Global Response Analysis
of the Jack-up Platform Odin
Tran Viet Hai
Master Thesis
presented in partial fulfillment of the requirements for the double degree:
“Advanced Master in Naval Architecture” conferred by University of Liege "Master of Sciences in Applied Mechanics, specialization in Hydrodynamics,
Energetics and Propulsion” conferred by Ecole Centrale de Nantes
developed at University of Rostock in the framework of the
“EMSHIP” Erasmus Mundus Master Course
in “Integrated Advanced Ship Design”
Ref. 159652-1-2009-1-BE-ERA MUNDUS-EMMC
Principal Supervisor:
Practical Supervisor:
Reviewer:
Prof. Patrick Kaeding, University of Rostock
Mr. Sebastian Wenzel, HOCHTIEF Solutions AG
Prof. Philippe Rigo, University of Liege
Rostock, February 2014
Tran Viet Hai
Master Thesis developed at University of Rostock Page ii
Thesis topic
GLOBAL RESPONSE ANALYSIS
OF THE JACK-UP PLATFORM ODIN
Fig. 1: Jack-up platform Oding during mainenance works.
For the installation and maintenance of offshore wind farms HOCHTIEF Solutions’ branch Civil
Engineering and Marine and Offshore isoperating a fleet of jack-up vessels. The operational
profile of a jack-up vessel can be divided into three modes:
1. The floating mode: The vessel acts as a barge or a cargo ship transporting heavy load
components on its main deck.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page iii
2. The operational mode: The hull is jacked out of the water at the offshore site being
exposed to moderate loads from wind waveand current. Major loads are introduced by the main
crane during heavylift activities.
3. The survival mode: All cranes are in resting position while strong wind and wave loads
are acting on the jacked up vessel.
All three modes of operation are weather restrictedregarding wave heights and wind speed. The
site specific extension of the weather limitations without compromising the safety is a constant
challenge in the operationand a key factor for lowering the costs in the offshore wind industry.
The Odin, the first vessel in service, has undergone several conversions according to specific
project requirements. The scope of the thesis is to conduct a global response analysis of the
jacked-up platform in the operational and survival mode. The objective is to determine envelopes
of feasible conditions depending on water depth, leg penetration, and deck load components.
The following items are to be covered:
1. Write a concise introduction covering a descriptionof the vessel, crane, a typical site
specification and operational mode.
2. Create a FE model consisting of beam and shell elements dedicated to geometric nonlinear
analysis as specified the appropriate rule books (see below). While the hull may be simplified by
beam elements special care has to be taken modeling the legs and their connection to the hull in
the jacking system.
3. Establish sets of environmental load conditions:
a. Weight distribution
b. Crane working loads
c. Wind loads
d. Wave and current loads
A hydrostatic program and several in-house tools may be used to shorten calculations.
Tran Viet Hai
Master Thesis developed at University of Rostock Page iv
4. Conduct the following FE-analyses:
- Static calculations
- Modal analysis
- Harmonic analysis
- Transient analysis
- Determination of the dynamic amplification factor (DAF)
5. Based on three given load cases define an operational profile (envelope of environmental
conditions) for three water depth.
6. Optional: Based on the findings in the above suggest structural improvements to extend the
operational limitations and quantify the improvement on the bases of additional operational days
in a provided seaway statistics.
The calculations are supported and supervised by experienced structural engineers and have to
fulfill the requirements in DIN ISO 19905-1and/or SNAME 5-5A - Guidelines for Site Specific
Assessment of Mobile Jack-Up Units. The calculation of the leg penetration and the spudcan-
soil-interaction is not to be included in the calculations. FE calculations are to be conducted in
ANSYS Mechanical 14.5. Intermediate results and the way forward is to be discussed with the
supervisors in frequently scheduled meetings
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page v
Declaration of Authorship
I declare that this thesis and the work presented in it are my own and have been generated by me
as the result of my own original research
Where I have consulted the published work of others, this is always clearly attributed.
Where I have quoted from the work of others, the source is always given. With the exception of
such quotations, this thesis is entirely my own work.
I have acknowledged all main sources of help.
Where the thesis is based on work done by myself jointly with others, I have made clear exactly
what was done by others and what I have contributed myself.
This thesis contains no material that has been submitted previously, in whole or in part, for the
award of any other academic degree or diploma.
I cede copyright of the thesis in favour of the University of Rostock.
Date: 15th
January 2014 Signature:
Tran Viet Hai
Master Thesis developed at University of Rostock Page vi
ACKNOWLEDGEMENTS
This thesis could not have been finished without guidance of many professors, my
supervisors, senior engineers and support from my family. It is my great pleasure to
acknowledge people who have given me help and encouragement.
First of all, I would like to offer my special thanks to Professor Rigo and Professor Bronsart
for giving me the chance to participate in EMSHIP program – Master in Naval Architecture and
to continue my study in Germany. Without any doubts, that has laid the foundation for this
thesis.
I cannot find words to express my gratitude to the board of managers of Civil Engineering
Marine and Offshore Department – HOCHTIEF Solutions AG, especially to Doctor Stempinski
who has given me the great chance to work with the jack-up Odin. Without this favor, the thesis
would have remained a dream.
I owe my deepest gratitude to my principal supervisor, Professor Kaeding and my practical
supervisor, senior engineer Mr. Wenzel, for excellent guidance, patience and caring throughout
the time. I have greatly benefited from their experience and knowledge.
It gives me great pleasure in acknowledging the support and guidance of senior engineers of
Civil Engineering Marine and Offshore Department – HOCHTIEF Solutions AG, especially Ms.
Gómez Ruiz, Mr. Rama and Mr. Tollenaar. Without this help, my jack-up model would consist
of nothing more than four spudcans.
Finally, I would like to thank my family. For me, their encouragement has been always an
important energy source.
This thesis was developed in the frame of the European Master Course in “Integrated
Advanced Ship Design” named “EMSHIP” for “European Education in Advanced Ship
Design”, Ref.: 159652-1-2009-1-BE-ERA MUNDUS-EMMC.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page vii
ABSTRACT
A jack up vessel is a type of mobile platform which is capable of elevating its hull form
above the water surface. A Jack up vessel is normally used in offshore construction area for the
purposes of transportation, installation and maintenance. Odin, named after the Nordic Father
God, is one platform in the fleet of HOCHTIEF solutions AG. The jack up is used for offshore
projects in different locations. Hence, it is necessary to understand the behaviour of the Odin
under different environmental conditions.
The operational profile of a jack up vessel can be divided into three main modes, namely
floating mode, operational mode and survival mode. The scope of the thesis is to conduct a
global response analysis of the Odin in the operational and survival modes. The main objective is
to establish the envelopes of feasible environmental conditions depending on water depth, leg
penetration, and deck load components.
In order to fulfil the goal, the jack-up Odin is modelled and analysed using the ANSYS
APDL software package. The finite element model (FEM) of the Odin is built based on detail
equivalent structure calculations. Finite element analyses conducted include linear static
analyses, nonlinear static analyses and dynamic analyses. Also, dynamic amplification factors
(DAF) are determined for each environmental load case. Sub-structuring technique is assessed
and applied to most of analyses to reduce the computation time.
The work is performed complying with requirements of SNAME 5-5A - Guidelines for Site
Specific Assessment of Mobile Jack-Up Units. The parts which are not covered by the
guidelines are performed complying with other guidelines, namely DNV-RP-C205 –
Environmental Conditions and Environmental Loads and EUROCODE 3 – Design of steel
structures
The main finding of the thesis is the ultimate weather conditions regarding wave heights and
wind speeds for different water depths and leg penetrations. Besides, suggestions for structural
improvements are also made in order to extend the operational limitation.
Tran Viet Hai
Master Thesis developed at University of Rostock Page viii
Table of Contents
ACKNOWLEDGEMENTS ..................................................................................................... vi
ABSTRACT ............................................................................................................................ vii
I INTRODUCTION ............................................................................................................ 1
1.1. Jack Up Rig Configuration ....................................................................................... 1
1.1.1. Ship hull ............................................................................................................. 1
1.1.2. Legs and Footing ............................................................................................... 2
1.1.3. Equipment .......................................................................................................... 5
1.2. Operational Profile .................................................................................................... 5
1.3. Jack Up Platform Odin.............................................................................................. 8
II. GUIDELINE and REQUIREMENT .............................................................................. 12
2.1. General .................................................................................................................... 12
2.2. Guidelines and requirements applied ...................................................................... 12
III. GENERAL INPUT DATA ......................................................................................... 13
3.1. Material Data .......................................................................................................... 13
3.2. Environmental Input Data ....................................................................................... 14
3.2.1. Wind data ......................................................................................................... 14
3.2.2. Wave and Current Data ................................................................................... 15
3.2.3. Marine Growth ................................................................................................ 15
3.2.4. Hydrodynamic Coefficients ............................................................................. 16
3.2.5. Water Level and Air-gap ................................................................................. 16
3.3. Weights and COGs Input Data ............................................................................... 17
3.3.1. Deck Load and Tanks ...................................................................................... 17
3.3.2. Legs and Spudcans .......................................................................................... 17
3.3.3. Light Ship without Legs or Spudcan ............................................................... 17
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IV. FINITE ELEMENT MODEL ..................................................................................... 18
4.1. Global Coordinate system ....................................................................................... 18
4.2. Hull model .............................................................................................................. 19
4.2.1. Hull model ....................................................................................................... 19
4.2.2. Hull Plating ...................................................................................................... 21
4.2.3. Hull Stiffness ................................................................................................... 23
4.2.4. Blocks of plates and stiffness .......................................................................... 25
4.3. Leg and Spudcan Model ......................................................................................... 26
4.3.1. Leg model ........................................................................................................ 26
4.3.2. Ocean Pipe ....................................................................................................... 27
4.3.3. Spudcan Model ................................................................................................ 28
4.4. Seabed reaction point and Foundation Fixity ......................................................... 28
4.5. Leg hull connection................................................................................................. 29
4.6. Weight Adjustment ................................................................................................. 29
4.7. Full Model and Sub-structuring Model................................................................... 31
V. LOAD APPLICATION.................................................................................................. 32
5.1. Self-Weight ............................................................................................................. 32
5.2. Crane Loads ............................................................................................................ 32
5.3. Wind Loads ............................................................................................................. 33
5.4. Wave and Current Loads ........................................................................................ 35
VI. ANALYSIS METHOD .............................................................................................. 37
6.1. Analysis Method – Step 1 ....................................................................................... 37
6.2. Analysis Method – Step 2 ....................................................................................... 38
6.2.1. Dynamic Analysis and Damping Ratio ........................................................... 39
6.2.2. Dynamic Amplification Factor (DAF) ............................................................ 41
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Master Thesis developed at University of Rostock Page x
6.3. Analysis Method – Step 3 ....................................................................................... 42
VII. ACCEPTANCE CRITERIA....................................................................................... 44
7.1. Leg Reserve ............................................................................................................ 44
7.2. Overturning Stability .............................................................................................. 44
7.3. Structural Ultimate Strength ................................................................................... 45
7.3.1. Leg Inclination ................................................................................................. 45
7.3.2. Leg Checking ................................................................................................... 45
VIII. FINDING .................................................................................................................... 50
8.1. Main Results ........................................................................................................... 50
8.2. Results for Operational Condition 1 ....................................................................... 51
8.2.1. Input Data ........................................................................................................ 51
8.2.2. Leg Reserve Check .......................................................................................... 51
8.2.3. Natural Frequency & Period ............................................................................ 52
8.2.4. The Critical Combination ................................................................................ 52
8.2.1. Dynamic Amplification Factor (DAF) ............................................................ 53
8.2.2. Checking Results ............................................................................................. 56
8.3. Results for Survival Condition 1............................................................................. 57
8.3.1. Input Data ........................................................................................................ 57
8.3.2. Leg Reserve Check .......................................................................................... 57
8.3.3. Natural Frequency & Period ............................................................................ 58
8.3.4. The Critical Combination ................................................................................ 58
8.4. Results for Operational Condition 2 ....................................................................... 59
8.4.1. Input Data ........................................................................................................ 59
8.4.2. Leg Reserve Check .......................................................................................... 59
8.4.3. Natural Frequency & Period ............................................................................ 60
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page xi
8.4.4. The Critical Combination ................................................................................ 60
8.4.5. Dynamic Amplification Factor (DAF) ............................................................ 61
8.4.6. Checking Results ............................................................................................. 64
8.5. Results for Survival Condition 2............................................................................. 65
8.5.1. Input Data ........................................................................................................ 65
8.5.2. Leg Reserve Check .......................................................................................... 65
8.5.3. Natural Frequency & Period ............................................................................ 66
8.5.4. The Critical Combination ................................................................................ 66
8.5.5. Dynamic Amplification Factor (DAF) ............................................................ 67
8.5.6. Checking Results ............................................................................................. 70
8.6. Results for Operational Condition 3 ....................................................................... 71
8.6.1. Input Data ........................................................................................................ 71
8.6.2. Leg Reserve Check .......................................................................................... 71
8.6.3. Natural Frequency & Period ............................................................................ 72
8.6.4. The Critical Combination ................................................................................ 72
8.6.5. Dynamic Amplification Factor (DAF) ............................................................ 73
8.6.6. Checking Results ............................................................................................. 76
8.7. Results for Survival Condition 3............................................................................. 77
8.7.1. Input Data ........................................................................................................ 77
8.7.2. Leg Reserve Check .......................................................................................... 77
8.7.3. Natural Frequency & Period ............................................................................ 78
8.7.4. The Critical Combination ................................................................................ 78
8.7.5. Dynamic Amplification Factor (DAF) ............................................................ 79
8.7.6. Checking Results ............................................................................................. 82
IX. DISCUSSION ............................................................................................................. 83
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Master Thesis developed at University of Rostock Page xii
9.1. Result Analysis ....................................................................................................... 83
9.1.1. Wave period and Natural period ...................................................................... 84
9.1.2. Wave Length and Angle of Attack .................................................................. 87
9.2. Discussion of Natural Period / Frequency .............................................................. 91
9.2.1. Foundation Fixity ............................................................................................ 91
9.2.2. Weight Distribution ......................................................................................... 93
9.2.3. Pre-stressed Effect ........................................................................................... 95
9.2.4. Leg-Hull Connection ....................................................................................... 96
9.2.5. Summary .......................................................................................................... 97
X. CONCLUSION .............................................................................................................. 98
10.1. Thesis Summary...................................................................................................... 98
10.2. Limitation .............................................................................................................. 100
BIBLIOGRAPHY ................................................................................................................. 102
APPENDIX A – EQUIVALENT STRUCUTRE
APPENDIX B – SUBSTRUCTURING MODEL ASSESSMENT
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List of Figures
Figure I-1 Jack up vessel in floating mode (after HGO InfraSea Solutions GmbH & Co. KG,
2013) ............................................................................................................................................... 1
Figure I-2 Jack up vessel in elevated mode (after HGO InfraSea Solutions GmbH & Co. KG,
2013) ............................................................................................................................................... 2
Figure I-3 Jack Up with three legs (after ZENTECH, Inc 2011) .............................................. 3
Figure I-4 Jack up with Trussed Legs (after HGO InfraSea Solutions GmbH & Co. KG,
2013) ............................................................................................................................................... 4
Figure I-5 Jack up with Cylindrical Legs (after HOCHTIEF Solutions AG, 2013) ................ 4
Figure I-6 Arriving and Fixing final position process (after Bennett & Associates, L.L.C,
Offshore Technology Development, Inc, 2005) ............................................................................. 6
Figure I-7 Preloading, at full air gap and operational mode (after Bennett & Associates,
L.L.C, Offshore Technology Development, Inc, 2005) .................................................................. 7
Figure I-8 Odin jack up platform in HOCHTIEF Fleet (after HOCHTIEF Solutions AG,
(2013) HOCHTIEF Fleet) ............................................................................................................... 8
Figure I-9 Odin jack up platform (after HOCHTIEF Solutions AG, (2013) Project success on
a safe basis: Jack-up platform Odin) ............................................................................................... 8
Figure I-10 General Arrangement – Jack up Odin (after HOCHTIEF Solutions AG, (2009)
Odin Drawing: General arrangement) ............................................................................................ 9
Figure I-11 Deck Plan – Jack up Odin (after HOCHTIEF Solutions AG, (2009) Odin
Drawing: General arrangement) ..................................................................................................... 9
Figure I-12 Crane working range diagram (after HOCHTIEF Solutions AG, (2009) Jack-up
Barge Odin: Liebherr BOS 7500-300 D Litronic,) ....................................................................... 10
Figure IV-1 Global Coordinate System ................................................................................. 18
Figure IV-2 Hull Model 1 ...................................................................................................... 19
Figure IV-3 Hull Model 2 ....................................................................................................... 20
Figure IV-4 Hull Model 3 ....................................................................................................... 20
Figure IV-5 Deck/Jack house plating .................................................................................... 21
Figure IV-6 Bottom plating ................................................................................................... 21
Figure IV-7 Fore part plating ................................................................................................. 21
Figure IV-8 Aft part plating ................................................................................................... 21
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Master Thesis developed at University of Rostock Page xiv
Figure IV-9 Portside plating .................................................................................................. 22
Figure IV-10 Starboard Side plating ...................................................................................... 22
Figure IV-11 Hull stiffness ..................................................................................................... 23
Figure IV-12 Hull stiffness – around jack house .................................................................... 23
Figure IV-13 Block – Plates and stiffness 1 .......................................................................... 25
Figure IV-14 Block – Plates and stiffness 2 ........................................................................... 25
Figure IV-15 Equivalent element shape - 3D ......................................................................... 26
Figure IV-16 Equivalent leg section ....................................................................................... 26
Figure IV-17 Equivalent leg section - FEM ........................................................................... 26
Figure IV-18 Ocean pipe ........................................................................................................ 27
Figure IV-19 Leg with ocean pipe .......................................................................................... 27
Figure IV-20 Spudcan model .................................................................................................. 28
Figure IV-21 Spudcan model-FEM ........................................................................................ 28
Figure IV-22 ODIN Full Model ............................................................................................. 31
Figure IV-23 ODIN Sub-structuring Model ........................................................................... 31
Figure VI-1 Analysis method – Step 1 ................................................................................... 37
Figure VI-2 Analysis Method – Step 2 ................................................................................... 38
Figure VI-3 Analysis method – Step 3 ................................................................................... 42
Figure VII-1 Effective leg section .......................................................................................... 46
Figure VII-2 Effective leg section - FEM ............................................................................... 46
Figure VIII-1 Critical combination ......................................................................................... 52
Figure VIII-2 Base Shear – Static Analysis ............................................................................ 53
Figure VIII-3 Base Shear – Dynamic Analysis ...................................................................... 54
Figure VIII-4 Total base shear comparison - Static and Dynamic analyses ........................... 55
Figure VIII-5 Dynamic amplification factor (DAF) ............................................................... 55
Figure VIII-6 Moment distribution over legs ......................................................................... 56
Figure VIII-7 Shear force distribution over legs ..................................................................... 56
Figure VIII-8 Critical combination ......................................................................................... 60
Figure VIII-9 Base Shear – Static Analysis ............................................................................ 61
Figure VIII-10 Base Shear – Dynamic Analysis .................................................................... 62
Figure VIII-11 Total base shear comparison - Static and Dynamic analyses ......................... 63
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page xv
Figure VIII-12 Dynamic amplification factor (DAF) ............................................................. 63
Figure VIII-13 Moment distribution over legs ....................................................................... 64
Figure VIII-14 Shear force distribution over legs................................................................... 64
Figure VIII-15 Critical combination ....................................................................................... 66
Figure VIII-16 Base Shear – Static Analysis .......................................................................... 67
Figure VIII-17 Base Shear – Dynamic Analysis .................................................................... 68
Figure VIII-18 Total base shear comparison - Static and Dynamic analyses ......................... 69
Figure VIII-19 Dynamic amplification factor (DAF) ............................................................. 69
Figure VIII-20 Moment distribution over legs ....................................................................... 70
Figure VIII-21 Shear force distribution over legs................................................................... 70
Figure VIII-22 Critical combination ....................................................................................... 72
Figure VIII-23 Base Shear – Static Analysis .......................................................................... 73
Figure VIII-24 Base Shear – Dynamic Analysis .................................................................... 74
Figure VIII-25 Total base shear comparison - Static and Dynamic analyses ......................... 75
Figure VIII-26 Dynamic amplification factor (DAF) ............................................................. 75
Figure VIII-27 Moment distribution over legs ....................................................................... 76
Figure VIII-28 Shear force distribution over legs................................................................... 76
Figure VIII-29 Critical combination ....................................................................................... 78
Figure VIII-30 Base Shear – Static Analysis .......................................................................... 79
Figure VIII-31 Base Shear – Dynamic Analysis .................................................................... 80
Figure VIII-32 Total base shear comparison - Static and Dynamic analyses ......................... 81
Figure VIII-33 Dynamic amplification factor (DAF) ............................................................. 81
Figure VIII-34 Moment distribution over legs ....................................................................... 82
Figure VIII-35 Shear force distribution over legs................................................................... 82
Figure IX-1 Static (purple) and Dynamic (aqua blue) Base Shear – Case 1 .......................... 85
Figure IX-2 Static (purple) and Dynamic (aqua blue) Base Shear – Case 2 .......................... 85
Figure IX-3 Legs’ Positions and Distances ............................................................................ 87
Figure IX-4 Wave loads on legs – Case 1............................................................................... 89
Figure IX-5 Wave loads on legs – Case 2............................................................................... 89
Figure IX-6 Wave loads on legs – Case 3............................................................................... 89
Figure IX-7 Wave loads on legs – Case4................................................................................ 89
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Master Thesis developed at University of Rostock Page xvi
Figure IX-8 Leg cross section used for ultimate strength check ............................................ 90
Figure IX-9 Weight distribution & Natural Frequency .......................................................... 94
Figure X-1 Odin Full Model ................................................................................................... 98
Figure X-2 Odin Sub-structuring model ................................................................................. 98
Figure X-3 Numerical damping effect .................................................................................. 101
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List of Tables
Table I-1 Technical data of Jack up platform Odin ............................................................... 11
Table II-1 Guideline and requirement applied ....................................................................... 12
Table III-1 Steel S355 properties ........................................................................................... 13
Table III-2 Sea water properties ............................................................................................. 13
Table III-3 Air properties ....................................................................................................... 13
Table III-4 Height coefficient ................................................................................................ 14
Table III-5 Shape coefficient ................................................................................................. 14
Table III-6 Hydrodynamic Coefficient .................................................................................. 16
Table III-7 Deck load and Tank Weight ................................................................................ 17
Table III-8 Legs and Spudcans Weight ................................................................................. 17
Table III-9 Light Ship Weight ............................................................................................... 17
Table IV-1 Plating Thickness ................................................................................................ 22
Table IV-2 Flat bar profile ...................................................................................................... 24
Table IV-3 Holland Profile ..................................................................................................... 24
Table IV-4 T-Bar profile ......................................................................................................... 24
Table IV-5 Equivalent leg section properties ......................................................................... 27
Table IV-6 Spudcan dimensions and properties .................................................................... 28
Table IV-7 Leg-Hull connection springs ................................................................................ 29
Table IV-8 FEM model weight .............................................................................................. 30
Table IV-9 Weight and COGs Comparison ........................................................................... 30
Table VII-1 Effective leg section properties .......................................................................... 46
Table VIII-1 Main Results ...................................................................................................... 50
Table VIII-2 Input data ........................................................................................................... 51
Table VIII-3 Natural Frequency & Period .............................................................................. 52
Table VIII-4 Leg Reaction ...................................................................................................... 56
Table VIII-5 Overturning Stability Check .............................................................................. 56
Table VIII-6 Input data ........................................................................................................... 57
Table VIII-7 Natural Frequency & Period .............................................................................. 58
Table VIII-8 Input data ........................................................................................................... 59
Table VIII-9 Natural Frequency & Period .............................................................................. 60
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Master Thesis developed at University of Rostock Page xviii
Table VIII-10 Leg Reaction .................................................................................................... 64
Table VIII-11 Overturning Stability Check ............................................................................ 64
Table VIII-12 Input data ......................................................................................................... 65
Table VIII-13 Natural Frequency & Period ............................................................................ 66
Table VIII-14 Leg Reaction .................................................................................................... 70
Table VIII-15 Overturning Stability Check ............................................................................ 70
Table VIII-16 Input data ......................................................................................................... 71
Table VIII-17 Natural Frequency & Period ............................................................................ 72
Table VIII-18 Leg Reaction .................................................................................................... 76
Table VIII-19 Overturning Stability Check ............................................................................ 76
Table VIII-20 Input data ......................................................................................................... 77
Table VIII-21 Natural Frequency & Period ............................................................................ 78
Table VIII-22 Leg Reaction .................................................................................................... 82
Table VIII-23 Overturning Stability Check ............................................................................ 82
Table IX-1 Main Results ......................................................................................................... 83
Table IX-2 Natural Frequency & Period ................................................................................ 84
Table IX-3 Wave Input Data................................................................................................... 84
Table IX-4 Results .................................................................................................................. 86
Table IX-5 Critical Angle of Attack and Wave Length Combination .................................... 88
Table IX-6 Wave Input Data................................................................................................... 88
Table IX-7 Results .................................................................................................................. 90
Table IX-8 Natural Period Comparison – Foundation fixity .................................................. 92
Table IX-9 Natural Period Comparison – Weight distribution ............................................... 94
Table IX-10 Natural Period Comparison – Pre-stressed Effect .............................................. 95
Table IX-11 Natural Period Comparison – Pre-stressed Effect .............................................. 96
Table X-1 Main Results .......................................................................................................... 99
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 1
I INTRODUCTION
1.1. Jack Up Rig Configuration
A jack up vessel is a type of mobile platform which is capable of elevating its hull form
above the water surface. A Jack up vessel is normally used in offshore construction area for the
purposes of transportation, installation and maintenance. Jack up vessels mainly work as
exploratory drilling platform and wind farm service platform. The vessels consist of ship hull,
movable legs, spudcans and equipment.
