## 1 Introduction  
High-speed railways have provided remarkable mobility in densely populated areas, with bridges playing a vital role in their design. Long-span bridges help high-speed railway lines cross large rivers, deep valleys, bays, and other natural barriers [1]. To avoid the adverse impacts of expansion joints on crossing trains, high-speed bridges can only have expansion joints at the girder ends of the main bridge structures. The long length and complex temperature field of the jointless bridge are in conflict with the low limits required for temperature-induced displacements. Hence, the temperature effects on bridge displacements--especially at the girder end--must be investigated, which is the focus of this article.  
The study of the temperature effects on long-span bridges is an important focus of civil engineers, who wish to master the behavior of bridge structures under both day-night and seasonal temperature changes. Some researchers have investigated the temperature behavior of the bridge structure usingfinite element (FE) simulations [2; 3]. Considering the complicated nature of the actual temperature field in a bridge during operation, additional studies have attempted to analyze the thermal effects on bridge structures based on measured data and long-term monitoring data [4; 5; 6; 7; 8; 9]. Furthermore, scholars have explored the behavior and performance of bridge structures under diurnal temperature loads via the validation of FE results using monitoring data [10; 11; 12]. Analysis of the temperature-induced behavior of bridge structures has solved a variety of engineering problems for many major infrastructure systems by employing such continuous studies.  
However, such studies have typically focused on the mechanical behavior of the girder end under service loads, especially under temperature loads, which are typically minimal [13; 14]. With the advancement of displacement-measurement technology [15; 16] and time-frequency analytical techniques [17; 18; 19; 20], the time-frequency and long-term characteristics of bridges can now be analyzed based on structural health monitoring (SHM) data. Due to the redundancy and complexity of train-bridge systems [21; 22; 23], girder expansion on the longitudinal direction must be unimpeded, and the transverse dislocation between two girder ends (the main bridge and ramp bridge) is not allowed.  
Based on long-term SHM data, this article investigates the longitudinal behaviors and girder end reliability of a jointless steel-truss arch railway bridge in operation. The time-frequency and long-term characteristics of the longitudinal displacements of the bearings and expansion joints are analyzed. The influence of the bridge's longitudinal displacements due to the environmental temperature is demonstrated based on the monitoring data. The wear lifetimes of the bearings caused by cumulative longitudinal sliding displacements are predicted. The relative transverse displacements of the bridge girder end are calculated using the monitoring data from the longitudinal displacements. The mechanical behaviors of the expansion device under the relative transverse displacements are simulated via FE modeling. The fatigue reliability of the expansion devices and the reliability of crossing trains under the in-service relative transverse displacements are studied, which can help bridge engineers to maintain this high-speed railway bridge during diurnal operation.