## 1 Introduction
[PERSON] and [PERSON] [19] analyzed the characteristics of the temperature distribution in bridge structures and proposed a finite element mesh generation algorithm based on Delaunay triangulation for adaptive finite element analysis to calculate the temperature field of bridge structures. [PERSON] et al. [20] developed a finite element model for typical concrete casting blocks under solar radiation, analyzing the impact of solar radiation on the temperature field of low-heat concrete at the surface of casting blocks to monitor the temperature gradient on the concrete structure. [PERSON] et al. [21] measured the temperature of truss bridges and determined that solar radiation intensity was an important factor affecting the temperature difference distribution of truss bridges. In summary, the study of temperature distribution in concrete structures has progressed from simplified linear models to complex numerical simulations that take into account various factors. These studies not only improve the accuracy of the temperature field simulation in structures but also provide an important basis for engineering design and structural maintenance. While there has been progress in studying the temperature fields of concrete structures, current research mainly focuses on the temperature distribution in commonly shaped bridge sections (like T-shaped, trough-shaped, I-shaped, and box-shaped, etc.). [PERSON] et al. [22] obtained the temperature distribution of T-shaped girder bridges through field measurements and analyzed the impact of temperature gradients on bridges. That is, short-term temperature gradients will not lead to stresses that exceed the cracking limit of the beam cross section, but the long-term cumulative effect can surpass the tensile strength of concrete, leading to structural cracks. [PERSON] et al. [23] performed year-long temperature monitoring on a box-shaped girder bridge to study vertical and horizontal temperature gradients under varying environmental conditions and proposed a second-order curve model for temperature distribution. [PERSON] et al. [24] established a temperature simulation model for trough-shaped girder bridges by considering the atmospheric environment, bridge orientation, and bridge direction, and a temperature difference model for the box room and bottom slab of trough-shaped girder bridges was proposed by analyzing the variation pattern of the temperature field in trough-shaped girder bridges. [PERSON] [25] studied the effects of seasonal temperature changes on the long-term performance of composite bridges, emphasizing the importance of accurately assessing temperature effects to prevent concrete cracking. [PERSON] et al. [26] analyzed the temperature gradients of I-shaped girder bridges under solar radiation through field tests, identifying temperature fluctuations, low wind speeds, and lack of precipitation as key environmental factors affecting temperature gradients, and disclosed the phenomenon of nonlinear temperature gradients under uneven temperature conditions. [PERSON] et al. [27] studied the effects of temperature changes on the dynamic characteristics of T-shaped girder bridges and elucidated the mechanisms by which temperature affects the dynamic responses of structures. [PERSON] et al. [28] monitored the temperature changes of three box-shaped girder bridges in different climatic regions and used data regression techniques to establish the prediction model for temperature distribution based on actual data. [PERSON] [29] studied the effects of temperature changes on the displacement of supports in long-span truss continuous bridges and demonstrated the nonlinear hysteresis effects between structural temperature and bridge support displacements through the analysis of field data. Although many studies have focused on the temperature distribution in commonly shaped bridge sections, research on the characteristics of temperature distribution in U-shaped girder bridges is relatively limited.