## Introduction

The complex structures of a railway track comprise of rails, sleeper-fastenings, sleepers and ballast all enthroning on the sub grade. This complex structure is similar to other civil engineering structures, which are steadfastly rooted in the ground. Railway track can be considered to be floating on the foundation. Thus the study of stresses and the plan of a railway track are regularized by its own laws which are in turn founded on the theory of elasticity.

In fact sleepers, rails, and counterweight constitute a track or superstructure which is placed upon a sub-grade. Sub-grade actually is used to put up with and allocate the inflicted loads with lessened unit forces and leave a smooth stand in which the super-structure can be placed. The track furnishes an uninterrupted elastic back up for static and dynamic wheel loadings and diffuses them with decreased unit forces to the subsoil. Conceptions of the spread of force by a railway track are set up upon the rationales of elasticity tailored by altering assumptions and test results.

## Images

## Elastic Theory

The unanimously acknowledged hypothesis founded on the considerations of elastic backing, presumes that the superstructure and its backup will sidetrack to some extent under the weight but come back to their original arrangement when the load is dispatched. Each constituent of the railway track is submitted to a frequently applied deflecting and winding loads as wheels of train pass. The consequence of different stresses is computed by regarding the track as an elastic member of a whole. The entire elastic property of the superstructure is presented by track modulus (Source: S.C.Saxena and S.P.Arora, A Text Book of Railway Engineering, 1975, Dhanpat Rai Publications).

## Track Modulus that is “μ”

Track modulus is an indicator for rigidity of track (i.e. opposition to bend) and is stated as load per unit length of the rail expected to develop a unit depression in the track. The modulus of the track is contingent on the gauge, the kind and thickness of sleepers, the kind of rails, the sort and division of ballast and sub grade (Source: S.C.Saxena and S.P.Arora, A Text Book of Railway Engineering, 1975, Dhanpat Rai Publications).

In order to find the track stresses the track modulus is applied in different equations. Several researches have been conducted and all the studies have revealed that a primary load of about 4 tonnes ensues in larger initial deflection. This deflection results in a gap between the rail and sleeper, between sleeper and ballast and annuls in ballast related on the maintenance of the track. The initial modulus at the initial range of 4 tonnes is known as Initial Track Modulus (ITM) and that beyond the range of 4 tonnes load is in fact elastic range and is known as the Elastic Modulus (EM). The calculation of stresses in track with the use of this double modulus gives more practical outcomes and therefore the Indian Railways has adopted this mode (Source: S.C.Saxena and S.P.Arora, A Text Book of Railway Engineering, 1975, Dhanpat Rai Publications).

## Images

The following measures of modulus are followed for computation of track stresses on Indian Railways based on extensive testing (Source: S.C.Saxena and S.P.Arora, A Text Book of Railway Engineering, 1975, Dhanpat Rai Publications).

1.For B.G.Track the standard track of

90R rails:

Sleeper density = M + 3

Ballast cushion = 200 mm

Its Initial Track Modulus (μi) = 70 kg/cm/cm

Elastic Track Modulus (μe) = 300 kg/cm/cm

52 kg rails

Sleeper density = M+6

Ballast cushion = 250 mm

Its Initial Track Modulus (μi) = 120 kg/cm/cm

Elastic Track Modulus (μe) = 300 kg/cm/cm

2.M.G.Track

Rails of 50R 60R and 75R

Sleeper density = M+3

Ballast cushion = 200 mm

Its Initial Track Modulus (μi) =50 kg/cm/cm 120 kg/cm/cm

Elastic Track Modulus (μe) = 250 kg/cm/cm

Notes:

1. Where ‘M’ is number of sleeper per rail length. Rail length for B.G.track is 13 m and for M.G. track is 12 m.

2. For computation of μ for B.G. Initial load is 4 tonnes while for M.G. track, it is 3 tones. (Source: S.C.Saxena and S.P.Arora, A Text Book of Railway Engineering, 1975, Dhanpat Rai Publications).