Report - PEER - University of California, Berkeley

Figure 6. Idealized capacity spectrum assumed for this study.Spectral acceleration (m/s 2 )161412108642Idealization usedSKR, stiff, 3kmIZT(X), rock, 8kmIZT(Y), rock, 8kmYPT(X), soft, 5kmYPT(Y), soft, 5km00.0 0.5 1.0 1.5 2.0Period (secs)Figure 7. Idealized demand spectrum used for study, and Kocaeli spectra.In Figure 6, a u and d y are the spectral acceleration and displacement at yield, andµ 1 and µ 2 are the displacement ductility ratios to first loss of capacity and to fracture;they are assumed to be log-normally distributed random variables with a coefficientof variation β c . c is the ratio of lower to upper yield plateaux strengths, taken as fixedfor a given simulation. The mean 5% damped demand spectrum was taken as theidealized spectrum of figure 7, but this was also treated as log-normally distributed.Table 2 shows the various cases considered, and Table 3 the adopted parametervalues. For the two base cases, called ‘brittle’ and ‘ductile’, a u and d y were givensimilar mean values to those used for 4-7 storey RC frames in the TCIP study referredto previously, but with the yield strength a u increased by about 50% to allow for theeffect of masonry infill. The mean values of µ 1 , µ 2 and c and also coefficient ofvariation (β) values were chosen more arbitrarily, but look reasonable, for example inrelation to standard values proposed in FEMA 356 or HAZUS. The relationshipsbetween peak deflection and damage state shown in Table 4 were also based onHAZUS; note that these values were taken as constant (i.e., not lognormally varying).404