The Response Equations for a Cross-Tie Track

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ACTA Mechanica
The Response Equations for a Cross-Tie Track. Early analyses of the lateral response of cross-tie railroad tracks are based on the assumption that the rail-tie structure responds like a beam in bending. Because of the difficulties encountered in determining the lateral bending stiffness of a cross-tie track, a more recent approach is to model the rail-tie structure as a beam in bending that is also subjected to continuous resistance moments, transmitted to the rails by the fasteners. Also this approach exhibits a number of shortcomings. To date there are no generally accepted equations for the lateral response of the cross-tie track. The main purpose of the present paper is to derive such equations. Since the rail-tie structure consists of a repeated pattern of identical units, the corresponding difference equations are derived first. Then, by a limiting process, in which the tie spaces tend to zero. The difference equations are reduced to differential equations. This approach yields equations with well-defined coefficients, in terms of the geometrical and mechanical parameters of the track structure. Difference and differential equations are derived for the track response in the lateral, as well as the vertical plane. The derived equations are then discussed and compared with those suggested by other investigators.
Publisher version:
Cross-tie track, Lateral response
Kerr, A. D., & Zarembski, A. M., “The Response Equations for a Cross-tie Track”, ACTA Mechanica, 40, 253-276, 1981.