## 2 Materials and Methods
Previous studies have shown that inelastic behavior can significantly increase the lateral displacement responses of low-rise (short-period) buildings; whereas, for tall (long-period) buildings, inelastic behavior can reduce the lateral displacement responses to some extent (see [48; 49; 50; 51] for example). Therefore, the results of the present study are valid for the case of buildings responding elastically. Moreover, in this study, soil-structure interaction effects are neglected assuming that the soil underneath the foundations is infinitely rigid. The inherent damping of the building is modeled using 5% Rayleigh damping. This assumption provides reasonable results when the building responds elastically. For the case of inelastic buildings, modified versions of Rayleigh damping have been proposed in the literature (see [52; 53; 54; 55]). Six different earthquake records have been used in the analyses, i.e., the Tabas, Imperial Valley, Loma Prieta, Landers, Kobe, and Kocaeli earthquakes (see Table 1 for details). The peak lateral displacements of independently vibrating buildings under each seismic excitation have been firstly determined. The analysis has been conducted using a Matlab-based software. The results of the time history dynamic analysis are summarized in Table 2. The graphical representation of the results is also shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Earthquake** & **Date** & **Magnitude** & **Station** & **PGA (cm/s\({}^{2}\))** \\ \hline Tabas & 1978 & 7.4 & Tabas & 821 \\ Imperial Valley & 1979 & 6.5 & Calexico & 284 \\ Loma Prieta & 1989 & 6.9 & Presidio & 360 \\ Landers & 1992 & 7.3 & Baker & 765 \\ Kobe & 1995 & 7.2 & JMA & 338 \\ Kocaeli & 1999 & 7.6 & Sakarya & 369 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The properties of earthquake records used in the analysis. Figure 2: Model of three-story building located close to a two-story structure (arrangement 3-2). Figure 4: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Arrangement** & **Imperial Valley** & **Kobe** & **Loma Prieta** & **Kocaeli** & **Landers** & **Tabas** \\ \hline
5-2 & 29 & 15 & 48 & 58 & 53 & 67 \\
5-3 & 50 & 13 & 60 & 63 & 70 & 80 \\
5-4 & 65 & 17 & 65 & 65 & 75 & 80 \\
5-5 & 0 & 0 & 0 & 0 & 0 & 0 \\
5-6 & 56 & 26 & 74 & 74 & 67 & 69 \\
6-1 & 17 & 8 & 25 & 25 & 25 & 30 \\
6-2 & 30 & 18 & 45 & 50 & 56 & 55 \\
6-3 & 48 & 14 & 47 & 70 & 60 & 60 \\
6-4 & 55 & 25 & 73 & 74 & 65 & 65 \\
6-5 & 56 & 26 & 74 & 74 & 67 & 69 \\
6-6 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._It can be seen from Table 3 that zero seismic gaps have been obtained for the cases when two identical buildings (arrangements: 1-1, 2-2, 3-3, 4-4, 5-5, 6-6) have been considered under different earthquakes. This situation results from the fact that the ground motions acting on both structures have been considered to be uniform and the in-phase structural vibrations take place in such a case. It should be underlined, however, that the out-of-phase vibrations of identical structures (with exactly the same heights and natural periods) might occur in reality if the spatial seismic effects related to the propagation of the seismic wave play an important role [56; 57]. These effects, which result in non-uniform earthquake excitation, include the following: difference in the arrival times of seismic wave at various locations (wave passage effect), loss of coherency of seismic wave due to scattering in the heterogeneous medium of the ground as well as due to differential superimposition of waves arriving from an extended source (incoherence effect), and spatially varying local soil conditions (site response effect) [58].