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M.S.E., BARIPADA- 757001

DEPARTMENT OF CIVIL ENGINEERING

SUBJECT- R&B ENGINEERING

Chapter- Geometric Design

HORIZONTAL CURVES

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SEMESTER- 5TH

​

By

By- Er. Saroj Kumar Nayak

(Lect. In Civil Engineering Department)

AY:2021-2022

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  • NECESSITY ARISES DUE TO PHYSICAL & GEOGRAPHICAL FEATURES
  • NECESSARY EVIL
  • CURVE IS A LINE OF WHICH NO PART IS STRAIGHT AND WHICH CHANGES DIRECTION WITHOUT ANGLES
  • POSITIVE IMPEDIMENTS FOR HIGHER SPEEDS

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ANGULARITY OF AXLE WHILE NEGOTIATING A CURVE

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  • PLAY HELPS THE WHEEL NEGOTIATE CURVE
  • A BOGIE WHICH CAN TAKE RADIAL POSITION ON THE CURVES IS BETTER
  • GUIDANCE SHALL BE FROM THE TRACK GUIDANCE AND NOT FLANGE CONTACT

Angle of attack

α

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CURVE DESIGNATION

  • CURVES ARE DESIGNATED BY THEIR RADII, EXCEPT ON IR & US RAIL ROADS
  • ON IR DEGREE OF CURVE FOR DESIGNATION
    • RADII FOR CALCULATION

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DEGREE OF CURVE IS THE ANGLE SUBTENDED BY 30.5m CHORD AT THE CENTRE

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D = 1750/R

100 feet=30.5m

D

R

R

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ON IR, THE CURVES ARE MEASURED BY VERSINE- WHICH IS MID CHORD OFFSET ON 20m CHORD

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2R

V*(2R-V) = C/2*C/2

2RV=C2/4

V = C2/8R

C

V

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PARAMETERS OF CURVES

  • RADIUS, R AND DEGREE OF CURVE, D
  • ACTUAL CANT Ca
  • CANT DEFICIENCY Cd
  • CANT EXCESS Cex
  • EQUILIBRIUM CANT Ce / EQUILIBRIUM SPEED Ve
  • RATE OF CHANGE OF ACTUAL CANT rca
  • RATE OF CHANGE OF CANT DEFICIENCY rcd
  • CANT GRADIENT, i
  • LENGTH OF TRANSITION, L

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EFFECTS OF CURVES

  • VEHICLE RUNNING AT A SPEED OF V IN A CURVE OF RADIUS R EXPERIENCES A CENTRIFUGAL FORCE = MV2/R
  • UNDESIRABLE EFFECTS
    • POSSIBLE PASSENGER DISCOMFORT
    • POSSIBLE DISPLACEMENT OF LOADS
    • RISK OF VEHICLE OVERTURNING

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EFFECTS OF CURVES

  • RISK OF DERAILMENT
  • HIGH LATERAL FORCE RESULTING IN MAINTENANCE PROBLEMS
    • CURVE RESISTANCE
    • WEAR OF RAIL & WHEEL FLANGE
    • LATERAL FORCE ON TRACK STRUCTURE

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COMPENSATION FOR CURVATURE ON GRADIENT

  • COMPENSATION ALLOWED ON GRADIENTS DUE TO CURVATURE
    • 70/R
    • 0.04% PER DEGREE

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SUPERELEVATION / CANT

  • THE EFFECT OF CENTRIFUGAL FORCE IS ELIMINATED/REDUCED BY RAISING THE OUTER RAIL BY A SPECIFIED AMOUNT.

THIS RAISING OF OUTER RAIL OVER INNER RAIL IS CALLED SUPERELEVATION/CANT

  • THE FORCE DUE TO THE RAISING OF THE OUTER RAIL IS EXERTED INWARDS AND IS CALLED CENTRIPETAL FORCE

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VEHICLE ON A CANTED TRACK

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W

G

SE

Centrifugal Force

Centripetal Force Wsinθ

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EQUILIBRIUM CANT

WHEN ON CIRCULAR MOTION , IF THE RESULTANT OF WEIGHT & CENTRIFUGAL FORCE IS PERPENDICULAR TO THE PLANE OF RAIL & PASSES THROUGH THE CENTRE OF TRACK, THE CORRESPONDING SPEED IS CALLED EQUILIBRIUM SPEED & THE CANT IS CALLED EQUILIBRIUM CANT

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EQUILIBRIUM CANT

  • IRPWM STIPULATION
    • EQUILIBRIUM SPEED IS TO BE DECIDED BY CE CONSIDERING
      • MAX. SPEEDS OF FAST & SLOW MOVING TRAINS
      • PERMANENT SPEED RESTRICTION
      • JUNCTIONS
      • STOPPING PLACES
      • GRADIENT AFFECTING SPEED OF GOODS TRAIN

