factors) and" P =0.89 for the required probability (based on the 135 lowest safety
factors) .
With a value of of Psr' and Ps/ at the same point, we can define a scale factor/f as
the ratio of these two numbers
.f = c (7-3)
This ratio can be used to correct the response surface approximation during the
optimization process. Once an optimum design is found with a givenJ fa new accurate
MCS can be calculated at the optimum, a new value of f can be calculated from Equation
(7-3) at the new point, and the process repeated until convergence. As further refinement,
we have also updated the response surface for the intermediate probability, centering it
about the new optima.
Beam Design Example
The following cantilever beam example (Figure 7-1) is taken from Wu et al. (2001)
to demonstrate the use of probabilistic sufficiency factor.
L=100"
=I W
Figure 7-1. Cantilever beam subj ect to vertical and lateral beading
There are two failure modes in the beam design problem. One failure mode is
yielding, which is most critical at the corner of the rectangular cross section at the fixed
end of the beam
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