Report - PEER - University of California, Berkeley

(4) The inelastic responses ofthe reduced SDF are related to theamplification factors of thespectrum by the equivalentlinearization method, modifiedcapacity spectrum method (CSM),and identify the level of thecapacity earthquake, thedeterministic performance index,defined as the factor when theresponse attains to the limit states.The inelastic responses by CSMcan be calculated numerically orgraphically, as shown in Figure 1,but also it should be noted that theestimated response can explicitlybe formulated by simple equationsbase on the poly-linear relations ofthe spectrum. The CSM forestimation may be modified soS aDemand Spectrafor Inelastic (h eq =15%)for Elastic (h eq =5%)T 5% T 7% Transition CurveT 10%Performance PointT 15% Capacity SpectrumS d5%h eq at Performance Point7% 10% 15%h eqFigure 1. Capacity spectrum method(CSM) for estimation of inelastic responseof SDF.that the equivalent period can be made optimum (shorter) instead of the secantstiffness to the peak as adopted in the new BSL. A factor of 0.82 for the equivalentperiod is recommended, and this can simply be considered by shifting the earthquakespectrum to the longer side by the factor as shown in Figure 2.300T c/α T=1.054sS V(cm /s)T200c=0.864sdT100 c/α TdT c第 Standard 2 種 地 盤 告 示 Earthquake安 全 限 界 スペクトル等 Shifted 価 線 形 化 計 for 算 用 CSM 応 答 スペクトル00.0 0.5 1.0 1.5 2.0 2.5T(s)equivalent stiffnessfor CSMsecant stiffnessto peakpeakresponseFigure 2. Shift of velocity spectrum of the standard earthquake taking optimumequivalent stiffness for CSM instead of secant stiffness to peak displacement.32