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This paper presents the results of a large parametric study concerning the evaluation of the critical local buckling coefficient for thin-walled rectangular hollow section (RHS) members subjected to combined axial load and biaxial bending, accounting for web-flange interaction. The calculation of the half-wavelength leading to the minimum critical local bifurcation load is performed by means of a Generalized Beam Theory specialization, which makes it possible to quickly solve a large set of cases. In particular, taking advantage of the small half-wavelength of local buckling, it is assumed that the stresses are uniformly distributed along the member length, making it possible to resort to semi-analytical solutions using sinusoidal half-wave amplitude functions for the GBT cross-section deformation modes. On the basis of the results obtained, the key parameters governing local buckling are identified, leading to easy-to-use charts and closed-form formulae to determine the local buckling coefficient. [ABSTRACT FROM AUTHOR]