# Fatigue Performance of Different Rib-To-Deck Connections Using Traction Structural Stress Method
## 2 Validation of the Numerical Simulation Method  
### Traction Structural Stress Method  
Traditional evaluation methods using the nominal stress method were applied for the fatigue life prediction of the welded components for a long time. The prediction results were usually conservative because the stress concentration effect of welded components was not considered. In the tradition numerical studies, the hot spot stress of the interested zone of the structure was mesh-size sensitive based on the extrapolation method of the stress. Furthermore, the notched stress of the weld toe of the weld seam was determined based the size of the notch. In order to overcome the limitations of the traditional analysis methods of the weld seam, traction structural stress method was proposed by [PERSON] [17; 18; 19] based on the fracture structure mechanism and Paris Law. The method was proved to be mesh-size insensitive and accurate for the fatigue performance prediction by comparing the fatigue test results from this method with the traditional methods. The proposed method [17; 18; 19] explained the crack initiation and propagation direction accurately. Later, the method was applied to predict the fatigue life of coastal pipes and pressure vessels. The inner stress of the weld toe along the direction of the thickness was divided into the normal stress, \(\sigma_{x}(y)\), and shear stress in plane, \(\tau_{xy}(y)\), as shown in Figure 1. Based the equilibrium conditions of forces and moments, the normal stress was simply divided into the membrane stress, \(\sigma_{m}\), and bending stress, \(\sigma_{b}\). The in-plane shear stress was simplified as the vertical shear stress, \(\tau_{m}\). However, the effect of the shear stress was generally ignored as it would have little influence on the propagation of the fatigue cracks. The traction structural stress was defined as the sum of the membrane stress \(\sigma_{m}\) and bending stress \(\sigma_{b}\), as in Equations (1)-(3). The nodal forces and moments of the nodes of the weld seam and weld elements can be obtained, as shown in Figure 2.  
\[\sigma_{m}=\frac{1}{t}\sum_{i=1}^{n}F_{i} \tag{1}\]  
\[\sigma_{b}=\frac{6}{t^{2}}\sum_{i=1}^{n}F_{i}\times(y_{i}-t/2) \tag{2}\]  
\[\sigma_{s}=\sigma_{m}+\sigma_{b} \tag{3}\]The propagation of a fatigue crack considered both short and long cracks. The relative crack length was represented with the combination of short cracks and long cracks using the united Paris Law. The stress intensity factor \(K\) in Equation (4) represented the stress intensity of fatigue tip and was calculated as in Equation (4). The equivalent structural stress range could be calculated using Equation (5) by considering the effect of the thickness, \(t\), the ratio of bending stress to traction structural stress, \(r\), and the traction structural stress range, \(\Delta\sigma_{y}\). Besides, the equivalent structural stress range, \(\Delta S_{s}\), versus fatigue cyclic life \(N\), namely the master \(S\)-\(N\) curve, was determined by considering the parameter \(C_{d}\), \(h\) and \(m\) based on the data analysis of the fatigue test results as shown in Equation (6). The parameter \(r\) stands for the ratio of the bending structural stress to the structural stress. \(I(r)\) is the parameter of loading mode and the thickness of base metal and can be calculated as shown in Equation (7). \[da/dN=C\dot{M}_{kn}^{n}\Delta K_{n}^{m} \tag{4}\]  
\[\Delta S_{s}\frac{\Delta\sigma_{s}}{t^{(2-m)/2m}.I(r)^{1/m}} \tag{5}\]  
\[N=\left(\Delta S_{s}/C_{d}\right)^{1/h} \tag{6}\]  
\[I(r)^{\frac{1}{h}}=2.155r^{6}-5.04r^{5}+4.80r^{4}-2.07r^{3}+0.56r^{2}+0.01r+1. 543 \tag{7}\]  
The master \(S\)-\(N\) curve method was applied for the fatigue behavior prediction of various types of welded structures with the only one curve. The effect of stress concentration on the zone of interest, the thickness of base metal and various loading modes were considered in the master \(S\)-\(N\) curve.