Abstract This paper is aimed to discuss the conceptual troubles currently appearing in the codified rules to account for second-order effects in the seismic design of structures. First of all, starting from SDOF systems, the distinction between second-order effects in the elastic range and second-order effects in the plastic range is clarified. Moreover, the attention is focused on the conceptual difference occurring between a parameter measuring the structural proneness to second-order effects and a demand parameter measuring the safety level against the phenomenon of dynamic instability. Successively, the critical issues concerning the behaviour occurring in real MDOF structures when compared to SDOF systems is pointed out underlining the uncoupling between second-order effects in the elastic range and second-order effects in the plastic range, due to the influence of the collapse mechanism typology. The codified rules to account for second-order effects in Eurocode 8 are analysed showing why they are conceptually wrong giving rise to a lot of unjustified problems in the seismic design of steel MRFs. Recent proposals to improve Eurocode 8 are also analysed. Finally, it is shown how relevant studies already existing in the technical literature can be exploited in order to set up code provisions having a sound theoretical background. Finally, a new proposal, accounting for the influence of the collapse mechanism, for codification of P − Δ effects in seismic design is presented.

Highlights ● In the case of SDOF systems, the stability coefficient is the only one parameter needed to measure the structural proneness to second-order effects both in the elastic range and in the plastic range. ● The stability coefficient adopted by Eurocode 8 is not a parameter measuring the structural proneness to second-order effects. ● Dynamic instability is a phenomenon related to the seismic displacement demand. ● In the case of real MDOF structures, the structural proneness to second-order effects in the plastic range of behaviour is dependent on the collapse mechanism. ● A new proposal for codification of effects in seismic design is proposed. ● The proposal novelty is that it accounts for the need of amplifying the seismic design forces, directly accounting for the influence of the collapse mechanism typology.