TP%2315_f08 - CE 3102 Fall 2008 Thought Problem 15 From a...

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CE 3102 Fall 2008 Thought Problem 15 From a number of laboratory tests on beams of A285 steel, the number of loading cycles to fatigue failure appear to be well-modeled by a lognormal distribution with an estimated mean of 430,000 cycles and a standard deviation of 215,000 cycles. All tests were run at 36,400 psi. It is anticipated that beams in a bridge, for which you are the engineer of record, will be subjected to a loading equivalent to 300,000 cycles at approximately 36,400 psi during the life of the bridge. Estimate the probability that fatigue failure will occur before the bridge is retired.
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CE 3102 Fall 2008 Thought Problem 15 Instructor’s Partial Solution Let Y denote the random variable used to model the number of cycles before fatigue failure occurs. We want to know ) 000 , 300 ( Y P From the problem statement we know: 000 , 215 000 , 430 ] [ = = = Y Y Y E σ μ If we let X be the log transform of Y, then from the definition of log-normal random
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TP%2315_f08 - CE 3102 Fall 2008 Thought Problem 15 From a...

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