transitioncurve-210816162648.pdf

survey

1. Transition Curve & Superelevation
Batch 2019 QUEST Larkana
2019 Batch

2. Transition Curve
•AcurveofVariableRadiusisknownas
Transitioncurve.
•Transitioncurveisacurveinplanwhichis
providedtochangethehorizontalalignment
fromstraighttocircularcurvegraduallymeans
theradiusoftransitioncurvevariesbetween
infinitytoRorRtoinfinity.

3. •Assoonasavehiclecommencesmotionona
circularcurvefromastraightlinetrack,itis
subjectedtoasuddencentrifugalforce,which
notonlycausesdiscomforttothepassengers
butalsodistortsthetrackalignmentand
affectsthestabilityoftherollingstock.
•Inordertosmoothentheshiftfromthe
straightlinetothecurve,transitioncurvesare
providedoneithersideofthecircularcurveso
thatthecentrifugalforceisbuiltupgradually.

4. Transition Curve
•Atransitioncurveis,therefore,thecureforan
uncomfortableride,inwhichthedegreeof
thecurvatureandthegainofsuperelevation
areuniformthroughoutitslength,starting
fromzeroatthetangentpointtothespecified
valueatthecircularcurve.Thefollowingare
theobjectivesofatransitioncurve.

5. Transition Curve

6. Objectives of Transition Curve
•Todecreasetheradiusofthecurvature
graduallyinaplannedwayfrominfinityatthe
straightlinetothespecifiedvalueofthe
radiusofacircularcurveinordertohelpthe
vehiclenegotiatethecurvesmoothly.
•Toprovideagradualincreaseofthe
superelevationstartingfromzeroatthe
straightlinetothedesiredsuperelevationat
thecircularcurve.

7. •Toensureagradualincreaseordecreaseof
centrifugalforcessoastoenablethevehicles
tonegotiateacurvesmoothly.
•Tointroduceextrawideninggradually
•Toprovidecomfortforthedriverthatisto
enablesmoothvehicleoperationonroad.
•Topreventthepossibilityofoverturningof
vehiclesonhorizontalcurve.
•Toimproveindesignspeedonhorizontal
curves.
•Reducewearandtearofrailsection.

8. Properties Of Transition Curve
•1)RateofchangeofSuperelevationmust
equaltothatcurve.
•2)RadiusofTransitioncurveatjunction
shouldequaltoradiusofcircularcurve.
•3)Mustmeetthecircularcurvetangentially.
•4)LengthofTransitionCurveisinversely
proportionaltoRadius.

9. Types Of Transition Curve
•a) Spiral or clothoid
•b) Cubic parabola
•c) Lemniscates

10. Spiral or clothoidIdeal Transition
Curve Why?
•Rateofchangeorcentrifugalaccelerationis
consistent(smooth)and
•RadiusofthetransitioncurveisInfinityatthe
straightedgeandchangestoR(Ls∝1/R)at
thecurvepointandcalculationandfield
implementationisveryeasy.
•Itsatisfiesthatrateofchangeofcentrifugal
accelerationisconstant.

11. Ideal Curve

12. LemniscateCurve

13. All in One

14. Length Of Transition Curve
For mountainous and steep terrain
Ls = V²/R

15. Length Of Transition Curve
•b)BydefiniteRateofSuperelevation
•Ls=nh/100
•Whern=rateofSuperelevation1innandh=
superelevation
•C)ByArbitraryGradientLs=hv/x
•Wherex=timerateincm/secwhichcanvarey
from2.5cm/secto5cm/sec.

16. Length Of Transition Curve
•D)Basedonrateofchangeofsuperelevation
andextrawidening:
•Ls=(W+We)nh
•Themaximumofaboveconditionswillbe
consideredasthelengthoftransitioncurve.

17. Shift and Length

18. Superelevation
•Theinwardtransverseinclinationprovidedto
thecross-sectionofthecarriagewayat
horizontalcurvedportionofaroadiscalled
superelevation,cantorbanking.
•Inotherwordssuperelevationisraisingof
outeredge(ofcurvedportionofroadof
railway)withrespecttoitsinneredgeiscalled
superelevation.Itisgenerallydenotedbythe
‘e

19. Superelevation

20. Superelevation

21. Objective of providing superelevation
•1.Tocounteracttheeffectofcentrifugalforce
actingonthemovingvehicletopullthesame
outwardonahorizontalcurve.
•2.Tohelpafastmovingvehicletonegotiatea
curvedpathwithoutoverturningandskidding.
•3.Toensuresafetyofthefastmovingvehicle.
•4.Topreventdamagingeffectontheroad
surfaceduetoimproperdistributionofload.

22. Advantages of providing superelevation
•Itpermitsrunningofvehicleathighspeedona
curvedpathorastraightpathwithoutanydanger
ofoverturningandthusresultsintoincreased
volumeoftraffic.
•Italsohelpstokeepthevehicletotheirproper
sideonthepavementandthuspreventscollision
ofvehiclesmovinginoppositedirectionona
curvedportionoftheroad.
•Itprovidesdrainageofthewholewidthofthe
roadtowardstheinnerside.Thus,thereisno
necessityofprovidingsidedrainontheouterside
oftheroad.

23. Superelevation Formula

24. Superelevation Formula

25. Superelevation Formula

26. Superelevation Formula

27. From width and superelevation rate or
rising slope
•e, or h = 1/n x width of road

28. Rate Of Superelevation

31. Ex:1
•Calculatethelengthoftransitioncurvefor
V=65kmph,R=220m,rateofintroductionof
superelevationis1in150,W+We=7.5m.
(Hint:c=0.57)
•[Answer:Ls1=47.1m,Ls2=39m(e=0.07,
pavementrotatedwithreferenceto
centerline),Ls3=51.9m,Ls=52m]

32. Ex:2
•NHpassingthroughrollingterrainofheavy
rainfallarea,R=500m.Designlengthof
Transitioncurve.(Hint:Heavyrainfall.
Pavementsurfacerotatedwithrespectto
inneredge.V=80kmph,W=7.0m,N=1in150)
[Answer:c=0.52,Ls1=42.3,Ls2=63.7m(e=
0.057,W+We=7.45),Ls3=34.6m,Ls=64m]