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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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Figs. 4.18 and 4.19 show the response of the bridge with different number of vehicles but the same driving speed V=20 m/s. The bridge response has slight change with different vehicles numbers in a more than straightforward manner. It is probably because that there are multiple excitations from vehicles in different locations on the bridge when there is more than one vehicle. Such slight change of the bridge response with different vehicle numbers, however, may become significant when there are many vehicles on the same bridge together. More specific research on the response of the bridge under real transportation loading and wind are deserved, which will be reported later by the authors. The vertical acceleration of the bridge is also shown in Fig. 4.20. The bridge vertical acceleration responses are quite close when the number of vehicles changes except slight suppression effect with the existence of vehicles. Figs. 18-20 suggest that the existence of vehicles on the bridge may have some suppression effect on the bridge response in high winds if they are located in some places on the bridge (e. g. the middle point of main span).

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The bridge response with vehicles under low wind speed is also studied. In comparison to high wind speed, the bridge response is affected by the driving speed of vehicles when wind speed is as low as 5 m/s. With the moving of the vehicles towards the middle point of the span, the curves also show a downward tendency, which is an indication of static displacement of the bridge due to the vehicle gravity (Figs. 4.21 and 4.22). It shows that when wind speed is low, wind effect does not dominate the bridge response like the case when wind speed is high. Under low wind speed, alternatively, the roughness and the static gravity effect of vehicles have become dominant on the bridge response. In this case, different driving speeds may cause totally different response of the bridge.

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The bridge response with vehicles without considering any wind effect is studied to further confirm aforementioned conclusions (Figs. 4.23 and 4.24). In the figures, vehicle static gravity effect dominates the vertical displacement of the bridge. For each driving speed, the bridge displacement of monitoring (middle point of main span) reaches the peak when the vehicles pass the monitoring location. For driving speed of 20 m/s, the curve is roughly symmetric about the peak point of 24 seconds when the vehicles pass the mid-span. It can also be found that the two curves reach the peak values at different time. Such differences on the curves, however, are not obvious when there are wind action on the bridge and the vehicles, for example, Figs. 4.16-4.17.

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Fig. 4.24 Torsional displacement of the bridge with vehicles without considering wind effect

4.5 Concluding Remarks A framework for vehicle-bridge-wind aerodynamic analysis is developed to consider different types and arbitrary number of vehicles on the bridge. Each vehicle is modeled with several rigid bodies, mass blocks, and spring-damping systems. The vehicle model is suitable for modeling different types of cars and trucks up to five axles. This framework provides a tool to systematically investigate bridge and vehicle performance in strong winds, such as bridge flutter and buffeting, and vehicle vibration and instability, considering the interaction of bridge, vehicles, and winds. A comprehensive analysis of vehicle accidents on bridges and highways, such as overturning and lateral sliding, are on-going taking advantage of this analytical framework. These results will be reported in the near future.

To demonstrate the capability of the established analytical framework, the present study investigates numerically the dynamic performance of vehicles and the bridge under strong winds and also compared with the results in low wind speed, considering three identical 2-axle vehicles running on a prototype long-span bridge. Effects of different driving speeds and number of vehicles on the dynamic performance of vehicles and bridge are studied. Dynamic wind loading and road roughness loading are applied on the bridge and quasi-steady wind force and road roughness loading are acting on the vehicles. Based on the present numerical analysis, following

conclusions can be drawn:

The vehicle driving speed does affect the relative vertical response of vehicles. The rolling relative response is dominated by direct static wind action on the vehicles and only slightly changes with the different driving speeds.

93 The absolute response of vehicles is dominated by the bridge response and thus varies little with driving speed when wind speed is high. Compared with vehicles on the road, vehicles responses are amplified on the bridge especially when the vehicle approaches the middle point of the main span. Vehicles show stronger relative response under high wind speed, which justifies again the importance of study on the vehicle safety under strong winds.

The relative response of the vehicle is hardly affected by the existence of other vehicles, however, the absolute responses of vehicles change with the number of vehicles on the bridge.

Multiple-vehicle simulation on the bridge is still necessary to realistically assess the response of vehicles as well as the bridge.

The vehicles on the bridge could reduce the dynamic response of the bridge in some cases under high winds. It is possibly due to the beneficial effects of eccentric gravity of vehicles, which caused some suppression effect of vibration. However, the effects may depend on many facts, such as positions of vehicles on the bridge, vehicle number, wind speed, and driving speed.

More studies are needed to draw a general conclusion.

The bridge response is not sensitive to the vehicle with different driving speed when wind speed is high because the wind-induced response dominates the bridge response. However, when wind speed is low, the bridge response is dominated by the static component induced by the gravity of vehicles and dynamic part contributed by road roughness. Different driving speed has more significant effect on the bridge response when wind speed is low.

4.6 Matrix Details of the Coupled System Please be noted that those terms not listed in the upper triangle of matrices are zero terms. The matrices are symmetric and the lower triangle terms of matrices are thus not given here.

