## 3 Research Method
### Numerical Simulation
The radiation calculation formulas of the model are as follows (1988):  
\[I_{bn}=Ae^{-B/sinh} \tag{4}\]  
\[I_{dh}=Cl_{bn} \tag{5}\]  
where \(I_{bn}\) is the direct solar radiation intensity on the surface normal (W/m\({}^{2}\)), \(I_{dh}\) is the diffuse solar radiation intensity on the horizontal surface (W/m\({}^{2}\)), \(h\) is the solar altitude angle, and \(A\), \(B\), \(C\) are the apparent solar irradiation, atmospheric extinction coefficient and diffuse radiation factor, respectively. The three empirical coefficients are all functions of monthly variation and are obtained on the basis of the measured data for solar radiation in the United States. The Hottel model is a clear sky model suitable for conditions with visibility higher than 23 km and altitude lower than 2500 m. In the Hottel model, the transmittance of direct solar radiation (\(\tau_{b}\)) and the transmittance of diffuse solar radiation (\(\tau_{d}\)) are applied in order to calculate solar radiation, as shown in Equations (6) and (7). \[I_{bh}=\tau_{b}I_{0} \tag{6}\]  
\[I_{dh}=\tau_{d}I_{0} \tag{7}\]  
Figure 2: Three basic components of solar radiation. where \(I_{bh}\) is the direct solar radiation intensity on the horizontal surface (W/m\({}^{2}\)), and \(I_{0}\) is the solar radiation intensity at the outside tangent plane of the atmosphere (W/m\({}^{2}\)). In 1976, [PERSON] [99] established the model and proposed a formula for calculating the transmittance of direct solar radiation based on the altitude and solar altitude angle; this formula is \(\tau_{b}=a_{0}+a_{1}e^{-k/sinh}\). \(a_{0}\), \(a_{1}\), \(k\) are all empirical coefficients in consideration of climate types. The transmittance of diffuse solar radiation is usually calculated using the formula \(\tau_{d}=0.271-0.294\tau_{b}\), proposed by [PERSON] and [PERSON] [100] in 1960. The direct solar radiation decreases exponentially as sunlight passes through the atmosphere. When studying the temperature stress of bridge structures under solar radiation, [PERSON] [101] followed the Bouguer-Lambert Law and provided method for calculating the direct solar radiation at the earth's surface using the power exponent model. In 1983, [PERSON] [102] established a systematic power exponent model to calculate direct solar radiation, and this model can be represented as the following formula:  
\[F_{avg}=(1-cos\alpha)/2 \tag{2}\]0  
\[F_{avg}=(1-cos\alpha)/2 \tag{2}\]1  
\[F_{avg}=(1-cos\alpha)/2 \tag{2}\]2  
where \(k_{T}\) is the transmittance factor, which expresses the scatter of the light in a pure atmosphere, as well as the absorption of certain wavelengths by the atmosphere; \(t_{u}\) is the atmospheric turbidity factor, which expresses the attenuation of direct solar radiation under different atmospheric conditions; \(m\) is the air mass factor, which gives the relative path length of the radiation through the atmosphere; and \(k_{a}\) is relative atmospheric pressure. Since then, many scholars have used [PERSON]'s method to calculate direct solar radiation, including [PERSON] [103], [PERSON] [104], [PERSON] [105], etc. Compared with the other two models, the ASHARE model is the most complex, and its three empirical coefficients require long-term meteorological observation data from different sites to be obtained in order to apply them to the corresponding areas. In addition, the atmospheric turbidity factor also needs to be obtained through meteorological information from the corresponding areas. However, around the globe, the empirical coefficients of the Hottel model have been provided for detailed values, corresponding to climate types. Therefore, under application conditions, the Hottel model can be used in areas with insufficient meteorological data. The shadow of steel structures under sunlight directly affects the direct solar radiation absorbed by the structure's surface, and the analysis of the shadow effect is one important step in ensuring the accuracy of the simulation of temperature fields.