Report - PEER - University of California, Berkeley

where, A is the sum of the horizontal cross-sectional area of transversal walls for eachfloor. F is the area of structure for each floor.From Fig.1, we can see that the hysteretic model is characterized by fiveparameters: the initial stiffness K 0 , the hardening stiffness K 1 , the softening stiffnessK 2 , the crack strength Q c , and the ultimate strength Q u , which can be determined fromexperimental data. The relationships between K 2 and K 1 , Q u and Q c are more or lessfixed. And their variability is very small and can be omitted. So only K 0 , K 1 and Q care treated as independent random variables in this analysis. In terms of K 0 and astrain-hardening ratio α 1 , K 1 can be expressed as K1 = α1K0 , so α1is treated as anindependent random variable instead of K 1 . Moreover, there is no pinching effect inthe inelastic reloading stiffness of the hysteretic model. Variation of the inelasticunloading stiffness has some effect on energy-dissipation under cyclic loadings, buthas negligible effect on the maximum deformation of structures. So it is reasonable toassume the unloading stiffness K’ 0 as deterministic.The coefficients of variation of K 0 , α 1 , Q c and ξ for the brick wall with andwithout constructional columns are listed in Table 2, respectively (Zhang 2002).Figure 1. Hysteretic model of brick wall.Table 2. Parametric uncertainties of structural modelCoefficient of variation ofmodel parametersβK Oβα 1βQ cβξBrick wall withoutconstructional columnsBrick wall withconstructional columns0.30 0.33 0.30 0.300.30 0.42 0.20 0.30411