DESIGN OF HORIZONTAL CURVES - IRC 38-1988

POWER POINT PRESENTATION

PREPARED BYEr. K.MARIAPPAN,B.E.,

ASSISTANT DIVISIONAL ENGINEER (H),INVESTIGATION, VIRUDHUNAGAR.

TERRAIN CLASSIFICATION

SL

NO

TERRAIN

CLASSIFICATION

CROSS SLOPE OF THE

COUNTRY IN %

1 PLAIN 0-10

2 ROLLING 10-25

3 MOUNTAINOUS 25-60

4 STEEP Greater than 60

Terrain is classified by the general slope of the country across the highway

alignment, for which the criteria given in table should be followed;

DESIGN SPEED FOR VARIOUS CLASSIFICATION OF ROADS

SL

NO

ROAD

CATEGORY

DESIGN SPEED KM/HOUR

PLAIN TERRAINROLLING

TERRAIN

MOUNTAINOUS

TERRAINSTEEP TERRAIN

RULING

DESIGN

SPEED

MIN

DESIGN

SPEED

RULING

DESIGN

SPEED

MIN

DESIGN

SPEED

RULING

DESIGN

SPEED

MIN

DESIGN

SPEED

RULING

DESIGN

SPEED

MIN

DESIGN

SPEED

1 NH & SH100 80 80 65 50 40 40 30

2 MDR80 65 65 50 40 30 30 20

3 ODR 65 50 50 40 30 25 25 20

4 VILLAGE ROADS 50 40 40 35 25 20 25 20

Normally “ruling design speed” should be the guiding criterion for correlating

the various geometric design features. “Minimum design speed” may, however,

be adopted in sections where site conditions, including costs, do not permit a

design based on the “ruling design speed”.

CAMBER / CROSS FALL VALUES FOR DIFFERENT ROAD

SURFACE TYPES

SL NO SURFACE TYPES CAMBER / CROSS FALL

1

High Type Bituminous Surfacing

& Cement Concrete 1.7 - 2.0

2 Thin Bituminous Surfacing 2.0 - 2.5

3 WBM & Gravel 2.5 - 3.0

4 Earth 3.0 - 4.0

• When a vehicle travels around a curve of constant radius atconstant speed, it exerts radially an outward force known asthe Centrifugal Force.

• Centrifugal Force P = where,

W = Weight of the Vehicle

V = Speed of the Vehicle in kmph

R = Radius of the curve in m

Note: P & W have the same units.

CENTRIFUGAL FORCE

WV2

127R

• The forces acting on the vehicle When it travels around a curve are,

i ) The Centrifugal Force acting radially outwards,

ii ) The wt. of the vehicle acting vertically downwards, and

iii ) The upward reaction of the road on the vehicle.

For Equilibrium, the Centrifugal Force must be counteracted

a ) either by lateral friction developed between the tyre and the road surface alone

b ) by the inward tilt of the road surface known as superelevation alone (or)

c ) partially by superelevation or partially by lateral friction while the weightof the vehicle is balanced by the reaction of the road on the vehicle.

CENTRIFUGAL FORCE

Case 1: When No Superelevation Provided

When the surface is levellaterally, i.e., when there is nocamber or Superelevation.The Centrifugal Force has tobe resisted by the frictionbetween tyres and roadsurface. There will be unequaldistribution of pressure onthe wheels, the outer wheeltaking more as shown in fig.

Case 2: When Superelevation equals to

Centrifugal Force

When Superelevation exactlyequals to Centrifugal Force,there will be equaldistribution of pressurebetween the wheels.

A – Angle of Superelevation

Case 3: When CentrifugalForce is counteracted partlyby Superelevation and partlyby lateral friction :

When the Centrifugal Force iscounteracted partially bySuperelevation and partiallyby lateral friction, thepressure on the wheels willbe intermediate betweenthose mentioned in case 1and case 2.

