13.9. From past records of highway construction and maintenance costs, a state highway de- partment determines the following cost relationships for two-lane bituminous high- ways within the state: c₁(x) = 0.1.x20 Cm(x) = 3.0- X where the equations hold for (0.5 ≤ x ≤ 10.0) and where x= pavement thickness (inches); c(x)= annualized construction cost (millions of dollars per mile per year); and C(x)= annual maintenance cost (millions of dollars per mile per year). (a) In words, describe the basic tradeoff decision that the highway department must make. (b) Determine the optimal pavement thickness, justifying the type of point found. (c) If pavement thickness can be specified only in whole inches, what is the best pave- ment thickness, considering normal variance in pavement thickness caused by field construction conditions? How sensitive is the optimal cost to small changes in thickness?

13.9. From past records of highway construction and maintenance costs, a state highway de- partment determines the following cost relationships for two-lane bituminous high- ways within the state: c₁(x) = 0.1.x20 Cm(x) = 3.0- X where the equations hold for (0.5 ≤ x ≤ 10.0) and where x= pavement thickness (inches); c(x)= annualized construction cost (millions of dollars per mile per year); and C(x)= annual maintenance cost (millions of dollars per mile per year). (a) In words, describe the basic tradeoff decision that the highway department must make. (b) Determine the optimal pavement thickness, justifying the type of point found. (c) If pavement thickness can be specified only in whole inches, what is the best pave- ment thickness, considering normal variance in pavement thickness caused by field construction conditions? How sensitive is the optimal cost to small changes in thickness?

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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Question

13.9. From past records of highway construction and maintenance costs, a state highway de-
partment determines the following cost relationships for two-lane bituminous high-
ways within the state:
c(x) = 0.1.x20
Cm(x) = 3.0-¹
X
where the equations hold for (0.5 ≤ x ≤ 10.0) and where
x= pavement thickness (inches);
c(x)= annualized construction cost (millions of dollars per mile per year); and
C(x)= annual maintenance cost (millions of dollars per mile per year).
(a) In words, describe the basic tradeoff decision that the highway department must
make.
(b) Determine the optimal pavement thickness, justifying the type of point found.
(c) If pavement thickness can be specified only in whole inches, what is the best pave-
ment thickness, considering normal variance in pavement thickness caused by field
construction conditions? How sensitive is the optimal cost to small changes in
thickness?

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