## 2 Previous Studies
### Bridges  
There are many factors leading to the complex temperature fields in bridge structures, such as solar radiation, atmospheric temperature, and wind speed [39; 40]. The significant structural thermal effect is caused by the complex temperature fields of bridges, which can result in potential safety hazards [41; 42]. The study of the temperature fields and effects of bridges is important and valuable for ensuring their safety during operation. The temperature fields of steel truss bridges under solar radiation is significantly non-uniform due to the effect of the self-shadow of members and the shadow between members, and this non-uniformity is not only reflected in the temperature difference between steel truss members, but also in the temperature differences within the cross-sections of each steel truss member [43; 44]. Through the comparative analysis of test results from the Dashengguan Yangtze Bridge, the static strain variations of steel truss members are mainly caused by temperature and trains, and the correlation between the temperature field and the remaining static stress shows good linear characteristics after removing train-induced static strain [45]. The large horizontal rotation angles at the beam ends of railway bridges can lead to the variation of track geometry state and damage of rail fastening systems [46]. Based on the long-term monitoring data of several railway steel truss bridges, the non-uniform temperature distribution of steel trusses is the key factor leading to the horizontal rotation angle, especially for the transverse temperature difference between the bottom chord trusses and the transverse temperature difference between the top chord trusses [47; 48]. For steel box girders in bridge structures, the temperature along its longitudinal direction is relatively uniform, but the temperature distribution through the cross-section is significantly non-uniform due to the shadow effect [49]. Based on Eurocode 1 for thermal actions [50], non-uniform temperature distributions through the cross-section can be divided into a uniform temperature component, a vertical temperature difference component, and a horizontal temperature difference component. On the basis of the temperature field monitoring data of the Normandy Bridge's steel box girder over 34 months, [PERSON] discovered that there was a difference, which was caused by solar radiation, between the daily maximums of the uniform temperature component and the air temperature, but that their daily minima were in good agreement [51; 52]. Many studies have shown that vertical temperature difference is usually significantly higher than horizontal temperature difference in normal cases; therefore, only the vertical temperature difference must be considered in these cases. The functions of quintic parabola, quadratic and cubic polylines have been used to describe the vertical temperature gradient curve modes for steel box girders in various studies [53; 54; 55]. However, the large horizontal temperature difference must also be considered in particular cases; for example, it reaches up to a maximum of 18 \({}^{\circ}\)C for the Humber Bridge based on the measured data [56]. Six horizontal temperature difference models were proposed by [PERSON] for the top plate of steel box girders on the basis of the monitoring data from the Runyang Cable-Stayed Bridge [57]. Throughout the life cycle of steel box girders, they are under outdoor conditions and are directly exposed to solar radiation; thus, the adverse effects of non-uniform temperature distribution are not only reflected during the construction period, but also during the service period. The steel box girders in bridge structures are usually assembled from several prefabricated sections. During the construction process, the non-uniform temperature distributions can result in the thermal deformation of prefabricated sections, which can lead to dislocations between the two prefabricated sections to be connected, which may directly affect closure accuracy and construction quality [58].