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Seabed irregularities (unevenness) during installation(residual tension on span creation is closely linked to thepipe weight).

Subsequent scouring(sand wave) and movement.Seabed topography and composition (type of soil), wave

and current action and pipe properties.

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Type of Span

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End Condition Using in Free SpanFixed- Pinned end condition may be assumed forsingle spans. Fixed- Fixed may only be assumed if

validated be observed support condition."Fixed/Pinned" in this case is assumed to be theaverage of "Fixed/Fixed and "Pinned/Pinned"bending moments, on the basis that the endfixities of a span are somewhere between the twocases but it is difficult to determine exactly where.

When calculating permissible span lengths, theassumed end conditions have a large impact on

the results.The fixed/pinned assumption may not be accurate when, for example, a pipeline spans between tworock ridges. The support conditions might then becloser to pinned/pinned; though the adjacentsections of pipe will provide some restraint so thatthe pipe section is not truly pinned/pinned.

Analytically, it is only possible to accurately determine these effects with the use of anadvanced finite element analysis to accurately model the span support conditions and axialeffects.It is obviously impractical to perform this type of analysis on every span along the pipeline route.However, it may be possible to build a "typical" FEmodel to determine the magnitude of theseeffects and modify the limiting span criteria.

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II. Criteria for Span Condition

Static Stress Vortex SheddingInduced Vibration:

In Line; Cross Flow;

Bar Buckling Fatigue.

A. DNV-1981

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1. Static Stress Checked individual stress components, and the totalcombined stress condition is also limited to maximumpercentage of the material SMYS (percentage is variable according to pipeline loading condition).

2. Vortex Induced Vibration

VIV dependent upon the pipe and span characteristics, fluid flow around a pipeline span can result in vorticesoccurring on the wake side of the pipe. If vortices areof sufficient frequency, they can produce significantpipeline oscillations.The parameter assessment VIV is Reduced Velocity (V r ).

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0 < Vr < 2.2 symmetric vortex shedding producing "In-Line" oscillations, i.e. parallel to fluid flow.

2.2 < V r < 3.5 alternate vortex shedding causing "In-Line"oscillations (unstable);

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4.8 < Vr < 12.0 alternate vortex shedding causing CrossFlow" oscillations i.e. perpendicular to fluid flow.

3. Bar BucklingFor a restrained pipeline, the pressure andtemperature induced axial force (compressive), if of sufficient magnitude, may lead to beam modebuckling of the pipeline

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4. Fatigue As mentioned previously, vortex shedding inducedspan vibrations may be broadly divided into twocategories:

In-line;

Cross-flow.Cross flow vibrations by their nature are almost alwayshigh amplitude and consequently their occurrenceshould be avoided at all costs , while in-line vibrations

are generally of smaller amplitude and may bepermissible. The criteria for permitting in-line vibrations fall within assessment of the pipelinefatigue and fatigue usage requirements.

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III. CalculationPermissible span lengths for a pipeline

are calculated based on each of thefollowing criteria:

Static stress

Vortexshedding (in-

line vibrations)

Vortexshedding (crossflow vibrations)

Bar buckling.

For each of these criteria the permissiblespan length should generally be calculatedfor each of the following four load cases:

Empty

Water filled

Hydrotest

Operation

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III. Calculation

2. Static stressDue to its self-weight and lateral hydrodynamicloading.The combined stresses should be checked againstthe allowable levels of stress given in the relevantcodes, i.e. is not to exceed thepermissible value.

What are aand b?

.ep

= usage factory as defined table below .F = specified minimum yeild strength

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III. Calculation

Is function likes Operation ?

How about Functional andenvironmental ?

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III. Calculation

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III. Calculation

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III. Calculation

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III. Calculation3. Vortex Shedding

a. Cross-Flow Vortex Shedding

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III. CalculationThe Reduced Velocity ( V r ) parameter see figure below:

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III. Calculationb. In-Line Vortex Shedding

Stability parameter is controlling the motion , K S

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III. CalculationEffective mass (m e) is function of Ca (add mass

coefficient).

Submerged Weight(W sub)

The relationship between V R

and the stability parameter, K S1

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III. Calculation

The Reduced Velocity for In-line VortexShedding as figure A. 3 The calculation In-Line Vortex Sheddingmethod is now thesame as for the CrossFlow. i.e.

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Other MethodThe natural frequency based on document ANALYSIS OF SPANS FOR SUBMERGEDPIPELINES (Shell):

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III. Calculation4. Bar Bucking

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III. Calculation5. Fatigue

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B. DNV-F105

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Methodology

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Methodology1. The fundamental natural frequency (first Eigen

frequency) may be approximated by

2. The reduced velocity, V R , is defined as:

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Methodology3. Onset Span Lengths :

Given(for In Line Onset spanLength) finding Leff:

Given(for Cross flow Onset span Length) finding Leff

What is this mean Onset ? Check all the MathCAD file , the span length due to onset span length isbigger/smaller span length due to Screening criteria.

