Report - PEER - University of California, Berkeley

DirectionX-directionY-directionSkeweddirection(60°)Table 1. Limit deformations and seismic capacity indices.Limit stateBase shearcoefficientOverall limitdeformationInter-storylimitdeformationSeismiccapacityindexServiceability 0.160 1/412 1/355 (5F) 0.30Reparability I 0.245 1/151 1/117 (4F) 1.05Reparability II 0.255 1/98 1/75 (4F) 1.54Safety 0.265 1/57 1/45 (4F) 2.35Serviceability 0.192 1/823 1/631 (9F) 0.26Reparability I 0.378 1/183 1/146 (9F) 1.00Reparability II 0.395 1/120 1/120 (9F) 1.74Safety 0.408 1/76 1/67 (9F) 2.75Safety - 1/57 - 3.23Therefore, the ultimate capacity would have enough margin of deformability upto the safety limit, in case of the design with the statically required capacity and thestandard design spectrum in the BSL. In other words, the “limit strength designmethod” allows the design such that the required lateral strengths may be less thanrequired conventionally, if the deformability up to the safety limit is ensured.However, it is not recommended in the Guidelines to make these margins less byselecting less capacity, but to designate these higher performance levels for properdescription in the market. It should be noted that this is the result in case of ideallyregular type of building with ensured overall mechanism, when the error of estimationmight probably be minimum. The factored design of wall and columns based on thecapacity design philosophy should be reemphasized. There still need furtherinvestigation both on demand and capacity, such as, extreme ground motion, inelasticresponses of irregular structures, nonlinear soil-structure interaction and so on.The risk analysis was carried out for this example with design service life of 50years: at first, the probabilities of exceeding the capacity earthquake were evaluatedin X and Y directions, respectively, as 12% and 7.6% for reparability I, 1.5% and0.18% for reparability II, 0.21% and 0.13% for safety limit sates. This is the casewhen the soil amplification is evaluated in detail and reduction of velocity spectrum,i.e., the constant displacement spectrum is assumed over certain period. This could beunderestimation, therefore, the constant velocity was assumed over the peak andevaluated alternatively then: 18% and 7.6% for reparability I, 6.5% and 2.0% forreparability II, 0.92% and 0.41% for safety limit sates. Because data were availableonly for the reliability of safety limit evaluation, the model was applied: theprobability of exceeding the safety limit in Y direction was evaluated as 3.6% and1.4% for the first and the latter assumptions in the spectrum shape. The accuracy inevaluating the limit states must and the earthquake hazard must be made higher in thefuture. It is expected that the proposed method will be made use of in practice, such assetting rates of earthquake disaster insurance or life-cycle cost analysis.37