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An Introduction to Rail Thermal Force Calculations Article 1 TECHNICAL ARTICLE AS PUBLISHED IN The Journal January 2017 Volume 135 Part 1 If you would like to reproduce this article, please contact: Alison Stansfield MARKETING DIRECTOR Permanent Way Institution [email protected] PLEASE NOTE THE OPINIONS EXPRESSED IN THIS JOURNAL ARE NOT NECESSARILY THOSE OF THE EDITOR OR OF THE INSTITUTION AS A BODY. TECHNICAL An introduction to AUTHORS: Constantin Ciobanu rail thermal force CEng, FPWI Principal Track Engineer calculations WSP | Parsons Brinckerhoff Levente Nogy CEng, MICE, FPWI Senior Design Engineer Network Rail Article 1 This article is the first in a series of articles THE PHYSICS OF RAIL THERMAL For a positive thermal variation of ΔT= 27°C intended to present complementary EXPANSION the compression force would be 500 kN. information to what is currently available This is the equivalent of an average freight car weighing 50 tonnes, pressing axially on a in the formal continuous welded rail (CWR) When exposed to temperature variations, the single CEN60 rail ( ). training courses and Railway Group or steel rail tends to vary in length and, if nothing figure 3 Network Rail Company Standards. This is constraining this length variation, the rail’s The rail alone is unable to withstand this high first article presents the general principles mid-point will stay fixed and each abutting compression force without deflecting at some and theoretical considerations on the rails half-rail length will expand equally by ΔL/2 affected by thermal variation. point along its length and thus the entire track (figure ).1 superstructure must be designed to provide the required stability and to avoid buckling in hot INTRODUCTION The total length variation can be computed as: weather and rail breaking in cold weather. ΔL = α•L•ΔT This series of articles will discuss the general principles and theoretical considerations Where: TRACK PARAMETERS on railway track which is subjected to INFLUENCING RAIL THERMAL thermal effects. These can be used by Track - ΔL is rail extension BEHAVIOUR Engineers for a better understanding of the - α is the expansion coefficient of the rail steel physics behind the rails’ behaviour when = 1.15•10-5 per °C for normal grade rail The behaviour of the track due to temperature subjected to temperature variations and can (NR/L2/TRK/3011). variations is influenced by numerous and also help to understand the specifications - L is the rail length complex parameters (UIC Code 720). This and requirements mandated in the current - ΔT is the rail temperature variation article focuses on a simplified approach standards covering the management of jointed and considers only the main parameters in respectively CWR track. Multiple thermal force If the temperature is increasing, the rail will evaluating the rail thermal behaviour: diagrams will be presented for both jointed expand. If the temperature is decreasing, the track and CWR applications. rail will be subjected to a negative expansion – • Installation parameters a contraction. The standard nominal rail length • Rail type is defined for +15°C and length measured at • Rail temperature other temperatures is corrected to take into • Track longitudinal resistance account the expansion or contraction of the rail • Joint minimum and maximum gap - for (BS EN 13674-1:2011). jointed track • Joint resistance - for jointed track On the other hand, if the expansion is not • Expansion joint gap or adjustment switch permitted and both ends of the rail are fixed, gap - the range of thermal “breathing” the thermal variation ΔT will generate a of the devices used on the transitions constant compression internal force, N (figure between sections of CWR track or 2). between CWR track and jointed track. This internal force is defined by: The entire process presented here presumes N = (α•E •ΔT)•A = σ•A an ideal and homogenous track structure. Where: - E is the steel’s elasticity modulus Table 1: Cross sectional area (A) for (2.1•108 kN/m²) - A is the area of the rail section different rail types used in the UK - σ is the normal stress generated by the temperature variation, ΔT. 24 TECHNICAL INSTALLATION PARAMETERS TRACK LONGITUDINAL RESISTANCE Track installation defines the starting point of the track thermal behaviour. From this When the rail tends to move longitudinally, perspective, the main track installation either due to temperature variations or due parameters are the following: to other factors, the track will oppose this Figure 1: Free rail thermal movement through a force called track • joint installation gap and installation expansion longitudinal resistance (or track creep temperature for jointed track resistance). • stress free temperature (SFT) for CWR track This track longitudinal resistance has three levels of action (figure ).4 RAIL TYPE 1. LONGITUDINAL RESISTANCE The rail type influences the thermal behaviour P BETWEEN THE RAIL AND THE through the cross sectional area (A) which 1 defines the amount of thermal force