Practice Quiz

Surveying FS

Category - Math & Science

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The elevation of Sta 5+00 on a 2% grad line is 250.00 ft and the elevation of Sta 15+00 on a 4% line is 246.00 ft. What is the station and elevation at which the two grade lines intersect?
  1. 9+00, 262.00 ft
  2. 11+00, 262.00 ft
  3. 11+00, 274.00 ft
  4. None of the above
Explanation
Answer: B - The two grade lines intersect at Sta 11+00 and elevation 262.00 ft.

Solution

Use asymmetrical vertical curve properties to solve for point of intersection (PI) and elevation.

1. Calculate elevation difference between the points

250.00 ft - 246.00 ft = 4.00 ft

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

G1 x- G2 (separation - x) = -elevation distance

2x - (4) (10) + 4x = -4.0 ft

6x = 36

X = 6 ft (6+00 Sta) PI = 5+00 + 6+00 = 11+00

3. Calculate elevation by using line equation

Elevation PI = 250.00 ft + 2%(6 Sta) = 250.00 ft + 12.00 ft = 262.00ft
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