## 3 Load Effect Calculation Method of Corroded Reinforcement Bridges
### Performance Function of Flexural Bearing Capacity  
The limit state of flexural bearing capacity of the \(i\)-th beam can be expressed as,  
\[Z=R_{i}-S_{Gi}-S_{Qi}, \tag{22}\]  
where \(R_{i}\) is the resistance of the \(i\)-th beam; \(S_{Gi}\) is the load effect generated by the secondary dead load, which obeys normal distribution; and \(S_{Qi}\) is the load effect produced by vehicle load on the \(i\)-th beam.  
It is worth noting that the \(M_{a}\) in Equation (12) is equal to the sum of the largest vehicle load \(S_{Qi}\) and dead load \(S_{Gi}\). \(M_{a}\) in Equation (12) has a direct effect on the effective moment of inertia of reinforced concrete bridge after corrosion, and the effective bending moment of inertia also affects the lateral distribution of vehicle load. The LLD coefficient in turn  
Figure 1: The most unfavorable position and LLD influence line of Beam 1.  
affects \(M_{a}\) in Equation (12). Therefore, the iterative algorithm combined with the Monte Carlo method is used to calculate the reliability index of bridges in this paper.  
Figure 2 shows the reliability calculation method for the corroded reinforcement bridge combined with inspection data of concrete strength and concrete cover thickness, which takes into consideration the influence of reinforcement corrosion on vehicle load effect. The inspection results of concrete strength and concrete cover thickness should be obtained at first and taken into the computational procedure as inputs. The reliability assessment established in this work is based on the Monte Carlo method, and the iterative algorithm is also employed due to the interaction between the effective bending moment of inertia and the LLD coefficient. The allowable error and the parameters of the Monte Carlo method and the iterative algorithm should be determined at first. Using the inspection results, the initial time of reinforcement corrosion can be calculated by the reinforcement corrosion model. When the corrosion occurs, the reinforcement corrosion rate and degree can be computed. Then, we can calculate and obtain the moment of inertia and cracking moment with reinforcement corrosion. According to the above results, the LLD coefficient \(m_{0}\) of the first iteration is calculated by the modified eccentric compression method, which is used to compute the maximum bending moment \(M_{a}\). The effective bending moment of inertia \(I_{ce}\) of the corroded reinforcement bridge is obtained by Equation (12) to Equation (15). Therefore, the LLD coefficient can be recalculated based on \(I_{ce}\) and marked as \(m_{1}\). If the absolute difference between \(m_{0}\) and \(m_{1}\) is less than the allowable error, it demonstrates \(m_{1}\) is the actual value of the LLD coefficient of corroded reinforcement bridge. It will be recorded and used to compute the flexural bearing capacity reliability. When the absolute difference is greater than the allowable error, \(m_{1}\) is assigned to \(m_{0}\). \(M_{a}\) and \(I_{ce}\) will be recalculated until the absolute difference is less than the allowable error. When the termination condition of Monte Carlo method is met, it will terminate the algorithm and output the reliability index.  
Figure 2: Flow chart of reliability calculation.