plasticity, multi-layered reinforced concrete beam, limit state, multimodulus behavior, deflection, bending moment, elastic foundation, viscous base, loads of explosive type.

Originally, fundamentals of the theory of limit equilibrium and dynamic deformation of building structures of metal and concrete were developed by A. A. Gvozdev [1]–[3] and evolved by his followers [4]–[7]. Forming the basis for the calculation model of an ideal rigid-plastic material made it possible to determine in many cases the ultimate load of bearing capacity and upper (kinematically possible) or lower (statically valid) values for a wide class of different structures by simple methods. Thus, with reference to concrete structures the most important property of concrete to resist significantly different tension and compression was not considered. This circumstance was taken into account in work [8] for reinforced concrete beams under conditions of quasi-static loading. In building practice there are often situations when the deformation is accompanied by the resistance of the environment [9]–[10], and the problem is about the assessment of the bearing capacity of the structure and reducing the level of its damage in the presence of such resistance when exposed to dynamic loads. In the framework of classical limit equilibrium theory by A. A. Gvozdev this issue was not considered, and in this paper it is investigated for reinforced concrete beams on elastic and visco-elastic foundation.

Nemirovsky Yuri Vladimirovich, e-mail: nemirov@itam.nsc.ru, Dr. Sci. Phys. & Math., Professor, Institute of Theoretical and Applied Mechanics S. Christianovich Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia.

Tikhonov Sergey Vladimirovich, e-mail: strangcheb@mail.ru, Candidate of Phys. & Math., Assoc. Professor, Department of Matematical Analysis, Algebra and Geometry, I. Yakovlev Chuvash State Pedagogical University, Cheboksary, Russia.