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Transcript of Fatigue Analysis [Compatibility Mode]
Deterministic and Spectral Fatigue Analysis
FATIGUE ANALYSISFATIGUE ANALYSIS
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
1
Deterministic and Spectral Fatigue AnalysisContents Introduction Global Response Models
Structural Model Hydrodynamic Model
Fatigue Analysis methods Fatigue analysis steps Deterministic Method
Wave scatter data Hydrodynamic Model Foundation Model Jacket appurtenances
Structural Response Methods Static Analysis
Wave scatter data Directional Distribution
Spectral method Stress Transfer function Selection wave frequencies Static Analysis
Pseudo-Static Analysis Wave Response Analysis Free Vibration Analysis Mass Modeling
Selection wave frequencies Centre of Fatigue Damage Wave Spectra Linear System Fatigue Damage Mass Modeling Fatigue Damage
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
2
Deterministic and Spectral Fatigue AnalysisSTRUCTURAL MODELThe structural model should include allnecessary stiffness contributing elementsincluding the following.
Primary Structure of jacket and deck Conductors Piles Piles
Following items shall be modeled to include the hydrodynamic loads only
Caissons Boat landing A d Anodes Secondary structures such as walkway,
handrail and pad-eyes.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
3
Deterministic and Spectral Fatigue AnalysisFOUNDATION MODELThe foundation model for the jacketstructures can be any one of the followingthree types.
Equivalent pile stub or depth of fixity Super Element at pile head Non-linear pile soil interaction Non linear pile soil interaction
Conductors shall be modeled as non-load sharing element as they suppose to t f th l d t th j k t d tl t transfer the load to the jacket and partly to soil.
Usual practice is to model the conductors Usual practice is to model the conductors up to a 10 diameter as the depth of fixity. Pile soil interaction can also be performed with appropriate boundary condition at the jacket – conductor interface.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
4jacket conductor interface.
Deterministic and Spectral Fatigue Analysis
Nonlinear Soil Springs Linearised Pile head SpringsEquivalent Pile Stub22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
5Nonlinear Soil Springs Linearised Pile head SpringsEquivalent Pile Stub
Deterministic and Spectral Fatigue AnalysisSUPER ELEMENT
Super element is a 6x6 stiffness matrix attached to the pile head.The non-linear soils springs applied to the pile all along the lengthis condensed to pile head.p
The is obtained by carrying out a static analysis of the platformwith representative horizontal load that corresponds to the fatiguesea state. Since the fatigue sea state contains several wave loads,the representative sea state is taken as the center of fatiguedamage sea state.
The center of fatigue damage sea state shall be calculatedusing the wave scatter data assuming a Rayleighdistribution of the sea statedistribution of the sea state.
Once this 6x6 matrix is obtained, the analysis of thestructure can be carried out.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
6
structure can be carried out.
Deterministic and Spectral Fatigue AnalysisNON-LINEAR PILE SOIL INTERACTIONNon-linear behaviour of soil is modeled using load displacementcharacteristics for skin friction, end bearing and lateral reaction.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
7
Deterministic and Spectral Fatigue Analysis
t-z curve for deformationt z curve for deformation of a pile under vertical axial loading
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
8
Deterministic and Spectral Fatigue AnalysisJacket AppurtenancesHydrodynamic model of the following appurtenances shall beincluded in the simulation of wave loading on jacket structures
Hydrodynamic coefficients for structural elements Hydrodynamic coefficients for structural elements Circular cylinders Non-circular members
H d d i d l f d t t Hydrodynamic model for secondary structures
Caissons Boat landingg Anodes Secondary structures such as walkway, handrail and pad-eys.
Marine growth Marine growth
Appropriate Mass models for dynamic analysis
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
9
Deterministic and Spectral Fatigue AnalysisHydrodynamic ModelEven though the weight of the non-structural items has been calculated and applied accurately, the following characteristics shall be simulated so that the wave/current loads and the buoyancy effects are taken care correctly Buoyancy Actual Dimensions for wave load calculation Equivalent Hydrodynamic coefficients
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
10
Deterministic and Spectral Fatigue AnalysisAnodes
The wave loads on the anodes shall be considered carefully and the number and shape of anodes affect this considerably. Following methods are in use for the calculation of equivalent wave loads due to the presence of anodes.
Equivalent Cd and Cm Equivalent increase in Member Diameter
Typically the increase is around 5 to 10% depending on the number and distribution of anodes in the jacket.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
11
Deterministic and Spectral Fatigue AnalysisBoat Landing and Barge BumpersBoat Landing shall usually be modeled since large number of the members aretubular and only fenders shall be treated carefully. However, for preliminaryanalyses, the boat landing can be treated as equivalent tube with diameter and Cdand Cm of the total boat landing approximately.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
12
Deterministic and Spectral Fatigue AnalysisBOAT LANDING AND BARGE BUMPER MODEL
Barge Bumper
Boat Landing
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
13
Deterministic and Spectral Fatigue AnalysisMudmat and Supports
Mud mat is not modeled in thein place analysis. However,some times it may be worthsome times it may be worthmodeling if large number ofexternal braces supporting themud mat are required.
These braces will induceadditional wave loads
Hence case to case basis, oneshall make a decision to includethe mud mat system or not.
Mudmat Bracesthe mud mat system or not.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
14
Deterministic and Spectral Fatigue AnalysisBuoyancy Tanks Bouyancy
Buoyancy Tanks are provided during installation to enhance the floatation properties of the
y yTanks
jacket.
These tanks are not required ft th i t ll ti i after the installation is
complete.
However not always these However, not always these tanks can be removed.
If these tanks are left If these tanks are left permanently, then the wave loads on these tanks shall be considered.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
15
Deterministic and Spectral Fatigue AnalysisANODES BOUYANCY TANKS
Bouyancy Tank Pile Guide
Skirt Sleeve
Anode
Mudmat
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
16
Deterministic and Spectral Fatigue AnalysisEquivalent Diameter Method
Drag Area Known
This method predicts the drag component correctly but does not include the inertia
L
Knowncomponent. This method is easy to apply as the member diameter can be increased for wave load calculation only L
Anode
LndLd anodes' A*)(
wave load calculation only
Original Structural Member
Lwhere
n – number of anodesd d’
n number of anodes
Aanodes – surface area of anodes
Surface area of Anode includes the area of core and anode
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
17
Deterministic and Spectral Fatigue AnalysisEquivalent Cd and Cm MethodIn this method, the equivalent Cd’ and Cm’ are calculated and applied for each member.
As both drag and inertia components are taken in to account, this method is t th th th th dmore accurate than the other methods.
Equivalent Cd’In this method, the equivalent Cd’ and Cm’ are calculated and applied for each
'
*A *Ca da
dmd
T
nC CA
member
Cd’ – Equivalent Drag Coefficient with effect of anodes
Cdm – Drag Coefficient of the original member
Cda – Drag Coefficient of anode
n – Number of anodes in the member
Aa – Surface area of anode
AT – Total surface area of member and anodes22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
18AT Total surface area of member and anodes
Deterministic and Spectral Fatigue AnalysisEquivalent Cm’
*V *Ca ma
nC C
In this method, the equivalent Cd’ and Cm’ are calculated and applied for each member
' mmm
T
C CV
Cm’ – Equivalent Inertia Coefficient with effect of anodes
Cmm – Inertia Coefficient of the original member
Cma – Inertia Coefficient of anode
n – Number of anodes in the member
Va – Volume of anode
VT – Total volume of member and anodes
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
19
Deterministic and Spectral Fatigue AnalysisWalkways and handrailsThe tubular members for walkways and handrails shall be included in the calculation of equivalent Cd and Cm calculationsCaissons and RisersNormally the Risers and Caisson will be modeled as part of the structural model but can be deleted after the generation of environmental loads. Some of the commercial software have the
bilit t t h i l ticapability to carry out such simulationLaunch CradleLaunch Cradle has different dimensions
d h ll b t t d f ll f th and shall be treated carefully for the calculation of the environmental loads and buoyancy.
