## 5 Fatigue Life Calculation of Jiangyin Bridge Based on the Stress Integration Approach
### Fatigue Life Calculation of Jiangyin Bridge Based on the Stress Integration Approach
The fatigue life calculation steps are shown in Section 5.4, and the fatigue life of WT-4 is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Statistics Value** & \(L_{1}\) **(mm)** & \(L_{2}\) **(mm)** & \(L_{3}\) **(mm)** & \(\alpha_{1}\) (\({}^{\circ}\))** & \(\alpha_{2}\) (\({}^{\circ}\))** & \(\alpha_{3}\) (\({}^{\circ}\)) \\ \hline Mean & 9.68 & 10.5 & 15.68 & 37.14 & 40.92 & 101.94 \\ Minimum & 5.4 & 6.3 & 10 & 25.11 & 28.38 & 94.59 \\ Maximum & 12.7 & 16.2 & 20 & 48.32 & 52.21 & 105.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean, minimum and maximum values of the weld size. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Weld Types** & \(\alpha_{1}\) & \(\alpha_{2}\) & \(\alpha_{3}\) & **L1** & **L2** & **L3** & **Area** \\ \hline WT-1 & 30 & 50 & 100 & 5.2 & 8 & 10.28 & 20.57 \\ WT-2 & 40 & 40 & 100 & 8 & 8 & 12.26 & 31.51 \\ WT-3 & 50 & 30 & 100 & 12.3 & 8 & 15.76 & 48.28 \\ WT-4 & 40 & 40 & 100 & 10 & 10 & 15.32 & 49.24 \\ WT-5 & 40 & 40 & 100 & 12.5 & 12.5 & 19.15 & 76.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Size of five weld types (unit: mm). Figure 20: Weld types. Figure 21 shows the following:  
(1) The fatigue life of the stress integration approach with slope \(m_{2}=5\) is close to that of the extrapolated hot spot stress approach. However, the fatigue life with slope \(m_{2}=3.125\) is less than half that of the extrapolated hot spot stress approach. Therefore, the slope of the master S-N curve at high cycles significantly affects the bridge fatigue life, and the slope \(m_{2}=5\) is more reasonable. (2) The fatigue lives of WT-1, WT-2, WT-3, WT-4 and WT-5 are approximately 51 years, 69 years, 113 years, 84 years and 100 years, respectively, and only reach approximately 100 years under a standard vehicle load. Thus, the change of the weld size can obviously affect the bridge fatigue life. The fatigue life of the most favorable condition, WT-3, is 2.2 times that of the most unfavorable, WT-1. (3) The comparison of WT-1, WT-2 and WT-3 shows that the fatigue life increases obviously with the decrease of the angle \(\alpha_{2}\) between the weld and the deck. The fatigue life increases by approximately 50% with the decrease of angle \(\alpha_{2}\) by 10 degrees. (4) The comparison of WT-2, WT-4 and WT-5 shows that when the weld angles remain the same, the fatigue life increases with the increase of the weld area. The fatigue life increases by approximately 20% with the weld area increasing by 56% (or the length of three sides increasing by 25% with the same proportions). (5) The comparison of WT-3 and WT-5 shows that the fatigue life decreases with the increase of \(L_{2}\), when the length of \(L_{1}\) is approximately equal. The fatigue life decreases by approximately 12% with the increase of \(L_{2}\), by 56%. Although the weld area increases in this case, the fatigue life decreases due to the increased angle \(\alpha_{2}\) between the deck and the weld. (6) Therefore, the change of weld size caused by weld manufacturing errors can obviously affect the actual bridge fatigue life. The fatigue life of five different weld types varies from 51 years to 113 years under a standard vehicle load. The weld fatigue life increases with the decrease of the angle \(\alpha_{2}\) between the deck and the rib and the increase of the weld area. The most favorable weld type is WT-3, with the angle \(\alpha_{2}\) of 30 degrees and the area of 48 mm\({}^{2}\).