1.1.1. Ship hull
The ship hull is the working area which gives room for transported units and facilitates
installing or maintaining process. The hull of the platform is watertight and creates buoyancy
when the jack up rig is in the floating mode.
Figure I-1 Jack up vessel in floating mode (after HGO InfraSea Solutions GmbH & Co. KG, 2013)
For jack up rig, the size and geometry of the platform matters. On one hand, a larger platform
provides larger work areas, more room for equipment and people. It also has larger loading
capacity and thereby performing better on site. On the other hand, the larger size also brings back
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Master Thesis developed at University of Rostock Page 2
several disadvantages. One of those drawbacks is the higher wind, wave and current loads acting
on the platform. Besides, the larger weight would also create challenge to the elevating system.
Figure I-2 Jack up vessel in elevated mode (after HGO InfraSea Solutions GmbH & Co. KG, 2013)
Last but not least, when the jack up rig is in elevated mode, the natural period would depend
on the weight. For the heavier platform, the dynamic effects may be more serious and thereby
playing havoc with the structure system. The geometry of the platform is also important since in
the floating mode, the jack up rig acts like a vessel and therefore the geometry links directly to
the stability, maneuverability and velocity of the vessel.
1.1.2. Legs and Footing
The legs and footing of jack up vessels are movable and able to penetrate into the seabed and
thereby allowing the jack up to transform from a vessel into a platform or vice versa.
In the elevated mode, the legs and footing system is the structure system that carries the load
of the platform, equipment as well as the load created during the working process. The legs and
footing system also ensure the stability to resist lateral loads which result from wind, waves and
currents.
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 3
In order to transform into the floating mode, the legs are lift up. This makes the center of
gravity move up and reduces the stability of the jack up rig. Another problem is that since the
jack up rig navigates in this mode, the lateral loads and moments created by wind acting on legs
may be significant. When the two problems combine, the stability of the jack up rig is even in a
more critical condition.
For that the proper design of legs and footing system is really important. On one hand, the
larger the legs and footing system, the stronger the structure becomes. On the other hand, the
larger the system, the less stable the jack up rig in floating mode. In addition, the loads of waves
and currents acting on the jack up rig in elevated mode are also larger.
There are several types of legs and footing systems. Each has a different stiffness and thereby
affecting differently the natural period of jack up rig in elevated mode, especially when the water
depth is high.
Figure I-3 Jack Up with three legs (after ZENTECH, Inc 2011)
In general, a jack up rig may have three or four legs. Both types of jack up have advantages
and disadvantages. A jack up rig with three legs requires less area and therefore gives more
space to equipment and crews on board. In addition, due to the fact that the type of jack up rig
has one leg less, the loading capacity in floating mode is higher and the lateral loads and
moments acting on legs are smaller compared to the jack up with four legs. However, the four-
legged unit also has its own strong points as it provides a stronger structure and thereby
facilitating activities on board in elevated mode.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 4
The two main types of leg are cylindrical legs and trussed legs. Cylindrical legs are hollow
steel tubes which may be reinforced with stiffeners. The type of legs requires less area on
platform but is less efficient in terms of steel utilization compared to trussed legs. In other words,
the trussed legs system needs more room on deck but proves stronger structure with the same
amount of steel. Due to the fact, the cylindrical legs system is not normally used for water depth
exceeding 100 meters.
Figure I-4 Jack up with Trussed Legs (after
HGO InfraSea Solutions GmbH & Co. KG, 2013)
Figure I-5 Jack up with Cylindrical Legs (after
HOCHTIEF Solutions AG, 2013)
For footing system, spudcans are widely used. The system keeps the jack up rig stable by
penetrating into the seabed. The spudcan can be kept dry or flooded like ballast tanks. This
system helps the jack up rig to operate well on seabed with different soil profiles and sloping
bottoms.
Another option for jack up rig is mat footing system which connects all the Jack Up Unit’s
legs to one common footing. The typical shape of mat footing system is rectangular, flat both on
the top and bottom. Ballast tanks are a part of this footing system that help adjust the transiting
process of the jack up rig. The main advantage of mat footing is that its large size help jack up
rig stand on weak soil. Besides, in the floating mode, the mat footing provides buoyancy and
thereby increasing load carrying capability. The drawback of the system is that it cannot work on
unclear seabed. In addition, the process of pumping water in or out of ballast tanks needs to be
done carefully in order to keep the jack up rig stable. This process also requires additional
equipment on board.
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 5
1.1.3. Equipment
The equipment of a jack up rig can be divided into three groups, namely “marine
equipment”, “elevating equipment” and “work equipment”.
The marine equipment consists of normal tools, machines that can be found and any other
kind of vessel such as engine, power generator, communication tools, etc. One important notice
is that marine equipment is technically considered lightweight of jack up rig.
Elevating equipment is the system that gives the jack up rig the ability to raise or lower the
ship hull. Elevating equipment may me pin and hole system or rack and pinion system. The pin
and hole system is more simple but it does not allow the hull to be positioned at certain positions
because the holes on legs are fix. In contrast, the rack and pinion system is able to position the
hull form at continuous positions. The jack up platform Odin uses a pin and hole elevating
system.
Work equipment of each jack up rig is different. It depends on the mission and the jack up
itself. Work equipment can be pumping equipment, drilling equipment, lifting equipment, etc.
Due to its feature, this equipment affects the design of a jack up rig. For example, in case of jack
up platform Odin, the design calculation must cover the load created by the crane which is work
equipment aboard. For that the structure under the crane is stronger than in other parts of the hull
form.
1.2. Operational Profile
The operational profile of jack up vessels can be divided into three main modes as follows:
1. The floating mode: The vessel acts as a barge or a cargo ship transporting heavy load
components on its main deck.
2. The operational mode: The hull is jacked out of the water at the offshore site being
exposed to moderate loads from wind wave and current. Major loads are introduced by the main
crane during heavy lift activities.
3. The survival mode: All cranes are in resting position while strong wind and wave loads
are acting on the jacked up vessel.
All three modes of operation are weather restricted regarding wave heights and wind speed
Tran Viet Hai
Master Thesis developed at University of Rostock Page 6
In detail, according to Bennett & Associates, L.L.C, Offshore Technology Development, Inc,
(2005) a jack up rig has to go through many steps in order to move away from one location and
operate in another location.
The first step should be changing location. A jack up rig can be transported from one location
to another as a floating body (wet tow) or as a cargo on deck of another vessel (dry tow). In this
step, all the legs of the jack up are raised up and therefore creating adverse effects on the
stability.
Figure I-6 Arriving and Fixing final position process (after Bennett & Associates, L.L.C, Offshore
Technology Development, Inc, 2005)
When getting near the final position, leg soft pinning should be performed in order to avoid
collision with other structures. The jack up must be hold temporarily away from its’ working
position. The process is done by lowering one or some legs down until the spudcans just touch
the seabed. The friction created by the contact between spudcans and seabed needs to be
adequate so that the jack up rig is under good control.
After soft pinning the legs, the jack up rig is pulled to the designed position by tugs or other
means. At the final position, the legs are lowered more so that the jack up rig is fixed.
When the final position is fixed, the jack up rig starts its transition. The goal is to turn the
jack up rig into a platform with a designed distance to the water surface level which is called
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 7
“full air gap”. Besides, the soil also needs to be reinforced by preload process so that the
foundation is strong enough to support the unit during operational process or in severe weather
condition. However, since most of jack up rigs have no ability to elevate the platform directly to
full air gap with full preload, the platform is first raised to a smaller air gap before preload
process. This process is called jacking up.
Figure I-7 Preloading, at full air gap and operational mode (after Bennett & Associates, L.L.C,
Offshore Technology Development, Inc, 2005)
Once the ship hull is out of water to a certain air gap, the preload process is carried on so that
the soil can be loaded. The purpose of the process is to reinforce the foundation and thereby
supporting the jack up rig in operational mode or in severe weather condition.
Right after the preload process is completed, the preload which normally is water is pumped
out. After that the platform is raised up to full air gap.
When the platform reaches full air gap, the working activities can be started. In this mode,
the jack up rig suffers from load created not only by winds, waves and currents but also load
created by work equipment.
Under severe weather condition, the wind, wave and current induced loads become critical.
For that all equipment needs to be stopped working and in some cases, crews need to be
evacuated.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 8
1.3. Jack Up Platform Odin
Odin jack up, named after the Nordic Father God, is one platform in the fleet of HOCHTIEF
solutions AG. Apart from Odin, the company also has larger jack up vessels namely Thor, Vidar
and Innovation, the largest jack up vessel of the company.
Figure I-8 Odin jack up platform in HOCHTIEF Fleet (after HOCHTIEF Solutions AG, (2013)
HOCHTIEF Fleet)
The jack up was used for the first German offshore
transformer station where the depth is over 30m, for
the wind energy plants off Borkum when the pile
foundations were laid for the tripods. Odin had also
worked for the project of HOCHTIEF solutions AG
when they expanded the container terminal as an
international freight trade hub in Bremerhaven.
Currently, the jack up platform Odin is being used
in many projects worldwide on many missions such
as soil investigation or installation of offshore
foundations for building state-of-the-art wind
farms. The jack up has been in service since 2004
and operated in area with water depth up to 35 m.
Figure I-9 Odin jack up platform (after
HOCHTIEF Solutions AG, (2013) Project
success on a safe basis: Jack-up platform Odin)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 9
The following figures show the general arrangement and deck plan of the Odin.
Figure I-10 General Arrangement – Jack up Odin (after HOCHTIEF Solutions AG, (2009) Odin
Drawing: General arrangement)
Figure I-11 Deck Plan – Jack up Odin (after HOCHTIEF Solutions AG, (2009) Odin Drawing:
General arrangement)
Tran Viet Hai
Master Thesis developed at University of Rostock Page 10
The figure below shows the working range diagram of the crane on deck of the jack-up
platform Odin.
Figure I-12 Crane working range diagram (after HOCHTIEF Solutions AG, (2009) Jack-up Barge
Odin: Liebherr BOS 7500-300 D Litronic,)
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 11
The table below shows the technical data of Jack up platform Odin
CLASSIFICATION GL + 100 A5 K50
MAIN DIMENSIONS HULL
Length 46.10 m
Width 30.00 m
Height 4.60 m
LEG DIMENSIONS
Length 60.00 m
Cross section 2.00m x 2.00m
Spudcans 3.25m x 3.25m
OPERATIONAL CONDITION
Draft (without spudcans) 3.25 m
Draft (with spudcans) 5.50 m
Operating depth 35.00 m
Deck load 15.00 - 30.00t/m2
Hoisting capacity 900 t/leg
Hoisting speed Up to 2.50 m/min
2 Moon Pools Øi 0.555 m
CRANE
LIEBHERR BOS 7500 – 300 D Litronic
Maximum range 65 m
Lifting capacity at maximum range 29.6 ton
Table I-1 Technical data of Jack up platform Odin
*Source:
- HOCHTIEF Solutions AG, (2009) Odin Drawing: General arrangement
- HOCHTIEF Solutions AG, (2009) Jack-up Barge Odin: Liebherr BOS 7500-300 D
Litronic
- HOCHTIEF Solutions AG, (2013) Project success on a safe basis: Jack-up platform
Odin
- HOCHTIEF Solutions AG, (2009) Odin Drawing: Jack-up legs extension
- HOCHTIEF Solutions AG, (2009) Odin Drawing: Steel Plans
Tran Viet Hai
Master Thesis developed at University of Rostock Page 12
II. GUIDELINE and REQUIREMENT
2.1. General
As required, the thesis is carried on under the requirements in DIN ISO 19905-1 and/or
SNAME 5-5A - Guidelines for Site Specific Assessment of Mobile Jack-Up Units. For the parts
which are not covered by DIN ISO 19905-1 and/or SNAME 5-5A, other codes are applied. The
detail of guidelines and requirements applied is presented in this chapter.
2.2. Guidelines and requirements applied
The table below shows the guidelines used in this thesis and the specific parts of the thesis
they are applied for.
GUIDELINE APPLIED PART
SNAME 5-5A - Assessment Input
Data
Wind input data
Wave input data
Current input data
DNV-RP-C205 Drag Coefficients
Added mass Coefficients
SNAME 5-5A - Calculation methods-
Hydrodynamic and Wind Forces
Wind Force
Hydrodynamic Force
SNAME 5-5A - Calculation methods
– Structural Engineering
Seabed reaction point
Foundation Fixity
Hull modeling
Legs modeling
Leg-Hull connection modeling
SNAME 5-5A – Determination of
Responses
Dynamic Amplification Factor
Quasi-Static Extreme Response with Inertial Load Set
DNV-RP-C205 Leg Reserve Check
SNAME 5-5A- Acceptance Criteria Load factors
Overturning Stability Check
EUROCODE 3 – Design of steel
structures
EN 1993-1-1 and EN 1993-1-5
Structural analysis
Effective Cross Section
Ultimate Strength Check
Table II-1 Guideline and requirement applied
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III. GENERAL INPUT DATA
3.1. Material Data
Steel S355
Properties Value
Density 7850 kg/m3
Yield Strength fy,k = 335 N/mm2
Young’s modulus of elasticity E = 2.1E11 N/m2 = 2.1E5 N/mm2
Poisson Ratio 0.3
Table III-1 Steel S355 properties
*Source: HOCHTIEF Solutions AG – Civil Engineering Marine and Offshore Department,
(2013) Odin profile document
Sea water
Properties Value
Density 1025 kg/m3
Yield Strength N/A
Young’s modulus of elasticity N/A
Poisson Ratio N/A
Table III-2 Sea water properties
Air
Properties Value
Density 1.2224 kg/m3
Yield Strength N/A
Young’s modulus of elasticity N/A
Poisson Ratio N/A
Table III-3 Air properties
Tran Viet Hai
Master Thesis developed at University of Rostock Page 14
3.2. Environmental Input Data
3.2.1. Wind data
According to SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up
Units, 3.Assessment Input Data, 3.4 Wind, the wind velocity should be 1 minute sustained for
the assessment return period, related to a reference level of 10.0m above mean sea level.
The height coefficients applied to calculated wind force are determined based on SNAME 5-
5A, Guidelines for Site Specific Assessment of Mobile Jack-Up Units, 4. Calculation Methods
– Hydrodynamic and Wind Forces. The height coefficients are shown in the table below
Height (m) Height coefficient
0-15 1.00
15-30 1.18
30-45 1.30
45-60 1.39
60-75 1.47
75-90 1.53
90-105 1.58
105-120 1.62
120-135 1.66
135-150 1.70
150-165 1.74
165-180 1.77
180-195 1.80
Table III-4 Height coefficient
The shape coefficients applied to calculated wind force are determined based on SNAME 5-
5A, Guidelines for Site Specific Assessment of Mobile Jack-Up Units, 4. Calculation Methods
– Hydrodynamic and Wind Forces. The shape coefficients are shown in the table below
Shape coefficient
Hull form Cs = 1
Legs Cs = Cd = 1.5
Table III-5 Shape coefficient
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3.2.2. Wave and Current Data
The wave and current data are determined based on SNAME 5-5A, Guidelines for Site Specific
Assessment of Mobile Jack-Up Units, 3.Assessment Input Data, 3.5 Wave and 3.6 Current. For
that the wave height is expressed in terms of maximum wave height and the relation between
maximum wave height and significant wave height is as follows:
Eq. 1
Where
- is the significant wave height
- is the maximum wave height
The range of associated wave period is determined as follows:
√ √ Eq. 2
Where
- is the significant wave height
- is the associated wave period
3.2.3. Marine Growth
Marine growth is determined based on SNAME 5-5A, Guidelines for Site Specific
Assessment of Mobile Jack-Up Units, 3.Assessment Input Data, 3.9 Marine Growth. For that
no marine growth is applied as the legs of the jack-up platform Odin are cleaned often.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 16
3.2.4. Hydrodynamic Coefficients
The hydrodynamic coefficients are determined based on DNV-RP-C205 – Environmental
Conditions and Environmental Loads. In detail, the added mass coefficients are chosen from
Appendix D – Added Mass Coefficients, table D-1. The drag coefficients are chosen from
Appendix E – Drag Coefficients, table E-1.