Dimensions W and H shall be specified for appropriate wave load calculations
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
20
Deterministic and Spectral Fatigue AnalysisShear and Yoke PlatesSkirt Piles are normally connected to the jacket legs using plated connection for simplicity and economical.
F h h f i d i f b l b b h ki l Further, the fatigue design of tubular members between the skirt sleeve and the jacket leg may be more difficult to handle.
These plated connections need to be modeled as accurately as possible These plated connections need to be modeled as accurately as possible to simulate the load path correctly using finite elements.However, Drag are shall be provided to simulate the wave/current loads
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
21
Deterministic and Spectral Fatigue Analysis
SHEAR PLATE / YOKE PLATE CONNECTION
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
22
Deterministic and Spectral Fatigue AnalysisStructural Response Analysis Methods
S i A l i
Global response of structure can be performed by any one of themethods.
Static Analysis Static Analysis (Pseudo-Static) Dynamic Wave Response Analysis (Frequency Domain) Dynamic Wave Response Analysis (Time Domain) Dynamic Wave Response Analysis (Time Domain)
All the above methods uses a linear stress – strain principleswithin elastic limit and assumes small displacement assumptions
f l l f d ff h f llas most of practical applications in fixed offshore structures fallwithin this region.
The methodology governing equations simplifying assumptionsThe methodology, governing equations, simplifying assumptionsare described. Each has its own advantages and disadvantages.Hence selection of method depends on the type of structure andits loading pattern.22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
23
g p
Deterministic and Spectral Fatigue AnalysisStatic Analysis Static analysis can be performed when the loads are static (notvarying with time). This method is very similar to simple stiffnessmethods. For very large structures, matrix methods are employed.
where K is the stiffness matrix
K X F 3
3EI WL
Th b tiF is the force vector
X is the displacement vector
This type of assumptions are true when the natural periods
The above equationdepicts a cantilever with Was end load.
This type of assumptions are true, when the natural periods(frequency) of structure is away from the loading (frequency).
Typical example of natural period of jacket less than 2 sec, is awayyp p p j , yfrom the wave period of say 10 sec. Hence the loads due to wavecan be assumed to be static. However, this needs to consideredcarefully if the wave periods is less than 10 sec.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
24
Deterministic and Spectral Fatigue AnalysisPseudo-Static Analysis Pseudo-Static analysis are performed when the loads are varyingwith time. In this method, the dynamic loads are approximated byconsidering the maximum amplitude of the load in a wave cycle.
However, the effect of dynamic interaction between the structureand the load is taken in to consideration approximately by using adiscrete Dynamic Amplification Factor (DAF)discrete Dynamic Amplification Factor (DAF).
h h ff ( l )
K X F DAFwhere K is the stiffness matrix (elastic)
F is the force vectorX is the displacement vectorDAF is the dynamic amplification factorDAF is the dynamic amplification factor
It is to be noted that this method is approximate as it considers only thefirst mode and there may be other local modes contributing todynamics22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
25dynamics.
Deterministic and Spectral Fatigue AnalysisDYNAMIC AMPLIFICATION FACTOR (SDOF)
Dynamic amplification of astructure can be calculated using aapproximate equivalent model of
1
pp qthe structure using Single Degreeof Freedom System (SDOF).
22
2
1DAF1 2N n
T TT T
TN – Natural Period of the structure
T – Wave PeriodT Wave Period
– Structural Damping Ratio
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
26
Deterministic and Spectral Fatigue AnalysisDYNAMIC AMPLIFICATION FACTOR (DAF)
9
10
Damping = 0.1%
6
7
8
D i 15%
Damping = 5%
3
4
5
Damping = 100%
Damping = 50%
Damping = 15%
DA
F
1
2
3
00 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Frequency Ratio = TN / T
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
27
Deterministic and Spectral Fatigue AnalysisWave Response analysisIf the natural period of the platform is close to the fatigue waves,assumption of equivalent static analysis does not hold good. Simplecalculations for DAF using SDOF model for will result in very conservativeor non-conservative results depending on the assumptions made onaverage wave periods for the calculation of DAF. Hence a Dynamic WaveResponse analysis needs to be performed.
Wave response analysis is performed using mode superposition principlesWave response analysis is performed using mode superposition principles.The details of this method can be referred in standard text books.However, brief details are given below. The equation for computation ofresponse is K X M X C X F where M is the structural mass matrix
C is the structural damping matrixX and are displacement velocity and acceleration vectorsXXX, and are displacement, velocity and acceleration vectors
The solution to the above can be performed using iterative methods suchWilson-theta or Newton-Raphson methods. But this cannot be combined withpile soil interaction which is another iterative technique.
XX
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
28
Deterministic and Spectral Fatigue AnalysisFree Vibration Analysis
0K X M X
Free vibration analysis of multi-element framed structures can be performed usingthe following equation. The above equation can be
written in a simple form for ai l d f f d
single degree of freedomequation as
/K M
Using the above, mass [M] and stiffness matrices [K]can be generated, which can be used for furtheranalysis for dynamic responses. Further, mode /K My y pshapes (normalized displacements) and Eigenfrequencies () are also extracted from the aboveanalysis.
H d i l i b f d i t t i l diHence a dynamic wave response analysis can be performed in two stages includingPile Soil Interaction analysis (PSI).
0K X M X Free Vibration Analysis
K X M X C X F Dynamic Response Analysis
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
29
Deterministic and Spectral Fatigue AnalysisMass ModellingSince the dynamic analysis involves accurate modeling of mass, following items shall be included in the model for their mass contribution in addition to the primary structure with stiffness. Deck Plate Platforms Monorails
Boat Landing Anodes Barge Bumper
Padeyes Equipment Walkways
Padeyes Mudmat Walkways
Handrails Grating Piping
Handrails and Grating Risers and Caissons Launch Cradlep g
Supports Crane Boom rest
Flooding and Grouting pipes Bouyancy Tanks Shear / Yoke Plates
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
30
/
Deterministic and Spectral Fatigue AnalysisFATIGUE ANALYSIS METHODS DETERMINISTIC METHODS (STATIC OR DYNAMIC) Wave Induced Motion InducedMotion Induced
SPECTRAL METHODS (STATIC OR DYNAMIC) Wave InducedWave Induced Wind Induced
Deterministic or Spectral methods, one can include dynamicff d d h f d l deffects depending on the type of structure and loading. For
example, fixed structures such as jacket may not be sensitive todynamic loading and hence quasi-static methods is sufficientwhere as slender fixed structures such as monopod complaintwhere as slender fixed structures such as monopod, complainttower may require dynamic response as the natural period mayfall within the wave energy regime.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
31
Deterministic and Spectral Fatigue AnalysisFATIGUE ANALYSIS STEPSThe various steps involved in the fatigue analysis of offshorestructures is listed below irrespective of the method. The majordifference comes in the response evaluation. The reminder of the
d i h t i il
Structural Model
procedure is some what similar.
