## 1 Introduction  
Recently, various investigations and studies on prestressed concrete (PC) girder bridges where corrosion has occurred have been conducted [1; 2; 3]. The studies have shown that the corrosion that occurred on bridges in use was due to the tendons not being properly protected from corrosion-inducing components such as air, water, and chloride. In addition, it was not easy to find corrosion due to grout, so there were many cases where corrosion was only found after abnormalities had been discovered in the structure. [PERSON] and [PERSON] [4] carried out a loading test on corroded pre-tensioned concrete girders recovered from a 45-year-old bridge. The test results showed that the performance of corroded PC girders had been overestimated compared to the strength and displacement calculated based on design theory. This was the same for all specimens, and the difference increased linearly according to the degree of corrosion. [PERSON] et al. [5] fabricated bonded fully PC beams with accelerated corrosion using electrochemical techniques. After flexural tests had been conducted, the results showed that the flexural strength had been reduced by up to 10%, and that the ductility and initial stiffness were reduced compared to the non-corroded specimens. The reduction in load-carrying capacity due to corrosion was also can be found in conventional reinforced concrete structures [6; 7]. This study also proposed an evaluation method for the deformation behavior of corroded PC beams using the strain compatibility method and statistical corrosion model. [PERSON] et al. [8] conducted similar tests on PC beams corroded by means of electrochemical techniques. The specimens had different levels of corrosion and were categorized by the mass loss of the corroded strands. The results showed that low corrosion levels led to a sharp ductility reduction and the crushing of the concrete, while severe corrosion of the strands led to the local rupture of wire. The author tried to evaluate the ultimate force using the stress block approach for concrete; however, it had limitations in that the sectional reduction could not be considered in the calculation. [PERSON] et al. [9] studied the effect of insufficient grout and strand corrosion on PC beams. The author also electrochemically accelerated strand corrosion, and the level of corrosion was measured by mass loss. The result showed that strand corrosion in non-grounded ducts led to pretension loss, a reduction in cracking load, a reduced number of cracks, and a larger crack spacing. The studies introduced above did not consider the quantitative residual capacity of corroded strands, despite it being necessary to predict the behaviors of corroded PC beams. [PERSON] et al. [10] conducted loading tests on corroded PC beams and tensile tests on artificially corroded strands. The author also measured the sectional loss using a contour gauge to define the relationship between the sectional loss due to corrosion and tensile behavior. This was used to evaluate the global behavior of corroded PC beams using the strain compatibility method. A major difference in this study compared to other research was the adoption of the quantitative evaluation of corroded strands, which enabled the reasonable prediction of the residual capacity of corroded PC beams. There has been much research on the mechanical properties of corroded strands [11; 12; 13; 14; 15]. These studies have tried to specify the corrosion behavior of strands based on visual inspection, mass loss, and section loss. [PERSON] et al. [16] suggested an equivalent material model of corroded strands based on research and finite element analysis, and [PERSON] et al. [17] developed this model using a probabilistic approach. Eventually, a previous study [18] conducted tensile tests on a total of 86 corroded strands taken from existing corroded PC bridges and proposed empirical mechanical properties. The study also introduced a method for evaluating the strength of corroded PC beams.