Question

The wind gust at a building site is of concern during the erection of a steel building. Suppose the daily maximum wind velocity at a particular site can be modeled as a Gaussian random variable with a mean velocity of 40 mph and a c.o.v. of 25%.

(a) If the erection of a building can be completed in a period of 3 months, what is the most probable maximum wind velocity that can be expected during the erection of the building?

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(b) If the shoring system used in the erection can withstand a wind gust velocity of 70 mph, what is the probability that the shoring system will be inadequate to withstand the maximum wind velocity during the erection of the building?

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(c) What would be the mean and c.o.v. of the maximum wind velocity during the erection of the building?

Answer 1

(a)

Express the cumulative distribution function of asymptotic form for the Type I distribution of the largest value of n.

Here, sample size is n, and parameters are and .

Find the parameter

Here, sample size is n and standard deviation of velocity is .

Substitute 91 for n and 10 for , to find .

Find the parameter

Here, sample size is n, and mean velocity is .

If the erection of the building completes in 3 months period, then sample size would be 91.

Substitute 91 for n and 40 for , to find .

Hence, the most probable maximum wind velocity excepted during the erection of the building is

(b)

Find the probability that the shoring system damage during the erection of the building.

Here, probability is P, cumulative distribution function of asymptotic form for the Type I distribution of the largest value of n is .

Substitute for .

Substitute 0.3 for , 70 for y and 42.1 for , to find .

Hence, the probability that the shoring system damage during the erection of the building is

(c)

Find the mean wind velocity during the erection of the building.

Here, the mean wind velocity during the erection of the building is , Euler’s number is and distribution parameters are and .

Euler’s number value is 0.5772.

Substitute 42.1 for , 0.5772 for and 0.3 for , to find .

Hence, the mean wind velocity during the erection of the building is

Find the coefficient of variation of wind velocity.

Here, distribution parameter is , mean wind velocity is and coefficient of variation of wind velocity is .

Rearrange the above equation, to find .

Substitute 0.3 for and 44 for , to find .

Hence, the coefficient of variation of wind velocity during the erection of the building is