A NUMERICAL ANALYSIS OF FIXED OFFSHORE STRUCTURE...

A NUMERICAL ANALYSIS OF FIXED OFFSHORE STRUCTURE SUBJECTED

TO ENVIRONMENTAL LOADING IN MALAYSIAN WATER

TAN CHUN CHAI

A thesis submitted in fulfillment of the

requirements for the award of the degree of

Master of Engineering (Mechanical)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

DECEMBER 2005

ACKNOWLEDGEMENT

While the motivation and hard work in pursuing a master degree must come

from within, interactions with others have stimulated and sustained me both

professionally and personally during my research career. I want to acknowledge

many people whose professional help and personal support has made it possible for

me to complete this research work. I wish to express my sincere appreciation to my

thesis supervisor, Associate Professor Dr. Iberahin Jusoh for his encouragement,

guidance, critics and friendship.

My special thanks to Mr. Ahmad Jafri for his assistant and guidance on finite

element of tubular joint. Appreciation is extended to my sponsor, Ministry of

Science, Technology and Innovation for providing scholarship to my study. My

fellow postgraduate students should also be recognised for their support especially

Miss Doris Chin Chong Leng. I would like to express my gratefulness to my family

for their continuous love and support throughout my life.

ABSTRACT

This research focused on the response of the jacket structure to environmental

loading. The jacket was modelled as a space frame using ANSYS finite element

package. Meanwhile, the estimation of extreme value of environmental parameters

based on data on Malaysia waters was carried out using MINITAB. Response of the

structure under environmental loading was performed using static analysis.

Interaction ratios of the members are computed based on API RP2A–WSD (1993)

using MATLAB. The sensitivity of the jacket structure to variation in design

parameters was investigated. From global stress analysis, one of the structure’s

member on a complex multiplanar leg joint, appeared to have a high utilisation of

stress when assessed using API RP2A–WSD (1993). Therefore, a nonlinear finite

element analysis of the multiplanar joint has been carried out to determine both the

absolute load capacity of the joint, the effect of the out–of–plane loads and braces

and relate these back to the strength of the critical brace acting as a Y joint. This

study presents the analytical methods and results together with a calibration of the

analysis against test data for Y joints. A systematic study of stresses in tubular Y

joints has also been conducted using finite element analysis which covers axial

loading, in–plane bending and out–of–plane bending. For each mode of loading, and

for both chord and brace sides of the intersection, stress concentration factors and its

distributions are calculated for selected locations. The validity of this approach is

demonstrated by comparing the finite element results with the predictions of other

previously published parametric equations.

ABSTRAK

Penyelidikan ini bertumpu kepada tindak balas struktur luar pantai terhadap

beban persekitaran. Permodelan struktur luar pantai yang terdiri daripada kerangka

dilakukan dengan menggunakan kaedah unsur terhingga ANSYS. Selain itu,

anggaran nilai parameter persekitaran yang ekstrim berdasarkan data di perairan

Malaysia dilakukan dengan menggunakan MINITAB. Tindak balas struktur luar

pantai terhadap beban persekitaran dianalisis secara statik. Nisbah beban terhadap

kapasiti elemen dikira berdasarkan API RP2A–WSD (1993) dengan MATLAB.

Kepekaan struktur luar pantai terhadap parameter yang digunakan dalam rekabentuk

dikaji. Daripada analisis tegasan, salah satu elemen yang terdapat pada sambungan

kaki struktur didapati mempunyai nilai nisbah penggunaan tegasan yang tinggi

apabila disemak dengan API RP2A–WSD (1993). Oleh itu, analisis kaedah unsur

terhingga tak linear sambungan multiplanar dijalankan untuk menentukan kedua–dua

nilai mutlak kapasiti beban pada sambungan, kesan beban dan cabang luar planar dan

mengaitkan semula kepada kekuatan elemen kritikal yang berfungsi sebagai

sambungan Y. Kajian ini mempersembahkan kaedah analitikal dan output bersama

dengan kalibrasi yang dilakukan terhadap data ujikaji sambungan Y. Kajian tegasan

yang sistematik juga dilakukan ke atas sambungan Y dengan menggunakan analisis

kaedah unsur terhingga yang meliputi beban paksi, momen dalam planar dan momen

luar planar. Bagi setiap jenis beban, dan untuk kedua–dua belah pertemuan

sambungan, faktor penumpuan tegasan dikira untuk lokasi yang tertentu. Kesahan

metodologi ini dipersembahkan dengan membuat perbandingan di antara output

daripada analisis kaedah unsur terhingga dengan persamaan parametrik yang

diterbitkan oleh penyelidik lain.

