## 2 Experimental  
### Basic Principle of Structural Temperature Field  
* Heat conduction. According to the basic principles of thermodynamics, temperature transfer is always from high temperature to low temperature. For any point in the structure, its temperature is a three-dimensional function of time change. According to [PERSON]'s heat conduction theory, the general form of the three-dimensional transient heat conduction differential equation of the structure is obtained [23; 24]:  
\[\lambda\bigg{(}\frac{\partial^{2}\text{T}}{\partial x^{2}}+\frac{\partial^{2 }\text{T}}{\partial y^{2}}+\frac{\partial^{2}\text{T}}{\partial z^{2}}\bigg{)} =c\gamma\frac{\partial\text{T}}{\partial t}+Q \tag{1}\]  
where \(\gamma\) is the density of the material, kg/m\({}^{3}\); \(c\) is the specific heat of the material, J/(kg\(\cdot\)K); \(\lambda\) is the thermal conductivity, W/(m\(\cdot\)K); T is the temperature of any point (x, y, z); \(t\) is time, s; \(Q\) is the internal heat source intensity, W/m\({}^{3}\). The cross-sectional variation in SCCB along the longitudinal bridge is not obvious, and the heat conduction along the bridge axis can be ignored. Therefore, the sunshine temperature field of the composite beam can be simplified as a two-dimensional transient temperature without an internal heat source, as shown in Equation (2):  
\[\rho c\frac{\partial T}{\partial t}=\lambda\bigg{(}\frac{\partial^{2}T}{ \partial x^{2}}+\frac{\partial^{2}T}{\partial y^{2}}\bigg{)} \tag{2}\]
* Convective heat transfer. Convective heat transfer is heat exchange between a solid surface and its surrounding fluid due to temperature differences. The factors affecting the heat convection intensity include the contact area between the media, the properties of the media, the flow velocity, the flow space size, the structure, and the fluid temperature. According to [PERSON]'s law, heat transfer is proportional to the contact area and temperature difference in the structure [25]:  
\[q_{c}=h_{f}(T_{\text{S}}-T_{\text{B}}) \tag{3}\]  
where qc is heat transfer, W/m\({}^{2}\); hf is the convective heat transfer coefficient; TS is atmospheric surface temperature; TB is bridge structure surface temperature. * Thermal radiation. Radiant heat transfer occurs between objects of different temperatures, when the temperature of the system is consistent, the radiant heat transfer is still in progress, but in a state of dynamic equilibrium. The radiant heat transfer between the two systems can be calculated using the Steffen-Boltzmann equation [26,27]:  
\[h_{r}=\sigma\varepsilon\Big{[}(T_{S}+273.15)^{2}+(T_{B}+273.15)^{2}\Big{]}(T_{S} +T_{B}+546.3) \tag{4}\]  
where \(\varepsilon\) is the emissivity of the actual object, whose value is always less than 1; \(\sigma\) is the Steffen-Boltzmann constant, whose value is 5.67 \(\times\) 10\({}^{-8}\) w/m\({}^{2}\). * System temperature difference. According to GBT51234-2017 Urban Rail Transit Bridge Design Code [28], the temperature difference in the system should be calculated from the closing time of the structure, and the difference between the closing temperature and the extreme minimum temperature and extreme maximum temperature over the years should be taken, respectively [28]  
\[ \begin{cases}\Delta T_{1}=T_{H_{1}-}T_{L_{1}}\\ \Delta T_{2}=T_{H_{2}-}T_{L_{2}}\end{cases}  \tag{5}\]  
where \(\Delta T_{1}\) and \(\Delta T_{2}\) are, respectively, the overall temperature rise difference, \({}^{\circ}\)C; \(T_{H_{1}}\) and \(T_{H_{2}}\) are, respectively, the extreme maximum temperature in the past year and the maximum temperature during the closing, \({}^{\circ}\)C; \(T_{L_{1}}\) and \(T_{L_{2}}\) are the lowest temperature and the extreme minimum temperature during the closing in the past years, \({}^{\circ}\)C.  
* Temperature gradient. Temperature gradient refers to the change in temperature per unit length in a certain direction in space. It describes the spatial change rate of the temperature field, and its calculation formula is as follows [28].