Computation of distribution factor

Abstract: Currently professionals use the charts from the Manual of Railway Engineering to get a percentage of load carried by single tie i.e., distribution factor. There are two charts – one gives nominal values of distribution factor for wood, steel, and concrete tie and the other one gives conservative values of distribution factor for concrete tie only. The charts are developed for some specific values of track modulus (lbs./in./in.) and tie spacing. The professionals have to interpolate a value of distribution factor for other values of track modulus and tie spacing. The charts give the same value of distribution factor for any rail section e.g., 115 RE, 136 RE etc. on the assumption that the effect of rail stiffness is small compared to other factors e.g., track modulus, tie spacing although the rail stiffness influences the distribution of load. Thus, three factors – track modulus, bending stiffness of rail and tie spacing affect the distribution of load. From the knowledge of track modulus and bending stiffness of rail the characteristic length can be computed by a well-established formula. For the sake of easy computation and to overcome the aforementioned deficiencies, a simple formula is derived in terms of characteristic length and tie spacing to compute the distribution factor. The formula is based on beam on an elastic foundation model and gives distribution factor for any rail section, track modulus and tie spacing