## 3 Influence of Different Simulation Methods for Internal Thermal Boundary Conditions
### Average Effective Temperatures of Cross-Sections  
Based on the aforementioned meteorological data under historically extreme temperature conditions and the Air Element Method, the FEMs of the concrete closed girder cross-sections were established to predict the peak average effective temperatures of the cross-sections under historically extreme temperature conditions (hereafter referred to as \(T_{\text{E}}\)). The one-year measured average effective temperatures of the cross-sections can be obtained from the field test (hereafter referred to as \(T_{\text{M}}\)). The maximum and minimum effective temperatures of highway concrete bridges were recommended by the Chinese code JTG D60-2015 [50] (hereafter referred to as \(T_{\text{C}}\)). China is partitioned into four climatic regions that are categorized as severe cold, cold, warm, and \"other\" regions [50]. Handan is in the cold region, with the highest \(T_{\text{C}}\) of 34 \({}^{\circ}\)C and the lowest \(T_{\text{C}}\) of \(-10\)\({}^{\circ}\)C; Shenzhen is in the warm region, with the highest \(T_{\text{C}}\) of 34 \({}^{\circ}\)C and the lowest \(T_{\text{C}}\) of \(-3\)\({}^{\circ}\)C; and Fuzhou is in the \"other\" region, with the highest \(T_{\text{C}}\) of 34 \({}^{\circ}\)C and the lowest \(T_{\text{C}}\) of \(0\)\({}^{\circ}\)C. Comparisons of \(T_{\text{M}}\), \(T_{\text{C}}\), and \(T_{\text{E}}\) are illustrated in Figure 24.  
Figure 23: Numerical hourly beam solar radiation and diffuse solar radiation under the highest historical temperature conditions: (**a**) Shenzhen; (**b**) Handan; (**c**) Fuzhou. Figure 24: _Cont._  
The comparisons of \(T_{\text{M}}\), \(T_{\text{C}}\), and \(T_{\text{E}}\) for the box girder cross-section are illustrated in Figure 24a. It can be observed that the highest \(T_{\text{M}}\) was close to the highest \(T_{\text{C}}\) (a difference of 0.9 \({}^{\circ}\)C), and these values were lower than the highest \(T_{\text{E}}\) (differences of 4.9 \({}^{\circ}\)C for \(T_{\text{M}}\) and 5.8 \({}^{\circ}\)C for \(T_{\text{C}}\)). The lowest \(T_{\text{M}}\) was much higher than the lowest \(T_{\text{E}}\) (a difference of 12.2 \({}^{\circ}\)C) and the lowest \(T_{\text{C}}\) (a difference of 17.8 \({}^{\circ}\)C). The variation of \(T_{\text{C}}\) was close to that of \(T_{\text{E}}\) (a difference of only 0.2 \({}^{\circ}\)C), and they were larger than that of \(T_{\text{M}}\) (differences of 16.9 \({}^{\circ}\)C for \(T_{\text{C}}\) and 17.1 \({}^{\circ}\)C for \(T_{\text{E}}\)). It can be predicted that the longitudinal thermal movement of the concrete box girder under historically extreme temperature conditions would be underestimated by considering the variation of \(T_{\text{M}}\). The variations of \(T_{\text{C}}\) (37.0 \({}^{\circ}\)C) and \(T_{\text{E}}\) (37.2 \({}^{\circ}\)C) were almost the same. However, assuming that the datum temperatures (\(T_{0}\)) were the same, the thermal expansion of the concrete box girder calculated by the difference between the highest \(T_{\text{C}}\) and \(T_{0}\) would be smaller than that calculated by the difference between the highest \(T_{\text{E}}\) and \(T_{0}\), while the thermal contraction of the concrete box girder calculated by the difference between \(T_{0}\) and the lowest \(T_{\text{C}}\) would be larger than that calculated by the difference between \(T_{0}\) and the lowest \(T_{\text{E}}\). The comparisons of \(T_{\text{M}}\), \(T_{\text{C}}\), and \(T_{\text{E}}\) for the small box girder cross-sections are illustrated in Figure 24b. It can be observed that the highest \(T_{\text{E}}\) (44.7 \({}^{\circ}\)C) was significantly higher than the highest \(T_{\text{M}}\) (a difference of 8.8 \({}^{\circ}\)C) and the highest \(T_{\text{C}}\) (a difference of 10.7 \({}^{\circ}\)C); meanwhile, the lowest \(T_{\text{E}}\) (\(-\)18.2 \({}^{\circ}\)C) was significantly lower than the lowest \(T_{\text{M}}\) (a difference of 20.2 \({}^{\circ}\)C) and the lowest \(T_{\text{C}}\) (a difference of 8.2 \({}^{\circ}\)C).