A law for the temperature-induced stress distribution in continuously welded rail

A new model is presented for the calculation of the rail extension, the friction created by sleeper fastenings and the temperature-induced stress for continuously welded rail (CWR) under free conditions and the calculation and analysis of temperature-induced stress when the temperature is changing and the rail is anchored. The mechanism for generating friction and the phenomenon of rail creep (extension) on site are used to establish a law that states that the friction force of the fasteners is distributed from the center of the CWR section towards the two ends in increasing scale; this observation is used to derive a formula for calculation of the distribution of the friction force in CWR fastenings. Formulas for calculating the temperature-induced stress and its distribution are also derived. The presented results show that the distribution of temperature-induced stress is cone-shaped in the absence of rail creep (extension), and with creep it presents a tangent and a cone shape in anchored sections. A comparison with the traditional temperature-induced stress distribution pattern in a rail of a tangent constitutes an argument against the established methods. The results reported in this paper should play an important role in guiding site maintenance activities.