(b) Estimate the probability of failure using basic (brute force) Monte Carlo simulation. Plot the estimated probability of failure p as a function of the number of random realizations (samples) N of R and S for two different seed numbers and compare it with the exact probability of failure PF- For three different values of N, plot the random realizations of R and S superimposed on some contour lines of the joint PDF of R and S and the limit-state surface. Comment on your results. Hint: Use the Matlab function "normrnd" to generate random realizations of a normal random variable. (c) Repeat parts (a) and (b) for the case when R and S are jointly normal with the following probability distribution parameters (or statistics) in consistent units: Comment on your results. HR = 12, σR = 3 μs = 5, σs = 2 PRS = 0.40 Perform a sensitivity study of p, with respect to PR and comment on your results. Hint: Use the Matlab function "mvnrnd" to generate random realizations of R and S pairs. In a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables associated with a failure mode of the structure of interest are normally distributed and statistically independent with the following probability distribution parameters (or statistics) in consistent units: MR = 12, σR = 3 μs = 5, σs = 2 (a) Determine the exact probability of failure pF ·
(b) Estimate the probability of failure using basic (brute force) Monte Carlo simulation. Plot the estimated probability of failure p as a function of the number of random realizations (samples) N of R and S for two different seed numbers and compare it with the exact probability of failure PF- For three different values of N, plot the random realizations of R and S superimposed on some contour lines of the joint PDF of R and S and the limit-state surface. Comment on your results. Hint: Use the Matlab function "normrnd" to generate random realizations of a normal random variable. (c) Repeat parts (a) and (b) for the case when R and S are jointly normal with the following probability distribution parameters (or statistics) in consistent units: Comment on your results. HR = 12, σR = 3 μs = 5, σs = 2 PRS = 0.40 Perform a sensitivity study of p, with respect to PR and comment on your results. Hint: Use the Matlab function "mvnrnd" to generate random realizations of R and S pairs. In a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables associated with a failure mode of the structure of interest are normally distributed and statistically independent with the following probability distribution parameters (or statistics) in consistent units: MR = 12, σR = 3 μs = 5, σs = 2 (a) Determine the exact probability of failure pF ·
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 1.2DP
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Transcribed Image Text:(b) Estimate the probability of failure using basic (brute force) Monte Carlo simulation. Plot the estimated
probability of failure p as a function of the number of random realizations (samples) N of R and S for
two different seed numbers and compare it with the exact probability of failure PF-
For three different values of N, plot the random realizations of R and S superimposed on some contour
lines of the joint PDF of R and S and the limit-state surface.
Comment on your results.
Hint: Use the Matlab function "normrnd" to generate random realizations of a normal random variable.
(c) Repeat parts (a) and (b) for the case when R and S are jointly normal with the following probability
distribution parameters (or statistics) in consistent units:
Comment on your results.
HR = 12, σR = 3
μs = 5, σs = 2
PRS = 0.40
Perform a sensitivity study of p, with respect to PR and comment on your results.
Hint: Use the Matlab function "mvnrnd" to generate random realizations of R and S pairs.
Transcribed Image Text:In a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables
associated with a failure mode of the structure of interest are normally distributed and statistically
independent with the following probability distribution parameters (or statistics) in consistent units:
MR = 12, σR = 3
μs = 5, σs = 2
(a) Determine the exact probability of failure pF ·
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