PCRailway Engineering Lab update!!

8/7/2019 PCRailway Engineering Lab update!!

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Department of Transportation Engineering & Management, UET Lahore 2


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(Generally tunnels are provided

(Alignment on either side of tunnel is steeper

(not more than ruling grade) shorter tunnel(To achieve the objective of as straight & Level

track as possible, length of track is increased

& grades are kept upto ruling grades, this iscalleddevelopment.



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Direction ofTravel is reversed

for a shortdistance


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(To gain elevation up or down hill, alignment

makes a half circle loop into valley followed

by half circle loop round the hill side

(Excessive cutting & filling is avoided



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Zig zag railway at Lithgow


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(When zig zag development is not feasible for

very steep slopes

(To stop train gradually, without using brakes,vertical curve is provided

(Train stops at switch point (station yards)



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(Track rises on a steady curve until it has

completed a 360 degree loop, passing over

itself until it gains height(Train does not need to stop & reverse

direction



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(Suitable

for narrow

valleys(Swings

around

slope of

valley



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(Curves around slopes of a hill



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(Estimate of traffic in terms of passengers &

wagons

(Possibility of development of naturalresources

(Places of tourism

(Traffic history

(2 3 tentative routes are marked



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(Topography(Towns, existing facilities, crossings(

Geological characteristics(Maximum flood levels(Availability of material(Probable radii of curves

(Total track length(Approximate earth work(Approx. cost of construction of each probable

line



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(2 3 routes are selected for preliminary

survey

(Recommends only one route(Data collected:

(Elevations (levels)

(River crossings

(Existing track

(Land ownership

(Climatic conditions



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(Topographic map is completed

(Longitudinal section of alignment

(Typical cross sections(Length of track

(Gradients

(Cost of subgrade



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(Preliminary survey Paper location (grades,

curves, contours, crossings, etc)

(Finally decided alignment is surveyed in detail(From paper to ground pegs are fixed at

regular intervals

(Demarcation of land width

(Centreline of culverts, bridges

(Position of buildings



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( Geometry Science of properties & relations of lines, surfaces & solids

DesignFinal layout or plan

Geometric Design

Deals with the geometry of track alignment in vertical & horizontalplanes.

Horizontal plane: straight portion, curves, degree, radius

Vertical Plane: Vertical curve, gradient

Combination: Superelevation



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(Superelevation (Cant) Difference in heightbetween the inner & outer rails on the curve

(Equilibrium speed the speed at which the effectof centrifugal force is exactly balanced by the

superelevation provided.

(Maximum permissible speed Highest speed

which may be allowed on a curved track taking intoconsideration the radius of curvature, actual cant,

cant deficiency, cant excess & length of transition

curve



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(Cant Deficiency when a train travels on a

curved track at a speed higher than the

equilibrium speed then cant deficiency occurs.

(Cant Excess when a train travels on a curved

track at a speed lower than the eq. speed, cant

excess occurs



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(Cant Gradient (& Cant Deficiency

Gradient) the amount by which a cant (or

deficiency of cant) is reduced or increased in agiven length of transition

Examples:

1. A gradient of1 in 500 means that cant (or cant

deficiency) of1 mm is attained (or lost) in every 500

mm length of transition

2. 1 in 60

3. 1 in 360Department of Transportation Engineering & Management, UET Lahore 33


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(Rate of Change of Cant (or Cant deficiency)

o The rate at which the cant (or cant deficiency) is

increased with time while passing over the transition

curve.

Examples:

1. 40 mm per second means that a vehicle when travelling

at maximum permitted speed will experience a change incant (or cant deficiency) of 40 mm in each second of

travel over the transition.

2. 2 per second



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( R= Radius of curve (m)

( C= Length ofChord (m)

( V = Versine on chord length C (m)

( By geometry,


A B

F

D

O

ER

C V

R

CV

CRV

VNeglecting

CVRV

CCCVRV

OBAOODOF

8

42

""4

2

422)2(

2

2

2

22

2

!

!

!

