# Prediction of Remaining Fatigue Life of In-Service Bridge Cranes
## 5 Project Examples  
We conducted special equipment inspection on the bridge crane in a certain machinery factory building. the fatigue load spectrum of the bridge crane was obtained using the above method and the remaining fatigue life of the bridge crane was predicted. The maximum rated lifting capacity of the prototype is 40/16 t, with a span of 21.6 m at both ends and a working level of A3. The main beam structure material is Q235 steel. The characteristic parameter data of this bridge crane were collected for 15 d of operation, and the obtained characteristic parameter samples were subjected to probability distribution fitting and goodness-of-fit tests to find out the model that best portrayed the distribution characteristics of the characteristic parameters [28]. As shown in Table 2, \(\alpha\), \(\beta\), and \(\gamma\) are  
Figure 7: Residual fatigue life evaluation process. the random variable, scale parameter, and shape parameter of the three-parameter Weibull distribution, respectively. Using the LHS method [3; 4], a feature parameter sample set is generated containing 300 random number sample points in Matlab, as shown in Figure 8.  
Figure 9 shows the stress-time history of a lifting cycle between simulation and on-site testing used to compare the accuracy of the simulation. The lifting weight is 40 t, the lifting distance is 2.99 m, the unloading position is 10.49 m, and the lifting height is 10 m. The simulation results show that the maximum stress of the trolley at the mid-span position is 56.9 MPa, while the actual on-site test results show a maximum mid-span stress of 62.45 MPa, with a difference of 8.89%. This proves that the data obtained from the simulation is more accurate. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Characteristic Parameter** & **Maximum Likelihood Estimated Parameter Values** \\ \hline Lifting weight & \(\alpha=7.960\) & \(\beta=0.926\) & \(\gamma=3.330\) \\ Lifting position & \(\alpha=6.210\) & \(\beta=2.054\) & 0 \\ Unloading location & \(\alpha=6.314\) & \(\beta=1.963\) & 0 \\ Whether the car is over the span & \(\alpha=0.586\) & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distribution of characteristic parameters of QB40/16 t overhead cranes. Figure 8: The random sample set of feature parameters. As shown in Figure 10, the number of lifting and unloading times of the measured bridge crane for 10 days was counted, and the average daily lifting and unloading times \(n=25\) were obtained. We performed dynamic simulation through a simulation model to obtain the stress-time history of the fatigue failure point of the measured bridge crane. Figure 11 shows the stress-time history curves of the 25 lifting cycles listed. Figures 12 and 13 show the 8-level stress spectrum mean and 8-level stress spectrum amplitude obtained from the 4-day lifting cycle simulation using Matlab's two-point rainflow counting method. Under this working condition, the stress cycle tends to exhibit a  
Figure 11: Stress–time course curves for 25 lifting cycles. Figure 10: Statistics of lifting times within 10 days. Figure 9: Comparison of simulation and experiment for one cycle. pulsating cycle. By calculation, the stress ratio R = 0.40-0.99 was obtained, and the stress ratios were all greater than 0. So far, there is no unified standard to determine the boundary of the initial crack formation stage in the total crack propagation life of the crane box beam structure. In engineering applications, the initial crack length \(a_{0}\) is generally recognized as a microcrack caused by welding. According to the literature [29; 30; 31], the value range of \(a_{0}\) is approximately 0.5-2.0 mm. Here, the initial crack length \(a_{0}\) is taken as 0.5 mm. According to the experimental data, the critical crack length \(a_{c}\) value [15; 16] in the range of 80-120 mm is more appropriate; here, the value of \(a_{c}\) is taken to be 100 mm. C,m are material constants--according to literature [21], for Q235 steel, \(c\) = 2.61 \(\times\) 10\({}^{-13}\), m = 3.