ce-451

1. * /2"
"cE 4' I
(! fract< Fittings and Fastenings
Introduction
The pLrrpose olproviding fitrings and lastenings is to hold the rail in proper position for the
smooth running of trains.
-fhesc
fittings and fastenings join rail with rail as weil as fix the
slccpers with rail.
.Shvtmswn rVaf,ar old, 2t
Purpose & Tvpe
L Rail to Rai)joining
2. Rarl to rvoodcn sleepers fitting
3. llail to stcel trough sJccpers
4. Rail to cast iron sleepers
5. Elastic lastenings to bc
used with concrete. steel
and wooden sleepers
Details offiulng andfastenings
Frsh plates. Combination fish plates, bolts and nuts
Dog spikes. Fang holts, screw spikes, Bear.rg plates
Loose Jaws. keys & lincrs
Tie bars and cotters
Ehstic or Pandrol clip. tRN 202 ctip. iRN ZOZ
clip. H.M. fastening, M.C.l.tnserr, Rubber pacis
and Nylon liners
and sleeper: It ihould be
of vertical and horizontal
Requirements of an ideal fastening:
Follou'ing are thc requiremcnts ofan ideal fastening connecting rail
(l) capcble ofabsorbing shocks and r ibrotrons.
(2) capable of giving protection to sleeper against the actions
forces.
(3) capable of securing correct gauge at first assembly and of maintaining the gauge
subscqucntly.
(4) capable of giving sufficient insulation in case of electrified sections.
151 capablc of rcsrsting creep.
(6) consist ofa smail number ofcomponents.
(7) easy to fix and to adjust.
(8) so designed that it is possible to remove it on)y by special tools.
(9) not affecr rhe rlil or slceper edversely in any respect.
( I 0) non-corrosive, durable and above all cheap.
The inrporlant littings and fastertrngs commonly used are as follows.

2. RAII-TO RAII, IIASTENING
Fish plales
Rails are to bc conncctcd at their cnds. This is achicved by means of a pair of fish-plates per
rail. Holes are drilled througlr the plates and the wcb of rails and ther.r, fish bolts and nuts arc
providcd in thcse holes. When bolts and nuts are tightencd up, the rarls are joined together
and a continuous track is fonned.
F:rnctiort. The function ofa fish plate is to hoid two rails together both in the horizontal
antl vert ical plancs.
Ftc tn I t:tH Pt )Tt:
Dcsigir: 1'he stcel used lor fish plates should have a minimum tensile strength between 36
and 42 Tons sq. inch with mininium elongation of 20%. The fish plates are designed to have
loughly the sanre strength as thc rail section and as such the sectional areas of two fish plates
connecting the rail ends is kept about the same as that of the rail section. As fish plates are
not as deep as rail, the strength of a pair of fish plates is less than that of rail section and is
about 55% ilonll, ve(ica) bending is taken into consideration. The fish plates are so designed
that the fishing angles at the top and bottom surface coincide with those of the rail section so
as to have a perltct contact with the rail,
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FIC. 10,2 fISH PIATE FOR 9O.R RAILS

3. Gencrally, altenrate holes of fish-plates are made elongated or oval-shaped so that the bolts lll
thc rails will not be tumed by vibrations. Also, bolts are provided altenratively inside antl
outside the rail. Thus, alternatively, the hole in the fish-plate wiil be oval-shaped on one srdc
and circular on the other srde. Also, the holes in rails are nrade of larger diatletcr, gcncrally 5
nrrn to 6 ntnt, to allorv the rail to expand or contract with temperature
Combination I'ish PIate
Cornbinationorjunctionfishplatsareusedlorconnectingtwodifferentrailsections'lncase
of conrpoutrd fislr-plates, spccial junction chairs will be used so as to satisfy the two
conditiolrsntentionedpreviously'Junclionchairsrequiredwillbelwoinnumber-onefor
each sidc, right-hand and left-hand. Junction chairs rest on sleepers and fang-bolts are used to
jorn junction chairs to wooden sieepets'
Junctlon
Choir
s:
Plon
Compound
Fro.
FithPlote Lclt ort
flsh-platc
6-8
The fish-plares are macle thicker at the centre than at the ends where the rail section gets
changed and also, the outer fish-plate is n.rade 6 mm thicker than the inner fish-plate A11 the
lou, firh-plrt., required lor compound fish-plate will be different because the following two
conditions are to be satisfied:
(i) 'l'ops of rails should rentain in the same level'
(ii) (laugc lilccri l'lltrst bc i11 tlie same line'
R-/OUT
DIRECNON
LIGHTEA BAIL
KEY PLAN OF FISH PI "IE
HEAV'EB PA]L
€ '11
Roil
45
I Gou'1e foce

4. ,/
In ordcr to facilitate tlrc Lrndcrstanding lor thc rcquircd
Tlrc fislr-platcs are knorvn as left inside, left outside,
dircctiorr is obtaincd by lacing the heavier rail as shown
fish-plutc,,
"",rui,,
codc is lollowcri,
right inside and right outside. The
in key plan in fig. 6-9.
Light Rails
Lei( Oul
Compowrd fish-plate
Flc. 6-9
f tc 10.4.fl/rRKt/(; or LoMRINATIO, I.l5 ?tArES
It should be noted that no space is allowed for expansion.
-- -)-- -
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HEAVI€F ftAIL SECIION UAPTIA, RAIL 5 ECTIOh
rIG, IO,3 COMAIN^TION FISH PIATE
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5. Fittings for Wooden Sleepers
Spike
Spikes are used lor fixing rail to the wooden sreepers. They can be used with or without
bearing-plates below the rails.
Rcquirtntcnts of a gootl spikc:
A good spike should fulfill the following requirements:
( l) 'I'he spike should hord rhe rair in position and it should have enough resistance to
ntotion to rctain its position.
(2) The spike should be cheap.
(3) The spike should be such thar it can be easily fixed and removed.
Types of spiAcs:
various lypes of spikes havc bcen used, t.e common being dog-spikes, screw-spikes, round-
spikes and elastic-spikes.
Dog- Spike
Fig 6-r l shows a typical dog-spike used on the Indian Rairways. To ext-ract the spike, lugs
are provided i. rhe rread ofthe spike. The shape of the spike has given its name as c10g-spike.
The section ofthe spike is square and the rower end is brunt, pointed or chisel-shaped.
,{rrangcmcnt of dos-spikes
Frc. 6-12 -
€
E
@
The spikes should be driven irr a staggering manner as shown in frg. 6-12.If the spikes are
placed directly opposite to each other, they have a rendency to sprit the sleeper and they wilr
have less holding power. The direction of staggering in uny on" particular sreeper shourd be
reverscd as shown in fig. 6_12.
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Dog-spikc
lic. 6- l I

