A numerical element for vehicle–bridge interaction analysis of vehicles experiencing sudden deceleration

Train sudden deceleration (braking) that causes sliding in wheels could impact the design of rail components, supports, bearings, and bridge substructure. Despite the availability of research on the vehicle–bridge interaction (VBI) analysis of vehicles with constant velocity, few studies have investigated the effect of vehicle longitudinal acceleration on VBI and more research is required. In this study, the effect of vehicle horizontal acceleration is incorporated into an available numerical procedure developed for VBI analysis of vehicles with constant velocity, and a modified numerical element is proposed. The effect of acceleration is considered as external loads acting on each part of the vehicle masses. Using suitable transformation matrices and defining a new parameter called acceleration parameter, the vertical contact forces are reformulated. Subsequently, a new formulation for a VBI element containing the effect of vehicle acceleration is obtained. VBI elements are those bridge elements in contact with wheels of moving vehicle. Numerical results are presented to evaluate the importance of the proposed VBI element, and to investigate the vehicle and the bridge responses. Considerable effect was observed on vehicle vertical contact forces, vehicle vertical acceleration, and somewhat on midspan deflection. Minor effect was observed on bridge midspan acceleration, for which the effect of vehicle initial velocity is prominent, not the vehicle acceleration.