The results of studies of monolithic reinforced concrete frames of multi-storey buildings and reinforced concrete frames simulating fragments of such frames in over-extreme limit states caused by special actions are presented. Two options for reinforcing the beams of the frames are considered: with double reinforcement, which ensures the operation of the beam when the force flows in the frame and, accordingly, the sign of the moment change; option with double reinforcement and installation of additional indirect reinforcement in the support zones of the beams for the entire height of the section. Primary and secondary design models were built using volumetric finite elements for concrete and reinforcement rods. The obtained design parameters of deformations, crack patterns and frame failure patterns for all options are compared with each other and with the results of testing physical models of these structures. To assess the effect of mixed reinforcement on the limiting deformations of compressed concrete in over-extreme limit states, based on the theory of plasticity of concrete and reinforced concrete G.A. Geniyeva, deformation dependencies are constructed for a typical reinforced concrete element reinforced with rods in one direction and meshes in the other two under uniaxial compression and volumetric deformation. It has been established that the use of indirect reinforcement in combination with double longitudinal reinforcement in bending elements under static-dynamic loading conditions significantly increases the ultimate deformation of the compressed zone. This reinforcement option can working way to protect monolithic reinforced concrete frames of multi-storey buildings from progressive collapse under special actions.