An analysis is presented for the determination of the range of “safe” temperature increases in a railroad track, in order to prevent vertical buckling. A general nonlinear formulation of the problem is derived by using the theory of elasticity, the principle of virtual displacements and the variational calculus for variable matching points. In order to simplify the solution it is shown, on a closely related problem, that a number of highly nonlinear terms may be neglected without affecting the final results. The obtained nonlinear formulation for the railroad track is simplified accordingly. The resulting nonlinear equations are then solved, in closed form, and the obtained results are presented graphically.

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