## 3 Theoretical Analysis
### The Fatigue Equivalent of the Taxiway Bridge Based on the S-N Curve  
The stress-life curve (S-N curve) takes the fatigue strength of the material standard specimen as the ordinate and the logarithm lgN of the fatigue life as the abscissa to represent the relationship between the fatigue strength and the fatigue life of the standard specimen under the characteristic cycle characteristics. The S-N curve can reflect the relationship between the fatigue strength and the fatigue life. When studying the fatigue strength of the structure, the S-N curve of its constituent materials plays an important role in the operation cycle, fatigue characteristics, and applicable redundancy of the whole structure [21]. For the superstructure of the studied taxiway bridge, the fatigue of the bridge deck is mainly reflected in the fatigue of the reinforcement and concrete. The repeated aircraft load changes the structural and material parameters of the taxiway bridge, resulting in a reduction in the bearing capacity and the maximum deflection exceeding the specification requirements. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Aircraft Type**} & \multirow{2}{*}{**Aircraft Weight in Different Conditions/kN**} & \multicolumn{2}{c}{**Load**} & \multirow{2}{*}{\
\begin{tabular}{c} **Number of** \\ **Coefficient of** \\ **the Main Main Learning** \\ **Gears** \\ **Landing Gear** \\ \end{tabular} } & \multicolumn{2}{c}{**Number of**} & \multicolumn{2}{c}{**Single-Wheel Load of Main**} & \multirow{2}{*}{
\begin{tabular}{c} **Conversion** \\ **Factor Kit** \\ \end{tabular} } \\  & & & **Conditions/kN** & & & & & \\  & & & **Conditions/** & & & & \\  & & & **Conditions/** & & & & \\ \hline \multirow{3}{*}{B737-300} & Basic weight & 326.02 & \multirow{3}{*}{0.950} & \multirow{3}{*}{2} & \multirow{3}{*}{2} & \multirow{3}{*}{122.81} & \multirow{3}{*}{0.72} \\  & Maximum landing & & & & & & & \\  & weight & & & & & & \\  & Maximum ramp & & & & & & \\  & weight & & & & & & \\  & Basic weight & 414.30 & & & & & 98.40 & 0.91 \\ B737-800 & Maximum landing & & & & & & 157.65 & 0.93 \\  & weight & & & & & & 188.24 & 0.80 \\  & weight & & & & & & 48.13 & 0.44 \\  & Basic weight & 405.29 & & & & & 76.59 & 0.45 \\ A320-200 & Maximum landing & & & & & & 91.91 & 0.39 \\  & weight & & & & & & 124.66 & 1.15 \\  & Basic weight & & & & & & 187.77 & 1.10 \\ B77-300 & Maximum landing & & & & & & 237.22 & 1.00 \\  & weight & & & & & 108.72 & / \\  & Basic weight & & & & & 108.72 & / \\ B747-400 & Maximum landing & & & & & 170.03 & / \\  & weight & & & & & & 236.69 & / \\  & Maximum ramp & & & & & & \\  & weight & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The single-wheel load conversion of different aircraft types. According to the design drawings, the main beam in the superstructure of the taxiway bridge adopts C50 concrete, and the prestressed steel strand is \(\Phi\)15 high strength low relaxation steel strand. Through on-site core drilling sampling, compression, splitting, and fatigue tests are carried out. By querying the existing research and specifications [29; 30; 31], the results of hundreds of load tests in the laboratory are compared with the results in the existing literature and specifications. It is found that they are consistent. Therefore, the fatigue parameter values and S-N curves obtained by referring to the existing research and specifications are shown in Table 3.  
As shown in Figure 6, the abscissa cycle times represent the times of repeated application of aircraft load, and the ordinate represents the yield stress of the reinforcement under the application of the repeated aircraft load, the tensile stress of concrete on the lower surface of the bridge deck, and the compressive stress of concrete on the upper surface of bridge deck along the action line of aircraft.