6. ,{
The liurlbcr of dog spikc
Locution
norrnally uscd is as [ollorvs:
Nunbcr of Dog Spikes
;
5
gr
w
On straight track ...... 2 (one on either side and duly staggered)
On curved track . 3 (2 outside and I inside)
Joint sleepers, bridges ...... 4 (2 outside and 2 inside)
l{ou nd Spikcs:
Round Spikcs alc Lrsed lor fixing thc rails with slecpers using anti-creep bearing plates. The
rountl spikes have bcconrc obsolctc now.
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FIG. 10.5, I)OG SPIKE, ROUND SPIKE AND FANG BOLT
Screrv Spikes
Figs. 10.6 & 6- 13 slrow a typical section of a screw-spike. The holiling power of a scr.ew-
spike is nearly double tl.ran that of a dog-spike. The head is circular with a square projection.
The sides ol the spike are tapered and provided with threads. The screw-spikes can resist
lateral thrust in a bettcr way than the dog-spikes. However, as the screw-spikes. are costly,
dog-spikes are rvidely useil. The driving operatrons are more or less the same as in case of
dog-spikes.
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7. 'lhcy arc also uscd on bridgcs and platlonr lirrcs. As pcr cxtant instructions, platc scrcws and
rail screws should be uscd in prelerence to round spikes and dog spikes to conserve the lifc of
wootlcn sleepcrs.
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F!'i. ) 0.6, SCREIY SPIKES
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Scrcw-spike
Fro. 6-13
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Elastic-spike
ErG.6-15
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Ror.urd-spikc
Frc. 6- 14
E lastic-spikes:
Fig. 6- l5 shows an elastic-spike. They are available in a variety of patented forms. A steel
spring and a specially shaped head are provided in,these spikes. These provisions give a
bettcr grip with the loot of thc rail and it results irr reduced wear and tear ol rail, less noise
and less creep. ln order to prevent corrosion, all elastic-spikes should be preferably
galvanized. These spikes are cornmonly used on the British Railways. The usual practice is
to provide tkee elastic-spikes per base-plate, lwo being on the gauge side.

8. Fang-bolts:
'l'his is an altemativc l.o rotntd-spikcs. BLrt tlris arrangerncnt is found to be nrore eflectivc. At
present, the tcndency is rlot to use fang-bolts due to th,e lact that there is considerable
difficLrlty in fixrng and rcrtroving the ftrng-bolt. Fig. 6- 16 shows a typic:rl farrg-bolt.
:t
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Hook-bolt
Ftc.6-17
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llook-bol(s:
Hook-bolts are uscd to fix sleepers to girders of the bridges. Rails are fixed with sleepers as
usual by means ofdog-spikes or screw-spikes. Holes are bored in the sleeper and the head of
the hook-bolt grips rvith the flange ol the girder. Usually, two hook-bolts are found to be
quite adequate for each sleeper.
Ch a irs and kel s:
For double hcaded and burr ircaded rails, chairs are required to hold them in position. The
chairs are invariably made of cast-irorr and they hclp in distributing the load from the rails to
the slecpcrs. All chairs co,sist of lwo jaws and a rail seat. The web of the rail is held tightly
against the inner Jarv of the chair and a key is driven between the rail and the outerjaw ofthe
chair as shown in fig. 6- 1 8 and fig. 6-21 , The rail seat on the chair is tilted inwards to. suit the
tilting of rails which is ger-rerairy l in 20. The chairs are fixed with the sleepers by means of
three spikes, two of
"vhich
are on the gauge side or by means of two through bolts.
The lieys requircd to keep the rair in proper position may be of wood or metar ard they rnay
be either straight or tapered. wooden kcys are cheap. But they are likely to be stolen and are
liable to be attacked by vermins. Hence, number of metal keys or various pattems are found
out, the cornnrort metirl used being steel. The initial cost of steel keys is high. But their life is
about ten tirnes rrore than wooden keys and hence at presenr, steel keys are prefened to
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fleootion

9. 6/,!9. Stdc
taner )oa ol choir
ts H R.ot
I wooden he!
Chair and }ey for B.H. rail
Fro. 6- 18
Stcwart's kcv
Frc. 6- 19
rvoodcn keys. Fig. 6- l9 :atld fig. 6-22 show Stewarr key and spring coiled key respecrively.
Stewan key is a steel plate bent in the fonn of letter E and a steel wedge, as shown in Fig. 6-
20, is introduced at the ends to kcep the key tight against the rail web and the outerjaw of the
chair.
Sleurort (d!
Gouge Srde
Outet Jaa of Cl]pir
lnner Jaa ol choir
Spihe
II-l
Ll/FII
tllIU---' fh-l-8mm
Wedge
Fro. 6-20
.|
E
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Chair and kcy for
Frc. 6-21
B.H. rail
Opcn coilcd key
Frc.6-22
! oder )o@ ol chor
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tlc. to.la. c.l at:art.-6I'LA! L toi a.H RArL
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10. t,
Bcaring-plates;
C'hairs for flat lboted rails are knorvn as beuring-plotes. Formerly, flat looted rails wcte
clircctly fixcd to tltc slccpcrs r.vitlt dog-spikcs. IJul at prcscnt, bcar-ing-platcs at'c lllaccd llclow
the rails on tracks carrying heavy vehicles at high speed, ntainly because of the following
udwtntuges:
(l) Beuring urea: The bearing alca on tlie sleepels is increascd and ltence, thc intellsiry of
loading is reduced.
(2) Rail-cuttitrg.. The abrasion by rail to contact surface of sleeper is known as rnll-
cutting. lt is lound that this tendency of rail is prevented by bearing-plates.
3) Soil cutting on cuntes;or.r curves, due to lateral pressure on the side of the head, there
is tcndcncy to ovcrtunl thc outcr rail. i'lcnce, a conccntratcd pressure is developed on
the outcr edgc of the base ol sleeper. This results in soil cuttirlg on cun'cs and is
prevented by use ol bcaring-plates on curves.
(4) Stabilin,: Spikes are driven through holes in the bearing-plates and this enables the
spikes on each side ol the rail to nlutually support each other. Hence, the overall
stability ol the track is increased by using bearing-plates.
5) lleur oJ'spikes; The rvcar of spikes by vertical vibrations of rails. against thern is
grcatly reduced tvhen bcaring-plates are used.
((>) Maintcnance: It is possible to ntaintain the gauge in a better way when bearing-plates
itre ttscd.
(7) Cost: The cost o f bcaring-p latcs is small as compared to reduction in maintenance of
track, incrcase in lile ofslcepcrs altd smooth running oftrains.
5l mnr
(JSrnml
--l + l.- ( l6r'rn )
Flat bcaring-plate
Fro, 6-23
Bearing-plates may be of cast-iron, wrought iron or stecl. Cast-iron bearirtg-plates
cheaper, but they are iiable to be easily t1;maged. Wrought iron bcaring-plates
occasionally adoptcd whilc bcaring-platcs ofstecI arc very comrnon.
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11. Bearing-plates are extensively used in countries like America where heavy vehicles are
running at high speed on treated softwood sleepers. But in India, as liardwood sleepers are
used, bearing-plates arc used at special places such as rail joints on curyes and on bridges,
under points and crossings, on ash-pits, etc.
Bearing-plates may be cither/at or canted. Flat bearing-plates are used in tumout track and
suclr othcr places rvhcrc rails are to be laid flat. In ail other cases. canled bearing-plates are
adoptcd.
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Carted bearing-plate
I'IG, 10,7. (:ANTED TT... AEARING PLA'II.: T'OR
Fro. 6-24
Fig. 6-23, 6-24 & l0.l show respcctively the flat and canted bearing-plates used on the Indian
Rail,,vays. Dimensions mcr:tioncd outside the bracket are for B.G. while inside the bracket are
lor M.G.
E last ic Fasten ings
Necessitl,Jor Elastic Fas t en in gs
The prinrary purpose of a fastening is to fix the rail with the sleeper. The fixing of the raii
to the sleeper rnay be done directly or indrrectly with the help of the fastenings, but in the
process the fastening is subjected to severe vertical, lateral and longitudinal forces. The
forccs, which arc prcclorninantly dynamic, increase rapidly witlr incrcasing loirds and
specds. In addition, vibrations are generated by moving loads mainly on account of
geometrical irregularities of track and due to forces set up by the imbalance in the rolling
stoc k.
The traditional rigid fastening, which has to certain extent fulfilled its task for quite some
time, is not able to meet the present challenge of heavy dynamic lorces effectively. Due to
shocks and vibrations caused by moving loads, the rigid fastenings get loose, an interplay
between the cornponents ol the track develops, track parameters get affected and a rapid
deterioration of thc track starts. There is a need, as such, of a fastening wliich can safeguard
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12. lhe track parautcters aud dampelt the vibrations. An elastic fastening is possibly an answel
for thc problcm.
Requirements of an Elastic Fastening
An ideal elastic fastening should be able to meet the following requirements :
(1) lt should provirJe sufJicient elasticity to absorb the vibrations and shocks caused
by moving loads
It slroulcl have adetluttte toe load wliicl.r should not reduce undcr scrvice
It should be o I '!r and forget " type to require least maintenance.
It should bc of thc typc that it can be used and re-used without losing its
propertl es
(5) It should have as few pttrts as possible, which are easy to be manufaclured, laid
ancl maintained.
(6) lt should be of the type that it cannot bc taken out a:td as svch is free from
s bol gc or theft.
t7) tt should be of universctl type so that it can be used on wooden, steei or concrete
sleepers I
(8) It should be cltettpartd have a Long l{e.
J
Type of Etastic Fasteuirrgs
(i) Paudrol Clip or Elastic l{ail Clip
pandrol PR 401 clip (also called Elastic rail clip) is a standard type olelastic fastening. It is a
"fit and forget" type of lastening and very little attention is required to maintain the same.
Fig. 10.15 Pandrol clip or Elastic rail clip
The toe load is quite adequate to ensure that no relative movement between rail and sleepcr is
possible. The Pandrol clips can be driven with the help of an ordinary 4 pound hammer and
requires no special tools. In order to ensure that correct toe load is exerted, the Pandrol Clip
should be driven to such an extent that the outer leg of the clip flush with the outer face ofthe
C.I. insert. The clip fixed on the rail is shown in an isometric view in figure 10.16.
(2)
(3)
(4)

