## 3 Research, Results, and Discussion
### Seismic Collapse Performance of Steel Ordinary Moment Frames  
Nonlinear static analyses (pushover) are performed using lateral forces with a vertical distribution following the fundamental mode shape of a frame according to FEMA P695 [29] methodology. Figure 4 shows the pushover curves of OMFs, from which overstrength factor (\(\Omega\)) and period-based ductility (\(\mu_{T}\)) are determined using the following equations:  
\[\Omega=V_{max}/V_{design} \tag{1}\]  
Figure 3: Numerical model for model structure: (a) Model configuration of steel OMF; (b) detail of the beam-to-column connection model. \[\mu_{T}=\delta_{u}/\delta_{y,eff} \tag{2}\]  
\[\delta_{y,eff}=C_{0}\frac{V_{max}}{W}\Big{[}\frac{g}{4\pi^{2}}\Big{]}(\max(T,T_{ 1}))^{2} \tag{3}\]  
where \(V_{max}\) is the maximum base shear, \(V_{design}\) is the design base shear force, \(\delta_{y,eff}\) is the effective yield roof displacement, and \(\delta_{u}\) is the maximum roof displacement measured when the strength decreases to 0.8 \(V_{max}\). Figure 4a,c shows the pushover curves of 9-story and 15-story OMFs. The cyclic curves of OMFs does not vary significantly according to the application of wind loads. The maximum strength and lateral stiffness of W44- and W51-OMFs are similar with those of corresponding W0-OMFs. Figures 3d and 4b show floor displacement normalized by building height (\(\delta_{i}/H\)). As mentioned in the previous section, the consideration of wind load in design leads to an increase in member sections, especially for lower stories. Since in upper stories, member sections do not increase unlike in the lower stories, significant damage could occur in the upper stories during earthquakes. This phenomenon is more prominent when OMFs approach collapse state (see Figure 4b,d). Figure 5 shows the values of \(\Omega\) and \(\mu_{T}\) for individual OMFs. As shown in this figure, the \(\Omega\) value of OMFs does not vary according to structural height and level of wind loads. All steel OMFs have \(\Omega\) values of about 2.0, which is less than the value of system overstrength factor (\(\Omega_{0}=3.0\)) specified for steel OMF in ASCE 7 [1]. The \(\mu_{T}\) value of OMFs tends to decrease gradually with increasing building height. It is also observed that \(\mu_{T}\) increases with an increase in the level of wind loads. Figure 4: Result of pushover analysis for 9- and 15-story steel OMFs: (**a**,**c**) Pushover curves; (**b**,**d**) normalized floor displacement (\(\delta_{i}/H\)) of W0- and W51-OMFs at specific normalized roof displacements until collapse stage. Figure 6 shows the distribution of damage in the 15-story OMFs designed without and with wind loads (44 m/s and 51 m/s) near collapse. As shown in this figure, damage is concentrated in upper stories for the W44- and W51-OMFs, whereas for the W0-OMF, damage is more widely distributed in the lower stories than that for the W44-, and W51-OMFs. This could be the reason that the maximum shear force of W0-OMF is similar to those of the corresponding W44-, and W51-OMFs (Figure 4a,c), although the member sections for the W0-OMF are less than those of the W44-, and W51-OMFs. All 15-story OMFs (W0-, W44-, and W51-OMFs) experience yielding and fracture mainly in exterior beams and interior panel zones. The fracture in the interior panel zones can be attributed to the fact that OMF panel zones are designed for the force demand from  
Figure 5: Overstrength factor (\(\Omega\)) and period-based ductility (\(\mu_{T}\)) of steel OMFs obtained from pushover analyses, (**a**) The \(\Omega\) values, (**b**) The \(\mu_{T}\) values. Figure 6: Plastic hinge distribution in pushover analysis for 15-story OMFs near collapse: (**a**) The 15-story W0-OMF; (**b**) 15-story W44-OMF; (**c**) 15-story W51-OMF. the load combinations specified in ASCE 7 [1] instead of that developed from the plastic moments of nearby beams.