Probabilistic theory of plastic mechanism control: Design and seismic assessment

This paper reports an application of the Probabilistic Theory of Plastic Mechanism Control (P-TPMC) to a steel Moment Resisting Frames (MRFs) assumed as a case study. The validation of the accuracy of the proposed design methodology is given through non-linear dynamic analyses. In particular, the aim of the non-linear dynamic analyses is to check the collapse mechanism developed by the structures designed by P-TPMC. In fact, it is expected that the percentage of structures exhibiting a collapse mechanism of global type completely developed or compatible with it agrees with the fixed probability given as design achievement of P-TPMC. In other words, if the probability of having a collapse mechanism different from the global one is the 10% the aim of the non-linear dynamic analysis is to check if at least the 90% of the analysis output is entirely in agreement with the global mechanism. The analysis results are given in terms of the number of plastic hinges developed in columns and beams. Each mechanism showing a lower number of plastic hinges on beams and first storey column bases is considered as compatible with a global mechanism while if plastic hinge also appears on columns of other storeys the mechanism has been considered partial. The most significant part of analyses leads to the development of a collapse mechanism of global type. In quantitative terms, the percentage of success in achieving a collapse mechanism of global type is about 91% thus confirming the reliability of the design exploiting the P-TPMC.