Iterative-R: A reliability-based calibration framework of response modification factor for steel frames

This study introduces a general reliability-based, performance-based design framework to design frames regarding their uncertainties and user-defined design goals. The Iterative-R method extracted from the main framework can designate a proper R (i.e., response modification factor) satisfying the design goal regarding target reliability index and pre-defined probability of collapse. The proposed methodology is based on FEMA P-695 and can be used for all systems that FEMA P-695 applies. To exemplify the method, multiple three-dimensional, four-story steel special moment-resisting frames are considered. Closed-form relationships are fitted between frames' responses and the modeling parameters. Those fits are used to construct limit state functions to apply reliability analysis methods for design safety assessment and the selection of proper R. The frameworks' unique feature is to consider arbitrarily defined probability density functions of frames' modeling parameters with an insignificant analysis burden. This characteristic enables the alteration in those parameters' distributions to meet the design goal. Furthermore, with sensitivity analysis, the most impactful parameters are identifiable for possible improvements to meet the design goal. In the studied examples, it is revealed that a proper R for frames with different levels of uncertainties could be significantly different from suggested values in design codes, alarming the importance of considering the stochastic behavior of elements' nonlinear behavior.