# Seismic Design and Performance Assessment of Frame Buildings Reinforced by Dual-Phase Steel
## 4 Design and Seismic Performance Assessment of DPD2 and B500B Buildings
### Description of Analysed Buildings  
The 4-, 8- and 11-storey reinforced-concrete frame buildings (Figure 8) were designed and analysed. The building structures were designed for the gravity and seismic load combinations prescribed by Eurocode 0 [29]. The design peak ground accelerations amounted to 1.2\(\cdot\)0.30 g = 0.36 g (soil type B), 1.15-0.25 g = 0.29 g (soil type C) and 1.2\(\cdot\)0.25 g = 0.30 g (soil type B), respectively, for the 4-, 8- and 11-storey buildings. The behaviour factor was assumed to equal 3.9, which is defined in Eurocode 8 for multi-storey multi-bay frames designed for ductility class medium (DCM). Concrete C30/37 was prescribed in the design of the 4- and 8-storey buildings, whereas C35/45 was selected in the case of the 11-storey building. Selected properties of the structures and their design parameters are presented in Table 4. The largest design base shear-weight ratio was observed for the 4-storey building (15.5%), whereas the smallest Fb/W ratio was observed for the 11-storey building (5.2%). Figure 7: Base shear—displacement at height 1.53 m relationship observed during cyclic test and that obtained from simulation of cyclic response of a column reinforced with DPD2 using (**a**) basic and (**b**) calibrated model. The average longitudinal reinforcing ratios of columns and beams in the critical zone (zone of the plastic hinge) of each storey are shown in Figure 9. As the design yield strength of the DPD2 reinforcing steel \(\langle f_{y\text{\tiny{td}},DPD2}=348\) MPa) is lower than that of the B500B reinforcing steel (\(f_{y\text{\tiny{td}},B500B}=435\) MPa), the required amount of DPD2 reinforcement is significantly increased for most of the structural elements. The highest longitudinal reinforcing ratios of the columns can be observed for 4-storey buildings, followed by the 8- and 11- storey buildings. The longitudinal reinforcing ratios of the columns of the 4-storey building varied between 1.5% and 2.0%, and were equal to approximately 1% in the case of the 11-storey building. In the critical zones of the columns of the 4-storey building, the amount of longitudinal reinforcement of DPD2 building is, on average, higher by a factor of 1.24 than the amount of longitudinal reinforcement of the B500B building. This result is practically equal to the ratio between the design yield strengths of the two types of steel (i.e., \(f_{y\text{\tiny{td}},B500B}/f_{y\text{\tiny{td}},DPD2}=435\) MPa/348 MPa = 1.25). For an 8-storey building, the factor is slightly smaller and amounts to 1.20. On the other hand, the longitudinal reinforcement of the columns of the 11-storey DPD2 and B500B building are practically the same, which is a consequence of the fact that the reinforcement in the columns of both \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Building** & **Total Mass (t)** & **Period \(T_{1}\) [s]** & \(a_{\text{\tiny{td}},B,R}\) [g]** & **Soil Factor** & \(\text{\tiny{S}}_{\text{\tiny{td}}}\)**D(T1) [g]** & \(\text{\tiny{F}}_{\text{\tiny{b}}}\)**/W** \\ \hline
4-storey & 339 & 0.68 & 0.30 & 1.2 & 0.66 & 15.5\% \\
8-storey & 2338 & 1.21 & 0.25 & 1.15 & 0.36 & 7.7\% \\
11-storey & 10,221 & 1.67 & 0.25 & 1.2 & 0.23 & 5.2\% \\ \hline \end{tabular}
\end{table} 
Table 4: Total mass, first vibration period, reference peak ground acceleration, soil factor, spectral acceleration corresponding to first vibration mode from the elastic spectrum and design base shear-weight ratio of 4-, 8- and 11-storey buildings. Figure 8: Elevations, plan views and reinforcement in typical columns and beams of (**a**) 4-, (**b**) 8- and (**c**) 11-storey buildings. variants of buildings is governed by the minimum requirements of Eurocode 8 [23] (i.e., the amount of longitudinal reinforcement should be higher than 1% of the area of the concrete cross-section). The highest longitudinal reinforcing ratios of beams can be observed for the 11-storey building, followed by the 4- and 8- storey buildings.