## 4 Numerical Example  
The numerical demonstration provided serves solely as an illustrative tool. It comprises assumed parameters, as delineated in Figure 4: specifically, \(\mathrm{l_{k}}=50\) m, \(\alpha=60^{\circ}\), \(\mathrm{\psi=2^{\circ}}\), \(\mathrm{\xi_{k}}=6\) cm. Importantly, it should be noted that these parameters do not correspond to any real-world bridge scenario. The requisite data are computed based on the coordinates of the endpoints, specifically pertaining to the cable support positions, both pre- and post-tensioning of strands. These calculations are conducted within the context of the global coordinate system adopted for the bridge model under consideration. As per Equations (1) and (2), prior to the tensioning process, the tension force in the cable at the active anchor point is negligible, while it registers at 8.0 kN at the fixed anchor situated in the pylon due to the cable's inherent weight. Following the completion of tensioning, applying the designed force of \(\mathrm{Z_{k}}=1200\) kN, the tension force in the cable reaches 1200 kN at the active anchor, whereas it elevates to 1208.0 kN at the fixed anchor. During this stage, auxiliary measures, such as a supplementary strand or other temporary supports like scaffolding, are employed to maintain the cable's alignment.  
The force applied at the jack deviates from the tensioning force within the strand under the active anchor due to the loss incurred during wedge insertion. For the cable under examination, and with a wedge insertion averaging 7 mm, the additional force by which the initial force at the jack (design force in the strand) is increased amounts to 4% of \(\mathrm{Z_{u}}=100\) kN. The attributes of the anchors and strands associated with the cable being studied align with those of cables utilized in the \"SPB SUPER prestressing system\", developed at the IMS Institute in Belgrade, Serbia [37]. This system was employed in the construction of the pedestrian bridge spanning the Nisava River in Nis (Figure 1). The treated cable consists of 12 parallel seven-wire strands with a nominal diameter of 16 mm. Cable end anchorage was performed using S12/16 type anchors (normal and fixed). Cable anchorage at the pylon head was accomplished with a fixed anchor. Anchoring the cable into the bridge deck structure was performed via a normal (active) anchor, through which individual strand tensioning was performed.  
The materials for the stay cable consist of sheathed strands of type EN10138-3-Y1860 S7-16 (Table 1), factory-coated with grease and encased in a hard high-density polyethylene (HDPE) coating (Table 2).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Characteristic** & **Symbol** & **Value** \\ \hline Diameter (steel) & d & 15.7 mm \\ \hline Total diameter (steel + grease + HDPE) & D & 19.1 mm \\ \hline Area of strand (steel) & \(\mathrm{A_{u}}\) & 150 mm\({}^{2}\) \\ \hline Strand mass (steel + grease + HDPE) & \(\mathrm{m_{s}}\) & 1.29 kg/m \\ \hline Relaxation class & - & 2 (low relaxation level: \textless{2.5\%}) \\ \hline Characteristic tensile strength & \(\mathrm{f_{pk}}\) & 1860 N/mm\({}^{2}\) \\ \hline Characteristic failure force & \(\mathrm{F_{pk}}=\mathrm{A_{u}}\cdot\mathrm{f_{pk}}\) & 279 kN \\ \hline Characteristic value of yield force at which & \(\mathrm{F_{p}}\,\mathrm{0.1}\) & 246 kN \\ permanent 0.1\% elongation occurs & \(\mathrm{0.45\,F_{pk}}\) & 12.55 kN \\ \hline Modulus of elasticity & E & \(\mathrm{1.94\,(\pm 0.01)\times 10^{5}\,MPa}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of geometric and mechanical characteristics of considered strand.