Purpose <p>The study investigates the impact of concrete's viscous resistance parameters on the deformation and failure of reinforced concrete framed structures under a static-dynamic loading regime in an accidental situation.</p> Methods <p>To account for the stages of concrete deformation under long- and short-term loading, a modified version of Maxwell's viscoelastic model was adopted. In this model, the linear-elastic element is substituted with a nonlinear-elastic element, whose deformations are defined by a polynomial function. The constants of the concrete model are determined by considering the duration of the normal operation stage and the structure's age at the time of the accidental event.</p> Results <p>This paper expounds upon the physical and geometric postulates that pertain to the deformation of reinforced concrete structures in accidental design situations involving the loss of bearing capacity in a frame element. An analysis of documented cases of partial or complete collapse of facilities due to accidental actions enabled the identification of the boundaries of potential local collapse for the purpose of a robustness check. A mathematical model of an equivalent single-degree-of-freedom (SDOF) system was proposed to calculate the dynamic response of a reinforced concrete structural system in the event of a sudden column failure, accounting for the nonlinear viscoelastic behavior of concrete. The proposed model was utilized to analyze the influence of nonlinear viscoelastic resistance parameters and static load levels during the initial long-term stage of operation on the response of the frame in the zone of potential local collapse.</p> Conclusions <p>The developed model can be used to assess the robustness of reinforced concrete frame substructures in scenarios involving sudden column removal, considering the alterations in the viscoelastic properties of concrete throughout the life cycle.</p>