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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