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

ACKNOWLEDGEMENT iii

ABSTRACT iv

ABSTRAK v

TABLE OF CONTENTS vi

LIST OF TABLES xii

LIST OF FIGURES xv

LIST OF SYMBOLS xxi

LIST OF APPENDICES xxv

1 INTRODUCTION 1

1.1 Research Significance 1

1.2 Research Objectives 2

1.3 Outline of Thesis 3

2 LITERATURE REVIEW PART I:

ENVIRONMENTAL LOADING ON FIXED

OFFSHORE STRUCTURES 6

2.1 Introduction 6

2.2 Historical Development of Oil and Gas in

Malaysia 7

2.3 Historical Development of Offshore

Structures 8

2.4 Classification of Offshore Structures 9

2.4.1 Fixed Structures 10

2.4.2 Mobile Structures 11

2.4.3 Compliant Structures 12

2.5 Type of Loading on Offshore Structures 13

2.6 Environmental Loading 14

2.6.1 Design Environmental Conditions 16

2.6.1.1 Oceanographic Conditions 17

2.6.1.2 Wind Conditions 18

2.6.1.3 Estimation of Extreme Values 19

2.6.2 Evaluation of Water Particle Motion 26

2.6.2.1 Wave Theories 27

2.6.2.2 Wave–Current Interaction 38

2.6.3 Evaluation of External Loads 41

2.6.3.1 Wave Force 41

2.6.3.2 Transverse Force 44

2.6.3.3 Wind Force 46

2.7 Summary 48

3 LITERATURE PART II: TUBULAR JOINTS 68

3.1 Introduction 68

3.2 Brief History of Tubular Joints 69

3.3 Classification of Tubular Joints 70

3.4 Joint Types 71

3.5 Behaviour of Tubular Joint under Operating

Loads 72

3.6 Stress Analysis of Tubular Joints 75

3.6.1 Thin–Shell Finite Elements 76

3.6.2 Three–Dimensional Isoparametric

Finite Elements 78

3.6.3 Nonlinear Analysis 79

3.7 Behaviour of Tubular Joint under Static Loads 80

3.8 Fatigue Performance of Tubular Joints 82

3.8.1 Stress Concentration Factor Equations 83

3.8.2 S–N Curves 91

3.8.3 Palmgren–Miner Cumulative Damage

Rule 92

3.9 Summary 93

4 STRUCTURAL MODEL AND

ENVIRONMENTAL CONDITIONS AT

SOTONG FIELD 101

4.1 Introduction 101

4.2 Model of Jacket Structure 101

4.2.1 Description of the Structure 102

4.2.2 Element of Jacket Structure 103

4.3 Environmental Conditions at Sotong Field 105

4.3.1 Estimation of Extreme Wave and

Associated Period 105

4.3.1.1 Basic Data 106

4.3.1.2 Statistical Analysis of

Extreme Significant Wave

Height 106

4.3.1.3 Maximum Individual Wave

Height and Associated Period 108

4.3.2 Wind Loads 110

4.3.3 Current and Its Profile 112

4.4 Concluding Remarks 112

5 STRUCTURAL ANALYSIS 122


5.2 Analysis Procedure 122

5.3 Results of Structural Analysis 123

5.3.1 In–Place Analysis 124

5.3.2 Base Case Analysis 125

5.3.3 Extreme Case Analysis 127


6 SENSITIVITY STUDY IN STRUCTURAL

RESPONSE 156


6.2 Base Design Criteria 157

6.3 Selection of Parameters 157

6.3.1 Wave Theory 158

6.3.2 Force Coefficients 159

6.3.2.1 Drag Coefficient 159

6.3.2.2 Inertia Coefficient 160

6.3.3 Environmental Parameters 161

6.3.3.1 Wave 161

6.3.3.2 Current and Its Profile 162

6.3.3.3 Wave–Current Interaction 163

6.3.3.4 Wind 163

6.4 Result of Sensitivity Studies 164

6.4.1 Wave Theory Sensitivity 164

6.4.2 Wave Force Coefficients Sensitivity 164

6.4.3 Wave Height Sensitivity 165

6.4.4 Wave Period Sensitivity 166

6.4.5 Current Velocity Sensitivity 166

6.4.6 Wave–Current Interaction Sensitivity 167

6.4.7 Wind Load Sensitivity 167


7 ULTIMATE STRENGTH ASSESSMENT OF

A MULTIPLANAR JOINT 179


7.2 Joint Configuration, Loading and Strength

Definitions 180

7.3 Scope of the Analytical Investigation 180

7.4 Finite Element Model of Multiplanar Joint 181

7.5 Analysis of Results 184

7.5.1 Complete Joint–All Braces Loaded 185

7.5.2 Complete Joint–Only Brace 251 Loaded 186

7.5.3 Y Joint–Brace 251 Subjected to All

Six Load Components 187

7.5.4 Y Joint–Brace 251 Subjected to

Axial Load Only 187

7.6 Comparison of Results 188


8 STRESS CONCENTRATION FACTORS FOR

Y JOINT 202


8.2 Joint Configuration 203

8.3 Finite Element Model of Y Joint 203

8.4 Results of Stress Analysis 205

8.5 Comparison of Results 207


9 DISCUSSIONS 219


9.2 Environment Modelling 219

9.3 Structural Analysis 221

9.4 Sensitivity of Jacket Structure 222

9.5 Strength Assessment of a Multiplanar Joint 223

9.6 Stress Concentration Factors for Y Joint 224

10 CONCLUSIONS AND SUGGESTIONS FOR

FUTURE RESEARCH 226


10.2 Conclusions 226

10.3 Suggestions for Future Research 228

REFERENCES 230

APPENDIX A – Structural Model 238

APPENDIX B – Structural Configuration 247

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Existing platforms water depth distribution 49

