## 2 Comparative Fatigue Tests of Rib-to-Deck Joints  
A series of fatigue tests have been carried out to investigate the fatigue strength of RD joints in OSD with TEUs [13; 14]. A total of eleven specimens have been tested using the cyclic loads, including five CU specimens and six TEU specimens. Figure 1a shows the sectional view of the two types of specimen. Among the specimens, three CU specimens and four TEU specimens are tested with the central loading [13], as shown in Figure 1b. Further, the eccentric loading has been applied to two CU specimens and two TEU specimens [14], as shown in Figure 1c. The specimens are fabricated with the structural steel Q345 qD [28] under the same welding process. As a common practice, each specimen consists of an 8 mm-thick U-rib and a 16 mm-thick deck plate, connected by the one-sided welding. As shown in Figure 1a, part of the rib wall (i.e., 2 mm) is left unwelded in order to avoid the weld-melt-through, which is harmful to the fatigue strength of joints. Compared with the CU specimens, the penetrated depth of the rib wall is increased from 6 mm to 10 mm (i.e., around 67%) in the TEU specimens. As a result, the weld leg length on the deck side is increased from 11 mm to 15 mm. Meanwhile, a smooth transition is achieved near the welding joint in TEU specimens, which could further reduce the local stress concentration in the joint. The specimens are supported on a testing platform with bearing rubber plates to allow for rotation displacement. Constant amplitude loads have been applied by the actuator located at the centre of the specimen, as shown in Figure 1b. Dye penetration (DP) checks have been conducted to detect the crack during loading. In all the specimens, the same cracking pattern has been observed: the crack first initiates at the deck toe near the end and then propagates along both the length and thickness of the deck plate. Figure 2 shows the typical cracking pattern of the RD joint, including the result of  
Figure 1: Fatigue test of rib-to-deck specimens: (**a**) Sectional view (Unit: mm); (**b**) Test set-up of central loading; (**c**) Test set-up of eccentric loading. DP checks during loading and the macro-section cut after the test. Since the crack occurs at the weld toe on the deck side in all the eleven specimens tested, the following investigation has been mainly focused on the deck toe-failure. Meanwhile, the \"thickness penetration\" criterion is employed to define the failure of the specimens: once the fatigue crack could be identified from both the top and bottom surfaces of the deck plate, the crack is regarded as a penetrated crack and failure of the specimen is achieved. Correspondingly, the number of loading cycles at the time is considered as fatigue life. The stress range measured near the deck toe is taken as the fatigue strength since it is the initiation point of cracks. The fatigue strength of the specimens is expressed in terms of the nominal stress approach and the hot spot stress approach, respectively [29; 30]. Due to the physical limitation on the size of strain gauges, the \"0515\" rule suggested by [PERSON] et al. [30] has been applied to determine the hot spot stress. In another words, the hot spot stress is determined through linear extrapolation based on the two reference points, which are 0.5\(t\) and 1.5\(t\) (where the parameter \(t\) is the plate thickness) away from the weld toe line, respectively. Generally, the design of stress-life curves are derived under a specified survival probability and then used in the fatigue evaluation, in dealing with the variation in fatigue strength. As a result, the conservative result can be expected at the given survival rate. In this study, the design curves have been derived though the regression analysis based on the stress-life model shown in Equation (1):  
\[log\ N=log\ C-m\cdot log\ \Delta\sigma \tag{1}\]  
where \(N\) is number of the failure cycles; \(C\) and \(m\) are the material constant and power index; \(\Delta\sigma\) is the applied stress range.