13. '
The Pandrol clip or Elastic rail clip can be fixed on wooden, steel, cast ilon and coucrcte
slccpcrs with thc hclp of basc platc and witl.r some other ancillary fittings, Pandrol clips are
nraximunr used u rtlr concrctc slccpers.
Cortccrte sleepers u'ith Pandrol/Elastic clips : In case of concrete sleepers, malleable cast
iron inserts are inserted directly into the sleepers during their manufacture. The Pandrol clip
is fixed in the holes of the C.l. insert. A 4.5 mm thick grooved rubber pad has been provided
under the rail seat to nrakc it double elastic. Insulated liners have also been provided for the
purposc of insu lation.
Drawbacks of Panlro! Clip; The Pandrol Clip suffers from the following drawbacks:
(l) No adjustment olgauge rs possible.
(2) The Pandrol Clip has a point contact and causes indentation on the foot of the rail
duc to heavy toe load and small contact area.
(3) It does not provide enough safeguard lor theft or sabotage because it can be taken
out by ordinary hammer.
FIG. IO.I7 PANDROL CUP WITH CONCRETE SI.EEPER
-i '',
.
FIG, ]0.16 PANDROL CUP FIXED TO MIL SEAT.
*.

14. fl: ,lLT;:Hf l un
'ru"i'
rastening designed bv R D'S o' to suit two block RCC sleeper'
'I'hc assembly is clcsigncd lbr a toc loaJol'1000 Kg (l Tonnc) and toc clcflection of l8'5mm'
The assembly has got creep resistance generally equal to 507o ofthe tolal toe load oithe rail'
'the clip holds the track gauge easily and elfectively The inner legs rest against rail bottom
flange to provide
"n "f
uttt"
'g"gt check After the clip is placed in position' the nut is
tightened ro depress t1.,. inn.rl.gl *ith respect.to the toe till the inner legs touch the sleeper
surface. This stage corespondsio ttre designed toe load and the toe load deflection' At this
stage, no furthcr tightcning is possiblc The nr'rt is not expected to get loose quickly' as the
tension in the bolt does not
"'y "a.'
during summer' iRN 202 clip has the advantage that
the rail can be changccl withoLrt rcmoving thc fastening simply by loosening the bolt and '
pushing the rail out
(iii) Lock SPikcs
Lock spikes are manufacttlred by M/s Lock Spike Ltd' London' The spike or round spike lor
use ofrvooden sleepers. ,, ," o ri,u. r65 mm (6.5 inches) rong having 16 mm (5/8") diameter
rouncl scctiotr. 'fhe spike, which zrppears to have good future' is still under trial'
lhc spikc . whrch afJpeus lo haYc 8o('d l'ulurc' is slill undcr ttial'
na. n.n. tocx suxe
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FIC. IO,I8 1RN.2O2 CI)P
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15. ( ir') Spring Steel Clip
The assembly consists of a double elastic fastening used on Prestressed Concrete Sleeper. In
this assembly, the rail rcsts on a grooved rlbber pad and is held venically by a pair of spring
clips at each rail seat. The clip is pressed by a nut tightened on a22 mm bolt which is inserted
fronr the under side o f sleeper.
(v) H.M. Fasten ing
HM lastening basically consists of lour coach screws, which are tightened against the plastic
dorvels of the PRC sleepers and press the W. clip assembly to give desired toe load. Each clip
weighs about 510 gm and can give a toe load of about I tome. Gauge- is maintained with the
help of angled guide places. A thin insulated shim is plated between the angled plate and
concrete sleepers. A grooved rubber pad is provided below the seat to give necessary
dampening efflect and resistance to lateral movement ofrails.
The HM f'astening can be used for 52 kg as well as for 60 kg rails by using suitable size of
angled guide plates and insulating shims.
CEN-IFIE ILNE OF R.4]L
aat 8€gl()tl
FIG, 10,22 TTM IIASTENING
L'IC. IO.2O. SPRINC STEDL CUP
':
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16. M.C.l I nse rts
Mallcable Cast lron (M.C.l.) inscrl.s are fixcd drrectly into thc concrctc slccpcrs durirtg
nranulacture. The inserts are of two types:
( I ) Stenr type M.C.l. insert lor use in normal Pre-tension concrete slqepers.
(2) Catc typc M.C.I. insert lor use in Post-tension concrete sleepers.
Rubber Pads
A rubber pad is an integral part o[ an elastic fastening. lt is providcd betwccn rails and
slcepers to pcrform the lollorving duties.
(i) lt absorbs the shocks.
(ii) lt danlpens and absorbs the vibrations.
(iii) It resists lateral movements ofthe rails.
(iv) lt prevents abrasion ofthe bottom surlace olthe rail, which otherwise comes
in direct contact with the sleepers.
(v) lt provides electrical insulation between the rails in an electrified area.
a
o.u
T
FIC. 10.23 RUBBER PAD
The grooves provide uniform distribution of the in the sleepers and help in lirniting lateral
expansion of the nrbber under dynamic loads.
Cornposite Lirrers
Nylon insulating Iiners are being mostly used on Indian Railways. They are, however, getting
cnrshed under the toe load exerted by Pandrol clips. To eliminate such premature failure, the
following two types of composite liners have been evolved by R.D.S.O.
(i) Composite liner r.vith rnalleable cast iron and nylon components
(ii) Cornposite lincrs with M.S. and n,rrlon components
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17. :p
These lincrs have becn evolved on the basis of the design adopted on British Raihvays, where
thesc are reported to have given trouble-free service for the last lew years.
Class Filled Nylon Liners
RDSO has developecl sonrc lime back glass filled nylon liners of4 mm thickness particularly
for track circuited areas an<l sections, subject to sevete corrosion. These glass filled nylon
liners are considered to be technically superior because these are in srngle piece, have longer
life and are free from con'osion. These liners are on extensive use on Indian Rail ways
particularly rvith ERC clip assembly on 60 kg and 52 kg rails and PRC sleepers.
t'l<;. t0)5 GIASS I:ILLt ),VI',LON r-lN/R
The experience has shown that GFN-66 Iiners arc breaking particularly in yards where these
liners have been fitted in ERC clip assembly on concrete sleepers due to rusting of the rail
surface and uneven seating. To avoid breakage of GFN-66 liners, it is necessary that while
initial laying, proper prccautions should be taken to ensure that rail surfaces are cleared off
rust etc. and the liners arc madc to sit evenly on the I in 6 sloping surface ofthe rail flange.
Pilfer proof Etastic Fastenings for Concrete Sleeper
The presenl design of elastic fastening (Pandrol clip) is such that the same can be renioved
easily by single stroke of hammer.
A pilfer-proo I elastic fastening may be defined as an elastic fastening system which is easy to
fit in the assembly but provides some difficulty for its removal without damage to tile system.
The design of a pilfer-proof elastic rail fastening consists of an elastic clip of almost the sanle
design and introduction of a new fitting called "Pilfer-proof'.
: .,-: ,-l -rl.r ' -L

