# Influence of Directionality on the Seismic Response of Typical RC Buildings
## 3 Definition of Case Studies
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Seismic** & **Mw** & **Epicenter** & **Scordinates** & **Station** & **Direction** & **PGA (g)** & **PGV** & **PGD (cm)** & **Significant** \\ \hline Valparaiso & 8.0 (CSN) & 33.207\({}^{\circ}\) S & Melipilla & Longitudinal & 0.53 & 40.30 & 6.03 & 29.35 \\  1985 & 7.4 (USGS) & 71.663\({}^{\circ}\) W & San Isidro & Transverse & 0.69 & 34.20 & 12.01 & 29.35 \\  & & & & Longitudinal & 0.72 & 43.20 & 6.91 & 45.40 \\  & & & & Transverse & 0.71 & 43.40 & 5.54 & 45.40 \\ \hline Bio-Bio 2010 & 8.8 (CSN) & 36.122\({}^{\circ}\) S & Angol & Longitudinal & 0.94 & 37.50 & 3.40 & 54.01 \\  & & & Transverse & 0.70 & 34.30 & 7.00 & 54.01 \\  & & & Concepcion & Longitudinal & 0.61 & 44.70 & 21.10 & 78.15 \\  & & & San Pedro & Transverse & 0.65 & 38.10 & 20.10 & 78.15 \\  & & & Longitudinal & 0.54 & 43.30 & 9.80 & 66.49 \\  & & & Transverse & 0.63 & 68.60 & 13.90 & 66.49 \\ \hline Coquimbo & 8.4 (CSN) & 31.573\({}^{\circ}\) S & El Pedregal & Longitudinal & 0.69 & 30.60 & 19.80 & 52.74 \\  2015 & 8.3 (USGS) & 71.674\({}^{\circ}\) W & Tololo & Transverse & 0.57 & 26.20 & 15.60 & 52.74 \\  & & & Longitudinal & 0.24 & 31.80 & 14.50 & 53.72 \\  & & & Transverse & 0.35 & 38.20 & 11.60 & 53.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Set of strong motions used to perform the nonlinear response analysis [32]. Figure 5: Definition of axes according to the angle of incidence [29]. Figure 6: Design elastic spectrum in displacements, amplified by 17% with both average response spectra and those obtained for the records used in the investigation. Figure 7: Plan of archetypes used for analysis of the influence of the angle of incidence: (**a**) Archetype 1 plan, torsionally flexible; (**b**) Archetype 2 plan, torsionally rigid; (**c**) Archetype 3 plan, unidirectional eccentricity; (**d**) Archetype 4 plan, flexible. The four archetypes chosen correspond to reinforced concrete structures configured using different typologies, ranging from very stiff (building with shear walls, Archetype 2) to structures of intermediate stiffness (frame building with a core of shear walls, archetype 1) to flexible structures (frame building, Archetype 4). An archetype that presents a high plan irregularity was intentionally introduced, so that the effect of such irregularity could be studied along with the directionality of the applied seismic components. Figure 8 shows the isometric views of the four archetypes studied; note the irregular distribution of the shear walls of Archetype 3, which generates unidirectional eccentricity (according to the \(x\) axis). The irregularity of Archetype 3 is proposed in a way that influences the dynamic results. This strategy has been used in structures with another type of irregularity in plan [39]. All the Archetypes designed comply with the normative prescriptions that govern the maximum admissible drifts for the different structural typologies. Likewise, all the Archetypes, except naturally Archetype 3, satisfy the design requirements that limit irregularity in plan. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Denomination** & \(f_{e}\) **or \(F_{y}\)[MPa]** & \(E\) [GPa] & \(\
u\) & \(\gamma\)[kg/m\({}^{3}\)] \\ \hline Concrete & G25 & 25 & 25.7 & 0.2 & 2500 \\ Steel & A630-420H & 420 & 200 & 0.3 & 7850 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of concrete and reinforcement steel. Figure 8: Isometric views of the archetypes studied: (**a**) Archetype 1 with a semi-rigid structure made up of frames and a core of shear walls, (**b**) Archetype 2 with a rigid structure made up of shear walls, (**c**) Archetype 3 with a semi-rigid structure made up of frames and shear walls distributed asymmetrically, and (**d**) Archetype 4 with a flexible structure made up of frames. The results of the linear elastic analysis of the archetypes were obtained considering a fraction of 5% of the critical damping.