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describing nonstationary process.
The acceleration time history a(t) is normalized using its maximum amplitude a max . The normalized
nonstationary acceleration time history is as fellows:
V(t)a s (t)
(2)
So, the nonstationary acceleration time history is:
where, A p is a given peak ground acceleration.
= A p a m (t) (3)
4 UNCERTAINTIES OF EARTHQUAKE LOAD AND STRUCTURAL MODEL
The parameters of structural model considered in this analysis are the viscous damping ratio and the
hysteretic model parameters. The viscous damping ratio of brick structures can be expressed as [2]:
where, A is the sum of horizontal cross sectional area of transversal walls for each floor. F is the area
of structure for each floor.
The hysteretic model is characterized by five parameters: the initial stiffness KO, the hardening
stiffness KI, the softening stiffness KI, the crack strength Q c , and the ultimate strength Q u . These
parameters can be determined by the experimental data. In this analysis, KQS KI and Q c are treated as
independent random variables. In terms of KI and a stain hardening ratio otj, KI can be expressed as K
= -aiKi. The relationship between Q u and Q c is more or less fixed, and its variability is very small. So
it is omitted. There is not pinching effect in inelastic reloading stiffness of the hysteretic model. The
degree of inelastic unloading stiffness has some effect on energy-dissipation under cyclic loadings, but
it hasn't effect on the maximum deformation of structures. So it is reasonable to assume the unloading
stiffness K o as deterministic.
The coefficients of variation of KO, a, Q c and ^ for the brick walls with and without constructional
columns are listed in table 2, respectively [2].
TABLE 2
PARAMETRIC UNCERTAINTIES OF STRUCTURAL MODEL
(4)
Coefficient of variation
of model parameters
&
Pa,
Po.
P<
Brick wall without
constructional columns
0.30
0.33
0.30
0.30
Brick wall with
constructional columns
0.30
0.42
0.20
0.30
The artificial wave is obtained by transforming the mean response spectrum into the power spectrum.
So the parameters of earthquake model include the mean response spectrum, the duration of
earthquake ground motion and the damping ratio. We take the standard response spectrum in Chinese
"Code for seismic design of buildings"(GBJll-89) as the mean response spectrum. The former is