Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines

Abstract

This paper presents a formal probabilistic framework for seismic design and assessment of structures and its application to steel moment-resisting frame buildings. This is the probabilistic basis for the 2000 SAC Federal Emergency Management Agency ͑FEMA͒ steel moment frame guidelines. The framework is based on realizing a performance objective expressed as the probability of exceeding a specified performance level. Performance levels are quantified as expressions relating generic structural variables ''demand'' and ''capacity'' that are described by nonlinear, dynamic displacements of the structure. Common probabilistic analysis tools are used to convolve both the randomness and uncertainty characteristics of ground motion intensity, structural ''demand,'' and structural system ''capacity'' in order to derive an expression for the probability of achieving the specified performance level. Stemming from this probabilistic framework, a safety-checking format of the conventional ''load and resistance factor'' kind is developed with load and resistance terms being replaced by the more generic terms ''demand'' and ''capacity,'' respectively. This framework also allows for a format based on quantitative confidence statements regarding the likelihood of the performance objective being met. This format has been adopted in the SAC/FEMA guidelines.

Optimal Friction Coefficients for Isolated Structures Depending on the Soil Condition

“…The lognormality assumption permits to estimate, with a limited number of samples, the response at different percentile levels, which is very useful for system reliability assessment. It also permits to obtain a closed-form analytical estimate of the seismic risk [59].…”

Q-Factor Verification of a 6-Storey Concentrically Braced Frame via the Innoseis Risk-Based Approach

“…The risk-based assessment is performed according to the Cornell et al [20] fragility-hazard convolution approach ( Figure 6) to determine λ DS , i.e., the mean annual frequency (MAF) of exceeding the damage state (DS, being either SD or GC) of interest:…”

Record-to-Record Variability in the Seismic Response of Rc Walls Buildings Subjected to Ground Motions Matched to the Conditional Spectrum

“…For example, the annual rate of exceeding a limit state inter-storey drift ratio, idr, can be determined through numerical integration of Equation 1, adapted from [1]:…”

“…In simplistic terms |dλ(x)| can be considered as the rate of events occurring within an infinitesimal intensity range dx about x. Alternatively, closed form solutions exist whereby the annual probability of exceeding a given level of demand can be approximated. For example, as shown in Equation 2, again adapted from [1]: (2) where λ(x edp ) is the hazard rate corresponding to a median response equal to edp, k is related to the slope of the hazard curve, b is used to described the relationship between intensity and the median conditional response and β is the dispersion in the engineering demand parameter (EDP) being examined.…”

“…In the case of Equation 1 this uncertainty manifests itself in the P(IDR>idr|IM=x) term, whereas in Equation 2 the uncertainty is incorporated directly as the term β, which is the standard deviation of the logarithms of the EDP. Note that both epistemic and aleatory uncertainty in demand and capacity should be considered [1]; however, this paper will be limited to consideration of the aleatory component in demand, or record-to-record variability, only.…”