breaking wave loads and stress analysis of jacket

Breaking Wave Loads and Stress Analysis

of Jacket Structures Supporting Offshore

Wind Turbines

A thesis submitted to the University of Manchester for the degree of

Doctor of Engineering in the Faculty of Engineering and Physical

Sciences

2012

Louise Devaney

School of Mechanical, Aerospace and Civil Engineering

2

I. Contents

I. Contents ....................................................... 2

II. List of Figures .............................................. 8

III. List of Tables .............................................. 15

IV. List of Symbols and Abbreviations .......... 17

V. Abstract ...................................................... 20

VI. Declaration ................................................. 21

VII. Copyright Statement .................................. 21

VIII. Acknowledgements ................................... 22

Chapter 1 Introduction ................................................ 23

1.1 Motivation for Research ...................................................... 23

1.2 Aims of the Project .............................................................. 24

1.3 Industrial Relevance of the Project ..................................... 25

1.4 Outline of Thesis Structure ................................................. 26

Chapter 2 Design of Offshore Wind Support

Structures ..................................................................... 27

2.1 Introduction ......................................................................... 27

2.2 Overview of Support Structure Options for Offshore Wind

Turbines ...................................................................................... 27

2.2.1 Monopiles .............................................................................................................28

2.2.2 Jackets .................................................................................................................29

2.2.3 Tripods .................................................................................................................31

2.2.4 Gravity Bases .......................................................................................................32

2.2.5 Concepts from the Offshore Wind Accelerator competition .................................33

2.2.6 Summary ..............................................................................................................37

2.3 Preliminary Design of Support Structures ........................... 37

2.3.1 Introduction ...........................................................................................................37

2.3.2 Natural Frequency Check ....................................................................................38

2.3.3 Serviceability Limit State Design ..........................................................................40

I. Contents

3

2.3.4 Ultimate Limit State Design ..................................................................................40

2.3.5 Fatigue Limit State Design ...................................................................................41

2.3.6 Areas for Further Work .........................................................................................47

2.4 Summary ............................................................................ 48

Chapter 3 Wind and Wave Loading on Monopile

Foundations ..................................................................... 50

3.1 Introduction ......................................................................... 50

3.2 Overview of Wave Theory ................................................... 50

3.2.1 Linear Wave Theory .............................................................................................51

3.2.2 Stream Function and Transfer Function Methods................................................51

3.2.3 Calculation of wave forces with the Morison equation .........................................52

3.3 Investigation into Wave Loading on a Monopile Foundation 53

3.3.1 Overview of Investigation by Luck and Benoit .....................................................53

3.3.2 Overview of Investigation into Applicability of Linear and Nonlinear Wave

Theories .............................................................................................................................56

3.3.3 Methodology .........................................................................................................56

3.3.4 Results .................................................................................................................58

3.3.5 Conclusions ..........................................................................................................62

3.4 Experiments into the Impact of Breaking Waves on a

Monopile Foundation .................................................................. 63

3.4.1 Introduction ...........................................................................................................63

3.4.2 Review of work on breaking waves ......................................................................63

3.4.3 Methodology .........................................................................................................64

3.4.4 Results .................................................................................................................68

3.4.5 Conclusion ............................................................................................................71

3.4.6 Recommendations ...............................................................................................71

3.5 Investigation into Wind and Wave Loading on a Monopile for

Two Different Turbine Capacities ................................................ 72

3.5.1 Methodology .........................................................................................................72

3.5.2 Results .................................................................................................................73

3.5.3 Conclusion ............................................................................................................78

3.5.4 Recommendations ...............................................................................................78

3.6 Summary ............................................................................ 78

I. Contents

4

Chapter 4 Review of Stress Concentration Factors for

Uniplanar and Multiplanar Tubular Joints ..................... 80

4.1 Introduction ......................................................................... 80

4.2 Development of Parametric Equations for SCFs for Tubular

Joints .......................................................................................... 81

4.2.1 SCFs for uniplanar tubular joints ..........................................................................81

4.2.2 SCFs for multiplanar joints ...................................................................................97

4.3 Development of FE Models ............................................... 103

4.3.1 Early FE models – using shells ..........................................................................103

4.3.2 Advanced FE models – solid elements ..............................................................105

4.3.3 Processing results ..............................................................................................106

4.3.4 Conclusions ........................................................................................................108

4.4 Summary .......................................................................... 108

Chapter 5 Finite Element Modelling of Uniplanar and

Multiplanar Tubular Joints ............................................ 111

5.1 Introduction ....................................................................... 111

5.2 Methodology ..................................................................... 112

5.2.1 Overview of Model Verification Process ............................................................112

5.2.2 Modelling Considerations ...................................................................................113

5.2.3 FE Model Details ................................................................................................114

5.2.4 Reporting of stresses .........................................................................................121

5.2.5 Model Verification Strategy ................................................................................122

5.3 Results of Model Verification ............................................. 122

5.3.1 Checks on the nominal stress ............................................................................122

5.3.2 Mesh Convergence Study ..................................................................................126

5.3.3 Efthymiou vs OTH ..............................................................................................128

5.3.4 FE models checked against OTH ......................................................................131

5.3.5 FE models checked against Efthymiou ..............................................................136

5.3.6 FE models checked against independent models .............................................137

5.4 Evaluation of Results ........................................................ 138

5.4.1 Summary of results ............................................................................................138

5.4.2 Potential inconsistencies in modelling approaches ...........................................139

5.4.3 Summary ............................................................................................................145

5.4.4 Conclusion ..........................................................................................................146

I. Contents

5

Chapter 6 Investigation into Effects of Loading of

Multiplanar Braces on Brace-Chord Intersection Stress

Distribution ................................................................... 147

6.1 Introduction ....................................................................... 147

6.2 Summary of SCF Calculations Using Efthymiou ............... 147

6.3 Investigation 1 – Comparison of Stresses in Uniplanar and

Multiplanar Tubular K Joints ...................................................... 150

6.3.1 Methodology .......................................................................................................150

6.3.2 Results ...............................................................................................................151

6.3.3 Conclusions ........................................................................................................156

6.4 Investigation 2 – Behaviour of Multiplanar Tubular Joints . 157

6.4.1 Introduction .........................................................................................................157

6.4.2 Methodology .......................................................................................................157

6.4.3 Results ...............................................................................................................158

6.4.4 Conclusions ........................................................................................................166

6.5 Investigation 3 – Carry-Over of Loads to Neighbouring

Braces for Multiplanar Joints ..................................................... 167

6.5.1 Introduction .........................................................................................................167

6.5.2 Methodology .......................................................................................................167

6.5.3 Results ...............................................................................................................168

6.5.4 Conclusions ........................................................................................................172

6.6 Overall Conclusion ............................................................ 172

Chapter 7 Parametric Study and Regression Analysis

to Develop Multiplanar Tubular Joint SCF Equations 174

7.1 Introduction ....................................................................... 174

7.2 Parameter Study Methodology .......................................... 175

7.2.1 Pre-processing ...................................................................................................175

7.2.2 Post-processing of data .....................................................................................178

7.3 Regression Analysis Methodology .................................... 179

7.3.1 Ranges of data for the analysis..........................................................................179

7.3.2 Modifying Efthymiou coefficients and equations ................................................182

7.3.3 Developing a new set of equations ....................................................................183

7.3.4 Validating the reliability of equations ..................................................................184

I. Contents

6

7.3.5 Development of equations for implementation ...................................................185

7.4 Results of Regression Analysis ......................................... 188

7.4.1 Selected equations .............................................................................................188

7.4.2 Factors for converting equations ........................................................................191

7.5 Comparison of final equations ........................................... 195

7.5.1 Summary of axial results ....................................................................................204

7.5.2 Summary of IPB results .....................................................................................205

7.5.3 Summary of OPB results ....................................................................................205

7.6 Evaluation of Converted Equations ................................... 206

7.6.1 Summary of results ............................................................................................208

7.7 Overall Summary, Conclusions and Future Work ............. 212

7.7.1 Overall Summary ...............................................................................................212

7.7.2 Conclusion ..........................................................................................................213

7.7.3 Further work .......................................................................................................214

Chapter 8 Design of Tubular Joints – Superposition

of SCFs to Determine Hot Spot Stresses for Multiplanar

Tubular Joints ................................................................ 216

8.1 Introduction ....................................................................... 216

8.2 Hot Spot Stress Prediction using Finite Element Analysis . 217

8.3 Hot Spot Stress Calculations ............................................ 218

8.3.1 Using the Efthymiou Equations ..........................................................................218

8.3.2 Using New Sets of Equations .............................................................................218

8.4 Results .............................................................................. 221

8.4.1 Analysis of results ..............................................................................................222

8.4.2 Overall discussion of results ..............................................................................230

8.5 Summary, Conclusions and Future Work .......................... 231

8.5.1 Summary ............................................................................................................231

8.5.2 Conclusions ........................................................................................................231

8.5.3 Future Work ........................................................................................................232

Chapter 9 Discussions, Conclusions and Future

Work ................................................................... 235

9.1 Introduction ....................................................................... 235

9.2 Wind and Wave Loading on Monopile Foundations .......... 235

I. Contents

7

9.2.1 Summary ............................................................................................................235

9.2.2 Discussion ..........................................................................................................236

9.2.3 Conclusions ........................................................................................................237

9.2.4 Future Work ........................................................................................................237

9.3 Investigation into the Behaviour of Multiplanar Tubular Joints .

......................................................................................... 237

9.3.1 Summary ............................................................................................................237

9.3.2 Discussion ..........................................................................................................239

9.3.3 Conclusions ........................................................................................................241

9.3.4 Future Work ........................................................................................................242

Appendix A – Flow chart for preliminary design of

offshore wind turbine support structures ................... 243

References ................................................................... 245

Final word count (including footnotes and end notes): 60,690

8

II. List of Figures

Figure 1-1: Offshore wind resource in Europe (taken from

http://www.wwindea.org/technology/ch02/imgs/2_2_2_img11.jpg, accessed 03.06.2012) .........23

Figure 2-1: Monopile foundation with its components and attachments (source: GL Garrad

Hassan available and online http://www.wind-energy-the-facts.org/en/part-i-technology/chapter-

5-offshore/wind-farm-design-offshore/offshore-support-structures.html) ....................................28

Figure 2-2: Diagram of jacket structure showing its features with appurtenances (source: GL

Garrad Hassan and available online http://www.wind-energy-the-facts.org/en/part-i-

technology/chapter-5-offshore/wind-farm-design-offshore/offshore-support-structures.html) .....29

Figure 2-3: Example of a cast joint taken from http://www.gusswerkstoff.de/221.jpg (accessed

25.02.2012) ..................................................................................................................................30

Figure 2-4: Diagram of tripod structure showing its features (source: GL Garrad Hassan and

available online http://www.wind-energy-the-facts.org/en/part-i-technology/chapter-5-

offshore/wind-farm-design-offshore/offshore-support-structures.html) ........................................31

Figure 2-5: Tripod used in the Global Tech 1 project in Germany taken from

http://www.owt.de/03_referenzen/pix/2009/01.jpg (accessed 19.02.2012) .................................32

Figure 2-6: Gravity base structure with appurtenances (source: GL Garrad Hassan and


offshore/wind-farm-design-offshore/offshore-support-structures.html) ........................................33

Figure 2-7: Suction bucket monopile from Universal Foundations taken from

http://www.carbontrust.co.uk/emerging-technologies/current-focus-areas/offshore-

wind/pages/foundation-design.aspx (accessed 19.02.2012) .......................................................34

Figure 2-8: Twisted jacket concept from Keystone taken from



Figure 2-9: Gravity base structure from Gifford, BMT and Freyssinet taken from



Figure 2-10: Tribucket design by SPT Offshore & Wood Group taken from



Figure 2-11: Soft to stiff frequency intervals of a three bladed, constant rotational speed wind

turbine with frequency on the x-axis and dynamic amplification factor (DAF) displayed on the y-

axis ...............................................................................................................................................38

Figure 2-12: Variation of DAF with frequency ratio, taken from Barltrop and Adams [21] ...........39

Figure 2-13: Section through weld for fabrication mismatch, taken from DNV-RP- C203 [19] ....43

Figure 2-14: Section through weld for changes in thickness, taken from DNV-RP- C203 [19] ...43

Figure 2-15: Classification of simple planar joints taken from DNV-RP-C203 [19] .....................44

Figure 2-16: Geometries for different types of joint .....................................................................45

II. List of Figures

9

Figure 2-17: Definition of geometrical parameters taken from DNV-RP-C203 [19] .....................46

Figure 3-1: Definition of wave parameters for a sinusoidal wave taken from Novak et al, 2001

[26] ...............................................................................................................................................51

Figure 3-2: Schematic for determining forced exerted on a cylinder submerged in water depth, d

.....................................................................................................................................................52

Figure 3-3: Diagram of flume with cylinder tested in the laboratories taken from Luck and Benoit,

2004 [25] ......................................................................................................................................54

Figure 3-4: Maximum and minimum measured forces on the monopile according to wave height

H, water depth d, gradient m and period T taken from Luck and Benoit, 2004 [25] ....................55

Figure 3-5: Calculated force vs. measured force (maximum and minimum) taken from Luck and

Benoit, 2004 [25]. Lines show gradients of 1, 1/2 and 1/4 ..........................................................56

Figure 3-6: Calculated force from nonlinear wave theory against measured force by Luck and

Benoit [25] ....................................................................................................................................58

Figure 3-7: Measured and calculated forces vs. wave height for water depth d = 0.3m with

maximum theoretical force represented by blue curve ................................................................60

Figure 3-8: Measured and calculated forces vs. wave height for water depth d =0.4m with





maximum theoretical force given as blue curve ...........................................................................61

Figure 3-11: Experimental setup – section through flume with cylinder and equipment .............64

Figure 3-12: Experimental setup – plan view of flume with cylinder and equipment ...................64

Figure 3-13: Experimental setup – section through flume with cylinder, ramp and equipment ...65

Figure 3-14: Section through cylinder showing wave forces applied and its equivalent static

system ..........................................................................................................................................66

Figure 3-15: Picoscope trace for wave gauges placed at two positions in the flume (see Figure

3-11) .............................................................................................................................................67

Figure 3-16: Picoscope trace for strain gauges at the top and bottom of the cylinder for non-

breaking waves ............................................................................................................................67

Figure 3-17: Picoscope trace for strain gauges at the top and bottom of the cylinder for breaking

waves ...........................................................................................................................................68

Figure 3-18: Comparison of experimental and calculated results for non-breaking waves .........69

Figure 3-19: Comparison of experimental and calculated results for breaking waves ................69

Figure 3-20: Comparison of data determined from experimental results (LCD+PKS) and the

results from Luck and Benoit (ML+MB) using linear wave theory ...............................................70

Figure 3-21: Comparison of data determined from experimental results (LCD+PKS) and the

results from Luck and Benoit (ML+MB) using nonlinear wave theory .........................................70

Figure 3-22: Graph of a comparison of hub loading experienced during operation by a 2MW and

5MW turbine from cut-in speed of 4m/s to cut-out speed of 25m/s .............................................74

II. List of Figures

10

Figure 3-23: Graph of the moments due to wind and wave loading for a 2MW and 5MW turbine

with wind speed U = 8m/s ............................................................................................................75


with wind speed U = 10m/s ..........................................................................................................75









Figure 4-1: Chord saddle SCF variation with β ratio taken from Lalani et al [46] ........................89

Figure 4-2: OPB on K-joints at brace saddle locations – comparison with FE results and SCFs

determined from simplified formulae (taken from Karamanos et al [53]) .....................................95

Figure 4-3: Configuration of KK-joints tested – note geometries – taken from Romeijn [57] ......98

Figure 4-4: Comparison between numerical and experimental hot spot strains taken from

Romeijn [57] .................................................................................................................................99

Figure 4-5: Direction of positive multiplanar modes used in van Wingerde’s analysis taken from

van Wingerde et al [54] ..............................................................................................................100

Figure 4-6: Composition of meshes in Reber’s model taken from Reber [43] ...........................104

Figure 4-7: Example of shell model using combination of 8-node and 16-node elements with

weld modelled ............................................................................................................................105

Figure 4-8: Typical weld details modelled in FE software using brick elements for tubulars and

welds taken from Choo and Qian [63] ........................................................................................106

Figure 4-9: Definition of the geometric stress zone in tubular joints taken from DNV-OS-J101

[12] .............................................................................................................................................107

Figure 4-10: Location of weld singularity for hot spot stress extrapolation dependent on element

types used in tubular joint FE models taken from DNV-OS-J101 [12] .......................................108

Figure 5-1: Weld geometry details for different brace inclinations from GL Garrad Hassan .....115

Figure 5-2: Stress extrapolation regions defined on both brace and chord of T joint in ANSYS

Workbench .................................................................................................................................115

Figure 5-3: Divisions on a uniplanar T joint to allow for different mesh density generation and

mesh symmetry taken from ANSYS Workbench .......................................................................116

Figure 5-4: Definition of stresses in welded structures taken from DNV-OS-J101 (2010) [12] .117

Figure 5-5: Meshing controls assigned to a uniplanar T joint taken from ANSYS Workbench .118

Figure 5-6: Variation in mesh sizes for different regions in the joint taken from ANSYS

Workbench .................................................................................................................................120

Figure 5-7: Types of elements available in ANSYS Workbench................................................121

II. List of Figures

11

Figure 5-8: Stress plots for T-joint under axial load with fixed scale demonstrating nominal

stress of around 0.7N/mm2 present in brace (taken from ANSYS Workbench) ........................123

Figure 5-9: Stress plots for T-joint under IPB with fixed scale demonstrating nominal stress of

around 0.8N/mm2 present in brace (taken from ANSYS Workbench) .......................................124

Figure 5-10: Stress plots for T-joint under OPB with fixed scale demonstrating nominal stress of

around 0.8N/mm2 present in brace (taken from ANSYS Workbench) .......................................125

Figure 5-11: Variation in stresses at key locations on the brace and chord under different

loadings ......................................................................................................................................126

Figure 5-12: Stress plot for fine density mesh for T joint under OPB in ANSYS Workbench ....127

Figure 5-13: Stress plot for medium density mesh for T joint under OPB in ANSYS Workbench

...................................................................................................................................................128

Figure 5-14: Plot of SCF_FE/SCF_EFT for different load cases and locations around the brace-

chord intersection .......................................................................................................................136

Figure 5-15: Geometric and local stresses for a tubular joint indicating the extrapolation points

(ECSC method) and stress jump at weld toe taken from Radenkovic (1981) [66] ....................140

Figure 5-16: Stress extrapolation points in tubular joints in accordance with the ECSC procedure

taken from Haagensen and Macdonald (1998) [67] ..................................................................140

Figure 5-17: Stress plot for T joint under OPB in ABAQUS .......................................................144

Figure 6-1: Positive axes directions applied to loadings on braces of tubular joints .................150

Figure 6-2: Joint geometry and loading used for ANSYS and Efthymiou analyses with screen-

print of joint from ANSYS Workbench showing directions of load application ...........................151

Figure 6-3: Chordside stresses for Brace A determined by Efthymiou and both uniplanar and

multiplanar ANSYS models ........................................................................................................152

Figure 6-4: Braceside stresses for Brace A determined by Efthymiou and both uniplanar and


Figure 6-5: Chordside stresses for Brace B determined by Efthymiou and both uniplanar and


Figure 6-6: Braceside stresses for Brace B determined by Efthymiou and both uniplanar and


Figure 6-7: Chordside stresses for Brace C determined by Efthymiou and both uniplanar and


Figure 6-8: Braceside stresses for Brace C determined by Efthymiou and both uniplanar and


Figure 6-9: Chordside stresses for Brace D determined by Efthymiou and both uniplanar and


Figure 6-10: Braceside stresses for Brace D determined by Efthymiou and both uniplanar and


Figure 6-11: Section through chord showing different planes and out-of-plane angle, φ, for a

multiplanar KK joint with 90º angle between planes ..................................................................157

II. List of Figures

12

Figure 6-12: Variation in braceside stress distribution in Brace A when varying IPB in Brace A

only with fixed loads applied to other braces (out-of-plane angle = 60º) ...................................158

Figure 6-13: Variation in braceside stress distribution in Brace B when varying IPB in Brace A


Figure 6-14: Variation in braceside stress distribution in Brace C when varying IPB in Brace A


Figure 6-15: Variation in braceside stress distribution in Brace D when varying IPB in Brace A


Figure 6-16: Variation in chordside stress distribution in Brace A when varying IPB in Brace A


Figure 6-17: Variation in chordside stress distribution in Brace B when varying IPB in Brace A


Figure 6-18: Variation in chordside stress distribution in Brace C when varying IPB in Brace A


Figure 6-19: Variation in chordside stress distribution in Brace D when varying IPB in Brace A


Figure 6-20: Variation in braceside stress distribution in Brace A when varying IPB in Brace A


Figure 6-21: Variation in braceside stress distribution in Brace B when varying IPB in Brace A


Figure 6-22: Variation in braceside stress distribution in Brace C when varying IPB in Brace A


Figure 6-23: Variation in braceside stress distribution in Brace D when varying IPB in Brace A


Figure 6-24: Variation in chordside stress distribution in Brace A when varying IPB in Brace A


Figure 6-25: Variation in chordside stress distribution in Brace B when varying IPB in Brace A


Figure 6-26: Variation in chordside stress distribution in Brace C when varying IPB in Brace A


Figure 6-27: Variation in chordside stress distribution in Brace D when varying IPB in Brace A


Figure 6-28: Braceside stress distribution plot for all braces with Brace A under 100kN axial load

...................................................................................................................................................168

Figure 6-29: Chordside stress distribution plot for all braces with Brace A under 100kN axial

load.............................................................................................................................................169

Figure 6-30: Braceside stress distribution plot for all braces with Brace A under 10kNm IPB load

...................................................................................................................................................169

Figure 6-31: Chordside stress distribution plot for all braces with Brace A under 10kNm IPB load

...................................................................................................................................................170

II. List of Figures

13

Figure 6-32: Braceside stress distribution plot for all braces with Brace A under 10kNm OPB

load.............................................................................................................................................170

Figure 6-33: Chordside stress distribution plot for all braces with Brace A under 10kNm OPB

load.............................................................................................................................................171

Figure 7-1: Dimensioning requirements for tubular K joints according to GL IV-2 – Taken from

GL IV-2 [69] ................................................................................................................................176

Figure 7-2: Application of loads to KK joint model in ANSYS Workbench for use in the

Parameter Set function ..............................................................................................................177

Figure 7-3: Definition of locations around brace-chord intersection for post-processing of results

...................................................................................................................................................178

Figure 7-4: Variation of SCF with each individual parameter for different values of brace

inclination, θ at location 3 braceside under axial loading ...........................................................180

Figure 7-5: SCF predictions for new equation at location 1 for braceside SCFs under axial load

with out-of-plane angle 60º ........................................................................................................184

Figure 7-6: Comparison of modified Efthymiou coefficients, modified Efthymiou equation and the

new equation against original Efthymiou for braceside stresses at location 3 under AXL load 185

Figure 7-7: Stress plot for an axially loaded brace on a multiplanar joint with out-of-plane angle

60º taken from ANSYS Workbench ...........................................................................................192

Figure 7-8: Graphs comparing SCFs from the Efthymiou equation and from ANSYS for each

parameter for braceside stresses at location 5 under axial load ...............................................196

Figure 7-9: Graphs comparing SCFs from the modified Efthymiou coefficients and from ANSYS

for each parameter for braceside stresses at location 5 under axial load .................................197

Figure 7-10: Graphs comparing SCFs from the modified Efthymiou equation and from ANSYS

for each parameter for braceside stresses at location 5 under axial load .................................198

Figure 7-11: Graphs comparing SCFs from the new equation and from ANSYS for each

parameter for braceside stresses at location 5 under axial load ...............................................199

Figure 8-1: Example joint in ANSYS Workbench indicating the brace lettering system and the

application of loads and their pattern .........................................................................................217

Figure 8-2: Variation of carry-over factor (COF) with α for Brace B braceside stresses at location

1 for axial load applied to Brace A with out-of-plane angle, φ = 60º ..........................................220

Figure 8-3: Variation of carry-over factor (COF) with τ for Brace B braceside stresses at location

1 for axial load applied to Brace A with out-of-plane angle, φ = 60º ..........................................220

Figure 8-4: Hot spot stress distribution around brace-chord intersection for braceside stresses

on Brace A .................................................................................................................................222


on Brace B .................................................................................................................................223


on Brace C .................................................................................................................................223


on Brace D .................................................................................................................................224

II. List of Figures

14

Figure 8-8: Hot spot stress distribution around brace-chord intersection for chordside stresses

on Brace A .................................................................................................................................224


on Brace B .................................................................................................................................225


on Brace C .................................................................................................................................225


on Brace D .................................................................................................................................226

15

III. List of Tables

Table 3-1: Model scale and representative size for water depths and time periods used in

investigation .................................................................................................................................54

Table 3-2: Ratio of measured force to calculated force in terms of the kd value ........................62

Table 4-1: SCF comparison of experimental techniques for axial loading with τ = 0.5, β = 0.53, γ

= 14.3, α = 13.3, θ = 90°/45°, ζ = -0.4 (Taken from Smedley and Fisher [49]) ............................90

Table 4-2: SCF comparison of experimental techniques for overlapped joint with τ = 0.5, β =

0.53, γ = 14.3, α = 13.3, θ = 90°/45°, ζ = -0.4 (Taken from Smedley and Fisher [49]) ................91

Table 4-3: Conclusions from Lloyd’s Register of Shipping [1] study ...........................................93

Table 4-4: Simplified multiplanar correction factors for CHS KK-connections taken from van

Wingerde at el [54] .....................................................................................................................101

Table 5-1: Comparison of SCFs derived using the Efthymiou equations and SCFs taken from

OTH 354 for a range of geometries selected from the database ..............................................130

Table 5-2: Geometries modelled in ANSYS Workbench with SCFs derived by Efthymiou and

obtained from FE model (Table 1 of 2) ......................................................................................132

Table 5-3: SCFs from FE, Efthymiou and OTH report [1] compared with each other for

geometries given in Table 5-2 (Table 1 of 2) .............................................................................133

Table 5-4: Geometries modelled in ANSYS Workbench with SCFs derived by Efthymiou and

obtained from FE model (Table 2 of 2) ......................................................................................134

Table 5-5: SCFs from FE, Efthymiou and OTH report [1] compared with each other for

geometries given in Table 5-4 (Table 2 of 2) .............................................................................135

Table 5-6: Comparison of SCFs for joint 3 modelled in ANSYS Workbench and ABAQUS with

each method, Efthymiou and data from the OTH report [1] .......................................................137

Table 5-7: Comparison of SCFs using different elements .........................................................142

Table 7-1: Possible sets of equations for the analysis of SCFs for multiplanar tubular joints –

note that the validity ranges can be found in section 7.3.1* B = Braceside SCFs, ^ C =

Chordside SCFs .........................................................................................................................187

Table 7-2: Factors to be applied to equations for multiplanar joints with axial load applied to one

brace only for both chord and braceside stresses .....................................................................193

Table 7-3: Factors to be applied to equations for multiplanar joints with in-plane bending applied

to one brace only for both chord and braceside stresses ..........................................................194

Table 7-4: Factors to be applied to equations for multiplanar joints with out-of-plane bending

applied to one brace only for both chord and braceside stresses .............................................195

Table 7-5: Summary of extreme values of ratio of SCFs from each equation and from ANSYS

...................................................................................................................................................200

Table 7-6: Summary of mean values of ratio of SCFs from each equation and from ANSYS and

percentage of results greater than 1 or within 10% of ANSYS ..................................................201

Table 7-7: Scores for reliability of SCFs from each equation based on maximum, minimum and

mean values for ratio EQN/ANS ................................................................................................201

III. List of Tables

16

Table 7-8: Scores for reliability of SCFs from each equation based on % of results greater than

1 and within 10% values for ratio EQN/ANS ..............................................................................202

Table 7-9: Maximum, minimum and mean values for SCF_EQN/SCF_ANS for validity range 2

...................................................................................................................................................207


...................................................................................................................................................207


...................................................................................................................................................208

17

IV. List of Symbols and Abbreviations

Greek symbols

α Geometrical parameter for joint design

β Geometrical parameter for joint design

∆σi Stress range for FLS calculations

φ Angle measured around brace-chord intersection from crown toe

φ Out-of-plane angle

γ Geometrical parameter for joint design

γ' Effective unit weight of soil

η Free surface elevation

η Usage factor

θ Brace inclination

ρ Density of water

σ Stress

σhot spot Hot spot stress

σnominal Nominal stress

τ Geometrical parameter for joint design

υ Kinematic viscosity

ξ Critical damping ratio

ζ Gap parameter for joint design

Roman symbols

A Cross-sectional area

a

Intercept of design S-N cruve with log(N) axis

a Wave amplitude

C

Chord end fixity parameter

CD Drag coefficient

CM Added-mass coefficient

d Brace diameter

D Chord diameter

D Pile diameter

d Water depth

Dfat Accumulated fatigue damage

F

Force exerted on submerged structure

g Acceleration due to gravity (9.81m/s2)

g Gap between in-plane braces for K joint

H Wave height

Hb Maximum height of breaking wave

Hmax

Maximum wave height

Hs Significant wave height

I

Second moment of area

k

Number of stress blocks

k Wave number


18

KC Keulegan-Carpenter number

L Chord length

L Wavelength

m

Gradient of slope for seabed

m Negative slope S-N curve

N3h Number of waves in a 3 hour period

Ni

Number of cycles to failure at constant stress range

ni

Number of stress cycles in block i

Re Reynold's number

SCFANS

SCF from ANSYS Workbench

SCFEft

SCF from Efthymiou

SCFp

Predicted SCF

t Brace thickness

T Chord thickness

T Time period

tref Reference thickness

Ts

Significant period of wave

U Flow velocity

U Wind speed

Um Maximum velocity of wave at still water level

Abbreviations

API American Petroleum Institute

AXL Axial

CHS Circular Hollow Section CIDECT

Comité International pour le Développment et l'Etude de la Construction Tubulaire

COF Carry-over factor

DAF Dynamic Amplification Factor

DEL Damage equivalent load

dlc Design load case

DNV Det Norske Veritas

DOF

Degrees of Freedom

DSFM Dean Stream Function Method or Fourier Theory

EDF

Electricité de France

FE Finite element

FEED Front End Engineering Design

FLS Fatigue Limit State

HAT Highest astronomical tide

HSE

Health and Safety Executive

IEC International Electrotechnical Commission

IPB In-plane bending

ISFM Irregular Stream Function Method

LIN Linear wave theory

LR

Lloyd's Register of Shipping

MTFM Modified Transfer Function Method


19

OPB Out-of-plane bending

ORNL

Oak Ridge National Laboratory

RHS

Rectangular hollow sections

SCF Stress concentration factor

SLS Serviceability Limit State

SWL

Still water line

UEG

Underwater Engineering Group

ULS Ultimate Limit State

Breaking Wave Loads and Stress Analysis of Jacket Structures Supporting Offshore

Wind Turbines

The University of Manchester Doctor of Engineering

08.06.2012 20 Louise Claire Devaney

V. Abstract

In terms of future power generation in UK and Germany, offshore wind is the next big player with 40GW [2] and 32GW [3] capacity planned for installation in both countries respectively by 2030. The latest Round 3 of sites owned by the Crown Estate explore deeper water depths of up to 78m in the Irish Sea [4]. Foundations for offshore wind structures consume around 25% of the total project cost [5] therefore the design of support structures is the subject of this thesis. The current state-of-the-art support structure options available for offshore wind turbines have been outlined in this thesis with an evaluation of the preliminary design of monopile and jacket solutions. This assessment resulted in further studies into the loading acting on a monopile foundation along with research into the fatigue design of multiplanar tubular joints for jacket structures. Mathematical modelling of linear and nonlinear waves combined with the Morison equation was completed to check the effects of breaking waves on a monopile foundation. Results indicated that measured forces were up to a factor of 2.5 times greater than calculated values, which suggests that loads could be underpredicted if the effects of breaking are not considered. The theoretical maximum wave height before breaking was then linked to wind speed and a comparison of overturning moments from the two loads was made. Wave loads dominated at water depths of around 30m for lower wind speeds but this depth decreased to around 12m as wind speeds approached cut-out of 25m/s. For deeper water depths and larger capacity turbines, jackets are the preferred design solution. Joint design in FLS is the critical aspect of jacket design with castings often required to provide adequate capacity. A review of stress concentration factors (SCF) for tubular joints indicated that the coded approach, which uses SCF equations for uniplanar joints, could be missing the multiplanar effects. Finite element (FE) modelling of multiplanar tubular joints was completed using ANSYS Workbench to examine the effects of loading in out-of-plane braces. Carry-over of stress from the loaded brace of the joint to unloaded neighbouring braces was observed which implies the importance of modelling joints as multiplanar geometries. A parameter study in ANSYS Workbench covering 1806 different geometrical configurations and loads was carried out with a regression of the data to give new sets of SCF equations for multiplanar tubular joints. SCFs from these equations were improved compared to Efthymiou but difficulties were encountered when superimposing the output (including Efthymiou). Further work on the superposition of individual load cases was therefore recommended for future work.

21

VI. Declaration

No portion of the work referred to in the thesis has been submitted in support of an application

for another degree or qualification of this or any other university or other institute of learning.

VII. Copyright Statement

i. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and she has given

The University of Manchester certain rights to use such Copyright, including for

administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents

Act 1988 (as amended) and regulations issued under it or, where appropriate, in

accordance with licensing agreements which the University has from time to time.

This page must form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other

intellectual property (the “Intellectual Property”) and any reproductions of copyright

works in the thesis, for example graphs and tables (“Reproductions”), which may

be described in this thesis, may not be owned by the author and may be owned by

third parties. Such Intellectual Property and Reproductions cannot and must not be

made available for use without the prior written permission of the owner(s) of the

relevant Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any

relevant Thesis restriction declarations deposited in the University Library, The

University Library’s regulations (see

http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s

policy on Presentation of Theses

22

VIII. Acknowledgements

I will be gratefully indebted to Phil Hoult, my industrial supervisor, and Dan Butterworth at GL

Garrad Hassan for providing outstanding, unrivalled knowledge in the field of offshore wind and

a rather unique insight in the wonderful world of engineering consultancy. Many thanks go to

Huw Traylor, Jerome Jacquemin, Fred Davison and the Excel Wizard, Nathan Muir at GL

Garrad Hassan for helping me out with the technical side of things, from programming macros

to acquiring project site data. Thanks also go to the Loads Group in GL Garrad Hassan in

particular to Andy Cordle, Tim Camp and Graeme McCann for providing support with Bladed.

I would like to thank Prof. Peter Stansby at the University of Manchester for assistance and

guidance on all things academic. Your encouragement, particularly in the last few months of the

project, was reassuring and motivated me into completing the thesis. Thanks go to Dr Tim

Stallard who helped me out with all the Matlab coding and gave sound advice on what was

required academically. I would also like to thank Armando Alexandre for buying me beer and

advising me on Matlab when it became confusing and Ashley Park for managing to fit doing

model verification in ABAQUS for me into his busy schedule. And I can’t forget to mention Prof.

Nick Jenkins, who has now moved on to Cardiff University, and thank him for organising the

project and finding sponsors five years ago.

Finally, I would like to thank the teams at ANSYS in Horsham and Sheffield for putting up with

my constant enquiries at the start of my foray into the world of FE modelling. Many thanks in

particular go to Steve Varnam and Mark Leddin who helped me with one-to-one tuition and

expertise in the Mechanical and DesignModeler components of ANSYS Workbench.

Many thanks to all you wonderful people! And not forgetting Anne, Clare, Fraser, Susie, Rob

and my mother, Anne, who have all been extremely supportive throughout the last four and half

years. Thank you!

23

Chapter 1 Introduction

1.1 Motivation for Research

With the best wind resources in Europe, as indicate in Figure 1-1, offshore wind has been put at

the heart at the UK government’s energy strategy for meeting increasing energy requirements

and to fulfil EU targets of generating 15% of the country’s total energy demand by renewables

by 2020. This has been calculated as around 40% of electricity generated in the country must

come from renewable energy meaning an eight-fold increase on the 2008 value of 5% is

required in the coming years [6]. The Carbon Trust estimates that offshore wind could

contribute to 25% of the UK’s electricity generation by 2020 [7].

Figure 1-1: Offshore wind resource in Europe (taken from

http://www.wwindea.org/technology/ch02/imgs/2_2_2_img11.jpg, accessed 03.06.2012)


24

Currently 1.3GW of operating capacity has been installed around the coast of the UK and this is

planned to increase to 18GW by 2020 and possibly to as much as 40GW by 2030 [8]. With this

huge expansion of Initial offshore wind farm projects were founded in shallow waters at

nearshore sites using monopile foundations supporting turbines with a capacity of 3.6MW. The

new Crown Estate Round 3 sites move into deeper water depths with one of the deepest sites

being in 78m of water in the Irish Sea [4], different support structure concepts need to be

implemented in order to withstand the increased wave loading on the structure. The Beatrice

Demonstrator project was one of the first projects to look into deeper waters and is founded on

jacket structures in a water depth of 45m.

With the design codes for offshore wind turbine support structures largely transferred from the

offshore oil and gas industry, potential improvements in the design methodologies could help in

the reduction of costs associated with foundation design. Offshore wind turbine support

structures are dynamic structures with additional cycle loading due to the motion of the rotor of

the turbine when comparing with offshore oil and gas structures. Current design methods for

the manned offshore oil and gas structures implement large safety factors top ensure that the

design is conservative and has adequate capacity to withstand the harsh environments out at

sea. The safety factors applied to offshore wind support structures are less generous therefore

it is important that the design methodologies are sufficient for this application.

Another factor concerning the offshore wind industry at present is the cost of the foundations.

Evaluations of current wind farms indicate that foundation costs could be as much as 25% of

total project costs [5]. A reduction of 1% in the total foundation costs could lead to significant

savings per MW – if costs of a foundation are estimated at €350k per MW (average investment

costs for Nysted and Horns Rev wind farms [9]), a reduction in 1% would lead to €3.5k per MW

or, for a 400MW wind farm, €1.4M on the total project costs. It may be such that improvements

to design methodologies could result in higher foundation costs but would prevent further

significant remedial works required if more robust structures are developed. During the

development of the project, a key design flaw has been observed with the majority of installed

monopile foundations where slippage has occurred at the grouted connection. Out of the 998

turbines installed in the North Sea in 2010 600 structures have experienced cracking in the

grouted connection which has resulted in a review of the design codes [10]. Estimates for

repairs to each structure come in at around €120,000 per turbine [10] which could have

significant cost implications to the wind farm owner. Ensuring that the support structures are

adequately designed initially could lead to project cost savings in the long term.

1.2 Aims of the Project

In short, the aim of the research is to gain a better understanding of the behaviour of offshore

wind turbine support structures and develop improved design techniques. Areas which have

been identified for improvement are outlined in Chapter 2 of the thesis after completion of a


25

review of the design methodologies currently used in the preliminary design of offshore wind

turbine support structures.

As highlighted in the previous section, design flaws have already been observed for monopile

foundations which have resulted in costly repair work. With projects moving further offshore into

deeper water depths and harsher environments, it is vital that the behaviour of wind turbine

support structures is fully understood and that the design codes are sufficient for application.

Unlike offshore oil and gas platforms, offshore wind turbine support structures are likely to be

unmanned and are therefore designed to different levels of safety as outlined in ISO 19902 [11].

Loadings on the structure also play an important role in the correct design of the structure and

any underestimate in loading could result in insufficient structural capacity.

The aims of the project are therefore:

• Evaluation of the preliminary design of state-of-the-art support structures for offshore

wind turbines highlighting areas for improvement

• Improvements to modelling of the loadings on the structure where possible

• Improvements to critical design methods highlighted from the review of preliminary

design methods

1.3 Industrial Relevance of the Project

Foundation design is a hot topic in the field of offshore wind as deeper waters begin to be

explored for the latest round of site development. Concerns with the adequacy of design codes

have been raised after reports of grouted connections for monopile structures slipping in

service. This has resulted in DNV amending its guidance on grouted connection design for

monopiles in the latest copies of the standard DNV-OS-J101 [12]. As the recommendations for

the design of offshore wind turbine support structures have been largely transferred from the oil

and gas industry, where structures are manned therefore requiring higher levels of safety, the

offshore wind industry has begun to question the validity of these codes for application to a

different design problem.

