2. Question asked in GTU‐Theory
Question asked in GTU Theory
1) Describe the procedure of setting out of simple
) esc be t e p ocedu e o sett g out o s p e
circular curve by (i) Perpendicular offset from
tangent, and (ii) Rankine’s method of tangential
l
angle.. Dec‐2009
2) Why transition curves are introduced on
h i t l f hi h il ? D
horizontal curves of highways or railways? Dec‐
2009
3) Describe the method of setting a circular curve
3) Describe the method of setting a circular curve
by the method of offsets from the long chord.
Dec‐2010
20 September 2013
3. Question asked in GTU‐Theory
Question asked in GTU Theory
4) Discuss the method of setting out a circular curve
) g
with two theodolite. What are its advantages
and disadvantages over Rankine’s method Dec‐
2010
2010
5) What are the elements of simple circular curve?
Define with figure and give their relationship.
March‐2010
6) Why are curves provided? State various types of
curves with sketch
curves with sketch.
7) Draw the neat sketch of simple circular curve
showing various elements of it. Dec‐2011
g
20 September 2013
4. Question asked in GTU‐Theory
Question asked in GTU Theory
8) Enumerate the parts of a compound curve
8) Enumerate the parts of a compound curve
and describe the relationship between them
Jan‐2013
Jan 2013.
9) What is vertical curve? Explain different types
of vertical curves Jan 2013
of vertical curves. Jan‐2013.
10) Explain following terms (i) Compound curve
(ii) P i f i i (iii) T Di
(ii) Point of intersection (iii) Tangent Distance
(iv) Mid Ordinate May‐2012.
20 September 2013
5. Lecture outline
Lecture outline
• Introduction
Introduction
• Theory and setting out methods of simple
circular curve
circular curve
• Elements of compound and Reverse curve.
• Transition curve
• Transition curve
• Types of Transition curve
C bi d
• Combined curve
• Types of vertical curve.
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29. Definition and Notation of Simple Curve
• 1) Back tangent or First Tangent ‐ AT₁
– Pervious to the curve
d d
2) Forward Tangent or Second tangent‐ B T₂
‐ Following the curve.
3) Point of Intersection ( P.I.) or Vertex. (v)
If the tangents AT₁ and BT₂ .are produced they
ill t i i t ll d th i t f
will meet in a point called the point of
intersection
4)Point of curve ( PC ) Beginning Point T of a
4)Point of curve ( P.C.) –Beginning Point T₁ of a
curve. Alignment changes from a tangent to
curve.
20 September 2013
30. Definition and Notation of Simple Curve
) f
• 5) Point of Tangency ‐ PT
– End point of curve ( T₂ ) is called..
6) Intersection Angle (Ø )
) g (Ø )
‐ The Angle AVB between tangent AV and tangent VB is
called...
7) Deflection Angle (∆ )
7) Deflection Angle (∆ )
The angle at P.I. between tangent AV and VB is called..
8)Tangent Distance –
It is the distance between P.C. and P.I.
9) External Distance – CI
The distance from the mid point of the curve to P.I.
The distance from the mid point of the curve to P.I.
It is also called the apex distance.
10) Length of curve – l
I i h l l h f f PC PT
It is the total length of curve from P.C. to P.T.
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31. Definition and Notation of Simple Curve
11) Long Chord
11) Long Chord
– It is the chord joining P.C. to P.T., T₁ T₂ is a long chord.
12) Normal Chord:
A chord between two successive regular station on a curve is
A chord between two successive regular station on a curve is
called normal chord. Normally , the length of normal chord is 1
chain ( 2o mt).
13) Sub chord
The chord shorter than normal chord ( shorter than 20 mt) is
called sub chord)
14) Versed sine – Distance CD
The distance between mid point of long chord ( D ) and the apex
point C, is called versed sine. It is also called mid‐ ordinate ( M).
15) Right hand curve:
If the curve deflects to the right of the direction of the progress
of survey.
16) Left hand curve
If th d fl t t th l ft f th di ti f th
If the curve deflects to the left of the direction of the progress
of survey.
20 September 2013
33. Designation of curve
( 2) By Degree of Curvature ( D )
Chord Definition Arc Definition
The Angle subtended at
the centre of curve by a
h d f 30 20 i
The Angle subtended at
the centre of curve by an
chord of 30 or 20 mt. is
called degree of
curvature.
arc of 30 or 20 mt.
length is called degree of
curve.
If an angle subtended at
the centre of curve by a
Used in America, canada,
India etc
20 September 2013
the centre of curve by a
chord of 20 mt is 5° , the
curve is called 5° curve
India etc.
34. Relation between Radius and degree of curve.
( ) B h d d fi iti
(a) By chord definition
The angle subtended at the centre of curve
by a chord of 20 mt. is called degree of curve.
R = radius of curve.
D = degree of curve.
