## 3 Residual Mechanical Properties of Corroded Strands  
In previous research [18], residual mechanical properties were introduced based on the tensile test results of 86 corroded strands. From these results, it was found that the yield properties were not significantly affected by corrosion, and that the ultimate properties could be defined using empirical expressions. Figure 7 shows the ultimate strength and strain of the 86 corroded strands with respect to the wire-unit section loss--the wire-unit section loss being the section loss of the most corroded wire in a strand. The reason for the use of wire-unit section loss as a parameter was that the ultimate properties (shown in Figure 7) were defined as \"when the first wire ruptured during the tensile tests\". The residual ultimate strength (shown in Figure 7a) illustrates a relationship in which the strength decreases linearly as the cross-sectional loss increases. A 5% fractile line, expressed as Equation (6), is proposed to account for this deviation. The fractile line is defined as the \"residual ultimate strength\" of the corroded strands. According to study on the corrosion-induced failure mechanism of prestressing steel [18], corrosion can cause stress concentration in pit corrosion, and local corrosion attack in the form of pitting or wide pitting corrosion, and the load bearing capacity may get lost at an early stage due to brittle fracture. Since the environmental conditions causing corrosion are different for each bridge and for each prestressing steel, the amount of local stress concentration is unpredictable. However, the decrease in elongation capacity of prestressing steel strand due to corrosion is required to be defined to evaluate  
Figure 6: Deconstruction of CB1 after the loading test. (**a**) Side view, (**b**) failed section of 1 st corroded strand, (**c**) failed section of 2 nd corroded strand. deteriorated behavior of corroded PC beams. Therefore, the term ultimate strain was used as an indicator of the average decrease in tensile capacity due to corrosion induced section loss so that the tensile capacity could be expressed by the material model, even though ultimate strain of \"metal\" has no correlation with corrosion induced section loss. The ultimate strains of corroded strands could be obtained by dividing the elongation by the target length. According to the previous research [16], it has been found that the elongation capacity of the corroded strand decreases linearly and rapidly at around 5% of cross-sectional loss, using finite element analysis. This was also observed in a few tensile test specimens as shown in Figure 8, which shows five examples of tensile test results and their corrosion features with \"wire-unit section loss (type of strand)\". The test results imply that there can be a large reduction in elongation capacity of corroded strands even in moderate corrosion of 5% section loss. Figure 8: Tensile test results of corroded strands. Figure 7: Tensile test results of corroded strands, (**a**) relationship between the ultimate load and the wire-unit section loss, (**b**) relationship between the ultimate tensile strain and the wire-unit section loss. Unlike the previous research [18], a new approach to the residual ultimate strain of the corroded strands was considered as shown in Figure 7b. With cross-sectional losses within 5%, the ultimate strain tended to decrease linearly; however, it sharply decreased with large deviations, after which it converged to a certain value. Therefore, the relationship between the residual ultimate strain and the section loss could be defined by dividing it into \"before\" and \"after\" 5% loss categories. Because the total elongation of 7-wire strands should not be less than 3.5%--according to the American Society for Testing and Materials standard ASTM A416 [26]--the residual ultimate strain for section loss less than 5% was defined by a straight line connecting 7.52% of the ultimate strain of non-corroded strands and 3.5% of ASTM A416 [26].