!v!

v!v


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Transition Curve36

Department of Transportation Engineering & Management, UET Lahore


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(What is Transition?

Change from one state or condition to another

(Requirement1. Straight section throughout is not always

possible

2. Curves may be introduced to by pass

obstacles or avoid cutting

3. Suppose a curve is provided with a tangent,

what will happen?



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(Increase the radius of curvature graduallyfrom that of the original circular curve until

the radius is infinitely large at the point wherecurve merges into the straight(Increase in curvature must be

Continuous

UniformRapid

(Superelevation: from no cant to full cantgradually within length of transition curve



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(ThreeWays:Case A:Case A: Full cant may be continued through the

whole length of the circular curve & the runoffinthe cant located entirely on the tangent at each

end

Case BCase B Full cant may be applied through thecentral portion of the circular curve & diminish to

zero at the two tangent pointsCase C:Case C: The cant may be located partly on

tangent & partly on the curve having its meanvalue at the tangent points.



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(No matter which of these three are adopted,

the cant is correct at only one point in the run-

off, at all other points it is either too great ortoo small.

(This excess ordeficiency of cant produces &

accounts for the objectionable lurches,

resistances & shocks which are noticeable to

passengers when a train travelling at speed

enters or leaves a curve



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Department of Transportation Engineering & Management, UET Lahore41

W

GNo curve, no

centrifugal force, radial

acceleration & trainweight are balanced

equally on both rails

Start ofSimple

circular curve

Case ACase A(1) Far(1) Farbefore thebefore the

tangenttangentpoint: nopoint: nocantcantappliedapplied


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Up to the tangent pointload on low rail is

greater than on thehigh rail (zero

centrifugal force)

W

e

Axle springs of low rail aredepressed & high rail

extended

Case A:Case A:(2)(2)SomewhatSomewhatbefore the tangentbefore the tangentpoint cant is startedpoint cant is started

being applied andbeing applied andreaches toreaches to

maximum value atmaximum value attangent pointtangent point


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Train

Horizontal centrifugal forcecombined with the vertical gravity

force results in equal loads on therails if equation shown holds true

Case A:Case A:(3) Just after(3) Just aftertangent point istangent point is

passedpassed

W

C

LURCH!! Axle springs of low

rail extended & high raildepressed


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Train

5/8 of train load is takenby the outer rail just

beyond the tangentpoint; line of action of

resultant force displaced

Start ofSimple

circular curve

Case BCase B(1) Just(1) Justbeyondbeyond

tangent pointtangent point

W

T

C


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PC PT

Point of fullsuperelevation

T

W

C

Inward LURCH!! Resultant

force swings back to centre

Case BCase B(2) Point of full(2) Point of fullsuperelevationsuperelevation

is reachedis reached


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(Before the tangent point the load on inner rail

is higher than on outer one & then are

equalized once the point of full superelevationis arrived.


Before the

tangent

point


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(Increase the radius of curvature graduallyfrom that of the original circular curve untilthe radius is infinitely large at the point wherecurve merges into the straight

(Increase in curvature must beContinuous

UniformRapid Superelevation: from no cant to full cant

gradually within length of transition curve



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(Amount of cant at any point correspond to

radius at that point

(Three conditions govern design:

Length

Rate of increase in radius

Rate of increase in superelevation



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(Cubic spiral

(Lemniscate

(Clothoid(Cubic Parabola Used for railways



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0 1 827

64

125

216

343

512

729

1000

0 1 2 3 4 5 6 7 8 9 10


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(If r denotes the radius of curvature at any point

whose ordinates are x, y then,

(When x = 0, r = infinity (no curvature)

(When x = L, r = R (Radius ofCircularCurve)

(As y = cx3 Y = x3/6RL

(Where Y is the offset from tangent to any point on

transition curve



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(Several ways to determine the length of

transition curve, two of them are:

1. Relating length to the cantfor the givenradius R& maximum (or avg.) speed by

attaining this cant at a certain rate (cant

gradient)

2. Relating length to the radius of circular

curve & speed of train upon it



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(1949: Track committee of the Railway Executive of

