Abstract
Short span railway bridges are prone to resonate caused by dynamic train axle loads, which were usually modeled as moving point loads on the bridge in many numerical studies. In reality, the axle weight of the train is a spread load for the bridge deck because of the transfer of the track structure. Previous numerical studies indicated that the spread axle load distributed through the track structure significantly reduces bridge responses compared to the point load model. In this study, the reduction effect is investigated analytically by solving the moving load problem for both the point load and the spread load cases. The analytical solution reveals that bridge responses from the spread load model can be obtained by filtering bridge responses from the point load model. The filter function is exactly the Fourier transform (FT) of the load spreading function. Based on this relationship, a reduction coefficient reflecting the load spreading effect on bridge responses is derived. Through numerical examples, the accuracy of this proposed reduction coefficient is validated not only for the moving load models but also for vehicle‐bridge interaction (VBI) problems.
Highlights
Short span railway bridges are prone to resonate caused by dynamic train axle loads, which were usually modeled as moving point loads on the bridge in many numerical studies
The reduction effect is investigated analytically by solving the moving load problem for both the point load and the spread load cases. e analytical solution reveals that bridge responses from the spread load model can be obtained by filtering bridge responses from the point load model. e filter function is exactly the Fourier transform (FT) of the load spreading function
Besides the vehicle-bridge interaction (VBI) effect, moving load (ML) models do not account for the effect of the track structure on bridge responses. ese effects include the following [16]: (1) the vibration of the track structure, (2) additional constraints applied on the bridge ends by the track, and (3) axle load distributed through track
Summary
Received 26 April 2018; Revised 1 August 2018; Accepted 8 August 2018; Published 12 September 2018. Previous numerical studies indicated that the spread axle load distributed through the track structure significantly reduces bridge responses compared to the point load model. E third effect of the track structure, redistribution of the point axle loads, has been shown to reduce the bridge responses considerably, especially for short span cases. E UIC document [22] provided a graph of the reduction coefficient through numerical simulations with the specific load distribution width of 2.5 m and 3 m All these existing studies on the load spreading effect were carried out numerically in the time domain for specific load shapes. Is frequency domain method helps to reveal the mechanism of the vibration reduction provided by spreading of the axle load and leads to more concise formulas that are applicable to various load distribution shapes. 2ζ i ωb,i v dqi(ι) dι ω2b,iqi pi(ι)
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