## 5 Probabilistic Seismic Performance Assessment of the Gantry Crane  
### Seismic Input in the Trolley-Travel Direction  
As illustrated above, the probabilistic seismic demand model (PSDM) was built for the gantry crane, and five groups of capacity limit states were constructed to evaluate the performance of the steel structure. In this section, three major working conditions of the gantry crane, i.e., Case 1, Case 2, and Case 3, subjected to ground motions input in the trolley-travel direction are investigated. As mentioned in Section 3, the three working conditions were fully-loaded trolley located in the midspan of the girder, fully-loaded trolley located in cantilever beam close to the flexible legs, and fully-loaded trolley located in cantilever beam close to the rigid legs in sequence. Meanwhile, the three thresholds at the joints of girders and legs were utilized since the seismic records were input in the trolley-travel direction. As 20 ground motions were utilized to take the uncertainties of seismic records into account fully, adequate raw data could be obtained for the probability seismic assessment by incremental dynamic analysis (IDA). To evaluate the effects of seismic records in the trolley-travel direction completely, the selected ground motions are all input along the trolley-travel direction of the gantry crane in this section. Figure 9 depicts the IDA curves of the gantry crane in terms of the PGA and the maximum LDR value for three working conditions, respectively. This figure also shows the limit states predefined in different colors. In general, it is worth noting that there existed obvious discrepancies between the IDA curves, which indicated that the uncertainties of seismic records were fully investigated in the PSDM. Moreover, when the curves reached the serviceability line in the three working conditions, the values of the minimum PGA were 0.21 g, 0.17 g, and 0.18 g, respectively. The data meant the gantry crane in Case 1 had the best seismic performance, while the gantry crane in Case 2 had the worst. However, regarding the other two lines, the gantry crane performed best in Case 2. These results indicated that working conditions had specific effects on the seismic performance of the gantry crane. It should be noted that with the increasing of PGA from 2 g to 2.5 g, the maximum LDR decreased, and the ground motion's ID number was seven in all cases. The phenomenon happened in all three figures, but was an individual case in 20 examples, respectively. The data shown in Figure 9 could be transformed in the log-normal space. Regression analysis of In(LDR) and In(PGA) was utilized to calculate the values of b and c in Equation (3). Figure 10 depicts the fragility curves of the gantry crane calculated by Equation (3). As mentioned in [54], the exceedance probabilities should be 63.2%, 10%, and 2% in resisting the frequent, fortification, and rare earthquakes in 50 years, respectively. The maximum accelerations of the design spectra of the frequent, fortification, and rare earthquakes are also drawn in Figure 10, which were developed by considering the site conditions of the gantry crane. The corresponding maximum spectral accelerations were 0.24 g, 0.68 g, and 1.2 g. Moreover, the values of logarithmic standard deviation for all the working conditions are listed in Table 4, and Columns 2, 3 and 4 show the deviation values when the ground motions were input in the X-direction (trolley-travel). Generally, the higher the magnitude of the earthquake, the greater the dispersion of the response. When the gantry crane was in Case 1, as can be seen in Figure 10a, in the frequent earthquakes, the probability of SA was approximately 25%, which met the needs of seismic capacity provided by the Chinese seismic design code for buildings. However, in the fortification and rare earthquakes, the probabilities of DC and CP were 24% and 3.2%, respectively. Compared with the corresponding exceedance probabilities, the gantry crane, designed by the current Chinese code of cranes, could not meet the requirements.