Structural Model
Deterministic Spectral
Structural Model Wave Climate (Scatter Data) Hydrodynamic Model Wave Load Estimation Non-linear Pile Soil Interaction
Structural Model Wave Climate (Scatter Data) Centre of fatigue damage wave Drag Linearization Foundation Linearization Non linear Pile Soil Interaction
Structural Response Dynamic effects (if required) Cyclic Stress Estimation SCF Calculation
Foundation Linearization Structural Response Dynamic effects (if required) Cyclic Stress Estimation SCF Calculationa u a o
Hot Spot Stress Computation Estimate of N using S-N curve Selection of Factor of Safety Fatigue Damage Calculations
a u a o Hot Spot Stress Computation Estimate of N using S-N curve Selection of Factor of Safety Fatigue Damage Calculations
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
32
g g g g
Deterministic and Spectral Fatigue Analysis
DETERMINISTIC DETERMINISTIC METHOD
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
33
Deterministic and Spectral Fatigue AnalysisDeterministic Method
Deterministic analysis is based on thediscrete wave scatter data with waveheight and period and associatedheight and period and associatednumber of occurrences for each seastate. This method is suitable if thedistribution of wave energy is awaygy yfrom the natural period of the structure.Two methods are adopted dependingthe dynamic characteristics of thestructure.
Static Response Dynamic Response
If the natural period of the structure isless than 3 seconds, normally thedynamic effects can be ignored.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
34
Deterministic and Spectral Fatigue Analysis
All wave directions All sea states
1 1
inDN
1 1j i iN
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
35
Deterministic and Spectral Fatigue Analysis
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
36
Deterministic and Spectral Fatigue AnalysisDirectional distribution of wave height and period
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
37
Deterministic and Spectral Fatigue Analysis
1.25%2.39%
27 38%27.38%
0.31%28.00%
0 42%0.42%13.67%
26.54%
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
38
Deterministic and Spectral Fatigue Analysis
NORTH DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)NORTH DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)HMAX(m)
Zero Crossing PeriodTotal1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5
0.465 338 25145 6701 372 0 0 0 0 0 0 0 0 32557
1.395 0 22186 132098 16856 4561 879 100 50 17 0 0 0 1767462 325 0 59 14474 14469 2940 1206 292 31 9 6 0 0 334872.325 0 59 14474 14469 2940 1206 292 31 9 6 0 0 334873.255 0 0 497 1351 1906 803 324 162 7 0 0 0 50504.185 0 0 0 16 25 59 39 20 8 0 0 0 1675.115 0 0 0 1 2 13 23 13 6 1 0 0 586.045 0 0 0 0 0 0 0 0 0 0 0 0 06 975 0 0 0 0 0 0 0 0 0 0 0 0 06.975 0 0 0 0 0 0 0 0 0 0 0 0 07.905 0 0 0 0 0 0 0 0 0 0 0 0 08.835 0 0 0 0 0 0 0 0 0 0 0 0 09.765 0 0 0 0 0 0 0 0 0 0 0 0 010.695 0 0 0 0 0 0 0 0 0 0 0 0 011.625 0 0 0 0 0 0 0 0 0 0 0 0 012.555 0 0 0 0 0 0 0 0 0 0 0 0 013.485 0 0 0 0 0 0 0 0 0 0 0 0 014.415 0 0 0 0 0 0 0 0 0 0 0 0 015.345 0 0 0 0 0 0 0 0 0 0 0 0 016.275 0 0 0 0 0 0 0 0 0 0 0 0 017.205 0 0 0 0 0 0 0 0 0 0 0 0 018.135 0 0 0 0 0 0 0 0 0 0 0 0 019.065 0 0 0 0 0 0 0 0 0 0 0 0 0
Total 338 47390 153770 33066 9433 2961 777 276 46 8 0 0 248065
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
39
Deterministic and Spectral Fatigue Analysis
NORTH EAST DIRECTION (JOINT DISTRIBUTION OF Hmax and T )NORTH EAST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)HMAX(m) Zero Crossing Period Total
1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 248 18392 4901 272 0 0 0 0 0 0 0 0 238131.395 0 12968 77213 9853 2666 514 58 29 10 0 0 0 1033112.325 0 13 3132 3131 636 261 63 7 2 1 0 0 72462.325 0 13 3132 3131 636 261 63 7 2 1 0 0 72463.255 0 0 24 67 94 40 16 8 0 0 0 0 2494.185 0 0 0 17 26 63 41 21 9 0 0 0 1775.115 0 0 0 0 0 3 6 3 1 0 0 0 156.045 0 0 0 0 0 4 18 15 6 2 0 0 456.975 0 0 0 0 0 0 0 0 0 0 0 0 07.905 0 0 0 0 0 0 0 0 0 0 0 0 08.835 0 0 0 0 0 0 0 0 0 0 0 0 09.765 0 0 0 0 0 0 0 0 0 0 0 0 010.695 0 0 0 0 0 0 0 0 0 0 0 0 011.625 0 0 0 0 0 0 0 0 0 0 0 0 012.555 0 0 0 0 0 0 0 0 0 0 0 0 013.485 0 0 0 0 0 0 0 0 0 0 0 0 014.415 0 0 0 0 0 0 0 0 0 0 0 0 015.345 0 0 0 0 0 0 0 0 0 0 0 0 016.275 0 0 0 0 0 0 0 0 0 0 0 0 017.205 0 0 0 0 0 0 0 0 0 0 0 0 018.135 0 0 0 0 0 0 0 0 0 0 0 0 019.065 0 0 0 0 0 0 0 0 0 0 0 0 0
Total 248 31373 85272 13339 3423 884 202 83 28 4 0 0 134856
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
40
Deterministic and Spectral Fatigue Analysis
EAST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)EAST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)HMAX(m)
Zero Crossing PeriodTotal1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5
0.465 31 2284 609 34 0 0 0 0 0 0 0 0 29571.395 0 2565 15270 1949 527 102 12 6 2 0 0 0 204312.325 0 7 1744 1743 354 145 35 4 1 1 0 0 40353.255 0 0 148 404 569 240 97 49 2 0 0 0 15094.185 0 0 1 47 75 178 116 59 25 1 0 0 5025.115 0 0 0 3 6 47 80 45 20 5 0 0 2066.045 0 0 0 0 1 16 74 61 25 8 1 0 1876.975 0 0 0 0 0 1 21 30 13 3 1 0 697.905 0 0 0 0 0 1 17 46 24 3 1 0 918.835 0 0 0 0 0 0 2 18 15 2 0 0 369.765 0 0 0 0 0 0 0 15 25 4 1 1 4610.695 0 0 0 0 0 0 0 4 12 5 0 0 2211.625 0 0 0 0 0 0 0 0 0 0 0 0 012.555 0 0 0 0 0 0 0 0 0 0 0 0 013.485 0 0 0 0 0 0 0 0 0 0 0 0 014.415 0 0 0 0 0 0 0 0 0 0 0 0 015.345 0 0 0 0 0 0 0 0 0 0 0 0 016.275 0 0 0 0 0 0 0 0 0 0 0 0 017.205 0 0 0 0 0 0 0 0 0 0 0 0 018.135 0 0 0 0 0 0 0 0 0 0 0 0 019.065 0 0 0 0 0 0 0 0 0 0 0 0 0
Total 31 4856 17772 4180 1533 730 455 336 163 32 3 1 30091
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
41
Deterministic and Spectral Fatigue Analysis
SOUTH EAST DIRECTION (JOINT DISTRIBUTION OF H and T )SOUTH EAST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)HMAX(m) Zero Crossing Period Total1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 38 2818 751 42 0 0 0 0 0 0 0 0 36491.395 0 3257 19392 2474 670 129 15 7 2 0 0 0 259462.325 0 8 1905 1904 387 159 38 4 1 1 0 0 44073.255 0 0 149 404 570 240 97 49 2 0 0 0 15104.185 0 0 1 36 57 136 89 45 19 1 0 0 3845.115 0 0 0 11 24 184 315 176 77 20 0 0 8086.045 0 0 0 0 3 33 152 125 52 17 2 0 3856.975 0 0 0 0 0 6 89 126 52 11 2 0 2877.905 0 0 0 0 0 2 53 146 77 8 2 0 2908.835 0 0 0 0 0 0 4 44 36 4 1 1 909.765 0 0 0 0 0 0 0 12 19 3 1 1 3610.695 0 0 0 0 0 0 1 11 31 14 0 0 5711.625 0 0 0 0 0 0 0 6 19 8 0 0 3411.625 0 0 0 0 0 0 0 6 19 8 0 0 3412.555 0 0 0 0 0 0 1 4 28 17 0 0 5113.485 0 0 0 0 0 0 0 13 25 21 0 0 5914.415 0 0 0 0 0 0 0 16 24 8 0 0 4815.345 0 0 0 0 0 0 0 23 35 0 0 0 5816 2 0 0 0 0 0 0 0 0 9 0 0 0 916.275 0 0 0 0 0 0 0 0 9 0 0 0 917.205 0 0 0 0 0 0 0 0 6 3 0 0 918.135 0 0 0 0 0 0 0 0 5 5 0 0 919.065 0 0 0 0 0 0 0 0 0 0 0 0 0
Total 38 6083 22197 4871 1711 890 857 808 520 141 8 2 38126
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
42
Deterministic and Spectral Fatigue AnalysisSOUTH DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)max z
HMAX(m) Zero Crossing Period Total1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 75 5544 1477 82 0 0 0 0 0 0 0 0 71781.395 0 112592 670387 85545 23147 4461 505 253 84 0 0 0 8969732 325 0 1664 407678 407527 82800 33973 8229 877 242 182 0 0 9431722.325 0 1664 407678 407527 82800 33973 8229 877 242 182 0 0 9431723.255 0 0 15689 42686 60190 25363 10229 5130 225 0 0 0 1595114.185 0 0 44 2018 3198 7608 4983 2544 1060 47 0 0 215025.115 0 0 0 22 50 378 648 362 158 41 1 0 16606.045 0 0 0 1 11 121 553 452 189 63 7 1 13986.975 0 0 0 0 1 19 285 403 166 34 7 1 9177.905 0 0 0 0 0 3 68 187 98 11 3 0 3718.835 0 0 0 0 0 1 16 172 142 15 5 2 3539.765 0 0 0 0 0 0 1 32 53 9 1 2 9810.695 0 0 0 0 0 0 2 29 82 36 0 1 15011.625 0 0 0 0 0 0 1 12 35 14 0 0 6211.625 0 0 0 0 0 0 1 12 35 14 0 0 6212.555 0 0 0 0 0 0 1 2 12 8 0 0 2213.485 0 0 0 0 0 0 0 5 9 8 0 0 2114.415 0 0 0 0 0 0 0 17 26 9 0 0 5115.345 0 0 0 0 0 0 0 32 47 0 0 0 7916.275 0 0 0 0 0 0 0 0 57 0 0 0 5717.205 0 0 0 0 0 0 0 0 19 9 0 0 2818.135 0 0 0 0 0 0 0 0 14 14 0 0 2719.065 0 0 0 0 0 0 0 0 0 9 9 0 17Total 75 1197991095275 537881 169396 71927 25522 10507 2718 508 32 7 2033647
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
43
Deterministic and Spectral Fatigue AnalysisSOUTH WEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)
HMAX(m)Zero Crossing Period
Total1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 4 312 83 5 0 0 0 0 0 0 0 0 4041.395 0 13043 77660 9910 2681 517 59 29 10 0 0 0 103909
2.325 0 505 123751 123705 25134 10313 2498 266 73 55 0 0 2863003.255 0 0 14828 40344 56887 23971 9668 4848 213 0 0 0 1507594.185 0 0 156 7208 11422 27174 17800 9088 3786 169 0 0 768025.115 0 0 0 799 1802 13775 23575 13171 5757 1500 29 10 604196.045 0 0 0 23 314 3541 16167 13215 5514 1851 199 15 408396.975 0 0 0 0 25 463 6974 9852 4066 838 163 31 224127.905 0 0 0 0 13 113 2419 6630 3465 382 100 6 131288.835 0 0 0 0 0 12 329 3521 2918 311 97 49 72379.765 0 0 0 0 0 0 30 910 1514 269 41 46 281010.695 0 0 0 0 0 0 25 357 1013 440 0 8 184411.625 0 0 0 0 0 0 11 141 433 173 0 0 75712.555 0 0 0 0 0 0 14 41 258 163 0 0 47613.485 0 0 0 0 0 0 0 31 61 51 0 0 14314.415 0 0 0 0 0 0 0 18 27 9 0 0 5415.345 0 0 0 0 0 0 0 7 11 0 0 0 1816.275 0 0 0 0 0 0 0 0 74 0 0 0 7417 205 0 0 0 0 0 0 0 0 95 48 0 0 14317.205 0 0 0 0 0 0 0 0 95 48 0 0 14318.135 0 0 0 0 0 0 0 0 31 31 0 0 6119.065 0 0 0 0 0 0 0 0 0 24 24 0 48
Total 4 13860 216478 181994 98278 79878 79569 62125 29320 6314 653 165 768637
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
44
Deterministic and Spectral Fatigue AnalysisWEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)
HMAX(m)Zero Crossing Period
Total1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 4 307 82 5 0 0 0 0 0 0 0 0 3971.395 0 17691 105333 13441 3637 701 79 40 13 0 0 0 1409352.325 0 490 120085 120040 24389 10007 2424 258 71 53 0 0 2778183.255 0 0 19826 53942 76061 32051 12926 6482 284 0 0 0 2015734.185 0 0 342 15852 25118 59759 39146 19986 8325 371 0 0 1689005.115 0 0 0 2573 5805 44370 75937 42425 18545 4832 94 31 1946136.045 0 0 0 94 1279 14444 65947 53906 22492 7549 811 62 1665846.975 0 0 0 0 125 2306 34749 49085 20257 4176 810 156 1116657.905 0 0 0 0 60 542 11625 31864 16655 1837 482 30 630958.835 0 0 0 0 0 58 1555 16644 13793 1469 461 230 342109.765 0 0 0 0 0 0 171 5107 8502 1512 228 257 1577810.695 0 0 0 0 0 0 72 1027 2914 1266 0 24 530311.625 0 0 0 0 0 0 20 266 819 328 0 0 143312.555 0 0 0 0 0 0 16 48 307 194 0 0 56513.485 0 0 0 0 0 0 0 52 104 87 0 0 24314.415 0 0 0 0 0 0 0 10 15 5 0 0 2915.345 0 0 0 0 0 0 0 4 5 0 0 0 916.275 0 0 0 0 0 0 0 0 9 0 0 0 917.205 0 0 0 0 0 0 0 0 12 6 0 0 1818.135 0 0 0 0 0 0 0 0 18 18 0 0 3519.065 0 0 0 0 0 0 0 0 0 0 0 0 0Total 4 18487 245667 205947 136475 164238 244669 227204 113141 23702 2886 791 1383212
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
45
Deterministic and Spectral Fatigue AnalysisNORTH WEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz)
HMAX(m)Zero Crossing Period
Total1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.50.465 414 30790 8205 456 0 0 0 0 0 0 0 0 398661.395 0 181700 1081870 138052 37354 7199 815 408 136 0 0 0 14475342.325 0 1409 345282 345153 70127 28773 6969 743 205 154 0 0 7988163.255 0 0 12156 33074 46635 19651 7926 3974 174 0 0 0 1235904.185 0 0 36 1666 2640 6281 4114 2101 875 39 0 0 177515.115 0 0 0 37 83 635 1087 607 265 69 1 0 27856.045 0 0 0 0 1 16 74 61 25 8 1 0 1876.975 0 0 0 0 0 3 50 71 29 6 1 0 1627 905 0 0 0 0 0 0 4 10 5 1 0 0 197.905 0 0 0 0 0 0 4 10 5 1 0 0 198.835 0 0 0 0 0 0 0 4 4 0 0 0 99.765 0 0 0 0 0 0 0 6 10 2 0 0 1810.695 0 0 0 0 0 0 0 2 5 2 0 0 911.625 0 0 0 0 0 0 0 2 5 2 0 0 912 555 0 0 0 0 0 0 0 0 0 0 0 0 012.555 0 0 0 0 0 0 0 0 0 0 0 0 013.485 0 0 0 0 0 0 0 0 0 0 0 0 014.415 0 0 0 0 0 0 0 0 0 0 0 0 015.345 0 0 0 0 0 0 0 0 0 0 0 0 016.275 0 0 0 0 0 0 0 0 0 0 0 0 017 205 0 0 0 0 0 0 0 0 0 0 0 0 017.205 0 0 0 0 0 0 0 0 0 0 0 0 018.135 0 0 0 0 0 0 0 0 0 0 0 0 019.065 0 0 0 0 0 0 0 0 0 0 0 0 0Total 414 213900 1447548 518438 156841 62559 21039 7988 1739 283 4 1 2430755
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
46
Deterministic and Spectral Fatigue Analysis
SPECTRAL METHODSPECTRAL METHOD
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
47
