Assume that the peak wind-induced pressure during a wind storm on a high-rise building is given as P=CRV² where: C = the drag coefficient; R = air mass density (slugs/ft³); V= the maximum wind speed (ft/sec); and P = pressure (lb/ft²). C, R, and V are statistically independent. They are lognormally distributed with the following respective means (μ) and c.o.v.'s (coefficient of variation; 8): Hc = 1.80 HR=2.3 × 10-³ Hy = 120 Hint: coefficient of variation is given as the ratio of the standard deviation (a) to the mean (u). (a) P is lognormal. Find its parameters, AP and p. (b) Find P (P > 30); that is, probability of P exceeding 30 lb/ft². Assume that the wind resistance of the building (denoted as B) is lognormal with the following mean and c.o.v. 8c = 0.20 R = 0.10 8y = 0.45 Ag = 0 = Pin 8 = E(In B) {B=w = nB = √V (In B) HB = 90 88 = 0.15 (e) Find the parameters of B, Às and . (d) Find the probability of failure during a wind storm. (e) The occurrences of wind storms follow a Poisson process with a mean rate of once every 5 years. Find the probability of failure of the structure in 25 years. (Hint: read the problem as at least one failure occurring in 25 years). P87 of Ch4 slides_If R and S have lognormal distribution: Y = R/S Z = In Y = In R-In S Py = P(Z <0] Z-N(min-min sina + ains) 8 = Min-Min S
Assume that the peak wind-induced pressure during a wind storm on a high-rise building is given as P=CRV² where: C = the drag coefficient; R = air mass density (slugs/ft³); V= the maximum wind speed (ft/sec); and P = pressure (lb/ft²). C, R, and V are statistically independent. They are lognormally distributed with the following respective means (μ) and c.o.v.'s (coefficient of variation; 8): Hc = 1.80 HR=2.3 × 10-³ Hy = 120 Hint: coefficient of variation is given as the ratio of the standard deviation (a) to the mean (u). (a) P is lognormal. Find its parameters, AP and p. (b) Find P (P > 30); that is, probability of P exceeding 30 lb/ft². Assume that the wind resistance of the building (denoted as B) is lognormal with the following mean and c.o.v. 8c = 0.20 R = 0.10 8y = 0.45 Ag = 0 = Pin 8 = E(In B) {B=w = nB = √V (In B) HB = 90 88 = 0.15 (e) Find the parameters of B, Às and . (d) Find the probability of failure during a wind storm. (e) The occurrences of wind storms follow a Poisson process with a mean rate of once every 5 years. Find the probability of failure of the structure in 25 years. (Hint: read the problem as at least one failure occurring in 25 years). P87 of Ch4 slides_If R and S have lognormal distribution: Y = R/S Z = In Y = In R-In S Py = P(Z <0] Z-N(min-min sina + ains) 8 = Min-Min S
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![Problem 3
Assume that the peak wind-induced pressure during a wind storm on a high-rise building is given
as
where:
C = the drag coefficient;
R = air mass density (slugs/ft³);
V = the maximum wind speed (ft/sec); and
P = pressure (lb/ft²).
C, R, and V are statistically independent. They are lognormally distributed with the following
respective means (μ) and c.o.v.'s (coefficient of variation; 8):
P=CRV²
AB = 0 = 4ln B = E(In B)
B = @= nB = √√√V(In B)
Hint: coefficient of variation is given as the ratio of the standard deviation (a) to the mean (u).
(a) P is lognormal. Find its parameters, and čp.
(b) Find P (P > 30); that is, probability of P exceeding 30 lb/ft².
Assume that the wind resistance of the building (denoted as B) is lognormal with the following
mean and c.o.v.
GIAR
Hc = 1.80
HR=2.3 × 10-3
Hy = 120
(c) Find the parameters of B, A and B.
(d) Find the probability of failure during a wind storm.
(e) The occurrences of wind storms follow a Poisson process with a mean rate of once every 5
years. Find the probability of failure of the structure in 25 years.
(Hint: read the problem as at least one failure occurring in 25 years).
+
&c = 0.20
R = 0.10
Sy = 0.45
ns
P87 of Ch4 slides_If R and S have lognormal distribution:
Y = R/S
Z = In Y = In R - In S
Pr = P(Z <0]
Z-N (min R-min si R + ins)
Min - Mins
B =
MB = 90 g = 0.15](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8418b63-998a-4633-ab56-cc26560878f4%2F57cda0a6-bc6e-4c2c-884e-990688dd84c7%2Fekr6iwc_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3
Assume that the peak wind-induced pressure during a wind storm on a high-rise building is given
as
where:
C = the drag coefficient;
R = air mass density (slugs/ft³);
V = the maximum wind speed (ft/sec); and
P = pressure (lb/ft²).
C, R, and V are statistically independent. They are lognormally distributed with the following
respective means (μ) and c.o.v.'s (coefficient of variation; 8):
P=CRV²
AB = 0 = 4ln B = E(In B)
B = @= nB = √√√V(In B)
Hint: coefficient of variation is given as the ratio of the standard deviation (a) to the mean (u).
(a) P is lognormal. Find its parameters, and čp.
(b) Find P (P > 30); that is, probability of P exceeding 30 lb/ft².
Assume that the wind resistance of the building (denoted as B) is lognormal with the following
mean and c.o.v.
GIAR
Hc = 1.80
HR=2.3 × 10-3
Hy = 120
(c) Find the parameters of B, A and B.
(d) Find the probability of failure during a wind storm.
(e) The occurrences of wind storms follow a Poisson process with a mean rate of once every 5
years. Find the probability of failure of the structure in 25 years.
(Hint: read the problem as at least one failure occurring in 25 years).
+
&c = 0.20
R = 0.10
Sy = 0.45
ns
P87 of Ch4 slides_If R and S have lognormal distribution:
Y = R/S
Z = In Y = In R - In S
Pr = P(Z <0]
Z-N (min R-min si R + ins)
Min - Mins
B =
MB = 90 g = 0.15
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 41 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON