Probabilistic Theory of Plastic Mechanism Control for Steel Moment Resisting Frames

This work aims at the development of an advanced method for the seismic design of Moment Resisting Frames (MRFs) based on a target value of the failure probability in the attainment of a collapse mechanism of global type for stochastic frames (considering the aleatoric uncertainty of the material properties). Therefore, the method herein presented constitutes the probabilistic version of the Theory of Plastic Mechanism Control (TPMC) already developed for frames with deterministic material properties. With reference to MRFs whose members have random values of the yield strength, when structural collapse is of concern, the failure domain is related to all the possible collapse mechanisms. Within the probabilistic TPMC, the term “failure” does not mean the attainment of a structural collapse, but the development 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. The limit state function corresponding to each event is represented by a hyperplane in the space of random variables, so that the failure domain is a surface resulting from the intersection of the hyperplanes corresponding to the limit states representing the single failure events. Since 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 considering that the limit states are events located in series, the probability of failure can be computed by means of Ditlevsen bounds. This approach has been validated by means of Monte Carlo simulations. In order to achieve a predefined level of reliability in the attainment of the design goal, the reliability analysis is repeated for increasing values of the overstrength factor of the dissipative zones to be used in TPMC, aiming to its calibration. Finally, on the basis of the results of a parametric analysis, a simple relationship to compute the value of the overstrength factor needed to include the influence of random material variability in the application of TPMC is proposed.