18. Fasten in gs per sleeper
Thc nulnbcr of various Iittings and
ord irrary or corrrclrtional lirstcrrings
10.4.
fastcnings pcr slccpcr lor diffcrcnt typcs ol slccpcrs lor
as wcli as clastic lastcning arc suntrr.rarizcd in the Tablc
Table 10.4 Numbeir of Fastenings
Type of
slecper
Orclinury Fas tcnings
per.sleepcr
Elastic Fastening per
sleeper
Nos.
Wooden
2. Concrete
3. Steel
trougll
4.CST/9
Dog spikes or
Screrv spikes
Kevs for C.l.
bearing p lates
No ordinarv Fastenings
Keys
Loosc Jaws
Plates
Tie Bar
Cotters
Keys
8
8
4
4
4
2
I
4
4
C.I. Bearing plates
Plate screws
Pandrol clips
Rubber pads
Pandrol lips
Nylon liners
Rubber pads I
M.C.l inserts I
Modified ioose ia*. I
"l
Pandroi clir.rs I
Rubber pads i
PandroJ clips I
Rubber pads I
2
8
4
2
4
4
2
4
4
4
2
4
2
..
ii, l.
,
{

19. CURVATURE OF TRACK
,,Nccessity of a curve
A curve is to Provided
-l to bYPass obstlc lcs
-.1 to conllcct tlesirctl oI ilnPortilltt ]ocatiotrs
u to havc llat gradicrlt
: to nlirlcll rvitlt tltc teIIlrirt ilg
For infbrnration, ir nray be rlored tlrat the rvor'ld's iongest corrpletely straight railway line exists
in Australia. lt is'197 knr long'
2rarr backs ol cu rr t
o Reduce speed., linrit lengtlr of train & prevent use ofthe heaviest types of locouottves'
o Increases tlack lllailltenallce cost'
:-.:l'lattrpcr'slnoothri'lillgclualityanclthcrcbyirlilLtccdisconrfortlothepassellger'
: lttcrcitsc proIahilit y ol'(lcrillll]lclll
t&B
As lar.as possiblc, rSeTu-rvcs s5oulil be avoiclcci at the lbllowi'g places:
c Bridge s ancl trtnnels
:..r APPloaclte s to l.rlrclgcs
o DecP cuttin gs
! SteeP grad iellts
I S ratiotts itrld Yards
u Lcvel-c rossitlgs'
Desigrt;ttion ol rt ctt rve :
Asimplecurvcisdestgtrateclcitlrcrbyitsdegrceorbyitsradius.Tlreclegreeofacurveistlre
anglesubtendedatthecenterbyachordof3048cnr(100|t)Iength,Thqs,infig.|2-1.,ifAB=
3048cnr(100ft)andZA1B=.lo,tlrecurveisofldegreeandwithtlresamelengtlroflB,if
.aAoB =6o,,re curve is of 6 ciegrees. It can be easiiy understood that the greater the degree of
curyatllre, the snlaller will be its radius'

20. A
Desigrration ol a curve
Fro. l2-l
The value olthe degree of the cun,c can be loLtnd out as inclicated below:
(i) Circumference ol a circle = 2rR
(ii) Angle subrended at rhe centre
by a circle having the above circumference = 360"
(iii) Anglc subtcnde<i ar t.he ccntre
by a 30.5 m chord or <legree o[ curve
360"
=_x30.5
2rR
= l75O / R approx,(Risinmerres)
(iv) Angle subtentled a( the centrc by o =iQ1 ,, 166
2nR,
l00fectarcordegrceot curi'c -lllln,isinfeet)
R,,,
Itt casc rvhctt raciiLts is vet'v latgc, ln arc ola circlc is alnrost equal to the lord cotlnectiltg the
r'wo cnds of tlre a|c. The dcgrcc ol'thc curvc is thr,r.s given by the following lormula:
Where R is in
Where R, is in
o=n8
^ 5730
u=-R;
metres.
f'eet
A 2o curve has. thercfore,
5730
ot --7:- -
,. .. I 7.50
a raolu s o, 2
2865 f'eet
= 8T5 rnetres
D| t4d. ShonlJ l lloqLtc
:

21. ,,Rclationship bclrvecn Radius arrd Versine of a curve
The rclatior.rship bclrvccn raclir.rs rrrrl versine can be established as indicated belorv. (Fig. 13.1)
a E
/p- .a* "- ---",N
c
-l-
s+
)1".
)..1G I ],1 RI:IATION RT:TIYEEN RADIUS & VERSINE OF A CURVE
Let R be rhc Radius ()l the curve.
Lct C hc thc lcngth ollhe chord.
Lct V bc lhe vcrsinc ol a chord ol length C.
As AC and DI arc two chords rneering pcrpendicular at common point B,
rt ean ['c provcd fr(rrr) srrr]plc tco tctry that.
ABxBC=DIlxBE
.r V(2R- v)=!x L
22
'C:or 2RV - V- =
4
V being vcry'small, V2 can be neglecred,
r-l
'"2RV=:-
.,0
C.
orV=-
8R ........... (i)
In the above eqLration V, C & R are in tire sanre unit say ln or cnr. TI.ris general equation can be
uscd to find out tllc vcrsitlcs, oncc the clrord and radius of a curve are l<nown.
Case I. ( Values in metric units)
The formula 1i) can be written
u
=c'
100 8R
Wherc, R is radius in ,C is Chord in metres, V is versines in cms.
Dr. Md. Shot,Bul Hoque
/|
---/ _L
I
f ,"i
i:}.

