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ADVANCE ENGINEERINGSURVEYING (3+1)
Lecture 1: Introduction and
Highway and Railway curves
Dr. Mohsin Siddique
Asst. Prof.
Dept. of Civil EngineeringFAST-NU
11/09/2012
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CIVIL ENGINEERING DRAWING & GRAPHICS
CH (1+2)
• Objective:
• To acquire knowledge of control surveys and their use in advance
branches of surveying.• To apply principles of surveying in related field problems.
• Course Contents:
• Hydrographic Surveys: Objectives of hydrographic survey andelectronic charting, Vertical control, Depth and Tidalmeasurements, Position-fixing techniques, Sounding plan,
Horizontal control, Processing.
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CIVIL ENGINEERING DRAWING & GRAPHICS
CH (1+2)
• Control Surveys: Geodesy, UTM and other Map Projections,
Coordinate Systems and Datum, Horizontal control techniques,Survey markers, Observations on Polaris, Computation techniquefor azimuth determination and Gyro-theodolite.
• urvey ng pp cat on: g way an a way urves, outesurveys, Circular curves, Setting out circular curve by variousmethods, Compound curves, Reverse, Vertical, Parabolic curves,Design considerations, Spiral curves, Approximate solution forspiral problems, Super-elevation.
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CIVIL ENGINEERING DRAWING & GRAPHICS
CH (1+2)
• Books Recommended
• 1. Basik. N.N., Advance Engineering Surveying
• 2. Wolf P.R. & Ghilani C. D., Elementary Surveying – Ann ro uc on o eoma cs, 11
P
on, ren ce a , ,2004.
• 3. Thomas, M. Lillesand & Ralph W. Kiefer (2005), Remote Sensingand Images Interpretation, 5th
PP edition, John Wiley & Sons, Inc.
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Highway and Railway Curves
Introduction
• During the survey of thealignment of a project involving
road or railways, the direction of the line may change due to someunavoidable circumstances.
• The angle of the change in
rect on s nows s nown asdeflection angle.
• For it to be possible for a vehicleto run easily along the road orrailway track, the two possible
straight lines (the original lineand the deflected line) areconnected by an arc which isknow as curve of the road or
track.
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Highway and Railway Curves
Introduction
• During the survey of thealignment of a project involving
road or railways, the direction of the line may change due to someunavoidable circumstances.
• The angle of the change in
rect on s nows s nown asdeflection angle.
• For it to be possible for a vehicleto run easily along the road orrailway track, the two possible
straight lines (the original lineand the deflected line) areconnected by an arc which isknow as curve of the road or
track.
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Highway and Railway Curves
Types▫ 1. Horizontal Curves
When the curve is provided in the horizontal
plane it is called horizontal curve
▫ 2. Vertical Curves
And if the curve is provided in the vertical
plane it is termed as vertical curve
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Highway and Railway Curves
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Highway and Railway Curves
Definition and Explanation of Different Terms
• Degree of Curve
• The angle a unit Chord of
length 30m subtends at thecentre of the circle formed by the curve is known as thedegree of the curve. It is
.
• A curve may be designatedaccording to either
▫ Radius or
▫ Degree of the curve
When the unit chord subtends an angle of 1 degree , it is called one-
degree curve and when the angle is 2 degree it is called two-degree curve
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Highway and Railway Curves
Relation between Radius and Degree of curve
• Let AB be the unit chord of 30m, O the center, R the radius
and D the degree of the curveas shown in fig.
ROAHere =
( )2 / sin
15
152Dsin
OACTriangleFrom
D/2AOC
mm;
D
R
ROA AC
=
==
=∠
==
(radian) D/2sinD/2
small,veryisDWhen
≈
( )( ) D D R
1719
180 / 2 /
15==
π
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Highway and Railway Curves
Superelevations• When a particle moves in a circular
path, then a force know as centrifugalforce acts upon it, and tends to push it
away from the center.
• Similarly when a vehicle suddenly moves from a straight path to a curved
path, the centrifugal force tends to pushthe vehicle away from the road. This is because there is no component force tocounterbalance this centrifugal force.