Deterministic and Spectral Fatigue AnalysisSPECTRAL ANALYSIS TECHNIQUES
The spectral analysis used for the determining stressresponse to sea state loadings.
The analysis is used to properly account for the actualdistribution of wave energy over the entire frequencyrange.range.
The spectral approach can be subdivided based upon themethod used to develop transfer functions.p
Static Transfer Function Methods Dynamic Transfer function methods
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
48
Deterministic and Spectral Fatigue AnalysisREGULAR WAVE IN FREQUENCY DOMAIN
Transfer functions developed using regular waves in thefrequency domain.
Characterize the wave climate using either the two, three, four or eight parameter format.
Select a sufficient number of frequencies to define all the peaks and valleys inherent in the jacket response transfer functions.
Select a wave height corresponding to each frequency. A Select a wave height corresponding to each frequency. A constant wave steepness that is appropriate for the wave climate can be used. A minimum height of one foot and a maximum height equal to the design wave height should be used.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
49
Deterministic and Spectral Fatigue AnalysisGENERATION OF TRANSFER FUNCTION
A)Wave Period Selection
Multiples of natural period of structurep p Sufficient number of periods mean natural period Wide range covering scatter of wave height in the field.
B) Wave Height
Wave height shall be as 1/20 to 1/25 of wave length. This means with limiting wave steepness in deep waterThis means with limiting wave steepness in deep water.
C) Methods
Regular wave in time domain. Regular wave in frequency domain. Regular wave in time domain.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
50
Deterministic and Spectral Fatigue AnalysisSELECTION OF WAVE FREQUENCY FOR TRANSFER FUNCTION
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
51
Deterministic and Spectral Fatigue AnalysisStress Range Transfer FunctionCompute a stress range transfer function at each point where fatiguedamage is to be accumulated for a minimum of four platformdirections.
For jackets with unusual geometry or where wave directionalityor spreading or current is considered, more directions may berequired
At each frequency, a point on the transfer function is determinedby passing an Airy wave of the appropriate height through thestructure and dividing the response stress range by the waveheight.
A sufficient number of time steps in the wave cycle at whichmembers stresses are computed should be selected todetermine the maximum brace hot spot stress range.
A minimum of four hot spot locations at both the brace andchord side of the connection should be considered.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
52
Deterministic and Spectral Fatigue AnalysisSpectral RepresentationSpectral analysis is useful inrepresenting the sea state energyaccurately as approximation is discretey ppwave scatter data is removed. Againthe response can be generated eitherof the methods discussed above.
If the structure system respondsdynamically to the incident loads,
t l l i ith d i ff tspectral analysis with dynamic effectsis suitable.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
53
Deterministic and Spectral Fatigue Analysis
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
54
Deterministic and Spectral Fatigue AnalysisCentre of Fatigue Damage WaveThe partial damage, Di, j caused by a particularsea state is hence proportional to the number ofoccurrences of the sea state, ni, j, and thesignificant wave height, HS, raised to the power( ) f h l f h S N P i li(m) of the slope of the S-N curve. Proportionalityto the number of stress cycles in the sea statetranslates into an inversely proportionalrelationship to the mean zero crossing period, TzConsequently:Consequently:
, j 1, j
1
0.50.5
mi i i
ij j
N H HD
T T
The above calculation is repeated for eachsea state in the wave scatter diagram toproduce a damage scatter diagram with
TZ mean zero-crossing periodHS significant wave heightTC central value of the mean zero crossing periodHC central value of the significant wave height
relative damages in the state bins.
HC central value of the significant wave heightDi, j fatigue damage from sea states with Hi<Hs<Hi+1 and Tj<Tz<Tj+1Di fatigue damage from sea states with Hi<Hs<Hi+1Dj fatigue damage from sea states with Tj<Tz<Tj+1D fatigue damage from sea states falling within indicated range of Hs and Tz
22-Jul-13 55 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
Deterministic and Spectral Fatigue AnalysisCENTRE OF FATIGUE DAMAGE SEASTATE
i
siiS D
HDH Significant wave height at the
centre of damage
i
siiz D
TDT Zero crossing period at the
centre of damage
sd HH 86.1Significant wave height at the centre of damage
Zero crossing period at the centre of damage zd TT 27.1
Using the above wave height and period, an analysis of the structure can be carried out which represents the same cumulative effect.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
56
Deterministic and Spectral Fatigue Analysis
All wave directions All sea statesinD
N
1 1j i iN
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
57
Deterministic and Spectral Fatigue AnalysisWave Scatter Data
T P t S tt Di
Wave scatter data is the information relating wave height, period and theoccurrences for defining the sea state at a particular site during a specified period.This can be expressed in following two ways.
Two Parameter Scatter DiagramThis is specified as a relationship between the number of occurrences for aparticular wave height (Hmax) and period (Tz) The specified waves shall bemaximum wave height with zero crossing period for that group of occurrences.Two parameter scatter data can be developed for each direction and used for thedeterministic fatigue analysis using the relationship between wave direction () andwave period (Tz).
Directional Scatter DataDirectional scatter data includes three parameters : Significant wave height (Hs),Peak Period (Tp) and the mean direction.
