Report - PEER - University of California, Berkeley

For a real structure, the task of defining these uncertainty bounds considering thevarious random variables involved is a complex process requiring many analyses. Asan alternative to this complex process, it is possible to estimate the confidence boundsby assuming that the variability can be represented by a standard distribution,typically lognormal, and by selecting a coefficient of variation based on either expertjudgment or the variability observed in analysis of a limited number of standardstructures. This will likely be the approach adopted by ATC-58 project, withengineers guided into performing analyses of the structure at several intensity levelsand then applying standard variability measures to the computed response based onstructure type and characteristics.Damage is related to response through structural fragility functions, whichindicate the probability that a structure will experience damage greater (or less) than acertain level, given that it experiences certain response, as measured by the EDP.Fragilities are expressed as probability distributions, rather than deterministicrelationships in order to account for the uncertainty inherent in the process ofpredicting structural damage as a function of structural response. This uncertainty isassociated with such factors as the random character of structural response toindividual ground motion records and the inability of simple EDPs to distinguishbetween this response variation and the damage it causes. For example, two differentground motions may each produce 3% peak interstory drift demand in a structure,however, one ground motion may cycle the structure to this drift level one time thenrestore the structure to small oscillations about its neutral position while the secondground motion may cycle the structure to this drift level several times and leave thestructure displaced nearly to this level. Clearly the latter motion will be moredamaging of the structure than the first, though the value of the EDP is the same.Such effects are not predictable unless the precise ground motion and structuralresponse is known. Other sources of uncertainty include lack of precise definition ofmaterial strength and construction quality.In the ATC-58 project we propose to parameterize damage by tracking thecondition of individual structural elements and components, as well as by tracking theglobal state of the building structure. For example, for moment-resisting steel frames,local damage measures include panel zone yielding, beam plastic hinging, beamflange buckling, and welded joint fracturing, while measures of global damage arevarious levels of residual interstory drift (e.g., 1%, 2%, 3%, etc. up to collapse) on astory by story basis. Each of these damage states (e.g., beam flange buckling, orresidual drift of 2%) has different implications with regard to potential injury, repaireffort and cost, and occupancy interruption. Figure 5 presents representative fragilitycurves for damage states for moment-resisting steel frame structures developed basedon data generated under the FEMA/SAC program (Roeder, 2000) and Figure 6presents a similar fragility curve for global damage states. The consequences of eachof these individual damage measures must be aggregated on a system basis, over theentire structure.96