## 2 Flexural Tests on Corroded PC Beams
### Fabrication of Test Specimens
The test considered two cases of corrosion at midspan and one case of corrosion near the support, and the result showed significant reduction in load-carrying capacity in the former case, but not in latter case. However, a recent study [21] showed that corrosion caused bond strength degradation and global strength decrease, even though the location was not midspan, and [PERSON] et al. [22] also found that tendon rupture of a full-sized PC girder exhibited reduced flexural stiffness in unbonded cases. Therefore, CB2, CB3, and CB4 were prepared to observe the effect of corrosion near the support on global behavior, especially with respect to the bond degradation behavior because there was doubt that the severe corrosion near support can cause deteriorated flexural behavior of PC beams. CB2 had the largest tendon-unit section loss, CB3 had the largest wire-unit section loss, and CB4 had the smallest section loss among them. Considering the results of the tensile test of corroded strands [18], the cross-sectional loss higher than that of Table 1 was less meaningful (so not considered) because a significant elongation capacity decrease occurred. The study on bond behavior of corroded strand [23] proposed effective bond length for corroded strands under flexural load considering single strand, and Equations (4) and (5) were derived to obtain effective bond length to give effective prestress in this paper. This means that the bond strength does not decrease if the cross section is out of the length and means that the global flexural behavior does not change if the length does not reach the midsection. Since the PC beams considered herein had three strands, the \(R(\eta)\) can be considered with three sectional losses: wire-unit section loss, strand-unit section loss, and tendon-unit section loss. Based on those three sectional losses, effective bond length of Equation (4) was calculated as shown in Table 1.  
\[A_{sl,1}=\ 2r^{2}\bigg{[}\arccos\bigg{(}1-\frac{d_{p}}{2r}\bigg{)}-\frac{1}{2} \sin\bigg{(}2\arccos\bigg{(}1-\frac{d_{p}}{2r}\bigg{)}\bigg{)}\bigg{]} \tag{1}\]  
\[A_{sl,2}=\ r^{2}\Bigg{[}2\Bigg{\{}\arccos\!\left(-\frac{d_{p}}{2r}\right)\Bigg{\}}- \pi-sin\!\left\{2\arccos\!\left(-\frac{d_{p}}{2r}\right)\right\}\Bigg{]} \tag{2}\]  
\[A_{sl,3}=\ r^{2}\Bigg{[}\arccos\!\left(1-\frac{d_{p}}{r}\right)-\frac{1}{2}sin \!\left\{2\arccos\!\left(1-\frac{d_{p}}{r}\right)\right\}\Bigg{]} \tag{3}\]  
where \(A_{sl,1-3}\) are the losses of sectional areas according to the type of pit configuration, \(r\) is the radius of the wire, and \(d_{p}\) is the pit depth (from 0 to 2\(r\)) measured by a depth gauge at the deepest location  
Figure 1:0  
\[R(\eta)=\ \left\{ \begin{array}{cc}1.0&\eta\ \leq\ 6\%\\ 2.03e^{-0.118\eta}&\eta\ >\ 6\%\end{array} \right. \tag{5}\]  
where \(l_{eb}\) and \(F_{pe}\) are the effective bond length and prestressing force of strands, respectively; \(R(\eta)\) is the normalized maximum bond stress; \(L_{p}\) is the circumference of a strand (=4/3\(\pi d_{s}\)), and \(d_{s}\) is the diameter of a strand; \(\eta\) is strand-unit section loss due to corrosion; \(\tau_{max}\) is the maximum bond stress taken as \(1.25\sqrt{f_{ck}}\) and \(2.5\sqrt{f_{ck}}\) for the good and other bond condition, respectively. Figure 4 shows the test setup. The test was conducted under three-point bending with simple supports, the span length between the supports being 2500 mm. A hydraulic jack applied the load to a steel beam of width 200 mm (to distribute the stress concentration), and a load cell was located between them. Another the load cell was installed between the end of beam and the anchor to establish the initial prestressing force, which was 400 kN (on average). The PC beams were loaded until concrete crushing at the top was observed, or the strength decreased by 10% after the peak strength. Table 2 shows the mechanical properties of materials used in the PC beam specimens.