SEISMIC ANALYSIS OF STEEL WIND TURBINE OWERS › bitstream › 1807 › ... · SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - iii - ACKNOWLEDGEMENTS I would

SEISMIC ANALYSIS OF STEEL WIND TURBINE TOWERS

IN THE CANADIAN ENVIRONMENT

by

Elena Nuta

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Graduate Department of Civil Engineering

University of Toronto

© Copyright by Elena Nuta (2010)

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - ii -

Seismic Analysis of Steel Wind Turbine Towers in the Canadian Environment

Master of Applied Science (2010)

Elena Nuta

Department of Civil Engineering

University of Toronto

ABSTRACT

The seismic response of steel monopole wind turbine towers is investigated and their risk is

assessed in the Canadian seismic environment. This topic is of concern as wind turbines are

increasingly being installed in seismic areas and design codes do not clearly address this aspect of

design. An implicit finite element model of a 1.65MW tower was developed and validated.

Incremental dynamic analysis was carried out to evaluate its behaviour under seismic excitation, to

define several damage states, and to develop a framework for determining its probability of damage.

This framework was implemented in two Canadian locations, where the risk was found to be low for

the seismic hazard level prescribed for buildings. However, the design of wind turbine towers is

subject to change, as is the design spectrum. Thus, a methodology is outlined to thoroughly

investigate the probability of reaching predetermined damage states under seismic loading for future

considerations.

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - iii -

ACKNOWLEDGEMENTS

I would firstly like to express my gratitude to Professor J. A. Packer and to Professor C.

Christopoulos for their guidance and the countless meetings that ensured my project was always on

track. I see now, in retrospect, how paramount this guidance was, and I thank you both.

Special thanks go out to Andrew Voth and Dr. Gilberto Martinez-Saucedo, for many hours of

help working out finite element modelling glitches, and to Lydell Wiebe and Nabil Mansour, for

their willingness to always discuss thesis concerns with me. I would also like to thank my many

officemates, research group members, and colleagues for enriching my graduate experience and

providing conversation and laughter.

Financial support has been provided by Ontario Graduate Scholarships (OGS), the National

Sciences and Engineering Research Council of Canada (NSERC), and the Steel Structures Education

Foundation (SSEF). I also gratefully acknowledge the Ontario Centres of Excellence (OCE), and

the Fraunhofer Centre Windenergie und Meerestechnik, Bremerhaven, Germany where I spent the

summer of 2008 as an intern.

Last but not least, I thank the people most important in my life. To my awesome parents,

Floarea and Mihai Nuta, thank you for teaching me to always aim high and for supporting me

always. To my beautiful sister and brother-in-law, Gabriela Nuta and Andrew Orel-Golla, thank you

for making sure I had enough distractions to stay sane and for accommodating my erratic schedule.

To my loving boyfriend, Michael Colalillo, thank you for your motivation, understanding,

encouragement, time, and patience during this time; and of course, thank you for the pasta dinners.

To all my friends, thank you for the unwavering mental support and for never doubting me.

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - iv -

TABLE OF CONTENTS

ABSTRACT .............................................................................................................................. ii ACKNOWLEDGEMENTS .................................................................................................... iii TABLE OF CONTENTS ........................................................................................................iv LIST OF TABLES................................................................................................................... ix LIST OF FIGURES................................................................................................................. xi LIST OF SYMBOLS AND ABBREVIATIONS.....................................................................xv

CHAPTER 1: INTRODUCTION................................................................................................... 1 1.1 Overview of Thesis................................................................................................................................ 1 1.2 Wind Turbine Type, Components, and Terminology .........................................................................2

CHAPTER 2: LITERATURE REVIEW..........................................................................................4 2.1 International Standards ........................................................................................................................4

2.1.1 International Electrotechnical Commission (IEC) .................................................................4 2.1.2 Germanischer Lloyd (GL) ........................................................................................................5 2.1.3 Det Norske Veritas (DNV) ......................................................................................................5 2.1.4 Other European Standards.......................................................................................................7

2.2 Canadian Standards ..............................................................................................................................7 2.2.1 CAN/CSA-C61400-1:08, Wind Turbines – Part 1: Design Requirements..............................7 2.2.2 CAN/CSA S37-01, Antennas, Towers, and Antenna-Supporting Structures..........................8 2.2.3 CAN/CSA S473-04, Steel (Fixed Offshore) Structures............................................................8 2.2.4 CAN/CSA S16-09, Design of Steel Structures .........................................................................8

2.3 Book Publications.................................................................................................................................8 2.4 Current Research on Wind Turbine Towers ........................................................................................9

2.4.1 Comparison of Seismic Analysis Methods: Frequency-Domain vs. Time-Domain..............9 2.4.2 Shell Buckling......................................................................................................................... 10 2.4.3 Dynamic Soil-Structure Interaction Effects............................................................................11

2.5 Summary ............................................................................................................................................. 12

CHAPTER 3: FINITE ELEMENT MODEL DEVELOPMENT AND VALIDATION ......................... 13 3.1 Geometry of Wind Turbine Towers.................................................................................................... 13 3.2 Finite Element Analysis Program ...................................................................................................... 13 3.3 Material Properties.............................................................................................................................. 14 3.4 Choice of Elements............................................................................................................................. 16

TABLE OF CONTENTS

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - v -

3.4.1 Shell Elements ........................................................................................................................ 16 3.4.1.1 Classical Plate Theory............................................................................................ 16

3.4.2 Solid Elements........................................................................................................................ 17 3.4.2.1 Elastic Beam Theory ............................................................................................. 18

3.4.3 Solid-Shell Interaction............................................................................................................ 18 3.5 Connection Modelling ........................................................................................................................ 18 3.6 Tubular Members under Bending...................................................................................................... 19

3.6.1 FE Model for Pure Flexure .................................................................................................... 21 3.6.1.1 Mesh Sensitivity ..................................................................................................... 22 3.6.1.2 Refinement of Mesh............................................................................................... 23 3.6.1.3 Results and Analysis of Tubular Members under Pure Flexure........................... 24

3.6.2 FE Model of a Cantilever Tower under Bending .................................................................. 27 3.6.2.1 Results and Analysis of Cantilever Tower under Bending ................................... 28 3.6.2.2 Stiffening Effect of a Flange .................................................................................. 29 3.6.2.3 Effect of Local Imperfections on Flexural Behaviour........................................... 30

3.7 Tubular Members under Axial Compression..................................................................................... 31 3.7.1 FE Analyses for Validation of Axial Buckling Behaviour ..................................................... 32

3.7.1.1 FE Models for Validation of Axial Buckling Behaviour ....................................... 32 3.7.1.2 Eigenvalue Buckling Analysis ............................................................................... 32 3.7.1.3 Nonlinear Buckling Analysis – Geometric and Material Nonlinearities ............. 33 3.7.1.4 Geometric Imperfections for Global Buckling...................................................... 33 3.7.1.5 Geometric Imperfections for Local Buckling ....................................................... 33 3.7.1.6 Results and Analysis of Cantilever Tower under Axial Compression .................. 34

3.7.2 Summary of Modelling Decisions.......................................................................................... 36 3.8 Time-History Analysis under Seismic Excitation.............................................................................. 36

3.8.1 Damping in ANSYS ............................................................................................................... 37 3.8.1.1 Comparison of Effect of Damping ........................................................................ 38 3.8.1.2 Aerodynamic Damping.......................................................................................... 41

3.8.2 Incremental Nonlinear Analysis ............................................................................................ 41 3.8.2.1 Failure Mode.......................................................................................................... 42

3.9 Summary ............................................................................................................................................. 43

CHAPTER 4: PRELIMINARY ANALYSIS OF VESTAS WIND TURBINE TOWER...........................45 4.1 Structure Characteristics..................................................................................................................... 45

4.1.1 Dimensions And Details ........................................................................................................ 45 4.1.1.1 Discontinuities ....................................................................................................... 45

4.1.2 Mass........................................................................................................................................ 48 4.1.3 Mode Shapes .......................................................................................................................... 49 4.1.4 Damping................................................................................................................................. 49

TABLE OF CONTENTS

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - vi -

4.2 Finite Element Model of Vestas Wind Turbine Tower ..................................................................... 49 4.3 Pushover Analysis ............................................................................................................................... 52

4.3.1 Background ............................................................................................................................ 52 4.3.2 Pushover Analysis of Wind Turbine Tower........................................................................... 53

4.3.2.1 Imposed Imperfections.......................................................................................... 54 4.3.3 Results of Pushover Analysis ................................................................................................. 55

4.3.3.1 Interpretation of Pushover Analysis Results ......................................................... 57 4.4 Summary ............................................................................................................................................. 57

CHAPTER 5: NONLINEAR TIME-HISTORY ANALYSIS OF THE VESTAS WIND TURBINE TOWER

........................................................................................................................................58 5.1 Earthquake Suite................................................................................................................................. 58

5.1.1 Earthquake Input in Time-History Analyses ........................................................................ 62 5.1.2 Scaling of Earthquake Records.............................................................................................. 62

5.2 Results of LA01 & LA02 (Imperial Valley, 1940, Elcentro) ................................................................ 63 5.2.1 Intensity and Damage Measures ........................................................................................... 63

5.2.1.1 Peak Displacement ................................................................................................ 64 5.2.1.2 Peak Rotation......................................................................................................... 65 5.2.1.3 Peak Stress ............................................................................................................. 66 5.2.1.4 Residual Deformation............................................................................................ 67

5.2.2 Displaced Shape ..................................................................................................................... 67 5.2.3 Time-History Displacement Response ................................................................................. 69 5.2.4 Orbit Plots .............................................................................................................................. 70 5.2.5 Definition of Damage States for Wind Turbine Towers ....................................................... 72

5.2.5.1 0.2% Residual Out-of-Straightness........................................................................ 72 5.2.5.2 First Yield............................................................................................................... 72 5.2.5.3 1.0% Residual Out-of-Straightness........................................................................ 72 5.2.5.4 First Buckle / Loss of Tower................................................................................. 72

5.3 Summary of Results for LA Earthquake Suite ................................................................................... 73 5.3.1 Incremental Dynamic Analysis Curves.................................................................................. 74

5.3.1.1 Assessment of Damage Measures ......................................................................... 74 5.3.1.2 Average Damage Measures ................................................................................... 75

5.3.2 Location of Buckle for 4th Damage State............................................................................... 75 5.3.3 Definition of Fragility Curves ................................................................................................ 76 5.3.4 Effect of Vertical Earthquake Component ............................................................................ 79 5.3.5 Effect of Damping.................................................................................................................. 80 5.3.6 Validation of Connection Modelling...................................................................................... 81

5.4 Summary ............................................................................................................................................. 83

TABLE OF CONTENTS

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - vii -

CHAPTER 6: INCREMENTAL ANALYSIS FOR TWO CANADIAN SITES ......................................85 6.1 Eastern Canada Site............................................................................................................................ 85

6.1.1 Simulated Time-History Records for the Eastern Canada Site ............................................ 86 6.1.2 Earthquake Suite for the Eastern Canada Site ...................................................................... 86

6.2 Western Canada Site ........................................................................................................................... 89 6.2.1 Simulated Time-History Records for the Western Canada Site............................................ 89 6.2.2 Earthquake Suite for the Western Canada Site ..................................................................... 90

6.3 Methodology for Scaling Records for IDA......................................................................................... 93 6.3.1 Efficiency of Method.............................................................................................................. 94

6.4 Results for Eastern Canada Site ......................................................................................................... 96 6.5 Results of Time-History Analysis for Western Canada Site .............................................................. 97

6.5.1 Incremental Dynamic Analysis Curves.................................................................................. 97 6.5.1.1 Average Damage Measures ................................................................................... 98

6.5.2 Fragility Curves ...................................................................................................................... 99 6.6 Summary ........................................................................................................................................... 100

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS........................................................101

REFERENCES..................................................................................................................... 103

APPENDIX A: RESULTS OF INCREMENTAL TIME-HISTORY ANALYSIS FOR LA

EARTHQUAKE SUITE.................................................................................. 107 A.1 LA03 & LA04 (Imperial Valley, 1979, Array #05)............................................................................ 108 A.2 LA05 & LA06 (Imperial Valley, 1979, Array #06)............................................................................. 111 A.3 LA07 & LA08 (Landers, 1992, Barstow)...........................................................................................114 A.4 LA09 & LA10 (Landers, 1992, Yermo)..............................................................................................117 A.5 LA11 & LA12 (Loma Prieta, 1989, Gilroy) ....................................................................................... 120 A.6 LA13 & LA14 (Northridge, 1994, Newhill)...................................................................................... 123 A.7 LA15 & LA16 (Northridge, 1994, Rinaldi RS) ................................................................................. 126 A.8 LA17 & LA18 (Northridge, 1994, Sylmar)........................................................................................ 129 A.9 LA19 & LA20 (North Palm Springs, 1986) ...................................................................................... 132 A.10 IDA Curves for Investigated Intensity Measures ........................................................................... 135

APPENDIX B: SEISMIC HAZARD FOR TWO CANADIAN SITES............................................ 138 APPENDIX C: RESULTS OF THE WESTERN CANADA EARTHQUAKE SUITE........................141

C.1 WCan01 (Magnitude 6, 8 – 13 km) .................................................................................................. 142 C.2 WCan02 (Magnitude 7, 10 – 26 km) ................................................................................................ 144 C.3 WCan03 (Magnitude 7, 10 – 26 km) ................................................................................................ 146

TABLE OF CONTENTS

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - viii -

C.4 WCan04 (Magnitude 7, 10 – 26 km) ................................................................................................ 148 C.5 WCan05 (Magnitude 7, 10 – 26 km) ................................................................................................ 150 C.6 WCan06 (Magnitude 7, 30 – 100 km) .............................................................................................. 152 C.7 WCan07 (Cascadia Record, Magnitude 9, 112 – 201 km)................................................................ 154 C.8 Fragility Curves for Additional Intensity Measures........................................................................ 156

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - ix -

LIST OF TABLES

Table 3.1: Cross-sectional slenderness limits (D/t) of circular hollow sections in bending 20 Table 3.2: Slenderness limits (D/t) of circular hollow sections in axial compression for non-slender

behaviour, using E = 200000 MPa 31 Table 3.3: Summary of results of time-history analyses for the UCSD tower comparing different damping

values 38 Table 3.4: Summary of results of incremental time-history analyses for the UCSD tower 42 Table 4.1: Mass of Vestas wind turbine tower 48 Table 5.1: Properties of LA earthquake suite records 59 Table 5.2: Summary of displacement results of time-history analyses subjected to LA01 & LA02 (Imperial

Valley, 1940, Elcentro) 63 Table 5.3: Minimum, average, and maximum values of damage measures at each damage state 75 Table 5.4: Location of buckle for the LA earthquake suite 76 Table 5.5: Intensity measures (magnification factors) of each earthquake analysis and statistics for all the

damage states for the LA earthquake suite 77 Table 5.6: Properties of earthquake records for analyses that included a vertical component 79 Table 5.7: Variation of peak displacement compared to 1% damping for LA11 and LA12 (Loma Prieta,

1989, Gilroy) 80 Table 5.8: Properties of bolts used in intermediate flanges of Vestas wind turbine tower 82 Table 5.9: Characteristics of wind turbine tower flanges 83 Table 6.1: Spectral hazard values (Sa(T)) and peak ground acceleration (PGA) for the Eastern Canada site,

2% probability of exceedance in 50 years 85 Table 6.2: Scale factors and PGA of earthquake records chosen for the Eastern Canada site 87 Table 6.3: Spectral hazard values (Sa(T)) and peak ground acceleration (PGA) for the Western Canada site,

2% probability of exceedance in 50 years 89 Table 6.4: Scale factors and PGA of earthquake records chosen for the Western Canada site 91 Table 6.5: Summary of results of time-history analyses for the Eastern Canada suite 96 Table 6.6: Summary of results of time-history analyses for the Eastern Canada suite with magnification

factor of 10 96 Table 6.7: Minimum, average, and maximum values of damage measures at each damage state for the

Western Canada site 99 Table 6.8: Probability of exceedance of particular damage states for varying seismic event intensities 100

Table A. 1: Summary of displacement results of time-history analyses subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05) 108

Table A.2: Summary of displacement results of time-history analyses subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06) 111

Table A.3: Summary of displacement results of time-history analyses subjected to LA07 & LA08 (Landers, 1992, Barstow) 114

Table A.4: Summary of displacement results of time-history analyses subjected to LA09 & LA10 (Landers, 1992, Yermo) 117

LIST OF TABLES

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - x -

Table A.5: Summary of displacement results of time-history analyses subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy) 120

Table A.6: Summary of displacement results of time-history analyses subjected to LA13 & LA14 (Northridge, 1994, Newhill) 123

Table A.7: Summary of displacement results of time-history analyses subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS) 126

Table A.8: Summary of displacement results of time-history analyses subjected to LA17 & LA18 (Northridge, 1994, Sylmar) 129

Table A.9: Summary of displacement results of time-history analyses subjected to LA19 & LA20 (North Palm Springs, 1986) 132

Table C.1: Summary of results of time-history analyses for WCan01 142 Table C.2: Summary of results of time-history analyses for WCan02 144 Table C.3: Summary of results of time-history analyses for WCan03 146 Table C.4: Summary of results of time-history analyses for WCan04 148 Table C.5: Summary of results of time-history analyses for WCan05 150 Table C.6: Summary of results of time-history analyses for WCan06 152 Table C.7: Summary of results of time-history analyses for WCan07 154

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xi -

LIST OF FIGURES

Figure 1.1: Typical horizontal-axis wind turbine 2 Figure 3.1: Engineering and true stress-strain curve from Voth (2010) for cold-formed circular HSS 15 Figure 3.2: Stress-strain curves used in subsequent analyses 15 Figure 3.3: Geometry of shell element used to represent tower walls (ANSYS, 2007) 16 Figure 3.4: Geometry of 20-noded solid element used to represent flanges (ANSYS, 2007) 17 Figure 3.5: Geometry of wind turbine tower ring flanges 18 Figure 3.6: Bolted flange connections of wind turbine tower (Vestas, 2006) 19 Figure 3.7: Schematic and descriptions of FE models for validation of pure flexure 21 Figure 3.8: Normalised moment-curvature response of FEA of VF-el for various mesh sizes using uniform

mesh and perfect geometry/loading 22 Figure 3.9: Refined mesh configuration 23 Figure 3.10: Incorrect buckling configuration due to perfectly symmetrical model and loading 24 Figure 3.11: Normalised moment-curvature response of FE model VF-el compared with experimental results

from Elchalakani et al. (2002) 25 Figure 3.12: Local buckling failure of CHS under pure bending, D/t = 111 25 Figure 3.13: Normalised moment-curvature response of FE models VF-1 and VF-el (D/t = 111) 26 Figure 3.14: Normalised moment-curvature response of FE models VF-2 (D/t = 286) 27 Figure 3.15: Local buckle failure of very slender CHS under pure bending (D/t = 286) 27 Figure 3.16: Schematic and descriptions of FE models for validation of bending behaviour 28 Figure 3.17: Normalised moment-curvature response of FE models VB-1 (D/t = 111), VB-2 (D/t = 276),

and VBS-1 (stiffened) 29 Figure 3.18: Investigation of location of buckle 30 Figure 3.19: Effect of local imperfections on cantilever tower under bending 31 Figure 3.20: Schematic and descriptions of FE models for validation of axial compression 32 Figure 3.21: Assessment of influence of geometric imperfections for local buckling 34 Figure 3.22: Axial loading analysis FE results of VA-1 (D/t = 111) with and without local imperfections 35 Figure 3.23: Axial loading analysis FE results of VA-2 (D/t = 286) with and without local imperfections 35 Figure 3.24: Details of small wind turbine tested at UCSD 37 Figure 3.25: Acceleration at top of nacelle for the reference earthquake for various damping ratios 39 Figure 3.26: Acceleration at upper joint for the reference earthquake for various damping ratios 40 Figure 3.27: Displacement response of incremental time-history analysis of small wind turbine 42 Figure 3.28: Buckled shape of UCSD wind turbine tower – analysis at a magnification factor of 10 43 Figure 4.1: Details at base of Vestas wind turbine tower 46 Figure 4.2: Wind turbine tower dimensions and layout (Vestas, 2006) 47 Figure 4.3: D/t ratio of Vestas wind turbine tower sections along the height with CSA (2009b) cross-section

classification in bending 48 Figure 4.4: Mode shapes of Vestas tower in horizontal direction 49 Figure 4.5: Mesh of Vestas wind turbine tower 51 Figure 4.6: Direction of pushover analyses 54

LIST OF FIGURES

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xii -

Figure 4.7: Multimode load pattern for pushover analysis of Vestas wind turbine tower 54 Figure 4.8: Load-displacement curves for pushover analysis at 0° for material properties with gradual

yielding and with yield plateau 55 Figure 4.9: Buckled failure of Vestas wind turbine tower subjected to pushover analysis at 0° 56 Figure 4.10: Peak load for pushover analysis acting at various angles 56 Figure 4.11: Top displacement at peak load for pushover analysis acting at various angles 56 Figure 5.1: Elastic acceleration response spectra for earthquake suite considered 60 Figure 5.2: Elastic displacement response spectra for earthquake suite considered 60 Figure 5.3: Accelerograms of 20 scaled ground motion records of the LA earthquake suite 61 Figure 5.4: Top view of tower showing definition of angle in plan view 64 Figure 5.5: Displaced shape of wind turbine tower used to determine the peak rotation for LA01 & LA02

(Imperial Valley, 1940, Elcentro) 66 Figure 5.6: Displaced shape of wind turbine tower at various magnification factors for LA01 & LA02

(Imperial Valley, 1940, Elcentro) 68 Figure 5.7: Bucked shape of Vestas wind turbine tower analysis for LA01 & LA02 (Imperial Valley, 1940,

Elcentro) 69 Figure 5.8: Incremental time-history displacement response of Vestas wind turbine tower subjected to

LA01 & LA02 (Imperial Valley, 1940, Elcentro) at hub height 70 Figure 5.9: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA01 & LA02 (Imperial

Valley, 1940, Elcentro) 71 Figure 5.10: Incremental dynamic analysis curves for three damage measures: peak displacement, peak

rotation, and residual displacement 74 Figure 5.11: Fragility curves for LA earthquake suite for magnification factor intensity measure 78 Figure 5.12: Fragility curves for LA earthquake suite for PGV intensity measure 78 Figure 5.13: Fragility curves for LA earthquake suite for PGA intensity measure 79 Figure 5.14: Orbit in x-z plane (in mm) for varying damping values of wind turbine tower: 0.5%, 1.0% and

1.5% of critical 81 Figure 5.15: Geometry of bolted connection of tower flange 82 Figure 6.1: 2005 NBCC UHS for the Eastern Canada site for 2% in 50 years and average spectra of 4

record sets of simulated earthquakes 86 Figure 6.2: Accelerograms of 14 scaled ground motion records for the Eastern Canada site 88 Figure 6.3: Acceleration response spectra for the Eastern Canada earthquake suite for 2% in 50 years

probability of exceedance 89 Figure 6.4: 2005 NBCC UHS for the Western Canada site for 2% in 50 years and average spectra of 4

record sets of simulated earthquakes 90 Figure 6.5: Accelerograms of 14 scaled ground motion records for the Western Canada site 92 Figure 6.6: Acceleration response spectra for the Western Canada earthquake suite for 2% in 50 years

probability of exceedance 93 Figure 6.7: Flowchart of scaling procedure for the Canadian earthquake suites 95 Figure 6.8: Incremental dynamic analysis curves for Western Canada suite 97 Figure 6.9: Fragility curves for Western Canada site for the magnification factor intensity measure 99

Figure A.1: Peak displaced shape of wind turbine tower subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05) 108

LIST OF FIGURES

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xiii -

Figure A.2: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05) at hub height (80m) 109

Figure A.3: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05) 110

Figure A.4: Peak displaced shape of wind turbine tower subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06) 111

Figure A.5: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06) at hub height (80m) 112

Figure A.6: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06) 113

Figure A.7: Peak displaced shape of wind turbine tower subjected to LA07 & LA08 (Landers, 1992, Barstow) 114

Figure A.8: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA07 & LA08 (Landers, 1992, Barstow) at hub height (80m) 115

Figure A.9: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA07 & LA08 (Landers, 1992, Barstow) 116

Figure A.10: Peak displaced shape of wind turbine tower subjected to LA09 & LA10 (Landers, 1992, Yermo) 117

Figure A.11: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA09 & LA10 (Landers, 1992, Yermo) at hub height (80m) 118

Figure A.12: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA09 & LA10 (Landers, 1992, Yermo) 119

Figure A.13: Peak displaced shape of wind turbine tower subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy) 120

Figure A.14: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy) at hub height (80m) 121

Figure A.15: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy) 122

Figure A.16: Peak displaced shape of wind turbine tower subjected to LA13 & LA14 (Northridge, 1994, Newhill) 123

Figure A.17: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA13 & LA14 (Northridge, 1994, Newhill) at hub height (80m) 124

Figure A.18: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA13 & LA14 (Northridge, 1994, Newhill) 125

Figure A.19: Peak displaced shape of wind turbine tower subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS) 126

Figure A.20: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS) at hub height (80m) 127

Figure A.21: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS) 128

Figure A.22: Peak displaced shape of wind turbine tower subjected to LA17 & LA18 (Northridge, 1994, Sylmar) 129

Figure A.23: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA17 & LA18 (Northridge, 1994, Sylmar) at hub height (80m) 130

Figure A.24: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA17 & LA18 (Northridge, 1994, Sylmar) 131

LIST OF FIGURES

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xiv -

Figure A.25: Peak displaced shape of wind turbine tower subjected to LA19 & LA20 (North Palm Springs, 1986) 132

Figure A.26: Incremental time-history displacement response of Vestas wind turbine tower subjected to LA19 & LA20 (North Palm Springs, 1986) at hub height (80m) 133

