lec 6_vertical alignment
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8/6/2019 Lec 6_Vertical Alignment
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Dr. Lina Shbeeb
Vertical alignment
Transportation Engineering
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8/6/2019 Lec 6_Vertical Alignment
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Dr. Lina Shbeeb
Vertical alignmentVertical Curves are used to provide a gradual change from
one tangent grade to another, so that vehicles may smoothlynavigate changes in grade as they travel the highway.
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8/6/2019 Lec 6_Vertical Alignment
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Dr. Lina Shbeeb
Vertical alignment Vertical alignment consists of grade tangents
connected with parabolic curves. The desirable maximum grades and gradient
changes depend on the facility type and vehiclecharacteristics.
The desirable grade as function of facility type: 2% for freeways
6% for local street
Higher grades are unavoidable at location with difficulttopography.
The length of vertical curve is measured along thehorizontal alignment. A point on the curve isspecified by its station location on the horizontalalignment and its elevation from a datum.
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Dr. Lina Shbeeb
Maximum grades by highway function
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Dr. Lina Shbeeb
Vertical alignment Grades vertical slope from reference station
upgrade positive
downgrade - negative
Crest, sag curves
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Dr. Lina Shbeeb
Vertical alignment Vertical point of intersection (VPI): The point where the grade
line intersect Vertical point of tangency (VPT): The point where the grade
vertical curve ends
Vertical point of curvature (VPC) The point where the grade
vertical curve beigns
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Dr. Lina Shbeeb
Vertical design element It important to find the vertical elevation at each station
particularly VPC,VPI and VPT.
External distance E needs to be calculated to estimate
their elevation.
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Dr. Lina Shbeeb
Vertical alignment
Total change in grade
Vertical curvature
External distance
Vertical offset
High(low) point of curve
Elevation of any P
12 GGA !
|| A
LK !
ftALE800
!
2
4
!
L
xEy
0X u
!21
1
GG
LGX
yxG
!
100
1VPCofelevation
X is the distance along
the horizontal alignment
from PVC to the point of
interest
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Dr. Lina Shbeeb
General considerations
Reasonable upgrades without significant
loss in speed is 4-5 %
@ 70 mph design speed max grade is5%
@ 30 mph design speed max grade is 7-
12%
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Dr. Lina Shbeeb
Vertical alignment example A 600-ft curve connects a +4% grade to a 2% grade
at station 25+60.55 and elevation 648.64 ft. Calculate
the location and elevation of the VPC, the middle of the
curve, the VPT, and the curve elevation at stations
24+00 and 27+00
?? ? ?
?
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Vertical alignment example
Total change in grade
Vertical curvature
External distance
Vertical offset
High(low) point of curve
Elevation of any P
%612
!! GGA
1006
600!!!
|| A
LK
ftAL
54800
6006
800.!
!!
2
4
!
L
x
y
400
21
1!
!
!
6
(4)600
GG
LGX
2
1
4100
!
L
xx
G
VPCofelevation
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Dr. Lina Shbeeb
Vertical alignment example
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Dr. Lina Shbeeb
Calculation of vertical curve length
In most cases, sight distance will govern forhighways. The equations used to calculate
minimum lengths of vertical curves based on
sight distance depend on whether the sight
distance is greater than or less than thevertical curve length.
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Dr. Lina Shbeeb
Crest Vertical Curves, S > L
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Dr. Lina Shbeeb
Crest Vertical Curves, S < L
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Dr. Lina Shbeeb
Crest Vertical Curves
For first condition: S < L
For second condition: S > L
where L = minimum length of vertical curve
S = sight distance
A = algebraic difference in grades (gradient)
h1 = height of eye above roadway surface
h2 = height of object above roadway surface
A
HHSL
2
21 )(2002
!
2
21
2
)(200 HH
ASL
!
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Dr. Lina Shbeeb
Crest Vertical Curves
If the height of eye, h1, is 3.5 ft and height of object,
h2, is 0.5 ft respectively, as used for SSD, then
For first condition: S < L
For second condition: S > L
ASL
13292 !
1329
2
SAL !
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Dr. Lina Shbeeb
Sag vertical curve: headlight sight distance
Headlight beam of automobile at 2 ft ( or 600 mm),
with 1o upward divergence from longitudinal axis of
roadway.
S is actually the distance between the vehicle and
point where the 1o angle of light beam intersects the
surface of the roadway. For first condition: S < L
For second condition: S > L
A
ShSL
)tan(2002
F!
)tan(200
2
Sh
SAL
F!
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Dr. Lina Shbeeb
Headlight Sight Distance
For safety the length of a sag vertical curve
should be long enough so that the light beam
distance is nearly the same as the SSD. Therefore SSD is used for "S" in the above
equations.
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Dr. Lina Shbeeb
Vertical Curves The procedures for designing a crest vertical curve
are the following:
Step 1: Determine the minimum length of curve to
satisfy sight distance requirements
Step 2: Determine from the layout plans the station
and elevation of the PVI, that is the point where thegrades intersect.
Step 3: Compute the elevations of the PVC (or BVC)
and end of vertical curve (EVC or PVT).
Step 4: Compute the offsets y from the tangent tothe curve at equal distances, usually 100 feet or 20 m
apart.
Step 5: Compute elevations on the curve.
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