolds numbers Re > 4000, the fluid flow is turbulent and the Darcy friction factor should be calculated using one of the turbulent flow equations. In the transition region 2000 < Re < 4000, the flow is unstable and the friction loss cannot be reliably calculated.

Minor losses can be entered as either a K friction factor, a length, or length over diameter ratio. The minor losses are used to account for pipeline fittings such as bends, tees, valves etc.. :sg:For air the gas specific gravity SG = 1.0. For low pressure air the compressibility factor is assumed equal to one.

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Related Modules :

CALCULATOR MODULE : DNVGL RP C203 Tubular Fatigue Stress   ±
DATA MODULE : ASME B31.1 Power Piping Allowable Stress ( Open In Popup Workbook )   ±
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