Round 3 of the Crown Estate’s offshore wind farm development sites aim to expand offshore

wind in the UK further with sites providing as much as 9GW in the case of Dogger Bank. These

new sites are being located further offshore in harsher environments therefore the correct

design of structures is vital to prevent costly repair and maintenance. Fatigue plays an

important role in the design of jacket structures and with jackets being implemented for sites

further offshore wind deeper water depths, failure of the structure through fatigue would be

difficult to monitor and rectify. A better of understanding of the behaviour of these structures is

important to ensure the success of the offshore wind industry.


26

GL Garrad Hassan has been involved in the preliminary design of support structures providing

Front End Engineering Design (FEED studies) to clients requiring jacket and monopile

structures for their wind farms. The company aims to become involved in the detailed design of

jacket structures for future offshore wind farm projects therefore knowledge on key aspects of

structural design, such as the design of tubular joints, would be build on technical competence

and provide additional tools for engineering.

1.4 Outline of Thesis Structure

The thesis covers a range of topics applicable to the design of offshore wind farms. Chapter 2

looks into the design of support structures with a short summary of support structure options

provided. The preliminary design of offshore wind turbine support structures is covered in this

chapter with a focus on monopile and jacket foundations, which are the state-of-the-art

foundation types used in offshore wind farms today and planned for future projects.

An investigation into wind and wave loading applied to a monopile foundation has been

described in Chapter 3. Experiments on a cylinder representing a monopile foundation were

completed with wind loads determined using Bladed. A comparison of overturning moments

acting on the support structure due to each individual load was made to assess the point at

which wave loads begin to dominate.

Resulting from the review of the design of support structures, the main topic for the research

was selected as multiplanar tubular joint design. Chapters 4 to 8 cover the work completed on

this subject with a literature review provided in Chapter 4 and FE modelling of tubular joints

outlined in Chapter 5. Several investigations into the behaviour of multiplanar tubular joints

were covered in Chapter 6 in order to verify that this differed from uniplanar joints. With the

carry-over effects of braces in another plane identified as a result of the study, a parameter

study for a wide range of multiplanar tubular joint configurations was planned. A regression

analysis was completed using the data from the parameter study and this is described in

Chapter 7. The equations arising from this chapter were then used to design a multiplanar

tubular joint using typical loading patterns experienced by a joint of an offshore wind turbine

jacket structure. Results and analysis of this can be found in Chapter 8.

To conclude the thesis, Chapter 9 gives an overall summary of the work completed and makes

recommendations for future work. Findings in the previous chapters are discussed and

concluded.

27

Chapter 2 Design of Offshore

Wind Support Structures

2.1 Introduction

Support structure design is one of the major topics in the field of offshore wind simply due to the

relatively large costs involved in the design and fabrication of suitable foundations. As indicated

in Chapter 1, support structures can form around 25% of the overall costs of an offshore wind

farm [5] therefore evaluation of the design could lead to reduction in project cost. Several

support structure options are available with the applicability of each dependent on site

conditions and the size of the turbine for employment.

Experience from the offshore oil and gas sector in support structure design has been transferred

across to the wind industry to provide concepts for foundations of offshore wind turbines.

Jackets, which have been predominantly used in offshore oil and gas operations, are one of the

options for exploration into deeper water depths as well as tripod foundations. For shallower

water depths, the monopile foundation has been favoured for turbines of capacity up to 5MW.

Other options are available and these will be summarised in this chapter along with the

preliminary design of monopile and jacket structures.

2.2 Overview of Support Structure Options for

Offshore Wind Turbines

As mentioned briefly in the introduction, three main support structure options have been

employed in offshore wind farm projects so far: monopiles, jackets and tripods. Other options

are available although many of these are in the conceptual stage and are as a result of the

Offshore Wind Accelerator competition by the Carbon Trust [6]. Concrete gravity base

structures have been used in some shallower nearshore projects, such as the Middelgrunden

offshore wind farm in Denmark, and have been suggested by some as an alternative to steel

construction for deeper sites [13]. Floating turbines are also being considered for deeper water

depths in Norway [14] but are unlikely to be implemented in the sites selected for the Crown

Estate’s Round 3.

Chapter 2 Design of Offshore Wind Support Structures

28

A short overview of the three main support structures will be given in this section with a

summary of other possible options arising from the Offshore Wind Accelerator competition.

2.2.1 Monopiles

For the majority of offshore wind farm projects in Rounds 1 and 2 sites owned by the Crown

Estate in the UK, the monopile foundation has been favoured as shallower water depths and

smaller capacity turbines make this structure the most cost effective solution. Monopile

foundations comprise simply a pile, which is a steel pipe driven into the seabed, transition piece

fixed into position with a grouted connection and the tower onto which the turbine is mounted.

Figure 2-1 shows a diagram of the structure and its components.

Figure 2-1: Monopile foundation with its components and attachments (source: GL

Garrad Hassan available and online http://www.wind-energy-the-facts.org/en/part-i-

technology/chapter-5-offshore/wind-farm-design-offshore/offshore-support-

structures.html)

Monopiles are typically 4m to 6m in diameter and are mostly driven into the seabed although

drilling may be required in harder ground. A transition piece is fitted to the pile once in position

by grouting between the pile outer wall and the transition piece inner wall. The tower is then

bolted into position at the work platform, which forms part of the transition piece. Grouted

connections are used to ensure that the tower and transition piece is level as there is the

possibility that the pile becomes inclined through the pile-driving process.


29

Appurtenances to the structure include boat landings, J tubes and platforms. The boat landings

and platforms are required for maintenance of the structure and turbine whereas the J tubes,

which can be external or internal, carry the cabling from the nacelle to the seabed.

Due to the size of the diameters required for monopile structures, the foundation is subjected to

scour. This is estimated at 2.5 times the diameter which, for a 6m diameter monopile, can be

significant and change the structural response if neglected. Scour protection is therefore

utilised in most cases around the pile at the seabed. This can be formed of rocks or geotextiles

around the circumference of the structure.

2.2.2 Jackets

Using the technology from the offshore oil and gas industry, jacket structures of circular hollow

sections (CHS) welded together with fabricated or cast nodes at the joints. A diagram of a

typical jacket structure can be found in Figure 2-2.

Figure 2-2: Diagram of jacket structure showing its features with appurtenances (source:

GL Garrad Hassan and available online http://www.wind-energy-the-facts.org/en/part-i-

technology/chapter-5-offshore/wind-farm-design-offshore/offshore-support-

structures.html)


30

Jackets comprise three or four legs, which can be of diameters between 864mm and 1200mm

depending on the configuration, site conditions and the capacity of the turbine used. The legs

are held together by diagonal braces which have smaller diameters and wall thicknesses than

the legs. Piles are typically driven into the seabed either through the jacket legs or by using a

template positioned on the seabed if piles sleeves or grout pins are used. As with the monopile

foundation, a grout is used to connect the jacket to the piles with shear keys provided to give

redundancy in the structure and to improve the axial capacity at the pile head. A transition

piece connects the tower to the jacket by means of bolted connections to the top flange.

The same appurtenances can be seen on jacket as for the monopile diagram given in Figure

2-1. Note that scour protection may or may not be required for the jacket configuration – this

depends on the stiffness of the soil.

Braces are connected to the legs of the jacket using either fabricated or cast nodes. For the

case of fabricated joints, the tubular sections are prepared accordingly to account for the

different weld profile around their circumferences. The brace members are then welded to the

jacket using, in most cases, a single-sided full penetration weld. If it’s not possible to achieve a

suitable fatigue life of the joint using a fabricated connection, castings can be used instead.

Cast nodes are single components which provide an improved detail in fatigue reducing the

need for complex weld details. The legs and braces are connected to the cast node by means

of circumferential welds giving a simpler connection for design. A sample cast joint can be

found in Figure 2-3 below.

Figure 2-3: Example of a cast joint taken from http://www.gusswerkstoff.de/221.jpg

(accessed 25.02.2012)


31

2.2.3 Tripods

Tripods have been used in combination with the Multibrid M5000 turbine in the Alpha Ventus

project in Germany and are basically squat versions of jackets with fewer braces. A diagram of

a tripod structure can be found in

Figure 2-4.

Figure 2-4: Diagram of tripod structure showing its features (source: GL Garrad Hassan

and available online http://www.wind-energy-the-facts.org/en/part-i-technology/chapter-5-

offshore/wind-farm-design-offshore/offshore-support-structures.html)

A central column in the tripod acts transfers the loads from the tower through diagonal braces to

the pile sleeves which carry load to the driven piles. The diagram shows that the diagonal

braces are of constant diameter. For the wind farms with tripod support structures, the braces

have tended to be conical as shown in Figure 2-5 with large diameters connecting with the

central column.

The tower is connected to the top flange of the tripod structure by bolts and a grouted

connection is used as in the case of jackets to fix the tripod level in position.


32

Figure 2-5: Tripod used in the Global Tech 1 project in Germany taken from

http://www.owt.de/03_referenzen/pix/2009/01.jpg (accessed 19.02.2012)

2.2.4 Gravity Bases

Typically used for shallow water depths, gravity bases are essentially large concrete structures

reliant upon their weight to overcome the moments and forces generated by the environment

and turbine. A diagram of a typical gravity base structure can be found in Figure 2-6.


33

Figure 2-6: Gravity base structure with appurtenances (source: GL Garrad Hassan and


offshore/wind-farm-design-offshore/offshore-support-structures.html)

The concrete structures tend to be hollow to reduce the weight of the structure for easier

transportation and installation. Seabed preparation is required in most cases to ensure that

settlement of the structure is reduced. After this stage, the gravity base is placed in position and

its hollow structure is filled with ballast providing the overall design weight. Scour protection is

essential for gravity bases due to the large diameters involved, which can be as great as 22m

[15].

2.2.5 Concepts from the Offshore Wind Accelerator

competition

Over 100 entries were submitted to the Carbon Trust’s Offshore Wind Accelerator competition

which looked into establishing innovative foundation designs that could lead to a reduction in

offshore wind farm costs by 30% [6]. From the 100 designs submitted, the following structures

were selected as viable design solutions:

2.2.5.1 Suction bucket monopile

This design solution utilises suction bucket foundations which have been implemented in the

past by the offshore oil and gas industry. Air is sucked out of the foundation once in position on


34

the seabed which creates a pressure difference causing the bucket to sink into the ground. The

design was favoured by the Carbon Trust due to its suitability for deeper waters (30m to 60m),

simple construction and installation and easy decommission. To remove the foundation, water

is pumped back into the bucket making it rise out of the ground leaving no trace.

Figure 2-7: Suction bucket monopile from Universal Foundations taken from


wind/pages/foundation-design.aspx (accessed 19.02.2012)

2.2.5.2 Twisted jacket

This concept was devised by Keystone and is a preferred solution due to the reduction in

material required. The jacket is constructed from steel and composite materials and is suitable

for water depths between 30m and 60m. A computed generated image of the structure can be

found in Figure 2-8.


35

Figure 2-8: Twisted jacket concept from Keystone taken from



2.2.5.3 Slipformed gravity base

Essentially a gravity base structure but with the advantage of being able to install the entire

structure complete with turbine resulted in this option being chosen by the Carbon Trust. A

bespoke unmanned vessel is required for installation, which can be advantageous as

bottlenecks in the supply chain with the offshore wind industry are a result of a lack of suitable

vessels. An image of the foundation option can be found in Figure 2-9.


36

Figure 2-9: Gravity base structure from Gifford, BMT and Freyssinet taken from



2.2.5.4 Self-installing tribucket

As with the gravity base structure given in section 2.2.5.3, the tribucket design from SPT

Offshore & Wood Group can be transported complete with turbine and installed using an

unmanned vessel. The structure appears to be a tripod or braced monopile with suction

buckets which allows for easy installation and decommissioning compared with piling.

Figure 2-10: Tribucket design by SPT Offshore & Wood Group taken from




37

2.2.6 Summary

At the end of 2009, the Crown Estate announced the winners of bidding for projects located in

nine different zones in waters around the UK. Round 3, as this phase of development of

offshore wind is known, ventures into much deeper waters than previous demonstrator projects.

Sites selected for Round 3 explore deeper waters with the greatest water depth of up to 78m in

Zone 9 in the Irish Sea [16]. The majority of wind farms operating in the UK are founded on

monopiles in water depths of up to 23m [4] (Thanet Offshore Wind Farm) however limitations

may exist on the practicalities of implementing such foundations in deeper waters. The

contribution from waves on overturning moments increases with depth therefore suitable

monopile diameter sizes for providing adequate resistance could become unfeasible.

Offshore wind turbines on jacket structures have been built as demonstrator projects in the UK

(Beatrice) and Germany (Alpha Ventus). The Beatrice demonstrator project was constructed in

a water depth of 45m and supports a REpower 5M turbine. With jackets and monopiles being

established solutions for offshore wind turbine support structures, the preliminary design of

these structures will be covered in this chapter to gain a better understanding of the design

processes required. The other solutions provided in the preceding section are innovative

concepts and are yet to be implemented in major projects therefore there is a degree of

uncertainty about the viability of the designs for up and coming projects.

2.3 Preliminary Design of Support Structures

2.3.1 Introduction

GL Garrad Hassan has been involved in the preliminary design of support structures including

monopiles, jackets, tripods and gravity bases. At FEED (Front End Engineering Design) study

level for steel structures, primary steel member sizes are estimated based on the requirements

set out in the appropriate design codes for Serviceability Limit State (SLS), Ultimate Limit State

(ULS) and Fatigue Limit State (FLS). This section intends to give a brief overview of the design

requirements for jacket and monopile foundations in SLS, FLS and ULS. For further details,

please refer to the flow chart provided in the appendix.

Note that the analysis completed for both monopiles and jackets uses a static analysis with

dynamic amplification factors applied to convert from a static to a dynamic design solution. An

integrated approach to the design of wind turbine support structures is possible using

commercial software such as Bladed or FLEX 5 which allow for a time series approach. Design

codes used in the analysis include IEC 61400 [17] for load cases, API RP 2A [18] and DNV

standards DNV-RP-C203 [19] for fatigue analysis recommendations and DNV-OS-J101 [12] for

general offshore support structure design.


38

2.3.2 Natural Frequency Check

When designing an offshore wind turbine support structure, it is important that the structure itself

has a natural frequency which falls into the frequency ranges specified by the turbine

manufacturer. These frequency ranges are so defined to account for the frequency of one

blade and all three blades of the turbine completing a full rotation, otherwise known as the 1P

and 3P frequencies respectively. If the structure’s natural frequency approaches either of these

frequencies, the risk of amplification of the structure’s response increases therefore leading to

potential failure. This dynamic amplification linked to rotor frequencies is demonstrated in

Figure 2-11 below.

Figure 2-11: Soft to stiff frequency intervals of a three bladed, constant rotational speed

wind turbine with frequency on the x-axis and dynamic amplification factor (DAF)

displayed on the y-axis

The DAF represents the ratio of the dynamic response and the static response magnitudes due

to an applied loading [20]. As resonance is approached, the value of DAF tends towards higher

values depending on the level of damping present in the structure. For structures with little or

no damping, the DAF will head towards infinity, whereas heavily damped structures will

experience minimal amplification effects. Figure 2-12 taken from Barltrop and Adams, shows the

variation of DAF with regards to the frequency ratio for different levels of damping, ξ [21].


39

Figure 2-12: Variation of DAF with frequency ratio, taken from Barltrop and Adams [21]

The three ranges considered for support structure design are:

1. Soft-soft - Very flexible structure with low natural frequency. Few structures are

designed to fall into this category as it can be difficult to achieve the required

frequency with sufficient structural integrity due to the small frequency window.

2. Soft-stiff - Most offshore wind turbine support structures are designed to fall into the

soft-stiff frequency range. Structures have a degree of flexibility to them without

compromising strength.

3. Stiff-stiff - The natural frequency of a stiff-stiff structure would be above the 3P limit

resulting in an inflexible, stiff structure.

The soft-stiff region of the graph in Figure 2-11 has been aimed for with regards to the natural

frequency of the monopile structure. The natural frequency of the structure will be required to

fall into a frequency range of 0.25 to 0.35Hz.

Estimates of the structure’s dimensions (diameter, wall thickness and member lengths) as well

as geometrical configuration for a jacket structure (number of bays, legs and braces) need to be

made to give an initial structure for further iterations. Structural analysis packages can be used

to evaluate the mode shapes of the given structure. To ensure that the mode shapes are

calculated correctly, the soil strata need to be modelled using p-y springs for both monopiles

and jackets with additional t-z and q-z springs for jacket structures. P-y springs represent the


40

soil’s lateral resistance which is key for monopile structures due to overturning moments

creating lateral loads dominating the loading on the structure. Jacket structures are axially

dominated structures therefore t-z and q-z springs need to be considered. For all springs, the

resistance of the soil, either p, t or q, is determined for a deflection in the y or z directions and

then a suitable equivalent spring stiffness calculated.

2.3.3 Serviceability Limit State Design

For SLS design, extreme loads are modelled and capacity checks are carried out. A partial

safety factor of 1 applies to all environmental loads.

For SLS design, the ability of the pile to carry service loads, or extreme unfactored loads, is the

key design aspect for consideration. Using LPile with the overturning moment and shear forces

determined for the extreme loading situation, checks on the top deflection with regards to

embedment length were completed. An optimisation of the pile design was carried out checking

different embedment lengths and the deflection imposed at the seabed.

The pile needs to have enough capacity to withstand and provide lateral resistance against the

overturning moments and shear forces generated by the wind and wave loading. Two

requirements as outlined in the standard need to be achieved to ensure that the pile can

function under lateral loading [12]:

1. Total lateral pile resistance should be greater than the design lateral load

2. Lateral displacement at the pile head should not exceed some specified limit

A value for the maximum lateral displacement at the seabed and also set criteria for checking

the embedment length is typically selected by the designer based on previous experience.

2.3.4 Ultimate Limit State Design

The aim of ULS checks on jacket and monopile structures is to determine the overall strength of

the structure and its capacity to sustain the extreme loading it’s exposed to. Extreme loads

determined in the SLS analysis can be used however for a more detailed analysis using

software packages like Bladed or Flex5, the following design load cases (dlc) taken from IEC

61400 [17] can be used:

• IEC dlc1.6a – normal wind turbulence model with severe sea state under power

production

o Two wind speeds used – optimum operating speed and maximum operating

speed (12m/s and 30m/s)

o Turbulence intensity calculated to IEC 61400 Part 3


41

o Maximum significant wave height and significant time period for waves

o Additional constrained wave in the Bladed model corresponding to the severe

wave height

• IEC dlc2.1 – normal wind turbulence model with normal sea state under power

production with turbine faults

o Same wind speeds and turbulence intensities as IEC dlc1.6a

o Significant wave heights and time periods correspond to hub wind speeds

o Turbine faults included such as blade pitch seizure and yaw errors

• IEC dlc6.1a – Extreme turbulent wind model with extreme sea state under idling

condition

o Turbine not in operation therefore idling condition needs to be specified in

Bladed

o Maximum wind speed used for the site with different directionality to account for

yaw error – 50 year 1 hour value

o Maximum significant wave height factored to give extreme sea state

o Waves travelling in different directions

o Also includes a constrained nonlinear extreme wave corresponding to the

extreme wave height

A series of checks are carried out in order to determine the reaction of the structure to axial,

bending and shear loading. Design checks can be carried out to DNV-OS-J101 with safety

factors of 1.35fγ = applied to environmental loads [12].

To summarise, the main checks completed under ULS involve individual members’ resistance to

bending and buckling. The various criteria are provided in the flow chart in Appendix A. An

optimisation of member wall thickness is generally the preferred approach as this does not

affect the level of loading on the structure. Increasing member diameters attracts a larger wave

load and is avoided unless a wall thickness optimisation has proved unsuccessful.

For jacket design, ULS tends not to be the critical design consideration as the members in the

structure do not attract large bending moments in comparison to a monopile structure. The

large overturning moments generated by wave forces on a monopile structure means that ULS

design plays a bigger role in the selection of sectional sizes. A proficient understanding of the

wave loads acting on the structure is therefore particularly important in the case of the monopile.

2.3.5 Fatigue Limit State Design

FLS design considers the resistance of the structure to typical normal loads during its entire

lifetime, which can be 20 or 25 years depending on the selected turbine. Fatigue is highly

important in the design of offshore wind structures due to the cyclic nature of the loading

exerted on the structure. The key design features which are likely to succumb to fatigue are the


42

welds between sections and any appurtenances or discontinuities in the structure such as holes

and thickness changes. For jacket structures, the resistance of tubular joints to axial and

bending loads is critical for FLS design.

DNV-OS-J101 [12] and DNV-RP-C203 [19] are used in conjunction with one another to

establish the combined fatigue life of the welds and other stress concentrators down the length

of the structure. DNV-OS-J101 [12] gives a brief overview of determining the fatigue life checks

using S-N curves with DNV-RP-C203 [19] adding further information about detailed fatigue

analysis.

Fatigue failure occurs when a material is cyclically loaded up to the point at which crack growth

occurs through the thickness of the material. The basis for analysis has been obtained from

laboratory testing on samples of structural steel under cyclic loading where the steel has been

repeatedly stressed until failure occurs. S-N curves have been developed from this data for

fatigue failure which look at the 97.6% rate of survival for structural steel with thickness, tref of

25mm for welded connections other than tubular connections, 32mm for tubular connections

and 25mm for bolts [19]. S-N curves are given for the three main scenarios with which this

project concerns [19]:

• Structural steel cyclically-loaded in air

• Structural steel cyclically-loaded in seawater with cathodic protection

• Structural steel cyclically-loaded but susceptible to free corrosion

Assessment of the effect of fatigue loading on the structure is the summation of the fatigue

damages on individual variable stress ranges according to Palmgren-Miner’s damage rule [19]

as given below.

( )1 1

1k kmi

fat i i

i ii

nD n

N aσ η

= =

= = ∆ ≤∑ ∑ (2-1)

Where Dfat is the accumulated fatigue damage, a is the intercept of the design S-N curve with

the logN axis, m is the negative slope of the S-N curve, k is the number of stress blocks, ni is

the number of stress cycles in stress block i, Ni is the number of cycles to failure at constant

stress range ∆σi and η is the usage factor.

The loading on the structure is interpreted from wind and wave scatter tables with the wave data

split into a number of design waves, from which a stress range can be determined for members

and joints in the structure. For wind loading, information can be taken from the turbine

manufacturer’s specification usually in the form of damage equivalent loads (DELs) for 2x106

cycles for the lifetime of the turbine. Alternatively, as with ULS design, Bladed or Flex5 can be

used to complete a rainflow cycle count with the following dlcs taken from IEC 61400 [17]:


43

• IEC dlc1.2 – Normal operation under power production

o Range of wind speeds from cut-in speed at 4m/s to cut-out speed at 30m/s

o Different turbulence intensities calculated according to IEC 61400 Part 3

o Combined wind and wave scatter table used therefore several waves with

different properties for each wind speed

• IEC dlc6.4 – Turbine on standby with normal turbulence model and normal sea state

o Two wind speeds above and below cut-out and cut-in wind speeds respectively

o Wave scatter table linked to wind speeds

o Wind and wave directionality varies

Stress concentration factors, or SCFs, apply to any misalignments, changes in thickness or

holes, appurtenances or discontinuities in the structure including tubular joints. SCF is defined

as the ratio of the hot spot stress range over the nominal stress range [19]. With Class D welds,

SCFs need to be ascertained for thickness correction and fabrication and thickness mismatch.

Diagrams of these discontinuities can be found in Figure 2-13 and Figure 2-14.

Figure 2-13: Section through weld for fabrication mismatch, taken from DNV-RP- C203

[19]

Figure 2-14: Section through weld for changes in thickness, taken from DNV-RP- C203

[19]


44

For tubular joints, the Efthymiou equations [22, 23], which are available in [19], are used to

determine SCFs. Tubular joints are defined by the pattern of loading applied to the connection

and not by the geometrical configuration as indicated in Figure 2-15 below.

Figure 2-15: Classification of simple planar joints taken from DNV-RP-C203 [19]

For each joint configuration, as given in Figure 2-16, a set of equations for SCFs apply for axial,

in-plane bending (IPB) and out-of-plane bending (OPB) load cases. The SCF equations are

dependent on geometrical parameters as indicated in Figure 2-17.


45

Figure 2-16: Geometries for different types of joint

(a) KT joint

(b) T/Y joint (c) T joint

(e) K joint

(d) X joint


46

Figure 2-17: Definition of geometrical parameters taken from DNV-RP-C203 [19]

To determine the hot spot stress range on the structural detail, the nominal stress range is

factored by the SCF.

hot spot nominalSCF.σ σ= (2-2)

This value is then used along with a suitable S-N curve in the Palmgren-Miner rule, as given in

equation 2-1, to calculate the anticipated fatigue damage. In order for the structure to fulfil FLS

requirements, the value of the damage needs to be less than 1. If the value for damage is

greater than 1, the fatigue life can be extended by grinding the welds or by increasing the

β = d/D

α = 2L/D

γ = D/2T

τ = t/T

βA = dA/D

τA = tA/T

ζ = g/D

βB = dB/D

τB = tB/T


47

thickness of the section. For tubular joints, different methods of fabrication can improve the

fatigue life such as use of castings instead of welded joints. For changes to the design detail,

different S-N curves are used to account for the changes in material properties, for example.

2.3.6 Areas for Further Work

2.3.6.1 Support structure concepts

As mentioned briefly at the start of the chapter, scope is available for innovation in terms of

support structure design with the aim of reducing costs of the foundations, which has been

highlighted as a problem for offshore wind farm projects. With technology transferred from the

oil and gas industry and the additional dynamic loadings on an offshore wind turbine support

structure resulting from the motion of the rotor, new and innovative concepts may be more

appropriate for this new application. The Carbon Trust devised a competition to encourage

engineers working in the industry to submit new and innovative support structure designs with

the aim of reducing foundation costs by 30% [6]. With over 100 designs submitted, many

concepts are available therefore making it potentially difficult to devise an original and

innovative concept. Improvements to current support structure concepts have therefore been

recommended for this thesis as opposed to developing an original support structure design.

2.3.6.2 Loadings on structure

Ensuring that the correct loadings are determined for the structure is particularly important for

extreme loads in SLS and ULS as underestimates could result in inadequate structural capacity

or a an over-engineered design. Insufficient axial capacity has already been observed for a

large number of offshore wind farms founded on monopile support structures therefore

highlighting the possibility that loads could be underestimated. An area for assessment covered

in this thesis concerns the combined wind and wave loading on a monopile foundation with an

evaluation of breaking waves on the structure.

Due to the high costs of constructing and operating an offshore wind farm, areas in which cost

savings could be made are of interest to the industry. In conjunction with GL Garrad Hassan’s

Offshore Group, a paper [24] looking into the potential cost savings in support structures due to

different methods of modelling wake effects was published for the European Wind Energy

Conference in Warsaw in April 2010. An alternative method for calculating turbulence

intensities using the Frandsen method was carried out – the Park method is usually used in

such calculations. The resulting turbulence intensities were used to perform a preliminary

design of a jacket structure in FLS for a 5MW turbine.

A wall thickness optimisation was completed using the DELs resulting from the loads

calculations for wind data using both the Frandsen and Park turbulence intensities. The two


48

jacket structures were compared for differences in weight and it was observed that a 7%

reduction in primary steel was possible when using the Frandsen method. Further information

on this short study can be found in the conference paper [24].

2.3.6.3 FLS design

With deeper water depths being explored for the latest Round 3 sites of the Crown Estates

offshore wind farm developments, a shift towards jacket and tripod as selected foundation

structures can be observed. From the preliminary design of jacket structures it was noted that

these structures are fatigue sensitive and the dimensioning of members is dependent on FLS

design. For the design of tubular joints in FLS, difficulties were observed gaining adequate

resistance to fatigue loading when considering a fabricated joint and therefore castings were

used instead.

An assessment of the existing design equations by Efthymiou provided in the DNV design

standards [12, 19] indicate that the equations concern uniplanar joints only. The joints forming

the jacket structure supporting an offshore wind turbine comprise multiplanar tubular joints

therefore the behaviour of these structures could differ to uniplanar configurations. As indicated

previously, offshore wind turbine support structures are unmanned and therefore require a lower

level of safety compared with offshore oil and gas platforms. The reduction in partial safety

factors and the use of uniplanar SCF equations could lead to the incorrect design of the

structure in fatigue therefore further investigation into the effects of multiplanar loading on

tubular joints is recommended.

2.4 Summary

A range of support structures for offshore wind turbines are available with the viability of each

foundation type dependent on site conditions. Generally monopiles and gravity bases are the

preferred solution for shallower water depths with gravity bases more likely to be used for sites

with favourable ground conditions. As deeper waters are explored, the feasibility of monopiles

reduces as large diameters are required to withstand the increased overturning moments from

waves. Pile sizes are restricted by the equipment available for installation, such as pile driving

hammers, and fabrication. For deeper water sites and larger capacity turbines, jacket and tripod

structures become viable design solutions. Other innovative designs are available however the

feasibility of concepts such as the twisted jacket as given in Figure 2-8 on page 35 is still being

examined at present. The preliminary design of established solutions was therefore covered in

the thesis.

Offshore wind turbine support structures need to be designed to suitable standards such as

DNV or Germanischer Lloyd for compliance in SLS, ULS and FLS. For both monopile and

jacket structures, the following applies:


49

• Design checks to SLS determine the pile design such as embedment length

• Member sizes (diameters generally) are established by ULS design checks

• Wall thicknesses of sections depend on FLS

Monopile structures are subjected to large overturning moments and their design is

predominantly governed by ULS member checks. FLS dominates for jacket design due to the

number of welded joints in the structure. Due to the sensitivity of the joints in fatigue, it is not

always possible to use simple fabricated details for jackets with casting often used to provide

sufficient FLS capacity. Research into the improvement of joint design for tubular structures is

therefore recommended as a direction for the research in this thesis. Studies into the modelling

of waves on the support structures have also been completed to check the validity of application

of theory to a monopile foundation.

50

Chapter 3 Wind and Wave

Loading on Monopile Foundations

3.1 Introduction

As mentioned previously in Chapter 2, a variety of support structure options are available for

offshore wind turbines, the simplest of these, in terms of design and fabrication, being the

monopile foundation. A short study in response to experiments on wave loading on monopiles

[25] was completed checking the validity of linear and nonlinear wave theory combined with

Morison equation to model the effects of wave impact on monopile structures. It was noted that

the waves used in the experiment were likely to be predominantly breaking waves, which led to

an increase in load on the structure, therefore experimental work checking the impact of

breaking waves on a cylinder was carried out. Breaking and non-breaking waves were

generated in the flume in the Hydraulics Laboratory at the University of Manchester and were

compared against forces resulting from using linear and a nonlinear Fourier series stream

function wave theory combined with the Morison equation.

Further work was then completed linking the maximum possible wave heights to wind speed for

a range of water depths from shallow water depth of 5m up to water depth of 60m. The Miche

criterion was used to establish the maximum wave height before the wave breaks relative to the

wind speed to give the overturning moment applied to the monopile. Using the operational wind

speeds, a Bladed analysis was completed for two different turbine capacities supported on a

monopile structure. The overturning moment at hub height was taken from the Bladed output

and compared against the plots for the moment due to waves.

3.2 Overview of Wave Theory

The motion of a wave can be described using linear or nonlinear wave theories which give the

wave’s profile and particle velocities and accelerations. Understanding the wave’s kinematics

allows for the determination of the force it exerts on the submerged structure. The process of

analysing the wave’s behaviour is the same for both linear and nonlinear methods but the

complexity of the approach increases with the nonlinear methods. For linear theory, simplifying

assumptions reduce the steps of the calculation of the wave’s motion which can lead to less

accurate results depending on how well the wave’s profile matches a sinusoidal form.

Chapter 3 - Wind and Wave Loading on Monopile Foundations

51

3.2.1 Linear Wave Theory

Regular waves which are sinusoidal in shape can be modelled by using linear wave theory, also

known as Airy waves. An example of a linear wave with definition of wave characteristics can

be found in Figure 3-1.

Figure 3-1: Definition of wave parameters for a sinusoidal wave taken from Novak et al,

2001 [26]

Where H is the wave height, a is the wave amplitude, η is the free surface elevation and L is the

wavelength

The simplifying assumptions in the derivation of the theory mean that the surface profile of a

wave, wave number and other characteristics can be calculated without too much difficulty.

Linear wave theory is considered to be sufficient for modelling most waves associated with

engineering purposes and is a good theory to build on when modelling ocean waves, however

as the steepness of the wave, H/L, increases, nonlinear approaches may be more necessary

[26, 27].

Linear wave theory is most suited to deeper water depths and smaller wave heights where the

motion of water particles in the wave is considered to be more regular. The theory goes on the

assumption that the particle velocities of the wave can be modelled as sinusoidal functions and

this gives a good approximation for deep ocean waves. Where the theory falls down is in the

evaluation of shallow and intermediate water depths or with wave heights that are comparatively

large to the water depth. In these situations, the surface elevation changes from a sinusoidal

shape to

3.2.2 Stream Function and Transfer Function Methods

Several nonlinear wave theories were adopted for the investigation by Luck and Benoit [25]

where stream functions and transfer functions were used to define sets of nonlinear equations.

The theories covered in [25] include Dean Stream Function Method or Fourier Theory (DSFM)

H y

x

η a

L

L

Still Water Line, SWL


52

[28-30], Modified Transfer Function Method (MTFM) and Irregular Stream Function Method

(ISFM). Whereas linear theory uses a number of simplifying assumptions to reduce the particle

velocity and surface profile expressions to sinusoidal functions, the various nonlinear methods

use stream functions or velocity potentials to satisfy Laplace’s equation and the boundary

conditions (kinematic and dynamic free surface) [31]. This results in more complex equations

for implementation but can lead to better predictions of the wave’s surface profile particularly for

shallow to intermediate water waves with steeper profiles.

3.2.3 Calculation of wave forces with the Morison

equation

A suitable model to represent the submerged part of the monopile is a cylinder of diameter D

positioned vertically in a depth of water, d. The cylinder is split into a finite number of sections

suitable enough to adequately model the effects of the wave on the structure as Figure 3-2

shows.

Figure 3-2: Schematic for determining forced exerted on a cylinder submerged in water

depth, d

Where U is the flow velocity of the wave and F is the force exerted on the structure for an

element size of dz

The number of elements selected affects the reliability of the results therefore the larger number

of elements, the more accurate the result with convergence for large enough numbers. Each

section is analysed individually and the sum of the forces for each section calculated to give the

overall load on the monopile.

To calculate the force on the cylinder, the particle velocities and accelerations associated with

the wave need to be calculated using either a linear or nonlinear method as outlined previously.

dz

F

n divisions

U

SWL

d


53

The Morison equation as given below [26] uses these velocities and accelerations over the

period of the wave to determine the force on a section of the cylinder:

dt

duDCuDuC

dy

dFMD

i

42

2ρπρ+=

(3-1)

where CD is the drag coefficient and CM the added mass coefficients associated with cylinder, D

is the diameter of the cylinder and ρ is the density of water, which can be assumed to be

1000kg/m3 for freshwater and 1025kg/m

3 for seawater.

The analysis is carried out for different positions along the length of the submerged cylinder

upon which the wave acts. Particle velocities and accelerations are calculated for each section

of the cylinder with the wave force according to Morison calculated. The total load acting on the

cylinder is the summation of the force for each section examined.

3.3 Investigation into Wave Loading on a

Monopile Foundation

3.3.1 Overview of Investigation by Luck and Benoit

A paper published by Luck and Benoit [25] in 2004 detailing a study carried out in Electricité de

France’s (EDF) laboratories was the basis for this investigation. A series of experiments were

carried out by Luck and Benoit on a model scale (1:25 geometric, 1:5 for time and velocity)

cylinder in a flume representing a monopile driven into a 2.5% or 5% slope nearshore sea bed.

Waves of varying wave heights and time periods were propagated towards the cylinder in

different water depths and the maximum and minimum forces and surface profiles of the waves

were recorded. The type of wave also varied throughout the investigation with breaking, non-

breaking and post-breaking waves generated in the laboratory. The following water depths and

time periods were used in the experiment:


54

Model Scale Full Scale

Wate

r dep

th,

d [m

]

0.3 7.5

0.4 10

0.6 15

0.8 20

Tim

e p

eri

od,

T [s]

1.6 8.0

1.8 9.0

2.1 10.5

2.4 12.0

Table 3-1: Model scale and representative size for water depths and time periods used in

investigation

A schematic diagram of the flume containing the monopile can be found in Figure 3-3.

Figure 3-3: Diagram of flume with cylinder tested in the laboratories taken from Luck and

Benoit, 2004 [25]

As Figure 3-3 shows a cylinder of 0.2m diameter was placed in a flume at a height of 0.4m from

the base. This model size equates to a full scale diameter of 5m.

Results show the total maximum and minimum horizontal force on the cylinder graphically as

given in Figure 3-4.


55

Figure 3-4: Maximum and minimum measured forces on the monopile according to wave

height H, water depth d, gradient m and period T taken from Luck and Benoit, 2004 [25]

Luck and Benoit assessed the results of the experiment and compared them with the following

theories [25]:

1. Linear theory (LIN)

2. Dean Stream Function Method or Fourier Theory (DSFM)

3. Modified Transfer Function Method (MTFM)

4. Irregular Stream Function Method (ISFM)

The results of the analyses using linear and nonlinear methods are given in Figure 3-5 which

shows plots of the measured forces on the cylinder against the calculated values. From

examination of the graphs, it appears that the measured forces from the non-breaking waves

are between one or two times the calculated forces. Breaking wave conditions give forces

anywhere between three times the calculated values and one times the calculated load

depending on the wave theory used.


56

Figure 3-5: Calculated force vs. measured force (maximum and minimum) taken from

Luck and Benoit, 2004 [25]. Lines show gradients of 1, 1/2 and 1/4

3.3.2 Overview of Investigation into Applicability of

Linear and Nonlinear Wave Theories

Using the data provided in Luck and Benoit [25], a series of calculations using linear Airy wave

theory and modified nonlinear Fourier series method were used to check the load applied to the

structure. It is not clear in the publication which results given in [25] correspond to the forces

from breaking, non-breaking and post-breaking waves provided in Figure 3-5. For the purpose

of application of wave theories, non-breaking waves are assumed.

3.3.3 Methodology

Two FORTRAN programs modelling linear wave theory (Airy waves) and nonlinear wave theory

(SAWW_FORCE by Buss and Stansby [32]) were used to calculate the forces on a cylinder to

Morison’s equation. Each program carries out a series of iterations in order to determine the


57

wave number which is then used in subsequent iterations to calculate the force on the cylinder.

The output from each program gives the force, moment and line of action at regular intervals

over one time period. Maximum and minimum measured forces were determined from the

graphs shown in Figure 3-4 with corresponding values for wave height measured.

Both the linear and nonlinear wave programs were run with experimental data for all water

depths. To be able to calculate the force from Morison’s equation, the correct drag and added

mass or inertia coefficients need to be identified. Inertia coefficients relate to added mass

coefficients with the following relationship:

1−= ma CC (3-2)

To determine both coefficients, the Keulegan-Carpenter number (KC) was estimated for the fluid

flow. The nonlinear program, SAWW_FORCE, was initially run using the drag and inertia

coefficients as stated in the Luck and Benoit paper (2004) with Cd ≈ 0.7 and Cm ≈ 1.8 [25].

Maximum velocities were extracted from output data files therefore allowing Reynold’s number

and the Keulegan-Carpenter to be calculated.

D

TUKC m=

(3-3)

ν

DU m=Re (3-4)

Where Um is the maximum velocity of the wave at still water level, T is the time period, D is the

diameter of the member and ν is the kinematic viscosity of the fluid.

Sarpkaya [33] gives information on how to determine the drag and inertia coefficients of flows

around cylinders using graphical methods. β-values for a given flow and cylinder need to be

calculated in order to ascertain which graph should be used. This parameter can be calculated

as follows:

KC

Re=β

(3-5)

β-values for the test data range between 25000 and 16667 therefore the graph with a β-value of

18000 was selected as the mean value for the data examined. Approximate values for both

coefficients were determined from the graph as Cd = 0.5 and Cm = 2.0 for the KC range of 3.1 to

25.3.


58

3.3.4 Results

Both linear and nonlinear theories were compared with one another and with the experimental

results from Luck and Benoit. A graph of measured force against calculated force was

developed in order to check whether there was much variation in these forces. Figure 3-6

below shows this variation with graphs of y = x, y = 0.5x and y = 0.25x plotted to show the range

of results.

Figure 3-6: Calculated force from nonlinear wave theory against measured force by Luck

and Benoit [25]

As Figure 3-6 shows, nonlinear theory tends to underestimate the force exerted on a cylinder

with most forces being between 1 and 0.5 times the value of the measured force. Results which

are underpredicted can be assumed to fall within the breaking or post-breaking waves category

however, as mentioned previously, it is not clear from Luck and Benoit’s report which points

correspond to these wave types.

