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Pipeline Cross Section 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 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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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 : Line Pipe Cross Section   ±

Calculate pipe internal and external diameter, cross section area and EI from pipe schedule diameter and wall thickness.

Use the Result Table option to display the results for the selected pipe diameter. For multi layer pipes (line pipe with outside layers and or inside layers), the results for each layer are displayed in the output view at the bottom of the page. Change the number of layers on the setup page.

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CALCULATOR MODULE : Plastic Pipe Cross Section   ±

Calculate plastic pipe diameter, wall thickness, tolerances, dimension ratio, unit mass (mass per length), and total mass from pipe schedule diameter and wall thickness or dimension ratio.

Use the Result Table option to display the results for the selected pipe diameter. The dimension ratio is based on the Renard R10 series. The standard dimension ratio SDR equals R10 + 1 and is calculated from the outside diameter divided by the pressure design wall thickness. The standard internal dimension ratio SIDR equals R10 - 1 and is calculated from the inside diameter divided by the pressure design wall thickness.

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CALCULATOR MODULE : Line Pipe Section Modulus   ±

Calculate pipeline EI and section modulus.

The section modulus is equal to the moment of inertia divided by the length from the centroid to the outer fibre (the outside radius).

`Zs = I / Y `

where :

Zs = Section Modulus
I = Moment Of Inertia Or Second Area Moment
Y = Length To Outer Fiber

The section modulus can be used to calculate the maximum bending stress from the bending moment

`SB = (BM) / (Zs) `

where :

SB = Bending Stress
BM = Bending Moment

For a pipe the the outer fiber length Y = the pipe radius. For combined stress calculations, the pipe mid wall radius can be used as the outer fiber length. This is based on the non linear stress distribution through the pipe wall. A mid wall approximation from DNVGL is also included.

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CALCULATOR MODULE : Line Pipe Concrete Stiffness Factor   ±

Calculate pipe concrete stiffness factor and effective EI from the concrete beam EI ratio.

The concrete stiffness factor is used to account for the effect of the concrete layer on the pipe EI. The concrete stiffness factor is calculated from the ratio of concrete EI over pipe EI in accordance with DNVGL RP F105. The effective EI can be calculated for asphalt coating, PE/PP coating, user defined coating factor Kc, user defined concrete stiffness factor CSF, or from the sum of the internal and external EI.

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

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CALCULATOR MODULE : Line Pipe Diameter Wall Thickness And Mass Schedule   ±
CALCULATOR MODULE : Hot Pipeline Mass And Weight   ±

Calculate high temperature pipeline unit mass (mass per length), and total mass from length.

The mass per joint can be calculated from the joint length. Construction quantities can be calculated from the total pipe length. Pipe unit mass (mass per length) and pipe unit weight (weight per length) can be calculated for multi layer pipelines (dry empty, dry full, wet empty and wet full pipelines). For multi layer pipelines, the first internal layer is the line pipe. Change the number of layers on the setup page.

Use the Result Table option to display a table of pipe mass and weight versus schedule wall thickness for the selected diameter.

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