2.2 Planned platforms water depth distribution 49

2.3 Selected probability distributions 50

2.4 Results of linear wave theory 51

2.5 Shallow and deep water approximation to

linear wave theory 52

2.6 Results of Stokes fifth–order wave theory 53

2.7 The coefficients for Stokes fifth–order

wave theory 54

2.8 Values of hydrodynamic coefficient for

circular cylinders 55

3.1 Basic dimensions for simple joint 94

3.2 Non–dimensional geometric parameter for

tubular joint 94

4.1 Data on significant wave height at the Sotong

field for the years 1941–1990 113

4.2 Comparison of goodness of fit test for various

distributions (significant wave height) 113

4.3 Data on wind speed at the Sotong field for the

years 1941–1990 114

4.4 Comparison of goodness of fit test for various

distributions (wind speed) 114

4.5 Design specification applied for the base case

and extreme case model 115

5.1 Base shear and overturning moment for

in–place analysis 129

5.2 Base shear and overturning moment for base

case analysis 129

5.3 Selected structural elements for ultimate strength

analysis 129

5.4 Stress utilisation ratio for selected element at

node I and node J (base case) 130

5.5 Base shear and overturning moment for extreme

case analysis 131

5.6 Stress utilisation ratio for selected element at

node I and node J (extreme case) 132

6.1 Base design criteria 169

6.2(a) Static strength sensitivity studies (base case) 170

6.2(b) Static strength sensitivity studies (extreme case) 171

6.3 Normalised maximum base shear 172

6.4 Normalised maximum overturning moment 173

7.1 Geometry of the multiplanar joint 190

7.2 Loads in member local axis system extracted

from global analysis of jacket structure 190

7.3 Ratio of ultimate axial load to ultimate load

capacity of analysis 4 191

8.1 Stress concentration factors values at crowns,

saddle and hot–spot on brace and chord 210

8.2 Comparison between results of meshes to

show extent of convergence 210

8.3 Comparison of predicted stress concentration

factors for axial loading 211


factors for in–plane bending 211


factors for out–of–plane bending 212

9.1 Comparison of typical design wave parameter

for Malaysia’s water (100–year return period) 220

LIST OF FIGURES

FIGURE NO. TITLE PAGE

2.1 Jacket platform 56

2.2 Gravity platform 57

2.3 Typical jack–up rig 58

2.4 Typical semi–submersible vessel 59

2.5 Guyed tower 60

2.6 Tension leg platform (TLP) 61

2.7 Articulated tower 62

2.8 Definition sketch for a progressive wave train 62

2.9 Range of wave theories giving the best fit to

the dynamic free surface boundary condition 63

2.10 Ranges of suitability for various wave theories

as suggested by Le Mehaute 63

2.11 Various methods of combining a current profile

with the variation in instantaneous water depth

due to wave action 64

2.12 Classification of wave force calculation methods 65

2.13 Definition sketch for wave forces on cylinder 65

2.14 DC versus KC number for various values of Re

and frequency parameter ( KCRe=β ) 66

2.15 MC versus KC number for various values of Re

and frequency parameter ( KCRe=β ) 66

2.16 Flow patterns at various values of KC 67

3.1 Typical tubular joints 95

3.2 Stiffened joint 96

3.3 Typical jacket framing configurations 97

3.4 Notation for joint configurations 97

3.5 Weld defects 98

3.6 Punching shear concept 98

3.7 Finite element mesh and stress contours for a

K joint 99

3.8 Reserve strength of a tubular connection 99

3.9 Empirical design curve for punching shear 100

3.10 Fatigue S–N curve 100

4.1 Structural model 116

4.2 PIPE 59 immersed pipe 116

4.3 PIPE 59 velocity profile for wave–current

interaction 117

4.4 Element load vector effects 117

4.5 Extreme Value distribution for significant

wave height 118

4.6 Log–Normal distribution for significant

wave height 118

4.7 Weibull 2–Parameter distribution for

significant wave height 119

4.8 Extreme Value distribution for wind speed 119

