## 3 Experiment Result and Analysis  
Figure 8 presents the displacement of the anchorage. Where, the number means the number of the tendon, H means the horizontal displacement, and V means the vertical displacement. The maximum displacement that occurred as shown in Figure 8 was 0.5 mm, and the safety of the anchorage was secured even when the load increased. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multirow{2}{*}{**Jacking Order**} & \multicolumn{4}{c}{**Tendon Force (kN)**} & \multicolumn{2}{c}{**Anchorage Displ. (mm)**} \\ \cline{3-7}  & & **Jacking Force** & **Setting Loss** & **Elastic Loss** & **Horizontal** & **Vertical** \\ \hline T1 & 3 & 184.8 & 172.8 & 172.0 & 0.06 & 0.05 \\ T2 & 2 & 180.0 & 171.0 & 168.3 & 0.03 & 0.01 \\ T3 & 1 & 179.5 & 169.3 & 164.5 & 0.02 & 0 \\ T4 & 4 & 181.5 & 175.5 & 175.5 & 0.02 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tendon force and anchorage displacement. Figure 7: Displacement according to prestressing. Figure 9 presents the stress of the external tendon as the load increases. The mechanical properties of the external tendon are 15.2 mm in diameter, 138.7 mm\({}^{2}\) in area, 222 kN yield load, and 261 kN tensile load. As experimental results, the yield was confirmed at about 210 kN, and the failure of the external tendon occurred around 230 kN. This is different from the theoretical mechanical properties, and it is judged as an experimental error caused by not aligning with the tendon when installing the loadcell. Figure 10 presents the load-displacement relationship of the girder before and after strengthening. Before strengthening, the girder was additionally loaded with only 570 kN. After strengthening with all external tendons jacking, the girder was loaded with 1028 kN, according to the progress of the bending crack. The experiment after strengthening ended with failure of the external tendon, not with the dropout of the anchorage. Until the end of the experiment, detachment or cracking of the anchorage was not observed, suggesting that the tensile strength of the strands was sufficient when designing the anchorage. Figure 8: Anchorage displacement. Figure 9: External tendon force. When a crack occurs on the surface of concrete, the values measured using the attached strain gauge fluctuate rapidly. Hence, the measured value after the occurrence of the crack is unreliable. Accordingly, to compare the behavioral characteristics before and after strengthening, the strengthening performance was compared through the deflection measurement result, reflecting the overall behavioral characteristics and using the strain gauge attached by exposing the internal tendon after crushing the concrete surface. For the analysis of the experimental values, the effective cross-sectional second moment analysis method was applied as in Equation (1) [35]. This is calculated by simplifying the load-displacement relationship of the cracked member into two straight lines with slopes of \(I_{g}\) and \(I_{cr}\). Compared to the simplified calculation, when the effective cross-sectional second moment was applied, \(I_{e}\) was closer to the experimental value. \[I_{e}=I_{cr}+\left(\frac{M_{cr}}{M_{a}}\right)^{3}\left(I_{g}-I_{cr}\right) \tag{1}\]  
Figure 10: Load-displacement relationship: (**a**) Before strengthening; (**b**) After strengthening. where, \(I_{e}\) represents the effective section secondary moment, \(I_{cr}\) represents the crack section secondary moment, \(M_{cr}\) represents the bending cracking moment of the section, \(M_{a}\) represents the maximum bening moment acting on the member, and \(I_{g}\) represents the non-cracked section secondary moment. \(I_{g}\) was calculated as the second moment of the entire section, and \(I_{cr}\) was calculated as in Equation (2) from the crack moment. The slope of the graph calculated using \(I_{g}\), \(I_{e}\), and \(I_{cr}\) after cracking is presented in Table 3. Each result has a similar meaning for stiffness.