## 3 Experiment Result and Analysis
The slope of the theoretical value presented in Figure 10 has the same meaning as stiffness. As shown in Table 3, there is only a slight difference according to the crack load, but the slope of the theoretical value is the same, so it is difficult to confirm the actual strengthening effect before cracking. \[M_{cr}=f_{r}Z_{2}+P_{e}\bigg{(}\frac{Z_{2}{}^{2}}{A_{c}}+e_{p}\bigg{)} \tag{2}\]  
where, \(M_{cr}\) represents the bending cracking moment of the section, \(f_{r}\) represents the concrete tensile strength, \(Z_{2}\) represents section constant, \(P_{e}\) represents prestressing force, \(A_{c}\) represents concrete section area, and \(e_{p}\) represents distance to tendon. It was confirmed that the slope of the load-displacement relationship changed at approximately 240 kN before strengthening and at approximately 470 kN after strengthening, resulting in concrete cracking and an increase of approximately 50% of the crack load. However, as shown in Figure 10b, the graph of the pre-crack load-displacement relationship before and after strengthening was identical. This means that the stiffness is the same, so it was difficult to compare the stiffness before and after the stiffness to confirm the strengthening effectiveness. Therefore, in the case of a real bridge, it is difficult to determine the crack load through an experiment; hence, it is concluded that confirming the reinforcing effect before cracking would be challenging. In addition, when comparing the amount of deflection generated by the same load before and after strengthening, it can be seen that the amount of deflection after applying strengthening decreases as shown in Table 4. At 400 kN, the deflection before strengthening was 39.7 mm, whereas after strengthening, a deflection of 30.3 mm occurred, confirming a strengthening effect of approximately 23.7%. In addition, at 470 kN, when cracks occur, the deflections before and after strengthening were 51.7 mm and 37.2 mm, respectively, and the strengthening effect was measured to be 28%; it was judged that the strengthening effect increased as the load increased. In the final loading phase before and after strengthening, a deflection of 77.1 mm and 51.3 mm occurred, respectively, confirming a 33% strengthening effect. Therefore, for the deteriorated bridge used in this experiment, the load carrying capacity increased by approximately 33% with an external prestressing of 180 kN for four tendons. Figure 11 presents the load-strain relationship occurring in the internal tendons before and after strengthening. The load-strain relationship of the internal tendons was also similar to the load-displacement relationship, so it was difficult to confirm the reinforcement effect as the slope before and after reinforcement was the same before cracking. However, the strengthening effect confirmed through the load-displacement relationship presented in Table 4 and the strengthening effect confirmed through the load-strain relationship presented in Table 5 was slightly different in value. The strain of the internal tendon was 555 \(\mu\)\(\epsilon\) at 400 kN before strengthening. After strengthening, a strain of 366 \(\mu\)\(\epsilon\) was gener \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Slope (kN/mm)**} \\ \cline{2-4}  & \(I_{g}\) & \(I_{e}\) & \(I_{cr}\) \\ \hline Before strengthening & 11.7 & 5.3 & 1.1 \\ After strengthening & 11.9 & 6.2 & 2.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of slope. ated, confirming a reinforcement effect of approximately 34.1%. In addition, at 470 kN, where cracks occur, the strains before and after strengthening were 741 \(\upmu\varepsilon\) and 452 \(\upmu\varepsilon\), respectively, and a strengthening effect of 39% was measured. In the final loading phase before and after strengthening, strains of 1115 \(\upmu\varepsilon\) and 698 \(\upmu\varepsilon\) occurred, respectively, confirming a 37.4% strengthening effect.