# Performance Evaluation of a Long-Span Cable-Slayed Bridge Using Non-Destructive Field Loading Tests
## 3 Experimental Results and Analysis
### Displacement Analysis for the Field Loading Test of Pingnan Xiangsizhou Bridge  
The calibration coefficient (\(\eta\)) is an important index to evaluate the bearing capacity and working state of a bridge. If \(\eta\) is greater than 1, the structural design strength is considered to be insufficient and unsafe. The calibration coefficient (\(\eta\)) for the field loading test of Pingnan Xiangsizhou Bridge was calculated using Equation (8):  
\[\eta=V_{C}/V_{D}, \tag{8}\]  
where \(V_{C}\) is the tested result and \(V_{D}\) is the designed value. In order to compare the experimentally measured displacement results and the theoretically calculated displacement values, the six loading cases listed in Table 1 were selected, and the displacement of the main girder for Pingnan Xiangsizhou Bridge under the six loading cases was also analyzed. The comparison results of the displacement values and calibration coefficients are shown in Table 4.  
As shown in Table 4, according to Case No. 1, the calculated displacement on the left side of the bridge section at the maximum positive moment of the first span for Pingnan Xiangsizhou Bridge under symmetrical load was 6.73 mm, and the corresponding measured displacement was 4.5 mm. On the other hand, the calculated displacement on the right side of the bridge section for Pingnan Xiangsizhou Bridge was 6.73 mm, and the corresponding measured displacement was 4.28 mm. It can be seen from Table 4 that the experimentally measured displacement values on both sides of the bridge section were less than the theoretically calculated displacement values; this is because ordinary reinforcement and steel strand were not considered in the finite element model established for the bridge loading test, leading to the projected stiffness in the finite element model being less than that of the actual bridge; therefore, the experimentally measured displacement and strain values were smaller than the theoretically calculated values. At the same time, the corresponding calibration coefficients of both sides for Case No. 1 were 0.67 and 0.64, which are less than 1. For Case No. 2, the experimentally calculated displacement on the left side of the bridge section at the maximum negative moment of the first span for Pingnan Xiangsizhou Bridge under eccentric load was 7.24 mm, and the corresponding theoretically measured displacement was 4.18 mm. Meanwhile, it can be seen that the theoretically calculated displacement on the right side of the bridge section for Pingnan Xiangsizhou Bridge was 5.03 mm, and the corresponding experimentally measured displacement was 2.91 mm. The corresponding calibration coefficients of both sides for Case No. 2 were 0.58, which are also less than 1. The above displacement analysis results show that the first span of Pingnan Xiangsizhou Bridge has greater stiffness than its designed value. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Left**} & \multicolumn{4}{c}{**Right**} \\ \cline{2-7}
**Case No.** & **Measured** & **Calculated** & **Calibration** & **Measured** & **Calculated** & **Calibration** \\  & **(mm)** & **(mm)** & **Coefficient** & **(mm)** & **(mm)** & **Coefficient** \\ \hline
1 & 4.5 & 6.73 & 0.67 & 4.28 & 6.73 & 0.64 \\
2 & 4.18 & 7.24 & 0.58 & 2.91 & 5.03 & 0.58 \\
3 & 80.5 & 116.79 & 0.69 & 54.6 & 91.13 & 0.60 \\
4 & 68.22 & 103.18 & 0.66 & 67.92 & 103.18 & 0.66 \\
9 & 287.13 & 328.25 & 0.87 & 270.68 & 328.25 & 0.82 \\
10 & 340.23 & 379.06 & 0.90 & 250.63 & 277.94 & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between measured and calculated displacement values and calibration coefficients. Similarly, the experimentally measured deflection values of the second span and the third span of Pingnan Xiangszhou Bridge were less than the theoretically calculated values, and the corresponding calibration coefficients were less than 1, indicating that the second span and the third span of Pingnan Xiangszhou Bridge have greater stiffness than their designed values.