This paper reports a parametric stress analysis of various configurations of rack plate stiffened multi-planar welded KK joints using the finite element method. The KK joint finds application in the leg structure of offshore oil and gas jack-up platforms. The rack plate works as a stiffener which reduces the stress concentration at the brace/chord intersection. This could be an immense contribution to the increase in fatigue life of the joint, but other hot spot sites are introduced into the joint. The rack is also used for raising and lowering of the jack-up hull which gives the jack-up platform its jacking capability. Over 120 models using a combination of shell and solid elements have been built and analysed with ABAQUS. Non-dimensional joint geometric parameters (b, c and X) are employed in the study, with the new parameter X being defined as the ratio of rack thickness to chord diameter. Stress concentration factors (SCFs) are calculated under applied axial and OPB (out-of-plane bending) loading. Three critical SCF locations are identified for each load case, with each location becoming the most critical based on the combination of the nondimensional parameters selected for the joint. This is important as careful design can shift the critical SCF from an area inaccessible to NDT to one that can be easily inspected. The SCF values extracted from the models are used to derive six parametric equations through multiple regression analysis performed using MINITAB. The equations describe the SCF at the different locations as a function of the non-dimensional ratios. The equations not only allow the rapid optimisation of multi-planar joints but also can be used to quickly identify the location of maximum stress concentration and hence the likely position of fatigue cracks. This in itself is an invaluable tool for planning NDT procedures and schedules.