57_HWKTTE 4004c

# 57_HWKTTE 4004c - 47 Another commonly accepted...

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47 Another commonly accepted relationship between the reliability index, β , and the probability of failure, p f , has been developed by Rosenblueth and Esteva (1972) using the relationship for values between 2 and 6. Reliability Index, β , vs. Probability of Failure, p f (Comparison of Methods) 1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 01234567 Reliability index, β p f = 460 exp (-4.3 β ) Esteva et al. (1972) True value Withiam et al. (1997) Figure 5-5. Comparison of Esteva and Withiam Methods to Obtain Reliability Index, β . (29 β 3 . 4 exp 460 - = f p (5-27) Figure 5-5 presents a comparison of the results for both, the Rosenblueth and Esteva method and the Withiam method, to determine the reliability index, β . It can be observed that Rosenblueth and Esteva approximation method will yield good values of probability of failure for values of reliability index between 2.0 and 6.0 as recommended by the author of the method.

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48 Resistance factor, φ . Once the reliability index, β , a resistance factor, φ, may be calculated. Assuming lognormal distributions of load and resistance in Eq. 5-5
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57_HWKTTE 4004c - 47 Another commonly accepted...

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