Finite element analysis of the thermal interaction of continuously welded rails with simply supported bridges considering nonlinear stiffness

The thermal interaction of continuously welded rails with railway bridges has attracted the wide attention of researchers. In this paper, the model of a continuously welded rail and a bridge with longitudinal nonlinear stiffness has been considered. The detailed mechanics equation of the rail on the bridge and the embankment with longitudinal nonlinear stiffness has been presented using the finite element analysis. The validity of the presented model and the compiled program is illustrated. The influences of nonlinear stiffness, span number of the bridge, constant longitudinal restoring force, bridge bearing arrangement, and the span length of the bridge on the additional longitudinal stress and displacement of rails are investigated for multispan simply supported bridges. The results show that (1) the responses of rails for the nonlinear stiffness are less than those for the linear stiffness; (2) when the bridge span reaches a certain number, the maximum additional longitudinal stress and the displacement of the rail tend to be constant; (3) with the increase of the value of the constant longitudinal restoring stress, the maximum additional longitudinal stress and the displacement of the rail increase; (4) the maximum additional longitudinal stress of the rail on multispan simply supported bridges can be reduced by using alternate bearings on one pier; and (5) the maximum additional longitudinal stress and displacement of the rail increase with the increase of the span length of the bridge.