4.9 Log–Normal distribution for wind speed 120

4.10 Weibull 2–Parameter distribution for wind

speed 120

4.11 Current velocity profile 121

5.1 Environmental load on offshore structure 133

5.2 Global coordinate system of the structure 133

5.3 Stress utilisation ratio for in–place analysis

(nodes I and J) 134

5.4 Variation of base shear and overturning moment

with wave phase angle for base case 135

5.5(a) Stress utilisation ratio at nodes I and J for base

case (wave phase angle: 0, 360) 136

5.5(b) Stress utilisation ratio at nodes I and J for base

case (wave phase angle: 45) 137

5.5(c) Stress utilisation ratio at nodes I and J for base


5.5(d) Stress utilisation ratio at nodes I and J for base


5.5(e) Stress utilisation ratio at nodes I and J for base


5.5(f) Stress utilisation ratio at nodes I and J for base


5.5(g) Stress utilisation ratio at nodes I and J for base


5.5(h) Stress utilisation ratio at nodes I and J for base


5.6 Variation of stress utilisation ratio at nodes I

and J for selected elements with wave phase

angle (base case) 144


with wave phase angle for extreme case 145

5.8(a) Stress utilisation ratio at nodes I and J for

extreme case (wave phase angle: 0, 360) 146

5.8(b) Stress utilisation ratio at nodes I and J for

extreme case (wave phase angle: 45) 147

5.8(c) Stress utilisation ratio at nodes I and J for


5.8(d) Stress utilisation ratio at nodes I and J for


5.8(e) Stress utilisation ratio at nodes I and J for


5.8(f) Stress utilisation ratio at nodes I and J for


5.8(g) Stress utilisation ratio at nodes I and J for


5.8(h) Stress utilisation ratio at nodes I and J for


5.9 Variation of stress utilisation ratio at nodes I

and J for selected elements with wave phase

angle (extreme case) 154

5.10 Percentage difference in stress utilisation ratio

at nodes I and J for extreme case compared to

the base case (wave phase angle: 45) 155


with wave height for base case and extreme case 174


with wave period for base case and extreme case 175


with depth average current for base case and

extreme case 176

6.4 Base shear and overturning moment sensitivity

for base case 177

6.5 Base shear and overturning moment sensitivity

for extreme case 178

7.1 Configuration of a typical multiplanar joint on

jacket structure 192

7.2 General loading of structural element 193

7.3 Finite element mesh of multiplanar joint 193

7.4 Finite element model of multiplanar joint 194

7.5 Stress/strain relationship 194

7.6 Nodes at intersection of chord and brace 251 195

7.7 Location of elements on chord and brace 251 195

7.8 Elements on chord (only brace 251 shown) 196

7.9 Elements on chord (only brace 251 shown) 196

7.10(a) Development of stresses around chord (joint

with all braces loaded) 197

7.10(b) Deformation of chord below brace 251 (joint

with all braces loaded) 197

7.11(a) Development of stresses around chord (joint

with only brace 251 loaded) 198

7.11(b) Deformation of chord below brace 251 (joint

with only brace 251 loaded) 198

7.12(a) Displacement at node 5478 (Y joint with brace

251 subjected to all load components) 199

7.12(b) Deformation of chord below brace 251 (Y joint

with brace 251 subjected to all load components) 199

7.13(a) Displacement at node 5478 (Y joint with brace

subjected to axial load) 200

7.13(b) Deformation of chord below brace 251 (Y joint

with brace subjected to axial load) 200

7.14 Comparison of Y joint finite element (FE) result

with test database 201

8.1 Subdivision of the tubular joint into a number of

regions suitable for mesh generation 213

8.2 Typical example of finite element mesh used to

model tubular joint 213

8.3 Details of modes of loading used for finite

element joint analyses 213

8.4 Comparison of SCFs distribution between chord

and brace under axial loading 214


and brace under in–plane bending 214


and brace under out–of–plane bending 215

