Deterministic and Spectral Fatigue Analysis
22-Jul-13
1
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Contents
Introduction Global Response Models Structural Model H drod namic Model Foundation Model Jacket appurtenances Structural Response Methods Anal sis Static An Pseudo-Static Analysis Wave Response Analysis Free Vibration Analysis Mass Modelin
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Fatigue Analysis methods Fatigue analysis steps Deterministic Method Wave scatter data Directional Distribution Spectral method Stress Transfer function Sele lect ctio ion n wav wave e fre fre uenc uencie ies s Se Centre of Fatigue Damage Wave Spectra Linear System Fati ue Dama e
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Contents
Introduction Global Response Models Structural Model H drod namic Model Foundation Model Jacket appurtenances Structural Response Methods Anal sis Static An Pseudo-Static Analysis Wave Response Analysis Free Vibration Analysis Mass Modelin
22-Jul-13
2
Fatigue Analysis methods Fatigue analysis steps Deterministic Method Wave scatter data Directional Distribution Spectral method Stress Transfer function Sele lect ctio ion n wav wave e fre fre uenc uencie ies s Se Centre of Fatigue Damage Wave Spectra Linear System Fati ue Dama e
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis STRUCTURAL MODEL The structural model should include all necessary stiffness contributing elements inc includ luding ing the the fo foll llow owin ing g.
Primary Structure of jacket and deck Conductors
Following items shall be modeled to include the hydrodynamic loads only
Caissons Boat landing no es Secondary structures such as walkway, handrail and pad-eyes.
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis FOUNDATION MODEL The foundation model for the jacket structures can be any one of the following thre three e type ypes.
Equivalent pile stub or depth of fixity Super Element at pile head -
Conductors shall be modeled as non-load sharing element as they suppose to rans er e oa o e ac e an par y o soil. up to a 10 diameter as the depth of fixity. fixity. Pile soil interaction can also be performed with appropriate boundary condition at the – . 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SUPER 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 length is condensed to pile head. The is obtained by carrying out a static analysis of the platform with representative horizontal load that corresponds to the fatigue sea state. Since the fatigue sea state contains several wave loads, the representative sea state is taken as the center of fatigue damage sea state.
The center of fatigue damage sea state shall be calculated using the wave scatter data assuming a Rayleigh . Once this 6x6 matrix is obtained, the analysis of the structure can be carried out. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis NON-LINEAR PILE SOIL INTERACTION Non-linear behaviour of soil is modeled using load displacement characteristics for skin friction, end bearing and lateral reaction.
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis of a pile under vertical axial loading
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Jacket Appurtenances Hydrodynamic model of the following appurtenances shall be included in the simulation of wave loading on jacket structures Circular cylinders Non-circular members
y ro ynam c mo e
or secon ary s ruc ures
Caissons Boat landin Anodes Secondary structures such as walkway, handrail and pad-eys.
Appropriate Mass models for dynamic analysis
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Hydrodynamic Model Even 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
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Anodes 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.
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Boat Landing and Barge Bumpers Boat Landing shall usually be modeled since large number of the members are tubular and only fenders shall be treated carefully. However, for preliminary analyses, the boat landing can be treated as equivalent tube with diameter and Cd and Cm of the total boat landing approximately.
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis BOAT LANDING AND BARGE BUMPER MODEL Barge Bumper
Boat Landing
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Mudmat and Supports Mud mat is not modeled in the in place analysis. However, some times it ma be worth modeling if large number of external braces supporting the mud mat are required. These braces will additional wave loads
induce
Hence case to case basis, one shall make a decision to include
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Mudmat Braces
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Buoyancy Tanks
Bou anc Tanks
Buoyancy Tanks are provided during installation to enhance the floatation properties of the jacket. These tanks are not required a ter t e nsta at on s complete. , tanks can be removed.
permanently, then the wave loads on these tanks shall be considered. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis ANODES BOUYANCY TANKS Bouyancy Tank
Pile Guide
Skirt Sleeve
Anode
Mudmat
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Equivalent Diameter Method This method predicts the drag component correctly but does not include the inertia component. This method is easy to apply as the member diameter can be increased for
Drag Area
Anode '
d
( dL) n * A anodes Original Structural Member
where – Aanodes – surface area of anodes
d
d’
Surface area of Anode includes the area of core and anode 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Equivalent Cd and Cm Method In 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 more accura e an e o er me o s.
Equivalent Cd’ In this method, the equivalent Cd’ and Cm’ are calculated and applied for each member
C
'
d
C
n * A *C
dm
a
da
A
T
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 – 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Equivalent Cm’ In this method, the equivalent Cd’ and Cm’ are calculated and applied for each member
n*V*C a
m
'
mm
ma
V
T
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
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Walkways and handrails The tubular members for walkways and handrails shall be included in the calculation of equivalent Cd and Cm calculations
Caissons and Risers Normally 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 capa y o carry ou suc s mu a on
Launch Cradle Launch Cradle has different dimensions an s a e rea e care u y or e calculation of the environmental loads and buoyancy. Dimensions W and H shall be specified for appropriate wave load calculations 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Shear and Yoke Plates Skirt Piles are normally connected to the jacket legs using plated connection for simplicity and economical. urt er, t e at gue es gn o tu u ar mem ers etween t e s rt s eeve and the jacket leg may be more difficult to handle.
to simulate the load path correctly using finite elements. However, Drag are shall be provided to simulate the wave/current loads
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SHEAR PLATE / YOKE PLATE CONNECTION
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Structural Response Analysis Methods Global response of structure can be performed by any one of the methods.
tat c na ys s Static Analysis (Pseudo-Static) Dynamic Wave Response Analysis (Frequency Domain)
All the above methods uses a linear stress – strain principles within elastic limit and assumes small displacement assumptions as most o practica app ications in ixe o s ore structures a within this region. , , are described. Each has its own advantages and disadvantages. Hence selection of method depends on the type of structure and its loadin attern. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Static Analysis Static analysis can be performed when the loads are static (not varying with time). This method is very similar to simple stiffness methods. For very large structures, matrix methods are employed.
K X F where
3 EI W L 3
K is the stiffness matrix F is the force vector X is the displacement vector
e a ove equat on depicts a cantilever with W as end load.
, (frequency) of structure is away from the loading (frequency). T ical exam le of natural eriod of acket less than 2 sec is awa from the wave period of say 10 sec. Hence the loads due to wave can be assumed to be static. However, this needs to considered carefully if the wave periods is less than 10 sec. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Pseudo-Static Analysis Pseudo-Static analysis are performed when the loads are varying with time. In this method, the dynamic loads are approximated by considering the maximum amplitude of the load in a wave cycle. However, the effect of dynamic interaction between the structure and the load is taken in to consideration approximately by using a .
