## 4 Structural Analyses for Selected Materials  
Older masonry structures' load-bearing systems differ from contemporary engineering ones. The behavior of masonry structures is very complex as it consists of elements made of various materials (units, joints, unit-joint interaction), creating a material of heterogeneous characteristics. Modeling masonry structures is a very complex task and a compromise between computational time and accuracy has to be made [81]. When assessing and creating masonry structures, modeling masonry walls is crucial. Numerical modeling with finite elements in masonry structures represents quite a long computational process [13; 82]. Three modeling approaches, namely, a detailed micro-modeling approach, a simplified micro-modeling approach, and a macro-modeling approach, can be used to simulate masonry walls. Figure 4 illustrates these models. A FEM model of the reference minaret was generated using the macro modeling technique for this investigation. One of the most utilized methods in structural studies \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Earthquake Level** & \(\mathrm{\mathbf{S_{S}}}\) & \(\mathrm{\mathbf{S_{1}}}\) & \(\mathrm{\mathbf{F_{S}}}\) & \(\mathrm{\mathbf{F_{1}}}\) & \(\mathrm{\mathbf{S_{DS}}}\) & \(\mathrm{\mathbf{S_{DI}}}\) & \(\mathrm{\mathbf{T_{A}}}\) & \(\mathrm{\mathbf{T_{B}}}\) & \(\mathrm{\mathbf{T_{AD}}}\) & \(\mathrm{\mathbf{T_{BD}}}\) \\ \hline DD-1 & 1.19 & 0.31 & 0.90 & 0.80 & 1.07 & 0.25 & 0.05 & 0.23 & 0.02 & 0.08 \\ DD-2 & 0.61 & 0.17 & 0.90 & 0.80 & 0.55 & 0.14 & 0.05 & 0.25 & 0.02 & 0.08 \\ DD-3 & 0.24 & 0.08 & 0.90 & 0.80 & 0.22 & 0.06 & 0.06 & 0.28 & 0.02 & 0.09 \\ DD-4 & 0.18 & 0.06 & 0.90 & 0.80 & 0.16 & 0.04 & 0.06 & 0.28 & 0.02 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the seismic parameters for different earthquake ground motion levels. Figure 3: Horizontal/vertical elastic design spectrum used for the structural analysis. of masonry constructions is the macro modeling methodology. This modeling must distinguish the binding material (mortar, etc.) utilized in the construction and the building elements. The masonry unit's and mortar's features were homogenized and recognized as composite masonry material in this modeling. Macro modeling is more convenient in practice as it requires less memory and time [7, 83, 84, 85, 86]. According to the assumptions set out by the software [83] utilized for the numerical modeling, the sign harmony and direction assumptions of the components employed in the finite element structural models are illustrated in Figure 5.  
As shown in Figure 5, S22 is vertical stress in the (Y) direction, S11 is vertical stress in the (X) direction, S33 is vertical stress in the (Z) direction, and (S12 = S21) are shear stresses in the X-Y plane. Modeling and structural analyses for the sample minaret were performed using the ABAQUS software package. In this study, the minaret is considered separate from the mosque. The stairs were taken into account in the structural analyses and drawn together with the outer wall to avoid possible problems with the mesh. In order to make comparisons, the wall thicknesses were chosen at 40 cm for each material. Since height is one of the important factors affecting earthquake vulnerability in minarets, this value was chosen as a variable. Nine different minaret heights have been selected, such as 19.40 m, 21.40 m, 23.40 m, 25.40 m, 27.40 m, 29.40 m, 31.40 m, 33.40 m, and 35.40 m. In some figures and tables, the minaret model of 25.40 m in height has been considered an example. In the structural model, quadratic tetrahedral elements (C3D10) were chosen as the mesh type. The sample masonry minaret model consists of 17,673 elements and 33,325 nodes. Notably, 3D models of the sample minaret (H = 25.40 m) obtained from the software are shown in Figure 6.  
Figure 5: Sign alignment and direction assumptions. Figure 6: Sample minaret dimensions and 3D models (H = 25.40 m).