engineering surveying - ii ce313 · nomenclature of simple curves 12) external ... the interval...

Engineering Surveying - II CE313Route Survey

Lecture 03

Muhammad Noman

Route Survey

Route surveying is comprised of all survey operations required for design and construction of engineering works such as highways, pipelines, canals, or railroads.

Curves

Curves are provided in the line of communications in order that the change of direction at the intersection of the straight lines shall be gradual.

Straight (tangent) sections of most types of transportation routes, such as highways, railroads, and pipelines, are connected by curves in both the horizontal and vertical planes.

Curves

Curves are provided whenever a road changes its direction from right to S (vice versa) or changes its alignment from up to down (vice versa).

The curves are generally circular arcs, but parabolic curves are often used in many countries

The lines connected by curve are Tangential to it and are called tangential straight.

T1 and T2 are tangent points

B is the intersection point or vertex.

Curves

Types of Curves

There are two types of Curves:

i) Horizontal Curve

ii) Vertical Curve

Types of Horizontal Curves

1. Simple Curve:

It consists of a single curve/Arc connecting two tangents or vertex.

It is the type most often used.


2. Compound Curve:

A compound curve consists of two arc/curves of different radii bending in the same direction and laying on the same side of their common tangent i.e. their center being on the same side of the curves.


3. Reverse Curve:

A reverse curve is composed of two arcs of equal of unequal radii, bending in opposite direction with common tangent at their junction. Their centers lying on opposite sides of the curve.


4. Transition Curve:

A track transition curve, or spiral easement, is a calculated curve on a section of highway, or railroad track, where a straight section changes into a curve. It is designed to prevent sudden changes in lateral or centripetal acceleration.

Nomenclature of Simple Curves

1. Tangents or Straights: The straight lines AB and BC which are connected by the curves are called the tangents or straights to curves.

2. Point of Intersection: (PI.) The Point B at which the 2 tangents AB and BC intersect or Vertex (V) .


3) Back Tangent: The tangent line AB is called 1st tangent or Rear tangents or Back tangent.

4) Forward Tangent: The tangents line BC is called 2nd tangent or Forward tangent.


5) Tangents Points: The points T1 and T2 at which the curves touches the straights.

• 5.a) Point of Curve (P.C): The beginning of the curve T1 is called the point of curve or tangent curve (T.C).

• 5.b) Point of tangency (C.T): The end of curve T2 is called point of tangency or curve tangent (C.T).


6) Angle of Intersection: (I) The angle ABC between the tangent lines AB and BC. Denoted by I.

7) Angle of Deflection (∅): Then angle B`BC by which the forward (head tangent deflect from the Rear tangent.

8) Tangent Length: (BT1 and BT2) The distance from point of intersection B to the tangent points T1 and T2. These depend upon the radii of curves.


9) Long Cord: The line T1T2 joining the two tangents point T1 and T2 is called long chord. Denoted by l.

10) Length of Curve: the arc T1FT2 is called length of curve. Denoted by L.

11) Apex or Summit of Curve: The mid point F of the arc T1FT2 is called Apex of curve and lies on the bisection of angle of intersection. It is the junction of lines radii.


12) External Distance (BF): The distance BF from the point of intersection to the apex of the curve is called Apex distance or External distance.

13) Central Angle: The angle T1OT2

subtended at the center of the curve by the arc T1FT2 is called central angle and is equal to the deflection angle.

14) Mid ordinate (EF): It is a ordinate from the mid point of the long chord to the mid point of the curve i.e. distance EF. Also called Versed sine of the curve.


If the curve deflect to the right of the direction of the progress of survey it is called Right-hand curve and if to the left, it is called Left-hand curve.

The Δ BT1T2 is an isosceles triangle and therefore the angle

∟ BT1T2 = ∟ BT2T1 = ∅/2

Elements of Simple Curve

Degrees of Curves

Degree of curve is defined in 2 ways

1) Arc Definition

2) Chord Definition

Degrees of Curves

Location of Tangent Points

To Locate T1 and T2

1) Fix the direction of tangents, produce them so as to meet at point B.

2) Set up theodolite at point B and measure T1BT2 (I). Then deflection angle ∅ = 180˚ – I

3) Calculate tangents lengths by

BT1 = BT2 = R tan(∅/2)

4) Locate T1 and T2 points by measuring the tangent lengths backward and forward along tangent lines AB and BC.

Location of Tangent Points

5) The chainage of T1 is obtained by subtracting the tangent length from the known chainage of the intersection point B. And the chainage of T2 is found by adding the length of curve to the chainage of T1. 6) Then the pegs are fixed at equal intervals on the curve. 7) The interval between pegs is usually 30m or one chain length. 8) The pegs along the centre line of the work should be at equal interval from the beginning of the line up to the end. 9) The first peg on the curve is fixed at such a distance from the first tangent point (T1) that its chainage becomes the whole number of chains i.e. the whole number of peg interval. 10) The length of the first sub chord is thus less than the peg interval and it is called a sub-chord.

Problem 01

Two tangents intersect at chainage of 6 +26.57. It is proposed to insert a circular curve of radius 1000ft. The deflection angle being 16˚38’. Calculate:a) Chainage of tangents points b) Lengths of long chord

a) Solution: Tangent length = BT1 = BT2 = R tan(∅/2) BT1 = BT2 = 1000 x tan(16˚38`/2) = 146.18 ftLength of curve = L = 𝜋 R ∅/180˚ L = 𝜋 x 1000 x 16 ˚38`/180˚ = 290.31ft

Problem 01

Chainage of point of intersection =6 + 26.56

minus tangent length =-1 + 46.18

chainage of T1 = 4 + 80.39

plus L =2 + 90.31

Chainage of T2 =7 + 70.70

b) Lengths of long chord

Length of chord = l = 2 R sin(∅/2)

l = 2 x 1000 x sin(16˚38`/2) = 289.29 ft

Problem 02

Assignment 01 a: Two tangents intersect at chainage of 14 + 87.33, with a deflection angle of 11˚21’ 35’’. Degree of curve is 6˚. Calculate chainage of beginning and end of the curve.

