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The notch stress intensity factor (NSIF) based analytical frame is applied to the slit tips (or weld roots) of welded joints with inclusion of the T-stress component. This T-stress can be determined from FE models evaluating the ligament stresses close to the pointed slit tip. An alternative analytical frame is presented for the corresponding keyhole notches based on analytical solutions from the literature, which are applied to the ligament stresses.\ud \ud In the slit tip models, the mean local strain energy density (SED) with inclusion of the T-stress effect is determined analytically and numerically in comparison, using two different fatigue-relevant control radii, R(0) = 0.28 mm and R(0) = 0.15 mm, the former value well proven for thick-sheet welded joints made of structural steel. The latter smaller value is tentatively proposed for thin-sheet welded joints, in the direction suggested in the recent literature where a reduction of the microstructural support length for laser beam welds and resistance spot welds is recommended. The FEM-based and analytical stress concentration factors (SCF) for the lap joint keyhole model and also the SED values for the corresponding pointed slit tips are found to be in good agreement. The J-integral consisting of the first and second component (the latter containing the T-stress) is compared with the corresponding SED values