PurposeThis article presents a geometrically non-linear finite element formulation for the analysis of planar two-layer beam-columns taking into account the inter-layer slip and uplift.Design/methodology/approachThe co-rotational method is adopted, in which the motion of the element is decomposed into a rigid body motion and a small deformational one. The geometrically linear formulation can be used in the local frame and automatically be transformed into a geometrically nonlinear one. In co-rotational frame, both layers are assumed to be discretely connected at the element ends. Slips and uplifts are assumed to be small. Consequently, the condition of non interpenetration between the layers can be treated using a node-to-node contact algorithm. The resolution methods such as penalty (PM) and augmented Lagrangian method (ALM) with Uzawa updating scheme can be used.FindingsThe non-penetration condition between the layers of composite beams can be formulated by using contact law. It is found that despite a low convergence rate of augmented Lagrangian method compared to penalty method, the former prevents the unrealistic penetration. Besides, it is shown that the buckling load of the composite beam-column is largely affected by the uplift stiffness of the connectors.Originality/valueThe proposed finite element model is capable of simulating accurately the geometrically non-linear behavior of planar two-layer beam-columns taking into account the inter-layer slip and uplift. Regarding uplift, the non-penetration condition is strictly enforced by considering rigorous contact conditions at the interface. The constraint problem is solved using the penalty method or the augmented Lagrangian method with the Uzawa updating scheme.