52 kg





and W



52 kg

(SH and





and ST










GMT stands for gross million tonnes per km/annum.

^ 60-kg rails are to be used on all routes identified for carrying 22 t axle load wagons.

* The existing 90 R rails may be allowed to remain for speeds not exceeding 110 km/h.

1 52/90 represents 52 kg/90 UTS (ultimate tensile strength) rail section.

Second-hand 52-kg rails may be used on a case-to-case basis, with the prior approval of the Railway Board, depending upon the quality of released rails available.

For routes identified for running 22.1 t axle load wagons, a sleeper density of 1660 per km should be maintained.

B Where primary renewals are undertaken and there is potential for LWR tracks, sleeper density may be kept as 1540.

B EF stands for elastic fastening.

1111 CST-9 sleepers can also be provided as an interim measure.

Head-hardened rails should be used for (i) local lines where there is an EMU stock running, (ii) sections with gradients steeper than 1 in 150 and/or curves sharper than 2°, and (iii) locations where the rate of wear of rails necessitates rail renewal at a frequency of10 years or so. These rails should be laid on continuous and long stretches.

The various track standards for private sidings are listed in Table 5.2


Track standard

Sidings with operating speeds of more than 80 km/h

Track structure as specified for D routes

Sidings with operating speeds of more than 50 km/h and up to 80 km/h

Track structure as specified for E routes

Where BOX'N or 22.1 t axle wagon ply and operating speed exceeds 30 km/h

52 kg Indian Railway Standards T-12 second quality rails or 52 kg second hand rails

For sidings with operating speeds of up to 30 km/h

52-kg Indian Railway Standards T-12 third quality rails or 52 kg second hand rails

Track structure for MG routes

Tracks on MG routes have been classified based on speed and GMT in categories Q, RI, R2, R3, and S routes. The S route of MG has been further classified as S1, S2, and S3 routes as per the details given below.

(a) Routes with a through movement of freight traffic are identified as S1 routes.

(b) Uneconomic branch lines are identified as S3 routes.

(c) Routes that are neither S1 nor S3 are identified as S2 routes.

The track standards being followed on MG routes are given in Table 5.3.

Table 5.3 Recommended track structures for MG lines


Q routes for speeds | > 75 km/h, GMT > 2.5

R routes for speeds up to 75 km/h

S routes for speeds < 75 km/h and GMT < 1.5


R1 routes, GMT > 5

R2 routes, GMT 2.5-5

R3 routes, GMT 1.5-2.5


90 R new

90 R new

90 R (SS) or 75 R new

90 SS or 75 R new

SS rails of 90 R for S1 and 75 R for for S2 and 60 R for S3

With EF







*As an








interim measure of up to

110 km/h


M + 7 or

M + 7 or

M + 7 or

M + 4 or

M + 4 or



1540 per

1540 per

1540 per

1380 per

1380 per

LWR is




km and M + 7* or 1540 per km

km and M + 7* or 1540 per km




300 mm*

300 mm*

250 mm*

250 mm*

150 mm*

* For


or 250 nm

or 250 nm

or 200 nm

or 200 nm

or 200 nm with SWR or 250 mm*

speeds of 100 km/h or above

The following are MG track standard specifications.

(a) Heavy haul routes identified for the movement of 14 t axle load wagons should be laid to the minimum standard prescribed for R1 routes even if these routes are classified in lower categories.

(b) Concrete sleepers, wherever provided, should have a minimum ballast cushion of 250 mm.

(c) New rails should be laid as LWR and concrete sleepers should be used for LWR as far as possible.

(d) Released rails of a higher section of (up to 90 R) may be used if the prescribed sections of rails are not available.

(e) Released BG CST-9 (Central Standard Track, 9th series) sleepers (90 R) may be used for secondary renewals on Q and all other routes of MG.

Maintenance of Permanent Way

The permanent way is the backbone of any railway system, and the safety and comfort of the travelling public primarily rests on its proper maintenance. Till a decade ago, the Indian Railways tracks were mostly manually maintained by beater packing as per a fixed timetable round the year. In recent years, however, on account of heavier and faster traffic and due to economic considerations, modern methods of track maintenance such as measured shovel packing, mechanized maintenance, and directed track maintenance have been tried and are in vogue on some sections of Indian Railways, particularly on high-speed routes.

