When performing a nonlinear time-history analysis of a reinforced concrete structure, it is necessary for the used structural model to dissipate the correct amount of energy. For the sake of computational efficiency, viscous damping models are still commonly used to account, partially or not, for non-viscous dissipations (e.g. friction between the crack surfaces, bond slip at the steel-concrete interface). In order to improve the physical relevance of such a substitution, an evolving equivalent viscous damping ratio estimated for a simply supported reinforced concrete beam is proposed in this paper. This work takes place in the scope of a moderate seismicity context for which steel yielding is not expected. The results are not directly identified from experimental results but rather from numerical simulations carried out thanks to an equivalent single-degree-of-freedom model, itself calibrated by means of quasi-static experiments. To begin with, the experimental setup used to calibrate the single-degree-of-freedom model and the equivalent viscous damping ratio assessment method are presented. Then, the single-degree-of-freedom model and the identification procedure are exposed. The resulting outputs are presented and commented. Finally, numerical experiments are performed in order to obtain equivalent viscous damping ratio values corresponding to a given maximum time-history curvature and a curvature demand.