Redundancy in Earthquake-Resistant Design

The effects of redundancy on the probability of structural failure are analyzed, emphasizing relationships with the over-strength and ductility ratios. The introductory remarks make reference to the difficulties that exist in defining and quantifying the effects of redundancy in the particular context of earthquake-resistant design. Two different definitions of redundancy are proposed. These definitions are used to evaluate the effects of redundancy on the probability of structural failure in each of the four following cases: (1) strength-based design and critical regions [plastic hinges (PHs)] with infinite deformation capacity; (2) strength-based design and critical regions (PHs) with finite deformation capacity; (3) displacement-based design and critical regions (PHs) with finite deformation capacity; and (4) energy-based design. The results obtained in these analyses lead to the conclusion that, although redundancy can result in several beneficial effects on the earthquake response, a component of the reduction factor R due to redundancy (R_R), as suggested in recent publications, cannot be established independently of the over-strength and ductility of the structural system. Furthermore, to take advantage of the redundancy based on its “probabilistic effect,” it is necessary: (1) to decrease the coefficient of variation of the demand relatively to the coefficient of variation of the supplied capacity; (2) to increase the over-strength; (3) to increase the plastic rotation capacity, i.e., the ductility; and (4) to guarantee a minimal rotation capacity in all members of the structural system so that they can follow the displacement of the structure without failure and allow other elements to dissipate the earthquake input energy.