PQ = 20 mt. = Length of chord.
g
From Triangle PCO
20 September 2013
38. Elements of simple circular curve
Elements of simple circular curve
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39. Elements of Simple circular curve
• T₁ = P.C.= Point of tangency=Point of curve.
• T₂ = P.T.= Second point of tangency.
T₂ P.T. Second point of tangency.
• V or I = P.I. = Point of intersection.
∆ D fl ti l
• ∆ = Deflection angle.
• Ø = Intersection angle.
• R = Radius of curve.
• CD= Mid ordinate (M)
CD Mid ordinate (M)
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40. Example 1
• A circular curve has a radius of 150 mt and 60⁰
deflection angle. What is its degree(i) By arc
deflection angle. What is its degree(i) By arc
definition and 9ii) by chord definition.
• Solution:
• Solution:
(i) By arc definition Assuming chord length 30mt
20 September 2013
46. Setting out of single Circular curve
• First step‐ Locate tangent point
• ‐ By tape measurements.
‐Intersection of both tangents point V‐ Point
of intersection.
‐ Set theodolite at V and measure angle Ø
Ø
‐ Ø ( Measure by theodolite)
‐ Calculate tangent length
‐ Fix point T₁T₂
20 September 2013
47. Setting out of single Circular curve
• Chainage of tangents:
• ‐ Point A is the starting point of chain line
• Chainage of point V, B, D are measured from
point A.
p
• ‐ Chainage of T₁ = Chainage of V‐ T ( Tangent length)
• T Chainage of T + Length of curve (l)
• T₂ =Chainage of T₁ + Length of curve (l)
20 September 2013
48. Setting out of single Circular curve
N l h d d S b h d
• Normal chord and Sub chord:
• ‐For alignment pegs are driven.
h di b i ll 20
• The distance between two pegs is normally 20m
• Peg station are called main stations.
• The chord joining the tangents point T₁ and the first
main peg station is called First sub chord.
All th h d j i i dj t t ti
• All the chord joining adjacent peg stations are
called full chord or normal chord.
• The length of normal chord is 20 mt
• The length of normal chord is 20 mt.
• The point joining last main peg station and tangent
T₂ is called last sub chord
T₂ is called last sub chord.
20 September 2013
49. Methods of Setting out of single Circular curve
• Two Methods
• 1) Linear Methods
• 2) Angular Methods.
• 1) Linear Methods
( ) ff d f h l h d
• ‐ (i) By offsets or ordinate from the long chord.
• (ii) By successive bisection of arcs or chords.
• (iii) By offsets from the tangents.
• (iv) By offsets from the chord produced
(iv) By offsets from the chord produced.
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50. (i) By offsets or ordinate from the long chord.
R = Radius of curve
R = Radius of curve
O0 = Mid ordinate
Ox = Ordinate at distance x
T1, T2 = tangents point
L = Length of long chord.
20 September 2013
51. (ii) By successive bisection of arcs or chords.
• T1 T2= L
• T1‐T2= L
• T1‐C = L
• T2‐C = L
• C‐C1, C‐C2=L
,
• C1‐T1, C2‐T2=L
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52. (iii) By offsets from the tangents.
• Two types
• Radial offset Perpendicular offset
p
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53. Angular Method
• Used when length of curve is large
• More accurate than the linear methods
• More accurate than the linear methods.
• Theodolite is used
• The angular methods are:
1) Rankine method of tangential angles.
OR
One theodolite method
2) Two theodolite method.
20 September 2013
54. Obstacles in setting out simple curves
• Case –I -When P.I. is inaccessible
C II Wh P C i i ibl
• Case –II -When P.C. is inaccessible
• Case –III -When P.T. is inaccessible
• Case –IV - When both P.C. and P.T. is
inaccessible.
• Case –V - When obstacles to chaining.
20 September 2013
56. Requirement of transition curve
• Tangential to straight
M t i l t ti ll
• Meet circular curve tangentially
• At origin curvature should zero.
• Curvature should same at junction of circular
curve.
• Rate of increase of curvature = rate increase of
super elevation.
p
• Length of transition curve = full super
elevation attained
elevation attained.
20 September 2013
57. Purpose of transition curve
p
• Curvature is increase gradually.
• Medium for gradual introduction of
• Medium for gradual introduction of
superelevation
• Provide Extra widening gradually
• Provide Extra widening gradually
• Advantages
• Increase comfort to passenger on curve
• Increase comfort to passenger on curve
• Reduce overturning
• Allow higher speed
• Less wear on gear, tyre
20 September 2013
58. Types of transition curve
• Cubic parabola
• For railway
• ‐ For railway
• Spiral or Clothoid
‐ Ideal transition
‐ Radius α Distance
• Lemniscates
‐ Used for road
‐ Used for road
20 September 2013
60. Length of vertical curve
Length of vertical curve
• Total change of grade
Total change of grade
• Length of vertical curve =‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
• Rate of change of grade
• Rate of change of grade
• g2 – g1
• = ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
• r
• g1, g2 = Grades in %
• r = Rate of change of grade
20 September 2013
