«A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of ...»
DYNAMIC PERFORMANCE OF BRIDGES AND VEHICLES
UNDER STRONG WIND
Submitted to the Graduate Faculty of the
Louisiana State University and
Agricultural and Mechanical College
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
The Department of Civil and Environmental Engineering
B.S., Tongji University, 1994
M.S., Tongji University, 1997 May 2004
DEDICATIONTo my parents, my wife and my son ii
ACKNOWLEDGMENTSI am indebted to Professor Steve Cai, my advisor, for his active mentorship, constant encouragement, and support during my Ph. D study at LSU and KSU. It has been my greatest pleasure to work with such a brilliant, considerate and friendly scholar.
I also want to express my sincere gratitude to Professor Christopher J. Baker of The University of Birmingham. The advice obtained from him on the vehicle accident assessment was very helpful and encouraging. The advice and help given by Dr. John D. Holmes on the time-history simulations are particularly appreciated. I also want to thank Professor Marc L.
Levitan, the director of the Hurricane Center at LSU, for his very helpful courses on hurricane engineering and his great work as a member of my committee. Gratitude is also extended to Professor M. Gu at Tongji University and Professor C. C. Chang at Hong Kong University of Science and Technology for their continuous encouragement and support.
Thanks are also extended to my other committee members: Professor Dimitris E.
Nikitopoulos of Mechanical Engineering, Professor Jannette Frandsen of Civil Engineering, and Professor Jaye E. Cable of Oceanography & Coastal Sciences for very helpful suggestions in the dissertation.
The Graduate Assistantship offered by Louisiana State University and the National Science Foundation (NSF) made it possible for me to proceed with my study.
Last but not the least, I would like to thank my beloved wife and my son for their strong support. The dissertation could not have been completed without their encouragement, their love and their patience.
TABLE OF CONTENTSDEDICATION
1.1 Wind Hazard
1.2 Bridge Aerodynamics
1.3 Vehicle Dynamic Performance on the Bridge under Wind
1.4 Structural Control on Wind-induced Vibration of Bridges
1.5 Present Research
CHAPTER 2. MODAL COUPLING ASSESSMENTS AND APPROXIMATED PREDICTIONOF COUPLED MULTIMODE WIND VIBRATION OF LONG-SPAN BRIDGES.................. 10
2.2 Mathematical Formulations
2.3 Approximated Prediction of Coupled Buffeting Response
2.4 Numerical Example
2.5 Concluding Remarks
CHAPTER 3. EVOLUTION OF LONG-SPAN BRIDGE RESPONSE TO WINDNUMERICAL SIMULATION AND DISCUSSION
3.2 Motivation of Present Research
3.3 Analytical Approach
3.4 Numerical Procedure
3.5 Numerical Example
3.6 Concluding Remarks
CHAPTER 4. DYNAMIC ANALYSIS OF VEHICLE-BRIDGE-WIND DYNAMICSYSTEM
4.2 Equations of Motion for 3-D Vehicle-Bridge-Wind System
4.3 Dynamic Analysis of Vehicle-Bridge System under Strong Wind
4.4 Numerical Example
4.5 Concluding Remarks
4.6 Matrix Details of the Coupled System…………………………………………………...94
CHAPTER 5. ACCIDENT ASSESSMENT OF VEHICLES ON LONG-SPAN BRIDGES INWINDY ENVIRONMENTS
5.2 Dynamic Interaction of Non-Articulated Vehicles on Bridges
5.3 Accident Analysis Model for Vehicles on Bridges
5.4 Numerical Example
5.5 Concluding Remarks
CHAPTER 6. STRONG WIND-INDUCED COUPLED VIBRATION AND CONTROL WITHTUNED MASS DAMPER FOR LONG-SPAN BRIDGES.
