A proposed bridge across a stream is to be supported at the two ends and a central pier. To avoid damage, the settlement of the three supports must be similar and within certain allowances. Through computer modeling the estimated mean settlements and their standard deviations have been estimated to be:SupportMean Settlement (cm)Standard Deviation (cm)Left End4.51.0Center Pier4.81.5Right End3.51.75The maximum allowable settlement for each of the supports is 6.0 cm. For each support individually, determine the probability that the settlement will exceed this maximum allowable value. Show your work.Assuming that the three supports settle independently, what is the probability that all three settle more than the allowable amount? Show your work.Again, assuming that the supports settle independently, what is the probability that at least one of the supports settles more than the allowable amount? Show your work.

Consider the given data. The formula to calculate the normal deviation is given by, z=δ-δmeanσ Here,…

Answered: A proposed bridge across a stream is to…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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A proposed bridge across a stream is to be supported at the two ends and a central pier. To avoid damage, the settlement of the three supports must be similar and within certain allowances. Through computer modeling the estimated mean settlements and their standard deviations have been estimated to be:

Support	Mean Settlement (cm)	Standard Deviation (cm)
Left End	4.5	1.0
Center Pier	4.8	1.5
Right End	3.5	1.75

The maximum allowable settlement for each of the supports is 6.0 cm. For each support individually, determine the probability that the settlement will exceed this maximum allowable value. Show your work.
Assuming that the three supports settle independently, what is the probability that all three settle more than the allowable amount? Show your work.
Again, assuming that the supports settle independently, what is the probability that at least one of the supports settles more than the allowable amount? Show your work.

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