Three Proposals for Characterizing MDOF Nonlinear Seismic Response

Seismic Reliability-Based Design of Inelastic Structures With Different Values of the Post-Yielding Stiffness Isolated by FPS

“…The probabilities f P exceeding different LSs at each level of the IM, are numerically computed for each combination of the structural properties (1280 equivalent structural systems) and then fitted through lognormal distributions [20]. In this phase, as for the softening systems and with the aim to consider both the collapse and not-collapse cases for each parameter combination at each IM level, the total probability theorem allows to estimate the probability exceeding a limit state at each intensity measure level considering the collapse number [69] as follows: (12) where N is the total number of analyses for the structural system at each IM level, and not collapse N is the number of numerical simulations without any collapse. The first term of Eq.…”

“…The first term of Eq. (12) defines the probability exceeding a LS corresponding to not-collapsing structural models [69]. The fragility curves are plotted in Fig.s 4-7 showing the exceedance probabilities f P versus the ground motion intensity.…”

Spo2frag V1.0: Software for Pushover-Based Derivation of Seismic Fragility Curves

“…6). 2 In cases where the user wishes to include (additional) modelling uncertainty into the calculation, two alternative options are available in the relevant GUI panel. First option is to define a logarithmic standard deviation U  for mean logarithmic capacity  at one of the predefined limit states.…”

“…In the case of structure-specific studies, the trend is to rely increasingly on analytical derivation for these fragility functions. State-of-the-art in analytical fragility estimation is the use of non-linear dynamic analyses -for example, incremental dynamic analysis (IDA, [1]), the cloud method [2] or multi-stripe analysis [3]. However, despite the advantages of the analytical approaches over the damage probability matrices and empirical fragility curves employed earlier, their chief disadvantage remains the computational burden involved [4], which may include the selection and manipulation of hazard-consistent ground motion records.…”

An Area-based Intensity Measure for Incremental Dynamic Analysis

“…Peak ground acceleration (PGA) has a long history and it is the most widely used IM by many researchers. Bazzurro et al (1998) proposed S a (T 1 ), the elastic spectral acceleration at period T 1 (the fundamental period or the 1st period of a structure, hereinafter the same), as an IM. Vamvatsikos and Cornell (2002) summarized and compared both IMs of PGA and S a (T 1 ).…”