# Geometrical Parametric Study on Steel Beams Exposed to Solar Radiation
## 4 Finite Element Modeling
### Verification with Experimental Records
The W12 sections exhibit the highest temperatures due to the thinner flanges, while W24 \(\times\) 84 exhibited the lowest temperature owing to its thickest flange among the four sections. The thickness of the top flange of the W12 sections is 16.25 mm, while those of W24 \(\times\) 104 and W24 \(\times\) 84 are 19.05 and 19.56 mm, respectively. Thicker section means longer heat transfer time from the heated surface to the section's core, which means slower gain of temperature. The same observations are applicable for the bottom flange as shown in Figure 8. The bottom flange receives the heating solar radiation from the top surfaces of the flange and the reflected component from the bottom surface of the flange. The above discussion comparing between the two groups of specimens relies on the sole effect of flange thickness. For better understanding, there should be a physical quantity that can by a good comparison tools between the four sections. The heating of the top surface is not solely affected by flange thickness, where the increase of flange width (\(W_{t}\)) leads to higher accumulated absorbed energy. Thus, both flange width and flange thickness are effective. When the temperature variation behavior at the peak temperature hours (12:00 to 15:00) was compared with the ratio of flange width to flange thickness (\(W_{t}\)/\(t_{t}\)), no specific trend was clear, which is mainly due to giving equal weights for both flange width and flange thickness. The flange thickness should be given a higher influence weight as it is the main controller of temperature at this time of day. Therefore, the temperature variations were investigated with the ratio of flange width to the square of flange thickness (\(W_{t}\)/\(t_{t}\)\({}^{2}\)) as shown in Figure 9. It is obvious in the figure that the top surface temperature increases with the increase of the quantity \(W_{t}\)/\(t_{t}\)\({}^{2}\). The section W12 \(\times\) 58 with the highest \(W_{t}\)/\(t_{t}\)\({}^{2}\) value of 0.96 exhibited the highest top surface temperature at noon hours, while the section W24 \(\times\) 84 with the lowest \(W_{t}\)/\(t_{t}\)\({}^{2}\) value of 0.60 showed the lowest temperatures at the same time. This means that the top surface temperature increases with the increase of top flange width and the decrease of its thickness but is more affected by flange thickness than flange width. The temperature variation of the top and bottom surfaces (Figures 7 and 8) is obvious to be uniform with time. Oppositely, Figure 10 shows that the temperature distributions of the mid-depth of the web exhibit some sharp edges that reveal local drop or rise of temperatures. This is attributed to the location of the measured temperature, where the web (especially the upper part) receives solar radiation intensities with different amounts from those received by the top surface. This fluctuation in the received amount of solar radiation, and hence the fluctuation of web temperature is directly attributed to the shading effect from the top flange, where shaded areas receive a much smaller fraction of solar radiation than exposed areas. The mid-depth temperature at noon hour is a function of the previously received solar energy during the late morning hours, in addition to the amount of energy transferred from the top surface through web during noon hour. As shown in Figure 10, the noon temperatures is significantly affected by the received solar energy (and hence web temperature) from 8:00 to 12:00. This temperature is also affected by the heat absorbed by the totally exposed top surface, which heats up the web owing to the high thermal conductivity of steel. The amount of received heat by the top surface, as discussed in Figures 7-9 is controlled by the top flange width and thickness, while the bath of the mid-depth is half the section's depth (\(H/2\)).