This paper describes analyses to examine the lateral deflection of railroad track subjected to quasi-static loading. Rails are assumed to behave as beams in bending. Movement of the track in the lateral plane is constrained by idealized resistance characteristics, while movement in the vertical plane is resisted by a continuous, linear and elastic foundation. These analyses are based on solving the ordinary differential equations for beam deflections. In certain cases, convenient mathematical expressions may be used to represent idealized lateral resistance characteristics and derive closed-form equations to relate lateral force as a function of track lateral deflection. However, in general, the idealized lateral resistance characteristic may be nonlinear, in which case numerical methods are required to examine the lateral load versus track lateral deflection behavior. In these general cases, a Fourier series technique is used to solve the governing equations numerically.
The analysis of track lateral deflection subjected to quasi-static loads may be applied to examine track shift. For example, lateral resistance of track may be measured using Track Lateral Pull Tests (TLPT). The Fourier method is also used to examine the relationship between lateral and vertical wheel loads and track lateral shift.