undefined | unit 4 curves

Unit - 4

Curves

Q1) Explain Horizontal and Vertical curve?

A1) Horizontal curve:

Definition: The curves which are provided at turning points so as to get gradual change in the direction of alignment of a road or a track are termed as horizontal curves.

Note that these curves are in the horizontal plan. In railway track, the minimum radius of a horizontal curve should be 175 m for broad gauge.

Horizontal as well as vertical, curves in case of road must ensure safety, comfort and convenience of the traffic.

Vertical Curve:

Definition: The curves which are provided in the alignment of road or track at change of gradient is termed as vertical curves.

Necessity of vertical curves: It gives adequate visibility and safety to the traffic.

It gives gradual change in grade or slope.

It gives adequate comfort to the passengers.

Q2) Explain about Simple curve?

A2)

The curve which consists of a single arc of a circle of which two straight tangents further connects and brings about a deflection of the road through an angle '0' is called as simple curve. See Fig. for better understanding.

Simple curve is normally represented by the length of its radius or by the degree of curve.

This type of curve is provided at every change in alignment of the road or railway à track in a plain and in hilly areas.

$H:\unit 4 survey\IMG_20210528_183612.jpg$

Fig.: Simple curve

Q3) Explain about Compound curve?

A3)

A curve of having the series of two and more simple curves of different radii curving in the same direction is called as compound curves. Refer to the Fig.

for better understanding.

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Fig.: Compound curve

In compound curves, the two adjacent curves will have a common tangent "BC" as shown in Fig.

The centers of two adjacent curve lie on the same side of the curve as shown in Fig.

To avoid the cutting through hard rocks, heavy cutting or filling in the alignment of road or track, compound curves are provided.

Q4) What are the advantage and disadvantage of reverse curve?

A4) Advantages of reverse curve:

This type of curve is oftenly used in the alignment of a hill road.

It is also used in the layout of railway spur tracks and cross-over.

Disadvantages of reverse curve:

The use of reverse curve is not suitable on highways where the speeds are high.

This type of curve is also not suitable in the main railway lines due to high speed.

There is sudden change of direction in reverse curve and this makes passangers more uncomfortable.

Steering is dangerous on highways and driver has to be very cautious.

Q5) What are the types of vertical curve?

A5) There are Two types of vertical curve:

Summit Curve

Valley Curve

Summit curves:

Definition: The curves which are having convex surface on upward side is termed as summit curves.

Vertical curves are used manly when rising gradient intersects a falling grade or when rising gradient meets another rising gradient or when rising gradient meets a horizontal road or when falling gradient meets at a steeper falling gradient. Refer Fig. for better understanding.

Fig. shows the different situations where summit curves are provided.

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Fig.: A rising gradient intersecting a falling gradient

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Fig.: A rising gradient meeting another rising gradient

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Fig.: A rising gradient meeting at horizontal road

Valley curves:

Definition: The curves which are having the convex surface on downward side Fig. shows the different situations where valley curves are termed as valley curve.

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Fig.: A falling gradient intersecting a rising gradient

$H:\unit 4 survey\IMG_20210528_183829.jpg$

Fig.: A falling gradient meeting another falling gradient

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Fig.: A falling gradient meeting a horizontal road

Q6) Explain about simple circular curve?

A6)

Refer the Fig. for understanding the various terms of notation for a simple circular curve.

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Fig.: Simple circular curve (Right hand curve)

The common notation which are normally preferred for simple circular curve are as follows:

BC and AB are the two tangents drawn to the curve at T1, and T2, respectively. In short, BC and AB are two straight called as tangents.

The two tangents AB and BC are intersected at the B which is called as point of intersection. In short, B is the point of intersection of tangents AB and BC.

In Fig., the curve deflects to right side. Therefore, it is called as right-hand curve.

$H:\unit 4 survey\IMG_20210528_183940.jpg$

Fig.: Simple circular curve (left hand curve)

4. In Fig., the curve deflects to left side. Therefore, it is called as left-hand curve.

5. In Fig., BC is first tangent and also called as back tangent. AB is second tangent and also called as forward tangent. In Fig.AB is first or back tangent at T₁ and BC is second or forward tangent at T₁.

6. T1, and T2, are the tangent points. T1, shows the starting of the curve and T2, shows the end of the curve.

7. In fig., I is an angle of intersection and 0 is a deflection angle.

8. BT1, and B T2, are the lengths of tangent.

9. T1, T2, is a long chord of length 'L'.

10. The arc 'T1ET2' is a length of curve.

11. The mid point 'E' is apex of summit of the curve T1ET2

12. BE is the distance of apex.

13. The angle 'T1OT2' = The deflection angle ''.

14. DE is a versed sine of the curves.

Q7) Explain about Compound curve?

A7)

A curve of having the series of two and more simple curves of different radii curving in the same direction is called as compound curves. Refer to the Fig. for better understanding.

In compound curves, the two adjacent curves will have a common tangent 'BC' as shown in Fig.

The centers of two adjacent curve lie on the same side of the curve as shown in Fig.

To avoid the cutting through hard rocks, heavy cutting or filling in the alignment of road or track, compound curves are provided.

