# Fatigue Reliability Analysis of Rib-To-Deck Joints Using Test Data and In-Situ Measurements
## 4 In-Situ Measurement-Based Fatigue Reliability Analysis
### Derivation of Stress Spectra Using In-Situ Measurement  
An OSD bridge in Chengdu, China was selected as the prototype for the further analysis of fatigue reliability. The prototype bridge consists of a 68 m-long main span and two 45 m-long side spans, which is a typical layout for urban steel bridges in China. The OSD system had been used in the bridge, carrying a fast lane, a middle lane and a slow lane. The sectional view of the prototype bridge is shown in Figure 10. Two critical details have been selected for the analysis, which are close to the frequent footprint of vehicles. In order to consider the uncertainty in vehicles passing through the bridge, the stochastic traffic model proposed in [27] was applied in deriving the stress spectra of the chosen details. The model consists of both the vehicle model including the vehicle-related properties and the lateral distribution of vehicles, which are described as random variables. Table 4 briefly illustrates the framework of the stochastic traffic model, and details could be found in [27]. In the vehicle model, the property is modelled by random variables using the in-situ measurement in [40; 41]. According to the measurement, the vehicles can be divided into six different categories based on configuration, as briefly shown in Figure 11. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Property** & **Description** \\ \hline \multirow{4}{*}{Vehicle model} & Axle number & The number of axles in a vehicle \\  & Axle spacing & The distance between the center of axles \\ \cline{1-1}  & Axle weight & The weight of each axle in a vehicle \\ \cline{1-1}  & Axle track & The distance between wheels in the same axle \\ \cline{1-1}  & Footprint & The contact area of wheels on the deck \\ \hline \multirow{2}{*}{Lateral distribution} & Occupancy rate & The distribution of the vehicle in different lanes \\ \cline{1-1}  & In-lane position & The lateral position of the vehicle within a lane \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Illustration of the stochastic traffic model [27]. Figure 10: Sectional view of the prototype bridge. Apart from the vehicle model, the occupancy rate in the lateral distribution can be also determined after the in-situ measurement shown in Figure 11. Besides, the distribution of the vehicle centre suggested in Eurocode 1 [42] has been used for the in-lane position. A multi-scale finite element (FE) model of the prototype bridge was established using ANASYS software [43] to calculate the stress spectra of the chosen critical details, as shown in Figure 12. The FE model was established with the 3-dimensional shell element SHLL93 [44], including the global model of the entire bridge, the sub-model of the interested segment, and the local refined model of the critical details. In the global model, relatively coarse meshing was used to balance accuracy and efficiency since its task is to simulate the boundary condition of the interested segment. Compared with the global model, a much more refined meshing was applied to the sub-model, which serves as a transition between the coarse global model and the highly refined local meshing of the critical details. It is worth stating that the multi-point-constrain (MPC) method [45] was used to connect the global model and sub-model, through which the influence of difference on meshing size can be minimized. In the sub-model, the highly refined meshing (with the minimum size of 2 mm) was employed near the critical details to ensure the accuracy of stress results. Figure 11: Vehicle category and occupancy rate [41]. Figure 12: Multi-scale finite element model of the prototype bridge. In the FE model, all the shell elements are arranged in the middle plane, as suggested by [PERSON] [36]. In solving the hot spot stress, the extrapolation method and reference points were kept the same as in the fatigue test, i.e., the \"0515\" rule. Since the local bending has influence mainly on the local nonlinear stress peak rather than the structural hot spot stress, the welds were not explicitly modelled.