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Wind-Induced Vibration of Stay Cables PUBLICATION NO. FHWA-HRT-05-083 AUGUST 2007 Research, Development, and Technology Turner-Fairbank Highway Research Center 6300 Georgetown Pike McLean, VA 22101-2296 Foreword Cable-stayed bridges have become the form of choice over the past several decades for bridges in the medium- to long-span range. In some cases, serviceability problems involving large amplitude vibrations of stay cables under certain wind and rain conditions have been observed. This study was conducted to develop a set of consistent design guidelines for mitigation of excessive cable vibrations on cable-stayed bridges. The project team started with a thorough review of existing literature; this review indicated that while the rain/wind problem is known in sufficient detail, galloping of dry inclined cables was the most critical wind-induced vibration mechanism in need of further experimental research. A series of wind tunnel tests was performed to study this mechanism. Analytical and experimental research was performed to study mitigation methods, covering a range of linear and nonlinear dampers and crossties. The study also included brief studies on live load-induced vibrations and establishing driver/pedestrian comfort criteria. Based on the above, design guidelines for the mitigation of wind-induced vibrations of stay cables were developed. As a precautionary note, the state of the art in stay cable vibration mitigation is not an exact science. These new guidelines are only intended for use by professionals with experience in cable-stayed bridge design, analysis, and wind engineering, and should only be applied with engineering judgment and due consideration of special conditions surrounding each project. Gary L. Henderson Office of Infrastructure Research and Development Notice This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation. The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers' names appear in this report only because they are considered essential to the objective of the document. Quality Assurance Statement The Federal Highway Administration (FHWA) provides high-quality information to serve Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement. Technical Report Documentation Page 1. Report No. FHWA-RD-05-083 2. Government Accession No. 3. Recipient’s Catalog No. 5. Report Date August 2007 4. Title and Subtitle Wind-Induced Vibration of Stay Cables 6. Performing Organization Code 7. Author(s) Sena Kumarasena, Nicholas P. Jones, Peter Irwin, Peter Taylor 8. Performing Organization Report No. 10. Work Unit No. 9. Performing Organization Name and Address Primary Consultant: HNTB Corporation 75 State St., Boston, MA 02109 352 Seventh Ave., 6 th Floor, New York, NY 10001-5012 In association with: John Hopkins University Dept. of Civil Engineering, Baltimore, MD 21218-2686 Rowan Williams Davies and Irwin, Inc. 650 Woodlawn Road West, Guelph, Ontario N1K 1B8 Buckland and Taylor, Ltd. Suite 101, 788 Harborside Drive, North Vancouver, BC V7P3R7 11. Contract or Grant No. DTFH61-99-C-00095 13. Type of Report and Period Covered Final Report September 1999 to December 2002 12. Sponsoring Agency Name and Address Office of Infrastructure R&D Federal Highway Administration 6300 Georgetown Pike McLean, VA 22101-2296 14. Sponsoring Agency Code 15. Supplementary Notes Contracting Officer’s Technical Representative (COTR) Harold Bosch, HRDI-07 16. Abstract Cable-stayed bridges have become the form of choice over the past several decades for bridges in the medium- to long-span range. In some cases, serviceability problems involving large amplitude vibrations of stay cables under certain wind and rain conditions have been observed. This study was conducted to develop a set of consistent design guidelines for mitigation of excessive cable vibrations on cable-stayed bridges. To accomplish this objective, the project team started with a thorough review of existing literature to determine the state of knowledge and identify any gaps that must be filled to enable the formation of a consistent set of design recommendations. This review indicated that while the rain/wind problem is known in sufficient detail, galloping of dry inclined cables was the most critical wind-induced vibration mechanism in need of further experimental research. A series of wind tunnel tests was performed to study this mechanism. Analytical and experimental research was performed to study mitigation methods, covering a range of linear and nonlinear dampers and crossties. The study also included brief studies on live load-induced vibrations and establishing driver/pedestrian comfort criteria. Based on the above, design guidelines for mitigation of wind-induced vibrations of stay cables were developed. 17. Key Words cable-stayed bridge, cables, vibrations, wind, rain, dampers, crossties 18. Distribution Statement No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161 19. Security Classif. (of this report) Unclassified 20. Security Classif. (of this page) Unclassified 21. No of Pages 281 22. Price Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized ii SI* (MODERN METRIC) CONVERSION FACTORS APPROXIMATE CONVERSIONS TO SI UNITS Symbol When You Know Multiply By To Find Symbol LENGTH in inches 25.4 millimeters mm ft feet 0.305 meters m yd yards 0.914 meters m mi miles 1.61 kilometers km A REA in 2 square inches 645.2 square millimeters mm 2 ft 2 square feet 0.093 square meters m 2 yd 2 square yard 0.836 square meters m 2 ac acres 0.405 hectares ha mi 2 square miles 2.59 square kilometers km 2 V OLUME fl oz fluid ounces 29.57 milliliters mL gal gallons 3.785 liters L ft 3 cubic feet 0.028 cubic meters m 3 yd 3 cubic yards 0.765 cubic meters m 3 NOTE: volumes greater than 1000 L shall be shown in m 3 MASS oz ounces 28.35 grams g lb pounds 0.454 kilograms kg T short tons (2000 lb) 0.907 megagrams (or "metric ton") Mg (or "t") TEMPERATURE (exact degrees) o F Fahrenheit 5 (F-32)/9 Celsius o C or (F-32) / 1.8 ILLUMINATION fc foot-candles 10.76 lux lx fl foot-Lamberts 3.426 candela/m 2 cd/m 2 FORCE and PRESSURE or STRESS lbf poundforce 4.45 newtons N lbf/in 2 poundforce per square inch 6.89 kilopascals kPa APPROXIMATE CONVERSIONS FROM SI UNITS Symbol When You Know Multiply By To Find Symbol LENGTH mm millimeters 0.039 inches in m meters 3.28 feet ft m meters 1.09 yards yd km kilometers 0.621 miles mi A REA mm 2 square millimeters 0.0016 square inches in 2 m 2 square meters 10.764 square feet ft 2 m 2 square meters 1.195 square yards yd 2 ha hectares 2.47 acres ac km 2 square kilometers 0.386 square miles mi 2 V OLUME mL milliliters 0.034 fluid ounces fl oz L liters 0.264 gallons gal m 3 cubic meters 35.314 cubic feet ft 3 m 3 cubic meters 1.307 cubic yards yd 3 MASS g grams 0.035 ounces oz kg kilograms 2.202 pounds lb Mg (or "t") megagrams (or "metric ton") 1.103 short tons (2000 lb) T TEMPERATURE (exact degrees) o C Celsius 1.8C+32 Fahrenheit o F ILLUMINATION lx lux 0.0929 foot-candles fc cd/m 2 candela/m 2 0.2919 foot-Lamberts fl FORCE and PRESSURE or STRESS N newtons 0.225 poundforce lbf kPa kilopascals 0.145 poundforce per square inch lbf/in 2 *SI is the symbol for th International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. e (Revised March 2003 ) iii TABLE OF CONTENTS EXECUTIVE SUMMARY 1 CHAPTER 1. INTRODUCTION 5 BACKGROUND 5 PROJECT OBJECTIVES AND TASKS 7 CHAPTER 2. COMPILATION OF EXISTING INFORMATION 9 REFERENCE MATERIALS 9 INVENTORY OF U.S. CABLE-STAYED BRIDGES 9 CHAPTER 3. ANALYSIS, EVALUATION, AND TESTING 11 MECHANICS OF WIND-INDUCED VIBRATIONS 11 Reynolds Number 11 Strouhal Number 11 Scruton Number 12 Vortex Excitation of an Isolated Cable and Groups of Cables 12 Rain/Wind-Induced Vibrations 13 Wake Galloping for Groups of Cables 14 Galloping of Dry Inclined Cables 15 WIND TUNNEL TESTING OF DRY INCLINED CABLES 16 Introduction 16 Testing 17 Results Summary 18 OTHER EXCITATION MECHANISMS 20 Effects Due to Live Load 20 Deck-Stay Interaction Because of Wind 21 STUDY OF MITIGATION METHODS 23 Linear and Nonlinear Dampers 23 Linear Dampers 24 Nonlinear Dampers 25 Field Performance of Dampers 26 Crosstie Systems 28 Analysis 30 Field Performance 33 Considerations for Crosstie Systems 35 Cable Surface Treatment 36 FIELD MEASUREMENTS OF STAY CABLE DAMPING 37 Leonard P. Zakim Bunker Hill Bridge (over Charles River in Boston, MA) 37 Sunshine Skyway Bridge (St. Petersburg, FL) 40 BRIDGE USER TOLERANCE LIMITS ON STAY CABLE VIBRATION 42 iv CHAPTER 4. DESIGN GUIDELINES 45 NEW CABLE-STAYED BRIDGES 45 General 45 Mitigation of Rain/Wind Mechanism 45 Additional Mitigation 45 Minimum Scruton Number 45 External Dampers 46 Cable Crossties 46 User Tolerance Limits 47 RETROFIT OF EXISTING BRIDGES 47 WORKED EXAMPLES 48 Example 1 48 Example 2 52 CHAPTER 5. RECOMMENDATIONS FOR FUTURE RESEARCH AND DEVELOPMENT 55 WIND TUNNEL TESTING OF DRY INCLINED CABLES 55 DECK-INDUCED VIBRATION OF STAY CABLES 55 MECHANICS OF RAIN/WIND-INDUCED VIBRATIONS 55 DEVELOP A MECHANICS-BASED MODEL FOR STAY CABLE VIBRATION ENABLING THE PREDICTION OF ANTICIPATED VIBRATION CHARACTERISTICS 56 PREDICT THE PERFORMANCE OF STAY CABLES AFTER MITIGATION USING THE MODEL 57 PERFORM A DETAILED QUANTITATIVE ASSESSMENT OF VARIOUS ALTERNATIVE MITIGATION STRATEGIES 58 IMPROVE UNDERSTANDING OF INHERENT DAMPING IN STAYS AND THAT PROVIDED BY EXTERNAL DEVICES 58 IMPROVE UNDERSTANDING OF CROSSTIE SOLUTIONS 59 REFINE RECOMMENDATIONS FOR EFFECTIVE AND EC ONOMICAL DESIGN OF STAY CABLE VIBRATION MITIGATION STRATEGIES FOR FUTURE BRIDGES 59 APPENDIX A. DATABASE OF REFERENCE MATERIALS 61 APPENDIX B. INVENTORY OF U.S. CABLE-STAYED BRIDGES 81 APPENDIX C. WIND-INDUCED CABLE VIBRATIONS 87 APPENDIX D. WIND TUNNEL TESTING OF STAY CABLES 101 v APPENDIX E. LIST OF TECHNICAL PAPERS 153 APPENDIX F. ANALYTICAL AND FIELD INVESTIGATIONS 155 APPENDIX G. INTRODUCTION TO MECHANICS OF INCLINED CABLES 213 APPENDIX H. LIVE-LOAD VIBRATION SUBSTUDY 225 APPENDIX I. STUDY OF USER COMFORT 257 REFERENCES AND OTHER SOURCES 261 vi LIST OF FIGURES Figure 1. Graph. Comparison of wind velocity-damping relation of inclined dry cable 19 Figure 2. Graph. Cable M26, tension versus time (transit train speed = 80 km/h (50 mi/h)) 20 Figure 3. Graph. Time history and power spectral density (PSD) of the first 2 Hz for deck at midspan (vertical direction) 22 Figure 4. Graph. Time history and power spectral density (PSD) of the first 2 Hz for cable at AS24 (in-plane direction) deck level wind speed 22 Figure 5. Deck level wind speed 22 Figure 6. Photo. Damper at cable anchorage. 23 Figure 7. Drawing. Taut cable with linear damper. 24 Figure 8. Graph. Normalized damping ratio versus normalized damper coefficient: Linear damper 25 Figure 9. Graph. Normalized damping ratio versus normalized damper coefficient (β = 0.5) 26 Figure 10. Photo. Fred Hartman Bridge 27 Figure 11. Photo. Cable crosstie system. 29 Figure 12. Photo. Dames Point Bridge. 30 Figure 13. Chart. General problem formulation. 31 Figure 14. Chart. General problem formulation (original configuration) 31 Figure 15. Graph. Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 1. 32 Figure 16. Graph. Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 5. 32 Figure 17. Graph. Comparative analysis of network vibration characteristics and individual cable behavior: Fred Hartman Bridge 33 Figure 18. Chart. Fred Hartman Bridge, field performance testing arrangement 34 Figure 19. Drawing. Types of cable surface treatments. 36 Figure 20. Graph. Example of test data for spiral bead cable surface treatment. 37 Figure 21. Photo. Leonard P. Zakim Bunker Hill Bridge 37 Figure 22. Graph. Sample decay: No damping and no crossties. 39 Figure 23. Graph. Sample decay: With damping and no crossties. 39 Figure 24. Graph. Sample decay: With damping and crossties. 40 Figure 25. Photo. Sunshine Skyway Bridge. 40 Figure 26. Photo. Stay and damper brace configuration 41 Figure 27. Photo. Reference database search page. 61 Figure 28. Photo. Reference database search results page 62 Figure 29. Photo. U.S. cable-stayed bridge database: Switchboard. 82 Figure 30. P hoto. U.S. cable-stayed bridge database: General bridge information. 83 Figure 31. Photo. U.S. cable-stayed bridge database: Cable data 84 Figure 32. Photo. U.S. cable-stayed bridge database: Wind data. 85 Figure 33. Graph. Galloping of inclined cables 92 Figure 34. Drawing. Aerodynamic devices. 94 Figure 35. Drawing. Cable crossties 98 Figure 36. Drawing. Viscous damping. 98 Figure 37. Drawing. Material damping 99 vii Figure 38. Drawing. Angle relationships between stay cables and natural wind (after Irwin et al.). (27) 103 Figure 39. Photo. Cable supporting rig: Top. 105 Figure 40. Photo. Cable supporting rig: Bottom. 105 Figure 41. Drawing. Longitudinal section of the propulsion wind tunnel 107 Figure 42. Drawing. Cross section of the wo rking section of propulsion wind tunnel. 108 Figure 43. Photo. Data acquisition system 109 Figure 44. Photo. Airpot damper. 111 Figure 45. Drawing. Cross section of airpot damper 112 Figure 46. Photo. Elastic bands on the spring coils. 113 Figure 47. Drawing. Side view of setups 1B and 1C 115 Figure 48. Drawing. Side view of setups 2A and 2C 116 Figure 49. Drawing. Side view of setups 3A and 3C 117 Figure 50. Photo. Cable setup in wind tunnel for testing 118 Figure 51. Graph. Amplitude-dependent damping (A, sway; B, vertical) with setup 2C (smooth surface, low damping) 125 Figure 52. Graph. Divergent response of inclined dry cable (setup 2C; smooth surface, low damping). 126 Figure 53. Graph. Lower end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s) 126 Figure 54. Graph. Top end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s) 127 Figure 55. Graph. Lower end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s) 127 Figure 56. Graph. Top end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s) 128 Figure 57. Graph. Trajectory of setup 2C at U = 32 m/s (105 ft/s). 128 Figure 58. Graph. Lower end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes 129 Figure 59. Graph. Top end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes 129 Figure 60. Graph. Lower end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes 130 Figure 61. Graph. Top end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 mi nutes 130 Figure 62. Graph. Lower end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes 131 Figure 63. Graph. Top end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 mi nutes 131 Figure 64. Graph. Lower end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes 132 Figure 65. Graph. Top end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 mi nutes 132 Figure 66. Graph. Lower end X-motion, time history of setup 2A at U = 19 m/s (62 ft/s) 133 Figure 67. Graph. Top end X-motion, time history of setup 2A at U = 19 m/s (62 ft/s) 133 Figure 68. Graph. Lower end Y-motion, time history of setup 2A at U = 19 m/s (62 ft/s) 134 Figure 69. Graph. Top end Y-motion, time history of setup 2A at U = 19 m/s (62 ft/s) 134 Figure 70. Graph. Lower end X-m otion, time history of setup 1B at U = 24 m/s (79 ft/s). 135 Figure 71. Graph. Top end X-motion, time history of setup 1B at U = 24 m/ s (79 ft/s). 135 viii Figure 72. Graph. Lower end Y-motion, time history of setup 1B at U = 24 m/s (79 ft/s) 136 Figure 73. Graph. Top end Y-motion, time history of setup 1B at U = 24 m/s (79 ft/s) 136 Figure 74. Graphic. Lower end X-motion, time history of setup 1C at U = 36 m/s (118 ft/s). 137 Figure 75. Graph. Top end X-motion, time history of setup 1C at U = 36 m/ s (118 ft/s). 137 Figure 76. Graph. Lower end Y-motion, time history of setup 1C at U = 36 m/s (118 ft/s). 138 Figure 77. Graph. Top end Y-motion, time history of setup 1C at U = 36 m/s (118 ft/s) 138 Figure 78. Graph. Lower end X-motion, time history of setup 3A at U = 22 m/s (72 ft/s) 139 Figure 79. Graph. Top end X-motion, time history of setup 3A at U = 22 m/s (72 ft/s) 139 Figure 80. Graph. Lower end Y-m otion, time history of setup 3A at U = 22 m/s (72 ft/s) 140 Figure 81. Graph. Top end Y-motion, time history of setup 3A at U = 22 m/s (72 ft/s) 140 Figure 82. Graph. Trajectory of setup 2A at U = 18 m/s (59 ft/s), first 5 minutes. 141 Figure 83. Graph. Trajectory of setup 2A at U = 18 m/s (59 ft/s), second 5 minutes. 141 Figure 84. Graphic. Trajectory of setup 2A at U = 19 m/ s (62 ft/s). 142 Figure 85. Graphic. Trajectory of setup 1B at U = 24 m/s (79 ft/s). 142 Figure 86. Graphic. Trajectory of setup 1C at U = 36 m/ s (119 ft/s). 143 Figure 87. Graph. Trajectory of setup 3A at U = 22 m/s (72 ft/s). 143 Figure 88. Graph. Wind-induced response of inclined dry cable (setup 2A; smooth surface, low damping). 144 Figure 89. Graph. Wind-induced response of inclined dry cable (setup 1B; smooth surface, low damping). 144 Figure 90. Graph. Wind-induced response of inclined dry cable (setup 1C; smooth surface, low damping). 145 Figure 91. Graph. Wind-induced response of inclined dry cable (setup 3A; smooth surface, low damping). 145 Figure 92. Graph. Wind-induced response of inclined dry cable (setup 3B; smooth surface, low damping). 146 Figure 93. Graph. Critical Reynolds number of circular cylinder (from Scruton). (27) 146 Figure 94. Graph. Damping trace of four different levels of damping (setup 1B; smooth surface). 147 Figure 95. Graph. Effect of structural damping on the wind response of inclined cable (setup 1B; smooth surface). 147 Figure 96. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 3A; low damping). 148 Figure 97. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 1B; low damping) 148 Figure 98. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 2A; low damping). 149 Figure 99. Graph. Amplitude-dependent damping in the X-direction with setup 2A (frequency ratio effect). 149 Figure 100. Graph. Amplitude-dependent damping in the Y-direction with setup 2A (frequency ratio effect). 150 Figure 101. Graph. Wind-induced response of inclined cable in the X-direction with setup 2A (frequency ratio effect). 150 Figure 102. Graph. Wind-induced response of inclined cable in the Y-direction with setup 2A (frequency ratio effect). 151