The hydrodynamic coefficients are shown in the table below.
Angle of Attack
(degree)
Drag Coefficient
Cd rough
Drag Coefficient
Cd smooth
Added Mass Coefficient
Ca
0 1.2 1.2 1.51
45 1.5 1.2 1.51
90 1.2 1.2 1.51
135 1.5 1.2 1.51
180 1.2 1.2 1.51
225 1.5 1.2 1.51
270 1.2 1.2 1.51
315 1.5 1.2 1.51
Table III-6 Hydrodynamic Coefficient
3.2.5. Water Level and Air-gap
According to SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up
Units, 3.Assessment Input Data, 3.7 Water Level and Air-gap, the water level and minimum
air-gap maybe calculated as follows:
- Lowest astronomical tide: LAT
- Highest astronomical tide: HAT
- Mean astronomical tide: MAT = ½ (LAT +HAT)
- Extreme still water level: SWL = MHWS + Storm Surge
- Extreme negative water level: SWL = MLWS + Negative Storm surge
- Air-gap = HAT + Storm Surge + Wave Crest + 1.5m
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3.3. Weights and COGs Input Data
This weight assessment of the ODIN is out of scope of this thesis. The weight and COGs are
taken as input data which is referred from Germanisher Lloyd’s, (2013) Jack-up platform Odin:
Weight assessment. The COGs shown below are in local vessel coordinate system:
- The X-axis points from Aft to Fore, X=0 at Aft
- The Y-axis points from Centerline to Portside, Y=0 at Centerline
- The Z-axis points from Bottom to Deck, Z=0 at Bottom
3.3.1. Deck Load and Tanks
The table below shows the weight and COGs of the deck load and tank weight
Item Weight (kg) Weight (t) x (m) y (m) z (m)
Deck load and tank 373500 373.5 27.01 1.017 3.067
Table III-7 Deck load and Tank Weight
3.3.2. Legs and Spudcans
The table below shows the weight and COGs of legs and spudcans
Item Weight (kg) Weight (t) x (m) y (m) z (m)
LEG_AFTPS_1 146820 146.82 3.15 12.000 27.913
LEG_AFTSB_3 146820 146.82 3.15 -12.000 27.913
LEG_FWDSB_4 146820 146.82 38.85 -12.000 27.913
LEG_FWDPS_2 146820 146.82 38.85 12.000 27.913
SPUDCAN AFTPS_SP1 12810 12.81 3.15 12.000 -1.399
SPUDCAN AFTSB_SP3 12810 12.81 3.15 -12.000 -1.399
SPUDCAN FWDSB_SP4 12810 12.81 38.85 -12.000 -1.399
SPUDCAN FWDPS_SP2 12810 12.81 38.85 12.000 -1.399
Table III-8 Legs and Spudcans Weight
3.3.3. Light Ship without Legs or Spudcan
The table below shows the weight and COG of the light ship
Item Weight (kg) Weight (t) x (m) y (m) z (m)
LIGHTSHIP 2728325 2728.33 20.605 0.037 7.116
Table III-9 Light Ship Weight
Tran Viet Hai
Master Thesis developed at University of Rostock Page 18
IV. FINITE ELEMENT MODEL
4.1. Global Coordinate system
The global coordinate system is described as follows:
- The X-axis points from Aft to Fore, X=0 at Aft
- The Y-axis points from Centerline to Portside, Y=0 at Centerline
- The Z-axis points from Bottom to Deck, Z=0 at Mean water level
Figure IV-1 Global Coordinate System
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 19
4.2. Hull model
The hull form is modeled by shell element SHELL281 and beam elements BEAM188.
Equivalent stiffness is calculated and applied to build the hull form. The areas around jack
houses are fully modeled. The crane is simplified and modeled by shell elements SHELL281.
The details about equivalent structure calculation are presented in Appendix A – Equivalent
Structure.
4.2.1. Hull model
The model of the hull form is shown in the following figures.
Figure IV-2 Hull Model 1
Tran Viet Hai
Master Thesis developed at University of Rostock Page 20
The model of the hull form is shown in the following figures.
Figure IV-3 Hull Model 2
Figure IV-4 Hull Model 3
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 21
4.2.2. Hull Plating
The following figures show the different plate types of the hull form. Each color corresponds to a
different thickness.
Figure IV-5 Deck/Jack house plating
Figure IV-6 Bottom plating
Figure IV-7 Fore part plating
Figure IV-8 Aft part plating
*Note: The colors in the above figures correspond to the thickness of the plating defined in Table
IV-1 Plating Thickness
Tran Viet Hai
Master Thesis developed at University of Rostock Page 22
The following figures show the different plate types of the hull form. Each color corresponds to a
different thickness.
Figure IV-9 Portside plating
Figure IV-10 Starboard Side plating
*Note: The colors in the above picture correspond to the thickness of the plating defined in Table
IV-1 Plating Thickness
The thickness of plates is defined by color as in the table below
Item Thickness (mm)
Grey 8 mm
Yellow 12 mm
Green 20 mm
Blue 30 mm
Red 40 mm
Table IV-1 Plating Thickness
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 23
4.2.3. Hull Stiffness
As presented in the Appendix A - Equivalent Structure, equivalent stiffness is calculated and
applied to build the hull form. The areas around jack houses are fully modeled.
The element shapes of the hull stiffness are shown in the figures below
Figure IV-11 Hull stiffness
Figure IV-12 Hull stiffness – around jack house
Tran Viet Hai
Master Thesis developed at University of Rostock Page 24
The tables below show the list of stiffeners used in the model. Not all stiffeners used in the
model are from the drawing of the ODIN. Some of the stiffeners are the equivalent stiffness
(eqv) calculated in Appendix A - Equivalent Structure.
Flat Bar Height (mm) Thickness (mm)
FB920x34 (eqv) 920 34
FB700x18 (eqv) 700 18
FB500x42 (eqv) 500 42
FB500x18 (eqv) 500 18
FB480x22 (eqv) 480 22
FB245x34 (eqv) 245 34
FB240x22(eqv) 240 22
FB220x26 (eqv) 220 26
FB160x46 (eqv) 160 46
FB 120x7 120 7
Table IV-2 Flat bar profile
Holland Profile b (mm) s (mm) c (mm) r (mm)
HP 280x11 280 11 40 12
HP 200X9 200 9 28 8
HP 120X8 120 8 17 5
Table IV-3 Holland Profile
T-Bar Profile WEB FLANGE
Height (mm) Thickness (mm) Height (mm) Thickness (mm)
WEB 1200x9 FB 300x20 1200 9 300 20
WEB 1000x10 FB 300x20 1000 10 300 20
WEB 1000X8 FB 300X20 1000 8 300 20
WEB 800x8 FB 200x20 800 8 200 20
WEB 500x12 FB 200x20 500 12 200 20
WEB 400x10 FB 150x20 400 10 150 20
WEB 300x8 FB 100x10 300 8 100 10
WEB 250x8 FB 120x20 250 8 120 20
WEB 250x8 FB 100x10 250 8 100 10
WEB 250x8 FB 100x8 250 8 100 8
Table IV-4 T-Bar profile
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 25
4.2.4. Blocks of plates and stiffness
Examples of the element shapes of some of the blocks are shown in the figures below.
Figure IV-13 Block – Plates and stiffness 1
Figure IV-14 Block – Plates and stiffness 2
Tran Viet Hai
Master Thesis developed at University of Rostock Page 26
4.3. Leg and Spudcan Model
4.3.1. Leg model
An equivalent leg is used in the model of the Odin. The method and detail calculation applied
to determine the equivalent leg are presented in Appendix A - Equivalent Structure.
The element shape of a part of the equivalent leg is presented in the figure below.
Figure IV-15 Equivalent element shape - 3D
The figures below show the main dimension of the equivalent leg section and its FEM model.
Figure IV-16 Equivalent leg section
Figure IV-17 Equivalent leg section - FEM
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 27
The table below shows the main properties of the equivalent leg section. The difference
between the calculated section and the section modeled is also presented in the table.
Equivalent Leg Section
Values (m/m2/m4) Ratio
Items Calculated
Section
Modeled
Section
Modeled /
Calculated
Area 0.25901 0.25620 98.9%
Iyy 0.13479 0.13467 99.9%
Iyz 0 0 N/A
Izz 0.16826 0.16675 99.1%
Table IV-5 Equivalent leg section properties
4.3.2. Ocean Pipe
As a limitation of ANSYS APDL, ocean load can only be computed on ocean pipe section.
Hence, ocean pipes are modeled along the leg to transfer the ocean load to the model. For that
the elements PIPE288 are used. Very small values are attributed to the stiffness and the weight of
the pipes so that the stiffness and the weight of the model are unchanged. The diameter of the
pipe is 2m. The equivalent added mass coefficients and drag coefficients are input to ANSYS in
order to achieve the same added mass and ocean load acting on the structure. The figures below
show the element shape of a part the ocean pipe and a part of the leg with the ocean pipe.
Figure IV-18 Ocean pipe
Figure IV-19 Leg with ocean pipe
Tran Viet Hai
Master Thesis developed at University of Rostock Page 28
4.3.3. Spudcan Model
The spudcan is modeled with beam elements BEAM188. Very high values are attributed to
the stiffness of the spudcan. The geometry of the model is the same with the real spudcan
without the bracket. The spudcan and a part of the leg are presented in the figures below.
Figure IV-20 Spudcan model
Figure IV-21 Spudcan model-FEM
The table below shows the main dimension and properties of the spudcan.
Spudcan
Total height 1.4m
Base height 0.45m
Base section 3.31x3.31m
Upper part height 0.95m
Upper part section 2.112x2.112m
Stiffness Infinite
Table IV-6 Spudcan dimensions and properties
4.4. Seabed reaction point and Foundation Fixity
As required in SNAME, the seabed reaction point and the foundation fixity is modeled as
follows:
Connection type: Pin joints (unable to sustain bending moments)
Position of the reaction point:
- At vertical axis of the leg/Spudcan
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- At Half of the predicted penetration (when SPD is partly penetrated)
- At Half of SPD height (when SPD is fully penetrated)
4.5. Leg hull connection
The leg-hull connection is modeled by linear springs. Each spring acts only in one direction.
For that the spring elements COMBIN14 are used. The detail about spring system is as follows
The table below shows the position and stiffness of the spring system.
Position Spring Stiffness (kN/mm)
Bottom
Horizontal (X)
Horizontal (Y)
1000
1000
Main Deck Horizontal (X)
Horizontal (Y)
1000
1000
Leg vertical axis Vertical (Z) 1000
Table IV-7 Leg-Hull connection springs
4.6. Weight Adjustment
Due to the fact that only the structure part of the ship is modeled, the weight of the model
cannot be equal to the real weight of the ship. Thus, the weight of the model needs to be adjusted
order to achieve the same weight and COGs with the weight and COGs presented in 3.3.
Weights and COGs Input Data.
For that different material densities are applied to different parts of the model. Besides, the
mass element MASS21 is applied in the model. The mass elements are linked to parts of the
model by Contact Technique – Multipoint Constraints and Assemblies. The target elements
TARGE170 and contact elements CONTA175 are used to perform the contact technique.
The tables below show COGs in local vessel coordinate system:
- The X-axis points from Aft to Fore, X=0 at Aft
- The Y-axis points from Centerline to Portside, Y=0 at Centerline
- The Z-axis points from Bottom to Deck, Z=0 at Bottom
Tran Viet Hai
Master Thesis developed at University of Rostock Page 30
The table below shows the weight and COGs of the model after adjusting
Item Weight (kg) Weight (t) x (m) y (m) z (m)
Light Ship + Deck Load
and Tank 3101825 3101.825 21.376 0.156 6.628
LEG_AFTPS_1 146820 146.82 3.15 12.000 27.913
LEG_AFTSB_3 146820 146.82 3.15 -12.000 27.913
LEG_FWDSB_4 146820 146.82 38.85 -12.000 27.913
LEG_FWDPS_2 146820 146.82 38.85 12.000 27.913
SPUDCAN AFTPS_SP1 12810 12.81 3.15 12.000 -0.9
SPUDCAN AFTSB_SP3 12810 12.81 3.15 -12.000 -0.9
SPUDCAN FWDSB_SP4 12810 12.81 38.85 -12.000 -0.9
SPUDCAN FWDPS_SP2 12810 12.81 38.85 12.000 -0.9
Table IV-8 FEM model weight
The table below shows the difference between weight, COGs of the model after adjusting
and weight, COGs from Germanisher Lloyd’s weight assessment data (refer to Table III-7 Deck
load and Tank Weight, Table III-8 Legs and Spudcans Weight and Table III-9 Light Ship
Weight).
Item Weight (kg) Weight (t) x (m) y (m) z (m)
Light Ship + Deck Load
and Tank 0 0 0 0 0
LEG_AFTPS_1 0 0 0 0 0
LEG_AFTSB_3 0 0 0 0 0
LEG_FWDSB_4 0 0 0 0 0
LEG_FWDPS_2 0 0 0 0 0
SPUDCAN AFTPS_SP1 0 0 0 0 0.5
SPUDCAN AFTSB_SP3 0 0 0 0 0.5
SPUDCAN FWDSB_SP4 0 0 0 0 0.5
SPUDCAN FWDPS_SP2 0 0 0 0 0.5
Table IV-9 Weight and COGs Comparison
As can be seen, the only difference between the two data sets is the Z coordinate of the COG
of the Spudcan. However, this difference does not affect any results. It is because in both cases,
the COGs of the Spudcan is below the model boundary connection point and therefore do not
participate in any analyses.
Thus, the weight of the model after adjusting totally matches the Germanisher Lloyd’s
weight assessment data.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 31
4.7. Full Model and Sub-structuring Model
The Odin full model is built as presented above. The full model and its sub-structuring model
are used for all analyses performed in this thesis. The detail about sub-structuring model is
presented in Appendix B - Sub-structuring Model Assessment. The figures below show element
shapes of the two models.
Figure IV-22 ODIN Full Model
Figure IV-23 ODIN Sub-structuring Model
Tran Viet Hai
Master Thesis developed at University of Rostock Page 32
V. LOAD APPLICATION
The loads acting on the jack-up platform Odin consist of self-weight, crane loads, wind loads
and hydrodynamic loads (wave and current loads). The load factors applied to each type of load
are determined based on SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile
Jack-Up Units, 8.Acceptance Criteria.
For that the required load factors are as follows:
- γ1 = 1.00 – Applies to non-varying weight loads
- γ2 = 1.00 – Applies to maximum or minimum variable loads applicable to check
being carried out
- γ3 = 1.15 – Applies to environmental loads
- γ4 = 1.00 – Applies to dynamic loads in combination with γ3
5.1. Self-Weight
The weight distribution of the model is adjusted as presented in 4.6. Weight Adjustment. The
self-weight then is applied to the model by acceleration with the magnitude equal to the
acceleration of gravity g = 9.81m/s2
The load factor applied to the self-weight is γ1 = 1.00
5.2. Crane Loads
As presented in Figure I-12 Crane working range diagram and Table I-1 Technical data of
Jack up platform Odin, the maximum range of the crane is 65m and the lifting capacity at that
range is 29.6 tons. The force and the moment acting on the crane base are calculated for the
maximum range and the associated lifting capacity. Nodal force and moment are applied to a
node at crane pedestal height and then distributed equally to crane base by means of Contact
Technique – Multipoint Constraints and Assemblies. The target elements TARGE170 and
contact elements CONTA175 are used to perform the contact technique.
The angle of the crane is determined based on the wind and wave direction in order to account
for the worst load combination (maximum over-turning moment).
Since the crane is in resting position in survival modes, crane loads are only applied to the model
in operational modes. The load factor applied to the crane loads is 1.15
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 33
5.3. Wind Loads
Wind loads are computed and applied separately for the legs and the hull form as the shape
coefficients for the legs and the hull form are different.
A macro file is created to compute and apply the wind loads acting on legs, from water surface to
the bottom of the jack up. For that the wind load acting on each leg element is automatically
computed for different angles of attack and then applied directly to the nodes of those elements
as nodal forces.
Another macro file is created to compute and apply the wind loads acting on the hull form to the
model. For that the wind force acting on each shell element is automatically computed as the
projected area is determined based on the area and the normal vector and the height coefficient is
determined based on the center of geometry of the area associated with that shell element. The
equivalent total forces and moments are then calculated and applied to the center of gravity of
the hull form as nodal force. The wind forces and moments are then distributed to parts of the
hull form by means of Contact Technique – Multipoint Constraints and Assemblies. The target
elements TARGE170 and contact elements CONTA175 are used to perform the contact
technique.
Due to lack of information about cargo on deck which results in extra wind force, it is assumed
that the total wind force acting on the hull form and the cargo is equal to 1.5 times the wind force
acting on the hull form.
The wind loads acting on the model are computed based on SNAME 5-5A, Guidelines for Site
Specific Assessment of Mobile Jack-Up Units, 4.2 Wind Force Calculation as follows:
Eq. 3
Where
: The wind force acting on the block considered
: The pressure at the center of the block
: The projected area of the block
Tran Viet Hai
Master Thesis developed at University of Rostock Page 34
Wind pressure Pi can be calculated as follows:
Eq. 4
Where
: The pressure at the center of the block
: Density of Air
: The 1 minute sustained wind velocity at reference elevation
: Height coefficient
: Shape coefficient
*Note:
- Density of air is given in Table III-3 Air properties.
- Height coefficient is given in Table III-4 Height coefficient
- Shape coefficient is given in Table III-5 Shape coefficient
The load factor applied to the wind loads is 1.15
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 35
5.4. Wave and Current Loads
The wave and current loads are calculated complying with SNAME 5-5A, Guidelines for
Site Specific Assessment of Mobile Jack-Up Units, 4.3 Hydrodynamic Forces. Also, according
to SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up Units, 4.4 Wave
Theories and Analysis Methods, for practical purposes the Stokes’ 5th
order wave theory can be
applied for intermediate water depth.
For that when the Morison’s equation can be applied providing:
Eq. 5
Where
: The wave length
: Reference diameter of member
The hydrodynamic forces as vector can be calculated as follows:
| | Eq. 6
Where
: Hydrodynamic force per unit length
: Water density
: Reference diameter of member
: Drag coefficient
: Relative fluid particle velocity resolved normal to the member axis
: Inertia coefficient
: Cross sectional area of member
: Fluid particle acceleration normal to member
Tran Viet Hai
Master Thesis developed at University of Rostock Page 36
According to Theory Reference for the Mechanical APDL and Mechanical Applications, 13.7
Hydrodynamic Loads on Line Elements, the ocean loads acting on elements calculated by
ANSYS APDL are also based on when the Morison’s equation.
For that the distributed hydrodynamic load on elements can be calculated as follows:
{ } | | | | Eq. 7
Where
{ } : Hydrodynamic force per unit length
: Water density
: Reference diameter of member
: Drag coefficient
: Relative fluid particle velocity resolved normal to the member axis
: Inertia coefficient
: Cross sectional area of member
: Fluid particle acceleration normal to member
: Tangential drag coefficient
: Tangential relative particle velocity vector
From Eq. 6 and Eq. 7 the method ANSYS APDL uses to calculate ocean loads is complying
with SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up.
For that the hydrodynamic loads can be computed by ANSYS APDL. Ocean environment
modeled by the commands OCDATA, OCTABLE, OCTYPE. The wave theory is determined as
Stokes’ 5th
order. Drag coefficient and inertial coefficient are as in Table III-6 Hydrodynamic
Coefficient. Tangential drag coefficient is set as 0. Ocean pipes are modeled to transfer the ocean
loads on the model as described in 4.3.2 Ocean Pipe.
The load factor applied to the ocean loads is 1.15
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 37
VI. ANALYSIS METHOD
In this thesis, the envelopes of feasible conditions are determined through three main steps.
The first step is to determine the most critical angle of attack & wave phase combination. The
second step is to determine the dynamic amplification factor (DAF). The last step is to analyse
the model with inertial force and other effects.
The detail about each step is presented in the following parts of the thesis.
6.1. Analysis Method – Step 1
The purpose of this step is to determine the most critical angle of attack & wave phase
combinations. For that static analyses and modal analyses are conducted.
Figure VI-1 Analysis method – Step 1
First of all, a static analysis is conducted with only self-weight and buoyancy. The wind forces,
hydrodynamic forces and crane loads are not available in this analysis. The purpose of this
analysis is to get the initial condition without effects of wind or wave.
