55_HWKTTE 4004c - f is in terms of reliability index F u...

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45 If the resistance, R, and load, Q, are both lognormally distributed random variables and are statistically independent, it can be shown that the mean values of g(R, Q) is + + = 2 2 1 1 ln R Q COV COV Q R g (5-22) and its standard deviation is (29 (29 [] 2 2 1 1 ln Q R g COV COV + + = ξ (5-23) Substituting Equations 5-22 and 5-23 into Equation 5-21, the relationship for the reliability index, β , can be expressed as (29 (29 (29 [ ] (29 (29 [] 2 2 2 2 1 1 ln 1 / 1 ln Q R R Q COV COV COV COV Q R + + + + = β (5-24) Equation 5-24 is very convenient because it depends only on statistical data and not on the distribution of the combined function g(R, Q). A very precise definition of probability of failure, p
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Unformatted text preview: f , is in terms of reliability index, F u ( β29 (Withiam et al. 1997). ( 29 u f F p-= 1 (5-25) 46 Figure 5-4. Reliability Definition Based on Standard Normal Probability Density Function In the latter equation, F u (x) is the standard normal cumulative distribution function. ( 29 dx x F u --= ∫ ∞ 2 2 1 exp 2 1 1 β π (5-26) A graphical representation of Equation 5-26 is presented in Figure 5-4. The shaded area in Figure 5-4 represents the probability of failure, p f , to achieve a target reliability index, β T ....
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This note was uploaded on 10/19/2011 for the course TTE 4004c taught by Professor Hass during the Spring '11 term at University of Florida.

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55_HWKTTE 4004c - f is in terms of reliability index F u...

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