This data is normally used for spectral distribution of wave energy represented byHs and Tp for each direction.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
58
Deterministic and Spectral Fatigue AnalysisTwo Parameter Wave Scatter Data
n00 n01 n02 n03 n04 . . . . nr0
n10 . . . nr1
0H1
H2
0 T1 T2 T3 T4 T5 T6 T7 T8 T9
n20 . . nr2
n30 . . nr3
n40 n 4
H2
H3
H4
H n40 nr4
. nr5
. nr6
H5
H6
H7
. nr7
. nr8
nc0 nc1 nc2 nc3 nc4 nc5 nc6 nc7 nc8 n
H8
H9
n00, n01,. . . are number of occurrences for each set of wave height and periodnc0, nc1,. . . are summation for each wave period andnr0, nr1,. . . are summation for each wave height andn is the total number of occurrences for all wave height and period22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
59n is the total number of occurrences for all wave height and period
Deterministic and Spectral Fatigue AnalysisDirectional distribution for wave height
N NE E SE S SW W NW Total
d00 d01 d02 d03 d04 . . . nh0
d n
0H1
d10 . . . nh1
d20 . . nh2
d30 . . nh3
H2
H3
H4
d40 nh4
. nh5
. nh6
H5
H6
H h6
. nh7
. nh8
n n n n n n n n n
H7
H8
H9
nd1 nd2 nd3 nd4 nd5 nd6 nd7 nd8 nd00, d01,. . . are number of occurrences for each set of wave height and directionnd0, nd1,. . . are summation for each direction and nh0, nh1,. . . are summationfor each wave height and n is the total number of occurrences.22-Jul-13 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
60
g
Deterministic and Spectral Fatigue AnalysisLINEAR SYSTEMResponse of a linear system can be described by
R f Z f F fwhereZ(f) = Response transfer functionF(f) = Fourier Transform of forcing functionR(f) = Fourier Transform of ResponseR(f) = Fourier Transform of Response
If the forcing function has many number of sinusoidal function with unit amplitude, such as decomposed Random waves, then for each
1 1 1 1 1 1R f Z f F f
forcing function, the above equation can be written as,
i i iR f Z f F f
In matrix notation, it can be written as
22-Jul-13 61 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
Deterministic and Spectral Fatigue AnalysisMultiplying the variable and retaining the diagonal terms
2i i i iR f R f H f H f F f
For a stationary random process of y(f) the power spectral density For a stationary random process of y(f), the power spectral density Sy(f) is y2(f) and hence the displacement can be written as
2 S f df
2
0yy t S f df
2
0RMS i FY R f S f
RMS value of displacement
0whereSy(f) = Power spectral density of responseSF(f) = Power spectral density forcing function.22-Jul-13 62 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
Deterministic and Spectral Fatigue AnalysisSPECTRAL RESPONSE OF JACKET STRUCTUREThis transfer function approach can be applied to a realistic system such as jacket structure response (in this case stress at a particular point in the structure). Following assumptions are made in the development of stress transfer function Sea state is assumed to be a
stationary Gaussian randomprocess. The stationary process
transfer function.
has the joint probabilitydistribution that des notchange with time or space.
The Spectra representing the The Spectra representing thestate is assumed to be narrowbanded.
The stress response of the Incident h i ht
Transfer f ti fjacket structure can be
simulated by RayleighDistribution for a narrow bandwave spectra.
wave height spectra
function of stresses
wave spectra.22-Jul-13 63 Prof. S. Nallayarasu
Department of Ocean Engineering Indian Institute of Technology Madras-36
Deterministic and Spectral Fatigue AnalysisSPECTRAL RESPONSE OF JACKET STRUCTURETh t t t th l ti f th j k t h ll b t d b t i l The sea state at the location of the jacket shall be represented by a typical spectra of either P-M, or JONSWAP type.The spectrum shall bedivided in to several subdivided in to several subsegments as shown infigure each with aconstant frequency rangedf and energy densitySHi(f).
This procedure isThis procedure isrepeated for alldirections with eachdirection represented by
t ith diff ta spectrum with differentsignificant wave heightand peak period
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
64
Deterministic and Spectral Fatigue Analysis
From the definition of linear system for the transfer function the
2 2R Z f F f
From the definition of linear system for the transfer function, the transfer function Zi (f) and the forcing function Fi(f) can be related as
RMS R f 2 2
0iRMS i iR Z f F f RMS Response of
structure
Replacing spectral density of forcing function with S (f) spectral Replacing spectral density of forcing function with SHi(f) – spectral density of wave height, the equation can be written as
0
iRMS i HZ f S f
RMS stress response of structure
0
Stress transfer functionPower spectral density of wave
22-Jul-13 65 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
Deterministic and Spectral Fatigue Analysis
The expected number of cycles n(s) associated with the spectrum during the
DdN b f l li d
p y ( ) p gdesign life (DL) can be calculated for each sea state induced stress (s) in which theterm dL is the fraction of spectrum of the sea state that prevails and Tz is the zerocrossing period.
iz
LLi T
Ddsn )(Number of cycles applied for each stress state (s)
The response in terms of stress at a particular location in the jacket and
dffSfH )()(2RMS stress range
The response in terms of stress at a particular location in the jacket andcorresponding zero crossing period can be written as
T
dffSfH
i
ii
RMS
HiRMS )()(0
RMS stress range
dffSfHfT
i
i
i
Hii
RMSz
)()(220
Zero crossing period
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
66
Deterministic and Spectral Fatigue AnalysisUsing Rayleigh probability distribution function (PDF) of the stress range at a
2
2
2 exp)( sssp
location in the jacket, the probability of the stresses in terms of RMS responsestress can be expressed as
RMSRMS
The partial fatigue damage due to stress range between s and s+ds using the S-Ncurve and the number of cycles that corresponding sea state n(s) can be computedas
dsspsNsnsdD )()()(
2)()(
The cumulative fatigue damage due to stress ranges in the complete spectrum canbe computed by integrating between 0 and frequencies of the spectrum
0 2
2
2 exp)()()( dss
sNspsnD
ii RMSRMS Cumulative fatigue damage
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
67
Deterministic and Spectral Fatigue AnalysisProbability Distribution of Stress ResponseThe probability distribution of stress response using Rayleigh distribution is shown in figure.
2
2
2 exp)( sssp RMSRMS
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
68
Deterministic and Spectral Fatigue AnalysisLinearisation of Wave ForcesIn linearizing the applied wave force, drag forces are approximated by sinusoidallyvarying forces and inundation effects are approximated or neglected. As a result,the equations of motion can then be solved without performing direct time
ff f fintegration. For typical small waves the effects of linearization are not of greatimportance; however, for large waves they may be significant if inundation effectsare neglected
CDVVDCF 1 2
M i E ti aCVVDCF WMwDT 4
2
Morison Equation
The square term in the drag part of the Morison can be linearized using stochastic principles
21 82 4T w d V w m
DF C V C a
Linearized Morison Equation
principles.
where V is the standard deviation of the velocity obtained using Gaussian process probability density function.
