Analytical Evaluation of Structural Component Limit State Probabilities

Abstract

Probabilistic seismic assessment requires extensive computational effort resulting from variability both in input ground motions and mechanical properties. Nonetheless, such methodologies are of considerable importance, namely for pre-earthquake disaster planning or development of retrofitting programs. A framework for the analytical definition of closed form expressions for exceedance probabilities of structural component limit states, defined by limit values of structural response parameters, is proposed herein. The definition of these expressions is based on the probabilistic representation of the ground motion intensity and on the establishment of suitable expressions characterizing the evolution of structural demand with increasing earthquake intensity. Distinction is made between deformation-based and force-based structural parameters in the definition of such relations. Within the proposed framework, the limit states are defined by single deterministic thresholds of structural response quantities at the component level, as defined in structural codes. Different approaches are also discussed to account for the randomness of the mechanical properties and ground motion input within the proposed methodology. An application of the assessment of different limit state probabilities of members from a reinforced concrete building is presented, for which limit states and limit state capacities are defined according to the upcoming Part 3 of the Eurocode 8. Although the presented application only deals with member chord rotation and shear force limit state probabilities, the proposed methodology can be generalized to other deformation-based and force-based structural parameters.