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The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r

The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.5P: To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the...
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The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r<s} in the (r,s) plane. (b) Reevaluate the probability of failure by using each of the following formulas: PF = √FR(S)fs(s)ds 0 PF = [[1-Fs (r)] fr (r)dr
Transcribed Image Text:The resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {r<s} in the (r,s) plane. (b) Reevaluate the probability of failure by using each of the following formulas: PF = √FR(S)fs(s)ds 0 PF = [[1-Fs (r)] fr (r)dr
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