## 2 Methodology
### Analysis and Design of Archetypes
These special shear walls are characterized by ductile behavior, subject to the following design provisions:  
* Limiting the wall slenderness by prescribing a minimum thickness (\(b_{w}\geq h/16\)), where \(h\) is the story height. * Limiting the maximum axial compression to \(P_{u}\leq 0.35f_{c}^{\prime}A_{g}\), where \(f_{c}^{\prime}\) is the specified compressive strength of the concrete, and \(A_{g}\) is the gross cross-sectional area. * Requiring boundary element confinement (with \(b_{w}\geq 30\) cm) when the compressive strain \(\varepsilon_{c}\geq 0.3\%\) under the design roof displacement \(\delta_{u}\). * When confinement of the boundary element is required, limiting the maximum concrete compressive strain to 0.8% under the design roof displacement \(\delta_{u}\). It should be emphasized that based on the aforementioned design provisions, none of the archetypes required boundary element confinement. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Building Typology** & \multicolumn{2}{c}{\(\mathbf{0}^{\circ}\)} & \multicolumn{2}{c}{\(\mathbf{15}^{\circ}\)} & \multicolumn{2}{c}{\(\mathbf{30}^{\circ}\)} & \multicolumn{2}{c}{\(\mathbf{45}^{\circ}\)} \\ \hline
**Direction** & **X** & **Y** & **X** & **Y** & **X** & **Y** & **X** & **Y** \\ \hline Seismic weight (\(1D+0.25L\)) [KN] & \multicolumn{2}{c}{39,224.20} & \multicolumn{2}{c}{38,387.43} & \multicolumn{2}{c}{34,787.70} & \multicolumn{2}{c}{31,698.63} \\ Fundamental period [s] & 0.57 & 0.36 & 0.54 & 0.34 & 0.48 & 0.30 & 0.40 & 0.25 \\ Response reduction factor \(R^{\ast}\) & 7.22 & 5.94 & 7.05 & 5.77 & 6.72 & 5.46 & 6.26 & 5.03 \\ Elastic base shear \(Q_{R-1}\) [KN] & 24552.89 & 29,108.04 & 24,357.76 & 27,710.15 & 23,527.58 & 24,748.20 & 21,923.25 & 20,859.29 \\ Maximum inelastic base shear \(Q_{max}\) [KN] & 57656.96 & 5765.96 & 5642.95 & 5642.95 & 5113.79 & 5113.79 & 4659.70 & 4659.70 \\ Minimum inelastic base shear \(Q_{min}\) [KN] & 2745.69 & 2745.69 & 2687.12 & 2687.12 & 2435.14 & 2435.14 & 2218.90 & 2218.90 \\ Design base shear \(Q_{Design}\) [KN] & 3400.06 & 4897.40 & 3454.75 & 4800.96 & 3501.69 & 4531.40 & 3502.44 & 4149.91 \\ Inelastic spectral acceleration \(\xi_{s}\) [\(m/s^{2}\)] & 1.31 & 1.93 & 1.42 & 1.97 & 1.60 & 2.10 & 1.81 & 2.28 \\ Inelastic spectral displacement \(S_{du}\) [cm] & 7.41 & 3.38 & 6.76 & 2.99 & 5.71 & 2.42 & 4.37 & 1.56 \\ Computed roof displacement \(\delta_{u}\) [cm] & 9.63 & 4.39 & 8.79 & 3.88 & 7.43 & 3.14 & 5.69 & 2.03 \\ Maximum interstory drift in CM [\%] & 0.0510 & 0.0330 & 0.0450 & 0.0260 & 0.0500 & 0.0300 & 0.0390 & 0.0200 \\ Maximum interstory drift [\%] & 0.0010 & 0.0003 & 0.0013 & 0.0006 & 0.0016 & 0.0006 & 0.0006 & 0.0003 \\ \hline \end{tabular}
\end{table} 
Table 4: Modal response spectral analysis results. Figure 5: Elastic and inelastic spectra for the \(0^{\circ}\) building archetype. Another important aspect of the design was the application of the capacity design approach to both beams and walls, as introduced in ACI 318-19 [61]. Under this design methodology, brittle failure modes are prevented by ensuring, in a deterministic manner, the development of a ductile failure mechanism, typically one controlled by flexural behavior [62,63].