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[画像:(2) Estimate the required increase in the reinforcement ratio, p, to increase the reliability index to ẞFORM = 3. (3) Estimate the change in FORM if the coefficient of variation of f, is increased to 0.15, while its mean is kept fixed. (4) What are the 8 and sensitivity vectors (see p. 215 of Course Reader). Rank the importance of the basic random variables in terms of the relative sensitivity of BFORM or PR, to their uncertainty (measured by their standard deviation). II. Using the sensitivity measures with respect to the mean and standard deviation of random variable f obtained from FERUM, derive the sensitivity of ẞ and p with respect to the parameters A and λ of random variable f. Check your solutions with those obtained from FERUM. III. Using the general-purpose reliability analysis program FERUM, determine the SORM estimates (both using "curvature fitting" and "point fitting") of the reliability index ẞ and failure probability Pr compare them with the corresponding FORM results and comment. IV. Using the general-purpose reliability analysis program FERUM, estimate the failure probability using Monte Carlo simulation. Specify NMCs = 500,000 realizations and a target sample coefficient of variation (cov) of the estimate of the failure probability of 5 percent. The Monte Carlo simulation stops after NMCs realizations or after the sample coefficient of variation falls below the target value cov, whichever arrives first. Compare the Monte Carlo Simulation estimate of the failure probability with the FORM and SORM estimates obtained in parts I and III, respectively, and comment. V. Repeat Part I assuming a statistical correlation coefficient between random variables b and d of 0.80 and compare the FORM estimates of the reliability index and failure probability with those obtained under Part I. Provide your FERUM input file with your solution. >]
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Transcribed Image Text:(2) Estimate the required increase in the reinforcement ratio, p, to increase the reliability index to ẞFORM = 3. (3) Estimate the change in FORM if the coefficient of variation of f, is increased to 0.15, while its mean is kept fixed. (4) What are the 8 and sensitivity vectors (see p. 215 of Course Reader). Rank the importance of the basic random variables in terms of the relative sensitivity of BFORM or PR, to their uncertainty (measured by their standard deviation). II. Using the sensitivity measures with respect to the mean and standard deviation of random variable f obtained from FERUM, derive the sensitivity of ẞ and p with respect to the parameters A and λ of random variable f. Check your solutions with those obtained from FERUM. III. Using the general-purpose reliability analysis program FERUM, determine the SORM estimates (both using "curvature fitting" and "point fitting") of the reliability index ẞ and failure probability Pr compare them with the corresponding FORM results and comment. IV. Using the general-purpose reliability analysis program FERUM, estimate the failure probability using Monte Carlo simulation. Specify NMCs = 500,000 realizations and a target sample coefficient of variation (cov) of the estimate of the failure probability of 5 percent. The Monte Carlo simulation stops after NMCs realizations or after the sample coefficient of variation falls below the target value cov, whichever arrives first. Compare the Monte Carlo Simulation estimate of the failure probability with the FORM and SORM estimates obtained in parts I and III, respectively, and comment. V. Repeat Part I assuming a statistical correlation coefficient between random variables b and d of 0.80 and compare the FORM estimates of the reliability index and failure probability with those obtained under Part I. Provide your FERUM input file with your solution. >
[画像:In the reliability analysis of a reinforced concrete beam under bending, the limit-state function is defined as M where p = 0.02 is the reinforcement ratio and the remaining variables are uncertain with the following statistical description: Random Variable Distribution Mean Coefficient of Variation b [in] beam width normal 10 0.05 d [in]: depth to reinforcement normal 18 0.10 f, [ksi]: yield stress of steel f[ksi] compressive strength of concrete lognormal 47 0.12 lognormal 3.5 0.20 77 [-] shape factor for stress block diagram uniform 0.60 0.05 M [k-in]: applied bending moment Type I, Largest Value (Gumbel) 1000 0.20 Assume the above random variables to be mutually statistically independent. I. Using the general-purpose reliability analysis program FERUM, determine the FORM estimate of the reliability index and failure probability P, the coordinates of the most likely failure point, u and x", and the sensitivity measures with respect to the mean and standard deviation of each random variable. Use these results to make the following estimates by hand calculation: (1) Estimate the changes in FORM and PR if the mean of M is increased to 1100 [k-in].]
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Transcribed Image Text:In the reliability analysis of a reinforced concrete beam under bending, the limit-state function is defined as M where p = 0.02 is the reinforcement ratio and the remaining variables are uncertain with the following statistical description: Random Variable Distribution Mean Coefficient of Variation b [in] beam width normal 10 0.05 d [in]: depth to reinforcement normal 18 0.10 f, [ksi]: yield stress of steel f[ksi] compressive strength of concrete lognormal 47 0.12 lognormal 3.5 0.20 77 [-] shape factor for stress block diagram uniform 0.60 0.05 M [k-in]: applied bending moment Type I, Largest Value (Gumbel) 1000 0.20 Assume the above random variables to be mutually statistically independent. I. Using the general-purpose reliability analysis program FERUM, determine the FORM estimate of the reliability index and failure probability P, the coordinates of the most likely failure point, u and x", and the sensitivity measures with respect to the mean and standard deviation of each random variable. Use these results to make the following estimates by hand calculation: (1) Estimate the changes in FORM and PR if the mean of M is increased to 1100 [k-in].
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