A discussion on the beam on elastic foundation theory

Abstract

A railway track is a structural composure of many elements. Railway track analyses requires analyses for the interaction between these elements and the interaction between the track and the vehicle passing over the track. Various design models have been developed to simplify the analysis of railway tracks and to establish appropriate design criteria. Winkler's representation of the subgrade support as a continuous structure with independent springs was adapted to railway tracks by Zimmermann that further evolved into what is known as the Beam on Elastic Foundation Theorem (BOEF) today. A soil and structure interaction model based on BOEF theorem, frequently used by engineers to analyze the response of continuously supported structures on bearing layers, provides estimates for the distribution of deflections, bearing pressure, shears and moments along a continuously supported structure, such as a plate, by subgrade. This study aims to provide an in-depth and an explicit solution to the 4th order differential equation of BOEF and serve as a resource for those who are interested in this topic. This study will also present the historical development of the BOEF model, its use in railway track analysis, as well as its underlying assumptions in terms of structural behavior.