Methods of Curve Ranging (Simple Curves)

The methods for setting out curves may be divided into 2 classes according to the instrument employed .

1) Linear or Chain & Tape Method

2) Angular or Instrumental Method

1) Linear or Chain & Tape Method

These methods use the chain surveying tools only.

These methods are used for the short curves which doesn’t require high degree of accuracy.

These methods are used for the clear situations on the road intersections.

a) By offset or ordinate from Long chord

b) By offset from the Tangents

c) By offset from the Chords produced

a) By offset or ordinate from Long chord

Divided the long chord into even number of equal parts.

Set out offsets as calculated from the equation at each of the points of division. Thus obtaining the required points on the curve.

𝑂𝑥 = 𝑅2 − 𝑥2 − 𝑅2 − (𝑙2)2

Problem 03:

Assignment 1b: Calculate the ordinate at 7.5 m interval for a circular curve given that l = 60 m and R = 180 m, by offset or ordinate from long chord.

b) By Offsets from the Tangents

In this method the offsets are setout either radially or perpendicular to the tangents BA and BC according to as the center O of the curve is accessible or inaccessible.


i) By Radial Offsets: (O is Accessible)

• Measure a distance x from T1 on back tangent or from T2 on the forward tangent.

• Measure a distance Ox along radial line A1O.

• The resulting point E1 lies on the curve.

𝑂𝑥 = (𝑅2+𝑥2) − 𝑅


ii) By Offsets Perpendicular to Tangents (O is Inaccessible)

• Measure a distance x from T1 on back tangent or from T2 on the forward tangent.

• Erect a perpendicular of length Ox.

• The resulting point E1 lies on the curve.

𝑂𝑥 = 𝑅 − (𝑅2−𝑥2)

c) By Offsets from Chord Produced

O1 = 𝐶12

2𝑅

O2 =𝐶2

2𝑅(C1+C2)

On =𝐶𝑛

2𝑅(Cn-1+Cn)

2) Angular or Instrumental Method

i) Rankine’s Method of Tangential Angles

ii) Two Theodolite Method

i) Rankine’s Method

METHOD:

1.Fix the theodolite device to be at point T1 and directed at point B.

2.Measure the deflection angles 𝛿1 and the chords C1.

3.Connect the ends of the chords to draw the curve.


C1= T1D = 2 π R δ1/180

δ1 = C1 ∗ 180/ 2 π R (degree)

δ1 = C1 ∗ 180 ∗ 60/2 π R (min)

δ1 = 1718.9 ∗C1/𝑅

δ2 = 1718.9 ∗C2/𝑅

δn = 1718.9 ∗Cn/𝑅


• Δ1= δ1

• Δ2 = δ1 + δ2 = Δ1 + δ2

• Δ3 = δ1 + δ2 + δ3 = Δ2 + δ3

• Δ4 = δ1 + δ2 + δ3 + δ4 = Δ3 + δ4

• Δn = δ1 + δ2 +…………. + δn = Δn-1 + δn

Check:

Total deflection angle BT1T2 = φ/2 ,

φ = Deflection angle of the curve

This Method give more accurate result and is used in railway & other important curve.

Problem 04:

• Two tangents intersect at chainage 2140 m . ∅= 18˚24`. Calculate all the data necessary for setting out the curve, with R = 600 m and Peg interval being 20 m by:

• 1) By deflection angle ∅

• 2) offsets from chords.

Problem 04:

Tangent length = BT1 = BT2 = R tan(∅/2)

BT1 = BT2 = 600 x tan(18˚24`/2)

= 97.18 m

Length of curve = L = 𝜋 R ∅/180˚

L = 𝜋 x 600 x 18 ˚24`/180˚ = 192.68 m

Chainage of point of intersection = 2140 m

minus tangent length = 97.18 m

chainage of T1 = 2042.82 m

plus L = 192.68 m

Chainage of T2 = 2235.50 m

Problem 04: Length of 1st chord = C1 = 2060 – 2042.82 = 17.18 m

C2 = C3 = C4 = C5 = C6 = C7 = C8 = C9 = 20 m

C10 = 2235.50 – 2220 = 15.15 m

Problem 04:

Problem 04:

2) By Offsets from Chords

O1 = 𝐶12

2𝑅= 17.182

2 ∗600= 0.25 m

O2 =𝐶2

2𝑅(C1+C2) =

20

2 ∗600(17.18+20) = 0.62 m

O3 =𝐶3

2𝑅(C2+C3) =

20

2 ∗600(20+20) = 0.67 m

O3 = O4 = O5 = O6 = O7 = O8 = O9

O10 =𝐶10

2𝑅(C9+C10) =

15.50

2 ∗600(20+15.50) = 0.46 m

ii) Two Theodolite Method

• This method is used when ground is not favorable for accurate chaining i.e. rough ground or very steep slope.

• It is based on the fact that angle between tangent & chord is equal to the angle which that chord subtends in the opposite segments.

Obstacles in Setting Out Simple Curve Assignment 1cThe following obstacles occurring in common practice will be considered.

1) When the point of intersection of Tangent lines is inaccessible.

2) When the whole curve cannot be set out from the Tangent point, Vision being obstructed.

3) When the obstacle to chaining occurs.

• Thank You

engineering surveying - ii ce313 · nomenclature of simple curves 12) external ... the interval...

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