developed FASTENING in the rail due to the temperature variation. At this level, the longitudinal resistance is (See table 1) generated by the friction between the rail and the fastening components. The European RAIL TEMPERATURE Norm BS EN 13841 mandates that the fastening longitudinal resistance on ballasted The rail temperature has a direct influence track should be at least 7 kN per fastening. Figure 2: Restrained rail thermal on the rail thermal stress and force. The rail For a normal sleeper interval of 600 mm, temperature is in relation to the air temperature expansion this is equivalent to a distributed longitudinal but is also influenced by other factors. The resistance of around 12 kN/m of rail. The location of the track has a significant impact fastenings used for high speed railway track - if the rail is exposed to direct sunlight it (V>250 km/h) are required by the same norm will absorb more caloric energy and its to provide a minimum longitudinal resistance of temperature will be higher compared to a rail 9 kN (around 15 kN/m of rail). (See image 2) located in shadow, in a cutting or a tunnel, or embedded in a material with thermal insulation At installation and in ideal conditions, all properties. Exposure to wind, humidity or fastenings can provide a certain toe load and condensation can also cause a difference consequently a longitudinal resistance. But between the rail temperature and the often, for old types of fastenings (images conventional air temperature. 3, 4) this toe load cannot be maintained at a constant reliable level throughout the service In the summer, the rail temperature can be up life of the fastening. Consequently, for such to 15-20°C higher and in the winter can go 5°C fastenings the longitudinal resistance is usually below the conventional air temperature. Based ignored in the evaluation of the track thermal on this and on the annual weather temperature response. variations, various railway administrations have adopted their own specific temperature ranges. Special fastening systems are sometimes installed on very long bridges with direct fixing, On the Network Rail railway infrastructure or in other specific cases, to provide a reduced this range is considered to be [-14°C, 53°C] longitudinal resistance and separate the Figure 3: Rail thermal force (NR/L2/TRK/3011).This gives a possible thermal expansion forces of the track from the maximum annual rail temperature variation of ones of the supporting structure. An example is 67°C. In continental Europe, for the countries the Pandrol Zero Longitudinal Restraint (ZLR – of temperate-continental climate, the rail image 5) that is designed to provide practically temperature range is [-30°C, 60°C]. This gives no longitudinal fastening resistance. a potential maximum annual rail temperature variation of 90°C. 2. LONGITUDINAL RESISTANCE The rail coating and colour also influences its P2 BETWEEN THE FASTENING caloric absorption properties. A rail painted AND THE SLEEPER in white reflective coating, exposed to direct sunlight can be up to 6-10°C cooler than an The highest longitudinal resistance is uncoated rail (Ritter, Al-Nazeer - 2014). encountered between the fastening and the Painting the rails white to reduce the rail sleeper. For Pandrol fastenings, the clip’s temperature is a method used efficiently in the shoulder is embedded in the sleeper’s concrete Figure 4: The three levels of action UK and around the world (image 1). so no relative movement will happen at this of the track longitudinal resistance level. The alternative screwed fastening is similarly good and generally all modern fastenings are designed to have a very high longitudinal resistance at this level. Since the resistance at this level is significantly higher than the other two, in the calculations that model the railway track thermal behaviour, no movement is considered to happen between 25 TECHNICAL the fastening and the sleeper in which it is practically embedded. 3. LONGITUDINAL RESISTANCE P3 BETWEEN SLEEPER AND BALLAST This resistance is dependant on a complex set of factors e.g. the type, shape, dimensions and weight of the sleeper, the ballast volume, compaction and content of fines. The friction forces at this level are not homogeneous along the track – there can be spots with high or low resistance, even for apparent similar track conditions. Consequently, the longitudinal resistance at this level is usually the lowest and the most difficult to control. This resistance is typically considered in the range of 6 (tamped) to 10 (consolidated) kN/sleeper (Van – 1996), the equivalent of 5 to 8 kN/m of rail. The track longitudinal resistance is the minimum of these three resistances (P1, P2, P3) Image 1: White coated rails on Italian main lines (Milano Afori railway and the track movement due to temperature station) variation will take place at that lowest resistance level. For modern superstructure and ballasted track, usually, the lowest longitudinal resistance is between the sleeper and the ballast.
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