During their lifetimes, tramway networks become increasingly susceptible to mechanical damage in the form of rail fractures. Understanding the underlying reasons, and initiating appropriate countermeasures may be facilitated by (computational) modeling tools. The development of such tools calls for a sound theoretical foundation. The latter is still largely missing, as the cross-sectional shapes of grooved rails employed in tramway networks differ significantly from those of (in this regard) well-investigated railroad systems. As a first step towards closing this knowledge gap, we here report on a novel beam theory approach allowing to compute typical shear stress distributions throughout the cross sections of grooved rails. Based on classical concepts, such as Bernoulli and Saint-Venant beam kinematics, cross-sectional boundary value problems for the related shear stress distributions are derived, and corresponding solutions are obtained in the form of 2D Finite Element approximations. This way, it is revealed that practically relevant loading scenarios induce distinctive shear stress concentrations. Remarkably, the positions of the latter agree well with fracture patterns observed in situ.

Introduction

In many urban areas, the tramway network is the backbone of the local public transport system [1–۴]. Hence, the reliability of tramway networks is key for the functionality of public life in such areas. The primary causes for disturbances are fractured rails [5,6], as well as degradation due to wear and environmental influences [7,8]. It is evident that rail fractures occur if the loads acting onto the rails induce stress states which exceed the strengths of the steels the rails are made of. A purely experimental approach to the challenge of predicting where and when fractures occur turns out as difficult (if not impossible), given the huge dimensions of the problem (in terms of both size and load magnitude). This calls for computational approaches, and the current state of the art in the field may be briefly sketched as follows: The contact forces between wheel and rail have been quantified for different types of rails (i.e. railroad, subway, and tramway) [5,9–۱۱]. Other modeling approaches are concerned with the estimation of residual stresses. This is often done based on the Finite Element (FE) method, with the main focus lying on Vignole rails [12–۱۸], and an only marginal amount of work spent on tramway rails [19]. Residual stresses have been shown to arise in the rails from the straightening and bending processes prior to mounting the rails [10,12–۱۸,۲۰,۲۱], and change, over time, due to the overrunning by wheels [9–۱۱,۲۲–۲۴], hence under standard operation conditions [22–۲۵]. Numerical methods have also been developed for crack propagation analysis in Vignole rails, either under consideration of residual stresses [27,26], or neglecting the latter [24,28].