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Publication Number:  FHWA-HRT-14-049    Date:  August 2014
Publication Number: FHWA-HRT-14-049
Date: August 2014


Mitigation of Wind-Induced Vibration of Stay Cables: Numerical Simulations and Evaluations

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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 wind-rain conditions have been observed. This study was conducted in response to State transportation departments' requests to develop improved design guidance for mitigation of excessive cable vibrations on cable-stayed bridges. The study included finite element modeling of representative individual cables as well as networks of cables to simulate dynamic behavior and evaluate various mitigation details such as dampers and crossties. The results of this study will be made available to the DC-45 Cable-Stayed Bridge Committee for the Post-Tensioning Institute for consideration during their periodic updates of the Guide Specification, Recommendations for Stay Cable Design, Testing, and Installation.(1)

This report will be of interest to bridge engineers, wind engineers, and consultants involved in the design of cable-stayed bridges. It is the first in a series of reports addressing aerodynamic stability of bridge stay cables that will be published in the coming months.

Jorge E. Pagán-Ortiz
Director, Office of Infrastructure
Research and Development


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.

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1. Report No.


2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle

Mitigation of Wind-Induced Vibration of Stay Cables: Numerical Simulations and Evaluations

5. Report Date

August 2014

6. Performing Organization Code
7. Author(s)

Sunwoo Park and Harold R. Bosch

8. Performing Organization Report No.


9. Performing Organization Name and Address

Genex Systems, LLC
2 Eaton Street, Suite 603
Hampton, VA 23669

10. Work Unit No. (TRAIS)

11. Contract or Grant No.
12. Sponsoring Agency Name and Address

Office of Infrastructure R&D
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101-2296

13. Type of Report and Period Covered

Laboratory Report
December 2003–December 2008

14. Sponsoring Agency Code


15. Supplementary Notes
The Contracting Officer's Technical Representative (COTR) was Harold R. Bosch, HRDI-50.
16. Abstract

Cable-stayed bridges have been recognized as the most efficient and cost effective structural form for medium-to-long-span bridges over the past several decades. With their widespread use, cases of serviceability problems associated with large amplitude vibration of stay cables have been reported. Stay cables are laterally flexible structural members with very low inherent damping and thus are highly susceptible to environmental conditions such as wind and rain/wind combination.

Recognition of these problems has led to the incorporation of different types of mitigation measures on many cable-stayed bridges around the world. These measures include surface modifications, cable crossties, and external dampers. Modifications to cable surfaces have been widely accepted as a means to mitigate rain/wind vibrations. Recent studies have firmly established the formation of a water rivulet along the upper side of the stay and its interaction with wind flow as the main cause of rain/wind vibrations. Appropriate modifications to exterior cable surfaces effectively disrupt the formation of a water rivulet.

The objective of this study is to supplement the existing knowledge base on some of the outstanding issues of stay cable vibrations and to develop technical recommendations that may be incorporated into design guidelines. Specifically, this project focuses on the effectiveness of cable crossties, external dampers, and the combined use of crossties and dampers. Finite element simulations are carried out on the stay cable systems of constructed stay cable bridges under realistic wind forces in order to address these issues. Explicit time-history analysis enabled the performance of stay cable systems with different mitigation strategies to be assessed and compared for their relative advantages and disadvantages.

17. Key Words

Cable-stayed bridges, Cables, Vibrations, Wind, Rain, Dampers, Crossties, Hazard mitigation, Simulation

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, VA 22161.

19. Security Classification (of this report)


20. Security Classification (of this page)


21. No. of Pages


22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized


SI* (Modern Metric) Conversion Factors






A Cross-sectional area of a string, beam, or cable.
a Vibration parameter for a classical beam.
C Damper coefficient.
Cn Amplitude of in-plane displacement due to vibration.
Copt Optimal damping coefficient.
c Phase velocity (of a taut string).
d Distance along cable of damper from deck.
D Diameter of a cable.
E Young's modulus (modulus of elasticity of cable material).
F Horizontal wind force.
Fi Frequency of ith mode.
f Fundamental natural frequency.
g Gravitational acceleration constant.
H Axial tension force in a string or cable.
h Horizontal component of tension force due to vibration.
I Moment of inertia.
i Mode number.
k Stiffness coefficient.
K Stiffness of crosstie between two cables.
KG Stiffness of crosstie between cable and ground or bridge deck.
kn Wave number of the nth mode of vibration.
L Length of string, cable, or beam.
Le Effective length of cable.
m Mass of cable per unit length.
n Mode number.
T Time interval for a wind load.
t Time.
Ux Horizontal transverse in-plane displacement calculated from a wind load.
Vavg Average horizontal wind speed.
x Distance.
y Transverse in-plane displacement due to vibration.
ys Transverse in-plane displacement due to weight.
α Correction factor for sag-extensibility effects.
αn Phase angle of time-dependent part of transverse in-plane displacement due to vibration.
βn Bending stiffness correction factor for nth mode of vibration.
ζi Damping ratio of the ith mode of vibration.
θ Inclination angle of the cable.
κ Non-dimensional normalized damping coefficient.
λ2 Non-dimensional sag-extensibility parameter.
μ Mass parameter.
ξ Flexural stiffness parameter.
ρ Mass density per unit volume.
ρL Cable mass per unit length.
ω1 Natural angular frequency of the first mode of vibration.
ωn Natural angular frequency of the nth mode of vibration.
ωnb Natural angular frequency of a classical beam in the nth mode of vibration.
ωns Natural angular frequency of a taut string in the nth mode of vibration.