Design the curve, of An equal tangent vertical curve is to be constructed between grades of -2.0% (initial) and 1.0% (final). The PVI is at station 11 + 000.000 and at elevation 420 m. Due to a street crossing the roadway, the elevation of the roadway at station 11 + 071.000 must be at 421.5 m. GIVEN DIMENSIONS ON THE ATTACHED PICTURE From the given valuesPVC station = 11 +000.000- /PVC elevation = PVI elevation - G₁ X = 420+ 0.01Lx = (11 +071.000) - (11 +000.000)- /x = 71 +0.5La=b=G₁ -0.02=C = 420 + 0.01LG₂-G 0.01-(-0.02)21.21.=0.015Ly = ax²+bx+c421.5 = 0.015 (71+0.5L)² + (−0.02) (71 +0.5L) +420 + 0.01LLsimply the equation1.855 =75.613+0.00375LL0.00375L² - 1.855L + 75.615 = 0L = 449.842 mLength of curve =449.842 mStation of PVC = (10+775.079)Elevation of PVC = 424.49842 mStation of PVT =(11+224.921)Elevation of PVT = 422.24981 m

Initial Grade = -2.0%Final Grade = +1.0%PVI1 (Point of Vertical Intersection 1): Station 11+000.000,…

Answered: Design the curve, of An equal tangent…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Design the curve, of An equal tangent vertical curve is to be constructed between grades of -2.0% (initial) and 1.0% (final). The PVI is at station 11 + 000.000 and at elevation 420 m. Due to a street crossing the roadway, the elevation of the roadway at station 11 + 071.000 must be at 421.5 m.

GIVEN DIMENSIONS ON THE ATTACHED PICTURE

From the given values
PVC station = 11 +000.000- /
PVC elevation = PVI elevation - G₁ X = 420+ 0.01L
x = (11 +071.000) - (11 +000.000)- /
x = 71 +0.5L
a=
b=G₁ -0.02
=
C = 420 + 0.01L
G₂-G 0.01-(-0.02)
21.
21.
=
0.015
L
y = ax²+bx+c
421.5 = 0.015 (71+0.5L)² + (−0.02) (71 +0.5L) +420 + 0.01L
L
simply the equation
1.855 =
75.613
+0.00375L
L
0.00375L² - 1.855L + 75.615 = 0
L = 449.842 m
Length of curve =449.842 m
Station of PVC = (10+775.079)
Elevation of PVC = 424.49842 m
Station of PVT =(11+224.921)
Elevation of PVT = 422.24981 m

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