Methods of setting out a simple circular curve

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Luma Khalid E-mail : [email protected] .edu.iq Engineering Surveying 3 rd Stage Methods of setting out a simple circular curve

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Surveing 4th Stagecircular curve
• Tangential angles method (or Deflection angles method)
• Tangent offsets method
• Chord offsets method
• Location from P.I
5
Δ
P.c
P.I
P.T
Δ
O
Station Total Chord Length Single Chord Length
Stat. P.C 0:00’ 0.00 0.00
Stat. (1) 1=
*D = 2*R* 1 = 2*R*
i
Stat. (2) 2= i
+ D = 2*R* 2 = 2*R*
Stat. (3) 3= i
+ 2D = 2*R* 3 = 2*R*
Stat. (4) 4= i
= 2*R* 4 = 2*R*
Stat. P.T 4= i
= 2*R*
( − ) = 2 − 2
= − 2 − 2
2 )2
X Y
0.00
2 )2
tanΔ 2−R sin
α=tan−1 1− cos
tanΔ 2−sin
Single Chord Length
tanΔ 2−sin 1
tanΔ 2−sin 2
tanΔ 2−sin 3
tanΔ 2−sin 4
tanΔ 2−sin Δ
Δ

Example
• Setting out a horizontal circular curve by all methods if you know :
• Δ=43:24’ , D= 4:30’ and Stat. P.I=38+20
• Deflection angles method for 20 m
• Tangent offsets method for 10 m
• Chord offsets method for 10 m
• Location from P.I divided Δ over 5
Elements of a Simple Circular curve
• R = 573
• Stat. P.T = stat P.C + L =
• 37 + 69.33 + 00 + 96.45 = 38 +65.78
Setting out a horizontal circular curve by Deflection angles method)
• =
• = 10.67 127.33
Setting out a horizontal circular curve by Deflection angles method)
Station Central angle Deflection angle()
Total Chord Single Chord
Stat. P.C 37 + 69.33 00 00 00 00 00 0.00 0.00
37 + 80 = 4:48’ 2:24’ 10.66 10.66
38 + 00 + 2D =13:48’
6:54’ 30.59 19.98
11:24’ 50.34 19.98
15:54’ 69.77 19.98
Δ = =43:24’
Setting out a horizontal circular curve by Tangent offsets method
X Y = R - −
0 0
10 0.39
20 1.58
30 3.58
40 6.45
50 10.23
Setting out a horizontal circular curve by Chord offsets method
X = 2 − 2 - 2 − (

Point α Single Arch Length
Single Chord Length
5 43.40: 136:36’=180:-Δ