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Equilibrium Speed

  • Russian Formula:

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    • ni: no of trains, wi: weight of such train, Vi: speed of such train, m: types of trains

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ACTUAL CANT Ca

  • MAINTENANCE CRITERIA
    • HIGH CANT WILL CAUSE ROLLING OF BALLAST & FLATTENING OF INNER RAIL
  • OVERTURNING AT INNER RAIL
    • NOT VERY SENSITIVE TO WIND FORCE
  • SAFETY AGAINST DERAILMENT
    • EMPTY WAGON STOPPED & STARTED
  • COMFORT CRITERIA
    • NO APPRECIABLE DISCOMFORT UPTO 180 mm
  • LIMITED TO 1/8 TO 1/10 OF DYNAMIC GAUGE

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MAXIMUM VALUE OF CANT

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IRPWM PROVISIONS

  • EQUILIBRIUM CANT (406(1)(a))
    • C=GV2/(127 R)
  • MAXIMUM CANT (406(1)(d)(i))
    • 165 MM FOR GROUP A, B AND C ROUTE
    • 185 MM FOR STRUCTURES
    • 140 MM FOR GROUP D AND E ROUTE

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Cant Deficiency

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CANT DEFICIENCY Cd�

  • SAFETY
    • UPTO 175 mm SAFE WITH CRITICAL WIND VELOCITY
  • COMFORT CRITERIA
    • DISCOMFORT IF UNBALANCED LATERAL ACCELERATION IS GREATER THAN 0.1g
    • CANT DEFICIENCY SHOULD BE LESS THAN 0.1G
  • OBSERVED VALUE OF ULA IS MORE THAN THE THEORETICAL VALUE

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MAXIMUM VALUE OF CANT DEFICIENCY

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Cant Excess

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CANT EXCESS Cex

  • NO COMFORT CONSIDERATION
  • MAINTENANCE CONSIDERATION
    • EXCESS WEAR ON INNER RAIL
    • MORE THE VOLUME OF GOODS TRAFFIC LESSER WOULD BE CANT EXCESS
  • WORKED OUT FOR BOOKED SPEED OF GOODS TRAINS.
    • NORMALLY 65 KMPH ON BG.

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Cant Excess values�

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SNCF

IMPORTANCE

TONNAGE PER DAY

CANT EXCESS

VERY IMP.

>45000

70

IMPORTANT

25,000 TO 45,000

80

MEDIUM

10,000 TO 25,000

90

UNIMPORTANT

<10,000

100

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DB 

IMPORTANCE

TONNAGE PER DAY

CANT EXCESS

VERY IMP.

>60,000

50

IMPORTANT

30,000 TO 60,000

70

MEDIUM

10,000 TO 30,000

90

UNIMPORTANT

<10,000

110

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IRPWM PROVISIONS

  • CANT DEFICIENCY(406(2))
    • FOR GROUP A AND B ROUTES FOR SPEEDS IN EXCESS OF 100 KMPH FOR NOMINATED STOCK RUNS WITH PERMISSION OF CE : 100 MM
    • FOR OTHERS : 75 MM
  • CANT EXCESS (406(3))
    • 75 MM

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MAXIMUM VALUE OF Cex

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TRANSITION CURVE

  • TRANSITION CURVE IS AN EASEMENT CURVE INTRODUCED BETWEEN STRAIGHT & CURVED TRACK TO FACILITATE GRADUAL CHANGE OF VERSINES & SUPERELEVATION
  • ON INDIAN RAILWAYS, IT IS CUBICAL PARABOLA WITH THE EQUATION:

Y = KX3

  • THE SPIRAL, WHICH CHANGES THE DIRECTION ANGLE UNIFORMLY, IS THE IDEAL TRANSITION
  • THERE IS NOT MUCH DIFFERENCE IN THE LAYOUT OF THE SPIRAL AND CUBIC PARABOLA UNTIL THE DEFLECTION FROM STRAIGHT IS APPROX 4 M.

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TRANSITION CURVES

  • CURVATURE VARIES UNIFORMLY WITH DISTANCE
  • VERSINES VARY UNIFORMLY
  • CANT VARIES UNIFORMLY

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VERSINE AND CANT DIAGRAM OF A CURVE

Ca

V

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SHIFT ON TRANSITION CURVE

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CIRCULAR

CURVE WITHOUT TRANSITION

TRANSITION CURVE

C

D

B

E

F

G

A

L/2

L/2

S/2

S

EXTENDED CIRCULAR CURVE

CIRCULAR

CURVE WITH TRANSITION

H

TANGENT

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THANK YOU