metrical Curve is 200 m. Find: Elevation of the highest point of the curve. Elevation of point T, which is 20 away from the highest point to the left direction.
metrical Curve is 200 m. Find: Elevation of the highest point of the curve. Elevation of point T, which is 20 away from the highest point to the left direction.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
The elevation of PC, PI and PT of a simple curve are 90.00, 93.00 and 88.50 meters respectively. The length of this Symmetrical Curve is 200 m.
Find:
- Elevation of the highest point of the curve.
- Elevation of point T, which is 20 away from the highest point to the left direction.
Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off all pertinent answers as well as the final anwer to three decimal places.
Transcribed Image Text:Fundamentals of Surveying (Route Surveying)
PROPERTIES AND FORMULAS OF VERTICAL
VERTICAL CURVES
PARABOLIC CURVE
L/2
L/2
Back tangent
Squared Property of Parabola
A = g2 - gi
y
H
gi
n Forward tangent
x2
H
a
I hi
Summit
g2
b
h2
Rate of change of slope is constant
92 - 91
r = :
When using the formula, grades
PT
are expressed in percent (%) not
S1
S2
in decimal.
Maximum offset
L
H =
(91 – 92)
gi
8
Area = c
g2
rise = run x slope
Grade Diagram
b= g:L
a =
Elements of Vertical Curve
vertical distance = area under the grade
PC=
point
of
curvature,
also
known
diagram
as BVC (beginning of vertical curve)
hi =
h2=g2S2
PT = point of tangency, also known as EVC (end of
vertical curve)
PI = point of intersection of the tangents, also
SYMMETRICAL PARABOLIC CURVE
called PVI (point of vertical intersection)
Locating the highest (or lowest points) on the curve:
L= length of parabolic curve, it is the projection of
From the PC
the
curve
onto
a
horizontal
surface which
corresponds to the plan distance.
= S
91 - 92
S1 = horizontal distance from PC to the highest
From the PT
(lowest) point of the summit (sag) curve
S2 = horizontal distance from PT to the highest
92L
S =
92 - 91
(lowest) point of the summit (sag) curve
hh = vertical distance between PC and the highest
UNSYMMETRICAL PARABOLIC CURVE
(lowest) point of the summit (sag) curve
h2 = vertical distance between PT and the highest
Locating the highest (or lowest points) on the curve:
Condition #1: When L191
(lowest) point of the summit (sag) curve
>H
2
From the PT
gi = grade (in percent) of back tangent (tangent
through PC)
S = 92l2?
2H
g2 = grade (in percent) of forward tangent (tangent
through PT)
A = change in grade from PC to PT
Condition #2: When 191
< H
From the PC
a = vertical distance between PC and PI
b = vertical distance between PT and PI
2
H=vertical distance between PI and the curve
S =
2H
Other Formulas
Curve:
from positive grade (%) to
(91 – 92)L1L2
2 (L1 + L2)
Summit Curve
H =
negative grade (%)
Sag Curve - from negative grade (%) to positive
2HL2
grade (%)
L, =
(91 – 92)L2 – 2H
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