K X F DAF w ere
K is t e sti ness matrix e astic F is the force vector X is the displacement vector
It is to be noted that this method is approximate as it considers only the first mode and there may be other local modes contributing to . 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis DYNAMIC AMPLIFICATION FACTOR (SDOF) Dynamic amplification of a structure can be calculated using a approximate equivalent model of the structure using Single Degree of Freedom System (SDOF). DAF
1 T 2 T T T 2
N
2
n
2
TN – Natural Period of the structure –
– Structural Damping Ratio 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis DYNAMIC AMPLIFICATION FACTOR (DAF) 10 9 Damping = 0.1% 8
Damping = 5%
7 6 amp ng = 5
F A D4
Damping = 50% Damping = 100%
2 1 0 0
0.5
1
1.5
2
Frequency Ratio 22-Jul-13
27
2.5
3
3.5
4
= TN / T Prof. S. Nallayarasu Department of Ocean Engineering
4.5
5
Deterministic and Spectral Fatigue Analysis Wave Response analysis If the natural period of the platform is close to the fatigue waves, assumption of equivalent static analysis does not hold good. Simple calculations for DAF using SDOF model for will result in very conservative or non-conservative results depending on the assumptions made on average wave periods for the calculation of DAF . Hence a Dynamic Wave Response analysis needs to be performed. . The details of this method can be referred in standard text books. However, brief details are given below. The equation for computation of response is
K
X
M
X
C
X
where
F
M is the structural mass matrix C is the structural damping matrix , , The solution to the above can be performed using iterative methods such Wilson-theta or Newton-Raphson methods. But thi s cannot be combined with pile soil interaction wh ich is another iterative technique. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Free Vibration Analysis Free vibration analysis of multi-element framed structures can be performed using the following equation. The above equation can be 0 written in a simple form for a K X M X s ng e egree o ree om Using the above, mass [M] and stiffness matrices [K] equation as can be generated, which can be used for further analysis for dynamic responses. Further, mode shapes (normalized displacements) and Eigen frequencies () are also extracted from the above analysis.
ence a ynam c wave response ana ys s can e per orme Pile Soil Interaction analysis (PSI).
n two stages nc u ng
Free Vibration Analysis
K X M X 0
Dynamic Response Analysis
K X M X C X F
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Mass Modelling Since 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 Boat Landing Platforms Anodes Monorails Barge Bumper Padeyes Padeyes Equipment Mudmat Walkways Walkways Handrails Handrails and Grating Grating Risers and Caissons Piping Launch Cradle Supports Flooding and Grouting pipes Crane Boom rest Bouyancy Tanks Yoke Plates Shear 22-Jul-13
30
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis FATIGUE ANALYSIS METHODS
DETERMINISTIC METHODS (STATIC OR DYNAMIC)
Wave Induced Motion Induced
SPECTRAL METHODS (STATIC OR DYNAMIC)
Wave Induced Wind Induced
Deterministic or Spectral methods, one can include dynamic e ects epen ing on t e type o structure an oa ing. For example, fixed structures such as jacket may not be sensitive to dynamic loading and hence quasi-static methods is sufficient , tower may require dynamic response as the natural period may fall within the wave energy regime. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis FATIGUE ANALYSIS STEPS The various steps involved in the fatigue analysis of offshore structures is listed below irrespective of the method. The major difference comes in the response evaluation. The reminder of the proce ure s some w a s m ar. Spectral
Deterministic
Structural Model Wave Climate (Scatter Data) Hydrodynamic Model Wave Load Estimation Non-linear Pile Soil Interaction Structural Response Dynamic effects (if required) Cyclic Stress Estimation SCF Calculation Hot Spot Stress Computation Estimate of N using S-N curve Selection of Factor of Safety Fati ue Dama e Calculations 22-Jul-13
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Structural Model Wave Climate (Scatter Data) Centre of fatigue damage wave Drag Linearization Foundation Linearization Structural Response Dynamic effects (if required) Cyclic Stress Estimation SCF Calculation Hot Spot Stress Computation Estimate of N using S-N curve Selection of Factor of Safety Fati ue Dama e Calculations
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
METHOD
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Deterministic Method Deterministic analysis is based on the discrete wave scatter data with wave number of occurrences for each sea state. This method is suitable if the distribution of wave energy is away from the natural period of the structure. Two methods are adopted depending the dynamic characteristics of the structure. Static Response Dynamic Response If the natural period of the structure is less than 3 seconds, normally the dynamic effects can be ignored. 22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
D
All wave directions All sea states
j
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
i
ni i
Deterministic and Spectral Fatigue Analysis
22-Jul-13
36
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Directional distribution of wave height and period
22-Jul-13
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Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis 2.39%
1.25%
.
0.31% 28.00%
. 13.67% 26.54% 22-Jul-13
38
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis NORTH DIRECTION JOINT DISTRIBUTION OF Hmax and Tz HMAX(m)
1.5
3.5
2.5
0.465
338
1.395
0
25145
Zero Crossing Period 5.5 6.5 7.5 8.5
4.5
6701
372
22186 132098
9.5
10.5
11.5
Total
12.5
0
0
0
0
0
0
0
0 32557
16856
4561
879
100
50
17
0
0
0 176746
. 3.255
0
0
497
1351
1906
803
324
162
7
0
0
0
4.185
0
0
0
16
25
59
39
20
8
0
0
0
5050 167
5.115
0
0
0
1
2
13
23
13
6
1
0
0
58
6.045
0
0
0
0
0
0
0
0
0
0
0
0
0
7.905
0
0
0
0
0
0
0
0
0
0
0
0
0
8.835
0
0
0
0
0
0
0
0
0
0
0
0
0
.
0
0
0
0
0
0
0
0
0
0
0
0
0
10.695
9.765
0
0
0
0
0
0
0
0
0
0
0
0
0
11.625
0
0
0
0
0
0
0
0
0
0
0
0
0
12.555
0
0
0
0
0
0
0
0
0
0
0
0
0
13.485
0
0
0
0
0
0
0
0
0
0
0
0
0
14.415
0
0
0
0
0
0
0
0
0
0
0
0
0
15.345
0
0
0
0
0
0
0
0
0
0
0
0
0
16.275
0
0
0
0
0
0
0
0
0
0
0
0
0
17.205
0
0
0
0
0
0
0
0
0
0
0
0
0
18.135
0
0
0
0
0
0
0
0
0
0
0
0
0
19.065
0
0
0
0
0
0
0
0
0
0
0
0
0
47390 153770
33066
9433
2961
777
276
46
8
0
0
248065
Total
22-Jul-13
338
39
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis NORTH EAST DIRECTION JOINT DISTRIBUTION OF Hmax and Tz HMAX(m)
1.5
3.5
2.5
Zero Crossing Period 5.5 6.5 7.5 8.5
4.5
0.465
248
18392
4901
272
1.395
0
12968
77213
2.325
0
13
3132
3.255
0
0
4.185
0
0
5.115
0
0
0
6.045
0
0
6.975
0
0
7.905
0
8.835
0
9.765
10.5
0
0
0
0
0
9853
2666
514
58
29
3131
636
261
63
7
24
67
94
40
16
8
0
17
26
63
41
21
0
0
3
6
3
0
0
0
4
18
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9.5
11.5
Total
12.5
0
0
0 23813
10
0
0
0 103311
2
1
0
0
0
0
0
0
249
9
0
0
0
177
1
0
0
0
15
15
6
2
0
0
45
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7246
0
0
0
0
0
0
0
0
0
0
0
0
0
10.695
0
0
0
0
0
0
0
0
0
0
0
0
0
11.625
0
0
0
0
0
0
0
0
0
0
0
0
0
12.555
0
0
0
0
0
0
0
0
0
0
0
0
0
13.485
0
0
0
0
0
0
0
0
0
0
0
0
0
14.415
0
0
0
0
0
0
0
0
0
0
0
0
0
15.345
0
0
0
0
0
0
0
0
0
0
0
0
0
16.275
0
0
0
0
0
0
0
0
0
0
0
0
0
17.205
0
0
0
0
0
0
0
0
0
0
0
0
0
18.135
0
0
0
0
0
0
0
0
0
0
0
0
0
19.065
Total
22-Jul-13
0
0
0
0
0
0
0
0
0
0
0
0
0
248
31373
85272
13339
3423
884
202
83
28
4
0
0
134856
40
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis EAST DIRECTION JOINT DISTRIBUTION OF Hmax and Tz HMAX(m)
1.5
3.5
2.5
Zero Crossing Period 5.5 6.5 7.5 8.5
4.5
0.465
31
2284
609
1.395
0
2565
15270
2.325
0
7
1744
3.255
0
0
148
4.185
0
0
1
5.115
0
0
6.045
0
0
34
9.5
0
0
0
0
1949
527
102
12
6
1743
354
145
35
4
404
569
240
97
49
47
75
178
116
59
0
3
6
47
80
45
0
0
1
16
74
61
10.5 0
11.5
Total
12.5
0
0
0
2957
2
0
0
0 20431
1
1
0
0
4035
2
0
0
0
1509
25
1
0
0
502
20
5
0
0
206
25
8
1
0
187
6.975
0
0
0
0
0
1
21
30
13
3
1
0
69
7.905
0
0
0
0
0
1
17
46
24
3
1
0
91
8.835
0
0
0
0
0
0
2
18
15
2
0
0
36
9.765
0
0
0
0
0
0
0
15
25
4
1
1
46
0
4
12
5
0
0
22
10.695
0
0
0
0
0
0
11.625
0
0
0
0
0
0
0
0
0
0
0
0
0
12.555
0
0
0
0
0
0
0
0
0
0
0
0
0
13.485
0
0
0
0
0
0
0
0
0
0
0
0
0
14.415
0
0
0
0
0
0
0
0
0
0
0
0
0
15.345
0
0
0
0
0
0
0
0
0
0
0
0
0
16.275
0
0
0
0
0
0
0
0
0
0
0
0
0
17.205
0
0
0
0
0
0
0
0
0
0
0
0
0
18.135
0
0
0
0
0
0
0
0
0
0
0
0
0
19.065
0
0
0
0
0
0
0
0
0
0
0
0
0
31
4856
17772
4180
1533
730
455
336
163
32
3
1
30091
Total
22-Jul-13
41
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SOUTH EAST DIRECTION JOINT DISTRIBUTION OF Hmax and Tz HMAX(m)
1.5
3.5
2.5
Zero Crossing Period 5.5 6.5 7.5 8.5
4.5
0.465
38
2818
751
42
1.395
0
3257
19392
2.325
0
8
1905
3.255
0
0
4.185
0
0
5.115
0
0
0
6.045
0
0
0
6.975
0
0
7.905
0
0
8.835
0
9.765
10.5
0
0
0
0
0
2474
670
129
15
7
1904
387
159
38
4
149
404
570
240
97
49
1
36
57
136
89
45
11
24
184
315
176
0
3
33
152
125
0
0
0
6
89
0
0
0
2
53
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12.555
0
0
0
13.485
0
0
14.415
0
0
15.345
0
16.275
17.205
18.135 19.065
10.695
11.5
Total
12.5
0
0
0
2
0
0
0 25946
1
1
0
0
4407
2
0
0
0
1510
19
1
0
0
384
77
20
0
0
808
52
17
2
0
385
126
52
11
2
0
287
146
77
8
2
0
290
4
44
36
4
1
1
90
0
0
12
19
3
1
1
36
0
0
1
11
31
14
0
0
57
0
0
0
1
4
28
17
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
38
6083
22197
4871
1711
890
9.5
3649
.
Total
22-Jul-13
42
13
25
21
0
0
59
16
24
8
0
0
48
23
35
0
0
0
58
0
0
9
0
0
0
9
0
0
6
3
0
0
9
0
0
0
5
5
0
0
9
0
0
0
0
0
0
0
0
857
808
520
141
8
2
38126
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SOUTH DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz) HMAX(m)
1.5
3.5
2.5
0.465
75
1.395
0
5544
4.5
5.5
1477
82
112592 670387
Zero Crossing Period 6.5 7.5 8.5
9.5
10.5
11.5
Total
12.5
0
0
0
0
0
0
0
0
7178
85545
23147
4461
505
253
84
0
0
0 896973
0
0 159511
. 3.255
0
0
15689
42686
60190
25363
10229
5130
225
0
4.185
0
0
44
2018
3198
7608
4983
2544
1060
47
0
0
5.115
0
0
0
22
50
378
648
362
158
41
1
0
1660
6.045
0
0
0
1
11
121
553
452
189
63
7
1
1398
6.975
0
0
0
0
1
19
285
403
166
34
7
1
917
7.905
0
0
0
0
0
3
68
187
98
11
3
0
371
8.835
0
0
0
0
0
1
16
172
142
15
5
2
353
9.765
0
0
0
0
0
0
1
32
53
9
1
2
98
10.695
0
0
0
0
0
0
2
29
82
36
0
1
150
11.625
0
0
0
0
0
0
1
12
35
14
0
0
62
12.555
0
0
0
0
0
0
1
2
12
8
0
0
22
13.485
0
0
0
0
0
0
0
5
9
8
0
0
21
14.415
0
0
0
0
0
0
0
17
26
9
0
0
51
15.345
0
0
0
0
0
0
0
32
47
0
0
0
79
16.275
0
0
0
0
0
0
0
0
57
0
0
0
57
17.205
0
0
0
0
0
0
0
0
19
9
0
0
28
18.135
0
0
0
0
0
0
0
0
14
14
0
0
27
19.065
0
0
0
0
0
0
0
0
0
9
9
0
17
119799 1095275 537881 169396
71927
25522
10507
2718
508
32
7
2033647
Total
22-Jul-13
75
43
Prof. S. Nallayarasu Department of Ocean Engineering
21502
Deterministic and Spectral Fatigue Analysis SOUTH WEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz) HMAX(m)
1.5
3.5
2.5
4.5
5.5
Zero Crossing Period 6.5 7.5 8.5
9.5
10.5
11.5
Total
12.5
0.465
4
312
83
5
0
0
0
0
0
0
0
0
1.395
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 286300
3.255
0
0
14828
40344
56887
23971
9668
4848
213
0
0
0 150759
4.185
0
0
156
7208
11422
27174
17800
9088
3786
169
0
0
76802
5.115
0
0
0
799
1802
13775
23575
13171
5757
1500
29
10
60419
6.045
0
0
0
23
314
3541
16167
13215
5514
1851
199
15
40839
6.975
0
0
0
0
25
463
6974
9852
4066
838
163
31
22412
7.905
0
0
0
0
13
113
2419
6630
3465
382
100
6
13128
8.835
0
0
0
0
0
12
329
3521
2918
311
97
49
7237
9.765
0
0
0
0
0
0
30
910
1514
269
41
46
2810
10.695
0
0
0
0
0
0
25
357
1013
440
0
8
1844
11.625
0
0
0
0
0
0
11
141
433
173
0
0
757
12.555
0
0
0
0
0
0
14
41
258
163
0
0
476
13.485
0
0
0
0
0
0
0
31
61
51
0
0
143
14.415
0
0
0
0
0
0
0
18
27
9
0
0
54
15.345
0
0
0
0
0
0
0
7
11
0
0
0
18
16.275
0
0
0
0
0
0
0
0
74
0
0
0
74
18.135
0
0
0
0
0
0
0
0
31
31
0
0
61
19.065
0
0
0
0
0
0
0
0
0
24
24
0
48
13860 216478 181994
98278
79878
79569
62125
29320
6314
653
165
768637
404
.
Total
22-Jul-13
4
44
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis WEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz) HMAX(m)
1.5
3.5
2.5
4.5
5.5
0.465
4
307
82
5
1.395
0
17691
105333
2.325
0
490
3.255
0
0
4.185
0
0
342
5.115
0
0
0
6.045
0
0
6.975
0
7.905
0
8.835
0
9.765
0
10.695 11.625
8.5
9.5
10.5
11.5
Total
12.5
0
0
0
0
0
0
0
0
13441
3637
701
79
40
13
0
0
0 140935
120085
120040
24389
10007
2424
258
71
53
0
0 277818
19826
53942
76061
32051
12926
6482
284
0
0
0 201573
15852
25118
59759
39146
19986
8325
371
0
0 168900
2573
5805
44370
75937
42425
18545
4832
94
31 194613
0
94
1279
14444
65947
53906
22492
7549
811
62 166584
0
0
0
125
2306
34749
49085
20257
4176
810
156 111665
0
0
0
60
542
11625
31864
16655
1837
482
30
63095
0
0
0
0
58
1555
16644
13793
1469
461
230
34210
0
0
0
0
0
171
5107
8502
1512
228
257
15778
0
0
0
0
0
0
72
1027
2914
1266
0
24
5303
0
0
0
0
0
0
20
266
819
328
0
0
1433
12.555
0
0
0
0
0
0
16
48
307
194
0
0
565
13.485
0
0
0
0
0
0
0
52
104
87
0
0
243
14.415
0
0
0
0
0
0
0
10
15
5
0
0
29
15.345
0
0
0
0
0
0
0
4
5
0
0
0
9
16.275
0
0
0
0
0
0
0
0
9
0
0
0
9
17.205
0
0
0
0
0
0
0
0
12
6
0
0
18
18.135
0
0
0
0
0
0
0
0
18
18
0
0
35
19.065
0
0
0
0
0
0
0
0
0
0
0
0
0
4
18487
245667
205947
136475
164238
244669
227204
113141
23702
2886
791
1383212
Total
22-Jul-13
45
Zero Crossing Period 6.5 7.5
Prof. S. Nallayarasu Department of Ocean Engineering
397
Deterministic and Spectral Fatigue Analysis NORTH WEST DIRECTION (JOINT DISTRIBUTION OF Hmax and Tz) HMAX(m)
1.5
2.5
Zero Crossing Period
3.5
0.465
414
30790
1.395
0
2.325
0
1409
3.255
0
0
4.185
0
5.115
0
6.045 6.975
4.5
5.5
8205
456
181700 1081870
6.5
7.5
8.5
9.5
10.5
11.5
Total
12.5
0
0
0
0
0
0
0
0
39866
138052
37354
7199
815
408
136
0
0
0 1447534
345282
345153
70127
28773
6969
743
205
154
0
0 798816
12156
33074
46635
19651
7926
3974
174
0
0
0 123590
0
36
1666
2640
6281
4114
2101
875
39
0
0
0
0
37
83
635
1087
607
265
69
1
0
0
0
0
0
1
16
74
61
25
8
1
0
187
0
0
0
0
0
3
50
71
29
6
1
0
162
8.835
0
0
0
0
0
0
0
4
4
0
0
0
9
9.765
0
0
0
0
0
0
0
6
10
2
0
0
18
10.695
0
0
0
0
0
0
0
2
5
2
0
0
9
11.625
0
0
0
0
0
0
0
2
5
2
0
0
9
13.485
0
0
0
0
0
0
0
0
0
0
0
0
0
14.415
0
0
0
0
0
0
0
0
0
0
0
0
0
15.345
0
0
0
0
0
0
0
0
0
0
0
0
0
16.275
0
0
0
0
0
0
0
0
0
0
0
0
0
18.135
0
0
0
0
0
0
0
0
0
0
0
0
0
19.065
0
0
0
0
0
0
0
0
0
0
0
0
0
213900 1447548
518438
156841
62559
21039
7988
1739
283
4
1
2430755
17751
2785
.
.
.
Total
22-Jul-13
414
46
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
22-Jul-13
47
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SPECTRAL ANALYSIS TECHNIQUES The spectral analysis used for the determining stress response to sea state loadings. The analysis is used to properly account for the actual distribution of wave energy over the entire frequency . The spectral approach can be subdivided based upon the method used to develo transfer functions.
Static Transfer Function Methods Dynamic Transfer function methods
22-Jul-13
48
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis REGULAR WAVE IN FREQUENCY DOMAIN Transfer functions developed using regular waves in the frequency 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.
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
49
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis GENERATION OF TRANSFER FUNCTION A)Wave Period Selection
Multi les of natural eriod of structure 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. .
C) Methods 22-Jul-13
Regular wave in time domain. Regular wave in frequency domain. Regular wave in time domain. 50
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SELECTION OF WAVE FREQUENCY FOR TRANSFER FUNCTION
22-Jul-13
51
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Stress Range Transfer Function Compute a stress range transfer function at each point where fatigue damage is to be accumulated for a minimum of four platform directions.
For jackets with unusual geometry or where wave directionality or spreading or current is considered, more directions may be required
At each frequency, a point on the transfer function is determined by passing an Airy wave of the appropriate height through the structure and dividing the response stress range by the wave height.
A sufficient number of time steps in the wave cycle at which members stresses are computed should be selected to determine the maximum brace hot spot stress range.
A minimum of four hot spot locations at both the brace and chord side of the connection should be considered.
22-Jul-13
52
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Spectral Representation Spectral analysis is useful in representing the sea state energy accuratel as a roximation is discrete wave scatter data is removed. Again the response can be generated either of the methods discussed above. If the structure system responds dynamically to the incident loads, spec ra ra ana ys ys s w ynam c e ec s is suit suitab able le..
22-Jul-13
53
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
22-Jul-13
54
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Centre of Fatigue Damage Wave The partial damage, Di, j caused by a particular sea state is hence proportional to the number of occurrences of the sea state, ni, j, and the significant wave height, HS, raised to the power m o t e s op ope o t e - curve. roport on ona ty to the number of stress cycles in the sea state translates into an inversely proportional relationship to the mean zero crossing period, Tz Conse uentl :
D i , j
N i , j 0 .5 H i
0 .5 T j
H i 1
T j 1
m
The above calculation is repeated for each sea state in the wave scatter diagram to produce a damage scatter diagram with relative damages in the state bins.
TZ HS TC
mean zero-crossing period significant wave height central value of the mean zero crossing period
Di, j Di D j D
fatigue fatigue fatigue fatigue
22-Jul-13
damage damage damage damage
from from from from 55
sea sea sea sea
states states states states
with Hi
Deterministic and Spectral Fatigue Analysis CENTRE OF FATIGUE DAMAGE SEASTATE Significant wave height at the centre of damage
H S
Zero crossing period at the centre of damage
T z
Significant wave height at the centre of damage Zero crossing period at the centre of damage
D H i
si
Di
DiT si
D i
H d
1.86 H s
T d
1.27T z
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
56
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis
D
All wave directions All sea states
j 1
22-Jul-13
57
Prof. S. Nallayarasu Department of Ocean Engineering
i 1
ni i
Deterministic and Spectral Fatigue Analysis Wave Scatter Data Wave scatter data is the information relating wave height, period and the occurrences for defining the sea state at a particular site during a specified period. This can be expressed in following two ways. wo arame er ca er agram This is specified as a relationship between the number of occurrences for a particular wave height (Hmax) and period (Tz) The specified waves shall be maximum wave height with zero crossing period for that group of occurrences. Two parameter scatter data can be developed for each direction and used for the deterministic fatigue analysis using the relationship between wave direction ( ) and wave period (Tz). Directional Scatter Data Directional scatter data includes three parameters : Significant wave height (H s), Peak Period (Tp) and the mean direction. This data is normally used for spectral distribution of wave energy represented by Hs and Tp for each direction. 22-Jul-13
58
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Two Parameter Wave Scatter Data 0
T1
0
H1
H3 H4
T2
T4
T3
n00
n01
n02
n03
n10
.
.
.
n20
.
.
n30
.
T5
n04
T6
.
T7
.
T8
.
T9
.
nr1 nr2
.
nr3 r
5
H6 H7 H8 H9
nr0
.
nr5
.
nr6
.
nr7
.
nr8
nc0
nc1
nc2
nc3
nc4
nc5
nc6
nc7
nc8
n
n00, n01,. . . are number of occurrences for each set of wave height and period nc0, nc1,. . . are summation for each wave period and nr0, nr1,. . . are summation for each wave height and 22-Jul-13
59
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Directional distribution for wave height 0 H1 H2 H3 H4 H5 H6
N
NE
E
SE
S
SW
W
NW
Total
d00
d01
d02
d03
d04
.
.
.
nh0
10
.
.
.
d20
.
.
d30
.
h1
nh2 .
nh3
d40
nh4
.
nh5
.
n
.
nh7
.
nh8
7
H8 H9
d1
d2
d3
d4
d5
d6
d7
d8
d00, d01,. . . are number of occurrences for each set of wave height and direction nd0, nd1,. . . are summation for each direction and nh0, nh1,. . . are summation for each wave height and n is the total number of occurrences. 22-Jul-13
60
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis LINEAR SYSTEM Response of a linear system can be described by
R f
Z f F f
where Z(f) = Response transfer function F(f) = Fourier Transform of forcing function
If the forcing function has many number of sinusoidal function with unit amplitude, such as decomposed Random waves, then for each forcing function, the above equation can be written as,
R1 f1 Z1 f1 F1 f 1 In matrix notation, it can be written as
Ri f 22-Jul-13
61
Zi f Fi f Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Multiplying the variable and retaining the diagonal terms
Ri f Ri f Sy(f) is
y2(f)
2 H f H f F i f i
, and hence the displacement can be written as
y
t
y
0
RMS value of displacement
Y RMS
Ri2 f S F f
where Sy(f) = Power spectral density of response SF(f) = Power spectral density forcing function. 22-Jul-13
62
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis SPECTRAL RESPONSE OF JACKET STRUCTURE This 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 . Sea state is assumed to be a stationary Gaussian random process. The stationary process has the oint probability distribution that des not change with time or space. state is assumed to be narrow banded. The stress response of the jacket structure can be simulated by Rayleigh Distribution for a narrow band 22-Jul-13
63
Incident wave e g spectra
Prof. S. Nallayarasu Department of Ocean Engineering
Transfer unc on o stresses
Deterministic and Spectral Fatigue Analysis SPECTRAL RESPONSE OF JACKET STRUCTURE e sea s a e a e oca on o e ac e s a spectra of either P-M, or JONSWAP type.
e represen e
The spectrum shall be segments as shown in figure each with a constant frequency range df and energy density SHi(f). repeated for all directions with each direction represented by a spec rum w eren significant wave height and peak period 22-Jul-13
64
Prof. S. Nallayarasu Department of Ocean Engineering
y a yp ca
Deterministic and Spectral Fatigue Analysis , transfer function Zi (f) and the forcing function Fi(f) can be related as
esponse o structure
RMSi
i
i
0 Hi
–
density of wave height, the equation can be written as
RMS stress response of structure
RMSi
Z f S i
H
f
Stress transfer function Power spectral density of wave 22-Jul-13
65
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis The ex ected number of c cles n s associated with the s ectrum durin the design life (DL ) can be calculated for each sea state induced stress (s) in which the term d L is the fraction of spectrum of the sea state that prevails and Tz is the zero crossing period.
