Keywords: floating-type, cable-stayed bridge, train braking, axle gravity loads of moving trains, four track bridge, combined railway and highway bridge.

In floating cable-stayed bridges, there are no direct connections in the longitudinal direction between the deck and the pylon towers. Because of this, there are no negative bending moments in the deck at the location of the pylon and the internal forces caused by the temperature change, shrinkage, and creep are very small. In addition, the longitudinal vibration of the deck under seismic and train excitations is allowed and this leads to energy dissipation. However, because of the lack of direct connections between the deck and the pylon towers in the longitudinal direction, the deck may vibrate excessively under sufficiently intensive excitation. The excessive vibration may in turn affect the normal functions of bridges and even cause damage to bridges and so has to be controlled. To do this, it is essential to understand the longitudinal vibrating behaviour of the deck in a floating-type cable-stayed bridge.

The longitudinal vibration response of the deck of floating-type railway bridges subjected to train braking and axle gravity loads of moving trains have been investigated in this paper. Firstly, based on an established model of longitudinal train braking forces, current design codes, and vehicle parameters, the longitudinal dynamic loading due to train braking is formulated. Secondly, a "track-fastener and board-sleeper-ballast-grid-bridge longitudinal nodes" model for the transmission of train braking forces is developed to describe the transmission of the braking forces from the tracks to the nodes of the deck. Thirdly, by considering effects of the axle gravity loads of moving trains, the finite element method is used to obtain the time histories of both the braking forces acting on the track and of the bridge nodal forces induced by braking and axle gravity loads of moving trains. Fourthly, the developed procedure is used to analyze the dynamic response of the Tian Xingzhou cable-stayed bridge over the Yangtze River [1] to train braking and axle gravity loads of moving trains. It has been concluded that:

1. The deck of a floating-type railway bridge may experience large longitudinal displacements and consequently large additional bending moments may be produced at the bottom of the pylon towers, which may adversely affect the safety and working state of the bridge.
2. The longitudinal vibration responses of the deck produced by train braking and axle gravity loads of moving trains may be considered in two stages: a braking stage, which has the characteristic of large displacement and low velocity, and a free attenuating vibration stage.
3. The longitudinal vibration responses of the deck of the Tian Xingzhou Yangtze River Bridge to the train braking and axle gravity loads of moving trains may result in large displacements and may affect the serviceability of the bridge.

1

W.L. Qu et al., "Intelligent hybrid control for longitudinal vibration of deck of Tian Xingzhou cable-stayed bridge due to earthquake, train braking and train axle load", Research Report, Wuhan University of Technology, Wuhan, China, 2007.

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