# Seismic Design and Performance Assessment of Frame Buildings Reinforced by Dual-Phase Steel
## 4 Design and Seismic Performance Assessment of DPD2 and B500B Buildings
### Pushover Analyses  
The capacity of the buildings was investigated using pushover analyses, which were performed by utilising the modal pattern of lateral forces. The resulting pushover curves are presented in Figure 11. The pushover curves are provided for the X direction only because the pushover curves for the Y direction are similar. Thus, the presentation of more results does not affect the conclusion of the study. The maximum strength of DPD2 buildings is higher than that of the B500B buildings, and it is observed at a higher roof displacement. The DPD2 buildings become more flexible at the initiation of the nonlinear behaviour, which begins with the cracking of concrete. After the yielding of columns at the base, the pushover curves of B500B buildings are practically horizontal, whereas hardening is more pronounced in the case of DPD2 buildings. All these differences in the pushover curves of DPD2 and B500B buildings are primarily the consequences of variations in the stress-strain relationship of the two types of steel. DPD2 steel bars are more deformable than the B500B bars, but they are not characterised by the yielding plateau, which is typical of the conventional reinforcing steel (i.e., for Tempcore steel B500B). However, to achieve the appropriate strength of DPD2 buildings, the quantity of steel had to be increased in the design. If the amount of steel in DPD2 buildings was equal to that designed for B500B buildings, then the strength would be significantly lower (see the pushover curve of DPD2 buildings designed as B500B buildings in Figure 11). The maximum base shear (\(F_{max}\)) and the roof displacement at the near-collapse (NC) limit state (\(d_{NC}\)) are listed in Table 5 and serve as a precise analysis of the described observations. The maximum strength of DPD2 buildings is from 6 to 10% higher than that of B500B buildings. On the other hand, the maximum strength of B500B buildings is from 9 to 14% higher than that observed for DPD2 buildings designed as B500B buildings. The near-collapse roof displacements \(d_{NC}\) were estimated by assuming that the near-collapse limit state at the structural level is attained when the near-collapse is observed in the first column. From Table 5, it is clear that the \(d_{NC}\) increases with the number of stories (Table 5). However, the trend regarding the difference in the \(d_{NC}\) of DPD2 and B500B buildings is not clear. A significantly and slightly higher \(d_{NC}\) can be observed, respectively, for 4- (45.7 cm) and 8-storey (65.0 cm) DPD2 buildings, whereas in the case of the 11-storey building, the \(d_{NC}\) was observed to be slightly higher for the B500B building. Note that the latter observation is not the consequence of the mechanical characteristics (i.e., stress-strain  
Figure 11: Pushover curves of variants of (**a**) 4-, (**b**) 8- and (**c**) 11-storey buildings. Diamond-shaped points on each of the pushover curves correspond to near-collapse displacement. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Building** & **Designed According to** & \(F_{max}\) **[kh]** & \(d_{NC}\) **[cm]** & \(S_{e,NC}\) **[g]** \\ \hline \multirow{3}{*}{4-storey} & B500B & 1113 & 40.0 & 2.84 \\  & DPD2 & 1203 & 45.7 & 3.20 \\  & DPD2—designed as B500B & 1018 & 42.0 & 2.89 \\ \hline \multirow{3}{*}{8-storey} & B500B & 2974 & 62.4 & 1.48 \\  & DPD2 & 3273 & 65.0 & 1.49 \\  & DPD2—designed as B500B & 2672 & 64.9 & 1.42 \\ \hline \multirow{3}{*}{11-storey} & B500B & 9402 & 69.7 & 0.91 \\  & DPD2 & 9968 & 64.5 & 0.83 \\ \cline{1-1}  & DPD2—designed as B500B & 8272 & 71.8 & 0.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum base shear (\(F_{max}\)), near-collapse roof displacement (\(d_{NC}\)) and median spectral accelerations at first vibration period, causing a near-collapse limit state (\(S_{e,NC}\)). curve) of the DPD2 bars.