This paper presents a formal probabilistic framework for seismic design and assessment of structures and its application to steel moment-resisting frame buildings. This is the probabilistic basis for the 2000 SAC Federal Emergency Management Agency ͑FEMA͒ steel moment frame guidelines. The framework is based on realizing a performance objective expressed as the probability of exceeding a specified performance level. Performance levels are quantified as expressions relating generic structural variables ''demand'' and ''capacity'' that are described by nonlinear, dynamic displacements of the structure. Common probabilistic analysis tools are used to convolve both the randomness and uncertainty characteristics of ground motion intensity, structural ''demand,'' and structural system ''capacity'' in order to derive an expression for the probability of achieving the specified performance level. Stemming from this probabilistic framework, a safety-checking format of the conventional ''load and resistance factor'' kind is developed with load and resistance terms being replaced by the more generic terms ''demand'' and ''capacity,'' respectively. This framework also allows for a format based on quantitative confidence statements regarding the likelihood of the performance objective being met. This format has been adopted in the SAC/FEMA guidelines.

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Nonlinear static and dynamic analyses are utilized by engineers for performance-based seismic risk evaluation of new and existing structures. In this context, nonlinear component modeling criteria are typically based on ASCE 41 guidelines. Experiments on wide-flange steel columns suggest that the ASCE 41-13 nonlinear component models do not adequately reflect the expected steel column behavior under cyclic loading. To help bridge the gap between state-ofthe-art research and engineering practice, this paper proposes new modeling criteria for the first-cycle envelope and monotonic backbone curves of steel columns for use in nonlinear static and dynamic frame analysis. The proposed nonlinear provisions include new parameters for concentrated hinge models to facilitate modeling of strength and stiffness deterioration of steel columns under seismic loading. The associated variability in the model parameters is also quantified to facilitate reliability analyses and development of probabilistic acceptance criteria for design. Recommendations are made to account for the influence of bidirectional lateral loading and varying axial load demands on the steel column's hysteretic behavior. Also proposed is an increase in the compression axial force limit for characterizing columns as forceversus deformation-controlled in line with the new ASCE 41 provisions. The proposed modeling parameters are validated against test data and continuum finite element analyses, and they are proposed for consideration in future updates to ASCE 41 requirements for nonlinear static and dynamic analyses of steel frame buildings with wide-flange columns.

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