LONG WELDED RAILS By G S Yadav IRSE

LONG WELDED RAILS By G S Yadav, IRSE 1994 PB 2, IRICEN 7420041112 gsyadav@iricen. gov. in

BASIC CONCEPTS: RAIL LENGTH As regards to rail length ( length of rail between two joints) track can be classified as below : 1. Free rail : rails of 13 m or 26 m length ( used on bridges on which LWR is not permitted. Also used on sharp curves on which LWR/SWR is not permitted) 2. SWR : rails ( welded or otherwise) of 39 m length (Used at locations where LWR is not permitted such as grades steeper than 1 in 100) 3. LWR : rails of 250 m length or more Note : CWR is basically LWR that is carried through station yards.

• Long Welded Rail (LWR) is a welded rail, the central part of which does not undergo any longitudinal movement due to temperature variations. A length of greater than 250 metre on Broad Gauge (BG) and 500 metre on Metre Gauge (MG) will normally function as LWR. The maximum length of LWR under Indian conditions shall normally be restricted to one block section

BASIC CONCEPTS: RAIL SLEEPER FASTENINGS On functional basis the rail sleeper fastenings can be classified as below : 1. Rail free fastenings ( RFF), and 2. Creep resistant fastenings (CRF) or resilient rail fastenings or elastic rail fastenings RFF are mainly used on girder bridges to isolate track from bridge deck in such a manner that interplay of forces in Track and Bridge deck is avoided CRF are used with PSC sleepers at almost all locations. On IR, Pandrol clips , also known as Elastic Rail Clips along with Grooved Rubber Pads and Liners are used

THEORY OF LWR (1) Concept of Rail Temperature : tmin , tmax, tmean ; Different Temp Zones (2) Concepts of thermal behaviour of metals ( linear thermal expansion) : Derivation of formula for thermal force in a restrained rail (3) Concepts of Track Resistance : Longitudinal, Lateral and torsional resistance : Factors affecting longitudinal resistance , Graph of longitudinal resistance. Longitudinal resistance offered by fastenings as well as by ballast. (4) Force diagram in LWR : BL, fixed portion and local stress transition locations, effect of bridges etc. Derivation of formula for BL, Breathing lengths for different temperature zones (5) Movement at free end of LWR : derivation of Formula (6) Concept of hysteresis (7) Lateral track stability ( Buckling Behaviour) (8) Rail Structure Interaction ( LWR on Bridges)

Rail Temperature • Rail temperature is the temperature of the Rail at site as recorded by an approved type of Rail thermometer. • Ambient temperature is the temperature of air in shade at the same place. • Mean Rail temperature (tm) for a section is the average of the maximum (tmax) and minimum rail temperature (tmin) recorded for the section • Installation Temperature (ti) is the average rail temperature during the process of fastening the rails to the sleepers at the time of installation of the LWR • Destressing Temperature(td) is the average rail temperature during the fastening of the rails to the sleepers after de-stressing LWR w/out use of rail tensors. • Stress Free Temperature (t 0) is the temperature of destressing when rail tensor is used. At this temperature the LWR will be truly stress free.

Rail Temperature • Indian Railways has been divided in 4 temperature zones as under : ZONE I II III Range Of Rail Temperature 40 to 500 C 51 to 600 C 61 to 700 C IV 71 to 760 C

Rail Temperature MAP OF INDIA SHOWING RAIL TEMPERATURE ZONES ZONE Range Of Rail Temperature I 40 to 500 C II 51 to 600 C III 61 to 700 C IV 71 to 760 C The range of rail temperature obtaining at a station and the annual mean rail temperature have been indicated outside and inside the brackets respectively

Exercise on Rail Temperature • At Bikaner station the range of rail Temperature is 750 C and mean rail temperature is 310 C. Calculate minimum and maximum rail temperature at this station

Ballast resistance • Longitudinal ballast resistance R gets mobilised when there is relative displacement of sleepers with respect to Ballast in the longitudinal direction • Lateral ballast resistance comes into play when track has tendency to get displaced in the lateral direction due to build up of compressive forces. • Maintenance operations on track have significant adverse effect on ballast resistance • Condition of ballast ( clean or caked up), consolidation state of ballast, condition of sleepers ( new or worn out at bottom) etc have significant impact on ballast resistance

Ballast resistance R u Longitudinal Ballast Resistance in Loaded Condition 25. 5 kg/Rail/cm ( 50 KN/m) Longitudinal Ballast Resistance in Unloaded condition 12. 74 kg/Rail/cm ( 25 KN/m)

Concepts of thermal behaviour of metals ( linear thermal expansion) + ΔT ΔL 2 L ΔL 2 FREE THERMAL EXPANSION 1. When a free Rail ( rail fastened with RFF) of length L is subjected to rise in temperature of ΔT, it expands freely by ΔL. 2. As thermal movement is not restrained , there is no build up of reaction forces in the Rail 3. Reaction forces will build up if expansion of Rail is restrained 4. This type of situation exists with Rail free Fastenings such as on Girder Bridges

