## 9 Results and Discussion  
### Positive Thermal Gradient Profiles for the Climate Regions  
This study aims to first develop and optimize positive vertical thermal gradient profiles for different climate regions. To achieve this, eight standard steel I girders were used in parametric studies to accurately determine the vertical thermal gradient variations. Positive thermal gradient profiles were developed based on extreme positive vertical thermal gradient variations for different climate regions as shown in Table 3. Figure 7 shows the maximum vertical thermal gradient profiles of the standard steel girders for the climate regions. The thermal gradient profiles have the same pattern regardless of the climate regions and selected standard steel girders. The maximum thermal gradient variations occurred at approximately 1:00 pm due to higher air temperatures and direct solar radiation on the top surface of the steel girder during this time, and the web was shaded and prevented from direct solar radiation. Thus, this leads to maximizing the thermal gradient differences (variations). Generally, Figure 7 shows that the maximum thermal gradient variations at the steel girder's top and bottom surfaces decrease with a decrease in the steel girder depth. A shorter steel girder means that the amount of heat transferred from the top steel girder's surface to the mid-depth section is faster than the heat transfer for the longer girders. This leads to higher heating of the mid-depth web and thus reduces the vertical thermal gradient variation.  
By comparing the steel girders of each standard steel pair, the steel girder with a wider flange shows higher thermal gradient variations, attributed to the shadowing effect of the flange overhang. The wider flange of the girder exposes the flange to more shadowing effect, meaning that the web is not exposed to direct solar radiation. Thus, the web's heating is slowed down, resulting in a higher thermal gradient difference. Regardless of the climate regions, the thermal gradient variations in W36 \(\times\) 282 are slightly higher than the thermal gradient variations observed for W30 \(\times\) 191. This is attributed to the higher flange thickness of W36 \(\times\) 282. A higher flange thickness slows the heat transfer from the top surface to the web's mid, thus reducing the thermal gradient difference.  
Figure 7: _Cont_.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Climate Region**} & \multicolumn{6}{c}{**Standard Steel I-Griders**} \\ \cline{2-9}  & **W36 \(\times\) 282** & **W36 \(\times\) 232** & **W30 \(\times\) 191** & **W30 \(\times\) 148** & **W18 \(\times\) 86** & **W18 \(\times\) 71** & **W10 \(\times\) 26** & **W10 \(\times\) 19** \\ \hline Region 1 & 11.537 & 10.572 & 11.31 & 10.373 & 8.219 & 7.482 & 5.838 & 5.268 \\ \hline Region 2 & 11.358 & 10.345 & 11.21 & 9.862 & 7.898 & 7.284 & 5.613 & 5.08 \\ \hline Region 3 & 11.572 & 10.666 & 11.382 & 10.473 & 8.634 & 7.479 & 5.936 & 5.363 \\ \hline Region 4 & 11.365 & 10.53 & 11.263 & 9.899 & 7.972 & 7.36 & 5.667 & 5.121 \\ \hline Region 5 & 9.443 & 8.828 & 9.346 & 8.346 & 6.438 & 6.062 & 4.539 & 4.106 \\ \hline Region 6 & 9.891 & 9.249 & 9.718 & 8.761 & 6.801 & 6.381 & 4.799 & 4.167 \\ \hline Region 7 & 9.524 & 8.989 & 9.398 & 8.511 & 6.688 & 6.282 & 4.744 & 4.286 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Extreme positive vertical thermal gradient variations (°C) for different climate regions.