# Estimation of Live Load Distribution Factor for a PSC I Grider Bridge in an Ambient Vibration Test
## 3 Estimation of Live Load Distribution Factor Using the Vehicle Loading Test
### Vehicle Loading Test  
The static loading test is currently used in measuring LLDF. In this study, the dynamic loading test was conducted to examine the possibility of estimating LLDF using the displacement response of traveling vehicles. In addition, the vehicles traveled at 10, 60, and 100 km/h to identify the difference in LLDF depending on the vehicle velocity in the dynamic loading test, and the results were compared with the LLDF measured in the static loading test. Each load case (LC) of the vehicle loading test is shown in Table 2. The static loading test was conducted in LC1, LC5, and LC9 and the dynamic loading test in the remaining LCs. Figure 6 shows the positions of the vehicles in the static and dynamic loading tests. Loading was applied on lane 1, lane 2, and both lanes 1 and 2. In the dynamic loading test, the vehicles passed the same positions as in the static loading test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & \multicolumn{4}{c}{**Axial Load [ton]**} & \multirow{2}{*}{**Total [ton]**} \\ \cline{2-3} \cline{5-5}  & **Front** & **Middle** & **Rear** & \\ \hline
1 & 7.02 & 10.30 & 10.01 & 27.33 \\
2 & 7.95 & 9.99 & 9.94 & 27.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Weight of the vehicles used in the vehicle loading test. Figure 4: LVDT installation positions. Figure 5: Specifications of the vehicles used in the vehicle loading test. To reduce the error in the LLDF measured in the vehicle loading test, the test was repeated three times in each LC and the average was used as a representative value. Figure 7 shows the displacement response measured using the LVDTs from the dynamic loading test when the vehicle velocity was 60 km/h. The displacement response of the static component was extracted using EMD. Table 3 shows the maximum displacement of the static component extracted using EMD. Maximum displacement occurred at G2 for loading on lane 1, at G3 for loading on lane 2, and at G3 for loading on lanes 1 and 2. In the dynamic loading test results shown in Table 3, displacement of the static component that represents the stiffness of the bridge decreased as the vehicle velocity increased, confirming the increase in displacement of the high-frequency component caused by the interaction between the bridge and the vehicles. Figure 8 compares the LLDF\({}_{sta}\) measured in the static loading test with the LLDF\({}_{dyn}\) measured in each LC in the dynamic loading test according to the vehicle velocity. \[error=\frac{\mathrm{LLDF}_{dyn}-\mathrm{LLDF}_{sta}}{\mathrm{LLDF}_{sta}} \tag{7}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**LC** & **Lane** & **Vehicle** & **Velocity [km/h]** \\ \hline
1 & & & stop \\
2 & 1 & 1 & 10 \\
3 & & & 60 \\
4 & & & 100 \\ \hline
5 & & & stop \\
6 & 2 & 2 & 10 \\
7 & 2 & 2 & 60 \\
8 & & & 100 \\ \hline
9 & & & stop \\
10 & 1,2 & 1,2 & 60 \\
12 & & & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: LC of the vehicle loading test. Figure 6: Vehicle loading positions in the vehicle loading test: (**a**) Static loading test; (**b**) Dynamic loading test. Figure 7: Measured displacement response and static displacement component in LCs with a vehicle velocity of 60 km/h: (a) LC 3; (b) LC 7; (c) LC 11. Figure 9 shows the error between the LLDF\({}_{dyn}\) measured in the dynamic loading test and the LLDF\({}_{sta}\) measured in the static loading test obtained using Equation (7). LLDF\({}_{sta}\) can be regarded as an accurate value that represents a bridge's structural stiffness characteristics. As shown in Figure 9, an error between 0.12% and 4.40% based on the static loading test can be seen in each LC. LLDF\({}_{dyn}\) was found to have excellent reliability because the error was less than 5%. The results of the dynamic loading test showed no significant difference in LLDF depending on the vehicle velocity. It was also confirmed that the dynamic loading test showed no significant difference in LLDF\({}_{sta}\).