# Solar Radiation Parameters for Assessing Temperature Distributions on Bridge Cross-Sections
## 6 Influence of Solar Radiation on Temperature Distribution on Bridge Grider Cross-Sections  
### Box Grider Bridge  
#### 6.1.1 Finite Element Model  
One 8-span continuous prestressed concrete box girder bridge in Fuzhou was chosen as case study. The dimensions of girder cross-section and the installation locations of temperature sensors are illustrated in Figure 9. The thickness of the concrete overlay is 80 mm. Four temperature sensors were installed near the external surfaces of the top flange (A-T), east web (A-E), west web (A-W) and bottom flange (A-B) to measure the air temperature at different parts of the box girder. One temperature sensor was hung in the box girder (A-I) to measure the air temperature inside the box girder. Six temperature sensors were installed in the concrete within the east web, west web and bottom flange, of which three were near the external surface (EW-1, WW-1 and B-1) and three were near the internal surface of each component (EW-2, WW-2 and B-2). The meteorological data, including hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period was from 1 April 2010 to 31 March 2011 and the time increment between measurements was one hour.  
The software Midas was chosen to establish the finite element model of the cross-section of box girder (Figure 9) based on a heat-conduction model. A 2D plane strain element can used for steady-state or transient analyses. The ambient air temperature data were obtained from the temperature sensors installed near the external surfaces of the box girder. 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 box girder. 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 box girder was considered by using the following rules and assumptions: (a) The external surface of the top flange is influenced by both the beam and diffuse solar radiation. (b) The external surfaces of the two webs are in the shadow due to the top flange. Therefore, they are influenced by the diffuse solar radiation and ground reflection only. (c) The undersides of the top and bottom flanges are influenced by the ground reflection alone. The boundary condition of the internal surface of the box girder in the finite element model was set based on the measured temperature obtained from the temperature sensor hung in the box girder (A-I). For the thermal parameters of the concrete, specific heat of 960 J/(kg \({}^{\circ}\)C), heat conductivity of 1.5 W/(m \({}^{\circ}\)C), and density of 2400 kg/m\({}^{3}\) were used [60]. The finite element mesh size was set as 0.02 m. There were 21,000 and 19,337 nodes and elements, respectively, as illustrated in Figure 10. Each node had a single temperature degree of freedom.  
Figure 9: Layout of cross-section of box girder (cm).