Global Response Analysis of the Jack-up Platform Odin Viet Hai - URO... · guidelines are performed...

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


“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.


“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


“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page ix

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


6.2.1. 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


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


8.2.2. Checking Results ............................................................................................. 56

8.3. Results for Survival Condition 1............................................................................. 57

8.3.1. Input Data ........................................................................................................ 57





8.4.1. Input Data ........................................................................................................ 59




“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page xi





8.5.1. Input Data ........................................................................................................ 65







8.6.1. Input Data ........................................................................................................ 71







8.7.1. Input Data ........................................................................................................ 77






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


“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page xiii

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


“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 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-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


“EMSHIP” Erasmus Mundus Master Course, period of study September 2012 – February 2014 Page xvii

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





Tran Viet Hai

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 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


“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

Tran Viet Hai

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.



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


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.



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


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



“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


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)



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


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,)



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


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



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


Poisson Ratio N/A

Table III-3 Air properties

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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



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.

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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


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



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


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


LIGHTSHIP 2728325 2728.33 20.605 0.037 7.116

Table III-9 Light Ship Weight

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IV. FINITE ELEMENT MODEL

4.1. Global Coordinate system

The global coordinate system is described as follows:



- The Z-axis points from Bottom to Deck, Z=0 at Mean water level

Figure IV-1 Global Coordinate System



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

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The model of the hull form is shown in the following figures.





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

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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



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

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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



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

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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



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

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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



- 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:




Tran Viet Hai


The table below shows the weight and COGs of the model after adjusting


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).


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.



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

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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



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

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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



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


: 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

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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


: 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



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).

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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.


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



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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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



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

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: 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


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



: 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.

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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



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


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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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



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

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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


- 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



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

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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


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.



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


=15m: Water Depth


m: The height of main hull


=15m: The air-gap

SATISFIED

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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




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

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legs. These results are given by dynamic analyses.

Figure VIII-3 Base Shear – Dynamic Analysis

*Note:



The maximum base shear (aqua color) given by dynamic analysis is 2.53E+06 N



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 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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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:

(

)

(

)

(

⁄)(

⁄) (

⁄)



8.3. Results for Survival Condition 1

8.3.1. Input Data



Value

Water Depth 15m

Leg Penetration 3m

Air-gap 5m





Current Speed 1.5 m/s






Where


=25m: Water Depth




=5m: The air-gap

SATISFIED

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1 0.3410 2.93

2 0.3462 2.89

3 0.4626 2.16





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.




8.4.1. Input Data



Value

Water Depth 20m

Leg Penetration 3m

Air-gap 15m





Current Speed 1 m/s






Where


=20m: Water Depth




=15m: The air-gap

SATISFIED

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1 0.1802 5.55

2 0.1892 5.28

3 0.2520 3.97







Value



Wave period 5.52s












*Note:




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*Note:









*Note:






4.43E+05 2.19E+06 4.95


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respectively)





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




X Axis 1.35E+07 3.92E+08 0.03

Y Axis 1.68E+08 5.70E+08 0.29



(

)

(

)

(

⁄)(

⁄) (

⁄)




8.5.1. Input Data



Value

Water Depth 20m

Leg Penetration 3m

Air-gap 5m











Where


=20m: Water Depth




=5m: The air-gap

SATISFIED

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1 0.2659 3.76

2 0.2742 3.65

3 0.3647 2.74







Value



Wave period 4.58s

Crane Working Angle N/A











*Note:




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*Note:









*Note:






8.67E+05 2.36E+06 2.72


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respectively)





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




X Axis 9.35E+06 3.92E+08 0.02

Y Axis 1.06E+08 5.70E+08 0.19



(

)

(

)

(

⁄)(

⁄) (

⁄)