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5.1 Introduction While little statistical information has been collected and published, threats of strong winds on the safety of vehicles have been realized and reported around the world (Scibo-rylski 1975;

Coleman and Baker 1990; Baker 1987; Baker and Reynolds 1992). In the United States, the gust winds have also been found to be very important contributors to the accidents of vehicles especially trucks. For example, on March 24, 2001, two trucks collided and one driver was killed on the highway in Madison, Indiana and wind effect was identified to be one potential cause (IDOT, 2001). On January 7, 2003, a tractor-trailer ran off the Interstate 81 in Frederick County, Virginia due to the strong winds (Winchester Star News, 2003). On May 30, 2003, a truck loaded with cattle overturned on I-29 in Iowa when the wind blew it off the road (Iowa channel news, 2003). On February 1, 2002, on the interstate 95/495 near Largo, Maryland, the National Transportation Safety Board believed that the accident was contributed by multiple factors, one of which was also gust wind (NTSB, 2003).

Different from scattered accidents, series concurrent accidents due to the strong winds may turn out to be a catastrophe. On November 10, 1998, south-central and southeast Wisconsin's counties experienced strong winds with sustained wind speed of 30-40 mph gusted to 60-70 mph. In only 17 hours, there were more than 40 semi-trucks that were reported to overturn or side slipping off the highways in that area according to the report (NWS, 1998). Some vehicles that were pushed sideways by gusts also caused multiple vehicle accidents. Transportation was unavoidably delayed and one Interstate highway was reported to be totally closed because of the accidents. Many small cars were pushed into the ditches, one of them was observed as “partially airborne” (NWS, 1998).

In hurricane haunted areas, strong winds can be expected in windy season. In addition to the loss of each individual accident, the more serious issue in hurricane-prone area is that accidents constantly happening on the highways will greatly delay or even obstruct the important transportation line before or upon the landfall of hurricanes. Transportations are usually very busy and more important for hurricane preparations at those moments compared with ordinary days. If accidents happen frequently when evacuations are in progress, the whole evacuation process will be significantly delayed and the safety of those people, who cannot be evacuated in time due to the transportation interruptions, will be inevitably put on stake.

While very little statistical data of accidents on bridges have been collected, vehicles on bridges are more vulnerable to the cross gusts than on roads (Baker and Reynolds, 1992). The reasons include that many vehicles experience a suddenly strengthened crosswind when they just entered the bridge that is usually more open than the road. This is especially true when compared with roads with trees, hills or bushes on both sides. Another critical situation for vehicles on bridges is when vehicles just pass by bridge towers. The vehicle may experience a very short period of no crosswind action and then crosswind action resumes since the bridge towers may block the crosswind on the vehicles temporarily. For long-span bridges, the strong dynamic response of the bridge due to the interaction with wind and vehicles will also contribute to the accidents. To reduce accidents, some safety measures like setting an appropriate driving speed limit and criteria to close the bridge/highway during windy period have been adopted (Baker, 1987). However, in the past, the decision of setting driving speed limit and closing the 101 transportation on bridges and highways arrives is mostly based on intuition or subjective experience (Irwin, 1999). The driving speed limit could be too high to be safe or too low to be efficient. Determination of suitable safety approaches at different situations deserves a more rational research.

Baker et al. have made explorative studies on the performance of high-sided vehicles in crosswinds on roads (Baker 1986, 1991a, 1991b, 1999); In his representative early work, Baker (Baker, 1986) proposed the fundamental equations for wind action on vehicles without considering the dynamic response of the vehicles in most directions. Through the adoption of meteorological information the percentage of the total time for which allowable wind speed is exceeded can thus be found and quantification of accident risk has been made considering driver behavior performance (Baker 1991b, 1999). In addition to wind tunnel tests on several particular vehicle models to identify the wind force on vehicles (Coleman and Baker 1990), some useful statistical information about actual accidents in British was also collected and analyzed (Baker and Reynolds, 1992). All of the above analyses, however, were limited to vehicles on the road.

Moreover, the vehicle was modeled with a rigid body with only two degrees of freedom and thus no dynamic vibration excited by road roughness and wind forces were considered. The road roughness effect, the vertical acceleration, pitching and rolling acceleration of the vehicles were assumed to be zero in the existent model (Baker, 1986, 1999). Such simplifications may be reasonable for vehicles on the road. However, the dynamic interaction effects are very important for the vehicles on bridges and should be incorporated into the accident analysis. A more general and more realistic accident analysis model which can be used for vehicles on bridges and on roads is very desirable. To the knowledge of the writers, however, no existing accident model is so far available for such purpose.

In Chapter Four, a three-dimensional coupled bridge-vehicle-wind system was developed and analyzed (Cai and Chen 2004). Each vehicle was modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers. Dynamic interaction analysis is then conducted on the vehicle-bridge system to predict the “global” bridge and vehicle dynamic responses without considering accident occurrences. The results of the global bridge-vehicle vibrations serve as the basis for the present accident analysis of the “local” vehicle vibrations.

The present study aims at building a framework of general vehicle accident analysis model, which can be used for vehicles on bridges and on roads. Excitations from the road roughness and the wind loading are incorporated. The proposed model is applicable for vehicles on the road with curves, cambers, and grades. After setting up some accident criteria and driving behavior model, the accident risk can be assessed with the derived accident-related responses. To present the methodology, a truck model and a prototype bridge are chosen as the example of applications.

5.2 Dynamic Interaction of Non-Articulated Vehicles on Bridges This section summarizes the procedures of interaction analysis of bridge-wind-vehicle for the convenience of discussion. Details are referred to Chapter Four.

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