huangyhg

aisc lrfd probability of failure
does anyone know if the aisc manual indicates the probability of failure in percent when using the lrfd method. many books that i have do not indicate it. i am suprised that with all the modeling and statistical analyses done with lrfd over the past 25 years this failure ratio issue appears to be very silent. i am sure it must be very small. any tips will be greatly appreciated.
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i don't know the exact number, or if a single number exists (probably doesn't), but you should read the following aisc ej papers on the subject. i think you could dig some numbers out if you try.
pinkham and hansell, 1qtr78
galambos and ravindra, 1qtr78
there are probably others, but i would start there.
i have no idea why, but i have the number 1/500 in the back of my head.. i could be completely wrong, though.. (and i know it's kind of high)
in an aisc article dated july 1972 galambos shows the failure probability involving calculus with a double intergral. essentially its the area under two bell curves intersecting at their base. it stops short of giving a typical example or answer.
cap4000-
that is the generic failure probability for any material. one bell curve is the reduced strength curve (this is the peak of one of the bell curves, however, there is the possibility that the strength can go lower due to lower material strength, tolerances in properties, etc... - this is why we use the entire bell curve, not just the peak that we use in calculations).
the other bell curve is the same exact idea, but on the load side. again, there is some possibility that the ultimate loads could exceed 1.2dl and 1.6ll (or less than), thus the bell curve.
the failure zone is the intersection of the two curves, or where the load curve is greater than the strength curve.
again, this is just a generic representation and not unique to steel (unless he put a specific number to it, which you said he didn't).
additionally, i don't think you can put a specific number on it because the ll/dl ratios always change and i don't believe that the 1.2 and 1.6 factors represent an equivalent failure percentage.
the aisc steel manual discusses this in depth. see commentary section b3.3 (page 16.1-214 in the 13th ed.).
the following link on pages 10 and 11 gives a realistic basis for the probability for a ductile beam gravity load failure of about 1 in 100,000 per year. note that the probability of exceeding the design load is about 5% per year.
if you do a search for galambos or bruce ellingwood, you'll find numerous papers on the subject. i finished my graduate program using many of their methods to get to a φ factor for lrfd design of composite metal decks.
basically the combination of variabilities between load and φ factors creates an order of probability called a beta (β) factor. these β factors correlate with the probability of failure.
however, since there are different load combinations and various (rounded off) load factors you get different probabilities of failure that change with different d/l load ratios, etc.

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