Dynamic behavior of track (rack)-bridge system under running vehicle and temperature load in rack railway

Significant diurnal temperature variations in mountainous rack railways cause stiffness mismatches between the rack structure and simply supported bridges, leading to critical failures like bolt loosening and rack fractures. This study develops a dynamic model of the vehicle-rack-bridge system based on train-track-bridge interaction theory, integrating gear-rack meshing and wheel-rail contact mechanisms. The model analyzes the dynamic response of bridges with varying spans under combined thermal and dynamic loading. Numerical simulations, conducted using finite element analysis, reveal peak vibration accelerations of 1.3 m/s² for the rack, 3.0 m/s² for the rail, 1.2 m/s² for the sleeper, and 0.1 m/s² for the bridge, with maximum stresses of 3 MPa in the rack, 8 MPa in the rail, and 25 MPa in connecting bolts. The results show significant span-dependent amplification of stress and strain in the rack system under thermo-mechanical loading, exceeding material strength limits at 60-meter spans. An innovative elastic connection method is proposed to mitigate stress concentrations effectively, enhancing system durability. This study introduces a novel approach to modeling complex thermo-mechanical interactions in rack railway systems, validated through extensive simulations, and provides a practical solution for improving structural resilience, offering theoretical guidance for optimizing rack-bridge system design to ensure operational safety in extreme environmental conditions.