ENVIRONMENTAL EFFECTS ON A SUSPENSION BRIDGE’S PERFORMANCE Robert James Westgate July 2012 Department of Civil and Structural Engineering The University of Sheffield A thesis submitted for the Degree of Doctor of Philosophy in Engineering Environmental Effects on a Suspension Bridge’s Performance DECLARATION This thesis is submitted for the degree of Doctor of Philosophy in the Department of Civil and Structural Engineering at the University of Sheffield. The thesis is based on independent work performed by the Author between October 2008 and July 2012 under the supervision of Professor James M. W. Brownjohn. All the ideas and work are original except where referenced in the text and detailed in the “Division of work” sections of several chapters. The work contained in the thesis has not previously been submitted for any other qualification. Robert James Westgate July 2012 2 Environmental Effects on a Suspension Bridge’s Performance ABSTRACT Current Structural Health Monitoring (SHM) research uses changes in a bridge’s behaviour to locate and quantify the damage in a structure. However the structural responses are also linked to environmental effects, such as its temperature and the traffic load. In order to understand a typical suspension bridge’s behaviour to environmental conditions, studies on the Tamar Suspension Bridge’s response to temperature and traffic are contained in this thesis. This was achieved by observing data collected from long-term monitoring systems installed on the structure, and simulated responses derived from a three-dimensional finite element model of the bridge. The data of the bridge have shown that the profile of the suspension bridge reconfigures when the temperature of its structure increases, causing the deck to sag and expand. The natural frequencies of the bridge were noted to drop during the day. Transient thermal responses were also indentified; the differing rates of warming up between the deck, towers and cables manifested in the structural responses of the bridge. Phenomena caused by the temperature differential across the bridge’s surface were also studied. Investigations on the effect of traffic demonstrated its additional mass causes the natural frequencies to decrease for certain modes. This was identifiable in the time series data, where the largest reduction in frequencies is during rush hours. The investigations have shown that the changes the modal frequencies and modal mass are dependent on the eccentricity of the traffic flow on the bridge, which may increase or decrease depending on the mode shape. The loading of an abnormally heavy trailer on the bridge has also demonstrated the deformation to the bridge’s quasi-static shape as the vehicle travelled across. The location of the vehicle on the bridge was also able to affect the modal properties of the suspension bridge, according to simulated results. 3 Environmental Effects on a Suspension Bridge’s Performance ACKNOWLEDGEMENTS I would like to express my gratitude to Prof. James Brownjohn for his guidance, knowledge and support throughout my study here at the University of Sheffield. I also owe a lot to Dr. Ki-Young Koo, not only for his work with the monitoring systems and database on the Tamar Suspension Bridge, but I could not have asked for a better colleague and friend for my research. Plus he can drive! Special thanks go to the staff at the Tamar Bridge and Torpoint Ferry Joint Committee for giving us access to their bridge for our research. I am very thankful for the love and support from Helen Leung, for making me very happy and being my rock. I would like to thank my mum, dad, brother Steven and the rest of my family for always being in my heart, and giving me the drive to work. I would also like to thank my colleagues in the Vibration Engineering Section for their friendship and support. These include Dr. Donald Nyawako, Dr. Vito Racic, Dr. Chris Jones, Dr. Chris Middleton, Malcolm Hudson, Nima Noormohammadi, Nicky de Battista, Prof. Paul Reynolds, Prof. Aleksander Pavic, Sharon Brown and many others. 4 Environmental Effects on a Suspension Bridge’s Performance ACKNOWLEDGEMENT OF WORK FROM OTHER AUTHORS Some of the work within this thesis was not produced by Robert Westgate, but from people whom he collaborated with to produce the research. The following section is for the reader to acknowledge which work was provided by other sources. The installation and maintenance of the VES monitoring system on the bridge is credited to Ki- Young Koo, as well as the processing of Robotic Total Station signals to acquire the monitored quasi-static properties of the structure, and the processing of accelerometer signals to acquire the monitored dynamic properties of the structure. Ki-Young Koo also managed the monitoring equipment on the bridge during a site investigation which monitored the transit of a heavy vehicle (in Chapter 8). In Chapter 2, Figure 2.9 and Figure 2.10 are taken from a 4th year undergraduate coursework by A. Spencer and M. Roberts. In Chapter 4, Figure 4.1 and Figure 4.2 were created by Ki-Young Koo. 5 Environmental Effects on a Suspension Bridge’s Performance CONTENTS Declaration ..............................................................................................................2 Abstract ...................................................................................................................3 Acknowledgements ..................................................................................................3 Acknowledgement of work from other authors ........................................................ 5 Contents ..................................................................................................................6 List of figures ......................................................................................................... 12 List of tables .......................................................................................................... 19 Nomenclature for Chapters 2 to 5, 7 and 8 .............................................................. 21 Nomenclature for Chapter 6 and Appendix A .......................................................... 24 Chapter One: Introduction to the Research ............................................................. 26 1.1 Structural Health Monitoring ............................................................................... 27 1.2 Motivation for the study ...................................................................................... 27 1.3 Organization ......................................................................................................... 29 Chapter Two: A History of Numerical Analyses used for Suspension Bridges: A Literature Review .................................................................................................................. 30 2.1 Introduction ......................................................................................................... 31 2.2 History .................................................................................................................. 31 2.2.1 Catenary derivation ........................................................................... 31 2.2.2 Navier’s theory .................................................................................. 34 2.2.3 Rankine theory .................................................................................. 35 2.2.4 Elastic theory ..................................................................................... 36 2.2.5 Deflection theory ............................................................................... 37 2.2.6 Relaxation theory .............................................................................. 38 2.2.7 Response to point loads .................................................................... 40 2.2.8 Linear dynamic response of cable ..................................................... 42 2.2.9 Dynamic response with stiffening frame .......................................... 45 2.3 Application of Finite Element models .................................................................. 46 6 Environmental Effects on a Suspension Bridge’s Performance 2.3.1 Construction of models ......................................................................46 2.3.2 Case studies of FE models applied to suspension bridges .................52 2.4 Sensitivity to structural parameters .....................................................................53 2.4.1 Site investigations ..............................................................................53 2.4.2 Updating parameters .........................................................................54 2.4.3 Adjustment of parameters .................................................................56 2.5 Structural Health Monitoring ...............................................................................57 2.6 Environmental Effects Upon Suspension Bridges ................................................58 2.6.1 Thermal Conditions ............................................................................59 2.6.2 Traffic and vehicle mass .....................................................................61 2.6.3 Wind Conditions ................................................................................62 2.7 Summary ..............................................................................................................62 References .....................................................................................................................63