Two-Dimensional Progressive Collapse Analysis on Reinforced Concrete Frame Structures Based on the Lumped Damaged-Plasticity Method
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Progressive collapse, a chain reaction or propagation of failures following damage to a relatively small portion of a structure, has drawn attention from researchers and the public because it leads to severe loss of life and property. Collapse of the Ronan Point apartment in 1968, terrorist attacks at the Murrah Federal Office building in 1995, and the tragedy of World Trade Center on September 11th, 2001 are examples of progressive collapse. However, the current procedures of progressive collapse analysis are limited by types of buildings or calculation efficiencies. This paper introduces the lumped damaged-plasticity method as an efficient and accurate method to check the resistance of two-dimensional (2-D) reinforced concrete frame structures in progressive collapse analysis. The lumped damaged-plasticity method is based on a simplification of continuum damage mechanics, which introduces a damage variable. This damage variable abstracts damage at the microscale, such as the density of microcracks and microvoids, and its influence on the behavior of the material at the continuum level. Unlike theories of continuum damage mechanics, in the following model all the damage and plasticity in a beam or column element are concentrated at both ends of the element. A yield surface and a damage surface are developed to describe the evolution of plastic rotation and damage. Catenary action is included into this method to account for the main resistance mechanism after flexural failure. A reinforced concrete cantilever beam and a 2-D frame structure were used to demonstrate static analysis by the lumped damaged-plasticity method. Results are compared with other models for the cantilever beam, and with experimental data for the frame structure. Dynamic progressive collapse analysis results on the frame structure are also shown. While further research is needed, the lumped damaged-plasticity method is shown to be an efficient and accurate method to check resistance of 2-D RC structures in progressive collapse analysis.