ni ( s )
um er o cyc es app e for each stress state (s)
L
L
T zi
e response n erms o s ress a a par cu ar oca on n corresponding zero crossing period can be written as
RMS stress ran e
0
RMS i
Zero crossing period
22-Jul-13
zi
66
2 i
e ac e
H i
0
2
2
f i H i ( f ) S H i ( f )df
Prof. S. Nallayarasu Department of Ocean Engineering
an
Deterministic and Spectral Fatigue Analysis Using Rayleigh probability distribution function (PDF) of the stress range at a location in the jacket, the probability of the stresses in terms of RMS response 2 stress can be expressed as
s
p( s )
2 RMS
exp
s
2 RMS
The partial fatigue damage due to stress range between s and s+ds using the S-N curve and the number of cycles that corresponding sea state n(s) can be computed as
dD( s )
n( s)
N s
p( s )ds
The cumulative fatigue damage due to stress ranges in the complete spectrum can be computed by integrating between 0 and frequencies of the spectrum Cumulative fatigue damage
22-Jul-13
D 67
n s 2 RMS i
0
p s N ( s )
exp
s
2
2 RMS ds
Prof. S. Nallayarasu Department of Ocean Engineering
i
Deterministic and Spectral Fatigue Analysis Probability Distribution of Stress Response The probability distribution of stress response using Rayleigh distribution is shown in figure.
p ( s )
22-Jul-13
s 2 RMS
exp
s
2
2 RMS
68
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Linearisation of Wave Forces In linearizing the applied wave force, drag forces are approximated by sinusoidally varying forces and inundation effects are approximated or neglected. As a result, the equations of motion can then be solved without performing direct time integration. For typical small waves the effects of linearization are not of great importance; however, for large waves they may be significant if inundation effects are neglected 2 or son
T
quat on
1
2
D
D w
M
4
W a
The square term in the drag part of the Morison can be linearized using stochastic . Linearized Morison Equation
FT
1 2
wCd
8
VV
D 2 4
wCm a
where V is the standard deviation of the velocity obtained using Gaussian process probability density function. 22-Jul-13
69
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Jacket Models
22-Jul-13
70
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Directional distribution of significant wave height and pea per o
22-Jul-13
71
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis 2.39%
1.25%
.
0.31% 28.00%
. 13.67% 26.54% 22-Jul-13
72
Prof. S. Nallayarasu Department of Ocean Engineering
Deterministic and Spectral Fatigue Analysis Hs(m) 0.25 0.75 .
1.91
3.18
4.45
5.72
0.0027
0.2000
0.0533
0.0030 0.0000
0.0000
0.0000
0.0000 0.2130
1.2683
0.1618
0.0084
0.0010
.
.
.
.
6.99 0.0438 .
Peak Period 8.26 9.53
.
.
10.80
Total
12.07
13.34
14.61
15.88
0.0000
0.0000
0.0000
0.0000
0.0000 0.2590
0.0005
0.0002 0.0000
0.0000
0.0000 1.6970
.
.
.
.
.
.
1.75
0.0000
0.0000 0.0060
0.0163
0.0230
0.0097
0.0039
0.0020
0.0001 0.0000
2.25
0.0000
0.0000 0.0000
0.0002
0.0003
0.0007
0.0005
0.0002
0.0001
2.75
0.0000
0.0000
0.0000 0.0000
0.0000
0.0002
0.0004
0.0002
0.0001
0.0000
0.0000
0.0000
3.25
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
3.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
4.25
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
4.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
5.25
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
5.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
6.25
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
6.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
7.25
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
7.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
8.25
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
8.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
9.25
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
9.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
10.25 Total
22-Jul-13
0.0000
0.0000 0.0610
0.0000 0.0000
0.0000 0.0020 0.0010
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
0.0027
0.4137
1.4906
0.3442
0.1002
0.0327
0.0090
0.0032
0.0005
0.0001
0.0000
0.0000
73
Prof. S. Nallayarasu Department of Ocean Engineering
2.3970
Deterministic and Spectral Fatigue Analysis Hs(m) 0.25 0.75
.
1.91
3.18
4.45
5.72
0.0019
0.1444
0.0385
0.0021 0.0000
0.0000
0.0000
0.0000 0.1230
0.7324
0.0935
0.0049
0.0006
.
.
.
.
6.99 0.0253 .
Peak Period 8.26 9.53
.
.
10.80
13.34
14.61
15.88
0.0000
0.0000
0.0000
0.0000
0.0000 0.1870
0.0003
0.0001 0.0000
0.0000
0.0000 0.9800
.
.
.
1.75
0.0000
0.0000 0.0003
0.0008
0.0011
0.0005
0.0002
0.0001
0.0000 0.0000
2.25
0.0000
0.0000 0.0000
0.0003
0.0004
0.0011
0.0007
0.0004
2.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
3.25
0.0000
0.0000
0.0000 0.0000
0.0000
0.0001
0.0004
3.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
4.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
4.75
0.0000
0.0000
0.0000
0.0000
0.0000
5.25
0.0000
0.0000
0.0000
0.0000
0.0000
5.75
0.0000
0.0000
0.0000
0.0000
6.25
0.0000
0.0000
0.0000
0.0000
6.75
0.0000
0.0000
0.0000
7.25
0.0000
0.0000
0.0000
7.75
0.0000
0.0000
8.25
0.0000
0.0000
8.75
0.0000
9.25 9.75 10.25 Total
22-Jul-13
Total
12.07
.
.
.
0.0000
0.0000 0.0030
0.0001
0.0000 0.0000
0.0000 0.0030
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0003
0.0001
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
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
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
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
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
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
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
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 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 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 0.0000
0.0010
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
0.0019
0.2676
0.8071
0.1325
0.0342
0.0095
0.0026
0.0011
0.0004
0.0001
0.0000
0.0000
74
Prof. S. Nallayarasu Department of Ocean Engineering
1.2570
Deterministic and Spectral Fatigue Analysis Hs(m) 0.25 0.75
1.91
3.18
4.45
5.72
0.0002
0.0178
0.0047
0.0003 0.0000
0.0000
0.0000
0.0000 0.0251
0.1495
0.0191
0.0010
0.0001
.
.
.
.
.
6.99 0.0052 .
Peak Period 8.26 9.53
.
.
10.80
13.34
14.61
15.88
0.0000
0.0000
0.0000
0.0000
0.0000 0.0230
0.0001
0.0000 0.0000
0.0000
0.0000 0.2000
.
.
.
