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.

5.3.1 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



Maintenance of Permanent Way | RAILWAY ENGINEERING | Forces Acting on the Track