# Strengthening Effect of the External Prestressing Method That Simulated a Deterioration Bridge
## 3 Test Result  
As the load increased, crack, yield, and failure occurred in stages. The crack load is the load in which a crack occurs due to an abnormality in the tensile strength of the concrete at the bottom of the specimen as deflection increases. The yield load is the load at which the reinforcing bar yields after the crack is transferred from the concrete to the reinforcing bar. The failure load is the load when the structure is completely destroyed, e.g., anchorage dropout. The crack load was calculated theoretically at the point where the stress of concrete generated at the bottom of the beam reaches the modulus of rupture of the concrete, as shown in Equation (1). The load was converted through the moment-load relationship of a simple beam with two loads [34]. \[M_{cr}=f_{r}I_{g}/y_{t} \tag{1}\]  
where, \(M_{cr}\) denotes the crack moment, \(f_{r}\) denotes the modulus of rupture, \(I_{g}\) denotes the moment of inertia, and \(y_{t}\) denotes the distance from the center axis of the section to the tensile edge. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Name of Specimen**} & \multirow{2}{*}{**Design P\({}_{\text{e}}\) (kN)**} & \multicolumn{2}{c}{**Measured P\({}_{\text{e}}\)(kN)**} \\ \cline{3-4}  & & & **T1** & **T2** \\ \hline
5 & C40-D22-EP & 100 & 82 (82\%) & 78 (78\%) \\
6 & C40-D19-EP & 100 & 69 (69\%) & 69 (69\%) \\
7 & C20-D22-EP & 50 & 32 (64\%) & 28 (56\%) \\
8 & C20-D19-EP & 50 & 33 (66\%) & 35 (70\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of introducing external prestress force. Figure 6: Load and sensor position. The yield load was calculated at the point where the reinforcement strain on the tensile side reached the yield strain of 2000 \(\mu\epsilon\), while the neutral axis was considered assuming that the section remains plane. Then, the strain rates of concrete and compression reinforcement were calculated. According to the failure shape, the non-strengthened specimen showed a typical form of flexural failure through compressive failure after the tensile reinforcement yielding, as shown in Figure 7a. The test was terminated owing to the detachment of the anchorage resulting from the failure of the surrounding concrete and the overturning of anchorage after yielding, as shown in Figure 7b. The prestress force was lost even after the load was removed, and the deflection was not recovered. The anchorage detachment occurred because the sufficient shear force was not secured as some anchor bolts did not reach the anchorage depth (see Section 2.2). Moreover, the number of anchor bolts was only designed for introducing the prestressing force due to the increase in the size of the anchorage and the number of anchor bolts, even though it needs to be designed according to the stress that the anchorage needs to bear until member failure. In addition, in the case of post-installed anchors, the center spacing and edge distance of 6 times or over of the anchor diameter need to be secured. However, the center spacing of anchor bolts was at a minimum of 70 mm, which did not satisfy the central spacing regulations, as shown in Figure 4a. Additionally, the side anchor bolts constrained the concrete cover and detached together with the anchorage, as shown in Figure 8a, which is determined to be the result of the reduction of the section of concrete due to the anchor bolts inserted from the left and right sides of the same height, as shown in Figure 8b. This is considered to have been caused by the narrow width of the specimen compared to the thick lower flange of the general bridge. The crack, yield, and failure loads of the specimen are summarized in Table 3, and the load-displacement relationship is shown in Figure 9. The load-displacement relationship of the non-strengthened specimen without strengthening is shown in Figure 9a, and a similar load-displacement relationship was shown according to the arrangement of tensile reinforcement regardless of the concrete compressive strength.