## 4 Conclusions  
The aging of the railway bridge infrastructure and the modernization of the train fleets worldwide necessitates regular safety assessment of railway bridges. Vital in this assessment procedure is the vehicle-bridge interaction and the ability of the numerical models to reflect the dynamic properties of the vehicles and bridges. Although elastomeric bearings are ubiquitous in railway bridges, research that quantifies their effect on the bridge response is scarce. This study, which aims to understand and quantify the effect of bearing stiffness on the dynamic response of railway bridges, is motivated by this scarcity. A finite element code that can take vehicle-bridge interaction into account is developed to analyze the behavior of railway bridges with varying bearing stiffness values. The code is then verified using the existing literature. The developed code conducts the vehicle-bridge interaction analysis at a relatively low computational cost compared to commercially available software paving the way to the parametric study reported in this article. Single- and multi-span bridges with varying bearing stiffness values were modeled using the developed software, and their dynamic response under vibrations induced by passenger trains traveling with different speeds was computed. As a result of the numerical analysis conducted, the following conclusions can be drawn. Figure 16: Fourier Amplitude Spectrum of the accelerations at the middle of the second span for the three-span bridge. Different colors correspond to different bearing stiffness values. * The bearing stiffness has a significant influence on the dynamic response on railway bridges at all train speeds considered in the study. Not only the amplitudes of the accelerations varied with the changes in the train speed but also the locations of the maximum accelerations shifted considerably. * The vertical stiffness of the bearings can be assumed to be infinite when its value exceeds \(1\times 10^{8}\) kN/m as neither the bridge frequency nor the acceleration response of the bridge is affected once the vertical bearing stiffness exceeds this value. * Even when the first and second mode frequencies of the bridge is not affected by the variations in the bearing stiffness, the subtle change in the higher mode frequencies can lead to significant changes in the acceleration response. For the single-span bridge analysed, only the third mode frequency of the bridge was slightly changed when the bearing stiffness was reduced from \(1\times 10^{8}\) kN/m to \(1\times 10^{7}\) kN/m while the frequencies of the first two modes remained the same. However, this subtle change combined with the change in the third vertical mode shape led to a significant increase in the acceleration response as well as in a shift in the location of the maximum acceleration. * For the multi-span bridges, the bearings at the ends of the bridge and the middle supports have a significantly different impact. When all bearings are infinitely rigid, the accelerations at each of the bearings are naturally zero. As the bearing stiffness is decreased, the accelerations at the end bearing increase rapidly, and the maximum accelerations are recorded at these edges. On the other hand, the accelerations over the middle bearings remain the lowest values over the entire bridge for all the bearing stiffness values considered. * The acceleration response of the bridges was not significantly influenced by the train speed for the speeds considered in this study when the bearing stiffness is lower than \(1\times 10^{8}\) kN/m. The effect of train speed in acceleration response is more pronounced for higher bearing stiffness values. * For certain bearing stiffness values, the finite element analysis can suffer from instabilities at the boundaries, and the results for these cases should be evaluated carefully. However, once the bearing stiffness values drop below \(1\times 10^{7}\) kN/m, these instabilities disappear.