# Seismic Design and Performance Assessment of Frame Buildings Reinforced by Dual-Phase Steel
## 4 Design and Seismic Performance Assessment of DPD2 and B500B Buildings
### Results of Seismic Performance Assessment  
The observations from the pushover analyses were verified by means of nonlinear response history analyses. For this purpose, incremental dynamic analysis (IDA) [46] was performed, aiming to estimate the spectral acceleration causing the near-collapse limit state, which was attained when a near-collapse rotation was observed in the first column, as defined in the previous section. The spectral acceleration at the first vibration period was adopted for the intensity measure. The ground motions for IDA were selected based on a conditional spectrum approach [47], using a SHARE seismic hazard model [48]. The mean magnitude and mean distance were obtained from seismic hazard disaggregation for Ljubljana and for spectral acceleration, which corresponded to a return period of 2475 years (\(S_{e,2475}\)) and the first vibration period of the structure. Consequently, the selected sets of ground motion are building-specific. For each building, 30 ground motions (see Figure 12) were selected from the combined NGA [49] and RESORCE [50] strong ground motion databases, which contain 9188 ground motions. All of 30 ground motions correspond to events with magnitudes between 4.5 and 7, and source-to-site distances between 5 and 50 km. For the analysis of the 4- and 11- storey buildings, the ground motions were recorded on soil with a shear-wave velocity \(v_{s,30}\) between 360 and 800 m/s, whereas, in the case of an 8-storey building, the \(v_{s,30}\) was between 180-360 m/s. The resulting median spectral accelerations causing the near-collapse limit state \(S_{e,NC}\) are presented in Table 5, whereas the median IDA curves are shown in Figure 13. The median IDA curves of DPD2 and B500B buildings are highly similar. Slight differences can be observed in a range close to dynamic instability. The median spectral acceleration causing the near-collapse limit state \(S_{e,NC}\) of the 4-storey DPD2 building was observed to be higher than that of the DPD2 building, whereas the opposite can be observed for the 11-storey building. This trend was expected because, in the case of frame buildings, the deformation capacity controls the ground motion intensity, causing the near-collapse limit state. Therefore, the IDA curves of 8-storey DPD2 and B500B buildings are practically equal, because this was also the case for the near-collapse roof displacement of buildings observed in the pushover analysis. It is interesting to note that the seismic performance, in terms of the median IDA curves of DPD2 designed as B500B buildings, is not significantly reduced, although the maximum strength of these buildings is significantly smaller than for the other buildings. Namely, the seismic performance of the medium-to-long period building is controlled by the deformation capacity, which was quite similar for variants of the investigated buildings (Figure 11). To determine whether the life safety objective was fulfilled, the \(S_{e,NC}\) were compared to the risk-targeted spectral acceleration causing the NC of structure \(S_{e,NC,a}\), which was calculated according to [51], and represents the target median value of spectral acceleration causing the NC limit state. To calculate \(S_{e,NC,a}\) the target (acceptable) annual probability of collapse \(P_{C,a}\) was set to \(10^{-4}\) (0.5%/50 years). This is a rather high value, but it is close to the values adopted in some other codes [52]. The seismic hazard curves for spectral acceleration at the first vibration period of the building, which are also required to calculate \(S_{e,NC,a}\), were obtained utilising the SHARE seismic hazard model [48]. The dispersion of the spectral acceleration causing the collapse \(\beta_{S_{e},C}\) was assumed to be 0.40 [53], and the limit-state reduction factor \(\gamma_{ls}\), which transforms \(S_{e,C}\) to \(S_{e,NC}\), was assumed to equal 1.15 [53].