Parametric Study of Influence of Structure Stiffness and Vehicle Characteristics on Dynamic Amplification

Abstract

This work presents the results of a parametric study on the dynamic amplification or impact factor due to transit vehicles. The study was performed on a single span simply supported bridge composed of prestressed concrete bulb tee girders with a concrete deck and direct fixation track. The study varied the key parameters affecting the structural response of the bridge, viz. stiffness of the bridge, vehicle speed and axle configuration. The bridge was numerically modeled using CSI-Bridge software. Stiffness was manipulated in the models by varying the elastic modulus of the concrete. Vehicle speed varied form quasi-static speed of 0.45 m/s (1 mph) to 35.32 m/s (79 mph) in increments of 1.34 m/s (3 mph). Different axle configurations were obtained by modeling trains consisting of different numbers of cars as well as considering different light rail vehicle types. Light rail vehicles defined by transit agencies in Denver, Boston, Washington DC, Phoenix and Houston were considered, which provided a total of 22 different configurations. Vehicle lengths as well the number of axles and spacing between axles varied. The moving loads were modeled using a linear elastic time history analysis. It was assumed that the rail was connected to the bridge deck at distinct points represented by the rail clip connections at approximately 0.76 m (30 inches) on-center. The magnitude of the axle load at a point ramped up from zero to maximum as the axle traveled from the preceding rail clip to the point under consideration and then decreased to zero as the axle traveled onto the following connection point. This triangular variation with time was modeled as a time dependent ramp function which was applied to the different light rail vehicle trains. The time between the start and end of the ramp function was dependent on the speed of the vehicles and train speed was modeled by changing the time base of the ramp function. Dynamic impact was estimated from the models from the ratio of the maximum deflection at midspan under time dependent moving load to the deflection due to a static load analysis. The results showed that the dynamic impact effects on the structure vary greatly with speed and configuration of the vehicle. While the effects generally increased with vehicle speed, the change was not linear and showed in general more than one peak value within the speed range selected. The maximum computed dynamic effect did not occur at the highest speed. The dynamic effect was also dependent on vehicle configuration, with a clear difference in responses between two axle and three axle cars. The overall length of the vehicle had less of an effect. The results were compared to the impact factors typically used by transit agencies and showed that in general for normal ranges of structure stiffness the Agency criteria are conservative or extremely close for vehicle speeds under 35.3 m/s (79 mph). However, the ACI equation for dynamic impact which is the only equation that incorporates vehicle speed and structural stiffness is usually conservative at higher speeds but may be unconservative at lower and medium speeds and does not reflect effects of axle configuration.