## 5 Comparison and Discussion
### Comparison between the Methods Using Monte-Carlo Simulation  
The strain-compatibility method resulted in relatively more accurate estimations because the \(f_{ps}\) approximation method could not include the rapid strain reduction. Furthermore, the material model--as shown in Figure 11b--resulted in the initial stiffness reduction in the corroded strands.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Maximum Loads of...**} \\ \cline{2-4}
**ID** & **Experiment** & **Strain Compatibility (Difference)** & \(f_{ps}\)**Approximation (Difference)** \\ \hline \multirow{2}{*}{**CB1**} & 289.84 kN & 290.27 kN & 299.22 kN \\  & (when 1 st wire failure) & (0.14\%) & (3.23\%) \\ \hline \multirow{2}{*}{**CB2**} & 339.08 kN & \multirow{2}{*}{346.48 kN} & \multirow{2}{*}{363.66 kN} \\  & 352.07 kN & & \\ \cline{1-1} \cline{4-4} \cline{5-5} \cline{  
Therefore, the three separate models of the strands (in Figure 9) simulated the flexural strength with large variations of total area losses due to corrosion.  
To calculate the difference in strength evaluation of the corroded PC beams, between the strain-compatibility method and the \(f_{\text{ps}}\) approximation method, Monte-Carlo simulation was conducted. The Monte-Carlo simulation is a traditional probabilistic technique and is very useful to evaluate the probability of failure [31]. Random variables for the simulation were the section losses of the strands in the interval of 0 to 30% and applied to the three strands separately. Consequently, the total interval of variables was (0%, 0%, 0%)-(30%, 30%, 30%). Based on the section loss, the material models were changed based on Figure 11.  
Figure 12 shows the results of the Monte-Carlo simulation on CB1 with respect to 1000 random variables. Because the \(f_{\text{ps}}\) approximation method considered only the ultimate strength of the most corroded strand, there was no variation at the same point of cross-sectional loss. Point A denotes the strength at 30% loss, which was 299.22 kN. On the other hand, the strain compatibility method showed a different flexural strength even in the same section loss of the most corroded strand, because it reflected three different corrosion properties, and the variation increased with the amount of section loss. Point B shows the flexural strength to be 282.78 kN when the three strands exhibited section losses of (30%, 30%, 30%). The difference between A and B was 5.81%. When it comes to existing PC beams, only the outer strands in tendons can be inspected for section loss; therefore, it is required to assume that all strands have the same section loss as the inspected most corroded strands. B represents this situation--the result of A provides a somewhat overestimated strength. In addition, this gap could be larger in full-sized PC girders because those had dozens of strands in a tendon  
Figure 13 shows the suggested decision-making flow for flexural strength evaluation. Starting with the 5% section loss, the difference in the strength evaluations between the two methods increased, so only the strain compatibility method was proposed when the section loss exceeded 5%. For practical use, we recommend the use of the \(f_{\text{ps}}\) approximation method in cases where the section loss is less than 5%, or else to the use the strain compatibility, with the assumption that the measured greatest section loss is equal to those of the unmeasurable strands.