Practice Quiz

Civil Engineering PE

Category - Transportation

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The elevation of Sta 10+00 on a 2.5% grade line is 204.00 feet (ft) and the elevation of Sta 20+00 on a 3% line is 200.00 ft. What is the station at which the two grade lines intersect?
  1. Sta 6+00
  2. Sta 10+00
  3. Sta 16+00
  4. Sta 20+00
Explanation
Answer: C - The two grade lines intersect at Sta 16+00.

Solution: Use Asymmetrical Vertical Curve properties to solve for Point of Intersection (PI)

Given G1 = 2.5

G2 = 3

Step 1: Calculate elevation difference between the points

204.00 ft - 200.00 ft = 4.0 ft

Step 2: Use grade lines to show the elevation distance and solve for location of PI

G1x- G2 (separation - x) = -elevation distance

2.5 x - (3) (10 - x) = -4.0 ft à 2.5 x - 30 + 4 x = -4 à 6.5 x = 26

x = 4 Sta point of intersection = 10+00 + 4+00= 16+00
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