# Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading
## 7 Conclusions  
In this paper, a guyed radio mast's size and shape optimization process was carried out to identify the equilibrium solution that guarantees the lighter optimized model, verifying strength, instability, and deformation requirements. The paper considers a detailed evaluation of the variable loads according to the Eurocodes recommendations. Furthermore, the OAPI was used to perform a structural analysis with the finite element software SAP2000 by considering the non-linearity of the cables. The optimization was \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**SCENARIO G—Optimized Solution**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 168.3 & 3 & 6000 & 73 \\ Pole 2 (6–12 m) & 168.3 & 4 & 6000 & 97 \\ Pole 3 (12–18 m) & 168.3 & 3 & 6000 & 73 \\ Pole 4 (18–24 m) & 168.3 & 3 & 6000 & 73 \\ Pole 5 (24–30 m) & 168.3 & 3 & 6000 & 73 \\ \hline \multicolumn{5}{c}{Total Mass [kg]} & \(\Sigma\) & 391 \\ \hline Mass variation [kg] & \(-1050\) & Mass variation [\%] & \(-72.88\) \\ \hline \multicolumn{5}{c}{**SCENARIO G—Design proposed according to the product list**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 168.3 & 4 & 6000 & 97 \\ Pole 2 (6–12 m) & 168.3 & 4 & 6000 & 97 \\ Pole 3 (12–18 m) & 168.3 & 3 & 6000 & 73 \\ Pole 4 (18–24 m) & 168.3 & 3 & 6000 & 73 \\ Pole 5 (24–30 m) & 168.3 & 3 & 6000 & 73 \\ \hline \multicolumn{5}{c}{Total Mass [kg]} & \(\Sigma\) & 414 \\ \hline Mass variation [kg] & \(-1026\) & Mass variation [\%] & \(-71.22\) \\ \hline \multicolumn{5}{c}{**Ntrial = 3**} \\ \hline \(t_{1}\) & \(t_{2}\) & \(t_{3}\) & \(t_{4}\) & \(t_{5}\) & OF \\ [mm] & [mm] & [mm] & [mm] & [KN] \\ \hline
3 & 4 & 4 & 3 & 3 & 34.985 \\ \hline
3 & 4 & 3 & 3 & 3 & 34.751 \\ \hline
3 & 4 & 3 & 4 & 3 & 34.985 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Scenario G results: optimized solutions for the different independent executions (Ntrial) and proposed industrial one, according to the product list. carried out using a genetic optimization algorithm. Eight scenarios (labeled from A to H) were investigated, considering different arrangements of the geometric characteristics of the central pole and cables. The input parameters were increased from Scenario A to H to achieve the best fitness value of the self-weight. From Scenario A to H, the mass reduction index generally increased with the computational effort except in scenarios B and E, in which the input parameter did not represent the best vector design for the structural optimization. At this stage, the best design solution was evaluated from the database of cross-sections inside the finite element software. Though Scenario A provides the worst structural solution in terms of objective function, it represents the most convenient optimization strategy due to its low computational effort; on the contrary, Scenario H exhibits the best fitness value with the lowest self-weight, but it represents the most time-consuming solution. The best solution is achieved when the thickness values of each member, which, composed of the central pole, are included in the optimization process. An improvement of the structural behaviour against instability is observed with increasing thickness. This verification is critical for this structure, mainly subjected to normal stresses resulting from self-weight and pre-stressing cable force. The entire optimization process seems to not be sensible to the pole diameter, chosen as the input parameter of the design vector. Although the final results of the FEM analyses are based on the Italian standards, other codes (e.g., Eurocodes, American code, etc.) can be selected from the SAP2000 settings. However, since no detailed analysis was carried out and many standards are based on the semi-probabilistic approach, the final results should be similar, even with different code formulations.