Dynamic characteristics of slender suspension footbridges

Due to the emergence of new materials and advanced engineering technology, slender footbridges are increasingly becoming popular to satisfy the modern transportation needs and the aesthetical requirements of society. These structures however are always &quotlively" with low stiffness, low mass, low damping and low natural frequencies. As a consequence, they are prone to vibration induced by human activities and can suffer severe vibration serviceability problems, particularly in the lateral direction. This phenomenon has been evidenced by the excessive lateral vibration of many footbridges worldwide such as the Millennium Bridge in London and the T-Bridge in Japan. Unfortunately, present bridge design codes worldwide do not provide sufficient guidelines and information to address such vibrations problems and to ensure safety and serviceability due to the lack of knowledge on the dynamic performance of such slender vibration sensitive bridge structures. A conceptual study has been carried out to comprehensively investigate the dynamic characteristics of slender suspension footbridges under human-induced dynamic loads and a footbridge model in full size with pre-tensioned reverse profiled cables in the vertical and horizontal planes has been proposed for this purpose. A similar physical suspension bridge model was designed and constructed in the laboratory, and experimental testings have been carried out to calibrate the computer simulations. The synchronous excitation induced by walking has been modelled as crowd walking dynamic loads which consist of dynamic vertical force, dynamic lateral force and static vertical force. The dynamic behaviour under synchronous excitation is simulated by resonant vibration at the pacing rate which coincides with a natural frequency of the footbridge structure. Two structural analysis software packages, Microstran and SAP2000 have been employed in the extensive numerical analysis. Research results show that the structural stiffness and vibration properties of suspension footbridges with pre-tensioned reverse profiled cables can be adjusted by choosing different structural parameters such as cable sag, cable section and pretensions in the reverse profiled cables. Slender suspension footbridges always have four main kinds of vibration modes: lateral, torsional, vertical and longitudinal modes. The lateral and torsional modes are often combined together and become two kinds of coupled modes: coupled lateral-torsional modes and coupled torsionallateral modes. Such kind of slender footbridges also have different dynamic performance in the lateral and vertical directions, and damping has only a small effect on the lateral vibration but significant effect on the vertical one. The fundamental coupled lateral-torsional mode and vertical mode are easily excited when crowd walking dynamic loads are distributed on full bridge deck. When the crowd walking dynamic loads are distributed eccentrically on half width of the deck, the fundamental coupled torsional-lateral mode can be excited and large lateral deflection can be induced. Higher order vertical modes and coupled lateral-torsional modes can also be excited by groups of walking pedestrians under certain conditions. It is found that the coupling coefficient introduced in this thesis to describe the coupling of a coupled mode, is an important factor which has significant effect on the lateral dynamic performance of slender suspension footbridges. The coupling coefficient, however, is influenced by many structural parameters such as cable configuration, cable section, cable sag, bridge span and pre-tensions, etc. In general, a large dynamic amplification factor is expected when the fundamental mode of a footbridge structure is the coupled lateral-torsional mode with a small coupling coefficient. The research findings of this thesis are useful in understanding the complex dynamic behaviour of slender and vibration sensitive suspension footbridges under humaninduced dynamic loads. They are also helpful in developing design guidance and techniques to improve the dynamic performance of such slender vibration sensitive footbridges and similar structures and hence to ensure their safety and serviceability