Mechanical maintenance of the track has been introduced on about 14,500 km of high-density BG routes and the rest of the track is maintained through manual labour. The labour force directly employed for this task is about 190,000. About 3000 km of track is being maintained at present by measured shovel packing, which is an improved method of manual packing. A need-based directed track maintenance system, which initiates maintenance work only when there is actual requirement, is being increasingly introduced in order to eliminate unnecessary maintenance work. It makes the labour force more productive. About 20,000 km of track is covered by this system.

A major portion of the track, however, continues to be maintained on a predetermined cyclic programme by the manual method of maintenance, i.e., better packing. The full details of these methods of maintenance have been discussed in subsequent chapters.

Track Utilization

With the introduction of high-capacity bogie wagons and the replacement of steam locomotives with more powerful diesel and electric locomotives, the tracks have been subjected to heavier axle loads and higher operating speeds. During the period 1950-51 to 1994-95 the average density of traffic (in terms of net million tonne kms per route km) has increased from 5.24 to 18.40 millions on BG and from 1.19 to 2.65 millions on MG. The increased track loading has necessitated improvement in the track structure and maintenance practices, specially over high-density and high-speed routes.

Track as an Elastic Structure

In the year 1888, Zimmerman propounded the theory that the track is an elastic structure. Rails are continuous beams carried on sleepers, which provide elastic support. The elastic nature of the rail supports affects the distribution of the wheel load over a number of sleepers in a rather complicated manner. The mode of distribution of load depends on the stiffness of the rails as well as the elasticity of the bed (sleepers and the ballast and formation taken together) on which the rail rests.

Track Modulus

Track modulus, like the modulus of elasticity, is an index of measurement of resistance to deformation. It is defined as the load in kilograms per unit rail length required to produce one unit depression in the rail bottom. The unit of track modulus is kg/cm2.

The Research, Designs and Standards Organisation (RDSO) of Indian Railways has carried out a large number of investigations to determine the track modulus and vertical bending stresses in rails due to static loads on BG and MG tracks. These empirical studies reveal that the rail depression immediately below the load is not directly proportional to the load in the entire load range. Due to slacks and voids in the track structure, the track depression is disproportionately higher in the initial stages of loading. These slacks and voids get closed under the initial load and thereafter further depression per unit load is smaller and becomes proportionate to the increase in the load. It is found that an initial load of 4 t for BG and 3 t for MG gives the best results.

There are, thus, two well-designed load ranges, and the value of the track modulus is not able to completely define the load-depression characteristics of a track. The complete relationship can be expressed by assuming that a linear load-depression relationship exists in the initial stage of the load and that there are two values of track modulus-one is the initial track modulus (U) and the other is the elastic track modulus (Ue).

The track modulus varies with the gauge as well as with the track standard, namely, the type of rails, sleepers, sleeper density, and ballast cushion. The values of track modulus adopted on Indian Railways are given in Table 5.4.

Table 5.4 Details of track modulus


Track standard

Initial track modulus (kg/cm2)

Elastic track modulus (kg/cm2)


90 R rails, N + 3 SD and 200 mm ballast cushion



52-kg rails, N + 6 SD 250 mm ballast cushion




Rails 60 R and 75 R; sleeper density N + 3 and 200 mm ballast cushion



Forces Acting on the Track

A rail is subjected to heavy stresses due to the following types of forces.

(a) Vertical loads consisting of dead loads, dynamic augment of loads including the effect of speed, the hammer blow effect, the inertia of reciprocating masses, etc.

(b) Lateral forces due to the movement of live loads, eccentric vertical loading, shunting of locomotives, etc.

(c) Longitudinal forces due to tractive effort and braking forces, thermal forces, etc.

(d) Contact stresses due to wheel and rail contact.

(e) Stresses due to surface defects such as flat spots on wheels, etc.

Vertical Loads

Dead load of vehicles at rail-wheel contact

The value of dead load is usually taken from the axle-load diagram. It is, however, brought out that for various reasons the actual wheel loads, even in the static state on a level and perfect track, may be different from the nominal values. Cases have sometimes come to notice where a steam locomotive had a higher axle load than the nominal load or had different right and left wheel loads.