8.6.1. Input Data



Value

Water Depth 25m

Leg Penetration 3m

Air-gap 15m





Current Speed 1 m/s






Where


=25m: Water Depth




=15m: The air-gap

SATISFIED

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1 0.1522 6.57

2 0.1607 6.22

3 0.2130 4.69







Value



Wave period 6.22s












*Note:




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*Note:









*Note:






4.12E+05 1.87E+06 4.54


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respectively)





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




X Axis 1.54E+08 3.92E+08 0.39

Y Axis 1.28E+07 5.70E+08 0.02



(

)

(

)

(

⁄)(

⁄) (

⁄)




8.7.1. Input Data



Value

Water Depth 25m

Leg Penetration 3m

Air-gap 5m











Where


=25m: Water Depth




=5m: The air-gap

SATISFIED

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1 0.2141 4.67

2 0.2232 4.48

3 0.2950 3.39







Value



Wave period 4.92s

Crane Working Angle N/A











*Note:




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*Note:









*Note:






9.63E+05 4.25E+06 4.41


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respectively)





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




X Axis 2.43E+06 3.92E+08 0.01

Y Axis 1.74E+08 5.70E+08 0.31



(

)

(

)

(

⁄)(

⁄) (

⁄)



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.


Water

Depth

Leg


Wind

Speed

Current

Speed

Wave Height

Max







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.

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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



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



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

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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.



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


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



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-7 Wave loads on legs – Case4

*Note:


- 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


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



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


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.



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


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



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.



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



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


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



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.



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


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.



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.


Water

Depth

Leg


Wind

Speed

Current

Speed

Wave Height

Max







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


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



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


BIBLIOGRAPHY

ANSYS, Inc, (2012) Advanced analysis techniques guide

ANSYS, Inc, (2012) ANSYS parametric design language guide

ANSYS, Inc, (2012) Basic analysis guide

ANSYS, Inc, (2012) Command reference

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



HOCHTIEF Solutions AG, (2009) Odin Drawing: General arrangement

HOCHTIEF Solutions AG, (2009) Odin Drawing: Jack-up legs extension

HOCHTIEF Solutions AG, (2009) Odin Drawing: Jack-up legs foundation plate

HOCHTIEF Solutions AG, (2009) Odin Drawing: Jack-up systems

HOCHTIEF Solutions AG, (2009) Odin Drawing: Legs and Guides

HOCHTIEF Solutions AG, (2009) Odin Drawing: Steel plans

HOCHTIEF Solutions AG, (2009) Odin Drawing: Steel plans crane pedestal

HOCHTIEF Solutions AG, (2013) HOCHTIEF Fleet

HOCHTIEF Solutions AG, (2013) Project success on a safe basis: Jack-up platform Odin

HOCHTIEF Solutions AG, (2013) The basis for a new energy era: Jack-up vessel Vidar

HOCHTIEF Solutions AG – Civil Engineering Marine and Offshore Department, (2013) Odin

profile document

SNAME – The Society of Naval Architects and Marine Engineers, (2012) Technical & Research

Bulletin 5-5A: Guidelines for site specific assessment of mobile jack-up units

ZENTECH, Inc (2011) Zentech R-550D jack-up drilling rig

Tran Viet Hai


Appendix A

Equivalent Structure


“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


“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-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


“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



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


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.



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


Tran Viet Hai


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





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


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).



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


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.



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


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



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


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.



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


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



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


- 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


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.



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


- : The slopes at position X= 0, X = L1, X = L1+ L2 respectively

Tran Viet Hai


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


- M: Bending moment






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


- Ieqv : The inertial moment of equivalent section




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


- M: Bending moment



- Ieqv : The inertial moment of equivalent section




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


Tran Viet Hai


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



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%


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


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



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


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 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



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


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


“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


“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


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


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



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.


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:




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


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



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

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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.


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:






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



Average error is 0.23%

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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


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


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.



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


4.3.2. Reaction Force

Reaction force in X direction from full model and sub-structuring model

Fx (N) Errors


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


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


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.



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.

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