Figure A.27: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA19 & LA20 (North Palm Springs, 1986) 134

Figure A.28: IDA curves for various intensity measures and peak displacement damage measure 135 Figure A.29: IDA curves for various intensity measures and residual displacement damage measure 136 Figure A.30: IDA curves for various intensity measures and peak rotation damage measure 137

Figure C.1: Peak displaced shape of wind turbine tower subjected to WCan01 142 Figure C.2: Incremental time-history displacement response of Vestas wind turbine tower subjected to

WCan01 at hub height (80m) 143 Figure C.3: Peak displaced shape of wind turbine tower subjected to WCan02 144 Figure C.4: Incremental time-history displacement response of Vestas wind turbine tower subjected to






WCan07 at hub height (80m) 155 Figure C.15: Fragility curves for the Western Canada earthquake suite for PGV intensity measure 156 Figure C.16: Fragility curves for the Western Canada earthquake suite for PGA intensity measure 156

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xv -

LIST OF SYMBOLS AND ABBREVIATIONS

AISC American Institute of Steel Construction

BSI British Standards Institution

CEN European Committee for Standardization (Comité Européen de Normalisation)

CSA Canadian Standards Association

GL Germanischer Lloyd

IEC International Electrotechnical Commission

NBCC National Building Code of Canada

CHS circular hollow section

DBE design-based earthquake

DM damage measure

DOF degree-of-freedom

DS damage state

FE finite element

FEA finite element analysis

FEM finite element method

HSS hollow structural section

IDA incremental dynamic analysis

IM intensity measure

LP load pattern

MCE maximum considered earthquake when referring to the Los Angeles area

MF magnification factor

PGA peak ground acceleration

PGV peak ground velocity


SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xvi -

SRSS square root of the sum of the squares

SSI soil-structure interation

UHS uniform hazard spectra

A cross-sectional area

Ab nominal area of bolt

]c[ damping matrix

D outside diameter of a CHS

Dm centreline diameter of a CHS

E Young’s modulus of elasticity

I moment of inertia

Fc elastic compressive buckling stress defined based on Fy and D/t

( ))t(F dynamic load vector

Fu ultimate tensile stress

Fy yield tensile stress

Fy,eff effective yield tensile stress calculated to meet Class 3 D/t limits

g acceleration due to gravity, 9.81m/s2

h height above base

H hub height

hf height of stiffening flange from base of tower

]k[ stiffness matrix

t thickness

tf thickness of stiffening flange

Ti period of mode i

Lr length of member having refined finite element size

]m[ mass matrix


SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xvii -

M moment

MFDS1 magnification factor at damage state 1

Mp plastic moment of a cross-section

Mu moment at ultimate capacity

My yield moment of a cross-section

n factor used in predicting scale factors that account for nonlinearity of response

P load

Pe Euler buckling load

Pu load at ultimate capacity

S elastic section modulus

SAtarg target spectral acceleration

SAsim spectral acceleration of simulated ground motion record

se element size

Tu ultimate bolt capacity

wf width of stiffening flange

)x( nodal displacement vector

)x( & nodal velocity vector

)x( && nodal acceleration vector

Z plastic section modulus

α coefficient used in Rayleigh damping

iα modal participation factor of mode i

β coefficient used in Rayleigh damping

∆ lateral deflection

∆max peak lateral deflection

∆max,avg,DS1 average peak lateral deflection for the first damage state


SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - xviii -

∆res residual lateral deflection

∆top lateral deflection at top of tower

ε true-strain; parameter used in slenderness limits

εnom engineering strain

εu ultimate strain at fracture

iζ modal damping ratio of mode i

θ rotation of tower as defined in Section 5.2.1.2

θmax maximum rotation of tower as defined in Section 5.2.1.2

θplan angle of tower in plan view (or top view, or x-z plane)

κ curvature

κp curvature at plastic moment: Mp/EI

µ average/mean, used in defining fragility curves

σ true-stress; standard deviation used in defining fragility curves

σnom engineering stress

σmises Von Mises stress

iϕ mode shape of mode i, normalized to mass matrix

ωi circular frequency of a mode i

SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - 1 -

CHAPTER 1: INTRODUCTION

Wind energy has gained popularity worldwide as many countries aim to increase the production

of clean energy. As Canada follows suit, Canadian design codes are largely adopting international

standards for the design of wind turbine components. However, several gaps are evident due to

Canada’s unique environment. One such gap is the assessment of seismic risk pertaining to wind

turbine towers, as the major developments of wind turbines have been in non-seismic areas. The

seismic risk is of particular importance to owners of wind turbine developments, especially wind

turbine farms, since all the towers are identical. This means that a seismic event would affect all the

towers in the same manner – if one fails, they all fail. Such a failure would result in severe financial

losses, as well as social implications if wind energy takes over more of the energy production in

Canada.

Thus, the need for research in this area has become evident. Wind turbine towers are different

from other structures because they are characterized by a very tall and slender tubular tower. This

geometry results in a structure that cannot respond in a ductile manner, thus the wind turbine

tower’s capacity when subjected to dynamic loads must be characterized.

1.1 OVERVIEW OF THESIS

This thesis begins with a review of existing literature on wind turbine towers, specifically

pertaining to seismic provisions and behaviour under seismic loads. International design codes for

wind turbines are presented, along with Canadian design codes for steel structures that may be

applicable to wind turbine towers. Some of the current research on seismic response of wind

turbine towers is also presented, noting that none of the existing research has evaluated the seismic

event that may cause failure of a typical wind turbine tower.

Chapter 3 describes the development and validation of a finite element model and methods

employed. Most of the validation analyses are carried out on a simple tubular member of constant

cross-section. Chapter 4 provides details of the typical wind turbine tower analysed in this thesis

and describes a preliminary analysis of the tower that was carried out using pushover analysis. The

tower was then subjected to incremental dynamic analyses, based on an earthquake suite for the Los

Angeles area in California, USA. These analyses were used to derive a methodology for determining

the seismic hazard of steel wind turbine towers. Damage states of the wind turbine tower were

defined and fragility curves were created for each damage state, indicating the probability that a



given intensity measure will cause exceedance of a particular damage state. Thus, a framework was

set up to assess the seismic hazard for wind turbine towers in any location.

The culmination of this project was the incremental dynamic analysis and seismic risk evaluation

at two Canadian locations. One location was in Western Canada, representing the most severe

seismic hazard in the country, and one was in Eastern Canada, representing a milder seismic hazard

but one where several wind farm developments are underway.

1.2 WIND TURBINE TYPE, COMPONENTS, AND TERMINOLOGY

Several types of wind turbines exist, but the most prevalent have a horizontal-axis rotor with

three blades and are supported by a thin-walled steel tower. This type of wind turbine is depicted in

Figure 1.1 and the main components of the wind turbine are labeled.

Figure 1.1: Typical horizontal-axis wind turbine

The rotor is made up of blades that are attached to a hub. Wind turbines are often referred to

by their “hub height”, which represents the height from the base to the centre of the rotor. The hub

height of the wind turbine tower analysed in this thesis is 80 m, which is a typical height. The

nacelle is behind the hub, and it contains the gearbox, generator, shafts, and other machinery. The

Main Wind Turbine Components:

Rotor Nacelle Tower Foundation



tower is made of a thin-walled tubular steel monopole and the foundation for onshore wind turbines

is typically an octagonal reinforced concrete slab. As previously mentioned, this thesis focuses on

the steel tower of the wind turbine.


CHAPTER 2: LITERATURE REVIEW

2.1 INTERNATIONAL STANDARDS

Several standards for the design and safety requirements of wind turbines exist. The most

significant ones are discussed in this section, and particular attention is given to any seismic design

or analysis provisions.

2.1.1 INTERNATIONAL ELECTROTECHNICAL COMMISSION (IEC)

The International Electrotechnical Commission (IEC) is the leading organization that compiles

international standards for electrical technologies. The IEC documents act as a basis for national

standardization and also as a reference for international contracts. Founded in 1906, the IEC did

not become involved in the wind turbine industry until 1988, when a technical committee, TC 88,

was formed to compile guidelines for wind turbines. This technical committee has developed the

IEC 61400 series, which is comprised of 10 guidelines that cover various topics related to wind

turbine generators. The bulk of the design process for onshore wind turbines is addressed by Part 1,

“Design Requirements.”

Furthermore, the IEC specifies project and type certification schemes for wind turbines in the

IEC WT 01 document “IEC System for Conformity Testing and Certification of Wind Turbines,

Rules and Procedures.” This document refers to all of the IEC 61400 series technical standards,

while also referring to several standards from the International Organization for Standardization

(ISO) (IEC, 2001).

IEC61400-1, Wind Turbines – Part 1: Design Requirements

This part of IEC61400 specifies minimum design requirements to assure the engineering

integrity of wind turbines (IEC, 2005). Wind turbine classes are defined based on the reference

wind speed and the turbulence intensity that the wind turbine is expected to experience. The primary

consideration is wind loading, for which several wind conditions are described. Other

environmental conditions are also specified, wherein earthquakes are considered as one of the

“extreme other environmental conditions” (IEC, 2005). The standard wind turbine classes have no

minimum earthquake requirements, but assessment of earthquake conditions is outlined in Clause

11.6. Seismic analysis may be required depending on site-specific conditions, and earthquake

assessment is not required in locations that are excluded by the local seismic codes due to weak

seismic action. In locations where seismicity may be critical, the seismic loading must be combined



with a specified operational loading that occurs frequently during the turbine’s lifetime and that is

considered to be significant enough (IEC, 2005).

IEC 61400 specifies that the seismic loading be based on the ground acceleration for a 475-year

recurrence period and that response spectrum requirements be defined by the local building codes.

The evaluation of the seismic loads may be carried out either in the frequency-domain or in the

time-domain. Furthermore, a simplified conservative approach to calculate the seismic loads is

provided in Annex C, but this approach is only recommended if the tower is the only part of the

wind turbine that will experience significant loading due to seismic action (IEC, 2005).

2.1.2 GERMANISCHER LLOYD (GL)

Germanischer Lloyd (GL) is a certification organization based in Germany. They use their own

guidelines, as discussed below, in addition to the IEC standards and the German Institute for

Standardization (DIN) standards to certify wind turbines and their components. Their services are

offered worldwide.

GL Wind 2003, IV – Part 1, Guideline for the Certification of Wind Turbine Towers

This guideline is used in the design and certification of wind turbines. It is largely similar to

IEC61400-1, but it also describes the design process for each component of the wind turbine

separately. This guideline outlines the national requirements of several countries: Germany,

Denmark, France, the Netherlands, and India (GL, 2003).

The earthquake requirements in this guideline are very similar to those of IEC 61400-1.

Earthquakes are included in the list of design load cases, with a few minimum load cases specified.

If there are no local regulations regarding earthquake analysis, designers are referred to Eurocode 8

or the earthquake chapter in the American Petroleum Institute (API) recommended practice

document RP 2A (GL, 2003). Similarly to IEC 61400-1, the analysis may be either carried out in the

frequency-domain or the time-domain. The minimum number of modes that must be considered is

three. For analysis carried out in the time-domain, a minimum number of six simulations must be

performed per load case.

2.1.3 DET NORSKE VERITAS (DNV)

Det Norske Veritas (DNV) is an independent foundation that was established in Norway, but is

now considered an international body. DNV works with the IEC and other European standards

organizations to provide project certification, type certification, and risk management for the wind



turbine industry. These certification services are based on IEC WT 01. Aside from its involvement

with the IEC, the DNV develops its own standards, which are used to provide a link between

standards for wind turbines, standards for offshore structures, and several other building codes.

Several documents have been published by the DNV. The one that is most comprehensive for

onshore wind turbines is a guideline written by the DNV and Risø National Laboratory in Denmark,

“Guidelines for Design of Wind Turbines” (DNV and Risø, 2002). The DNV also publishes

standards, recommended practice documents, and classification notes. The DNV documents that

may be helpful in wind turbine tower design include:

• DNV-OS-J101, Design of Offshore Wind Turbine Structures

• DNV-OS-J102, Design and Manufacture of Wind Turbine Blades

• DNV-OS-C101, Design of Offshore Wind Turbine Structures, General (LFRD Method)

• DNV-OS-C201, Structural Design of Offshore Units (WSD Method)

• DNV-RP-C201, Bucking Strength of Plated Structures

• DNV-RP-C202, Bucking Strength of Shells

• DNV-RP-C203, Fatigue Design of Offshore Steel Structures

DNV/Risø, Guidelines for Design of Wind Turbines

These guidelines were created through the cooperation of DNV and Risø National Laboratory

to provide a unified basis for the design of wind turbines. The book provides fairly detailed

guidance on all technical items that need to be covered. It is mostly based on meeting the

requirements of the IEC, and also some Danish, Dutch, and German codes (DNV and Risø, 2002).

The earthquake requirements discussed in these guidelines are very similar to those from the

IEC. Pseudo response spectra are suggested as the method of determining the earthquake loads.

Although accelerations in one vertical and two horizontal directions generally need to be analysed,

the guideline suggests some simplifying assumptions. Since the vertical acceleration is not expected

to create much of a dynamic response, the tower may be analysed using the load created by the

maximum vertical acceleration to determine if buckling will be critical. Furthermore, the two

horizontal directions can be simplified to one horizontal direction, because the dynamic system is

fairly symmetrical. A simple model of the wind turbine is suggested as a vertical rod with a

concentrated mass on top. The mass consists of the nacelle and rotor mass and ¼ of the tower

mass (DNV and Risø, 2002). This simplified analysis could be used as a preliminary analysis for



designers to determine if earthquake loading might be critical and thus if a more detailed analysis is

necessary.

2.1.4 OTHER EUROPEAN STANDARDS

Other European standards have been fairly harmonized with the IEC codes and thus further

discussion of these is unnecessary.

2.2 CANADIAN STANDARDS

As the number of wind turbines being constructed in Canada increases, there has been much

discussion regarding which codes are applicable to the design of Canadian wind turbine towers.

Hatch Acres (2006) carried out a code review and gap analysis for wind turbines, assessing several

aspects of design of international and Canadian codes. The seismic provisions of relevant Canadian

design codes are discussed in this section.

2.2.1 CAN/CSA-C61400-1:08, WIND TURBINES – PART 1: DESIGN REQUIREMENTS

This standard is almost identical to the IEC standard of the same name, with a few Canadian

deviations. It was adopted by the Canadian Standards Association (CSA) in March 2008.

Furthermore, it replaces the 1987 standard, CAN/CSA-F416:87, Wind Energy Conversion Systems

(WECS) – Safety, Design, and Operation Criteria.

Canadian Modifications to IEC61400-1

The CSA-C61400-1 has introduced a few changes to make the IEC61400-1 suitable for Canada.

The main changes are due to the external conditions that the wind turbine will experience. More

severe icing and temperature conditions are acknowledged. The CSA has added several notes to the

earthquake-related clauses of the IEC, instructing designers how to obtain seismic loads, design

spectral accelerations, and seismic design data (CSA, 2008). Additionally, the National Building

Code of Canada (NBCC) is referenced in several instances, one of which is for the determination of

the seismic loads.

The CSA acknowledges that the NBCC does not address earthquake forces acting vertically, and

identifies this as a problem because wind turbines may have vibration modes with significant mass

participation factors in the vertical directions. However, the vertical component of a seismic event

is most likely not significant, but is investigated and discussed in Section 5.3.4. Furthermore, there is

a discrepancy between the recurrence period of the seismic event to be used in design. The



IEC61400-1, and thus the new CSA-C61400-1, suggests a 475-year recurrence period, whereas the

NBCC requires a 2500-year return period.

2.2.2 CAN/CSA S37-01, ANTENNAS, TOWERS, AND ANTENNA-SUPPORTING

STRUCTURES

This standard applies to structural antennas and towers. It does have a few requirements

regarding the effects of earthquakes and the dynamic effects of wind, but this code’s applicability to

this thesis is mostly related to determining the resistance of the tower (CSA, 2001).

2.2.3 CAN/CSA S473-04, STEEL (FIXED OFFSHORE) STRUCTURES

This is a standard that specifies the requirements for the design and fabrication of fixed steel

offshore structures, but is in the process of being replaced by an adopted ISO standard (CSA,

2009a). It acknowledges that supplementary requirements may be necessary for unusual structures,

which would be the case for wind turbine towers. It is more applicable to offshore wind turbines,

although some design information is applicable to onshore wind turbine towers as well, such as the

resistance of large, fabricated slender cross-section tubes under compression and bending (CSA,

2004). It also provides significant information about fatigue details relating to tubular joints and

various connection details.

2.2.4 CAN/CSA S16-09, DESIGN OF STEEL STRUCTURES

This standard provides rules and requirements for the design, fabrication, and erection of steel

structures based on limit states design. It specifically defines “steel structures” as structural

members and frames, and it is apparent that it is principally intended for buildings (CSA, 2009b).

Although this standard is frequently referenced by other CSA Structural Standards, it is not very

useful for the design and analysis of wind turbine structures. The one area where it may be useful is

for fatigue design, as it provides information regarding several fatigue details that are present in wind

turbine towers.

2.3 BOOK PUBLICATIONS

In recent years, several books about wind turbines have been published, most of which are very

detailed and valuable to designers of wind turbines. However, most also have little or no mention of

the effects of earthquakes on wind turbines. A few books of note are listed here:

• Wind Energy Handbook (2001), by T. Burton, D. Sharpe, N. Jenkins, E. Bossanyi



• Wind Energy Explained – Theory, Design and Application (2002), by .J.F. Manwell, J.G.

McGowan, A.L. Rogers

• Wind Turbines: Fundamentals, Technologies, Application, Economics (2006), by Erich Hau

• Aerodynamics of Wind Turbines (2000), by M.O.L. Hansen

2.4 CURRENT RESEARCH ON WIND TURBINE TOWERS

The majority of recent publications on wind turbine towers originates from universities and

research centres, with few contributions from the private sector. Some of this research that is

related to seismic behaviour of wind turbines is presented in this section.

2.4.1 COMPARISON OF SEISMIC ANALYSIS METHODS: FREQUENCY-DOMAIN VS. TIME-DOMAIN

Frequency-domain methods are typically favoured in design due to their ease of implementation.

Time-domain analyses have a higher computational demand and are often used in analysis of

structures, rather than in their design. Time-domain analyses are increasingly being used in the wind

turbine industry.

Currently, several wind turbine simulation software packages exist. The purpose of such

software is to analyse wind turbines under several loading cases to determine the design loads. They

range from basic to very sophisticated and are generally proprietary to companies, which carry out

the analyses and only provide the results. The more sophisticated packages can create a full

aeroelastic model of the wind turbine, including the blades, and subject it to turbulent wind loading.

The newest addition to most of these packages is wave and current loading, as offshore turbines are

becoming commonplace (van Wingerde et al., 2006; Lüddecke et al., 2008). A few companies also

recognize the need to incorporate earthquake loading into these software packages, as more wind

turbines are being erected on seismically active sites. Garrad Hassan in the UK is one such

company. Their software, GH Bladed, can apply an accelerogram (real or synthesized) to a model

along with other normal loading (Witcher, 2005). The ground motion is applied in any direction and

a secondary ground motion may be applied at 90° to the first. The structural dynamics of the wind

turbine are represented using a limited-degree-of-freedom modal model, and all forces and moments

at specified locations are output, as well as torques at critical locations (Witcher, 2005).

This time-domain method was validated against the frequency-domain, which is more

commonly employed. Witcher concluded that both methods were adequate, but discrepancies arose



when the system damping was not close to that of the design spectra, which is typically 5%. For

operating wind turbines, the aerodynamic damping is close to 5% (Witcher, 2005), and thus both

methods yield very similar results. For turbines that are not operating, the aerodynamic damping is

much lower. Most building codes do not provide a method to correct the level of damping when

using the frequency-domain method, so the time-domain method provides an advantage over the

frequency method because the correct level of damping can be applied (Witcher, 2005). Therefore,

Witcher (2005) concluded that conducting seismic analysis in the time-domain is acceptable, and in

fact preferred, because the correct aeroelastic interaction can be modelled.

A similar investigation was carried out by Windrad Engineering GmbH and Nordex Energy

GmbH (Ritschel et al., 2003). The method of modal approximation was compared with a time-

domain approach using the simulation program Flex5. The main reason for investigating this

comparison is because they believe modal approximation is not an adequate method for obtaining

design loads, especially the rotor and nacelle loads, as modal approximation ignores any action above

the tower top (Ritschel et al., 2003). Thus, any system modes which might take into account the

interaction of the tower and the blades are not considered. The results of this investigation suggest

that the modal approach is very conservative for the lower part of the tower (Ritschel et al., 2003).

Regarding the machine loads on the nacelle and the rotor, the time-domain method predicts high

vertical forces, which are not predicted by the modal approximation method because the vertical

component is ignored (Ritschel et al., 2003).

Both the time-domain method and the frequency-domain method were deemed to be adequate.

In this thesis, the time-domain method is used as the intent is to obtain information about the

response of the wind turbine tower, rather than to obtain design loads.

2.4.2 SHELL BUCKLING

Local bucking in the shell of the wind turbine tower using static, buckling, and seismic analyses

was investigated by Bazeos et al. (2002). They also assessed the influence of the door opening on

the overall behaviour of the tower. Furthermore, the effects of soil-structure interaction were also

investigated and are discussed in the next section.

Bazeos et al. (2002) found that the static analysis yielded positive results. The wind turbine was

subjected to pseudo-aerodynamic loads corresponding to survival conditions along with gravity load,

and the maximum stresses were found to be well below yield (Bazeos et al., 2002). The static

analysis also showed acceptable stress values throughout the tower and a maximum horizontal

deflection less than 1% of the total height, which is acceptable. The buckling analysis predicted local



buckling would occur at 1.33 times the static load (Bazeos et al., 2002). Lastly, seismic analyses were

carried out and the first mode was found to dominate the response to the seismic excitation, as was

expected. The maximum stresses were found to be very low for this analysis as well. Thus, Bazeos

et al. (2002) concluded that seismic analysis does not produce a critical response for this type of

structure. However, the magnitude of the design earthquake was not specified, making it difficult to

assess the results of these studies.

Shell buckling was also investigated by Lavassas et al. (2003), where the design of a prototype

steel wind turbine tower was evaluated. Shell buckling was not assessed under seismic loading. It

was concluded that assessment of shell buckling according to design codes is somewhat ambiguous.

Additionally, a simplified linear model was deemed insufficient because the stress concentrations at

the base of the tower are ignored.

2.4.3 DYNAMIC SOIL-STRUCTURE INTERACTION EFFECTS

Researchers have identified the importance of analyzing the soil-structure interaction (SSI) when

assessing the seismic resistance of wind turbines. Although the wind turbine tower was identified as

the most important structural component when analyzing dynamic response (Zhao and Maisser,

2006), the interaction between the structure, the foundation, and the soil around was also considered

to be very significant (Bazeos et al., 2002; Zhao and Maisser, 2006).

Time-history analysis was used for the seismic analysis to analyse the soil-structure interaction

effects, as it is applicable to both elastic linear and non-linear analysis. A weak earthquake was used

in the analysis by Zhao and Maisser (2006). The wind speeds, also as a time-history, were used to

determine the thrust and the torque on the tower top. For these loads, Zhao and Maisser (2006)

found that the peak tower displacement was dominated by the wind forces. The inclusion of SSI

resulted in reduced fundamental frequencies of the wind turbine. Thus, it was concluded that soil-

structure interaction has a large influence on the dynamic characteristics of the wind turbine tower,

particularly in areas with flexible soil, and that this interaction should be included in dynamic analysis

of wind turbines (Zhao and Maisser, 2006). This conclusion was also reached by Bazeos et al.

(2002).

Design codes generally specify response spectra depending on the soil characteristics. Thus it

may not be necessary to include SSI effects if seismic analysis is carried out in the frequency-domain.

For time-domain analyses, the soil-structure interaction should be assessed if the wind turbine

structure is erected on flexible soil.



2.5 SUMMARY

The existing codes offer some guidelines for seismic analysis of wind turbine towers, but

generally more guidance is needed, especially for areas of high seismicity. Some private companies

have identified this need and are incorporating seismic analysis in their wind turbine analysis

software. However, most existing research is concerned with verifying that a given wind turbine can

sustain low or moderate seismic loadings without assessing the limits of the wind turbine tower’s

seismic capabilities. Therefore, this thesis will focus on characterizing these limits for Canadian

locations by employing the finite element method (FEM).

The following chapter describes an essential part of any project that employs FEM: the

development and validation of the finite element model.


CHAPTER 3: FINITE ELEMENT MODEL DEVELOPMENT AND

VALIDATION

Numerical models are useful for predicting the behaviour of complex structures or structures

with unusual loading, for which analytical methods are difficult to employ, and can be used to assess

the seismic capabilities of such structures. However, any numerical model must first be deemed

reliable. Material models, element formulations, and failure mechanisms must be verified and shown

to represent realistic behaviours.

Numerical models can be validated using a variety of methods. If experimental results are

available, those results are often used to calibrate the model. Otherwise, the validation must rely on

comparison with values calculated from various theoretical formulations. It must also be shown that

the post-peak behaviour is consistent with experimental results and that the expected failure

mechanism can be captured.

When dealing with wind turbines, very few experimental tests have been performed on the

supporting structure. The validation of any numerical study must hence be segmented, yet must

demonstrate accuracy and reliability.

3.1 GEOMETRY OF WIND TURBINE TOWERS

Tubular steel wind turbine towers are typically very tall and slender. The particular tower that is

discussed and analysed in detail in this thesis is 78 m tall, with a centreline diameter, Dm, of

3650 mm for almost the entire bottom half of the tower. The diameter then tapers down to

2800 mm at the top. The thickness of the tower varies along the height, from 35 mm at the base to

10 mm at the top. Details of the Vestas wind turbine tower are provided in Chapter 4.

