# Solar Radiation Parameters for Assessing Temperature Distributions on Bridge Cross-Sections
## 6 Influence of Solar Radiation on Temperature Distribution on Bridge Grider Cross-Sections
### Side-by-Side Box Girder Bridge  
#### 6.2.1 Finite Element Model  
One 6-span concrete continuous bridge in Zhangzhou with a cross-section consisting of 11 side-by-side box girders was chosen as case study. The thickness of the concrete overlay is 100 mm. The dimensions of girder cross-sections and the installation locations of temperature sensors are illustrated in Figure 15. Six temperature sensors were installed in the concrete within the top flanges (1-T and 11-T), webs (1-W and 11-W) and bottom flanges (1-B and 11-B) of box girders #1 and #11. The meteorological data, including ambient air temperature, hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period was from 30 July 2014 to 3 August 2014 and the time increment between measurements was set as one hour. The 2D plane strain element in Midas-FEA was chosen to establish the finite element model of the cross-sections of side-by-side box girders (Figure 15). The ambient air temperature data were obtained from the automated meteorological station. The solar radiation was calculated using the estimation models described earlier. The effects of solar radiation and convective and radiative heat transfer were considered at the external surfaces of the side-by-side box girders. The surface heat transfer coefficient and the temperature of the surrounding fluid medium were input as boundary conditions for the finite element model. The influence of the solar radiation on different parts of the side-by-side box girders was considered by using the following rules and assumptions: (a) The external surfaces of the top flanges are influenced by the beam solar radiation and diffuse solar radiation. (b) The webs in the shadow are influenced by the diffuse solar radiation and ground reflection. (c) The webs not in the shadow are influenced by the beam solar radiation, diffuse solar radiation and ground reflection. (d) The undersides of the top and bottom flanges are not influenced by the solar radiation or ground reflection, because the space below the side-by-side box girders is small obtained by the field observation. No temperature gauge was hung inside the side-by-side box girders. Therefore, the boundary condition of the internal surfaces of the side-by-side box girders was simulated using the 2D plane strain element with the thermal parameters of the air (0 \({}^{\circ}\)C and 100 \({}^{\circ}\)C) for the finite element model. The thermal parameters of the concrete were discussed earlier. For the air (at 0 \({}^{\circ}\)C), a specific heat of 714.8 J/(kg \({}^{\circ}\)C), heat conductivity of 0.023 W/(m \({}^{\circ}\)C) and density of 1.293 kg/m\({}^{3}\) was used. For the air (at 100 \({}^{\circ}\)C), a specific heat of 716.9 J/(kg \({}^{\circ}\)C), heat conductivity of 0.030 W/(m \({}^{\circ}\)C) and density of 0.946 kg/m\({}^{3}\) were used [61]. It can be found observed that the influence of temperature on the thermal parameters of the air is small. Therefore, the thermal parameters of the air (at 100 \({}^{\circ}\)C and air 0 \({}^{\circ}\)C) were input into the finite element models in summer and winter, respectively. The finite element mesh size was set as 0.02 m. There were 27,370 and 27,190 nodes and elements, respectively, as illustrated in Figure 16. Each node had a single temperature degree of freedom. Figure 15: Layout of cross-section of side-by-side box girder (cm). 2.2 Influence of Solar Radiation on Temperature Distribution on Cross-Section of Side-by-Side Box Girder  
The monitoring period on 31 July 2014 was a sunny day with high solar radiation. Comparisons of temperature-time curves obtained experimentally or from finite element model with or without the consideration of solar radiation are illustrated in Figure 17 (31 July 2014). The hollow points denote the measured data, the solid line denotes the calculated curves with the consideration of solar radiation, and the dashed line denotes the calculated curves without consideration of solar radiation.