A calculated model of a building frame fragment is presented for calculating the dynamic additional loading of structural elements in the zone of possible local destruction after the failure of one of the structures. To model such a fragment, a substructure isolated from a structural system of the building frame was used in the form of a two-span statically indeterminate continuous beam under various boundary conditions on the extreme supports, loaded with a specified design load. The sudden removal of the middle supporting column of the substructure is modelled by reducing to zero for some short-time the internal force in this column, obtained when calculating the entire frame of the building. The use of level calculated schemes and analytical description of the movement of reinforced concrete substructure with variable stiffness due to cracking for determining the dynamic additional loading of frame elements of a multi-story building after the failure of one of the structures allows to define the parameters of the dynamic response of the substructure and simulate in more detail the zones of possible local destruction of the building under the considered special action. The developed algorithm for calculating physically and structurally nonlinear reinforced concrete systems can be used for the calculated analysis of the frame of multi-story buildings when designing their protection against progressive collapse.

Solving problems associated with protecting buildings from progressive collapse and minimizing resources is becoming increasingly important. In many countries, ensuring such protection is set in accordance with the requirements of national regulatory documents and, therefore, researches aimed at developing effective ways to protect constructive systems from progressive collapse under special actions are relevant. In this regard, the present work presents studies of the influence of energy dissipation in constructive reinforced concrete elements during their sudden structural rearrangement caused by the removal of one of the supporting elements. The hysteretic dispersion accompanying the nonlinear load-unload cycle of the cross-section during crack formation is taken into account. The damping mechanism of reinforced concrete elements of the constructive system is described by the equivalent viscous damping model, based on the hypothesis of proportionality of the damping force and the oscillation velocity. Approbation of the calculated model is carried out in relation to the reinforced concrete frame structures, the physical models of which were tested under the considered loading regime. A comparison of the experimental and calculated parameters shows the effectiveness of the proposed model for assessing the dynamic response of reinforced concrete structures with cracks under the static-dynamic loading regime.

The results of experimental and theoretical researches of crack resistance, development and growth of cracks of a fragment of a reinforced concrete multi-storey frame of a monolithic building with prestressed beams for a special emergency impact caused by a sudden removal of one of the load-bearing elements are presented. Removal of the middle column of the frame was considered as an emergency impact. Analysis of the pattern cracking in the frames with a prestressed beam before and after a special impact is carried out against the pattern cracking in an unstressed frame structure. Based on the increments of cracks width in the beam, the coefficient of dynamic additional loading in prestressed frame structures from a special impact was calculated. The obtained results of experimental and theoretical researches of the crack resistance of frame structures in considered influences can be used in the development of methods for protecting the frames of monolithic multi-storey buildings against progressive collapse.

The stress-strain state in RC elements of statically indeterminate structural systems under sudden restructuring is considered in this article. The solution of the problem on determining the parameters of a static-dynamic deformation diagram of prestressed RC elements was obtained on the energy basis excluding the structure dynamics instrument the problem. The deformation dependences for the pre-stressed flexural RC element are determined using the diagram method presented in the research of. For the possibility of obtaining an analytical expression of the desired moment convenient for practical application of the construction of the “moment-curvature” diagram for the pre-stressed element is performed using the simplest deformation dependence. The calculation analysis of the deformation of such a structural systems was performed using the level of primary and secondary design models.

An analytical condition for crack resistance of a specific plane stress reinforced concrete element with prestressed reinforcement is considered in this article. The specific concrete element is reinforced with orthogonally located prestressed rods that coincide with the directions of the coordinate axes. The crack resistance condition is constructed by generalizing of G.A. Geniev theory of plasticity of concrete and reinforced concrete on the region of existence of tensile stresses: “tension-tension” and “compression-tension”. A graphical interpretation of this condition is presented for a plane stressed element depending on the angle between the main force and the coordinate axes. As an example, the crack resistance condition of the support zone of a prestressed concrete beam of a monolithic reinforced concrete frame is considered.