CCS355 Neural Network & Deep Learning UNIT III notes and Question bank .pdf
Unit 5 Curves (1).pptx
1. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
2. Lectureoutline
d
• Introduction
• Theory and setting out methods of simple
circular curve
• Elements of compoun and Reverse curve.
• Transition curve
• Types of Transition curve
• Combined curve
• Types of vertical curve.
29. o
DefinitionandNotationof S
impleCurve
1) Back tangent or First Tangent ‐ AT₁
– Previous to the curve
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 will meet
in a point called the point f intersection
4)Point of curve or Commencement ( P.C.) –Beginning Point
T₁ of a curve. Alignment changes from a tangent to
curve.
30. n
• 5) Point of Tangency ‐ PT
– End point of curve ( T₂ ) is called..
6) Intersection Angle (Ø )
‐ The Angle AVB between tange t AVand tangent VB is
called...
7) Deflection Angl (∆ )
The angle at P.I.between tangent AVand 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.
It is also called the apex distance.
10) Length of curve – l
It is the total length of curve from P
.C.to P
.
T.
DefinitionandNotationof S
impleCurve
31. 11) Long Chord
– It is the chord joining P
.C.to P
.
T
.,T₁ T₂ is a longchord.
12) Normal Chord:
A chord between two successive regular station on a curve is called normal chord.
Normally , the length of normal chord is 1 chain ( 20 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 the curve deflects to the left of the direction of the progress of survey.
DefinitionandNotationof S
impleCurve
32. Designationof curve
h
The sharpness of the curve is designated by two ways.
( 1 ) By radius ( R)
( 2) By Degree of Curvature ( D )
( 1 ) By radius ( R)
Curve is known by the lengt of its radius‐ R
33. Designationof curve
Chord Definition
The Angle subtended at
the centre of curve by a
chord of 30 or 20 mt. is
called degree of
curvature.
If an angle subtended at
the centre of curve by a
chord of 20 mt is 5° , the
2
c0S
ue
p
rt
e
vm
eb
e
r
is2
c3
aled5° curve
( 2) By Degree of Curvature ( D )
Arc Definition
The Angle subtended at
the centre of curve by an
arc of 30 or 20 mt. length
is called degree of curve.
Used in America, canada,
India etc.
34. 20S eptember 2013
R
elationbetweenRadiusanddegreeof curve.
(a) By chorddefinition
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.
From Triangle PCO
35. When D is small,
R
elationbetweenRadiusanddegreeof curve.
may taken equal to
R = ---- ---
-----------
1719
D
37. Example 1
• A circular curve has a radius of 150 mt and 60⁰
deflection angle. What is its degree(i) By arc
definition and 9ii) by chord definition.
• Solution:
(i) By arc definition Assuming chord length 30mt
38. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
39. v
Elementsof S
implecircular cur e
• 1) Length of curve ( l)
• * If curve is designated by Radius:
l = Length of arc T₁ C T₂
= R * ∆ ‐ When ∆ is in Radian
‐ When ∆ is in degree.
* If curve is designated by degree:
• Length of arc =20 mt.
• Length of curve
40. 2) Tangent length ( T):
• VT₁ and VT₂ are the tangents
length Elements of simple
circular curve
• T = VT₁ = VT₂ = tangent length
• From ∆ VT₁O
Elements of Simple circular curve
41. u
Elements of Simple circular c rve
3) Length of chord ( L ):Elements of simple
circular curve
• In the figure T₁ ,T₂ is a long chord.
• Length of long chord =L =T₁T₂ = 2 * (T₁ D).
• From triangle T₁DO,
42. a
V
E= OV‐OC ( OC = R)
Elementsof S
implecircular curve
4) External Distance ( E ): or Apex distance
• In the figure VC is an extern l distance.
• External distance = E= VC= O –OC Length of
• From triangle VT₁O.
43. O
Elementsof S
implecircularcurve
5) Mid ordinate ( M ): = Distance – CD
• Also known as versed sine of the curve.