Dynamic augment of vertical loads

On account of vertical impact due to speed and rail vibrations, etc., the dynamic load is much more than the static load. The dynamic wheel load is obtained by increasing the static wheel load by an incremental amount given by the speed factor. Till 1965 Indian Railways used the 'Indian Formula' for calculating the speed factor. This formula is the following:


Speed factor = ~m (5.1)

where V is the speed in miles per hour and jl is the track modulus in psi.

After 1966, the 'German formula' given by Schram was adopted, which is as follows.

(a) For speeds up to 100 km/h:


Speed factor =- (5.2)

30,000 v 2

(b) For speeds above 100 km/h:

45V2 15V3

Speed factor =------ (5.3)

105 107

where V is the speed in km/h.

At a speed of 60 mph, the Indian formula gives a speed factor of 55%, whereas the German formula, as used by RDSO, gives a speed factor of 30%. Investigations have been carried out by RDSO and different values of speed factors have been recommended for different types of vehicles running at different speeds.

Hammer blow effect

The centrifugal forces due to revolving masses in the driving and coupled wheels of a locomotive, such as crank pins, coupling rods, and parts of the connecting rod, are completely balanced by placing counterweights near the rim of the wheel, diametrically opposite to the revolving masses. The reciprocating masses of the piston, piston rod, cross head, and part of the connecting rod, by virtue of their inertia and oscillatory movement, produce alternating forces in the direction of the stroke and tend to cause the locomotive to oscillate sideways and nose across the track. In order to reduce this nosing tendency, a weight is introduced onto the wheels at the opposite side of the crank. The horizontal component of the centrifugal force of this added weight balances the inertial force in the line of stroke, but the vertical component throws the wheel out of balance in the plane perpendicular to the line of stroke. The vertical component of the centrifugal force of the weight introduced to balance the reciprocating masses causes variation in the wheel pressure on the rail, and is called the hammer blow. The heavier the weight added to balance the reciprocating masses, the greater the hammer blow.

The hammer blow effect occurs only in the case of steam locomotives. The hammer blow can be calculated as follows (Fig. 5.2):

M 2

Hammer blow = - r(2pn) sin Q (5 4)


Steam effect, hammer blow effect and effect of inertia of reciprocating masses
Fig. 5.2 Steam effect, hammer blow effect and effect of inertia of reciprocating masses

where M is the net overweight in lbs, r is the crank pin diametre in ft, n is the number of revolutions of the wheel per second, and Q is the crank angle.

Steam effect

A steam locomotive works by converting coal energy into steam energy. Steam pressure acts on the piston and is transmitted to the driving wheels through the

crank pins and connecting rod. The vertical component of the crank pins and connecting rod is at an angle to the piston rod. Its value is given by the formula

where L is the length of the connecting rod in inches, h is the height of the cross head above the centre line of the driving wheel in inches, and Q is the crank angle,

i.e., the angle traversed by the crank since the beginning of the stroke.

The steam effect (Fig. 5.2) does not scynchronize with the hammer blow effect due to overbalance and is additional to the hammer blow only during some part of the revolution of the crank shaft.

Inertia of reciprocating masses

The reciprocating masses, due to their inertia and acceleration, alter the forces on the piston, and hence the force in the connecting rod is also affected during the revolution of the wheel.

where M is the mass of the reciprocating parts, L is the length of the connecting rod, n is the number of revolutions per second, h is the height of the cross head above the centre line of the driving wheel, and Q is the crank angle.

The maximum combined force of the hammer blow, the steam effect, and inertia for each driving wheel and the hammer blow effect of the coupled wheels do not act simultaneously due to the phase difference in the angular position of the counterweights in the coupled and driving wheels. The maximum combined effect of these forces is obtained by summing up the three curves for one complete revolution of the wheel.

Bending stresses on the rail due to vertical loads

The general theory of bending of rails is based on the assumption that the rail is a long bar continuously supported by an elastic foundation. Due to vertical loads, the rail is subjected to bending or flexural stresses. The bending stresses that a rail is subjected to as a result of vertical loads are illustrated in Fig. 5.3. The theory of stresses in rails takes into account the elastic nature of the supports. Based on this theory, the formula for bending moment is

where M is the bending moment, P is the isolated vertical load, l = (EI/ m)1/4 is the characteristic length, EI is the flexural stiffness of the rail, m is the track modulus, and x is the distance of the point from the load.