Using the Miche criterion, it was possible to identify the maximum possible wave height before

the wave breaks to help identify which waves given in the Luck and Benoit paper were breaking.

The Miche criterion is as follows [34]:

y = x

y = 0.5x

y = 0.25x


59

)tanh(142.0 kdLH b = (3-6)

Where Hb is the maximum wave height before breaking, k is the wave number, L is the

wavelength and d is the water depth

The theoretical maximum wave height was then used for a range of wave in each of the water

depths given to determine the maximum force exerted on the structure. Graphs were plotted

with this information and compared against the data from the Luck and Benoit paper to check

which waves could be considered to be breaking and non-breaking. Figure 3-7, Figure 3-8,

Figure 3-9 and Figure 3-10 show graphs of the results with the blue curve the line of best fit for

the maximum possible force and wave height without waves breaking.

As the graphs show, nearly all measured results are positioned well above the theoretical

maximum line. Experimental measured data points are shown as pink markers of varying

shape for different time periods with nonlinear results given as green data points. The

exception appears to be when the wave height is small for the water depth although data points

seem to be dotted in random places especially with shallow water depths. The measured set of

data closest to the calculated values is for the water depth of 0.8m where the majority of the

experimental points are within 1.5 times that of the theoretical values achieved from

SAWW_FORCE program [32].


60


maximum theoretical force represented by blue curve

Figure 3-8: Measured and calculated forces vs. wave height for water depth d =0.4m with



61



Figure 3-10: Measured and calculated forces vs. wave height for water depth d = 0.8m

with maximum theoretical force given as blue curve


62

Ratios of the measured to calculated force were determined by grouping values in terms of the

wave property, kd. The following maximum values were established for the data set:

kd Fmeas/Fcalc

0.50 2.9

0.75 2.5

1.00 2.3

1.25 1.8

1.50 1.1

Table 3-2: Ratio of measured force to calculated force in terms of the kd value

For shallower water depths, or lower wave numbers, the measured and calculated forces were

nearly three times different (measured force three times larger than calculated). As the water

depth increases, this reduces to almost unity indicating that waves in this region may not be

breaking and that nonlinear wave predictions are reasonable.

3.3.5 Conclusions

For shallow water depths, calculated forces for waves modelled with nonlinear theory are up to

a third smaller than those measured. Deeper water depths give better results with the ratio of

measured and calculated wave forces between 1.1 and 1.8. This indicates that the nonlinear

wave theory implemented in the SAWW_FORCE program by Buss and Stansby [32] gives

reasonable predictions of the force exerted on a cylinder for deeper water depths. What also

can be inferred from the analysis is that breaking waves may increase the force predictions from

the Morison equation by up to a factor of three.

The experiments carried out by Luck and Benoit involved breaking, non-breaking and post-

breaking waves. From the information provided in the publication [25] it is difficult to establish

which data points are for the breaking and non-breaking waves. Differences in forces

determined by nonlinear wave theory in the SAWW_FORCE program and the measured values

are likely to be as a result of waves breaking on the cylinder. Forces exerted on a submerged

object by a travelling wave will be larger if the wave is breaking or has broken, which could

explain why calculated forces are much smaller.

Due to the lack of clarity in the data given in [25], an investigation into waves breaking on

cylinder was carried out to check the level of amplification in this load.


63

3.4 Experiments into the Impact of Breaking

Waves on a Monopile Foundation

3.4.1 Introduction

Experimental work was completed to check the hypothesis that waves breaking on a cylinder

exert three times as much force as non-breaking waves computed using linear and nonlinear

wave theories and the Morison equation. A cylinder was placed in the flume at University of

Manchester and breaking and non-breaking waves were impacted against the structure. The

forces exerted on the cylinder, which was used to represent a monopile foundation, were

measured and compared with the forces resulting from analyses with linear and nonlinear wave

theories and the Morison equation.

3.4.2 Review of work on breaking waves

A short review of work in the field of load amplification due to breaking waves was completed to

verify this hypothesis. Swift [35] examines the behaviour of breaking waves and presents a

mathematical model for the calculation of the free surface profile, particle velocities and

accelerations leading onto a modified version of the Morison equation where a slamming

coefficient is considered to take account of the increase in load. The impact forces on the

cylinder is said to depend upon the dynamic properties of the cylinder in addition to the wave’s

characteristics.

Experimental work was completed by Wienke and Oumeraci [36] into plunging breakers. It is

implied in the introduction that a factor of 2.5 should be applied to the forces from the Morison

equation to make it valid for breaking waves (reference is made to the Shore Protection Manual,

1984) and the use of a slamming coefficient to increase loads is discussed later in the

publication. Pressures were measured at different points around the cylinder which was

inclined at different angles. Results were used to develop 2D and 3D models for the impact

load based on Wagner [37] which indicated that breaking forces depend on the wave’s celerity,

C.

The Coastal Engineering Research Centre (CERC) (1977) recommends the use of a drag

coefficient of 2.5 times the original for the case of waves breaking in the Morison equation, as

identified by Apelt and Piorewicz [38]. This paper looks into experimental work on breaking

waves on cylinder with measurements of wave forces made relative to the water depth. It was

concluded that sinusoidal linear wave theory significantly underestimates the force impact on

the cylinder.


64

To conclude, breaking waves acting on a cylindrical structure generate a greater force than

what would be expected from non-breaking waves. The papers covered in this short literature

review indicate that a factor of around 2.5 should be applied to forces arising from the Morison

equation. Experimental work has therefore been carried out by the author to check the

magnitude of wave force amplification due to breaking waves.

3.4.3 Methodology

A cylinder of 90mm attached to a central column with calibrated strain gauges located near the

top and bottom was placed in a flume with water depth of approximately 500mm. This

compares with a cylinder of 200mm diameter and water depths from 0.3m to 0.8m in the Luck

and Benoit experiments [25]. To measure the water depth as waves propagated along the

length of the flume, wave gauges were placed at around 500mm upstream and at the centreline

of the cylinder with an offset of 200mm to reduce the gauge's interaction with the wave. These

gauges were also calibrated with the output of all measurements to an oscilloscope trace using

Picoscope software. Diagrams of the experimental setup can be found in Figure 3-11 and

Figure 3-12.

Figure 3-11: Experimental setup – section through flume with cylinder and equipment

Figure 3-12: Experimental setup – plan view of flume with cylinder and equipment

A B


65

To generate breaking waves on the structure, a ramp was positioned next to the edge of the

base plate of the cylinder. This ensured that waves would break onto the structure and not

beforehand. Figure 3-13 shows the positioning of the ramp in the flume.

Figure 3-13: Experimental setup – section through flume with cylinder, ramp and

equipment

Initially regular non-breaking waves were generated for a range of frequencies and wave

heights. Strains were measured at the top and bottom of the cylinder for the first five waves

generated in order to avoid superposition of reflecting waves from the end of the flume.

Positioning strain gauges at the top and bottom of the cylinder measures the moments at these

points but also allows the overall force exerted on the cylinder to be found and its line of action.

Figure 3-14 gives a section through the cylinder used in the experiments. A central rod is fixed

to the base of the structure and it is on this rod that the cylinder is attached. Note that the

cylinder is bolted onto the end of the rod and makes no connection or contact with the base

plate – a gap is indicated between the cylinder and base plate in Figure 3-14. With waves

hitting the cylinder, the load is transferred to the central rod but due to the bolted connection

present at the top of the cylinder and end of rod, a moment is generated. The attachment of the

central rod to the base plate is a fixed boundary condition therefore an opposing moment will be

generated at this location also. With reference to Figure 3-14, the following load balance can be

assumed:

L

MMFMFLM 21

12

+=⇒−=

A B


66

Figure 3-14: Section through cylinder showing wave forces applied and its equivalent

static system

For each frequency, three recordings of five waves were made and averages of time period,

moments and force with its associated line of action were calculated. Both linear and nonlinear

(Fourier series approximation) analyses were used to model the waves generated in the flume

in order to check the validity of both methods.

A similar methodology was applied to the breaking wave experiments. The ramp was placed in

the flume as shown in Figure 3-13 and a series of waves was generated. Results where the

wave broke before hitting the structure were excluded. Again both linear and nonlinear wave

theories were used as a basis of comparison between values.

The output from the Picoscope software for both the wave gauges and strain gauges for

breaking and non-breaking waves can be found in Figure 3-15 to Figure 3-17.

L

Cylinder

Central rod

Bolt connecting cylinder to rod

Base plate


67

Figure 3-15: Picoscope trace for wave gauges placed at two positions in the flume (see

Figure 3-11)

Figure 3-16: Picoscope trace for strain gauges at the top and bottom of the cylinder for

non-breaking waves


68

Figure 3-17: Picoscope trace for strain gauges at the top and bottom of the cylinder for

breaking waves

3.4.4 Results

Results were grouped in terms of their kd values (the product of wave number and water depth)

and compared with experimental data as shown in Figure 3-18 and Figure 3-19. The graphs

show that for non-breaking sinusoidal waves, the linear and nonlinear calculated forces are

similar to measured forces - ratios of measured to calculated forces vary from 0.95 to 1.27

averaging at around 15% variance. Comparing this with the safety factors applied to

environmental loads according to DNV-OS-J101, a factor of 1.35 must be applied to wind and

wave loading [12], therefore the results safely fulfil this requirement. Figure 3-19 shows that

the effects of breaking result in loads much greater than those calculated using linear and

nonlinear wave theories.


69

Figure 3-18: Comparison of experimental and calculated results for non-breaking waves

Figure 3-19: Comparison of experimental and calculated results for breaking waves

Due to the amplification effect breaking has on the structure, the ratio of measured to calculated

force was ascertained in order to gain an understanding of how these compare with what was

determined previously. Figure 3-20 and Figure 3-21 show similarities between the results from

the experiments and those from Luck and Benoit. A greater range of kd values were examined

by Luck and Benoit hence the higher magnification of forces due to breaking waves. For higher


70

kd values (greater than 1.0) it appears that the experimental results are slightly higher than Luck

and Benoit’s particularly for application of linear wave theories. Results from both sets of

experimental work seem similar for kd values between 0.7 and 1.0 for linear and nonlinear wave

theories.

Figure 3-20: Comparison of data determined from experimental results (LCD+PKS) and

the results from Luck and Benoit (ML+MB) using linear wave theory

Figure 3-21: Comparison of data determined from experimental results (LCD+PKS) and

the results from Luck and Benoit (ML+MB) using nonlinear wave theory


71

3.4.5 Conclusion

For the case of non-breaking waves, the experimental forces exerted on the monopile

foundation were similar to those obtained from linear and nonlinear wave theories with actual

forces around 15% larger than calculated values. From Figure 3-18, it can be seen that both

wave theories slightly underestimate measured forces with linear forces slightly greater than

nonlinear values, roughly 5% larger.

Experimental results indicate that there is an increase in the force exerted on a monopile

foundation when the effects of breaking are considered. Results from the initial study into the

wave loading on a monopile foundation, where test data from Luck and Benoit was compared

against the forces determined using linear and nonlinear wave theory combined with the

Morison equation, indicated that waves breaking on the structure could be as much as three

times larger than those determined by the theory. This level of load magnification was observed

but was less severe with an amplification of load around 2.5 times the theory dependent on the

value of kd. On examination of the individual data points grouped by kd values, it appeared that

results from the author and Luck and Benoit were similar. Different levels of magnification could

be attributed to different values of kd with Luck and Benoit examining a larger range of kd. The

KC range for the tests was 2 and 10.

Linear and nonlinear wave theories combined with the Morison equation for modelling the force

exerted on a monopile give reasonable results for predicting the effects of regular waves

impacting with the structure. Once waves begin to break on the foundation and substructure,

linear and nonlinear wave theories do not account for the increase in magnitude of force due to

this phenomenon. Results are magnified by a factor of up to 2.5 compared with the theory

therefore caution should be taken with Morison’s equation in regions where breaking waves are

a possibility.

3.4.6 Recommendations

The investigation into wave breaking examines the potential increase in force which these

waves exert on a monopile foundation compared to the forces exhibited by non-breaking regular

linear and nonlinear waves. A range of support structure options are available for offshore wind

turbines therefore similar investigations checking whether this magnification of force due to

breaking waves phenomenon is recommended. Jacket and tripod structures are now being

explored as viable options for future offshore wind farms which are planned for deeper water

depths. Monopiles foundations are considered to be limited with regards to fabrication and its

financial implications with building larger and larger sections therefore studies examining the

wave forces on a variety of support structures should be considered for future work.


72

3.5 Investigation into Wind and Wave Loading

on a Monopile for Two Different Turbine

Capacities

Using the theoretical maximum wave height and linking this with wind speed, a short study into

wind and wave loading on a monopile foundation was completed. The question of which load

dominates for a range of water depths was the focus for the study. Two turbines were

examined; a 2MW and a 5MW turbine, the models of which were predefined in the Bladed

demo. The maximum wave height for the operational wind speeds of the two turbines was

determined using the Rayleigh Distribution. Nonlinear wave theory and the Morison equation

were used to generate wave loading on the structure and a direct comparison between loadings

was completed.

3.5.1 Methodology

Models of 2MW and 5MW turbines supplied with the software, Bladed, have been utilised in

order to determine the maximum wind loading at a range of different speeds. In order to

simplify this assessment, a constant wind speed of 20m/s has been used in Bladed in order to

develop a wind speed versus hub loading curve for each of the turbines. Nonlinear stream

function wave theory has been used to determine the force exerted on a monopile foundation

over one wave period allowing the maximum force to be found [32] .

In order to link the wind speeds to the maximum wave heights, formulae from the Shore

Protection Manual [39], specifically the Rayleigh Distribution has been used in analysis where:

hs NHH 3max ln2

1=

(3-7)

where Hmax is the maximum wave height, Hs is the significant wave and N3h is the number of

waves expected in a three hour period

The significant wave height is calculated using the following equations:

22.1 UgH s =

(3-8)

8.12

=U

gTs

π (3-9)

with U as wind speed and Ts as the significant period of the wave.


73

The theoretical maximum wave height ascertained from the Rayleigh Distribution is compared

with the Miche criterion [34] given in section 3.3.4.

The lower of the two values is then considered to be the maximum wave height applicable to the

specified wind speed. Water depths ranging from 5m to 60m at regular 5m intervals were

examined for the maximum force and moment applied to a monopile foundation. A modified

nonlinear Fourier series computation using the SAWW_FORCE program developed by Buss

and Stansby [32] was implemented to complete the wave loading analysis. This analysis for

wave loading is that of a static analysis therefore further modification is required to ensure that

the effects of the rotor's motion are considered.

To convert a static analysis using the nonlinear Fourier series computation into a dynamic

analysis, the wind turbine's frequency range needs to be known and a suitable DAF calculated.

A range from 0.25-0.35Hz has been assumed for both turbines based on a frequency ranges

specified by a series of different turbine manufacturers. Before calculating the DAF for a

structure, the natural frequency of the structure and a suitable critical damping ratio need to be

determined. Given the estimated range for the turbines, a natural frequency of each support

structure has been assumed to be 0.3Hz. The critical damping ratio for a turbine varies

depending on the operational mode experienced in the analysis. Since the maximum hub

loading has been determined for steady operational loads, the rotor is in motion therefore a

higher critical damping ratio applies in this case. For the case of the turbine shutting down,

either due to cut-out wind speeds observed or failure of the turbine, the critical damping ratio

can be assumed to be negligible so a value of 0.01 ≤ ξ ≤0.02 can be assumed. In the case of

operational loads, a critical damping ratio of 0.07 has been assumed to be reasonable due to

the wind speeds assessed and the range of damping ratios considered for shutdown mode.

For wind loading on the structure, Bladed has been used to determine the hub loading at

varying wind speeds. Operational wind speeds were examined with results for cut-in wind

speeds of 3m/s to cut-out wind speed at 25m/s. The wind loading from Bladed takes into

account the effects of aerodynamic damping from the motion of the turbine and the amplification

of wind loads due to the structure's response therefore a DAF did not need to be applied.

3.5.2 Results

The maximum hub loading experienced by the 2MW and 5MW turbine was observed at wind

speeds of 11.5m/s and 12m/s respectively. Once this maximum hub loading is achieved, which

coincides with peak power production, the hub loading tails off as shown in Figure 3-22.


74

Figure 3-22: Graph of a comparison of hub loading experienced during operation by a

2MW and 5MW turbine from cut-in speed of 4m/s to cut-out speed of 25m/s

Graphs of the overturning moments due to wind and wave loading for different wind speeds

were developed in order to ascertain the depth at which the wave loading dominates. These

graphs can be found in Figure 3-23 to Figure 3-28. Note that the hub loading stays fixed for a

designated wind speed as the force associated with this loading stays constant, as indicated in

Figure 3-22.


75

Figure 3-23: Graph of the moments due to wind and wave loading for a 2MW and 5MW

turbine with wind speed U = 8m/s




76






77





For lower wind speeds, the wave loading appears to dominate in water depths from around 25m

up to 35m for both turbines. As the wind speed increases up to peak power production, the hub

loading reaches a peak and then decreases (see Figure 3-22) therefore allowing the wave


78

loading to dominate at much shallower water depths. Figure 3-26 shows that the wave loading

is the major force at a water depth of roughly 12.5m for both turbines. As the wind speed

increases to cut-out speeds of 25m/s and the hub loading decreases, the maximum wave

heights due to either the Miche criterion or the Rayleigh Distribution increase leading to the

wave loading dominating at water depths of around 10m. Figure 3-27 and Figure 3-28 indicate

that the overturning moments due to wind loading appear small compared with those due to

waves for water depths over 25m, particularly for the 5MW turbine.

3.5.3 Conclusion

Linking wind and wave loads using the Rayleigh Distribution and the Miche criterion gives limits

on the maximum wave height attainable for a particular water depth. Each of the graphs in

section 3.5.2 show a variation in gradient for the wave loading over the water depth range

examined in this investigation. The higher the wind speeds, the more pronounced this change

is with a peak forming in the shape of the graph at the point at which the Rayleigh Distribution

values for maximum wave heights takes over. This limits the maximum wave height to the

same value for the rest of the water depths leading to the steady gradient observed.

Generally nominal wave loadings for both turbines tend to dominate at around 30m water

depths before peak power production is reached. Once this has been observed, the wind

loading dominates at shallower water depths leading to the conclusion that overturning

moments due to wave loading appear small compared to those generated by wind as the wind

speeds approach the cut-out speed of 25m/s

3.5.4 Recommendations

The case of maximum power production, which is the point at which the hub loading is at a

maximum during operation, may not necessarily be the worst case scenario with regards to

extreme loads on the turbine structure. Wind turbines operate in a relatively small window of

wind speeds from 4m/s to 25m/s. Extreme wind speeds could be much higher than 25m/s,

even up to 60m/s if considering a 1 in 100 year extreme gust. Potential future work on this

subject would be to look at the case of extreme gusts and their associated wave heights for a

range of water depths.

3.6 Summary

Understanding the effects wave loading has on the overall loading on an offshore wind turbine

support structure is vital to its design. Investigations into modelling the wave loading on a

monopile foundation based on data from Luck and Benoit [25] indicated that measured wave

loads were up to a factor of three larger than those determined through linear and nonlinear

modified Fourier series [32] methods. It was implied that the amplification in loads was due to

wave breaking phenomenon therefore experiments were carried out at the University of


79

Manchester to clarify this possibility. The results of experimental work indicated that the effects

of breaking lead to a magnification of forces experienced on the monopile due to waves

however the factor by which linear and nonlinear wave forces need to be modified by was less

than anticipated. Magnification of forces arising from linear and nonlinear wave theories were at

most a factor of 2.5 of the data obtained from experimental work.

Combined wind and wave loading studies indicated that wave loading dominates at around the

same water depths for both a 2MW and 5MW turbine. For nominal forces, the wave loading

was the dominant force between depths of 25m and 35m for lower wind speeds with wind

loading becoming small as cut-out speed was approached.

Further studies into wave loads and their effects on alternative support structures, in particular

the effects of breaking waves, is a desirable for future work. Examining gusts and wind speeds

greater than the cut-out speed of 25m/s for combined wind and wave loading may indicate that

the extreme wind loading conditions may be outside the operational window for an offshore

wind turbine. Future work could examine the effects of these loads and compare them with the

associated wave loading for dominant forces

80

Chapter 4 Review of Stress

Concentration Factors for

Uniplanar and Multiplanar Tubular

Joints

4.1 Introduction

Rounds 1 and 2 of the Crown Estate’s bidding for offshore wind farm sites has resulted in the

majority of structures built being monopiles. Water depths encountered in the demonstrator and

initial offshore wind farm projects have been relatively shallow with Round 3 projects exploring

depths of up to 60m. Monopiles have limitations for implementation in deeper waters with

unfeasible structure diameters required for compliance with ULS and FLS design criteria. The

Beatrice Demonstrator project was the first of its kind to utilise a four-legged jacket in a water

depth of 45m. Preliminary design of four-legged jackets has been carried out and summarised

in section 2.3 with an analysis of a three-legged jacket completed in Bladed as part of a study

into wake modelling, the detail of which can be found in [24].

Observations from examination of preliminary design procedures on for jacket structures

indicate that cast connections are often required for joints to provide adequate capacity in FLS.

Tubular joint design in the FLS involves examining the stress ranges the structure is likely to

have to withstand during its lifetime and translating this into an expected life based on S-N curve

data. SCF equations, or the Efthymiou equations, are applied to nominal stresses to give the

hot spot stress at eight key locations around the brace-chord intersection. The Efthymiou

equations [22, 23] are based on parameter studies completed using finite element models to

predict the increase in stress due to discontinuities in the structure at the joints. These

equations allow the engineer to determine the hot spot stress expected at the weld toe of a

range of tubular connections, for example K, KT and Y joints, without having to use finite

element software.

Chapter 4 Review of Stress Concentration Factors for Uniplanar and Multiplanar

Tubular Joints

81

This chapter gives an overview of the work completed on tubular joint design indicating where

improvements can be made. Better modelling of tubular joints could improve the design of

jacket structures and may lead to cost savings.

4.2 Development of Parametric Equations for

SCFs for Tubular Joints

The concept of providing a comprehensive set of parametric equations is such that it enables

the engineer to design tubular joints in FLS without the need for finite element (FE) modelling.

Early work on the development of equations focused on full scale testing of steel models in

order to determine the stress distribution around welded connections between tubulars. Due to

the cost of such testing, later investigations involved a combination of testing small scale acrylic

models and developing FE models, which utilised results from physical testing as a means of

model verification. The outcome of this research resulted in a range of different parametric

equations for determining the stress concentration at saddle and crown locations of the chord

and braces.

Design codes such as DNV-OS-J101 [12] have adopted the Efthymiou equations as the

standard for designing tubular connections. These equations were developed in the 1980s and

have not been superseded by any other form. Recent work has looked into the development of

equations for predicting the stress distribution around the weld however, these equations are

rather cumbersome. As the Efthymiou equations look at braces in one plane only, there may be

errors present in the design of tubular connections as jacket structures comprise multiplanar

braces. Some work has been completed on multiplanar connections however, this is limited.

The following section will give an overview of the work completed on both uniplanar and

multiplanar joints.

4.2.1 SCFs for uniplanar tubular joints

Work has been carried out on the design of unstiffened and stiffened uniplanar tubular

connections since the 1960s. Unstiffened connections only have been examined in this thesis

due to the complexity of stiffened tubular joints. As work has progressed on the subject,

equations have become more complicated and later works have resorted to simplifying existing

equations in order to make them easier for the engineer to use.

4.2.1.1 Beale and Toprac (1967)

In 1967, research was carried out by Beale and Toprac [40] in response to limited guidance on

the design of tubular connections given in industry standards. A series of ten steel welded

specimens (4 T, 3 Y and 3 K joints) were axially loaded in a test rig in order to assess the stress


Tubular Joints

82

distributions present around the weld toe. The specimens were tested in the elastic range and

to failure so that the failure modes could be observed. Regression analysis was used to

develop the first set of principal stress equations in the form of [40]:

5432

1

kkkkk τγβασ = (4-1)

Parameters associated with the geometry of joint are as follows:

T

t

D

d

T

D

D

L==== τβγα ; ;

2 ;

2

(For geometry, please refer to Figure 2-17 on page 46)

The resulting four equations allow the engineer to gain a very rough estimate of the stresses at

the saddle and crown locations on brace and chord for any form of joint under axial loading.

Tubular connections in the offshore environment are likely to be exposed to other forms of

loading and each type of joint (T, Y, X, K and KT) is likely to exhibit different behaviour.

4.2.1.2 Visser (1974)

FE models were developed by Visser [41] in order to verify and make amendments to API

approaches for the design of tubular connections. Visser examines the use of thin-shell

elements to model tubular joints in FE software to determine the distribution and magnitude of

stresses in areas of stress concentration. An equation for calculating SCFs in T and K joints

was derived from a parametric study and the hot spot stress resulting from testing a range of

joint configurations.

4.2.1.3 Kuang et al (1975)

Fatigue cracking in tubular connections on offshore oil and gas platforms prompted Kuang et al

[42] to investigate stress concentrations at simple tubular joints. FE models of T, K and KT

joints were developed and examined by [42] to generate a series of parametric equations

expanding on those developed by Toprac and Beale, Visser and Reber [40, 41, 43].

Results from the FE models were verified by carrying out specimen testing which was

completed by the Oak Ridge National Laboratory (ORNL). As welds were not modelled in FE,

an idealised steel joint was built and loaded. To idealise the joint, a series of annealing and

surface boring was carried out. A total of 966 individual strain gauges were attached to the

structure to measure the stress distribution and magnitudes [42]. Correlation between results

was reasonable – discrepancies between results were assumed to be due to FE models not

containing weld details.


Tubular Joints

83

The final component of the study was to develop a series of parametric equations expanding on

those established by Toprac and Beale, Visser and Reber [40, 41, 43]. Key parameters, which

could influence the behaviour of the joint under loading, were defined as follows [42]:

• T/D (chord thickness/chord diameter) influences the radial flexibility of the chord

• d/D (brace diameter/chord diameter) governs the stress distribution

• t/T (brace thickness/chord thickness) indicates the relative bending stiffness therefore

governing the bending stress

• θ (angle of inclination of brace to chord) determines the mechanism of load transfer in

the joint

Kuang et al [42] outline the procedures for determining the SCF equations. A series of log scale

plots for each of the above identified parameters bar θ was carried out:

• Plot SCF against D

Tand determine slope 1m

• Plot 1m

D

T

SCF

against

D

dand determine slope 2m

• Plot

21 mm

D

d

D

T

SCF against

T

t and determine slope 3m

• Determine a0 from the above plot and the relation:

yxam =3

0 where

T

tx = and

=

21 mm

D

d

D

T

SCFy

• Construct the empirical equation in the form:

321

0

mmm

T

t

D

d

D

TaSCF

=

A total of 18 equations were developed by Kuang et al [42] for predicting the maximum SCF in

the chord and braces of T, Y, K and KT joints. These equations form the basis of Efthymiou’s

which use superposition of SCFs determined by different loadings on braces. It is noted that the

equations do not specify the locations of maximum stress however it is indicated that, from FE

models, these locations were either at or adjacent to the intersection of the mid-surface of the


Tubular Joints

84

brace and chord. Limitations for the validity of SCF equations dependent on parameters were

as follows [42]:

0.015 ≤ T/D ≤ 0.06

0.2 ≤ t/T ≤ 0.8

0.3 ≤ d/D ≤ 0.8

0.01 ≤ g/D ≤ 1.0

0.05 ≤ D/L ≤ 0.3

0° ≤ θ ≤ 90°

All FE models used for the study fall into the above ranges. Comparisons were made with the

outcomes of using equations developed by Beale and Toprac, Visser and Reber along with the

output from FE modelling. Results indicate that the Kuang et al equations give a better

estimation of SCF.

4.2.1.4 Wordsworth and Smedley (1978)

Acrylic model testing was used by Wordsworth and Smedley [44] as part of the Lloyd’s Register

of Shipping’s programme of research into SCFs for tubular joints. Experimental work was

carried out on a series of T, Y and X joint acrylic specimens which were tested with axial, in-

plane (IPB) and out-of-plane bending (OPB) loads with the aim of expanding on existing SCF

parametric equations. Simply supported acrylic samples with strain gauges positioned around

the location of the weld toe were tested in order to identify the locations of maximum stress.

The effects of the chord length were examined with the observation that increasing chord length

resulted in an increase in bending stress which therefore changed the position of hot spot

stress. Due to the nature of the specimens, it was not possible to mimic the effects of welds

and so a weld correction factor was applied to the results.

A set of ten empirical parametric equations were developed with the locations of hot spot stress

stated for each equation – it is possible to use the principle of superposition to calculate SCFs at

different locations. Common equations apply to T and Y joints. Restrictions apply to the validity

of these equations. Note that the output from the SCF equations was compared with results

from experiments however it was not verified with work by others.

Further work was carried out by Wordsworth using the same acrylic modelling approach for non-

overlapped K and KT joints [45]. SCF formulae were expanded upon to give a further ten

equations for joints under axial, IPB and OPB and a weld leg length correction factor was

determined. No useful information has been given in both Wordsworth papers showing

experimental results or variation of SCF with the different parameters.


Tubular Joints

85

4.2.1.5 Efthymiou and Durkin (1985)

Efthymiou and Durkin [23] began their work on developing a comprehensive set of SCF

equations for T/Y and gap/overlap K joints, the latter of which had no equations at the time of

research. The work was in response to the differences between output from parametric

equations devised by Kuang et al [42] and Wordsworth and Smedley [44]. The main difficulties

with the existing sets of parametric equations were identified as follows [23]:

1. Significant differences between predictions from Kuang et al and Wordsworth and

Smedley for certain simple joints and loadings

2. No equations exist for certain load types in simple K and KT joints

3. No equations exist for overlapped braces

4. Limited information on SCFs in stiffened joints

5. Limited information on SCFs in multiplanar joints

FE models were developed for 150 different joint configurations. Models were verified by using

an alternative FE analysis software, which resulted in good agreement (within 6%) for chord

SCFs however brace SCFs were consistently higher (15-25%) [23]. Two identical full-size steel

T joints were tested as a further validation of the models with good correlation noted between

results.

For T/Y joints around 70 different configurations were subjected to axial, IPB and OPB load

cases [23]. The effects of end-fixity conditions were examined along with possible ovalisation of

the chord due to bending as a result of chord length. Different correction factors have been

developed for cases for α < 12 (where α = 2L/D) for application to SCFs [23]:

F1: for axially loaded joints with fixed chord-ends

F2: for axially loaded joint with pinned chord-ends

F3: for OPB in T/Y joints

F4: for short chords

Eleven SCF equations were determined for T/Y joints for different loading and fixity conditions

using stresses extrapolated to the weld toe (note that previous investigations did not clarify

whether this approach was adopted) and maximum principal stresses. For axial loading, SCF

equations were developed for the brace and chord saddle and crown. Short chord correction

factors apply to saddle SCFs. With IPB and OPB, the SCF equations feature only for brace and

chord crown and saddle respectively.


Tubular Joints

86

Efthymiou and Durkin compared the output of their SCF equations to those from Kuang et al

[42] and Wordsworth and Smedley [44] along with the output from FE models. Discrepancies

exist between each of the studies, particularly under axial loading conditions, however similar

graph shapes for chord SCF versus β can be observed for Wordsworth and Smedley and the

results of FE modelling. Poor correlation between the Kuang et al output and the FE results

could be due to the limitations of geometries and end-fixity conditions in axial and OPB cases.

About 100 K joints, including overlapping joints, with nine different loading cases were

investigated by Efthymiou and Durkin [23]. The majority of joints examined had identical brace

inclinations with configurations mostly of 45°/45°. Some brace inclinations of 30°/30° and

60°/60° were studied along with unequal brace inclinations of 90°/45°, also known as N joints.

Fifteen equations were developed for gap/overlap K joints under axial, IPB, OPB loading

introducing an additional ζ parameter, where ζ = g/D. Short chord correction factors apply to

cases where loads are unbalanced or present in one brace only for gap and overlap joints under

axial and OPB loading.

All the Efthymiou equations are valid for the following geometrical parameters [23]:

0.2 ≤ β ≤ 1.0

0.2 ≤ τ ≤ 1.0

8 ≤ γ ≤ 32

4 ≤ α ≤ 40

20° ≤ θ ≤ 90°

-(0.6β)/sinθ ≤ ζ ≤ 1.0 (for overlapping joints)

4.2.1.6 Efthymiou (1988)

To complete his work on parametric SCF equations, Efthymiou developed further equations to

cover SCFs for X and KT joints [22]. Influence functions have been developed by Efthymiou to

allow the engineer to compute the hot spot stress in any planar joint subject to end loading

conditions. Multiplanar effects were modelled in the analysis with the conclusion that these

have little impact on the fatigue life of the joint.

FE models of X and KT joints were developed in the program PMBSHELL with nine load cases

applied as follows:

1. balanced loads (axial, OPB, IPB)

2. one-brace-only loaded with axial, OPB, IPB loadings

3. unbalanced loads (axial, OPB, IPB)


Tubular Joints

87

Additional SCF equations were developed for T/Y joints expanding on those by Efthymiou and

Durkin in 1985. These extra equations include measures for chord-end fixity conditions with the

inclusion of a chord-end fixity parameter, C.

Influence functions were developed by Efthymiou as an alternative approach to deriving hot

spot stress. When a nominal unit stress is applied to a brace of the joint, the hot spot stress at a

certain location on another brace of the joint can be computed. The method of superposition

can then be implemented for each brace by multiplying the nominal stress by the outcome of the

influence function for each brace and adding them together. A range of influence functions for

X, K and KT joints under axial load and OPB can be found in Tables 5 to 7 in [22].

Efthymiou [22] puts forward the argument for using influence functions over SCF equations.

Efthymiou claims that the influence functions allow for easier assessment of complex

geometrical configurations as there is no need to determine whether loading conditions are

balanced or unbalanced. Using the SCF approach may result in a conservative estimate of hot

spot stress as the effects of OPB and multiplanar braces could be underestimated or neglected.

A comparison of hot spot stress determined by SCF equations and influence functions was

made by Efthymiou for a range of joint configurations. For the case of K and KT joints where

the OPB stresses are significant, the use of SCF equations resulted in a considerable

overprediction of hot spot stress. As the SCF equations assume that the OPB moments are

unbalanced the SCF adopted for analysis would be much larger and thus give a greater hot

spot stress than what would be calculated using influence functions.

SCF equations developed by Efthymiou are still the more favoured approach to designing

tubular joints. Further work has been completed by other authors on the subject however the

design code DNV-RP-C203 [19] still recommends the use of Efthymiou.

4.2.1.7 Lalani et al (1986)

So far, the majority of research into tubular connections had been based on FE modelling with

some acrylic specimen testing. Because of this, over 50 elastic test were carried out on large

scale steel models by Lalani et al [46] in order to address whether existing parametric formulae

give reliable estimates of SCFs. Lalani et al discuss the uncertainty and problems with the SCF

method and note that the following apply [46]:

1. Design codes give different definitions of hot spot stress

2. 103 parametric equations exist the output of these depending on which equations is

used

3. Variations in the methods used to determine combine hot spot stress i.e. load

combination techniques


Tubular Joints

88

4. Limited SCF equations exist for overlapping, multiplanar and stiffened joints

Note that only points i) and ii) were examined for the Lalani et al study.

A critical review of existing parametric formulae by Kuang et al [42], Gibstein [47], Wordsworth

[44], UEG (Underwater Engineering Group), Buitrago et al and Efthymiou [22, 23] was carried

out and formed the initial component of the study. It was noted by Lalani et al that

inconsistencies are present on which individual parameters bear influence on SCFs in the

aforementioned formulae. Validity ranges are also inconsistent for each set of equations. A

graph of chord saddle SCF versus β ratio was constructed for an axially loaded T joint and can

be found below:

Lalani et al reviewed published data on SCFs for steel joints excluding tests on unrealistically

sized joints and reported values for 49 T/Y, 14 DT/X and 20 K/YT joints. 137 different SCF

values could be calculated using the various formulae. Recommendations for the most reliable

equations for predicting stress concentration were made based on the results from loading

comparable steel sections. The Efthymiou, Wordsworth and UEG equations gave the best

relative correlation however not all joint configurations are covered. Lalani et al recommend the

use of the UEG equations, which are derived from those developed by Wordsworth; however

the document seems to be unavailable at present.

A useful graph depicting the variation of chord SCF with β can be found in the paper and is

given in Figure 4-1 . The graph shows the great differences between all existing parametric

equations but does not offer a comparison of these with the data acquired from the full scale

testing.


Tubular Joints

89

Figure 4-1: Chord saddle SCF variation with β ratio taken from Lalani et al [46]

4.2.1.8 Hellier, Connolly and Dover (1990)

Additional research highlighting the disparities between SCFs derived by different equations

and experimental results was completed by Hellier, Connolly and Dover [48] and Smedley and

Fisher [49].

Nearly 900 thin-shell FE models of T and Y joints were developed and tested by Hellier,

Connolly and Dover [48]. Output from the models was verified with results from steel model

tests and the predictions arising from previously derived equations. Parametric equations were

developed using statistical regression software.

Hellier, Connolly and Dover [48] compared the output of their equations with those by Kuang

[42], Wordsworth and Smedley [44] and Gibstein [47] and the results of steel tests. Analysis

suggested that Kuang, Wordsworth/Smedley and Gibstein underpredicted SCFs frequently with

44%, 13% and 34% of results underpredicted respectively. For the case of Hellier, Connolly

and Dover, the majority SCFs were slightly overpredicted with only 3% of cases underpredicted.


Tubular Joints

90

It was suggested by Hellier, Connolly and Dover that an overprediction of SCF was preferable in

order to attain a level of safety in design.

Data is provided of a select number of joints giving the parameters, SCFs from different

equations and those from steel testing resulting in a ratio of steel tests to derived SCFs. FE

models may be flawed as weld details have not been modelled and there is no discussion on

methods of extrapolation to the weld toe. It can only be assumed that SCFs have been taken

directly from brace-chord intersections which could lead to erroneous results. Hellier, Connolly

and Dover, however, acknowledge the potential for errors due to FE models concluding that

values of SCF may be overestimated [50].

4.2.1.9 Smedley and Fisher (1990)

Over 350 additional acrylic joint specimens were tested with the main emphasis on ring-

stiffened joints. Verification of tests on samples was made by two separate independent FE

analyses using PMBSHELL and PAFEC along with further testing of 2 full scale steel complex

tubular joints.

A comparison of the SCFs from steel and acrylic specimen testing and those determined by FE

modelling was undertaken by Smedley and Fisher [49]. As the acrylic models and the FE

models from the PAFEC program did not include weld details, a direct comparison was made

between these methods and with the outcomes from PMBSHELL and the steel models. It was

noted that exclusion of the weld fillet in FE and acrylic models resulted in an increase in SCF of

up to 18% for an unstiffened joint. Measured SCF values were compared with the predicted

values from Efthymiou and Durkin [23], Wordsworth [44, 45] and Kuang [42]. The following

table of results was generated for an overlapped K joint:

Table 4-1: SCF comparison of experimental techniques for axial loading with τ = 0.5, β =

0.53, γ = 14.3, α = 13.3, θ = 90°/45°, ζ = -0.4 (Taken from Smedley and Fisher [49])

For unstiffened tubular joints, the following could be summarised [49]:

Configuration Location on joint Steel Acrylic PAFEC PMB-

SHELL

Unstiffened joint Chord Saddle

Chord Crown

Brace Saddle

Brace Crown

24.2

8.1

14.1

1.8

23.9

7.0

13.5

1.6

21.9

6.8

15.0

1.5

23.5

7.3

12.7

-


Tubular Joints

91

1. Acrylic specimens’ SCFs were approximately 10% larger on the chordside and 20%

larger on the braceside when compared with steel specimens – it was assumed that this

was due to neglecting weld details

2. For T/Y joints under axial load with β = 0.8, SCFs were underpredicted by all equations

especially for large γ

3. Kuang equations give good approximation for SCF in validity limits however

extrapolation for values outside range results in overprediction

4. Good predictions of SCFs occur for the case of OPB using Wordsworth & Smedley and

Efthymiou & Durkin

5. Hot spot stress locations may differ – for IPB, the maximum SCF could be located away

from the crown

Eight overlapped joints were examined by Smedley and Fisher comprising 4 N joints (θ =

90°/45°) and 4 K joints (θ = 60°/60°) the results of one of these tests can be can found in

Table 4-2.