• To counter balance the centrifugal force,the outer edge of the road or railway israised to some height, so that the sinecomponent of the weight (W sinΘ) of the vehicle may counter balance the
overturning force.
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Highway and Railway Curves
Superelevations
• The height through which the outer edgeof the road or railway is raised is known
as superelevations or cant.• In the figure, P is the centrifugal force,
W sinΘ is the component of the weightof the vehicle and h is the supere evat on g ven to roa or ra way.
• For Equilibrium
bhwhen
gR
WV
b
hW
gR
WV W
==⇒<<
=⇒=
θ θ θ
θ
tansin;1
;sin22
RailwaysFor
RoadsFor
2
2
gRGV h
gR
bV h
=
=
• b=width of the road (m)
• G=distance between centreof rail (gauge) (m)
• R=radius of curve (m)• g=acceleration due to
gravity (9.8m/s/s)
• Speed of vehicle (m/s)
• Superelevation (m)
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Highway and Railway Curves
Centrifugal Ratio
• The ratio between centrifugal force and the weight of the vehicle isknow as centrifugal ratio
Ratio(CR)lCentrifuga22
===gR
V
gRW
WV
W
P
8
1railwaysinCRforvalueAllowable
4
1roadsinCRforvalueAllowable
=
=
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Highway and Railway Curves
Types of Horizontal Curves
• Simple Circular Curve: When a curve consists of a
single arc with a constantradius connecting twotangents, it is said to be acircular curve.
• Compound Curve: When acurve consists of two or morearcs with different radii, it iscalled a compound curve.
• Such a curve lies on the sameside of a common tangent andthe centers of different arcs lieon the same side of their
respective tangents.
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Highway and Railway Curves
Types of Horizontal Curves• Transition Curve: A curve of
a variable radius is known as
transition curve.• It is also called a spiral curve oreasement curve.
• It railways, such a curve isprov e on o s es o a
circular curve to maintainsuperelevations.
• Excessive superelevations may cause wear and tear of the rail
section and discomfort topassengers.
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Highway and Railway Curves
Types of Horizontal Curves• Lemniscate curve: A
lemniscate curve is similar to
transition curve and isgenerally adopted in city roads where the deflection angle islarge.
,
of such curve.• The curve is designated by
taking a major axis OD, minoraxis PP’ with origin O and axes
OA and OB.• OP(ρ) is known as the polar ray
and α as the polar angle
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Notation Used with Circular Curve
• AB & BC are known as thetangents to the curve
• B is known as the point of theintersection or vertex.
• The angle φ is know as theangle of deflection
• e ang e s ca e t e ang eof intersection
• Points T1 and T2 are known astangent points
• Distance BT1 and BT2 are
known as tangent lengths• AB is called the rear tangent
and BC is called the forwardtangent
• When the curve deflects to theright, it is called a right-handcurve and when it deflects to
left, it is said to be a left-handcurve.
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Notation Used with Circular Curve
• The straights line T1DT2 isknown as long chord
• The curve line T1ET2 is said to be the length of curve
• The mid-point E of the curveT1ET2 is known as apex orsumm o e curve
• The distance BE is known asapex distance or externaldistance
• The distance DE is called the
versed sine of the curve• R is the radius of the curve
• Angle T1OT2 is equal to thedeflection angle φ
• The point T1 is known as beginning of the curve or thepoint of the curve
• And End of the curve (T2) isknown as the point of tangency
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Properties of Simple Circular Curve
• If the angle of intersection isgiven as I , then
I −=180φ • If radius is not given, then
D R / 1719=
Where D is degree of curve
• Tangent length BT1 or BT= ( )2 / tan φ R
• Length of curve=length of arc T1ET2
180
o R
Rφ π
φ =
• Again length of curve
giveniscurveof Ddegreeif
30
D
φ =
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Properties of simple circular curve
• Length of long chord
( ) ( )2sin22sin1212 φ φ ROT DT ==
• Apex distance=BE=OB-BE
( ) ( ) )12(sec2sec −=− φ φ R R R
• Versed sine of curve
)2cos1(2cos φ φ −=−=
−=
R R R DE
ODOE DE
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