## 8 Discussion
### Results Compared with Nominal Stress Method  
As most fatigue assessment in the field of civil engineering is based on nominal stress, it is necessary to compare the results obtained by nominal stress and equivalent structural stress so that the advantage and disadvantage can be concluded. In nominal stress assessment, the multi-scale FE model is replaced by a global one, as shown in Figure 15, where beams and columns are completely simulated by element BEAM188 and the local model with element SOLID45 is no longer necessary. It is no doubt that analysis using this global model costs far less computing resources and time, at a cost of the confusion of selecting the proper S-N curve and inability of considering the local concentration. According to the IIW Recommendations [15], as there are so many curves involved during the selection of a desirable S-N curve, it seems that only approximate welded joint detail can be found. Finally, FAT36 curve is found to be the most proper S-N curve, which is described in Table 6 and shown as Equation (28) and illustrated in Figure 16.  
\[\Delta\sigma_{nom}{}^{m^{\prime}}N_{nom}=C_{nom} \tag{28}\]  
where \(\Delta\sigma_{nom}\) is the nominal stress range, \(N_{nom}\) is the number of failure cycles under the action of stress range \(\Delta\sigma_{nom}\), \(C_{nom}\) is a constant and \(m^{\prime}\) is the negative reciprocal of S-N curve slope in double logarithmic coordinates, which can be found in Table 7.  
Figure 14: Comparison results of two methods: (**a**) Annual damage; and (**b**) Fatigue life. Based on FAT36 curve, the nominal stress can be determined by elementary theories of structural mechanics based on linear-elastic behavior. Nominal stress \(\sigma_{nom}\) is the average stress in the plate at weld toe of the structural detail, which can be defined as:  
\[\sigma_{nom}=\frac{N}{A}+\frac{M_{x}}{I_{x}}+\frac{M_{y}}{I_{y}} \tag{29}\]  
where \(N\) is the axial force, \(A\) is the section area of the plate, \(M_{x}\) and \(M_{y}\) are the moment in the two mutually perpendicular directions on the plate section, and \(I_{x}\) and \(I_{y}\) are the inertia moment of the \begin{table}
\begin{tabular}{c c c} \hline
**FAT36 Curve** & **Description** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Description of FAT36 curve. Figure 16: FAT36 curve. Figure 15: Global FE model. plate section. These parameters, which are all time series, can be obtained through the global FE model. With the same wind time series utilized, time history analysis is performed. The rain-flow counting method and Palmgren-Miner linear accumulating damage rule are utilized once again to convert the varied amplitude range to an effective range, which is shown as Equation (30), and cycle number \(n_{50 nom}\) during this 50 s can be obtained:  
\[\Delta\sigma_{nom}=\left[\frac{\sum_{i=1}^{k}{n_{i}^{\prime}(\Delta\sigma_{nom })}^{m^{\prime}}}{N_{apnom}}\right]^{1/m^{\prime}} \tag{30}\]  
where \(N_{apnom}\) is the cycle number during this 50 s, \(\Delta\sigma_{nom}\) is the \(i\)-th nominal stress range causing fatigue damage in the stress spectrum, and \({n_{i}}^{\prime}\) is the number of cycles under stress range \(\Delta\sigma_{nom}\). Based on the effective nominal stress range \(\Delta\sigma_{nom}\), the number of failure cycles \(N_{nom}\) under the action of \(\Delta\sigma_{nom}\) can be calculated by Equation (28) and the fatigue damage during this 50 s can be obtained by Equation (21). Thus, the annual fatigue damage \(D_{annualnom}\) and fatigue life \(T_{nom}\) can be calculated according to Equations (22) and (23) and the results are shown in Table 8.  
According to Table 8, it can be found that the result obtained by nominal stress varies greatly from and falls in between the results based on equivalent structural stress method of different locations of the weld.