P =

= = e + f where;

= Centrifugal Ratio

e = Superelevation

f = co-efficient of lateral friction

WV2

127R

V2

127RPW

PW

The value of Coefficient of Lateral Friction (f) is a function of

• speed of the vehicle,

• the type and condition of the road surface,

• the condition of the tyres,

• the weather conditions at the time of contact between tyre androad,

• the temperature of the road surface and etc,.

Tests indicate that the safe value of

f = 0.15

LATERAL FRICTION BETWEEN THE TYRE AND ROAD SURFACE

Superelevation is defined as raising of outer edge over the

inner edge in curve portion of Highway and Railway to balance

the Centrifugal Force. It is denoted by „e‟.

Also, superelevating the curves results in economies in

maintenance. This is because skidding and unequal pressure on

the wheels of the vehicle cause damage of road surface which

necessitate frequent attention to the surface.

SUPERELEVATION

• Max Allowable Superelevation = 7 % in Plains

(Restricted to 7 % to provide convenience to slow moving vehicleslike bullock carts )

• Max Allowable Superelevation = 10 % in Hilly areas not effectedby snow.

• Max Allowable Superelevation = 7 % in Hilly areas effected bysnow .

• Max Allowable Superelevation = 4 % in Urban areas

SUPERELEVATION - LIMITS

Centrifugal Force P =

Centrifugal Ratio =

We assume that the Centrifugal Ratio is to be balanced orcounteracted by Superelevation (e) and lateral friction (f).

i.e., = e + f

= 0.07 + 0.15 or 0.10 + 0.15

= 0.22 for Plains and 0.25 for Hilly Regions

For Plains R = x 0.22

R = 0.0358 V2

MINIMUM CURVE RADIUS

WV2

127R

V2

127RPW

V2

127

V2

127R

V2

127R

R = 0.0358 V2

MINIMUM CURVE RADIUS

CATEGORY OF ROAD DESIGN SPEED IN KM/HMIN RADIUS OF CURVE

IN PLAIN & ROLLING IN M

SH 100 360

MDR 80 230

ODR 65 155

• Superelevation required to fully counteract the Centrifugal Force developed ifmore than 7% for sharp curves and this will cause inconvenience to slow movingvehicles. Since the superelevation is limited to 7% for practical reasons maximumlateral friction would have to be relied upon when sharpest possible curve istraversed.

• Share of Centrifugal ratio by Superelevation and lateral friction :

e = 0.07 & f = 0.15 ; e + f = 0.22

Share of ‘e’ in counteracting the Centrifugal Force = 0.07/0.22 X 100

= 32%

Share of ‘f’ in counteracting the Centrifugal Force = 0.15/0.22 X 100

= 68%

SHARE OF SUPERELEVATION & LATERAL FRICTION TO

BALANCE THE CENTRIFUGAL FORCE

• It has also been observed that a majority of the vehicles using a Highway travelat less than the design speed. Design of superelevation for mixed trafficconditions is complex problem as different vehicles ply on the road with a widerange of speeds.

• To superelevate the pavement upto the maximum limit so as to counteract thecentrifugal force fully, neglecting the lateral friction is safer for fast movingvehicles.

• But for slow moving vehicles this may quite inconvenient.

• On the contrary to provide lower value of superelevation thus relying more onthe lateral friction would be unsafe for fast moving vehicles.

• Therefore, as a compromise and from practical considerations it is suggestedthat the superelevation should be provided to fully counteract the CentrifugalForce developed at 75% of the design speed by neglecting lateral frictiondeveloped.

SUPERELEVATION FOR MIXED TRAFFIC

e + f =

e + 0 = For Mixed Traffic

e =

a) The value given by this equation is subject to a maximum of 7%.

b) Also, the ‘e’ given to the surface of a road should not be less than the camberrequired for the drainage of the surface water of the road.

Minimum camber = 1.70% for BT

c) When the value of the ‘e’ given by the above equation is less than thatrequired for the drainage, the normal cambered profile may be continued in thecurve portions also without providing any Super Elevation.