Table 4-2: SCF comparison of experimental techniques for overlapped joint with τ = 0.5, β

= 0.53, γ = 14.3, α = 13.3, θ = 90°/45°, ζ = -0.4 (Taken from Smedley and Fisher [49])

* Derived by superposition on balanced OPB and single OPB

^ CS = Chordside

& BS = Braceside

4.2.1.10 Lloyd’s Register of Shipping (1997)

With no clear agreement on which SCF equations should form the basis of the tubular

connection design, Lloyd’s Register of Shipping (LR) produced a document [1] which aimed to

critically assess all available equations, nominate their preferred approach and develop a new

Specimen Maximum measured SCF Predicted SCF

Load. Location Steel

joint

Acr.

model

PA-FEC PMB-

SHELL

Efthy.

/Durk.

Words. Kuang

Bal. axial CS^

BS&

1.6

2.3

1.5

2.7

1.8

1.8

2.1

2.9

2.7

3.3

4.1

3.6

3.1

4.1

Unbal

OPB

CS

BS

6.0*

5.5*

7.7

5.6

8.6

6.9

7.8

7.3

7.9

7.4

6.9

5.3

-

-

Bal. IPB Chord

Brace

1.2

2.7

1.5

2.7

1.3

2.9

1.5

3.8

2.5

2.6

2.5

2.6

2.5

2.8


Tubular Joints

92

set of equations. LR aimed to establish a database of SCF values resulting from all steel and

acrylic testing from previous studies and from this database derive a new set of SCF equations.

The following sets of equations were assessed by LR [1]:

1. Kuang et al [42]

2. Wordsworth and Smedley [44, 45]

3. Underwater Engineering Group (UEG)

4. Efthymiou and Durkin [22, 23]

5. Hellier, Connolly and Dover [48]

6. Smedley and Fisher [49]

It was assumed that all joints researched in the study have pinned boundary conditions,

although Efthymiou developed equations for different chord-end fixity conditions. The key

conclusions arising from the investigation are summarised in Table 4-3.

The paper also provides advice to the designer on key aspects of performing FE, acrylic and

steel testing. Further information on this can be found in Section 4.3, which looks into the

development of FE models.

A database of SCFs derived from realistic steel and acrylic tests is available in the LR report.

The report outlines acceptance criteria for SCF data which includes experimental details,

geometrical parameters used, applied load cases and repetitions. All SCFs in the database

have been standardised to conform to the HSE recommended method by application of a

number of correction factors.

SCF equations were also analysed against the database either against “pooled” steel and

acrylic results or each type of testing alone. A ratio of predicted SCF to recorded SCF was

calculated for each set of equations with the conclusion that the Efthymiou and LR equations

were the most reliable.


Tubular Joints

93

Kuang Wordsworth UEG Efthymiou Hellier Smedley C

om

men

ts

FE thin shells not observing HSE definition of HSS

Acrylic models without welds

Similar comments to Wordsworth apply

150 FE models covering K, KT, T/Y, X joints

Cover T/Y joints but have limited applicability β ≤ 0.8

Developed as mean fit equations to include levels of safety

No weld modelled

Uncertainties about extrapolation methods

Modification factor applied to β > 0.6 and γ >20

Includes short chord correction factors

Chord end fixity conditions not considered

SCFs @ saddle & crown: could under-estimate @ different locations

Restricted validity range

Braceside SCFs conservative

Some underpredictions of SCF

Beam bending not accounted for

Limited to γ = 12

Does not account for beam bending

Chordside SCFs give good estimates

Unbalanced OPB give good fit for symmetric K joints

Looks at realistic geometries

Use short chord correction factors – requires verification

Chord length not considered

Carry-over functions available for multiplanar braces

Equations for SCF at saddle and crown

Influence functions given

Poor performance for some T/Y joints

Only valid for R/T ≥ 12

Different values calculated for locations

Con-servative for K joints

Table 4-3: Conclusions from Lloyd’s Register of Shipping [1] study

4.2.1.11 Chang and Dover (1999)

The concept developing SCF distributions instead of SCF equations just for saddle and crown

locations on the brace and chord was first discussed by Chang and Dover [51, 52]. Thin-shell

analyses for 330 T and Y-joint configurations were carried out resulting in a database of SCFs

being created. From this database Chang and Dover derived SCF distribution equations which

allow the designer to determine the SCFs at any point along the brace-chord intersection.

These equations build on the work completed by Hellier, Connolly and Dover which attempted

to define equations for computing the hot spot stress regardless of location.

The final equations given by Chang and Dover relate the SCF stress distribution to the

parameters as a function of the angle measured around the intersection from crown toe, φ.


Tubular Joints

94

Although the equations appear to be in a simple form, as stated below, the coefficients

associated with the equations are complex and difficult to compute.

)++=) φφφ 2cos((SCF 210 CCC (4-2)

Using shell elements and, from what can be deduced from diagrams, a coarse mesh may affect

the reliability of the research. Further information about the suitability of FE models will be

discussed later in the report.

4.2.1.12 Karamanos, Romeijn and Wardenier (2000)

As indicated previously, the complexity of SCF equations, in particular the SCF distributions,

can make them difficult to compute. Karmanos, Romeijn and Wardenier [53] therefore

attempted to simplify a suitable set of equations for K joints resulting from an assessment of

those available at the time of research and from output of FE models.

A set of graphs were produced allowing the engineer to easily determine the SCF at different

locations on the chord and brace according to specific β and γ parameters. Accompanying

simplified equations are available with exponents X1 and X2 which are determined according to

the type of loading the joint is subject to.

),(

12=),,, θβ

τγθτγβ 0

21

SCF5.0

(SCF

XX

(4-3)

The equations and graphs take into account the carry-over bending effects which have been

considered previously by Efthymiou [23] and Smedley [49]. Carry-over bending is when a

stress concentration is observed near the weld of a neighbouring brace due to loading in

another brace. A normalised gap parameter, ζ, has been included in the analysis to account for

these effects.

A simplified calculation of SCF allows the engineer to compute information easily and quickly.

From the data given in the publication it appears that there is good correlation with FE analyses

and the output from the equations as shown in Figure 4-2. It must be noted, however, that this

graph displays only OPB results for one location – data for other locations and axial and IPB

load cases are not available. The publication does not offer any indication of how the output

from the equations compares with previous works.


Tubular Joints

95

Figure 4-2: OPB on K-joints at brace saddle locations – comparison with FE results and

SCFs determined from simplified formulae (taken from Karamanos et al [53])

4.2.1.13 van Wingerde, Packer and Wardenier (2001)

Continuing with the concept of providing a simplified approach to SCF calculations, van

Wingerde et al [54] developed a set of graphs and equations for CHS and RHS based on a

rational hot spot stress approach. FE models have been analysed in order to determine

simplified SCF formulae for uniplanar RHS (rectangular hollow sections) and CHS K joints and

multiplanar CHS K joints.

For the simplified calculations, van Wingerde et al utilise stresses perpendicular to the weld toe

instead of principal stresses. A series of graphs and a reduced number of simplified SCF

formulae have been developed which use the Eurocode 3 correction factors. Provided in the

paper is the graph for balanced axial load on a tubular K-joint only.

The three SCF equations arising from van Wingerde et al’s research is considered to be a

conservative approach to the design of tubular connections. Details into the FE modelling and

procedures followed to determine the simplified equations are not given in the paper.


Tubular Joints

96

4.2.1.14 Shao, Du and Lie (2009)

Continuing with the concept of determining SCF distributions as opposed to specific locations

such as brace crown, Shao, Du and Lie [55] attempted to develop a set of equations for

calculating this distribution around the weld of K-joints. FE analysis of 287 models combined

with full scale steel specimen testing formed the database of results from which a series of

complex equations similar to Chang and Dover [51].

Good correlation exists between FE models and specimen testing under axial, IPB and OPB

loading conditions. Plots of the SCF against the location around the weld in terms of angle φ

indicate a sinusoidal relationship for the various parameters under different loading conditions.

As with Chang and Dover [51], the equations for SCF distribution appear simple in form but

comprise complex coefficients for terms of the equation.

4.2.1.15 Lotfollahi-Yaghin and Ahmadi (2010)

Further work on stress distribution equations has been completed by Lotfollahi-Yaghin and

Ahmadi [56] with formulae determined for KT-joints. 105 FE models comprising 3D solid

elements and weld profiles were built and tested in ANSYS under balanced axial loading, the

output of which was compared with expected SCFs from LR equations. An equation for

determining the stress distribution around the weld toe of a KT joint under balanced axial load

was derived. The equation comprises a number of functions of different parameters and offers

a less complex formation as Chang and Dover [51] and Shao, Du and Lie [55] as indicated

below:

( ) ))))),(+),= θφζβγτβτ (((((SCF 654321 ffffff (4-4)

The individual functions of the above equation are much easier to manipulate than the

coefficients of previous SCF distribution equations but still offer a level of complexity to this

approach.

4.2.1.16 Conclusion

Significant research has been carried out into predicting SCFs numerically with recent works

looking into the concept of stress concentration distribution. Disparities between outputs from

the various SCF equations raise the question of whether these equations are reliable. These

differences arise from the various methods of modelling tubular joints in the finite element and

the use of acrylic and steel models. Exclusion of weld details in models may also be a reason

why some equations are more accurate than others. The most widely used equations are from

Efthymiou who modelled weld details in FE analyses. Efthymiou also examined the effects of

loading in multiplanar braces, which will be discussed in the following section.


Tubular Joints

97

4.2.2 SCFs for multiplanar joints

As indicated in the last section, there is substantial work completed on uniplanar joints with a

range of modelling and testing and various SCF equations. DNV-RP-C203 recommends the

use of the Efthymiou equations for the design of tubular connections however these equations

look at uniplanar joints only with the option of utilising a carry-over factor for multiplanar braces.

There is some debate as to whether the presence of loading on a brace in a different plane has

any effect on the deformation of chord therefore work has been carried out by various authors

which will be outlined in this section.

4.2.2.1 Efthymiou (1988)

The “carry over” effects of multiplanar braces was first accounted for in Efthymiou’s work on

influence functions [22]. A set of influence functions were devised for determining the chord

and brace hot spot stress for both uniplanar and multiplanar braces. Efthymiou concludes in his

analysis that multiplanar effects “do not seem to be very important” [22] and that they only

increased or reduced the hot spot stress range by up to 15%.

4.2.2.2 Smedley and Fisher (1990)

To verify the assumption that uniplanar SCF equations were valid for calculating SCFs for

multiplanar joints, Smedley and Fisher carried out experimental work on acrylic specimens [49].

Three joints with multiplanar braces were examined for SCFs – one K and two KT joints. Four

different configurations applied to each:

1. One single plane joint

2. One 0° and 90° plane joint

3. One 0° and one 180° plane joint

4. One 90° and 180° plane joint

Results indicate that carry-over effects due to multiplanar braces could lead to an increase in

SCF over 100% for some loading conditions. IPB moments were observed to have little effects

on SCFs however. Efthymiou [22] concluded that loading on multiplanar braces had little effect

on the SCFs therefore there appears to be conflicting evidence on this matter.

4.2.2.3 Romeijn (1994)

A document published by Romeijn at Delft University of Technology aimed to provide guidance

on the fatigue design of multiplanar tubular joints for inclusion in Eurocode 3 [57]. The report

highlights the lack of work completed on multiplanar joints at the time of publication noting that


Tubular Joints

98

the only experimental work available on KK joints was limited. A reason for insufficient work on

the subject is the cost implications of fabricating such complex joint details for full scale testing.

Romeijn carried out experimental testing of four different multiplanar triangular lattice girders

fabricated from steel circular hollow sections. Overlap and gap KK joints were tested with the

braces of joint repeatedly stressed to failure to establish an S-N curve for multiplanar joints.

During the cycles of load, the strains at locations around the weld profile on both chord and

brace were measured at regular intervals to check whether changes in hot spot stress and

stress distribution occurred. The progression of cracks through members of the joint were

observed and noted with failure occurring mostly in the chord.

Figure 4-3: Configuration of KK-joints tested – note geometries – taken from Romeijn [57]

All experimental tests were checked numerically with FE models using 20 node solid or 8 node

shell elements. Welds were included in the models comprising solid elements. Hot spot strains

were the basis of the comparison between FE models and experimental results. Good

calibration between results was achieved as shown in Figure 4-4.


Tubular Joints

99

Figure 4-4: Comparison between numerical and experimental hot spot strains taken from

Romeijn [57]

A parametric study was completed for TT and XX joints based on 444 FE models for TT-joints

and 60 XX joints. For a jacket structure, XX joints are unlikely to be present therefore the focus

will be on KK joints for the purpose of this report. For TT joints with φop = 90° (where φop is the

angle between out-of-plane braces), SCF data exists from steel and acrylic models. For TT

joints with φop = 45°, 70° and 135°, no data exists. A comparison was made between FE

models of TT joints with φop = 90° and the acrylic models due to limited steel test data.

For those joint configurations where SCF exists, comparisons were made between the output

from Wordsworth and Smedley [45] and Efthymiou [22]. For Wordsworth and Smedley

equations, an acceptable agreement for SCFs on chord member was observed; however large

differences existed in SCFs for brace members. With the Efthymiou equations, large

differences in SCF results for saddle and crown locations of chord and brace member were

noted. Romeijn points out that the influence functions devised by Efthymiou assume the same

SCF value for both saddle locations on the brace, which is incorrect. Another problem was

identified with the Efthymiou influence functions - for chord and brace crown locations, influence

functions represent nominal chord bending stresses. These stresses are not hot spot stresses

and therefore it would be incorrect to make a direct comparison between the values arising from

Efthymiou and the results from FE models.


Tubular Joints

100

Romeijn completed a study into the carry-over effects due to the presence of out-of-plane

braces. The following was observed [57]:

• Influence of changes in γ and τ is generally small compared to changes in β and φop

• Chord and brace saddle locations, load cases Fbr,ax,b and Mbr,op,b cause large carry-over

effects especially with increasing β

• SCF results for the two saddle locations on both chord and brace can vary

• Carry-over effects for Mbr,ip,b are negligible

• Carry-over effects for Mbr,op,b are negligible for chord and brace crown locations

• Varying φ gives a harmonic function for SCFs due to carry-over effects with largest

SCFs found in the region forming the shortest gap

No attempt was made by Romeijn to generate influence functions or parametric equations for

multiplanar joints.

4.2.2.4 van Wingerde, Packer and Wardenier (2001)

In addition to the work completed on uniplanar joints, van Wingerde, Packer and Wardenier [54]

carried out a further study to determine influence factors based on the work of Karamanos et al

[58]1. These factors are formed from a geometrical and a load factor, which are applied to

uniplanar SCFs to modify values such that they represent the effects of loading in multiplanar

braces. Van Wingerde et al used this approach instead of trying to generate a new set of SCF

equations as due to an overwhelming number of permutations required both numerically and

experimentally, the analysis would yield an unmanageable number of SCF formulae. It was

considered that an approach similar to Efthymiou’s equations for uniplanar joints would either

give too many equations or yield equations limited in terms of loading conditions and geometry.

Figure 4-5: Direction of positive multiplanar modes used in van Wingerde’s analysis

taken from van Wingerde et al [54]

1 This reference was unavailable at the time of writing but has been noted as subsequent work

has arisen from the report


Tubular Joints

101

The correction factors determined from previous works apply to axial loads and to SCFs at

saddle locations only. A typical correction factor is given below.

fgeom = 1 – 0.7β1.5

Van Wingerde et al simplified these factors to give the following:

Chord Braces

Angle φ m ≥ 0 m ≤ -1 m ≥ 0 m ≤ -1

60° 90° 180°

1.0 1.0 1.0

1.2 1.2 1.0

1.0 1.0 1.0

1.3 1.3 1.0

Table 4-4: Simplified multiplanar correction factors for CHS KK-connections taken from

van Wingerde at el [54]

With reference to the Table 4-4 and Figure 4-5, angle φ represents the angle between

multiplanar braces and m represents the proportion of load between braces in different planes.

4.2.2.5 Smedley (2003)

P.A. Smedley carried out an assessment of Efthymiou’s equations [22] and the Smedley and

Fisher equations highlighting their limitations. The equations derived by Smedley and Fisher

(given in Lloyd’s Register of Shipping document [1]) were expanded upon to take into account

the influence of multiplanar braces.

It was noted that the Efthymiou equations give a comprehensive basis for the design of the

tubular connections with the effects of short chords and different end fixity conditions examined.

Smedley noted that inconsistencies exist between two papers in the public domain by Efthymiou

[22, 23] as indicated below [59]:

• K/KT joint equations under axial load with large separations are different to T joint

equations although both configurations of joint are essentially the same

• As β → 0, it is anticipated that chordside SCF → 0 and braceside SCF → 1. This is not

always the case with the equations

• For complex loadings, the influence function approach applied only to members under

axial load

• For braces with unequal section moduli, the influence functions under moment load are

incorrect


Tubular Joints

102

Smedley and Fisher published equations to give a better estimate of SCFs at less critical

locations compared to Efthymiou. Ring-stiffened joints were also examined however these

configurations are outside the scope of this report. Smedley acknowledges that these works do

not account for the effects of multiplanar braces.

In his 2003 paper, Smedley developed a set of SCF formulae based on Smedley and Fisher

equations including a factor of safety by applying one standard deviation to the mean formulae.

A database of over 1000 steel, acrylic and FE models developed by the TJ group was used to

optimise and refine the equations. The influence of out-of-plane braces was accounted for in

his analysis giving a set of equations for determining the stress in a reference brace due to a

loaded out-of-plane brace.

For axial, IPB and OPB, different XA coefficients are given depending on the location under

examination, i.e. chord or brace saddle or crown. The OP term in the equations takes into

account the angle between braces, the formulae associated with which depends on the location

under examination.

The paper gives a good overview of the approach adopted to calculate the SCFs arising from

multiplanar braces and will provide a reference point for future work. However, there is no

actual data presented in the paper therefore it is difficult to assess the reliability of the

equations.

4.2.2.6 Woghiren and Brennan (2009)

Recently work has been completed by Woghiren and Brennan on multiplanar stiffened tubular

KK joints with FE analyses completed and SCF equations developed [60]. Although stiffened

joints are outside the scope of project due to the potential cost increases and high number of

permutations, the paper gives advice on FE modelling and good provide a reference point when

developing ANSYS models.

4.2.2.7 Conclusions

Comparing the volume of work completed on uniplanar joints with that of multiplanar joints it is

clear that relatively little research into the effects of loading on multiplanar is available in the

public domain. A carry-over factor approach seems to be the most feasible method of

ascertaining SCFs for multiplanar braces where a factor is applied to SCFs arising from

uniplanar equations.

The reliability of the research is questionable as references in some papers are not in the public

domain and authors of papers do not always give results or make comparisons to other works.

An investigation into the effect loading on a multiplanar brace should be the starting point for


Tubular Joints

103

further work in order to determine whether this load has a stiffening effect or weakens the

overall stability of the joint. There is conflicting opinions on the impact of such loading present

in other planes with views that these loads have little effect on SCFs [22] and, on the converse,

claims that loads can double SCFs [49].

Guidance is provided by CIDECT on the design of multiplanar tubular joints for both CHS and

RHS in their Design Guide 8 [61]. This document recommends the use of uniplanar SCF

equations factored by the carry-over factors as determined by [54, 57, 58]. Only two load cases

have been covered in this design document for multiplanar KK joints, namely balanced axial

loads in the brace and axial and bending loads in the chord. Further work looking into other

loading cases (axial, IPB and OPB in one brace only, for example) is therefore recommended.

4.3 Development of FE Models

As computer capabilities improved over the years, the complexity of FE models has increased

leading to better methods of predicting hot spot stress by such means. FE models of tubular

joints were initially built up of shell elements with 8 degrees of freedom (DOF) with just the

tubular section models as this would lead to quicker run times. With software and hardware

improving, it was possible to build models with a combination of shell and solid elements with

welds modelled using the latter. This section will explore the possible methods of modelling

tubular connections and assess their suitability for implementation.

4.3.1 Early FE models – using shells

One of the first attempts at modelling tubular connections in FE was made by Reber [43] who

used shell elements to build models in order to determine the ultimate strength of tubular

connections. A common method of modelling tubular connections is to split the joint into

sections with different mesh densities used as shown in Figure 4-6.


Tubular Joints

104

Figure 4-6: Composition of meshes in Reber’s model taken from Reber [43]

Coarser meshes are used at non-critical regions where nominal stresses are exhibited. Mesh

density increases near the chord-brace intersection in order to improve the analysis at this point

where stress concentration occurs. Variations in mesh density are used as this reduces the run

times of the software’s analysis – a coarser mesh is requires less memory for analysis so it is

preferable to use this in regions where the results are not used.

Shell models without weld details were used by Kuang et al to develop a set of parametric

equations [42]. Meshes for a range of tubular K, T and KT joints were developed taking into

consideration the areas of stress concentration and discontinuities in the model. A method

called “substructuring” was adopted for brace-to-chord intersections. This uses a number of

junction nodes at this intersection which are incorporated into the model using static

condensation. Finer meshes were also implemented at this location to ensure adequate

modelling of stress concentration.

Efthymiou’s models used a combination of shell elements to generate the tubular joints with

weld details included [22, 23]. Three dimensional 16-node shell elements were used to model

the tubular thickness and 8-node shell elements represented the weld detail as shown in Figure

4-7. Models were built in PMBSHELL and analysed using a range of chord-end fixity conditions.

Most analyses carried out before the mid 1990s consisted of tubulars modelled as thin shell

elements with the majority of cases neglected weld details. SCFs were taken either directly


Tubular Joints

105

from the intersection of members or extrapolated linearly or non-linearly to the weld toe. Further

discussion about the extrapolation of stresses will be given later in the report.

It must be noted that studies into the accuracy of SCF equations [1] quote the Efthymiou

equations as being the most accurate. The inclusion of weld details may be the contributor to

the reliability of the equations.

Figure 4-7: Example of shell model using combination of 8-node and 16-node elements

with weld modelled

4.3.2 Advanced FE models – solid elements

Improvements in FE software allowed for 3D brick elements to be used which include the effects

of thickness in the properties of the element. Romeijn [57] recommended the use of brick

elements and modelling weld details as, determined from his analysis of shell and brick

elements, these gave a better approximation of SCFs. The conclusions from Romeijn’s study

were as follows:

16 Nodes –

Brace/Chord

8 Nodes –

Weld profile


Tubular Joints

106

• SCFs should be determined at the weld toe position and not the intersection of the

member wall outer surfaces

• Include weld shapes

• Solid elements to model weld recommended

• 20 node solid elements recommended over 8 node elements

• Use of transition elements not advised

• Length of 20 node element should be less than 1/16 of the total length of the

intersection area

• Need to compensate for influence of boundary conditions for determination of SCFs

Research completed on FE modelling of tubular joints from 1999 onwards uses 3D solid

elements in the majority of models. Chang and Dover [51] recommend 3D brick elements for

modelling of tubular joints as the possibility of including the weld detail in the model as a sharp

notch provides an improved representation of the stress detail, however their analysis was

formed of shell elements due to cost implications.

Karamanos et al [53] modelled tubular joints using 20 node and 8 node solid elements and

concluded that the 20 node element yielded better results. 20 node brick elements were used

to model both weld profiles and tubular joints. Other researchers to use 20 node brick elements

include Gho and Gao [62] and Choo and Qian [63]. Figure 4-8 shows a section through a

tubular joint modelled with brick element and containing weld details.

Figure 4-8: Typical weld details modelled in FE software using brick elements for

tubulars and welds taken from Choo and Qian [63]

4.3.3 Processing results

When extracting results of hot spot stress and SCFs from shell and solid models, attention must

be paid to the location from which SCF values are taken. The obvious but incorrect method is


Tubular Joints

107

to take stresses directly from the brace-chord intersection. Discontinuities in the model at this

location result in higher stresses recorded. In a welded tubular joint, the stresses at the weld

toe would be much higher than the actual hot spot stress as other stresses would also be

present in the weld. The welding process itself would generate residual stresses and extracting

result directly from the weld toe would include this value. Stresses present at this location

include the notch stress, geometric stress and the nominal stress in the brace.

SCFs therefore need to be extrapolated from a distance away from the intersection of tubular

walls to the location of the weld toe. DNV-OS-J101 gives guidance on carrying out this

procedure with the following figure taken from the document.

Figure 4-9: Definition of the geometric stress zone in tubular joints taken from DNV-OS-

J101 [12]

Stresses in the braces and chord of the joint are extrapolated linearly in the geometric stress

zone to the weld toe. For this reason, when modelling tubular joints in FE, a separate region is

defined for the extrapolation region.

DNV-OS-J101 also provides advice on the modelling of tubular joints in the finite element.

Figure 4-10 shows the locations recommended by DNV for the extrapolation of stresses based

on type of element used and whether weld details have been included in the FE model.


Tubular Joints

108

Figure 4-10: Location of weld singularity for hot spot stress extrapolation dependent on

element types used in tubular joint FE models taken from DNV-OS-J101 [12]

For a solid element FE model including weld detail, the DNV standard recommends extracting

stresses away from the weld toe and extrapolating back to this position. In the cases where no

weld profile has been included, it is recommended that stresses should be extrapolated back to

the intersection of the brace with the chord.

4.3.4 Conclusions

Solid elements are recommended for modelling tubular joints with weld details included over

using the traditional shell element approach. Modelling welds leads to more accurate results as

this gives a better representation of the joint’s behaviour. Stresses must be linearly

extrapolated to the weld toe and not taken at this location due to the increase in stress from

notch stresses. A further recommendation for FE modelling of tubular joints is to divide the joint

into sections so that the density of the mesh can be increased for regions of interest.

4.4 Summary

Extensive research has been completed in the field of uniplanar tubular joints however there is

comparatively less work available on the subject of multiplanar tubular joints. Despite the

further work on uniplanar joints, the Efthymiou equations are still the preferred SCF equations

and are referred to in offshore standards such as DNV-RP-C203 [19]. The Efthymiou equations

[22, 23] were based on a parameter study using FE models meshed with shell elements to

represent steel tubular T, Y, K and X joints where the braces were stressed with either axial,

IPB and OPB loads. Stresses were measured at upper and lower extrapolation points and were

extrapolated back to the weld toe to give the SCF. Further modelling using thin-shell elements

was completed by Hellier, Connolly and Dover [48] and Smedley and Fisher [49, 64] and the

results of which were compared against Efthymiou [22, 23] and others [42, 44, 45] in the Lloyd’s


Tubular Joints

109

Register of Shipping report, OTH 354 [1]. The conclusion from this report was that the

Efthymiou equations were considered the most reliable.

A mixture of experimental work and mathematical modelling has been carried out in the field of

fatigue of tubular joints. Steel and acrylic scaled joints were tested by [44, 46] and were

included in the database of SCFs provided in the OTH 354 report [1]. The database compiled

steel and acrylic test data along with SCFs from FE models, which will provide a useful resource

in the validation of FE models for future work.

Limited work has been completed on multiplanar tubular joints [22, 49, 54, 59, 60] in comparison

with the available information on uniplanar joints. FE and scale steel models have been tested

with no clear practical design approach. Discussed by [54] is the idea of using influence factors

which are applied to the out-of-plane braces to represent the behaviour of multiplanar braces.

No SCF equations were developed for the work into multiplanar joints although influence

functions were a concept mooted by Efthymiou for application to uniplanar and multiplanar joints

[22]. Conflicting agreement on whether loads in multiplanar braces have an overall effect on the

joint’s behaviour was also observed in the literature [22, 49].

Recent work on uniplanar joints looks into the concept of stress distribution plots instead of

SCFs applied to a single location [51-53, 55, 56] . Observed in [49] was a shift in location of hot

spot stress away from the crown and saddle locations for some geometrical configurations

therefore examination of stresses at these points only could be missing the maximum stresses.

Looking at the stress distribution around the brace-chord intersection would prevent these

peaks in stress being ignored and could improve the design of the joint. However, due to the

complexity of the stress distribution equations, this approach could be difficult to implement.

FE modelling methods were evaluated in this chapter. Throughout the development of work on

tubular joints, a range of methods have been adopted and can be summarised as follows:

1. Shell elements with no weld modelled where results are reported directly at the brace-

chord intersection

2. Shell elements with weld modelled and results reported at extrapolation points.

Stresses at the weld toe are determined by linear extrapolation

3. Solid elements with weld modelled and the same extrapolation procedure as previous

With the improvement in technology, it is possible to generate finer density meshes with solid

(brick) elements. It is recommended [22, 23, 57, 62, 63] that weld details should be modelled

and results taken from extrapolation points away from the discontinuities at the weld toe.

Efthymiou [22, 23] used 2D shell elements for the parameter study therefore an update on his


Tubular Joints

110

work with improved FE modelling techniques will form part of the investigation into multiplanar

tubular joints.

111

Chapter 5 Finite Element

Modelling of Uniplanar and

Multiplanar Tubular Joints

5.1 Introduction

As identified in the previous chapter, there appears to be conflicting agreement as to whether

the presence of braces in another plane has an effect on the overall behaviour of a steel tubular

joint [22, 49]. Limited and possibly outdated information is available on the subject however

new concepts and research have not been implemented in the design codes for offshore

structures. DNV-RP-C203 recommends that all joints on a structure are to be treated as

uniplanar joints and provides detail on the Efthymiou equations with further reference to the

influence functions as described in [22].

A parameter study where the various parameters as identified for the Efthymiou equations in

Chapter 4 are varied to cover the appropriate validity range was therefore planned for

completion in ANSYS Workbench. Before carrying out the parameter study the modelling

assumptions in ANSYS Workbench needed to be verified in order to check that the stresses

predicted by the model were as close to the actual stresses as possible. A series of uniplanar

joints were modelled with SCFs checked against those determined by the Efthymiou equations.

Further calibration was made against steel and acrylic test data in the HSE document, OTH354

[1] and by checking against a model developed by an independent FE analyst in ABAQUS. A

convergence study was completed to ensure that the mesh density in the area of interest was of

refined enough to give accurate results. Once a suitable mesh had been developed for the

uniplanar joints, models of multiplanar KK joints were developed. These models were then

used to check the behaviour of the multiplanar joints, the details of which will be outlined in the

following chapter.

Chapter 5 Finite Element Modelling of Uniplanar and Multiplanar Tubular Joints

112

5.2 Methodology

5.2.1 Overview of Model Verification Process

The first stage of the FE modelling process is to check whether the stress plots and the SCFs

associated with these and the nominal loading on the structure are being estimated correctly.

Three possible methods were identified as ways in which the assumptions selected for the FE

models could be checked. The following checks were carried out in order to verify the

assumptions applied to a uniplanar FE model:

1. T/Y and K joint geometries selected from OTH 354 [1] which were then modelled in

ANSYS with their SCFs checked against the values in the database in the document

2. Joint geometries of a similar size to those used in offshore jacket structures selected,

modelled in ANSYS and checked against the SCFs determined by using the Efthymiou

equations

3. An independent FE model built by an FE analyst at the University of Manchester using

ABAQUS FEA with SCFs checked against the author’s ANSYS models

To keep the model verification stage simple and because of the data available in the public

domain, uniplanar joints were selected for comparison. With the case of a T or a Y joint, fewer

components to the structure meant that it would be easier to perform a study on selected

geometries where convergence to a final stress was possible.

Initially T and Y joint geometries were selected from the OTH 354 [1] document where SCFs for

all locations (crown and saddle on both chord and braces) were available. These SCFs were

checked against DNV-RP-C203 [19] using the appropriate Efthymiou equations for the type of

loading applied and the joint configuration. The output from the FE models was checked

against both sets of SCFs with the aim of achieving values within ±5% of these values

preferably or ±10% as a limit.

A further method of validation was adopted with an additional FE model developed by an

independent FE modeller using ABAQUS FEA. A model from the OTH 354 document was

selected and modelled by an analyst, Ashley Park at the University of Manchester. The

dimensions, weld details and boundary conditions were kept constant with meshes generated

independently but with the aim of using the same element size, element type and aspect ratios.

As mentioned previously, a convergence study was completed in order to determine a suitable

element size with which the model can be meshed to give a good approximation of stresses

without using large amounts of computer memory. Reducing the number of elements and

nodes shortens the time for each run of the model so selecting an optimum element size for the


113

geometry is essential. For a uniplanar T joint configuration the element size in the region

nearest to the weld was reduced until the stress at the weld toe converged. It is possible for

some joint configurations to reduce the number of nodes and elements in the mesh by

modelling half and quarter models due to the symmetry in the model. Application of this method

was possible for uniplanar joints but could not be applied to multiplanar KK joint configurations

particularly when looking at loading combinations in one brace only. Because of the limitations

of using this method, full joints were modelled for both uniplanar and multiplanar configurations

with the convergence study carried out on a T joint.

5.2.2 Modelling Considerations

As indicated in Chapter 4, three main types of FE model have been implemented by different

authors in the past:

1. Shell elements with no weld modelled where results are reported directly at the brace-

chord intersection

2. Shell elements with weld modelled and results reported at extrapolation points.

Stresses at the weld toe are determined by linear extrapolation

3. Solid elements with weld modelled and the same extrapolation procedure as previous

Several sources [22, 23, 57, 62, 63] recommend that modelling the weld and using solid

elements in the FE package is the best approach. With significant improvements in computing

technology, fine meshes comprising solid brick elements can be easily handled by the computer

therefore all models considered for the analysis were built with solid elements. This ensures

that the thickness of the structure is modelled leading to a realistic behaviour of the structure

compared with the other methods given.

The method for reporting of stresses need to considered in the development of suitable models

for the parameter study. As detailed in Chapter 4, results can be reported in different locations

depending on the type of FE model implemented (see Figure 4-10). For an FE model using

solid brick elements with the weld detail modelled, DNV-OS-J101 [12] recommends reporting

stresses at points away from the location of stress concentration and extrapolating back to the

weld toe.

To ensure the validity of the output from the FE models, previous studies have used test data

and/or results from models of a joint in another FE package. A database of steel and acrylic

joint test data was compiled by Lloyd's Register of Shipping [1] and the information in this

document was used as a starting point for checking the assumptions made in the modelling.

The document gives results for a range of uniplanar X, T/Y and K joint configurations stating the


114

SCFs at the crown and saddle locations under different loading situations. FE models of a

selection of K and T/Y joints were developed using both fixed and pinned boundary conditions.

To summarise, the following must be considered in FE modelling of tubular joints:

• Type of element (shell or solid, tetrahedral or quadrilateral)

• Modelling of weld detail

• Boundary conditions (fixed-fixed, pinned-pinned, simply supported)

• Location for reporting of stresses

5.2.3 FE Model Details

5.2.3.1 Geometry and weld details

Initial models of uniplanar T/Y and K joints were built based on data from OTH 354 [1] in order

to verify the assumptions made within ANSYS Workbench. These models were generated

using solid elements with the weld details modelled. A fixed boundary condition was applied to

both ends of the chord initially. At the ends of the braces, plates with a high Young's Modulus

were included to allow for application of loads to the joint and to prevent any unrealistic

deformation in the braces.

As recommended by various sources [22, 23, 57, 62, 63], weld details were included in the

analysis. Due to the variation in experimental procedures, the authors of [1] decided to factor all

results from testing without weld details by a mean reduction factor for both chordside and

braceside values. Although there is no indication of the sizing of the welds in any of the test

data, information was taken from as-built drawings from GL Garrad Hassan's previous projects

(see Figure 5-1) and adapted for the different geometries. Welds were included in ANSYS as

additional material modelled with solid elements.

The weld sizing depends on the thickness of the brace as shown in Figure 5-1. The inclination

of the brace also affects the geometry of the weld, which results in a change of section around

the brace-chord intersection. Initial models kept the weld dimensions fixed however the change

in section could lead to spurious results adding stiffness to the overall behaviour of the joint.

Due to this change in the weld's geometry, different models had to be set up for the brace

inclinations as indicated in Figure 5-1.


115

Figure 5-1: Weld geometry details for different brace inclinations from GL Garrad Hassan

In order to generate meshes with some degree of symmetry, the model was divided into

sections so that nodes could be forced to be created at specific locations.

Establishing symmetry in the model allowed for modifications to be made to enable K and KK

joint geometries to be developed from the initial setup. Creating divisions in the model also

allows the user to assign additional mesh controls to specific edges and faces to further refine

the mesh. Results can also be reported on a construction path defined by an edge so the upper

and lower bounds of the extrapolation region were created as slices through the model.

Figure 5-2: Stress extrapolation regions defined on both brace and chord of T joint in

ANSYS Workbench


116

Figure 5-3: Divisions on a uniplanar T joint to allow for different mesh density generation

and mesh symmetry taken from ANSYS Workbench

As mentioned previously, due to discontinuities present at the weld toe on the FE model, it is

incorrect to simply extract stresses at this location. Linear extrapolation of stresses back to the

weld toe is the standard approach to FE modelling with the upper and lower bounds dependent

on the geometry of the joint.

Region 3

Region 1 Region 2

Region 4 Region 5


117

Figure 5-4: Definition of stresses in welded structures taken from DNV-OS-J101 (2010)

[12]

As shown in Figure 4-9 on page 107, the hot spot stresses at the weld toe are determined by

reporting stresses at the shown locations and linearly extrapolated back to give a lower stress.

The reason for this is to exclude any other stresses which could be present due to

discontinuities in the model. Figure 5-4 shows how these stresses are likely to build up in the

model.

For hot spot stress, the geometric stress in the section of the graph in Figure 5-4 is applicable.

As shown, the stress distribution on this section becomes linear therefore it is reasonable to

adopt a linear extrapolation of stresses back to the weld toe.

5.2.3.2 Using the Parameter Set function in ANSYS Workbench

ANSYS Workbench was used to develop the models due to the Parameter Set function

available in the program. This function allows geometries to be developed such that individual

dimensions can be defined by user specified parameters. The models were set up so that

changing any of the following parameters would allow the model to be regenerated with all

members and extrapolation points positioned correctly.

Parameters which could be changed:

• Brace diameter


118

• Brace thickness

• Brace inclination

• Chord diameter

• Chord thickness

• Chord length

• Angle between planes

5.2.3.3 Meshing

With the model divided up into sections, it was possible to assign meshing controls to edges,

faces and bodies in the different regions. With the latest version of ANSYS, these controls

could be based on parameters in the Parameter Set so that sizing controls would vary when the

overall dimensions of the joint altered. A fine density mesh was used in the region of stress

concentration with the mesh density becoming coarser as the model progressed further from

this location. Implementing a change in mesh density reduces the computer time greatly as the

overall number of nodes and elements forming the mesh is decreased.

With reference to Figure 5-3, region 1: the area of interest in terms of stress concentration, body

sizing controls were assigned to this region in order to generate a fine density mesh. The

element size was set as a parameter which was dependent on the diameter of the brace. Fixing

this setting to be dependent on a dimension ensures that consistency in the modelling

technique is carried through the investigation. As the diameter of the chord increases, the

element size increases making sure that the same number of elements are used in the stress

analysis.

Figure 5-5: Meshing controls assigned to a uniplanar T joint taken from ANSYS

Workbench


119

Other sizing controls applied to region 1 include edge sizing around the braces and the

extrapolation region, which again are dependent on parameters in the Parameter Set. This was

set up to ensure that a consistent number of elements and nodes around the extrapolation

region was present so that the post-processing of results was simplified when looking at stress

distribution plots.

The reliability of the output from an FE model depends highly on the validity of the meshes

assigned to the geometry. Poor quality meshes can lead to erroneous results. Checks on the

aspect ratio of elements were carried out in the Mechanical part of ANSYS Workbench and a

mesh convergence study was also carried out. The mesh density around the brace-chord

intersection was increased until the stresses determined from the model converged to a

solution. As the number of elements and nodes increased, the duration of running the ANSYS

Solver increased therefore a suitable element size was selected to ensure that the stresses

reported were close to that determined by the convergence study. For further information on

the convergence study, see section 5.3.2 on page 126.

The aspect ratio of elements used in the mesh also affects the reliability of results. For areas of

detail, an aspect of ratio of 1:1 is recommended and this can be increased from 1:3 to 1:5 in

regions where the results are not critical.

The choice of element for an FE model can also alter the output of stresses. Literature on the

subject of FE modelling of tubular joints recommend the use of 20-noded solid brick elements

as these yield the most reliable results [57]. However, due to the complexity of the geometry

involved in the modelling of multiplanar tubular joints with the weld detail included, it was not

always possible to develop a mesh comprising 20-noded quadratic elements. In ANSYS

Workbench, meshes can be generated automatically once sizing, mapped meshing and pinch

controls have been assigned. The software selects a suitable element for the geometry and its

controls and then uses this information to generate meshes with suitable aspect ratios. If the

model has been built with wall thickness in the DesignModeler component of ANSYS

Workbench, the software automatically selects a 3D element. For a complex geometry,

including the multiplanar joint configuration with weld details included, the automatic meshing

tends to opt for tetrahedral meshes and requires very specific mesh controls to produce a

quadratic mesh, which proved difficult and time consuming for most of the K and Y joint

configurations modelled. However, where possible, joints were modelled with both quadratic

and tetrahedral meshes with similar element sizes to check whether results differed.


