Ductility capacity models for buckling-restrained braces using a bayesian methodology

Buckling-restrained braces (BRBs) have recently become popular for use in the primary lateral-force-resisting systems of structures located in high seismic regions of the United States. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Concentrically-braced frames (CBFs) incorporating BRBs are known as buckling-restrained braced frames (BRBF). Since BRBFs are a relatively new structural system in the U.S., current design provisions require qualification tests to demonstrate acceptable BRB performance. Numerous isolated BRB tests have been conducted in support of building projects, and several large-scale BRBFs have also been tested. In general, these experiments have shown that BRBs exhibit robust cyclic performance and possess large ductility capacity. Although procedures for predicting BRB maximum ductility demands have been developed [19], no generally accepted method exists for predicting the cumulative plastic ductility (CPD) capacity of BRBs, where CPD capacity is defined by the cumulative plastic deformation sustained before fracture of the steel core. In addition, CPD capacity has been shown to be dependent on loading history; Carden [9] and Fahnestock have observed that braces which undergo large maximum deformations exhibit lower CPD capacity than those braces which undergo relatively smaller maximum deformations. Furthermore, other important parameters affecting capacity have not been clearly identified yet. As an effort to answer these needs, this paper develops ductility capacity models for BRBs using a Bayesian methodology. As one of the few CPD capacity models available, Takeuchi developed a deterministic fatigue model. This model can account for the effect of loading history on BRB CPD capacity by dividing the imposed brace deformations into skeleton and Bauschinger parts as described by Benavent-Climent. By contrast to the deterministic approach by Takeuchi, this research effort employs a Bayesian methodology, which is probabilistic in nature. Through this method, test observations are used to update the capacity model parameters based on the probabilities that the observed results would be predicted by the model. The result is a model that relates CPD capacity to selective predictive parameters. Although subjective information to select a distribution prior to the updating is not available, a Bayesian methodology is selected because the method (1) produces unbiased models, (2) is flexible in regards to model form, (3) can accommodate both failure and non-failure test specimens, (4) quantifies the model error probabilistically, and (5) provides the ability to identify important parameters affecting capacity.