22. C2 x 100
orV=_-
8R
12 5C2 125C2
OfV=.-afitSOf--lrllll
R R .(ii)
Case Il. (Vulut-s in .f' p's' rtrtirs )
Srnrilarllj u'hcn Il, is ra<Jir't: in tcct C, is chorcl in lect' V
'
rs vcrsine in
Thc fornrula (i) carl be writte n as
v,= ci
t2 8R,
I 5C:
<.rr, V, = -;- ( rnches )
' tt .. (iii)
FrortrtltcfornlLrla(ii)artci(iii),rlicr.acliusofthecuryecatrbecalculated,otlcetheversitreand
clrotLl lc rrgth IIU kl'lort'
Detertuinatiou of Degree of the Curve in tlte Field
Forrlcrernrinirtstltetlcr]rct'oflltecrtrvcirrthcfield.acirordlengthofeitlterll.8nloro]ltiS
,.rop."aThc,c"...ctlrcclrorcilcng|its,rvhcrctlrer.elatiorisl-ripbetweetrthedegreeandversirreof
a cun,e is very silttplc as indicated belorv:-
(a) Versint rttt tt chttrd oJ' I l B nrctre's
t2.-5Cr
y =
''' "- ettrslronr litrnlula(ii)
N
1750 ^
P= "'" from Prrra l-3.2
R
Frorn thc abtrve two equations. the tlegrce of'the curve lbr a
chord can be dctcrmincd;
* 1750
D= -R
Substituing valua of R =
I I .8 metres
12.5C'
--v -
Dr. Md. Shotttsrl Ilotlrc
Ac,!.1

23. ^
1750V 1750V
t2.5C7 12.5(1t.8):
= V appro.r. (cms)
(b) Versine on a chorcl of 62 ft.)
- - ^2l.-)(_- vr =T inches from l.ormula(iii)
^ 5730 ^
U = _;_ trom para 13.2
Kr
The degrce of the curve lor a 62 ft. chord is as given below:
D _ 5730
R)
Substituting valueof'R, = {$ incrr.s
,_, 5730V1
u - __--_--_-i
=
l 5c;
= V, approx.
5730Vr
1.5(6D2
(inches)
This irrpoftarrt relarionsirip is urilizecl in finding out the degree of the curve at any point by
tlcasuring vctsincs citltcr in ctrr ott a cltord ol'I1.8 n')ctcrs lcngth or in inclrcs on a c6oril of (r2
li length. l'he cLtlvc is of as ttrany clegree as thele are cm or inches of the versine for the above
chord lcngths.
y Tvpes ofcurvcs and linriting ratlius or clcgree ofcurvature
Thc curvature uay be in the lornt of sinrple cilcular cur,,es or conpound and r.everse cul.ves or
vcrtical curves. A transition crrrvc is provided at the starling point of the circular curve to have
col)stalll rate of change ol radial accelelatjon. The radiLrs of transition curve varies {l-o n.r
infinity at the junction lvith the straight to the radius of circular curve at the junction with the
circular cttrve. Various tlansitioll curvcs are found out. Vertical curves are introdLrced in
vcrtical planc irr thc lbrnt ol'a 1;arabola.
The largest degree or the smallest radius ofcurve on a track is decided by keeping in view the
objcctrons mentionccl prcviously. ln Irrdia. the degrees ofcurvature are limited io iO, to ana aO
lor E.G., M.G. and N.c. respectivery. on important broad gauge li.es, the curves are flat and
they rarely excced 3o.
Dr. Mtt. Sh tlts|t Haqte
Pt
t ,l

24. I'ransitiolr cll rves:
T,Purposc of a 'fransitiott Curve (l:rg I 3. t0)
As soon as a vehicle eltters a cilcLrliu curve taking off fronr a straight, it rs subjected to a
sudclcli cctttritirgal Ibrcc. ,,vlticlr rrot orrly causcs disconrlbrt to pusscngcrs but distorts Lr.ack
aligttntcnt and a1'lccts tllc strbllily ol'r'olling srock. In ordcr to proviclc snrootl.r cntry to thc
curve' tratlsitioll ctlrvcs arc Ptovi<lctl orr cilher sidc ola circular curve so that thc ccrrtrifirgal
Ibrcc is built up gradually by running out the super-elevation slowly at a unilorm rate. A
ttattsitiott curve is. thercfote, lt1 ause tcul c'urvc irt rvhich the degree olthe curvature and gain
ofsuper clevation are ttnilornt tlrloughout its lcngth, starting tiom zero at the tangent point to
the specified valrre at tlre circular.curve.
'l'hc Ibllowing alc thc objcctivcs ol'a tr.ansition cur.vc:_
o 'fo decrease the radius of citrvattLre gradualJy in a planned rvay from infinity at the
straight to that of thc circLtlar cr.rlve to l.relp the vehicle to negotiate a cu1e smoothly.
o To provide a gradual illcrcase of the super-elevation startjng fiom zero at the straight to
the desired super-elcvation at tlte circrrlar cLrrve.
T'IC IJ IA TRANSITION CURVE :
To errable rlre vclrrcl.s lo r)esolilte a cur.r'e snroolhly cnsLrring a gradual increase or
decrease of centrifrrgtt lorccs.
T llequire nrcnts of an ideul trarrsitiott curve
o lt shor-rld be tangential ro rhe srraight i.e. it should srart from straight with zero
e u IViIIU IC.
o It shoulcl join tlrc cilcular curve tangentially i.e. at the encl it sirould have the same
curvitlurc its lllal. oJ tlls cir.cLtlar cLtrvc.
g fhe curvature shoirld i'lcr-c:rsc ar the same rate as the super-elevatior.r irtcreases.
c The length of tl.re trarrsition curve should be adequate to attain the full super-elevation,
rvhich itrcreases gradually at a specified rate.
Forms of transitiott curye:
Various lorms of transition curves are lcund out such as Euler.,s spiral, Froud,s cubic parabola,
etc. The latter is widelv adopred in rai)way track. The equation representing Froud's cubic
6/
Dt. t4d. Shonsul Hogue

25. cu rvc
r = distancc ol arry poi't or1 the tangent fr.o,r comnrencerlrent of the curve
R = ratlirrs ofcircullr crrlr e
[- = totill length ol'tratrsitiot) curve
Lengtlr of transitiorr curve:
The lengrh of a transition cu.ve is trie centre Iine rengtrr aro,g the Eaek between the starting
point on the straight and thc nrecting point on the junction *itr,, tto.ir.rrur.u.u.. Fo,. th.
lndian Rai'vays, this length is rvorke. oLrt by applying the following for.mulas:
(l) L=7.20e
(2) L:0.073C1 x V,,,,.
(3) L:0.073c x V,,,,,
where L : Lenglh oItrarrsitrorr curvc in m
e ,= Actual supcr--elcvation or caltt in cn]
Ca = Cant deficiency lor nraxinrurn speecl in cm
/ = MaxirlLrnt speed in kmph
parabola is as Ib IIorvs:
y = '/(oRL)
Whcrc y = perpcrrdicular.ol'l!ct ol lr.atlsitiorr cLrrve
elcvation.
(b) The greatest lcngth as workcd out fi.onr
Shift:
In order to fit the transrtion curve, the nlain
distance. This distance is ternrcd as1Lry' and
at a distance x li.onr contlnencenrent ol'lhc
is based on the rate
of change of super-
all the three cqLratiol.ls should be adopred.
...
,9*ftuina poiuts should be rrored:
(a) Equation ( l) is basetl on an arbirrary gr.adient while equation (2)
of changc of cunt tlcllcicncy. Ecluation (3) is based ou tlte fate
circulal curve is to
for a cubic parabol
be n.roved tnwards by a cerlain
a, it is worked out by applying
Dr. i4tt. Sh,,,$ul lloqtft
0€ANOlJtLrs

