Probability Applications

Timothy J. Ross and Jonathan L. Lucero 203
Figure 9.6. Sensitivity of building deflection to seismic load and response to uncertainties
in structural modeling (Seible and Kingsley (1991)).
and disjoint data can be quantified and manipulated using fuzzy sets and fuzzy algebra in
a manner which reflects the degree of imprecision in the original information and data. A
fuzzy set approach is illustrated in the following examples; similar sets of examples were
provided earlier in Wong, Ross, and Boissonnade (1987).
9.7 Examples
These examples focus on the definition of damage and the relationship between structural
response and damage for the beams and columns of the reinforced-concrete multistory frame
To narrow the scope of the discussion, suppose the variable governing the failure (or safety)
of the frame structure is x = ^, where 9 is the column rotation of the frame at the top
of the first floor and d is the base displacement of the structure. This is a simplification
of the problem and is used for illustration only. (The frame structure is capable of several
failure modes, and each mode may be governed by more than one response parameter.) A
relationship between the variable x and the damage of the structure is required to continue
the analysis. Alternately, a definition of damage or failure is required in order to assess the
safety of the multistory frame structure (Figure 9.1). It is helpful to consider this example
in an order of progress going from all deterministic data/models to imprecise data/models.