This paper investigates the efficacy of the collar plate in improving the Local Joint Flexibility (LJF) of thin-walled circular hollow section (CHS) K-joints under axial loads. Initially, a finite element model (FEM) was created and verified against data from 14 available experimental tests. Subsequently, an extensive series of 136 unreinforced and reinforced K-joints was simulated to analyze the influence of parameters such as collar plate dimensions (η and λ), brace angle (θ), and joint geometry (β, ξ, and γ) on the LJF factor (fLJF) and the fLJF ratio (χ). The FEMs incorporated plate-to-member contact and weld modeling. Findings indicate that the utilization of the plate reduces the fLJF by 73 %. Additionally, it was observed that plate length significantly affects the fLJF compared to plate thickness. While the impact of γ, θ, and ξ on χ is marginal, β, η and λ emerge as a noteworthy determinant of χ. Despite the pivotal role of fLJF in joint behavior, there exists a gap in studies and equations specifically addressing fLJF in collar-plate reinforced K-joints under axial loads. To address this gap, leveraging the FE results, a design equation is proposed. This equation is subsequently validated with high coefficients of determination and standards set by the UK Department of Energy.