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Islamic University of Gaza
Civil Engineering Department
Surveying II
ECIV 2332
By
Belal Almassri
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Chapter 9
Route Surveying – Part 5
- Transition Curve Layout Using The Theodolite.
- Preliminary work and calculations.
- Setting out the curves.
- The whole procedure.
- Example 9.4 .
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Transition Curve Layout Using The
Theodolite: In order to lay out a combination of circular curve
and transition curve, the following procedure is used:
1. Preliminary work and calculations.
- Transition Curve.
- Circular Curve.
2. Setting out the curve.
- Left transition curve.
- Right transition curve.
- Circular curve.
- Common tangent between transition and circular curves.
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Transition Curve Equations
Length of transition curve (L):
- Past experience or uniform rate or equation
- a: Rate of change of radial acceleration in
m/sec^3 (0.3 – 0.5).
- R: Circular curve radius.
- V: Design speed in m/sec.
aR
vL
3
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Transition curve shift (S):
- The amount of distance that the circular
curve is shifted inward to be adopted
with the transition curve.
- L: Length of transition curve.
- R: Circular curve radius.
R
LS
24
2
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The total length of the tangent Ts or P-T line:
- The total length from the point of the intersection PI to the start point of the transition T can be computed through the following formula:
- L: Length of transition curve.
- S: Shift of transition curve.
- R: Radius of circular curve.
- Δ: Central Angle.
2)
2tan()(
LSRPT
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Chainage of TS ( T ͦ ) and SC ( T1):
Chainage of T ͦ = Chainage of PI - P T ͦ
Chainage of T1 = Chainage of T ͦ + L
Lengths of partial chords for the left
transition curves:
- C ≤ R/40
- C1 to be as computed in circular curves.
- C2 = L – (C1+ nC), n: intermediate
chords.
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Deflection angles of the transition curve:
- Angle of T1 (the spiral angle):
- Deflection angle of transition curve:
- CHECK! .....Sum of di =
180.
2R
Ls
180.
6
2
LR
Cd i
i
3
s
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Underground . . .
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The Whole Calculations Procedure:
1. Find R and Δ of the circular curve.
2. Find L, S and PT ͦ of the transition curve.
3. Find Chainage of T ͦ , T1, T2 and T3.
4. Find the Partial chords and the
deflection angles for the following:
- Right transition curve.
- Circular Curve.
- Left Transition Curve.
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Example 9.4
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Vertical Curves
Def: A parabolic curve that is applied to
make a smooth and safe transition between
two grades on a roadway or a highway.
VPC: Vertical Point of Curvature
VPI: Vertical Point of Intersection
VPT: Vertical Point of Tangency
G1, G2: Tangent grades in percent
A: Algebraic difference in grades
L: Length of vertical curve
VPI
VPC VPT
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There are two kinds of vertical curve:
SummetVertical Curves: Type I and Type II.
Sag Vertical Curves : Type III and Type IV.
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Information needed for vertical curves
design:
1. Gradients g1 and g2.
2. Chainage and elevation of VPI.
3. Length of the curve L.
Sight Distance:
The length of the roadway visible to driver.
1. Stopping sight distance. (S.S.D)
2. Passing sight distance. (P.S.D)
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Stopping Sight Distance (SSD) is the
viewable distance required for a driver to
see so that he or she can make a
complete stop in the event of an
unforeseen hazard.
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V: Velocity in m/s
t: Perception and reaction time (2.5 sec)
f: coefficient of friction for roads
i: gradient (Up is +ve, Down is –ve)
g: gravity (9.81m/s^2)
)(2.
2
ifg
VtVSSD
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Passing Sight Distance (PSD) is the clear
distance that the driver must view in
order to be able safely pass the car in
front of him. (PSD=2. SSD)
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Vertical Curve Calculations
Location of Max/Min elevation on the
curve:
Elevation of any point on the curve:
A
Lgx 1
maxmin/
2
12
xL
AxgHH VPCM
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Chainage and elevation of VPC and VPT:
2
2
2
2
2
1
LCHCH
LgHH
LCHCH
LgHH
VPIVPT
VPIVPT
VPIVPC
VPIVPC
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Length of Vertical Curve:
Method 1:
K: Rate of curvature. (By Tables)
A: Difference of gradients.
Method 2: depends on the sight distance,
gradient difference: Equations (9.46, 9.47,
9.48, 9.50) from the text book.
AKL .
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Example 9.7