For several of the validation analyses, the model was of a simpler member having a constant

diameter and thickness, so that the theoretical closed-form solution for each analysis could be

calculated and compared to the finite element analysis (FEA) result.

3.2 FINITE ELEMENT ANALYSIS PROGRAM

For this thesis, ANSYS was chosen to carry out the numerical analyses, as it offers the non-

linear capabilities that are deemed necessary to capture all the aspects of the response of the wind

turbine tower that is being studied.

CHAPTER 3: FINITE ELEMENT MODEL DEVELOPMENT AND VALIDATION


3.3 MATERIAL PROPERTIES

Typical steel wind turbine towers are made from flat steel plates which are rolled into cylindrical

or conical pieces, and then welded longitudinally (Danish Wind Industry Association, 2003). The

cylindrical or conical pieces are then welded together circumferentially into sections of 20 to 30 m in

height, generally a length that is easily transportable. Each of these sections has flanges at the ends,

and the sections are bolted together on site as the tower is erected. Due to this fabrication process,

the material properties of the tower are similar to cold-formed tubular members. The stress-strain

curve of the material shows a low proportional limit, followed by gradual yielding, no clear yield

plateau, and significant strain hardening.

The material properties used for the analyses in this thesis come from the average of several

coupon tests of cold-formed circular HSS sections performed by Voth (2010). No material data

from an actual wind turbine tower was available. In the ANSYS analyses herein, the true-stress (σ)

vs. true-strain (ε) curve has been employed. This was obtained by modifying the engineering stress-

strain curve (σnom, εnom), as obtained from a tensile coupon test, in the following manner:

)1ln( nomε+=ε (Equation 3.1)

)1( nomnom ε+σ=σ (Equation 3.2)

These equations are only valid until necking of the coupon test occurs. After that point, the

stress distribution is no longer a simple uniaxial case, but a complex triaxial case (Aronofsky, 1951).

The method used by Voth (2010) to determine the post-necking material behaviour was developed

by Matic (1985). It was refined by Martinez-Saucedo et al. (2006), who suggested that the Matic

material properties should only be used in the post-necked region of the stress-strain curve. The

finite element (FE) material properties were thus determined through an iterative process, wherein

several FE analyses of a coupon with the Matic material properties were carried out and compared

with the experimental stress-strain behaviour and rupture. The resulting true stress-true strain curve

is shown in Figure 3.1, as is the experimental stress-strain curve and the onset of necking.



0

100

200

300

400

500

600

700

800

0 0.1 0.2 0.3 0.4 0.5Strain (mm/mm)

Stress (MPa)

True stress-strain curve

Engineering stress-strain curve

Figure 3.1: Engineering and true stress-strain curve from Voth (2010) for cold-formed circular HSS

For the subsequent analyses, three sets of material properties were used, shown in Figure 3.2.

The first, gradual yielding, is the aforementioned true stress-strain curve from Voth (2010). The

second, having a yield plateau, was adapted from Voth (2010) by modifications as shown in Figure

3.2. The third curve is bilinear, was obtained from Elchalakani et al. (2002), and was only employed

in a few analyses that were geometrically comparable to an experimental specimen.

0

100

200

300

400

500

600

700

800

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Strain (mm/mm)

Stress (MPa)

Gradual Yielding (from Voth, 2010)

Stress-Strain Curve with Yield PlateauBilinear (from Elchalakani et al., 2002)

Figure 3.2: Stress-strain curves used in subsequent analyses

E = 211449 MPa Fy = 389 MPa Fu = 833 MPa εu = 1.1

E = 190900 MPa Fy = 408 MPa Fu = 510 MPa εu = 0.27

Yield plateau: 0.02 mm/mm

0

100

200

300

400

500

0 0.002 0.004 0.006 0.008

E

1

after necking



3.4 CHOICE OF ELEMENTS

The elements selected for this analysis are 8-noded shell elements and 20-noded solid elements,

which are further described in the following subsections. Furthermore, mass elements and rigid link

elements were employed, and it was verified that these elements exhibit the desired behaviour.

3.4.1 SHELL ELEMENTS

The wall of the tower was represented with 8-noded shell elements (SHELL281 in ANSYS), as it

was deemed that this element could likely reflect the behaviour of the tower, essentially a thin

conical shell structure. Due to the large diameter-to-thickness ratio along the tower height, the

tower wall acts fairly independently from the rest of the tower and more like a thin shell, with

potential for local buckling. This element has six degrees-of-freedom (DOFs) at each node –

translations in the x, y, and z directions, and rotations about the x, y, and z axes. A schematic of the

element and its DOFs is shown in Figure 3.3. The deformation shapes are quadratic, making this

shell element well-suited to model curved shells (ANSYS, 2007). The out-of-plane stress varies

linearly through the thickness and the transverse shear stresses are assumed to be constant through

the thickness.

Figure 3.3: Geometry of shell element used to represent tower walls (ANSYS, 2007)

Another element was also investigated (SHELL93 in ANSYS). Its geometry is identical to that

of the chosen shell element, but has fewer capabilities, albeit still adequate for modelling a tubular

tower. However, the SHELL281 element was chosen, as it has nonlinear stabilization properties,

which improves the stability of local buckling during static analyses (ANSYS, 2007). This element

was found to be more stable during transient analyses as well.

3.4.1.1 CLASSICAL PLATE THEORY

The elastic behaviour of thin plates is described by classical plate theory, also known as

Kirchhoff’s plate theory. This theory has several assumptions and limitations (Szilard, 2004).

I M

P

O

L

K N

J

Z

Y X

zo yo

xo



Several of the assumptions are analogous to the properties of the shell element previously described.

Classical plate theory is a small-deflection theory, so the transverse deflections are assumed to be

small. The deflection limit is considered to be 1/10th of the thickness. When the deflection exceeds

this limit, some of the assumptions are violated and the theory is no longer as reliable – the

behaviour of the plate begins to be governed by membrane action, rather than plate bending action.

A simple numerical analysis showed good agreement of the shell element with the classical plate

theory. The displacements obtained from the FE analyses were slightly higher than those predicted

by classical plate theory. The difference between the FEA and classical plate theory became more

evident when material nonlinearities were included in the analysis. However, once the difference

was significant, the classical plate theory was past its small-deflection limit, which is expected

because the theory does not account for any nonlinearity.

3.4.2 SOLID ELEMENTS

The wind turbine tower has flanges at the base of the tower and at several locations along the

height of the tower, as well as at the top. These allow the tower to be more easily erected and also

stiffen the tower. The flanges were modelled using a 3-dimensional solid element that has 20 nodes

(SOLID95 in ANSYS). The geometry of this element is shown in Figure 3.4. This solid element

was chosen for two reasons: it is well suited to model curved boundaries, as it has a mid-side node;

and it is directly compatible with the shell element that was chosen. One face of the solid element

has the same nodes and node placement as the shell element, resulting in easy and clean meshing of

the flanges. Due to the connectivity to the shell wall, each flange only has one element through the

thickness, which is also a typical feature of 20-noded solid element modelling.

Figure 3.4: Geometry of 20-noded solid element used to represent flanges (ANSYS, 2007)

M

Y

Q

J

R

K

A

O

W

P X

U

B N

V

S Z

T

L

I

Z

Y X



3.4.2.1 ELASTIC BEAM THEORY

As the main effect of the flanges is to stiffen the shell and thus prevent it from moving in the

circumferential direction, a beam analysis was carried out to evaluate the solid element’s flexural

capabilities. The dimensions of the beam were similar to the width and depth of the flanges on a

wind turbine tower, and the length was about 1/6th of the circumference of a tower having a 3 m

diameter. It was found that even a very coarse mesh captured the Von Mises stress distribution well.

Thus, one element through the thickness of the flange and two elements through the width were

deemed adequate and were used in the modelling of the flanges.

3.4.3 SOLID-SHELL INTERACTION

There is one discrepancy between the shell and solid elements which arises from the rotational

degree of freedom that does not exist in the solid element. To ensure full connectivity between the

shell and the solid, an overlap of the two elements was used, as shown in Figure 3.5. The increased

mass due to this overlap is not significant, as the wall is quite thin.

(a) (b) (c)

Figure 3.5: Geometry of wind turbine tower ring flanges (a) dimensions (b) node locations (c) area of overlap

3.5 CONNECTION MODELLING

As discussed in the previous section, the tower is made up of sections that are bolted together

using flanges. The flanges of the Vestas wind turbine tower are shown in Figure 3.6. The flanges

are stocky and stiff, so prying of the connection is not likely to occur. The bolted connections are

thus not modelled. However, the flanges are modelled to simulate the stiffness they lend to the

tower, but are assumed to be fully connected and monolithic. The bolt holes are not modelled, as

the bolt material almost entirely fills the bolt hole. The stiffening effect of these flanges is discussed

further in 3.6.2.2. The maximum stresses at the flange connection during seismic analysis are later

verified to ensure that the assumptions stated here are not violated (Section 5.3.6).



Figure 3.6: Bolted flange connections of wind turbine tower (Vestas, 2006)

3.6 TUBULAR MEMBERS UNDER BENDING

Flexural member cross-sections are classified by many codes based on their cross-sectional

slenderness, which governs a section’s ability to carry moment. If elements of the cross-section that

are in compression are too slender, the flexural member may not reach its global flexural capacity,

but may instead buckle locally. Many codes describe the slenderness of tubular elements in flexural

compression in terms of classes, where the limits are defined based on the diameter-to-thickness

ratio (BSI, 2000; CEN, 2005; CSA, 2009b). Other codes also base their limits on the diameter-to-

thickness ratio, but describe flexural members as compact, non-compact, or slender (AISC, 2005;

Standards Australia, 1998).

Class 1 sections, also known as compact, are capable of reaching and maintaining a plastic

moment, and can thus provide sufficient rotation for plastic design. Class 2 sections, sometimes



known as semi-compact, will reach their plastic moment but are not capable of maintaining it and

thus have limited rotation capacity. Class 3 sections, also known as non-compact, are capable of

reaching their yield moment but not their plastic moment. Finally, Class 4 sections, also described as

slender sections, will experience elastic local buckling in areas of the section that are loaded in

compression and thus will likely not be able to reach the yield moment.

The limits of each class for circular hollow sections are shown in Table 3.1 for several codes.

There appear to be some fairly high discrepancies between the codes described in the table. CSA

S16 has similar but less conservative D/t limits compared to Eurocode 3, except for the major

Class3/Class 4 breakpoint.

Table 3.1: Cross-sectional slenderness limits (D/t) of circular hollow sections in bending using E = 200000 MPa

Class 1, or Compact Class 2 Class 3,

or Non-Compact Class 4,

or Slender

CSA S16 (2009b)

yF13000

yF

18000

yF66000

yF

66000tD>

CSA S473 (2004)

yF14200

– yF

62000

yF62000

tD

>

AISC (2005) y

y F14000F/E07.0 = –

yy F

62000F/E31.0 = yF

62000tD>

BS 5950 (2000)*

y

2

F1100040 =ε

y

2

F1375050 =ε

y

2

F38500140 =ε

yF38500

tD>

AS 4100 (1998)**

yF12500

– yF

30000

yF30000

tD>

Eurocode 3 (2005)***

y

2

F1175050 =ε

y

2

F1645070 =ε

y

2

F2115090 =ε †

yF21150

tD>

* in BS 5950, yF/275=ε

** taken from Zhao et al. (2005)

*** in Eurocode 3, yF/235=ε

† Eurocode 3 conservatively adopts the same limit as in axial compression (see Table 3.2)

Sections of wind turbine towers fall within the limits of Class 3 and Class 4. The bottom part of

the wind turbine tower that will be analysed in this thesis after the completion of the validation

analyses is class 3 in flexure according to CSA S16, while most of the tower’s height is well past the

Class 4 limit.



3.6.1 FE MODEL FOR PURE FLEXURE

Several analyses were carried out to determine if ANSYS can capture the flexural behaviour of a

tubular member made up of shell elements. For the validation of pure flexural behaviour, the FE

model was of a short cantilevered tubular member having a constant cross section that was

subjected to pure bending moment. The member was dimensioned as shown in Figure 3.7 to obtain

five FE models: VF-el, VF-1a, and VF-1b had the same geometry but used all three material

properties described in Section 3.3; VF-2a and VF-2b had the same geometry but were more slender

and used the gradual yielding and the yield plateau material properties, respectively. The length-to-

diameter ratio was 4, which is well over the recommended minimum value of L/D=2 necessary to

eliminate the effect of load fixtures on bending properties (Elchalakani et al., 2002). The base of the

member was fully fixed. The nodes at the top of the member were all rigidly connected to simulate

another fixture, but were not fixed globally, allowing the application of a moment at the top of the

member. A schematic of this model is shown in Figure 3.7. All three models are Class 4 by

Eurocode 3 (CEN, 2005), but VF-el and VF-1 are Class 3 by CSA (2009b) and AISC (2005).

Figure 3.7: Schematic and descriptions of FE models for validation of pure flexure

One of the models, VF-el, was created such that its geometric ratios would be directly

comparable to experimental specimen B2 from Elchalakani et al. (2002), which had an L/D=4 and a

D/t=110. To ensure that all parameters were equal, the analysis of model VF-el was carried out

using material properties from tensile coupon test results for specimen B2: E=190,900 MPa, Fy =

408 MPa, Fu=510 MPa, and εu=0.27 (Elchalakani et al., 2002). Due to the lack of a stress-strain

curve, the material properties used in the analysis were bilinear, as shown in Figure 3.2.

Four additional models were created. Model VF-1 (a and b) were identical to model VF-el in

dimensions and boundary conditions, but used the gradual yielding and the yield plateau material

VF-1a t = 18mm D/t = 111

*gradual yielding

VF-1b t = 18mm D/t = 111

*yield plateau

D = 2000mm L = 8000mm L/D = 4

VF-2a t = 7mm D/t = 286

VF-el t = 18mm D/t = 111 *bilinear material properties D L

t

M

VF-2b t = 7mm D/t = 286



properties described in Section 3.3. This provided an indication of how sensitive the model is to

changes in material properties. Models VF-2 (a and b) had a thickness of 7mm and D/t of 286, and

were also carried out using the same material properties as VF-1. Model VF-2 (a and b), having a

very slender section, was investigated because its diameter-to-thickness ratio was similar to the

highest diameter-to-thickness ratio found on the wind turbine tower.

3.6.1.1 MESH SENSITIVITY

The analysis of model VF-el was carried out several times in order to determine the mesh

fineness and configuration that best captured the expected local buckling failure mechanism.

Initially, analyses were carried out using a uniform mesh of well-proportioned elements, as depicted

in Figure 3.8. The curvature, κ, was calculated as described in Elchalakani et al. (2002). The

normalised moment-curvature response of the analysis of model VF-el using this mesh

configuration with various element sizes, se, is shown in Figure 3.8. The mesh having an element

size-to-thickness ratio (se/t) of 9.6 produced convergence, as a finer mesh yielded approximately the

same moment-curvature response. The response of the mesh with se/t = 11.5 was also quite good.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

Normalised Curvature, κ/κp

Normalised Moment,

M/Mp

Figure 3.8: Normalised moment-curvature response of FEA of VF-el for various mesh sizes

using uniform mesh and perfect geometry/loading

Any of the element sizes used, even up to se/t of 19.2, were accurate in the elastic range, having

the same initial stiffness as the experimental specimen B2 (Elchalakani et al., 2002). Furthermore, all

M

se

se/t = 19.2

se/t = 14.4

se/t = 11.5

se/t = 9.6

se/t = 8.2

se/t = 7.2

My/Mp



mesh sizes showed that the member began to yield when the yield moment, My, was reached, and all

mesh sizes captured the failure mechanism, although the coarser meshes over-estimated the post-

peak capacity. Thus, a coarse mesh may be used in areas that remain elastic or that experience only

limited yielding.

3.6.1.2 REFINEMENT OF MESH

A second mesh configuration was evaluated to decrease computation time and to establish that a

fine mesh is only required for critical parts of the model. The mesh was refined at the centre of the

member where the buckle was expected to occur. The refined elements had a ratio of se/t = 9.6, the

aforementioned value that was considered converged. As shown in Figure 3.9, the mesh had

elements with a good aspect ratio at the middle of the member for a specified refined length, Lr, and

elements with an aspect ratio of 3:1 at the end of the member. The moment-curvature response of

model VF-el using refined lengths of 0.5D, D, and 1.5D, was found to be identical to the response

obtained using the uniform refined element mesh.

Figure 3.9: Refined mesh configuration

However, due to the model having perfectly symmetrical geometry and loading, difficulties were

sometimes encountered. Instead of forming one buckle, two buckles would sometimes form, as

shown in Figure 3.10. Thus, a small imperfection was introduced. An out-of-straightness was

created using two opposing displacements, applied at a distance of se (or se/2 for the coarser

meshes) above and below midheight. The displaced geometry was then used for the subsequent

flexural analysis. The total out-of-straightness was varied from 1% of the shell thickness to 5% of

the shell thickness, t, to see the influence on the response curve. The effect of various imperfections

was evaluated, and it was found to decrease the peak capacity of the member by only 1.5%. The

M

Lr



post-peak response was somewhat improved for the coarser meshes, but was unchanged for the

finer meshes.

Figure 3.10: Incorrect buckling configuration due to perfectly symmetrical model and loading

Thus, the mesh size used in this thesis was based on the findings of this section. In critical

locations where local buckling may occur, a mesh size up to 12 times the thickness is adequate. The

mesh may be coarser in non-critical locations, as it does not cause any loss of accuracy.

3.6.1.3 RESULTS AND ANALYSIS OF TUBULAR MEMBERS UNDER PURE FLEXURE

The normalized moment-curvature response of model VF-el is shown in Figure 3.11. As

previously described, this model was created such that it would be geometrically comparable to the

experimental results of specimen B2 from Elchalakani et al. (2002). Although the shape of the

response curve is similar, the agreement is not ideal as the peak is over-estimated by 9%. This is

believed to be due to imperfections of the experimental specimen. Due to the small scale of the

specimen (D = 110 mm, t = 1 mm), imperfections would have been hard to measure, but could be

significant. Elchalakani et al. (2002) did not discuss this in their publication. In addition, the FE

model used a bilinear stress-strain curve, since the true stress-strain curve was not reported by

Elchalakani et al. (2002).



0

0.2

0.4

0.6

0.8

1

0 1 2 3 4Normalised Curvature, κ/κp

Normalised Moment,

M/Mp

Figure 3.11: Normalised moment-curvature response of FE model VF-el

compared with experimental results from Elchalakani et al. (2002)

Despite these differences, the failure mode was captured quite well, as can be seen from Figure

3.12. Elchalakani et al. (2002) note that local buckling generally occurs away from the fixture, where

ovalisation is prevented. This finding is consistent with the results of the FEA. However, it can be

seen in Figure 3.12 (a) that the local buckle of specimen B2 formed close to the fixture, indicating

the possibility that larger imperfections were present at that location, causing the failure to occur

there.

(a) (b)

Figure 3.12: Local buckling failure of CHS under pure bending, D/t = 111 (a) Specimen B2 (Elchalakani et al., 2001) (b) FE model VF-el

Experimental Results, Specimen B2

(Elchalakani et al., 2002)

My/Mp

FEA Results, VF-el



The FE models VF-1a and VF-1b, which were geometrically identical to VF-el but used

different material properties, had very different response curves from VF-el. The responses of all

three models are shown in Figure 3.13. It can be seen that the difference in material properties

greatly influences the moment-curvature response. Due to the bilinear material properties of VF-el,

its response was almost linear until the peak load was achieved. Meanwhile, the gradual stress-strain

curve used for VF-1a resulted in a curvilinear response up to the peak load. The yield plateau used

in VF-1b caused it to fail much earlier than VF-1a. The post-peak response of the three models was

similar, quickly shedding the load as a local buckle formed. Furthermore, the peak load achieved by

VF-1a was much higher than that of VF-el and VF-1b, and was in fact only 2.5% less than the

plastic moment. This corresponds to Class 3 behaviour, where Mp > Mult > My, which is predicted

by CSA S16 (2009b) and AISC (2005), but incorrectly predicted by Eurocode 3 (CEN, 2005) which

classifies this cross-section as Class 4 in flexure.

0

0.2

0.4

0.6

0.8

1


Normalised Moment,

M/Mp

Figure 3.13: Normalised moment-curvature response of FE models VF-1 and VF-el (D/t = 111)

The moment-curvature responses of FE models VF-2a and VF-2b are shown in Figure 3.14.

Both models fail very abruptly, VF-2a at a moment 7% greater than the yield moment and VF-2b at

a moment only 2.4% greater than the yield moment. The buckled shape is shown in Figure 3.15.

For this very slender section, the material properties don’t influence the response as much as for

the previously discussed models, as can be seen from the insignificant difference between the two

response curves. This is expected because Class 4 sections experience elastic local buckling and thus

My/Mp

VF-1a, gradual yielding

VF-el, bilinear material properties

VF-1b, yield plateau



the post-yield material properties should not influence the response. However, the attainment of

the yield moment, My, is somewhat surprising because VF-2 is classified as Class 4, or slender (CSA,

2009b, AISC, 2005, and CEN, 2005).

0

0.2

0.4

0.6

0.8

1


Normalised Moment,

M/Mp

Figure 3.14: Normalised moment-curvature response of FE models VF-2 (D/t = 286)

Figure 3.15: Local buckle failure of very slender CHS under pure bending (D/t = 286)

3.6.2 FE MODEL OF A CANTILEVER TOWER UNDER BENDING

After establishing a good mesh size and ensuring that the local buckling failure can be captured

in ANSYS, a more realistic problem to investigate was that of a cantilever tower under bending, a

My/Mp

VF-2a, gradual yielding

VF-2b, yield plateau



load case that a wind turbine tower is regularly subjected to. To validate the ability of the program

to capture the behaviour of what is essentially a cantilevered beam made of shell elements, two

models were created, VB-1 and VB-2. These two models have cross-sectional dimensions similar to

VF-1 and VF-2, respectively, but the length of the member is much longer, 60 m. No initial

imperfections were added to the geometry, as asymmetry is created by the load due to the shear

variation along the length. A schematic is shown in Figure 3.16, along with details of the FE

models.

A flange of proportions similar to a wind turbine tower flange was added to model VB-1 at the

location where the buckle formed, creating a third model, VBS-1. The geometry of the flange and

details of the model are shown in Figure 3.16. All three models were analysed twice: once with

material properties having gradual yielding, and a second time with material properties having a yield

plateau.

Figure 3.16: Schematic and descriptions of FE models for validation of bending behaviour

3.6.2.1 RESULTS AND ANALYSIS OF CANTILEVER TOWER UNDER BENDING

The response curves of all three models described above are plotted in Figure 3.17. In each

case, the moment is taken at the base to reflect the capacity of the tower and not necessarily that of

the section that fails. The response curves of the unstiffened towers are very similar to their pure

flexure counterparts. The peak load of VB-1 appears to be higher than the peak load achieved in

pure flexure. However, this is not true because the moment in Figure 3.17 is the base moment and

not the moment at the section where the tower buckled, at 4.5 m from the base. Hence, the plotted

moment, M, is proportional to the applied lateral load, P. The peak load of VB-2 is the same as that

achieved in pure flexure. The buckle of VB-2 formed much higher, at 8.6 m from the base. Thus

the peak moment at the location of failure was much less than that achieved in pure flexure, which is

to be expected.

D = 2000mm L = 60m

VB-2 t = 7mm D/t = 276

VB-1 t = 18mm D/t = 111 D L

t

P

VBS-1 t = 18mm D/t = 111 hf = 4.48m wf = 94mm tf = 35mm

wf

tf

hf



The material properties affect the response of the cantilever towers significantly as can be seen

from the figure. This influence is less severe for the more slender member, VB-2.

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25

Normalised Lateral Deflection, ∆/L

Normalised Moment,

M/Mp

Figure 3.17: Normalised moment-curvature response of FE models

VB-1 (D/t = 111), VB-2 (D/t = 276), and VBS-1 (stiffened)

3.6.2.2 STIFFENING EFFECT OF A FLANGE

The stiffening flange did not have the desired effect. Without the flange, the ovalisation caused

due to the bending of the tower decreased the stiffness of the tower some distance away from the

base, with the maximum ovalisation occurring at 5.2 m from the base. The variation of the applied

moment was linear and thus the weakest section along the tower height was not at the base, which

had the highest moment but also the highest stiffness, but instead at 4.48 m from the base, which

had a lower stiffness than the base. This is shown in Figure 3.18 (a). The addition of the flange was

thought to push the formation of the buckle further up the tower and thus increase its capacity.

However, the section having the lowest stiffness was at 11.2 m from the base, a location where the

moment was too low to cause failure, as is shown in Figure 3.18 (b). Thus, the failure occurred at

the base where the moment was highest and the capacity of the tower was actually decreased due to

the addition of the flange.

My/Mp VB-1

VBS-1

VB-2

gradual yielding yield plateau

Material Properties:



0

10

20

30

40

50

60

0 15000 30000

Moment (kNm)

Height from Base (m)

0

10

20

30

40

50

60

0 15000 30000

Moment (kNm)


(a) VB-1 (b) VBS-1

Figure 3.18: Investigation of location of buckle

Nonetheless, model VBS-1 showed that the flanges of the wind turbine tower may have a

significant impact on its behaviour and should be included in the FE model of the Vestas wind

turbine tower.

3.6.2.3 EFFECT OF LOCAL IMPERFECTIONS ON FLEXURAL BEHAVIOUR

As demonstrated in upcoming Section 3.7.1.5, local imperfections can be added by using the

geometry from high-frequency mode shapes whereby one buckle (or half the sine wave) is 1.5D and

the depth of the wave is equal to the thickness of the tube. Although the initial analyses had no

local imperfections, it was considered worthwhile to investigate the response of the cantilever towers

under bending once local imperfections are added. Figure 3.19 shows the effect of adding local

imperfections to models VB-1 and VB-2.

