## 3 Required Performance and Resistance Capacity Considering Environmental Factors
### Resistance Capacity Based on Statistical Characteristics  
The resistance capacity of a bridge is used as a significant index for bridge maintenance. In order to compute the resistance capacity, which reflects the statistical properties of a bridge structure, uncertainty variables that form the resistance capacity must be considered. These include the statistical characteristics (\(\lambda_{MF},V_{MF}\)) of materials and sections resulting from construction and the statistical characteristics (\(\lambda_{P},V_{P}\)) [14] resulting from the discrepancy between the model and actual structure. When the bridge resistance capacity is computed based on reliability theory, such uncertainty variables must be reflected. In this study, all variables in the resistance capacity equation for the PSC-I girder that describe materials and sections were regarded as probabilistic variables. A Monte Carlo simulation with 100,000 samples was performed to infer the statistical characteristics of the materials and sections. The bias factor (\(\lambda_{R}\)) and coefficient of variation (\(V_{R}\)) of the resistance capacity considering the statistical characteristics of materials, sections, and modeling can be computed as follows [15]:  
\[\lambda_{R}=\lambda_{MF}\lambda_{P}, \tag{17}\]  
\[V_{R}=\sqrt{\left(V_{MF}\right)^{2}+\left(V_{P}\right)^{2}}, \tag{18}\]  
where \(\lambda_{P}\) is the bias factor of modeling, \(\lambda_{MF}\) is the bias factor of the material and fabrication, \(V_{P}\) is the coefficient of variation of modeling, and \(V_{MF}\) is the coefficient of variation of the material and fabrication.  
The probabilistic characteristics of the materials and the section properties should be considered. Statistical characteristics such as the area of the PS tendon, area of the reinforcing bars, effective depth, and height of the concrete section were taken from National Cooperative Highway Research Program 368 (NCHRP 368) [14]. The material properties of concrete and steel structures, such as the concrete compressive strength, reinforcing steel tensile strength, and PS strand breaking stress, were taken from [PERSON] and Szerszen [16]. The probabilistic characteristics of the resistance capacity were estimated through a Monte Carlo simulation run 100,000 times in total. Table 10 presents the statistical characteristics of the resistance capacity considering both the statistical characteristics and modeling error variables of the material and fabrication. The flexural resistance of the PSC-I girder was calculated to be 1.053 times greater than the nominal strength on average.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Categories**} & \multirow{2}{*}{**Girder**} & \multicolumn{2}{c}{**Live Load Distribution Factor**} \\ \cline{3-4}  & & **Lane 1 (\(C_{Lane1}\))** & **Lane 2 (\(C_{Lane2}\))** \\ \hline \multirow{3}{*}{PSC-I girder bridge} & G1 & 0.124 & 0.312 \\  & G2 & 0.153 & 0.302 \\ \cline{1-1}  & G3 & 0.219 & 0.181 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Lateral load distribution coefficients for lanes.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Girder**} & \multicolumn{2}{c}{**Non-Exceedance Probability 95\%, (kN-m)**} \\ \cline{2-4}  & **Light Traffic** & **Normal Traffic** & **Heavy Traffic** \\ \cline{2-4}  & **10,000, 15\%** & **20,000, 25\%** & **40,000, 35\%** \\ \hline \hline G1 & 1730.4 & 1847.2 & 1912.5 \\ G2 & 1775.3 & 1902.8 & 1950.1 \\ G3 & 1585.9 & 1645.2 & 1648.3 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Annual extreme load considering the AADT and heavy vehicle proportion (heavy vehicle distribution = 15:85, lane 2).