120

Figure 5-6: Variation in mesh sizes for different regions in the joint taken from ANSYS

Workbench


121

a) Quadratic solid 20node elements with different aspect ratios (LHS 2:7, RHS 1:1)

b) Tetrahedral meshing with mostly aspect ratios of 1:1

Figure 5-7: Types of elements available in ANSYS Workbench

5.2.4 Reporting of stresses

As mentioned previously, results were reported on the upper and lower bounds of the

extrapolation regions (see Figure 5-2). This allowed for the results to be output for coordinates

around the brace and chord. With the modelled divided as shown in Figure 5-3, the crown and

saddle locations were defined on the extrapolation paths so it was possible to convert the

coordinates into an angle from 0º to 360º making the extrapolation of results easier. Another

advantage of including extrapolation regions in the model was that the meshing tool in ANSYS

was forced to generate nodes at exactly where stresses were to be reported. This ensures that

the actual stresses at the upper and lower extrapolation bounds are given as opposed to

averaged stresses when reporting between nodes.

a 3.6a a


122

5.2.5 Model Verification Strategy

The model verification process was divided into the following stages:

1. Check nominal stresses present in the loaded brace

2. Check data in the OTH database against Efthymiou

3. Select suitable joint geometries from the OTH database and build joints in ANSYS

4. Model joints with different density meshes to see whether large jumps in stress occur

5. Perform separate calculations with tetrahedral and quadratic meshes where possible to

identify variation in results

6. Compare selected joints against the OTH and Efthymiou SCFs – ratios of SCFs from

the models and calculated SCFs used as a means of comparison with the aim of

achieving results within ±5% of OTH or Efthymiou if possible

7. Validate model further by comparing output of joint built in another FE program by Park

– use same criteria for comparison as mentioned in step 5

5.3 Results of Model Verification

5.3.1 Checks on the nominal stress

A simple check on the nominal stress applied to the brace was the first stage in the model

verification process. The loading applied to all joints was as follows:

1. Axial load of 1000N applied in compression

2. Shear force of 100N applied to the centre of the plate at brace ends to give IPB

3. Shear force of 100N as for IPB but in different direction for OPB

For joint configuration 3, taken from the OTH report [1], the following dimensions were used:

• Chord diameter = 168mm

• Chord thickness = 6.27mm

• Chord length = 882mm

• Brace diameter = 89.04mm

• Brace thickness = 5.33mm

• Brace length = 441mm

This gives a nominal stress of 0.71N/mm2 for the axial load case. For bending, the stress will

vary depending on the location selected so the stress halfway down the brace at a distance of

approximately 220mm will be 0.79N/mm2.

Stress plots in ANSYS are given in Figure 5-8 to Figure 5-10 for the T-joint described above.

The scale on the plots has been altered to around 0.05N/mm2 above and below the expected

nominal stresses to give a better indication of where the nominal stresses occur.


123

Figure 5-8: Stress plots for T-joint under axial load with fixed scale demonstrating

nominal stress of around 0.7N/mm2 present in brace (taken from ANSYS Workbench)


124

Figure 5-9: Stress plots for T-joint under IPB with fixed scale demonstrating nominal

stress of around 0.8N/mm2 present in brace (taken from ANSYS Workbench)


125

Figure 5-10: Stress plots for T-joint under OPB with fixed scale demonstrating nominal

stress of around 0.8N/mm2 present in brace (taken from ANSYS Workbench)


126

Under axial load, the region of nominal stress is observed in the upper part of the brace with

increasing stress as the brace-chord intersection is approached. A stress of around 0.71N/mm2

is recorded in this upper region of the brace.

For the bending cases, a smaller region with the calculated nominal stress is observed. This is

due to the stress’s dependency on the moment generated, which varies with the location on the

brace. The stress calculated in these cases was for approximately the midpoint on the brace

and the plots confirm that the nominal stress of 0.79N/mm2 can be found at this location for both

IPB and OPB.

5.3.2 Mesh Convergence Study

Using the T-joint for the nominal stress check, a mesh convergence study was completed with

the number of nodes and elements in the model increased until stresses converged within 1% of

each other. The following graph shows the variation of stress with the number of nodes used in

the FE analysis. Stresses plotted on the graph have been taken from the upper and lower

bounds of the extrapolation region and linearly extrapolated back to the weld toe.

Figure 5-11: Variation in stresses at key locations on the brace and chord under different

loadings


127

The results in Figure 5-11 indicate that the variation in stress reduces as the number of nodes

increases. A flattening in the curves can be seen as more elements and nodes are used in the

FE model which could infer that the stresses are converging to a solution. Analysis of the

percentage change in stress with each iteration indicates that results are converging with a 1%

difference between the last sets of results.

Figure 5-12 and Figure 5-13 show two different meshes with elements sizes of 1.5mm and 3mm

respectively. These two figures show fine and medium density meshes used in the mesh

convergence study with Figure 5-12 corresponding to the converged results and Figure 5-13

showing the results for a number of nodes around 270000. Stress plots appear to be very

similar with the hot spot stresses identified in the same location. When examining the increase

in stress for the minimum principal stress however, a jump in stress of 6% can be observed.

The runtimes associated with the finely meshed model were much higher than for the model

with 3mm sized elements in the area of interest. A balance would therefore need to be struck

between accuracy and runtime hence an intermediate element size is recommended where,

with reference to Figure 5-11, a number of nodes between 800,000 and 1,000,000 could be

achieved.

Figure 5-12: Stress plot for fine density mesh for T joint under OPB in ANSYS Workbench


128

Figure 5-13: Stress plot for medium density mesh for T joint under OPB in ANSYS

Workbench

With the checks on the nominal loads in the braces in the ANSYS model matching the

calculated nominal stresses as indicated in section 5.3.1 and stresses converged to within 1%

of previous values, it could be inferred that the assumptions used in the author’s models are

sufficient to achieve reliable results. Modification of the models’ properties are required for

application to a KK joint and a suitable element size must be selected to produce reliable results

but with reasonable runtimes.

Further checks against published data, the Efthymiou equations and an independent model in

another FE package have been made and are outlined in the next pages of this chapter.

5.3.3 Efthymiou vs OTH

Comparing the data compiled in OTH 354 [1] with that from Efthymiou showed that there were

disparities between the two sets of numbers. Data in Table 7-10 shows that there are

significant variations in SCFs determined by Efthymiou and steel or acrylic testing. The ratio of

SCFs from the OTH document and by Efthymiou was taken with results within 5% of each other

coloured blue in the table. Results outside the ±10% range have been coloured red for easy

identification.

Only a handful of results are within 5% of each other with the majority of results either

underestimating or overestimating SCFs. There appears to be no logical pattern in these

variations however it seems that the chord crown SCF under axial load for steel and acrylic test


129

data is around 70% of that of the test data. For IPB, SCFs appear to be higher on the whole for

both chord and brace locations with braceside crown SCFs around 50% higher. This variation

in SCF values for both methodologies makes it difficult to establish against which method all FE

models should be checked.


130

Tab

le 5

-1:

Co

mp

ari

so

n o

f S

CF

s d

eri

ved

usin

g t

he E

fth

ym

iou

eq

uati

on

s a

nd

SC

Fs t

aken

fro

m O

TH

354 f

or

a r

an

ge o

f g

eo

metr

ies s

ele

cte

d f

rom

th

e

data

base


131

5.3.4 FE models checked against OTH

As shown in Table 7-1, SCFs were not always available for all locations under different loads so

joints with the most information were selected from the database. Different meshes were used

on the models with either tetrahedral or quadratic elements forming the mesh. For each mesh

implemented, the number of nodes and elements as well as the duration of the calculation was

recorded. This allowed for the optimisation of the FE model for the parameter study as a

suitable element size could be selected which ensured that calculations’ durations were kept to

a minimum but stress outputs were accurate enough.

Results for all models in the verification process are given in Table 5-2 to Table 5-5, which

provide the following information:

• Geometry selected – dimensions of brace and chord

• Information about the ANSYS calculation (duration, number of elements/nodes, type of

element used)

• SCFs from ANSYS, OTH report, Efthymiou

• Ratio of SCFs for comparison

For models where the node and element numbers were not recorded, a value of 0 has been

given.

With reference to the tables, the joints examined for which steel and acrylic test data were

available were joints 3, 8 and 9. Results were mixed with brace crown SCFs for joint 3 under

axial load consistently reported by test data as 33% of that obtained in the ANSYS analysis.

For joint 3 reasonable predictions of SCF were achieved for IPB load case at the brace crown

when comparing with the test data however chord crown SCFs were around a third higher than

values reported in OTH 354.

Brace crown SCFs under axial load for joint 8 compared better against the OTH data with

results close to the measured SCFs. Reasonable results were achieved for chord and brace

saddles under OPB and chord and brace crowns under OPB for the T joint 8 with results closer

to the measured values when using a von Mises stress plot (models 8a – 8c). The von Mises

model takes an average of stresses in all directions so results were much lower when compared

with the maximum principal stresses.

A Y joint was modelled for joint 9 with tetrahedral meshing used due to the geometry. For SCFs

at all locations, poor correlation with the data in the OTH report was observed. Further checks

were completed with the output from these models against Efthymiou to confirm whether errors

were present in the modelling assumptions.


132

Tab

le 5

-2:

Geo

metr

ies m

od

elled

in

AN

SY

S W

ork

be

nch

wit

h S

CF

s d

eri

ved

by

Eft

hym

iou

an

d o

bta

ined

fro

m F

E m

od

el (T

ab

le 1

of

2)


133

Tab

le 5

-3:

SC

Fs f

rom

FE

, E

fth

ym

iou

an

d O

TH

rep

ort

[1]

co

mp

are

d w

ith

each

oth

er

for

geo

metr

ies

giv

en

in

Tab

le 5

-2 (

Tab

le 1

of

2)


134

Tab

le 5

-4:

Geo

metr

ies m

od

elled

in

AN

SY

S W

ork

be

nch

wit

h S

CF

s d

eri

ved

by

Eft

hym

iou

an

d o

bta

ined

fro

m F

E m

od

el (T

ab

le 2

of

2)


135

Tab

le 5

-5:

SC

Fs f

rom

FE

, E

fth

ym

iou

an

d O

TH

rep

ort

[1]

co

mp

are

d w

ith

each

oth

er

for

geo

metr

ies

giv

en

in

Tab

le 5

-4 (

Tab

le 2

of

2)


136

5.3.5 FE models checked against Efthymiou

A total of 11 models were generated with different geometries for checking against the

Efthymiou equations, the results of which are given in Table 5-2 to Table 5-5. Results varied for

each of the joints (either T or Y joint) however it was consistently noted that brace crown SCFs

for braces under IPB were much lower than the predictions by Efthymiou. These values varied

between as low 32% and a maximum of 89% of the Efthymiou SCFs. Predictions of chord

crown SCFs under axial load were reasonable for most of the cases examined however results

were still outside the maximum ±10% range.

The ratio of SCF from the FE models and the SCF from Efthymiou were calculated for all

models examined and plotted for each location and load case. Figure 5-14 below shows the

variation in the SCFs with the boundaries for results within ±5% and ±10% depicted by thick and

thin red lines respectively.

Figure 5-14: Plot of SCF_FE/SCF_EFT for different load cases and locations around the

brace-chord intersection

As shown in the figure above, few results fell within the desired boundaries. One of the

geometries was selected for further verification against models generated in another FE

program by Park.


137

5.3.6 FE models checked against independent models

A simple T joint was selected for modelling in ABAQUS by Ashley Park at the University of

Manchester. Weld details were modelled along with fixed boundary conditions applied the ends

of the chords. Results were reported at the extrapolation points and calculated back to the weld

toe for comparison. The following results were obtained:

Table 5-6: Comparison of SCFs for joint 3 modelled in ANSYS Workbench and ABAQUS

with each method, Efthymiou and data from the OTH report [1]

NB. LCD represents the author’s model built in ANSYS, OTH stands for the Lloyd’s Register of Shipping [1] database

and the ABAQUS FE model results by Ashley Park are denoted by the initials AP

For evaluation of results, the output from joint 3E, highlighted in red in the table above, were

used. The number of nodes and elements had been increased to allow for convergence of

stresses and results differed from previous values by at most 4%. The mesh refinement

process was terminated after this run as the high number of nodes and elements resulted in

computations with durations of greater than 1.5 hours. Models completed by the author were

labelled as “LCD” whereas output from models generated by Park in ABAQUS was denoted as

“AP”. Comparison of these two models have been highlighted in yellow under “LCD vs AP” in

the table.

Reasonable correlation between the FE models was achieved for chordside SCFs with results

within 10% of each other. For OPB and IPB, the output was less successful with brace crown

SCFs for IPB around 22% lower for models generated in ANSYS compared with the ABAQUS

output.

When comparing against Efthymiou, the two models fare well for chordside SCFs under axial

load and it can be noted that both models produced smaller brace crown SCFs. Differences

can be observed for OPB SCFs with the ANSYS models closer to Efthymiou for chordside


138

stresses and ABAQUS closer to the braceside SCFs determined by Efthymiou. Brace crown

SCFs under IPB for both models appear to be lower than that calculated using the Efthymiou

equations.

A further check of the two models was carried out against the data provided in the OTH report.

It appears that, on the whole, the SCFs predicted by both models were around 20% higher than

those given in the database. Only chord saddle SCFs under axial load were similar to the OTH

report and, for both models, brace crown SCFs under axial load were over 4 times higher than

the measured values.

5.4 Evaluation of Results

5.4.1 Summary of results

There was significant variation in the results produced in the model verification process;

however, convergence in SCFs was achieved for a selected joint so that a suitable element size

could be selected for the models in the parameter study. A further convergence test was

completed for a multiplanar KK joint to reinforce confidence in the modelling techniques used.

SCFs given in the OTH data report varied considerably compared to those predicted by

Efthymiou and it was concluded that no clear pattern of variation emerged. Few SCFs were

within 5% of each other and it seemed that IPB SCFs were overpredicted by Efthymiou for most

cases. When comparing output from the FE models with OTH data, SCFs were mostly lower for

the FE models but, again, disparities could be seen for different geometries therefore making it

difficult to ascertain whether inconsistencies were present in the model.

Further checks were made against the Efthymiou equations and results were also varied. It was

clear that, for all the geometries examined, the IPB brace crown SCFs were much smaller in the

FE models. Brace crown SCFs under axial loading were also lower compared to Efthymiou

however it was noted in the HSE document, "Offshore Installations: Guidance on design,

construction and certification" [65], that the Efthymiou equation gives a conservative estimate

for SCF at brace crown under axial loading.

A T joint was selected randomly and modelled in ABAQUS for comparison against ANSYS,

OTH and Efthymiou. Again, variation could be seen in all of the methods but both FE models

gave lower SCFs for brace crown SCFs under both axial and IPB load cases when compared

with Efthymiou.


139

With variation noted for all the model verification processes performed, differences in the

modelling assumptions must exist. This section will identify and discuss which factors could be

causing this variation in results.

5.4.2 Potential inconsistencies in modelling

approaches

5.4.2.1 Extrapolation

The variation in stresses and SCFs derived by the different methods could be attributed to

approaches specific to each type of modelling used. One area of concern surrounds the

extrapolation of stresses, namely whether a linear or nonlinear method has been used and the

locations at which the stresses have been reported. With the Efthymiou equations reference is

made to the "ECSC agreed procedure" which is outlined in [66]. Figure 5-15, taken from [66],

shows the geometric and local stresses near the weld on a tubular joint. The locations for

reporting stresses are indicated in the diagram but the actual values of these positions are not

given. Defined in Figure 5-16 is the upper extrapolation point on the chord at the saddle

location which is positioned at a 5° angle with its origin at the centre of the brace and chord,

starting at the weld toe and progressing down the chord.

Because the lack of clarity about the locations of stress extrapolation points given in the

Radenkovic paper, further documents detailing the "ECSC agreed procedure" were sought. A

further diagram given in Figure 5-16 and taken from [67] indicates the dimensions for the upper

and lower extrapolation points.

For the brace, the extrapolation points are:

1

11

2 1

2

Crown: Upper extrapolation point, 0.65

0.2 for 4mmCrown: Lower extrapolation point,

otherwise 4mm

Saddle: Upper extrapolation point,

Saddle: Lower extrapolation point,

A rt

rt BB

A A

B

=

>=

=

1B=

For the chord, the extrapolation points are given as follows:

Chapter 5 Finite Element Modelling of


Crown: Lower extrapolation point,

Saddle: Upper extrapolation point, 5 ang


Figure 5-15: Geometric and local stresses for a tubular joint indicating the extrapolation

points (ECSC method) and stress jump at weld toe taken from Radenkovic (1981)

Figure 5-16: Stress extrapolation points in tubular joints in accordance with the ECSC

procedure taken from Haagensen and Macdonald (1998)

Finite Element Modelling of Uniplanar and Multiplanar Tubular Joints

140

43

33

4


0.2 for 4mmCrown: Lower extrapolation point,

otherwise 4mm

Saddle: Upper extrapolation point, 5 angle from weld toe with

A RTrt

rt BB

A

=

>=

= °

4 3

origin at centre of chord

Saddle: Lower extrapolation point, B B=

Geometric and local stresses for a tubular joint indicating the extrapolation

points (ECSC method) and stress jump at weld toe taken from Radenkovic (1981)

Stress extrapolation points in tubular joints in accordance with the ECSC

procedure taken from Haagensen and Macdonald (1998) [67]


0.2 for 4mm

otherwise 4mm

le from weld toe with

>

origin at centre of chord/brace

Geometric and local stresses for a tubular joint indicating the extrapolation

points (ECSC method) and stress jump at weld toe taken from Radenkovic (1981) [66]

Stress extrapolation points in tubular joints in accordance with the ECSC


141

It is unclear whether the dimensions as indicated in the Haagensen and Macdonald paper have

been adopted by Efthymiou for his study. The locations have not been explicitly stated in the

paper so there is a possibility that these could differ from Haagensen and Macdonald. What is

clear, however, from [22, 23] is the method of extrapolation adopted:- Efthymiou states that a

linear extrapolation between the points identified has been used to determine the stresses at

the weld toe.

DNV-OS-J101 [12] outlines the recommended extrapolation procedure given in Appendix D of

the standard (for reference, see Figure 4-9 on page 107). This follows a similar approach to

Efthymiou with the same locations for upper and lower extrapolation cited for extrapolation

points in the brace. With chord extrapolation points, the locations differ with a simpler approach

used for the saddle upper extrapolation point.

For the brace, the extrapolation points are:

1

1

2 1

2 1


Crown: Lower extrapolation point, 0.2



A rt

B rt

A A

B B

=

=

=

=

For the chord, the extrapolation points are given as follows:

43

3

4 3

4 3


Crown: Lower extrapolation point, 0.2



A RTrt

B rt

A A

B B

=

=

=

=

Unlike the ECSC procedure the location of stress extrapolation points does not vary as

progression is made around the brace perimeter.

Extrapolation procedures outlined in the OTH 354 report [1] follow the ECSC agreed procedures

as used by Efthymiou. The document specifically states that the methodology is applied to the

positioning of strain gauges on steel and acrylic test specimens however it could be inferred that

this same procedure applies to reporting stresses in FE models. Another extrapolation method

by Gurney is detailed in [1] where a minimum strain gauge distance of 0.4T applies to both

braceside and chordside stresses.


142

With reference to Figure 4-9 on page 107 and Figure 5-4, the reason for using extrapolation of

stresses is to ensure that the geometric stress is used and not the notch stress resulting from

stress concentration. If a different extrapolation point outside the geometric stress zone is used,

there is a possibility that the nominal stress is used instead which could lead to a smaller stress

extrapolated back to the weld toe. Checking the values of SCF from Efthymiou with those from

the FE models for chord crown locations indicates that results are mixed and therefore

inconclusive with regards to influence of extrapolation points.

5.4.2.2 Use of different elements

Advances in computer technology means that today's hardware is capable of dealing with FE

packages generating models with potentially millions of nodes and elements, although run times

for such configurations could be lengthy. State-of-the-art technology has the ability to deal with

a higher number of solid elements, such as bricks, therefore allowing the effects of thickness of

a structure to be accurately modelled. When Efthymiou completed his research in 1988, FE

packages predominantly worked with shell elements and relatively coarse meshes in

comparison with models developed recently. Differences in SCFs obtained from the Workbench

models and those determined using the Efthymiou equations could be as a result of the choice

of element in both models. Literature on the subject of FE modelling [57] recommends using

20-noded solid elements for modelling of tubular joints.

Where possible different elements (tetrahedral and quadratic) were used with a similar element

size to check the influence of element type on the stresses in the model. The results are

summarised in Table 5-7:

Table 5-7: Comparison of SCFs using different elements

Changing the type of element changes the number of nodes and the number of elements in the

structure if the same element size is used. For the majority of results given in the table above,

there is little difference between extrapolated SCFs with most values within 5% of each other.


143

5.4.2.3 Boundary conditions

The work completed by Efthymiou [22] includes a chord-end fixity parameter, C, which is

modified depending on the boundary conditions (i.e. fixed, pinned).

Where: 0.5 1.0 Typically 0.7C C≤ ≤ =

For a joint with fixed-fixed boundary conditions, a value of 0.5C = applies. When both ends of

the chord are pinned, 1.0C = is used.

For all data compiled in the OTH document [1] the assumption for all test data surveyed, the

chord ends were pinned at both ends. This approach was adopted due to the lack of

information given on chord length, chord-end fixity or test rig structure in the literature

surrounding the subject.

When checking the output from FE models with the Efthymiou equations, a chord-end fixity

parameter of 0.5 was applied to the SCFs where appropriate as fixed-fixed boundary conditions

were used in the models. The influence of incorrect boundary conditions can be ruled out as a

source of error when examining outputs with Efthymiou as this can be clearly specified. With

regards to the modelling completed in ABAQUS, the same fixity conditions were used but

element size varied, which could account for the variation in results.

However for results compared with the database, due to the uncertainty of the conduct of

experiments, there is potential for variation in the FE output and the data given. Changing the

chord end fixity conditions to pinned-pinned or simply supported would change the amount of

deflection in the chord particularly at the crown locations. This is due to the additional

movement available in the structure with the possibility for the joint to rotate at its supports for a

pinned-pinned system and also to move along the length of the chord for the simply supported

case. On examination of the results for the FE models checked against OTH, stresses at the

crown location for the majority of cases were higher in the report than the extrapolated ANSYS

stresses. It could therefore be inferred that the joints in the OTH report were supported

differently than the fixed-fixed condition used in the FE models.

5.4.2.4 Mesh density

There is likelihood that mesh density could be attributed to the variation in the SCFs determined

by Efthymiou and by ANSYS and ABAQUS FEA. As mentioned in Section 5.4.2.2, when

Efthymiou completed his study, it wasn’t possible to generate fine density meshes with the

technology available at the time. For the models produced in ANSYS, different density meshes

were modelled with the aim of achieving stress convergence as the meshes became finer. With

the meshes using an element size of anything up to 1/100th of the brace diameter and over

Chapter 5 Finite Element Modelling of

1,000,000 nodes, the chance for disparity between SCFs as a result of mesh density is highly

likely when comparing against Efthymiou.

For comparisons against different FE models, the ele

contributing to the variation in SCFs.

used in the study for ANSYS, where an element size of 1.5

interest. This mesh density allowed for convergence of results however the run time of the

model was excessive.

element size was increased for the parameter stud

implemented in the mesh, as shown in

The model produced in ABAQUS is given in

for OPB applied to the brace. Differences to note from the three models are the use of element,

the element size and the extents of the fine density mesh region. For the ABAQUS model, the

fine density mesh region covers a smaller area than the ANSYS model particularly when looking

at brace crown locations. On examination of SCFs at this location (see

that the values taken from the ABAQUS

SCFs. Brace saddle SCFs for both axial and OPB load cases were also higher

40%. Use of larger elements in the proximity of the extrapolation regions at this point could be

cause of this increase

Figure 5-17: Stress plot for T joint under OPB in ABAQUS

Finite Element Modelling of Uniplanar and Multiplanar Tubular Joints

144


likely when comparing against Efthymiou.

For comparisons against different FE models, the element type and mesh size could be

contributing to the variation in SCFs. Figure 5-12 on page 127 shows the finest density mesh

used in the study for ANSYS, where an element size of 1.5mm was used in the region of


model was excessive. A balance between mesh density and run time was required so the

element size was increased for the parameter study. An element size of 3mm was also

implemented in the mesh, as shown in Figure 5-13 on page 128.

The model produced in ABAQUS is given in Figure 5-17. All figures given show the stress plots



mesh region covers a smaller area than the ANSYS model particularly when looking

at brace crown locations. On examination of SCFs at this location (see

that the values taken from the ABAQUS model were around 20-30% higher than the ANSYS

SCFs. Brace saddle SCFs for both axial and OPB load cases were also higher


cause of this increase in stress.

: Stress plot for T joint under OPB in ABAQUS



ment type and mesh size could be

shows the finest density mesh

mm was used in the region of


A balance between mesh density and run time was required so the

y. An element size of 3mm was also

. All figures given show the stress plots



mesh region covers a smaller area than the ANSYS model particularly when looking

at brace crown locations. On examination of SCFs at this location (see Table 5-6), it appears

30% higher than the ANSYS

SCFs. Brace saddle SCFs for both axial and OPB load cases were also higher – around 30-



145

Chord crown and saddle results were good for axial load cases and reasonable for bending

cases with SCFs within ±10% of each other for axial loads and ANSYS SCFs 15% higher for

OPB and IPB. As the area of fine density meshing continues further on the chord, there is the

possibility that better correlation between the models exists because of this. Important to note

from the ABAQUS analysis was that the results were not converged to a solution which could be

another reason for differences in stress between the ANSYS and ABAQUS models.

5.4.2.5 Inclusion of weld detail

Welds were included in the analysis of the joint in the FE programs and in the parameter study

completed for the Efthymiou equations. For the OTH report, a weld fillet correction factor taken

from the document, “Finite element analysis for Task 4A of Lloyd’s project – Stress

concentration factors in tubular complex joints” [68], was applied to chordside and braceside

stress (0.95 and 0.86 respectively) for results where no weld details were modelled. The

presence of a weld in the model stiffens the joint therefore reducing the stress at the brace-

chord intersection. Different weld profiles used in the models could lead to a variation in the

stresses extrapolated back to the weld toe.

Comparing the two FE models given in Figure 5-13 and Figure 5-17, the weld details look

similar (and should be the same) although it could be said that the profile at the saddle location

appears smaller for the ABAQUS model. However, if a variation between weld profiles exists,

this could be considered to be minimal therefore having little effect on the stresses in the model.

It is more likely that the region of fine meshing plays a greater role in the disparity between

results.

For comparisons made against Efthymiou and the OTH report, differences in SCFs obtained

could be attributed to the modelling of the weld profile. In both papers [22, 23], the weld

dimensions are not mentioned or referenced so the weld geometry adopted by Efthymiou in his

parametric study cannot be ascertained. A similar difficulty with the data provided by Lloyd’s [1]

– a mixture of models with and without weld profiles form the database, factors have been

applied to non-welded models and it is not identified which models are which.

5.4.3 Summary

To summarise, the differences in SCFs for each of the methods could be attributed to:

Efthymiou

• Element type and mesh density – shells used and possibly coarse meshes

• Unknown weld profile

• Possibly different extrapolation points

• Boundary conditions can be ruled out as possible variation in modelling assumptions –

this is included in the Efthymiou equations by a chord-end fixity parameter


146

OTH Report

• Different location of strain gauges – could lead to smaller stresses extrapolated to weld

toe

• May or may not include weld profiles – no information on this however models without

weld details were factored to account for this

• No information in the report on boundary conditions however the authors of the report

have assumed all joints to be pinned at their chord ends

ABAQUS modelling

• Different element sizes used which could contribute to the variations in SCFs

• Convergence study not performed due to computational limits

• Extents of fine density mesh region smaller for brace saddle locations which could

attribute to different SCFs

• Tetrahedral mesh used – this should bear little influence on the SCFs but should be

noted

• Fixed-fixed boundary condition used to support chord-ends so inconsistencies due to

boundary effects can be ruled out

• Model in ABAQUS did not reach convergence

5.4.4 Conclusion

Differences were observed in the all the model verification methods described in this chapter

with no particular pattern in these variations. The factors which could be attributing to the

disparity between SCFs determined by the various methods have been identified and

acknowledged in order to develop a reliable FE model for the parameter study. Results for

Park’s model in ABAQUS were acceptable for chord saddle and crown locations under axial

load but less comparable with the ANSYS model for brace locations. A possibility for this

variation is the region of fine density meshing which extends further for the ANSYS models.

Despite the variation in the model calibration and verification processes completed, confidence

was established in the modelling techniques implemented for the parameter study. This

confidence can be confirmed by the achievement of convergence to a final stress with a fine

density mesh. This was completed for a T joint and also for a KK joint where models were

meshed with an element size around 100th of the brace diameter. For the T joint, as the mesh

increased, there was at most a 4% difference in SCFs however most of the values reported

around the brace-chord intersection within 1% of each other.

147

Chapter 6 Investigation into

Effects of Loading of Multiplanar

Braces on Brace-Chord

Intersection Stress Distribution

6.1 Introduction

After establishing a suitable mesh size for the FE model which allowed for good predictions of

stress but reasonable runtimes, a series of small studies were completed to check the

behaviour of multiplanar tubular joints. An important point arising from the literature review was

the level of uncertainty about whether the presence of braces in another plane had an effect on

the overall performance of the joint. Conflicting arguments from Efthymiou [22] and Smedley

and Fisher [49] where multiplanar effects are considered to have little effect on the SCFs [22] or

double the SCFs [49] means that further clarification on the subject is required.

A multiplanar KK joint was examined with typical fatigue loads in ANSYS and compared against

the same geometry but analysed as two uniplanar joints. The uniplanar analysis was completed

in ANSYS and using the Efthymiou equations with stresses superimposed. One load in one

brace only from the loading pattern was then varied in the multiplanar model in order to check

the effect of individual loads on the stress plot for the entire joint. As it was observed that

varying one load in one brace had a knock-on effect on the stresses in all braces, a single load

(either axial, IPB or OPB) was applied to the joint to check how much load was carried over into

the neighbouring braces.

6.2 Summary of SCF Calculations Using

Efthymiou

Efthymiou completed a parametric study into the behaviour of uniplanar tubular joints under a

range of loading patterns to determine the SCFs at the crown and saddle locations for both

braceside and chordside stresses. A range of SCF equations are available for different joint

Chapter 6 Investigation into Effects of Loading of Multiplanar Braces on Brace-Chord


148

types under different loading patterns. For the case of a K joint, which will be analysed as both

a uniplanar and multiplanar KK configuration, the loading can be treated as follows:

• Balanced axial load - loads in both braces are within 10% of each other [19]

• Unbalanced IPB and OPB loads - similar magnitude loads are required but are applied

in the same direction

• Axial, IPB or OPB load in one brace only - other loads must be superimposed

In order to determine the SCFs at the weld toe, each brace subjected to loading is isolated and

the SCFs calculated depending on loading type and joint configuration. Loads are divided into

their constituent components with SCFs calculated for the brace under axial, in-plane-bending

(IPB) and out-of-plane bending (OPB). SCFs are calculated at the crown and saddle locations

on the chord and brace according to type of loading experienced by the joint. For IPB, the

maximum hot spot stress is expected to occur at the crown location whereas the position moves

to the saddle for OPB. A total of fourteen equations apply to gap K joints for calculation of SCFs

applicable to braceside and chordside stresses [22, 23].

Axial load in one brace only

Chord saddle -

25.0

1 ))2(sin()1(8.0()(sin((311.1( θβτβαθβγτ 221.621.1 −6)−+))0.52)−−= CSCFcsA (6-1)

Chord crown - θατββτγ sin) 2 3)−(+0.65)−5(+(2.65= 20.2CSCFccA (6-2)

Brace saddle - )−1.10.10.52 0.96)−−+= αθββαγτ 01.07.2(

)(sin(25.1187.0(3.1bsASCF (6-3)

Brace crown - 1.2)−(+−0.011+)−+= 21.2 αβτββγ 3)045.04exp(12.0(3 CSCFbcA (6-4)

IPB in one brace only

Chord crown - 0.7)−0.85 )= θγβτ β

(sin45.168.01(

ccISCF (6-5)

Brace crown - 1.16)−(0.06)−0.4 )+= γβ θγβτ (sin65.01

77.009.1(

bcISCF (6-6)

OPB in one brace only

Chord saddle - )]8.0exp((08.01[)(sin5.0

xSCFcsO −)−)1.05−(1.7= 1.63 βγθβγτβ (6-7)

Brace saddle – )47.099.0(...

))]...8.0exp((08.01()(sin[5.0

40.05−0.54−

1.63

0.08+−

−)−)1.05−(1.7=

ββγτ

βγθβγτβ xSCFcsO (6-8)

where - β

θζ sin1+=x



149

Efthymiou equations taken from DNV-RP-C203 2010 Appendix B [19].

Hot spot stresses are determined at both saddle and crown locations for axial loads by factoring

the nominal stresses applied to the brace by the appropriate SCF. In order to determine the

overall hot spot stress acting at eight locations around the joint on both the chord and brace

(see Figure 6-1), hot spot stresses are superposed using the following equations given in [19].

1 SCF SCFAC x MIP my

σ σ σ= + (6-9)

2

1 1 1(SCF SCF ) 2 SCF 2 SCF

2 2 2AC AS x MIP my MOP mz

σ σ σ σ= + + − (6-10)

3 SCF SCFAS x MOP mzσ σ σ= − (6-11)

4



σ σ σ σ= + − − (6-12)

5 SCF SCFAC x MIP my

σ σ σ= − (6-13)

6



σ σ σ σ= + − + (6-14)

7 SCF SCFAS x MOP mzσ σ σ= + (6-15)

8



σ σ σ σ= + + + (6-16)

The stresses apply to crown and saddle locations with intermediate positions accounted for as

shown in Figure 6-1.

An important point to note about the application of the Efthymiou equations is that the selection

of equation is not necessarily dependent on the geometrical configuration of the joint. Joint

classification depends on the loading pattern therefore a joint which has the geometry of a K

joint could be loading such that the equations for an X joint are more suitable. Figure 2-15 on

page 44 shows how this can be possible.



150

Figure 6-1: Positive axes directions applied to loadings on braces of tubular joints

6.3 Investigation 1 – Comparison of Stresses in

Uniplanar and Multiplanar Tubular K Joints

6.3.1 Methodology

A realistic set of loads for a single joint in a jacket structure resulting from the review of

preliminary design methods in Chapter 2 was used to develop ANSYS models. The joint

selected was modelled as both a uniplanar and multiplanar joint with two analyses completed

for loading in each plane for the uniplanar joint. Results were taken at the upper and lower

bound of the extrapolation region, which was defined on the models, and stresses were

extrapolated back to the weld toe. These stresses were plotted for both chordside and

braceside locations on the brace-chord intersection for each of the four braces and compared

against each other and the resulting hot spot stresses from the Efthymiou equations.

The loads and dimensions of the joint in question were taken from the jacket structure analysed

as part of the work completed on the preliminary design procedures as outlined in Section 2.3

and are given in Figure 8-2.

1 2

3

4 5

6

7

8

y

z

x out of page

1 2

3

4 5

6

7

8 1

2

3

4 5

6

7

8 1

2

3

4 5

6

7

8

N

N out of page

MIP MOP

Axial force In-plane bending

moment

Out-of-plane

bending moment

Positive axes

directions



151

Figure 6-2: Joint geometry and loading used for ANSYS and Efthymiou analyses with

screen-print of joint from ANSYS Workbench showing directions of load application

For the uniplanar joint, the loads for Braces A and B were applied to one model and loads for

Braces C and D applied to the other model. The same methodology was used for the analysis

of the joint by Efthymiou.

6.3.2 Results

Graphs were plotted of the stress distribution around the brace-chord intersection for both

braceside and chordside stresses for all three methods. The stress distribution plots can be

found in Figure 6-3 to Figure 6-10.

Joint Geometry

Chord diameter 2000 mm

Chord thickness 45 mm

Chord length 17750 mm

Brace diameter 759 mm

Brace thickness 25.4 mm

Brace length 8875 mm

Brace inclination 45 º

Gap 1000 mm

Angle between planes 60 º

Joint Loading

Brace A Axial 38361 N

Brace A OPB 12385 N

Brace A IPB 599 N

Brace B Axial 99318 N

Brace B OPB 4651 N

Brace B IPB 1093 N

Brace C Axial 66812 N

Brace C OPB 2154 N

Brace C IPB 43 N

Brace D Axial 284850 N

Brace D OPB 1775 N

Brace D IPB 3830 N

Brace A

Brace B

Brace C

Brace D



152

Figure 6-3: Chordside stresses for Brace A determined by Efthymiou and both uniplanar

and multiplanar ANSYS models

Figure 6-4: Braceside stresses for Brace A determined by Efthymiou and both uniplanar




153

Figure 6-5: Chordside stresses for Brace B determined by Efthymiou and both uniplanar


Figure 6-6: Braceside stresses for Brace B determined by Efthymiou and both uniplanar




154

Figure 6-7: Chordside stresses for Brace C determined by Efthymiou and both uniplanar


Figure 6-8: Braceside stresses for Brace C determined by Efthymiou and both uniplanar




155

Figure 6-9: Chordside stresses for Brace D determined by Efthymiou and both uniplanar


Figure 6-10: Braceside stresses for Brace D determined by Efthymiou and both uniplanar


As shown in the graphs, a variation between each of the three methods can be observed. The

difference in the stress plot may depend on the loading applied to the brace and whether one of



156

the load types dominates. What can be clearly concluded from the study is that the presence of

braces in another plane has an effect on the stresses in the joint either stiffening or weakening

the joint.

For Brace A, a reduction in hot spot stress can be observed for the multiplanar model at location

7 on both brace and chordsides when comparing against both the uniplanar ANSYS model and

the stresses derived by Efthymiou. A similar effect can be observed for Brace B, where the

uniplanar ANSYS model gives higher stresses at the saddle locations 3 and 7 for chordside

stresses. For the braceside stresses, however, a higher stress is found in Brace B at location 7

in the multiplanar model.

Stresses in Brace C appear to be greatly reduced on the chordside when considering braces in

another plane. A slight reduction in stress can be observed when comparing the two ANSYS

models on the braceside. Efthymiou appears to significantly underpredict the stresses on the

braceside and misses one of the peaks for chordside stresses.

The distribution around the brace-chord intersection for the ANSYS uniplanar joint differs

considerably when comparing against the multiplanar model. Crown location 1 is in

compression for the uniplanar joint and experiences a small level of stress whereas the stress

for the multiplanar joint is double and in tension. Maximum hot spot stresses for the uniplanar

joint occur roughly at the intermediate locations 4 and 6. For the multiplanar joint, the maximum

hot spot stresses are at locations 3 and 8.

On the whole, the Efthymiou equations give reasonable predictions of hot spot stress with the

shape of the stress distribution similar to the ANSYS multiplanar model. For Braces B and C,

the second peak in the stress distribution plot is greatly reduced when comparing with the

multiplanar model. For most of the loading patterns, Efthymiou appears to be conservative

however stresses are underpredicted for Brace C.

6.3.3 Conclusions

Modelling a multiplanar KK joint as two separate uniplanar joints could result in the

overprediction or underprediction of stresses depending on the loading pattern applied to the

joint. The presence of braces in another plane can either provide a weakening or stiffening

effect resulting in a different behaviour of the joint under load. It is observed from the analysis

performed that saddle stresses were reduced for the multiplanar joint when compared with the

uniplanar FE model. This indicates that proximity of the additional material to the neighbouring

braces has an effect on the stresses at this location.



157

The prediction by Efthymiou appeared to be on the whole conservative for the joint studied in

this chapter. An important observation from the study is that the Efthymiou equations

occasionally fail to predict a second peak in the hot spot stress distribution. If this stress was to

become the maximum hot spot stress, using the Efthymiou equation could result in an

incorrectly dimensioned joint being designed with a smaller thicknesses selected.

6.4 Investigation 2 – Behaviour of Multiplanar

Tubular Joints

6.4.1 Introduction

With the variations observed in the different modelling methods adopted for part 1 of the

investigation, a study into the behaviour of multiplanar joints was completed in order to check

the stiffening and weakening effects. Loads were applied to all braces and the magnitude of

one load in one of the braces was varied to see how this changed the stress distribution pattern

around the brace-chord intersection. This was completed for the multiplanar joint only with out-

of-plane angles (i.e. the angle between each plane) of 60º and 90º (see Figure 6-11below).

