The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.

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The annual maximum load (in tons) on a structure is normal distributed with mean
and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure
(R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13
tons, with probabilities 0.3, 0.6, and 0.1, respectively.
a) Compute the failure probability of the system in any year.
b) Determine the reliability of the structure over its 30-year life span.
c) Compute the expected number of failure events over the lifetime.
d) Compute the safety margin and safety factor for the structure.
Transcribed Image Text:The annual maximum load (in tons) on a structure is normal distributed with mean and standard deviation 6 tons and 2.7 tons, respectively. The strength (i.e., resistance) of the structure (R) is a discrete random variable with three possible outcomes: R = 10 tons, R = 11.5 tons, and R = 13 tons, with probabilities 0.3, 0.6, and 0.1, respectively. a) Compute the failure probability of the system in any year. b) Determine the reliability of the structure over its 30-year life span. c) Compute the expected number of failure events over the lifetime. d) Compute the safety margin and safety factor for the structure.
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