Analysis of Crosstie Track in Lateral Plane Using New Track Equations

The analysis of a crosstie railroad track in the lateral plane has traditionally been based on the theory of a beam on an elastic foundation, in which the bending rigidity of the track structure is assumed to be twice the rigidity of a single rail, and the ballast resistance is represented by a linear Winkler foundation with modulus k. The traditional analysis ignores the contribution of the ties and rail-tie fasteners to the bending stiffness of the track and the nonlinearity of the ballast resistance. In the present paper the analysis of an infinitely long crosstie track subject to a concentrated lateral load is presented. The analysis is based on the new track equations derived by Kerr and Zarembski in 1981. These equations explicitly account for the contribution of the rails, ties, and fasteners to the bending stiffness of the track. A bilinear approximation is assumed in modeling the lateral resistance due to the ballast. A closed form solution for the track deflection is obtained using the new equations, for displacements in the linear regime. A closed-form solution is obtained for the nonlinear response, using a simplified set of track equations. A method for determining the model track parameters is presented that is based on a least-squares fit to experimental load-deflection data. Results show that the analytical solution accurately predicts the measured data, for the full range of loads and over the entire length of the track.