26. thc Ibllou,ing
rvhere
lirnr u la:
s = L'?(24R)
S = Shilt
L = Length ol'tr.ansition curve
Il. = Radius ol'cir.cular. curve.
Probletn l.
A trutsitiott curyc is lo be use<l to
struight. Tlte lcrtgtlt of tlu rtitttsitiort
ttt interval.
Solution:
FIG.I3.I ). SHIFT
ioin rltt' crtLl: oJ.t /ottr tlegtcc circttlat curvc wirlt tha
(ut t L' is l :0 ttt. Wurl out the rltift trtt,l olfsets Ltr cvcty 30
F*--30 n--+i<-30 m *)i+-3O m_i+-JO m..+r
ts.+ 6O m--:*--6O nr --_____-X
Trans.ition curve
Fro. I2-2
Dr i4l Shontntl Hoqnt
liv, ){ -_
ct RcuL^r cur/{ <
-
-tL//^{ -x
'. 4-
W 'lo/,
I
t
I
Circulor

27. .&: I{adius
J : Shilr :
OITlct at 30
Oilsct a c 60
Offsct at 90
OIhct at 120
-
t-ea
'2+R 2+ x 437 - '"'
303
m:--
6r120x437"
603
nI::
-
{b ( 120 x 437 "
.- 903
6x120x437"
1203
nt.
100: B-58 cn.
100 : 66.65 t*.
100 : 231.79 ,*,
o)
!=
Gq
" 17+6..50
or curve - =_ar- -.136.625, say 437 m.
, *,,
L: l2oir'
L : 7.20e
: 7.20 x 10 : 72*.
L:OO73.fPV^;,
: 0.073 x 7.60 x B0
L:0.07'3e x V,no,
6x 120 x 437
: 4438 m......:............(Z)
liffE sEg zo ,*.
- - .,. lsrD'
Cdnt ' -
,*, tr^
Prohlent 2.
Firttl ott tlta lanvllr of t,Lrrtsitr,u ttl tt'fot'tr lJ.G. cttrt,c of rltr.ce tlagrces., ltut,ittg, ((trt oJ
l0 <ttr. The r r t cr.t i r t t t r r r r ltar.nti.t.sihlt,.t.tt,ttl ott tlt<,<.ttn,e is g0 ltut p.tt.
Solutiort.
S u pet'elevation, Crnt dcficiencl aud Cant erccss fbr curvcs
,.- Sluperclevutiorr ot ( utrt (Crt)..
As lar as a train is rLllltlitlg alottg lr straiglrt track, the heads of the rails nrLrst be kept absolLrtcly
at tl'rc sa'nc Icvcl Btrt u'hctt rt is rlto'rtls on cr CLrrvcd path, it has 2r corlslarrt radial accelcr.atio.
which produces ccntrilugal fbrce. ln order to counteract this force, the outer rail of the track is
raised slightly higher than trre iruer rair. This is known as super-erevation or catlt.
S Lrper-elevat ion or cant is the clifference in height between the outer and the i*er rail on a
curve lt is provided by gradually lilting the outer rail above tl.re level of the inner rail. The
inner rail is considerecr as the reference rair and is norma y maintained n, iu-origira r.rar.
Thc inner rail is also kttowrt its thc gradient rail. The nrarn fr.rnctions of sr-rper-elevati-on are:
(l) To havc a better drsrriburion of loarl on both rails.
(2) To reduce the rvear anci tear olrails and roliing stock.
: 0 073 x l0 x B0 : 59.46 m..... ...... .. (3)
Adoptrng the grearcsr ol(l), (l), (3). the iengrh of transitiorr curve will be72nt.
), ".,
Dr. Ml. Shu sul Haque

28. 7
(3) To neutralize thc eflect ol lateral lorces.
(4) To provide conrfort to passengers.
Thc aptount ol srrpcr-c leva{ ion crn r'asilv he rvorkecl otlt theoretically as shown below. See fig'
r2-1.
Ie
1
Super.elevation
Fro. l2-3
It is cvident thal. lotatiorl rvill take piace about veltical axis and since centrifilgal force acls at
right angles to the axis of rotatiotr, its tlirection rvill be horizontal.
Lcl lY = Werght ol'lttor ittg tr;lilt
r' = Vclocity itr trtc(tcs per secotrd
P = Centrilugal lbrce lctrng on tlte vehicle through its ceirtre ofgravity
.g = Acccleratiott clLte to gravity itl trl/sec2
,( ' I{l(litrs of ctttr c ttt tlt
C = Caugc ol (rack itt ttl
c == SLrPcr-clcvutiolt itt ctrl
a - Angle ol'illclitlrliorr
S = Lcngtlr of irrclincil surfacc.
Raclial accclcrariorr, g = /l/R
Forcc, P == ln.lss x accelcration
'I hcn,
Wuz
P -':-'- ... .....(l)'-Tn
Also, resolving thc lorces along the inclined sullace, we
gct, Pgs5a: W sinc.
Wu2 G -. c
-:W. -"grRSJ
It may be noted that it is not accurate to say G as gaugc oftrack in hg. l2-3.
Dr. lttd. ShaDtsuL l!oqre

29. (2)
Il tr/: Vclociry in km
/ l/ x 100000z
llrcn,r:l-- | ' 60x60 I
per hour'
Gx 100
98i xfix 100
For Il.G.,
S.E.
For M.G.,
For N.G.,
e l,'
Y' X l.b ll)
1.27 x R
Iz! x 1.00
1.27 x R
t8t5#. v
t)-a
O8O
R
ut/
Vr x O i62 V2
-l.zT
^-t{
=- 0 6a
-n
'v
The anrount olsttper-elevatiorl or cant obtained by eqLration (3) is knorvn as equilibrilm super-
elevuliort or equilibriun cu tt t.
The super-elevatioll can bc calculated only lbr a parlicuiar speed wheleas in actual practrce,
dilfercrrt trains al dil'lercnt spcetis will be usirrg thc cur:vature with super-elevation. Hence
super-elevation should be such as Lo accommodate these variations of speed from time to time.
For this purpose. a speed is rvorked out deperrding on the trumber of trairrs running at differeut
speeds. This specd is knor'n as the
'veighted
average. Fo. i.stance, suppose on l particular
track, the speerls ol varrorrs tr.;rirrs:rre as lollorvs:
Nunrber o f trains
l0
8
4
Total 22
1'lrcn,
wcighccd avcrage
Specd oItlains irr knrlth
50
55
60
:(r0 Is0) +
s00 + 440 +
(8_x s5) +_14 x-90:)
22
240
I lB0
.oo
= 53.64 kmph
Hence, deviation from tlre r':raximunr speed = (60_00 - 53.64) = 6.36 kmph
l, ..i
fl,'
Dt' Mtl Shottsul tloqu(

