# Size and Shape Optimization of a Guyed Mast Structure under Wind, Ice and Seismic Loading
## 7 Conclusions
\begin{tabular}{c c} \hline \hline  & \multicolumn{2}{c}{**Load Combination**} \\ \hline ULS Max\({}_{1}\) & \(1.3\cdot G_{1}+1.5\cdot G_{2}+1.5\cdot Wind_{1}+1.5\cdot 0.5\cdot Ice_{1}+1.5 \cdot 0\cdot Q_{M}\) \\ \hline ULS Max\({}_{2}\) & \(1.3\cdot G_{1}+1.5\cdot G_{2}+1.5\cdot Q_{M}+1.5\cdot 0.6 Wind_{1}+1.5\cdot 0.2 Ice_{1}\) \\ \hline ULS Min\({}_{1}\) & \(1\cdot G_{1}+0.8\cdot G_{2}+1.5\cdot Wind_{1}+1.5\cdot 0.5 Ice_{1}+1.5\cdot 0Q_{M}\) \\ \hline Quake\({}_{1}\) & \(E+G_{1}+G_{2}+0\cdot Wind_{1}+0 Ice_{1}+0Q_{M}\) \\ \hline ULS Max\({}_{2}\) & \(1.3\cdot G_{1}+1.5\cdot G_{2}+1.5\cdot Wind_{2}+1.5\cdot 0.5\cdot Ice_{2}+1.5 \cdot 0\cdot Q_{M}\) \\ \hline ULS Max\({}_{2}\) & \(1.3\cdot G_{1}+1.5\cdot G_{2}+1.5\cdot Q_{M}+1.5\cdot 0.6 Wind_{2}+1.5\cdot 0.2 Ice_{2}\) \\ \hline ULS Min\({}_{1}\) & \(1\cdot G_{1}+0.8\cdot G_{2}+1.5\cdot Wind_{2}+1.5\cdot 0.5 Ice_{2}+1.5\cdot 0Q_{M}\) \\ \hline Quake\({}_{2}\) & \(E+G_{1}+G_{2}+0.8\cdot Wind_{2}+1.5 Ice_{2}+1.5Q_{M}\) \\ \hline \hline \end{tabular}   
**Figure A1. ** Cont. Figure 11: Scenarios A, B. In blue, orange, and green, the average PRs, respectively, at the initial condition, after optimization, and the design solution. Figure 13: Scenarios E, F, H. In blue, orange and green, the average PRs, respectively, at the initial condition, after optimization, and the design solution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**SCENARIO B–Optimized Solution**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 149 & 12.5 & 6000 & 252 \\ Pole 2 (6–12 m) & 138 & 12.5 & 6000 & 231 \\ Pole 3 (12–18 m) & 126 & 12.5 & 6000 & 210 \\ Pole 4 (18–24 m) & 115 & 12.5 & 6000 & 189 \\ Pole 5 (24–30 m) & 103 & 12.5 & 6000 & 168 \\ \hline \multicolumn{5}{c}{Total Mass [kg]} & \(\Sigma\) & 1051 \\ \hline Mass variation [kg] & \(-\)389 & Mass variation [\%] & \(-\)27.02 \\ \hline \multicolumn{5}{c}{**SCENARIO B–Design proposed according to product list**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 168.3 & 12.5 & 6000 & 288 \\ Pole 2 (6–12 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 3 (12–18 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 4 (18–24 m) & 114.3 & 12.5 & 6000 & 188 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Scenario B results: optimized solutions for the different independent executions (Ntrial) and the proposed industrial one according to the product list. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{5}{c}{**SCENARIO A–Optimized Solution**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 121 & 12.5 & 6000 & 201 \\ Pole 2 (6–12 m) & 121 & 12.5 & 6000 & 201 \\ Pole 3 (12–18 m) & 121 & 12.5 & 6000 & 201 \\ Pole 4 (18–24 m) & 121 & 12.5 & 6000 & 201 \\ Pole 5 (24–30 m) & 121 & 12.5 & 6000 & 201 \\ \hline \multicolumn{5}{c}{Total Mass [kg]} & \(\Sigma\) & 1003 \\ \hline Mass variation [kg] & \(-\)437 & Mass variation [\%] & \(-\)30.36 \\ \hline \multicolumn{5}{c}{**SCENARIO A–Design proposed according to the product list**} \\ \hline Element & d [mm] & t [mm] & L [mm] & Mass [Kg] \\ \hline Pole 1 (0–6 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 2 (6–12 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 3 (12–18 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 4 (18–24 m) & 139.7 & 12.5 & 6000 & 235 \\ Pole 5 (24–30 m) & 139.7 & 12.5 & 6000 & 235 \\ \hline \hline \multicolumn{5}{c}{Total Mass [kg]} & \(\Sigma\) & 1176 \\ \hline Mass variation [kg] & \(-\)264 & Mass variation [\%] & \(-\)18.36 \\ \hline \multicolumn{5}{c}{**Ntrial = 5**} \\ \hline \hline \multicolumn{5}{c}{\(\Phi_{\rm opt}\) [mm]} & \multicolumn{2}{c}{OF [kN]} \\ \hline
**121** & \multicolumn{2}{c}{40.758} \\ \hline
121 & \multicolumn{2}{c}{40.758} \\ \hline
122 & \multicolumn{2}{c}{40.849} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Scenario A results: optimized solutions for the different independent executions (Ntrial) and the proposed industrial one, according to the product list.