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?
A)9+00, 262.00 ft
B)11+00, 262.00 ft
C)11+00, 274.00 ft
D)None of the above

Question

Quizplus · Accepted Answer

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

The Elevation of Sta 5+00 on a 2% Grad Line