## 3 Influence of Different Simulation Methods for Internal Thermal Boundary Conditions
### Adjacent Box Girder  
#### 3.3.1 Influence on the Hourly Temperature Curves  
Due to space limitations, the measured hourly temperature curves obtained from the temperature sensors installed on the adjacent box girder #3 (3-T, 3-W, and 3-B as illustrated in Figure 7) were selected for comparison with the numerical hourly temperature curves calculated by the FEMs considering different simulation methods for the internal thermal boundary conditions, as shown in Figure 18. The solid points denote the measured data, and the solid lines with hollow points denote the calculated curves. The RMSE and MAPE of the numerical hourly temperature curves of the adjacent box girder cross-sections obtained from the FEMs with different simulation methods for the internal thermal boundary conditions are illustrated in Figure 19. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Methods**} & **Ambient Temperature Method** & **Mean Temperature Method** & **Air Element Method** \\ \hline Measured value & & 28.4 & \\ Numerical value & 29.5 & 28.6 & 28.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparisons of the highest \(T_{\text{AVG}}\) of the small box girder cross-sections obtained from the field test and the FEMs with different simulation methods for the internal thermal boundary conditions (Unit: \({}^{\circ}\)C). Figure 17: Comparisons of the maximum vertical temperature gradients of the small box girder cross-sections obtained from the FEMs with different simulation methods for the internal thermal boundary conditions. In Figures 18 and 19, it can be observed that the trends and the times at which the maximum temperatures occurred are similar for the measured and numerical hourly temperature curves of 3-T, 3-W, and 3-B. The influence of the Ambient Temperature Method on the trends of the numerical  
Figure 19: The RMSE and MAPE of the numerical hourly temperature curves of the adjacent box girder cross-sections obtained from the FEMs with different simulation methods for the internal thermal boundary conditions: (**a**) RMSE; (**b**) MAPE. Figure 18: Comparisons of the hourly temperature curves of the adjacent box girder cross-sections obtained from the field test and the FEMs with different simulation methods for the internal thermal boundary conditions: (**a**) 3-T in the top flange; (**b**) 3-W in the web; (**c**) 3-B in the bottom flange. hourly temperature curves of the bottom flanges on the adjacent box girders is much smaller than that on the box girder or small box girders. This is because the area of the cavities in the adjacent box girders illustrated in Figure 7 is quite small. Compared with the measured hourly temperature curves, the numerical curves calculated by the Measured Temperature Method (the maximum RMSE was 1.1 \({}^{\circ}\)C, and the maximum MAPE was 2.6%) and the Air Element Method (the maximum RMSE was 1.2 \({}^{\circ}\)C, and the maximum MAPE was 3.0%) provided the closest agreement. When there is a lack of measured temperatures inside the cavities, the numerical hourly temperature curves calculated by the Air Element Method provided a closer agreement with the measured curves than the curves calculated by the Ambient Temperature Method (the maximum RMSE was 2.0 \({}^{\circ}\)C, and the maximum MAPE was 4.8%) and the Mean Temperature Method (the maximum RMSE was 1.7 \({}^{\circ}\)C, and the maximum MAPE was 4.2%). The measured hourly temperature curves of all temperature sensors installed in the adjacent box girder cross-sections were compared with the numerical hourly temperature curves calculated by the FEM using the Air Element Method as the simulation method for the internal thermal boundary condition, as shown in Figure S3.