SUPERELEVATION FOR MIXED TRAFFIC

V2

127R

(0.75V)2

127R

V2

225R

SUPERELEVATION FOR MIXED TRAFFIC

METHOD OF BUILDING SUPERELEVATION –

STAGE I

• The normal camberedsurface on a straight reachof road is changed into asuperelevated surface intwo stages.

• In the first stage, the outerhalf of the camber isgradually raised until it islevel.

• Then the levelled outerhalf is further raised to aslope equal to camber.Thus the super elevationequal to camber stage isobtained.

METHOD OF BUILDING SUPERELEVATION –

STAGE II

In the second stage one of thefollowing three methods maybe adopted depending uponthe site conditions:

1. The surface of the road isrotated about the point A,lowering the inner edge andraising the outer edge. In thiscase the level of the centerlineof the road remains practicallyunchanged.

2. The surface of the road isrotated about the inner edge.This will raise the centre andouter edge simultaneously.

3. The surface of the road isrotated about the outer edge.This will lower the centre andinner edge simultaneously.

Min radius for any design speed R = 0.0358V2

From; e = = 0.07

R = 0.06349V2

Therefore, for curves whose radii liebetween 0.06349V2 and 0.0358V2, the maximumsuperelevation is attained at a point on thetransition curve whose radius is equal to0.06349V2.

This involves calculation and marking ofthe point on the transition curve where theradius is equal to 0.06349V2 in the field andproviding superelevation with zero at the startof the curve and 7% at this point B shown infigure. In this case the field set out is littlecomplicated.

Therefore, superlevation should beuniformly increased from zero at the start of thecurve to its full designed value at the end of thetransition.

METHOD OF BUILDING

SUPERELEVATION

V2

225R

• On horizontal curves, especially when they are not of very large radii, it is common towiden the pavement slightly more than the normal width.

• When a vehicle passes a straight road, the rear wheels follow the same track as that of thefront wheels. It is not so while negotiating a curve.

• An automobile has rigid wheel base and only the front wheels can be turned. On curves,the rear wheels do not follow the same path as that of the front wheels. This phenomenonis called off tracking.

• Normally, the rear wheels follow the inner path on the curve as compared with those ofthe corresponding front wheels.

• This means that if the inner front wheel takes a path on the inner edge of a pavement athorizontal curve, the inner rear wheel will be off the pavement on the inner shoulder.

EXTRA WIDENING AT CURVES

Extra Widening at curves has two components of 1. Mechanical Wideningand 2. Psychological Widening.

MECHANICAL WIDENING:

• The extra widening required to account for the off-tracking due to the rigidity ofwheel is called mechanical widening.

Wm = ; l = Length of wheel

n = No. of lanes

R = Radius of curve

PSYCHOLOGICAL WIDENING:

• Extra width of pavement is also provided for psychological reasons such as, toallow for the extra space requirements, for overhangs of vehicles and to providegreater clearance for overtaking vehicles.

Wps =

Total extra widening = Wm + Wps = +

• Normally extra widening at curves for the two lanes needs when the radius is lessthan 300m.

EXTRA WIDENING AT CURVES

nl2

2R

V9.5√R

nl2

2RV

9.5√R

EXTRA WIDENING AT CURVES

Flat Curve Sharp Curve

Curves are defined as arcs, with some finite radius, providedbetween intersecting straights to gradually negotiate a change indirection.

This change in direction of the straights may be in ahorizontal or a vertical plane, resulting in the provision of ahorizontal or a vertical curve, respectively.

Curves are basically classified as horizontal or vertical curves,the former being in the horizontal plane and the later in thevertical plane.

The horizontal curves are further classified as simple circular,compound, reverse, transition, combined and broken-back curves.

CURVES

SIMPLE CIRCULAR CURVE

A curve connecting twointersecting straights having aconstant radius all throughout itslength is known as simple circularcurve. The radius of the circledetermines the “sharpness” or“flatness” of the curve. The largerthe radius, the “flatter” the curve.