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
69
Deterministic and Spectral Fatigue AnalysisJacket Models
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
70
Deterministic and Spectral Fatigue AnalysisDirectional distribution of significant wave height and
k i dpeak period
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
71
Deterministic and Spectral Fatigue Analysis
1.25%2.39%
27 38%27.38%
0.31%28.00%
0 42%0.42%13.67%
26.54%
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
72
Deterministic and Spectral Fatigue Analysis
NORTH DIRECTION (JOINT DISTRIBUTION OF HS and TP)NORTH DIRECTION (JOINT DISTRIBUTION OF HS and TP)Hs(m)
Peak PeriodTotal1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.88
0.25 0.0027 0.2000 0.0533 0.0030 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.25900.75 0.0000 0.2130 1.2683 0.1618 0.0438 0.0084 0.0010 0.0005 0.0002 0.0000 0.0000 0.0000 1.69701 25 0 0000 0 0007 0 1630 0 1629 0 0331 0 0136 0 0033 0 0004 0 0001 0 0001 0 0000 0 0000 0 37701.25 0.0000 0.0007 0.1630 0.1629 0.0331 0.0136 0.0033 0.0004 0.0001 0.0001 0.0000 0.0000 0.37701.75 0.0000 0.0000 0.0060 0.0163 0.0230 0.0097 0.0039 0.0020 0.0001 0.0000 0.0000 0.0000 0.06102.25 0.0000 0.0000 0.0000 0.0002 0.0003 0.0007 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.00202.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0004 0.0002 0.0001 0.0000 0.0000 0.0000 0.00103.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00003.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00003.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00004.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00004.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00005.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00005.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0027 0.4137 1.4906 0.3442 0.1002 0.0327 0.0090 0.0032 0.0005 0.0001 0.0000 0.0000 2.3970
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
73
Deterministic and Spectral Fatigue Analysis
NORTH EAST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)NORTH EAST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)Hs(m)
Peak PeriodTotal1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.88
0.25 0.0019 0.1444 0.0385 0.0021 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.18700.75 0.0000 0.1230 0.7324 0.0935 0.0253 0.0049 0.0006 0.0003 0.0001 0.0000 0.0000 0.0000 0.98001 25 0 0000 0 0001 0 0359 0 0359 0 0073 0 0030 0 0007 0 0001 0 0000 0 0000 0 0000 0 0000 0 08301.25 0.0000 0.0001 0.0359 0.0359 0.0073 0.0030 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000 0.08301.75 0.0000 0.0000 0.0003 0.0008 0.0011 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.00302.25 0.0000 0.0000 0.0000 0.0003 0.0004 0.0011 0.0007 0.0004 0.0001 0.0000 0.0000 0.0000 0.00302.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00003.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0003 0.0001 0.0000 0.0000 0.0000 0.00103.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00003.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00004.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00004.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00005.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00005.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0019 0.2676 0.8071 0.1325 0.0342 0.0095 0.0026 0.0011 0.0004 0.0001 0.0000 0.0000 1.2570
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
74
Deterministic and Spectral Fatigue Analysis
EAST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)EAST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)Hs(m)
Peak PeriodTotal1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.88
0.25 0.0002 0.0178 0.0047 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.02300.75 0.0000 0.0251 0.1495 0.0191 0.0052 0.0010 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.20001 25 0 0000 0 0001 0 0203 0 0203 0 0041 0 0017 0 0004 0 0000 0 0000 0 0000 0 0000 0 0000 0 04701.25 0.0000 0.0001 0.0203 0.0203 0.0041 0.0017 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.04701.75 0.0000 0.0000 0.0022 0.0059 0.0083 0.0035 0.0014 0.0007 0.0000 0.0000 0.0000 0.0000 0.02202.25 0.0000 0.0000 0.0000 0.0008 0.0012 0.0028 0.0019 0.0009 0.0004 0.0000 0.0000 0.0000 0.00802.75 0.0000 0.0000 0.0000 0.0001 0.0001 0.0009 0.0016 0.0009 0.0004 0.0001 0.0000 0.0000 0.00403.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0016 0.0013 0.0005 0.0002 0.0000 0.0000 0.00403.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0004 0.0002 0.0000 0.0000 0.0000 0.00103.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0004 0.0002 0.0000 0.0000 0.0000 0.00104.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0010 0.0005 0.0001 0.0000 0.0000 0.00204.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0004 0.0000 0.0000 0.0000 0.00105.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0001 0.0000 0.0000 0.00105.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0005 0.0002 0.0000 0.0000 0.00106.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0002 0.0430 0.1767 0.0463 0.0189 0.0103 0.0077 0.0064 0.0036 0.0008 0.0001 0.0000 0.3140
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
75
Deterministic and Spectral Fatigue Analysis
SOUTH EAST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)( p)Hs(m)
Peak PeriodTotal1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.88
0.25 0.0004 0.0263 0.0070 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.03400.75 0.0000 0.0331 0.1973 0.0252 0.0068 0.0013 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.26401.25 0.0000 0.0001 0.0229 0.0229 0.0047 0.0019 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.05301.75 0.0000 0.0000 0.0023 0.0062 0.0087 0.0037 0.0015 0.0007 0.0000 0.0000 0.0000 0.0000 0.02302.25 0.0000 0.0000 0.0000 0.0006 0.0009 0.0021 0.0014 0.0007 0.0003 0.0000 0.0000 0.0000 0.00602.75 0.0000 0.0000 0.0000 0.0002 0.0004 0.0034 0.0059 0.0033 0.0014 0.0004 0.0000 0.0000 0.01503.25 0.0000 0.0000 0.0000 0.0000 0.0001 0.0007 0.0032 0.0026 0.0011 0.0004 0.0000 0.0000 0.00803.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0019 0.0026 0.0011 0.0002 0.0000 0.0000 0.00604.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0011 0.0030 0.0016 0.0002 0.0000 0.0000 0.00604.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0010 0.0008 0.0001 0.0000 0.0000 0.00205.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0001 0.0000 0.0000 0.00105.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0005 0.0002 0.0000 0.0000 0.00106.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0006 0.0002 0.0000 0.0000 0.00106.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0003 0.0000 0.0000 0.00107.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0009 0.0007 0.0000 0.0000 0.00207.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0002 0.0000 0.0000 0.00108.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0012 0.0000 0.0000 0.0000 0.00208.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0004 0.0595 0.2295 0.0554 0.0216 0.0133 0.0156 0.0164 0.0111 0.0030 0.0002 0.0001 0.4260
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
76
Deterministic and Spectral Fatigue AnalysisSOUTH DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)
