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Chapter 1. Introduction

BACKGROUND

Cable-stayed bridges are a relatively new structural form made feasible with the combination of advances in manufacturing of materials, construction technology, and analytical capabilities that took place largely within the past few decades.

The first modern cable-stayed bridge was the Stromsund Bridge built in the 1950s in Sweden. Its main span measures 183 m (600 ft), and its two symmetrical back spans measure 75 m (245 ft) each. There are only two cables on each side of the tower, anchored to steel I-edge girders.

Today, cable-stayed bridges have firmly established their unrivalled position as the most efficient and cost effective structural form in the 150-m (500-ft) to 460-m (1,500-ft) span range. The cost efficiency and general satisfaction with aesthetic aspects has propelled this span range in either direction as both increasingly shorter and longer spans are being designed and constructed. The record span built to date is the Tatara Bridge connecting the islands of Honshu and Shikoku in Japan; its main span measures 890 m (2,920 ft). In Hong Kong, the planned Stonecutters Bridge will have a 1,000-m (3,280-ft)-long main span. The early engineering approach to stay cables essentially was derived and hybridized from already established engineering experience with suspension cables and posttensioning technology.

Stay cables are laterally flexible structural members with very low fundamental frequency (first natural mode). Because of the range of different cable lengths (and thus the range of frequencies), the collection of stay cables on a cable-stayed bridge has a practical continuum of fundamental and higher mode frequencies. Thus, any excitation mechanism with any arbitrary frequency is likely to find one or more cables with either a fundamental or higher mode frequency sympathetic to the excitation. Cables also have very little inherent damping and are therefore not able to dissipate much of the excitation energy, making them susceptible to large amplitude build-up. For this reason, stay cables can be somewhat lively by nature and have been known to be susceptible to excitations, especially during construction, wind, and rain/wind conditions.

Recognition of this susceptibility of stay cables has led to the incorporation of some mitigation measures on several of the earlier structures. These included cable crossties that effectively reduce the free length of cables (increasing their frequency) and external dampers that increase cable damping. Perhaps because of the lack of widespread recognition of stay cable issues by the engineering community and supplier organizations, the application of these mitigation measures on early bridges appears to have been fairly sporadic. However, those bridges incorporating cable crossties or external dampers generally have performed well.

Field observation programs have provided the basis for characterization of stay cable vibrations and the environmental factors that induce them.^(2,3,4) Peak-to-peak amplitudes of up to 2 m (6 ft) have been reported, with typical values of around 60 cm (2 ft). Vibrations have been observed primarily in the lower cable modes, with frequencies ranging approximately from 1 to 3 Hz. Early reports described the vibrations simply as transverse in the vertical plane, but detailed observations suggest more complicated elliptical loci.

High-amplitude vibrations have been observed over a limited range of wind speeds. At several bridges in Japan, the observed vibrations were restricted to a wind velocity range of 6 to 17 m/s (13 to 38 mi/h).⁽⁵⁾ More recent field measurements revealed large-amplitude vibrations at around 40 m/s (90 mi/h). The wind speed did not reach values high enough to determine whether these vibrations were also velocity restricted.⁽⁴⁾

The stays of the Brotonne Bridge in France were observed to vibrate only when the wind direction was 20–30° relative to the bridge longitudinal axis.⁽²⁾ On the Meiko-Nishi Bridge in Japan, vibrations were observed with wind direction greater than 45° from the deck only on cables that declined in the direction of the wind.⁽³⁾ However, instances have also been reported subsequently of simultaneous vibration of stays with opposite inclinations to the wind.⁽⁶⁾

From field observations it became evident that these large oscillation episodes occurred under moderate rain combined with moderate wind conditions, and hence were referred to as "rain/wind-induced vibrations."⁽³⁾ Extensive research studies at many leading institutions over the world have undoubtedly confirmed the occurrence of rain/wind-induced vibrations. Totally unknown before its manifestation on cable-stayed bridges, the mechanisms leading to rain/wind-induced vibrations have been identified. The formation of a so-called water rivulet along the upper side of the cable under moderate rain conditions and its interaction with wind flow have been solidly established as the cause through many recent studies and wind tunnel tests. (See references 3, 7, 8, and 9.)

Based on this understanding, exterior cable surface modifications that interfere with water rivulet formation have been tried and proven to be very effective in the mitigation of rain/wind-induced vibrations. Particularly popular (and shown to be effective through experimental studies) are the double-spiral bead formations affixed to the outer surface of the cable pipes.⁽⁸⁾ Cable exterior pipes with such surface modifications are available from all major cable suppliers with test data applicable to the particular system. This type of spiral bead surface modification has been applied on many cable-stayed bridges both with and without other mitigation measures such as external dampers and cable ties. From the observations available to date, the bridges incorporating stay cables with effective surface modifications appear to be generally free of rain/wind-induced vibrations.

At the time of the present investigation, it was evident that the rain/wind problem essentially had been solved, at least for practical provisions for its mitigation. The Scruton number, identified later in the report, is generally accepted as the key parameter describing susceptibility of a given cable to rain/wind-induced vibrations. Raising the Scruton number by increasing damping or, alternatively, the use of cable crossties has been recognized as the standard solution for the mitigation of rain/wind-induced vibrations. Generally, these are applied in combination with a proven surface modification.

However, there was no such clarity with respect to other potential sources of cable vibration. High-speed galloping of inclined cables (discussed later) was the foremost issue that limited the designer’s options. The only effective method available for satisfying the existing criteria on galloping was to raise the natural frequency of cables through the use of cable crossties. However, the inclined dry cable galloping criteria being used was postulated on such a limited set of data that its application was frequently brought into question.

Thus, to meet the project objective of formulating design guidelines, some further experimental and analytical work was needed to supplement the existing knowledge base on stay cable vibration issues.

PROJECT OBJECTIVES AND TASKS

The charter of the project team, established early in the development of the program, consisted of the following objectives:

• Identify gaps in current knowledge base.
• Conduct analytical and experimental research in critical areas.
• Study performance of existing cable-stayed bridges.
• Study current mitigation methods.
• Develop procedures for aerodynamic performance assessment.
• Develop design and retrofit guidelines for stay cable vibration mitigation.

Overall project goals were translated into tasks A through F:

• Task A: Synthesize available information—reference database (appendix A, chapter 2); descriptions of wind-induced cable vibrations (appendix C, chapter 3).
• Task B: Take inventory of U.S. cable-stayed bridges—inventory database (appendix B, chapter 2).
• Task C: Perform analysis/evaluation/testing—wind tunnel testing of dry inclined cables (appendix D, chapter 3); study of mitigation methods (appendix E, appendix F, chapter 3); study of other excitation mechanisms (appendix H, chapter 3); field measurements of stay cable damping (chapter 3); study of user comfort (appendix I); calculations on mechanics of inclined cables (appendix G).
• Task D: Develop guidelines for design and retrofit (chapter 4).
• Task E: Formulate recommendations for future research (chapter 5).
• Task F: Document the project.

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