An office building is planned with a lateral-force-resisting system designed for earthquake resistance in aseismic zone. The seismic capacity of the proposed system, expressed as a force factor, is assumed tofollow a lognormal distribution with a median of 6.5 and a standard deviation of 1.5. The ground motionfrom the largest expected earthquake at the site is estimated to correspond to an equivalent force factor of 5.5.(a) What is the estimated probability that the building will experience damage when subjected to the largest expected earthquake? (b) If the building survives (i.e., experiences no damage) during a previous moderate earthquake with aforce factor of 4.0, what is the updated probability of failure of the building under the largest expectedearthquake?(c) Suppose future occurrences of the largest expected earthquake follow a Poisson process with a mean return period of 500 years. Assuming that damage events from different earthquakes are statisticallyindependent, what is the probability of the building will survive without damage over a 100-year designlife?(d) Suppose the office building is part of a complex of five identical structures, each designed with thesame level of earthquake resistance. What is the probability that at least four of the five buildings willsurvive a 100-year design life without damage? Assume that survival events among the buildings aremutually statistically independent. Note: According to the Poisson random (in time) occurrence model, the number of Poisson eventoccurrences N(t) in the time interval (0, t) is a discrete random variable with the followingprobability mass function:where l = average number of Poisson even occurrences per unit time (or mean occurrence/arrivalrate of the Poisson events).

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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An office building is planned with a lateral-force-resisting system designed for earthquake resistance in a
seismic zone. The seismic capacity of the proposed system, expressed as a force factor, is assumed to
follow a lognormal distribution with a median of 6.5 and a standard deviation of 1.5. The ground motion
from the largest expected earthquake at the site is estimated to correspond to an equivalent force factor of 5.5.
(a) What is the estimated probability that the building will experience damage when subjected to the largest expected earthquake?

(b) If the building survives (i.e., experiences no damage) during a previous moderate earthquake with a
force factor of 4.0, what is the updated probability of failure of the building under the largest expected
earthquake?
(c) Suppose future occurrences of the largest expected earthquake follow a Poisson process with a mean return period of 500 years. Assuming that damage events from different earthquakes are statistically
independent, what is the probability of the building will survive without damage over a 100-year design
life?
(d) Suppose the office building is part of a complex of five identical structures, each designed with the
same level of earthquake resistance. What is the probability that at least four of the five buildings will
survive a 100-year design life without damage? Assume that survival events among the buildings are
mutually statistically independent.

Note: According to the Poisson random (in time) occurrence model, the number of Poisson event
occurrences N(t) in the time interval (0, t) is a discrete random variable with the following
probability mass function:

where l = average number of Poisson even occurrences per unit time (or mean occurrence/arrival
rate of the Poisson events).

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