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Recent rapid advances in mesh-insensitive structural stress procedures are summarized in this report. In addition to their effectiveness in reliably calculating structural stresses for both simple weld details and complex structures, the mesh-insensitive structural stress procedure provides an effective mean for drastically simplifying stress intensity factor solutions for welded joints, by extending the structural stress definition for characterizing notch effects at welds. The results achieved so far and significant implications are summarized below: (1) The mesh-insensitive structural stresses can be consistently related to fatigue behavior in welded joints and the calculation methods can be readily implemented as processing procedures (2) As a stress based transformation process, the mesh-insensitive structural stress methods map complex 3D geometry and loading mode to a simple strip geometry subjected to a simple structural stress state.