Analysis of structural-nonlinear vibrations of reinforced concrete frame

The paper presents mathematical models of vibrations and an algorithm for calculating a discrete dissipative system (DDS) at shutdown of a structural element caused by shock or impulse loading. Within the framework of time analysis theory, the paper proposes the derivation of solving equations of the reaction of the DDS, which is before the onset of the dynamic load P(t) (at t = t0) both in the state of motion and in the position of static equilibrium. The internal friction of the material was determined based on the theory of elastic viscous resistance according to the model of disproportionate damping. The recording of the dynamic reaction equations of the design model take into account the parameters of its static component. The results are illustrated by the example of fluctuations in the model of a 3-storey reinforced concrete frame building when the corner column of the lower floor is destroyed by a pulse load of the type of explosion (outside the building). The paper presents a detailed analysis of the destruction of the angular column of the frame with the determination of the destructive load. Stress surfaces are constructed for the variants of destruction of the original and damaged models (with angular and adjacent columns). For variants of destruction of the initial and damaged models (with the corner and neighboring columns) stress surfaces are constructed under the variation of impulse force parameters: changing the angle of the explosion direction to the horizontal and its duration in time.