1.75
0.0000
0.0000 0.0022
0.0059
0.0083
0.0035
0.0014
0.0007
0.0000 0.0000
2.25
0.0000
0.0000 0.0000
0.0008
0.0012
0.0028
0.0019
0.0009
2.75
0.0000
0.0000
0.0000 0.0001
0.0001
0.0009
0.0016
3.25
0.0000
0.0000
0.0000 0.0000
0.0000
0.0003
0.0016
3.75
0.0000
0.0000
0.0000
0.0000 0.0000
0.0000
4.25
0.0000
0.0000
0.0000
0.0000 0.0000
0.0000
4.75
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
5.25
0.0000
0.0000
0.0000
0.0000
0.0000
5.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0002
6.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
6.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
7.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
7.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
8.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
8.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
9.25
0.0000
0.0000
0.0000
0.0000
0.0000
9.75
0.0000
0.0000
0.0000
0.0000
0.0000
10.25 Total
Total
12.07
.
.
.
0.0000
0.0000 0.0220
0.0004
0.0000 0.0000
0.0000 0.0080
0.0009
0.0004
0.0001
0.0000
0.0000
0.0040
0.0013
0.0005
0.0002
0.0000
0.0000
0.0040
0.0003
0.0004
0.0002
0.0000
0.0000
0.0000
0.0010
0.0004
0.0010
0.0005
0.0001
0.0000
0.0000
0.0020
0.0000
0.0005
0.0004
0.0000
0.0000
0.0000
0.0010
0.0000 0.0000
0.0003
0.0005
0.0001
0.0000
0.0000
0.0010
0.0005
0.0002 0.0000 0.0000
0.0010
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
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 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
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
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0002
0.0430
0.1767
0.0463
0.0189
0.0103
0.0077
0.0064
0.0036
0.0008
0.0001
0.0000
22-Jul-13
75
Prof. S. Nallayarasu Department of Ocean Engineering
0.3140
Deterministic and Spectral Fatigue Analysis SOUTH EAST DIRECTION JOINT DISTRIBUTION OF Hs and T Hs(m) 0.25
1.91
3.18
4.45
0.0004
5.72
6.99
Peak Period 8.26 9.53
10.80
12.07
13.34
14.61
15.88
Total
0.0263
0.0070
0.0004 0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0340
0.75
0.0000 0.0331
0.1973
0.0252
0.0068
0.0013
0.0001
0.0001
0.0000 0.0000
0.0000
0.0000 0.2640
1.25
0.0000 0.0001
0.0229
0.0229
0.0047
0.0019
0.0005
0.0000
0.0000
1.75
0.0000
0.0000 0.0023
0.0062
0.0087
0.0037
0.0015
0.0007
0.0000 0.0000
0.0000 0.0000
2.25
0.0000
0.0000 0.0000
0.0006
0.0009
0.0021
0.0014
0.0007
2.75
0.0000
0.0000
0.0000 0.0002
0.0004
0.0034
0.0059
3.25
0.0000
0.0000
0.0000 0.0000
0.0001
0.0007
0.0032
3.75
0.0000
0.0000
0.0000
0.0000 0.0000
0.0001
4.25
0.0000
0.0000
0.0000
0.0000 0.0000
0.0001
4.75
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
5.25
0.0000
0.0000
0.0000
0.0000
5.75
0.0000
0.0000
0.0000
0.0000
6.25
0.0000
0.0000
0.0000
6.75
0.0000
0.0000
7.25
0.0000
0.0000
7.75
0.0000
8.25
0.0000
8.75
0.0000 0.0530
0.0000
0.0000 0.0230
0.0003
0.0000 0.0000
0.0000 0.0060
0.0033
0.0014
0.0004
0.0000
0.0000
0.0150
0.0026
0.0011
0.0004
0.0000
0.0000
0.0080
0.0019
0.0026
0.0011
0.0002
0.0000
0.0000
0.0060
0.0011
0.0030
0.0016
0.0002
0.0000
0.0000
0.0060
0.0001
0.0010
0.0008
0.0001
0.0000
0.0000
0.0020
0.0000
0.0000 0.0000
0.0003
0.0005
0.0001
0.0000
0.0000
0.0010
0.0000
0.0000 0.0000
0.0002
0.0005
0.0002 0.0000 0.0000
0.0010
0.0000
0.0000
0.0000 0.0000
0.0002
0.0006
0.0002 0.0000
0.0000 0.0010
0.0000
0.0000
0.0000
0.0000 0.0000
0.0001
0.0005
0.0003 0.0000
0.0000 0.0010
0.0000
0.0000
0.0000
0.0000
0.0000 0.0004
0.0009
0.0007 0.0000
0.0000 0.0020
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0003
0.0005
0.0002 0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0008
0.0012 0.0000
0.0000
0.0000 0.0020
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
9.25
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
9.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
10.25 Total
0.0000 0.0010
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
0.0004
0.0595
0.2295
0.0554
0.0216
0.0133
0.0156
0.0164
0.0111
0.0030
0.0002
0.0001
22-Jul-13
76
Prof. S. Nallayarasu Department of Ocean Engineering
0.4260
Deterministic and Spectral Fatigue Analysis SOUTH DIRECTION (JOINT DISTRIBUTION OF Hs and Tp) Hs(m) 0.25
1.91
3.18
4.45
5.72
Peak Period 8.26 9.53
10.80
12.07
13.34
14.61
15.88
0.0008
0.0602
0.0161
0.0009 0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0780
0.0000
0.0000 10.4510
0.0025 0.0000
0.0000 12.8550
6.99
0.75
0.0000 1.3119
7.8110
0.9967
0.2697
0.0520
0.0059
0.0029
0.0010 0.0000
1.25
0.0000 0.0227
5.5565
5.5544
1.1285
0.4630
0.1122
0.0120
0.0033
Total
1.75
0.0000
0.0000 0.2606
0.7092
0.9999
0.4214
0.1699
0.0852
0.0037 0.0000
0.0000
0.0000 2.6500
2.25
0.0000
0.0000 0.0008
0.0367
0.0581
0.1383
0.0906
0.0463
0.0193
0.0009 0.0000
0.0000 0.3910
2.75
0.0000
0.0000
0.0000 0.0004
0.0009
0.0066
0.0113
0.0063
0.0028
0.0007
0.0000
0.0000
0.0290
3.25
0.0000
0.0000
0.0000 0.0000
0.0002
0.0025
0.0115
0.0094
0.0039
0.0013
0.0001
0.0000
0.0290
3.75
0.0000
0.0000
0.0000
0.0000 0.0000
0.0004
0.0065
0.0092
0.0038
0.0008
0.0002
0.0000
0.0210
4.25
0.0000
0.0000
0.0000
0.0000 0.0000
0.0001
0.0017
0.0045
0.0024
0.0003
0.0001
0.0000
0.0090
4.75
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0004
0.0039
0.0032
0.0003
0.0001
0.0001
0.0080
5.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0010
0.0016
0.0003
0.0000
0.0000
0.0030
5.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0001
0.0008
0.0022
0.0010 0.0000 0.0000
0.0040