$H:\unit 4 survey\IMG_20210528_184002.jpg$

Fig.: Compound curve

Fig. shows T1D T2 is a two centred compound curve having two circular arcs T1D and DT2 meeting at a common point D known as the point of compound curvature.

$H:\unit 4 survey\IMG_20210528_184022.jpg$

Fig.: Two centered compound curve

T1 is the point of curve and T, is the point of tangency.

O1 and O2 are the centres of the two areas:

Let,

Rs =the smaller radius (T1O1)

R2= the longer radius (T2O2)

BC= common tangent

deflection angle between the rear and the common tangent.

=deflection angle between the common and the forward tangent.

total deflection angle.

ts=the length of the tangent to the arc (T, D) having a smaller radius.

Ts = tangent distance T1A corresponding to the shorter radius.

TL = tangent distance T2A corresponding to the longer radius.

From Fig. we have,

ts= T1B= BD= Rs

tl=T2C=CD+RL

From triangle ABC we have,

Ts=T1B+BA

=ts+(ts+tl)

Q8) Explain setting out by radial offsets?

A8)

Let Ox=Radial offset PN at any distance x along the tangent

T1P = x

From Δ T1 PO,

PO2 = T1O2+T1 P²

Ox= –R …. (1)

Fig.: setting out by radial offsets

In order to get an approximate expression for Ox, expand

Thus,

Ox=R-R

Neglecting the other terms except the first two, we get

Or Ox=x2/ 2R

When the radius is large

T1P2=PN(2R+PN)

X2=Ox(2R+Ox)

Neglecting Ox in comparison to 2R we get

Ox=x2/2R

Q9) Explain setting out by perpendicular offset?

A9)

$H:\unit 4 survey\IMG_20210528_184105.jpg$

Fig.: setting out by perpendicular offsets

Let DN=Ox= offset perpendicular to the tangent

T1D=x= measured along the tangent

Draw NN1 parallel to the tangent

From leEE1O, we have

E1O2=EO2-E1E2

(R-Ox)2=R2-x2

From which

Ox=R-

The corresponding approximate expression for Ox may be obtained by expanding the term. Thus,

Ox=R-R

Neglecting the other terms except the first two of the expressions

Ox=R-R+

Q10) Explain Successive bisection of chords?

A10)

Join the tangent point T₁, T, and bisect the long chord at D.

$H:\unit 4 survey\IMG_20210528_184124.jpg$

Fig.: Successive bisection of arcs

Erect the perpendicular DC and make it equal to the versed since of the curve. Thus

NO= R (1-)

=R-^2

Join T1N and T2N and bisect them at O1 and O2 respectively. At O1 and O2, set out perpendicular offsets N1O1=N2O2=R (1-

)

By the successive bisection of these chords, more points may be obtained.

Q11) Explain two theodolite method of deflection angle?

A11)

$H:\unit 4 survey\IMG_20210528_184224.jpg$

Fig.: Two theodolite method

In this method, two theodolites are used. One is at T1 and other at T2.

When the ground is unsuitable for chaining, this method is used.

This method is based on the principle that "The angle between the tangent and the chord is equal to the angle which that chord subtends in the opposite segment.

Thus, in Fig.

<PT1L= A=Deflection angle for L.

But LT2T1, is the angle subtended by the chord T, L in the opposite segment.

∴ angle LT2T1= angle PT1M =

Similarly, angle PT1L= = angle T1T2M

Hence the angle between the long chord and the line joining any point to T2 is equal to the deflection angle to the point measured with respect to the rear tangent.

Method of setting out the Curve:

Set up one transit theodolite at T1, and the other at T2.

Clamp both plates of each transit theodolite to zero reading.

In order to orient two transit theodolites correctly, theodolite at T1, must sight towards P with zero reading on vernier. Similarly, direct the line of sight of the other transit theodolite at T2, towards T1, when the reading is zero.

Set the reading of each of theodolite to the deflection angle (

) for the first point L. The line of sight of both the theodolites are thus directed towards L along T1L and T2 L respectively.

Move a ranging rod or an arrow in such a way that it is bisected simultaneously by cross- hairs of both the instruments Thus point L. is bisected.

To fix the second point M, set reading to A, on both the theodolite o bisect the ranging rod.

In order to locate all other points, repeat steps (4) and (5)

Q12) Explain advantages and disadvantages of two theodolite method?

A12) Advantage of two theodolite method:

This method is more accurate, since each point is fixed independently of the other

An error in setting out one point is not carried right through the curve as in the method of tangential angles.

Disadvantage of two theodolite method:

The only disadvantage of this method is it is costlier since two theodolites two surveyors are required.

Q13) Explain Transition curve?

A13)

The curve in which radius varies gradually from infinity to a finite value equal to that of the circular curve to be connected and vice versa is termed as transition curve.

These curves are commonly used in railway tracks between the circular curve and tangent so as to provide easy and gradual change in direction.

Necessity:

To provide gradual change in the radius of curvature.

To provide smooth entry of vehicle from a straight portion to curved portion.

To permit gradual application of the superelevation and extra widening at horizontal curves.

To provide safety to the vehicular traffic.

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