After that, static analyses are conducted with environmental loads. Self-weight, buoyancy, wind
forces and hydrodynamic forces are all applied. These analyses are performed for different
angles of attack and different wave phase.
In this thesis, 8 angles of attack are considered: 0, 45, 90, 135, 180, 225, 270, 315 degrees.
(Refer to Figure IV-1 Global Coordinate System for directions and angles). For each wave, 24
wave phases are considered with equal phase step of 15 degrees. (0, 15, 30, …, 330, 345
degrees).
Tran Viet Hai
Master Thesis developed at University of Rostock Page 38
Also, three associated wave periods are considered for each maximum wave height. These
wave periods are the maximum period (Tmax), the minimum period (Tmin) and the mean period
(Tmean) in the range of associated wave period defined in 3.2.2 Wave and Current Data. Thus,
there are 576 static analyses need to be conducted in this part for each maximum wave height.
From these analyses and the initial condition established by the static analysis with self-
weight and buoyancy the most critical angle of attack & wave phase combinations are
determined. These combinations give the maximum base shear or the maximum ratio of
overturning moment to stabilizing moment.
Besides, a modal analysis is also conducted. From the natural periods of the jack up another
critical angle of attack & wave phase combination may be added. This is when the critical angle
of attack & wave phase combinations determined before do not cover the angle of attack
associated with the oscillation mode with the natural frequency close to wave frequency.
The natural periods and frequencies are calculated for three main modes which are normally
oscillation modes corresponding to oscillation motion in X direction, Y direction and torsion
about Z direction. The angular frequencies in the first two modes which are more important are
then used to calculate mass matrix multiplier α and stiffness matrix multiplier β in step 2.
6.2. Analysis Method – Step 2
The purpose of this step is to determine the dynamic amplification factor (DAF). For that
static analyses and dynamic analyses are conducted.
Figure VI-2 Analysis Method – Step 2
All analyses in this step are performed with ocean load only. The wind force is not applied in
order to focus on wave and current loads. First, static analyses are performed for the wave and
current coming from the critical angles of attack determined in the first step. From these
analyses, the base shear and overturning moment due to wave and current loads can be calculated
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 39
without dynamic effects. After that, dynamic analyses are conducted to calculated base shears
and overturning moments with dynamic effects. If the natural frequencies of the model are out of
range of wave frequency, three values of wave periods will be applied (Tmax, Tmin and Tmean).
In case the natural frequencies of the model fall within the range of wave frequency, the wave
period will be chosen the same as the corresponding natural period.
6.2.1. Dynamic Analysis and Damping Ratio
In order to take into account dynamic effects, dynamic analyses need to be conducted. For
that, harmonic and transient analyses are performed for the critical angles of attack determined in
the first step.
As a limit of ANSYS APDL, it is not possible to conduct harmonic analysis along with sea
load from ocean environment. To overcome this challenge, the set command HROCEAN is used
along with Harmonic Ocean Wave Procedure (HOWP).
The basic equation solved by harmonic analysis and transient analysis is as follows:
{ ̈} { ̇} { } { } Eq. 8
Where
: Mass matrix
: Damping matrix
: Stiffness matrix
{ ̈}: Nodal acceleration vector
{ ̇}: Nodal velocity vector
{ }: Nodal displacement vector
{ }: Load vector
Another challenge is that the damping ratio is unknown and needs to be determined.
Nevertheless, measuring the damping ratio is out of the scope of this thesis. For that, an
assumption is made in which the damping ratio is taken as 0.05 the critical damping.
√ Eq. 9
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Master Thesis developed at University of Rostock Page 40
In order to achieve this ratio, the damping matrix (C) is applied by means of mass matrix
multiplier α and stiffness matrix multiplier β. In detail, according to Theory Reference for the
Mechanical APDL and Mechanical Applications, 13.5 Damping Matrices, the damping matrix
is calculated as follows:
∑[(
) ]
∑
Eq. 10
Where
: Damping matrix
: Mass matrix
: Stiffness matrix
: Mass matrix multiplier
: Stiffness matrix multiplier
: Variable stiffness matrix multiplier
: Stiffness matrix multiplier for material j
: Constant stiffness matrix coefficient for material j
: Circular excitation frequency
: Portion of structure stiffness matrix based on material j
: Element damping matrix
: Frequency-dependent damping matrix
The damping matrix created by only mass matrix multiplier α and stiffness matrix multiplier
β is as follows:
Eq. 11
From the modal analysis conducted in the first step, two main oscillation angular frequencies
ω1 and ω2 are determined. The mass matrix multiplier α and stiffness matrix multiplier β are
then calculated in order to satisfy the set of two equations as follows:
Eq. 12
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 41
Eq. 13
Where
: Damping ratio
: Mass matrix multiplier
: Stiffness matrix multiplier
: The angular frequency of mode 1 oscillation motion determined in step 1
: The angular frequency of mode 2 oscillation motion determined in step 1
The maximum base shear and the maximum ratio of overturning moment to stabilizing
moment over time are then determined from dynamic analyses. These base shears and ratios are
with dynamic effects.
6.2.2. Dynamic Amplification Factor (DAF)
The dynamic amplification factors (DAF) are then determined based on SNAME 5-5A,
Guidelines for Site Specific Assessment of Mobile Jack-Up Units, 7.3.6.3 Inertial load set
based on random analysis as follows:
Eq. 14
Where
DAF: Dynamic amplification factor
: The most probable maximum extreme from base shear and overturning
moment from dynamic analysis
: The most probable maximum extreme from base shear and overturning
moment from static analysis.
In detail, the dynamic amplification factors based on base shear (DAFS) and the dynamic
amplification factors based on overturning moment (DAFT) can be calculated as follows:
Eq. 15
Where
: Dynamic amplification factor based on base shear
: The total base shear from dynamic analysis
Tran Viet Hai
Master Thesis developed at University of Rostock Page 42
: The total base shear from static analysis
Eq. 16
Where
: Dynamic amplification factor based on overturning moment
: The overturning moment from dynamic analysis
: The overturning moment from static analysis
6.3. Analysis Method – Step 3
This step is the final step in that all loads and their load factors are applied to the model. The
inertial loads are also calculated and applied so that the dynamic effect can be taken. Non-linear
static analyses are performed in order to take into account the P-Δ effect.
Figure VI-3 Analysis method – Step 3
The inertial loads are calculated based on the dynamic amplification factors determined in
the second step. The increase in base shear due to dynamic effects which needs to be applied to
the model can be calculated as follows:
Eq. 17
Where
: The increase in base shear due to dynamic effects
: The total base shear from dynamic analysis
: The total base shear from static analysis
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 43
: Dynamic amplification factor based on base shear
The increase in base shear due to dynamic effects which needs to be applied to the model can
be calculated as follows:
Eq. 18
Where
: The increase in overturning moment due to dynamic effects
: The overturning moment from dynamic analysis
: The overturning moment from static analysis
: Dynamic amplification factor based on overturning moment
Thus, in order to take into account the dynamic effect forces and moments are calculated and
then applied to the center of gravity of the hull form. In detail, a couple of forces in X and Y
direction are determined to represent in both magnitude and direction. Moments are then
added in order to create taking into account the moments resulting from the couple of forces
added before. The forces and moments are then distributed to parts of the hull form by means of
Contact Technique – Multipoint Constraints and Assemblies. The target elements TARGE170
and contact elements CONTA175 are used to perform the contact technique.
The reaction forces and overturning moments given by nonlinear static analyses in this step are
then used for the overturning stability check and structural ultimate strength check.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 44
VII. ACCEPTANCE CRITERIA
7.1. Leg Reserve
According to DNV-RP-C205 the leg reserve must be greater than 1.5m. For that, the
following condition must be satisfied:
Eq. 19
Where
: The total length of a leg and its spudcan
: Water Depth
: The leg penetration
: The height of main hull
: The height of jack house
: The air-gap
7.2. Overturning Stability
The overturning stability checking is perform complying with SNAME 5-5A, Guidelines for
Site Specific Assessment of Mobile Jack-Up Units, 8.2 Overturning Stability. The overturning
axis shall be the most critical axis passing through any two leg reaction points.
The overturning stability can be calculated as follows:
Eq. 20
Where
: Overturning Moment
: The extreme overturning moment
: The dynamic overturning moment
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 45
The criterion for overturning stability is given as follows:
Eq. 21
Where
: Overturning Moment
: The dynamic overturning moment due to dead load including buoyancy
: The stabilizing moment due to the most onerous combination of minimum
variable load and center of gravity.
7.3. Structural Ultimate Strength
7.3.1. Leg Inclination
According to SNAME 5-5A, Guidelines for Site Specific Assessment of Mobile Jack-Up
Units, 5.4 Leg Inclination, an increase in effective moment must be added to the position at the
lower guide of each leg in order to take into account the leg inclination effect. This effect is
applied only to structural strength check.
The magnitude of the increase in moment due to leg inclination effect can be calculated as
follows:
Eq. 22
Where
: Increase in moment due to leg inclination effect
: Total horizontal offset of leg base with respect to hull – taken as 0.5%
: The factored vertical reaction at leg base
7.3.2. Leg Checking
As the ultimate strength check for the legs is not covered by SNAME 5-5A, Guidelines for
Site Specific Assessment of Mobile Jack-Up due to their rectangular shape, the leg checking part
is done complying with EUROCODE 3 – Design of steel structures, , EN 1993-1-1 and EN
1993-1-5.
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Master Thesis developed at University of Rostock Page 46
For that the leg section of the Odin is classified as class 4 and the effective area must be
calculated in order to take into account the buckling effect. The detail calculation for the
effective leg section is presented in Appendix A - Equivalent Structure.
The effective leg section used for ultimate strength checking is shown in the figures below.
Figure VII-1 Effective leg section
Figure VII-2 Effective leg section - FEM
Leg cross section properties are shown in the table below.
Items Value (m/m2/m4)
Area 0.18518
Iyy 0.10815
Iyz 0
Izz 0.15178
Centroid Y 0
Centroid Z 0
Table VII-1 Effective leg section properties
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 47
The effective leg cross section then can be used for structural ultimate strength check.
According to EN 1993-1-1, 6 Ultimate Limit States the yield criterion for elastic verification is
as follows:
(
)
(
)
(
)(
) (
)
Eq. 23
Where
: Yield strength or reduced yield strength (see *Note below)
: The design value of the local longitudinal stress at the point of consideration
: The design value of the local transversal stress at the point of consideration
: The design value of the local shear stress at the point of consideration
The normal stress caused by axial force can be calculated as follows:
Eq. 24
Where:
- F: The design value of the axial force
- A: The cross section area
The normal stress caused by bending moment can be calculated as follows:
Eq. 25
Where:
- M: The design value of the bending moment
- y: The perpendicular distance from the point of interest to the neutral axis
- I: The inertial moment about the neutral axis
Tran Viet Hai
Master Thesis developed at University of Rostock Page 48
The shear stress caused by shear force can be calculated as follows:
Eq. 26
Where:
- : The design value of the shear force
- S: The first moment of area about the neutral axis of that portion of the cross
section between the point of interest and the boundary of the cross-section
- I: The inertial moment about the neutral axis
- t: The thickness at the point of interest
*Note: Since the legs of the Odin are under combination of bending moment, shear force and
axial force, the reduced yield strength must be taken into account unless
Eq. 27
Where
: Design value of the shear force
: Design plastic shear resistance
Design plastic shear resistance can be calculated as follows:
√
Eq. 28
Where
: Shear area
: Yield strength of material
Shear area can be calculated as follows:
∑ Eq. 29
Where
: Web height
: Web thickness
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 49
The reduced yield strength then can be calculated as follows:
Eq. 30
Where
: Reduced yield strength
: Yield strength of material
: Reduction factor
The reduction factor can be calculated as follows:
(
)
Eq. 31
Where
: Design value of the shear force
: Design plastic shear resistance
Tran Viet Hai
Master Thesis developed at University of Rostock Page 50
VIII. FINDING
8.1. Main Results
As required, the model needs to be analyzed for three different water depths. For each water
depth, the model is tested for both operational and survival modes. The water depths are chosen
as 15m, 20m and 25m. The air-gaps are 15m and 5m for operational mode and survival mode
respectively.
The idea of this arrangement is that for each water depth, the Odin will jack down from
operational mode to survival mode when the weather turns heavy and threatens the safety of the
jack up in the operational mode. In detail, first the model in operational mode is analyzed with
different wave heights and associated wave periods. Envelop of weather condition is then
determined for this mode. The mode in survival condition will be tested only with wave heights
which are greater than the minimum wave height that is dangerous for the jack up in the
operational mode. Envelop of weather condition is then again defined for the survival condition
mode. In all cases, in order not to violate the air-gap condition, only wave under 7m height are
tested.
The table below shows the weather conditions that threaten the safety of the jack up in
different elevated conditions.
ELEVATED CONDITION HIGH-RISK WEATHER CONDITION
Water
Depth
Leg
Penetration Mode Air-gap
Wind
Speed
Current
Speed
Wave Height
Max
15m 3m Operational (1) 15m 12m/s 1m/s 2m – 4.2m
Survival (1) 5m 23m/s 1.5m/s None
20m 3m Operational (2) 15m 12m/s 1m/s 2.9m – 5.6m
Survival (2) 5m 23m/s 1.5m/s 3.3m – 3.5m
25m 3m Operational (3) 15m 12m/s 1m/s ≥3.7m
Survival (3) 5m 23m/s 1.5m/s 3.8m – 4.8m
Table VIII-1 Main Results
Due to the size of the thesis, detail results cannot be presented for all cases. Instead, for each
operational or survival mode, the results are presented for one critical weather condition only.
The details are shown in the next part of the thesis.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 51
8.2. Results for Operational Condition 1
8.2.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 15m
Leg Penetration 3m
Air-gap 15m
Maximum Wave Height 2.00m
Peak Wave Period 4.58s
Significant Wave Height 1.08m
Associated Wave Periods 3.57 ; 4.08 ; 4.58s
Current Speed 1 m/s
Wind Speed at 10m above sea level 12 m/s
Table VIII-2 Input data
8.2.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=15m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=15m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 52
8.2.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.2178 4.59
2 0.2268 4.41
3 0.3036 3.29
Table VIII-3 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.2.4. The Critical Combination
The highest environmental load (ocean load and wind) acting on the jack-up platform is
created by the combination shown in the following table.
Value
Angle of Attack – Wind 0 degree
Angle of Attack – Wave & Current 0 degree
Wave period 4.58s
Crane Working Angle 0 degree
Figure VIII-1 Critical combination
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 53
8.2.1. Dynamic Amplification Factor (DAF)
The dynamic amplification factor (DAF) is calculated by comparing the results given by
static analyses and dynamic analyses. (Refer to VI ANALYSIS METHOD for detail) The main
results are presented in the following figures.
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by static analyses.
Figure VIII-2 Base Shear – Static Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by static analysis is 3.95E+05 N
Tran Viet Hai
Master Thesis developed at University of Rostock Page 54
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by dynamic analyses.
Figure VIII-3 Base Shear – Dynamic Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by dynamic analysis is 2.53E+06 N
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 55
The figure below compares the results of total base shear of the four legs given by static
analyses (purple) and dynamic analyses (aqua blue).
Figure VIII-4 Total base shear comparison - Static and Dynamic analyses
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The dynamic amplification factor is given in the table below
Maximum Base Shear (N) Dynamic Amplification Factor
Static Analysis Dynamic Analysis
3.95E+05 2.53E+06 6.41
Figure VIII-5 Dynamic amplification factor (DAF)
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Master Thesis developed at University of Rostock Page 56
8.2.2. Checking Results
The maximum displacement of the jack-up in this case is 0.50m. The moment and shear
force diagrams are as follows. (The values of moment and shear force are given in Nm and N
respectively)
Figure VIII-6 Moment distribution over legs
Figure VIII-7 Shear force distribution over legs
The reaction forces of each leg are given in the following table:
Leg 1 Leg 2 Leg 3 Leg 4 Total
Fx (N) -7.27E+05 -7.33E+05 -7.27E+05 -7.31E+05 -2.92E+06
Fy (N) -1.14E+04 -1.35E+04 9.60E+02 2.39E+04 -1.16E+01
Fz (N) 6.49E+06 1.10E+07 6.36E+06 1.07E+07 3.46E+07
Table VIII-4 Leg Reaction
The Overturning Stability Check (satisfied if overturning/stabilizing < 1) is given as follows
About Overturning Moment (Nm) Stabilizing Moment (Nm) Overturning/Stabilizing
X Axis 2.36E+07 3.92E+08 0.06
Y Axis 1.82E+08 5.70E+08 0.32
Table VIII-5 Overturning Stability Check
The result for Leg Ultimate Strength Check (satisfied if < 1) is as follows:
(
)
(
)
(
⁄)(
⁄) (
⁄)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 57
8.3. Results for Survival Condition 1
8.3.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 15m
Leg Penetration 3m
Air-gap 5m
Maximum Wave Height 3.80m
Peak Wave Period 6.32s
Significant Wave Height 2.04m
Associated Wave Periods 4.92 ; 5.62 ; 6.32s
Current Speed 1.5 m/s
Wind Speed at 10m above sea level 23 m/s
Table VIII-6 Input data
8.3.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=25m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=5m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 58
8.3.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.3410 2.93
2 0.3462 2.89
3 0.4626 2.16
Table VIII-7 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.3.4. The Critical Combination
The model in this elevated mode is safe under all weather conditions except for the case the
wave reaches the platform and the condition of the air-gap is violated.
Safe with waves smaller than 7m height.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 59
8.4. Results for Operational Condition 2
8.4.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 20m
Leg Penetration 3m
Air-gap 15m
Maximum Wave Height 2.90m
Peak Wave Period 5.52s
Significant Wave Height 1.56m
Associated Wave Periods 4.30 ; 4.91 ; 5.52s
Current Speed 1 m/s
Wind Speed at 10m above sea level 12 m/s
Table VIII-8 Input data
8.4.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=20m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=15m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 60
8.4.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.1802 5.55
2 0.1892 5.28
3 0.2520 3.97
Table VIII-9 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.4.4. The Critical Combination
The highest environmental load (ocean load and wind) acting on the jack-up platform is
created by the combination shown in the following table.
Value
Angle of Attack – Wind 0 degree
Angle of Attack – Wave & Current 0 degree
Wave period 5.52s
Crane Working Angle 0 degree
Figure VIII-8 Critical combination
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 61
8.4.5. Dynamic Amplification Factor (DAF)
The dynamic amplification factor (DAF) is calculated by comparing the results given by
static analyses and dynamic analyses. (Refer to VI ANALYSIS METHOD for detail) The main
results are presented in the following figures.
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by static analyses.
Figure VIII-9 Base Shear – Static Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by static analysis is 4.43E+05 N
Tran Viet Hai
Master Thesis developed at University of Rostock Page 62
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by dynamic analyses.
Figure VIII-10 Base Shear – Dynamic Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by dynamic analysis is 2.19E+06 N
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 63
The figure below compares the results of total base shear of the four legs given by static
analyses (purple) and dynamic analyses (aqua blue).
Figure VIII-11 Total base shear comparison - Static and Dynamic analyses
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The dynamic amplification factor is given in the table below
Maximum Base Shear (N) Dynamic Amplification Factor
Static Analysis Dynamic Analysis
4.43E+05 2.19E+06 4.95
Figure VIII-12 Dynamic amplification factor (DAF)
Tran Viet Hai
Master Thesis developed at University of Rostock Page 64
8.4.6. Checking Results
The maximum displacement of the jack-up in this case is 0.67m. The moment and shear
force diagrams are as follows. (The values of moment and shear force are given in Nm and N
respectively)
Figure VIII-13 Moment distribution over legs
Figure VIII-14 Shear force distribution over legs
The reaction forces of each leg are given in the following table:
Leg 1 Leg 2 Leg 3 Leg 4 Total
Fx (N) -6.62E+05 -6.40E+05 -6.62E+05 -6.40E+05 -2.60E+06
Fy (N) -9.47E+03 -9.79E+03 6.28E+01 1.92E+04 2.68E+01
Fz (N) 6.28E+06 1.08E+07 6.15E+06 1.05E+07 3.38E+07
Table VIII-10 Leg Reaction
The Overturning Stability Check (satisfied if overturning/stabilizing < 1) is given as follows
About Overturning Moment (Nm) Stabilizing Moment (Nm) Overturning/Stabilizing
X Axis 1.35E+07 3.92E+08 0.03
Y Axis 1.68E+08 5.70E+08 0.29
Table VIII-11 Overturning Stability Check
The result for Leg Ultimate Strength Check (satisfied if < 1) is as follows:
(
)
(
)
(
⁄)(
⁄) (
⁄)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 65
8.5. Results for Survival Condition 2
8.5.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 20m
Leg Penetration 3m
Air-gap 5m
Maximum Wave Height 3.30m
Peak Wave Period 5.89s
Significant Wave Height 1.77m
Associated Wave Periods 4.58 ; 5.23 ; 5.89s
Current Speed 1.5 m/s
Wind Speed at 10m above sea level 23 m/s
Table VIII-12 Input data
8.5.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=20m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=5m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 66
8.5.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.2659 3.76
2 0.2742 3.65
3 0.3647 2.74
Table VIII-13 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.5.4. The Critical Combination
The highest environmental load (ocean load and wind) acting on the jack-up platform is
created by the combination shown in the following table.
