1. The document discusses three methods for setting out a simple circular curve in engineering and surveying projects: the tangential angle method, the tangent offset method, and the chord offset method. 2. The tangential angle method uses a theodolite to measure deflection angles and chords to lay out points along the curve. 3. The tangent offset method uses only a chain and tape, measuring offsets perpendicular to tangents to locate points for small curves where high accuracy is not required. 4. Similarly, the chord offset method divides a chord between the PC and PT into segments and measures offsets perpendicular to locate points along the curve.

1. Engineering
Surveying
‫ﺍﻟﺒﺴﻴﻂ‬ ‫ﺍﻟﺪﺍﺋﺮﻱ‬ ‫ﺍﻟﻤﻨﺤﻨﻲ‬ ‫ﺗﺴﻘﻴﻂ‬ ‫ﻃﺮﻕ‬
Methods of Setting-Out a Simple
Circular Curve
M. Sc. Ahmed Q. Hameed
Lecturer at Surveying Engineering Department
Collage of Engineering / Middle Technical University
Email / ahmedhaloub2@yahoo.com

2. Concepts:
At the end of this lecture. Students will be able to….
Methods of Setting a Simple Circular Curve:
1- Tangential Angles Method (Deflection Angles Method).
2- Tangent Offset Method.
3-Chord Offset Method.

3. • The curve setting-out is to determine the horizontal positions of the
curved points on the ground so that they form the required curve
when connected to each other.
• To locate intersection point (P.I.) and tangent points (P.C.- P.T.).
Introduction
T
T
P.C
P.I
P.T
Case 1:-
• Set up theodolite at point P.I.
• Locale P.C. & P.T.points by fixed direction
of tangents and measuring the tangent
lengths backward and forward along tangent
line T₁ & T₂

4. • To locate intersection point (P.I.) and tangent points (P.C.- P.T.).
Introduction
T
T
P.C
P.I
P.T
Case 2:-
• Set up theodolite at point P.I.Directing along
the previously installed tangent and measure
angle (Ø = 180-∆).
180-∆
• Locale P.C. & P.T.points by fixed direction
of tangents and measuring the tangent
lengths backward and forward along tangent
line T₁ & T₂

5. • To locate intersection point (P.I.) and tangent points (P.C.- P.T.).
Introduction
T
T
P.C
P.I
P.T
Case 3:-
• Make the intersection of two tangents by
using the theodolite.
• Locale P.C. & P.T. points by fixed
direction of tangents and measuring the
tangent lengths backward and forward
along tangent line T₁ & T₂ .

6. 0+50
0+00
1+00
2+00
2+30
3+00
4+00
4+30
5+00
6+00
6+30
The station (chainage) is the horizontal distance as measured along
with a combination of curves and straight lines between two points
The stations in vertical curve:1+50
L = 400 m
Introduction

7. 20m
15+80
15+60
15+40
16+15
15+25
• The station of P.C is
obtained by subtracting the
tangent length from the
known station of the
intersection point P.I, and
the station of P.T is found
by adding the length of
curve to the station P.C,
then the pegs are fixed at
equal intervals on the
curve. The interval
between pegs is usually
20m.
T
T
R
R
∆
P.C
P.I
o
20m
20m
P.T20m
20m
16+00
L = 90 m
Lᵢ L
ғ
The stations in horizontal curve:
Introduction
ϴ=2D

8. •
Important Relationships for Circular Curves for Setting-Out
T
T
R
R
ϴ₂=2D
P.C
P.I
o
P.T
∆
ϴƒϴᵢ
ϴ₁=2D
Ø Ø
∆

9. • In this method the curve is set out tangential angle often called
deflection angle with a theodolite and tape.
• Working method:-
Tangential AngleMethod
1- Fix the theodolite device to be at
point P.C and directed at point P.I.
2- Measure the deflection angle (Ø)
and chord C.
3- Connect the ends of the chords to
draw the curve.
T
T
R
R
P.C
P.I
20m
P.T
ϴƒ
ϴᵢ
ϴ₁=2D
L
i
L f
Øᵢ
Ø₁
؃
∆

10. •
Tangential AngleMethod
R
R
ϴᵢ
P.C
Lᵢ
C
o
R
R
ϴ=2D
P.C
20m
C

11. • The calculations are completed by the table
below…
Station Deflection
Angle
Total Chord (m)
C=2R sin Ø
Single Chord
(m) C=2R sin Ø
P.C.
↓
P.T.

12. •

13. Station Deflection Angle
Total Chord (m) C=2R
sin Ø
Single Chord (m) C=2R sin
Ø
P.C.
37+69.33
0ᵒ 00” 0.00
0.00
37+80
38+00
38+20
38+40
38+60
P.T.
38+65.78

14. ϴ₂=2D
ϴƒ
ϴᵢ
ϴ₁=2D
o
P.C
P.I
P.T
ϴ₂=2D
ϴ₂=2D

15. Tangent Offset Method.
• In this method only chain and tape are used, where the curve is of
small length and there is no need for greater accuracy. Often know
as coordinate method.
• Working Method:
1. The T₁ is the horizontal x-axis, the
R is the vertical y-axis and the P.C
is a point of the origin.
2. Measure a distance-x from P.C. on
T₁ such as (X₁, X₂,...).
3. Erect perpendicular at each x-
distance such as (Y₁, Y₂,...)

16. •
Tangent Offset Method.
Point x
1 x₁ = y₁=
2 x₂ = y₂=
3 x₃ = y₃=
4 x₄ = y₄=
↓ ↓ ↓

17. Chord Offset Method.
• In this method only chain and tape are used, where the curve is of
small length and there is no need for greater accuracy.
• Working Method:
1. Locate the chord (P.C-P.T) and
divide it by suitable distances.
2. Measure distances such as (10, 15,
20)m at left and right of chord
center and mark a number of
points 1, 2,...etc.
3. Erect perpendicular at each x-
distance such as (Y₁, Y₂,...).

18. •
Chord Offset Method.
Point x
1 x₁ = y₁=
2 x₂ = y₂=
3 x₃ = y₃=
4 x₄ = y₄=
↓ ↓ ↓