# Geometrical Parametric Study on Steel Beams Exposed to Solar Radiation
## 4 Finite Element Modeling
### Verification with Experimental Records  
As disclosed in the previous sections, the experimental temperature records of the seven thermocouples were used to verify the finite element thermal analysis. Comparisons were made between the predicted temperatures from the finite element analysis at the same locations of the fielded test thermocouples with the recorded test temperatures of these thermocouples. The comparisons were made at 48 time steps, each of 30 min, along the full hours of the selected sunny day, which was 14 June. The test recoding of temperature at time intervals of 30 min allowed for more accurate temperature comparisons with 48 points/day. Figure 6 shows the comparisons of four selected thermocouples, which are the top and bottom surfaces (TS and BS), the top web thermocouples (W1) and the bottom flange one (BF). Figure 6 shows that the behavior of temperature with time of both TS and BS is similar to the experimental behavior with slight differences. The temperature rises during the day hours reaching a maximum range between 11:00 and 14:00, and then drops with time until the temperature is almost equalized at midnight. The differences between the predicted and recorded temperatures of TS and BS were in the range of 0.06 to 4.01 \({}^{\circ}\)C within the 48 time steps, which were mostly the highest among the seven thermocouples. Figure 6 shows the comparisons at the web thermocouples W1 (30 mm below the top flange) and BF (top surface of bottom flange). The same above addressed notes can be adopted here, where minor differences can be noticed between the time-dependent variations of predicted and recorded temperatures. The temperature differences at W1 were in the range of 0.07 to 3.81 \({}^{\circ}\)C, while those at BF were in the range of 0.06 and 3.93 \({}^{\circ}\)C. It should be noticed that the highest differences were occurred at similar time intervals for all thermocouples as shown in Figure 6, which means that differences between temperature gradients are much less. Along the 48 time steps of the selected days, the differences between the recorded and predicted vertical temperature gradients ranged between zero during cold hours and 1.2 \({}^{\circ}\)C during shiny hours. The same analysis procedure was also followed and verified recently for different configurations of steel-concrete composite girders and concrete girders [46; 47; 48; 49]. \begin{table}
\begin{tabular}{c c c c c} \hline
**Dimensions (mm)** & **W24 \(\times\) 104** & **W24 \(\times\) 84** & **W12 \(\times\) 58** & **W12 \(\times\) 50** \\ Height (\(H\)) & 612.14 & 612.14 & 309.88 & 309.88 \\ Web thickness (\(t_{w}\)) & 12.7 & 11.938 & 9.144 & 9.398 \\ Flange width (\(W_{i}\)) & 325.12 & 229.108 & 254 & 205.232 \\ Flange thickness (\(t_{t}\)) & 19.05 & 19.558 & 16.256 & 16.256 \\ \hline \end{tabular}
\end{table} 
Table 2: Dimensions of the analyzed standard steel beams. Figure 6: Verification of predicted finite element temperatures with test records: (**a**) TS and BS; (**b**) W1 and BF. Figure 7 shows that the top-surface temperatures of the four sections are almost the same during the cold (night) time, which is also obvious for the bottom-surface temperatures as shown in Figure 8. This is mainly attributed to the high thermal conductivity of steel that accelerates heat expulsion from the section core through surfaces. Adding the influence of the small thickness of web and flanges compared to concrete sections, which reduces the heat transfer path resulting in faster cooling. The cooling during the night hours is attributed to the exchange with air via surface convection and the heat dissipation via surface long-wave radiation. Owing to the large surface area to volume ratio of the steel sections, quick surface cooling takes place. After receiving a significant amount of solar radiation beyond 8:00, the top surface gets warmer and differences between the four sections become clearer, especially at the noon hour as shown in Figure 7. However, the differences at this time are not so significant.