*4.2. Temperature Longitudinal Correlation Analysis*

The analysis of statistical values, such as the annual mean and annual maximum temperatures, showed that there was a significant temperature gradient along the longitudinal direction of the bridge. To investigate the connection between surface temperatures at different longitudinal locations, correlation analysis was necessary. In order to evaluate the non-uniformity of the longitudinal temperature distribution, for each section measurement point (T1~T8), correlation analysis was performed with the same measurement points at other longitudinal positions, respectively. The position of S6 (mid-span) was taken as the reference point, where the correlation coefficient [47] could be defined as:

$$R\_x(y) = \frac{\mathbb{Cov}[\mathbf{x}(t, y\_1), \mathbf{x}(t, y\_2)]}{\sqrt{\mathbb{Cov}[\mathbf{x}(t, y\_1)]} \cdot \sqrt{\mathbb{Cov}[\mathbf{x}(t, y\_2)]}} \tag{4}$$

where, *x* denoted the surface temperature of the steel box girder, *Cov*[] was the operator of covariance, *t* corresponded to time, and *y*<sup>1</sup> and *y*<sup>2</sup> represented different longitudinal measuring points.

Figure 12 shows the correlation analysis results and reveals that: (1) On the main span, the correlation coefficient decreased as the distance from S6 increased. This indicated that S6 had a greater effect on the temperature of S5 and S7 compared to S4 and S8. (2) The lowest correlation was found at the bridge tower. This is probably a result of the variability in the spatial distribution of cross-sections due to differences in the duration and intensity of the solar radiation received. The solar radiation at the bridge tower would be absorbed more by the tower, so the correlation coefficient of the S4 and S8 cross-sections was the lowest. (3) The sudden increase in the correlation coefficients of cross-sections S3 and S9 at the side span position indicated that solar radiation had a more dominant effect than the shading effect on the bridge tower. (4) The temperature correlation coefficient was generally higher on the right side of the mid-span than on the left side, meaning that the temperature was more uniform on the right side than on the left side. In addition, the upstream and downstream sides showed different temperature correlation characteristics. These differences may be related to the differences in bridge orientation, section form and material properties.

**Figure 12.** Correlation analysis of the measurement points in the mid-span section with those in other locations.

The longitudinal correlation analysis showed again that the longitudinal temperature distribution was non-uniform. These results were more comprehensive than previous studies with limited point comparisons. Therefore, using single-point measurement data to represent the temperature field may lead to overestimating or underestimating the temperature effect at different bridge spanwise locations. As a result, the temperature effects of large-span bridges could not be assessed accurately.
