Dynamic Analysis Of Long-span Bridge Subjected To Wind And Train

Long-span bridges are so susceptible to wind actions due to their high flexibility characteristic that large displacement and vibration will be induced with the action of strong wind loads. If a railway bridge is built to span river or sea, its dynamic response to the action of wind and train should be studied to ensure the safety of bridge structure and the running train. Furthermore, the nonlinear characteristics will be more and more obvious with the increase of bridge span, which further adds the difficulty of analysis for the coupled wind-train-bridge system. Based on the research background review of the dynamic interaction of bridge with running train and the wind induced vibrations of long-span bridges, a nonlinear wind-train-bridge model is established considering the geometric nonlinearities of the long-span bridge, and a corresponding computer code is written. In this way, the dynamic actions of both wind and running train to the long-span bride are studied synthetically. The main contents of this paper are as following:1. The current construction state and the current study of long-span bridges in the world are summarized, including a review of the rapid development of long span bridges with different style, the research background of the dynamic interaction of bridge with running trains, the wind-induced vibrations of bridges, and the nonlinear analysis of long-span bridges. The significance and necessary of studying this problem by regarding the wind, running train and long-span bridge to a coupled system are set out.2. The effect of train speed varying is studied based on the coupling vibration of train and bridge system. The distribution curve of the bridge maximum deflection versus vehicle speed is given, with which the varying tendency of maximum displacement with speed varying is explained. The calculated results show that the tendency of the bridge displacement time history does not change when the train runs with varying speed, and the values of the maximum displacements have little difference. Therefore, for simplification of study, the speed varying of train can be ignored.3. The dynamic characteristics of fluctuating winds are analyzed. Wind forces, including steady-state, buffeting and self-excited forces acting on the bridge, and steady-state, buffeting ones acting on the train, are simulated in time domain by harmonic superposition technique. A dynamic model of wind-train-bridge system is established, by considering27degrees-of-freedom for the4-axle train, and adopting the modal superposition technique for the bridge model, while the geometric nonlinearity is considering further. The framework for solving the coupled dynamic train-bridge system subjected to wind action is proposed. A computer code is written, and some skills in writing the code are introduced.4. The proposed framework is then applied to a real long-span steel truss arch bridge across the Jiujiang River. The natural frequencies and node modes of the bridge are gained via modal analysis. The effect of static wind loads and fluctuating wind loads are calculated through applying different wind loads. The dynamic responses of the bridge are calculated with different wind velocity, and the influences of wind velocity and train speed are synthetically analyzed. The conclusions obtained are given below:(1) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement.(2) The vertical displacements reduce with increase of wind velocity, while the lateral and torsional displacements increase, and the accelerations of the bridge in both directions increase with wind velocity.(3) Both train speed and wind velocity have great influence on the dynamic responses of the bridge.5. Considering the nonlinear relation between displacement and strain, a dynamic model of simply-supported bridge with moving wheel-sprung mass is established, and the dynamic differential equations of bridge with generalized coordinates are derived, which is solved by the Newmark numerical integration and the direct interactive method. The proposed analysis model is validated with a real highway bridge. On this basis, the analysis method is investigated for nonlinear dynamic responses of non-simply-supported bridges subjected to running train, which is the basic study for the nonlinear analysis of complex train model and long-span bridge. The influence of initial force in the hangers and large displacement effect of the Jiujiang Yangtze River Bridge are calculated. By taking the Wufengshan suspension bridge with the main span1120m as an example, and considering the geometric nonlinear characteristics of the long-span suspension bridge, the nonlinear dynamic responses of wind-train-bridge system are analyzed. The influences of structure geometric nonlinearity, wind velocity and train speed are analyzed, and are compared with those of the Jiujiang steel arch bridge. The corresponding conclusions are as following:(1) The initial forces of gravity and dead load in the main cable and·suspenders may increase the structural stiffness and the frequencies of the bridge, but not influence its vibration, modes.(2) The geometric nonlinearity of the structure does not influence the shape of bridge displacement and acceleration histories, but reduces the maximum values of the responses.(3) The static wind makes the bridge to produce a biased lateral displacement, and the fluctuating wind makes it to vibrate around the static displacement. The wind load effect to the Wufengshan suspension bridge is the same to the Jiujiang steel arch bridge.(4) The bridge vibration will be exacerbated under higher wind velocity. The lateral and torsional displacements and accelerations are affected significantly by wind velocity. The vertical responses will be exacerbated when the wind velocity is high enough, which is different to the results of the Jiujiang steel arch bridge.(5) Train speed has certain influences on the dynamic response of the bridge, and especially the influence to the vertical displacement is obvious. While the lateral and torsional displacements and accelerations are more sensitive to the wind velocity.(6) Influence of the large displacement increases with the bridge displacement, but it is not a linear relation between the nonlinear error and displacement.