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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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