Abstract: The lateral rigidity of a sharply curved bridge (SCB) pier has an important impact on regularities of the track in modern tram lines. A spatial calculation model for SCB-CWR (continuous welded rail) interaction is established by the grounds of the finite element method. Taking the example of a curved steel-concrete composite bridge with spans of 35 m+40 m+40 m+35 m, the effects of different factors on TAI (track alignment irregularity) are analyzed. The results show that the coupling between longitudinal and lateral SCB-CWR interactions can cause middle and long wave TAI. The amplitude of TAI shows a positive correlation with longitudinal rigidity of a pier, with the variation range of rail temperature and, with the maximum force of fastener longitudinal resistance, but a negative correlation with lateral rigidity of a pier, with curve radius and, with the yield displacement of fastener longitudinal resistance. The most significant factor is curve radius. When the radius increases from 150 m to 600 m, the amplitudes of TAI determined by the mid-chord offset method and by the differential offset method reduce by more than 60%. The lateral rigidity thresholds of piers for common curved continuous beam bridges in modern tram lines are ascertained respectively. The thresholds of steel-concrete composite bridges are 1.2~2.0 times greater than that of reinforced concrete bridges. Optimizing design stress-free rail temperature or using small resistance fastener which can effectively reduce the amplitude of TAI and the lateral rigidity thresholds of piers are recommended to be applied during the design of CWR on SCB.