• Federal Highway Administration >
• Publications >
• Research Publications >
• 05083 >
• Nondestructive Evaluation >
• Wind-Induced Vibration of Stay Cables

Wind-Induced Vibration of Stay Cables

PDF files can be viewed with the Acrobat® Reader®

Table of Contents

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.

Metric Conversion Chart

TABLE OF CONTENTS

• EXECUTIVE SUMMARY
• CHAPTER 1. INTRODUCTION
  • BACKGROUND
  • PROJECT OBJECTIVES AND TASKS
• CHAPTER 2. COMPILATION OF EXISTING INFORMATION
  • REFERENCE MATERIALS
  • INVENTORY OF U.S. CABLE-STAYED BRIDGES
• CHAPTER 3. ANALYSIS, EVALUATION, AND TESTING
  • MECHANICS OF WIND-INDUCED VIBRATIONS
    • Reynolds Number
    • Strouhal Number
    • Scruton Number
    • Vortex Excitation of an Isolated Cable and Groups of Cables
    • Rain/Wind-Induced Vibrations
    • Wake Galloping for Groups of Cables
    • Galloping of Dry Inclined Cables
  • WIND TUNNEL TESTING OF DRY INCLINED CABLES
    • Introduction
    • Testing
    • Results Summary
  • OTHER EXCITATION MECHANISMS
    • Effects Due to Live Load
    • Deck-Stay Interaction Because of Wind
  • STUDY OF MITIGATION METHODS
    • Linear and Nonlinear Dampers
    • Linear Dampers
    • Nonlinear Dampers
    • Field Performance of Dampers
    • Crosstie Systems
    • Analysis
    • Field Performance
    • Considerations for Crosstie Systems
    • Cable Surface Treatment
  • FIELD MEASUREMENTS OF STAY CABLE DAMPING
    • Leonard P. Zakim Bunker Hill Bridge (over Charles River in Boston, MA)
    • Sunshine Skyway Bridge (St. Petersburg, FL)
  • BRIDGE USER TOLERANCE LIMITS ON STAY CABLE VIBRATION
• CHAPTER 4. DESIGN GUIDELINES
  • NEW CABLE-STAYED BRIDGES
    • General
    • Mitigation of Rain/Wind Mechanism
    • Additional Mitigation
    • Minimum Scruton Number
    • External Dampers
    • Cable Crossties
    • User Tolerance Limits
  • RETROFIT OF EXISTING BRIDGES
  • WORKED EXAMPLES
    • Example 1
    • Example 2
• CHAPTER 5. RECOMMENDATIONS FOR FUTURE RESEARCH AND DEVELOPMENT
  • WIND TUNNEL TESTING OF DRY INCLINED CABLES
  • DECK-INDUCED VIBRATION OF STAY CABLES
  • MECHANICS OF RAIN/WIND-INDUCED VIBRATIONS
  • DEVELOP A MECHANICS-BASED MODEL FOR STAY CABLE VIBRATION ENABLING THE PREDICTION OF ANTICIPATED VIBRATION CHARACTERISTICS
  • PREDICT THE PERFORMANCE OF STAY CABLES AFTER MITIGATION USING THE MODEL
  • PERFORM A DETAILED QUANTITATIVE ASSESSMENT OF VARIOUS ALTERNATIVE MITIGATION STRATEGIES
  • IMPROVE UNDERSTANDING OF INHERENT DAMPING IN STAYS AND THAT PROVIDED BY EXTERNAL DEVICES
  • IMPROVE UNDERSTANDING OF CROSSTIE SOLUTIONS
  • REFINE RECOMMENDATIONS FOR EFFECTIVE AND ECONOMICAL DESIGN OF STAY CABLE VIBRATION MITIGATION STRATEGIES FOR FUTURE BRIDGES
• APPENDIX A. DATABASE OF REFERENCE MATERIALS
• APPENDIX B. INVENTORY OF U.S. CABLE-STAYED BRIDGES
• APPENDIX C. WIND-INDUCED CABLE VIBRATIONS
• APPENDIX D. WIND TUNNEL TESTING OF STAY CABLES
• APPENDIX E. LIST OF TECHNICAL PAPERS
• APPENDIX F. ANALYTICAL AND FIELD INVESTIGATIONS
• APPENDIX G. INTRODUCTION TO MECHANICS OF INCLINED CABLES
• APPENDIX H. LIVE-LOAD VIBRATION SUBSTUDY
• APPENDIX I. STUDY OF USER COMFORT
• REFERENCES AND OTHER SOURCES
  

