## 3 Numerical Examples  
To investigate the performance of the proposed design procedure, two plan-asymmetric 20-story RC frame buildings are chosen. [PERSON] et al. [PERSON] et al. (2019) stated that moment-resisting frames will be ineffective in resisting seismic loading above the 20-story limit. Hence, the case studies are imposed on this recommendation. Case-I has same-plan configuration while Case-II has different-plan configuration along the height. Both cases have different bay widths in orthogonal directions as shown in Figures 4 and 5. Columns and beams have dimensions of 800 mm \(\times\) 800 mm and 800 mm \(\times\) 300 mm, respectively, for all stories for the frames in the \(y\)-direction. In the \(x\)-direction, the beam dimensions are 500 mm \(\times\) 300 mm for all stories. All stories are 3.5 m high. The seismic load acting on all beams is 15 kN/m, excluding the frame members' weight. A characteristic cylinder strength, \(f^{\prime}{}_{c}\), of 30 MPa for the concrete, a characteristic yield strength of 413.7 MPa, and an ultimate strength of 620.5 MPa for the rebar are used. The characteristic concrete and rebar strengths are factored by 1.3 and 1.1, respectively, to obtain the corresponding expected material strengths. In this study, it is desired that a basic safety objective must be fulfilled according to the Federal Emergency Management Agency (FEMA-356) standard [PERSON] et al. (2019). Therefore, the buildings when subjected to Design Basis Earthquake (DBE) and Maximum Considered Earthquake (MCE) hazard levels, the Life Safety (LS) and Collapse Prevention (CP) performance levels were not exceeded, respectively. To achieve the performance levels LS and CP, the mean NTTA story drifts shall not be higher than 2 percent and 4 percent, respectively (Table C1-3 of FEMA 356). Mean NTTA plastic hinge rotations shall not exceed the allowable FEMA 356 plastic hinge rotations (Tables 6.8 and 6.9 of FEMA 356). The case studies are located near San Andreas Fault having coordinates of \(37^{\circ}\) N, \(-122^{\circ}\) W. Class C (very dense soil and soft rock) is assumed for the soil type. The U.S. seismic design map is utilized to obtain the site's design spectral accelerations, \(S_{d1}\) and \(S_{ds}\), and long period, \(T_{L}\). These values are input in the PEER NGA-West 2 ground motion database [PERSON] et al. (2019) to generate the acceleration response spectrum for DBE. The acceleration response spectrum for MCE is 1.5 times the acceleration response spectrum for DBE. Again, the PEER NGA-West 2 ground motion database is used to select and scale eleven ground motions (Tables 1 and 2) to match the 5-percent damping DBE and MCE acceleration response spectra (Figure 6a,b). Figure 4: Case-I’s plan view. Figure 5: Case-II’s plan view for (**a**) 1 st-5 th story plan; (**b**) 6 th–13 th story plan; (**c**) 14 th–20 th story plan. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Result** & **Earthquake Name** & **Station Name** & **Magnitude** & **Mechanism** & **Peak Ground** & **Scale** & **Tp-Pulse** & **Arias Intensity** & **V530** & **5-95\%** \\
**ID** & **The** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** \\
2 & **The** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** & **In** \\
3 & **Cape Mendeno** & **“Fortuna-Fortuna Blvd** & 7.01 & & & & & & & & & & \\
4 & **“Landes** & **“Nern-Parting Blvd** & 7.28 & & & & & & & & & \\
5 & **“Kocaeli, Turkey** & **“Arcella** & 7.51 & & & & & & & & & \\
6 & **“Kocaeli, Turkey** & **“Ouczer** & 7.51 & & & & & & & & \\
7 & **“Kocaeli, Turkey** & **“Cebrav** & 7.51 & & & & & & & & \\
8 & **“Chi-Chi, Taiwan** & **“CHV006** & 7.62 & & & & & & & & \\
9 & **“Chi-Chi, Taiwan** & **“CHV006** & 7.62 & & & & & & & & \\
10 & **“Chi-Chi, Taiwan** & **“CHV006** & 7.62 & & & & & & & & \\
11 & **“Chi-Chi, Taiwan** & **“CHV024** & 7.62 & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected ground motions for Maximum Considered Earthquake (MCE).