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

� Subsequent scouring(sand wave) and movement.

�Seabed topography and composition (type of soil), wave and current action and pipe properties.

Type of Span

End Condition Using in Free Span� Fixed- Pinned end condition may be assumed for

single spans. Fixed- Fixed may only be assumed ifvalidated 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 onthe results.

� The fixed/pinned assumption may not be accuratewhen, 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 accuratelydetermine these effects with the use of anadvanced finite element analysis to accuratelymodel the span support conditions and axialeffects.

� It is obviously impractical to perform this type ofanalysis 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.

II. Criteria for Span Condition

Static StressVortex Shedding

Induced Vibration:

In Line; Cross Flow;

Bar Buckling Fatigue.

A. DNV-1981

1. Static Stress� Checked individual stress components, and the total

combined stress condition is also limited to maximumpercentage of the material SMYS (percentage isvariable 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”(Vr ).

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

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

�4.8 < Vr < 12.0 alternate vortex shedding causing “Cross

Flow" oscillations i.e. perpendicular to fluid flow.

�4.8 < Vr < 12.0 alternate vortex shedding causing “Cross

Flow" oscillations i.e. perpendicular to fluid flow.

3. Bar Buckling� For a restrained pipeline, the pressure and

temperature induced axial force (compressive), ifof sufficient magnitude, may lead to beam modebuckling of the pipeline

� For a restrained pipeline, the pressure andtemperature induced axial force (compressive), ifof sufficient magnitude, may lead to beam modebuckling of the pipeline

4. Fatigue� As mentioned previously, vortex shedding induced

span vibrations may be broadly divided into two categories:

� In-line;

� Cross-flow.

� Cross flow vibrations by their nature are almost always high amplitude and consequently their occurrence should be avoided at all costs, while in-line vibrations are generally of smaller amplitude and may be permissible. The criteria for permitting in-line vibrations fall within assessment of the pipeline fatigue and fatigue usage requirements.

III. CalculationPermissible span lengths for a pipeline

are calculated based on each of the following criteria:

Static stress

Vortex shedding (in-

line vibrations)

Vortex shedding (cross flow vibrations)

Bar buckling.

For each of these criteria the permissible span length should generally be calculated for each of the following four load cases:

Empty

Water filled

Hydrotest

Operation

III. Calculation

2. Static stress� Due to its self-weight and lateral hydrodynamic

loading.

� 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 “a” and “b” ?

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

III. Calculation

Is function likes Operation ?

How about Functional andenvironmental ?

III. Calculation

III. Calculation

III. Calculation

III. CalculationVortex Shedding3. Vortex Shedding

a. Cross-Flow Vortex Shedding

III. Calculation� The Reduced Velocity (Vr ) parameter see figure below:

III. Calculationb. In-Line Vortex Shedding� Stability parameter is controlling the motion , KS

III. Calculation

� Effective mass (me) is function of Ca (add mass coefficient).

� Submerged Weight(Wsub)

� The relationship between VR and the stability parameter, KS

� 1<Vr<3.5 and Ks<1.8 : resonant in-line vortex shedding include oscillationsmay occur.

• The possibility of fatigue damage from in-line VIVs may therefore be

ignored if this criteria is violation.� Vr > 4.7 and Ks <16 crow-flow oscillation may occur.

• Cross-flow VIVs may be assumed not to occur if this criteria is violation.

III. Calculation

� The Reduced Velocity for In-line Vortex Shedding as figure A.3

� The calculation In-Line Vortex Shedding method is now the same as for the Cross Flow. i.e.

Other Method� The natural frequency based on document “ANALYSIS OF SPANS FOR SUBMERGED

PIPELINES (Shell)”:

III. Calculation

4. Bar Bucking

III. Calculation

5. Fatigue

B. DNV-F105

Methodology

Methodology1. The fundamental natural frequency (first Eigen

frequency) may be approximated by

2. The reduced velocity, VR, is defined as:

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 is bigger/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 F105� Reduced Velocity for Cross Flow is defined in section 4.4.4 DNV RP F105

Methodology

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

The Cross-Flow natural frequencies fn,CF must fulfill:

5. Given f =f finding maximum 5. Given f1=fnIL finding maximum free span length due to Inline flow. Given f1=fnCL finding maximum free span length due to CrossFLow.

Methodology

2. Fatigue Criterion

� ??????????

3. ULS Criterion(Ultimate Limit State)

Local buckling check for a pipeline free span shall be in compliance with thecombined 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:

Methodology

Section D505

Section D505

�Axial Force

Where: H = Effective (residual) lay tension

Δ pi = Internal pressure difference relative to as laid

ΔΤ = 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

Methodology�Inertial Force :

Where:

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

: �The pressure containment resistance: F101-Eq5.8

�Characteristic collapse pressure is finding as: Eq. 5.10

�Plastic Collapse Pressure: F101-Eq5.12

�Elastic collapse pressure, see Eq. 5.11

MethodologyLoad-Controlled Combined Loading Check b) Load-Controlled Combined Loading Check

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

Applies for D/t2 <45, Pi>Pe

Where: Msd : The design moment is sum of maximum environmental bending moment 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:

Methodology� Normalised Moment

� Design effective axial force

� Normalised Effective Force

�Which calculation using Check?

γ.F=Functional Load factor (S4 G201)

γ.c=Condition Load factor (S4 G203)

Applies for D/t2 <45, Pi<Pe

c) Validity Check

Maximum length for response model validity

Cross flow deflection

a

Methodology and Summary

C. COMPARE TWO METHOD CALCULATION FREE SPAN LENGTH

Coefficient DNV 1981 DNV RP F105

1. ReducedVelocity

� Interpolate for figure (notaccurate)

� Equation (accurate)

2. StaticStress

�Comparison with Yielding Criteria,Von Misses Stress included allparameters as:�Bending Stress�Hoop Stress�Hydrodynamic Load�Longitudinal Stress�Thermal Stress�Poisson Stress

�ULS check (Combined LoadingCheck) based on parameters as:�Bending Moment�Hoop Stress�Hydrodynamic Load�Axial Force

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 ofmethod is not finding)

� Required when Screening Criteria isviolated.

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 <40m

Example

Example

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 λ and the water particle motion throughout the flow.

Supplementary (wave)

1. The different of wave theory

o if Ur<48.35, Airy theory / Airy Lagrange / Stocker 1st using sin/cos function

o Ur≥48.35 ,Cnoidal theory using Jacoby Eliptic function/ Stocker 2nd ,3rd ,4th ,….n

o Ur=∞ ,Limit solitary wave.

Fig 1:Ranges of validity for various wave theories.

Detail of the wave theory ref DNVRP C205

Supplementary (wave)

2. Defined Deep Water

� Deep water waves can be defined as those for which or more usefully:

� Shallow water waves can be defined as or

� Intermediate water as other section.

Supplementary (wave)

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 specific characteristics wave

� Frequency 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 depth

� Deep water;

� Shallow water;

3. Wave spectrum classification

Supplementary (wave)3. Wave spectrum classification

Supplementary (wave)4. Jonswap spectrum

The spectral density function