## 5 Temperature Field Analysis of Concrete Bridge Tower
### Temperature Field Analysis
#### 5.2.2 Local Temperature Difference Analysis of Tower Wall  
Figures 22-24 show the temperature change along the thickness direction of the east tower wall at the height of 125 m. It can be seen from the figure that the temperature change was relatively obvious at a range of 0.3 m from the external surface of the tower wall, and the temperature change was small in the remaining range because of the thermal insulation effect of concrete materials during the night and early morning periods. In the daytime, the radiation of the sun and the change in the ambient temperature made the temperature at a range of 0.3 m in the thickness direction change obviously, but the weak thermal conductivity of the concrete material led to the temperature in the thickness direction of the tower wall. The temperature at a range of 0.8 m from the external surface showed a gradual downward trend, while in the area beyond 0.8 m from the external surface, the temperature rose slightly due to the heat transfer and the thermal insulation of the concrete material itself.  
Figure 21: The temperature change curve of the outer surface of the tower wall at a height of 125 m and the temperature difference curve between the opposite faces of the tower column.  
Figure 23: The temperature variation curve at night in the thickness direction of the east tower wall at a 125 m height.  
Figure 22: The temperature change curve in the thickness direction of the east tower wall at a 125 m height in the early morning.  
Figure 25 shows the maximum variation of temperature difference at the same distance from the outer surface in the thickness direction of each wall in a day. It can be seen from the figure that the temperature change was more significant at a range of 0.3 m from the outer surface. When measured more than 0.8 m from the outer surface, the temperature change was less than 1 \({}^{\circ}\)C.  
The existing research shows that the temperature gradient distribution along the wall thickness direction of the concrete box structure under sunshine is close to the exponential  
Figure 24: The temperature variation curve in the thickness direction of the east tower wall at a 125 m height during the day.  
Figure 25: The maximum variation of temperature at the same distance from the external surface of the tower wall at a height of 125 m.  
As shown in Figure 27, the exponential function was used to fit the discrete temperature data, which can express the temperature change in the wall thickness direction well. The fitting results in the figures show that when the temperature value at 0.8m from the external surface was used as the parameter \(C\) in Formula (33) for fitting, the result was better than the fitting result obtained by using the temperature value of the internal surface as the parameter \(C\) in Formula (33). The minimum correlation coefficients of the fitting results of the two methods were 0.968 and 0.895, respectively. Therefore, it is recommended to use the temperature data at 0.8m from the outer surface as the parameter \(C\) in Formula (33) to fit the temperature data in the thickness direction. Because of the high fitting accuracy of the discrete temperature data of the concrete bridge tower in the wall thickness direction by Formula (33), the exponential loading mode shown in Figure 28 can be used to complete the application of temperature load in the calculation of the structural temperature effect.  
Figure 27: The fitting results of discrete temperature data. (**a**) The east tower wall; (**b**) the south tower wall; (**c**) the west tower wall; (**d**) the north tower wall; (**e**) the inner east tower wall; (**f**) the inner west tower wall. Note: The temperature fitting curve 1 in the figure is the result of fitting the temperature value at 0.8 m from the external surface as the parameter \(C\) in Formula (33); the temperature fitting curve 2 is the result of fitting the temperature value of the internal surface as the parameter \(C\) in Formula (33).