Accurate design rules are crucial for the safety, sustainability, and economy of steel structures. To predict the load-bearing capacity of sway structures, Eurocode 3, Part 1-1, uses individual member unity checks, which are assumed to include the interaction between members, related to their stability and plastic behaviour. To verify this assumption, basic (one-bay single-storey) 2D and 3D sway structures, and building-size 3D structures are simulated by nonlinear finite element simulations, and results are compared to Eurocode 3. The results show that as long as basic 2D and 3D structures are loaded such that all their members fail due to instability, the load-bearing capacity is predicted accurately by Eurocode 3. If, however, they are loaded to have members failing due to stability and plasticity, Eurocode 3 predicts the load-bearing capacity too low, i.e. conservatively, probably due to plasticity induced redistribution and hardening. For building-size 3D structures, it is shown that system eigenvalues, which may range from single member buckling, via coupled instabilities, to overall buckling, are important for load predictions, however, are not taken into account in all Eurocode 3 methods. In conclusion, Eurocode 3 seems to be safe, for stability and plasticity interaction effects, even for building-size structures. However, for economy, design rules should consider plastic redistribution, and building-size system stability should be taken into account by predicting member instability via system eigenvalues, also for stocky cases including plasticity.