8.7 Comparison of SCFs distribution between UCL

equations and FE data for axial loading (chord) 215


equations and FE data for axial loading (brace) 216


equations and FE data for in–plane bending

(chord) 216


equations and FE data for in–plane bending

(brace) 217


equations and FE data for out–of–plane bending

(chord) 217


equations and FE data for out–of–plane bending

(brace) 218

LIST OF SYMBOLS

na – Normal particle acceleration vector

AM – Annual maxima

BS – Base shear

c – Wave celerity

bC – Buoyancy coefficient

DC – Drag coefficient

LC – Lift coefficient

MC – Inertia coefficient

WC – Wind drag coefficient

WLC – Wind drag coefficient for long member

WSC – Wind drag coefficient for short member

d – Water depth

D – Diameter

BD – Brace outer diameter

CD – Chord outer diameter

eD – Outside diameter of the pipe with insulation

PMD – Cumulative damage ratio

E – Young’s modulus of steel

E – Mean square

pE – Encounter probability

EDF – Empirical distribution function

af – Nominal axial stress

bf – Nominal bending stress

Df – Drag force

If – Inertia force

Lf – Lift force

Sf – Frequency of vortex

F – Forces

FE – Finite element

FT–I – Fisher–Tippett Type I

FT–II – Fisher–Tippett Type II

FT–III – Fisher–Tippett Type III

F(x) – Cumulative probability distribution

bF – Allowable bending stress

WF – Wind force

yF – Yield stress

g – Gravity

G – Gust factor

H – Wave height

SH – Significant wave height

maxH – Maximum individual wave height

I – Turbulence intensity

IPB – In–plane bending

ID – Initial distribution

k – Wave number

KC – Keulegan–Carpenter number

L – Wave length

CL – Chord length

fL – Design lifetime of a structure

ML – Member length

M – Moments

OPB – Out–of–plane bending

OTM – Overturning moment

POT – Peak over threshold

( )XP – Probability of non–exceedance

( )xXP < – Probability that a randomly chosen observation X will

be below x

Q – Bernoulli constant

Q(X) – Probability of exceedance

Re – Reynolds number

S – Strouhal number

SS – Wave steepness

WS – Frontal area (facing the wind)

SCFs – Stress concentration factors

SWL – Still water level

t – Time

T – Wave period

RT – Return period

zT – Mean zero–crossing period associated with the extreme

storm

assT – Period associated with the design wave

u – Horizontal water particle velocity

nu – Normal relative particle velocity

tu – Tangential relative particle velocity

U – Steady velocity

CU – Current velocity

GU – Gust wind

WU – Wind speed

pV – Punching shear stress

w – Vertical water particle velocity

BWT – Brace wall thickness

CWT – Chord wall thickness

Z – Statistical constant

α – Ratio of chord length to chord radius

β – Frequency parameter

δ – Ratio of the brace diameter to chord diameter

ε – Perturbation parameter

φ – Velocity potential

ϕ – Angle between brace and chord

γ – Ratio of chord radius to the chord wall thickness

η – Free surface elevation

π – Pi

θ – Wave phase angle

ϑ – Angle around the intersection of joint

ρ – Density of steel

aρ – Air density

wρ – Water density

σ – Standard deviation

τ – Ratio of the wall thickness of the brace to that of the

chord

ω – Angular frequency

aω – Apparent angular frequency

rω – Relative angular frequency

ψ – Stream function

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Structural Model 238

B Structural Configuration 247

CHAPTER 1

INTRODUCTION

1.1 Research Significance

The demand for exploration and production of oil and gas has grown

worldwide during the past few decades in spite of its periodic down turns. As a

consequence of this general search to explore and exploit offshore energy resources,

new innovations and developments have taken place in structural form, equipment

technology, inspection, repair methodologies and economic field utilisation. Oil and

gas will continue as the most important source of energy remainder of this century

and well into the next century.

