# Geometrical Parametric Study on Steel Beams Exposed to Solar Radiation
## 6 Conclusions  
During the construction of steel frames of buildings, bridges or industrial structures, the frame might be left exposed to open-field conditions for a long time. With the presence of permanent fluctuating thermal loads like solar radiation and air temperature, unfavorable stresses would be induced, which might be not adequately considered in the design of the structure. The finite element analysis conducted in this study was directed to investigate the influence of geometrical parameters and shadowing effect on temperature gradients and thermal stresses induced from solar radiation in steel beams. Four ASTM standard sections were used to evaluate the effect of the investigated parameters. The results were presented at three distinguished times of solar radiation effect, which are sunrise, noon and sunset. The most important conclusions obtained from this investigation are as follows:  
1. The smaller W12 sections are obviously colder than the bigger W24 sections at sunrise and sunset and hotter than W24 sections at noon hour. This is due to the thinner web and flanges of W12 sections compared to W24 sections, which allows for faster cooling and heating. The temperature gradient along the section depth is controlled by the time-dependent temperature variation, which is strongly affected by the geometrical properties of the steel sections. 2. The maximum temperature of the top surface at noon hour is mostly affected by the geometrical parameters of the top flange. The maximum temperature increases as the top flange width increases and its thickness decreases. However, this variation is more  
Figure 16: Thermal stresses of the four sections: (**a**) At sunrise; (**b**) At noon; (**c**) At sunset. sensitive to flange thickness than flange width, where the maximum temperature of the top surface was found to be positively correlated to the ratio of flange width to the square of flange thickness (\(W_{\rm f}/t_{\rm f}^{2}\)). Section W12 \(\times\) 58 with the maximum \(W_{\rm f}/t_{\rm f}t^{2}\) value among the four steel sections (0.96) recorded the highest top surface temperature at noon hour, while the temperature of W24 \(\times\) 84, which has the lowest \(W_{\rm f}/t_{\rm f}t^{2}\) value of 0.60, was the lowest. 3. The temperature of the web's mid-depth at noon hour is mainly due to the huge amount of solar radiation received by the top surface during this period. The influential geometrical parameters are the area and thickness of the heated part, which is the top flange, and the path to the target point, which is the mid-depth of the web. The temperature of the centroid of the web at noon hours increases with the increase of the quantity \(2W_{\rm f}/Ht_{\rm f}\). The wider and thinner flange results in faster heating, while the shorter path (\(H/2\)) leads to faster heat conduction to the web's centroid from the top surface 4. The shading from the top flange on the web's temperature becomes effective during afternoon hours. Wider flanges impose deeper shadows that reduce the temperature of the web, while deeper sections are less influenced by flange's shading. The variation of temperature during afternoon hours affects that at sunset and is affected by the geometrical ratio of flange width to flange thickness (\(W_{\rm f}/H\)). 5. The vertical thermal stress distributions are directly influenced by the nonlinear temperature gradients at the same times. In addition, their maximum values are also related to the geometrical parameters that affect the heat transfer and temperature variation during the heating and cooling phases. The thicknesses of web and flange and the ratio of flange width to flange thickness are the most influential parameters. Conceptualization, S.R.A. ; Data curation, J.X. and J.L. ; Formal analysis, J.X. and Y.L. ; Funding acquisition, B.B. ; Investigation, S.R.A. and T.S.A.-G.; Methodology, S.R.A. and T.S.A.-G.; Project administration, Y.L. and B.B. ; Resources, S.R.A. and B.B. ; Software, S.R.A. ; Supervision, S.R.A. and B.B. ; Validation, Y.L., J.L. and B.B.