Concepts of thermal behaviour of metals ( linear thermal expansion) RESTRAINED THERMAL EXPANSION PN + ΔT P N L Thermal Force Diagram PN Compression Free thermal Expansion ΔL = Lα ΔT ( Linear thermal expansion of metals) As the expansion is now restrained, this will result in Thermal Strain = (Lα ΔT)/L = α ΔT Resultant Thermal Stress = E x Thermal Strain = E α ΔT Hooke’s Law Resultant Thermal Force P = AE α ΔT

Tutorial on Thermal Force Calculation • Calculate thermal force in 52 kg and 60 kg rail for 30 o. C rise in temperature. A for 52 kg = 66. 15 cm 2 A for 60 kg = 76. 86 cm 2 E = 2. 15 x 106 kg/cm 2 α = 1. 152 x 10 -5

Concepts of thermal behaviour of metals ( linear thermal expansion) 1. In track with elastic fastenings thermal movement is restrained due to: (1) friction between Rail and fastenings, and (2) longitudinal Ballast Resistance. 2. The elastic fastenings are designed in such a way that the resistance offered at Rail seat level is more than the longitudinal Ballast Resistance 3. In such a situation the induced thermal forces will try to move the track frame in longitudinal direction. This movement is resisted by longitudinal ballast resistance 4. The central portion of LWR, also called the fixed portion or non breathing length, behaves like a fully restrained rail with maximum thermal force as P =AEα ΔT 5. The condition of fixity at both ends of central portion of LWR is achieved gradually through gradual building up of longitudinal ballast resistance over a length called the Breathing Length. Tendency Of Rail Movement To avoid creep of Rails P 1+P 2 > P 3 P 2

Force Diagram in LWR: Gradual buiding up of resistence Longitudinal Resistance per sleeper ΔT Free rail end 1 p Rail tendency to expand 2 p 3 p 5 p 4 p Breathing Length Lb 6 p Thermal Force Diagram p R Compression P 7 p

Force Diagram in LWR Formula for Breathing Length : Maximum force in central portion of LWR Longitudinal ballast resistance = R kg/Rail/m The force in central portion builds up over the BL of length Lb Therefore, L x R = AEαΔT or , Lb = AEαΔT /R b

Breathing Lengths in Different Temperature Zones

Factors Affecting Force Diagram : Force/Stress Transitions Zones in Central Portion of LWR (A) Stress Transitions Zones Caused By Rail Temperature Changes : These can be encountered in areas of track where there is consistent rail temperature difference between adjacent LWR sections. Some of such locations are : 1. Tunnel portals 2. Transition from deep cutting to embankment 3. Transition from white painted rail to unpainted rail ( temperature difference of about 60 C 4. Transition from exposed to embedded rail ( like long level crossings) 5. Passage over a river ( on a bridge)

Factors Affecting Force Diagram : Force/Stress Transitions Zones in Central Portion of LWR (B) Stress Transitions zones generated by track structure changes : locations exhibiting track structure changes are : 1. Track passing over Bridge 2. Transition from ballasted to slab track or any other higher fixity track structure ( different type of sleepers with different type of fittings) 3. Change of rail section 4. Stress transitions over switches and crossings Note : Such stress transition zones in central portion of LWR cause longitudinal movement of sleepers to build up difference in forces in the adjacent portions. Thus packing of sleepers gets disturbed at such locations like in Breathing length.

Force Diagram in case of Fractures Force Diagram After Fracture

Thermal Movement at End of LWR ( at SEJ) • Movement at the end of LWR : • m = Lb α ΔT/2 ( half of free movement in BL) • = (AE α ΔT/R) α ΔT/2 • = AE (α ΔT)2 / 2 R • or, m = k (ΔT)2 Lb α ΔT/2

Tutorial on rail movement at free end ( SEJ) Find maximum movement at SEJ for following data : Sleepers PRC ( BG) Rail 52 kg Sleeper Density 1540 sleepers per km Zone IV with temperature Range of 760 C of mean temperature of 380 C R = 13. 28 kg/rail/cm E = 2. 15 x 106 kg/cm 2 A = 66. 15 cm 2 α = 1. 152 x 10 -5 td = tm + 100 C

HYSTERESIS

HYSTERESIS Discussion on Appendix V of LWR manual Typical Annual Hysteresis Loop for Zone IV with Temp range 760 C and mean temp 380 C

Tutorial On Hysteresis • Find the gap at SEJ at rail temperature of 550 C with the following data : • Rail Section 60 kg/m ( A = 76. 86 cm 2) • Type of sleepers PRC ( R = 13. 74 kg/cm/Rail) • Sleeper Density 1660 per km • Temperature Zone IV ( Range 760 C and Mean 380 C) • De-stressing Temperature 430 C • Gap at SEJ at Td 40 mm

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