With reference to offshore production facilities, any structures employed

must perform satisfactorily under service conditions while safely enduring extreme

environmental events. Environmental loads such as wind, wave, tide, current and

marine fouling are well known to be major contributor to the loading experienced by

any offshore structures. In addition, ice and earthquake are important in some

geographical location. Being of random in nature, the environmental loads chosen as

design loads must not less than the most probable severest load in a time period of

100 years. The ability to predict accurately the extreme environmental loading

remains an important factor in the continued safe and economic exploitation of the

hydrocarbon reserves.

Secondly, the sensitivity of the structural response due to the changes in

design parameters is still not well understood. The effect of variations in the design

parameters is dependent on both the range of values considered and sensitivity of

structural design to such variations. In this study, analyses are carried out to

investigate the sensitivity of the structure response to the variations in design

parameters.

One of the features of fixed offshore structures is the problem of tubular joint

design. A global stress analysis of the overall structure resolves applied gravity

loads and environmental loads into nominal axial and bending stresses in the various

members. If local scale stress analysis is performed on tubular connection, the hot–

spot stresses near the welded intersection are found several times higher than

nominal, often exceeding yield and may cause it to collapse. The local analysis may

involve rigorous shell theory, finite element analysis or experimental stress analysis.

In this study, finite element analysis has been used to investigate local stress and

ultimate static strength of tubular joint.

1.2 Research Objectives

The main objectives of the research presented in this thesis are:

a) To develop an environmental loading model for typical jacket structure in

Malaysia’s water.

b) To study the effects of variations in design parameters on the jacket structure.

c) To determine the load capacity of a multiplanar joint.

d) To perform stress analysis on Y joint.

1.3 Outline of Thesis

This thesis consists of nine chapters begin with the introductory chapter. The

literature reviews are divided into two chapters, which is Chapter Two and Chapter

Three. The division of the literature review is essential to give the readers a better

understanding of the research topic as both chapters discuss two different topics in

depth.

Chapter Two describes in detail the methods which are available to translate a

definition of environmental conditions into the resultant steady and time dependent

forces on the structure. This chapter is concerned with describing and developing

methods of calculating these forces for fixed offshore structures.

Chapter Three discusses the behaviour of tubular joints under operating loads

and static loads. The punching shear is used as a viewpoint from which to examine

various approaches to stress analysis of tubular joints, such as thin–shell finite

elements and three dimensional isoparametric finite elements.

Chapter Four describes the structural model of a typical four legged jacket

structure and the modelling of the environmental parameters where the structure is

situated. The statistical analysis of extreme is used to estimate extreme

environmental loading experienced by the structure.

Chapter Five studies the response of the jacket structure under extreme

environmental loading conditions. Analysis procedures are discussed and the

selections of critical member for further analysis are also discussed. Results from the

structural simulation studies in term of base shear and overturning moment, and the

utilisation ratio of structural members are presented.

Chapter Six investigates the sensitivity of jacket structure to uncertainties in

parameters used in design. The parameters which considered in this study are wave

theory, force coefficients, wave height and period, current and its profile, wave–

current interaction and wind. The design parameters were varied one at a time,

within appropriate ranges, and the effects of parameters which were considered to be

the measures of static strength was calculated.

In Chapter Seven, a series of nonlinear finite element analysis was carried out

to determine both the absolute load capacity of the joint, the effect of the out–of–

plane loads and braces and relate these back to the strength of the critical brace

acting as Y joint. This study presents the analytical methods and results together

with a calibration of the analysis against test data for Y joints.

Chapter Eight describes the modelling of Y joint using finite element and is

subjected to simple loadings of the axial, in–plane bending and out–of–plane bending

types, applied separately to the joints. The stress concentration factors and its

distributions obtained from the analyses were compared with the predictions of other

previously published parametric equations.

Chapter Nine presents the overall discussion on the research works which

emphasises on the environmental modelling, structural analysis, sensitivity of jacket

structure, strength assessment of a multiplanar joint and stress concentration factor

for Y joint.

The thesis is concluded in Chapter Ten, which comprises of the summary of

the works and recommendations for further research.

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