6.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0004
0.0011
0.0005 0.0000
0.0000 0.0020
6.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0000
0.0001
0.0005
0.0003 0.0000
0.0000 0.0010
7.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0002
0.0004
0.0004 0.0000
0.0000 0.0010
7.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0003
0.0005
0.0002 0.0000
0.0000 0.0010
8.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0008
0.0012 0.0000
0.0000
8.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0020 0.0000
0.0000
0.0000 0.0020
9.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0007
0.0003 0.0000
0.0000 0.0010
9.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0005
0.0005 0.0000
0.0000 0.0010
10.25
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
0.0008
1.3948 13.6449
7.2983
2.4574
1.0844
0.4101
0.1833
0.0542
0.0010
Total
22-Jul-13
77
0.0107
Prof. S. Nallayarasu Department of Ocean Engineering
0.0000 0.0020
0.0002 26.5400
Deterministic and Spectral Fatigue Analysis Hs(m) 0.25
1.91
3.18
4.45
0.0000
0.0031
0.0008
0.0000 0.0000
0.0000
0.0000
5.72
6.99
Peak Period 8.26 9.53
10.80
12.07
13.34
14.61
15.88
0.0000
0.0000
0.0000
0.0000
0.0000 0.0040
0.0000
0.0000 1.2860
0.0008 0.0000
0.0000 4.1630
0.75
0.0000 0.1614
0.9611
0.1226
0.0332
0.0064
0.0007
0.0004
0.0001 0.0000
1.25
0.0000 0.0073
1.7994
1.7988
0.3655
0.1500
0.0363
0.0039
0.0011
0.0859
0.0038 0.0000
1.75
0.0000
0.0000 0.2627
0.7148
1.0079
0.4247
0.1713
2.25
0.0000
0.0000 0.0033
0.1534
0.2430
0.5781
0.3787
0.1934
0.0805
0.0036 0.0000
0.0000 1.6340
2.75
0.0000
0.0000
0.0000 0.0193
0.0436
0.3333
0.5705
0.3187
0.1393
0.0363
0.0007
0.0002
1.4620
3.25
0.0000
0.0000
0.0000 0.0006
0.0082
0.0931
0.4252
0.3475
0.1450
0.0487
0.0052
0.0004
1.0740
3.75
0.0000
0.0000
0.0000
0.0000 0.0007
0.0126
0.1904
0.2690
0.1110
0.0229
0.0044
0.0009
0.6120
4.25
0.0000
0.0000
0.0000
0.0000 0.0003
0.0031
0.0660
0.1808
0.0945
0.0104
0.0027
0.0002
0.3580
4.75
0.0000
0.0000
0.0000
0.0000
0.0000 0.0004
0.0095
0.1017
0.0843
0.0090
0.0028
0.0014
0.2090
5.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0009
0.0272
0.0453
0.0081
0.0012
0.0014
0.0840
5.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0008
0.0112
0.0319
0.0138 0.0000 0.0003
0.0580
6.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0003
0.0043
0.0131
0.0053 0.0000
0.0000 0.0230
6.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0004
0.0013
0.0081
0.0051 0.0000
0.0000 0.0150
7.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0009
0.0017
0.0014 0.0000
0.0000 0.0040
7.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0007
0.0010
0.0003 0.0000
0.0000 0.0020
8.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0004
0.0006 0.0000
0.0000
0.0000 0.0010
8.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0020 0.0000
0.0000
0.0000 0.0020
9.25
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0027
0.0013 0.0000
0.0000 0.0040
9.75
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000 0.0010
0.0010 0.0000
0.0000 0.0020
10.25
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
0.0000
0.1719
3.0274
2.8095
1.7024
1.6017
1.8510
1.5471
0.7670
0.0181
Total
22-Jul-13
78
0.1690
0.0000
Total
Prof. S. Nallayarasu Department of Ocean Engineering
0.0000 2.6710
0.0047 13.6700
Deterministic and Spectral Fatigue Analysis WEST DIRECTION (JOINT DISTRIBUTION OF Hs and Tp) Hs(m) 0.25
1.91
3.18
0.0000 0.0031
4.45
5.72
6.99
Peak Period 8.26 9.53
10.80
12.07
13.34
14.61
15.88
Total
0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0040
0.75 0.0000 0.2033 1.2108 0.1545 0.0418 0.0081 0.0009 0.0005 0.0002 0.0000 0.0000 0.0000 1.6200 1.25 0.0000 0.0069
1.6879 1.6873 0.3428 0.1407 0.0341 0.0036 0.0010 0.0008 0.0000 0.0000 3.9050
1.75
0.0000 0.0000 0.3527 0.9596 1.3531 0.5702 0.2300 0.1153 0.0051 0.0000 0.0000 0.0000 3.5860
2.25
0.0000 0.0000 0.0074 0.3416 0.5413 1.2879 0.8436 0.4307 0.1794 0.0080 0.0000 0.0000 3.6400
2.75
0.0000 0.0000 0.0000 0.0617 0.1392 1.0638 1.8207 1.0172 0.4446 0.1159 0.0023 0.0008 4.6660
3.25
0.0000 0.0000 0.0000 0.0024 0.0325 0.3674 1.6773 1.3711 0.5721 0.1920 0.0206 0.0016 4.2370
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.25
0.0000 0.0000 0.0000 0.0000 0.0016
4.75
0.0000 0.0000 0.0000 0.0000 0.0000 0.0016 0.0442 0.4729 0.3919 0.0417 0.0131 0.0065 0.9720
5.25
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0050 0.1505 0.2506 0.0446 0.0067 0.0076 0.4650
5.75
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0022 0.0310 0.0879 0.0382 0.0000 0.0007 0.1600
.
.
.
.
.
.
0.0148 0.3180 0.8717 0.4556 0.0503 0.0132 0.0008 1.7260
.
.
.
.
.
.
.
.
6.75
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0015 0.0098 0.0062 0.0000 0.0000 0.0180
7.25
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0017
0.0034 0.0029 0.0000 0.0000 0.0080
7.75
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003
0.0005 0.0002 0.0000 0.0000 0.0010
8.25
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
.
.
.
.
.
.
.
.
.
.
.
.
.
.
9.25
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0003 0.0000 0.0000 0.0010
9.75
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0005 0.0005 0.0000 0.0000 0.0010
10.25 Total
22-Jul-13
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 0.0000 0.2133 3.2596 3.2072 2.4557 3.5154 5.8958 5.7736 2.9633 0.6216 0.0773 0.0221 28.0050
79
Prof. S. Nallayarasu Department of Ocean Engineering