According to Eqn (5.7), the bending moment is zero at points where x = pl/4, 3pl/4 and maximum where x = 0, pl/2, 3pl/2, etc.



pl/ 8

pl/ 4


pl/ 2


3plj 4



9 pl/8


FMB as a percentage of the maximum





















For calculating the stresses acting on the rail, first the maximum bending moment caused due to a series of loads moving on the rail is calculated as per Eqn (5.7). The bending stress is then calculated by dividing the bending moment by the sectional modulus of the rail. The permissible value of bending stress due to a vertical load and its eccentricity is 23.5 kg/mm2 for rails with a 72 UTS.

Stresses on the Track

Stresses on the track due to the various kinds of forces applied on it are discussed in the following sections.

Lateral forces

The lateral force applied to the rail head produces a lateral deflection and twist in the rail. Lateral force causes the rail to bend horizontally and the resultant torque causes a huge twist in the rail as well as the bending of the head and foot of the rail. Lateral deflection of the rail is resisted by the friction between the rail and the sleeper, the resistance offered by the rubber pad and fastenings, as well as the ballast coming in contact with the rail.

The combined effect of lateral forces resulting in the bending and twisting of a rail can be measured by strain gauges. Field trials indicate that the loading wheels of a locomotive may exert a lateral force of up to 2 t on a straight track particularly at high speeds.

Longitudinal forces

Due to the tractive effort of the locomotive and its braking force, longitudinal stresses are developed in the rail. Temperature variations, particularly in welded rails, result in thermal forces, which also lead to the development of stresses. The exact magnitude of longitudinal forces depends on many variable factors. However, a rough idea of these values is as follows:

(a) Longitudinal forces on account of 30-40% weight of locomotive of tractive effort for alternating current (ac).

(b) Longitudinal forces on account of 15-20% of weight of braking force of the locomotive and 10-15% weight of trailing load.

Tensile stresses are induced in winter due to contraction and compressive stresses are developed in summer due to compression. The extreme value of these stresses can be 10.75 kg/mm2 in winter and 9.5 kg/mm2 in summer.

Contact stresses between rail and wheel

Hertz formulated a theory to determine the area of contact and the pressure distribution at the surface of contact between the rail and the wheel. As per this theory, the rail and wheel contact is similar to that of two cylinders (the circular wheel and the curved head of the rail) with their axes at right angles to each other. The area of contact between the two surfaces is bound by an ellipse as shown in Fig. 5.4.

The maximum contact shear stress (F) at the contact point between the wheel and the rail is given by the empirical formula


where F is the maximum shear stress in kg/mm2, R is the radius of the fully worn out wheel in mm, and P is the static wheel load in kg + 1000 kg for on-loading on curves

Contact stress for the WDM2 locomotive Static wheel load (P) = 9400 + 1000 = 10,400 kg. Radius of worn out wheel for maximum wear of 76 mm (38 mm radius reduction):

Contact stresses between rail and wheel
Fig. 5.4 Contact stresses between rail and wheel

The contact stress for the WDM2 locomotive as such is 18.7 kg/mm2 The maximum value is, however, limited to 21.6 kg/mm2, which is 30% of the UTS value (72 kg/mm2) of the rail.

Surface defects

A flat on the wheel or a low spot on the rail causes extra stresses on the rail section. Empirical studies reveal that an additional deflection of about 1.5 times the depth of the flat or low spot occurs at the critical speed (about 30 km/h). Additional bending moment is caused on this account with a value of about 370,000 kg cm for the BG group A route with the WDM4 locomotive.

Stresses on a sleeper

The sleepers are subjected to a large number of forces such as dead and live loads, dynamic components of tracks such as rails and sleeper fastenings, maintenance standards, and other such allied factors. Based on the elastic theory, the maximum load on a rail seat is given by the following formula:

where P is the wheel load, m is the track modulus, S is the sleeper spacing, l is the characteristic length, and Z is the modulus of the rail section.

The maximum load on the rail seat is 30%-50% of the dynamic wheel load, depending on various factors and particularly the packing under the sleeper.

