A model for the mechanical behaviour of the railway track in the lateral plane

This paper deals with a mechanical model for the analysis of the railway track behaviour built by exploiting the periodicity of the track-structure. The starting point of this study are the inner forces transferring modes. They have been determined by the unit principal vectors analysis of the base cell transfer matrix. The main outcome on bending moments is that they are transferred through the track without deforming the sleepers and fasteners and are composed of two parts: the first one, referred as primary bending moment, is generated by the couple of axial forces acting on each nodal section while the second is due to the curvature changes of the rails. Shear forces are engendered by two independent mechanisms that are associated respectively with the unit changes of the total and primary bending moments. The constitutive properties of the equivalent medium are derived by an averaging and limiting process of the transferring modes strain energies, avoiding any a priori assumption on the kinematics of the substitute medium. Finally, the equilibrium equations are achieved by the virtual work principle. The proposed model is able to reproduce accurately the track behaviour in transferring its inner forces. However, solutions that are equilibrated but not kinematically admissible are obtained from it when transversal loads are applied. In additions, only boundary conditions compatibles with the track transferring modes can be satisfied. This inconsistency is eliminated by superposition of some corrective deformed shapes. These are derived by the eigenvectors of the transfer matrix pertaining to self-equilibrated systems of bending moments decaying along the track. The application field of the proposed track model is also discussed, and the results of a validation study carried out by F.E. analysis are finally presented.