In this article (and video above), we tackle a real-world scenario that could show up on the PE exam: Estimating concrete quantity for a canal lining. This question was created and solved by Engineer in training, Enrique Ivers, LEED Green Associate.
Question:
Construction documents call for a 500-foot-long canal, shown below, to be lined with 6” of concrete for erosion control. A 5% allowance is made for waste and over-excavation. How many cubic yards of concrete should be ordered?
Explanation:
This problem has several steps and potential snags. Let’s think about it and then go through each one:
1) We need to consider the cross-sectional area of the concrete at the base of the canal, the left leg, and the right leg.
2) We then must consider the distance the canal travels to find the volume.
3) Finally, we have to consider our waste factor.
The area of the left and right legs are equal. We’re given the height and told the slope of the legs is 1:1.
To find the hypotenuse, or the actual dimension of the leg, we must find the width:
Now we need to find the hypotenuse:
We can now find the cross-sectional area of the lining:
Next we calculate the volume of the lining:
The canal is 500 ft long, and we’ve calculated the cross sectional area above.
V=Area x Length
We must convert from cubic feet to cubic yards; there are 27 cubic feet in a cubic yard:
It would be tempting to take this 372.96cy and select answer B. After all, it is very close to 373cy, and the PE will expect us to round answers in this way.
BUT, don’t forget to take into account the whole problem. We’re told there’s a 5% waste factor.
Answer:
The correct answer is C.
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I hope you found this article helpful. In upcoming articles, I will solve some more PE exam practice problems and answer other questions from our subscribers. Pass the PE Exam videos will publish weekly, so be sure to click the subscribe button so you don’t miss something that could make a substantial difference in your exam result.
Lastly, I encourage you to ask questions in the comments of this video, or on this page and I’ll read and respond to them in future videos. So, if there’s a specific topic you want me to cover or answer, we have you covered.
I’ll see you next week… on Pass the PE Exam
Anthony Fasano, P.E.
Engineering Management Institute
Author of Engineer Your Own Success
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