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Surveying Engineering
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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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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
=
=
−=
−−
=
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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…
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