## 4 Structural Analyses for Selected Materials
### Suggested Empirical Natural Fundamental Periods  
Simple equations are often used to calculate the fundamental natural periods since it is only sometimes possible to make a detailed analysis of a building. Due to this issue, many researchers have proposed simplified equations. In these equations, the height of the building (H) is accepted as the basic parameter, and equations can be suggested with constants specific to the building material. For this purpose, many researchers have suggested the following relation depending on the material-dependent constants and the structure's height [92; 93; 94; 95; 96; 97]:  
\[\mathrm{T=cH^{b}} \tag{1}\]  
where H is the total height of the structures and c and b are constant. In this study, correlations have been developed for minarets made of different materials. In the equations, the first mode values were taken as references, and it was sufficient for the equation to provide the first mode period value in this study. In a time series analysis, a moving average is obtained only for a certain number of periodic averages, while the exponential moving average used in this study is a kind of moving average method that gives weight to the current frequency values. The empirical periods of natural stones defined in future studies can be obtained by using these relations. The relations between height and period obtained for different material types are given in Table 8.  
In general, the formula (\(\mathrm{T_{1}=C_{t}H^{0.75}}\)) for the first period of the minarets is suggested. Here, \(\mathrm{C_{t}=0.05}\), and H indicates the total minaret height. As can be seen from this formula, the material used in the minaret is not taken into account in the empirical period calculation. However, the recommended formulas for Ahlat stone, Bitlis stone, brick, and cut stone give the closest values to this empirical formula. While very high values are obtained for adobe, very low values are obtained for other remaining materials. Therefore, this study will be able to make important contributions in this respect.  
The formulas were created by adding the trendline to allow the curves to be calculated for different heights. At this stage, the power trendline \"which is the type of curve best used with datasets\" that \"compares measures that increase at a certain rate\" is used. The exponential curve and the power trendline, which are typically used to represent measurements that rise at a given rate, are quite similar; however, the power trendline has a more symmetrical arc. A strength trendline cannot be created if the data contains zero or negative values. Obtaining the natural vibration period depending on the height of each material considered in the study has been presented in Figure 9.  
Figure 8: Comparison of the natural fundamental period of the 1 st mode (H = 25.40 m).  
\begin{table}
\begin{tabular}{c c} \hline
**Material Type** & **Suggested Empirical Relation** \\ \hline Ahlat Stone & T = 0.0004H\({}^{2.3234}\) \\ C25 Concrete & T = 0.0001H\({}^{2.3222}\) \\ Bitils Stone & T = 0.0004H\({}^{2.3249}\) \\ K\(\ddot{\text{u}}\)feki Stone & T = 0.0002H\({}^{2.3253}\) \\ Diyarbakir Basalt & T = 0.0001H\({}^{2.3245}\) \\ Brick & T = 0.0004H\({}^{2.3252}\) \\ Andseite & T = 0.0002H\({}^{2.3254}\) \\ Natural Stone & T = 0.0003H\({}^{2.3271}\) \\ Cut Stone & T = 0.0004H\({}^{2.3267}\) \\ Adobe & T = 0.0008H\({}^{2.326}\) \\ Edremit Travertine & T = 0.0002H\({}^{2.3268}\) \\ Siphan Basalt & T = 0.0001H\({}^{2.3266}\) \\ Karam\(\ddot{\text{u}}\)rsel Od Stone & T = 0.0002H\({}^{2.3228}\) \\ \hline \end{tabular}
\end{table}
Table 8: Recommended period relations for the material types.  
Figure 9: _Cont._