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«A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of ...»

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Without considering the driver’s performance, the wind speed at which these accident criteria are exceeded (the so-called accident wind speed) was found to be a function of vehicle speed and wind direction. Using meteorological information, the percentage of the total time for which this wind speed is exceeded can be found. Some quantification of accident risk has been made. Based on Baker’s model, Sigbjornsson and Snajornsson (1998) tried the risk assessment of an accident which happened in Iceland through a reliability approach. In the approach, the so-called “safety index approach” was adopted to describe the risk of the accident and some valuable results were given. However, the driver’s behavior was not included in this analysis, which made the analysis not general enough for further application. As in Baker’s study, Sigbjornsson did not consider road roughness, which could be a very important factor affecting the dynamic behavior of vehicles on highway roads. In addition, no study has included vehicle performance on a bridge under strong wind.

During periods of high winds, it is a common practice to either slow down traffic or stop vehicle movement altogether at exposed windy sites such as long span bridges (Baker 1987).

Various criteria used to initiate traffic control differ substantially between sites. In some places, the “two-level” system is operated; vehicles are slowed down, and warning signs are activated when the wind speed exceeds a certain level. It seems that the various criteria for imposing traffic restrictions are, to an extent, rather arbitrary and ill-defined (Baker 1987). Baker (Baker

1986) suggested that an overturning accident may occur if, within the 0.5 s of the vehicle entering the gust, one of the tire reactions fell to zero. A side-slipping accident happens when the lateral displacement exceeded 0.5m, and a rotational accident happens when the rotational displacement exceeds 0.2 radians. These definitions are based on some assumptions, especially that within 0.5s, the driver of the vehicle would not react to correct the lateral and rotation 6 displacement. With the introduction of the driver behavior model, the assumption of 0.5 second can be eliminated (Baker 1994).

1.4 Structural Control on Wind-induced Vibration of Bridges When extreme wind such as a hurricane attacks the long span bridges, large vibration response may force the bridge to be closed to transportation for the safety of the bridge and of vehicles. An efficient control system is needed to guarantee the safety of the bridge, to prolong the opening time for traffic under mitigation conditions, and to reduce direct and indirect financial loss as well as civilian lives. In the past few decades, bridge engineers have had modest success in dealing with wind-induced vibrations by structural strengthening or streamlining/modifying the bridge geometry based on the results of experimental /analytical studies. However, with the increase in bridge-span length, wind-structure interaction is becoming increasingly important. The Akashi Kaikyo suspension bridge in Japan has set a new record of 1900 m in span length. An even longer span length of 5000 m for the Gibraltar Strait Bridge is under discussion (Wilde et. al 2001). Wind-induced vibrations become one of the major controlling factors in long-span bridge design. To meet the serviceability and strength requirements under wind actions, structural control will be the most economical and the only feasible alternative for these ultra-long-span bridges (Anderson and Pederson 1994).

The control strategies for wind-induced vibration of long-span bridges can be classified as structural (passive), aerodynamic (passive or active), or mechanical (passive or active) countermeasures. Passive structural countermeasures aim at increasing the stiffness of the structures by increasing member size, adding additional members, or changing the arrangement of structural members.

Passive aerodynamic countermeasures focus on selecting bridge deck shapes and details to satisfy aerodynamic behaviors. Examples are using shallow sections, closed sections, edge streamlining and other minor or subtle changes to the cross-section geometry (Wardlaw 1992). It was found that the aerodynamic countermeasures are more efficient than structural strengthening (Cai et al. 1999b). However, these passive aerodynamic countermeasures are not adequate for ultra long-span bridges and in extreme high wind, such as a hurricane.

Active aerodynamic countermeasures use adjustable control surfaces for increasing critical flutter wind velocity (Ostenfeld and Larsen 1992, Predikman and Mook 1997, Wilde and Fujino 1998, 2001). By adjusting the rotation of these control surfaces to a predetermined angle, stabilizing aerodynamic forces are generated. One of the disadvantages is that the control efficiency is sensitive to the rotation angles. A wrong direction of rotation, due to either the failure of control system or inaccurate theoretical predictions, will have detrimental effects on the bridge. Predicting a bridge’s performance under hurricane wind and designing a reliable/efficient control mechanism is still extremely difficult.

