# Fatigue Reliability Analysis of Rib-To-Deck Joints Using Test Data and In-Situ Measurements
## 2 Fatigue Tests of Rib-To-Deck Joints
### Test Result  
In all the tested specimens, the fatigue crack first initiates at the weld toe on the deck side, and then propagates along both the thickness and length of the deck plate, as shown in Figure 5. In the test, the failure of specimens is assumed when the fatigue crack penetrates through the thickness of the deck plate. After that, the test will be terminated, and the number of the loading cycles applied is taken as the fatigue life.  
Figure 4: Strain gauges installed on specimens.  
As aforementioned, dynamic gauges have been applied to monitor strain drops near the crack, which can in turn reflect the development of fatigue cracks during loading. Figure 6 shows the strain drops in the dynamic gauges installed on specimen TEU-10.  
The result indicated that two fatigue cracks were initiated at the two deck toes which were about 70 to 80 mm away from the center of actuator. With the increase in loading cycles, the two cracks propagated along both the depth and length of the deck plate. It can be found that the cracking pattern measured by the gauges is highly consistent with the visual observation. At the same time, the strain drops at the two crack-initiate sites, i.e., D-4 and D-18, are illustrated in detail in Figure 7. The strain drops of 10% can be observed after about \(1.2\times 10^{6}\) cycles in D-4 and \(1.43\times 10^{6}\) cycles in D-18, respectively. After that, the strain gradually drops with the loading cycles, from almost 170 MPa to about 30 MPa. It is interesting to note that, the strain drops in D-18 a bit later than in D-4. However, the value in D-18 meet that in D-4 after \(1.55\times 10^{6}\) cycles and then surpasses, since the slope of strain drops is increasing in D-18 while almost unchanged in D-4.  
Figure 5: Typical fatigue cracking pattern of tested specimens.  
Figure 6: Strain drops measured in TEU-10.  
Figure 7: Stress ranges measured at the two crack-initiate sites in TEU-10.  
In the tests, different cyclic loads have been applied on the different specimens. For comparison purposes, the measured stress-life data have been unified to the equivalent fatigue strength under the same equivalent fatigue life [36], as shown in Equation (2).  
\[\Delta\sigma_{\text{epp}}=\left(\frac{N_{\text{test}}}{N_{\text{app}}}\right)^{ \frac{1}{m}}\cdot\Delta\sigma_{\text{test}} \tag{2}\]  
where \(\Delta\sigma_{\text{app}}\) stands for the equivalent fatigue; \(\Delta\sigma_{\text{test}}\) and \(N_{\text{test}}\) are the measured stress range and corresponding failure cycles; \(N_{\text{app}}\) is the equivalent fatigue life, set as \(2\times 10^{6}\) cycles in this study; \(m\) is the material-related power index, assumed to be 3 as a common practice.  
Based on the above analysis, the stress-life data are summarized in Table 2, accompanied by the data of 11 specimens previously tested [10; 18].  
The test result suggests that the fatigue strength is relatively higher in the TEU specimens than in the CU specimens, indicating the effectiveness of TEUs in enhancing the fatigue performance of rib-to-deck joints. In terms of nominal stress, the average value of equivalent fatigue strength is 125 MPa in TEU specimens, i.e., 21.4% higher than the strength of 103 MPa in the CU specimens. In the case of hot spot stress, the average strength of TEU specimens and CU specimens is respectively 155 and 128 MPa, i.e., an enhancement of 21.1%. Meanwhile, it is also worth noting that the standard deviation of the two types of specimens are similar, which is slightly higher in TEU specimens. Due to the random nature in fatigue strength, the higher deviation can be attributed to the larger number of the tested TEU specimens.