30. :pcnding upon these lactors, the ttlaxittlttt't'l pcrn)issiblc value ol' su1;ct-cltr'lttit)tt
t.nuir.tJ b1 r'arious cotllllrics, c'g', in Britain, it is 190 nrtlr; itl Atncrica' iL is 152 mnll
dia, it is 165 rrrnl, 102 nrnr and 76 ntm lor B'C', M'G'' and N'C' r'espectivcly l'ltus
aximum value o f super-elevation a<Jopred in lndia is about onc-tenth of the gauge
is.
in
the
:ansition curves are used to obtaiD correct super-elevation at all points along the tlack Super-
cr,aliontsZcroattl]cbegrrlningol.tlrctratlsirioncut.vcatrditreachestlrefullvalueattlre
rnction of transiti<tn an<l cilculur ctrtvcs. Thetl, s Ltllet-elcvation iS kept constant along tl.re
rculztr curvc.
'
u nt deJic ie n c.t' ( C d,1 :
)ant deficiency occurs rvhcn a ttait't
quilibriunr speed. lt is the djflerence
peetl ancl thc aclLtal cant providcd
travels aroutrd a culve at a speed higher than tlte
between the theoretical cant required for such higher
a spccrl lorvet than the eqLrilibriLrtl
and >e theoretical cant reqtrired tbr
'.uttt
cxcess (C't'1 :
',,il
"^a"rt
occLIrs rvhclt ll tlilill llllvcls atotttrd a cttrvc at
;pced, lt is the dill'ercnce belrvccn the actual callt provided
;uch lorver speed.
ipeed of trairrs 0t) curvcs:
IhespcedoftrainslvhilcpassirrgovelaCLllvalLlledependsonseveralfactorssuchasthe
gauge, the sulter-elevatioll, thc plovision or abseuce oltransitiol.t cLlrve, the weight of trair.r, etc'
I-lencc, r,arious countrics havc <lcvclopcd ccrtain cnlpirical lormulas for obtaining the
nraxin rm value of speed. In Irrtjia, the lollowing lonrtulas ale adopted for u'orhiug out the sale
speeds on firs1 class broad gatrgc, nletle gattge zr:ld ttatrow gauge track:
For B.C. ancl M.C., t :4.4 x sqrt (R - 70)
For N.C.. V= i.(r x sqrl (R - 6)
The above lormrrlas are lor curvcs provided with trarlsition curves. For curves which ate'not
providccl rvith transition curvcs, tltc ntaxiniun.r pcrmissible spceds are trker.r as 0 80 I/
ln the above fonlulas,
/= maximum sPeed rn knrlrh
fl = Radius ,f,f cttrve il.l 11).
The above speecls arc to bc reduced lLrrther by 20%o,
this case, the nlax. value ol N.G. will be 40 krrph'
track is provideci rl'ith ballast ancl the rolling stock is
if transition cllryes are not provided and in
The above formulas are adopted when the
in good order.
'1i'
Dt t, . ShottlJul Hoqne

31. l) ellciel cy in su per-eleva I io tl:
Undcr ccrtain conrlitions, ir is nor possible to provic.lc tlrc cquilibrium cant. see fig. l2-4. A
branch line diverges ll-ont a tltailt Iine. ,,1P and 8Q are the itinet all<i outcl rails rcspcctivcly ol
nrain lilc arrrl 1lD urtrl .4('arc thc inncr unci ou{cr iails rcsl)ecli/cly ofbra:lch line. l-et 57 iir'ld .!-'
5c tllc ntol;ts of supcr'-e lcvatiorr rccltrilctl [or rnain and btattch lirlcs rcspcctivcly Following
co rrd rt ions slrotr ltl bc sattsll,-rl:
(l) considcring nlitin litle, ltoint li shoulcl be higher tltan poil1t,4 by the irnroLutt s;
(2) Consiclcring brattch litre, 1;oint z1 should be higher than point B by the amortnt S:
Deficicncy in super-elevation
Fro. l2'4
Ir is obvious rltal ir is intyrossible to comply with botli the corrditions sit.t.tu ltatreously and ilence,
urrdcr such circunrstanccs, a snrall rnlount. oldcliciency in super-elcvzrtiotr is pcruritted r.vittroLrt
corlesponding rcduciltg thc specd..Tiris is knorvn as cant tlefciency or cleJiciency itt super-
clct)ution and it rcprescnts tlre amount by whiclr the actual super-elevation falls sl.ro: t of thc
cquilibrium super-elevatiotl.
I)rocedLrre tor findirrg resltcctive speeds on
(l) The equilibriunr cant on branch
suitable speed on brar.rch line.
(2) Thc 1;crrnissiblc cant clc[icicncy is dedtrctecl fiom the equilibrium car.rt.
(3) -l-hc
rcsLrlt. (hus obtaincd will rc1:r'cscrrl lhc ncgal.ivc suPcr-clcvation to bc givcrr on tltc
brlnclr litr,;.
(4) Evidently, the negative cant on branch line will be equal to the maximum ctrlt
pernrittecl on tl)c rnair) llne.
(5) Perr-nissible cant dellciency is added to the maximum cant per'lrritted on the n.rain line
and co rrespondingly, the restlicted speed on rnain line is worked out.
The nraxirnurn clcficicncy in sLtpcr-c Icvat ion perrnitted in lndia is 76 mnr on B.C., 51 mnr on
M.G. and 38 mnr ou N.C.
r.naiu and branch lines will be as follows:
lirrc is calculated by ustral lonnula by assuming
so
Dr Mt Shn tstl tloq)Le

32. .4 6 tl<'grt'cs cttrt'c l>rurtc:ltcs <1/l.frurtt u 3 degrces ntctirt c,nrve in trn opposite clirection in the
lul out of u [J,G. .tanl. lf tltc :;ltctctl ott lhc brutth line is restrictetl to 35 l tph,. deLermine the
spaed rastrictiott r.trt tlrc ntttirt lirta. ..lsstrtnc pennissible leJiciencv in cunL us 76 mm.
S. E. fbr branch line :
: 5.534 cn.'dy'
Ncgative super-elevation == 5.5i4 - 7:60 = -2.066 cnr.
I'laxinrLrrn S. E. tltat can be gir e rr on ntain line = 2.066 cnt.
l-lrcoretical S.E. on nrain Iinc = 2.06(> +'7.60 - 9.666 cm.
H c n t,,',
9.606
- I.315 v'
--t 746.5013
I/ = 65.42 krn p.h. spccd on main line. Ats.
Problent 1.
I.llork out lhc naximum spud oJ a train on a B.G. track hauin.q
a culaaturc o1f tfuee degrccs anl ca oJ' 10 cn. Assume allowable canl
dejcietrl' as 76 mm.
Soluliort:
,t : Radius uf curv 1746 50
"
.: -_3_: :582.t7 m.
Theoretical cant : Actual cant + Cant dcficiency
: 10.00 + 7.60
- I 7.60 cm.
Tltcrr.
t/2
s,E.: l.3ls
1760: t.usx !5tJ2'17
V : BB km p.h. ....(t)
Accoldirrg to thc lorntula ot rlrc Indran Railway Board,
V : 4.4/R - i0
: +.+Vss[;[7 - zb
:99.62 kmph .. .. ... ... (2)
Adopting the lowcr ol ( l) and (2), rhc mnxir.nu* permissible speed of train will be gg kmph
| 3ts
#: 1.315 x
35?
n46lcold
L t:)
Dt'. M!1. Sh.t|tul Hoque