Value
Angle of Attack – Wind 0 degree
Angle of Attack – Wave & Current 0 degree
Wave period 4.58s
Crane Working Angle N/A
Figure VIII-15 Critical combination
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 67
8.5.5. Dynamic Amplification Factor (DAF)
The dynamic amplification factor (DAF) is calculated by comparing the results given by
static analyses and dynamic analyses. (Refer to VI ANALYSIS METHOD for detail) The main
results are presented in the following figures.
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by static analyses.
Figure VIII-16 Base Shear – Static Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by static analysis is 8.67E+05 N
Tran Viet Hai
Master Thesis developed at University of Rostock Page 68
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by dynamic analyses.
Figure VIII-17 Base Shear – Dynamic Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by dynamic analysis is 2.36E+06 N
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 69
The figure below compares the results of total base shear of the four legs given by static
analyses (purple) and dynamic analyses (aqua blue).
Figure VIII-18 Total base shear comparison - Static and Dynamic analyses
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The dynamic amplification factor is given in the table below
Maximum Base Shear (N) Dynamic Amplification Factor
Static Analysis Dynamic Analysis
8.67E+05 2.36E+06 2.72
Figure VIII-19 Dynamic amplification factor (DAF)
Tran Viet Hai
Master Thesis developed at University of Rostock Page 70
8.5.6. Checking Results
The maximum displacement of the jack-up in this case is 0.30m. The moment and shear
force diagrams are as follows. (The values of moment and shear force are given in Nm and N
respectively)
Figure VIII-20 Moment distribution over legs
Figure VIII-21 Shear force distribution over legs
The reaction forces of each leg are given in the following table:
Leg 1 Leg 2 Leg 3 Leg 4 Total
Fx (N) -6.81E+05 -7.75E+05 -6.83E+05 -7.72E+05 -2.91E+06
Fy (N) -1.36E+04 -1.53E+04 5.21E+03 2.37E+04 -1.55E+01
Fz (N) 6.97E+06 9.94E+06 6.83E+06 9.68E+06 3.34E+07
Table VIII-14 Leg Reaction
The Overturning Stability Check (satisfied if overturning/stabilizing < 1) is given as follows
About Overturning Moment (Nm) Stabilizing Moment (Nm) Overturning/Stabilizing
X Axis 9.35E+06 3.92E+08 0.02
Y Axis 1.06E+08 5.70E+08 0.19
Table VIII-15 Overturning Stability Check
The result for Leg Ultimate Strength Check (satisfied if < 1) is as follows:
(
)
(
)
(
⁄)(
⁄) (
⁄)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 71
8.6. Results for Operational Condition 3
8.6.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 25m
Leg Penetration 3m
Air-gap 15m
Maximum Wave Height 3.7m
Peak Wave Period 6.23s
Significant Wave Height 1.99m
Associated Wave Periods 4.85 ; 5.54 ; 6.23s
Current Speed 1 m/s
Wind Speed at 10m above sea level 12 m/s
Table VIII-16 Input data
8.6.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=25m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=15m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 72
8.6.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.1522 6.57
2 0.1607 6.22
3 0.2130 4.69
Table VIII-17 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.6.4. The Critical Combination
The highest environmental load (ocean load and wind) acting on the jack-up platform is
created by the combination shown in the following table.
Value
Angle of Attack – Wind 90 degree
Angle of Attack – Wave & Current 90 degree
Wave period 6.22s
Crane Working Angle 90 degree
Figure VIII-22 Critical combination
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 73
8.6.5. Dynamic Amplification Factor (DAF)
The dynamic amplification factor (DAF) is calculated by comparing the results given by
static analyses and dynamic analyses. (Refer to VI ANALYSIS METHOD for detail) The main
results are presented in the following figures.
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by static analyses.
Figure VIII-23 Base Shear – Static Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by static analysis is 4.12E+05 N
Tran Viet Hai
Master Thesis developed at University of Rostock Page 74
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by dynamic analyses.
Figure VIII-24 Base Shear – Dynamic Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by dynamic analysis is 1.87E+06 N
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 75
The figure below compares the results of total base shear of the four legs given by static
analyses (purple) and dynamic analyses (aqua blue).
Figure VIII-25 Total base shear comparison - Static and Dynamic analyses
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The dynamic amplification factor is given in the table below
Maximum Base Shear (N) Dynamic Amplification Factor
Static Analysis Dynamic Analysis
4.12E+05 1.87E+06 4.54
Figure VIII-26 Dynamic amplification factor (DAF)
Tran Viet Hai
Master Thesis developed at University of Rostock Page 76
8.6.6. Checking Results
The maximum displacement of the jack-up in this case is 0.75m. The moment and shear
force diagrams are as follows. (The values of moment and shear force are given in Nm and N
respectively)
Figure VIII-27 Moment distribution over legs
Figure VIII-28 Shear force distribution over legs
The reaction forces of each leg are given in the following table:
Leg 1 Leg 2 Leg 3 Leg 4 Total
Fx (N) 4.06E+04 -2.03E+04 1.57E+04 -3.60E+04 -1.30E+02
Fy (N) -4.95E+05 -4.93E+05 -6.55E+05 -6.68E+05 -2.31E+06
Fz (N) 1.10E+07 1.19E+07 4.96E+06 5.13E+06 3.30E+07
Table VIII-18 Leg Reaction
The Overturning Stability Check (satisfied if overturning/stabilizing < 1) is given as follows
About Overturning Moment (Nm) Stabilizing Moment (Nm) Overturning/Stabilizing
X Axis 1.54E+08 3.92E+08 0.39
Y Axis 1.28E+07 5.70E+08 0.02
Table VIII-19 Overturning Stability Check
The result for Leg Ultimate Strength Check (satisfied if < 1) is as follows:
(
)
(
)
(
⁄)(
⁄) (
⁄)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 77
8.7. Results for Survival Condition 3
8.7.1. Input Data
The input data for this condition are shown in the table below. Other input data are presented
in III GENERAL INPUT DATA.
Value
Water Depth 25m
Leg Penetration 3m
Air-gap 5m
Maximum Wave Height 3.80m
Peak Wave Period 6.32s
Significant Wave Height 2.04m
Associated Wave Periods 4.92 ; 5.62 ; 6.32s
Current Speed 1.5 m/s
Wind Speed at 10m above sea level 23 m/s
Table VIII-20 Input data
8.7.2. Leg Reserve Check
The leg reserve is checked as presented in VII ACCEPTANCE CRITERIA. The leg
reservation can be calculated as follows:
Where
: The total length of a leg and its spudcan
=25m: Water Depth
: The leg penetration
m: The height of main hull
: The height of jack house
=5m: The air-gap
SATISFIED
Tran Viet Hai
Master Thesis developed at University of Rostock Page 78
8.7.3. Natural Frequency & Period
A Modal analysis is performed in order to calculate the natural frequencies and natural
periods of the model in this condition. For this analysis the ocean is modeled without waves or
currents. The natural frequencies and natural periods are shown in the table below:
MODE Frequency (Hz) Period (s)
1 0.2141 4.67
2 0.2232 4.48
3 0.2950 3.39
Table VIII-21 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
8.7.4. The Critical Combination
The highest environmental load (ocean load and wind) acting on the jack-up platform is
created by the combination shown in the following table.
Value
Angle of Attack – Wind 0 degree
Angle of Attack – Wave & Current 0 degree
Wave period 4.92s
Crane Working Angle N/A
Figure VIII-29 Critical combination
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 79
8.7.5. Dynamic Amplification Factor (DAF)
The dynamic amplification factor (DAF) is calculated by comparing the results given by
static analyses and dynamic analyses. (Refer to VI ANALYSIS METHOD for detail) The main
results are presented in the following figures.
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by static analyses.
Figure VIII-30 Base Shear – Static Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by static analysis is 9.63E+05 N
Tran Viet Hai
Master Thesis developed at University of Rostock Page 80
The figure below shows the total base shear of the four legs and the base shear of individual
legs. These results are given by dynamic analyses.
Figure VIII-31 Base Shear – Dynamic Analysis
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The maximum base shear (aqua color) given by dynamic analysis is 4.25E+06 N
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 81
The figure below compares the results of total base shear of the four legs given by static
analyses (purple) and dynamic analyses (aqua blue).
Figure VIII-32 Total base shear comparison - Static and Dynamic analyses
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second.
The dynamic amplification factor is given in the table below
Maximum Base Shear (N) Dynamic Amplification Factor
Static Analysis Dynamic Analysis
9.63E+05 4.25E+06 4.41
Figure VIII-33 Dynamic amplification factor (DAF)
Tran Viet Hai
Master Thesis developed at University of Rostock Page 82
8.7.6. Checking Results
The maximum displacement of the jack-up in this case is 0.70m. The moment and shear
force diagrams are as follows. (The values of moment and shear force are given in Nm and N
respectively)
Figure VIII-34 Moment distribution over legs
Figure VIII-35 Shear force distribution over legs
The reaction forces of each leg are given in the following table:
Leg 1 Leg 2 Leg 3 Leg 4 Total
Fx (N) -1.20E+06 -1.28E+06 -1.20E+06 -1.27E+06 -4.95E+06
Fy (N) -1.07E+04 -1.11E+04 -2.18E+03 2.40E+04 2.30E-01
Fz (N) 5.61E+06 1.08E+07 5.50E+06 1.05E+07 3.24E+07
Table VIII-22 Leg Reaction
The Overturning Stability Check (satisfied if overturning/stabilizing < 1) is given as follows
About Overturning Moment (Nm) Stabilizing Moment (Nm) Overturning/Stabilizing
X Axis 2.43E+06 3.92E+08 0.01
Y Axis 1.74E+08 5.70E+08 0.31
Table VIII-23 Overturning Stability Check
The result for Leg Ultimate Strength Check (satisfied if < 1) is as follows:
(
)
(
)
(
⁄)(
⁄) (
⁄)
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 83
IX. DISCUSSION
In this part of the thesis, the interpretation of the finding is presented by analyzing the results.
After that, a suggestion for structure is made based on the interpretation. Finally, discussion of
natural frequencies of the model, which would be proven to be important in the previous parts, is
presented.
9.1. Result Analysis
From the many analyses conducted, it is can be concluded that the limited weather conditions are
always associated with leg ultimate strength check. In all cases, the overturning stability check
gives very safe results, below 0.4. (The limit value is 1). Besides, wave and current are identified
as the main cause of load acting on the structure. However, it is interesting that wave heights are
not the main factor that leads to critical weather condition.
ELEVATED CONDITION HIGH-RISK WEATHER CONDITION
Water
Depth
Leg
Penetration Mode Air-gap
Wind
Speed
Current
Speed
Wave Height
Max
15m 3m Operational (1) 15m 12m/s 1m/s 2m – 4.2m
Survival (1) 5m 23m/s 1.5m/s None
20m 3m Operational (2) 15m 12m/s 1m/s 2.9m – 5.6m
Survival (2) 5m 23m/s 1.5m/s 3.3m – 3.5m
25m 3m Operational (3) 15m 12m/s 1m/s ≥3.7m
Survival (3) 5m 23m/s 1.5m/s 3.8m – 4.8m
Table IX-1 Main Results
*Note: In order not to violate the Air-Gap condition, only wave under 7m are tested.
As can be seen from the table of main results (which was already presented in the VIII
FINDING), the critical wave height often fall within a particular range. A big wave is not
necessary a dangerous wave. It can even be noticed that waves with wave height over 6m are
rarely critical.
Instead, it is found that the total load is dominated by the relation between wave periods and the
natural periods of the model. In addition, the wave lengths and the angles of attack also have
great influence on the final results. The details are presented in the next part.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 84
9.1.1. Wave period and Natural period
Wave periods are the most important factor that affects the total wave load. If the wave
period is close to the natural period of the structure, it is very likely that the total load over the
structure is high due to dynamic effects.
In order to have a clearer understanding about this, an example is considered. In the example,
the final total wave loads acting on the structure (including dynamic effects) are calculated and
compared for two different cases. In the first case, the wave has a smaller wave height but a
wave period closer to the natural period of the structure. In the second case, the wave has a very
big wave height, but the wave the wave period is far from the natural periods of the model. The
details about the input data and results are presented as follows.
Natural frequencies and periods of the structure are shown in the following table.
Input Data Mode Frequency (Hz) Period (s)
Water depth: 25m
Air-gap: 5m
Leg Penetration: 3m
1 0.2141 4.67
2 0.2232 4.48
3 0.2950 3.39
Table IX-2 Natural Frequency & Period
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
The input data of the two waves are shown in the following table.
Wave Input Case 1 Case 2
Wave Height Max 3.8m 6m
Wave Period 4.92s 7.06s
Angle of Attack 0 degree 0 degree
Table IX-3 Wave Input Data
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 85
The results given by static and dynamic analyses for both cases are as follows:
Figure IX-1 Static (purple) and Dynamic (aqua blue) Base Shear – Case 1
Figure IX-2 Static (purple) and Dynamic (aqua blue) Base Shear – Case 2
*Note: The vertical axis indicates force in newton. The horizontal axis indicates time in second
Tran Viet Hai
Master Thesis developed at University of Rostock Page 86
The detail results are shown in the following table:
Wave
Height Max Wave Period
Maximum Base Shear (N) Dynamic
Amplification
Factor Static
Analysis
Dynamic
Analysis
Case 1 3.8m 4.92s 9.63E+05 4.25E+06 4.41
Case 2 6m 7.06s 8.32E+05 1.39E+06 1.67
Table IX-4 Results
As can be seen, though the difference in static analysis is not significant, the results from
dynamic analysis of the two cases are far different. The base shear in the case number 1 is over
three times the base shear of the case number 2 (4.25E+06N compared to 1.39E+06). It is
because in the case number 1 the wave period is close to the natural period of the structure and
that leads to high dynamic amplification factor (DAF) which is 4.41. In the case number 2, the
dynamic amplification factor is just 1.67.
For the chosen water depths, the natural period of the jack up ranges from 2.89s to 6.57s. These
periods are in the range of wave periods for the wave with wave height from 1.2m to 7m. As a
result, the high-risk weather conditions are normally associated with wave periods close to the
natural period of the jack up.
Also from this example, it can be seen that even the maximum base shear given by the static
analysis is greater in the case number 1. This is due to the relation between the wave length,
angle of attack and the distance between legs of the Odin. The detail is presented in the next part
of the thesis.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 87
9.1.2. Wave Length and Angle of Attack
The wave load acting on the structure is the combination of the wave loads acting on each
leg. These wave loads, however, are not constant but changing by time. Hence, the total wave
load on structure at a certain moment depends heavily on wave phases at the position of each leg
at that moment.
It is not challenging to predict that if the wave phases at each leg are the same, the maximum
wave loads on each leg happen at the same time and thereby creating a critical situation. The
figure and table below show the positions of the four legs and point out the combinations of
angle of attack and wave length in which wave phases at each leg are the same.
Figure IX-3 Legs’ Positions and Distances
Tran Viet Hai
Master Thesis developed at University of Rostock Page 88
The table below shows the critical combinations of angle of attack and wave length in which
wave phases at each leg are the same
Combination 1 Combination 2 Combination 3 Combination 4
Angle of Attack 0; 180 degrees 90; 270 degrees 37; 217 degrees 71; 251 degrees
Wave Length 35.7m 24m 14.323m 11.375m
Table IX-5 Critical Angle of Attack and Wave Length Combination
In order to have a clearer undersantding about the influence of the combination of angle of attack
and wave length an example is presented. In the example, the total wave load and the wave load
on each leg are calculated without dynamic effects for 4 cases. In the first case, the wave has a
smaller wave height but the angle of attack and the wave length are chosen to be close to the
critical combination 1 presented in Table IX-5 Critical Angle of Attack and Wave Length
Combination. In other cases, the waves have very big wave heights and come from different
directions.
Also in this example, the model consists of 4 legs only. The hull form is extracted in order to
remove the interaction between the legs so that the wave load on individual leg can be observed
in a better way. The connetions between legs and seabed are fix (all 6 degrees of freefom are
fixed). The details of input data and results are presented as follows.
The wave input data for 4 cases are shown in the table below:
Wave Input Case 1 Case 2 Case 3 Case 4
Wave Height Max 3.3m 6.8m 6.8m 6.8m
Wave Period 4.58s 6.70s 6.70s 6.70s
Wave Length 35.493m 71.529m 71.529m 71.529m
Angle of Attack 0 degrees 0 degrees 90 degrees 45 degrees
Table IX-6 Wave Input Data
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 89
The total wave loads (aqua blue) and the wave loads on each leg (other colors) are shown in the
figures:
Figure IX-4 Wave loads on legs – Case 1
Figure IX-5 Wave loads on legs – Case 2
Figure IX-6 Wave loads on legs – Case 3
Figure IX-7 Wave loads on legs – Case4
*Note:
- The vertical axis indicates force in newton.
- The horizontal axis indicates time in second
In the case number 1, the wave phases at each leg are almost the same, hence the wave loads on
individual legs in the graph are coincident. Similarly, in case number 2 and 3, only two lines
representing loads on individual legs can be seen. In the case number 4, wave phases at each leg
are all different so all lines can be seen clearly.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 90
The detail results are shown in the following table:
Case 1 Case 2 Case 3 Case 4
Wave Height Max 3.3m 6.8m 6.8m 6.8m
Maximum Load on one Leg 2.1E+5 N 4.3 E+5 N 4.3 E+5 N 5.4E+5 N
Total Maximum Load 8.3E+5 N 8.6E+5 N 11.2E+5 N 9.3E+5 N
Table IX-7 Results
It can be seen that though the wave heights in the case number 2, 3, 4 are over two times the
wave height in the case number 1 (6.8m compared to 3.3m), the total wave loads of all cases are
not much different.
For all the critical combination listed in Table IX-5 Critical Angle of Attack and Wave
Length Combination, the combination number 1 (angle of attack is 0 and wave length is 35.7m)
is the most dangerous one. It is because in other combinations the wave lengths are quite small
so that the associated wave heights are small as well.
The waves with wave height around 3.3m (like the wave chosen in this example) are very
dangerous to the Odin. It is because they may have not only the wave length close to 35.7m but
also the wave periods very close to natural period of the Odin in many elevated condition
(around 4.5s – 5.5s).
In addition, there is another important
reason that makes the waves coming with the
angle of attack of 0 degree dangerous. It is
because the legs of the Odin have lower
structure strength in bending about the global
Y axis. As presented in the Appendix A –
Equivalent Structure, the leg cross section
used for ultimate strength check has very
different value of inertial moments about
different axis.
Iyy = 0.10815m4 (bending about global y axis)
Izz = 0.15178 m4 (bending about global x axis)
Figure IX-8 Leg cross section used for ultimate
strength check
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 91
9.2. Discussion of Natural Period / Frequency
As presented in previous parts of the thesis, the relation between wave periods and natural
periods of the jack up has a major influence on analysis results. Hence, it is very important to get
correct natural frequencies of the jack up. In other words, it is necessary to build a model that
gives correct natural frequencies. However, as a matter of fact, there is always a certain gap
between a model and its’ original structure. Undoubtedly, some of differences will have the
influence on the natural frequencies calculated. The question is just what the differences are and
how much they affect the results.
In this part of the thesis, the influence on the natural frequencies will be discussed in
following topics:
- Foundation fixity
- Weight distribution
- Pre-stressed effect
- Leg-hull connection
9.2.1. Foundation Fixity
As required from SNAME, in case the data about soil-structure interaction is not available
the foundation fixity should be modeled as pin joints, and so are unable to sustain bending
moment. Also, because soil-spudcan interaction is out of the scope of this thesis, the foundation
fixity is modeled as pin joints.
This model, however, is not completely accurate. The foundation fixities are normally able to
sustain a certain bending moment, depending on the seabed characteristics and leg penetration.
Hence, the accurate model of foundation fixities should be somewhere between pin joints and
fixity (all six degree of freedoms are fixed).
In order to learn about the influence foundation fixity model on the natural periods, modal
analyses are conducted for models with foundation fixity of pin joints (Ux, Uy, Uz) and of fixity
(Ux, Uy, Uz, ROTx, ROTy, ROTz).
Tran Viet Hai
Master Thesis developed at University of Rostock Page 92
The results are presented in the table below.