Figure 6-11: Section through chord showing different planes and out-of-plane angle, φ,

for a multiplanar KK joint with 90º angle between planes

6.4.2 Methodology

Using the same model as in the previous study with the same mesh density and other modelling

assumptions, loads were varied in order to check how this affects the behaviour of the joint.

Initially the axial load was varied in stages and the stress distribution plot extrapolated back to

φ

Plane 1

Plane 2

Section

through chord



158

the weld toes was plotted for both chordside and braceside stresses. The same procedure was

carried out for IPB and OPB to check whether increasing load in one direction changed the

behaviour of the joint. This process was repeated for the same dimensioned joint with an out-

of-plane angle of 90º.

6.4.3 Results

The following sample graphs were established for the IPB case – similar behaviour was

observed for the OPB and axial load cases with the increasing loads creating an increase in

stress at the point of hot spot stress. For the axial load case, the amplitude of the peak hot spot

stresses increased with increasing load, likewise for OPB. The difference for IPB is that the

position of the peak hot spot stress shifts with the increase in loading. This can be seen in

Figure 6-12 to Figure 6-19 for the 60º out-of-plane case.

Figure 6-12: Variation in braceside stress distribution in Brace A when varying IPB in

Brace A only with fixed loads applied to other braces (out-of-plane angle = 60º)



159

Figure 6-13: Variation in braceside stress distribution in Brace B when varying IPB in


Figure 6-14: Variation in braceside stress distribution in Brace C when varying IPB in




160

Figure 6-15: Variation in braceside stress distribution in Brace D when varying IPB in


Figure 6-16: Variation in chordside stress distribution in Brace A when varying IPB in




161

Figure 6-17: Variation in chordside stress distribution in Brace B when varying IPB in


Figure 6-18: Variation in chordside stress distribution in Brace C when varying IPB in




162

Figure 6-19: Variation in chordside stress distribution in Brace D when varying IPB in


Figure 6-20: Variation in braceside stress distribution in Brace A when varying IPB in




163

Figure 6-21: Variation in braceside stress distribution in Brace B when varying IPB in


Figure 6-22: Variation in braceside stress distribution in Brace C when varying IPB in




164

Figure 6-23: Variation in braceside stress distribution in Brace D when varying IPB in


Figure 6-24: Variation in chordside stress distribution in Brace A when varying IPB in




165

Figure 6-25: Variation in chordside stress distribution in Brace B when varying IPB in


Figure 6-26: Variation in chordside stress distribution in Brace C when varying IPB in




166

Figure 6-27: Variation in chordside stress distribution in Brace D when varying IPB in


For a change in out-of-plane angle to 90º, it was observed that the stresses were overall higher

than for the 60º case. Figure 6-20 to Figure 6-27 show the variation in the hot spot stress

distribution for the joint with 90º out-of-plane angle.

The key observation to make from the graphs is that changing the loading in one brace has a

knock-on effect on neighbouring braces increasing the stresses around the brace-chord

intersection. This effect is more profound in the brace in the same plane as the increased

loading and more pronounced in the braces in the other plane for the out-of-plane angle of 60º.

For this joint configuration, the hot spot stress at location 3 on Brace B increases by around

7N/mm2 when increasing the load in Brace A by 20kN. In terms of increase in stress, a 20kN

increase in load generates an additional 20N/mm2 of hot spot stress around the brace-chord

intersection of the loaded brace, therefore the extra stress in Brace B can be considered to be

significant.

6.4.4 Conclusions

From the graphs given in section 6.4.3 it is clear that loads are carried over to neighbouring

braces particularly for braces in the same plane. The level of carry-over could be considered to

be significant for the brace in the same plane however it is difficult to establish this with other

loads applied. For the joint with an out-of-plane angle of 60º, the level of carry-over into the

braces in the other plane was much greater than for the joint with a 90º out-of-plane angle. This



167

can be justified as the braces in the other plane for the 60º case are closer together than for the

90º joint so more load is carried over to this set. The same applies to the brace in the same

plane with regards to the level of stress resulting from carry-over effects. It would be expected

that the carry-over stress reduces in this brace as the gap increases so the proximity of each of

the braces plays a role in stress carry-over.

As the Efthymiou equations consider joints as uniplanar configurations only, it can be suggested

that the application of such equations for multiplanar joints is invalid as the carry-over effects

are not considered. However, if the level of carry-over is considered to be small, the Efthymiou

equations could still be valid. The investigation in this section examined joints with all loads

applied to all braces whilst varying one load in one brace only therefore making it difficult to

ascertain the significance of the carry-over of stresses in neighbouring braces. Further

investigation into this effect with one load only applied to one brace was therefore completed

and described in the next section of this chapter.

6.5 Investigation 3 – Carry-Over of Loads to

Neighbouring Braces for Multiplanar Joints

6.5.1 Introduction

Loads were isolated to one brace only of the KK joint and the model was analysed to check how

the neighbouring braces were affected. A single axial, IPB or OPB load was applied to brace A

of the joint and the stress distribution plots were output as completed previously. A significant

level of loading was carried over to all of the neighbouring braces, which, if we consider

Efthymiou’s equations for a uniplanar K joint, the theory suggests does not occur. As with the

previous study for all loads applied to all braces, the magnitude of the load was increased to

assess the severity of the stresses incurred due to the carry-over of load into the neighbouring

braces.

According to Efthymiou, when examining a uniplanar K joint under loading in one brace only,

the equations recommend evaluating the loaded brace as a T joint. This implies that the loaded

brace only is affected by the force, which, as the results suggest, appears not to be the case.

These “carry-over” loads are present in all three braces which could either provide a weakening

or stiffening of the joint, depending on the loading pattern applied to these braces.

6.5.2 Methodology

Using the multiplanar models developed for the two preceding studies (for both φ = 60º and φ =

90º), all the loads were removed from all braces and replaced with a single axial, IPB or OPB



168

load on one brace (Brace A) only. These loads were varied in increments to check the level of

carry-over into the neighbouring braces. As with the previous investigations, the maximum

principal stresses were recorded at the upper and lower bounds of extrapolation regions and

extrapolated back to the weld toe for braceside and chordside hot spot stresses on all braces.

The hot spot stress distribution plot was then generated for both chordside and braceside

locations for all braces under the different levels of load.

6.5.3 Results

Increasing the load by increments results in a linear increase in stress in all braces, which is to

be expected because only one load is present in the structure. Due to this linear increase in

stress, graphs showing the stress distribution around the brace-chord intersection for one axial

load of 100kN and one bending load of 10kNm have been plotted. These graphs show the

stress distribution plot for braceside and chordside hot spot stresses and carry-over stresses for

all braces so a direct comparison can be made. Both the 60° and 90º cases have been plotted

on the same graphs using different line styles – a dashed line represents the 90º results.

Results can be found in Figure 6-28 to Figure 6-33. Note that the absolute values of stress have

been plotted so that results are displayed on the positive y-axis for easier comparison.

Figure 6-28: Braceside stress distribution plot for all braces with Brace A under 100kN

axial load



169

Figure 6-29: Chordside stress distribution plot for all braces with Brace A under 100kN

axial load

Figure 6-30: Braceside stress distribution plot for all braces with Brace A under 10kNm

IPB load



170

Figure 6-31: Chordside stress distribution plot for all braces with Brace A under 10kNm

IPB load

Figure 6-32: Braceside stress distribution plot for all braces with Brace A under 10kNm

OPB load



171

Figure 6-33: Chordside stress distribution plot for all braces with Brace A under 10kNm

OPB load

A considerable amount of load is carried over to Brace B, the brace in the same plane as the

load application, under increasing axial load. For IPB and OPB, the effects are less drastic but

still notable. With braceside and chordside stresses under axial load, more than 50% of the

load is carried over to Brace B, the neighbouring brace in a K-configuration at the location

where maximum stress occurs. A reduced level of carry-over stress is seen for the out-of-plane

braces however, under axial load, just over a third of this load is carried into Brace C.

For IPB and OPB, the largest carry-over is observed in the brace in the same plane with around

33% of stress in Brace A carried to the same location on Brace B for OPB and IPB. A reduced

peak stress can be noted for IPB where a 21N/mm2 exists at location 5 on Brace A chordside

but a much smaller stress of 3N/mm2 can be seen at the same location on Brace B.

Differences can be observed between the stress plots of the 60º and 90º configurations with the

largest variations present in the axial load case. Similar stress distribution plots are achieved

for out-of-plane angles φ = 60º and φ = 90º under OPB likewise for IPB.

In terms of fatigue design, incorrect assessment of the hot spot stress range could lead to an

incorrect assessment of the fatigue damage expected at the tubular joint. The Palmgren-Miner

rule states that the accumulated fatigue damage depends on the hot spot stress range to the

power of appropriate slope of the fatigue curve deployed (m = 3, 4 or 5 – usually 4 for jacket



172

structures). If a hot spot stress is underpredicted by 50%, this could result in an accumulated

damage a factor of 16 greater than anticipated. For underpredictions of 33%, this factor

reduces down to around 3.15 but could still lead to significant error in the prediction of fatigue

life of the joint.

6.5.4 Conclusions

When applying one load to one brace only, significant levels of carry-over can be observed in

neighbouring braces, particularly for the axial load case. For the brace in the same plane

(Brace B), as much as 50% of the load carries over to a similar position on the brace-chord

intersection when looking at the axial load case. Under IPB and OPB, this amount of carry-over

is reduced to around 20% and 32% respectively (see data report) but could be considered to be

significant in the overall behaviour of the joint. For out-of-plane braces, the level of carry-over is

reduced but is still near 50% for the axial load case and 20% for IPB and OPB.

6.6 Overall Conclusion

As the investigations show, the behaviour of multiplanar tubular joints differs to uniplanar joints

with the presence of braces in another plane providing a stiffening or weakening effect

depending on the loading pattern applied. Stress distribution plots from ANSYS indicated that,

for the loading pattern modelled, examining a multiplanar joint as two uniplanar joints

overestimated the hot spot stress distribution implying that the multiplanar joint was stiffer. This

could be attributed to a favourable carry-over of load into neighbouring braces, which may have

reduced the level of stress recorded in the multiplanar model.

Studies into the behaviour of multiplanar joints was completed in order to check how loads were

transferred into the different braces of a KK joint with out-of-plane angles φ = 60º and φ = 90º.

When applying a single load (axial, IPB or OPB) to one brace only, a significant level of load is

transferred to all three other braces. As much as 50% of the load is transferred into the brace in

the same plane for axial load, with around 20-33% of the stress in the loaded brace measured

in the neighbouring braces for the bending load cases. Different behaviour of the joint could be

observed for the two out-of-plane angles – the same stresses were reported in the braces in the

same plane but different stress plots were noted for the out-of-plane braces.

When analysing a uniplanar K joint using the Efthymiou equations, each brace is dealt with

individually and the carry-over of loads from the loaded brace to neighbouring braces is not

considered in the overall behaviour of the joint. For SCFs for loads applied to the K joint

individually (axial, IPB and OPB in one brace only), it should be noted that Efthymiou refers

back to the equations applicable to T/Y joints and therefore neglects any carry-over from the

brace in the same plane. Since jackets supporting offshore wind turbines are highly susceptible



173

to fatigue loading, a carry-over stress as high as 50% of the stress measured in the loaded

brace could potentially result in significant underestimation of hot spot stress and lead to a

higher damage sustained by the structure. This would result in early failure of the structure

through fatigue crack propagating as the result of cyclic loading.

174

Chapter 7 Parametric Study and

Regression Analysis to Develop

Multiplanar Tubular Joint SCF

Equations

7.1 Introduction

In order to develop a new set of equations for the calculation of stress concentration factors for

multiplanar tubular joints, a parameter study has been undertaken where each of the

parameters associated with tubular joints were amended to give a series of data points covering

the validity ranges as specified by Efthymiou [22, 23] and given in the DNV standard [19].

Using the parameter set function of ANSYS Workbench, 301 different geometrical

configurations under the three loads (axial, in-plane bending and out-of-plane bending) and with

both 60º and 90º out-of-plane angles were analysed with the maximum and minimum principal

stresses at the upper and lower bounds of the extrapolation regions output. Stresses were then

extrapolated back to the weld toe and determined for both brace- and chordside stresses

around the brace-chord intersection. These stresses were used to evaluate the SCFs around

the brace-chord intersection and at 8 specific locations as required by DNV-RP-C203 [19].

Using the data arising from the parameter study, a regression analysis was performed in order

to determine improved SCF equations. The analysis was conducted in three stages:

1. Modification of the original Efthymiou equations in terms of their coefficients using a

least squares fit of the data

2. Inclusion of additional parameters (where possible) and their accompanying coefficients

in the modified Efthymiou equations – coefficients determined again by a least squares

fit of the data

3. Construction of new equations by evaluating each parameter in turn resulting in an

equation of the form (additional terms, such as α2 or β

3 to be included where relevant):

ζθγτβα 654321SCF CCCCCC + ++++= (7-1)

Chapter 7 Parametric Study and Regression Analysis to Develop Multiplanar Tubular Joint SCF

Equations

175

Where C1 to C6 are constants

SCFs arising from each of the methods were compared with the original Efthymiou output and

each other to determine the best set of equations for analysis. For carry-over factors,

information was displayed graphically indicating whether the stresses arising from the

geometrical configuration and load type were compressive or tensile.

7.2 Parameter Study Methodology

7.2.1 Pre-processing

An examination of the parameters associated with tubular joint design was carried out in order

to determine suitable geometry for the study. The following parameters apply to a uniplanar K

joint (see Figure 2-17 on page 46).

• Chord length to chord diameter - D

L2=α

• Ratio of diameters - D

d=β

• Ratio of wall thicknesses - T

t=τ

• Chord diameter to chord thickness - T

D

2=γ

• Gap parameter - D

g=ζ

• Brace inclination - θ

For multiplanar KK joints, the above parameters are valid with an additional parameter to

account for the out-of-plane braces, φ, as indicated in Figure 6-11 on page 157.

The study examined KK joints with braces with the same dimensions and inclination and

therefore the number of parameters given in Figure 2-17 on page 46 can be reduced from 9 to 6

giving a total of 7 parameters for the analysis. Because four of the parameters are dependent

on chord diameter, D, it was decided that this dimension should not be changed initially as this

would make it difficult establishing a relationship between the individual parameters and SCF. It

was decided for the initial analysis to vary chord length, brace diameter, gap, brace inclination

and chord thickness with the option for changing chord diameter at a later date. Geometry was

selected based on the validity ranges for the Efthymiou equations excluding overlapping braces


Equations

176

for the zeta parameter. A minimum gap of 50mm was selected based on the following diagram

taken from the GL standard, Guideline for the Certification of Offshore Wind Turbines [69].

Figure 7-1: Dimensioning requirements for tubular K joints according to GL IV-2 – Taken

from GL IV-2 [69]

7.2.1.1 Modelling in ANSYS Workbench

Using the information obtained from the model verification stage, the ANSYS model was set up

with a suitable mesh size, boundary conditions and loads such that the parameter set function

could be used. As mentioned previously, the dimensions of the joint were parameterised such

that altering any one of the key dimensions would result in an automatic change in the geometry

of the structure. Mesh attributes were also parameterised so that the element size would be

proportional to a change in the brace diameter. This was to ensure that a similar mesh was

used for each geometry was analysed with an appropriate element size set to the brace

diameter divided by 17 for finely meshed areas.

To be able to parameterise the application of loads, the geometries were divided into batches

according to the brace inclination and analysed separately. The magnitudes of loads can be

parameterised in Workbench however it is not possible to define the sense of the load in this

way. Seven batches were set up in Workbench for brace inclinations between 30º and 60º in 5º

intervals. For axial loads, a 100kN force was applied to the end plate and aligned with the

length of the brace with all other loads set to 10-14

kN as indicated in Figure 7-2. For bending

loads, a 10kN force applies to load case examined with the other loads set to the same value of

10-14

kN as before.


Equations

177

Figure 7-2: Application of loads to KK joint model in ANSYS Workbench for use in the

Parameter Set function

Using smaller batches instead of analysing the 1806 models in one step has its advantages. If

errors were noticed in the model setup after the batch had begun, the run time of the batch was

much less so time would not be wasted waiting for its completion. During the model verification

process occasionally it was observed that the geometry would be generated without error in the

DesignModeler component of ANSYS Workbench but then would not open in Mechanical.

Advice was received from ANSYS indicating that this was a bug in the version of Workbench

used and not a user error. Because of this, running smaller batches meant that any

unsuccessful design points could be identified and then removed from the following batches.

Python scripts were provided by the ANSYS support team to allow the batch to continue when

an error as described in the previous paragraph was encountered. This script also output each

of the maximum and minimum principal stress plots around the brace-chord intersection on both

brace and chord as text files for post-processing. With each batch defined in a separate folder,

the data could be processed easily for each successful model.


Equations

178

7.2.2 Post-processing of data

Microsoft Excel was used to process the data files from the ANSYS Workbench batch jobs. The

output files from ANSYS gave the maximum and minimum principal stresses at the upper and

lower extrapolation regions for a quarter of the section (i.e. from crown location 1 to saddle

location 3 as shown in Figure 7-3). This identified the key locations around the brace and

chord ensuring that stresses could be computed at saddle, crown and intermediate locations.

The upper and lower bound stresses were extrapolated back to the weld toe giving the stresses

distributed around the brace’s circumference. In order to determine the intermediate locations,

the distance around the brace-chord intersection was computed in terms of angle in degrees

starting at location 1.

Figure 7-3: Definition of locations around brace-chord intersection for post-processing of

results

To calculate the SCFs the nominal stress was determined for each of the load cases. For axial

loads the nominal stress is:

Brace A

N A=nomσ (7-2)

For bending, the following equation applies:

Chord I

Mybenom =,σ

(7-3)

Where y is the distance to the neutral axis (D/2 for CHS) and I is the second moment of area

1 2

3

4 5

6

7

8

45º


Equations

179

The SCF at each location is therefore the extrapolated stress divided by the nominal stress.

SCFs were determined at each of the 8 locations as shown in Figure 7-3. Data was compiled

into text files for each of the locations and each of the load cases. The files contained the SCFs

and geometry in terms of each of the seven parameters altered (α, β, γ, ζ, τ, θ, and φ) under

each of the load cases.

7.3 Regression Analysis Methodology

Data was compiled from the parameter study performed in ANSYS Workbench and arranged

according to location, load type, brace and chord/braceside SCF. Initially, when comparing the

data against the original Efthymiou equation, all the data was included. Graphs of SCF versus

each individual parameter were plotted for both the outcomes from Efthymiou and the SCFs

determined by ANSYS in order to check whether certain data ranges needed to be examined

individually and therefore excluded from the overall data set.

7.3.1 Ranges of data for the analysis

After building graphs of SCF against each parameter individually for all sets of data, it was clear

that different relationships applied to the ranges of parameters. Efthymiou acknowledges this in

his work [22, 23] by providing a short-chord correction factor for joints where the chord length is

small compared to the chord diameter (for α < 12). Different short chord correction factors apply

to different load cases resulting in three factors for use. With the data collected from the

parameter study in ANSYS, plots of SCF against α indicated that a mostly linear relationship

could be observed for values of α less than 15. Depending on the load type and the location

(chord or brace, saddle or crown), the SCF either increased or decreased exponentially below

the limit of α < 15. Figure 7-4 shows how SCF changes with each parameter for a specific value

of brace inclination, θ and demonstrates this variation in SCF with change in α.

The data files were therefore edited to remove data points for α < 15 in order to establish the

linear relationship between SCF and the α parameter. Data were retained for short chords such

that further analysis could be carried out for these points.


Equations

180

Figure 7-4: Variation of SCF with each individual parameter for different values of brace

inclination, θ at location 3 braceside under axial loading


Equations

181

For plots of SCF against the brace inclination (θ), it was observed that there was a change in

relationship for values of θ < 45º. The change in pattern was likely to be a result of a change in

weld detail, which was modelled in the ANSYS DesignModeler program. As indicated

previously, with changes in brace inclination come alterations to the weld profile which is likely

to have an effect on the level of stress in the chord and braces. It was decided that the data

points for KK joints with braces inclined at 30º to 40º should be evaluated separately.

The following data ranges were analysed individually:

Validity ranges for dataset 1

15 ≤ α ≤ 40

0.2 ≤ β ≤ 0.4

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

45º ≤ θ ≤ 60º

φ = 60º


15 ≤ α ≤ 40

0.2 ≤ β ≤ 0.6

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

45º ≤ θ ≤ 60º

φ = 90º


15 < α

0.2 ≤ β ≤ 0.4

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

45º ≤ θ ≤ 60º

φ = 60º


15 < α

0.2 ≤ β ≤ 0.6

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

45º ≤ θ ≤ 60º

φ = 90º


Equations

182


15 ≤ α ≤ 40

0.2 ≤ β ≤ 0.4

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

30º ≤ θ < 45º

φ = 60º


15 ≤ α ≤ 40

0.2 ≤ β ≤ 0.6

8 ≤ γ ≤ 32

0.2 ≤ τ ≤ 1.0

30º ≤ θ < 45º

φ = 90º

Note that insufficient data was recorded for the ranges where α < 15 and 30º ≤ θ < 45º therefore

these ranges have been excluded from the analysis.

7.3.2 Modifying Efthymiou coefficients and equations

Once the correct data ranges were identified and the data compiled in text file accordingly, the

regression analysis was then performed using Matlab. The first stage in the regression analysis

was to check the data ranges against Efthymiou and then modify the coefficients in each of the

applicable equations.

Each of Efthymiou equations was evaluated in Matlab with all numerical factors set as variables

in the code. This meant that all the coefficients, constants and powers could be altered in order

to fit the equations better to the data. For those equations from Efthymiou where parameters

were excluded, plots of SCF against each individual parameter were examined in order to check

the assumption that the excluded parameter had no effect on SCF. If a clear relationship

between the SCF and the unused parameter existed, an additional term was added to the

equation, the form of which was assumed by judging the data trends.

The way in which the regression analysis was performed meant that the variables were

converged mostly to a solution where some SCFs were underpredicted and some

overpredicted. The least squares fit takes the original values as given in and calculated by the

Efthymiou equation and tries to reduce the difference between the calculated SCF and that

determined by ANSYS by altering the variables in the equation. When the SCF according to


Equations

183

Efthymiou (SCFEft) is greater than the SCF determined by ANSYS (SCFAN), the least squares is

likely to underpredict as the difference between the two values reduces.

Using the ratio of the SCF predicted by the new equation (SCFp) or SCFEft and SCFANS as the

basis of comparison for checking the validity of each set of equations, the distribution of results

around the unity line was an initial indicator of the reliability of results. With the limits of the

least squares fit set to distribute results equally above and below this line, the number of

underpredictions from the new equation can be, as mentioned before, around 50%. In terms of

actual design, it is better to be conservative and overpredict results or account for the

underpredictions with a partial safety factor. In this case, the limits of the regression analysis

were changed to ensure that the difference between SCFp and SCFANS could not be less than

zero and those values to which this applies are excluded from the analysis.

7.3.3 Developing a new set of equations

On first inspection of the Efthymiou equations, the complexity of some of the formulae stands

out particularly for the OPB cases as described by equations 25 and 26 in the DNV-RP-C203

standard. For such cases, the modification of the original equation becomes difficult therefore a

methodology separate from the original equations may be better suited to the data. Kuang et al

[42] outline their procedures for determining a set of parametric data from their data using a

logarithmic scale, assuming that the relationship between individual parameters and SCFs is

logarithmic. Adopting a similar approach to fit equations to the data arising from the parametric

study may result in more reliable equations than simply modifying Efthymiou’s complex

formulae.

Again using Matlab to perform this regression, plots of each parameter and their corresponding

SCF were developed such that the relationship with each individual parameter and SCF could

be determined. The order in which plots were assessed had an effect on the form of the

equations so this needed to be considered carefully in the analysis. The following methodology

was adopted:

1. Select the first parameter for evaluation and determine the relationship between SCF

and the parameter.

2. Using the new relationship for SCF and the first parameter, select the next parameter

for assessment and add the new SCFs from the SCFs for the data points.

3. Determine a relationship between the second parameter and amended SCF.

4. Continue the process until all parameters have been evaluated.

5. Determine a suitable constant in order to shift the data to the correct predictions of SCF.

6. Repeat the process changing the order of processing the parameters until the best fit to

the data is achieved.


Equations

184

Initially a straight line plot was fitted to the data to check the validity of the method.

Amendments were made to the code such that different order quadratics could be fitted to the

data if a linear best fit relationship didn’t capture enough of the data points. A systematic

approach was adopted in order to determine the best relationship between SCF and each

individual parameter where order of the polynomial was increased if the relationship didn’t fit the

data points well. Depending on the selected order, additional terms in the equation would be

included, for example if the relationship between α and SCF appeared to be a quadratic

polynomial, then two terms would apply for this parameter in the overall equation for SCF: an α2

term and an α term.

7.3.4 Validating the reliability of equations

In order to assess the validity of each of the individual equations, acceptance criteria were

defined. It was decided that, for the purpose of design, the number of underpredictions should

be minimised and that the ratio of the calculated SCF and the SCF determined from ANSYS

should be within +/-10%. Graphs were plotted showing the distribution of data points around

the unity line, where SCFp and SCFANS are equal, with ratio of SCFs on the y-axis and SCFANS

along the x-axis. A sample of these graphs can be found in Figure 7-5

Figure 7-5: SCF predictions for new equation at location 1 for braceside SCFs under axial

load with out-of-plane angle 60º


Equations

185

In order to compare the reliability of each of the equations against Efthymiou and each of the

newly derived formulae, data were binned into either 0.02, 0.05 and 0.1 bins of ratio of

SCFp/SCFANS depending on the spread of results. The number of data points falling within each

bin was identified therefore allowing the distribution of results around unity to be clearly

demonstrated. An example graph can be found in Figure 7-6 below.

Figure 7-6: Comparison of modified Efthymiou coefficients, modified Efthymiou equation

and the new equation against original Efthymiou for braceside stresses at location 3

under AXL load

Graphs were developed for each of the eight locations around the brace-chord intersection for

both braceside and chordside stresses under axial, in-plane bending and out-of-plane bending.

This process was completed for all validity ranges and used in evaluating the reliability of each

set of equations.

7.3.5 Development of equations for implementation

Initially it was planned to develop equations for all datasets however due to the approach

adopted for the parameter study, where certain dimensions were altered only, limited data was

available for some of the validity ranges. For θ = 30º difficulties were encountered with

automating the generation of geometries using the parameter set so models in this range had to

be developed individually.


Equations

186

In terms of developing a methodology for design, it was decided that the best approach would

be to generate equations for the validity ranges covering the greatest number of geometries and

then factor these for subsequent ranges. If equations were established for each validity range,

each load case and each location, a total of 96 equations would apply (see Table 10-1). The

number could be reduced using one equation for both saddle and for both crown locations and

then factoring the result to fall in line with the generated data. Table 10-1 outlines the possible

sets of equations which could be developed.

As indicated in Table 10-1, it was possible to generate up to 96 equations if all locations, load

cases and validity ranges were analysed separately. This reduces down to 32 equations if

SCFs for both out-of-plane angles 60º and 90º are evaluated individually but factors are used

for short chord effects and brace inclinations of less than 45º. The number of equations can be

reduced further by using one equation for both saddle and both crown locations (16 equations)

and factoring the SCFs accordingly for cases where SCFs vary at the two positions. Finally the

equations can be reduced to eight only by using the equations selected for the 60º out-of-plane

angle and factoring the SCFs to give suitable values for the 90º case, which was the chosen

methodology for the study.

Chapter 7 Parametric Study and Regression Analysis to Develop Multiplanar Tubular Joint SCF Equations

187

Tab

le 7

-1:

Po

ss

ible

sets

of

eq

uati

on

s f

or

the a

naly

sis

of

SC

Fs f

or

mu

ltip

lan

ar

tub

ula

r jo

ints

– n

ote

th

at

the v

alid

ity r

an

ge

s

can

be f

ou

nd

in

secti

on

7.3

.1*

B =

Bra

ce

sid

e S

CF

s,

^ C

= C

ho

rdsid

e S

CF

s


Equations

188

7.4 Results of Regression Analysis

7.4.1 Selected equations

A final set of eight equations for validity range 1 (φ = 60º, θ ≥ 45º, α ≥ 15) was selected based

on the following criteria comparing the ratio of SCFp and SCFANS:

• Number of results within +/-10% of SCFANS

• Number of results where SCFp/SCFANS is greater than 1 (minimising the number of

underpredictions)

• Distribution of results around the mean – eliminating use of equations where extreme

calculated SCFs exist (includes both over and underpredictions)

For the first two criteria, the percentage of results conforming to the criterion was determined so

as to make a comparison. For the purpose of design it was decided that it would be preferable

for SCFs to be overpredicted as opposed to underpredicted so the second statement was given

priority in the selection process. If the majority of results were distributed tightly around the

mean, the equation was favoured. Equations were chosen for the three different methods

(modified Efthymiou constants, modified Efthymiou equation and the new equation) for the 60º

out-of-plane angle results and were compared against each other and the original Efthymiou

equations.

Using the equations identified in the previous paragraph, the parameters associated with the

data for joints with an out-of-plane angle of 90º were used to calculate SCFs for the dataset.

The resulting SCFs were compared with the ANSYS SCFs by taking the ratio of the two SCFs

to give a correction or adjustment factor to apply to the equation. Again, as for the 60º out-of-

plane angle data, the results were compared with each other graphically such that the most

reliable equation could be selected. The same methodology was adopted for the other validity

ranges with suitable factors chosen for each validity range.

The selected equations using the three methods for regression are as follows. Note that only

two methods were used for OPB due to the complexity of the equations. It was not always

possible to change the coefficients only as some terms in the equation converged to zero which

nullified the SCFs. The terms affecting the output SCF were removed from these equations

leading to a simplified version.


Equations

189

7.4.1.1 Braceside crown SCFs for axial load in one brace only

Modified Efthymiou coefficients

4.1746)+(0.0185+

−0.0085+)+= 6.691221.

αβτ

ββγ

....

)...597.08871.3exp(6091.0(1251.2SCF 5762

(7-4)

Modified Efthymiou equation

)0019.01044.00006.0...

)...0581.0636989.0exp(49.0(0353.0(SCF 7235.41158.0

)++(−+

−0.00−)+.=6,3482ζαβτ

ββγθ

(7-5)

New equation

(7-6)

7.4.1.2 Braceside saddle SCFs for axial load in one brace only


0.0151)−0.0480.1704 0.0087))−++= αθββαγτ 0005.0(0762.0 )(sin(186.01106.0(0874.0SCF (7-7)


0.1058−

−(−0.016−0.0959

−

)0.114)(−++=

ζ

θββαγτ

4953.0...

...sin(1292.0152.0(3282.0SCF)0141.00004.014.0

(7-8)

New equation

(7-9)

7.4.1.3 Braceside crown SCFs for in-plane bending in one brace

only


)653.10582.0()(sin0061.04489.1SCF +)2.1536−(1.8266−3.4664+= γβ θγβτ (7-10)


θα

θγτβ γβ

sin0043.0...

..(sin116.07461.0SCF

+

)++−= 0.0796)+(0.0191)0.1451−(0.2981−0.3280.1974

(7-11)

1.8+−+3.6909−+

+43.8216+−+)0.004−−=23

23

ζζζβ

ββθγτγτα

4615.41388.74322.4...

...3085.200332.01469.0(30001.0SCF 2

7.332573.1601.3...

...2359.21.34410391028089.04561.00215.0SCF

+−+

−+++++=2

323

ζζ

ζβββθγτα


Equations

190

New equation

(7-12)

7.4.1.4 Braceside saddle SCFs for out-of-plane bending in one

brace only


))7054.03622.0(...

...)())(sin1736.12897.(SCF

18999425.0

1955.1

1.6461−0.

−0.08931.1539

0.3061++−

)0.2417(−1.0251+(1=

ββγτ

βγθβγτβ

(7-13)

New equation

(7-14)

7.4.1.5 Chordside crown SCFs for axial load in one brace only


θ

ατββτγ

sin...

...)4032.44264.0(SCF

9.8601)+

(0.361+8.2681)+(+= −2.55430.6768

(7-15)


θζ

ατββτγ

sin)...

...))5(SCF2036.2

32.031

65.20

0.8442−

22.178)−(0.3705+60.884−14.851(+(59.26= (7-16)

New equation

48.81.8023−+

−1312+0.0506++)0.0008(−= 232

-438....

...13262682.00599.0SCF

ζβ

ββθγτγτα

(7-17)

7.4.1.6 Chordside saddle SCFs for axial load in one brace only


0.1860.03941.196 )0.2)−+= θβγτ )(sin(2914.04305.0(SCF (7-18)

4.261407.0096.01.185...

...5.5123.4650019.00019.00182.00211.0SCF

−+−+

−+−+−=2

232

ζζβ

ββθθγτα

7.195351.03897.0288....

...4.8883.872356.00029.02557.00146.0SCF

++−−

+−+−+=2

232

ζζβ

ββθθγτα


Equations

191


1.6757

−0.09850.71581.0388

))+

+1.1337)++=

θα

ζβγτ

(sin0009.0....

...0743.0(7878.03388.0(SCF

(7-19)

New equation

(7-20)

7.4.1.7 Chordside crown SCFs for in-plane bending in one brace

only


1.2171)1.0313(0.4863−1.1763 )= θγβτ β (sin7643.14SCF (7-21)


θαθγτ β sin0046.0(sin0074.0SCF +)= 1.0895)1.0313−(2.2513−0.7106

(7-22)

New equation

(7-23)

7.4.1.8 Chordside saddle SCFs for out-of-plane bending in one

brace only


θαβ

θζβγ

θβγτβ

sin1243.0sin

4321.03007.0exp(7806.05742.0

))(sin(SCF 2365.0

+

+)+−

0.2071−(0.9844=

0.199

−−0.3919

(7-24)

New equation

10.5−+

0.5277−13.375+0.1038+0.3993+= 2

ζ

ζβθγτα

7327.0....

...029.0SCF (7-25)

7.4.2 Factors for converting equations

It was possible to reduce the overall number of equations for application if the same equation

was applied to different validity ranges but factored accordingly. This was also assumed to be

valid for examining saddle and crown locations for cases where a different value of SCF was

8.721036.14859.0....

...1.585177417721767.06403.00116.0SCF

−++

+−+++=2

23

ζζ

βββθγτα

5.861516.01046.06.7472168....

...20750332.02024.0)(0028.00015.0SCF

−++++

+++−=22

32

ζζββ

βθγτγτα


Equations

192

recorded for opposite locations. A key observation from the ANSYS output was that the

braceside SCFs for crown location 1 were consistently lower than the SCFs at location 5. For

joints with out-of-plane angles of 60º, a slight reduction in hot spot stress was noted for saddle

location 3 compared with saddle location 7. This could be attributed to the presence of

neighbouring braces at this location providing a stiffening effect. Figure 7-7 below shows this

variation in stress around the brace-chord intersection on an axially loaded brace with the

higher stresses present on the left-hand side of the loaded brace. The greater values of stress,

colour-coded red in the stress plot, cover a larger area on the left-hand side of the brace

implying that the stress is greater on this side.

Figure 7-7: Stress plot for an axially loaded brace on a multiplanar joint with out-of-plane

angle 60º taken from ANSYS Workbench

For intermediate values at locations 2, 4, 6 and 8, the superposition equations outlined in DNV-

RP-C203 and given in section 6.2 were used. These values were compared with the data from

ANSYS and factors applied where possible. Table 7-2 to Table 7-4 give the factors applied to

all equations. Note that data is given for validity ranges 1, 2, 5 and 6. Validity ranges 3 and 4,

which examine the effects of short chords, have been ignored due to the modelling of fixed

boundary conditions. As solid brick elements were used in ANSYS Workbench, it was only

possible to apply boundary conditions to faces of the model. Predefined boundary conditions

given in the software, such as simply supported, were unavailable so a fixed boundary condition

was applied to the entire chord-end face on both sides. This may have the effect of creating a

built-in reaction thus increasing the level of stress near the ends of the chord. Because of this

effect, the stresses determined for joints with an alpha parameter less than 15 have been

excluded from the analysis.

With reference to Table 7-2 to Table 7-4, for locations where no factor applies, a grey box is

shown. Typically for these cases, the equation selected for the general position (i.e. crown or

saddle) applies to that exact location and the corresponding SCF requires no further alteration.


Equations

193

Factors applied to equations at locations

Load VR Equation Brace/ Chord?

1 2 3 4 5 6 7 8

AXL 1 Modified

coefficients (MC)

Brace 0.22

1.12

AXL 1 Modified equation

(ME) Brace 0.22

1.08

AXL 1 New

equation (NE)

Brace 0.22

1.04

AXL 2 MC Brace 0.30

AXL 2 ME Brace 0.22

1.08

AXL 2 NE60 Brace 0.25

1.04


1.04

AXL 5 MC Brace 0.45

0.70

0.70

AXL 5 ME Brace 0.70

0.70

1.40

0.70

AXL 5 NE Brace 0.40

0.80

0.85

0.80

AXL 6 MC Brace 0.45 1.15 0.70 1.10 0.90

0.80 1.05

AXL 6 ME Brace 0.70

0.75

1.40

0.75


0.90

0.85


0.90

0.80

0.90

AXL 1 MC Chord 0.54

1.20

AXL 1 ME Chord 0.54

AXL 1 NE Chord 0.54

AXL 2 MC Chord 0.70

1.15

1.15

1.15

AXL 2 ME Chord 0.60

1.03

1.13

1.12

AXL 2 NE60 Chord 0.60

1.05

1.10

1.12


1.25

AXL 5 MC Chord 0.45

0.70 0.90 1.05

0.70

AXL 5 ME Chord 0.50

1.35

AXL 5 NE Chord 0.40

0.90 0.90

0.90 1.10

AXL 6 MC Chord 0.50

0.80

1.05 0.90 0.80

AXL 6 ME Chord 0.60

0.90

1.35 0.90 0.90


1.05 0.90 0.90


0.85

0.90 0.90 0.90

Table 7-2: Factors to be applied to equations for multiplanar joints with axial load applied

to one brace only for both chord and braceside stresses


Equations

194



1 2 3 4 5 6 7 8

IPB 1 MC Brace

1.95 0.50

1.22

0.50 1.95

IPB 1 ME Brace

1.95 0.50

1.22

0.50 1.95

IPB 1 NE Brace

1.95 0.50

1.22

0.50 1.95

IPB 2 MC Brace

1.80 0.40

1.20

0.40 1.80

IPB 2 ME Brace

1.85 0.40 0.90 1.20 0.90 0.40 1.80

IPB 2 NE60 Brace

1.80 0.40

1.10

0.40 1.80

IPB 2 NE90 Brace

1.85 0.40

1.20

0.40 1.85

IPB 5 MC Brace 1.65

0.20

0.75

0.20

IPB 5 ME Brace 1.80

0.20

0.80 0.90 0.20

IPB 5 NE Brace 3.00

0.20 1.50 1.20

0.20

IPB 6 MC Brace 1.65 1.25 0.20 2.00 0.60 1.30 0.20 1.20

IPB 6 ME Brace 1.80 1.20 0.20 2.00 0.65 1.30 0.20 1.20

IPB 6 NE60 Brace 2.30 1.20 0.20 1.80 0.75 1.30 0.20 1.20

IPB 6 NE90 Brace 1.70 1.30 0.20 2.00 0.60 1.30 0.20 1.30

IPB 1 MC Chord 0.80 1.40 0.10

0.10 1.40

IPB 1 ME Chord 0.80 1.40 0.10

0.10 1.40

IPB 1 NE Chord

1.40 0.10

1.22

0.10 1.40

IPB 2 MC Chord

1.20 0.06 0.80 1.20 0.80 0.06 1.10

IPB 2 ME Chord 0.80 1.50 0.09 0.90

0.90 0.09 1.50

IPB 2 NE60 Chord

1.50 0.08

1.10

0.08 1.30

IPB 2 NE90 Chord 0.80 1.50 0.08

0.08 1.50

IPB 5 MC Chord 0.80 1.20 0.10

0.80

0.10 1.20

IPB 5 ME Chord 0.80 1.20 0.09

0.80

0.10 1.20

IPB 5 NE Chord

1.50 0.10

1.10 1.10 0.10 1.20

IPB 6 MC Chord 0.80 1.40 0.08 1.10 0.90 1.10 0.08 1.40

IPB 6 ME Chord 0.85 1.35 0.08

0.08 1.20

IPB 6 NE60 Chord 0.90 1.50 0.08

1.10 1.10 0.08 1.20

IPB 6 NE90 Chord 0.75 1.30 0.08 1.15 0.75 1.15 0.08 1.30

Table 7-3: Factors to be applied to equations for multiplanar joints with in-plane bending

applied to one brace only for both chord and braceside stresses


Equations

195



1 2 3 4 5 6 7 8

OPB 1 ME Brace

0.70

0.70

OPB 1 NE Brace

0.70

0.70

OPB 2 ME Brace 0.03 0.70

0.15

0.70

OPB 2 NE60 Brace 0.03 0.80

0.12

0.70

OPB 2 NE90 Brace 0.02 0.70

0.14

0.70

OPB 5 ME Brace 0.10

0.15

OPB 5 NE Brace 0.10 0.90

0.15

0.90

OPB 6 ME Brace 0.03 0.90

0.15

0.90

OPB 6 NE60 Brace 0.03 0.90

0.15

0.90

OPB 6 NE90 Brace 0.03 0.90

0.14

0.90

OPB 1 ME Chord

0.95

0.95

0.95

0.95

OPB 1 NE Chord

0.85

0.85

0.85

0.85

OPB 2 ME Chord 0.04 0.80

0.02 0.80

0.90

OPB 2 NE60 Chord 0.04 0.80

0.02 0.75

0.90

OPB 2 NE90 Chord 0.04 0.80

0.02 0.80

0.90

OPB 5 ME Chord 0.06 0.80 0.80

0.06 0.70 0.80

OPB 5 NE Chord 0.06 1.10

0.90 0.06 0.90

OPB 6 ME Chord 0.06 0.90

0.80 0.06 0.80 0.90

OPB 6 NE60 Chord 0.06

0.80 0.06 0.70 1.10

OPB 6 NE90 Chord 0.04 0.90

0.80 0.05 1.05 0.90

Table 7-4: Factors to be applied to equations for multiplanar joints with out-of-plane

bending applied to one brace only for both chord and braceside stresses

7.5 Comparison of final equations

The equations and factors provided in sections 7.4.1 and 7.4.2 and cover either two or all three

of the methodologies used for the regression analysis resulting in a total of 22 available

equations. From these 22 equations, the most reliable equations need to be identified. Using

the same criteria as outlined in section 7.4.1, the SCFs arising from the equations were

compared against each other and against Efthymiou.