33. l)t<.tltlcut 5.
ll lrut:ltotrltl lx'lltc ctltiltlttrttttt (rttl on tt Nl.o. t rrrt'c r.{ 5" f<tt un ut'ct.tge,tpcctl r-tf 60 l;tttltltl
''llso firt<l tntt tlrc nttt.t.ittttrttt 1t<'rnti.s.riltle speecl uftcr ttllou ing tltc rttu.rirtttrrtt ccrttr tlt,ficicrc,.t..
Soltrtrotr.
^ 1746.50
o:
s
:349.30 m
V2
S.lr' : 6'99 -t)
:o8u* 60'
349.30
: 8.24 cm.
Theoretical canr : Actuai cant
:8.24 * 5.10
: I 3.34 cm.
I'hqr,
f Cant deficiency
S E. : 0.80 I:R
i i.-i4 = 0.,5.r. f /_jJ9.30
V -- 76.34 krrrph ....................,....... ( l)
According to the fonrrula of the Indian Railway Board,
V,:4.4/n:70
:4.4rl349.30
-
- 73,57 km p.h.
70
Adoptirrg rhe lorver or (l) and (2), rrre maxinrur, pernrissibre speed of trai, wi, be 73.57 kmph
t /Gra<le conlpellsation on curves:
The ntling gra(rie tis defineci as the nraxinrunr gradient to which a track may be laid in aparlicular section Now' jfa curvc is situated on a rLrling gradient, the total resistance would bethc addition ofresjstance due to cLrrvature and rhe resistarce due to ru)ing gradie,t. T-his wiLiincrease the resistance wrricrr is worked out on the consideration of gradient onry. In oriier toavoid resistances beyond a definite limit, gradients o, curves are reduced and suclr reduction isknorvtt as gru(!(' ('()ttlpL'ttsttltott utt turvts. Tlrcre lIc vlrious factot.s aflectirrg cur.ve fesrstance.BLrt it is taken as a perccntage per degrec of curve. The Indian Railways have adopted thcvalucs of gracle compcnsation on culves as
0.04 per cent per degree of curve on 8.G.,
0.03 pcr cent per degree of curve on M.G. and
0.02 per cent per degree of curve on N.G.
b;.,
Dr. Md. Sho,nsul Hoql,e

34. lrr U.S.r., lltc gritdc cortll)clrsirl io rl orr curves vlrrics Ilorll 0.03 to 0 05 pcr cent ller degrce'
dcpcndingotr Lllc rario oi-thc lcngth ol'curvc to thc lcngtir of the longcst traitl and also on the
pusirio,,
-of
ctttvc itt rclation to thc foot ol the gradient ln England' the usual grade
conlpensation oll curves is 0,04 per cent per degrec oi'ctlrve
P rohla nt 6.
II the ruling gratlient is 1 in 200 on n particttlrtr section of B'G' and if u curve of 4 degrees is
sttlote(! ott rhis rttlitrg grutlicttt tt ltttt should be rhe uctval ruling gradient'?
Solutiott:
Assumirrg gratle conrpetrsation ol1 B C as equal to 0-04 per cent pel degree of curve'
con]pctlsill.ioll alloued = 0 04 x '1 = 0 i6 pcr cellt'
Norv. 1 in 200 = 0.50%
Actuar gradienr allowed : 0.50 - 0.16 = 0.34% or 1 in 2g4 wi be the ruling gradient for the
c u rvc.
Ilending of rails ott curves:
Curves less thatr 3 dcgrecs ar-e considcrcd as flat cul ves and in tllis case, rails can be retainecl it.t
tliecttrr,cc]positionbyslccpcrsrr,hichat'elreldinplacebyballast'Iror.sharpcurvesof
curvatLllegleateltllal]3degt.ccs,itistlcsirablcrobcndtherailStocorrcctCLlrvattlle,lftherails
are not bent, rhe si<lc tlrrusl' on ballast at ti]c ends of tlre sleepers due to tlre rail rvhich acts like a
spring, is sufficicltt to lornl elbolvs and drsturb ihe alignllent of the track The amount by
rvhich the rail is to be bent cau easily be found out as shorvu in fig 12-5'
Bcnding of rails on curvcs
Frc. l2'5
Effect Of Curvature On Long Vehicle
Lct v = rise of rail at centrc; c: onc-hali' ol chord length; /? = radius ofcurve'
Then, c.r- c : t, (2R - t'): 2Rv - vr'
"
Neglecting v2, as this will be very small'
2 ,^
^v = c /z^
For a I2.80 nr rail length to be laid on a 4 degree curvature'
v:6.402 l(7x174(t.5014) = 0.0i633 m = 4 633 cm, say 47 mm
c
R"'
- OVEB THBOW
Dr. lt . Shu $ul Ho4ue
ENO !
P

35. Cuttirrg cf rails orr curves:
Gcnc-rally. rails arc lard irr such a way that rail joints are exactly opposite to each othcr. But
u'lrcn thc tails arc laid on a curve, the.ioints of oLlter rail gradually fallbehind the joints of
itrtel tail duc to thc l'act that the outer rail has to cover a lo:rger distance than the inner rail,
Hcnce. u'ltetr this dil'fcrencc bcconres equal to the distance between two bolt holes, generally
I I.l ntrtt, a picce ol- rail ctlLral to cloublc this length is cut off fronr the inner rail. Thus, the joint
t.rtt iltnct rarl rvrll lall bchind thc joint on outer lail by 114 mnr and aiter a certain length, the
joints rrill bc cxaclly oppttsil.c to each other. This is termcd as cuuing of rails on curves. lt
should bc retttentbctcd (hat cutting of rails r.vill not be required in case ofstaggered railjornts.
,/
I:IC. 13.21, CUTT|NG RAIL ON CURVES
idcn ing g:iugc 0n cln cs:
DLre ro rigiclity of'tlti: r.vheel basc, ir is sor'r'retintes found on the cLrrve that the rails are tilted
oLrlalds so that aclLlal gaLrgc is trtorc than thc thcoretical value. The y,hcel bcrse is defiled as
lhe distance bctrvectt trvo adjoinrng axlcs rvhich are held in a rigid frante. The nraximum valges
o1'rigrd u'hce I basc in lntlia on B.C. ancl M.G. arc 610 cur and 4gE cnr rcspectively. To prevell
this tcndency, lhc gauge ol'the triicli is sontetimes widened on shaip cLrrves. The anlount of
rvidcning ofgauge depcrrds on the radius of the curve, gauge and the rigid wheel base of the
r elricles Iikcly lo r.rsc ll)d track.
various lornrulas a'c availablc lor finding out rlle extra width ofgauge required on
in arry case, this cxtra wiclth shoLrld not exceed 25 rnm on 1676 mm and 1435 rnn.r
l6 nrnr orr thc M.C. Sonrc of thcsc rulcs at.e r.:tentioned belorv.
Rula I :
d _ LB_+ L_),_x t25
f
d = Extra rvidth of gauge in mnt
a = Rigid wheel base in rn
L = Lap of flange in m
R: Radius ofcurvc in nr.
cuives. But
gauges and
rvhe re
Dt. lil. Sh u:it4 tloty|

36. (lhccli rail on curve (lrig. I3.221
clrccli rails a'c blrsicaly p'o'idcd on sha.p c.rvcs o.l trre inncr rail to reducc tire raterar *,ear,
oll tllc ou{cl rails. Thcy itlso Prc'cn1 tl)c or.rlcr l,hecl flange lionr :rroLr,tirrg o. the outer rail and
thus decrease lhe crrarrccs of ticrairnrert or'thc pr.irics. chec* :.airs we:lr oLlt quite rast but as
thesc are nortrlally rvorn rails Lrnil lor' lriD Iinc tr.aclis, frrrlhcr $,car of chccli rails is rror
cons idcrcd objec rionab le.
t:t(;. I t.22 (' L:(:K R ttt_ 0,y cuRvr.:s
As pcr l)rcsent stil;rrlations
cLrn,cs slrarpo tltan S" olt
lor chcck rail is ul4 nrnt fbr.
chccli lails ar.c ltroi,icleci on
E.C. 100 on N4.C. and l4o
B .C. and 4I nrnr [or. N.G.
Lhc gaLrge lace s icie
on N.C. ltl in rur unt
of the inner rails on
c learance plescribed
tr'. i4tl. Sllot s ll l.l0qu?