For VB-1, a Class 3 section in flexure, the effect of adding local imperfections decreased the

peak load achieved by only 4.5%, but the post-peak response was significantly different. The effect

was much less significant for VB-2, a very slender section.

M

My along height

M

My along height



0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25


Normalised Moment,

M/Mp

Figure 3.19: Effect of local imperfections on cantilever tower under bending

The very gradual post-peak response of VB-1 with the addition of local imperfections is not the

desired response, as it does not agree with experimental observations (Elchalakani et al., 2002).

Thus, local imperfections will not be included in the Vestas wind turbine tower model because their

addition affects the bending response of the cantilever tower in an unlikely manner.

3.7 TUBULAR MEMBERS UNDER AXIAL COMPRESSION

Members subjected to axial compression are not divided into 4 classes, as is the case for

bending. Instead, there is only one limit which defines if a section is Class 4, or slender. If the

cross-sectional slenderness falls above this limit, the member cannot achieve its global flexural

buckling capacity due to local buckling. The cross-sectional slenderness limits of various codes are

shown in Table 3.2. There is good agreement between the codes on the definition of a slender CHS

cross-section in axial compression.

Table 3.2: Slenderness limits (D/t) of circular hollow sections in axial compression for non-slender behaviour, using E = 200000 MPa

CSA S16 (2009b)

AISC (2005)

BS 5950 (2000)

AS 4100 (1998)**

Eurocode 3 (2005)

Slenderness Limit yF

23000

yF22000

yF

22000

yF20500

yF

21150

** taken from Trahair and Bradford (1998)

gradual yielding yield plateau

Material Properties:

My/Mp VB-1

VB-2

VB-1 with local imperfections

VB-2 with local imperfections



3.7.1 FE ANALYSES FOR VALIDATION OF AXIAL BUCKLING BEHAVIOUR

Axial compression analyses were carried out to determine the ability of the FEA program to

capture axial compression buckling. Although axial loading is rarely a concern for wind turbine

towers, it must be considered since seismic analysis may include a vertical component, which may

affect the very slender sections at the top of the tower as well as those at the base.

3.7.1.1 FE MODELS FOR VALIDATION OF AXIAL BUCKLING BEHAVIOUR

Two FE models were initially created and analysed for this validation, VA-1 and VA-2. The

models are identical to VB-1 and VB-2, but the loading is different: axial compression plus a small

lateral load to induce sway. This lateral load of 0.005P corresponds to the “notional lateral load” of

CSA S16 Clause 8.4.1 (CSA, 2009b). A schematic of this model is shown in Figure 3.20. Four other

models were created based on VA-1 and VA-2. One set had local imperfections and no lateral load

(VA-1-S and VA-2-S), and another set had local imperfections and the 0.005P lateral load as well

(VA-1-SL and VA-2-SL). Due to the much lower slenderness limits in axial compression, both VA-

1 and VA-2 members are Class 4 in axial compression according to all codes included in Table 3.2.

Figure 3.20: Schematic and descriptions of FE models for validation of axial compression

3.7.1.2 EIGENVALUE BUCKLING ANALYSIS

Also known as classical Euler buckling analysis, this type of analysis predicts the theoretical

buckling strength of an ideal elastic structure by computing the structural eigenvalues of the defined

system. The FEA result for the Euler buckling load, Pe, was within 0.5% of the calculated Euler

buckling load for both VA-1 and VA-2.

D = 2000mm L = 60m k = 0.5

VA-1 t = 18mm D/t = 111 Plat = 0.005P *no local imperfections

D L

t

P

Plat

VA-2 t = 7mm D/t = 276 Plat = 0.005P

VA-1-S Plat = 0 *local imperfections – sinusoidal: wave length = 1.5D wave depth = t

VA-2-S Plat = 0

VA-1-SL Plat = 0.005P

VA-2-SL Plat = 0.005P



3.7.1.3 NONLINEAR BUCKLING ANALYSIS – GEOMETRIC AND MATERIAL

NONLINEARITIES

Euler buckling analysis over-predicts the elastic buckling load of a structure because it does not

account for imperfections and initial out-of-straightness of columns. Equations have been

developed to account for this and to predict a more realistic capacity of a column against buckling.

To determine this value using finite element analysis, a geometric non-linear, large-deflection static

analysis must be employed. The load is gradually increased until a load is reached where the

structure is unstable. This type of analysis may also include nonlinear material properties, to

approach the behaviour of a real column.

3.7.1.4 GEOMETRIC IMPERFECTIONS FOR GLOBAL BUCKLING

To simulate some initial imperfections to induce global buckling, a lateral load of 0.5% of the

axial load was added at the top of the cantilever tower. According to CSA S16-09 (2009b), 0.5% is

an adequate notional load to simulate such translational effects in a structure. This value was

furthermore confirmed by running two analyses with an initial out-of-straightness of 5 mm and of

10 mm at the top of the cantilever tower. Both analyses followed the same load-deflection path.

Conversely, an analysis with only 0.1% lateral load was found to differ significantly from the other

cases investigated.

3.7.1.5 GEOMETRIC IMPERFECTIONS FOR LOCAL BUCKLING

Imperfections were also added along the height of the tower to make local failure possible in the

case that local buckling occurred before global buckling.

To determine the amount of local imperfections required to induce local buckling, model VA-1

was reduced to a quarter of its initial length. Its geometry was then updated with high-frequency

mode shapes having three to six buckles (or 1.5 to 3 sine waves) along the length of the member.

The length of the sine wave was thus varied from 2.5D to 1.25D. Additionally, the depth of the

wave was varied from 0.25t to 2t. There was no lateral load at the top to induce global buckling.

The effect of varying the sine wave length and depth is shown in Figure 3.21.



0

0.2

0.4

0.6

0.8

1

0 0.01 0.02 0.03 0.04∆/L

P/AFy

1.25D1.5D1.88D2.5D

0

0.2

0.4

0.6

0.8

1

0 0.01 0.02 0.03 0.04∆/L

P/AFy

0.25t0.5t t2t

(a) (b)

Figure 3.21: Assessment of influence of geometric imperfections for local buckling (a) variation of sine wave length (b) variation of sine wave depth for 1.5D wave length

A sine wave length of 1.5D and a depth of t were deemed adequate at representing local

imperfections for subsequent analyses.

3.7.1.6 RESULTS AND ANALYSIS OF CANTILEVER TOWER UNDER AXIAL COMPRESSION

The normalized load-displacement responses of the axial compression FE validation analyses are

shown in Figure 3.22 and Figure 3.23. Also shown in the figures are the axial compression

capacities of VA-1 and VA-2, calculated in three ways: using CSA S16 (2009b) and Fy as specified;

using CSA S473 (2004); and using CSA S16 (2009b) and Fy as an effective yield stress, Fy,eff,

determined from the diameter-to-thickness ratio meeting the class 3 limit (CSA, 2009b).



0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16


Normalised Axial Load,

P/Pe

Figure 3.22: Axial loading analysis FE results of VA-1 (D/t = 111)

with and without local imperfections

0

0.2

0.4

0.6

0.8

1

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07


Normalised Axial Load,

P/Pe

Figure 3.23: Axial loading analysis FE results of VA-2 (D/t = 286)

with and without local imperfections

None of the analyses experience local buckling prior to global buckling, thus expected Class 4

behaviour under axial compression was not captured by the FEA. Furthermore, there is not good

agreement between the FEA results and the code predictions, but the latter can be seen to have very

Pu/Pe Fy = specified (CSA S16)

Nonlinear Geometry / Linear Materials VA-1

Nonlinear Geometry / Nonlinear Materials

Pu/Pe Fy = Fy,eff, meets Class 3 D/t limit (CSA S16)

Pu/Pe Fy = Fc, based on D/t (CSA S473)

VA-1-S VA-1 VA-1-SL

Nonlinear Geometry / Linear Materials VA-2

Nonlinear Geometry / Nonlinear Materials

VA-2-S VA-2 VA-2-SL

Pu/Pe Fy = specified (CSA S16)

Pu/Pe Fy = Fy,eff, meets Class 3 D/t limit (CSA S16)

Pu/Pe Fy = Fc, based on D/t (CSA S473)



differing estimates for compression strength for Class 4 sections anyway. The prediction from CSA

S473 is most consistent for VA-1 and VA-2 (the two pure compression load cases, see Figure 3.20).

The only models that surpass the code predictions for pure axial compression are those with no

lateral load but with local imperfections, VA-1-S and VA-2-S, as might be expected.

3.7.2 SUMMARY OF MODELLING DECISIONS

This chapter has thus far described the various analyses that have validated the following

modelling decisions:

• The 8-noded shell elements were chosen for the thin wall of the tower, the 20-noded solid

elements were chosen for the flanges, and rigid link elements were used to attach the nacelle

and rotor point mass elements. A good mesh size in critical areas is provided by square-

shaped (aspect ratio close to 1) elements having element size-to-thickness ratio up to 12. A

coarser mesh is acceptable in non-critical areas, where elements aspect ratios of up to 3 are

used.

• To represent material properties, the gradual yielding curve from Voth (2010) is used for all

subsequent models. Furthermore, material properties with a yield plateau are employed for a

few models to further assess sensitivity to material properties.

• Flanges are deemed important in capturing the failure mode and are thus included.

• Global or local imperfections are not added in any wind turbine tower models as the primary

loading is bending, for which imperfections were deemed unnecessary or unhelpful.

3.8 TIME-HISTORY ANALYSIS UNDER SEISMIC EXCITATION

The main purpose of this validation was to determine if the time-history analysis method used in

ANSYS is adequate to capture the earthquake response, and also to identify appropriate damping

values for a wind turbine. An incremental analysis was also conducted.

A full-scale shake table test of a small wind turbine was carried out at the University of

California, San Diego (Prowell et al., 2008 and 2009). The turbine was 22.6 m tall and was made up

of three sections of constant cross-section connected by conical joints. A schematic of the turbine is

shown in Figure 3.24. A simple FE model was created using shell elements and additional mass

elements, uniformly distributed throughout the tower, to reach the mass specified by Prowell et. al.

(2008). Modal analysis in ANSYS estimated the first modal period to be 0.58 sec, which is in good

agreement with the experimentally observed first mode of 0.59 sec (Prowell et al., 2008).



The model was subjected to the same ground motions as the shake table test corresponding to

the results presented in Prowell et al. (2008), 143% of the east-west component of the 1992 strike-

slip Landers Earthquake. Recently, Prowell et al. (2009) have also presented results for the 100%

and 200% level of the Landers earthquake, but the analyses in this section were compared to the

2008 publication. The ground motion record, obtained from the US Geological Survey database,

was 80 sec long and the analyses had an addition 15 sec of free vibration.

Figure 3.24: Details of small wind turbine tested at UCSD

3.8.1 DAMPING IN ANSYS

The basic equation of motion that is solved during a transient dynamic analysis of any implicit

FE solver is expressed as:

( ))t(F)x](k[)x](c[)x](m[ =++ &&& (Equation 3.3)

where ]m[ = mass matrix

]c[ = damping matrix

]k[ = stiffness matrix

( ))t(F = dynamic load vector

)x( , )x( & , )x( && = nodal displacement, velocity, and acceleration vectors

6m

6m

6m

1.9m

1.9m

hub height: 22.6m

Top Section D = 1100mm t = 5.3mm

Middle Section D = 1600mm t = 5.3mm

Lower Section D = 1600mm t = 5.3mm

upper joint accelerometer

top of nacelle accelerometer



The damping matrix is generally difficult to evaluate. A common way of defining the damping

matrix is by using Rayleigh damping, which is a linear combination of the mass matrix and the

stiffness matrix using two coefficients, α and β:

]k[]m[]c[ β+α= (Equation 3.4)

The modal damping ratio, ζi, of a mode i can then be expressed in terms of the coefficients α

and β, and the circular frequency, ωi, of that mode as follows:

22i

ii

βω+

ωα

=ζ (Equation 3.5)

The above equation can be solved to obtain the desired damping ratio in two modes by solving

for the coefficients α and β to achieve the specified damping ratios. For subsequent analyses, the

damping value specified is for the first and second modes. However, it should be noted that this

may result in more damping of the higher modes.

3.8.1.1 COMPARISON OF EFFECT OF DAMPING

Based on experimental results, Prowell et al. (2008) calculated the amount of viscous damping to

be between 0.4 and 0.6% of critical for the small wind turbine described above. This is also similar

to the estimated value of 0.5% used by Bazeos et al. (2002) in their dynamic analysis of a wind

turbine. However, industry guidelines suggest the use of 1% of critical damping (IEC, 2005).

Several analyses were carried out with damping ratios tuned to the first and second modes at

0.5%, 1%, and 1.5% of critical. The FEA results and the experimental results are plotted in Figure

3.25 and Figure 3.26 for the acceleration at the top of the nacelle and at the upper joint, respectively,

for the first 20 sec of the earthquake. This duration was chosen to allow for comparison with the

results presented in Prowell et al. (2008). The duration of the earthquake record was 50 sec, and the

analysis was continued for an additional 15 sec to allow the tower’s vibrations to stop. Some results

of the time-history analyses with various damping values are listed in Table 3.3.

Table 3.3: Summary of results of time-history analyses for the UCSD tower comparing different damping values

Peak Displacement

Peak Stress

Residual Deformation

Damping

Ratio ∆max (% H) σmises (MPa) ∆res (% H)

Peak Acceleration at Hub Height**

0.5% 0.26 % 93 0.03 % 0.71g 1.0% 0.23 % 80 0.02 % 0.59g 1.5% 0.17 % 63 0.02 % 0.46g

** peak acceleration occurred after 20 sec and is not shown in Figure 3.25



-0.6

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Accelerationat Top

(g)

Recorded Experimental Values0.5% damping

-0.6

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Accelerationat Top

(g)

Recorded Experimental Values1% damping

-0.6

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Accelerationat Top

(g)

Recorded Experimental Values1.5% damping

Figure 3.25: Acceleration at top of nacelle for the reference earthquake for various damping ratios

(a) 0.5% damping (b) 1.0% damping (c) 1.5% damping

(a)

(b)

(c)



-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Accelerationat Upper Joint

(g)Recorded Experimental Values

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)


(g)0.5% damping

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)


(g)1% damping

-0.4

-0.2

0

0.2

0.4

0 2 4 6 8 10 12 14 16 18 20

Time (s)


(g)1.5% damping

Figure 3.26: Acceleration at upper joint for the reference earthquake for various damping ratios

(a) recorded experimental values (b) 0.5% damping (c) 1.0% damping (d) 1.5% damping

(a)

(b)

(c)

(d)



The agreement between the FE results and the experimental results is reasonable, considering all

the modelling assumptions – uniform distribution of additional mass, no modelling of the blades,

rigid fixity at the base. Prowell et al. (2008) presented better agreement in their publication from a

numerical model wherein the parked blades were included using beam elements, thus it is believed

that modelling the blades changed the higher mode influence and thus affected the response of the

upper joint, which is dominated by the higher modes. However, no details of the blades were

available, thus the influence of the blades cannot be assessed.

For the acceleration at the top of the nacelle (Figure 3.25), it appears that the experimental

results have a higher frequency content than the FE results for any level of damping. Furthermore,

while many peaks are captured, several peaks are not, and it appears that the lower damping value of

0.5% captures the peaks slightly better than the analyses with higher damping.

For the acceleration at the upper joint (Figure 3.26) the frequency content of the FE results

appears to be very similar to that of the experimental results. However, the experimental results

seem to be more muted, thus the higher damping value of 1.5% provides the response that is closest

to experimental results. It appears that even higher damping may produce a better response.

The response at the nacelle is closer to experimental results for a lower damping ratio, but the

response at the upper joint is closer to experimental results for a higher damping ratio. Thus, the

damping value of 1% of critical was chosen for further analyses, as a compromise between the

nacelle response and the upper joint response.

3.8.1.2 AERODYNAMIC DAMPING

During operation, the total damping of the wind turbine is increased, as the aerodynamic

damping experienced by the wind turbine is around 5% (Witcher, 2005). However, this thesis only

analyses a parked wind turbine, thus aerodynamic damping is ignored.

3.8.2 INCREMENTAL NONLINEAR ANALYSIS

The reference earthquake (143% of the east-west component of the 1992 strike-slip Landers

Earthquake) caused a peak relative displacement of 51 mm in the wind turbine and a maximum

stress of 80 MPa. As such, it was safely below yield. For the incremental analyses, the acceleration

of the reference earthquake was magnified by factors of 4, 8, and 10. A summary of results is

presented in Table 3.4 and the displacement response is shown in Figure 3.27.



Table 3.4: Summary of results of incremental time-history analyses for the UCSD tower

Peak Displacement

Peak Stress

Residual Deformation Magnification

Factor ∆max (% H) σmises (MPa) ∆res (% H)

Peak Acceleration at

Hub Height 1 0.23 % 80 0.02 % 0.59g 4 0.88 % 173 0.02 % 2.24g 8 2.22 % 406 0.32 % 2.79g 10 6.07 % 784 3.43 % 3.15g

Figure 3.27: Displacement response of incremental time-history analysis of small wind turbine

The response increased linearly up to the analysis with a magnification actor of 4. At a

magnification factor of 8, the response showed some non-linear behaviour and the wind turbine

tower remained slightly off-centre. At a magnification factor of 10, the tower experienced severe

yielding, buckled just above the lower joint, and was left with large residual deformation.

3.8.2.1 FAILURE MODE

At the magnification factor of 8, the tower was already showing signs of large ovalisation just

above the lower joint. The tower was thus expected to buckle at that location in subsequent

analyses. Moreover, the tower wall at that location had a significant angle change which is likely to

attract a buckling failure to that location. This was indeed found to be the case, as the tower

buckled at that location during the analysis with a magnification factor of 10. The buckled shape is

shown in Figure 3.28.



Figure 3.28: Buckled shape of UCSD wind turbine tower – analysis at a magnification factor of 10

3.9 SUMMARY

The finite element decisions described in this chapter have been validated and shown to capture

several behaviours that are essential to the analysis of a thin-walled steel wind turbine tower.

Geometric and material nonlinearities were incorporated, and the elements chosen were shown to

adequately represent the expected behaviours. Mesh sensitivity studies were carried out on fully

nonlinear models to determine that a ratio of element size-to-thickness of less than or equal to 12 is

required for areas where local buckling may occur, but that this ratio can be much higher in other

areas. Refinement of the mesh was found to be acceptable, but care must be taken that the

transition zone between mesh sizes does not affect the failure.

Comparison of one FE model for pure flexure with an experimental specimen suggested that the

FE analysis slightly over-estimated the peak capacity in flexure. However, the response path was as

expected and the failure mode was captured very closely. Comparison of geometrically-identical

models with different material properties showed that the numerical analysis is very much dependant

on the nonlinear material properties. Gradual yielding material properties were chosen for

subsequent analyses as they are considered representative of cold-rolled plates, as would be used in a

typical wind turbine tower.



Axial compression analyses did not exhibit the expected behaviour. Despite employing Class 4

sections, local buckling did not occur before global buckling, but this shortcoming is not critical,

however, because axial loading is not expected to be a major component of the seismic response.

Local imperfections were included in some of the validation analyses to assess their effect on the

response. For the flexural analyses, the addition of local imperfection was insignificant for the Class

4 section and produced a response curve for the Class 3 section that was not similar to experimental

results. For the axial buckling analysis, the addition of local imperfections was still unable to

produce local buckling. Thus, it was not deemed worthwhile to include them in the full wind

turbine tower model.

Lastly, time-history analysis of a small wind turbine tower was carried out and compared with

experimental results from a shake table test. The effect of damping was compared, incremental

analysis was carried out until the tower buckled, and the failure mode captured was as expected.

Thus the time-history analysis method in ANSYS was deemed adequate.

The following chapter employs these findings to create a finite element model of the wind

turbine tower, which is subjected to some preliminary analyses before the nonlinear time-history

analysis is carried out.


CHAPTER 4: PRELIMINARY ANALYSIS OF VESTAS WIND

TURBINE TOWER

4.1 STRUCTURE CHARACTERISTICS

4.1.1 DIMENSIONS AND DETAILS

The 1.65 MW Vestas wind turbine tower that is studied in this thesis is composed of 4 sections

made up of smaller pieces welded together. The height of the tower is 78.23 m and the hub height

is 80 m. Figure 4.1 and Figure 4.2 show the base details and tower geometry (diameter, thickness,

and length of all the pieces), respectively. The plastic moment is also shown and is based on average

section properties. It should be noted that the plastic moment of piece 2 of section 1 is somewhat

different in actuality due to the thickened door wall and the door itself. Furthermore, Figure 4.3

shows the D/t ratio along the height of the tower and the class of each segment, based on an

assumed Fy = 389 MPa. The nominal yield stress of the ASTM A709 steel is 50 ksi or 345 MPa, so

this assumed yield stress is realistic. The bottom 17.5 m of the Vestas tower is Class 3 and the rest of

the tower is Class 4 (CSA, 2009b).

4.1.1.1 DISCONTINUITIES

There are several discontinuities in the wind turbine tower. Some discontinuities are accounted

for in the FE model while others are not. The wind tower experiences changes in thickness along

the height. In actual towers, these changes are gradual, because the weld between each section is

specified to have a 1:4 slope (Vestas, 2006). In the FE model, this weld slope is not modelled.

Furthermore, the structure has two openings at the base: a door and a cable hole. The finite element

implemented herein leaves holes in the tower shell where the actual door and cable holes occur.

These details are shown in Figure 4.1 and are included in the model. The door section covers 1/6 of

the tower’s circumference and is 50 mm thick – about twice as thick as the rest of the wall at that

height in the tower. The bottom section, where the cable hole is located, is already quite thick

(35 mm) and there is also a lip around the hole. It is important to include these details, as they are

discontinuities and thus a source for stress concentrations.

CHAPTER 4: PRELIMINARY ANALYSIS OF VESTAS WIND TURBINE TOWER


(a) (b) (c)

Figure 4.1: Details at base of Vestas wind turbine tower (a) front view / door (b) side view door (c) back view / cable hole



.

Figure 4.2: Wind turbine tower dimensions and layout (Vestas, 2006)

11 2000 18 42600

10 1441 14 39200

9 1442 10 29400

8 2318 10 31400

7 2311 11 37200

4 6 2305 11 40000

5 2299 11 42900

4 2293 12 50000

3 2286 12 53400

2 2280 12 56800

1 2359 13 65400

9 2460 13 67300

8 2480 13 67300

7 2480 13 67300

6 2480 13 67300

3 5 2480 13 67300

4 2480 14 72500

3 2480 14 72500

2 2480 15 77700

1 2580 16 82900

4 2535 16 82900

2 3 2480 17 88100

2 2480 17 88100

1 2585 18 93200

9 2480 19 98400

8 2480 19 98400

7 2480 20 103600

6 2480 21 108800

1 5 2480 21 108800

4 2967 22 114000

3 2968 23 119100

2 2980 24 124300

1 1101 35 181300

78230 2282

76230 2650

74789 2718

73347 2786

71029 2895

68718 3004

66413 3112

64114 3220

61821 3328

59535 3436

57255 3543

54896 3650

52436

49956

47476

44996

42516

40036

37556

35076

32496 3650

29961

27481

25001

22416 3650

19936

17456

14976

12496

10016

7049

4081

1101

0 3650

height from Dm piece

base (mm) (mm) length (mm)

thickness (mm)

Mp (kNm) piece section



0

10

20

30

40

50

60

70

80

0 50 100 150 200 250 300

D/t ratio


Figure 4.3: D/t ratio of Vestas wind turbine tower sections along the height

with CSA (2009b) cross-section classification in bending

4.1.2 MASS

The mass of the Vestas wind turbine tower is summarized in Table 4.1. The tower mass is

computed by ANSYS based on the geometry and a density of steel of 7850 kg/m3. This value is

slightly greater than the hand-calculated value due to the slight overlap of solid and shell elements

discussed in Section 3.4.3. The nacelle and rotor masses are added as concentrated mass elements at

the hub height of 80 m. The centre of mass of the tower is at 52.73 m above the base.

Table 4.1: Mass of Vestas wind turbine tower

Component Mass (tonnes) Tower * 120 Nacelle 52 Rotor ** 43 Total 215 * tower mass: 113 tonnes specified in Vestas Specs 119 tonnes calculated by hand 120 tonnes computed by ANSYS ** rotor mass has 3.447m eccentricity from centreline of tower

class 3 class 4



4.1.3 MODE SHAPES

Modal analysis of the Vestas wind turbine tower revealed that the fundamental period was fairly

long, 3.17 sec, and had a modal mass ratio of 65%. The predominant period of typical earthquakes

(further discussed in Section 5.1) is approximately 0.3 sec. Figure 4.4 shows the first 3 modes of the

structure in the horizontal direction perpendicular to the rotor, and describes some of the modal

properties.

0

10

20

30

40

50

60

70

80


Figure 4.4: Mode shapes of Vestas tower in horizontal direction

4.1.4 DAMPING

As discussed in Section 3.8.1, the damping of the wind turbine tower was estimated to be 1% of

critical in the first and second mode. The damping is specified in ANSYS using Rayleigh damping,

which was also discussed in Section 3.8.1.

4.2 FINITE ELEMENT MODEL OF VESTAS WIND TURBINE TOWER

The Vestas wind turbine tower FE model was based on the validation models discussed in the

previous chapter. The flanges were made of 20-noded solid elements and the wall was made of 8-

noded shell elements. All nodes at the base were connected to one point at the origin using rigid

link elements. The nodes at the top were all connected to one point at the hub height (80 m), where

there was also a concentrated mass element representing the nacelle mass. This point was then

Modal Modal Participation Mass Period Factor Ratio

Mode 1 3.17 s 11.81 65% Mode 2 0.38 s 5.58 14% Mode 3 0.15 s -3.22 5% * modes normalized to mass matrix ** modes of horizontal direction perpendicular to rotor



rigidly connected to another point mass at the same height, but 3.447 m away from the centreline of

the tower. This point represented the rotor mass and is shown at the top of Figure 4.5.