A further method of comparison was to look at the unbinned data arising directly from the

Matlab regression. Graphical output from Matlab included a plot of SCFs from ANSYS and the

equations (new or Efthymiou) against each individual parameter to check that the equations

were predicting trends correctly. From these plots it could be easily identified whether the new

formulae and Efthymiou’s equations were producing good results. Example graphs of these

plots for SCFs at location 5 braceside under axial load can be found in

Figure 7-8 to Figure 7-11.


Equations

196

Figure 7-8: Graphs comparing SCFs from the Efthymiou equation and from ANSYS for

each parameter for braceside stresses at location 5 under axial load


Equations

197

Figure 7-9: Graphs comparing SCFs from the modified Efthymiou coefficients and from

ANSYS for each parameter for braceside stresses at location 5 under axial load


Equations

198

Figure 7-10: Graphs comparing SCFs from the modified Efthymiou equation and from

ANSYS for each parameter for braceside stresses at location 5 under axial load


Equations

199

Figure 7-11: Graphs comparing SCFs from the new equation and from ANSYS for each

parameter for braceside stresses at location 5 under axial load


Equations

200

Combined with the graphs showing the distribution of results around the mean, it was possible

to evaluate the reliability of the equations. It was not always the case that one methodology

gave the best equations for all load cases and locations. The results for testing the reliability of

the selected equations can be found in Table 7-5 to Table 7-8.

Table 7-5: Summary of extreme values of ratio of SCFs from each equation and from

ANSYS

(* VR = validity range, ^ EQN = equation, ‘ Br/Ch = Brace or Chordside SCF, 1 = Efthymiou, 2 = Modified Efthymiou

coefficients, 3 = Modified Efthymiou equation, 4 = New equation)


Equations

201

Table 7-6: Summary of mean values of ratio of SCFs from each equation and from ANSYS

and percentage of results greater than 1 or within 10% of ANSYS

Table 7-7: Scores for reliability of SCFs from each equation based on maximum,

minimum and mean values for ratio EQN/ANS

(* VR = validity range, ^ EQN = equation, ‘ Br/Ch = Brace or Chordside SCF, 1 = Efthymiou, 2 = Modified Efthymiou

coefficients, 3 = Modified Efthymiou equation, 4 = New equation)


Equations

202

Table 7-8: Scores for reliability of SCFs from each equation based on % of results greater

than 1 and within 10% values for ratio EQN/ANS

The information provided in Table 7-5 and Table 7-6 covers all equations determined by the

regression analysis. It also shows the variation in Efthymiou’s predictions and those arising

from the three different methods according to the location on the brace-chord intersection.

Further analysis of the results was made by scoring each of the equations out of ten for each of

the five criteria given in Table 7-7 and Table 7-8 and then ranked based on the final score out of

50. The following ranges were used to evaluate the data.

For maximum values of SCF_EQN/SCF_ANS

1.00 ≤ SCF Score = 1

1.00 < SCF ≤ 1.05 Score = 10

1.05 < SCF ≤ 1.10 Score = 9

1.10 < SCF ≤ 1.20 Score = 8

1.20 < SCF ≤ 1.30 Score = 7

1.30 < SCF ≤ 1.50 Score = 6

1.50 < SCF ≤ 1.75 Score = 5

1.75 < SCF ≤ 2.00 Score = 4

2.00 < SCF ≤ 2.5 Score = 3

2.50 < SCF ≤ 3.00 Score = 2

SCF > 3.00 Score = 1


Equations

203

For minimum values of SCF_EQN/SCF_ANS


0.60 < SCF ≤ 0.70 Score = 10

0.70 < SCF ≤ 0.75 Score = 9

0.75 < SCF ≤ 0.80 Score = 8

0.80 < SCF ≤ 0.85 Score = 7

0.85 < SCF ≤ 0.90 Score = 6

0.90 < SCF ≤ 0.95 Score = 5

0.95 < SCF ≤ 1.00 Score = 4

1.00 < SCF ≤ 1.05 Score = 3

1.05 < SCF ≤ 1.10 Score = 2


For mean values of SCF_EQN/SCF_ANS


0.70 < SCF ≤ 0.80 Score = 10

0.80 < SCF ≤ 0.85 Score = 9

0.85 < SCF ≤ 0.90 Score = 8

0.90 < SCF ≤ 0.95 Score = 7

0.95 < SCF ≤ 1.00 Score = 6

1.00 < SCF ≤ 1.05 Score = 5

1.05 < SCF ≤ 1.10 Score = 4

1.10 < SCF ≤ 1.20 Score = 3

1.20 < SCF ≤ 1.30 Score = 2


For percentage of results where SCF_EQN/SCF_ANS > 1 and percentage of results within +/-

10%

40 ≤ % of results Score = 1

40 < % of results ≤ 50 Score = 2










Equations

204

Using this system to rank the equations in terms of reliability indicates that, based on the criteria

used, the most reliable equations appear to be the new equations. For the majority of locations

and loads, Efthymiou seems to predict poorly ranking bottom. Similar results were achieved for

both modified Efthymiou coefficients and modified Efthymiou equations.

7.5.1 Summary of axial results

7.5.1.1 Efthymiou equations

• Overpredictions at locations 1 and 5 braceside with large spread of values

• Underpredictions at location 5 chordside with a larger distribution of values

• Generally poor predictions of SCFs for all axial locations both chord and braceside -

mostly overpredictions

7.5.1.2 Modified Efthymiou coefficients

• Large spread of results for location 1 braceside with the majority of results greater than

1 – poor predictions

• Braceside SCF predictions for all other locations reasonable with majority of results

predicting higher SCFs although around half of results within 10%

• Better predictions of chordside stresses than Efthymiou with mean

SCF_EQN/SCF_ANS around 1.07 and a greater number of results within 10% of

ANSYS values

7.5.1.3 Modified Efthymiou equations

• Similar results to modified Efthymiou coefficients but with a poorer prediction of

braceside SCFs at location 1

• Reasonable predictions of chordside SCFs with between 70% and 95% of safe

overpredictions and around 70% of results within 10% of ANSYS values

7.5.1.4 New equations

• Good predictions of SCFs for both chord and braceside locations

• Achieves up to 98% of results greater than the ANSYS values but with between 79%

and 99% of results within 10%


Equations

205

7.5.2 Summary of IPB results


• Efthymiou seems to overpredict all IPB SCFs for braceside locations with up to 97% of

results overpredicted

• At most only 10% of results for braceside SCFs are within 10% of those determined by

ANSYS

• Poor predictions of SCFs for location 1 chordside with 9% of results within 10% of

ANSYS values

7.5.2.2 Modified Efthymiou coefficients

• Chordside predictions seem more reliable than braceside estimates however some

values exist where chordside SCFs are as little as 50% of the ANSYS values

• Results appear to have a tighter distribution around the mean than for axial predictions


• Again, similar output to the modified Efthymiou coefficients

• Better predictions at location 1 braceside compared with the modified Efthymiou

coefficients


• Good predictions of SCF for both chordside and braceside locations

• Larger spread of results for chordside stresses with a minimum SCF_EQN/SCF_ANS of

0.51 – this seems to apply to all methods so maybe an anomalous result exists in the

data set

• Little variation between all three new methodologies in terms of the five criteria used in

assessment however the new equation gives a mean SCF_EQN/SCF_ANS closest to 1

7.5.3 Summary of OPB results


• Efthymiou gives better predictions of braceside SCFs with all results or the majority of

results greater than ANSYS for both saddle locations

• For chordside SCFs, Efthymiou appears to consistently underpredict results with the

majority of results outside of the +/-10% bracket – mean SCF_EQN/SCF_ANS ratio is

around 0.90 for both locations


Equations

206

• Compared to IPB, OPB predictions using Efthymiou seem more reliable as results show

a smaller distribution about the mean


• Braceside SCF predictions appear to be good with around 80% of results greater than

SCFs determined using ANSYS and within +/-10% of these values

• Less reliable outcome for chordside SCFs – around 50% of predictions were greater

than or within +/-10% of ANSYS SCFs

• Braceside SCFs appear to be relatively tightly distributed about the mean however with

chordside SCFs, overpredictions as high as 1.65 times the values from ANSYS are

possible


• Underpredictions limited with minimum SCFs as high as 0.95 times the ANSYS values

• Results tightly distributed around the mean for both chordside and braceside SCFs

• Braceside predictions appear to be more reliable with as many as 95% of results

greater than ANSYS values and 87% of results within 10% of these SCFs

7.6 Evaluation of Converted Equations

A series of factors were applied to the selected equations as given in section 7.4.1 to calculate

the SCFs at each of the eight locations around the brace-chord intersection for the other validity

ranges. Converting the modified Efthymiou coefficients and equations for different validity

ranges appeared to work reasonably well however problems were encountered when this was

applied to the new equation. For the majority of data points covered in the different validity

ranges, the new equation developed for validity range 1 could be utilised for a different validity

range by applying the factors given in Table 7-2.

For some data points, however, the predictions obtained from factoring these equations did not

work at all. Negative values of SCF were calculated for a small number of data points

particularly when converting between out-of-plane angles 60º and 90º. The distribution of

results about the mean was greater than for the original new equations with the majority of

results within 30% of ANSYS values but more extreme values were noted. These extremes

were the negative values and predictions anywhere up to 25 times the ANSYS values.

Maximum, minimum and mean values of the ratio SCF_EQN/SCF_ANS have been presented in

Table 7-9 to Table 7-11.


Equations

207

Table 7-9: Maximum, minimum and mean values for SCF_EQN/SCF_ANS for validity

range 2


range 5


Equations

208


range 6

7.6.1 Summary of results

The results for each of the methods adopted and their applicability to the validity ranges are

summarised as follows.

7.6.1.1 Summary of axial results - Efthymiou equations

• As with validity range 1, it appears that Efthymiou gives poor predictions for brace

location 1 for all other validity ranges

• Poor predictions are also made at location 5 braceside with SCF_EQN/SCF_ANS

values distributed widely and mean values around 3.5 for all validity ranges

• For locations 3 and 7, better predictions of SCF are achieved for both chordside and

braceside stresses in validity range 2 with mean values near to unity

• Compared with braceside predictions, chordside SCFs appear to be more reliable with

a smaller distribution of results and mean values of SCF_EQN/SCF_ANS closer to one

• For location 5 chordside it seems that Efthymiou underpredicts for validity ranges 2 and

6


Equations

209

7.6.1.2 Summary of axial results - Modified Efthymiou coefficients

• A large spread of results can be seen for location 1 braceside for all validity ranges with

a greater number of overpredictions for validity ranges 2 and 5

• Reasonable predictions of braceside and chordside SCFs at all other locations for

validity ranges 2 and 6

• Mean SCF_EQN/SCF_ANS values are greater than 1 for validity range 5 for both

chordside and braceside stresses indicating that there are slight overpredictions in SCF

using this method

7.6.1.3 Summary of axial results - Modified Efthymiou equations

• Large spread of results particularly for locations 1 and 5 for both chordside and

braceside stresses

• Good prediction of SCFs for both chordside and braceside locations 3 and 7 for validity

range 6

• For validity ranges 2 and 5, good predictions are made at either chordside or braceside

locations 3 and 7 but not both – mean values are higher than unity for some cases

7.6.1.4 Summary of axial results - New equations

• Negative values of SCF are achieved for some cases for both φ = 60º and φ = 90º -

these values may exist outside the data range of the original values

• Large spread of results for validity ranges 2 and 5 for both sets of equations – results

appear to be particularly poor for chordside stresses

• Better results achieved for validity range 6 with mean SCF_EQN/SCF_ANS closer to

unity and a smaller distribution of results

• No negative SCFs calculated for validity range 6

7.6.1.5 Summary of IPB results - Efthymiou equations

• On the whole, Efthymiou overpredicts the SCF at the two crown locations for all validity

ranges

• Worst predictions of SCF are for location 5, validity range 6 braceside where the mean

SCF_EQN/SCF_ANS is 3.72

• Poor prediction of SCF for all validity ranges and locations

7.6.1.6 Summary of IPB results - Modified Efthymiou coefficients

• Good predictions at location 1 braceside for all validity ranges

• Generally good predictions for all braceside and chordside locations for validity range 6

with SCFs averaging close to the ANSYS values


Equations

210

• Poor predictions of SCF for all chordside stresses for validity range 2 with the majority

of SCFs overpredicted

• Biggest distribution of results present for location 5 braceside for validity range 5 where

SCF_EQN/SCF_ANS varies between 0.82 and 3.01

7.6.1.7 Summary of IPB results - Modified Efthymiou equations

• Good predictions of SCF at chordside and braceside locations for validity ranges 2 and

6 – mean results close to 1 and small distribution of SCFs

• Predictions for validity range 5 are less reliable with a wider distribution of results for

both chordside and braceside stresses

• Mean SCF chordside predictions for validity range 5 around 33% larger than ANSYS

results

7.6.1.8 Summary of IPB results - New equations

• Unreliable predictions for all validity range 2 locations when employing φ = 60º - at

worst, results of SCF_EQN/SCF_ANS ranging from -1.59 to 24.57

• More reliable predictions of SCF achieved using φ = 60º for validity range 6 with mean

values close to ANSYS stresses and a smaller distribution of results

• Predictions using φ = 90º equations vary with reasonable approximations for validity

ranges 2 and 6 but negative SCFs arising when applied to validity range 5

7.6.1.9 Summary of OPB results - Efthymiou equations

• Efthymiou consistently underpredicts for chordside stresses at both saddle locations for

all three validity ranges with predictions around 90% of the ANSYS result

• Good predictions of braceside stresses for all validity ranges although there appears to

be a slight tendency to overpredict

• Distribution of results for both braceside and chordside SCFs tight around the mean

7.6.1.10 Summary of OPB results - Modified Efthymiou equations

• Large spread of results for all locations and validity ranges in comparison with the

Efthymiou equations

• For braceside stresses, SCFs as low at 16% of the ANSYS results were achieved

• Chordside predictions for all validity ranges appear to be better than braceside

estimates with mean values closer to ANSYS results


Equations

211

7.6.1.11 Summary of OPB results - New equations

• Generally better predictions achieved for braceside stresses using the φ = 60º set when

comparing to the modified equations however Efthymiou’s equations appear more

reliable

• For chordside stresses both the φ = 60º and φ = 90º equations slightly overpredict

SCFs – little difference between the two sets can be observed

• Out of the two equations it appears that φ = 90º give the best prediction (excluding

Efthymiou)

7.6.1.12 Overall summary

The method of factoring the equations established for one validity range in order to fit the data

for other validity ranges seems to be limited particularly for the new equation sets. Poor

predictions of SCF were obtained when applying the equations valid for φ = 60º to an out-of-

plane angle of 90º. This often resulted in a large spread of data with more extreme values

where the predicted SCF was anything up to 25 times larger than that determined using

ANSYS. Negative values of SCF resulted from the analysis therefore reinforcing the idea that

using factors to allow for the application of equations for different validity ranges is not the

correct approach.

Equations where the coefficients of the original Efthymiou equations were modified to fit the new

data set appeared to be the most reliable. This set of equations gave the smallest distribution of

predictions with mean values closer to the ANSYS SCFs. For OPB the modified Efthymiou

equations were less reliable with more underpredictions for braceside SCFs. The Efthymiou

equations performed best for all validity ranges under OPB with consistently good predictions of

braceside SCFs and a tight distribution of results around the mean.

Modified Efthymiou equations also performed reasonably well for most load cases, validity

ranges and locations. As the relationship between SCF and the additional terms introduced into

the equation was approximated, there could be flaws in applying the equations to further validity

ranges. Because of this, the equations with modified Efthymiou coefficients may be more

suitable for further application.

For all sets of equations, including Efthymiou, the predictions for crown location 1 braceside

under axial loading appear to be poor with a high number of overpredictions for all validity

ranges. Efthymiou performs particularly badly for this location as seen in the previous analysis

for validity range 1. Maximum SCFs as high as 42 times the ANSYS prediction can be seen for

the Efthymiou equations. Maximum estimated SCFs for the new sets of equations are relatively

more reliable with values averaging at around a factor of 3 overpredicted.


Equations

212

7.7 Overall Summary, Conclusions and Future

Work

7.7.1 Overall Summary

Three sets of equations were established using the data for validity range 1 where short chords

and brace inclinations of less than 45º were excluded for out-of-plane angles of 60º. A total of

eight equations with factors where applicable were determined for the load cases and braceside

and chordside stresses for each of the methodologies. These equations were compared

against each other and against the original Efthymiou equations in order to assess their

reliability. A set of criteria was determined for assessment including ensuring that the majority

of predictions fell within +/-10% of the ANSYS values and the number of underpredictions were

minimised.

For validity range 1, the most reliable set of equations appeared to be the new set where the

relationship between each parameter and SCF was established to give an overall equation

which included all of the available parameters.

In general, the reliability of all sets of equations was good for validity range 1. Underpredictions

were minimised and the number of extreme results, for example gross overpredictions, were

few. SCFs were distributed tightly around the mean, which was on the whole close to the

ANSYS calculations. The Efthymiou equations gave poor results in comparison to the new sets

of equations and a key observation was that the SCFs at crown location 1 were consistently

higher than the ANSYS SCFs.

It was decided that, due to limited data and in order to restrict the number of equations for

application by the engineer, the equations for validity range 1 could be factored for other validity

ranges, as given in section 7.3.1 on page 179. The factored equations were compared with the

output from Efthymiou and with each other to assess their reliability. Predictions using this

approach were poor in comparison to the results achieved for validity range 1 and, for some

locations and validity ranges, in comparison to the output from Efthymiou. What was

repeatedly observed for all sets of equations was the overprediction of SCFs at crown location

1, as identified for Efthymiou and validity range 1.

For this methodology, it was noted that the new set of equations, which proved to be the most

reliable for validity range 1, performed poorly with large ranges of results including negative

values of SCF. When using the equations valid for the out-of-plane angle, φ = 90º for different

validity ranges with the same angle between planes, the results were more reliable but still gave


Equations

213

inadequate predictions of SCFS compared to Efthymiou and the modified equations. The best

set of equations seemed to be the modified Efthymiou coefficients for axial and IPB load cases

with the original Efthymiou equations providing the best predictions for OPB.

7.7.2 Conclusion

The new sets of equations established for validity range 1, where short chord effects and brace

inclinations of less than 45º were excluded and the out-of-plane angle φ = 60º, using the a

regression method assessing each of the parameters individually gave the best results for that

data set. Modifying the Efthymiou equations, however, by changing the coefficients and

including additional terms in the equation also gave good predictions. All three methods

predicted the SCFs better than the Efthymiou equations for the validity range in question. This

could be a result of removing the data which did not fit to the range, giving a smaller field of data

to correlate.

When applying factors to the equations developed for validity range 1, the resulting SCFs were

poor in comparison to the data set from ANSYS. This implies simply that the methodology is

not valid. Examining the plots of SCF against individual parameters indicates that the

relationships between parameters vary with different validity ranges. For example, when

looking at the change in SCF and brace inclination, θ, it is clear that for brace inclinations less

than 45º, a different relationship between SCF and θ applies. A linear relationship between the

parameter α and SCF exists for values of α greater than 15. Short chord effects kick in for

values less than this which produces a log or exponential curve with a negative slope to the

linear part of the curve. This clearly demonstrates that there is the potential for different

relationships between individual parameters to occur for different validity ranges which could be

a contributor to the poor performance of the equations for different data sets.

For the modified Efthymiou equations and coefficients, the results were less drastic when

equations for one validity range were factored for another. As the Efthymiou equations were

established for a broader range of data, which could explain a lesser fit for some cases, there is

a likelihood that the modified equations fit the different ranges better because of this.

Predictions failed to meet the standards of the application to the original data range but were

vastly improved compared to the newly derived equations. When comparing to Efthymiou, the

equations performed less well, again presumably due to the wider data range for which

Efthymiou is valid. A recommendation for future work exploring further data ranges is to be

made as a result of this uncertainty.

To conclude, the new set of equations work well for a specific data range but cannot be factored

for application to different validity ranges. Caution should therefore be applied when using the

new equations for values outside the original validity range. Equations developed from the


Equations

214

original Efthymiou equations provide good estimates of SCF for the applicable validity range

and give reasonable predictions for other validity ranges. For OPB, however, the Efthymiou

formulae gave the best estimates of SCF compared to those derived using ANSYS.

7.7.3 Further work

The first stage of the regression analysis was to identify appropriate validity ranges so that

equations would fit better to the data. Because of the change in relationship between SCF and

some of the parameters for different data sets, it may not be a valid approach to simply factor

one set of equations for a specific validity range for application to a different range. A

recommendation for further would be to either include a broader range of data in the regression

analysis, so expanding on the data to include changes in chord diameter and brace thickness,

or to develop sets of equations for all validity ranges. The second approach would offer a more

accurate method but would require multiple equations for each location and load case under

consideration. This could, however, complicate the design process with a larger number of

equations to deal with.

Expanding the data set and changing the validity ranges could reduce the reliability of the

equations, as seen with Efthymiou for some data points. Further work investigating the

predictions resulting from sets of equations with different validity ranges would be useful to see

the variability between results. A regression analysis could be performed on the entire existing

data set and the SCFs arising from the equations compared against those from validity range 1.

Further checks on Efthymiou would be possible and would confirm whether the inaccuracies in

his approach are as a result of covering a wide range of data points.

The investigation looked into braces with the same inclination. In practice, it would be difficult to

achieved identical brace inclinations for an offshore jacket structure particularly for structures

with inclined legs. Further research into braces inclined at different angles on one joint is

recommended so the effects of the θ parameter can be fully investigated. As with uniplanar K

joints, changing the brace inclination of both braces would introduce an extra θ term and further

steps to the analysis but would offer more flexibility with design.

Fixed-fixed boundary conditions only were modelled in the parameter study. With the Efthymiou

equations, it is possible to estimate SCFs for a range of chord-end fixity conditions by

specification of a chord-end fixity parameter, C. For a fully fixed condition, C = 0.5 (as used in

the calculations) whereas a pinned-pinned connection would have a value of 1.0. Simply

supported end conditions would require a parameter of C = 0.7. Further investigation into how

chord-end fixity conditions affect the new sets of equations and whether an additional parameter

could be integrated into these is recommended. This would require expanding the data set to

include a range of joints with different support conditions in the ANSYS model.


Equations

215

The influence of chord loads was not taken into account for the parameter study. Early

investigations indicated that this could have an effect on SCFs for both chord and brace

locations. Inclusion of chord loads in the design process could complicate the already complex

methodology of estimating SCFs hence not examined as part of the investigation.

Consideration into how this would be incorporated into the design procedure and appropriate

FE modelling allowing development of the modified Efthymiou and new sets of equations may

provide improved predictions of SCFs.

216

Chapter 8 Design of Tubular

Joints – Superposition of SCFs to

Determine Hot Spot Stresses for


8.1 Introduction

Equations have been established for calculating the SCFs at different locations around the

brace-chord intersection for axial, IPB and OPB in one brace only. The procedure follows that

of Efthymiou where each brace is isolated and SCFs calculated based on a set of geometrical

parameters. According to DNV-RP-C203 [19] it is possible to superpose nominal stresses in

each brace factored by the corresponding SCF to give the overall hot spot stress pattern at the

weld toe for both chord and braceside. The equations of superposition are given in

In order to check the validity of the equations, a sample joint with a realistic loading pattern was

modelled in ANSYS using the same modelling assumptions as adopted for the parameter study.

Loading patterns for the joint were taken from the preliminary design of a jacket structure

performed in Chapter 2. The stresses around the upper and lower extrapolation regions were

output from ANSYS and extrapolated back to the weld toe to give the hot spot stress

distribution. Hot spot stresses at the 8 key locations could then be ascertained.

The same joint was analysed using SCFs calculated by Efthymiou and the three sets of

equations established in Chapter 7. Carry-over factors were estimated from the graphs

developed as a result of the parametric study and applied to the nominal stresses. For the

Efthymiou case, nominal stresses were factored by the SCFs and superposed to give the hot

spot stresses at eight locations. The same procedure was applied to the three alternative

methods and a further analysis, where the nominal stresses were also factored by the estimated

carry-over factors and then superposed, was carried out. Final plots showing the hot spot

stress distribution for chord and braceside locations were produced to check whether all four

methods predicted this correctly.

Chapter 8 Design of Tubular Joints – Superposition of SCFs to Determine Hot Spot

Stresses for Multiplanar Tubular Joints

217

8.2 Hot Spot Stress Prediction using Finite

Element Analysis

For the preliminary design of a jacket structure, the loading on the structure due to one of the

fatigue waves was determined using GL Garrad Hassan in-house spreadsheets and the

structural analysis package RISA, as outlined in Chapter 2. The following geometry and

corresponding parameters were selected for the analysis:

Geometry Parameters

Chord diameter D 2000 mm α 17.75

Brace diameter d 759 mm β 0.38

Chord thickness T 45 mm γ 22.22

Brace thickness t 25.4 mm τ 0.56

Chord length L 17750 mm ζ 0.50

Gap g 1000 mm

Brace inclination θ 45 º

Out-of-plane angle φ 60 º

The loading pattern applied to the braces in the directions as shown in Figure 8-1 was as

follows:

Figure 8-1: Example joint in ANSYS Workbench indicating the brace lettering system and

the application of loads and their pattern

Brace A AXL 38361 N

IPB 599 N

OPB 12385 N Brace B AXL 99318 N

IPB 1093 N

OPB 4651 N Brace C AXL 66812 N

IPB 43 N

OPB 2154 N Brace D AXL 2.85E+05 N

IPB 3830 N

OPB 1775 N

Brace A

Brace B

Brace C

Brace D



218

Using the same modelling methods as applied to the parameter study, the joint was evaluated

with the loading pattern as indicated above. Maximum and minimum principal stresses were

determined at the upper and lower extrapolation bounds as according to DNV-RP-C203 [19].

These stresses were then extrapolated back to the weld toe to give the overall hot spot stress

distribution around each of the four braces’ brace-chord intersections. All assumptions and

techniques used in the previous batch runs for the parameter study were implemented to ensure

the methodology remained consistent. This includes both the ANSYS analysis and post-

processing of data.

8.3 Hot Spot Stress Calculations

8.3.1 Using the Efthymiou Equations

The design code DNV-RP-C203 [19] outlines the approach for the design of uniplanar tubular

joints using the Efthymiou equations. On examination of the loading pattern for the joint, it is

clear that the load cases for loads in one brace only apply. For balanced axial and unbalanced

bending load cases, loads in adjacent braces must be within 10% of each other. The equations

as given in section 6.2 were used along with additional equations as given below:

Chord-end fixity parameters

7.0 typically,0.15.0 where

5/

2/

)5.0(2

3

2

1

=≤≤

=

=

−=

CC

CC

CC

CC

(8-1)

For OPB cases, an additional parameter, x, is required:

β

θζ sin1+=x

(8-2)

The equations for superposition as given in section 6.2 and taken from DNV-RP-C203 [19] were

then used to calculate the hot spot stresses at each of the eight key locations.

8.3.2 Using New Sets of Equations

8.3.2.1 Without carry-over factors

SCFs were calculated for each of the eight locations using the equations derived in section

7.4.1 and the equations of superposition. Where applicable, correction factors were applied to

the intermediate locations between crown and saddle as given in section 7.4.2. This was to



219

ensure a better prediction of the anticipated stresses at these locations. Nominal stresses

resulting from application of axial and bending stresses were then factored by the SCFs and

correction factors to give the hot spot stress distribution around the brace-chord intersection.

The analysis was completed for all sets of equations so a comparison could be made between

the predictions arising from each individual equation. Comparisons were also made against the

predicted hot spot stress distribution by Efthymiou and determined using ANSYS Workbench.

8.3.2.2 With carry-over factors

The same approach as described above in paragraph 8.3.2.1 was used to determine the hot-

spot stresses at the eight key locations but an additional stress was applied resulting from the

plots of carry-over factors. Carry-over factors calculated using the ratio of the stress in the

loaded brace and the stress in the brace in question were represented by a series of graphs.

For each parameter varied and for each load case, the variation in carry-over factor was plotted

against the parameter. A sample graph for brace B, the brace in the same plane to the loaded

brace, can be found in Figure 8-2.

As Figure 8-2 shows, the level of load carried over to the neighbouring brace depends on the

geometry of the joint. For the example given above, applying a tensile axial load to brace A

results in a compressive load at location 1, the severity of which depends on the value of alpha

selected. A negative value of carry-over factor could lead to an overall reduction in stress when

hot spot stresses are superimposed to give the final design values.

What can also be observed from the graph above is that the short chord effects also play a role

in carry-over factors with peak values found around α = 15. The carry-over factors appear to

reduce above and below this value for this case. For other parameters and other braces,

variations in the value of carry-over factors can be seen with the change in value of parameter.

In some cases, the sign of the carry-over factor can vary meaning that above and below certain

values of parameter, the load carried in the brace and chord can turn from compressive to

tensile or vice versa. An example of this can be shown in Figure 8-3.



220

Figure 8-2: Variation of carry-over factor (COF) with α for Brace B braceside stresses at

location 1 for axial load applied to Brace A with out-of-plane angle, φ = 60º

Figure 8-3: Variation of carry-over factor (COF) with τ for Brace B braceside stresses at

location 1 for axial load applied to Brace A with out-of-plane angle, φ = 60º



221

With these changes in carry-over factor (COF) dependent entirely on variations in geometry,

application of the graphs given in the data report would not be a valid approach for joints with

geometries outside the data range. However, for the joint examined in this chapter, the graphs

can be used as its geometry falls within the evaluated range of data. Although the data range is

limited for the COFs and the usability of the graphs in the data report is therefore reduced, the

graphs give a good indication of the relationships between each of the parameters and COF. A

recommendation for further work would be to perform a regression analysis on the existing data,

which could be supplemented by additional geometrical configurations, to produce a set of

equations for application.

For the joint selected, all parameters complied with the base parameters for the variation in α so

the graphs with COF versus α could be used for the analysis. For each of the braces, the COFs

were determined from the graphs given in the data report for each of the locations and load

cases. Taking the nominal stresses resulting from axial, IPB and OPB applied to each of the

braces, the level of load carrying over to neighbouring braces could then be calculated. Taking

brace A as an example, the loading pattern applied to the brace was as follows:

These forces could then be used to calculate the stresses in the brace, with a lever arm of

8875mm applied for bending load cases, which were as follows:

Brace A AXL 0.66 N/mm2

IPB 0.51 N/mm2

OPB 10.58 N/mm2

With the stresses established for the loaded brace, the carry-over stresses could be calculated

in the neighbouring braces by factoring the above stresses by the COFs. The summation of all

available stresses for each of the braces was then completed to give the stress distribution plot

around the brace-chord intersection on both braceside and chordside locations.

8.4 Results

Graphs were plotted for all the methods described in this chapter for chordside and braceside

stresses at the eight key locations to give a stress distribution around the brace-chord

intersection. Figure 8-4 to Figure 8-11 on the following pages show the hot spot stress

Brace A AXL 38361 N

IPB 599 N

OPB 12385 N



222

distribution for all braces on both the chordside and braceside. For the newly developed

equations, plots can be seen for results with and without carry-over factors.

8.4.1 Analysis of results

A variation in the reliability of predictions can be seen for all the methodologies implemented in

the analysis of the joint. This may depend on the loading pattern applied to the brace in

question and could be a case of better results predicted for one or more of the load cases

applied. For both chordside and braceside stresses on Brace A, results by all methods appear

to be satisfactory with each of the sets of equations predicting the shape of the stress

distribution curve well together with reasonable estimates of peak hot spot stresses.

Overpredictions can be seen for stresses at location 7 for chordside and braceside results on

Brace A, which at most are around 30-40% higher than the results reported in ANSYS.

Including COFs seems to reduce the peak stress at location 7 marginally with the smallest

prediction around 15% higher than the ANSYS output.

Figure 8-4: Hot spot stress distribution around brace-chord intersection for braceside

stresses on Brace A



223


stresses on Brace B


stresses on Brace C



224


stresses on Brace D

Figure 8-8: Hot spot stress distribution around brace-chord intersection for chordside

stresses on Brace A



225


stresses on Brace B


stresses on Brace C



226


stresses on Brace D

For the other three braces, the predictions are varied and do not match the hot spot stress

distribution plot from ANSYS as well as that achieved for Brace A. The prediction of the hot

spot stress plot using Efthymiou for Brace D braceside stresses appears incorrect with peak

stresses located at the points of minimum stress. Apart from the case of braceside stresses on

Brace D, the form of curves for Efthymiou and the new equations is very similar with peak and

trough hot spot stresses being located in nearly the same place each time. Variation in the

magnitude of stresses can be observed for each of the methodologies with COFs bearing some

influence on this where applied.

8.4.1.1 Brace A hot spot stress predictions

Loading pattern applied: AXL = 38.4kN, IPB = 5.3kNm, OPB = 109.9kNm

Nominal stresses: AXL = 0.66N/mm2, IPB = 0.51N/mm

2, OPB = 10.58N/mm

2

Dominant load: OPB

As discussed briefly in the previous section, the predictions of hot spot stress for the loading

pattern on Brace A seem reasonable when comparing to the ANSYS output and the results for

other braces. For the new sets of equations, predictions are slightly better for braceside

stresses compared with chordside stresses. Efthymiou predicts the chordside stresses well with



227

peak stresses at locations 3 and 7 within 10% of the ANSYS stress distribution. Note that the

stress at location 3 using Efthymiou is underpredicted when comparing with the ANSYS plot.

For braceside stresses with the new sets of equations, the peak hot spot stress prediction at

location 7 varies around 10% between the various methodologies used. Predictions of hot spot

stress are improved at location 3 with little variance between each of the equations. It appears

that the modified Efthymiou equations with COFs applied give the best prediction with the curve

of this plot close to that achieved by using ANSYS. From examination of the graphs for this

loading pattern it can be surmised that similar results can be achieved by using any of the sets

of equations for this particular geometrical configuration.

The dominant load for this loading pattern is OPB which can be determined by examining the

shape of the graph. When OPB is applied to a brace in isolation, peaks occur at locations 3 and

7 with compressive stresses at one location and tensile stresses at the other. Magnitudes of

stress should be close to one another. The shape of the graph follows this rule with peak

stresses having roughly the same order of magnitude. With OPB as the dominant load, it could

be assumed that the prediction of stresses is based mainly on the Efthymiou and other

equations and not on the equations of superposition. As the predictions for Brace A appear to

be better than for other braces, it could be inferred that the new sets of equations provide

reasonable predictions of hot spot stress for OPB in isolation. Also, the level of load

experienced by this brace was much higher than for the other braces indicating that carry-over

effects may not play a significant role in the overall stress distribution for the brace.

8.4.1.2 Brace B hot spot stress predictions

Loading pattern applied: AXL = 99.3kN, IPB = -9.7kNm, OPB = -41.3kNm

Nominal stresses: AXL = 1.70N/mm2, IPB = -0.93N/mm

2, OPB = -3.97N/mm

2

Dominant load: OPB

The predictions of hot spot stress for this load combination were poor in comparison with the

results for Brace A. Examining the magnitude of peak stress only and ignoring its location

implies that reasonable results for hot spot stress have been obtained using the equations,

including Efthymiou. Using maximum hot spot stresses only gives a difference between ANSYS

readings and the predictions of the equations of around 20% with the equations overpredicting

this stress. However the stress plots show a different picture with the hot spot stress at location

3 braceside roughly double the ANSYS output when using the newly established equations and

Efthymiou. Chordside predictions fare better but the variation between each of the equations is

much greater with Efthymiou providing the best predictions and the modified Efthymiou

coefficients without COFs overpredicting by around 90%.



228

For the braceside stress distribution, results appear to be similar for each of the new equations

devised. At location 3, the variation between the output of each of the new equations with or

without COFs is at most 8% however it seems that most of the curves overlie one another at

this position. For location 7, there is a greater difference between the three methods (new

equation, modified Efthymiou equation and coefficients) but no variation in stress when

implementing COFs. The carry-over effects play the greatest role at the crown location 1

increasing the hot spot stress at this location.

Similar values of hot spot stress are achieved at saddle locations 3 and 7 when considering the

ANSYS plot, implying that the OPB effects are dominating the stress distribution in the joint. A

key feature of the graph is the reduction in stress at crown location 1 for the new sets of

equations compared with Efthymiou. At this location, the stresses derived using the new

equations are closer to the ANSYS output indicating that axial and IPB effects are generating

stress here. Incorrect superposition of the loads; that is, the equations of superposition do not

superimpose the load pattern correctly; could be a contributor to the poor prediction of the

overall shape of the hot spot stress distribution plot.

8.4.1.3 Brace C hot spot stress predictions

Loading pattern applied: AXL = 66.8kN, IPB = 0.4kNm, OPB = 19.2kNm

Nominal stresses: AXL = 1.14N/mm2, IPB = 0.04N/mm

2, OPB = 1.84N/mm

2

Dominant load: OPB with AXL increasing peak stresses

Maximum hot spot stresses for this loading pattern occur at location 7 for both chordside and

braceside locations. For braceside maximum stress, all equations appear to greatly

underestimate this value. The modified Efthymiou coefficients with COFs applied give the best

prediction however this value of stress is approximately 17% lower than the values obtained

from ANSYS. Without applying COFs, the stresses are reduced further at this point indicating

that carry-over effects from other braces have a less favourable impact on stresses at location

7. Chordside stresses, however, are overpredicted at location 7 when applying the new sets of

equations and the COFs appear to worsen the predictions by increasing the stress significantly.

Without COFs applied, the maximum hot spot stress predicted by the new equations matches

the stress arising from ANSYS at this point. When applying the COFs, stress at location 7

chordside was at most around 40% greater than the output from ANSYS.

Another observation from the stress plots is that the second peak in the hot spot stress

distribution is not modelled when using the equations given in Chapter 7 and the Efthymiou

equations. This second reduced peak at location 3 is likely to be an effect of the axial load

applied to the brace and is reduced because of the compressive effects of OPB at this location.

For braceside stresses, the equations indicate a small level in load at this point, which can be



229

viewed as negligible for the modified Efthymiou cases. Carry-over effects increase the stress at

this point marginally so there is a possibility that either the superposition of axial loads is not

being accounted for sufficiently or that a greater influence of loads in neighbouring braces

applies. Similar behaviour can be concluded from the chordside stress plots; however the

COFs manage only to change the stress from compressive to tensile at this location which

therefore reduces its magnitude.

In terms of variation between the three new methodologies, little difference in stresses can be

seen when comparing the equations either with or without COFs applied for braceside stresses.

