Speed, Fatigue Test, and ${\mathrm{P}}_2$ Load Limit: Fatigue Strength of Railroad Rail

The allowable bending fatigue stress in a rail will determine the maximum allowable speed, which is then checked against the current operating speed. Therefore, some sensible value of allowable bending fatigue stress must be agreed upon. This paper establishes a relationship between reliability and bending fatigue stress. According to the American Railway Engineering and Maintenance-of-Way Association (AREMA), the recommended allowable bending fatigue stress is $124\mathrm{N}/{\mathrm{mm}}^2$ (18,000 psi). However, this recommendation is associated with low reliability and does not match the AREMA-recommended fatigue test load, which implies a stress of $97\mathrm{N}/{\mathrm{mm}}^2$ (14,042 psi). AREMA should review its recommended value of the allowable bending fatigue stress and fatigue test load. This paper explores the basis of the fatigue test span and formulates a fatigue test load. Additionally, the author suggests the upper limit of ${\mathrm{P}}_2$ load in this paper. The concerns associated with the heavy haul operation are discussed with suggestive measures to reduce rail/weld fracture failure rate. Therefore, this paper could be helpful to compute allowable speed, to assess reliability of rail traffic against fatigue failure of rail/weld, to compute fatigue test load and to limit the ${\mathrm{P}}_2$ load.