The mesh of the tower had an aspect ratio of 1 for the bottom section of the tower. Above the

bottom section, the aspect ratio was 3, but the mesh was refined as it approached the flanges such

that the ratio would be 1 near the flanges. The mesh had a highly variable element size-to-thickness

ratio (se/t) due to the variation in thickness. The mesh is shown in Figure 4.5, along with the

approximate se/t and the aspect ratio along the height. The element size was taken as the smaller

dimension of the elements. The element size-to-thickness ratio at the base was slightly higher than

the ratio decided upon in the previous chapter, but it was verified that this mesh was still able to

capture the desired buckling behaviour of the tower.

The material properties employed for the subsequent analyses are those having gradual yielding,

as discussed in Section 3.3.



Figure 4.5: Mesh of Vestas wind turbine tower

se/t se/t

11 11

16 16

24

24

23

24

25

23

24

25

24

24

24

24

24

24

24

24

23 23

23

21 21

20

20 20

19 19

19

18 18

17 17

17

16

15 15

15

14

14 13

13

9 9

aspect ratio ≈ 1

aspect ratio ≈ 2

aspect ratio ≈ 1

aspect ratio ≈ 3

aspect ratio ≈ 3

aspect ratio ≈ 1

aspect ratio ≈ 1

rotor mass element nacelle mass element



4.3 PUSHOVER ANALYSIS

4.3.1 BACKGROUND

Pushover analysis is a simplified inelastic analytical procedure that was developed to estimate the

seismic response of structures. Elastic analysis does not accurately predict forces and deformations

after a structure begins to be damaged during an earthquake. Inelastic time-history analysis is

considered one of the most realistic analytical approaches to evaluate the performance of a structure

during seismic activity, but it is also very complex and time-consuming (Tso and Moghadam, 1998).

Thus, pushover analysis was developed as the compromise between the two. There are several uses

for pushover analysis: to identify regions where inelastic deformations are expected to be high, to

identify strength irregularities, to obtain realistic estimations of force demands, to predict the

sequence of failure of the structural components, and to determine the capacity curve of the

structure (Antoniou and Pinho, 2004). There are also several interpretations on how to carry out

this type of analysis.

The conventional method is to apply and monotonically increase a predefined lateral load

pattern. This pattern is kept constant throughout the analysis. This procedure has been criticized

for certain limitations, such as its inability to account for the progressive stiffness degradation, which

leads to a significant increase in the period of the structure and in its modal characteristics.

Furthermore, it has been shown that deformation predictions can be quite inaccurate if higher

modes are important or if the structure is loaded heavily into the non-linear post-yield range

(Antoniou and Pinho, 2004). Another problem with conventional pushover analysis is that it does

not account for all sources of energy dissipation associated with a dynamic response, since it is a

static method. Only material straining is captured, while kinetic energy, viscous damping, and

duration effects are neglected.

Attempting to overcome these limitations, several pushover methods considering higher mode

effects have been developed: multi-modal pushover (MMP) (Sasaki et al., 1998), pushover results

combination (PRC) (Moghadam, 2002), modal pushover analysis (MPA) (Chopra and Goel 2002),

consecutive modal pushover (CMP) (Poursha et al., 2009). All the aforementioned higher mode

methods require several pushover analyses to be carried out corresponding to the different modes,

and then combine the results.

There are also a few methods that take the higher modes into account by determining an

invariant load pattern based on the higher mode shapes. The upper-bound pushover analysis

procedure (Jan et al., 2004) determines the load pattern by combining the first two modes based on



their modal participation factors, and the design elastic displacement response spectrum.

Furthermore, the method of modal combinations (MMC) (Kalkan and Kunnath, 2004) is similar to

the upper-bound method, but allows the inclusion of more modes and uses the elastic acceleration

spectrum. The simplest multimode load pattern is described by Barros and Almeida (2005) and is

obtained by the linear addition of the desired number of mode shapes scaled by their respective

modal participation factors.

The methods discussed above that take into account higher mode effects do not consider

damage accumulation and the resulting modification of the modal parameters. This has led to the

development of many fully adaptive methods, where the load distribution changes as the structure is

deformed. Unfortunately, many of these methods have been shown to provide only a slight increase

in accuracy, while demanding huge computational efforts (Antoniou and Pinho, 2004). At this level

of complexity and computational demand, it has been argued that it may be easier and more accurate

to carry out a non-linear time history analysis.

4.3.2 PUSHOVER ANALYSIS OF WIND TURBINE TOWER

Most of the pushover procedures discussed, even the conventional ones, have been developed

and validated for buildings and bridges. None have been tailored for a structure similar to a wind

turbine tower. As such, a very complex pushover analysis was not carried out. Instead, a multimode

load pattern (Barros and Almeida, 2005) was used to determine the capacity of the tower and to get

a rough idea of how the wind turbine tower structure behaves. The load pattern consisted of a

linear combination of the first three modes in the horizontal direction, as follows:

iiLP ϕα∑= (Equation 4.1)

where LP = load pattern

iα = modal participation factor of mode i

iϕ = mode shape of mode i, normalized to mass matrix

The resulting load pattern using the first three modes in the horizontal direction is shown in

Figure 4.7. The resultant of this force pattern acts at 45.9 m above the ground. The pushover

analysis was carried out at 22.5° intervals around the circumference of the tower (Figure 4.6) to

determine the weakest angle of incidence. Additionally, a pushover analysis was carried out without

modelling the door and cable hole at the bottom of the tower to determine if those details are

indeed necessary in the model of the Vestas wind turbine tower.



Figure 4.6: Direction of pushover analyses

Figure 4.7: Multimode load pattern for pushover analysis of Vestas wind turbine tower

4.3.2.1 IMPOSED IMPERFECTIONS

No data was available on actual imperfections from a wind turbine tower, thus no local or global

imperfections were added. The eccentricity of the rotor combined with the discontinuities in the

tower create some asymmetry, which is enough to trigger a failure.

Due to the variations in thickness and diameter along the tower’s height, the addition of local

imperfections would have entailed a lot of guesswork and could have caused a failure in a fictitious

location. It also could have generated an unrealistic response curve, as was the case for the

validation models discussed in Section 3.6.2.3. Based on those validation models, it is acknowledged

that not adding local imperfections may result in an over-prediction of the peak load of about 5%.

0°

22.5°

45°

67.5° 90°

112.5°

135°

157.5°

180°

door cable hole

X

Z



0

30000

60000

90000

120000

Base Moment(kNm)

4.3.3 RESULTS OF PUSHOVER ANALYSIS

The capacity curve (total load vs. top displacement) of the pushover analysis at 0° with gradual

yielding material properties is shown in Figure 4.8 and the failure mode is shown in Figure 4.9. The

peak resultant force that the tower could sustain was 2544 kN, corresponding to a base moment of

116.9 MNm. The failure consisted of buckling of the tower wall immediately above the door

section, the latter being much thicker than the surrounding tower wall. The capacity curve of the

same analysis but with material properties having a yield plateau is also shown in Figure 4.8. As with

the validation analyses, the peak capacity is reduced slightly, but the overall response of the tower is

very similar.

The capacity curve at the other angles of incidence was very similar to that at 0°, but the peak

load varied slightly. This variation is shown in Figure 4.10, and the variation of top displacement at

the peak load is shown in Figure 4.11. The lowest peak load is achieved when the angle of incidence

is 22.5°, followed by 45°. This is believed to be the case because the compression side is very close

to the corner of the thickened tower door section, so stress concentrations for those analyses are

almost exactly at the location where the buckle forms, thereby causing failure earlier than when the

tower is pushed in any other direction.

0

500

1000

1500

2000

2500

3000

0 2000 4000 6000 8000

Top Lateral Deflection (mm)

Total LateralLoad (kN)

Figure 4.8: Load-displacement curves for pushover analysis at 0° for material properties

with gradual yielding and with yield plateau

Mp

My

Material Properties: gradual yielding yield plateau



109000

113000

117000

121000Peak Base

Moment (kNm)

Figure 4.9: Buckled failure of Vestas wind turbine tower subjected to pushover analysis at 0°

2350

2450

2550

2650

0 22.5 45 67.5 90 112.5 135 157.5 180

Angle (deg)

Peak LateralLoad (kN)

Figure 4.10: Peak load for pushover analysis acting at various angles

3000

3500

4000

4500

0 22.5 45 67.5 90 112.5 135 157.5 180

Angle (deg)

Top Displacement at Peak Load

(mm)

Figure 4.11: Top displacement at peak load for pushover analysis acting at various angles

The analysis without the door and cable hole reached a peak load of 2630 kN at a displacement

of 4180mm, and also had a similar response curve to the one shown for the pushover analysis at 0°.

However, the failure was at a different location, above the fourth piece of section 1 at 10 m above

the base. Thus, the door and cable hole details were included in subsequent analyses to ensure that

no door or cable hole

no door or cable hole



the location of local buckling failures occurs according to the details of the actual wind turbine

tower.

4.3.3.1 INTERPRETATION OF PUSHOVER ANALYSIS RESULTS

The maximum base moment that can be sustained by the Vestas wind turbine tower before

collapse is 110 MNm, as approximated by the pushover analysis. The theoretically-calculated yield

moment of the section that failed is 93 MNm, and the plastic moment is 119 MNm. Thus, the

moment reached by the tower was 18% higher than the yield moment and 8% lower than the plastic

moment. This behaviour was expected because the bottom 17 m of the tower, which is where the

failure occurred, is Class 3 in bending.

Yielding of the material around the door opening begins at a top displacement of about

1900 mm, and yielding of the tower wall away from the openings begins at a top displacement of

2400 mm. Thus, for subsequent seismic analyses, residual displacements must be evaluated if the

top relative displacement is greater than 1900 mm.

4.4 SUMMARY

The Vestas wind turbine tower was presented in detail and modelling decisions were discussed.

Discontinuities in the tower were considered sufficiently asymmetric to trigger failures in the tower,

and additional imperfections were not added. The tower was subjected to a pushover analysis with a

multimode load pattern, and it was decided to include the door and cable hole details at the bottom

of the tower in order to capture any failure modes that may be affected by those details. The onset

of yielding at a top displacement of 1900 mm (or 2.4% of the hub height of 80 m) suggests that any

seismic excitation that produces a top displacement greater than that value will result in permanent

residual deformations. The following chapter investigates the response of the tower subjected to a

suite of ground motion records and further verifies the conclusions of the pushover analyses.


CHAPTER 5: NONLINEAR TIME-HISTORY ANALYSIS OF THE

VESTAS WIND TURBINE TOWER

The Vestas wind turbine tower was subjected to incremental nonlinear time-history analysis to

assess its response to seismic events. Also know as incremental dynamic analysis (IDA), this type of

analysis is characterized by a suite of earthquake records that represents the seismic hazard in a given

area. The structure is then subjected to increasing intensities of those records until failure is

reached. The earthquake suite employed in this chapter is used to assess the wind turbine tower’s

capacity until failure, to define limit states that describe the state of the structure as it is subjected to

increasing earthquake loads, and to assess the effect of damping and that of the vertical acceleration

component.

5.1 EARTHQUAKE SUITE

The earthquake records considered in the subsequent analyses were strong ground motions from

the Los Angeles (LA) area in California. This area was chosen to investigate the overall response of

the tower because it is highly seismic and has many historical records from which to assemble a suite

of records. A further study on the seismic response of the wind turbine tower in the Canadian

seismic environment is presented in the following chapter.

This suite of earthquakes is representative of earthquakes having a 475-year return period, or a

probability of exceedance of 10% in 50 years. This is typically defined as the design-based

earthquake (ASCE, 2005). The records were taken on firm soil conditions. These strong motion

ground records were developed for the SAC Phase 2 Steel Project (Somerville et al., 1997) with the

intent of providing response spectra and time-histories for use in case studies, trial applications, and

topical investigations.

These ground motion records were originally scaled by various factors in the SAC Phase 2 Steel

Project, and were then further scaled by a factor of 1.1 to match the mean of the earthquake

response spectra to the target spectrum obtained using the procedure prescribed in ASCE/SEI 7

(2005), assuming class D soil. These scaled records are considered the reference earthquakes and are

then magnified by factors of 1.5, 2, 3, etc. until collapse. Due to the damping factor of the target

response spectrum of 5%, the spectra of the earthquake records was also computed using 5%

damping. The acceleration response spectra are shown in Figure 5.1. There is good agreement

between the design response spectrum and the mean response spectrum, with slight deviations in

the constant acceleration period range. The maximum and minimum envelopes are also shown.



The displacement spectra were also computed because the fundamental period, T1, is long, thus

discrepancies between the design spectrum and the mean spectrum are hard to detect on the spectral

acceleration figure. The displacement spectra are shown in Figure 5.2, where it can be seen that the

deviation at the fundamental period is not significant.

The properties of the ground records in this earthquake suite are summarized in Table 5.1, and

the accelerograms of the 20 records are shown in Figure 5.3. The 20 ground motion records are

orthogonal components from 10 earthquakes. Typically, each record is considered independently,

because most buildings have separate orthogonal lateral-load resisting systems. However, the wind

turbine tower is one unit and the response in one direction can affect the response in the orthogonal

direction as well. Thus, ground motions in both orthogonal directions are applied simultaneously.

Table 5.1: Properties of LA earthquake suite records

Name

Record

Magnitude

Distance (km)

Duration (s)

Scale Factor

Predominant Period (s)

Scaled PGA (g)

LA01 0.292 0.507 LA02

Imperial Valley, 1940, Elcentro 6.9 10 53.48 2.211 0.333 0.743

LA03 0.224 0.433 LA04

Imperial Valley, 1979, Array #05 6.5 4.1 39.39 1.111 0.250 0.537

LA05 0.242 0.332 LA06

Imperial Valley, 1979, Array #06 6.5 1.2 40 0.924 0.225 0.258

LA07 0.268 0.463 LA08

Landers, 1992, Barstow 7.3 36 80 3.520 0.283 0.468

LA09 0.261 0.572 LA10

Landers, 1992, Yermo 7.3 25 80 2.387 0.219 0.396

LA11 0.205 0.732 LA12

Loma Prieta, 1989, Gilroy 7.0 12 40 1.969 0.247 1.066

LA13 0.395 0.746 LA14

Northridge, 1994, Newhill 6.7 6.7 60 1.133 0.357 0.723

LA15 0.212 0.587 LA16

Northridge, 1994, Rinaldi RS 6.7 7.5 14.95 0.869 0.205 0.638

LA17 0.311 0.626 LA18

Northridge, 1994, Sylmar 6.7 6.4 60 1.089 0.299 0.899

LA19 0.229 1.121 LA20

North Palm Springs, 1986 6.0 6.7 60 3.267 0.190 1.085



0

1

2

3

4

0 1 2 3 4

Period, T (s)

Spectral Acceleration,

Sa (g)

Figure 5.1: Elastic acceleration response spectra for earthquake suite considered

0

0.03

0.06

0.09

0.12

0 1 2 3 4

Period, T (s)

Spectral Displacement,

Sd (g/s2)

Figure 5.2: Elastic displacement response spectra for earthquake suite considered

Maximum Envelope

Mean of 20 Scaled Records

Minimum Envelope

Design Spectrum

Modal Periods T3 T2 T1

Maximum Envelope


Design Spectrum

Minimum Envelope




Figure 5.3: Accelerograms of 20 scaled ground motion records of the LA earthquake suite



5.1.1 EARTHQUAKE INPUT IN TIME-HISTORY ANALYSES

In the time-history validation analysis of the UCSD wind turbine (Section 3.8), acceleration was

applied directly to the base of the structure in one direction. However, for the Vestas wind turbine

tower, applying the acceleration in two horizontal directions caused severe convergence difficulties.

It was decided to convert the acceleration ground motion records to displacement records by

integrating twice. This displacement was then applied at the base in the x- and the z- directions (the

y-direction is the vertical direction). It was later verified that the acceleration experienced at the base

of the tower was indeed the same as the original accelerogram. At the end of the record, the

analyses were continued for an additional 60 sec of free vibration until the tower’s oscillations

diminished to near zero.

More than 80 analyses were carried out based on various increments of the 10 earthquakes in the

suite. This is discussed further in the next section. Each analysis was carried out by applying two

orthogonal horizontal components. Three analyses included the vertical component to assess its

influence. Six analyses were carried out with varied damping to assess the degree to which the

specified damping values affect the response. The damping of the tower was typically specified at

1% of critical for the first and second modes.

5.1.2 SCALING OF EARTHQUAKE RECORDS

There are concerns about the validity of scaling records because weaker records that have been

scaled up may not be representative of stronger records (Vamvatsikos and Cornell, 2002). However,

scaling ground motion records up or down by manipulating the amplitude of records is not

uncommon in practice or in research, and is increasingly done as incremental dynamic analysis gains

popularity. For this thesis, the accelerograms described in this section were taken as the reference

records. Although initially scaled to match the target spectrum, the records that match the spectrum

are considered to have a magnification factor of 1 when referring to the incremental dynamic

analyses that follow. The reference earthquake was magnified by factors 2, 3, 4, etc., until collapse

was reached. This type of stepped scaling algorithm is not extremely efficient (Vamvatsikos and

Cornell, 2002) as it may result in too many analyses in the linear part of the incremental dynamic

analysis curve and possibly not enough analyses when the structure is nearing collapse. However, it

was employed because of the uncertainty of the response of the wind turbine tower. A magnification

factor of 1.5 was also included in the analysis cases, as it represents the maximum considered

earthquake for the Los Angeles area.



5.2 RESULTS OF LA01 & LA02 (IMPERIAL VALLEY, 1940, ELCENTRO)

Several results were extracted from the incremental time-history analyses. The results from one

earthquake, LA01 & LA02 (Imperial Valley, 1940, Elcentro), are described in detail and are

presented in this section. This includes: a summary of the displacement results of the incremental

analyses, listed in Table 5.2; the displaced shape of the wind turbine tower at various magnification

factors, described and shown in Section 5.2.2; the incremental time-history displacement response,

described and shown in Section 5.2.3; and orbit plots as seen in plan view, discussed and shown in

Section 5.2.4.

Table 5.2: Summary of displacement results of time-history analyses subjected to LA01 & LA02 (Imperial Valley, 1940, Elcentro)

Peak Displacement

Peak Rotation

Peak Stress

Residual Deformation Factor

∆max (% H) θplan θmax σmises (MPa) ∆res (% H) θplan Damage State Reached

1 1.18 % 326° 0.057° 185 0.03 % 332°

1.5 1.63 % 326° 0.077° 253 0.03 % 320° 2 2.06 % 158° 0.091° 305 0.02 % 235°

2.9** 2.80 % 0.123 ° 389 0.02 % 0.2% Residual Out-of-Straightness & First Yield

3 2.92 % 322° 0.128° 400 0.23 % 315° 4 3.56 % 159° 0.167° 438 0.30 % 311°

4.4** 3.80 % 1.524° 521 1.00 % 1.0% Residual Out-of-Straightness 5 4.20 % 160° 3.716° 656 2.14 % 351° First Buckle / Loss of Tower 6 4.57 % 161° 4.135° 753 2.68 % 336° 7 4.99 % 162° 2.533° 750 2.48 % 180°

** interpolated values

The values listed in the table (peak displacement, peak rotation, peak stress, residual

deformation, and damage state) are described in detail in the following subsections. Detailed results

from the other earthquakes are presented in Appendix A, and a summary of all results from the LA

earthquake suite is presented in Section 5.3.

5.2.1 INTENSITY AND DAMAGE MEASURES

The results from an incremental dynamic analysis are typically presented as the damage measure

on the horizontal axis versus the intensity measure on the vertical axis.

The intensity measure is commonly the peak ground acceleration, the peak ground velocity, or

the 5% damped spectral acceleration of the structure’s first-mode period (Vamvatsikos and Cornell,

2002). The intensity measure should be chosen such that the dispersion of all the incremental time-

history analysis curves is minimized. For the earthquake suite used in this chapter, the intensity



measure employed was the magnification factor. Since all the earthquakes were chosen to represent

the design response spectrum, the magnification factor represents the intensity of the ground

motion with respect to the intensity of the design-based earthquake. Other intensity measures

investigated were the peak ground displacement, the peak ground velocity, and the peak ground

acceleration. The IDA curves employing all of these intensity measures are included in Appendix A,

Section A.10. It was found that the dispersion of the curves was smallest when the magnification

factor was used as the intensity measure, followed closely by the peak ground velocity.

The damage measure is typically the peak roof drift of a structure or its peak interstorey drift

angle (Vamvatsikos and Cornell, 2002). Several damage measures were considered: the peak

displacement, the peak rotation, and the residual displacement. These damages measures are

discussed below. Along with the peak stress, these damage measures constituted the results that

were obtained from the analysis and are presented in tabular format for all earthquakes.

5.2.1.1 PEAK DISPLACEMENT

For each analysis, the displacement at hub height (80 m) in the three orthogonal directions (x, y,

and z) was obtained for each time increment throughout the analysis. The resultant displacement

was computed based on the two lateral displacements, and the maximum displacement was thus

obtained for each analysis. The peak displacement (∆max) is described as a percentage of the hub

height and the angle of the wind turbine tower in plan view (θplan, shown in Figure 5.4). This angle

should not be confused with the angle of incidence employed in the previous chapter, where an

angle of incidence of 22.5° (equivalent to θplan=22.5° and θplan=337.5°) was found to be the weakest

direction of the tower. However, the angle of the tower in plan view was included in the results to

determine if there is a weaker direction.

Figure 5.4: Top view of tower showing definition of angle in plan view

door cable hole

X

Z

θplan



5.2.1.2 PEAK ROTATION

The rotation of the beam, θ, was computed at a specific time through the analysis, typically at the

time the peak displacement occurred. Initially, the rotation of the beam was computed at several

instances, but it was found that the peak rotation always occurred simultaneously with the peak

displacement if the tower buckled prior to the peak displacement occurrence.

To calculate the rotation, the displacement of the wind turbine tower was obtained at 33

elevations along its height. These elevations correspond to the dividing lines between the pieces of

the tower as described in Section 4.1.1. It is important to note that the distance between each point

is not the same. However, in the area of the tower that governs the peak rotation (from 1.1 m to

54.9 m in height), the average of this distance is 2.56m, and the minimum and maximum values are

2.46 m and 2.98 m, respectively. Thus, measuring the rotation of the tower based on these segments

is adequate. Furthermore, the displacement of the tower at each location along the height was taken

as the average of 12 evenly spaced points around the circumference at that elevation. This ensured

that the deformed shape represented the centreline of the tower and was not influenced by any

ovalisation that may have occurred.

The angle of each segment with respect to the vertical was determined. For the analyses where

the tower did not buckle, the peak rotation was computed as the greatest difference in this angle

between two adjacent segments. Figure 5.5 (a) shows the peak displaced shape for the IDA with a

magnification factor of 2, and it is evident that the transition between each segment is smooth and

thus the peak rotation was small. For the analyses where buckling did occur, the segments used to

determine the rotation are not adjacent, as the rotation of the segments very close to the buckle was

not considered accurate due to ovalisation of the tower and flattening on the tower wall on the side

opposite the buckle. Two or three segments were thus ignored. Two segments were ignored if the

buckle occurred exactly at the joint between two segments, while three segments were ignored if the

buckle occurred within one segment. For the IDA with magnification factor of 5, which had the

displaced shape at the peak rotation as shown in Figure 5.5 (b), three segments were ignored because

the buckle occurred within one segment, and the two above and below it were also influenced by the

effects described above. The two segments used to calculate the rotation are shown with a thick line

in the figure.



0

10

20

30

40

50

60

70

80

0 1 2

Lateral Displacement (m)

Height above Base (m)

0

10

20

30

40

50

60

70

80

0 1 2 3


Height above Base (m)

(a) (b)

Figure 5.5: Displaced shape of wind turbine tower used to determine the peak rotation for LA01 & LA02 (Imperial Valley, 1940, Elcentro)

(a) magnification factor 2 (b) magnification factor 5

5.2.1.3 PEAK STRESS

The peak stress listed is the peak Von Mises stress (σmises). Although this is not one of the

damage measures, it is included in the results summary tables because it indicates how much the

material has yielded. Prior to buckling, the peak stress typically occurs at the side of the door hole

opening on the inside of the tower. In the incremental analyses where the tower buckles, the peak

stress is typically at the location of the buckle.

height of

buckle

peak rotation, θmax



5.2.1.4 RESIDUAL DEFORMATION

The residual deformation (∆res) at hub height is stated as a percentage of the hub height and the

angle in plan view. As with the peak displacement, the angle in plan view of the residual

deformation was obtained and investigated to see if a particular direction typically sees the most

deformation.

In most cases, there was a small residual displacement even after analyses where the peak stress

does not exceed the yield stress of the material (Fy = 389 MPa). This occurs because the stress-

strain curve is slightly curvilinear until yield, as discussed in Section 3.3, due to the material

properties being similar to those of a cold-formed tubular member.

5.2.2 DISPLACED SHAPE

The displaced shapes of the wind turbine tower for all the incremental analyses for LA01 and

LA02 (Imperial Valley, 1940, Elcentro) are shown in Figure 5.6 (a) and (b) for the peak displacement

and the peak rotation, respectively. Typically, the peak displacement and rotation occur at the same

time. However, for this earthquake, the analyses with magnification factors 5 and 6 developed a

buckle some time after the peak displacement occurred, and also at a different location from the

buckle that formed for incremental analysis 7. This is likely due to higher mode effects. Due to this

behaviour, the incremental dynamic analysis curve for this earthquake (shown in Figure 5.10 along

with all of the earthquake curves) is not typical of the rest of the earthquakes, as it displays weaving

behaviour, where there is successive softening and hardening in the response of the tower as the

initial accelerograms are scaled up. Vamvatsikos and Cornell (2002) discussed this type of response

and noted that it is not only the intensity of the earthquake that influences the response, but also the

pattern and the timing of the earthquake. However, it was not expected that the wind turbine tower

would exhibit this behaviour, considering that its response is almost linear until failure. This was the

only earthquake for which the wind turbine tower behaved in this manner.



