Based on a number of numerical investigations into welding simulations, highly non-linear welding-induced residual stresses within high strength S690 welded H-sections have been evaluated successfully, and surface residual stresses along their flange / web junctions have been carefully calibrated against measured data. This modelling technique has been extended to cover residual stresses of cold-formed circular hollow sections recently, and also of cold-formed square hollow sections as described in this paper. Hence, a full presentation on the proposed approach of integrated and coordinated numerical simulations on various mechanical, heat transfer and thermomechanical, and stresses analyses on these cold-formed square hollow sections is described. Subsequent structural analyses of these models on both stocky and slender columns of these cold-formed square hollow sections are then carried out. Structural adequacy of the proposed approach is thoroughly demonstrated through a systematic calibration against various measured data – both temperatures and residual stresses of these sections induced during fabrication, and load-deformation curves of these sections under compression. It should be noted that the proposed approach provides a scientific mechanism to determine directly residual stresses due to transverse bending and longitudinal welding as initial materials imperfections in these high strength S690 cold-formed square hollow sections. With an adoption of the lowest eigenmodes of these columns as their initial geometric imperfections after adjusted with measured or design values of the member out-of-straightness, both the effects of initial materials and of initial geometric imperfections onto the structural performance of these columns are readily quantified separately.