Input Data Mode
Natural Periods T(s) Percentage
(Tfixity / Tpin joints) Pin Joints
(Ux, Uy, Uz)
Fixity (Ux, Uy, Uz,
ROTx, ROTy, ROTz)
Water depth: 15m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 4.59 2.23 48.6%
Mode 2 4.41 2.15 48.7%
Mode 3 3.29 1.59 48.4%
Water depth: 20m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 5.55 2.68 48.4%
Mode 2 5.28 2.56 48.5%
Mode 3 3.97 1.90 47.9%
Water depth: 25m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 6.57 3.17 48.2%
Mode 2 6.22 3.01 48.3%
Mode 3 4.69 2.24 47.6%
Table IX-8 Natural Period Comparison – Foundation fixity
*Note: In the table above, the mode 1, mode 2 and mode 3 correspond to oscillation motion
in X direction, Y direction and torsion about Z direction respectively.
As can be seen from the table above, there are huge differences in natural periods of models
with pin joint connections and of models with fixity connections. Interestingly, the ratio seems to
be constant. The models with fixity connection have the natural period around half of the natural
period of the model with pin joint connections.
Thus, the foundation fixity model has a significant influence on the natural frequency of the
jack up model. For that reason, the soil – spudcan interaction is very important and should be
investigated.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 93
9.2.2. Weight Distribution
One of the requirements in modeling is that a model must have the same weight and COGs
with its original structure. However, this condition does not ensure the correct weight
distribution of the model. In other words, we can have many models with the same weight and
COGs with the original structure but none of them have the same weight distribution.
Theoretically, this will have an influence on the accuracy of the natural frequencies calculated.
For natural frequency calculation, the damping force and external force are not included and
the equation of motion can be written as follows:
[ ]{ ̈} [ ]{ } { } Eq. 32
Where
[ ]: Mass matrix
[ ]: Stiffness matrix
{ ̈}: Acceleration vector
{ }: Displacement vector
For linear system, the displacement is harmonic of the form:
{ } { } Eq. 33
Where
{ } : Eigenvector representing the mode shape of the natural frequency i
Natural circular frequency i
t: Time
For that, the natural circular frequency ω must satisfy the following equation:
Determinant of [ ] [ ] |[ ] [ ]| Eq. 34
Where
[ ]: Mass matrix
[ ]: Stiffness matrix
Mass matrix plays an important role in determining natural frequency.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 94
This idea can be presented in a less complex way. Let’s consider simple systems as follows:
In Figure IX-9 Weight distribution &
Natural Frequency, the three systems have the
same weight and COGs. However, they do not
have the same natural frequency. This is also
important in modeling jack up. For practical
purposes, the weight of a model is adjusted by
means of density and mass points in order to
achieve the same weight and COGs with its
original structure. Similarly, that is not enough to
make sure the natural frequency calculated is
accurate.
Figure IX-9 Weight distribution & Natural
Frequency
In order to learn about this, modal analyses are conducted for many models at different
elevated modes. Each model has a different density of steel. The typical results are presented in
the table below.
Input Data
Water depth: 15m, Air-gap: 15m, Leg Penetration: 3m
Mode
Natural Periods T(s)
Steel Density
7850 kg/m3 Steel Density
1.4*7850 kg/m3
Steel Density
1.8*7850 kg/m3
Steel Density
2.2*7850 kg/m3
Mode 1 4.60 4.60 4.59 4.60
Mode 2 4.43 4.43 4.41 4.44
Mode 3 2.66 2.99 3.29 4.00
Table IX-9 Natural Period Comparison – Weight distribution
*Note: In the table above, the mode 1, mode 2 and mode 3 correspond to oscillation motion
in X direction, Y direction and torsion about Z direction respectively.
As shown in the table above, in case of the jack up Odin, the weight distribution only has
minor influences on the natural frequencies in mode 1 and mode 2. However, the influences on
natural frequencies in mode 3 are significant. Thus, the correct weight distribution is very
important in case the dominant oscillation motion is torsion about Z direction.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 95
9.2.3. Pre-stressed Effect
Since the weight of the hull form is great, the four legs of the Odin are always under large
compression. Hence, the pre-stressed effect may have influence on the natural frequency.
In order to learn about this influence, modal analyses are conducted with pre-stressed effect
for different elevated modes. In order to do this, a static analysis needs to be performed in
advance with option PSPRES, ON. The results for different cases are shown in the table below.
Input Data Mode
Natural Periods T(s) Percentage
(T2 / T1) Without Pre-stressed
Effects (T1)
With Pre-stressed
Effect (T2)
Water depth: 15m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 4.59 5.03 109.6%
Mode 2 4.41 4.78 108.5%
Mode 3 3.29 3.57 108.4%
Water depth: 20m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 5.55 6.24 112.6%
Mode 2 5.28 5.86 110.9%
Mode 3 3.97 4.40 110.8%
Water depth: 25m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 6.57 7.63 116.1%
Mode 2 6.22 7.08 113.7%
Mode 3 4.69 5.34 113.8%
Table IX-10 Natural Period Comparison – Pre-stressed Effect
*Note: In the table above, the mode 1, mode 2 and mode 3 correspond to oscillation motion
in X direction, Y direction and torsion about Z direction respectively.
As can be seen from the table above, with pre-stressed effect, the natural periods increase
around 12%. Besides, it can also be noticed that the effect has greater influences in case the
platform is at a higher position. In the first case, the total leg length under lower guide is 33m,
the natural periods increase around 9%. In the second case, these numbers are 38m and 12%. In
the third case, these numbers are 43m and 15%.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 96
9.2.4. Leg-Hull Connection
Leg-Hull connection is a very important part of the model. The interaction between the legs
and the hull is complex and not easy to be fully modeled. In order to understand about the
influence of the leg-hull connection on the natural frequency of the jack up, in this part, modal
analyses will be conducted to measure the natural periods for two jack-up models. In the first
model, the legs and hull are connected by spring systems as presented in 4.5. Leg hull
connection. In the second model, the legs and hull connection at the positions of upper and lower
guides is modeled as fixed connection (all 6 degrees of freedom are fixed). The results are shown
in the following table.
Input Data Mode Natural Periods T(s) Percentage
(T2 / T1) Spring Connection (T1) Fixed Connection (T2)
Water depth: 15m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 4.59 4.15 90.4%
Mode 2 4.41 3.88 88.0%
Mode 3 3.29 2.43 73.8%
Water depth: 20m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 5.55 5.08 91.6%
Mode 2 5.28 4.73 89.5%
Mode 3 3.97 2.83 71.3%
Water depth: 25m
Air-gap: 15m
Leg Penetration: 3m
Mode 1 6.57 6.08 92.5%
Mode 2 6.22 5.64 90.6%
Mode 3 4.69 3.22 68.6%
Table IX-11 Natural Period Comparison – Pre-stressed Effect
*Note: In the table above, the mode 1, mode 2 and mode 3 correspond to oscillation motion
in X direction, Y direction and torsion about Z direction respectively.
As can be seen from the table above, the leg-hull connection also has a significant influence
on the natural period of the model. In general, the jack-up models with fixed leg-hull connection
have smaller natural period. The differences in natural periods vary from mode to mode.
Concerning the mode 1 and 2, the jack-up models with fixed leg-hull connection give natural
periods around 10% less than the models with spring leg-hull connection. Regarding mode 3, this
gap is even much bigger, up to over 30%. Thus, it is very important to model properly the leg-
hull connection.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 97
9.2.5. Summary
From the analyses above, it can be concluded that the accuracy in natural frequencies or
periods of a jack up model is quite sensitive. It depends heavily on weight distribution, pre-
stressed effect and leg-hull connection model, and especially foundation fixity model.
The foundation fixity has the greatest influences on the accuracy of the natural periods. The
model with pin joints foundation may have the natural periods two times greater than the same
model with fixed foundation. This obviously cannot be neglected. Hence, it is absolutely
necessary to conduct investigation into the soil-spudcan interaction in order to model properly
the foundation fixity.
Although the influences of the weight distribution, pre-stressed-effect and the leg-hull
connection model on the natural periods are not as great as that of the foundation fixity, they are
also really significant. The differences in natural periods in each case can range from 10% to
30%. In combination, this can change the results of natural periods totally and thereby making
the whole calculation meaningless.
As presented in 9.1. Result Analysis, the relation between natural periods of the model and
the wave periods is the key factor affecting the accuracy of the final results. Thus, it is important
to understand and model the foundation fixity, the weight distribution, pre-stressed effect and the
leg-hull connection in a proper way.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 98
X. CONCLUSION
10.1. Thesis Summary
The purpose of this thesis is to establish the envelopes of feasible environmental conditions
for operational and survival modes for three different water depths. In order to fulfil the goal, the
jack-up Odin is modelled and analysed using the ANSYS APDL software package.
In order to make the computation feasible, the finite element model (FEM) of the Odin has
been built based on detail equivalent structure calculation. Many analyses had been performed in
ANSYS APDL to test and ensure the accuracy of the equivalent model.
Sub-structuring technique was applied to build sub-structuring model. Along with the full
model, sub-structuring model has been used in many analyses so that the computation time can
be reduced.
Figure X-1 Odin Full Model
Figure X-2 Odin Sub-structuring model
The models are analysed under different elevated modes and load cases. For each of three
different water depths, both operational and survival modes are analysed. Wind, wave and
current are assumed to come from the same direction. The angles of attack considered include 0,
45, 90, 135, 180, 225, 270, 315 degrees. For each wave, 24 wave phases are considered with
equal phase step of 15 degrees (0, 15, …, 330, 345 degrees). The angle of crane is taken to create
the most critical load case in combination with environmental load. Finite element analyses
conducted include modal analyses, linear static analyses, nonlinear static analyses, harmonic and
transient analyses.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 99
The work is performed complying with requirements of SNAME 5-5A - Guidelines for Site
Specific Assessment of Mobile Jack-Up Units. The parts which are not covered by the
guidelines are performed complying with other guidelines, namely DNV-RP-C205 –
Environmental Conditions and Environmental Loads and EUROCODE 3 – Design of steel
structures
The main results of high-risk weather condition are given in the following table.
ELEVATED CONDITION HIGH-RISK WEATHER CONDITION
Water
Depth
Leg
Penetration Mode Air-gap
Wind
Speed
Current
Speed
Wave Height
Max
15m 3m Operational (1) 15m 12m/s 1m/s 2m – 4.2m
Survival (1) 5m 23m/s 1.5m/s None
20m 3m Operational (2) 15m 12m/s 1m/s 2.9m – 5.6m
Survival (2) 5m 23m/s 1.5m/s 3.3m – 3.5m
25m 3m Operational (3) 15m 12m/s 1m/s ≥3.7m
Survival (3) 5m 23m/s 1.5m/s 3.8m – 4.8m
Table X-1 Main Results
*Note: In order not to violate the Air-Gap condition, only wave under 7m are tested.
It is also found that the total environmental load acting on the structure depends not only on
wave heights but also on the combination of angle of attack and wave lengths. The jack up is
more vulnerable to waves with wave length around 35.7m coming from the direction of 0 and
180 degrees. However, above all, the relation between wave periods and natural periods of the
model is predominant.
Again, the natural periods or frequencies of a model are very sensitive. They can be
influenced heavily by the way the model is built. The results of natural periods or frequencies
vary significantly depending on the models leg-hull connection, on whether the pre-stressed
effect included or not, on the weight distribution and especially on the foundation fixity model.
Based on the finding, suggestions have been made. Regarding structure improvement, the
parts of the legs around lower guides should be reinforced. Concerning the effectiveness of the
model, it is suggested that research should be carried out into soil-spudcan interaction.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 100
10.2. Limitation
Though effort has been made, limitations of this thesis are unavoidable. In this part of the
thesis, the limitation, its reasons and its influence on the results will be presented.
First and foremost, the model of foundation fixity is a limitation of the thesis. Since the soil-
structure interaction is out of the scope of this thesis, the foundation has been modeled as pin
joints connection as required from SNAME. However, in reality the model should be somewhere
between pin joints connection and fixed connection, depending on leg penetration and the
characteristic of seabed. Besides, as presented in previous parts of the thesis, the accuracy in
foundation fixity has a great influence on the accuracy of the results. For the reasons, this is the
most severe limitation of this thesis.
The model of leg-hull connection is also a limitation of the thesis. One reason is that the
structure inside the jack houses is complex and models of spring systems may not reflect all the
features of the connection. In addition, the model does not include the gaps between legs and
hull, which would make the behavior of leg-hull connection non-linear. The reason for this is a
limitation of current ANSYS APDL version, in which the non-linear effects are not able to be
included in all types of analysis, for instance modal analysis and harmonic analysis. As presented
in previous parts of the thesis, the leg-hull connection is a very important part of the model, thus
this limitation also affect adversely the accuracy of the results.
Another limitation is that analyses conducted do not include the pre-stressed effect. As
presented in previous parts of the thesis, this also have a considerable effect on the natural
periods and frequencies of the model. However, this option has not been activated because in the
current version of ANSYS APLD the pre-stressed effect is not able to be included in harmonic
analyses.
In this thesis, wind, wave and current are assumed to come from the same direction and
only 8 angles of attack considered. Besides, for each wave, only 24 wave phases are considered.
This is totally due to the time restriction of the thesis and can be improved. For example, if
waves are considered to come from 24 directions and 72 wave phases are analyzed, the accuracy
of the final results will be higher.
In addition, the wind force applied to the model is not accurate. This is because of the lack of
information about wind exposed area, which depends on the cargos on deck. In order to achieve
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 101
more accurate results, details about shapes and sizes of cargos should be given. Nevertheless,
from analyses conducted, it can be seen that the wind force does not account for a very
significant proportion of total load. Thus, this limitation may not have big influence on the final
results.
Lastly, the accuracy of the results is partly affected by damping phenomenon. Since the
damping ratio had not been measured, an assumption of 5% of critical damping has been made.
This may not be the right damping ratio of the jack up. Furthermore, from analyses conducted, it
is noticed that there may be effects of numerical damping. This can be seen clearer in the figure
below.
Figure X-3 Numerical damping effect
The figure above plots the base shear given by static analysis (aqua blue) and dynamic
analysis (purple). As can be seen, first the dynamic force increases due to dynamic effect. After
staying constantly for some time, this force starts to go down. This may be due to numerical
damping. Since no method has been applied to measure the numerical damping ratio in this
thesis, no specific conclusion is made on the influence on the accuracy of the results. However, it
is undoubtedly that estimating properly the damping ratio will help achieve more accurate
results.
Tran Viet Hai
Master Thesis developed at University of Rostock Page 102
BIBLIOGRAPHY
ANSYS, Inc, (2012) Advanced analysis techniques guide
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ANSYS, Inc, (2012) Contact technology guide
ANSYS, Inc, (2012) Element reference
ANSYS, Inc, (2012) Modeling and meshing guide
ANSYS, Inc, (2012) Structural analysis guide
ANSYS, Inc, (2012) Theory reference for the mechanical APDL and mechanical applications
Bennett & Associates, L.L.C, Offshore Technology Development, Inc, (2005) Jack up units: A
technical primer for the offshore industry professional
DNV – Det Norske Veritas, (2010) Recommende practice DNV-RP-C205: Environmental
conditions and environmental loads
European Standard, (2005) Eurocode 3: Design of steel structures – Part 1.1:General rules and
rules for building
European Standard, (2005) Eurocode 3: Design of steel structures – Part 1.5: Plated structural
elements
Germanisher Lloyd’s, (2013) Jack-up platform Odin: Weight assessment
HGO InfraSea Solutions GmbH & Co. KG, (2013) Heavy-lift jack-up vessel: Innovation –
Power of performance
HOCHTIEF Solutions AG, (2009) Jack-up Barge Odin: Liebherr BOS 7500-300 D Litronic
HOCHTIEF Solutions AG, (2009) Odin Drawing: Deck houses
HOCHTIEF Solutions AG, (2009) Odin Drawing: Deck layout
HOCHTIEF Solutions AG, (2009) Odin Drawing: Forecastle scantling
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page 103
HOCHTIEF Solutions AG, (2009) Odin Drawing: General arrangement
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HOCHTIEF Solutions AG, (2009) Odin Drawing: Jack-up systems
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Tran Viet Hai
Master Thesis developed at University of Rostock Page 104
Appendix A
Equivalent Structure
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - i
Table of Contents
I. GENERAL ....................................................................................................................... 1
II. PRINCIPLE AND CRITERIA......................................................................................... 2
2.1. Structural Strength .................................................................................................... 2
2.2. Principle and Criteria ................................................................................................ 5
2.2.1. The stress caused by Axial Force and Bending moment ................................... 5
2.2.2. The displacement caused by Axial Force and Bending moment ....................... 6
III. EQUIVALENT HULL FORM STRUCTURE ............................................................ 7
3.1. Bending mode of structure ........................................................................................ 7
3.1.1. Bending mode of Hull Form .............................................................................. 7
3.1.2. Bending mode of Jack Houses ........................................................................... 8
3.1.3. Bending mode of Bulkheads and Sidewalls ...................................................... 8
3.2. Calculation Method ................................................................................................... 9
3.2.1. Step 1: Calculating Cross Section Area ............................................................. 9
3.2.2. Step 2: Calculating Inertial Moment ................................................................. 9
3.2.3. Step 3: Determining dimension of equivalent members ................................. 10
3.3. Equivalent Hull Form Structure .............................................................................. 11
3.3.1. Original Structure and Equivalent Structure ................................................... 11
3.3.2. Equivalent Stiffener List .................................................................................. 13
IV. EQUIVALENT LEG MODEL ................................................................................... 14
4.1. Detail Leg Model .................................................................................................... 14
4.1.1. ODIN legs ........................................................................................................ 14
4.1.2. Detail FEM Model ........................................................................................... 15
4.2. Equivalent Leg Model............................................................................................. 16
4.2.1. Calculation Method ......................................................................................... 16
Tran Viet Hai
Master Thesis developed at University of Rostock A - ii
4.2.2. Equivalent FEM model .................................................................................... 22
4.3. Comparing detail legs and equivalent legs in ANSYS ........................................... 23
4.3.1. Testing model .................................................................................................. 23
4.3.2. Results and Comparison .................................................................................. 25
4.4. Conclusion .............................................................................................................. 25
V. EFFECTIVE LEG CROSS SECTION – BUCKLING EFFECT .................................. 26
5.1. Leg Section Classification ...................................................................................... 26
5.2. Effective Area Calculation ...................................................................................... 27
5.3. Effective Leg Section .............................................................................................. 28
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - iii
List of Figures
Figure II-1 Plate A .................................................................................................................... 2
Figure II-2 Plate B .................................................................................................................... 2
Figure II-3 Block A ................................................................................................................... 3
Figure II-4 Block B ................................................................................................................... 3
Figure III-1 Bending mode – Hull Form................................................................................... 7
Figure III-2 Bending mode – Jack Houses ............................................................................... 8
Figure III-3 Bending mode – Bulkhead and Sidewalls ............................................................. 8
Figure III-4 Original plate cross section ................................................................................. 11
Figure III-5 Equivalent plate cross section ............................................................................. 11
Figure III-6 Original hull cross section ................................................................................... 11
Figure III-7 Equivalent hull cross section ............................................................................... 11
Figure III-8 Deck plate – Detail model ................................................................................... 12
Figure III-9 Deck Plate – Equivalent model ........................................................................... 12
Figure IV-1 ODIN leg ............................................................................................................. 14
Figure IV-2 Section A ............................................................................................................. 15
Figure IV-3 Section B ............................................................................................................. 15
Figure IV-4 Section C ............................................................................................................. 15
Figure IV-5 Element shape-3D ............................................................................................... 15
Figure IV-6 Section A ............................................................................................................. 16
Figure IV-7 Section B ............................................................................................................. 16
Figure IV-8 Section C ............................................................................................................. 16
Figure IV-9 Non-constant beam under axial force ................................................................. 17
Figure IV-10 Leg block .......................................................................................................... 18
Figure IV-11 Moment over a block ........................................................................................ 18
Figure IV-12 Displacement over a block ................................................................................ 19
Figure IV-13 Equivalent element shape - 3D ......................................................................... 22
Figure IV-14 Equivalent leg section ....................................................................................... 22
Figure IV-15 Equivalent leg section - FEM ........................................................................... 22
Figure IV-16 Testing model – Axial force ............................................................................. 23
Figure IV-17 Testing model – Bending moment .................................................................... 24
Tran Viet Hai
Master Thesis developed at University of Rostock A - iv
Figure IV-18 Axial force diagram .......................................................................................... 25
Figure IV-19 Bending moment diagram ................................................................................. 25
Figure V-1 Internal compression part ..................................................................................... 26
Figure V-2 Effective leg section ............................................................................................. 28
Figure V-3 Effective leg section - FEM ................................................................................. 28
List of Tables
Table III-1 Equivalent stiffener list......................................................................................... 13
Table IV-1 Leg section properties .......................................................................................... 16
Table IV-2 Equivalent leg section properties ......................................................................... 21
Table IV-3 Equivalent leg section properties ......................................................................... 23
Table IV-4 Displacement – Detail leg and Equivalent leg ..................................................... 25
Table V-1 Section classification ............................................................................................. 26
Table V-2 Leg section Classification ...................................................................................... 26
Table V-3 Reduction factor and Effective cross section area ................................................. 28
Table V-4 Effective leg section properties ............................................................................ 28
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 1
I. GENERAL
One of the main questions in building a Finite Element Model (FEM) is how detail the model
should be. A detail model gives more accurate results, is easier to build (because the work is
simply modeling everything in the blue plans). However, the detail FEM model is more
expensive in many aspects as it needs more computer memory, time to build the model, time to
compute, etc. On the other hand, an equivalent model may give less accurate results, is harder to
build but much more practical as it requires less powerful computers, less time to calculate and
therefore being applicable to complex analyses such as dynamic or nonlinear static analyses.
