In-plane nonlinear localised lateral buckling under thermal loading of rail tracks modelled as a sandwich column

• A sandwich model is to determine the in-plane nonlinear localised lateral buckling of rail tracks.
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• A critical track length is proposed to study localised buckling.
• Both symmetric and antisymmetric buckling modes are investigated.
• Fasteners with large rotational stiffness substantially increases the lateral stability of the track structure.
• Design curves relating lateral out-of-straightness versus the safe temperature were determined.

The lateral buckling problem for continuous welded rail tracks under thermal loading has been well researched and is known to involve a localisation buckling phenomenon where only a limited region of the track buckles. In this paper, a sandwich column model is formulated to model the rail track-tie structure as sandwich column. The constitutive relations for the thermally induced stresses and finite strain are based on a hyperelastic constitutive model. A hyperbolic function for the nonlinearity of the axial and lateral resistance between the tracks and ballast was used. A critical track length is proposed beyond which the localisation is unaffected. Increasing the track length or changing the boundary conditions does not influence the localised buckling behaviour for track lengths beyond the critical length. The use of fasteners with large rotational stiffness substantially increases the lateral stability of the track-tie structure. Nonlinear numerical solutions are compared with the results in the literature. The variation in the axial compressive force within the localisation zone in the rail is studied and discussed. Parametric studies are performed on examples to identify the influence of track imperfections on the localised lateral buckling and safe temperature change.