ON THE RELATIONSHIP BETWEEN LOAD AND DEFLECTION IN RAILROAD TRACK STRUCTURE Sheng Lu, Richard Arnold, Shane Farritor* *Corresponding Author Department of Mechanical Engineering University of Nebraska Lincoln N104 Scott Engineering Center Lincoln, NE 68588-0656 Mahmood Fateh, Gary Carr Federal Railroad Administration Office of Research and Development 1200 New Jersey Avenue SE Washington, DC 20590 ABSTRACT Track Modulus, defined as ratio between the rail deflection and the vertical contact pressure between the rail base and track foundation, is an important parameter in determining track quality and safety. The Winkler model is a widely used mathematical expression that relates track modulus to rail deflection. The Winkler model represents railroad track as an infinitely long beam (rail) on top of a uniform, linear, and elastic foundation. The contact pressure between the rail base and track foundation increases linearly with vertical deflection. However, it is widely accepted that actual track deflection is highly non-linear. Several other models have been used to better represent the behavior of railroad track structure including a model that includes a shear layer and one that uses discrete supports. This paper presents a new model of track deflection where the elastic foundation beneath the rail has a cubic polynomial relationship between applied pressure and vertical deflection. This new cubic model is compared to other models of railroad track structure, including the Winkler, Pasternak, and Discrete Support models, as well as with experimental data. It is shown that the cubic model is a better representation of real track structure. INTRODUCTION Background The relationship between applied loads, track stresses, and track deformations are important factors to be considered in proper track design and maintenance. A representative mathematical model that accurately describes this relationship is desirable. Winkler proposed the use of an elastic beam theory to analyze rail stresses and calculation of a fundamental parameter, called the track modulus, which represents the effects of all the track components under the rail (1). Track Modulus (represented by u in this paper) is defined as the supporting force per unit length of rail per unit rail deflection (2). Track Stiffness (represented by k in this paper) is simply the ratio of applied load to