Since the objective of the thesis is to analyze the global response of the Jack up ODIN, it is
not necessary to build the detail FEM model. In addition, there are thousands of computations to
be run so it is worth saving a few seconds from each computation. For those reasons, an
equivalent model is more practical for this project.
Apart from that, as the ultimate strength check for the legs is not covered by SNAME 5-5A,
Guidelines for Site Specific Assessment of Mobile Jack-Up due to their rectangular shape, the
leg checking part is done complying with EUROCODE 3 – Design of steel structures. For that,
it is compulsory to determine the effective leg cross section in order to account for buckling
effect.
This appendix presents the equivalent structure, the effective leg cross section as well as all
the principles, the methods and the assumptions used.
Tran Viet Hai
Master Thesis developed at University of Rostock A - 2
II. PRINCIPLE AND CRITERIA
2.1. Structural Strength
It is necessary to understand that there is no equivalent structure which has the same strength
with the original structure in every way. In other words, the equivalent structure just has the
same strength with the original structure in a particular analysis.
In order to get a clearer picture about structural strength, a simple example of two plates
which have the same cross section area is considered.
Figure II-1 Plate A
Figure II-2 Plate B
Without taking into account buckling effect, as the two plates have the same cross section
area, even with no detail calculations we can claim that:
- The two plates have the same strength under axial force.
- The Plate A is stronger than the plate B under bending moment
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Thus, the structural strength of a component must be assessed based on the load case applied
or the structural mode of interest. If the two plates are under axial force only, without taking into
account the buckling effect, they have the same structural strength. However, if the bending
mode is dominant, the plate A has higher structural strength compared to the plate B.
Furthermore, the structural strength also depends on the part of the structure of interest. The
above analysis shows that the plate A always has similar or higher strength compared to the plate
B, but it is only correct when we consider the local structure. When considering a larger
structure part, the result may be different.
The two plates A and B are put in blocks as shown in Figure II-3 Block A and Figure II-4
Block B. The two blocks A and B have the same side walls.
Figure II-3 Block A
Figure II-4 Block B
Tran Viet Hai
Master Thesis developed at University of Rostock A - 4
Again, without taking into account buckling effect, as the two blocks have the same cross
section area and are both symmetrical, even with no detail calculations we can claim that:
- The positions of neutral axes of the two blocks are the same at mid-block.
- The two blocks have the same strength under axial force as they have the same cross
section area
- The block B is stronger than the block A under bending moment because they have the
same cross section area but the material is further away from the neutral axis in case of
the block B
In this case, the result is different. The plate B always gives similar or higher strength
compared to the plate A.
From the analysis above, it can be seen that the structural strength of a certain component
depends on many factors including the load case acting on the structure (axial force, bending
moment, shear force or combination of some or all of the force and moment) and the structure
part of interest (local or global structure). Hence, it would be not feasible to create an equivalent
component which has the same structural strength with the original component in every way.
Nevertheless, equivalent model can be created with the same structural strength for a particular
analysis. For example, in case the block A is considered as a column under only axial force, the
model of the plate B can be used instead of the plate A as it gives the same cross section area and
is simpler to be modeled. Also, in case of local analysis and the dominant effect on the plate A is
induced by bending moment, the plate B may be used instead as it is weaker and we are on the
safe side.
In this thesis, the equivalent components are also calculated in order to obtain an equivalent
model with the same structural strength for global analysis only. The detail is presented in the
next part of the appendix.
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2.2. Principle and Criteria
The principle and criteria are made based on the objective of the thesis which is to analyze
the global response of the Jack up ODIN. Also it is assumed that the dominant effects are
caused by axial force and bending moment. The effects caused by shear force or torsion are
insignificant compared to axial force and bending moment (which is correct in most cases)
As criteria, the stress and displacement in equivalent structure must be the same with stress
and displacement in the original structure respectively. (On the safe side, the stress and
displacement in equivalent structure may be higher than in original structure).
For a constant section beam, the stress and displacement caused by axial force and bending
moment can be calculated by the equations presented in the following part.
2.2.1. The stress caused by Axial Force and Bending moment
Stress caused by axial force:
Eq. 1
Where:
- Sigma 1: Stress due to axial force
- F: Axial force
- A: Cross section Area
Stress caused by bending moment:
Eq. 2
Where:
- Sigma 2: Stress due to Bending about a neutral axis
- M: Bending moment
- y: The perpendicular distance from the point of interest to the neutral axis
- I: The inertial moment about the neutral axis
Tran Viet Hai
Master Thesis developed at University of Rostock A - 6
The total stress caused by axial force and bending moment:
Eq. 3
Where:
- Sigma: Stress due to axial force and bending moment
- Sigma 1: Stress due to axial force
- Sigma 2: Stress due to bending moment
2.2.2. The displacement caused by Axial Force and Bending moment
Absolute displacement caused by axial force:
Eq. 4
Where:
- Delta: Absolute displacement caused by Axial Force
- F: Axial Force
- L: Beam length
- A: Cross section area
- E: Elastic modulus
Absolute displacement caused by bending moment :
∫∫
Eq. 5
Where:
- Delta: Absolute deformation caused by bending moment
- M: Bending moment
- I: The inertial moment about the neutral axis
- E: Elastic modulus
Global response analysis of the jack-up platform Odin
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III. EQUIVALENT HULL FORM STRUCTURE
3.1. Bending mode of structure
The bending mode of the structure is important to determine the neutral axis for calculating
the inertial moment. The bending mode of each part of the hull is assumed as below.
3.1.1. Bending mode of Hull Form
The hull form is considered bent about lines parallel
to the X and the Y axis as shown in Figure III-1
Bending mode – Hull Form. The bending mode
about lines parallel to the Z axis is neglected. The
whole hull form acts like a single plate.
The equivalent main deck, inner bottom and the
outer bottom must keep the strength of the hull
form unchanged in these bending modes. In detail,
the neutral axis position and the total inertial
moment (second moment) of the cross section of
the hull form after being simplified must remain the
same in both modes, bending about lines parallel to
X and Y direction.
Figure III-1 Bending mode – Hull Form
Tran Viet Hai
Master Thesis developed at University of Rostock A - 8
3.1.2. Bending mode of Jack Houses
The Jack Houses are considered bent about lines
parallel to the X and the Y axis as shown in
Figure III-2 Bending mode – Jack Houses. The
bending mode about lines parallel to the Z axis is
neglected. Each Jack House acts like a single
beam.
The equivalent Jack House’s walls must keep the
strength of the Jack Houses unchanged in these
bending modes. In detail, the neutral axis position
and the total inertial moment (second moment) of
the cross section of the Jack Houses after being
simplified must remain the same in both modes,
bending about lines parallel to X and Y direction.
Figure III-2 Bending mode – Jack Houses
3.1.3. Bending mode of Bulkheads and Sidewalls
Because the bending mode about lines parallel to
the Z axis of the Hull Form is neglected, all
vertical plates including Bulkheads and Sidewalls
are considered bent individually as shown in
Figure III-3 Bending mode – Bulkhead and
Sidewalls. Each plate including stiffeners acts like
a single plate.
Each equivalent plate must keep the strength of
the original plate unchanged in these bending
modes. In detail, the neutral axis position and the
total inertial moment (second moment) of the
cross section of the equivalent plate must remain
the same in its bending modes
Figure III-3 Bending mode – Bulkhead and
Sidewalls
(Depending on each plate, the bending modes may be about lines parallel to X,Y or Z direction).
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3.2. Calculation Method
The equivalent structure is calculated for different parts of the hull and they are considered as
beams with constant cross section. (Which is not true in case of the leg, details are presented in
IV EQUIVALENT LEG ). Thus, based on the principle and criteria presented, the equivalent
hull structure must have the same cross section area and the same inertial moment (or second
moment) with the original structure.
3.2.1. Step 1: Calculating Cross Section Area
The total cross section area is calculated by the following equation:
∑ Eq. 6
Where:
- Atotal: Total cross section area
- Ai: Unit cross section area
3.2.2. Step 2: Calculating Inertial Moment
Determining position of Neutral Axis
In the case of the jack up platform ODIN, all structure members are made of the same
materials and have the same Young’s Modulus of elasticity. Therefore, the Neutral Axis of a
cross section goes through the geometry center of that cross section. The direction of Neutral
Axis depends on the bending mode of interest as presented in
The distance from neutral axis to a reference line can be determined by the equation below.
∫
Eq. 7
Where:
- dreference: Distance from neutral axis to reference line
- d: Distance from the unit area to reference line
- A: Unit cross section area
- Atotal: Total cross section area
*Note: reference line can be any line which is parallel to the neutral axis.
Tran Viet Hai
Master Thesis developed at University of Rostock A - 10
Calculating Inertial Moment
As the position of the neutral axis is determined, the inertial moment can be calculated by the
following equation:
∫ Eq. 8
Where:
- I: Inertial moment
- d: Distance from unit area to Neutral Axis
- A: Unit cross section area
3.2.3. Step 3: Determining dimension of equivalent members
The equivalent members are determined based on two criteria as presented in II PRINCIPLE
AND CRITERIA. The equivalent component must have:
- The same cross section area with the original members
- The same inertial moment with the original members
To be on the safe side, the cross section area and inertial moment of the equivalent
component may be smaller but must not be higher than the original cross section area and inertial
moment respectively.
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3.3. Equivalent Hull Form Structure
3.3.1. Original Structure and Equivalent Structure
Typical drawings of original structure and equivalent structure are shown in figures below.
Figure III-4 Original plate cross section
Figure III-5 Equivalent plate cross section
Figure III-6 Original hull cross section
Figure III-7 Equivalent hull cross section
Tran Viet Hai
Master Thesis developed at University of Rostock A - 12
The figures below show the deck plate in detail model and in equivalent model
Figure III-8 Deck plate – Detail model
Figure III-9 Deck Plate – Equivalent model
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3.3.2. Equivalent Stiffener List
The table below shows the equivalent stiffness which is calculated and used in the equivalent
model.
Profile Height (mm) Thickness (mm) Section Area (cm2)
FB920x34 920 34 312.80
FB700x18 700 18 126.00
FB500x42 500 42 210.00
FB500x18 500 18 90.00
FB480x22 480 22 105.60
FB245x34 245 34 83.30
FB240x22 240 22 52.80
FB220x26 220 26 57.20
FB160x46 160 46 73.60
Table III-1 Equivalent stiffener list
*Note:
- For detail calculation, refer to the Equivalent Structure Excel File.
- For detail about the position of each stiffener, refer to the FEM model or the Appendix –
APDL Code
Tran Viet Hai
Master Thesis developed at University of Rostock A - 14
IV. EQUIVALENT LEG MODEL
As the ODIN is analyzed in elevated mode, the legs become extremely important and needs
to be modeled precisely. Nevertheless, due to the fact that the model is analyzed with different
water depths, leg penetrations and air-gaps, it is more convenient to use legs with a constant
cross section instead of the complex original legs which consist of three different types of cross
sections.
Thus, in order to be accurate and practical at a same time, the following solution is applied
which consists of three steps:
- Step 1: Model the original legs (detail model)
- Step 2: Model the equivalent legs using theoretical approach
- Step 3: Test and compare the detail model and the equivalent model in ANSYS
4.1. Detail Leg Model
4.1.1. ODIN legs
Each leg of the ODIN is 60m in length and consists of three different types of cross sections.
The following figures show one part of the legs of the ODIN.
Figure IV-1 ODIN leg
The three sections of the legs are presented in the following figures.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 15
Figure IV-2 Section A
Figure IV-3 Section B
Figure IV-4 Section C
4.1.2. Detail FEM Model
From the drawing, the detail models are then modeled. The element shape of the leg is
presented in the figure below.
Figure IV-5 Element shape-3D
Tran Viet Hai
Master Thesis developed at University of Rostock A - 16
The figures below shows the three section of the leg model.
Figure IV-6 Section A
Figure IV-7 Section B
Figure IV-8 Section C
The main properties of the section are presented in the table below.
Values (m/m2/m4)
Items Section A Section B Section C
Area 0.27297 0.23217 2.9276
Iyy 0.13497 0.13440 1.1901
Iyz 0 0 0
Izz 0.18222 0.14343 1.0415
Centroid Y 0 0 0
Centroid Z 0 0 0
Table IV-1 Leg section properties
4.2. Equivalent Leg Model
4.2.1. Calculation Method
The principle in modeling leg equivalent model is different from what has been performed
for the hull form. In case of the hull form, the equivalent structure is calculated for each part of
the hull which is considered a constant section beam. In case of the legs, the equivalent structure
is calculated for all parts of each leg at a same time. In other words, each non-constant section
leg must be turned into a constant section one.
For that, the criterion for equivalent structure is that the equivalent legs must give the same
deflection due to axial force and bending moment with the original legs. To be on the safe side,
the leg parts consisting of section C which is only 12mm long is considered insignificant and not
taken into account. The stress difference can be neglected in this part because the stress obtained
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 17
is not used to check the ultimate strength of the legs. The ultimate strength is checked with
moment, shear force and axial force for the effective leg cross section due to buckling effect as
required in EUROCODE 3 – Design of steel structures. The details are presented in V
EFFECTIVE LEG CROSS SECTION – BUCKLING EFFECT
Absolute displacement caused by axial force:
Though parts of the legs have different lengths and cross section
areas, they are all made of a same material, from the Eq. 4 the
displacement under axial force can be calculated as
Eq. 9
The equivalent leg has a constant section therefore the displacement
under axial force can be calculated as
Eq. 10
From Eq. 9 and Eq. 10 the equivalent cross section area can be
calculated as
Eq. 11
Where in Eq. 9, Eq. 10 and Eq. 11
- Delta ( : Absolute displacement caused by Axial Force
- F: Axial Force
- E: Elastic modulus
- A1: Cross section area of part consisting section A
- A2: Cross section area of part consisting section B
- Aeqv: Equivalent Cross section area
- L1, L2: Length corresponding to section with A1, A2
Figure IV-9 Non-
constant beam under axial
force
Tran Viet Hai
Master Thesis developed at University of Rostock A - 18
Absolute displacement caused by bending moment:
The legs of the ODIN can be divided into identical blocks as shown in Figure IV-10 Leg
block. The length of each block is d which is equal to 1.33m.
Figure IV-10 Leg block
As the length of a block is 1.33m (d=1.33m)
and the total length of a leg is 60m (L=60m),
the length of a block is small compared to the
total length (d<<L).
Thus, though the moment distribution along
the legs is not yet known, it can be assumed
that the moment variance over one block is
small. In other words, it is assumed that the
moment over one block is uniform.
Figure IV-11 Moment over a block
(In Figure IV-11 Moment over a block, the moment distribution along leg is just an example).
Take a certain block in the into consideration. The boundary condition at the starting point
of the block (X=0) is as follows:
- Slope ϴ = ϴ1
- Displacement
The next part of the appendix presents the method to calculate displacement of that block under
uniform moment and thereby calculating for the equivalent leg section.
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The figure below shows the displacement delta ( of a block under uniform moment
Figure IV-12 Displacement over a block
From Eq. 5 the displacement caused by bending moment over the non-constant section beam can
be calculated as
∫ ∫
∫ ∫
∫ ∫
Eq. 12
From Eq. 12 and the boundary condition the displacement can be calculated as
Eq. 13
Where in Eq. 12, Eq. 13
- Delta ( : Absolute deformation caused by bending moment
- M: Bending moment
- I1,I3: The inertial moment about the neutral axis of Section A
- I2: The inertial moment about the neutral axis of Section B
- L1, L2, L3: The length corresponding to section with I1, I2, I3 respectively
- E: Elastic modulus
- : The slopes at position X= 0, X = L1, X = L1+ L2 respectively
Tran Viet Hai
Master Thesis developed at University of Rostock A - 20
From the boundary condition, at X=0. Hence, the slope and slope can be
calculated as follows
∫
Eq. 14
Eq. 15
Eq. 16
Combine Eq. 13, Eq. 15 and Eq. 16 the displacement can be calculated as
Eq. 17
Where in Eq. 14, Eq. 15, Eq. 16, Eq. 17
- Delta ( : Absolute deformation caused by bending moment
- M: Bending moment
- I1,I3: The inertial moment about the neutral axis of Section A
- I2: The inertial moment about the neutral axis of Section B
- L1, L2, L3: The length corresponding to section with I1, I2, I3 respectively
- E: Elastic modulus
- : The slopes at position X= 0, X = L1, X = L1+ L2 respectively
From Eq. 5 the displacement of an equivalent block caused by bending moment can be
calculated as
∫ ∫
Eq. 18
Where:
- Delta ( : Absolute deformation of an equivalent block
- M: Bending moment
- L1, L2, L3: The length corresponding to section with I1, I2, I3 respectively
- Ieqv : The inertial moment of equivalent section
- E: Elastic modulus
Global response analysis of the jack-up platform Odin
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As the equivalent structure must give the same displacement, from Eq. 17 and Eq. 18 we have
Eq. 19
Eq. 20
Eq. 21
Where in Eq. 19, Eq. 20, Eq. 21
- Delta ( : Absolute deformation caused by bending moment
- M: Bending moment
- I1,I3: The inertial moment about the neutral axis of Section A
- I2: The inertial moment about the neutral axis of Section B
- Ieqv : The inertial moment of equivalent section
- L1, L2, L3: The length corresponding to section with I1, I2, I3 respectively
- E: Elastic modulus
- : The slopes at position X= 0, X = L1, X = L1+ L2 respectively
From Eq. 11 and Eq. 21 the equivalent cross section area and inertial moment Iyy, Iyz and
Izz can be calculated. The results are as follows
Values (m/m2/m4)
Items Section A Section B Equivalent Section
Area 0.27297 0.23217 0.25901
Iyy 0.13497 0.13440 0.13479
Iyz 0 0 0
Izz 0.18222 0.14343 0.16826
Table IV-2 Equivalent leg section properties
Tran Viet Hai
Master Thesis developed at University of Rostock A - 22
4.2.2. Equivalent FEM model
From the calculated values, the equivalent leg is modeled. The element shape of the leg is
presented in the figure below.
Figure IV-13 Equivalent element shape - 3D
The figures below show the main dimension of the equivalent leg section and its FEM model.
Figure IV-14 Equivalent leg section
Figure IV-15 Equivalent leg section - FEM
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“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 23
The table below shows the main properties of the equivalent leg section. The difference
between the calculated section and the section modeled is also presented in the table.
Equivalent Leg Section
Values (m/m2/m4) Ratio
Items Calculated
Section
Modeled
Section
Modeled /
Calculated
Area 0.25901 0.25620 98.9%
Iyy 0.13479 0.13467 99.9%
Iyz 0 0 N/A
Izz 0.16826 0.16675 99.1%
Table IV-3 Equivalent leg section properties
4.3. Comparing detail legs and equivalent legs in ANSYS
4.3.1. Testing model
Three testing models are built to compare the detail legs and the equivalent legs.
The first model is to check the difference in displacement under axial force as shown in
Figure IV-16 Testing model – Axial force. The length of each leg is 58.52m. The force applied
is 1000 kN. The leg-ground connection is fixed (all 6 DOFs)
Figure IV-16 Testing model – Axial force
Tran Viet Hai
Master Thesis developed at University of Rostock A - 24
The second and the third model are to check the difference in displacement under bending
moment as shown in Figure IV-17 Testing model – Bending moment. The length of each leg is
58.52m. A 1000 kN force is applied in X direction for the second model and in Y direction for
the third model. The horizontal bar connecting legs has very high stiffness. The leg-ground
connection is spin (free to rotate).
This model is chosen because its shape is similar to the real model of jack up platform in
elevated mode and the moment diagram and boundary condition are as suggested in SNAME.
Figure IV-17 Testing model – Bending moment
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 25
4.3.2. Results and Comparison
Static linear analyses are performed for the three models. The figures below show the
diagram axial force of the first model and the bending moment diagram of the third model (the
bending moment diagram of the second model is basically similar).