COMPOUND CURVE

when two or more simplecircular curves of different radii,turning in the same direction jointwo intersecting straights, theresultant curve is known as acompound curve. Surveyors oftenhave to use this curve because ofthe terrain.

REVERSE CURVE

When two simple circularcurves, of equal or different radii,having opposite direction ofcurvature join together, theresultant curve is known as areverse curve. For safety reasons,the surveyor should not use thiscurve unless absolutely necessary.

TRANSITION CURVE

It is a curve usually introducedbetween a simple circular curve anda straight, or between two simplecircular curves. It is also known as aneasement curve. It is widely used onhighways and railways, since itsradius increases or decreases in avery gradual manner.

BROKEN BACK CURVE

In the past,sometimes, two circularcurves having their centreson the same side andconnected with a shorttangent length were usedfor rail road traffic. Sincethey are not suitable forhigh speeds, they are not inuse nowadays.

ELEMENTS OF SIMPLE

CIRCULAR CURVE

T1 – Point of Curve

T2 – Point of Tangency

IT1 = IT2 – Tangent length

T1CT2 – Total length of curve

C – Apex or summit of curve

T1DT2 – Long chord

CD – Mid ordinate

IC – Apex distance

T1OT2 – Central Angle =Deflection angle ∆

SIMPLE CIRCULAR CURVE –IMPORTANT FORMULAE

a) Length of Curve L =

b) Tangent length T = R tan

c) Long chord L = 2R sin

d) Apex distance = R (sec – 1)

e) Mid ordinate = R (1 – cos )

R∆π180

∆2

∆2

∆2

∆2

Setting out a curve means locating various points at equal and convenientdistances along the length of a curve.

The difference between any two successive points is called peg interval.

The first and last chord, will be a sub chord and all other chords will be fullchords.

Before setting out a curve in the field, the P.I, the P.C. and the point oftangency are located.

SETTING OUT A SIMPLE CIRCULAR CURVES

Methods of Setting out the Simple Circular Curve

Linear Methods Angular Methods

1. Offsets from the long chord2. Perpendicular offsets from the tangent3. Radial offsets from the tangent4. Successive bisection of arcs5. Offsets from chord produced

1. One Theodolite Method2. Two Theodolite Method3. Tachometric Method (Similar to the

One Theodolite Method – Tachometeris used Instead of Theodolite)

1. OFFSETS FROM LONG

CHORD

PROCEDURE OF SETTING OUT :-

• Let it be required to lay a curveT1CT2 between the twointersecting straights T1I and T2I.

• R is the radius of the curve and Oo

the mid-ordinate.

• Ox is the offset at a point P at adistance x from the mid point M atthe long chord is computed by thefollowing formula.

Ox = Oo – x2 / 2R

• By assigning different values to x,the corresponding values ofoffsets Ox can be determined.

• The calculated offsets can be laidfrom the long chord and thepoints can be established in thefield which when joined producethe required curve.

2. PERPENDICULAR OFFSETS

FROM THE TANGENT

PROCEDURE OF SETTING OUT :-• Ox is the offset perpendicular to

the tangent at a distance x fromthe point of curve T1.

Ox = x2 / 2R

• By assigning different values to x,the corresponding values ofoffsets Ox can be calculated.

• These calculated offsets can belaid from the tangent at knowndistances x and the points can beestablished in the field whichwhen joined produce the requiredcurve.

• These method is suitable for smallvalues of the radius, length ofcurve and deflection angle.

App. expression

3. RADIAL OFFSETS FROM THE

TANGENT

PROCEDURE OF SETTING OUT :-• Ox is the radial offset to the

tangent at a distance x from thepoint of curve T1.

Ox = x2 / 2R

• By assigning different values to x,the corresponding values ofoffsets Ox can be calculated.

