## 2 Resistance Capacity and Performance Degradation Analysis  
### Resistance Capacity Evaluation of the Sample Bridge  
In this study, a PSC-I type girder bridge was specifically selected for examination in order to develop a method for analyzing the resistance capacity and performance degradation of bridges. The sample bridge was to be used in a two-lane expressway and comprised a single span that was 15 m in width. It was designed to satisfy the DB-24 load as outlined in the Korea highway bridge specifications [6]. The total span length of the sample bridge was set as 30 m.  
To determine the appropriate cross section of the PSC-I girder, the standard cross-section of a 30-m-long PSC-I girder provided by the Korea Express Corporation (Seoul, Korea) was utilized. Table 1 and Figure 1 present the data specifications and cross-sectional profiles of the sample bridge at the mid-span. The resistance capacity of the sample bridge was evaluated by calculating the flexural resistance, which is the material property that resists the effects of the two major loads applied to the structure: \begin{table}
\begin{tabular}{c c} \hline \hline
**Property** & **Value** \\ \hline Bridge width & 15 m \\ Cross-beam spacing & 5 m \\ Number of girders & 8 \\ Span length & 30 m \\ Girder height & 2000 mm \\ Girder width & 700 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Section properties of the pre-stressed concrete-I (PSC-I) bridge. Figure 1: Cross-section of the PSC-I bridge at the mid-span (mm). the dead load and live load. As discussed in the following sections, the resistance capacity of the PSC-I girder bridge was evaluated by using the flexural strength equation from the load-and-resistance factor design (LRFD) bridge design specifications [7]. The equations for the flexural strength of a PSC-I girder vary with the depth of the concrete stress block \(a\ (=c\beta)\) and the position of the compression flange \(h_{f}\). If the depth of the concrete stress block is shallower than the thickness of the compression flange (i.e., \(a<h_{f}\)), the equations for the flexural strength of a rectangular cross-section are used:  
\[M_{n}=A_{ps}f_{ps}\Big{(}d_{p}-\frac{a}{2}\Big{)}+A_{s}f_{s}\Big{(}d_{s}-\frac {a}{2}\Big{)}-A_{s}^{\prime}f_{s}^{\prime}\Big{(}d_{s}^{\prime}-\frac{a}{2} \Big{)}, \tag{1}\]  
\[\text{c}=\frac{A_{ps}f_{ps}+A_{s}f_{s}-A_{s}^{\prime}f_{s}^{\prime}}{0.85f_{c}^ {\prime}\beta_{1}b_{1}+kA_{ps}\frac{f_{ps}}{d_{p}}}, \tag{2}\]  
where \(A_{ps}\ (\text{mm}^{2})\) is the area of the pre-stressed (PS) tendon, \(A_{s}\ (\text{mm}^{2})\) is the area of the non-pre-stressed tension reinforcing bar, \(A_{s}^{\prime}\ (\text{mm}^{2})\) is the area of the compression reinforcing bar, \(f_{ps}\) (MPa) is the average stress in the PS tendon, \(f_{s}\) (MPa) is the stress in the mild steel tension reinforcing bar, \(f_{s}^{\prime}\) (MPa) is the stress in the mild steel compression reinforcing bar, \(f_{pu}\) (MPa) is the yield strength in the PS tendon, \(a\ (\text{mm})\) is the depth of the equivalent stress block, \(b_{1}\ (\text{mm})\) is the width of the compression face of the member, \(\text{c}\ (\text{mm})\) is the distance from the center of the longitudinal reinforcement to the nearest face of the concrete-encased shape on the bending plane, \(d_{s}\ (\text{mm})\) is the distance from the extreme compression fiber to the centroid of the non-pre-stressed tensile reinforcement, and \(\beta_{1}\ (\text{mm})\) is the stress block factor.