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Civil Engineering PE

Category - Transportation

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What is the elevation of the point of vertical tangency for an equal-tangent sag vertical curve with the following given information?

G1 = -2%, G2 = +4%, L= 300 ft, PVC Sta = 100+00, PVC Elev = 100.00 ft
  1. 96 ft
  2. 103 ft
  3. 128 ft
  4. None of the above
Explanation
Answer: B - the elevation of the point of vertical tangency for the given equal-tangent sag vertical curve is 103 ft.

Solution: Use the general parabolic formula for a vertical curve

y = ax2 + bx + c


Where a = (G2 - G1)/2L

Given, G1 = -0.02

G2 = +0.04

L = 300 ft

a = (0.04 - (-0.02))/2(300) = 0.0001

x = curve length = L = 300 ft

b = G1 = -0.02

c = PVC elevation = 100 ft

y = 0.0001 (300) 2 + (-0.02) (300) + 100 = 9 - 6 + 100 = 103 ft
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