## 1 Introduction  
Cable-supported bridges (cable-stayed bridges, suspension bridges, and cable-stayed suspension bridges) with large span characteristics have become the preferred structural form to meet the growing demand for transportation and specific purposes. The height of the tower structure, as an important component of a bridge, also needs to increase with the continuous increase in the span of such bridges. Since the bridge tower structure is always exposed to the atmospheric environment, temperature differences will occur between the surfaces of the bridge tower under the influence of external environmental conditions (solar radiation, atmospheric temperature, wind, and other factors), including the overall temperature difference between the external surfaces and the local temperature difference between the internal and external surfaces in the direction of the tower wall thickness, thus forming an uneven temperature field inside the structure. The temperature difference on the external surface of the bridge tower is caused by the shadow occlusion between different surfaces under solar irradiation, and the temperature difference will cause the bridge tower to deviate. The direction and size of the deviation of the bridge tower will change with the direction of solar light irradiation, which will undoubtedly increase the difficulty of monitoring the alignment of the bridge tower during the construction stage. The local temperature difference in the thickness direction of the tower wall is due to the large change in temperature of the external surface of the bridge tower with the change in atmospheric ambient temperature and the influence of solar radiation. The air in the inner cavity of the bridge tower is not flowing and the thermal conductivity of the concrete is poor, which leads to a change in the temperature of the internal surface of the bridge tower that is far less than the change in the external surface temperature. The actual monitoring data of the temperature field of the bridge tower show that the temperature difference formed in the thickness direction of the tower wall is often greater than 10 \({}^{\circ}\)C, and the temperature stress generated can reach the level of the live load [1; 2; 3; 4; 5]. The General Specifications for Design of Highway Bridges and Culverts (JTG D60-2015) [6] does not give a detailed description of the calculation of the temperature field of the bridge tower, while the Specifications for Design of Highway Cable-Stayed Bridges (JTG/T 3365-01-2020) [7] only suggests that the linear temperature difference between the opposite external surface of the bridge tower can be taken as \(\pm 5\)\({}^{\circ}\)C, but its applicability remains to be discussed. The European standard [8] suggests that the temperature difference between the opposite outer surfaces is recommended to be considered by \(\pm 5\)\({}^{\circ}\)C in the absence of detailed information, and the temperature difference between the inner and outer surfaces of the tower wall is recommended to be considered at 15 \({}^{\circ}\)C, but the temperature gradient distribution mode is not described in detail. The temperature gradient distribution of the bridge tower is mostly considered according to the gradient mode of other similar projects, which may be quite different from the actual structure. Therefore, the accurate calculation of the temperature field of the bridge tower structure under the action of sunlight and the exploration of its temperature field distribution law on this basis are of great significance for the reasonable design of bridge tower structures and the assurance of the construction quality. The temperature difference in the height direction of the bridge tower structure is often ignored, and a two-dimensional analysis method is used to calculate the temperature field to simplify the calculation in engineering. However, this method cannot accurately consider the impact of shadow shading, and the calculated results obviously cannot reflect the real structural deformation.