introduction to railways and highways curves by d.m siddique

7/30/2019 Introduction to Railways and Highways Curves By D.M Siddique

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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



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.




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.




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.



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.




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.




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




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




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




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.




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)




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

=

=




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.




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.




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



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.



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



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 =



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



THANK YOU

• Questions….

• Comments…

• Suggestions…

• Feel free to contact

[email protected]

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