Report - PEER - University of California, Berkeley

of sliding thresholds, are desirable. Table 1 shows the classification selected for thebench-mounted science equipment of interest in this study. Fragility curves are nowgiven in terms of their median m and coefficient of variation cov (log-standarddeviation/median) for incrementally calculated DMs and the equipment categoriesnoted in Table 1. Figure 6 shows a sample of these generalized curves for the lowbase resistance equipment (Category 1). It should noted, that for development of thesefragility curves, an incremental DM of 0.2 cm is selected.Table 1. Equipment categorized by their base resistanceCategory Description Science Equipment 3 Average µs Averageφ1 Low base resistanceLarge MicroscopeIndy0.35 0.902Low-medium base 38 cm CRTresistance43 cm CRT0.45 0.903Medium base Technicon AnalyzerresistanceIndigo, Octane0.65 0.954Medium-high base EppendorfresistanceCentrifuge0.70 0.905 High base resistance 48 cm CRT 0.85 0.95Figure 6. Lognormal parameters (m and cov) for DM = maximum relativedisplacement, bench-mounted equipment category 1 ( µ = 0.35,sφ = 0.90).Figure 6 illustrates that for a damage measure of 3cm or more the lognormalparameters follow a straight-line trend. Therefore, both m and cov, may be simplifiedby a least square regression. The median m may be simplified as a straight line of theform, m = b 1 DM +c 1 and the cov can be assumed as a straight line parallel to abscissa(i.e., cov = c 2 ). Using these simplified expressions for m and cov, re-arranging theterms of Equation 6 and neglecting smaller order terms, one can express the PHFA interms of the DM for a given probability of exceedence as a simple quadratic of theform:2PHFA = c1 + c2DM+ c3DM(10)3 Testing results of these equipment items presented in Ray Chaudhuri and Hutchinson (2004a)206