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1. The probability distribution function of the maximum annual wind speed v is g

ID: 3363834 • Letter: 1

Question

1. The probability distribution function of the maximum annual wind speed v is given by: F, (v) = expl , with =9.0 and V = 45 mph. Determine the design wind speed with a return period of 50 years (50-year wind speed). 2. Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram 3. A steel cable consists of eight high-strength steel strands. The strength of each strand can be modeled by a lognormal random variable with a mean value of 50 kips and a coefficient of variation of 10%. What is the probability that the weakest strand will have a strength less than 40 kips? Compute the same probability if the cable consists of 16, 32 and 64 strands 4. The annual maximum stage height in a river channel is modeled using a Type I asymptotic distribution of the largest value, with a mean value of 30 ft and a coefficient of variation of 10%. The stage height at which flooding will occur is 40 ft. What is the probability that the annual maximum stage height will exceed this level?

Explanation / Answer

A. The return period is a statistical measure of the average period of time expeted to pass between similar events.

B. Normal distribution z=(x-mean)/standard deviation

Since z=3 and z=6

Mean=60000. Standard deviation=5000

hence for z=3

3=(x-60000)/5000

X=15000+60000

=75000

When z=6

6=(x-60000)/5000

30000=x-60000

X=90000