This article, “An analytical solution to Track Bridge Interaction,” presents a comprehensive algebraic approach to the Track-Bridge Interaction (TBI) problem 1 . The core contribution is an analytical solution to the governing differential equations 2 , extending existing algebraic formulations by integrating three increasingly refined track restraint models: the fully plastic, gap plastic, and the linear elastic-plastic models 3 , 2 . This development provides a computationally efficient method for accurately assessing the additional stresses introduced into Continuous Welded Rail (CWR) due to bridge movement 4 . The resulting set of algebraic equations offers a rapid TBI analysis tool, which serves as a significant practical alternative to time-consuming Finite Element Models (FEMs) 5 . The analytical framework is powerful for performing sensitivity analysis on key design variables 6 and is ideally suited for studying the influence of parameter variations, such as comparing ballasted versus slab track systems 7 and assessing various deck stiffnesses 8 . This capability enables engineers to validate FEMs and rapidly optimize bridge and track designs to meet stringent safety and durability requirements for high-speed lines 9 . • Novel Analytical Solution : The article presents a comprehensive analytical approach to the Track Bridge Interaction problem, significantly extending and providing an algebraic solution to the governing differential equations. • Three Refined Track Bridge Interaction (TBI) Models : The core contribution is an algebraic solution based on three increasingly refined track restraint models: the fully plastic, gap plastic, and the linear elastic-plastic models. • Computational Efficiency : The resulting algebraic equations offer a powerful, rapid method for TBI analysis that is computationally efficient and provides a significant practical advantage over time-consuming Finite Element Models (FEMs). • Design Optimization Tool : The framework enables engineers to rapidly optimize bridge and track designs to meet stringent safety and durability requirements. • Validation and Sensitivity Analysis : The new set of equations can be used to validate FEMs and to perform sensitivity analysis on key design variables. • Parametric Study Capability : The analytical model is ideally suited for studying the influence of parameter variations, such as comparing ballasted versus slab track systems and investigating various deck stiffnesses.
Leon et al. (Fri,) studied this question.