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D, can be obtained by evaluating each aspect using the following equation.
D = (3)
Where w(#), w(Z), and w(F) is the "weight" of fuzzy set "H", "I", and "P, respectively.
Hence, The membership functions for comprehensive structural damage can be obtained by using the
fuzzy reasoning method based on the membership functions of fuzzy sets about three aspects. Based
on the membership functions, result can be simplified by applying the fuzzy maximizing decision
[Bellman and Zadeh, 1970]. The structural damage levels in the ground motion hazard level, whose
earthquake probability of occupancy 20% in 50 years and whose mean return period is 225 years, is
demonstrated with Table 1, whose result is "slight injure".
Table 1: Clients' demands transformation into damage leveis (performance levels) by Fuzzy Set Theory
—^—-^
Hazard to human
life
Loss of property
value
Required function
Damage levels
Weight
0.4
0.3
0.3
No injure
0.634
No loss
0.334
Keep overall
function
0.301
No damage
0.4441
Fuzzy membership
Slight injure
Injure of
fracture
Serious injure
0.366
0
0
Small loss
0.613
Keep main
function
0.585
Slight
damage
0.5058
Middle loss
0.053
Keep
essential
function
0.114
Small scale
damage
0.0501
Large loss
0
Keep limited
function
0
Middle scale
damage
0
Death
0
Almost total
loss
0
Guarantee for
life safety
0
Serious
damage
0
DETAILED DESIGN
Clients lay stress on the performance of a structure in large earthquake. Moreover, structural engineers
the capacity of a structure in inelastic range. In order to assure structural earthquake-resistant
performance, the distribution of strength through a building is more important than the absolute value
of the design base shear. A frame building would perform better under seismic attack, if it could be
assured weak beam / strong column mechanism, that is, plastic hinges would occur in beams rather
than in columns, or if the shear strength of members exceeded the shear corresponding to flexural
strength. This can be identified as structural performance levels based on multiple design criteria,
where the overall performance of the building is satisfied. Nevertheless, there are some factors that
have a hold on the performance, for example the uncertainties of dynamic environment, uncertainties