Elasto-plastic progressive collapse analysis based on the integration of the equations of motion

This paper considers the progressive collapse analysis of reinforced concrete structures based on the sudden removal of a load-bearing structural element and simulation of the dynamic structural behavior, taking into account the elasto-plastic properties of the material and the degradation of concrete during cracking. A specially developed finite element library is used, which includes triangular and quadrilateral shell finite elements of medium thickness, and a two-node finite element of a spatial frame, which take into account the discrete arrangement of reinforcement and various elasto-plastic material models for concrete and reinforcement. The novelty of the proposed approach lies in the formulation of both: the spatial frame and shell finite elements as a three-dimensional solid body with sequential application of the conventional hypothesis of the for Mindlin-Reissner shells of medium thickness, Timoshenko beams, and the elasto-plastic constitutive models. This makes it possible to achieve sufficiently high reliability of the results for engineering analysis, and on the other hand, a relatively simple implementation, which makes it possible to perform an elasto-plastic dynamic analysis of the entire design model of the structure, and not a separate fragment, in real time from the point of view of practical design. This approach is free from assumptions related to the introduction of a dynamic amplification factor into the quasi-static analysis, which is widely used to solve such problems. The paper provides a numerical example illustrating the effectiveness of using a special structure – an outrigger storey, to prevent progressive collapse, and a comparison of the nonlinear dynamic analysis and the linear one.