## 4 Fatigue Life Prediction of Bridge Cables  
### Vehicle Load Model  
According to the records from toll stations of the RCB [13], there were a total of 371,167 vehicles passing through the bridge during 28 July 2011 to 31 August 2011. Information including the types of vehicles, number of vehicles in each type, number of axles, and axle weights, _etc._, is obtained and analyzed. Taking the probabilistic properties of axle weights for example, as summarized in Table 2, there are mainly six types of vehicles crossing the bridge, and the axle weights of most types of vehicles are described by a single-peak probability density function (PDF); however, for the last three types, multi-peaks exist in the PDFs, and therefore, a weighted sum of PDFs are used to describe such distributions.  
Figure 8: Calculated and measured force increments of cables (load case 1).  
Figure 9: Force time-histories of the cable J13.  
Using the video camera, the transversal positions (_i.e._, outer lane, middle lane or inner lane) are also identified, as shown in Table 3. It is observed that 36.65 percent and 42.03 percent vehicles ran in the middle lane and inner lane (_i.e._, the fast lane), respectively; whereas 21.32 percent vehicles ran in the outer lane (_i.e._, the slow lane). For the vehicle type 1 for light weight, most of them (_i.e._, 41.23 percent) were in the fast lane, and only 9.7 percent were in the slow lane. However, for the vehicle type 6 with heavy weight, their lane occupation was just opposite to that of vehicle type 1. Most heavy trucks were in the middle lane and the slow lane, while only a small portion of them were in the fast lane.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Vehicle** \\ **Type** \\ \end{tabular} & \begin{tabular}{c} **Graphic Illustration** \\ \end{tabular} & \begin{tabular}{c} **Variable** \\ **Designation** \\ \end{tabular} & \begin{tabular}{c} **Distribution** \\ **Type** \\ \end{tabular} & \
\begin{tabular}{c} **Mean** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline \multirow{4}{*}{1} & \(AW_{11}\) & \(AW_{2}\) & \(AW_{11}\) & Lognormal & 10.54 & 3.12 \\  & \(A\)\(P_{11}\) & \(A\)\(W_{12}\) & Lognormal & 8.55 & 3.27 \\ \hline \multirow{4}{*}{2} & \(AW_{11}\) & \(AW_{21}\) & \(AW_{21}\) & Normal & 48.29 & 14.22 \\  & \(A\)\(P_{21}\) & \(A\)\(W_{22}\) & Normal & 78.54 & 36.48 \\ \hline \multirow{4}{*}{3} & \(AW_{11}\) & \(AW_{22}\) & \(AW_{22}\) & \(AW_{22}\) & Normal & 38.16 & 10.39 \\  & \(A\)\(W_{22}\) & \(A\)\(W_{22}\) & Normal & 35.66 & 12.87 \\  & \(A\)\(P_{21}\) & \(A\)\(P_{22}\) & \(A\)\(W_{22}\) & 115.10 & 65.54 \\ \hline \multirow{4}{*}{4} & \(AW_{11}\) & \(AW_{22}\) & \(AW_{22}\) & \(AW_{22}\) & 46.26 & 10.03 \\  & \(A\)\(P_{21}\) & \(A\)\(P_{22}\) & \(A\)\(P_{22}\) & 52.40 & 15.50 \\  & \(A\)\(P_{22}\) & \(A\)\(P_{22}\) & \(A\)\(P_{22}\) & 11.82 \\  & \(A\)\(P_{22}\) & \(A\)\(P_{22}\) & \(A\)\(P_{22}\) & 1.71 \\  & \(A\)\(W_{22}\) & Normal (0.30) & 52.23 & 13.92 \\  & \(A\)\(W_{22}\) & Normal (0.43) & 83.35 & 9.51 \\ \hline \multirow{4}{*}{6} & \(AW_{61}\) & \(AW_{61}\) & Lognormal & 53.86 & 5.95 \\  & \(A\)\(W_{62}\) & \(A\)\(W_{63}\) & Normal (0.13) & 35.35 & 4.79 \\  & \(A\)\(W_{64}\) & \(A\)\(W_{65}\) & Normal (0.07) & 22.68 & 3.20 \\  & \(A\)\(W_{66}\) & Normal (0.77) & 80.94 & 13.11 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Probabilistic properties of axle weights (dimensions in kN).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Vehicle Type**} & \multirow{2}{*}{**Percentage in Traffic Volume (\%)**} & \multicolumn{3}{c}{**Percentage in Each Lane (\%)**} \\ \cline{3-5}  & & **Outer Lane** & **Middle Lane** & **Inner Lane** \\ \hline
1 & 76.66 & 9.70 & 25.74 & 41.23 \\
2 & 0.65 & 0.36 & 0.26 & 0.03 \\
3 & 1.57 & 0.60 & 0.87 & 0.10 \\
4 & 1.64 & 0.92 & 0.67 & 0.04 \\
5 & 2.54 & 1.31 & 1.17 & 0.06 \\
6 & 16.94 & 8.43 & 7.94 & 0.57 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Constitution of vehicles.