## 6 Fatigue Assessment
In the local weld model which consists of a butt weld near the flange plate and a fillet weld near the web plate, five typical locations near the welds are selected, which are the lateral weld toe of the butt weld on the column (Location 1), upper weld toe of the butt weld on the column (Location 2), lower weld toe of the butt weld on the column (Location 3), the lateral weld toe of the fillet weld (Location 4) and the upper side of the fillet weld (Location 5), as shown in Figure 9. These locations are usually regarded as the dangerous locations where stress concentration exists. Based on the modified equivalent structural stress formulae and the master S-N curve stated above, the fatigue assessment of these five locations is carried out as follows. First, by area map and area operation technology involved in ANSYS, the integral parts in Equations (10) and (11) can be obtained and thus the membrane stress \(\sigma_{m3D}\) and bending stress \(\sigma_{b3D}\) can be calculated, which are variables related to time. According to Equation (12), the structural stress \(\sigma_{s3D}\) time-history can be obtained. Finally, the time-history of structural stress \(\sigma_{s3D}\) is converted to the time-history of the equivalent structural stress \(\Delta S_{e}\) according to Equation (13). Second, according to rain-flow counting method and Palmgren-Miner linear accumulating damage rule, the effective equivalent structural stress range \(\Delta S_{eq}\) which produces the same amount of fatigue damage during this 50 s time as the time-history of the equivalent structural stress \(\Delta S_{e}\) does is obtained according to Equation (19). The cycle number \(n_{50}\) during this 50 s time can also be obtaiend according to rain-flow counting method. As the formula of \(\Delta S_{eq}\) based on equivalent structural stress method is a little different from that based on hot spot stress method, the deduction procedure is detailed as follows. When undergoing varied amplitude loading, the accumulating damage is:  
\[D_{1}=\sum_{i=1}^{k}\frac{n_{i}}{N_{i}}=\sum_{i=1}^{k}\frac{n_{i}}{\sqrt[k]{ \frac{\Delta S_{e}}{\mathcal{C}}}} \tag{17}\]  
Figure 8: Master S-N curve. Figure 9: Five typical locations. where \(\Delta S_{ei}\) is the \(i\)-th equivalent structural stress range causing fatigue damage in the stress spectrum, \(n_{i}\) is the number of cycles under stress range \(\Delta S_{ei}\), and \(N_{i}\) is the number of failure cycles under the action of \(\Delta S_{ei}\). When undergoing constant amplitude loading, the accumulating damage is:  
\[D_{2}=\frac{\sum_{i=1}^{k}n_{i}}{N}=\frac{\sum_{i=1}^{k}n_{i}}{\sqrt[k]{\frac{ \Delta S_{ei}}{\mathbb{C}}}} \tag{18}\]  
To make these two equivalent, which means \(D_{1}=D_{2}\), the effective stress range based on equivalent structural stress method is calculated as:  
\[\Delta S_{eq}=C\cdot\left(\frac{\sum_{i=1}^{k}n_{i}}{\sum_{i=1}^{k}\frac{n_{i }}{\sqrt[k]{\frac{\Delta S_{ei}}{\mathbb{C}}}}}\right)^{h} \tag{19}\]  
Combined with the master S-N curve stated above, the number of failure cycles \(N_{eq}\) under the action of \(\Delta S_{eq}\) can be calculated by Equation (20) and the fatigue damage during this 50 s \(D_{50}\) is obtained by Equation (21):  
\[N_{eq}=\sqrt[k]{\frac{\Delta S_{eq}}{\mathbb{C}}} \tag{20}\]  
\[D_{50}=\frac{n_{50}}{N_{eq}} \tag{21}\]  
By extending it to the time of one year, the annual fatigue damage \(D_{annual}\) and fatigue life \(T\) of these six locations can be assessed by Equations (22) and (23):  
Figure 7:0  
Figure 7:1