## 2 Equivalent Structural Stress Method  
The equivalent structural stress method was first proposed by [PERSON] [9], who defined the structural stress \((\sigma_{s})\) to be the superposition of a membrane component \((\sigma_{m})\) and a bending component \((\sigma_{b})\):  
\[\sigma_{s}=\sigma_{m}+\sigma_{b} \tag{1}\]  
A typical T-filtel weld toe is illustrated in Figure 1, the stress distribution through the thickness at the weld toe is assumed to be monotonic with the peak stress occurring at the weld toe. Two reference sections are defined, Section A-A, where the normal structural stress \((\sigma_{s})\) is defined at the weld toe, and Section B-B, where a row of elements with same length of \(\delta\) which represents the distance between Sections A-A and B-B at the weld toe can be used in the FE model so both local normal stress \(\sigma_{x}(y)\) and shear stress \(\tau_{xy}(y)\) can be directly obtained from a FE solution. The plate thickness is \(t\) and the transverse shear of the structural stress components is ignored. The local coordinate is established as in Figure 1. By imposing equilibrium conditions that the force balances in \(x\) direction evaluated along B-B and moment balances in Section A-A at \(y=0\) between Sections A-A and B-B, the structural stress components \(\sigma_{m}\) and \(\sigma_{b}\) must satisfy the following conditions:  
\[\sigma_{m}=\frac{1}{t}\int_{0}^{t}\sigma_{x}(y)dy \tag{2}\]  
\[\sigma_{m}.\frac{t^{2}}{2}+\sigma_{b}.\frac{t^{2}}{6}=\int_{0}^{t}\sigma_{x}( y)ydy+\delta\int_{0}^{t}\tau_{xy}(y)dy \tag{3}\]It is clear that if element size (\(\delta\)) is small or transverse, shear, which is one of the integral terms on the right-hand side of Equation (3), is negligible, and the integral representations of \(\sigma_{b}\) and \(\sigma_{m}\) in Equations (2) and (3) can be directly evaluated at Section A-A in Figure 1.  
In hot spot stress or other local stress analysis, the stress values within some distance from the weld toe can change significantly with the changing meshing style while in the equivalent structural stress analysis the stress deduced from elementary structural mechanics theory will be less affected by the meshing style, so the first advantage of mesh-insensitive is achieved. By the effects of stress concentration, thickness of plates and loading on the fatigue life of welds being considered, and based on thousands of fatigue test data, the welded joint fatigue S-N curves based on the nominal stress are compressed into a single master S-N curve based on the equivalent structural stress which can be deduced from the structural stress \(\sigma_{s}\) above. As a result, the second advantage of unifying different curves is realized.  
This method has been applied to fatigue assessment of several types of welded joints including butt welds, fillet welds and spot welds and good correlation is proven [10; 11]. Later, [PERSON] extended this method to medium and low cycle fatigue assessment, by defining a structural strain parameter [12]. However, the appliance of this method to real three-dimensional complex structure is still tricky because, in three-dimensional circumstances, the formulae are a little different from Equations (2) and (3) and need modification. Besides, in a large scale structure, acquiring detailed stress time-history near welds needs multi-scale modeling technique, which is not an easy task.