6.2 Closed-Form Solution of Bridge-TMD System
6.3 Coupled Vibration Control with a Typical 2DOF Model
6.4 Analysis of a Prototype Bridge
6.5 Concluding Remarks
CHAPTER 7. OPTIMAL VARIABLES OF TMDS FOR MULTI-MODE BUFFETINGCONTROL OF LONG-SPAN BRDGES
7.2 Formulations of Multi-mode Coupled Vibration Control with TMDs
7.3 Parametrical Studies on “Three-row” TMD Control
7.4 Concluding Remarks
CHAPTER 8. WIND VIBRATION MITIGATION OF LONG-SPAN BRIDGES INHURRICANES
8.2 Equations of Motion of Bridge-SDS System
8.3 Solution of Flutter and Buffeting Response
8.4 Numerical Example: Humen Bridge-SDS system
8.5 Concluding Remarks
CHAPTER 9. CONCLUSIONS AND FURTHER CONSIDERATIONS
9.1 Summary and Conclusions
9.2 Future Work
The record of span length for flexible bridges has been broken with the development of modern materials and construction techniques. With the increase of bridge span, the dynamic response of the bridge becomes more significant under external wind action and traffic loads.
The present research targets specifically on dynamic performance of bridges as well as the transportation under strong wind.
The dissertation studied the coupled vibration features of bridges under strong wind. The current research proposed the modal coupling assessment technique for bridges. A closed-form spectral solution and a practical methodology are provided to predict coupled multimode vibration without actually solving the coupled equations. The modal coupling effect was then quantified using a so-called modal coupling factor (MCF). Based on the modal coupling analysis techniques, the mechanism of transition from multi-frequency type of buffeting to singlefrequency type of flutter was numerically demonstrated. As a result, the transition phenomena observed from wind tunnel tests can be better understood and some confusing concepts in flutter vibrations are clarified.
The framework of vehicle-bridge-wind interaction analysis model was then built. With the interaction model, the dynamic performance of vehicles and bridges under wind and road roughness input can be assessed for different vehicle numbers and different vehicle types. Based on interaction analysis results, the framework of vehicle accident analysis model was introduced.
As a result, the safer vehicle transportation under wind can be expected and the service capabilities of those transportation infrastructures can be maximized. Such result is especially important for evacuation planning to potentially save lives during evacuation in hurricane-prone area.
The dissertation finally studied how to improve the dynamic performance of bridges under wind. The special features of structural control with Tuned Mass Dampers (TMD) on the buffeting response under strong wind were studied. It was found that TMD can also be very efficient when wind speed is high through attenuating modal coupling effects among modes. A 3-row TMD control strategy and a moveable control strategy under hurricane conditions were then proposed to achieve better control performance.
vi CHAPTER 1. INTRODUCTION
The dissertation is made up of nine chapters based on papers that have either been accepted, or are under review, or are to be submitted to peer-reviewed journals, using the technical paper format that is approved by the Graduate School.
Chapter 1 introduces the related background knowledge of the dissertation, the research scope and structure of the dissertation. Chapter 2 discusses the modal coupling effect on bridge aerodynamic performances (Chen et al. 2004). Chapter 3 covers the evolution of the long-span bridge response to the wind (Chen and Cai 2003a). Chapter 4 discusses the dynamic analysis of the vehicles-bridge-wind system (Cai and Chen 2004a). Chapter 5 discusses the vehicle safety assessment of vehicles on long-span bridges under wind (Chen and Cai 2004a). Chapter 6 investigates the new features of strong-wind induced vibration control with Tuned Mass Dampers on long-span bridges (Chen and Cai 2004b). Chapter 7 studies the optimal variables of Tuned Mass Dampers on multiple-mode buffeting control (Chen et al. 2003). Chapter 8 investigates the wind vibration mitigation on long-span bridges in hurricane conditions (Cai and Chen 2004b). Chapter 9 summarizes the dissertation and gives some suggestions for future research.
This introductory chapter gives a general background related to the present research. More detailed information can be seen in each individual chapter.