• These calculated offsets can belaid from the tangent at knowndistances x and the points can beestablished in the field whichwhen joined produce the requiredcurve.

App. expression

4. SUCCESSIVE BISECTION OF

CHORD

PROCEDURE OF SETTING OUT :-• Let T1 & T2 be the tangent points.

The long chord T1T2 is bisected atD. Mid-ordinate is equal toR(1–cos∆/2). Thus point C isestablished.

• T1C & T2C are joined. T1C & T2C arebisected at D1 & D2 respectively.

• Perpendicular offsets D1C1 & D2C2

each will be equal to R(1–cos∆/4).

• These offsets are set out givingpoints C1 & C2 on the curve.

• By the successive bisection of thechords T1C1, C1C, CC2 & C2T2 morepoints may be obtained whichwhen joined produce the requiredcurve.

5. OFFSETS FROM THE CHORD

PRODUCED

• Calculate the length of the curve and find thelength of the first sub-chord, full chords andthe last sub-chord.

• Calculate all the offsets from O1 to On.

• T1a is the first sub-chord C1. From T1, a lengthequal to first sub-chord C1 (T1a’) is taken.

• The perpendicular offset O1 (aa’) is set out,there by getting point a.

• T1a is joined and produce by distance C2 (Fullchord length).

• The second offset O2 (bb’) is set out to getpoint b.

• Points a & b are joined and produce further bydistance C3 (Full chord length).

• The third offset O3 (cc’) is set out to get point c.

• The procedure is repeated till the curve iscompleted.

• This is the best method for setting out a longcurve by Linear method and is usuallyemployed for highways curves when atheodolite is not available. However, if onepoint is wrongly set, all the subsequent pointsget affected, limiting the use of this method.

On = (Cn-1 + Cn)

O1 = (Co + C1) =

O2 = (C2-1 + C2)

O2 = (C1 + C2) and

O3 = (C2 + C3)

Cn

2R

C1

2RC1

2

2R

C2

2R

C2

2R

C3

2R

ONE THEODOLITE METHOD –

RANKINES METHOD OF

DEFLECTION ANGLE

• A deflection angle to any point on the curve isthe angle of P.C. between the tangent and thechord from P.C. to that point. From the propertyof a circle, this deflection angle is equal to halfthe angle subtendedby the arc at the centre.

• Set up the theodolite exactly at T1. Set thevernier A to zero and bisect the P.I.

• Set the vernier A to read δ1. The line of site isthus directed along T1a.

• Hold the zero of the tape at T1, take the distanceC1 (T1a) and swing the tape with an arrow till it isbisected by theodolite. This gives first point a onthe curve.

• Set the second deflection angle δ2 so that theline of site is set along T1b.

• With zero of the tape held at a and an arrow atthe other end (chord distance = ab), swing thetape about a, till the arrow is bisected by the

theodolite at b. This gives the second point b onthe curve.

• The same step are repeated till the last point T2

is reached.

δ1 = Radians

δ1 = x x 60 min

δ1 = min

δ2 = min

δ3 = min

C1

2R

C1

2R180o

π1718.9 C1

R

1718.9 C2

R1718.9 C3

R

TWO THEODOLITE METHOD

This method is most convenientwhen the ground is undulating, rough andnot suitable for linear measurements.

Linear measurements arecompletely eliminated. Hence, this is themost accurate method.

FIELD PROCEDURE :-

• Set up one theodolite at T1 and the otherat T2. Set the vernier A of both thetheodolites to zero.

• Direct the theodolite at T1 towards I, andthe theodolite at T2 towards T1.

• Set an angle δ1 in both the theodolites soas to direct the line of sights towards T1a

and T2a thus the point a i.e., point ofintersection of the two line of sights, isestablished on the curve.

• Similarly point b is established by setting δ2

in both the theodolites and bisecting theranging rod at b.

• The same steps are repeated with differentvalues of δ to establish more points.

PRINCIPLE :

It is based on the principle thatthe angle between the tangent andthe chord is equal to the anglesubtended by the chord in theopposite segment.

