## 5 Seismic Risk Assessment of Novel SCPC Frame
### Incremental Dynamic Analysis (IDA)  
Incremental dynamic analysis (IDA) is one of potential parameter analysis methods used in performance-based seismic engineering to assess the seismic behavior of the structure with the increase of the ground motion intensity. The technique includes a series of nonlinear dynamic analysis using one or more seismic ground motions multiplied by a series of proportional coefficients, to cover a whole dynamic performance of the structures with multiple intensities from elastic state to collapse state. To plot the IDA curves, the intensity measure (IM) of earthquake waves and the engineering demand parameters (EDP) are required. In this paper, 21 near-fault ground motions recommended by PEER record database are selected to conduct the IDA and assess the seismic behavior of novel SCPC structure. Select the proportional strength measurement index such as the acceleration response spectrum value corresponding to the first model period \(S_{a}\left(T_{1}\right)\) as the intensity measure (IM), compared with other intensity measures such as the PGA and PGV. The EDP select the maximum inter-story drift ratio \(\theta_{max}\) and the maximum residual inter-story drift ratio \(\theta_{r,max}\) to reflect seismic response at the near-fault earthquake waves. The acceleration response spectrum value corresponding to the first model period \(S_{a}\left(T_{1}\right)\) change from 0.05 g to 0.6 g, at an interval 0.05 g. When applying the nonlinear dynamic history analysis on the novel SCPC frame, we can obtain the EDP index \(\theta_{max}\) and \(\theta_{r,max}\) for each near-fault earthquake wave. The relationship between the EDP \(\theta_{max}\) and \(\theta_{r,max}\) and the acceleration response spectrum value \(S_{a}\left(T_{1}\right)\) are displayed in Figure 18. The figures illustrate the peak inter-story drift ratio  
Figure 17: Maximum connection rotation and standardized PT force for each story. Figure 18: _M-_\(\theta_{r}\) hysteretic relationships of the beam end joint for the new frame. and the peak residual inter-story drift ratio for each earthquake wave has a certain degree of dispersion and the dispersion increases with the increase of the seismic intensity. For the probabilistic estimation of demand, the relationship between engineering demand parameters (EDP) and intensity measure \(S_{a}\) (T\({}_{1}\)) shows as follows:  
\[D=a(SI)^{b}\varepsilon, \tag{4}\]  
where \(a\) and \(b\) denote the regression coefficient of linear regression analysis, \(SI\) refers to acceleration response spectrum value corresponding to the first model period \(S_{a}\) (\(T_{1}\)), \(\varepsilon\) is lognormal distribution random variable with a median of 1.0 and logarithmic standard deviation of \(\beta_{d}\). According to the Formula (4), regression analysis is conducted for the structural demands (\(\theta_{max}\) and \(\theta_{rmax}\)) and the regression curves can be obtained shown as in Figure 19. The figures also reflect the linear regression results together with 16 th percentile and 84 th percentile lines. It can be observed from the regression curves that both EDP index \(\theta_{max}\) and \(\theta_{rmax}\) of the novel SCPC structure nonlinear increased approximately with the seismic intensity of near-fault earthquake waves. However, the dispersion of the peak residual inter-story drift ratio is significantly larger than the peak inter-story drift ratio. The logarithmic standard deviation of the maximum inter-story drift ratio and the maximum residual inter-story drift ratio are 0.3767 and 0.9172. It also presents the mean values of the peak story drift ratio of the novel SCPC frame are 0.34% and 0.83% at the two levels and the mean values of peak residual story drift ratios of the novel SCPC frame are 0.027% and 0.012% at the two seismic levels. The seismic vulnerability of structures is a characteristic of the structure, which means the possibility of the structure reaching a certain limit state or performance level with the increasing of seismic intensities.