Report - PEER - University of California, Berkeley

esponse, and the Response Database may be derived for a tri-linear or other shape ofpushover curve.W=m·gPForceFigure 4. Bi-linear model and response parameters.3.3.2 Statistical Estimation of Maximum ResponsekDisplacementStrength Ratio (S.R.) = P/WPeriod = 2π k / mAs indicated in Fig. 2, the mean (µ) and standard deviation (σ) of maximumdisplacement response from a series of inelastic dynamic response history analysesare collected and organized in tabular form. An example of the latter table, theresponse matrix of the mean value in Fig. 2, is represented in Appendix I. Each cell ofthe table contains six constants of a fifth order polynomial regression function andrepresents mean or standard deviation of the maximum displacements as a function ofearthquake intensity, as shown in Eq. (1).y = a+(1)543211⋅ x + a2⋅ x + a3⋅ x + a4⋅ x + a5⋅ x a6Where x is earthquake intensity and y is mean or standard deviation of the responsequantity.The analyst can instantly obtain mean values (µ) and standard deviation (σ) ofmaximum displacement as functions of earthquake intensity, provided that theresponse parameters (period and strength ratio) are prescribed and the responsedatabase is ready to be utilized. As an example of response estimation by the abovedescribedmethod, a set of plots of mean value (µ) and standard deviation (σ) forelastic-perfectly-plastic (EPP) structures with elastic period of 0.8 sec. and strengthratios (S.R.) of 0.1, 0.2 and 0.3 is shown in Fig. 5.9030Mean of max. displ (mm)6030S.R.= 0.1 S.R.= 0.2 S.R.= 0.3STDV of max. displ2010S.R.= 0.1 S.R.= 0.2 S.R.= 0.300 0.1 0.2 0.3 0.4 0.5PGA (g)(a) Mean (µ) of max. displ.00 0.1 0.2 0.3 0.4 0.5PGA (g)(b) Standard deviation (σ) of max. displ.Figure 5. Mean and standard deviation as functions of earthquake intensity.191