# Study on Solar Radiation and the Extreme Thermal Effect on Concrete Box Girder Bridges
## 2 Calculation Method of Solar Radiation and Field Temperature Observing
### Temperature Field Analysis and the Finite Element Numerical Simulation  
The measured time-temperature curves of each slab of the box girder are shown in Figure 8.  
The temperature variations show the temperature distribution of the measuring points in four slabs in the day. The maximum temperature appears in the top slab. Due to the pavement influence, there is a delay between the rise of measured temperature and solar radiation. The overall temperature of the left web (sunshine side) is higher than that of the right web (sheltered side), and the temperature changing range is also more extensive. The overall temperature of the bottom slab is the lowest but changes more obviously. It also illustrates that direct solar radiation has the most significant influence on the temperature field, and the depth of practical impact is about 30 cm. Figure 8: _Cont._  
Figure 7: (a) Diurnal variation of the measured air temperature; (b) Diurnal variation of solar radiation intensity. Since the temperature field distribution along the length of the bridge is almost consistent, 2D simulations of the temperature field at the mid-span section were carried. The simulation analysis of the solar effect is by ANSYS, the element size is 0.05 m, and the element type is used as PLANE 55/182, which is suitable for transient temperature analysis. The simulation time is selected from 6:00 to 19:00 according to the sunlight period, and the steady-state simulation result of the temperature field at 6:00 is as the initial condition. The load step was set as every other hour. After obtaining the temperature fields, the thermal-structure coupling method in ANSYS is used to calculate the temperature stress. According to the design information, the material properties of bridge girder concrete and the parameters of comprehensive heat convection are shown in Tables 2 and 3. According to the thermodynamic theory, the temperature boundary condition of the girder under solar radiant is unified as the third boundary condition. The integrated heat transfer coefficient \(h_{c}+h_{r}\) on the sunlight surfaces is calculated as Formula (13) and (14); the coefficient at different moments is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Density \(\rho\)** & **Specific Heat c** & **Thermal Conductivity \(\lambda\)** & **Elastic Module** & **Linear Expansion Coefficient** & **Poisson’s Ratio** \\ \hline
2600 kg/m\({}^{3}\) & 910 J/(kg.\({}^{\circ}\)C) & 2.7 W/(m.\({}^{\circ}\)C) & 3.45 \(\times\) 10\({}^{4}\) MPa & 1\(\times\) 10\({}^{-5}\)\({}^{\circ}\)C & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material thermal properties [29]. Figure 8: **(a)** The measured temperature variation of the top slab; **(b)** The measured temperature variation of the left web; **(c)** The measured temperature variation of the right web; **(d)** The measured temperature variation of the bottom slab. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Surface Albedo \(\tau_{e}\)** & **Wind Speed, \(v\)** & **Surface** & **Radiation** & **Inner Surface Integrated** & **Stefan–Boltzmann** \\  & **Emissivity \(\epsilon_{r}\)** & **Absorption \(\epsilon\)** & **Heat Transfer Coefficient** & **Constant C\({}_{0}\)** \\ \hline
0.2 & 1.5 m/s & 0.88 & 0.5 & 11.05 W/(m\({}^{2}\).\({}^{\circ}\)C) & 5.67 \(\times\) 10\({}^{-8}\) \\  & & & & W/(m\({}^{2}\).K4) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comprehensive heat convection parameters. The finite element calculation shows that the maximum temperature appears at the top deck under solar radiation, and the minimum temperature area appears inside the right part of the section. The comparison between the measured data and calculated results of some points in each slab is shown in Figure 10.