British railways recommended that 1 in 300 should beadopted as the steepest permissible cant gradient

(

6

as maximum permissible cant(2 per second as the max. permissible rate of gain &loss of cant (& of cant deficiency)

5Important: Rate of gain or loss of cant involves thespeed of a train & therefore the cant gradient variesaccording to this rate of gain or loss

5For any given rate: lower the speed steeper the cantgradient



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BRITISH RECOMMENDATIONS

Based on max. cant gradient (1 in 300);L = 25 e

Based on rate of gain of cant (& ofdeficiency) of 2 per second;

L = 0.65 e Vmax

L = 0.65 D Vmax

L = length of transition in feet e = cant in inches D = deficiency of cant in inches Vmax = Max. permissible speed in m.p.h.


INDIAN RECOMMENDATIONS

Based on arbitrary cant gradient (1 in 720);L = 7.20 e

Based on rate of change of cant deficiency;

L = 0.073 D Vmax

Based on rate of change of superelevation;

L = 0.073 e Vmax

L = length of transition in metres e = cant in cms. D = deficiency of cant in cms. Vmax = Max. permissible speed in k.m.p.h.

Greatest of the following within each set of recommendations


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(Due to centrifugal force on train, it has

angular acceleration on curve

(On transition curve, with change in radius theangular acceleration changes.

(What should be the rate of change of angular

acceleration which is unnoticeable to

passengers?



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0 1 827

64

125

216

343

512

729

1000

0 1 2 3 4 5 6 7 8 9 10

l

r

v


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( Ifl= length in feet of any element of the transition curve

whose radius = rin feet and v is the linear velocity in ft./sec.

of the train the angular acceleration is v2/r

( Time taken to move overlis l/v, the rate of change in angularacceleration is

(When r = R, the above expression will be equal to 1 and this is

a maximum.



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To fit the transitioncurve, circular curve is to

be shiftedinwards by acertain distance called

shift


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(ATC = Original Tangent & CircularCurve

(TS = Shift s or the amount by which the

curve is displaced inwards in order tointroduce transition curve ABP

(P = Point of change from transition to circular

curve

(B = Mid point ofTS & AT = TD


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( Y = 8TB = 4TS end ordinate is four times the shift( Versine = SV = C2/8R( Because VS = 3TS,

3 Shift = s =C2/24RorL2/24Rwhere L = Length of transition curveDepartment of Transportation Engineering & Management, UET Lahore 60

A T

C

S

B

PR

V

Q

D

C/2 C/2

Y


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(Find out the length of transition curve for a

four degree Broad Gauge circular curved track

having a cant of 15 cm. The maximumpermissible speed on the curve is 90 kmph.

(Find out the shift & offset at every 15 m

interval of length of curve

(Draw the transition curve

Assume maximum permissible cant deficiency as

75 mm



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Length of Transition CurveBasis Value Units

Cant gradient 108.00 metres

Rate of change

of cant deficiency49.28 metres

Rate of change

of superelevation98.55 metres



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(Shift = L2/24R

= 1082/24 x 4/1750

= 1.11 metres



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Interval(m)

Offsets(cm)

15 1.19

30 9.52

45 32.14

60 76.19

75 148.81

90 257.14

105 408.33



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1.1

.52

32.14

76.1

148.81

257.14

408.33

0

5

10

15

20

25

30

35

40

45

5055

60

65

70

75

80

85

0

5

100

105

0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00 450.00

R = 437.5 metres

ORIGINALCIRCULAR

CURVE


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(READ THIS TOPIC FROMGUPTAS

BOOK

(Effect of change of Gradients(Summit curves

(Valley curves

(Length of Vertical Curve



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hhDL

R

LB

v!

v

!

)(2

125)( 2

Rigid Wheel Base Distance between two adjoining axleswhich are held in a rigid frameDue to this rigidity, there is a tendency of outer wheels of

front axle to tilt the rail outwards hence widening the gaugefrom its actual valueTo prevent this, gauge is widened by engineers on curves

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PCRailway Engineering Lab update!!