Figure IV-18 Axial force diagram
Figure IV-19 Bending moment diagram
The displacements of the two legs in X, Y and Z direction are shown in the table below.
Displacement (m) Ratio (%)
Model Displacement Detail Leg Equivalent
Leg Equivalent leg / Detail Leg
Model 2 Ux 0.9497 0.9630 101.4 %
Model 3 Uy 1.1832 1.1891 100.5 %
Model 1 Uz -1.071E-03 -1.088E-03 101.6 %
Table IV-4 Displacement – Detail leg and Equivalent leg
4.4. Conclusion
As can be seen in Table IV-4 Displacement – Detail leg and Equivalent leg, the equivalent
model gives very good results as the errors remain less than 2%. Besides, the displacement given
by equivalent legs are always bigger than the displacement given by the detail legs. Hence we
are on the safe side.
For that reasons, the equivalent leg model is good and can be applied to the main project.
*Note: For more detail about the model test, refer to the Appendix – APDL Code
Tran Viet Hai
Master Thesis developed at University of Rostock A - 26
V. EFFECTIVE LEG CROSS SECTION – BUCKLING EFFECT
The effective leg cross section is calculated complying with EUROCODE 3 – Design of
steel structures, EN 1993-1-1 and EN 1993-1-5. The result is used for ultimate strength check.
5.1. Leg Section Classification
The effective section calculation depends on the class of the section. Hence the leg section
must be classified first. According to EN 1993-1-1 part 5.6 as the legs are under compression,
they can be classified as follows:
Classification Under compression
Class 1 c/t ≤ 33ε
Class 2 c/t ≤ 38ε
Class 3 c/t ≤ 42ε
Class 4 c/t > 42ε
Parameter √
Table V-1 Section classification
Figure V-1 Internal compression part
As the legs of the ODIN are made of Steel S355 with Yield Strength fy = 335 N/mm2.
√
Eq. 22
The length and average thickness of each side of the leg cross section can be calculated from
Figure IV-14 Equivalent leg section as follows
c (mm) t (mm) c/t 42ε
Side 1 1918.79 27.07 70.88 35.2
Side 2 1881.72 39.43 47.73 35.2
Table V-2 Leg section Classification
*Note: Side 1 represents the upper and lower sides of the legs. Side 2 represents the left and
right sides of the legs. For detail refer to Figure IV-14 Equivalent leg section
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 A - 27
It can be seen in Table V-2 Leg section Classification that c/t > 42ε in both cases. Thus the
leg section is classified as class 4 and the effective area must be calculated in order to take into
account the buckling effect.
5.2. Effective Area Calculation
According to EN 1993-1-5 part 4.4, the effective area can be calculated by the following
formula:
Eq. 23
Where:
- : Effective cross section area
- : Gross cross section area
- ρ: Reduction factor
The reduction factor can be calculated by the following formula:
Eq. 24
Where:
- : Stress ratio
- : Parameter
Parameter can be calculated by the following formular:
√
Eq. 25
Where:
- b: Internal flange
- t: Thickness
- ε: Parameter ε
- : Buckling factor related to
According to EN 1993-1-5, table 4.1 stress ratio is determined as and buckling factor
is determined as . From the Eq. 22 parameter ε = 0.8376.
Tran Viet Hai
Master Thesis developed at University of Rostock A - 28
The reduction factor and effective cross section area then can be determined from Eq. 23, Eq.
24 and Eq. 25. The table below shows the results for each side of leg cross section.
Reduction factor Gross cross section area
(mm2)
Effective cross section area
(mm2)
Side 1 0.5720 54139.07 30970.01
Side 2 0.8100 78851.66 63867.36
Table V-3 Reduction factor and Effective cross section area
*Note: Side 1 represents the upper and lower sides of the legs. Side 2 represents the left and
right sides of the legs. For detail refer to Figure IV-14 Equivalent leg section
5.3. Effective Leg Section
The effective leg section is shown in the figures below.
Figure V-2 Effective leg section
Figure V-3 Effective leg section - FEM
Leg cross section properties are shown in the table below.
Items Value (m/m2/m4)
Area 0.18518
Iyy 0.10815
Iyz 0
Izz 0.15178
Centroid Y 0
Centroid Z 0
Table V-4 Effective leg section properties
Appendix B
SUB-STRUCTURING MODEL
ASSESSMENT
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - i
Table of Contents
I. GENERAL ....................................................................................................................... 1
II. INPUT DATA .................................................................................................................. 2
2.1. Material Data ............................................................................................................ 2
2.2. Environmental Data .................................................................................................. 2
2.2.1. Wave and Current .............................................................................................. 2
2.2.2. Marine Growth and Hydrodynamic Coefficients .............................................. 2
2.3. Weights and COGs ................................................................................................... 3
2.4. Load Case.................................................................................................................. 3
III. MODEL DESCRIPTION ............................................................................................. 4
3.1. Full Model and Sub-structuring Model..................................................................... 4
3.1.1. Seabed Reaction Point and Foundation Fixity .................................................. 5
3.1.2. Leg Hull Connection ......................................................................................... 5
3.1.3. Air-gap and Leg Penetration.............................................................................. 5
3.2. Weight and COGs ..................................................................................................... 6
IV. RESULTS AND COMPARISON ................................................................................ 7
4.1. Modal analysis .......................................................................................................... 7
4.2. Static Linear Analysis ............................................................................................... 8
4.3. Static Non-linear Analysis ........................................................................................ 9
4.3.1. Convergence Path .............................................................................................. 9
4.3.2. Reaction Force ................................................................................................. 10
V. CONCLUSION AND APPLICATION ......................................................................... 11
Tran Viet Hai
Master Thesis developed at University of Rostock B - ii
List of Figures
Figure III-1 Hull Form .............................................................................................................. 4
Figure III-2 Super Element ....................................................................................................... 4
Figure IV-1 Full Model ............................................................................................................. 7
Figure IV-2 Sub-structuring Model .......................................................................................... 7
Figure IV-3 Convergence path – Full model ............................................................................ 9
Figure IV-4 Convergence path – Sub-structuring model .......................................................... 9
List of Tables
Table II-1 Steel S355 properties .............................................................................................. 2
Table II-2 Sea water properties ................................................................................................. 2
Table II-3 Wave and Current ................................................................................................... 2
Table II-4 Marine Growth and Hydrodynamic Coefficient ..................................................... 2
Table II-5 Weights and COGs - Input....................................................................................... 3
Table III-1 Number of Elements ............................................................................................... 4
Table III-2 Leg-Hull connection springs .................................................................................. 5
Table III-3 Air-gap and Leg penetration ................................................................................... 5
Table III-4 Weight and COGs of the model ............................................................................. 6
Table IV-1 Natural Periods ....................................................................................................... 7
Table IV-2 Reaction force Fx – Linear analysis ....................................................................... 8
Table IV-3 Reaction force Fy – Linear analysis ....................................................................... 8
Table IV-4 Reaction force Fz – Linear analysis ....................................................................... 8
Table IV-5 Reaction force Fx – Nonlinear analysis ............................................................... 10
Table IV-6 Reaction force Fy – Nonlinear analysis ............................................................... 10
Table IV-7 Reaction force Fz – Nonlinear analysis ................................................................ 10
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 1
I. GENERAL
Sub-structuring is an advanced technique which pre-calculates for a body and then use one
single matrix element to represent for the whole body. The single matrix element is called super
element.
There are several reasons for applying the sub-structuring technique to this project. First of
all, as the whole body is represented by a single element, the complexity of the model is reduced
significantly. Since there are thousands of computations needed to be performed, this obviously
saves a considerable amount of time.
In addition, the objective of the thesis is to perform the global analysis for the jack-up
platform ODIN. Hence, the detail analysis for the hull form, which contains most of the elements
in the model, is unnecessary. For that, the whole hull from can be transformed into a super
element without eliminating any important results.
Furthermore, it is also easier to get converged solutions in nonlinear analysis by using the
sub-structuring technique. It is because one of the reasons leading to diverged solutions is the
high local deformation or stress at certain parts of the body. By transforming the whole hull form
into a super element, such problems can be overcome.
Though the benefits of applying sub-structure technique are clear, there are also
disadvantages. Elements with Lagrange multipliers cannot be used in the body and that creates
certain challenges of modeling the jack-up. Besides, there are also errors in computation and how
significant are the errors depends on many factors such as the complexity of the model or the
way super elements are generated.
Thus, in order to apply the technique to this project the sub-structuring model (with the super
element) needs to be assessed. The assessment is performed by comparing the results from a full
model (without supper element) and its sub-structuring model. In this appendix, the two models
and the results of the reaction forces, the natural frequency given by modal analysis, static linear
analysis and static non-linear analysis are presented. These results are typical among many cases
performed.
Tran Viet Hai
Master Thesis developed at University of Rostock B - 2
II. INPUT DATA
2.1. Material Data
Steel S355
Properties Value
Density 7850 kg/m3
Yield Strength fy,k = 335 N/mm2
Young’s modulus of elasticity E = 2.1E11 N/m2 = 2.1E5 N/mm2
Poisson Ratio 0.3
Table II-1 Steel S355 properties
Sea water
Properties Value
Density 1025 kg/m3
Yield Strength N/A
Young’s modulus of elasticity N/A
Poisson Ratio N/A
Table II-2 Sea water properties
2.2. Environmental Data
2.2.1. Wave and Current
Water Depth 25.2 m
Wave Height max 1.5m
Significant Wave Height 0.79m
Wave Period 3.6 s
Current Speed 1 m/s
Table II-3 Wave and Current
2.2.2. Marine Growth and Hydrodynamic Coefficients
Marine Growth N/A
Inertial coefficient 1.51
Drag coefficient 1.5
Table II-4 Marine Growth and Hydrodynamic Coefficient
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 3
2.3. Weights and COGs
This report does not cover the weight assessment of the ODIN. The weight and COGs are
taken as input data which is referred from Germanisher Lloyd’s weight assessment document.
Item Weight (kg) Weight (t) x (m) y (m) z (m)
LIGHTSHIP 2728325 2728.33 20.605 0.037 7.116
LEG_AFTPS_1 146820 146.82 3.15 12.000 27.913
LEG_AFTSB_3 146820 146.82 3.15 -12.000 27.913
LEG_FWDSB_4 146820 146.82 38.85 -12.000 27.913
LEG_FWDPS_2 146820 146.82 38.85 12.000 27.913
SPUDCAN AFTPS_SP1 12810 12.81 3.15 12.000 -1.399
SPUDCAN AFTSB_SP3 12810 12.81 3.15 -12.000 -1.399
SPUDCAN FWDSB_SP4 12810 12.81 38.85 -12.000 -1.399
SPUDCAN FWDPS_SP2 12810 12.81 38.85 12.000 -1.399
Equipment and Tank 373500 373.5 27.01 1.017 3.067
Table II-5 Weights and COGs - Input
The COGs in the table above are given in local vessel coordinate system:
- The X-axis points from Aft to Fore, X=0 at Aft
- The Y-axis points from Centerline to Portside, Y=0 at Centerline
- The Z-axis points from Bottom to Deck, Z=0 at Bottom
2.4. Load Case
A same load case is applied to full model and sub-structuring model. The load case is determined
in order to simulate a typical real load case. The loads applied in the model are as follows:
- Self-weight and Pay Load by means of gravity, g = 9.81 m/s^2
- Wave load with Angle of attack of 0 degree
- Distributed load in X direction: 147000 N
- Distributed load in Y direction: 147000 N
Tran Viet Hai
Master Thesis developed at University of Rostock B - 4
III. MODEL DESCRIPTION
The purpose of this appendix is to compare the two models and thereby assessing the
accuracy of the sub-structuring model. Thus, the details about the full model are not presented in
this appendix.
3.1. Full Model and Sub-structuring Model
The full model used in this analysis is similar to the FEM model of the ODIN described in
the main report of thesis except for the air-gap and the leg penetration. The sub-structuring
model is the same with the full model except for the hull form. The sub-structuring model uses
one super element to represent the whole hull form. This super element is calculated from a sub-
structuring analysis.
The figures below show the hull form and the super element that represents the hull form
Figure III-1 Hull Form
Figure III-2 Super Element
By applying the sub-structuring technique, the number of elements has reduced significantly.
The table below shows the number of elements in the full model and its sub-structuring model.
Number of Elements
Full model 21536
Sub-structuring model 1378
Table III-1 Number of Elements
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 5
3.1.1. Seabed Reaction Point and Foundation Fixity
As required in SNAME, the seabed reaction point and the foundation fixity is modeled as
follows:
Connection type: Pin joints (unable to sustain bending moments)
Position of the reaction point:
- At vertical axis of the leg/Spudcan
- At Half of the predicted penetration (when SPD is partly penetrated)
- At Half of SPD height (when SPD is fully penetrated)
3.1.2. Leg Hull Connection
The leg-hull connection is modeled by linear springs. Each spring acts only in one direction.
The details about the spring system are as follows
Position Spring Stiffness (kN/mm)
Bottom
Horizontal (X)
Horizontal (Y)
1000
1000
Main Deck Horizontal (X)
Horizontal (Y)
1000
1000
Leg vertical axis Vertical (Z) 1000
Table III-2 Leg-Hull connection springs
3.1.3. Air-gap and Leg Penetration
According to SNAME, the minimum air-gap maybe calculated as follows:
- Lowest astronomical tide: LAT
- Highest astronomical tide: HAT
- Mean astronomical tide: MAT = ½ (LAT +HAT)
- Extreme still water level: SWL = MHWS + Storm Surge
- Extreme negative water level: SWL = MLWS + Negative Storm surge
- Air-gap = HAT + Storm Surge + Wave Crest + 1.5m
The table below shows the air-gap and the leg penetration in this analysis.
Air-gap 9m
Leg Penetration 3.5m
Table III-3 Air-gap and Leg penetration
Tran Viet Hai
Master Thesis developed at University of Rostock B - 6
3.2. Weight and COGs
Due to the fact that only the structure part of the ship is modeled, the weight of the model
cannot be equal to the real weight of the ship. Thus, the weight of the model is adjusted by
adjusting material density and adding mass points in order to achieve the same weight and COGs
with the real ship
The Weight and COGs of parts of the model after adjusting are shown in the following table.
Item Weight (kg) Weight (t) x (m) y (m) z (m)
Light Ship + Pay load 3101825 3101.825 21.376 0.156 6.628
LEG_AFTPS_1 146820 146.82 3.15 12.000 27.913
LEG_AFTSB_3 146820 146.82 3.15 -12.000 27.913
LEG_FWDSB_4 146820 146.82 38.85 -12.000 27.913
LEG_FWDPS_2 146820 146.82 38.85 12.000 27.913
SPUDCAN AFTPS_SP1 12810 12.81 3.15 12.000 -0.9
SPUDCAN AFTSB_SP3 12810 12.81 3.15 -12.000 -0.9
SPUDCAN FWDSB_SP4 12810 12.81 38.85 -12.000 -0.9
SPUDCAN FWDPS_SP2 12810 12.81 38.85 12.000 -0.9
Table III-4 Weight and COGs of the model
The COGs in the table above are given in local vessel coordinate system:
- The X-axis points from Aft to Fore, X=0 at Aft
- The Y-axis points from Centerline to Portside, Y=0 at Centerline
- The Z-axis points from Bottom to Deck, Z=0 at Bottom
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 7
IV. RESULTS AND COMPARISON
The results of reaction forces and the natural periods given by modal analysis, static linear
analysis and static non-linear analysis are compared between the two models.
Figure IV-1 Full Model
Figure IV-2 Sub-structuring Model
4.1. Modal analysis
The modal analysis is conducted without taking into account the pre-stressed effect. The
results of natural period given by the full model and the sub-structuring model are as follows
Natural Period (s) Errors
MODE Full model Sub-structuring model Absolute (s) Percentage (%)
1 5.419 5.412 0.006 0.119
2 5.173 5.144 0.028 0.545
3 3.851 3.850 0.001 0.023
Table IV-1 Natural Periods
*Note: In this case, the mode 1, mode 2 and mode 3 correspond to oscillation motion in X
direction, Y direction and torsion about Z direction respectively.
Average error is 0.23%
Tran Viet Hai
Master Thesis developed at University of Rostock B - 8
4.2. Static Linear Analysis
Reaction force in X direction from full model and sub-structuring model
Fx (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 -33634.0 -35994.0 2360.0 7.0
Leg 3 -37163.0 -35229.0 1934.0 5.2
Leg 2 -112240.0 -113720.0 1480.0 1.3
Leg 4 -112510.0 -110600.0 1910.0 1.7
Total force -295547.0 -295543.0 4.0 0.0
Table IV-2 Reaction force Fx – Linear analysis
Reaction force in Y direction from full model and sub-structuring model
Fy (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 -59634.0 -58335.0 1299.0 2.2
Leg 3 -43219.0 -41937.0 1282.0 3.0
Leg 2 -51602.0 -52736.0 1134.0 2.2
Leg 4 -32347.0 -33795.0 1448.0 4.5
Total force -186802.0 -186803.0 1.0 0.0
Table IV-3 Reaction force Fy – Linear analysis
Reaction force in Z direction from full model and sub-structuring model
Fz (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 9304900.0 9120000.0 184900.0 2.0
Leg 3 8485100.0 8670000.0 184900.0 2.2
Leg 2 9518700.0 9703600.0 184900.0 1.9
Leg 4 9384000.0 9199100.0 184900.0 2.0
Total force 36692700.0 36692700.0 0.0 0.0
Table IV-4 Reaction force Fz – Linear analysis
Average error of individual legs is 2.9%
*Note: The average error is taken as the average of the percentage errors not including the
total force.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 9
4.3. Static Non-linear Analysis
4.3.1. Convergence Path
Convergence path from static non-linear analysis of the full model and the sub-structuring
model are shown in the following figures.
Figure IV-3 Convergence path – Full model
Figure IV-4 Convergence path – Sub-
structuring model
As can be seen from the figures above, it is easier to get a converged solution with the sub-
structuring model. In case of the full model the cumulative iteration number is 15 while in case
of the sub-structuring model this number is only 8.
Tran Viet Hai
Master Thesis developed at University of Rostock B - 10
4.3.2. Reaction Force
Reaction force in X direction from full model and sub-structuring model
Fx (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 -33625.0 -36923.0 3298.0 9.8
Leg 3 -39935.0 -37157.0 2778.0 7.0
Leg 2 -110220.0 -111580.0 1360.0 1.2
Leg 4 -111570.0 -109730.0 1840.0 1.6
Total force -295350.0 -295390.0 40.0 0.0
Table IV-5 Reaction force Fx – Nonlinear analysis
Reaction force in Y direction from full model and sub-structuring model
Fy (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 -58849.0 -58241.0 608.0 1.0
Leg 3 -45603.0 -42909.0 2694.0 5.9
Leg 2 -50281.0 -51812.0 1531.0 3.0
Leg 4 -32021.0 -33791.0 1770.0 5.5
Total force -186754.0 -186753.0 1.0 0.0
Table IV-6 Reaction force Fy – Nonlinear analysis
Reaction force in Z direction from full model and sub-structuring model
Fz (N) Errors
Full model Sub-structuring model Absolute (N) Percentage (%)
Leg 1 9368100.0 9117600.0 250500.0 2.7
Leg 3 8352500.0 8604600.0 252100.0 3.0
Leg 2 9596700.0 9768400.0 171700.0 1.8
Leg 4 9376000.0 9202600.0 173400.0 1.8
Total force 36693300.0 36693200.0 100.0 0.0
Table IV-7 Reaction force Fz – Nonlinear analysis
Average error of individual legs is 3.7%
*Note: The average error is taken as the average of the percentage errors not including the
total force.
Global response analysis of the jack-up platform Odin
“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 B - 11
V. CONCLUSION AND APPLICATION
As presented in IV RESULTS AND COMPARISON the differences between results from a
full model (without supper element) and sub-structuring model (with supper element) are
insignificant.
In case of Modal Analysis the two models give almost the same results. The average error is
0.23% and the maximum error is just 0.55%.
In case of Static Analysis (both linear and nonlinear) there are only errors in reaction force of
individual legs. The total reaction forces are always the same for the two models. Regarding the
reaction force of individual legs, the results given by Static Linear Analysis are closer with the
average error of 2.9%. The sub-structuring model in static non-linear analysis gives less accurate
results as the average error is 3.7%.
For the reasons, in this thesis the sub-structuring technique is applied for all static linear
analyses including analyses for different wave directions, crane directions and wave phases. The
harmonic analyses are also performed by sub-structuring models as harmonic analyses actually
are also linear analyses.
Though the errors in static nonlinear analysis are also insignificant, the technique is not
applied to nonlinear analyses. It is because the number of nonlinear analyses is not as many as
the static analyses. Besides, nonlinear analyses are among the last analyses performed and it is
necessary to get results from the original full model.