# Low-Cost Assessment Method for Existing Adjacent Beam Bridges
## 5 Case Study
### Comparison between Calculation Results and Static Load Test Results  
In this section, the results obtained in Section 5.2 are verified by the static load test results of the three bridges.  
The static load test results of inspection reports of Baidong No. 2 Bridge and Changhong Tunnel K1 + 812 Bridge give the measured and theoretical values of the LLDF of each beam under central load conditions and two kinds of eccentric load conditions. The inspection report of Yunhe Bridge gives the theoretical and measured values of mid-pan deflection of each beam under central load conditions and two kinds of eccentric load conditions,  
\begin{table}
\begin{tabular}{c c} \hline
**Bridge** & **LDN** \\ \hline Changhong Tunnel K1 + 812 Bridge & \(LDN_{1}=\) 43.40 \\ \hline Baidong No. 2 Bridge & \(LDN_{2}=\) 67.41 \\ \hline Yunhe Bridge & \(LDN_{3}=\) 36.66 \\ \hline \end{tabular}
\end{table}
Table 6: \(LDN\) of Changhong Tunnel K1 + 812 Bridge, Baidong No. 2 Bridge, and Yunhe Bridge.  
\begin{table}
\begin{tabular}{c c c c} \hline  & & **(a)** & \\ \hline
**Beam-\(n\)** & \(VA_{i}\) & **Beam-\(n\)** & \(VA_{i}\) \\ \hline Beam-1 & 0.761 & Beam-10 & 0.312 \\ Beam-2 & 0.555 & Beam-11 & 0.216 \\ Beam-3 & 0.600 & Beam-12 & 0.120 \\ Beam-4 & 0.617 & Beam-13 & 0.048 \\ Beam-5 & 0.584 & Beam-14 & 0 \\ Beam-6 & 0.656 & Beam-15 & 0 \\ Beam-7 & 0.641 & Beam-16 & 0 \\ Beam-8 & 0.544 & Beam-17 & 0 \\ Beam-9 & 0.352 & Beam-18 & 0 \\ \hline \end{tabular}
\begin{tabular}{c c c} \hline
**(b)** & \\ \hline
**Beam-\(n\)** & \(VA_{i}\) & **Beam-\(n\)** & \(VA_{i}\) \\ \hline Beam-1 & 0.120 & Beam-10 & 0.664 \\ Beam-2 & 0.240 & Beam-11 & 0.768 \\ Beam-3 & 0.264 & Beam-12 & 0.784 \\ Beam-4 & 0.336 & Beam-13 & 0.760 \\ Beam-5 & 0.352 & Beam-14 & 0.760 \\ Beam-6 & 0.456 & Beam-15 & 0.856 \\ Beam-7 & 0.440 & Beam-16 & 0.840 \\ Beam-8 & 0.504 & Beam-17 & 0.880 \\ Beam-9 & 0.580 & - & - \\ \hline \end{tabular}
\begin{tabular}{c c} \hline
**(c)** & \\ \hline
**Beam-\(n\)** & & \(VA_{i}\) \\ \hline All beams & & 0.333 \\ \hline \end{tabular}
\end{table}
Table 5: (a) \(VA_{i}\) of the 13 m span of Changhong Tunnel K1 + 812 Bridge. (b) \(VA_{i}\) of Baidong No. 2 Bridge. (c) \(VA_{i}\) of Yunhe Bridge.  
which can be used to calculate the LLDF of each beam. See Figure 6a-c for lateral deflection influence lines obtained for the three tested bridges.  
Figure 6: (**a**) Lateral deflection influence lines of Changhong Tunnel K1 + 812 Bridge (13 m span). (**b**) Lateral deflection influence lines of Baidong No. 2 Bridge. (**c**) Lateral deflection influence lines of Yunhe Bridge.  
Equation (19) is proposed based on the concept of standard deviation to calculate the variation degree of the LLDFs of the three bridges. The result is shown in Table 7.  
\[VD_{ldf}=\sqrt{\frac{\left(\sum_{i=1}^{i=N}V_{ldf,i}\right)^{2}}{N}} \tag{19}\]  
where \(VD_{ldf}\) represents the variation degree of the LLDFs of the bridge, \(V_{ldf,i}\) represents variation in the LLDF of beam-\(i\), and \(N\) is the total number of beams. The selection principle of \(V_{ldf,i}\) is that for each beam, choose the largest difference among the three load conditions.  
The sequencing in bridge maintenance determined by Table 7 is the same as the result obtained in Section 5.2.