# Study on Solar Radiation and the Extreme Thermal Effect on Concrete Box Girder Bridges
## 4 The Estimated Extreme Temperature Condition of the Bridge in the Design Lifetime  
### Historical Meteorological Data  
The meteorological data are obtained from the nearest ground observation station (25.51\({}^{\circ}\) N and 107.33\({}^{\circ}\) E, altitude 980 m) of the bridge site. Summer (from June to August) air temperature data from 1990 to 2020 were collected and analyzed. The daily maximum air temperature \(T_{max}\), the daily maximum temperature difference \(\Delta T_{max}\), and daily average wind speed \(w_{a}\) in summer are shown in Figure 12.  
2.386, \(\mu=5.958\). The distribution functions of daily maximum air temperature and daily maximum temperature difference \(G(x)_{t}\), \(G(x)_{\Delta}\) are as  
\[G(x)_{t}=exp\left\{-\left[1-0.359\left(\frac{x-26.317}{2.814}\right)^{1/0.359} \right]\right\} \tag{20}\]  
\[G(x)_{\Delta}=exp\left\{-\left[1-0.157\left(\frac{x-5.958}{2.386}\right)^{1/0. 157}\right]\right\}. \tag{21}\]  
According to the Chinese code [30], a bridge structure's design lifetime is 100 years, so the extreme temperature data in the return period (\(T\)) of 100 years are considered a severe load condition. The estimated extreme temperature with a return period of 100 years was estimated as \(x_{p}\) when \(1-f(x)=1/T\). \[x_{p}=\left\{\left[-\log(1-p)\right]^{-\xi}-1\right\}\frac{\sigma}{\xi}+\mu \tag{22}\]  
Based on Formula (15), the smaller the wind speed is, the more significant the temperature difference inside the concrete box girder. Therefore, it is necessary to obtain a small value of wind speed. Since the generalized extreme value distribution is generally used to fit the maximum value, set the parameter of the daily minimum average wind speed \(Min\{v_{1},v_{2},\cdots,v_{n}\}=Max\{-v_{1},-v_{2},\cdots,-v_{n}\}\). The parameters of the wind speed are as, \(w_{a}:\;\xi=-0.479,\sigma=1.284,\mu=-2.560\); then, the distribution function of the wind speed \(G(x)_{wa}\) is as:  
\[G(x)_{t}=exp\left\{-\left[1-0.479\left(\frac{x+2.560}{1.284}\right)^{1/0.479} \right]\right\}. \tag{23}\]  
After calculation, when the regression period is more than 10 years, the daily minimum average wind speed variation is less than 0.4 m/s. As the wind speed on the girder surface changes rapidly and randomly, the probability of the minimum average wind speed appearing over a regression period of 100 years is too small, and the result will be too unfavorable. The return period of wind speed is taken as 10 years, and the minimum value is 0.49 m/s. Therefore, the estimated value of summer's daily maximum air temperature is obtained as 33.1 \({}^{\circ}\)C, the daily maximum temperature difference is 14.7 \({}^{\circ}\)C, and the wind speed is valued as is 0.5 m/s. As the solar radiation changes slight in summer, the extreme thermal condition is obtained by combining the same solar radiation in Section 3.1 and the temperature and wind factors above. Numerical Example of the Box Girder Thermal Effect under Solar Radiation and the Extreme Temperature Condition  
To study solar radiation and the extreme thermal effect on the concrete bridge girder, the temperature valve and wind speed obtained in the previous chapter were used for heat transfer process calculation. Since the solar radiation \(I_{o}\) changes about 1.2% in clear weather in summer, the solar condition remains the same. The hourly temperature of the day is calculated as Formula (22) [31]  
\[T_{a}(t)=0.5(T_{amax}-T_{amin})sin[(t-9)15^{\circ}]+0.5(T_{amax}+T_{amin}) \tag{24}\]  
where \(T_{amax}\) is the maximum air temperature in a day, and \(T_{amin}\) is the minimum air temperature in a day, which is valued as \(T_{amax}-\Delta T_{max}\). As there is a time difference \(t_{d}\) between the true solar time at the bridge site and the standard time (calculated by Formula (6)), and the measured maximum air temperature appears at 17:00, one-hour adjustment was applied to obtain the hourly air temperature for the numeral example.