## 5 Results
### Multi-Cycle Tensioning of Strands  
In contrast to single-cycle tensioning, the multi-cycle tensioning method applies a consistent force (\(Z_{\text{u}}\)) to each strand over multiple cycles to gradually achieve the desired tension and deformation in the stay cable. The intensities of the forces in the strands for each cycle, after applying the same force (100 kN) to each strand in every cycle, are calculated according to the algorithm in Figure 7 for the first cycle and the algorithm in Figure 8 for subsequent cycles. Table 4 presents the cable force and strand forces achieved in each strand during each cycle of the multi-cycle tensioning procedure, as well as the factor of realization (\(\gamma_{\text{k}}\)(\({}^{\text{d}}\))), which measures how close the actual cable force and deformation are to the designed specifications after each cycle. By analyzing this factor according to relation (5), it is determined that four cycles are necessary to achieve the designed cable force and deformation. This conclusion is supported by the incremental improvements in both tension forces and cable deformation metrics, from 86.8% after the first cycle to 100% by the fourth cycle. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Strand (i)**} & \multirow{2}{*}{\(Z_{\text{u}}\) [kN]} & \multicolumn{4}{c}{\(Z_{\text{i}}\)(\({}^{\text{d}}\) * [kN])} \\ \cline{3-6}  & & \(Z_{\text{i}}\)(\({}^{\text{d}}\)) & \(Z_{\text{i}}\)(\({}^{\text{d}}\)) & \(Z_{\text{i}}\)(\({}^{\text{d}}\)) & \(Z_{\text{i}}\)(\({}^{\text{d}}\)) \\ \hline
**1** & 100 & 72.457 & 96.450 & 99.620 & 99.967 \\
**2** & 100 & 75.299 & 97.010 & 99.716 & 99.975 \\
**3** & 100 & 78.062 & 97.521 & 99.773 & 99.980 \\
**4** & 100 & 80.751 & 97.984 & 99.822 & 99.985 \\
**5** & 100 & 83.370 & 98.400 & 99.863 & 99.988 \\
**6** & 100 & 85.922 & 98.768 & 99.897 & 99.991 \\
**7** & 100 & 88.410 & 99.089 & 99.925 & 99.993 \\
**8** & 100 & 90.838 & 99.364 & 99.947 & 99.995 \\
**9** & 100 & 93.208 & 99.592 & 99.965 & 99.997 \\
**10** & 100 & 95.524 & 99.774 & 99.979 & 100 \\
**11** & 100 & 97.787 & 99.910 & 100 & 100 \\
**12** & 100 & 100 & 100 & 100 & 100 \\ \hline \multicolumn{2}{c}{\(Z_{\text{k}}\)(\({}^{\text{d}}\) [kN] **} & 1041.628 & 1183.862 & 1198.507 & 1199.870 \\ \hline \multicolumn{2}{c}{\(\varepsilon_{\text{k}}\)(\({}^{\text{d}}\) [cm] ***)} & 5.208 & 5.920 & 5.993 & 6.000 \\ \hline \multicolumn{2}{c}{\(\gamma_{\text{k}}\)(\({}^{\text{d}}\) ***)} & 86.8\% & 98.66\% & 99.88\% & 100\% \\ \hline \hline \end{tabular}  
* tension force in the strand in the c-th tensioning cycle; ** tension force in the cable after completing the c-th tensioning cycle; *** cable shortening after completing the c-th tensioning cycle; *** factor of realization after completing the c-th tensioning cycle.  
\end{table} 
Table 4: Multi-cycle strand tensioning. Figure 11: Shortening of cable axis as a function of number of tensioned strands. Table 4 shows a gradual increase in tension forces for each strand (\(\text{Z}_{\text{i}}\text{(c)}\)) after completing each cycle. For instance, the tension in the first strand progresses from 72.457 kN at the end of the first cycle to 100 kN by the end of the fourth cycle. The overall cable tension increases from 1041.628 kN after the first cycle to 1199.870 kN by the fourth cycle, with cable shortening stabilizing at 6.000 cm. Figures 12 and 13 depict how cable tension and deformation evolve in achieving the desired cable performance over different tensioning cycles. Based on Figures 12 and 13, it can be concluded that in each subsequent tensioning cycle, the increase in cable force and deformation occurs at a slower rate. As the curve representing cable tension force or shortening of the cable axis approaches a horizontal line, it indicates that the strand forces are becoming more equalized, and the designed values of cable force and deformation are being reached.