Thermal buckling of ballasted tangent track

Euler type analysis usually used for compression members in structural engineering does not work for railroad track. Euler type analytical formulas for horizontal and vertical buckling endorsed in a recent literature is reviewed to demonstrate its weakness. Using definition of moment and curvature as well as principle of equilibrium, the author suggests formula for horizontal buckling load of railroad track and demonstrates validation in context with currently accepted values, published results, and past field tests. The buckling load from suggested formula agrees with the recent buckling load formula based on total energy theorem. A formula is suggested to study the effect of misalignment on critical temperature differential or critical load. A vertical buckling load formula is derived from horizontal buckling load formula. A buckling process is narrated through step by step computation. Formulas are suggested to compute the effect of track misalignment on critical buckling load and threshold radius of a vertical curve.