0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7

0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7

(a) (b)

Figure 5.6: Displaced shape of wind turbine tower at various magnification factors for LA01 & LA02 (Imperial Valley, 1940, Elcentro)

(a) at peak displacement (b) at peak rotation

The buckled shape of the wind turbine tower is shown in Figure 5.7 (a) and (b) for magnification

factors 5 and 7, respectively, at the time the peak stress was experienced. The buckled shape for

magnification factor 6 is not shown because it is very similar to that of magnification factor 5. The

global view of the tower in those figures is the side view of the buckled shape and not the side view

of the tower (as it was referred to in Section 4.1.1.1). The buckled shape appears very similar to the

buckle failures observed in the validation analyses and is very similar between all earthquakes. Thus,

the buckled shape is not shown for all analyses.



Figure 5.7: Bucked shape of Vestas wind turbine tower analysis for

LA01 & LA02 (Imperial Valley, 1940, Elcentro) (a) magnification factor 5, t = 44.64 s (b) magnification factor 7, t = 56 s

5.2.3 TIME-HISTORY DISPLACEMENT RESPONSE

The time-history displacement response of the Vestas wind turbine tower at hub height (80 m)

in orthogonal horizontal directions (x and z) is shown in Figure 5.8 (a) and (b) for the x- and z-

directions, respectively, for magnification factors 4 to 7. The response of the tower was fairly linear

up to the magnification factor of 4, thus the response for factors 1 to 3 are not plotted. For some

analyses, the response is linear up to a different magnification factor, thus the time-history

displacement response figures are not of the same factors for all earthquakes. It is apparent from

this figure that the failure of incremental analysis 7 was different from that of analysis 5 and 6, as the

buckle forms in the opposite x-direction. Once again, this behaviour is not typical, and the failures

side view front view opposite side view

(a)

(b)

side view front view opposite side view



of incremental analyses typically propagate in the same direction as the magnification factor is

increased.

Figure 5.8: Incremental time-history displacement response of Vestas wind turbine tower

subjected to LA01 & LA02 (Imperial Valley, 1940, Elcentro) at hub height (a) x-direction response for magnification factors 4 – 7 (b) z-direction response for magnification factors 4 – 7

5.2.4 ORBIT PLOTS

The orbit plots in the x-z plane for all magnification factors for LA01 & LA02 (Imperial Valley,

1940, Elcentro) are shown in Figure 5.9 (b) to (j). Figure 5.9 (a) shows the orientation of the tower

in plan view and the legend describing the stages in the orbit plots. The orbit plots differentiate

between the pre-peak, post-peak, and free vibration stages of the analysis, and the maximum

displacement is also indicated. The orbit plots show that the increase in the response is almost linear

until buckling occurs, as the shape of the orbit plot grows consistently with increasing magnification

factors up to buckling, at which point the shape changes drastically. They also show the

predominant direction of the tower’s oscillations. Furthermore, the orbit plots validate the use of

applying the two orthogonal earthquake components simultaneously, as it is apparent that the

tower’s oscillations are not primarily in one direction.

free vibration begins at 53.48s until 120s (not shown to completion)

(a)

(b)




Figure 5.9: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA01 & LA02 (Imperial Valley, 1940, Elcentro)

(a) top view of tower and legend (e) factor: 3 (i) factor: 7 (b) factor: 1 (f) factor: 4 (c) factor: 1.5 (g) factor: 5 (d) factor: 2 (h) factor: 6

door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5

(i) factor: 7

tower buckles

tower buckles



5.2.5 DEFINITION OF DAMAGE STATES FOR WIND TURBINE TOWERS

Limit states are typically defined using prescribed values to ensure safety of occupants and

stability of buildings. However, wind turbine towers do not fall in the same category as buildings, as

they are generally not occupied. Therefore, four damage states were defined instead of limit states

to provide an indication of the damage sustained by the wind turbine tower.

5.2.5.1 0.2% RESIDUAL OUT-OF-STRAIGHTNESS

The acceptable out-of-straightness for wind turbine towers is not well defined, but this value for

other structures varies in Canadian standards between 0.1% (CSA S473, 2004; CSA S16, 2009b) and

0.2 % (CSA S37, 2001). This out-of-straightness is typically defined for erection purposes. As

discussed in Section 5.2.1.4, there is some residual deformation before the yield stress is reached due

to the curvilinear material properties. Thus, an out-of-straightness limit of 0.1% was considered to

be too severe.

For this thesis, a residual out-of-straightness of 0.2% was taken as the first damage state. Linear

interpolation between the two analyses that enveloped a residual displacement of 0.2% of hub height

was carried out to determine the damage and intensity measures at this damage state.

5.2.5.2 FIRST YIELD

Linear interpolation between the two analyses that enveloped a peak yield stress, Fy = 389 MPa,

was carried out to define the values of the second damage state.

5.2.5.3 1.0% RESIDUAL OUT-OF-STRAIGHTNESS

Yielding of the tower typically falls within the 0.2% residual out-of-straightness (the first damage

state) and 1.0% residual out of straightness. Due to the uncertainty of the material properties of the

wind turbine tower, this damage states was investigated as well. Similar to the previous two damage

states, linear interpolation was employed to obtain the values that define 1% residual out-of-

straightness.

5.2.5.4 FIRST BUCKLE / LOSS OF TOWER

The last damage state corresponds to the first incremental analysis where the tower buckles.

The wind turbine tower is considered as a complete loss after this damage state is reached, given the

fact that the sections comprising the tower are class 3 or class 4. However, the tower is likely still

standing after the first buckle is formed. For this damage state, there is no linear interpolation, and



the lowest magnification factor that produced the buckling of the tower defined the intensity and

damage measures of this damage state.

Some of the incremental analyses were continued past the last damage state and a few buckled

very severely. The FE model was able to capture buckling failure for all of the earthquakes,

indicating a robust model.

5.3 SUMMARY OF RESULTS FOR LA EARTHQUAKE SUITE

Detailed results for each earthquake are provided in Appendix A. This section presents the

incremental dynamic analysis curves and the average damage measure for all the damage states, as

well as the location of the buckle along the tower height. The method for deriving a fragility curve

is outlined, and fragility curves are created for the LA earthquake suite. Also discussed in this

section is the effect of the vertical earthquake component, the effect of damping on the response of

the tower, and a validation of the modelling decisions for the bolted flange connections of the wind

turbine tower.

Furthermore, analysis of the results of the LA earthquake suite suggests that there is no pattern

in the angle of the tower in plan view for either the peak displacement or the residual displacement.

Thus, for subsequent analyses, these values will not be investigated.



5.3.1 INCREMENTAL DYNAMIC ANALYSIS CURVES

The incremental dynamic analysis curves for all earthquakes are shown in Figure 5.10. The IDA

curves were shown for three different damage measures: the peak displacement, the peak rotation,

and the residual displacement.

0

1

2

3

4

5

6

7

8

0 5 10 15Peak Displacement (% H)

Mag

nific

atio

n Fa

ctor

LA01 & LA02 (Imperial Valley, 1940, Elcentro)

LA03 & LA04 (Imperial Valley, 1979, Array #05)


LA07 & LA08 (Landers, 1992, Barstow)

LA09 & LA10 (Landers, 1992, Yermo)

LA11 & LA12 (Loma Prieta, 1989, Gilroy)

LA13 & LA14 (Northridge, 1994, Newhill)

LA15 & LA16 (Northridge, 1994, Rinaldi RS)

LA17 & LA18 (Northridge, 1994, Sylmar)

LA19 & LA20 (North Palm Springs, 1986)

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5Peak Rotation (°)

Mag

nific

atio

n Fa

ctor

0

1

2

3

4

5

6

7

8

0 1 2 3 4Residual Displacement (% H)

Mag

nific

atio

n Fa

ctor

Figure 5.10: Incremental dynamic analysis curves for three damage measures:

peak displacement, peak rotation, and residual displacement

5.3.1.1 ASSESSMENT OF DAMAGE MEASURES

The peak rotation is a good damage measure because it indicates very clearly when buckling

occurs. Although the response is not entirely linear up to that point, the increase in the peak

rotation once buckling occurs is very drastic in every case.

1st damage state: 0.2% residual out-of-straight 3rd damage state:

1.0% residual out-of-straight



The residual displacement is an important damage measure because it is used to define two of

the damage states. Also, the second damage state, representing the first yield limit, is also easily

identifiable using this damage measure, as those analyses typically have a residual displacement

between 0.2% and 1.0%. Of the three damage measures, the residual displacement has the least

dispersion, which is an important factor.

The peak displacement appears to be the least indicative damage measure. There are a few

analyses where the tower buckled and where the peak displacement IDA curves do not give any

indication of this, depending on the height where the buckle formed.

5.3.1.2 AVERAGE DAMAGE MEASURES

The average damage measures for each damage state for the LA earthquake suite are shown in

Table 5.3, along with the minimum and maximum values of the damage measures. It is apparent

that the spread of the damage measures in any damage state was quite significant.

Table 5.3: Minimum, average, and maximum values of damage measures at each damage state

Damage State

Peak Displacement ∆max (% H)

Peak Rotation θmax

Peak Stress

σmises (MPa)

Residual Displacement ∆res (% H)

0.2% Residual Out-of-Straightness

min: 1.85 % average: 2.50 %

max: 3.02 %

min: 0.089° average: 0.120°

max: 0.142°

min: 228 average: 341

max: 387 0.2 %

First Yield

min: 2.71 % average: 3.01 %

max: 3.46 %

min: 0.124° average: 0.144°

max: 0.163° 389

min: 0.20% average: 0.34%

max: 0.75%

1% Residual Out-of-Straightness

min: 3.71% average: 4.34 %

max: 4.88 %

min: 0.177° average: 0.532°

max: 1.524°


max: 531 1.0 %

First Buckle / Loss of Tower

min: 4.20 % average: 6.23 %

max: 8.23 %

min: 2.46° average: 2.99°

max: 3.72°


max: 743

min: 1.66 % average: 3.74 %

max: 6.22 %

5.3.2 LOCATION OF BUCKLE FOR 4TH DAMAGE STATE

Buckling of the wind turbine tower was expected to occur close to the base of the tower. Based

on the failure of the pushover analysis carried out in the previous chapter, the buckle should form

just above the door section. However, the time-history analyses suggest a different location. The

location of the first buckle is listed in Table 5.4 for the LA earthquake suite, and it is apparent that

the buckle is equally likely to form 10 m above the base, between the fourth and fifth pieces of the

wind turbine tower, and about 43 m above the base.



Table 5.4: Location of buckle for the LA earthquake suite

Earthquake Location of First Buckle

LA01 & LA02 44.9 m LA03 & LA04 10 m LA05 & LA06 10 m LA07 & LA08 10 m LA09 & LA10 4.1 m LA11 & LA12 43.5m LA13 & LA14 10 m LA15 & LA16 42.5 m LA17 & LA18 10 m LA19 & LA20 42.5 m

5.3.3 DEFINITION OF FRAGILITY CURVES

Statistics of incremental dynamic analyses can be used to generate fragility curves, which serve

the purpose of estimating the probability of reaching a defined damage state for a range of intensity

values (Nasserasadi et al., 2008).

The incremental analyses were carried out using linearly increasing magnification factors, as

discussed in Section 5.1.2. As a result, the damage states generally occurred between two particular

incremental analyses. Linear interpolation was thus used to determine the intensity measures at the

first three damage states. For the fourth damage state, which occurred at the first buckling of the

tower, the intensity measures of the analysis wherein buckling first occurred were used to define that

damage state. Table 5.5 lists the intensity measure (IM) when the damage state (DS) of interest was

attained for each earthquake, as well as the mean of the intensity measures for each damage state.

Also listed in the table are the natural logarithms of the intensity measures for each earthquake and

the standard deviation of the natural logarithms for each damage state. These values are calculated

because the fragility curve is characterized by a lognormal distribution and thus employs the mean of

the intensity measures and the standard deviation of the natural logarithms of the intensity measures

(Deierlein et al., 2008).



Table 5.5: Intensity measures (magnification factors) of each earthquake analysis and statistics for all the damage states for the LA earthquake suite

Earthquake IMDS1

ln(IM) IMDS2

ln(IM) IMDS3

ln(IM) IMDS4

ln(IM) LA01 & LA02 (Imperial Valley, 1940, Elcentro)

2.9 1.05

2.9 1.06

4.4 1.48

5 1.61


1.5 0.41

1.7 0.54

3.3 1.21

4 1.39


1.2 0.21

1.5 0.43

3.1 1.13

4 1.39

LA07 & LA08 ( Landers, 1992, Barstow)

1.8 0.58

2.6 0.95

3.7 1.30

5 1.61


2.2 0.78

3.1 1.14

4.5 1.51

6 1.79

LA11 & LA 12 (Loma Prieta, 1989, Gilroy)

3.5 1.25

3.8 1.32

7 1.95

8 2.08


3.6 1.28

3.9 1.35

5.5 1.54

7 1.95


2.7 1.01

3.4 1.23

4.7 1.42

6 1.79


2.4 0.87

2.8 1.02

4.1 1.65

5 1.61


2.7 0.98

4.6 1.53

5.2 1.45

7 1.95

Mean of IM (µ): 2.47 3.03 4.55 5.7 ln(µ): 0.903 1.107 1.515 1.740

Standard Deviation of ln(IM) (σ): 0.324 0.348 0.232 0.236 Summary of Damage States:

DS1: 0.2% residual out-of-straightness DS2: first yield

DS3: 1.0% residual out-of-straightness DS4: first buckle / loss of tower

The first step in generating the fragility curve is to define the statistics of the set of points that

the fragility curve describes. The mean, µ, is the average magnification factor (IM) when first yield is

reached for all earthquakes. As the fragility curve is characterized by a lognormal distribution, the

natural logarithm of the mean, ln(µ), is used in the definition of the fragility curve. Secondly, the

standard deviation, σ, is taken as the standard deviation of the natural logarithms of the

magnification factors. Using these statistics, the following lognormal distribution function defines

the probability that the damage will exceed the damage state at a given intensity measure:

)()ln()ln(21exp

21)|(

0IMdIM

IMIMDSdamagep

IM

−

−=≥ ∫ σµ

πσ (Equation 5.1)

For example, for the second damage state, first yield, the above equation employs 0.348 as the

standard deviation, σ, and 3.03 as the mean, µ. The fragility curve that then emerges from this

equation is shown in Figure 5.11, labeled as the 2nd damage state. The graph can then be used to



determine, for example, that the probability of exceeding first yield during an earthquake with a

magnification factor of 2 (i.e. twice as intense as the design-based earthquake) is 12%.

The fragility curves for the LA earthquake suite are shown in Figure 5.11 for all the damage

states. Considering that a magnification factor of 1.5 represents the maximum considered

earthquake, the fragility curves indicate that the only damage states that may be exceeded during the

maximum considered earthquake are the first damage state, at a probability of 6%, and the second

damage state, at a probability of 2%.

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10Magnification Factor

Pro

babi

lity

of E

xcee

danc

e

Figure 5.11: Fragility curves for LA earthquake suite for magnification factor intensity measure

Fragility curves for other intensity measures were also generated and are shown in Figure 5.12

for the peak ground velocity (PGV) intensity measure and in Figure 5.13 for the peak ground

acceleration (PGA) intensity measure.

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15PGV (m/s)

Pro

babi

lity

of E

xcee

danc

e

Figure 5.12: Fragility curves for LA earthquake suite for PGV intensity measure

1st damage state: 0.2% residual out-of-straightness 2nd damage state: first yield 3rd damage state: 1.0% residual out-of-straightness 4th damage state: first buckle / loss of tower

1st damage state: 0.2% residual out-of-straightness 2nd damage state: first yield 3rd damage state: 1.0% residual out-of-straightness 4th damage state: first buckle / loss of tower 26%

12%



0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15PGA (g)

Pro

babi

lity

of E

xcee

danc

e

Figure 5.13: Fragility curves for LA earthquake suite for PGA intensity measure

5.3.4 EFFECT OF VERTICAL EARTHQUAKE COMPONENT

The vertical earthquake component was included in a few analyses in order to determine the

extent to which it affects the response of the wind turbine tower. The analysis was that of the tower

subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy). The properties of the vertical component

are listed in Table 5.6, along with those of the horizontal components. The peak vertical ground

acceleration is 0.723 g, almost as high as that of one of the horizontal components. Thus, the

vertical component for this particular earthquake record is quite significant.

Table 5.6: Properties of earthquake records for analyses that included a vertical component

Name

Record

Magnitude

Distance (km)

Duration (s)

Scale Factor

Predominant Period (s)

Scaled PGA (g)

LA11 0.205 0.732 LA12 40 0.247 1.066

LA11V Loma Prieta, 1989, Gilroy 7.0 12

1.969

0.101 0.723

Despite including such a significant vertical earthquake component, the response of the tower

was barely affected. This is not surprising, as the normal stress created in the tower’s bottom

section under gravity loads is only 5 MPa. On the other hand, the peak normal stress in the same

section due to bending is 65 MPa for the reference earthquake (magnification factor = 1). The

maximum increase in the normal compressive stress of the elements at the bottom of the wind

turbine tower was 2.2 MPa for the reference earthquake, and 3.5 MPa at a magnification factor of 2.




5.3.5 EFFECT OF DAMPING

The wind turbine tower’s sensitivity to damping was assessed by running the same analysis with

varied damping values: 0.5%, 1%, and 1.5%. The seismic records LA11 and LA12 (Loma Prieta,

1989, Gilroy) were used for this purpose, at magnification factors 1, 2, and 4.

The peak and pre-peak response was not very heavily influenced, especially as the magnification

factor was increased. Table 5.7 presents the percent difference of the peak displacement of the

analyses with 0.5% and 1.5% damping, with respect to the 1% damping. It can be concluded that if

the peak response is the sole interest of a given analysis, then the amount of damping is not

extremely important.

Table 5.7: Variation of peak displacement compared to 1% damping for LA11 and LA12 (Loma Prieta, 1989, Gilroy)

Damping (% of critical) Factor 0.5 1.5

1 6.9% -5.3% 2 2.0% -2.3% 4 0.4% -1.3%

However, the post-peak time-history response of the wind turbine tower is very much

influenced by the amount of damping, as can be seen from the orbit plots in Figure 5.14.

Also investigated was the resulting residual displacement, which was almost identical between

the various damping values, although the analyses with lower damping oscillate for much longer in

free vibration before the tower comes to stillness. Once again, it seems that the damage measure

(residual displacement) is not greatly influenced by the amount of damping, but the path of the wind

turbine tower is significantly different.

Analyses with higher magnification factors were not carried out, but it is expected that the

importance of the damping value becomes even more apparent as the tower yields more severely

and eventually buckles.



Figure 5.14: Orbit in x-z plane (in mm) for varying damping values

of wind turbine tower: 0.5%, 1.0% and 1.5% of critical (a) magnification factor 1 (b) magnification factor 2 (c) magnification factor 4

5.3.6 VALIDATION OF CONNECTION MODELLING

As previously discussed, the bolted connections of the tower sections at the flanges were not

modelled, but the flanges themselves were included in the tower FE model to maintain the stiffness

added to the tower. The flange at the base of the tower need not be investigated, as it provides

many more bolts that are of a larger diameter than those used in the rest of the tower. The top

flange is also not investigated as the stresses are lower and because mechanical loads from the rotor

are assumed to govern. The intermediate flanges, however, are addressed in this section.

The bolts at the intermediate flanges are specified to have a minimum pretension of 510 kN

(Vestas, 2006). Properties of the bolts in the intermediate flanges of the tower are listed in Table

5.8.

(c)

(b)

(a)

door cable hole X

Z



Table 5.8: Properties of bolts used in intermediate flanges of Vestas wind turbine tower

Property Bolt M36, grade 10.9 Bolt diameter 36 mm Area of bolt, Ab 1018 mm2 Yield strength, Fy 940 MPa Tensile strength, Fu 1040 MPa Ultimate bolt capacity, Tu 794 kN

Analysis of the flange was carried out by taking a radial slice of the tower tributary to one bolt, as

shown in Figure 5.15, and then analyzing the slice as an L-flange. The flange was simplified as a

rectangular segment and the length of the flange, Lf, was determined using the diameter of the tower

at the middle of the flange width.

(a) Cross-section of tower (b) Simplified flange geometry

Figure 5.15: Geometry of bolted connection of tower flange

Some of the characteristics of the flange connections are listed in Table 5.9. As the L-flange is

statically determinate, the maximum moment in the flange is easily determined for any applied force

by multiplying it by the distance from the edge of the tower wall to the centre of the bolt. The

deflection of the flange can also be determined approximately using the model of a cantilevered

beam fixed at the centre of the bolt and applying a force at the tip. The separation of the flanges at

the outside of the tower is then twice the calculated deflection, as both flanges would deflect the

same amount. The flange total separation was calculated for a tower wall force of 510 kN (equal to

the pretension in the bolts) and is listed in Table 5.9 for each of the intermediate flanges. It is

important to note that the stress in the tower wall referred to in Table 5.9 is the normal (axial) stress

above or below the flange. This is not the same as the peak stress listed in the results tables for all

the analyses, which usually occurs near the door opening.

wf

Lf

tf

Cross-Section of Tower

Simplified Flange

wf

angle: 360°/(number of bolts)

b



Table 5.9: Characteristics of wind turbine tower flanges

intermediate flange 1



Number of bolts 112 112 84 Length of flange per bolt, Lf 98 mm 98 mm 132 mm Thickness of flange, tf 75 mm 70 mm 55 mm Width of flange, wf 172 mm 171 mm 140 mm Distance from tower wall to bolt, b 56 mm 58 mm 61 mm Amount of separation at bolt pretension force, i.e. applied force of 510 kN 0.08 mm 0.12 mm 0.21 mm

Stress in tower wall to produce a bolt force of 510 kN

(below / above) 262 / 276 MPa 311 MPa 287 MPa

Stress in tower wall to produce bolt tensile failure, Tu = 794 kN

(below / above) 408 / 431 MPa 485 MPa 447 MPa

The pretension of the bolts is exceeded at about the same time that the tower reaches the

second damage state, first yield (where yielding occurs at a stress concentration, not near the

flanges). Thus, any inelastic behaviour in the wind turbine tower will cause the bolt forces to exceed

the bolt pretension and elongate. This implies that any of the incremental analyses with a

magnification factor greater than that corresponding to the second damage state (first yield) may

violate the FE modelling assumption that the flanges remain rigidly connected.

The ultimate capacity of the bolts is never exceeded. At buckling, the peak tensile stress in the

tower above and below the flanges was approximately the yield stress of the material, 389 MPa,

which is lower than the stress in the wall required to produce bolt tensile failure (408 MPa to 485

MPa, see Table 5.9). As the stress above and below the flanges decreases drastically after the

formation of the buckle, the capacity of the connections is not exceeded.

5.4 SUMMARY

The limit states for the wind turbine tower were defined as 0.2% residual out-of-straightness,

first yield, 1.0% residual out-of-straightness, and first buckle. The last damage state, first buckle, was

deemed to result in a complete loss of the tower, because the tower remains with a kink at the

location of the buckle and is severely deformed. Considering these damage criteria, it was decided to

use the magnification factor for the intensity measure. The damage measures of peak displacement,

peak rotation, and residual displacement are maintained for subsequent analyses to be consistent.

Some result parameters were deemed unimportant and are not investigated in the next chapter.

Fragility curves were defined and sample fragility curves were created for the LA earthquake suite.

Some conclusions can be made regarding the behaviour of the tower under seismic loads.

Firstly, it was determined that it is not necessary to include the vertical acceleration component. The



increase in stresses with its inclusion is minimal. Secondly, a damping value of 1.0% for the first and

second modes was determined to be very influential in the post-peak response of the tower, but was

not significant in the peak and pre-peak response. For this thesis, 1% damping is used in

subsequent analysis and is considered adequate, but damping is a significant characteristic of wind

turbine towers that should be investigated and defined more precisely in future studies.

Lastly, the normal stress in the tower wall adjacent to the bolted flange plate connections of the

wind turbine tower was investigated. It was found that the bolt applied load reached the tensile

preload at approximately the same time that the tower first yields (away from flange connections, at

a stress concentration). Also, the ultimate tensile capacity of the bolts only marginally exceeds the

yield capacity of the tower wall at the connections.

Comparison of the nonlinear time-history analyses and the pushover analysis discussed in the

previous chapter indicate that existing pushover analysis methods are not an adequate replacement

for time-history analysis, when it comes to wind turbine towers. The buckle in the time-history

analyses did not form directly above the door section, as it did with the pushover analysis. Thus the

pushover analysis did not capture the correct failure mode. However, the prediction that first yield

would occur at a peak displacement of 2.4% of hub height was reasonable, as the average peak

displacement at which the yield stress was reached for the time-history analyses of the LA

earthquake suite was 3% of hub height.

As the model of the wind turbine tower has been fully validated and the framework set up for

the incremental dynamic analysis of a wind turbine tower, the following chapter applies this

framework to Canadian sites and determines the seismic risk that wind turbines face in Canada.


CHAPTER 6: INCREMENTAL ANALYSIS FOR TWO CANADIAN

SITES

The seismic design provisions of the National Building Code of Canada (NBCC, 2005) are

developed using the Uniform Hazard Spectra (UHS). The UHS represent the spectral acceleration

that has a specified probability of exceedance for each spectral period. Thus, the probability of

exceeding a UHS is constant at all periods (Adams and Atkinson, 2003). The incremental time-

history analyses will start with the reference earthquake that is matched to the spectrum, and will

then be incremented as described in Section 6.3.

