# Seismic Performance of Ductile Column with Rectangular Hollow Cross-Section in RC Building
## 4 Discussion
### Neutral Axis Location  
As explained earlier, the hollow-sectioned CM12 of the S-series, having an axial force ratio of 0.3, experienced an abrupt reduction in load-bearing capacity at the second loading cycle of \(R=2.0\%\), before the shear reinforcement yielding. At this time, concrete compressive failure, at the plastic hinge region near the column end, suddenly occurred, resulting in brittle failure. On the other hand, such a failure pattern did not develop in the hollow-sectioned CM2 of the N-series with an axial force ratio of 0.16.  
To comprehend the reason for this, the location of the neutral axis (\(x_{n}\)), at the ultimate flexural state, was investigated in the cross-sectional analysis, which was explained in Section 2. The calculated \(x_{n}\) at the ultimate flexural state, in CM2 and CM12, are shown in Figure 13. In CM2, with an axial force ratio of 0.16, the neutral axis has been found to be located on the flange of the cross-section, which means the concrete compressive stress does not work on the hollow section at the ultimate flexural state. Therefore, the compressive stress distribution of the concrete, at the plastic hinge region, is expected to be similar to that of a solid cross-section. However, in CM12, having an axial force ratio of 0.3, \(x_{n}\) increased due to higher compressive axial force, and the neutral axis has been estimated to be located on the web beyond the flange, which means that the concrete compressive stress acts on the hollow section at the ultimate flexural state. Therefore, if the neutral axis exists on the web of plastic hinge regions, the concrete compressive stress on the hollow section is likely to increase rapidly, due to the concrete crushing, at around the ultimate flexural state. This is the reason why the deformation capacity was drastically improved in the CM13, in which the position of the hollow sections was appropriately adjusted. Simultaneously, such adjustment, avoiding hollow sections from plastic hinge regions, would be an effective solution to ensure enough ductility against large compressive axial forces.  
In the previous studies [2], the structural performance of cylindrical bridge piers with circular hollow sections was investigated by introducing different axial force ratios. From the experimental results, the deformation capacity tended to reduce, when the neutral axis  
Figure 12: Equivalent viscous damping ratios: (**a**) N-series; (**b**) S-series.  
location exceeded the flange of hollow cross-sections, which is consistent with the results of rectangular cross-sections in this study. Although further study is required, the relationship between the magnitude of the compressive axial force and the neutral axis location at the ultimate flexural state is one of the important factors in determining the deformation capability and the application scope of RC columns with rectangular hollow cross-sections. If the neutral axis, at the flexural state, is expected to be located on the web of the hollow cross-section, as confirmed by the results of the hollow-sectioned CM13, the failure mode and ductility can be ensured by properly separating the hollow section from the plastic hinge region. Therefore, it is recommended that the position of the neutral axis against the design axial force, at the ultimate flexural state, be calculated and checked for the use of hollow-sectioned columns. At the same time, focusing on the total collapse buildings where the flexural hinges occur at the beam ends, these hollow-sectioned columns would be applicable to the second floor or higher, since no flexural hinges develop in those columns.