Mechanical countermeasures focus mainly on the flutter and buffeting controls with passive devices, such as tuned mass dampers (TMD). A TMD consists of a spring, a damper and a mass. It is easy to design and install and has been used in the vibration control of some buildings and bridges, such as Citicorp Center in New York, John Hancock tower in Boston, and the Normandy Bridge in France. In a typical passive TMD system, the natural frequency of the TMD is tuned to a pre-determined optimal frequency that is dependent on the dynamic 7 characteristics of the bridge system and wind characteristics (Gu et al. 1998, 2001, Gu and Xiang 1992).

1.5 Present Research The present research discusses the safety issues of long-span bridges and transportation under wind action. It covers three interrelated parts: Part I - multimode coupled vibration of long-span bridges in strong wind; Part II – vehicle-bridge-wind interaction and vehicle safety;

and Part III - bridge vibration control under strong wind.

Chapters 2 and 3 are devoted to Part I. With the increase of bridge span, the dynamic response of the bridge becomes more significant under external wind action and traffic loads.

Longer bridges usually have closer mode frequencies than those of short-span bridges. Under the action of aeroelastic and aerodynamic forces, the response component contributed by one mode may affect the aeroelastic effects on another mode when their frequencies are close, due to aerodynamic coupling. Such coupling effects among modes are usually gradually strengthened when wind speed is high. As an important phenomenon for long-span bridges under strong wind, modal coupling of a bridge under wind action is assessed in Chapter 2. A practical approximation approach of predicting the coupled response of the bridge under wind action is also introduced. Another part of research in the bridge aerodynamic is to investigate the phenomena of buffeting and flutter of bridges. Buffeting and flutter are usually treated as two different phenomena. Buffeting is believed to be a forced vibration, and flutter is usually treated as a system instability phenomena. Chapter 3 aims at establishing the connections between buffeting and flutter phenomena. It is believed in the current work that the two phenomena are continuous, and the evolution process from buffeting to flutter is investigated. In the meantime, the hybrid analysis approach introduced will also benefit the following analysis of vehiclebridge-wind interaction analysis.

Based on the work of Part I, Chapters 4 and 5 develop the analytical framework of vehicle-bridge-wind interaction (Part II). The previous works are mainly focused on the dynamic performance of vehicles on the road under wind action, or vehicle dynamic performance on the bridge without wind or with slight wind. In Chapter 4, a general analysis model is built for dynamic coupling analysis of a bridge and vehicles. With finite-element based dynamic analysis results, modal coupling assessment techniques introduced in Chapter 2 are adopted to choose those important modes to be included in the analysis. With limited key modes and the vehicle dynamic model, the dynamic response of the moving vehicle can be predicted at any time on the bridge under wind action. Part of the obtained dynamic response of vehicles is to be used in the following vehicle safety assessment part. Regarding vehicle safety assessment, all previous works are only for vehicles on the road. In Chapter 5, the general model of vehicle safety assessment on the bridge is introduced. With the safety assessment model, the accident risks corresponding to different accident types are assessed under different situations.

Chapters 6, 7, and 8 form Part III - vibration control. Bridges exhibit large dynamic response under strong wind. Excessive response may cause the safety problem of the bridge known as flutter. It may also cause serviceability problems and fatigue accumulation. So, in some circumstances, structural control is an important way to enhance the safety, serviceability, and durability of a bridge. In Chapter 6, the special features of structural control with Tuned Mass Dampers (TMD) on the buffeting response under strong wind are studied. In addition to 8 the well-known resonant suppression mechanism of TMD, it is also found that the TMD can be used to suppress the strong coupling effects among modes of a bridge when the wind speed is high. Such a new mechanism enables TMD to control the bridge buffeting efficiently even when wind speed is high. Following the work of Chapter 6, a 3-row TMD control strategy is proposed to achieve better control performance in Chapter 7. Finally, in Chapter 8, a moveable control strategy is introduced to facilitate the vibration control of long-span bridges under hurricane.

