A recently developed variational model that describes the nonlinear interaction between the global and local buckling of a thin-walled I-section strut under pure compression is extended to include semi-rigid flange--web connections. A formulation combining the Rayleigh--Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Cellular buckling, observed in the case where the web is assumed to provide no more than a simple support to the flanges, is found to be rapidly eroded by increasing the connection rigidity, although the local buckling wavelength still reduces as the post-buckling deformation is increased. The model is validated using finite element analysis; the results compare very well particularly when a high rigidity between the section web and flanges is simulated.