IT1a = δ1 = aT2T1

And IT1b = δ2 = bT2T1

When a vehicle travels from the straight to a curve of finiteradius, it is suddenly subjected to an outward centrifugal force.This cases a shock and sway to the passenger and the driver.

Thus, a transition curve is provided for the followingadvantages;

1. It allows a gradient transition of curvature from the tangent tothe circular curve or from the circular curve to the tangent.

2. The radius of curvature increases or decreases gradually.

3. It is provided for the gradual change in superelevation in aconvenient manner.

4. It eliminates the danger of derailment, overturning or side-slipping of vehicles, and discomfort to passengers.

TRANSITION CURVES

ELEMENTS OF TRANSITION CURVE

1. P.I. - Apex of a curve

2. Es - Apex distance

3. Rc – Radius of circular curve

4. ∆: Total deviation angle

5. 180 - ∆: Intersection angle

6. L.C. – Long chord

7. Shift (s) – The displacementof a circular curve from thestraight to provide room tointroduce a transition curve.

8. Ts – Tangent distance

9. T.P. & P.T. – Tangent points

10. Ls – Transition length

11. Lc – Length of circular curve

12. θs – The tangent deflectionangle for the transitioncurve.

13. ∆c – Deviation angle of thecircular curve.

CIRCULAR CURVE WITH TRANSITION

a. Lemniscate

b. Spiral (also called clothoid)

c. Cubic Parabola

All the three curves follow almost the samepath upto deflection angle of 4o and practicallythere is no significant different even upto 9o. In allthese curves the radius decreases as the lengthincreases.

But the rate of change of radius and hencerate of change of centrifugal acceleration is notconstant in the case of leminiscate and cubicparabola, especially at deflection angles higherthan 4o.

In spiral curve, the radius is inverselyproportional to the length and the rate of changeof centrifugal acceleration is uniform throughoutthe length. Thus the spiral fulfils the condition offan ideal transition curve.

The IRC recommends the use of the spiralas transition curve due to the following reasons,

1. The spiral curve satisfies the requirements of anideal transition.

2. The geometric property of spiral is such that thecalculations and setting out the curve in the fieldis simple and easy.

TYPES OF TRANSITION CURVES

OA = Lemniscate

OB = Spiral

OC = Cubic Parabola

The length of transition curve is design tofulfill two conditions.

1. Rate of change of centrifugalacceleration :

The rate of change of centrifugalacceleration should causediscomfort to drivers. From thisconsideration the length oftransition is given by;

Ls =

Where;

Ls = Length of transition in metres

V = Speed in Km/h

R = Radius of circular curve in metre

C = 80 / 75 + V (varies from 0.5 to 0.8)

MINIMUM LENGTH OF TRANSITION

2. Rate of change of superelevation :The rate of change of

superelevation should be such as not tocause discomfort to travelers. Rate ofchange should not be steeper than0.66% (1 in 150) for roads in Plain andRolling terrain and 1.66% (1 in 60) inMountainous / Steep terrain. From thisconsideration the length of transition isgiven by;

Ls =Where;

Ls = Length of transition in metresV = Speed in Km/hR = Radius of circular curve in metre

These equations have been derivedfor two lane roads, but these can beapplied equally to single lane roads andfour lane divided highways. For fourlaneundivided and six lane divided highwaysit would be preferable to increase thelength given by these equations by 50%.

