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The total sustained load on the concrete footing of a
Chapter 5, Problem 118E(choose chapter or problem)
Problem 118E
The total sustained load on the concrete footing of a planned building is the sum of the dead load plus the occupancy load. Suppose that the dead load X1 has a gamma distribution with α1 = 50 and β1 = 2, whereas the occupancy load X2 has a gamma distribution with α2 = 20 and β2 = 2. (Units are in kips.) Assume that X1 and X2 are independent.
a Find the mean and variance of the total sustained load on the footing.
b Find a value for the sustained load that will be exceeded with probability less than 1/16.
Questions & Answers
QUESTION:
Problem 118E
The total sustained load on the concrete footing of a planned building is the sum of the dead load plus the occupancy load. Suppose that the dead load X1 has a gamma distribution with α1 = 50 and β1 = 2, whereas the occupancy load X2 has a gamma distribution with α2 = 20 and β2 = 2. (Units are in kips.) Assume that X1 and X2 are independent.
a Find the mean and variance of the total sustained load on the footing.
b Find a value for the sustained load that will be exceeded with probability less than 1/16.
ANSWER:
Solution:
Step 1 of 3:
It is given that denotes the dead load,
denotes the occupancy load and total sustained load is sum of the dead load and the occupancy load.
Also it is given that ~Gamma distribution (
50,
2) and
~ Gamma distribution(
20,
2).
and
are independent.
Using this we need to find the required values.