11.10: Probabilistic theory of plastic mechanism control

This work aims at the development of an advanced method for the seismic design of Moment Resisting Frames (MRFs) based on the evaluation of the probability of failure in the attainment of a collapse mechanism of global type in case of stochastic frames. Therefore, the method presented constitutes the probabilistic version of the Theory of Plastic Mechanism Control (TPMC) already successfully developed for frames with deterministic material properties. With reference to MRFs whose members have random values of the yield strength, the failure domain derives from all the possible collapse mechanisms. Under the point of view of structural reliability analysis, the term failure means the attainment of a collapse mechanism different from the global one. The design requirements normally needed to prevent undesired collapse mechanisms are probabilistic events within the framework of the kinematic theorem of plastic collapse. At each event corresponds a limit state function representing a hyperplane in the space of the random variables, so that the failure domain is a manifold surface resulting from the intersection of the hyperplanes corresponding to the limit states of the single events. Because of plastic hinges in frame's members are common to many different mechanisms, the single limit state events are correlated. Therefore, by applying the theory of binary systems and taking into account that, from the structural reliability point of view, the limit states are events located in series, the probability of failure is computed by means of Ditlevsen bounds. © Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin.