Report - PEER - University of California, Berkeley

IDR 3[rad]σPFAIDR34(g)σ PFA4medianmedian0.100.62.00.6(a)0.08(b) (c)1.6(d)0.40.40.061.20.040.20.80.2c0.020.40.000.00.00.00 1020304050 0 1020304050 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1S d [cm]S d [cm]S a [g]S a [g]Figure 1. Variations of the probability parameters of EDPs with changes in theelastic displacement spectral ordinate, S d : (a) median of IDR1 (b) dispersion ofIDR1 (c) median PFA roof (d) dispersion of PFA roof .In this study the use three different parameters as IM’s was investigated. The firstone is the elastic displacement spectral ordinate of a single-degree-of-freedom,SDOF, system evaluated at the fundamental period of vibration of the building,S d (T 1 ). The second IM, is the maximum displacement ∆ i (T 1 ) of a bilinear SDOFsystem with the same period and strength as that of the building. The third parameterthat was studied as IM is the peak ground acceleration (PGA).The probability that a structural response parameter, referred in PEER asengineering demand parameters (EDP), exceeds a certain value conditioned on agiven ground motion intensity P(EDP|IM) is obtained by using the results of nonlinearresponse history analyses (Miranda and Aslani 2003). Ground motions arescaled, such that all have the same intensity measure and the analysis is repeated forincreasing levels of intensity. Figure 1 shows the variations of the median anddispersion of the interstory drift ratio at the first story, IDR 1 , and of the peak flooracceleration at roof level, PFA roof of a non-ductile seven-story reinforced concretebuilding. The figure shows changes in central tendency and dispersion of these tworesponse parameters for five increasing levels of elastic displacement intensity S d . Foreach intensity level 80 nonlinear response history analyses were performed. Gray dotsin the figure represent results for individual ground motions. It can be seen thatconsiderable variability exists in the response of the structure from one record toanother. In general, the response will increase as the ground motion intensityincreases; however, the trend is not necessarily linear. Several simplified approachesassume the dispersion to remain constant with changes in ground motion intensity. Asshown in the figure for the case of drift in the first floor, the level of dispersionexhibits a sharp increase with the increasing IM. However, dispersion will not alwaysincrease. For example, dispersion in upper stories was observed to decrease withincreasing IM. Figures 1c and 1d presents similar results but for the peak flooracceleration at the roof, PFA roof . In this case, the acceleration demand increases withincreasing S d , but the demand tends to saturate with increasing level of nonlinearity. Itcan be seen that dispersion sharply decreases with increasing level of ground motionintensity. It is noteworthy that the variations of the dispersion of the EDP withchanges in IM shown here are very large both for IDR 1 and PFA roof .153