# Fatigue Reliability Analysis of Rib-To-Deck Joints Using Test Data and In-Situ Measurements
## 2 Fatigue Tests of Rib-To-Deck Joints
### Test Setup  
The specimen is simply supported on a testing platform, with the actuator on the longitudinal center of the left joint, as shown in Figure 3a,b. In order to distribute the applied load and reacting force, rubber plates are installed between the loading actuator, specimen and supporting platform. Besides, a pressure-sensitive film is installed between the specimen and actuator, as shown in Figure 3b, to verify the uniformity of loading distribution. A coordinate system is introduced to illustrate the position of the actuator, shown in Figure 3a, with the origin at the left-front corner of the deck. Under the system, the coordinate of the center of the actuator is (455 mm, 300 mm). The specimens were cyclically loaded with the constant amplitude loads, using the hydraulic test device MTS system [34]. The loading frequency was set as 3.25 Hz, which is acceptable for the fatigue test of large civil structures. Various levels of cyclic loads were applied on the different specimens, to obtain stress-life (S-N) data under a wide range of stress levels. Meanwhile, the ratio of the maximum to the minimum loads was kept the same as the value in the previous test [18,19], i.e., 3.0. Table 1 summarizes the cyclic loads applied on each specimen. According to the test result of similar specimens in [10], fatigue cracking is highly expected to initiate at the deck-side weld toe at two potential cracking sites shown in Figure 3a. Based on this assumption, the stress gauge was set with special emphasis on the weld toe at the deck side, as shown in Figure 4.  
Both the nominal stress and hot spot stress were considered in the measurement. The hot spot stress is calculated by the extrapolation with the \"0515\" rule suggested by IIW [35], as shown in Equation (1). \[\sigma_{hs}=1.5\sigma_{0.5t}-0.5\sigma_{1.5t} \tag{1}\]  
where \(t\) stands for the thickness of the plate under consideration, i.e., the deck plate in this study; \(\sigma_{hs}\) is the hot spot stress; \(\sigma_{0.5t}\) and \(\sigma_{1.5t}\) are, respectively, the stress measured at the distance of 0.5 and 1.5 t away from the deck toe, i.e., D8-X and D24-X in this study. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**CODE** & **Maximum Load** & **Minimum Load** & **Range of Loads** \\ \hline CU6 & 15 & 50 & 35 \\ CU7 & 15 & 50 & 35 \\ TEU7 & 15 & 50 & 35 \\ TEU8 & 18 & 60 & 42 \\ TEU9 & 19 & 65 & 46 \\ TEU10 & 19 & 65 & 46 \\ TEU11 & 22 & 74 & 52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cyclic loads applied on each specimen (kN). Figure 3: Test setup: (**a**) schematic view and (**b**) photography. As per the rule, two reference points are used in calculating the hot spot stress, whose distances to the weld toe are 8 mm (named as D8-1 to D8-16) and 24 mm (named as D24-1 to D24-16), respectively. Since the cracking in the RD joint would result in strain drops in nearby gauges, the dynamic strain monitored during loading could be utilized to reflect the development of fatigue cracks [18]. Thus, additional dynamic gauges are deployed, which are named as D-1 to D-21. Due to the difference in the weld leg length between the CU specimen and TEU specimen, the distance between the strain gauges and loading point will be different. Since the mid-plane width of the two types of U-ribs is the same, it can be calculated from Figure 2b that the distance from the weld toe to the loading point in TEU specimens is 2 mm longer than that in CU specimens. Meanwhile, it can be determined from Figures 1 and 3 and the coordinate of the loading point that the distance from the weld toe to the loading point is 119 and 121 mm in the CU and TEU specimens, respectively. For the first-row reference gauges, which are 8 mm away from the weld toe, the distance between the loading point and gauges is, respectively, 127 mm and 129 mm in the two types of specimens, i.e., a difference of less than 1.6%. In the case of the second-row reference gauges, which are 24 mm away from the weld toe, the difference is no more than 1.4%.