rtical curve is required to pass through a fixed point that is located at station 314+00, elevation 2436.50 ft. the grades are g1 = -2.5% and g2 = +1.50%. The intersection of these grades is located at 315+00, elevation 2430.00 ft. Find: The elevation at station 310+00. The elevation at station 320+00. Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off all pertinen
rtical curve is required to pass through a fixed point that is located at station 314+00, elevation 2436.50 ft. the grades are g1 = -2.5% and g2 = +1.50%. The intersection of these grades is located at 315+00, elevation 2430.00 ft. Find: The elevation at station 310+00. The elevation at station 320+00. Draw and plot the curve. Compute all of the necessary elements of the curve. Include the proper units/dimensions and round-off all pertinen
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
A symmetrical vertical curve is required to pass through a fixed point that is located at station 314+00, elevation 2436.50 ft. the grades are g1 = -2.5% and g2 = +1.50%. The intersection of these grades is located at 315+00, elevation 2430.00 ft.
Find:
- The elevation at station 310+00.
- The elevation at station 320+00.
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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