Report - PEER - University of California, Berkeley

RESULTS, DISCUSSIONS AND CONCLUSIONSThe results are obtained for different normalized yield strength parameters C y , whichis described as the ratio of yield strength to the total weight mg. Four different C yvalues are considered: 0.1, 0.2, 0.3 and 0.4. The mean spectral distributions of the C 2coefficient are then classified for the stiff and soft soil sites, and for slightly (SL),moderately (MD) and severely (SV) deteriorating systems separately, resulting in sixcombinations. These spectral relations are shown in Figures 9.a-f. In all presentedresults, the C 2 coefficient are defined as the mean ratios of the maximum inelasticdisplacements of deteriorating to non-deteriorating (elasto-plastic) systems. Meanvalues are calculated over the dynamic responses to 20 ground motions.A general observation can be easily made on the effect of normalized yieldstrength C y from the set of six spectral graphics in Figures 9. There is no consistenttrend in the variation of C 2 with C y . This is somewhat expected because both thenumerator and the denominator of C 2 are equally influenced by the yield strength Cy.Therefore C 2 can be evaluated independent from the yield strength, accordinglyindependent from the ductility ratio. The definition of C 2 in FEMA 356 (2000) isconsistent with these observations.The slightly deteriorating systems (SL) defined herein are equivalent to Type-2frames in FEMA 356, where C 2 is assigned a constant value of unity. Figure 11.areveals that this is reasonable for stiff sites, however Figure 11.b does not confirm thisassumption for soft sites. An inverse exponential variation of C 2 from 1.5-2.0 at shortperiods, to 1.0 at periods in the vicinity of the site period T s is clearly observed fromFigure 9.b.Moderately and severely deteriorating systems (MD and SV) defined inaccordance with Figure 3 are classified as Frame Type-1 in FEMA 356, withoutfurther distinction. The spectral distributions of the C 2 coefficient for these systemsare shown separately in Figures 9.c-f, along with the values proposed in FEMA-356T s is taken as 0.5 second for stiff sites (NEHRP B, C), and 0.8 second for soft sites(NEHRP D, E), respectively, in constructing the FEMA curves.Before comparing the values proposed by FEMA with the calculated values,three different C 2 levels described in FEMA for immediate occupancy, life safety andcollapse prevention performances deserves critical attention. A target displacementhas to be related to the return period of the seismic hazard in a probabilisticassessment, whereas the performance limit states are for controlling the acceptance ofmember performances when the system attains the target displacement. Threedifferent levels for C 2 , and accordingly for the target displacement is confusing andnot practical in implementation.It can be observed from Figures 9.c-f that as deterioration level increases frommoderate to severe, C 2 displays an increasing trend over the entire period range. Thisis valid for both stiff and soft sites respectively. Further, mean C 2 approaches unity atlonger periods. The period where C 2 reaches unity is somewhat closer to T s for MDsystems whereas it is longer for the SV systems.430