Practice Quiz

Civil Engineering PE

Category - Transportation

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Which of the following is the depth of a sanitary sewer force main crossing at a right below the surface of an equal tangent 600 foot vertical curve, given the pipe elevation at Station 10+00 is 100 feet, the PVI at Station 13+85 is 109.0 feet, and the initial and final grades are +1.2% and -1.06%?
  1. 1.5 feet
  2. 12.1 feet
  3. 112 feet
  4. None of the above
Explanation
Answer: B - The depth of the sanitary sewer force main below the surface of the given vertical curve is 12.1 feet.

Solution:

Step 1: Use the offset formula (distance between curve and tangent)

Y = [G/ (200*L)]*x2

Given G = | 1.2-(-1.06)| = 1.26

L = 600 feet

x = 385 feet

Therefore,

Y = [1.26/ (200*300)]*3852 = 1.5 feet

Step 2: Determine PVC elevation

109.0 feet - (6/2 stations x 1.2 feet/station) = 105.4 feet

Step 3: Determine initial tangent above pipe

109.0 + (3.85 stations x 1.2 feet/station) = 113.6 feet

Step 4: Determine curve elevation at pipe crossing (initial tangent - offset)

113.6 - 1.5 = 112.1 feet

Step 5: Determine distance between curve elevation and top of pipe

112.1 - 100.0 = 12.1 feet
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