In order to assess the seismic response of the wind turbine tower for two Canadian locations, a

suite of earthquakes that are compatible with the NBCC UHS were required. Atkinson (2009)

created a series of simulated earthquake time histories over a range of magnitudes, distances, and site

conditions. There are several sets of time histories for Eastern and Western Canada. The

earthquake time histories are suitable for matching a target UHS for 2% probability of exceedance in

50 years. Atkinson (2009) provides a method of selecting records to create an appropriate suite.

6.1 EASTERN CANADA SITE

A few locations close to Toronto are currently being investigated for wind turbine farm

developments. The site that has the highest seismic risk is on the north shore of Lake Erie, south-

west of Dunnville, Ontario. The UHS for this location was obtained using the online seismic hazard

interpolator from Earthquakes Canada (http://earthquakescanada.nrcan.gc.ca/hazard), a subsection

of Natural Resources Canada. The 2005 NBCC seismic hazard calculation output from the online

interpolator is included in Appendix B. Alternatively, the same data can be found in the Geological

Survey of Canada Open File 5813 (Halchuk and Adams, 2008). The site class was taken as C, which

has been adopted by the 2005 NBCC as the reference ground condition for which the acceleration-

and velocity-based coefficients are taken as unity. The uniform hazard spectra for 2% in 50 years

for the Eastern Canada site are listed in Table 6.1.

Table 6.1: Spectral hazard values (Sa(T)) and peak ground acceleration (PGA) for the Eastern Canada site, 2% probability of exceedance in 50 years

Spectral Period

Spectral Acceleration

Sa(0.2) 0.324g Sa(0.5) 0.157g Sa(1.0) 0.057g Sa(2.0) 0.019g PGA 0.232g

CHAPTER 6: INCREMENTAL ANALYSIS FOR TWO CANADIAN SITES


6.1.1 SIMULATED TIME-HISTORY RECORDS FOR THE EASTERN CANADA SITE

Of the simulated earthquake time-histories from Atkinson (2009), there were four record sets

for site class C from which the earthquake suite could be assembled. The average spectral

acceleration for each set is shown in Figure 6.1, along with the target UHS for 2% probability of

exceedance in 50 years. The name of each set of earthquakes indicates the region, the magnitude,

the site class, and the distance to the epicentre.

0

0.3

0.6

0.9

1.2

1.5

1.8

0 1 2 3 4Period (s)


(g)

Target SpectrumEast7C1East6C1East6C2East7C2

Figure 6.1: 2005 NBCC UHS for the Eastern Canada site for 2% in 50 years

and average spectra of 4 record sets of simulated earthquakes

The period range over which the simulated spectra (SAsim) was matched to the target spectrum

(SAtarg) was specified from 0.1 sec to 3.3 sec, as it covers the first three modes of the wind turbine

tower. Atkinson (2009) suggests that the lower magnitude records can be used to match the UHS

for low periods (0.1 sec to 0.5 sec) as well as the PGA, while the higher magnitude records can be

used to match the UHS for longer periods (0.5 sec to 2 sec).

6.1.2 EARTHQUAKE SUITE FOR THE EASTERN CANADA SITE

Atkinson (2009) suggests assembling an earthquake suite from only one record set that provides

the closest match to the target UHS for the specified period range. Although this is best for design

of a structure, as it results in the most critical time-histories for the given structure, it was decided to

use records from more than one record set. Since the purpose of the earthquake suite for the wind

turbine tower analysis is to extract fragility curves for the various damage states, the earthquake suite

should cover all possible seismic events in the location of interest, and not just those that are most

T3 T2 T1 Modal Periods

Magnitude 7, Site Class C, 14-26km Magnitude 6, Site Class C, 11-17km Magnitude 6, Site Class C, 17-31km Magnitude 7, Site Class C, 42-100km



critical for the wind turbine tower. Furthermore, due to the wide range of period of the wind

turbine tower, there was no single record set that perfectly matched all periods of interest.

To pick the records that define the earthquake suite, the mean and standard deviation of

(SAtarg/SAsim) were computed for each simulated earthquake time-history and 7 records were chosen

based on these statistics. The aim was to use records with a low standard deviation so that the

simulated spectrum would have a good shape, but also records with a mean (SAtarg/SAsim) in the

range of 0.5 to 2.0, because the mean also acts as the scaling factor, and any factor outside that

approximate range may yield an unrealistic record (Atkinson, 2009). An additional criterion was to

ensure that the average spectrum of the chosen records was in good agreement with the target

spectrum. Fulfilling these requirements as best as possible, 14 earthquake time-histories were

chosen to act as orthogonal components of 7 earthquakes. As in the previous chapter, both

orthogonal components were applied simultaneously. Table 6.2 lists these earthquakes and presents

the scale factor (also the mean of SAtarg/SAsim) and PGA for each record. The accelerograms for

these records are shown in Figure 6.2.

Table 6.2: Scale factors and PGA of earthquake records chosen for the Eastern Canada site

Name Earthquake

Record Scale

Factor PGA Magnitude Distance

ECAN01 East 6C1 #40 East 6C1 #41

0.635 0.681

0.354g 0.280g 6 11-17 km


0.963 0.699

0.291g 0.188g


0.812 0.800

0.146g 0.138g

6 17-31 km


0.491 0.565

0.106g 0.112g


0.746 0.806

0.114g 0.096g


1.108 1.020

0.085g 0.111g


0.971 1.034

0.098g 0.108g

7 42-100 km

The average spectrum of the 14 records is shown in Figure 6.3, along with the minimum and

maximum envelopes. There is good agreement between the average response spectrum and the

target spectrum. Furthermore, the average of the PGA of the lower magnitude records is 0.233g,

which is very close to the 2005 NBCC value of 0.232g.



Figure 6.2: Accelerograms of 14 scaled ground motion records for the Eastern Canada site



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.5 1 1.5 2 2.5 3 3.5

Period (s)


(g)

Figure 6.3: Acceleration response spectra for the Eastern Canada earthquake suite

for 2% in 50 years probability of exceedance

6.2 WESTERN CANADA SITE

Many locations that are being investigated for wind turbine farms in Western Canada are

offshore and in the northern parts of British Columbia. While those areas are much more seismic

than Eastern Canada, they do not represent the most severe seismic risk in Canada. Thus, the site

that was investigated was offshore, just south of Victoria, BC. It is possible that there will be future

developments of wind turbine towers around this area. As it can be seen from the UHS values listed

in Table 6.3, the seismic risk in this area is much higher than that of the Eastern Canada site.

Table 6.3: Spectral hazard values (Sa(T)) and peak ground acceleration (PGA) for the Western Canada site, 2% probability of exceedance in 50 years

Spectral Period


Sa(0.2) 1.192g Sa(0.5) 0.803g Sa(1.0) 0.374g Sa(2.0) 0.183g PGA 0.594g

6.2.1 SIMULATED TIME-HISTORY RECORDS FOR THE WESTERN CANADA SITE

Figure 6.4 shows the average spectra of the record sets for Western Canada (Atkinson, 2009)

and the target spectrum for that site. The Cascadia subduction zone records are a very poor match

for the UHS, but they match the first mode of the wind turbine tower very closely. Thus, one

Maximum Envelope


Target Spectrum

Minimum Envelope




Cascadia earthquake was included in the analysis of the Western Canada site, but it was matched and

scaled based on the first modal period only, not the period range of 0.1 sec to 3.3 sec as previously

described. The rest of the earthquakes were still matched based on the period range of 0.1 sec to

3.3 sec. Thus, two Cascadia records were chosen along with twelve other records to provide 7

earthquake records to be used in the analysis of the Western Canada site.

0

0.3

0.6

0.9

1.2

1.5

0 1 2 3 4Period (s)


(g)

Target SpectrumWest6C1West7C1West6C2West7C2West9C

Figure 6.4: 2005 NBCC UHS for the Western Canada site for 2% in 50 years

and average spectra of 4 record sets of simulated earthquakes

6.2.2 EARTHQUAKE SUITE FOR THE WESTERN CANADA SITE

Table 6.4 lists the scale factors and the PGA of the chosen records, and Figure 6.5 shows the

accelerograms of the records.

T3 T2 T1 Modal Periods

Magnitude 6, Site Class C, 8-13km Magnitude 7, Site Class C, 10-26km Magnitude 6, Site Class C, 13-31km Magnitude 7, Site Class C, 30-100km

Magnitude 9, Site Class C, 112-201km (Cascadia Record)



Table 6.4: Scale factors and PGA of earthquake records chosen for the Western Canada site

Name Earthquake

Record Scale

Factor PGA Magnitude Distance

WCAN01 West 6C1 #19 West 6C1 #21

1.108 1.373

0.661g 0.731g 6 8-13 km


0.713 0.718

0.408g 0.339g


1.520 1.435

0.506g 0.436g


0.905 0.908

0.512g 0.445g


0.974 0.720

0.497g 0.495g

7 10-26 km


1.620 1.688

0.305g 0.400g 7 30-100 km

WCAN07 West 9C #14 * West 9C #15 *

0.754 1.025

0.099g 0.162g 9 112-201 km

*Cascadia records, scaled to match 1st modal period



Figure 6.5: Accelerograms of 14 scaled ground motion records for the Western Canada site



Figure 6.6 displays the average spectrum of the twelve records (excluding the Cascadia records,

WCan07) and the minimum and maximum envelopes, and also shows the spectra of the two

Cascadia records that were chosen. The agreement of the average spectrum is very good in the

period range of interest, 0.1 sec to 3.3 sec, while the agreement of the Cascadia records is good at

the first period.

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5

Period (s)


(g)

Figure 6.6: Acceleration response spectra for the Western Canada earthquake suite

for 2% in 50 years probability of exceedance

6.3 METHODOLOGY FOR SCALING RECORDS FOR IDA

For each record, the initial analysis was always the reference record that was matched to the

target spectrum. The second analysis was one that aimed to reach the first damage state, 0.2%

residual-out-of-straightness. The results from the previous chapter on the incremental dynamic

analyses of the LA earthquake suite were used to estimate the magnification factor needed for the

second analysis, so that an unnecessary amount of analyses was not carried out in the linear part of

the IDA curve.

There are several existing algorithms that ensure that the discrete points that make up the IDA

curve provide the desired coverage (Vamvatsikos and Cornell, 2002). However, for this thesis, the

damage states are the main interest rather than the full IDA curve. Thus, the method described

below was used to try and minimize the number of analyses needed while still capturing all the

damage states.

Maximum Envelope

Target Spectrum

Minimum Envelope



Cascadia Records



The increase of the peak displacement and the peak rotation was approximately linear until the

first or second damage state. These two damage measures were thus employed for determining the

magnification factor of the second analysis. A factor that accounts for slight nonlinearity of the

response, n, was determined. To do this, the average peak displacement at the first damage state,

∆max,DS1, was divided by the peak displacement of the reference earthquake, ∆max,ref, and was then

divided by the magnification factor at the first damage state, MFDS1. This was repeated for all

earthquake records and the average of all the records provided the factor necessary to account for

the slight nonlinearity of the response. The following equation summarizes this:

∆

∆= 1DS

refmax,

1DSmax, MF/averagen for all IDAs (Equation 6.1)

To determine the magnification factor necessary to reach the first damage state for subsequent

analyses, the above equation can be reworked to solve for the magnification factor, but using the

average peak displacement at which the first damage state was reached, ∆max,avg,DS1, instead of ∆max,DS1.

n/MFrefmax,

1DS,avgmax,,1DS ∆

∆=∆ (Equation 6.2)

The magnification factor can also be determined based on the peak rotation prediction, by

substituting rotation instead of displacement in the equations above. The magnification factor

actually employed in predicting the first damage state was the average of the two factors (based on

peak displacement and peak rotation).

6.3.1 EFFICIENCY OF METHOD

It was found that this method typically overpredicted the magnification factor for the first

damage state. The subsequent predictions of required magnification factors were based on linear

interpolation or extrapolation from the previous analyses, but still employing the n factor described

above. The linear interpolation was based on the residual displacement for the first and third

damage states, the peak stress for the second damage state, and the peak rotation and the peak stress

for the fourth damage state. The following flowchart (Figure 6.7) describes this process. There is

one condition: the difference between magnification factors should be at least 1, unless specifically

indicated otherwise. For example, if the prediction for the MF to achieve a particular damage state

is only greater than another magnification factor already analysed by 0.7, the subsequent analysis will

actually increase the magnification factor by 1.



Figure 6.7: Flowchart of scaling procedure for the Canadian earthquake suites

no

predict MF for DS1 from previous analyses, based on linear interpolation of

residual displacement

DS1 envelopedor reached within 5%?

linearly interpolate to obtain precise damage measures for DS3

predict MF for DS4 using methodology outlined above, considering the peak stress

DS4 reached? i.e. tower buckled?

no

yes

predict MF for DS2 from previous analyses, based

on linear extrapolation of peak stress


no

yes


predict MF for DS3 from previous analyses, based

on linear extrapolation of residual displacement


no

yes

predict MF for DS1 using methodology outlined

DS1 reached within 5%?

yes

no


yes

increase MF by 1

decrease MF by 1

tower buckled?yes

tower buckled? no

yes

no

START: initial analysis: records matching UHS, SF=1

FINISH DS4 has been reached at the

second-to-last analysis within a magnification factor of 1



6.4 RESULTS FOR EASTERN CANADA SITE

The analyses of the wind turbine tower at the Eastern Canada site with the records matched to

the UHS for that area produced a very slight response in the tower. The results are summarized in

Table 6.5.

Table 6.5: Summary of results of time-history analyses for the Eastern Canada suite

Peak Displacement

Peak Rotation

Peak Stress

Residual Deformation Analysis

∆max (% H) θmax σmises (MPa) ∆res (% H)

Estimated Magnification Factor Required to Reach

First Damage State ECan01 0.02 % 0.010° 46 0 % 62 ECan02 0.03 % 0.009° 44 0 % 51 ECan03 0.03 % 0.010° 43 0 % 58 ECan04 0.08 % 0.006° 44 0 % 29 ECan05 0.11 % 0.003° 44 0 % 34 ECan06 0.07 % 0.007° 43 0 % 28 ECan07 0.08 % 0.008° 43 0 % 25

The last column of the table presents the estimated magnification factors required to reach the

first damage state based on the methodology presented in the previous section. The estimated

factors range from 25 to 62; records are unrealistic when scaled to that extent. However, it was

determined from scaling the Western Canada records that predicting the magnification factors for

specific damage states is quite inaccurate. Thus, the Eastern Canada suite was analysed using an

incremental factor of 10 to determine if further analyses are necessary. Those results are presented

in Table 6.6.

Table 6.6: Summary of results of time-history analyses for the Eastern Canada suite with magnification factor of 10

Peak Displacement

Peak Rotation

Peak Stress

Residual Deformation

Analysis and Magnification

Factor ∆max (% H) θmax σmises (MPa) ∆res (% H) ECan01 x 10 0.24 % 0.014° 123 0 % ECan02 x 10 0.30 % 0.014° 126 0 % ECan03 x 10 0.26 % 0.017° 79 0 % ECan04 x 10 0.76 % 0.035° 140 0 % ECan05 x 10 1.06 % 0.056° 174 0.01 % ECan06 x 10 0.74 % 0.034° 114 0 % ECan07 x 10 0.76 % 0.036° 111 0 %

None of the analyses had a residual deformation greater than 0.2%, thus were well under the

first damage state at an intensity that was 10 times greater than that required for design. Due to the

findings in this section, no further incremental dynamic analyses of the Eastern Canada earthquake



suite were carried out, as it could be concluded that the seismic risk for this wind turbine tower at

that location is extremely low.

6.5 RESULTS OF TIME-HISTORY ANALYSIS FOR WESTERN CANADA SITE

The results tables and figures for the individual analyses of the Western Canada earthquake suite

are included in Appendix C. This section presents the resultant incremental dynamic analysis curves

for the Western Canada suite and the fragility curves for this wind turbine tower in Western Canada.

6.5.1 INCREMENTAL DYNAMIC ANALYSIS CURVES

The IDA curves are presented in Figure 6.8, employing the magnification factor as the intensity

measure and the peak displacement, peak rotation, and residual displacement as the damage

measures.

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10Peak Displacement (% H)

Mag

nific

atio

n Fa

ctor

WCan01 - West 6C1 #19 & #21

WCan02 - West 7C1 #7 & #9

WCan03 - West 7C1 #13 & #14

WCan04 - West 7C1 #25 & #26

WCan05 - West 7C1 #28 & #30

WCan06 - West 7C2 #13 & #14

WCan07 - West 9C #14 & #15

0

2

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1Peak Rotation (°)

Mag

nific

atio

n Fa

ctor

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5Residual Displacement (% H)

Mag

nific

atio

n Fa

ctor

Figure 6.8: Incremental dynamic analysis curves for Western Canada suite

Magnitude 6 8-13 km Magnitude 7 10-26 km

Magnitude 7 30-100 km

Magnitude 9 112-201 km

(Cascadia Record)



The dispersion of the IDA curves is quite high because the suite was made up of records from 4

records sets, as described in Section 6.2. Earthquake records from the same record set have very

low dispersion, as can be seen from the IDA curves for WCan02, WCan03, WCan04 and WCan05.

These four analyses were based on record set 7C1 (Magnitude 7 on Site Class C and at distance of

10-26 km).

The most significant outlier is WCan01, which is from the record set of ground motions at the

closest distance. That record set, 6C1, is characterized by high spectral accelerations in the low

frequency range. The results from WCan01 thus confirm that a lower magnitude earthquake record

at a close distance will have the least impact on the wind turbine tower, as suggested by Atkinson

(2009).

WCan06 and WCan07 are also of interest as they represent the opposite of WCan01, both

regarding the records and the results of the IDA. They are based on record sets of a higher

magnitude and at significantly larger distances, and the results constitute the most critical response

of the wind turbine tower. This is consistent for all the damage measures shown in Figure 6.8. It in

also interesting to note that the Cascadia Record (WCan07) was slightly less intense for the wind

turbine tower than the Magnitude 7, 30-100 km record (WCan06). This may be due to the influence

of higher modes, for which WCan06 was much more intense.

6.5.1.1 AVERAGE DAMAGE MEASURES

The average damage measures for the Western Canada earthquake suite for each damage state

are listed in Table 6.7, along with the minimum and maximum values of the damage measures. As

previously stated, the peak stress may appear very high; however, that is typically the stress at a stress

concentration, not in the tower wall. The averages listed are not very close to those of the LA

earthquake suite (Table 5.3 in the previous chapter), thus it is not surprising that predicting the

magnification factors was not very accurate.



Table 6.7: Minimum, average, and maximum values of damage measures at each damage state for the Western Canada site

Damage State

Peak Displacement ∆max (% H)

Peak Rotation θmax

Peak Stress

σmises (MPa)

Residual Displacement ∆res (% H)

0.2% Residual Out-of-Straightness

min: 1.76 % average: 2.06 %

max: 2.42 %

min: 0.094° average: 0.104°

max: 0.124°


max: 336 0.2 %

First Yield

min: 2.72 % average: 3.23 %

max: 4.38 %

min: 0.129° average: 0.165°

max: 0.223° 389

min: 0.38% average: 0.59%

max: 1.05%

1% Residual Out-of-Straightness

min: 3.58 % average: 4.07 %

max: 4.32 %

min: 0.205° average: 0.218°

max: 0.240°


max: 579 1.0 %

First Buckle / Loss of Tower

min: 4.71% average: 17.28 %

max: 86.11 %

min: 1.00° average: 14.55°

max: 89.50°


max: 798

min: 1.88 % average: 15.03 %

max: 86.11 %

6.5.2 FRAGILITY CURVES

The fragility curves for the different damage states for the Western Canada site are shown in

Figure 6.9. As decided in the previous chapter, the magnification factor was used as the intensity

measure. Additional curves for other intensity measures are shown in Appendix C.

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15Magnification Factor

Pro

babi

lity

of E

xcee

danc

e

Figure 6.9: Fragility curves for Western Canada site for the magnification factor intensity measure

The fragility curves suggest that the seismic risk for this wind turbine tower is extremely low for

the seismic hazard that was considered in this study. Considering that the magnification factor

represents the intensity of a seismic event with respect to the design-based earthquake (DBE), Table

6.8 summarizes the fragility curves by providing the probability of exceeding the damage states for

seismic intensities up to 5 times greater than the DBE.




Table 6.8: Probability of exceedance of particular damage states for varying seismic event intensities

Seismic Event Intensity Compared to DBE Damage State 2 3 4 5 6 0.2% Residual Out-of-Straightness 3.3% 26% 58% 80% 92% First Yield 0.1% 2.2% 13% 32% 54% 1% Residual Out-of-Straightness 0 0.1% 1.2% 6.6% 19% First Buckle / Loss of Tower 0 0 0 0.2% 1.5%

An earthquake having twice the intensity of the DBE, may cause exceedance of the first damage

state at a probability of 3.3% and of the second damage state at a probability of 0.1%. As previously

stated, this suggests an extremely low seismic risk for this wind turbine tower in Western Canada.

6.6 SUMMARY

Two Canadian locations were picked to assess the seismic risk of this wind turbine tower in

Canada. One location is in Eastern Canada on the north shore of Lake Erie, Ontario and is

currently being investigated for a wind turbine farm development. The second location is in

Western Canada, offshore of Victoria, BC. There are no current wind turbine developments in that

area, but it was still investigated as it represents the highest seismic risk in Canada.

Earthquake suites were assembled for each location based on simulated time-histories generated

by Atkinson (2009). The earthquake suites represent a range of earthquakes that may occur in each

area and that match the uniform hazard spectra for each location. The records of the earthquake

suite thus represent design-based earthquakes. Each record suite consisted of 14 time-histories that

represented the orthogonal components of 7 analyses.

The Eastern Canada site analyses at the design-based earthquake level resulted in an insignificant

seismic response. The analyses were then carried out at a magnification factor of 10 and the seismic

response was still very mild – none of the analyses reached the first damage state. Thus, it was

decided that further incremental analysis of the Eastern Canada location was unnecessary. However,

a significant uncertainly exists in the definition of the seismic hazard in Eastern Canada, especially

for long periods.

The Western Canada location was carried out so that all four damage states were reached.

Fragility curves were constructed and it was concluded that the seismic risk is very low.


CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS

This thesis investigated the behaviour of the tubular steel wind turbine tower of a typical

1.65MW parked wind turbine under seismic loading, and evaluated its seismic risk for two Canadian

locations. A finite element model was thoroughly validated and the expected failure mode, inelastic

buckling in flexure, was adequately captured. Earthquake suites were assembled and used to carry

out nonlinear incremental dynamic analysis. Fragility curves were defined for four potential damage

states of the wind turbine tower: 0.2% residual out-of-straightness, first yield at a stress

concentration, 1% residual out-of-straightness, and first buckle. The results obtained, discussed

shortly, represent the seismic hazard of the investigated wind turbine tower in a few locations.

However, the main contribution of this thesis is the framework that was set up to assess the seismic

risk of any tubular steel wind turbine tower subject to any level of seismic hazard.

The incremental analyses for either location in Canada suggest that the seismic risk for the wind

turbine tower that was investigated is very small. This is due to the long fundamental period of the

tower and the very short predominant period of most earthquakes. The response of the wind

turbine tower subjected to the Eastern Canada (Ontario) earthquake suite of records was almost

insignificant. The seismic response was very slight and did not reach the first damage state even

with a magnification factor of 10 with respect to the design-based earthquake. However, the design

spectrum in Eastern Canada has an extremely low spectral acceleration in the long-period range and

may change as the definition of the seismic hazard improves. The incremental analyses carried out

with the Western Canada earthquake suite, corresponding to the highest seismic risk in Canada,

suggest that the probability of exceeding 0.2% residual-out-of-straightness is only 3.3% after a

seismic event that is twice as intense as the design-based earthquake. Thus, the 1.65MW Vestas

wind turbine tower has a very low seismic risk in Canada under the current definition of the seismic

hazard.

However, the analyses demonstrated that these structures must be designed for large safety

factors against any overloading, as they are prone to collapse when the tower is excited beyond its

elastic limit. As the design of wind turbine towers is quickly evolving, with a tendency for taller

structures, the seismic response may become more critical. This thesis outlines a methodology to

carry out a thorough investigation into the probability of reaching predetermined damage states

under seismic loading.

Future research is required in several areas. The damping of wind turbine towers should be

determined more precisely, as it significantly influences the response path of the wind turbine tower

CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS


during a seismic event. The bolted flange connections of the wind turbine tower may also be further

investigated, as the flanges are expected to experience prying before the tower fails by buckling.

Furthermore, a pushover analysis suited to wind turbine towers may be developed. Lastly, there was

some uncertainty in the damage states defined. In future studies, the damage states of the wind

turbine tower may be re-defined in conjunction with requirements of other components of the wind

turbine to ensure safe operation.

.


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Poursha, M., Khoshnoudian, F., and Moghadam, A.S. 2009. “A Consecutive Modal Pushover Procedure for Estimating Seismic Demands of Tall Buildings.” Engineering Structures, Vol. 31, No. 2, pp. 591–599.

REFERENCES


Prowell, I., Veletzos, M., Elgamal, A., and Restrepo, J. 2008. “Shake Table Test of a 65 kW Wind Turbine and Computational Simulation.” 14th World Conference on Earthquake Engineering, Beijing, China, Paper ID 12-01-0178.

Prowell, I., Veletzos, M., Elgamal, A., and Restrepo, J. 2009. “Experimental and Numerical Seismic Response of a 65 kW Wind Turbine.” Journal of Earthquake Engineering, Vol. 13, No. 8, pp. 1172–1190.

Ritschel, U., Warnke, I., Kirchner J., and Meussen, B. 2003. “Wind Turbines and Earthquakes.” Proceedings of the World Wind Energy Conference (WWEC) 2003, Cape Town, South Africa.

