# Design Method of Primary Structures of a Cost-Effective Cable-Supported Photovoltaic System
## 5 Conclusions  
In this study, the bearing capacity and failure modes of the primary structures of a new CSPS were investigated in detail using FEM. A design method for a new structure was proposed based on the limit state design method. The primary conclusions of this study are as follows. (1) The proposed structure exhibited a strong load-bearing capacity. Case 180\({}^{\circ}\) is the controlling condition of cables 1 and 2, and Case 0\({}^{\circ}\) is the controlling condition of cable 3. When the internal forces of the three cables are equal to their resistance force, the wind load is supported by all three cables in Case 0\({}^{\circ}\), whereas only cables 1 and 2 bear the wind load when the wind load is greater than a certain critical value in Case 180\({}^{\circ}\). (2) The failures of the cables and triangle brackets are the two primary types of failures of the primary structure. The cross-sectional area of the cables is the most important factor affecting the load-bearing capacity of the structure and directly affecting the failure modes of the PV system. Case 0\({}^{\circ}\) is the controlling condition of the triangular brackets, the buckling or yielding of which is closely related to the outer diameter of the rods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{3}{c}{**Load Effect**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Self-Weight of PV Modules**} & \multicolumn{2}{c}{**Local Wind Load**} & \multirow{2}{*}{**Ultimate Limit State (R\({}_{\text{d}}\))**} & \multirow{2}{*}{**Serviceability Limit State (C)**} \\ \hline \multicolumn{5}{c}{Allowable deflection (m)} \\ \hline Axial force of Cables & Case 0\({}^{\circ}\) & 30 & 34 & \\
1, 2 (kN) & Case 180\({}^{\circ}\) & 30 & 68 & 125 \\ \hline Axial force of Cable 3 (kN) & Case 0\({}^{\circ}\) & 18 & 55 & 99 \\ \hline Axial force of triangle brackets (kN) & 4.3 & 6.5 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Required internal force of cables and triangle brackets. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Design Parameters** & \multicolumn{2}{c}{**Original Structure**} & \multicolumn{2}{c}{**Redesigned Structure**} \\ \hline Triangle brackets height \(h_{1}\) (m) & 1.5 & 1.5 \\ \hline Outer diameters of triangle brackets \([D]\) (m) & 0.03 & 0.025 \\ \hline Cross-sectional areas of Cables 1, 2 \(S_{1,2}\) (m\({}^{2}\)) & \multicolumn{2}{c}{\(0.97\times 10^{-4}\)} & \(1.83\times 10^{-4}\) \\ \hline Cross-sectional areas of Cable 3 \(S_{3}\) (m2) & \multicolumn{2}{c}{\(1.36\times 10^{-4}\)} & \(1.32\times 10^{-4}\) \\ \hline The resistance force of the cables \(R_{\text{kk}}\) (kN/m\({}^{2}\)) & \multicolumn{2}{c}{Case 0\({}^{\circ}\)} & 1.95 & 2.66 \\ \multicolumn{5}{l}{Case 180\({}^{\circ}\)} & \multicolumn{2}{c}{1.1} & 2.85 \\ \hline Design value of wind load capacity of the CSPS \(S_{\text{d}}\) (kN/m\({}^{2}\)) & \multicolumn{2}{c}{0.55} & 1.33 \\ \hline Midspan deflection (m) & \multicolumn{2}{c}{Case 0\({}^{\circ}\)} & 0.41 & 0.41 \\ \multicolumn{5}{l}{Case 180\({}^{\circ}\)} & \multicolumn{2}{c}{0.59} & 0.58 \\ \hline Steel consumption of cables and triangle brackets (t) & \multicolumn{2}{c}{30.1} & 25.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of parameters between the original structure and the redesigned structure per MW. (3) The proposed limit state design method was shown to be cost-effective, and the designed structure had less steel consumption and a strong load capacity. Conceptualization, H.D. and H.J. ; methodology, H.D. and H.J. ; formal analysis, H.D. and H.J. ; investigation, H.D. and H.J. ; data curation, H.D., X.H. and H.J. ; writing--original draft preparation, H.D., X.H. and H.J. ; writing--review and editing, all authors; supervision, X.H., [PERSON] ([PERSON]) and [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript.