This paper deals with modeling reinforced concrete (RC) frame structure in seismic motion with inelastic time- history analyses. Such analyses require the definition of an inelastic structural model - that is capable of dissipating part of the imparted seismic energy - and additional damping is generally added, e.g. Rayleigh damping. This additional damping has to be consistent with the inelastic structural model: it has to account for energy dissipation mechanisms not otherwise explicitly modeled. A consistent damping model is presented in this paper and the simulation of a 2D RC frame tested on a shaking table is performed with this latter damping model. Results are then used as a baseline to assess the consistency of another more common Rayleigh damping model.