Hs(m) Peak Period Total1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.880.25 0.0008 0.0602 0.0161 0.0009 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.07800.75 0.0000 1.3119 7.8110 0.9967 0.2697 0.0520 0.0059 0.0029 0.0010 0.0000 0.0000 0.0000 10.45101.25 0.0000 0.0227 5.5565 5.5544 1.1285 0.4630 0.1122 0.0120 0.0033 0.0025 0.0000 0.0000 12.85501.75 0.0000 0.0000 0.2606 0.7092 0.9999 0.4214 0.1699 0.0852 0.0037 0.0000 0.0000 0.0000 2.65002.25 0.0000 0.0000 0.0008 0.0367 0.0581 0.1383 0.0906 0.0463 0.0193 0.0009 0.0000 0.0000 0.39102.75 0.0000 0.0000 0.0000 0.0004 0.0009 0.0066 0.0113 0.0063 0.0028 0.0007 0.0000 0.0000 0.02903.25 0.0000 0.0000 0.0000 0.0000 0.0002 0.0025 0.0115 0.0094 0.0039 0.0013 0.0001 0.0000 0.02903.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0065 0.0092 0.0038 0.0008 0.0002 0.0000 0.02103.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0065 0.0092 0.0038 0.0008 0.0002 0.0000 0.02104.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0017 0.0045 0.0024 0.0003 0.0001 0.0000 0.00904.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0039 0.0032 0.0003 0.0001 0.0001 0.00805.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0016 0.0003 0.0000 0.0000 0.00305.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0008 0.0022 0.0010 0.0000 0.0000 0.00406.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0011 0.0005 0.0000 0.0000 0.00206.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0003 0.0000 0.0000 0.00107.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0004 0.0004 0.0000 0.0000 0.00107.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0002 0.0000 0.0000 0.00108.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0012 0.0000 0.0000 0.0000 0.00208.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0000 0.0000 0.0000 0.00209.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0003 0.0000 0.0000 0.00109.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0005 0.0000 0.0000 0.001010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0005 0.0000 0.0010
Total 0.0008 1.3948 13.6449 7.2983 2.4574 1.0844 0.4101 0.1833 0.0542 0.0107 0.0010 0.0002 26.5400
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
77
Deterministic and Spectral Fatigue Analysis
SOUTHWEST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)SOUTH WEST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)Hs(m) Peak Period Total1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.880.25 0.0000 0.0031 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00400.75 0.0000 0.1614 0.9611 0.1226 0.0332 0.0064 0.0007 0.0004 0.0001 0.0000 0.0000 0.0000 1.28601.25 0.0000 0.0073 1.7994 1.7988 0.3655 0.1500 0.0363 0.0039 0.0011 0.0008 0.0000 0.0000 4.16301.25 0.0000 0.0073 1.7994 1.7988 0.3655 0.1500 0.0363 0.0039 0.0011 0.0008 0.0000 0.0000 4.16301.75 0.0000 0.0000 0.2627 0.7148 1.0079 0.4247 0.1713 0.0859 0.0038 0.0000 0.0000 0.0000 2.67102.25 0.0000 0.0000 0.0033 0.1534 0.2430 0.5781 0.3787 0.1934 0.0805 0.0036 0.0000 0.0000 1.63402.75 0.0000 0.0000 0.0000 0.0193 0.0436 0.3333 0.5705 0.3187 0.1393 0.0363 0.0007 0.0002 1.46203.25 0.0000 0.0000 0.0000 0.0006 0.0082 0.0931 0.4252 0.3475 0.1450 0.0487 0.0052 0.0004 1.07403.75 0.0000 0.0000 0.0000 0.0000 0.0007 0.0126 0.1904 0.2690 0.1110 0.0229 0.0044 0.0009 0.61204.25 0.0000 0.0000 0.0000 0.0000 0.0003 0.0031 0.0660 0.1808 0.0945 0.0104 0.0027 0.0002 0.35804.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0095 0.1017 0.0843 0.0090 0.0028 0.0014 0.20905.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0272 0.0453 0.0081 0.0012 0.0014 0.08405.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0008 0.0112 0.0319 0.0138 0.0000 0.0003 0.05806.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0043 0.0131 0.0053 0.0000 0.0000 0.02306.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0013 0.0081 0.0051 0.0000 0.0000 0.01507.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0009 0.0017 0.0014 0.0000 0.0000 0.00407.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0010 0.0003 0.0000 0.0000 0.00208.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0006 0.0000 0.0000 0.0000 0.00108.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0000 0.0000 0.0000 0.00209.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0027 0.0013 0.0000 0.0000 0.00409.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0010 0.0000 0.0000 0.002010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0010 0.0010 0.0000 0.0020
Total 0.0000 0.1719 3.0274 2.8095 1.7024 1.6017 1.8510 1.5471 0.7670 0.1690 0.0181 0.0047 13.6700
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
78
Deterministic and Spectral Fatigue AnalysisWEST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)
Hs(m) Peak Period Total1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.880.25 0.0000 0.0031 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00400.75 0.0000 0.2033 1.2108 0.1545 0.0418 0.0081 0.0009 0.0005 0.0002 0.0000 0.0000 0.0000 1.62001.25 0.0000 0.0069 1.6879 1.6873 0.3428 0.1407 0.0341 0.0036 0.0010 0.0008 0.0000 0.0000 3.90501.75 0.0000 0.0000 0.3527 0.9596 1.3531 0.5702 0.2300 0.1153 0.0051 0.0000 0.0000 0.0000 3.58602.25 0.0000 0.0000 0.0074 0.3416 0.5413 1.2879 0.8436 0.4307 0.1794 0.0080 0.0000 0.0000 3.64002.75 0.0000 0.0000 0.0000 0.0617 0.1392 1.0638 1.8207 1.0172 0.4446 0.1159 0.0023 0.0008 4.66603.25 0.0000 0.0000 0.0000 0.0024 0.0325 0.3674 1.6773 1.3711 0.5721 0.1920 0.0206 0.0016 4.23703.75 0.0000 0.0000 0.0000 0.0000 0.0033 0.0610 0.9186 1.2976 0.5355 0.1104 0.0214 0.0041 2.95203.75 0.0000 0.0000 0.0000 0.0000 0.0033 0.0610 0.9186 1.2976 0.5355 0.1104 0.0214 0.0041 2.95204.25 0.0000 0.0000 0.0000 0.0000 0.0016 0.0148 0.3180 0.8717 0.4556 0.0503 0.0132 0.0008 1.72604.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0016 0.0442 0.4729 0.3919 0.0417 0.0131 0.0065 0.97205.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0050 0.1505 0.2506 0.0446 0.0067 0.0076 0.46505.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0022 0.0310 0.0879 0.0382 0.0000 0.0007 0.16006 25 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0006 0 0080 0 0246 0 0098 0 0000 0 0000 0 04306.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0006 0.0080 0.0246 0.0098 0.0000 0.0000 0.04306.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0015 0.0098 0.0062 0.0000 0.0000 0.01807.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0017 0.0034 0.0029 0.0000 0.0000 0.00807.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0002 0.0000 0.0000 0.00108.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008 75 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 0000 0 00008.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0003 0.0000 0.0000 0.00109.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0005 0.0000 0.0000 0.001010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0000 0.2133 3.2596 3.2072 2.4557 3.5154 5.8958 5.7736 2.9633 0.6216 0.0773 0.022128.0050
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
79
Deterministic and Spectral Fatigue AnalysisNORTH WEST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp)
Hs(m)Peak Period
Total1.91 3.18 4.45 5.72 6.99 8.26 9.53 10.80 12.07 13.34 14.61 15.880.25 0.0036 0.2657 0.0708 0.0039 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.34400.75 0.0000 1.923811.4545 1.4617 0.3955 0.0762 0.0086 0.0043 0.0014 0.0000 0.0000 0.000015.32601.25 0.0000 0.0172 4.2144 4.2128 0.8559 0.3512 0.0851 0.0091 0.0025 0.0019 0.0000 0.0000 9.75001.75 0.0000 0.0000 0.1624 0.4418 0.6230 0.2625 0.1059 0.0531 0.0023 0.0000 0.0000 0.0000 1.65102.25 0.0000 0.0000 0.0005 0.0246 0.0390 0.0927 0.0607 0.0310 0.0129 0.0006 0.0000 0.0000 0.26202.75 0.0000 0.0000 0.0000 0.0006 0.0013 0.0103 0.0176 0.0098 0.0043 0.0011 0.0000 0.0000 0.04503.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0016 0.0013 0.0005 0.0002 0.0000 0.0000 0.00403.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0012 0.0018 0.0007 0.0001 0.0000 0.0000 0.00404.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0005 0.0003 0.0000 0.0000 0.0000 0.00104.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00005.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0005 0.0001 0.0000 0.0000 0.00105.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00006.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00007.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00008.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00009.75 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.000010.25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
Total 0.0036 2.206715.9025 6.1454 1.9148 0.7933 0.2809 0.1112 0.0255 0.0040 0.0001 0.000027.3880
22-Jul-13 Prof. S. Nallayarasu Department of Ocean Engineering
Indian Institute of Technology Madras-36
80