0.0215V3

CR

2.7 V2

R

MINIMUM TRANSITION LENGTH S FOR DIFFERENT SPEED AND

CURVE RADII

TRANSITION CUM CIRCULAR

CURVE – IMPORTANT FORMULAE

a) Shift s =

b) Ts = R + S tan +

c) Length of Circular curve =

d) Total length of curve = + Ls

e) Apex distance = - Rc

f) θs = radians

= 28.65 x degrees

g) αc = θs

Ls2

24Rc

∆2

CIRCULAR CURVE WITH TRANSITION

Ls

2

πR∆180o

Rc+scos ∆/2

Ls

2Rc

Ls

Rc

13

πR∆c

180o

From the design of the curve, Ts the tangent distance, Es the apex

distance, Ls length of the transition, Rc the radius of the circular curve and∆s the tangent deviation of the transition, etc., are known. The start ofthe curve TP is fixed by measuring the Ts from the apex point. The curve islaid out in the field by any one of the following two methods;

1. Off-set Method.

2. Polar Deflection Method.

Usually the length of the tangent is divided into 10 or 20 equal partsand it is assumed that the length of the chord of each to the point is thesame as length along the curve. This assumption is correct for transitionlength of less than 120m even for sharp curves.

SETTING OUT A TRANSITION CURVES

1. OFFSET METHOD

• From the design of the curve, Tangentdistance Ts, Apex distance Es, Lengthof tansition Ls, Radius of the Circularcurve Rc, Tangent deviation of thetransition ∆s, etc., are known. Thestart of the curve T1 is fixed bymeasuring Ts from the apex point.

• Now, the perpendicular offsets to thetransition curve at different points arecomputed from the formula y =x3/6LR till the point B is fixed. x ismeasured along the tangent from thepoint T1 and the correspondingperpendicular offset y is setout, thusgiving a number of points on thetransition curve.

• Perpendicular offsets at x = L/4, L/2,3L/4 & L are also computed and laid inthe field.

• The process is repeated from theother tangent point T2, till point B’ isfixed.

• The circular curve BB’ can be laid byoffsets from the chord produced usingthe formula;

On = (Cn-1 + Cn)Cn

2R

2. METHOD OF DEFLECTION ANGLE

• Set the theodolite at T1 and direct theline of sight to I, and keep the vernierat zero.

• Set the vernier to the first deflectionangle α1, thus directing the line ofsight to the first point on thetransition curve.

α1 = min

• With the zero of the tape pinned atT1, measure a length l1 till it isbisected by the line of sight. The firstpoint is thus fixed.

• Set the angle α2 so that the line ofsight is directed to the second point.Now measure a distance l2 from thepoint T1 till it is bisected by the line ofsight, thus the second point is fixed.

• The procedure is repeated until thelast point B is set out. At the last pointB, α = 1/3 θs which gives a check onthe field work.

573l2

LR

• To set the circular curve, shift the theodoliteto the junction point B, direct the telecope tothe point T1, with vernier reading 360o -2θs/3.

The telescope is now rotated by an angle2/3θs till zero reading is obtained. Pn

transiting the telescope is now directedalong the tangent B1B produced. The circularcurve BB’ is now set from the point B by theusual method of deflection angle till thepointB’ is reached.

• The other transition curve from T2 is set up ina way similar to the first one.

SETTING OUT OF TRANSITION CURVE USING TABLES AS PER IRC 38-1988

• The setting out of a transition curve is carried out after calculating various elementsof the transition curve for the given deflection angles and radii.

• In practice, however, the alignment will be such that there are restrictions of terrainor a built up area which will not be free choice of the radius for the curve. Generally,the tangent distance Ts or the apex distance Es or both are the governing elements.There are various combinations of the radius of the curve and the length of thetransitions which will give the values of Es and Ts that are required. Thus for any oneset of field conditions to arrive at the best suitable value of Ls and Rc trail and errorwill be necessary. Therefore, table 10 (Appendix 3) of IRC 38 have been worked outto enable field engineers to select the maximum possible radius and length oftransition best suited to the filed conditions.

• Even under conditions where there are no restrictions in the field, calculation ofcurve functions are tedious. So curve functions for radii from 14 to 2500m andtransition length ranging from 15 to 140m have been worked out and given in tables10 (Appendix 3), 11 (Appendix 4), & 12 (Appendix 5). In the field generally curvessatisfying a range of the element that governs the design would be satisfactory.