From tension tests on 121 samples of ASTM A514 structural steel, the mean yield strength is 794 MPa and the standard deviation is 38.6 MPa. Assume that a normal distribution applies, and estimate the yield strength value for a reliability of 99%. (Data from [Kulak 72].)

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Accepted Answer

A reliability of 99% corresponds to a strength such that only 1%, or one out of 100, values are expected to be lower. From Table B.3(b),

Limiting Value of x	Percent Less Than Limit, P	Fraction Less Than Limit	Percent More Than Limit, R
(a) For integer numbers of standard deviations
μ	50	1/2	50
μ − σ	15.9	1/6	84.1
μ − 2σ	2.28	1/44	97.72
μ −3σ	0.135	1/740	99.865
μ − 4σ	0.00317	1/31,600	99.99683
(b) For particular values of probability
μ − 1.28σ	10	1/10	90
μ − 2.33σ	1	1/100	99
μ − 3.09σ	0.1	1/1000	99.9
μ − 3.72σ	0.01	1/10,000	99.99

this limit corresponds to μ − 2.33σ. If [latex] \bar{x}[/latex] and [latex] s_{x}[/latex] are employed as estimates of μ and σ, respectively, the 99% reliability value is

[latex]x_{99}=\bar{x} − 2.33s_{x}=794 − 2.33 imes38.6=704 MPa[/latex] Ans.

Question B.2: From tension tests on 121 samples of ASTM A514 structural st...

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