LIST OF FIGURES

• Figure 1. Graph. Comparison of wind velocity-damping relation of inclined dry cable
• Figure 2. Graph. Cable M26, tension versus time (transit train speed = 80 km/h (50 mi/h))
• Figure 3. Graph. Time history and power spectral density (PSD) of the first 2 Hz for deck at midspan (vertical direction)
• 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
• Figure 5. Deck level wind speed
• Figure 6. Photo. Damper at cable anchorage
• Figure 7. Drawing. Taut cable with linear damper
• Figure 8. Graph. Normalized damping ratio versus normalized damper coefficient: Linear damper.
• Figure 9. Graph. Normalized damping ratio versus normalized damper coefficient (β = 0.5)
• Figure 10. Photo. Fred Hartman Bridge
• Figure 11. Photo. Cable crosstie system
• Figure 12. Photo. Dames Point Bridge
• Figure 13. Chart. General problem formulation
• Figure 14. Chart. General problem formulation (original configuration)
• Figure 15. Graph. Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 1.
• Figure 16. Graph. Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 5.
• Figure 17. Graph. Comparative analysis of network vibration characteristics and individual cable behavior: Fred Hartman Bridge
• Figure 18. Chart. Fred Hartman Bridge, field performance testing arrangement
• Figure 19. Drawing. Types of cable surface treatments
• Figure 20. Graph. Example of test data for spiral bead cable surface treatment
• Figure 21. Photo. Leonard P. Zakim Bunker Hill Bridge
• Figure 22. Graph. Sample decay: No damping and no crossties
• Figure 23. Graph. Sample decay: With damping and no crossties
• Figure 24. Graph. Sample decay: With damping and crossties
• Figure 25. Photo. Sunshine Skyway Bridge.
• Figure 26. Photo. Stay and damper brace configuration
• Figure 27. Photo. Reference database search page
• Figure 28. Photo. Reference database search results page
• Figure 29. Photo. U.S. cable-stayed bridge database: Switchboard
• Figure 30. Photo. U.S. cable-stayed bridge database: General bridge information
• Figure 31. Photo. U.S. cable-stayed bridge database: Cable data
• Figure 32. Photo. U.S. cable-stayed bridge database: Wind data
• Figure 33. Graph. Galloping of inclined cables
• Figure 34. Drawing. Aerodynamic devices
• Figure 35. Drawing. Cable crossties
• Figure 36. Drawing. Viscous damping
• Figure 37. Drawing. Material damping
• Figure 38. Drawing. Angle relationships between stay cables and natural wind (after Irwin et al.).⁽²⁷⁾
• Figure 39. Photo. Cable supporting rig: Top
• Figure 40. Photo. Cable supporting rig: Bottom
• Figure 41. Drawing. Longitudinal section of the propulsion wind tunnel
• Figure 42. Drawing. Cross section of the working section of propulsion wind tunnel
• Figure 43. Photo. Data acquisition system
• Figure 44. Photo. Airpot damper
• Figure 45. Drawing. Cross section of airpot damper
• Figure 46. Photo. Elastic bands on the spring coils
• Figure 47. Drawing. Side view of setups 1B and 1C
• Figure 48. Drawing. Side view of setups 2A and 2C
• Figure 49. Drawing. Side view of setups 3A and 3C
• Figure 50. Photo. Cable setup in wind tunnel for testing
• Figure 51. Graph. Amplitude-dependent damping (A, sway; B, vertical) with setup 2C (smooth surface, low damping)
• Figure 52. Graph. Divergent response of inclined dry cable (setup 2C; smooth surface, low damping)
• Figure 53. Graph. Lower end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s)
• Figure 54. Graph. Top end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s)
• Figure 55. Graph. Lower end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s)
• Figure 56. Graph. Top end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s)
• Figure 57. Graph. Trajectory of setup 2C at U = 32 m/s (105 ft/s)
• 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
• 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
• 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
• Figure 61. Graph. Top end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes
• Figure 62. Graph. Lower end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes
• Figure 63. Graph. Top end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes
• Figure 64. Graph. Lower end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes
• Figure 65. Graph. Top end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes
• Figure 66. Graph. Lower end X-motion, time history of setup 2A at U = 19 m/s (62 ft/s)
• Figure 67. Graph. Top end X-motion, time history of setup 2A at U = 19 m/s (62 ft/s)
• Figure 68. Graph. Lower end Y-motion, time history of setup 2A at U = 19 m/s (62 ft/s)
• Figure 69. Graph. Top end Y-motion, time history of setup 2A at U = 19 m/s (62 ft/s)
• Figure 70. Graph. Lower end X-motion, time history of setup 1B at U = 24 m/s (79 ft/s)
• Figure 71. Graph. Top end X-motion, time history of setup 1B at U = 24 m/s (79 ft/s)
• Figure 72. Graph. Lower end Y-motion, time history of setup 1B at U = 24 m/s (79 ft/s)
