PSI - Issue 78

Matteo Tatangelo et al. / Procedia Structural Integrity 78 (2026) 73–80 where 1 is the annual reliability index (Cornell, 1969). Traditionally, the seismic design of a structure is carried out over a defined reference period . Therefore, in order to compute the cumulative failure probability =1 −� 1 − 1 � (Tatangelo et al., 2024b), the term (i.e. 1/ ) in (3) should be replaced using a Poisson process. Thus, is obtained approximately as follows ≅ 1 − � � 1 − , � ∙ � − 1 � ⋅ � 0.5 ∙ 1 2 ⋅ 2 �� (4) where E , t ref is the probability of exceeding a given value of seismic intensity in a fixed . Moreover, in order to know how much the seismic demand should be modified in order to satisfy the failure probability (or reliability index) the equation (4) can be, thus, reformulated by expressing the term � ̅� that may be called as target reliability factor and expressed as follows: � ̅� = � � 1 − �− ̅�� � (1 − , ) � � � −1 1 ⁄ ⋅ (0.5 ∙ 1 ⋅ 2 ) (5) where ̅ is the target reliability index in a certain . In order to explicitly consider the construction over-strength, that is due fundamentally to partial factors, a over strength factor 0 ≥ 1 is introduced so as to obtain a new target reliability factor ′ � ̅� as follows: ′ � ̅� = � ̅ � 0 ⁄ (6) Fig. 1 gives an example on how it is possible to define the reliability-targeted design spectrum, that is the capacity spectrum satisfying a certain reliability requirement, with 0 , edp � ̅� and e ′ dp � ̅� . 3. Parameters for derivation of failure probability In this section, a discussion of the parameters needed for the estimation of failure probability for Ultimate Limit State (ULS) with closed form equation (4), according to Italian standards NTC-18 (2018). In detail, the hazard slope 1 may be calculated, as suggested in FEMA 350 (2000), by considering the values of seismic hazard having exceedance probabilities of 2% and 10% in 50 years, as follows: 75

Fig. 1. Schematic representation of the , 0 and ′