1.1 Wind Hazard Wind is about air movement relative to the earth, driven by different forces caused by pressure differences of the atmosphere, by different solar heating on the earth’s surface, and by the rotation of the earth. It is also possible for local severe winds to be originated from local convective effects and the uplift of air masses. Wind loading competes with seismic loading as the dominant environmental loading for modern structures. Compared with earthquakes, wind loading produces roughly equal amounts of damage over a long time period (Holmes, 2001). The
major wind storms are usually classified as follows:
Tropical cyclones: Tropical cyclones belong to intense cyclonic storms which usually occur over the tropical oceans. Driven by the latent heat of the oceans, tropical cyclones usually will not form within about 5 degrees of the Equator. Tropical cyclones are called in different names around the world. They are named hurricanes in the Caribbean and typhoons in the South China Sea and off the northwest coast of Australia (Holmes, 2001).
Thunderstorm: Thunderstorms are capable of generating severe winds, through tornadoes and downbursts. They contribute significantly to the strong gusts recorded in many countries, including the United States, Australia and South Africa. They are also the main source of high winds in the equatorial regions (within about 10 degrees of the Equator), although their strength is not high in these regions (Holmes, 2001; Simiu and Scanlan, 1986).
Tornadoes: These are larger and last longer than “ordinary” convection cells. The tornado, a vertical, funnel-shaped vortex created in thunderclouds, is the most destructive of wind storms. They are quite small in their horizontal extent-of the order of 100 m. However, they 1 can travel for quite a long distance, up to 50 km, before dissipating, producing a long narrow path of destruction. They occur mainly in large continental plains, and they have very rarely passed over a weather recording station because of their small size (Holmes, 2001).
Downbursts: Downbursts have a short duration and also a rapid change of wind direction during their passage across the measurement station. The horizontal wind speed in a thunderstorm downburst, with respect to the moving storm, is similar to that in a jet of fluid impinging on a plain surface (Holmes, 2001).
Damage to buildings and other structures caused by wind storm has been a fact of life for human beings since these structures appeared. In nineteenth century, steel and reinforcement were introduced as construction materials. During the last two centuries, major structural failures due to wind action have occurred periodically and provoked much interest in wind loadings by engineers. Long-span bridges often produced the most spectacular of these failures, such as the Brighton Chain Pier Bridge in England in 1836, the Tay Bridge in Scotland in 1879, and the Tacoma Narrows Bridge in Washington State in 1940. Besides, other large structures have experienced failures as well, such as the collapse of the Ferrybridge cooling tower in the U. K. in 1965, and the permanent deformation of the columns of the Great Plains Life Building in Lubbock, Texas, during a tornado in 1970. Based on annual insured losses in billions of US dollars from all major natural disasters, from 1970 to 1999, wind storms account for about 70% of total insured losses (Holmes, 2001). This research addresses transportation-related issues due to hurricane-induced winds.
Hurricanes and hurricane-induced strong wind are, by many measures, the most devastating of all catastrophic natural hazards that affect the United States. The past two decades have witnessed exponential growth in damage due to hurricanes, and the situation continues to deteriorate. The most vulnerable areas, coastal countries along the Gulf and Atlantic seaboards, are experiencing greater population growth and development than anywhere else in the country.
In the United States, annual monetary losses due to tropical cyclones and other natural hazards have been increasing at an exponential pace, now averaging up to $1 billion a week (Mileti, 1999). Large hurricanes can have impacts that are national or even international in scope.
Damage from Hurricane Andrew was so extensive (total loss approximately $25 billion) that it caused building materials shortages nationwide and bankrupted many Florida insurance companies. Had Andrew’s track shifted just a few miles, it could have gone through downtown Miami, hit Naples on the west coast of Florida, and then devastated New Orleans. Projections for the total losses in this scenario are several times greater than the $25 billion in damages caused by Andrew. Losses of this magnitude threaten the stability of national and international reinsurance markets, with potentially global economic consequences. When a hurricane or tropical storm does strike the gulf coast, the results are generally devastating.