• Figure 73. Graph. Top end Y-motion, time history of setup 1B at U = 24 m/s (79 ft/s)
• Figure 74. Graphic. Lower end X-motion, time history of setup 1C at U = 36 m/s (118 ft/s)
• Figure 75. Graph. Top end X-motion, time history of setup 1C at U = 36 m/s (118 ft/s)
• Figure 76. Graph. Lower end Y-motion, time history of setup 1C at U = 36 m/s (118 ft/s)
• Figure 77. Graph. Top end Y-motion, time history of setup 1C at U = 36 m/s (118 ft/s)
• Figure 78. Graph. Lower end X-motion, time history of setup 3A at U = 22 m/s (72 ft/s)
• Figure 79. Graph. Top end X-motion, time history of setup 3A at U = 22 m/s (72 ft/s)
• Figure 80. Graph. Lower end Y-motion, time history of setup 3A at U = 22 m/s (72 ft/s)
• Figure 81. Graph. Top end Y-motion, time history of setup 3A at U = 22 m/s (72 ft/s)
• Figure 82. Graph. Trajectory of setup 2A at U = 18 m/s (59 ft/s), first 5 minutes
• Figure 83. Graph. Trajectory of setup 2A at U = 18 m/s (59 ft/s), second 5 minutes
• Figure 84. Graphic. Trajectory of setup 2A at U = 19 m/s (62 ft/s)
• Figure 85. Graphic. Trajectory of setup 1B at U = 24 m/s (79 ft/s)
• Figure 86. Graphic. Trajectory of setup 1C at U = 36 m/s (119 ft/s)
• Figure 87. Graph. Trajectory of setup 3A at U = 22 m/s (72 ft/s)
• Figure 88. Graph. Wind-induced response of inclined dry cable (setup 2A; smooth surface, low damping)
• Figure 89. Graph. Wind-induced response of inclined dry cable (setup 1B; smooth surface, low damping)
• Figure 90. Graph. Wind-induced response of inclined dry cable (setup 1C; smooth surface, low damping)
• Figure 91. Graph. Wind-induced response of inclined dry cable (setup 3A; smooth surface, low damping)
• Figure 92. Graph. Wind-induced response of inclined dry cable (setup 3B; smooth surface, low damping)
• Figure 93. Graph. Critical Reynolds number of circular cylinder (from Scruton).⁽²⁷⁾
• Figure 94. Graph. Damping trace of four different levels of damping (setup 1B; smooth surface)
• Figure 95. Graph. Effect of structural damping on the wind response of inclined cable (setup 1B; smooth surface)
• Figure 96. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 3A; low damping)
• Figure 97. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 1B; low damping)
• Figure 98. Graph. Surface roughness effect on wind-induced response of dry inclined cable (setup 2A; low damping)
• Figure 99. Graph. Amplitude-dependent damping in the X-direction with setup 2A (frequency ratio effect)
• Figure 100. Graph. Amplitude-dependent damping in the Y-direction with setup 2A (frequency ratio effect)
• Figure 101. Graph. Wind-induced response of inclined cable in the X-direction with setup 2A (frequency ratio effect)
• Figure 102. Graph. Wind-induced response of inclined cable in the Y-direction with setup 2A (frequency ratio effect)
• Figure 103. Graph. Comparison of wind velocity-damping relation of inclined dry cable
• Figure 104. Chart. Taut cable with a linear damper
• Figure 105. Graph. Normalized damping ratio versus normalized damper coefficient
• Figure 106. Chart. Cable with attached friction/viscous damper
• Figure 107. Chart. Force-velocity curve for friction/viscous damper
• Figure 108. Graph. Normalized damping ratio versus clamping ratio
• Figure 109. Graph. Normalized viscous damper coefficient versus clamping ratio
• Figure 110. Graph. Relationship between nondimensional parameters μ and κ with different values of the clamping ratio Θ_ci for a friction/viscous damper
• Figure 111. Graphic. Normalized damping ratio versus κ with varying μ
• Figure 112. Graph. Normalized damping ratio versus normalized damper coefficient (β = 0.5)
• Figure 113. Graph. Normalized damping ratio versus mode ratio (β = 1)
• Figure 114. Graph. Normalized damping ratio versus amplitude ratio (β = 0.5)
• Figure 115. Graph. Normalized damping ratio versus mode-amplitude ratio (β = 0)
• Figure 116. Chart. General problem formulation
• Figure 117. Chart. General problem formulation (original configuration)
• Figure 118. Graph. Eigenfunctions of the network equivalent to Fred Hartman Bridge (1st–8th modes)
• Figure 119. Graph. Comparative analysis of network vibration characteristics and individual cable behavior (Fred Hartman Bridge; NET_3C, original configuration; NET_3RC,infinitely rigid restrainers; NET_3CG, spring connectors extended to ground (restrainers 2,3))
• Figure 120. Chart. Generalized cable network configuration
• Figure 121. Chart. Twin cable with variable position connector
• Figure 122. Graph. Twin cable system, with connector location ξ = 0.35, example of frequency solution for linear spring model
• Figure 123. Graph. Typical solution curves of the complex frequency for the dashpot
• Figure 124. Chart. Intermediate segments of specific cables only
• Figure 125. Chart. Fred Hartman Bridge (A-line) 3D network
• Figure 126. Chart. Equivalent model
• Figure 127. Graph. Frequency solutions (1st mode) for the damped cable network (A-line)
• Figure 128. Graph. Complex modal form (1st mode) for the optimized system M1(uo)
• Figure 129. Graphic. Damping versus mode number for Hartman stays A16 and A23
• Figure 130. Graph. Stay vibration and damper force characteristics; stay A16
• Figure 131. Graph. Stay vibration and damper force characteristics; stay A23
• Figure 132. Chart. In-plane versus lateral RMS displacement for (A) AS16 and (B) AS23
• Figure 133. Chart. Sample Lissajous plots of displacement for two records from AS16
• Figure 134. Chart. Power spectral density of displacement of two records from AS16
• Figure 135. Graph. Sample Lissajous plots of displacement for two records from AS23
• Figure 136. Graph. Power spectral density of displacement of two records from AS23
• Figure 137. Graph. In-plane versus lateral RMS displacement for (A) AS16 and (B) AS23 after damper installation
• Figure 138. Graph. Lissajous and power spectral density plots of displacement for record A
• Figure 139. Graph. Modal frequencies of stays (A) AS16 and (B) AS23
• Figure 140. Graph. Second-mode frequency versus RMS displacement for stay AS16
• Figure 141. Graph. Estimated modal damping of stay AS16 showing effect of damper
• Figure 142. Graphic. Histogram of estimated damping for (A) mode 2 of AS16 and (B) mode 3 of AS23
• Figure 143. Graphic. Dependence of modal damping on damper force
• Figure 144. Graph. RMS damper force versus RMS displacements for (A) AS16 and (B) AS23
• Figure 145. Chart. Damper force versus displacement and velocity for a segment of a sample record
• Figure 146. Chart. Displacement and damper force time histories of a sample record
• Figure 147. Drawing. Incline stay cable properties
• Figure 148. Drawing. Definition diagram for a horizontal cable (taut string), compared to the definition diagram for an inclined cable
• Figure 149. Graph. Cable √T/m versus cable unstressed length: Summary of Alex Fraser,Maysville, and Owensboro bridges
• Figure 150. Graph. Cable frequency versus cable unstressed length: Summary of Alex Fraser, Maysville, and Owensboro bridges
• Figure 151. Photo. RAMA 8 Bridge (artistic rendering)
• Figure 152. Drawing. RAMA 8 Bridge computer model: XY, YZ, and ZX views
• Figure 153. Chart. Independent cable M26 discretization 10-segment model: XZ view
• Figure 154. Chart. Cable catenary
• Figure 155. Chart. Cable modes: XZ, YZ, and XY views (as defined in figure 152)
• Figure 156. Chart. Inextensible cable mode 1, in-plane: XY, YX, and XZ views
• Figure 157. Drawing. Cable M26 discretization: 10-segment model, isometric view. Only cables M26 are shown. Other cables not shown for clarity
• Figure 158. Drawing. Cable M26 discretization: 10-segment model, XZ view. Other cables not shown for clarity
• Figure 159. Chart. Fundamental bridge modes
• Figure 160. Chart. Additional bridge modes
• Figure 161. Chart. Four first modes of the cables; XY, YZ, and XZ views
• Figure 162. Chart. Four second modes of the cables; XY, YZ, and XZ views
• Figure 163. Chart. Four third modes of the cables; XY, YZ, and XZ views
• Figure 164. Chart. Nodes, members, and cables for comparison of results
• Figure 165. Graph. RAMA 8 Bridge model damping versus frequency
• Figure 166. Graph. Vertical displacements, velocities, and accelerations of node 427 versus time (train speed = 80 km/h (50 mi/h)
• Figure 167. Graph. Member 1211: Bending moment versus time (train speed = 80 km/h (50 mi/h))
• Figure 168. Graph. Cable M26: Tension versus time (train speed = 80 km/h (50 mi/h))
• Figure 169. Graph. Difference in cable tension for cable M26 between the dynamic train load case and static train load case versus time (train speed = 80 km/h (50 mi/h))
• Figure 170. Graph. Cable M26 tension spectra (train speed = 80 km/h (50 mi/h))
• Figure 171. Graph. Global coordinate displacements (A, B, C) of cable M26 nodes (mm) versus time (train speed = 80 km/h (50 mi/h))
• Figure 172. Chart. Transformation from global coordinates to coordinates along the cable
• Figure 173. Chart. Local coordinate displacements of nodes of cable M26 (mm).Displacements are shown for three nodes of the cable: At 1/4 span (closer to the tower),1/2 span, and 3/4 span (closer to the deck; train speed = 80 km/h (50 mi/h)
• Figure 174. Graph. Spectra for movements of cable M26 nodes: At 1/4 span (closer to the tower), 1/2 span, and 3/4 span (closer to the deck; frequency range = 0–2 Hz; train speed = 80 km/h (50 mi/h))
• Figure 175. Graph. Deck rotations and cable end rotations for cable M26: Dynamic (train speed = 80 km/h (50 mi/h)) and static
• Figure 176. Graph. Deck rotations and cable end rotations for cable M21: Dynamic (train speed = 80 km/h (50 mi/h)) and static
• Figure 177. Graph. Effect of mode (constant amplitude and velocity)
• Figure 178. Graph. Effect of velocity (constant amplitude)
• Figure 179. Graph. Effect of amplitude (constant velocity)

LIST OF TABLES

• Table 1. Dry inclined cable testing: Model setup
• Table 2. Dry inclined cable testing: Damping levels
• Table 3. Dry inclined cable testing: Surface condition
• Table 4. Stay and damper properties
• Table 5. Cable network modes (0-4 Hz) predicted by the model
• Table 6. Preliminary cable damping measurements: Leonard P. Zakim Bunker Hill Bridge
• Table 7. Preliminary cable damping measurements from the Sunshine Skyway Bridge
• Table 8. Data from table 4
• Table 9. Cable-stayed bridge inventory
• TTable 10. Bridges reporting cable vibration and mitigating measures
• TTable 11. Model setup
• Table 12. Different damping levels of the model
• Table 13. Surface condition
• Table 14. Limited-amplitude motion
• Table 15. Geometrical and structural characteristics of the Fred Hartman system
• Table 16. Individual cable frequencies (0–4 Hz) of the A-line side-span stays of the Fred Hartman Bridge (direct measurement)
• Table 17. Cable network modes (0–4 Hz) predicted by the model (A–line system)
• Table 18. Stay cable property comparison
• Table 19. Free independent extensible cable vibration versus theoretical inextensible
• Table 20. Free independent inextensible cable vibration periods: Theoretical values and values obtained by analysis
• Table 21. Cable vibration periods and frequencies: Theoretical values and values obtained by analysis
• Table 22. Vertical displacements due to live load
• Table 23. Bending moments due to live load
• Table 24. Cable forces due to live load
• Table 25. Cable end rotations and deck rotations

Next