## 3 Temperature Testing Results of Concrete Box Girder  
### Temperature Time-Varying Rules  
A local coordinate system is established on the measured cross-section based on the relative position of the sensors to determine the coordinates of each temperature measurement point and establish the coordinate index of the temperature sensors. The triangular meshing of the box girder's cross-section is performed using a Delaunay triangulation algorithm, as shown in Figure 4. This algorithm ensures that no circumscribed circle of any triangular mesh overlaps with other measuring points [26; 27]. By employing the finite element method with Lagrange shape function [28], interpolation and transformation are used to determine the temperature at arbitrary positions on the cross-section, thereby establishing a comprehensive database for measured temperature field across the entire  
Figure 3: Meteorological data. cross-section. A temperature nephogram depicting the three stages of the box girder's cross-section is illustrated in Figure 5.  
Based on the measured temperature data across the cross-section of the box girder, it is postulated that each measurement point represents an approximation of the average  
Figure 4: Triangulation of the concrete box girder. Figure 5: Temperature nephogram of box girder at three stages. temperature within its corresponding triangular area. Consequently, a weighted calculation formula for determining the average temperature of the cross-section is proposed as follows:  
\[\overline{T}=\sum_{i=1}^{n}T_{i}\,A_{i}/\sum_{i=1}^{n}A_{i} \tag{3}\]  
where \(\overline{T}\) denotes the mean temperature across the cross-section of the box girder; \(T_{i}\) represents the measured temperature value at the \(i\)-th temperature measurement point; \(A_{i}\) is the area represented by this measurement point; and \(n\) is the number of temperature measurement points. The curve in Figure 6 illustrates the temperature evolution of the box girder cross-section obtained by solving Equation (3). It is evident that the temperature variation curve exhibits noticeable fluctuations, while the temperature reduction curve of the concrete box girder remains remarkably smooth. As abrupt drops occur in air temperature, three significant cooling stages can be observed across the average temperature of the box girder's cross-section, as listed in Table 2. A comparison between Tables 1 and 2 reveals a lag in cooling for the box girder's cross-section following an abrupt drop in air temperature, with phase differences ranging from 0.23 h to 3.28 h. Notably, cooling stage I displays the smallest phase difference, whereas stage II exhibits the largest discrepancy. In stage I, temperature reduction commences at 17:46, when solar radiation intensity is relatively weak and has minimal impact on the box girder's temperature field. Conversely, stage II experiences a rise in temperatures starting at 12:43, when solar radiation values are high and steadily increasing. During this stage, solar radiation energy is absorbed by the box girder model, leading to the continuous elevation of cross-sectional temperatures and resulting in a larger phase difference. These findings highlight that solar radiation significantly influences the temporal disparity between air temperature reduction and box girder cooling. A noticeable difference can be observed in the termination times of air temperature reduction, whereas the cross-sectional temperature of the box girder initiates an upward trend at around 10:00 in the morning. Research findings indicate that, in this region, sunrise occurs at approximately 10:00 a.m. during January. Following sunrise, the concrete box girder undergoes heat absorption due to solar radiation influence, leading to the cessation of cooling. Moreover, within the same cooling stage, the maximum temperature of the concrete box girder remains lower than that of ambient air temperature; however, its minimum temperature surpasses that of ambient air temperature.