Finding Vr (Reduced Velocity) ?.Reduced Velocity for In Line Flow is defined in section 4.3.5 DNV RP F105Reduced Velocity for Cross Flow is defined in section 4.4.4 DNV RP F105

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Methodology

4. Screening Fatigue CriteriaThe In-line natural frequencies f n,IL must fulfill:

The Cross-Flow natural frequencies f n,CF mustfulfill:

5. Given f 1=f nIL finding maximumfree span length due to Inlineflow. Given f 1=f nCLfinding

maximum free span lengthdue to CrossFLow.

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Methodology2. Fatigue Criterion

??????????3. ULS Criterion(Ultimate Limit State)Local buckling check for a pipeline free span shall be in compliance with the

combined loading load controlled condition criteria in DNV-OS-F101, Sec.5 orsimilar stress-based criteria in a recognised code. Functional and environmentalbending moment, axial force and pressure shall be accounted for. Simplifications areallowed provided verification is performed by more advanced modeling / analyses incases where the ULS criteria become governing.

a) Input Data

Hoop Stress:

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Methodology

Section D505

Section D505

Axial Force

Where: H = Effective (residual) lay tension pi = Internal pressure difference relative to as laid = Temperature difference relative to as laid

Characteristic plastic axial force resistance :

Characteristic plastic moment resistance:

Drag Force : Where:

Other parameter is defined in DNV RP F105 , from section 5.4.4 to 5.4.8

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MethodologyInertial Force : Where:

Other parameter is defined in DNV RP F105 , from section 5.4.10 to 5.4.13

The pressure containment resistance :F101-Eq5.8Characteristic collapse pressure is finding as :Eq. 5.10

Plastic Collapse Pressure : F101-Eq5.12

Elastic collapse pressure, see Eq. 5.11

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Methodologyb) Load-Controlled Combined Loading Check

Pipe members subjected to bending moment, effective axial force andexternal overpressure shall be designed to satisfy the following equation:

Applies for D/t2 Pe Where: Msd : The design moment is sum of maximum environmental bendingmoment due to in-line and cross-flow VIV (Dynamic) and static bending moment

Submerged Weight

Pcr Critical buckling load (positive sign)

The stiffening effect of concrete (CSF)coating

may be accounted for by:

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MethodologyNormalised Moment

Design effective axial force

Normalised Effective Force Which calculation using Check?

.F=Functional Load factor (S4 G201)

.c=Condition Load factor (S4 G203)

Applies for D/t2

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aMethodology and Summary

C. COMPARE TWO METHOD CALCULATION FREE SPANLENGTH

Coefficient DNV 1981 DNV RP F105

1. Reduced Velocity

Interpolate for figure (notaccurate)

Equation (accurate)

2. Static

Stress

Comparison with Yielding Criteria,

Von Misses Stress included allparameters as:Bending StressHoop StressHydrodynamic LoadLongitudinal StressThermal StressPoisson Stress

ULS check (Combined Loading

Check) based on parameters as:Bending MomentHoop StressHydrodynamic Load Axial Force

S

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SummaryCoefficient DNV 1981 DNV RP F105

3. Dynamic Stress Maximum span length based on theexcitation frequency (due to Vr-Interpolatefor figure )

Maximum span length based on Screeningand Onset criteria

4. Bar Buckling Maximum span length based on axial force Not required, summary in ULS checks.

5. Fatigue Check Required (but the sequence calculation of method is not finding)

Required when Screening Criteria is violated.

6. Validity Check Not required Check the free span length is smaller140.D, deflection is invalid/Ok, Bucking isnot influence the response/ buckled(Onset Criteria).

7. Result Bigger (see example free span length 40m) Smaller (i.e the number is smaller

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Example

E l

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Example

l ( )

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Supplementary (wave)1. Analytic wave theories

Wave Theories are developed for constant water depth d. The objective of a wave theory is to determinethe relationship between T and and the water particle motion throughout the flow.

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Supplementary (wave)1. The different of wave theory

o if Ur

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Supplementary (wave)2. Defined Deep Water

Deep water waves can be defined as those for whichor more usefully:Shallow water waves can be defined as orIntermediate water as other section.

Supplementary (wave)

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Supplementary (wave)

Supplementary (wave)

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Supplementary (wave) All the wave theory: Airy, stocker, Cnoidal and Solitary are regular kinematics wave and waveperiod T remains constant but reality wave always random field.

I. Classification wave spectrum following s pecific characteristics waveFrequency spectrum;Direction spectrum;Energy Spectrum ;Height Spectrum.

II. Classification wave spectrum following geographical name or famous man

Pierson Mosskowitz spectrum first time (P-M);Pierson Mosskowitz spectrum second time;Bretschneider Mitsuyasu spectrum (B-M);

Jonswap spectrum (Joint North Sea Wave Observation Project);Neumann spectrum;Roll Fisher spectrum;Storckelov spectrum;Burling spectrum;Krulov spectrum;Bretschneider spectrum;Davidan spectrum.

III. Classification wave spectrum following water depthDeep water;

Shallow water;

3. Wave spectrum classification

S l t ( )

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Supplementary (wave)3. Wave spectrum classification

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Supplementary (wave)4. Jonswap spectrum

The spectral density function