# Fatigue Reliability Analysis of Rib-To-Deck Joints Using Test Data and In-Situ Measurements
## 4 In-Situ Measurement-Based Fatigue Reliability Analysis
### Result and Discussion  
Through the numerical approach illustrated in Section 4.2, the stress spectra of the two critical details were derived using in-situ measurement data. Figure 14a,b, respectively, shows the stress spectra of the two critical details D1 and D2 in terms of nominal stress. In both the spectra, the low-level stress range accounts for the largest portion. It is worth noting that the two details are in different lanes, while their stress spectra are highly similar. However, the similarity can be attributed to the almost same proportion of heavy trucks in the slow lane and middle lane. As shown in Figure 11, the occupancy rate is highly comparable in the two lanes for all the vehicle types except type V1, which represents lightweight vehicles. As generally acknowledged, lightweight vehicles have a very minor effect on the fatigue life of welded joints, even if their proportion are usually high in all the vehicles types. Meanwhile, after carefully checking the stress ranges from 5 to 30 MPa, it can be found that the stress ranges in the spectra of D2 are slightly higher than that of D1. Figure 13: Procedures for stress spectra derivation. Also, the stress spectra of the two details were derived in terms of hot spot stress, as shown in Figure 15a,b. Overall, the distribution and difference in the two types of spectra are almost the same as that in Figure 14a,b. However, the stress ranges in terms of hot spot stress are more continuous and even distributed than in terms of nominal stress. The result indicates that the hot spot stress-based spectra are able to reflect the randomness in vehicles more thoroughly than the nominal stress-based approach, through which a better accuracy can be expected for the prediction on fatigue life. Through incorporating the above stress spectra into the calculation method in Section 4.1, the fatigue reliability of the two critical details can solved. It is worth stating that the average daily traffic (ADT) is determined by the measurement data in [41], i.e., 5302 vehicles per direction per day. Besides, a design service life of 100 years is usually recommended for bridge structures [20; 22]. However, for some vital structures such as the Hong Kong-Zhuhai-Macao bridge, an extended design life of 120 years can be applied [47]. To this end, the design lifespan of 120 years has been used in the reliability analysis. Based on the above analysis, the fatigue reliability can be solved for the two critical details in the OSD using CUs and OSD using TEUs. Figure 16a,b illustrates the reliability solved in terms of nominal stress, relating to the critical details D1 and D2, respectively. Figure 14: Stress spectra in terms of nominal stress: (**a**) critical detail D1 and (**b**) critical detail D2. Figure 15: Stress spectra in terms of hot spot stress: (**a**) critical detail D1 and (**b**) critical detail D2. As suggested by JCSS [48], the target reliability of 2.3 and 1.3 can be used for service limit checks when the efforts for enhancement are low and high, respectively. Thus, prediction can be made on the fatigue life using the two values above as the upper limit and lower limit of target reliability. It is worth stating that the target of 2.3 can be treated as a warning sign that inspection is required when the reliability is below 2.3, while the target of 1.3 can serve as a criterion for the fatigue life prediction. According to the result, in the OSD using CUs, the fatigue reliability of D1 reaches the upper limit after 67 years but stays above the lower limit up to the end. Meanwhile, the fatigue reliability of D2 reduces to the upper limit after 56 years and then the lower limit after 104 years. The result means that the design fatigue life of D2 is estimated as 104 years in terms of nominal stress. By contrast, in the OSD using TEUs, the fatigue reliability of both the two details is well above the upper limit line. The comparison suggests the fatigue life of rib-to-deck joints can be notably improved through the application of TEUs in OSDs.