The distribution of load under the sleeper is not easy to determine. The pattern of distribution depends on the sleeper as well as on the firmness of the packing under the sleeper. As the ballast yields under the load, the pressure under the sleeper is not uniform and varies depending on the standard of maintenance. The following two extreme conditions may arise.

End-bound sleeper The newly compacted ballast is well compacted under the sleeper and the ends of the sleepers are somewhat hard packed. The deflection of the sleeper at the centre is more than that at the ends.

Centre-bound sleeper As trains pass on the track, the packing under the sleeper tends to become loose because of the hammering action of the moving loads. The sleeper thus tends to be loose under the rail seat. Alternatively, due to defective packing, the sleeper is sometimes hard packed at the centre.

Stresses on ballast

The load passed onto the sleeper from the rail is in turn transferred to the ballast. The efficacy of this load transmission depends not only on the elasticity of the sleeper but also on the size, shape, and depth of the ballast as well as the degree of compaction under the sleeper. Professor A.N. Talbot has analysed the pressure distribution in the ballast under the sleeper and investigations reveal that the pressure distribution curve under the sleeper would be shaped like bulbs as shown in Fig. 5.5. The following are the important conclusions drawn from Fig. 5.5.

(a) The pressure on the sleeper is maximum at the centre of its width. This pressure decreases from the centre towards the ends.

(b) The vertical pressure under the sleeper is uniform at a depth approximately equal to the spacing between the sleepers.

Pressure on formation or subgrade

The live as well as dead loads exerted by the trains and the superstructure are finally carried by the subgrade. The pressure on the subgrade depends not only on the total quantum of the load but also on the manner in which it is transferred to the subgrade. The spacing between the sleepers; the size, depth, as well as compaction of the ballast under the sleeper; and the type of subgrade play an important role in the distribution of pressure on the subgrade.

The values of maximum formation pressure permitted on Indian Railways are the following:

For motive power 3.5 kg/cm2 for BG

2.5 kg/cm2 for MG For goods wagons 3.0 kg/cm2 for BG

2.3 kg/cm2 for MG

Stresses in the ballast
Fig. 5.5 Stresses in the ballast

Relief of stresses

A train load consists of a number of wheel loads close to each other which act simultaneously on the rail. A single isolated wheel load creates much more bending moment in the rail as compared to a group of wheel loads, which on account of the negative bending moment under adjacent wheels provide what known as a 'relief of stresses'. The rail stresses in this case are comparatively smaller. The value of relief of stresses depends upon the distance of the point of contraflexure of the rail and the spacing between the wheels, but its value can be as high as 50%.

Permissible stresses on a rail section

The permissible bending stresses due to vertical load and its eccentricity, and lateral load on a rail section on Indian Railways is given in Table 5.5.

Table 5.5 Permissible bending stress



Permissible stress due to bending



Minimum ultimate tensile strength



The stresses on a rail are measured by any of the following methods depending upon the facilities available.

(a) Photo-elastic method

(b) Electric resistance strain gauge method

(c) Method employed using special test frame

At present, Indian Railways mostly uses the electric resistance strain gauges for measuring rail stresses.

Whenever a new locomotive or rolling stock design is introduced on the Railways, a detailed study is carried out followed by field trials to ensure that the permitted speed of the new locomotive or rolling stock does not cause excessive stresses on the track. The same stipulations are made whenever there is an increase in the speed or axle load of the existing locomotive or rolling stock design.

The various parameters and their limiting values required to be checked for BG are given in Table 5.6.

Table 5.6 Limiting values of stresses on BG


Permissible value

Bending stress on the rail

36.0 kg/mm2

Contact stress between the rail and the wheel

21.6 kg/mm2

Dynamic overloads at rail joints due to

27 t for locomotives and

unsuspended masses

19 t for wagons

Formation pressure

3.5 kg/cm2 for locomotives and 3.0 kg/cm2 for wagons

Fish plate stresses

30 kg/mm2

Bolt hole stresses

27 kg/mm2

Coning of Wheels

The tread of the wheels of a railway vehicle is not made flat, but sloped like a cone in order to enable the vehicle to move smoothly on curves as well as on straight tracks. The wheels are generally centrally aligned on a straight and level surface with uniform gauge, and the circumference of the treads of the inner and outer wheels are equal as can be seen in Fig. 5.6.

