## 3 Research, Results, and Discussion
### Seismic Collapse Performance of Steel Ordinary Moment Frames
The locations of the most significant damage in the 15-story W0, W44- and W51-OMFs are the fourth, ninth, and twelve stories, respectively, which are the same stories that experience the largest story drift (Figure 4b,d). It is noted that in all the OMFs in Figure 6, plastic hinges are not developed at the bottom of the first story columns. This indicates that steel OMFs, according to the current design procedure, may not have the maximum base shear capacity intended in seismic design standards. This is attributed to the fact that the \(\Omega\) values of all OMFs are smaller than overstrength factor (\(\Omega_{0}=3.0\)) specified for OMFs in ASCE 7 [1] (Figure 5a). For other OMFs with different numbers of stories, similar observations are obtained. An incremental dynamic analysis (IDA [42]) was also performed for the steel OMFs, from which collapse intensity and fragility curves were obtained. The fragility curve of the model frame was constructed according to the FEMA P695 [29] methodology. An ensemble of 44 far-field ground motions provided by FEMA P695 are used to perform the IDA. The hunt and fill algorithm [47] is used to efficiently conduct the IDA. Due to the limitations of the page, IDA curves for individual ground motions of all frames are not included, and the median IDA curves of each steel OMF are presented in Figure 7. Table 2 summarizes the parameter values obtained from the pushover analysis and the IDA. The collapse intensity (\(S_{CT}\)) of a structure is defined as a 5%-damped pseudo spectral acceleration \(PSA(T_{1},5\%)\) at \(T_{1}\), which leads to the global dynamic instability (GI) of a structure. When a structure reaches the GI state, the lateral displacement of the structure increases without bound by a slight increase in ground motion intensity. Figure 7: Median IDA curves for OMFs: (**a**) 9-story; (**b**) 12-story; (**c**) 15-story; (**d**) 18-story. The median collapse intensity (\(\hat{S}_{CT}\)) of W0-OMFs is generally similar with that of corresponding W44- and W51-OMFs, where \(\hat{S}_{CT}\) is the median value of \(S_{CT}\) for 44 ground motions (Figure 7). This indicates that the consideration of wind loads in design may not affect the seismic collapse intensity of OMFs. However, the record-to-record dispersion (\(\beta_{RTR}\)) of W44- and W51-OMFs is larger than that of W0-OMF. With increasing \(\beta_{RTR}\), the collapse probability of a structure increases. This indicates that the collapse probability of W44- and W51-OMFs is higher than that of corresponding W0-OMF. According to [PERSON] et al. [48], an increase in \(\beta_{RTR}\) leads to an increase in the collapse probability for low-intensity ground motions, and the effect of \(\beta_{RTR}\) on life-cycle collapse probability is significant. Additionally, with a decrease in \(T_{1}\), ground motion intensity demands at a given hazard level increases. The \(T_{1}\) values of OMFs designed with consideration of wind loads are shorter than those of corresponding OMFs designed without consideration of wind loads. Thus, the collapse performance of W44- and W51-OMFs could be less satisfactory than that of corresponding W0-OMF due to higher seismic intensity demands, similar seismic collapse intensity (capacity), and larger \(\beta_{RTR}\). Thus, an increase in member sections only in the lower stories of the structure due to the consideration of wind loads may adversely affect the seismic performance of OMFs. This indicates that when evaluating the seismic performance of OMFs, the effect of wind loads should be considered in the evaluation. In addition, this study inspects the distribution of elastic story drift ratios along the building height for 44 far-field ground motion sets [29]. The story drift ratio (\(SDR_{i}\)) is calculated as the story drift of the \(i\)th story divided by story height. Figure 8 shows the distribution of story drift ratios for 15-story W0- and W51-OMFs. A solid gray circle in the figure represents story drift ratios generated by individual ground motions.