• Mid ordinate =M= CD= OC‐OD
• From ∆T₁DO
M = C‐ OD
44. S
ettingout of singleCircularcurve
• 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 ( Measure bytheodolite)
‐ Calculate tangent length
‐ Fix point T₁T₂
45. o
S
ettingout of singleCircularcurve
• Chainage of tangents:
• ‐ Point A is the starting point of chain line
• Chainage of point V
,B, D are measured from
point A.
• ‐ Chainage of T₁ = Chainage of V‐ T ( Tangent length)
• T₂ =Chainage f T₁ + Length of curve (l)
46. h
d
d
o
S
ettingout of singleCircularcurve
• Normal chord and Sub c ord:
• ‐For alignment pegs are riven.
• 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 calle First sub chord.
• All the chord joining adjacent peg stations are
called full chord or normal chord.
• The length of normal ch rd is 20 mt.
• The point joining last main peg station and tangent T₂
is called last sub chord.
47. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
48. m
e
d
Methodsof S
ettingout ofsingleCircularcurve
Two Methods
• 1) Linear Methods
• 2) Angular Methods.
1) Linear Methods
• (i) By offsets or ordinate fro the long chord.
• (ii) By successive bisection of arcs or chords.
• (iii) By offsets from the tang nts (Radial & Perpendicular).
• (iv) By offsets from the chor produced.
49. (i) By offsets or ordinate
Let T1T2=L= the length of
the Long chord
ED= O0= the offset at mid-
point (e) of the long chord
(the versed sine)
PQ=Ox= the offset at
distance x from E
Draw QQ1 parallel to
T1 T2 meeting DE at Q1
from the long chord.
50.
51.
52. (i) By offsets or ordinate
R = Radius of curve
O0 = Mid ordinate
Ox = Ordinate at distance x
T1, T2 = tangents point
L = Length of long chord.
from the long chord.
53. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
54. c
• T1‐T2= L
• T1‐C = L
• T2‐C = L
• C‐C1, C‐C2=L
• C1‐T1, C2‐T2=L
(ii) By successive bisection of ar s or chords.
55. (iii) By offsets from the tangents .
• Two types
• Radial offset erpendicular offset
60. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
61. The angle of intersection of a circular curve is 45° 30' and its radius is 198.17
m. PC is at Sta. 0 + 700. Compute the right angle offset from Sta. 0 + 736.58
on the curve to tangent through PC.
Length of curve from PC to A:
s=736.58−
700
s=36.58 m
Angle subtended by arc s from the center of the curve:
s/θ=2πR/360∘
36.58/θ=2π(198.17)/360∘
θ=10.58∘
Length of offset x:
cosθ=(R−x)/R
x=R−Rcosθ=198.17−198.17cos10.58∘
x=3.37 m
62. Angular Method
• Used when length of curve is large
• More accurate than he linear methods.
• Theodolite is used
• The angular methods are:
1) Rankine method of tangential angles.
OR
One theodolite met od
2) Two theodolite met od.
3) Tacheometric method
72. Obstacles in setting out simple curves
• Case –I -When P.I. is inaccessible
• Case –II -When P. . is inaccessible
• Case –III -When P. . is inaccessible
• Case –IV -When b th P.C. and P.T. is
inaccessible.
• Case –V -When obstacles to chaining.
74. u
Requirement of transition curve
• Tangential to straight
• 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.
• Length of transition c rve = full super
elevation attained.
75. d
Purpose of transition curve
• Curvature is increase gradually.
• Medium for gradual introduction of superelevation
• Provide Extra widening gra ually
Advantages
• Increase comfort to passenger on curve
• Reduce overturning
• Allow higher speed
• Less wear on gear, tyre
76. Typesof transitioncurve
• Cubic parabola
• ‐ For railway
• Spiral or Clothoid
‐ Ideal transition
‐ Radius α Distance
• Lemniscates
‐ Used for road
78. Length of vertical curve =
Lengthofverticalcurve
T
otal change of grade
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
Rate of change of grade
g2 – g1
= ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
r
g1, g2 = Grades in %
r = Rate of change of grade
79. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
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91. UNIT V Curves and Modern Surveying
Surveying - 19CECN1303
Mr. S. Krishnakumar, AP /Civil
