SummaryThis paper presents a procedure for seismic design of reinforced concrete structures, in which performance objectives are formulated in terms of maximum accepted mean annual frequency (MAF) of exceedance, for multiple limit states. The procedure is explicitly probabilistic and uses Cornell's like closed-form equations for the MAFs. A gradient-based constrained optimization technique is used for obtaining values of structural design variables (members' section size and reinforcement) satisfying multiple objectives in terms of risk levels. The method is practically feasible even for real-sized structures thanks to the adoption of adaptive equivalent linear models where element-by-element stiffness reduction is performed (2 linear analyses per intensity level). General geometric and capacity design constraints are duly accounted for. The procedure is applied to a 15-storey plane frame building, and validation is conducted against results in terms of drift profiles and MAF of exceedance, obtained by multiple-stripe analysis with records selected to match conditional spectra. Results show that the method is suitable for performance-based seismic design of RC structures with explicit targets in terms of desired risk levels. 1 It has been extensively recognized 2 that, due to the large uncertainty affecting input motion and to a variable extent also structural properties, as well as response and capacity modelling, 3-5 performance should be evaluated probabilistically in PBSD to be really able to claim that "target performance is achieved," eg, with an acceptable value of the mean annual frequency (MAF) of exceedance. Research efforts directed at providing fully probabilistic, rigorous PBSD approaches, eg, Vamvatsikos and Papadimitriou 6,7 and Lagaros and Papadrakakis, 7 are so far characterized by a complexity that makes them unsuitable for practical design problems, or use nonlinear equivalent SDOF system as a proxy (with the obvious limitations), rather than a full MDOF. 8 On the other hand, practice-oriented implementations of PBSD do not model uncertainty explicitly, neither they express the results in probability terms, eg, Kappos and Stefanidou. 9 At an even lower level, design codes prescribe deterministic seismic design with "characteristic" values of capacity parameters, assuming that uncertainties on capacity and on response at a given seismic intensity are covered by "design factors," including partial load and resistance factors, 10 the desired risk level being implicitly attained in the design process by the combination of these factors. The more robust element of probability entering in the design is in the seismic action, which is defined through uniform hazard response spectra