# Long Welded Rails

Long Welded Rails [LWR] In order to avoid the expansion joints in rails welding of rails is done & stress-induced is arrested by fixtures and sleepers.
If one sleeper gives R resistance force. Then no. of Sleepers required to Resist the Force developed due to expansion of rail.

n= As×α×T×Es/R,
where As is a cross-section of one rail,
T = temperature in degree centigrade
Es = modulus of Elasticity of steel
α = coefficient of thermal expansion

Total minimum length of LWR = 2 ( n-1) S
Where S is the spacing of sleepers

### Theory of Long Welded Rails

It is accepted that metals expand and contract with an increase or decrease in temperature, i.e., bear thermal growth. Thus, a rail expands and contracts to rely upon the variations in temperature. The expansion of a rail could be an operation of the constant of the linear expansion of the rail material, the length of the rail, and also the variations within the rail temperature. Normally, an unfastened rail could go through changes in its duration similar to the versions in rail temperature, however as rails are mounted to sleepers, which in flip are embedded inside the ballast, their expansion and contraction because of temperature changes are restricted. The restraint placed on the thermal growth of rail provides rise to barred up internal stresses within the rail metal. The ensuing force, referred to as the thermal force, is given by the subsequent equation:

P = EAaT (eq1)
where,
P = force in tonnes,
E = modulus of elasticity of rail steel = 2.15 x 106 kg/cm2 or 2150 t/cm2,
A = cross-sectional area of steel in cm2 [ depends upon the individual rail section (for a 52-kg rail it is 66.15 cm2)]
a = coefficient of linear expansion = 0.00001152 per °C
T = temperature variation in °C

Substituting the values of E, A, a, and T, the force for each 1° increase of temperature for a 52-kg rail are often derived as follows:

P = (2.15 x 106) x 66.15 x 0.00 001152 x 1 x 10-3 = 1.638 t per °C
The values of E and a are mounted for every style of rail steel. the worth of the cross-sectional space depends upon the sectional weight of the rail. subbing the value of sectional weight in kg/m (eq1),

the force P also can be by the formula.
P = 31.5AT
where,
P =force in kilograms,
A = sectional weight in kg/m,
T = temperature variation in °C. For a 52-kg rail
P = 31.5 x 52 kg per unit °C , [1638 in kg] ,[ 1.638 t per °C]

### Longitudinal Thermal Expansion of Long Welded Rails (LWR) and Breathing Length

In the case of Long Welded Rails (LWR), the thermal enlargement of the rail takes place at the rail ends as a result of temperature variations and also the inability of the resisting force offered by the rail associated with the ballast to beat the same. a protracted welded rail continues to expand at its winds up thereto particular length at that an adequate resisting force is developed towards the center. A stage is finally reached at a selected length of the rail from its ends once the resistance offered by the track structure becomes adequate the thermal forces created as a result of temperature variations. there’s no alternation within the rail length on the far side this point. The accumulative price of the enlargement or contraction of those finish parts of the rail (breathing lengths) is given by the formula.
Long Welded Rails (LWR) = 2 ( n-1) S

##### What are the common lengths of rails?

The commonest length for BG rails is 13m(42’8”) though double-length rails (26m, 85’4”) are seen. Welded rail sections are of 2 types: Short Welded Rail or SWR that consists of simply two or 3 rails welded along and Long Welded Rail or LWR which covers something longer. Long Welded Rails (LWR) is often any length larger than doubly the respiration length, which allowed at the tip of the welded rail section which is unengaged to expand or contract because the temperature changes. (Beyond the breathing length, the rails don’t move as a result of the resistance of the fasteners and also the sleepers and ballast.) The respiration length varies with the temperature range, the sleepers, and also the style of rails, however is often 10m or less with concrete or steel sleepers.