At most there is around 8% difference in hot spot stresses at location 7 with graphs overlying

each other at crown location 1. Applying COFs shifts the graphs up around 20% at location 7

indicating that carry-over effects are significant at this location. For chordside stress plots, a

greater variance can be observed between each set of equations regardless of whether COFs

have been applied or not. In this case, application of COFs does not improve predictions

resulting in stresses being overpredicted at the key saddle location 7. Efthymiou performs badly

for both chordside and braceside stresses with significant underpredictions for maximum hot

spot stresses particularly for braceside values.

8.4.1.4 Brace D hot spot stress predictions

Loading pattern applied: AXL = 284.9kN, IPB = -34.0kNm, OPB = -15.8kNm

Nominal stresses: AXL = 4.87N/mm2, IPB = -3.27N/mm

2, OPB = -1.52N/mm

2

Dominant load: AXL

Axial loading appears to dominate for the loading pattern applied to Brace D. OPB effects

increase the peak at location 3 when using the theory of superposition for all of the equations

however this increase is much reduced for the output from ANSYS particularly for chordside

values. Efthymiou predicts a similar stress distribution as the other equations for chordside

stresses, however, the braceside predictions appear completely incorrect. Maximum stresses

appear at the crown location 1 whereas the ANSYS plot indicates that this should occur

between locations 2 and 3. Inspection of the SCFs at location 1 braceside indicates that this

value is much higher for the selected geometry than other SCFs therefore, with axial loads

dominating for this brace, the maximum stress has been shifted to this location. As noted in the

parameter study, Efthymiou consistently overpredicted the SCFs at location 1 under axial loads

therefore the overprediction at this point is likely to be a result of this. For chordside stresses,

Efthymiou predicts SCFs reasonably well hence an improved plot of stress distribution although

it must be noted that predictions by Efthymiou at location 1 are still higher than the ANSYS

estimates and those arising from the new sets of equations.



230

For other equations, similar shaped plots are achieved which match the shape of the ANSYS

results reasonably well. Peak stresses are significantly overpredicted particularly for chordside

stresses where the worst prediction for location 3 was around a factor of 1.7 greater than the

ANSYS predictions. Estimates of the hot spot stress at location 7 were much better with results

closer to the stress at this point. On the whole, the best prediction for Brace D on both chord-

and bracesides was the new equation with COFs applied however maximum stresses at

location 3 were around 50% higher for chordside hot spot stresses and around 30% higher for

braceside hot spot stresses.

8.4.2 Overall discussion of results

For the loading patterns on braces B, C and D, it appears that the new equations and the

Efthymiou equations together with the equations of superposition give a poor prediction of

maximum hot spot stresses and their locations. The shape of the hot spot stress distribution

curve is generally predicted reasonably well with peak stresses located roughly in the same

place as that determined using ANSYS and extrapolation of stresses to weld toe. However the

magnitude of these peak stresses varies from the ANSYS predictions for most cases with worst

estimates being overpredicted by anything up to 70%.

The best prediction of hot spot stress was achieved for Brace A, the loading on which was

dominated by OPB. Both axial and in-plane loads were negligible in comparison to the OPB

load case therefore the overall behaviour of the joint depended on OPB only. Values of stress

at locations 3 and 7 were overpredicted at these locations but the stress plot followed that of the

ANSYS results. Overpredictions at locations 3 and 7 were at most 50% higher than ANSYS

however the predictions for location 3 were closer to the ANSYS output.

What can be implied from the analysis is that the equations for SCFs combined with the

equations of superposition give poor predictions of the stress distribution plots. Brace A is

subjected to a large OPB loading which makes the nominal stresses due to axial and IPB load

cases negligible in comparison. For this case, the superposition equations can be ruled out as

having any effect on the predictions of hot spot stress distribution due to the dominance of the

OPB loading case. Reasonable predictions of hot spot stress were achieved for this brace, in

comparison with other braces, with the hot spot stress distribution matching that of the ANSYS

output. This implies that the equations for the OPB loading case alone, without use of the

superposition equations taken from [19] and outlined in section 6.2 on page 147, work well to

predict the hot spot stress distribution around the brace-chord intersection.

As reasonable predictions of hot spot stress were observed for the case where one load

dominated and other loads could be assumed as having a negligible effect, there is the

possibility that the equations of superposition could be affecting the reliability of the overall



231

predictions. Further work is therefore recommended to check the reliability of equations of

superposition outlined in DNV-RP-C203.

8.5 Summary, Conclusions and Future Work

8.5.1 Summary

Significant variations were observed in the peak hot spot stresses determined using Efthymiou

and the newly derived equations when compared with the results from ANSYS Workbench. The

best predictions were achieved for the loading pattern on Brace A where the OPB load

dominated indicating that the application of the equations of superposition could be flawed. No

particular set of equations stood out as offering the best prediction of the hot spot stress

distribution for both braceside and chordside stresses. On the whole, there was little variation

between the modified Efthymiou equations and coefficients and the new equations particularly

at locations where stresses were not at maximum values.

For braces B, C and D, the predictions of hot spot stress distribution using the various equations

missed secondary peaks which were identified from the extrapolated stresses as determined by

ANSYS. The magnitude of maximum stresses was predicted reasonably for braceside stresses

for the loading patterns on braces B and D and for chordside stresses on braces B, C and D,

however, the location of the peak stresses varied from the plots given by ANSYS. For

braceside stresses on Brace C, the stresses were significantly underpredicted even with COFs

applied indicating that the effects of carry-over may be greater than estimated from the graphs

given in the data report.

The influence of carry-over factors on the stress distribution plot varied for the different loading

patterns but in most cases application of the factors did not alter the maximum stresses greatly.

For intermediate locations and locations where the stress was much smaller than peak values,

the COFs had little effect on the stress. The case where carry-over seemed to play a significant

role in the predictions was for Brace C where both axial and OPB loading dictated the stress

patterns in the brace. Stresses due to the loading on this brace were smaller than that

experienced by all other braces implying that carry-over effects were much greater. For Brace

A, OPB loads gave much higher stresses than the loads applied to other braces (more than

double the maximum stress experienced in Brace D), therefore it could be assumed that the

brace was subjected to minimal carry-over effects.

8.5.2 Conclusions

When examining the loads in isolation, it appears that the method of using SCFs and the

equations of superposition to predict the hot spot stress distribution around the brace-chord



232

intersection work reasonably for the joint in examination. Brace A of the joint is almost

exclusively acted on by OPB, the resulting stress of which is more than double the maximum

stress in neighbouring braces, hence the good prediction of the hot spot stress profile and a

reasonable estimation of the maximum stress.

The poor predictions of hot spot stress in braces B, C and D compared with Brace A invites the

questions of whether the equations of superposition are adequate as well as whether the

influence of carry-over in these braces is more significant than anticipated from the graphs given

in the data report. Predictions of the values of maximum stresses were on the whole

reasonable using the equations derived in Chapter 7 however the location of this maximum was

often noted as the opposite crown or saddle location from what was indentified using ANSYS

Workbench. For the purpose of practical application, the maximum hot spot stress would be

determined using SCF equations and the equations of superposition and then further

calculations to determine the fatigue life of the joint would be carried out using this maximum.

Assessing the hot spot stress output from the equations on this basis, it could be said that the

new derived equations gave reasonable predictions for the loading patterns on Brace A in

particular.

Three different sets of equations were devised for the design of multiplanar tubular joints with

factors applied to intermediate locations or for different validity ranges outside that used for the

analysis. A greater variation between results was observed when comparing the calculated

values of SCF against the ANSYS SCFs. However when applying the equations to a loaded

joint, the variation in hot spot stress distribution for this particular case seemed little for all sets

of equations. At locations of peak stress, a larger difference can be seen between the

equations however, for each of the loading patterns the equation closest to ANSYS plot differs

therefore it cannot be inferred which of the equations performs best.

8.5.3 Future Work

A great level of uncertainty can be observed from the analysis completed on the design of

multiplanar tubular joints using equations derived from the parameter study and COFs.

Because of this uncertainty, further investigation into the application of COFs is required before

a concrete solution can be provided. Using the existing data, a regression analysis could be

performed to give a series of equations for COFs which would then be applied in conjunction

with the equations derived in Chapter 7. As the graphs in the data report indicate, it is likely that

a relationship between each of the parameters and the COF exists and therefore can be

established for data points outside the range when the regression analysis is completed. This

would expand on the limited data displayed in the graphs and could allow for a more accurate

estimation of the anticipated level of carry-over. Further FE modelling could also be carried out



233

with the individual loads applied in isolation as before in order to gain more certainty of the

variation of COFs with parameters.

Two possible sources of error in the analysis performed in this chapter can be identified as the

estimation of carry-over effects and its application together with the superposition of hot spot

stresses to give the overall hot spot stress distribution. Checks on the equations of

superposition are recommended in order to ascertain whether stresses due to axial, IPB and

OPB load cases are being combined correctly. If loads are not superimposed correctly, a range

of load patterns and geometrical configurations would need to be modelled so a new set of

equations of superposition can be established.

Only one joint configuration was examined for application of the new equations to determine the

hot spot stresses so it is difficult to conclude whether the poor performance of the complete

analysis applies to this joint configuration only or is common with a range of geometries and

loading patterns. It is therefore recommended that a wider range of joints are examined

ensuring that the spectrum of parameters are covered. The combination of loads and their

subsequent effects on the stresses induced in neighbouring braces also requires further

consideration. For the parameter study, loads were examined in isolation based on the

assumption that the stresses resulting from individual loads could be factored by SCFs and

superimposed to give the correct hot spot stress distribution around the brace-chord

intersection.

The following FE models could therefore be examined for clarification on this matter:

• Using the loading pattern and joint configuration examined in this chapter, build FE

models with loading pattern applied as individual loads

o Can check the accuracy of the equations derived in Chapter 7

o Superposition of load cases can therefore be examined – individual hot spot

stress distributions can be overlaid to give an overall stress pattern which can

compared with the ANSYS plot determined in this chapter

o Effects of carry-over can be clarified with carry-over stresses indicated in

unloaded braces

• Further loading pattern configurations applied individually and combined

o Expands on data set so new superposition equations could be developed if

required

o Additional data to reinforce existing data

• Range of geometries covering the equations’ validity range

o Again, reinforces existing data set



234

o Can confirm with additional data whether the poor prediction is to be expected

or whether an anomalous case was examined

235

Chapter 9 Discussions,

Conclusions and Future Work

9.1 Introduction

Aspects affecting the design of offshore wind turbines support structures have been examined

in this thesis with the aim of tackling design issues concerning the industry at present. Two

support structure options, monopiles and jackets, were covered as state-of-the-art and future

design possibilities for supporting large wind farms out at sea. The following concepts were

identified as problem areas and were investigated further in the thesis:

1. Wind and wave loading on monopile foundations – how breaking waves affect the

magnitude of forces exerted on the structure and when does wave loading dominate

during turbine operation

2. Fatigue life of jacket structures – whether design equations for predicting the stress

concentration factors for uniplanar tubular joints gave adequate estimates for hot spot

stresses in multiplanar joints

Fabricating and installing foundation structures for offshore wind farms consumes a significant

proportion of the total budget for an offshore wind project, sources indicate that this could be as

high as 25% of the overall project cost. Understanding the behaviour of support structures,

particularly when establishing wind farms in deeper waters with larger turbines, could lead to

improvements in the design process and maybe could result in weight savings in the structure.

Important is that structures are design correctly to prevent any further costly repair work later on

during operation of the wind farm.

9.2 Wind and Wave Loading on Monopile

Foundations

9.2.1 Summary

In response to a research paper published by Luck and Benoit [25] where a model monopile

foundation was loaded by waves in a flume, an investigation into the validity of using linear and

nonlinear wave theories to model waves was completed. Results from the investigation differed

Chapter 9 Discussions, Conclusions and Future Work

236

significantly to the published data and, on further inspection of the publication, it was concluded

that breaking waves were being exerted on the structure. Experimental work was completed to

check this hypothesis and to assess the effect of waves breaking on a monopile structure. A

further comparison of the forces predicted using a linear and non-linear wave theory together

with the Morison equation was made against the author’s test data confirming that waves

breaking on the structure generated as much as 2.5 times more force than according to the

theory.

Using GL Garrad Hassan’s commercial software, Bladed, an analysis of two different generic

turbines support by a monopile foundation was completed to check the influence of the wind

loading on the overturning moments on the structure. The moments at hub height were

recorded in Bladed for the turbine in operation and compared against the overturning moment

due to the maximum theoretical wave height to see which would dominate for different water

depths.

9.2.2 Discussion

Examining the results from Luck and Benoit [25] using linear Airy wave theory and a nonlinear

Fourier series method developed by Buss and Stansby [32] indicated that wave loads from the

experimental data were up to a factor of three different from the calculated values. A range of

breaking, non-breaking and post-breaking waves were examined in [25] however it was unclear

which waves were which. Checks on the data for maximum wave heights according to Miche

[34] implied that the majority of waves generated exceeded this criteria. With this conclusion it

was decided that experimental work needed to be carried out to check the level of magnification

anticipated from waves breaking on a monopile foundation.

A series of non-breaking and breaking waves were therefore generated in the Hydraulics

Laboratory at the University of Manchester to check linear and nonlinear wave theories and to

examine the level of magnification for waves breaking on the structure. For the non-breaking

waves, forces exerted on the cylinder in the flume were within 15% of the theory indicating that

predictions from both methods matched the data well. When breaking waves were generated, a

magnification of load was observed however this was slightly smaller than anticipated. At most,

the amplification of loads was around 2.5 times the theory.

Static wave loads were converted to dynamic loads using a dynamic amplification factor and the

overturning moments were compared with hub moments for a 2MW and a 5MW turbine

supported by monopiles under steady operational loads. The maximum theoretical wave height

for the operational wind speeds was used for comparisons and it was observed that, for lower

wind speeds, the wind loading dominated for water depths up to 30m. As the wind speed

increased, the wave loading increased with larger theoretical wave heights generating a greater

overturning moment on the structure. Conversely, the wind loading appeared less significant


237

compared to wave loads for higher wind speeds with the wave loading dominating at around

12m water depth for both turbines.

9.2.3 Conclusions

The effects of waves breaking on a submerged cylinder causes an amplification of loads on the

structure of up to 2.5 times the values determined using wave theory and the Morison equation.

A review of literature on the subject indicates that using the Morison equation in its present form

may not be suitable for modelling the magnification of loads due to breaking wave phenomenon

with recommendations of increasing the drag coefficient by a factor of 2.5. This falls in line with

the results from the experimental work completed on breaking waves.

Comparing wind and wave loads determined using the Miche criterion and the Rayleigh

Distribution indicated that for lower wind speeds, the wave loading dominates at deeper water

depths. As the wind speed increased, the maximum theoretical wave height increased leading

to a higher overturning moment on the structure. Operational wind speeds only were examined

for this study which meant that higher wind speeds resulting from gusts were not considered in

the analysis. There is a likelihood that wind loads would dominate for such conditions and

would be the critical load case for design.

9.2.4 Future Work

Monopile structures only were examined in the study therefore the work could be expanded to

cover different support structure options such as jackets and tripods. Scale models of the

support structures could be fabricated and subjected to breaking and non-breaking waves to

examine the level of amplification of force exerted on the structure for the two wave types. For

work on combined wind and wave loading, further design load cases could be examined with

gust loads a possibility.

9.3 Investigation into the Behaviour of


9.3.1 Summary

As a result of the work completed on preliminary design of support structures for offshore wind

turbines, research was carried out to assess the behaviour of multiplanar tubular joints. The

investigation comprised several stages as conflicting agreement [22, 49] on the behaviour of

multiplanar joints required further clarification. FE modelling of multiplanar KK joints was

completed in order to check whether the presence of braces in another plane had an effect on

the hot spot stresses at the weld toe. Comparisons of the hot spot stresses were made for

uniplanar models, multiplanar models and the stresses arising from the Efthymiou equations.


238

Differences in stress could be observed with a reduction in stress observed for the multiplanar

configuration. Further investigation into this indicated that significant levels of stress were being

carried over from the loaded brace to neighbouring braces (anything up to 50% for axial loads)

which could either have a stiffening or weakening effect on the joint depending on the loading

pattern applied. The Efthymiou equations neglected this carry-over particularly when analysing

a single loaded brace on a K joint - the equations for a T joint are recommended for use and no

carry-over into the adjacent brace is considered.

A parametric study of multiplanar KK tubular joints was completed using ANSYS Workbench to

form a database of stress concentration factors and carry-over data for a range of joints under

axial, IPB and OPB loads. This data was then used in a least-squares fit regression analysis

where the original Efthymiou equations were modified to fit the data by changing the

coefficients, including additional parameters or varying the relationship between the parameters

if a more suitable one could be applied.

Plots of the SCFs against each of the parameters for the values from ANSYS and the values

predicted by the new sets of equations indicating that modifying the Efthymiou equations didn’t

always yield good results. A different approach to regressing the data was applied with each

parameter examined individually and their relationship with SCFs established to give an

equation of the form:

ζθγτβα 654321SCF CCCCCC + ++++= (9-1)

Equations were established primarily for two data ranges based on the assumption that factors

could be applied to the resulting SCFs to give reasonable predictions for other ranges. The

different validity ranges were identified by examining the entire data set for changes in pattern

with changes in parameter. To reduce the number of equations, the same formula was used for

the two different crown and saddle locations and, as with the different validity ranges, factors

were calculated if a variation in SCF at these points occurred. Further calculations indicated

that this method worked reasonably for the modified equations but lead to extreme values of

SCF being calculated for the new sets of equations. These new equations performed better

than the modified Efthymiou equations for the data from which they were established implying

possibly that factoring equations for different data sets is not a valid assumption.

The equations arising from the parameter study are available in section 7.4.1 between pages

189 and 191 of the thesis. For the factors which convert the equations for applicability to

different data ranges, see section 7.4.2 on page 191. The validity ranges are outlined in 7.3.1

on page 179.


239

The final step of the multiplanar analysis was to use the new sets of equations to design a

multiplanar tubular joint and compare this against Efthymiou and the stresses determined using

ANSYS. Two assessments were completed – stresses superimposed without carry-over factors

and stresses superimposed with carry-over factors applied – to check the level of influence of

carry-over stresses have on the overall behaviour of the joint. Results indicated that there was

little variance between the three sets of equations and that the estimated carry-over stresses did

have an effect on the peak hot spot stresses. When comparing the hot spot stress distribution

plots of all braces for all sets of equations, including Efthymiou, with the stress distribution from

ANSYS, a variation in the form of the stress plots could be observed for three of the four loading

patterns applied to the braces. This could indicate that the equations of superposition, as given

in DNV-RP-C203 [19], may be incorrect therefore further work on this is recommended.

9.3.2 Discussion

Modelling multiplanar tubular joints as uniplanar configurations could be considered to be

incorrect as the presence of additional material in another plane has an effect on the overall

behaviour of the joint. For joints with an out-of-plane angle of 90º, this effect is reduced in

comparison with the 60º case where out-of-plane braces are closer to each other and therefore

hot spot stresses at the saddle location where the two planes meet are reduced. The initial

stages of the investigation examined the carry-over effects of multiplanar tubular joints

indicating that this was significant when isolating loads to one brace and applying them

individually. As much as 50% of the stress was seen to be carried over into neighbouring

braces for axial loads in one brace only, which would be neglected if analysing the joint using

the Efthymiou equations. This carry-over either offers a favourable or an unfavourable effect

on the overall hot spot stress distribution around the brace-chord intersection depending on the

magnitude, direction and type of loading applied to the joint. It cannot be simply summarised

that the effects of the presence of braces in another plane reduces the hot spot stress as this

depends entirely on the sense of the loading applied.

The results of the regression analysis indicate that the modified Efthymiou equations performed

on the whole better than the new sets of equations particularly when applying to different validity

ranges. When compiling the data arising from the parameter study, it was observed that

different relationships between parameters and SCFs applied to different ranges of the data.

This observation was clear for the alpha parameter, which depends on the chord length, when

considering joints with shorter chord lengths. Efthymiou indicates this change in relationship by

providing a set of short chord correction factors for application to the SCFs determined by the

main equations however this effect is considered to come into effect for a value of α of 12 and

not 15 as observed in the data produced for the parameter study. Other validity ranges

identified from the entire dataset were dependent on the brace inclination, θ, and the out-of-

plane angle, φ. These different validity ranges were as a result of the change in chordside


240

stresses for a change in φ as discussed previously and the change of weld profile for brace

inclinations of 40º and less.

Factoring one set of equations for application to different validity ranges therefore could be

considered as an invalid approach particularly if relationship between the SCFs and parameters

change. This was clearly observed when applying the new equations derived for an out-of-

plane angle of 60º for different out-of-plane angles and more acute brace inclinations as the

range of SCFs became greater with some results distributed reasonably around the mean but

more extreme values including negative values of SCF. The new equations functioned well for

the specific dataset, performing better than the two sets of modified Efthymiou equations

therefore reinforcing the idea that equations for a specific validity range cannot be implemented

with factors for other ranges.

A set of carry-over factors was recorded for the data obtained in the parameter study by taking

the ratio of stress extrapolated back to the weld toe for the loaded brace and the extrapolated

stress in brace under consideration. Tensile and compressive carry-over factors were

determined as mentioned previously, the carry-over stresses can either have a weakening or

stiffening effect on the overall behaviour of the joint. Graphs given in the data report show the

relationships between COF and each individual parameter indicating that a blanket value cannot

be used to model this effect. The joint selected for design fell within the data range analysed

therefore the graphs could be used to estimate the level of carry-over to the unloaded brace.

For joints outside the data range examined, further work would need to be completed to either

develop further graphs or a set of COF equations for application.

Application of the equations to a design situation resulted in a variation between the hot spot

stress distribution arising from all of the equations, including Efthymiou, and that determined

using ANSYS and extrapolation of stresses. The best results were obtained for Brace A of the

joint, which was subjected largely to OPB with other loads in the brace appearing to be

negligible in comparison. With one load dominating and reasonable plots of the hot spot stress

distribution predicted by all of the equations, stresses due to other loads are minimal therefore,

when superimposing these stresses, their influence is negligible. For all other braces, two or

more of the loads were of larger magnitudes compared to Brace A and the prediction of hot spot

stress distribution around the brace-chord intersection was poor. It could be assumed that, with

the good predictions of stress distribution in Brace A, the incorrect superposition of stresses

may attribute to the variation in stress patterns.

When considering the influence of COFs on the prediction of hot spot stresses, slight reductions

or increases in stress can be seen at either the saddle or crown locations. Comparing these

locations against the actual extrapolated stress output from ANSYS indicates that the level of

carry-over may be underpredicted for some locations. As the COFs were estimated from the


241

graphs arising from the parameter study, there could be a possibility that values were

underreported hence the lesser effect on the hot spot stress. Further work covering a wider

range of data with a regression analysis to develop equations for carry-over factors was

recommended to improve this approach.

9.3.3 Conclusions

To summarise this section, it was concluded that the effects of multiplanar braces were

significant enough to have an influence on the behaviour of the joint. Carry-over effects of

multiplanar braces were observed as the result of an investigation into the behaviour of

multiplanar tubular joints and were considered to be significant to bear influence on the joint’s

overall hot spot stress pattern. Completion of a parameter study and comparison of the data

arising from the study indicated that the Efthymiou equations excluded carry-over effects from

the analysis which may affect the overall hot spot stress distribution around the brace-chord

intersection.

As a result of the regression analysis, three sets of equations were derived for two validity

ranges. The SCFs arising from these equations were factored to apply to different validity

ranges with mixed results. Predictions from the new equations were particularly poor with

negative values of SCF achieved which therefore indicated that new equations should be

derived for each validity range and existing equations cannot be factored. This conclusion

could explain the variation in performance for the Efthymiou equations as the equations were

valid for a larger range of data.

COFs were established in graphical form using the ratio of stresses in the loaded brace and the

stress in the unloaded braces. These COFs appeared to vary with parameter therefore a single

value for carry-over could not be used. For braceside stresses, there was little variation in

SCFs and COFs when comparing the differences between out-of-plane angles 60º and 90º.

Variations in SCFs and COFs were observed for chordside stresses, however, with reductions

in stress for φ = 60º. This could be attributed to the proximity of the braces in the other plane

providing a stiffening effect.

Looking at the design of multiplanar joint with loading taken from a fatigue wave flowing through

a jacket structure, the prediction of hot spot stress using all the equations were largely

inaccurate. Good predictions of hot spot stress were observed in Brace A, which was subjected

to a greater OPB load such that the IPB and axial loads could be considered to be negligible.

Because of this observation it was hypothesised that the variation in the form of the stress plots

could be attributed to inaccuracies in the superposition of hot spot stresses.


242

9.3.4 Future Work

The following areas of research were recommended for future work:

• Expansion of the data from the parameter study to include the following variations:

o Changes to the chord diameter and brace thickness

o Modifications to the FE models so different brace inclinations for each of the

braces can be modelled

o Changes to the chord-end fixity to include pinned-pinned and simply supported

boundary conditions

o Different loading patterns on the braces, i.e. balanced and unbalanced load

cases, to check whether this improves the prediction of hot spot stresses

• Further regression analyses using the existing data set in whole without dividing into

different validity ranges – would be interesting to see whether data would be skewed

and predictions less reliable

• Development of COF equations from the existing data – could potentially be improved

with expanded data sets

• Development of SCF equations for the different validity ranges given in Chapter 7

• Exploration into the superposition of individual load cases to determine the overall hot

spot stress distribution

o Further work to confirm whether this a valid approach or whether balanced and

unbalanced load cases as given in the Efthymiou equations is a better

approximation

o FE models with different loading patterns to compare against those with

individual loads and superimposed

• Hot spot stress distribution equations instead of equations at the defined locations 1-8

• Influence of chord loads on the overall behaviour of the joint – if this has a significant

effect, thought would be required on how to include this in the design of tubular joints

• Further joint configurations to be examined to check the design procedure using the

new sets of equations for multiplanar joints

243

Appendix A – Flow chart for

preliminary design of offshore wind

turbine support structures

Appendix A – Flow chart for preliminary design of offshore wind turbine support structures

244

START

Estimate suitable dimensions for sections of support structure

Check natural frequency of

structure – is it within

manufacturer’s spec?

Select capacity of turbine for use

No

Yes

Build model of structure in RISA including soil properties

Determine extreme wind and wave loads on the structure

Determine p-y and t-z curves for soil profile

Build LPILE model

SLS Embedment Length Check Check top deflection of pile with embedment length in LPILE. Pile head deflection should not vary greatly with increase in embedment

length.

Is the deflection at the pile head suitable for the

embedment length?

Yes

No

SLS Embedment Length Check Increase or decrease the embedment length

accordingly

ULS Design Checks Select locations at which checks are to be

carried out

(Recommendations – Check at mudline, maximum bending moment)

ULS Design Checks Calculate the compressive, shear and bending stresses on the pile and the

hydrostatic pressure

ULS Design Checks Check for shear capacity

Compliant? ULS Design Checks

Alter section sizes accordingly

Yes

No

ULS Design Checks Check the section for hoop buckling

Compliant?

No

Yes

ULS Design Checks Check for combined axial and compressive

strength

ULS Design Checks Check for inelastic local buckling

ULS Design Checks Check with hoop stress

Is ?

ULS Design Checks Check combined axial compression, bending

and hydrostatic pressure:

FLS Design Checks Determine environmental loads

FLS Design Checks Calculate nominal stress at welds, tubular

joints and changes of thickness

FLS Design Checks Calculate SCFs

FLS Design Checks Factor the nominal stress by product of SCFs

– hot spot stress

FLS Design Checks Calculate damage

Is Dfat ≤ 1?

FLS Design Checks Alter section and weld sizes accordingly or

choose different S-N curve class where appropriate

Compliant?

Compliant?

Compliant?

Compliant?

STOP

No

No

No

Yes

Yes

Yes

Yes

No

Yes

No

Yes

245

References

1. Lloyd's Register of Shipping, Stress Concentration Factors for Simple Tubular Joints:

Assessment of Existing and Development of New Parametric Formulae, in Offshore

Technology Report. 1997, Health and Safety Executive: London.

2. Renewable UK. 10 facts about UK offshore wind. [Online] 2011 [cited 2012

12.02.2012]; Available from: http://www.bwea.com/offshore/index.html.

3. Anon. South Baltic Offshore Wind Energy Regions - Germany. [Online] 2012

12.02.2012 [cited; Available from: http://www.southbaltic-offshore.eu/regions-

germany.html.

4. 4C Offshore. Global Offshore Wind Farms Database. 2010 Online [cited 2010

08.07.2010]; Available from: http://www.4coffshore.com/offshorewind/.

5. Rasmussen, J.L., T. Feld, and P.H. Soerensen. Structural and economic optimisation of

offshore wind turbine support structure and foundation. [Online] [cited 2009

14.08.2009]; Available from: http://www.ramboll-wind.com/PDF/OMAE99.pdf.

6. Carbon Trust. Offshore Wind Accelerator. [Online] 2012 [cited 2012 19.02.2012];

Available from: http://www.carbontrust.co.uk/emerging-technologies/current-focus-

areas/offshore-wind/pages/offshore-wind.aspx.

7. Carbon Trust. Offshore Wind Accelerator - Overview. 2012 [cited 2012 03.06.2012];

Available from: http://www.carbontrust.com/our-clients/o/offshore-wind-accelerator.

8. Department of Energy & Climate Change, UK Renewable Energy Roadmap. 2011.

9. Wind Energy The Facts - Development and investment costs of offshore wind power.

[Online] 2012 [cited 2012 03.06.2012]; Available from: http://www.wind-energy-the-

facts.org/de/part-3-economics-of-wind-power/chapter-2-offshore-developments/.

10. Rajgor, G. Offshore Wind: Solid foundations for the future. [Online] 2012 [cited 2012

03.06.2012]; Available from: http://social.windenergyupdate.com/offshore-wind/offshore-

wind-solid-foundations-future.

11. International Standards Organisation, ISO 19902:2007 Petroleum and natural gas

industries - Fixed steel offshore structures. 2007.

12. Det Norske Veritas, Offshore Standard DNV-OS-J101 - Design of Offshore Wind

Turbine Structures. 2010, Høvik, Norway: Det Noske Veritas.

13. Lynch, D., Concrete plans for wind, in New Civil Engineer. 2010, EMAP: London.

14. Lloyd's Register. Norway: Consultancy for the world’s first full-scale floating wind

turbine, Hywind Demo. [Online] 2012 [cited 2012 19.02.2012]; Available from:

http://www.lr.org/sectors/power/News/206761-norway-consultancy-for-the-worlds-first-

fullscale-floating-wind-turbine-hywind-demo.aspx.

References

246

15. Zaaijer, M.B., Comparison of monopile, tripod, suction bucket and gravity base design

for a 6MW turbine, in Offshore Windenergy in Mediterranean and Other European Seas

(OWEMES conference). 2003: Naples, Italy.

16. The Crown Estate. Round 3 Developers. [Online] 2009 [cited 2010 08.07.2010];

Available from:

http://www.thecrownestate.co.uk/our_portfolio/marine/offshore_wind_energy/round3/r3-

developers.htm.

17. International Electrotechnical Commission, IEC 61400-3 Ed.1: Wind turbines - Part 3:

Design requirements for offshore wind turbines. 2007, IEC.

18. American Petroleum Institute, API RP 2A - Recommended Practice for Planning,

Designing and Constructing Fixed Offshore Platforms - Load and Resistance Factor

Design. 1997.

19. Det Norske Veritas, Recommended Practice DNV-RP-C203 - Fatigue Design of

Offshore Steel Structures. 2010, Høvik, Norway: DNV.

20. Twidell, J. and G. Gaetano, Offshore Wind Power. 2009: Multi-Science Publishing Co.

Ltd.

21. Barltrop, N.D.P. and A.J. Adams, Dynamics of Fixed Marine Structures. 1991: The

Marine Technology Directorate Ltd.

22. Efthymiou, M., Development of SCF Formulae and Generalised Influence Functions for

use in Fatigue Analysis, in Recent Developments in Tubular Joint Technology: OTJ'88.

1988: London, UK.

23. Efthymiou, M. and S. Durkin. Stress Concentrations in T/Y and Gap/Overlap K Joints. in

4th International Conference on Behaviour of Offshore Structures. 1985. Delft, The

Netherlands: Elsevier.

24. Jacquemin, J., et al., Large wind farm turbulence calculations using IEC 61400-1

Edition 3: Reaching consensus through dialogue and action, in European Wind Energy

Conference 2010. 2010: Warsaw, Poland.

25. Luck, M. and M. Benoit, Wave Loading on Monopile Foundation for Offshore Wind

Turbines in Shallow-Water Areas, in Coastal Engineering 2004. 2004, World Scientific

Publishing Co. Pte. Ltd.: Lisbon, Portugal. p. 4595.

26. Novak, P., et al., Hydraulic Structures. 3rd ed. 2001, London and New York: Spon

Press. 666.

27. Chadwick, A., J. Morfett, and M. Borthwick, Hydraulics in Civil and Environmental

Engineering. 4th ed. 2004, London and New York: Spon Press. 644.

28. Chappelear, J.E., Direct numerical calculation of wave properties. Journal of

Geophysics, 1961. 66: p. 501-508.

29. Dean, R.G., Stream function representation of nonlinear ocean waves. Journal of

Geophysics, 1965. 70: p. 4561-4572.

30. Rienecker, M.M. and J.D. Fenton, A Fourier approximation method for steady water

waves. Journal of Fluid Mechanics, 1981. 104: p. 119-197.

References

247

31. Dean, R.G., Stream Function Representation of Nonlinear Ocean Waves. Journal of

Geophysical Research, 1965. 70(18): p. 4561-4572.

32. Buss, G.Y. and P.K. Stansby, SAWW - a computer program to compute the properties

of steady water waves. 1982, University of Manchester Manchester.

33. Sarpkaya, T., Force on a circular cylinder in viscous oscillatory flow at low Keulegan-

Carpenter numbers. Journal of Fluid Mechanics, 1986. 165: p. 61-71.

34. Miche, R., Mouvement ondulatoires de la mer en profondeur constante ou decroissante.

1944: Annales des Ponts et Chaussees.

35. Swift, R.H., Prediction of Breaking Wave Forces on Vertical Cylinders. Coastal

Engineering, 1989. 13: p. 97-116.

36. Wienke, J. and H. Oumeraci, Breaking wave impact force on a vertical and inclined

slender pile - theoretical and large-scale model investigations. Coastal Engineering,

2004. 52: p. 435-462.

37. Wagner, H., Über Stoß- und Gleitvorgänge an der Oberfläche von Flüssigkeiten.

Zeitschriften für angewandte Mathematik und Mechanik, 1932. 12(4): p. 193-215.

38. Apelt, C.J. and J. Piorewicz, Laboratory Studies of Breaking Wave Forces on Vertical

Cylinders in Shallow Water. Coastal Engineering, 1987. 11: p. 263-282.

39. U.S. Army Coastal Engineering~Research Center, Shore Protection Manual. 1975,

Washington DC, USA.

40. Beale, L.A. and A.A. Toprac, Analysis of in-plane T, Y and K welded tubular

connections 1967, Welding Research Council: New York.

41. Visser, W., On the Structural Design of Tubular Joints, in Sixth Annual Offshore

Technology Conference. 1974: Houston, Texas. p. 881-894.

42. Kuang, J.G., A.B. Potvin, and R.D. Leick, Stress Concentration in Tubular Joints, in

Seventh Annual Offshore Technology Conference. 1975: Houston, Texas. p. 593-612.

43. Reber, R.J., Ultimate Strength Design of Tubular Joints, in Fourth Annual Offshore

Technology Conference. 1972: Houston, Texas. p. 447-459.

44. Wordsworth, A.C. and G.P. Smedley. Stress Concentrations at Unstiffened Tubular

Joints. in European Offshore Steels Research Seminar. 1978. Cambridge, UK.

45. Wordsworth, A.C. Stress Concentration Factors at K and KT Tubular Joints. in Fatigue

in Offshore Structural Steels: Implications of the Department of Energy's Research

Programme. 1981. London, UK: Thomas Telford Ltd.

46. Lalani, M., I.E. Tebett, and B.S. Choo. Improved Fatigue Life Estimation of Tubular

Joints. in 18th Annual Offshore Technology Conference. 1986. Houston, Texas.

47. Gibstein, M.B., Parametric stress analysis of T joints, in European Offshore Steel

Research Seminar. 1978.

48. Hellier, A.K., M.P. Connolly, and W.D. Dover, Stress concentration factors for tubular Y-

and T-joints. International Journal of Fatigue, 1990. 12(1): p. 13-23.

References

248

49. Smedley, P. and P. Fisher. A Review of Stress Concentration Factors for Tubular

Complex Joints. in Fourth International Symposium on Integrity of Offshore Structures

1990. University of Glasgow, Scotland: Taylor and Francis.

50. Hellier, A.K., et al., Prediction of the stress distribution in tubular Y- and T-joints.

International Journal of Fatigue, 1990. 12(1): p. 25-33.

51. Chang, E. and W.D. Dover, Prediction of stress distributions along the intersection of

tubular Y and T-joints. International Journal of Fatigue, 1999. 21(4): p. 361-381.

52. Chang, E. and W.D. Dover, Parametric equations to predict stress distributions along

the intersection of tubular X and DT-joints. International Journal of Fatigue, 1999. 21(6):

p. 619-635.

53. Karamanos, S.A., A. Romeijn, and J. Wardenier, Stress concentrations in tubular gap

K-joints: mechanics and fatigue design. Engineering Structures, 2000. 22(1): p. 4-14.

54. van Wingerde, A.M., J.A. Packer, and J. Wardenier, Simplified SCF formulae and

graphs for CHS and RHS K- and KK-connections. Journal of Constructional Steel

Research, 2001. 57(3): p. 221-252.

55. Shao, Y.B., Z.F. Du, and S.T. Lie, Prediction of hot spot stress distribution for tubular K-

joints under basic loadings. Journal of Constructional Steel Research, 2009. 65(10-11):

p. 2011-2026.

56. Lotfollahi-Yaghin, M.A. and H. Ahmadi, Effect of geometrical parameters on SCF

distribution along the weld toe of tubular KT-joints under balanced axial loads.

International Journal of Fatigue, 2010. 32(4): p. 703-719.

57. Romeijn, A., The Fatigue Behaviour of Multiplanar Tubular Joints. Heron, 1994. 39(3):

p. 1-82.

58. Karamanos, S.A., A. Romeijin, and J. Wardenier, CIDECT Report 7R-17/98 - Stress

concentrations and joint flexibility effects in multiplanar welded tubular connections for

fatigue design. 1998, Delft University of Technology: Delft, The Netherlands.

59. Smedley, P.A. Advanced SCF formulae for simple and multi-planar tubular joints. in

Tubular Structures X. 2003. Madrid, Spain: Swets and Zeitlinger.

60. Woghiren, C.O. and F.P. Brennan, Weld toe stress concentrations in multi-planar

stiffened tubular KK joints. International Journal of Fatigue, 2009. 31: p. 164-172.

61. Zhao, X.-L., et al., Design Guide for Circular and Rectangular Hollow Section Welded

Joints under Fatigue Loading, Comité International pour le Développment et l'Etude de

la Construction Tubulaire (CIDECT), Editor. 2001.

62. Gho, W.-M. and F. Gao, Parametric equations for stress concentration factors in

completely overlapped tubular K(N)-joints. Journal of Constructional Steel Research,

2004. 60(12): p. 1761-1782.

63. Choo, Y.S. and X.K. Qian, Neural Network-Based Evaluation of SCF Distribution at the

Intersection of Tubular X-Joints. Mechanics of Advanced Materials and Structures,

2007. 14(7): p. 511-522.

References

249

64. Smedley, P. and P. Fisher, Stress Concentration Factors for Ring-Stiffened Tubular

Joints. 1988, Lloyd's Register of Shipping.

65. HSE, Offshore Installations: Guidance on Design, Construction and Certification. 1995:

Health and Safety Executive (HSE).

66. Radenkovic, D. Stress analysis in tubular joints. in Steel in Marine Structures. 1981.

Paris.

67. Haagensen, P.J. and K.A. Macdonald, Fatigue design of welded aluminium rectangular

hollow section joints, in Tubular Structures VIII, Y.S. Choo and G.J. van der Vegte,

Editors. 1998, A.A. Balkema: Rotterdam, The Netherlands.

68. Efthymiou, M., Finite element analysis for Task 4A of Lloyd’s project - Stress

concentration factors in tubular complex joints, in Shell Report RKER.84.151. 1984.

69. Germanischer Lloyd, GL IV-2 Guideline for the Certification of Offshore Wind Turbines.

2005, Hamburg, Germany: Germanischer Lloyd.

breaking wave loads and stress analysis of jacket

Documents