## 8 Discussion
### Results Compared with Hot Spot Stress Method  
As hot spot stress theory has been widely used in fatigue assessment in the field of civil engineering and proven to be quite reliable. It is necessary to compare the results obtained by hot spot stress method and equivalent structural stress method so that the results obtained by equivalent structural stress can be verified. The hot spot stress represents the structural stress at the hot spot, which includes all stress raising effects of a structural detail and excludes all stress concentrations due to the local weld profile itself. There are mainly two types of hot spot and they can be defined as Type a, which is hot spot stress transverse to weld toe on plate surface, and Type b, which is hot spot stress transverse to weld toe at plate edge, as illustrated in Figure 12.  
When hot spot stress is used to calculate the structural stress, a surface stress extrapolation can be defined. For Type a hot spot, a linear extrapolation is adopted, where the hot spot stress \(\sigma_{\text{hsa}}\) can be calculated according to the stress of two reference points which are located 0.4\(t\) and 1.0\(t\) away from the hot spot (\(\sigma_{x_{1}},\ \sigma_{x_{2}}\)), where \(t\) is the thickness of the adjacent plate, as defined in Equation (24):  
\[\sigma_{\text{hsa}}=1.67\sigma_{x_{1}}-0.67\sigma_{x_{2}} \tag{24}\]  
For Type b hot spot, a linear extrapolation of three reference points is adopted, where the hot spot stress \(\sigma_{\text{hsb}}\) can be calculated according to the stress of three reference points which are located 4 mm, 8 mm and 12 mm away from the hot spot (\(\sigma_{x_{1}}^{\prime},\ \sigma_{x_{2}}^{\prime},\ \sigma_{x_{3}}^{\prime}\)), as defined in Equation (25):  
\[\sigma_{\text{hsb}}=3{\sigma_{x_{1}}}^{\prime}-3{\sigma_{x_{2}}}^{\prime}+{ \sigma_{x_{3}}}^{\prime} \tag{25}\]  
According to the IIW Recommendations [15], FAT90 curve is found to be the most proper S-N curve, which is shown as Equation (26) and illustrated in Figure 13.  
\[\Delta{\sigma_{hs}}^{m^{\prime}}N_{hs}=C_{hs} \tag{26}\]  
where \(\Delta{\sigma_{hs}}\) is the hot spot stress range, \(N_{hs}\) is the number of failure cycles under the action of stress range \(\Delta{\sigma_{hs}}\), \(C_{hs}\) 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 4.  
Figure 12: Two types of hot spot. After the time-history analysis is conducted and the hot spot stress is obtained as the procedure above, 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 (27). The cycle number \(n_{50 hs}\) during this 50 s can also be obtained. \[\Delta\sigma_{e}=\left[\frac{\sum_{i=1}^{k}{n_{i}^{\prime}(\Delta\sigma_{hsi})^ {m^{\prime}}}}{N_{eabs}}\right]^{1/\alpha^{\prime}} \tag{27}\]  
where \(N_{eabs}\) is the cycle number during this 50 s, \(\Delta\sigma_{hsi}\) is the \(i\)-th hot spot stress range causing fatigue damage in the stress spectrum, and \({n_{i}^{\prime}}\) is the number of cycles under stress range \(\Delta\sigma_{hsi}\). Based on the effective hot spot stress range \(\Delta\sigma_{e}\), the number of failure cycles \(N_{hs}\) under the action of \(\Delta\sigma_{hs}\) can be calculated by Equation (26) and the fatigue damage during this 50 s can be obtained by Equation (21). Thus, the annual fatigue damage and fatigue life can be calculated according to Equations (22) and (23) and the results are shown in Table 5. As can be concluded from the results obtained by equivalent structural stress method above, the fatigue life of the fillet weld connecting the web plate and the column is much longer than that of the butt weld connecting the upper beam flange plate and column, so, for simplicity, only the three locations near the butt weld connecting the upper beam flange plate and column are calculated in hot spot stress method.