Interface - The Journal of Wheel/Rail Interaction

RAIL STRESSES

Understanding Stresses in Rails (Part 1 of 2)
By Jude Igwemezie, Ph.D., P.Eng • January, 2007

Rail represents a significant part of any railway’s investment in annual track maintenance. At the end of its useful life, the scrap value of rail can be as little as 15% to 20% of its original cost. Proper management of this precious asset will have a positive impact on the user’s bottom line, operating ratio and net asset value. Understanding the stress environment will help determine the ultimate life expectancy of the rail.

To understand the stresses in rails, it is necessary to establish the loading environment of the rail. We often discuss train wheel loadings, but very few of us have actually measured wheel loading from a train. Figure 1 shows the vertical (two top graphs) and lateral (two bottom graphs) wheel loads measured on both rails under a coal train traveling at 16 mph on a 1% grade and 10-degree curve. (The graphs on the left column belong to the high rail; those on the right column belong to the low rail.) The track speed at the location was 25 mph. The train had two puller locomotives and two pusher locomotives. As expected, there is more vertical load on the low rail than on the high rail. Lateral loads were generally less than 15 kips on both rails, except for the occasional bad actor truck that generated up to 25-kip lateral loadings on the low rail. These loads are then distributed to the track components with reactions generated at the tie locations along the rail. The track also deforms under these loads.

Load Distribution in Track
There are four types of load distribution in track: vertical, lateral, longitudinal and torsional. These distributions can be treated individually and their effects summed. In this article, we will deal only with the vertical and lateral load distribution.

Load distribution in track has been a subject of study since the creation of the railway system. Though it may appear otherwise, a single wheel load is not carried by a single tie, nor is the wheel load between ties carried by the two adjacent ties. The implications of this statement are far reaching in that they impact the design and assessment of track components. Understanding load distribution allows for better assessment of the response of track components to wheel loading.

Figure 2 shows the vertical loading from one wheel and one truck on a typical track system. As can be seen, the load in each case is distributed over several ties. The adjacent wheel in the two-axle system clearly increases rail deflection — by 16%, in this case. In fact, under varied track support conditions, the increased deflection can range from about 10% in frozen track to 30% in mush track. With regard to the behavior of the rail, Figure 2 shows that the rail is deformed with an upward concavity. It also shows that the rail is in reverse bending with a downward concavity about three ties away from the wheel. These reversing deformations play into the total stress and fatigue cycles that the rail is subjected to. Overall, vertical load distribution and deformation of track is influenced by the tie spacing, ballast (track support stiffness), rail size and axle spacing. Lateral loading is also distributed over several ties, but the type of rail fastening and torsional rigidity of the rail play a significant role in the distribution. (Note that there are no lateral loads applied to the track in generating the displacements shown in Figure 2.)

Lateral load distribution, such as is shown in Figure 3, is affected by the lateral stiffness of the track and the amount of shoulder ballast that is available to resist the lateral load. The number of ties that participate in the distribution of the lateral loading is similar to the number of ties that participate in the distribution of the vertical load. Very often, lateral loading to the rail causes torsional distortion of the rail (shown in Figure 4). Because the rail is weaker in torsion than in vertical or lateral bending, torsional distortion occurs only one or two ties away from the axle load point.

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