9/20/2012

1

ADVANCE ENGINEERING SURVEYING (3+1)

Dr. Mohsin Siddique

Asst. Prof.

Dept. of Civil Engineering

FAST-NU

Lecture 4: Compound curve

20/09/2012

Compound curve

• Compound Curve: When a curve consists of two or more arcs withdifferent radii, it is called a compound curve.

• Such a curve lies on the same side of a common tangent and thecenters of different arcs lie on the same side of their respectivetangents.

9/20/2012

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Compound Curve

Notations

• AB= rear tangent

• BC= forward tangent

• DE=common tangent

• Φ= Deflection angle

• Φ1=Deflection angle between read and forward tangent

• Φ2=deflection angle between common and forward tangent

• O1= centre of short curve

• O2=centre of long curve

• Rs=radius of short curve

• RL=radius of long curve

• T1 and T2= tangent point of short curve

• T2 and T3=tangent points of long curve

Compound Curve

Notations

• Ts= total tangent length of short side

• TL=total tangent length of longer side

• Ts=tangent length of short curve

• tL=tangent length of long curve

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3

Compound Curve

Calculation of data

• 1. Deflection angle

• 2. short tangent

• 3. Long tangent

• 4 . Common tangent

21 φφφ +=

( )2/tansin

sin1

2

1

φφ

φss

ss

RDET

tBDDTBDT

+=

+=+=

( )2/tansin

sin2

1

3

φφ

φLL

LL

RDET

tBEETBET

+=

+=+=

( ) ( )2/tan2/tan 21 φφLs

Ls

RR

ttDE

+=

+=

Compound Curve

Calculation of data

• From triangle BDE

( )( ) ( )

φ

φ

φ

φ

φφφ

φφ

sin

sin

sin

sin

180sin180sin

sinsin

1

2

21

12

DEBE

DEBD

BEBD

BEBD

=

=

−=

−−

=

9/20/2012

4

Compound Curve

Calculation of data

• Curve length (short curve)

• Curve length (long curve)

• Deflection angle (short curve)

• Deflection angle (short curve)

o

sR

180

1φπ

o

LR

180

2φπ

s

s

R

C9.1718=δ

L

L

R

C9.1718=δ

• Chainage of T1= Chainage of B -Ts

• Chainage of T2= Chainage of T1 +short curve length

• Chainage of T3= Chainage of T2 + long curve length

Numerical 5

• Two tangents AB and BC intersect at B. Another line DE intersects AB and BC at D such that the angle DEC=140 degrees. The radius of the first curve is 200m and that of second curve is 300m. The chainage point B is 950m. Take full chord length as 20 and 30m for short and long curves respectively.

• Calculate all necessary data for setting out the compound curve

• Solution:

• Given data

• Chainage of point B=950m

• Full chord length=20m

o

o

o

704030

40140180

30150180

2

1

=+=

=−=

=−=

φ

φ

φ

mR

mRs

L300

250

=

=

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Numerical 5

• 1. Tangent length of short curve

• 2. Tangent length of long curve

• 3. Common tangent length

( )( ) mt

RDTDTt

s

ss

58.532/30tan250

2/tan 121

==

=== φ

( )( ) mt

RETETt

s

Ls

19.1092/40tan200

2/tan 223

==

=== φ

mDE

ETDTDE

77.16219.10958.53

22

=+=

+=

Numerical 5

• From triangle BDE

mDE

BE

mDE

DB

DEBEDB

61.86110sin

77.16230sin

110sin30sin

34.111110sin

77.16240sin

110sin40sin

110sin30sin40sin

===

===

==

mR

mR

o

o

L

o

o

s

44.209180

length curve long

72.104180

length curveShort

2

1

==

==

φπ

φπ

m

m

m

24.109944.2098.889T of Chainage

8.88972.10408.785T of Chainage

08.78592.164950T of Chainage

3

2

1

=+=

=+=

=−=

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Numerical 5

• Deflection angle for short curve

• Number of full chords=5 (5x20=100m)

• Length of final subchord

• 104.72-100=4.72m

43040chord-sub finalfor

200

72.49.1718chord-sub finalfor

35152chord fullfor

200

209.1718chord fullfor

′′′=

×=

′′′=

×=

o

o

δ

δ

δ

δ

• Deflection angle for long curve

• Number of full chords=6 (6x30=180m)

• Length of final subchord

• 209.44-180=29.44m

14842chord-sub finalfor

300

44.299.1718chord-sub finalfor

35152chord fullfor

300

309.1718chord fullfor

′′′=

×=

′′′=

×=

o

o

δ

δ

δ

δ

2/959514

43040351525

2/

1

1

φ

φδ

=′′′=∆

′′′+′′′×=∆

=∑=∆

o

ns

oo

ns

ns

2/959519

14842351526

2/

2

2

φ

φδ

=′′′=∆

′′′+′′′×=∆

=∑=∆

o

nL

oo

nL

nL

Setting out by deflection angle method

• One theodolite metod

• Two theodolite method

Reading Assignment: Read both methods from book.

9/20/2012

7

Numerical 6

• Two tangents AB and BC intersect at B. Another line DE intersects AB and BC at D such that the angle ADE=145o and angle DEC=130o. The radius of the first curve is 250m and that of second curve is 350m. The chainage point B is 1250m. Take full chord length as 30m for both short and long curves.

• Calculate all necessary data for setting out the compound curve

THANK YOU

• Questions….

• Comments…

• Suggestions…

• Feel free to contact

mohsin.siddique@nu.edu.pk