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Composite steel-concrete structures experience non-linear effects which arise from both instability-related geometric non-linearity and from material non-linearity in all of their component members. This paper therefore presents a numerical procedure capable of addressing geometric and material non-linearities at the strength limit state based on the refined plastic hinge method. The refined plastic hinge approach models the elasto-gradual-plastic material non-linearity with strain-hardening under the interaction of bending and axial actions. This produces a benign method for a beam–column composite element under general loading cases. Another main feature of this paper is that, for members containing a point of contraflexure, its location is determined and a node is then located at this position to reproduce the real flexural behaviour and associated material non-linearity of the member. The formulation with the refined plastic hinge approach is efficacious and robust, and so a full frame analysis incorporating geometric and material non-linearity is tractable. Following development of the theory, its application is illustrated with a number of varied examples.