Coning of wheels
Fig. 5.6 Coning of wheels

The problem, however, arises in the case of a curve, when the outer wheel has to negotiate more distance on the curve as compared to the inner wheel. Due to the action of centrifugal force on a curve, the vehicle tends to move out. To avoid this the circumference of the tread of the outer wheel is made greater than that of the inner wheel. This helps the outer wheel to travel a longer distance than the inner wheel.

The wheels of a railway vehicle are connected by an axle, which in turn is fixed on a rigid frame. Due to the rigidity of the frame, the rear axle has a tendency to move inward, which does not permit the leading axle to take full advantage of the coning. The rigidity of the frame, however, helps to bring the vehicle back into central alignment and thus works as a balancing factor.

The coning of wheels helps to keep the vehicle centrally aligned on a straight and level track also. Slight irregularities in the track do occur as a result of moving loads and the vagaries of the weather. The wheels, therefore, move from side to side and therefore the vehicles sway. Due to the coning of wheels, this side movement results in the tread circumference of one wheel increasing over the other. As both the wheels have to traverse the same distance, this causes one wheel to slide. Due to the resistance caused by the sliding, any further side movement is prevented. If there was no coning, the side movement would have continued and the flange of the wheel would have come in contact with the side of the rail, causing jerks and making the ride uncomfortable.

Coning of wheels causes wear and tear due to the slipping action. It is, however, useful as

(a) it helps the vehicle to negotiate a curve smoothly,

(b) it provides a smooth ride, and

(c) it reduces the wear and tear of the wheel flanges.

As far as the slip is concerned, it can be mathematically calculated as follows. 2nd

Slip =-G (5 10)

360 K '

where d is the angle at the centre of the curve fixed by the rigid wheel box and G

is the gauge in metres.

The approximate value of the slip for broad gauge is 0.029 metre per degree of the curve.

Tilting of Rails

Rails are tilted inward at an angle of 1 in 20 to reduce wear and tear on the rails as well as on the tread of the wheels. As the pressure of the wheel acts near the inner edge of the rail, there is heavy wear and tear of the rail. Lateral bending stresses are also created due to eccentric loading of rails. Uneven loading on the sleepers is also likely to cause them damage. To reduce wear and tear as well as lateral stresses, rails are titled at a slope of 1 in 20, which is also the slope of the wheel cone. The rail is tilted by 'adzing' the wooden sleeper or by providing canted bearing plates.


The permanent way consists of rails, sleepers, the ballast, sleeper fittings, and the subgrade. The strength of each of these components is essential for the safe running of trains. The stresses developed in each component due to the movement of wheel loads should be within permissible limits as specified for different types of tracks. The concept of load distribution in a railway track is based on the elastic theory, but most of the equations used to calculate stresses in the different components lack a theoretical background. The coning of wheels helps reduce the wear and tear of the wheel flanges, providing a smooth ride. The ill effects of coning on horizontal curves are reduced by laying the rails at a slope of 1 in 20.

Review Questions

1. What do you understand by a railway track or a permanent way? Mention the requirements of an ideal permanent way.

2. What are the component parts of a permanent way?

3. Draw a typical cross section of a BG double track in embankment and show therein all the components of the track.

4. What is meant by 'track modulus'? Indicate its usual range of values for a broad gauge track.

5. How is track modulus expressed? State the factors affecting it and give the values of at least one of these factors for the tracks in our country.

6. Draw a typical cross section of a permanent way. Explain briefly the functions of the various components of the railway track.

7. Discuss the necessity and effects of the coning of wheels.

8. What are the various types of stresses induced in a rail section? Explain briefly how these are evaluated.

9. Explain the following terms.

(a) Track modulus

(b) Coning of wheels

(c) Tilting of rails

(d) Permanent way




Rails are the members of the track laid in two parallel lines to provide an unchanging, continuous, and level surface for the movement of trains. To be able to withstand stresses, they are made of high-carbon steel. Standard rail sections, their specifications, and various types of rail defects are discussed in this chapter.

Tilting of Rails | RAILWAY ENGINEERING - Contents | Function of Rails