Keywords: bridge, train, wind, interaction, dynamic response, running safety.

With the rapid development of construction materials and technology, more and more long span suspension bridges have been being built in the world. The dynamic interaction between bridges and trains is an important problem to be solved for bridge design, which has been noticed and studied by researchers in China and abroad [1,2,3]. The long suspension bridges usually exhibit special characteristics of high flexibility and low structural damping, which are very susceptible to wind actions [3,4]. Railway trains may be prone to overturn when they are running over a suspension bridge exposed to a strong wind [3,5].

The Tianxingzhou Bridge, with the main span of 864m and two side spans of 96m each, is another long span rail-cum-road suspension bridge being built in Wuhan, China. The modal analysis on this bridge has been performed by the finite element analysis software ANSYS. The results show that the natural frequencies of the bridge are spaced very closely together. Its first 20 natural frequencies range from 0.1259 to 0.5706Hz, including 1 longitudinal vibration mode, 5 vertical modes, 9 lateral modes, and 5 coupling modes between lateral vibration and torsional vibrations [6].

A dynamic analysis model of the wind-bridge-train system is established, which consists of three sub-models: the dynamic model of a train, the dynamic model of a suspension bridge, and the wind loads on the bridge-train system. The train model consists of several locomotives and vehicles. Each locomotive and vehicle is composed of a car body, bogies, wheel-sets, and the spring and damping connections between the three components. For each 2-bogie 4-axle vehicle, the total degrees of freedom are 27. The detailed descriptions on the assumptions used in the model of the train, and the equations of motion for the vehicle can be found in [2,5].

A long suspension bridge consists mainly of bridge towers, piers, main girder, deck, cables, suspenders and anchorages. This study assumes that there is no relative displacement between the track and bridge deck. The suspension bridge is modeled as a three-dimensional system using the finite element method. The winds act as external forces on the bridge and the trains, which include both buffeting and self-excited forces. An efficient computer simulation technique based on the spectral representation method, by using the experimental aerodynamic coefficients and flutter derivatives [4], is proposed to simulate the wind velocity field for the bridge. The method is developed specifically for generating the span-wise turbulent wind velocities at location equally distributed along the bridge span.

In the wind-train-bridge model, the wind loads of bridge structures consist of the buffeting loads and the self-excited loads, whereas the wind loads of train vehicles consist of the steady-state wind loads and the buffeting loads.

The proposed formulations are applied to the Tianxingzhou suspension bridge. The whole histories of the train passing through the bridge under wind actions are simulated, with the train speeds 100-200km/h, and mean wind velocities 0-40m/s. The dynamic responses of the bridge, the running safety and stability indices of the train vehicles, and their distributions versus train speed and wind velocity, are obtained. The main results include:

1. Wind affects on the dynamic responses of the bridge prominently: both the displacements and accelerations of the bridge increase rapidly versus wind velocity. The lateral displacement responses of the bridge are mainly controlled by wind loads, which are more sensitive to the wind than the vertical ones. For such a long suspension bridge, the influence of train speed on the dynamic responses of the bridge girder is much smaller than wind velocity.
2. The dynamic responses of the car-body accelerations, derailment factors, offload factors, and turnover factors related to the running safety and stability indices of the train are all increase significantly with wind velocity. When the mean wind velocity reaches 25m/s or higher, the running safety parameters of the train vehicles exceed the allowances, to which great attention should be paid.
3. Most of the maximum safety and stability indices of the passenger cars are greater than those of the locomotive. It can be concluded that the passenger cars with lighter weights are more dangerous than the heavier locomotives when they move on the bridge under wind action.

1

Frýba L., "Vibration of solids and structures under moving loads", Thomas Telford, London, 1999.

2

Xia H., Xu Y.L., "Dynamic interaction of long suspension bridges with running trains", J Sound & Vibration, 237(2), 263-280, 2000. doi:10.1006/jsvi.2000.3027

3

Diana G., et al, "Wind effects on the dynamic behaviour of suspension bridge", International Report, Milano, 1986.

4

Cao Y.H., et al, "Simulation of stochastic wind velocity field on long-span bridges", J Engineering Mechanics, ASCE, 126(1), 1-6, 2000. doi:10.1061/(ASCE)0733-9399(2000)126:1(1)

5

Xia H., "Dynamic interaction of vehicles and structures", Science Press, Beijing, 2002.

6

Guo W.W., Xia H., Su G.Y., "Vibration analysis of Tianxingzhou long span suspension bridge scheme", Proc. ISSEYE, Tianjin, 319-324, 2002.

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