## 3 Results
### Geometrical Features  
In this type of defensive structures, resistance to gravity loads is not the decisive parameter in their design. In fact, assuming a standard specific weight for masonry of 20 kN/m\({}^{3}\), the average compressive stress is 0.2 MPa per 10 m of wall height. As seen in Table 3 the minimum estimated value of the compressive strength of the studied walls is 1.5 MPa, which suggests this type of wall could reach a height of up to 70.5 m. Accordingly, the main issue for this type of structure is the effect of horizontal loads, especially those relating to earthquake or wind. The high vulnerability of masonry towers against such loads depends particularly on geometric characteristics directly related to their design, such as the slenderness or the number and size of the openings. Pathological processes, such as loss of verticality or cracks in walls due, for instance, to differential settlement, are also relevant [38]. Figure 16: Elastic modulus of the masonry (E). Figure 17: Compressive strength of the masonry (f\({}_{\text{m}}\)). Figure 18 provides data on the slenderness of the towers in the survey. The values are shown together with the shape index, which indicates the ratio between the two main dimensions of the floor plan at level 0 (length/width). This index provides information about the homogeneity of how the structure behaves in relation to a given direction. To enable comparison between the different units, the data was classified according to the morphology of the tower in question. The analysis reveals that tower slenderness decreased over the centuries: Andalusian towers built prior to the 16 th century have a higher slenderness index than those built in later times. Thus, the average slenderness for medieval towers is around 1.80 compared to modern towers, which do not exceed 1.5. This reduced slenderness reaches its maximum expression with the modern \"horseshoe-shaped\" towers of the 18 th century, whose slenderness is around 0.8. Such lower slenderness is the result of adaptation to the gradual introduction of long-range weaponry in siege warfare constructions. By the 15 th century, weapons had acquired enough firepower to become a significant danger to defensive constructions, which needed to be adapted to withstand their impact by evolving towards more massive buildings, with no protruding edges, steep slopes and lower elevation from the ground. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Sample Towers**} & \multirow{2}{*}{**MQI**} & \multicolumn{2}{c}{**Elastic Modulus (MPa)**} & \multicolumn{2}{c}{**Compressive Strength (MPa)**} \\ \cline{3-6}  & & \(\mathbf{E_{min}}\) & \(\mathbf{E_{max}}\) & \(\mathbf{f_{m,min}}\) & \(\mathbf{f_{m,max}}\) \\ \hline Campanillas & 4.90 & 1284.93 & 1828.91 & 2.80 & 4.47 \\ Urique & 5.00 & 1307.46 & 1859.04 & 2.86 & 4.56 \\ Esteril & 1.20 & 675.46 & 999.14 & 1.22 & 2.14 \\ Jaral & 4.20 & 1137.74 & 1631.24 & 2.39 & 3.89 \\ Guadalmansa & 4.50 & 1198.64 & 1713.20 & 2.56 & 4.13 \\ Tramores & 3.50 & 1007.41 & 1454.93 & 2.05 & 3.39 \\ Duque & 3.50 & 1007.41 & 1454.93 & 2.05 & 3.39 \\ Sal & 6.00 & 1555.64 & 2189.03 & 3.58 & 5.56 \\ Agriculture & 2.00 & 776.22 & 1138.67 & 1.46 & 2.51 \\ Montelviche & 2.45 & 839.37 & 1252.55 & 1.62 & 2.75 \\ Viñuela & 1.75 & 743.22 & 1093.09 & 1.38 & 2.39 \\ Casasola & 5.00 & 1307.46 & 1859.04 & 2.86 & 4.56 \\ Manganeto & 2.80 & 892.01 & 1297.68 & 1.75 & 2.95 \\ Cantal & 5.00 & 1307.46 & 1859.04 & 2.86 & 4.56 \\ Ancon & 3.15 & 947.96 & 1374.06 & 1.89 & 3.16 \\ Derecha & 5.50 & 1426.16 & 2017.30 & 3.20 & 5.04 \\ Lagos & 5.25 & 1365.52 & 1936.55 & 3.02 & 4.79 \\ Chikches & 6.00 & 1555.64 & 2189.03 & 3.58 & 5.56 \\ Moya & 6.50 & 1696.87 & 2375.39 & 4.00 & 6.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mechanical Properties and Strength Characteristics of the Towers under Study. Figure 18: Slenderness and shape index for the towers under study.