Sasaki K.K., Freeman S.A., and Paret T.F. 1998. “Multi-Mode Pushover Procedure (MMP) – a Method to Identify the Effects of Higher Modes in a Pushover Analysis.” 6th US National Conference on Earthquake Engineering, Seattle, USA. Earthquake Engineering Research Institute, Oakland, USA, Proceedings Paper Reference 271.

Standards Australia. 1998. Steel Structures. Australian Standard AS 4100. Standards Australia, Sydney, Australia.

Somerville, P., Punyamurthula, S., and Sun, J. 1997. “Development of Ground Motion Time Histories for Phase 2 of the FEMA/SAC Steel Project.” Report No. SAC/BD-97/04, SAC Joint Venture, Sacramento, California, USA.

Szilard, R. 2004. Theories and Applications of Plate Analysis: Classical, Numerical, and Engineering Methods. John Wiley, Hoboken, USA.

Trahair, N. S., and Bradford, M. A. 1998. The Behaviour and Design of Steel Structures to AS 4100. 3rd Australian Edition. Spon Press, London, UK.

Tso, W.K., and Moghadam, A.S. 1998. “Pushover Procedure for Seismic Analysis of Buildings.” Progress in Structural Engineering and Materials, Vol. 1, No. 3, pp. 337–344.

Vamvatsikos, D, and Cornell, C.A. 2002. “Incremental Dynamic Analysis.” Earthquake Engineering and Structural Dynamics, Vol. 31, No. 3, pp. 491–514.

Vamvatsikos, D, and Cornell, C.A. 2004. “Applied Incremental Dynamic Analysis.” Earthquake Spectra, Vol. 20, No. 2, pp. 523–553.

van Wingerde, A.M., van Delft, D.R.V., Packer, J.A., and Janssen, L.G.J. 2006. “Survey of Support Structures for Offshore Wind Turbines.” 11th International Symposium on Tubular Structures, Québec City, Canada, Proceedings pp. 365-373.

Vestas. 2006. Wind Turbine Drawing 961000. V-82-1.65 MW HH80 IEC 2A US. Vestas Wind System A/S, Randers, Denmark.

Voth, A. P. 2010. Branch Plate-to-Circular Hollow Structural Section Connections. Ph.D. Thesis. University of Toronto, Toronto, Canada.

Witcher, D. 2005. “Seismic Analysis of Wind Turbines in the Time Domain.” Wind Energy, Vol. 8, No. 1, pp. 81-91.

Zhao X., and Maisser, P. 2006. “Seismic Response Analysis of Wind Turbine Towers Including Soil-Structure Interaction.” Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, Vol. 220, No. 1, pp. 53-61.

Zhao, X.L., Wilkinson, T., and Hancock, G. 2005. Cold-Formed Tubular Members and Connections: Structural Behaviour and Design. Elsevier Science Ltd., Oxford, UK.


APPENDIX A: RESULTS OF INCREMENTAL TIME-HISTORY

ANALYSIS FOR LA EARTHQUAKE SUITE

This appendix includes the result items for the LA earthquake suite except those for LA01 &

LA02, which were presented in Section 5.2:

• summary of displacement results in tabular format

• comparison of the peak displaced shape of all the magnification factors

• time-history displacement response at hub height for the higher magnification factors

• orbit plots for all magnification factors

In addition, this appendix presents several additional IDA curves for the three damage measures

(peak displacement, residual displacement, and peak rotation) and four intensity measures (peak

ground displacement, peak ground velocity, peak ground acceleration, and magnification factor).

APPENDIX A: RESULTS OF INCREMENTAL TIME-HISTORY ANALYSIS FOR LA EARTHQUAKE SUITE


A.1 LA03 & LA04 (IMPERIAL VALLEY, 1979, ARRAY #05)

Table A. 1: Summary of displacement results of time-history analyses subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05)

Peak Displacement

Peak Rotation

Peak Stress



1 1.81 % 25° 0.089° 274 0.03 % 315°

1.5 2.72 % 29° 0.136° 371 0.20 % 13° 0.2% Residual Out-of-Straightness 1.7** 3.00 % 0.145° 389 0.26 % First Yield

2 3.38 % 28° 0.157° 415 0.36 % 20° 3 4.38 % 28° 0.208° 454 0.66 % 35°

3.3** 4.76 % 1.223° 531 1.00 % 1.0% Residual Out-of-Straightness 4 5.51 % 198° 3.201° 681 1.66 % 198° First Buckle 5 8.58 % 27° 4.240° 750 6.9 % 26° 6 86.7 % 35° 89.09° 786 86.72 % 35°


0

10

20

30

40

50

60

70

80

0 2 4 6 8


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

Figure A.1: Peak displaced shape of wind turbine tower subjected to




Figure A.2: Incremental time-history displacement response of Vestas wind turbine tower

subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05) at hub height (80m) (a) x-direction response for magnification factors 3 – 6 (b) z-direction response for magnification factors 3 – 6

(a)

(b)





Figure A.3: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA03 & LA04 (Imperial Valley, 1979, Array #05)

(a) top view of tower and legend (e) factor: 3 (b) factor: 1 (f) factor: 4 (c) factor: 1.5 (g) factor: 5 (d) factor: 2 (h) factor: 6

door cable hole X

Z

(a)

(g) factor: 5

(b) factor: 1

(c) factor: 1.5

(d) factor: 2

(e) factor: 3

(f) factor: 4

(h) factor: 6

full collapse of tower



A.2 LA05 & LA06 (IMPERIAL VALLEY, 1979, ARRAY #06)

Table A.2: Summary of displacement results of time-history analyses subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06)

Peak Displacement

Peak Rotation

Peak Stress



1 1.88 % 201° 0.087° 292 0.04 % 20°

1.4** 2.64 % 0.131° 374 0.20 % 0.2% Residual Out-of-Straightness 1.5 2.76 % 23° 0.137° 386 0.22 % 18° First Yield 2 3.28 % 23° 0.159° 424 0.27 % 15° 3 4.58 % 17° 0.240° 466 0.68 % 20°

3.1** 4.78 % 0.477° 490 1.00 % 1.0% Residual Out-of-Straightness 4 6.46 % 10° 2.462° 90 3.73 % 5° First Buckle 5 10.30 % 8° 5.343° 712 9.19 % 12° 6 20.12 % 16° 11.315° 745 20.0 % 16°


0

10

20

30

40

50

60

70

80

0 2 4 6 8


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6






subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06) at hub height (80m) (a) x-direction response for magnification factors 3 – 6 (b) z-direction response for magnification factors 3 – 6

(a)

(b)




Figure A.6: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA05 & LA06 (Imperial Valley, 1979, Array #06)


door cable hole X

Z

(a)

(b) factor: 1

(c) factor: 1.5

(d) factor: 2

(e) factor: 3

(f) factor: 4

(g) factor: 5

(h) factor: 6



A.3 LA07 & LA08 (LANDERS, 1992, BARSTOW)

Table A.3: Summary of displacement results of time-history analyses subjected to LA07 & LA08 (Landers, 1992, Barstow)

Peak Displacement

Peak Rotation

Peak Stress



1 1.33 % 53° 0.067° 190 0.03 % 27°

1.5 1.96 % 53° 0.098° 262 0.13 % 35° 1.8** 2.34 % 0.117° 306 0.20 % 0.2% Residual Out-of-Straightness

2 2.62 % 50° 0.130° 339 0.26 % 30° 2.6** 3.27 % 0.161° 389 0.45 % First Yield

3 3.71 % 47° 0.181° 423 0.58 % 33° 3.7** 4.47 % 0.214° 452 1.00 % 1.0% Residual Out-of-Straightness

4 4.85 % 45° 0.231° 467 1.21 % 36° 5 7.60 % 3° 3.633° 689 5.62 % 18° First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5


LA07 & LA08 (Landers, 1992, Barstow)




subjected to LA07 & LA08 (Landers, 1992, Barstow) at hub height (80m) (a) x-direction response for magnification factors 3 – 5 (b) z-direction response for magnification factors 3 – 5

free vibration begins at 80s until 140s (not shown)

(a)

(b)




Figure A.9: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA07 & LA08 (Landers, 1992, Barstow)

(a) top view of tower and legend (e) factor: 3 (b) factor: 1 (f) factor: 4 (c) factor: 1.5 (g) factor: 5 (d) factor: 2

door cable hole X

Z

(a)

(b) factor: 1

(c) factor: 1.5

(d) factor: 2

(e) factor: 3

(f) factor: 4

(g) factor: 5



A.4 LA09 & LA10 (LANDERS, 1992, YERMO)

Table A.4: Summary of displacement results of time-history analyses subjected to LA09 & LA10 (Landers, 1992, Yermo)

Peak Displacement

Peak Rotation

Peak Stress



1 1.15 % 326° 0.058° 274 0.02 % 352°

1.5 1.62 % 134° 0.076° 248 0.12 % 39° 2 2.11 % 330° 0.104° 292 0.18 % 34°

2.2** 2.25 % 0.111° 308 0.20 % 0.2% Residual Out-of-Straightness 3 2.94 % 130° 0.145° 383 0.29 % 25°

3.1** 3.05 % 0.151° 389 0.36 % First Yield 4 3.74 % 121° 0.187° 425 0.78 % 43°

4.5** 4.16 % 0.206° 442 1.00 % 1.0% Residual Out-of-Straightness 5 4.56 % 37° 0.225° 458 1.21 % 41° 6 8.23 % 33° 2.694° 743 6.22 % 38° First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6






subjected to LA09 & LA10 (Landers, 1992, Yermo) at hub height (80m) (a) x-direction response for magnification factors 4 – 6 (b) z-direction response for magnification factors 4 – 6


(a)

(b)




Figure A.12: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA09 & LA10 (Landers, 1992, Yermo)


door cable hole X

Z

(a) (f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5



A.5 LA11 & LA12 (LOMA PRIETA, 1989, GILROY)

Table A.5: Summary of displacement results of time-history analyses subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy)

Peak Displacement

Peak Rotation

Peak Stress



1 0.82 % 158° 0.033° 143 0 % n/a

1.5 1.20 % 332° 0.058° 198 0.02 % 334° 2 1.54 % 331° 0.071° 256 0.05 % 324° 3 2.22 % 333° 0.101° 328 0.11 % 356°

3.5** 2.55 % 0.117° 369 0.20 % 0.2% Residual Out-of-Straightness 3.8** 2.71 % 0.125° 389 0.24 % First Yield

4 2.87 % 335° 0.132° 408 0.28 % 8° 5 3.38 % 335° 0.163° 428 0.40 % 19° 6 3.87 % 335° 0.188° 458 0.60 % 21° 7 4.42 % 335° 0.204° 501 0.92 % 23° 1.0% Residual Out-of-Straightness 8 44.7 % 352° 90° 721 44.7 % 352° First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7

factor: 8


LA11 & LA12 (Loma Prieta, 1989, Gilroy)




subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy) at hub height (80m) (a) x-direction response for magnification factors 5 – 8 (b) z-direction response for magnification factors 5 – 8

(a)

(b)

free vibration begins at 40s until 100s (not shown to completion)

free vibration begins at 40s until 100s (not shown to completion)



Figure A.15: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA11 & LA12 (Loma Prieta, 1989, Gilroy)

(a) top view of tower and legend (e) factor: 3 (i) factor: 7 (b) factor: 1 (f) factor: 4 (j) factor: 8 (c) factor: 1.5 (g) factor: 5 (d) factor: 2 (h) factor: 6

door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5

(i) factor: 7

(j) factor: 8



A.6 LA13 & LA14 (NORTHRIDGE, 1994, NEWHILL)

Table A.6: Summary of displacement results of time-history analyses subjected to LA13 & LA14 (Northridge, 1994, Newhill)

Peak Displacement

Peak Rotation

Peak Stress



1 0.86 % 45° 0.042° 140 0 % 55°

1.5 1.30 % 43° 0.063° 194 0.06 % 43° 2 1.66 % 41° 0.077° 247 0.08 % 15° 3 2.22 % 219° 0.106° 361 0.14 % 276°


4 3.06 % 220° 0.146° 398 0.24 % 276° 5 4.06 % 220° 0.199° 428 0.66 % 251°



0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7






subjected to LA13 & LA14 (Northridge, 1994, Newhill) at hub height (80m) (a) x-direction response for magnification factors 4 – 7 (b) z-direction response for magnification factors 4 – 7


(a)

(b)




Figure A.18: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA13 & LA14 (Northridge, 1994, Newhill)


door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5

(i) factor: 7



A.7 LA15 & LA16 (NORTHRIDGE, 1994, RINALDI RS)

Table A.7: Summary of displacement results of time-history analyses subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS)

Peak Displacement

Peak Rotation

Peak Stress



1 0.90 % 174° 0.042° 154 0 % 2°

1.5 1.30 % 348° 0.068° 214 0.03 % 342° 2 1.66 % 175° 0.076° 268 0.04 % 235°

2.7** 2.30 % 0.105° 343 0.20 % 0.2% Residual Out-of-Straightness 3 2.51 % 177° 0.115° 369 0.25 % 215°

3.4** 2.82 % 0.129° 389 0.39 % First Yield 4 3.26 % 180° 0.150° 417 0.59 % 213°

4.7** 3.89 % 0.177° 431 1.00 % 1.0% Residual Out-of-Straightness 5 4.19 % 179° 0.190° 438 1.20 % 206° 6 5.24% 176° 3.161° 665 3.45% 194° First Buckle 7 6.96% 190° 5.162° 679 5.65 % 195° 8 9.95% 171° 10.115° 668 8.77 % 186°


0

10

20

30

40

50

60

70

80

0 2 4 6 8


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7

factor: 8






subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS) at hub height (80m) (a) x-direction response for magnification factors 4 – 8 (b) z-direction response for magnification factors 4 – 8

(a)

(b)




Figure A.21: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA15 & LA16 (Northridge, 1994, Rinaldi RS)

(a) top view of tower and legend (e) factor: 3 (i) factor: 7 (b) factor: 1 (f) factor: 4 (j) factor: 8 (c) factor: 1.5 (g) factor: 5 (d) factor: 2 (h) factor: 6

door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5

(j) factor: 8

(i) factor: 7



A.8 LA17 & LA18 (NORTHRIDGE, 1994, SYLMAR)

Table A.8: Summary of displacement results of time-history analyses subjected to LA17 & LA18 (Northridge, 1994, Sylmar)

Peak Displacement

Peak Rotation

Peak Stress



1 1.39 % 216° 0.064° 183 0.01 % 179°

1.5 1.94 % 216° 0.092° 259 0.02 % 110° 2 2.57 % 216° 0.122° 336 0.07 % 205°


3 3.74 % 217° 0.173° 405 0.41 % 221° 4 4.69 % 217° 0.225° 477 0.72 % 223°

4.1** 4.88 % 0.546° 505 1.00 % 1.0% Residual Out-of-Straightness 5 6.01 % 219° 2.478° 673 2.69 % 225° First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5






subjected to LA17 & LA18 (Northridge, 1994, Sylmar) at hub height (80m) (a) x-direction response for magnification factors 4 – 5 (b) z-direction response for magnification factors 4 – 5


(a)

(b) free vibration begins at 60s until 120s (not shown)



Figure A.24: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA17 & LA18 (Northridge, 1994, Sylmar) (a) top view of tower and legend (e) factor: 3 (b) factor: 1 (f) factor: 4 (c) factor: 1.5 (g) factor: 5 (d) factor: 2

door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5



A.9 LA19 & LA20 (NORTH PALM SPRINGS, 1986)

Table A.9: Summary of displacement results of time-history analyses subjected to LA19 & LA20 (North Palm Springs, 1986)

Peak Displacement

Peak Rotation

Peak Stress



1 0.69 % 269° 0.032° 112 0 % 310°

1.5 1.04 % 269° 0.048° 144 0 % 356° 2 1.38 % 270° 0.065° 182 0.06 % 312°

2.7** 1.85 % 0.089° 228 0.20 % 0.2% Residual Out-of-Straightness 3 2.09 % 270° 0.101° 253 0.28 % 301° 4 2.82 % 270° 0.137° 299 0.53 % 297°

4.6** 3.26 % 0.163° 389 0.75 % First Yield 5 3.55 % 270° 0.180° 449 0.90 % 294°



0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 1.5

factor: 2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7






subjected to LA19 & LA20 (North Palm Springs, 1986) at hub height (80m) (a) x-direction response for magnification factors 4 – 7 (b) z-direction response for magnification factors 4 – 7 `


(a)

(b)




Figure A.27: Orbit in x-z plane (in mm) for Vestas wind turbine tower subjected to LA19 & LA20 (North Palm Springs, 1986)


door cable hole X

Z

(a)

(f) factor: 4

(g) factor: 5

(h) factor: 6

(b) factor: 1

(d) factor: 2

(e) factor: 3

(c) factor: 1.5

(i) factor: 7



A.10 IDA CURVES FOR INVESTIGATED INTENSITY MEASURES

The figures in this section show the incremental dynamic analysis curves for several intensity

measures. It can be seen that the ones having the least dispersion are those with the peak ground

velocity and the magnification factor as the intensity measure.

0

1

2

3

4

5


PG

D (

m)

0

2

4

6

8

10


PG

V (

m/s

)

0

2

4

6

8


PG

A (

g)

0

2

4

6

8


Mag

nific

atio

n Fa

ctor

Figure A.28: IDA curves for various intensity measures and peak displacement damage measure



0

1

2

3

4

5


PG

D (

m)

0

2

4

6

8

10


PG

V (

m/s

)

0

2

4

6

8


PG

A (

g)

0

2

4

6

8


Mag

nific

atio

n Fa

ctor

Figure A.29: IDA curves for various intensity measures and residual displacement damage measure



0

1

2

3

4

5

0 1 2 3 4Peak Rotation (°)

PG

D (

m)

0

2

4

6

8

10


PG

V (

m/s

)

0

2

4

6

8


PG

A (

g)

0

2

4

6

8


Mag

nific

atio

n Fa

ctor

Figure A.30: IDA curves for various intensity measures and peak rotation damage measure


APPENDIX B: SEISMIC HAZARD FOR TWO CANADIAN SITES

The following pages contain the reports of the online interpolator from Earthquakes Canada

(http://earthquakescanada.nrcan.gc.ca/hazard) for the two locations chosen in Canada: close to

Dunnville, Ontario to represent Eastern Canada, and offshore of Victoria, BC to represent Western

Canada.






APPENDIX C: RESULTS OF THE WESTERN CANADA

EARTHQUAKE SUITE

This appendix includes the result items for the Western Canada earthquake suite:

• summary of displacement results in tabular format

• comparison of the peak displaced shape of all the magnification factors

• the time-history displacement response at hub height for the higher magnification factors

Orbit plots are omitted, as they were not essential for determining the probability of damage. In

addition, fragility curves for the PGV and the PGA intensity measures are included in this appendix.

APPENDIX C: RESULTS OF THE WESTERN CANADA EARTHQUAKE SUITE


C.1 WCAN01 (MAGNITUDE 6, 8 – 13 KM)

Table C.1: Summary of results of time-history analyses for WCan01

Peak Displacement

Peak Rotation

Peak Stress


∆max (% H) θmax σmises (MPa) ∆res (% H) Damage State Reached

1 0.41 % 0.017° 87 0 %

5.1 1.91 % 0.086° 281 0.09 % 6.4** 2.24 % 0.103° 336 0.02 % 0.2% Residual Out-of-Straightness 7.1 2.41 % 0.111° 365 0.26 %

8.4** 2.72 % 0.129° 389 0.38 % First Yield 8.5 2.74 % 0.131° 398 0.39 % 12 3.44 % 0.195° 522 0.92 %

12.4** 3.58 % 0.205° 579 1.00 % 1.0% Residual Out-of-Straightness 13 3.77 % 0.218° 659 1.11 % 16 4.74 % 1.000° 565 1.88 % First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 7.1

factor: 5.1

factor: 8.5

factor: 12

factor: 13

factor: 16

0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 7.1

factor: 5.1

factor: 8.5

factor: 12

factor: 13

factor: 16

(a) (b)

Figure C.1: Peak displaced shape of wind turbine tower subjected to WCan01 (a) at peak displacement (b) at peak rotation



Figure C.2: Incremental time-history displacement response of

Vestas wind turbine tower subjected to WCan01 at hub height (80m) (a) x-direction response (b) z-direction response

free vibration begins at 7.61s

(a)

(b)





Peak Displacement

Peak Rotation

Peak Stress



1 0.64 % 0.031° 112 0 %

4.1 2.40 % 0.123° 302 0.19 % 0.2% Residual Out-of-Straightness 5.2 2.94 % 0.152° 369 0.37 %

5.9** 3.21 % 0.170° 389 0.48 % First Yield 7.6 3.93 % 0.217° 442 0.78 %



0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 4.1

factor: 5.2

factor: 7.6

factor: 9

factor: 10

Figure C.3: Peak displaced shape of wind turbine tower subjected to WCan02






(a)

(b)






Peak Displacement

Peak Rotation

Peak Stress



1 0.50 % 0.025° 77 0 %

3.8 1.93 % 0.095° 216 0.14 % 4.2** 2.17 % 0.106° 234 0.20 % 0.2% Residual Out-of-Straightness 5.2 2.76 % 0.135° 280 0.35 % 7.7 4.18 % 0.212° 383 0.95 %

7.9** 4.28 % 0.218° 386 1.00 % 1.0% Residual Out-of-Straightness 8** 4.38 % 0.223° 389 1.05 % First Yield 9 5.02 % 0.258° 406 1.37 % 11 7.66 % 3.258° 606 4.93 % First Buckle 12 48.8 % 87.4° 717 48.8 %


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 3.8

factor: 5.2

factor: 7.7

factor: 9

factor: 11

factor: 12






free vibration begins at 60.26s (not shown)

(a)

(b)






Peak Displacement

Peak Rotation

Peak Stress



1 0.52 % 0.030° 119 0 %

3.3** 1.76 % 0.094° 272 0.20 % 0.2% Residual Out-of-Straightness 3.5 1.85 % 0.098° 283 0.21 % 4.7 2.47 % 0.125° 364 0.33 %

5.3** 2.77 % 0.143° 389 0.44 % First Yield 6 3.12 % 0.164° 418 0.57 %

7.4** 3.86 % 0.218° 446 1.00 % 1.0% Residual Out-of-Straightness 9 4.67 % 0.278° 477 1.47 % 10 5.23 % 0.613° 712 2.19 %

10.5 5.65 % 1.436° 728 2.83 % First Buckle ** interpolated values

0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 3.5

factor: 4.7

factor: 6

factor: 9

factor: 10

factor: 10.5







(a)

(b)






Peak Displacement

Peak Rotation

Peak Stress



1 0.65 % 0.035° 134 0 %

2.8 1.84 % 0.096° 267 0.19 % 2.9** 1.89 % 0.099° 273 0.20 % 0.2% Residual Out-of-Straightness 3.8 2.51 % 0.127° 348 0.35 %

4.5** 2.91 % 0.146° 389 0.44 % First Yield 5 3.16 % 0.158° 415 0.50 %

7.1 4.14 % 0.203° 444 0.87 % 7.5** 4.32 % 0.215° 485 1.00 % 1.0% Residual Out-of-Straightness 8.5 4.84 % 0.250° 603 1.38 % 9.5 4.89 % 1.665° 698 2.68 % First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 2.8

factor: 3.8

factor: 5

factor: 7.1

factor: 8.5

factor: 9.5







(a)

(b)






Peak Displacement

Peak Rotation

Peak Stress



1 0.92 % 0.042° 155 0 %

2.2 1.92 % 0.099° 299 0.19 % 0.2% Residual Out-of-Straightness 3 2.62 % 0.134° 378 0.34 %

3.2** 2.81 % 0.144° 389 0.41 % First Yield 4 3.39 % 0.176° 422 0.60 % 5 4.08 % 0.201° 506 0.90 %



0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 2.2

factor: 3

factor: 4

factor: 5

factor: 6

factor: 7







(a)

(b)




C.7 WCAN07 (CASCADIA RECORD, MAGNITUDE 9, 112 – 201 KM)


Peak Displacement

Peak Rotation

Peak Stress



1 0.66 % 0.032° 108 0 %

2.8 1.90 % 0.096° 239 0.17 % 3** 2.01 % 0.101° 250 0.20 % 0.2% Residual Out-of-Straightness 4 2.77 % 0.139° 322 0.39 % 5 3.58 % 0.188° 380 0.78 %

5.3** 3.79 % 0.199° 389 0.91 % First Yield 5.4** 3.95 % 0.206° 395 1.00 % 1.0% Residual Out-of-Straightness

6 4.41 % 0.228° 415 1.27 % 7 5.34 % 0.289° 445 1.93 % 8 86.11 % 89° 798 86.11 % First Buckle


0

10

20

30

40

50

60

70

80

0 2 4 6


Hei

ght

abov

e B

ase

(m)

factor: 1

factor: 2.8

factor: 4

factor: 5

factor: 6

factor: 7

factor: 8






(Scale of this figure is 3 times smaller than the typical scale used in these types of figures)


(a)

(b) free vibration begins at 258.96s (not shown)



C.8 FRAGILITY CURVES FOR ADDITIONAL INTENSITY MEASURES

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8PGV (m/s)

Pro

babi

lity

of E

xcee

danc

e

Figure C.15: Fragility curves for the Western Canada earthquake suite for PGV intensity measure

0

0.2

0.4

0.6

0.8

1

0 3 6 9 12 15 18PGA (g)

Pro

babi

lity

of E

xcee

danc

e

Figure C.16: Fragility curves for the Western Canada earthquake suite for PGA intensity measure



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SEISMIC ANALYSIS OF STEEL WIND TURBINE OWERS › bitstream › 1807 › ... · SEISMIC ANALYSIS OF WIND TURBINE TOWERS IN THE CANADIAN ENVIRONMENT - iii - ACKNOWLEDGEMENTS I would