## 4 Structural Analyses Results
### Comparison of Natural Fundamental Periods  
In this part, the period values obtained according to the eigenvalue analyses were compared with the empirical ones predicted for each country. The time required for the undamped system to complete one vibration cycle is called the natural vibration period of the system. The more rigid one of the same mass with a single degree of freedom system will have a shorter natural period and a higher natural frequency. Similarly, of two structures of the same stiffness, the heavier (greater mass) has a lower natural frequency and a longer natural period. This value can be obtained both with approximate formulas and as a result of numerical analysis [143; 144; 145; 146]. The empirical relations and explanations stipulated in the corresponding design code for each country are given in Table 16. The comparison of these periods with the ones obtained from structural analyses is shown in Table 16. The empirical formulas used in Table 16 are directly taken from the seismic design codes currently used by countries. The fundamental periods obtained from the structural analyses for all countries were constant since the structural characteristics of the sample RC buildings models did not change. Empirically, the smallest period values were obtained for Albania, while the highest periods were obtained for Turkiye. The empirical periods suggested for Albania were lower than the periods obtained from the structural analysis. For the other five countries, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**County**} & **Number of** & **Empirical Formula** & **Empirical Period (s)** & **Structual Analyses** & **Description** \\  & **Storey** & & & **Period (s)** & \\ \hline \multirow{3}{*}{Albania} & 4 & & 0.242 & 0.402 & h—the height of the structure (in meters). \\  & 6 & \(T_{1}=(0.09h)/6^{1/2}\) & 0.362 & 0.597 & b—dimension of the building in parallel to the \\  & 8 & & 0.483 & 0.796 & applied forces (in meters). \\ \hline \multirow{3}{*}{Bosnia and Herzogevina} & 4 & & 0.484 & 0.402 & \\  & 6 & \(T=C_{\text{t}}\text{H}^{3/4}\) & 0.655 & 0.597 & C\({}_{\text{t}}\) is 0.075 for RC frame structures and H is the \\  & 8 & & 0.813 & 0.796 & total height of the building \\ \hline \multirow{3}{*}{Croatia} & 4 & & 0.484 & 0.402 & \\  & 6 & \(T=C_{\text{t}}\text{H}^{3/4}\) & 0.655 & 0.597 & C\({}_{\text{t}}\) is 0.075 for RC frame structures and H is the \\  & 8 & & 0.813 & 0.796 & total building height \\ \hline \multirow{3}{*}{Iran} & 4 & & 0.468 & 0.402 & \\  & 8 & & 0.674 & 0.597 & H is the total building height \\ \hline \multirow{3}{*}{Serbia} & 4 & & 0.484 & 0.402 & \\  & 6 & \(T=C_{\text{t}}\text{H}^{3/4}\) & 0.655 & 0.597 & C\({}_{\text{t}}\) is 0.075 for RC frame structures and H is the \\  & 8 & & 0.813 & 0.796 & total building height \\ \hline \multirow{3}{*}{Tarixipe} & 4 & & 0.645 & 0.402 & H\({}_{\text{N}}\) is the building’s total height; C\({}_{\text{t}}\) is the \\  & 6 & \(T_{\text{R}}=C_{\text{t}}\text{H}_{\text{N}}\text{}^{3/4}\) & 0.874 & 0.597 & correction coefficient. C\({}_{\text{t}}\) = 0.1 for RC building \\ \cline{1-1}  & 8 & & 1.084 & 0.796 & frames that built only beams and columns \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Comparison of the natural fundamental periods for selected countries.