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S a( T f) . Inoue (1990) provides the following empirical correlation coefficient, ρln Sa1ln Sa f, thatfills this need:ln Sa1ln Sa f( T ) − ln( 1/ T )ρ = 1−0.33ln 1/1f(5)Given this correlation expression, the standard deviation of S* can be defined as follows:σ2 22 2( 1 − α ) σln Sa+ α σln Sa+ 2ρ( )1 f ln Sa1ln Sa1 − α ασfln Saσln Sa f= (6)2ln S*1Most spectral attenuation relationships define empirical coefficients as a function of frequency orperiod that can be manipulated to calculate S* according to Eq. 4. For example, Abrahamson &Silva (1997) define an attenuation function as follows:n[ S ] a + a (m-m ) + a ( 8.5-m)+ [ a a (m-m )] ln(R)E ln =1 4 1 123+13 1(7)awhere the a-coefficients are tabulated by Abrahamsom & Silva, m is the earthquake magnitude,m 1 is a given base magnitude, and R is the distance from the epicenter to the site. SubstitutingEq. 7 into Eq. 4, one obtains the following relationship for modified coefficients that can beapplied in the otherwise standard attenuation relationship to obtain S*:a*x= a a(8)( 1−α )xT1+ αxT 2These new relationships can then be applied in a standard probabilistic site hazard analysis wherethe required performance is evaluated on the basis of this new intensity, S*.3. BUILDING TESTBEDSIn related research (Mehanny et al., 2000, 2001) several moment frame structures have beendeveloped and analyzed to exercise seismic assessment and design provisions for compositeconstruction. These frames are utilized here to provide the basis for calibrating the new intensitymeasure parameters, α and T f /T 1 , and illustrate their application in a probabilistic performanceassessment. The case study structures consist of three six-story frames and one twelve-storyframe, all of which are designed according to provisions of the International Building Code (ICC2000) and AISC Seismic Provisions (1997) for a site in a high seismic region of California. Dueto space limitations the frames are only briefly introduced here. For further details the reader isreferred to Mehanny et al. (2000, 2001).5