[BS en 13230-6] -- Railway Applications. Track. Concrete Sleepers and Bearers. Part 6. Design

Draft for Public Comment

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Draft BS EN 13230-6 Railway applications - Track - Concrete sleepers and bearers Part 6: Design

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EUROPEAN STANDARD NORME EUROPÉENNE

DRAFT prEN 13230-6

EUROPÄISCHE NORM February 2014 ICS 91.100.30; 93.100

English Version

Railway applications - Track - