Nghiên cứu & Hướng dẫn thiết kế giảm dao động gió cáp văng cầu (FHWA 2007)

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. Henderson Office of Infrastructure Research and Development Notice This document is disseminated under the sponsorship of the U.

Department of Transportation in the interest of information exchange. Government assumes no liability for the use of the information contained in this document. This report does not constitute a standard, specification, or regulation. 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. Government Accession No. Recipient’s Catalog No. Title and Subtitle 5.

Report Date Wind-Induced Vibration of Stay Cables August 2007 6. Performing Organization Code 7. Performing Organization Report No. Sena Kumarasena, Nicholas P.

Jones, Peter Irwin, Peter Taylor 9. Performing Organization Name and Address 10. Work Unit No. Primary Consultant: HNTB Corporation 11.

Contract or Grant No., Boston, MA 02109 DTFH61-99-C-00095 352 Seventh Ave., 6th 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 12.

Sponsoring Agency Name and Address 13. Type of Report and Period Covered Office of Infrastructure R&D Final Report Federal Highway Administration September 1999 to December 2002 6300 Georgetown Pike 14. Sponsoring Agency Code McLean, VA 22101-2296 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. Distribution Statement cable-stayed bridge, cables, vibrations, wind, No restrictions. This document is available to the public through rain, dampers, crossties the National Technical Information Service, Springfield, VA 22161 19. No of Pages 22.

Price Unclassified Unclassified 281 Form DOT F 1700.7 (8-72) Reproduction of completed pages authorized 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 AREA 2 2 in square inches 645.2 square millimeters mm ft2 square feet 0.093 square meters m2 2 2 yd square yard 0.836 square meters m ac acres 0.405 hectares ha mi2 square miles 2.59 square kilometers km2 VOLUME fl oz fluid ounces 29.57 milliliters mL gal gallons 3.785 liters L ft3 cubic feet 0.028 cubic meters m3 3 3 yd cubic yards 0.765 cubic meters m 3 NOTE: volumes greater than 1000 L shall be shown in m MASS oz ounces 28.35 grams g lb pounds 0.454 kilograms kg T short tons (2000 lb) 0.8 ILLUMINATION fc foot-candles 10.76 lux lx 2 2 fl foot-Lamberts 3.426 candela/m cd/m FORCE and PRESSURE or STRESS lbf poundforce 4.45 newtons N lbf/in2 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 AREA 2 2 mm square millimeters 0.0016 square inches in 2 2 m square meters 10.764 square feet ft 2 2 m square meters 1.195 square yards yd ha hectares 2.47 acres ac km2 square kilometers 0.386 square miles mi2 VOLUME mL milliliters 0.034 fluid ounces fl oz L liters 0.264 gallons gal 3 3 m cubic meters 35.314 cubic feet ft 3 3 m cubic meters 1.307 cubic yards yd 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 o C Celsius 1.8C+32 Fahrenheit F ILLUMINATION lx lux 0.0929 foot-candles fc cd/m2 candela/m2 0.2919 foot-Lamberts fl FORCE and PRESSURE or STRESS N newtons 0.225 poundforce lbf 2 kPa kilopascals 0.145 poundforce per square inch lbf/in *SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380. (Revised March 2003) ii TABLE OF CONTENTS EXECUTIVE SUMMARY. 5 PROJECT OBJECTIVES AND TASKS.

COMPILATION OF EXISTING INFORMATION. CABLE-STAYED BRIDGES. ANALYSIS, EVALUATION, AND TESTING .11 MECHANICS OF WIND-INDUCED VIBRATIONS. 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. 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.

25 Field Performance of Dampers. 33 Considerations for Crosstie Systems. 35 Cable Surface Treatment. 36 FIELD MEASUREMENTS OF STAY CABLE DAMPING.

Zakim Bunker Hill Bridge (over Charles River in Boston, MA). 37 Sunshine Skyway Bridge (St. 40 BRIDGE USER TOLERANCE LIMITS ON STAY CABLE VIBRATION.45 NEW CABLE-STAYED BRIDGES. 45 Mitigation of Rain/Wind Mechanism.

45 Minimum Scruton Number. 46 User Tolerance Limits. 47 RETROFIT OF EXISTING BRIDGES. 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 ECONOMICAL DESIGN OF STAY CABLE VIBRATION MITIGATION STRATEGIES FOR FUTURE BRIDGES.

DATABASE OF REFERENCE MATERIALS. CABLE-STAYED BRIDGES. WIND-INDUCED CABLE VIBRATIONS. WIND TUNNEL TESTING OF STAY CABLES.

LIST OF TECHNICAL PAPERS. ANALYTICAL AND FIELD INVESTIGATIONS. INTRODUCTION TO MECHANICS OF INCLINED CABLES. LIVE-LOAD VIBRATION SUBSTUDY.

STUDY OF USER COMFORT. 257 REFERENCES AND OTHER SOURCES. 261 v LIST OF FIGURES Figure 1. Comparison of wind velocity-damping relation of inclined dry cable.

Cable M26, tension versus time (transit train speed = 80 km/h (50 mi/h)). Time history and power spectral density (PSD) of the first 2 Hz for deck at midspan (vertical direction). Time history and power spectral density (PSD) of the first 2 Hz for cable at AS24 (in-plane direction) deck level wind speed. Deck level wind speed.

Damper at cable anchorage. Taut cable with linear damper. Normalized damping ratio versus normalized damper coefficient: Linear damper. Normalized damping ratio versus normalized damper coefficient (β = 0.

Fred Hartman Bridge. Cable crosstie system. Dames Point Bridge. General problem formulation.

General problem formulation (original configuration). Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 1. Eigenfunctions of the network equivalent to Fred Hartman Bridge: Mode 5. Comparative analysis of network vibration characteristics and individual cable behavior: Fred Hartman Bridge.

Fred Hartman Bridge, field performance testing arrangement. Types of cable surface treatments. Example of test data for spiral bead cable surface treatment. Zakim Bunker Hill Bridge.

Sample decay: No damping and no crossties. Sample decay: With damping and no crossties. Sample decay: With damping and crossties. Sunshine Skyway Bridge.

Stay and damper brace configuration. Reference database search page. Reference database search results page. cable-stayed bridge database: Switchboard.

cable-stayed bridge database: General bridge information. cable-stayed bridge database: Cable data. cable-stayed bridge database: Wind data. Galloping of inclined cables.

Angle relationships between stay cables and natural wind (after Irwin et al. Cable supporting rig: Top. Cable supporting rig: Bottom. Longitudinal section of the propulsion wind tunnel.

Cross section of the working section of propulsion wind tunnel. Data acquisition system. Cross section of airpot damper. Elastic bands on the spring coils.

Side view of setups 1B and 1C. Side view of setups 2A and 2C. Side view of setups 3A and 3C. Cable setup in wind tunnel for testing.

Amplitude-dependent damping (A, sway; B, vertical) with setup 2C (smooth surface, low damping). Divergent response of inclined dry cable (setup 2C; smooth surface, low damping). Lower end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s). Top end X-motion, time history of setup 2C at U = 32 m/s (105 ft/s).

Lower end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s). Top end Y-motion, time history of setup 2C at U = 32 m/s (105 ft/s). Trajectory of setup 2C at U = 32 m/s (105 ft/s). Lower end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes.

Top end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes. Lower end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes. Top end Y-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in the first 5 minutes. Lower end X-motion, time history of setup 2A at U = 18 m/s (59 ft/s) in second 5 minutes.