setting out of circular curves

7/23/2019 Setting Out of Circular Curves

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SETTING OUT OF CIRCULAR CURVES

Curves are used in linear project to (produce) provide a smooth change from one straight to

another straight

Project such as a roads, railways, canals, water & oil pipelines are curves for this purpose.

TYPES OF CURVES

1. Simple curve: these are circular curves of constant radius

A B

R R

2. Compound Curves – these are two or more consecutive.

Simple curves of different radii

R1 R2

R3



3. Reverse curves- these are two or more consecutive simple curves of the some of or

different radii with centres on opposite side of the common tanges (s)

R

R

4. TRanstional curves – Curves with a gradually varying radius ( offen refered to as

spirals)

R1 R2

5.

Combines curves – Consists of consecutive transition and simple curves transition

and simple curves

R R



This is the usually manner in which transition curves are used in roads and railway

design i.e link straight and circular curves or two branches of compound or reserve

curves.

Transition curves are also used to provide distances for applying the super elevation of

the road

6. Vertical curves – These are used to connect two intersecting straight (Gradients) in

vertical plane

Vertical curves can be circular or paraboloc

PROPERTIES OF CIRCULAR CURVES

I

Q=180-

T1 T2

90-

R

R D2

D1 Straight

O



Two straight and are connected by a circular curve of radious R.

The straight where projected forward meet at I the intersection point IP

The angle ∆ a is called the deflection Angle and equal the angle

subtended at the centre of the curve O.

The angle at pt I is called the apex angle

The curve commences at and ends at these pts are called the tangent

points.

Distance T1I and T2I are called tangent lengths and they are equal to

The length of the curve is T1 AT2 and it is obtained from the curve length =

( being in radians) Distance T1T2 is the main chord ( c) and it is given as

IA is called the apex distance and is given as

BA is the rise of the curve and is given as

=

THROUGH CHAINAGE

Through chaining is the horizontal distance from the start of the project of a

construction scheme. Normally straight part of the project is set out on 50m interval

while on the curve the marking is at half that interval.

Each peg is set out is marked by the thorough chainage on which it is placed e.g. if a peg

is placed at 3174.5m from the start of the project the peg is will be marked as 31+74.5 (

or 3+174.5) to indicate the chainage.

Setting Out of Circular Curves



The initial requisite for setting out any curve is:-

The location of the straight and their intersection points

The deflection angles or the radii and other some parameters e.g. tangent length

or length of curve

However these parameters can be derived from the deflection angle and radious

1. Setting Out Using Theodolite and Tape.

Also called deflection Angle method or Tangential Angle method

The curve is established by a series of chords.

IP

T1

Y

Z

The curves is established by a series of chords

T1X, XY,YZ etc thus the peg at pt X is fixed by sighting to the IP with theodalite

readings 00

Turning off the angle and measuring the chord length T,X along the line.

The instrument is set to lead to get direction to second peg at Y but the peg is

fixed by measuring the distance XY from X. peg at z measuring the distance XY

from X. Peg at Z is fixed by turning angle from T1 and measuring distance YZ

from Y. The process

continues until the whole curve is set out.

To IP

T1



A

R R

To get the setting out angle consider the figure and from OT,X if OA bisects

the chord T1X at right singles then from OT,A the angle AT,O = 1

Angle T,OA= 1=AOX

By radious are arc length

Approximate are T1X to chord T1X

Or

Example

Compute the setting out parameters on through chaninage basis of a curve given

the following

0 R= 200m

Chainage of IP = 22+59.59

Setting out to be 20m standard chord

Solution

Tangent length



=

= 53.59m

Curve length =

For setting out the curve on through chainage basis

1st subchord =14m

2nd , 3rd 4,th 5th, standard 20m

Final subchord = 10.72m

Calculate the deflection angles

1st suchord

Standard chord

Final Subchord



In tabula form (the setting Angles)

Chord Chord Length

(m)

Chainage

(m)

Deflection

angle 0’ ‘ “

Setting angle

0’ ‘ “

Remarks

1 14 22+20.00 2 00 19 2 00 19 Peg 1

2 20 22+40.00 2 51 53 4 52 12 Peg 2

3 20 22+60.00 2 51 53 7 44 05 Peg 3

4 20 22+80.00 2 51 53 10 35 58 Peg 4

5 20 23+00.00 2 51 53 13 27 51 Peg 5

6 10.72 23+10.72 1 32 08 14 59 59 T2

setting out of circular curves

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