Non-linear calculation results can be significantly different when considering monotone or cyclic analyses. The crack opening and re-closing phenomena are quite difficult to represent with non-linear constitutive models using finite elements methods. The comparison between seismic time-history and pushover analyses is performed in this paper using GLRC\_HEGIS non-linear global model for reinforced concrete mono-layer shell elements. It takes into account four different dissipative phenomena: concrete cracking, concrete damage, steel-concrete slip and steel yielding, by means of an analytical multi-scale analysis. This stress-resultant model is formulated for cyclic calculations in the framework of the thermodynamics of irreversible processes, in order to allow efficient numerical computations of earthquake engineering applications of RC buildings. This paper explores the validity range of this constitutive law through cyclic time-history analyses (that consider the crack opening and re-closing phenomena) and monotone pushover static analyses on asymmetric structures of CASH and SMART benchmarks. Pushover analysis is a nonlinear static procedure for evaluating the seismic margin of buildings accounting for their non-linear behavior. The pushover method used in this paper is the so-called Enhanced Direct Vectorial Addition (E-DVA) which defines the load pattern for the pushover analysis as a linear combination of load patterns proportional to the mode shapes. As this method is based on the application of a static force field with constant shape and increasing amplitude, only monotone non-linear phenomena are taken into account. The pushover and time-history analyses are performed (i) on the CASH benchmark model representing a multi-storey shear wall of a real nuclear power plant building structure and (ii) on the SMART benchmark mock-up representing a typical RC building of a nuclear facility. Several numerical comparisons are made at both global and Gauss points levels and are focused on the global mechanical behaviour and the computation of crack opening.