Method for Analyzing the Probability of Stability Failure of a RC Frame in an Accident Situation

Despite the general principles on reliability for structures have been stated in the international standard ISO 2394, the implementation of these principles in the design and construction practice faces with difficulties. One of the current problems is probabilistic robustness checking for buildings and structures. This study focuses on the development of a probabilistic model to calculate the risk of failure of a reinforced concrete frame due to stability failure of its elements in a scenario of sudden removal of a structural component. The critical forces for the eccentrically compressed structural components of the frame are determined using the displacement method, considering the two-stage static-dynamic loading regime due to the sudden column collapse. The study takes into account the change in stiffness of frame elements due to cracking during loading. In addition, it proposes the probabilistic equigradient-based model for the failure of the frame elements after the sudden removal of a column. The mathematical formulation of this model is that if some value is a critical force associated with some parameters satisfying a given condition, then the extremum of that value can be found using an auxiliary Lagrangian function. To illustrate the application of the model, the paper provides an example of the calculation of the stability failure probability of a reinforced concrete frame structure under the considered loading regime. The calculated critical force values were compared with the experimental data for the reinforced concrete frame tested for sudden column removal.