–  –  –

2.1 Introduction Bridges with record-breaking span lengths are currently being designed or expected worldwide in the future. For example, Messina Straits Bridge with a span length of 3,300 m is under design and Gibraltar Straits Crossing with a span length of 5,000 m is under discussion. Lighter and more aerodynamically profiled cross sections of decks are most commonly used for these increasingly more flexible long-span bridges. In these circumstances, the structural characteristics of the bridges tend to result in closer modal frequencies. As a result, the possibilities of modal coupling through aerodynamic and aeroelastic effects increase (Chen et al. 2000).

The mechanisms of modal coupling in the wind-induced vibrations of bridges have been studied (Cai et al. 1999; Namini et al. 1992; Thorbek and Hansen 1998; Katsuchi et al.

1998; Bucher and Lin 1988). Thorbek and Hansen (1998) once focused on the effect of modal coupling between vertical and torsional modes on the buffeting response and gave a general guideline regarding the need of including modal coupling in the calculations. They suggested that for suspension bridges with streamlined bridge deck sections and a ratio of 2-3 between the torsional and vertical natural frequencies in still air, the effect of modal coupling be taken into account in the calculation if the mean wind velocity exceeds approximately 60% of the critical flutter wind velocity. D'Asdia and Sepe (1998) and Brancaleoni and Diana (1993) also highlighted the importance of aeroelastic effects in the analysis of Messina Bridge and modal coupling effects were studied. Other previous works (Bucher and Lin

1988) also recognized the importance of conducting coupled multimode analysis.

For a long time, wind-induced buffeting response of bridges is obtained from the square root of the sum of the squares (SRSS) of single-mode responses (Simiu and Scanlan 1996), which is called “single-mode approach” hereafter. Single-mode response has been very attractive in engineering practice and preliminary analysis due to its convenience. However, since single-mode approach completely neglects the modal coupling effects among different modes, it sacrifices significantly the accuracy when modal coupling is not weak (Jain et al.

1996; Tanaka et al. 1994). In contrast, coupled multimode procedures take into account all the aeroelastic and aerodynamic coupling effects by solving simultaneous equations (Chen et al.

2000; Bucher and Lin 1988; Jain et al. 1996; Cai et al. 1999b). The calculation efforts vary with the total number of modes being included in the simultaneous equations.

Katsuchi et al. (1998, 1999) investigated the multimode behavior of the Akashi-Kaikyo Bridge with a span length of 1990 m by using the numerical procedures based on (Jain et al.

1996). The analytical results showed some strongly coupled aeroelastic behaviors that are consistent with the wind tunnel observations (Katsuchi et al. 1998, 1999). In their study, up to 25 and 17 modes were analyzed for the flutter and buffeting response, respectively. Through the comparison between the coupled multimode and single-mode analyses, it was found that only 6 key modes are important to the flutter analysis. Meanwhile, no significant difference 10 appeared between the buffeting results of coupled multimode analysis and single-mode analysis until the 10th mode was included (Katsuchi et al. 1999). This implied that it is only a few key modes that are crucial for the accuracy of coupled multimode analysis.

However, a rational method of assessing the modal coupling effect and thus identifying these key modes is still absent. One does not know if a coupled multimode analysis is needed, or how many key modes should be included before an actual coupled multimode analysis is conducted. As a result, the modes that are included in the multimode analysis can only be selected based on subjective judgment of modal properties and flutter derivatives.

Consequently, one may choose either too many or too few modes for the coupled analysis.

The former may include many unessential modes while the latter may miss some important ones. In recent years, finite element method (FEM) has become more and more popular for the aerodynamic analysis of bridges (Cai et al. 1999; Namini et al. 1992). Assessing the necessity of coupled multimode analysis and then including the key modes in the analysis will achieve better computation efficiency.

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