# Thin-Walled CFST Columns for Enhancing Seismic Collapse Performance of High-Rise Steel Frames
## 3 Seismic Performance of the Thin-Walled SMRFs
### Dynamic Analysis  
Time-history dynamic analysis on high-rise SMRFs under the Level 2 earthquakes is conducted to compare the seismic responses of the building using compact and thin-walled members. The ground  
Figure 6: Modelling of the CFST (concrete filled steel tubular) frame specimen. Figure 7: Comparisons between simulation results and experimental results. (**a**) Hysteretic curve when R \(\leq\) 2%; (**b**) Hysteretic curve when R = 5.  
motions C-San-EW is a long-period ground motion synthesized based on the characteristics of basin areas near the Pacific Ocean, and CHB009-NS was observed in the Great East Japan earthquake, 2011. Maximum story drift angle \(\theta_{\max,i}\) of the \(i\)th-story can be calculated by the horizontal drift of the \(i\)th-story divided by the story height. Figures 8 and 9 show the distributions of the \(\theta_{\max,i}\) for the SMRFs with various overall story levels. The seismic demand of Level 2 (\(\theta_{\max}\leq\) 0.01) was satisfied when subjected to Art-Hachi, El-Centro-NS, Hachinohe-NS and Tafe-EW waves, while the C-San-EW wave excited excessive story drifts on the 20S and 30S models. This means that the high-rise SMRFs fulfill the same seismic demand at design level regardless of the width-to-thickness ratios of members. The long-period component of earthquake waves obviously correlates with the first-mode period of high-rises which is controlled by the total number of stories. For instance, the C-San-EW wave shows extremely large excitation on the structures with 'first-mode' natural period \(T_{1}\) between 2 s and 4 s. In contrast, the maximum story drift angle subjected to the observed CHB009-NS is relatively small; even the wave is characterized with the long-period component. The collapse capacity of high-rise SMRFs with thin-walled FB members (20S-FB\({}_{\rm c}\)-FB\({}_{\rm b}\), where the subscripts c and b indicate column and beam components) is assessed based on the incremental dynamic analysis (IDA) method by excessively scaling the intensity of input ground motions. The IDA approach was proposed on the basis of the analogy with the incremental static push-over (SPO) analysis. IDA was developed by [29], and is widely used in collapse studies [30; 31]. The IDA method is capable of estimating the seismic performance of building structures covering the whole process  
Figure 8: Maximum story drift angle of high-rise SMRFs with compact members under Level 2 earthquakes. (**a**) 20S model; (**b**) 30S model; (**c**) 40S model. Figure 9: Maximum story drift angle of high-rise SMRFs with thin-walled members under Level 2 earthquakes. (**a**) 20S model; (**b**) 30S model; (**c**) 40S model. from elastic to ultimate global collapse eventually. Usually, the IDA approach requires a sufficient amount of input ground motions to run time-history analysis to eliminate the uncertainty from the variety of ground motions. In this study, since the high-rise building systems highly relate to the characteristics of long-period ground motions, the Art-Hachi with flat velocity spectral shape is used to provide stable excitations in the wide range of the long-period domain. Figure 10 shows the vertical distribution of the maximum story drift angle of thin-walled FB buildings with 20, 30 and 40 story levels. \(\phi\) is the incremental factor of the Art-Hachi wave. Note that higher buildings produce more significant component deterioration to enlarge the maximum story drift angle. The deterioration effects triggered by the local buckling amplify the \(\theta_{\text{max}}\) at lower stories and reduce the \(\theta_{\text{max}}\) at higher stories because the inflexion point changes the deflection pattern. For instance, the inflexion point is located at the fifth floor for the 20S-FB\({}_{\text{c}}\)-FB\({}_{\text{b}}\) building when the \(\phi\) is scaled to 3. Thus, the width-to-thickness ratio (FB rank) of beam and column components overtly has effects on the seismic responses when the plastic deformation extensively develops.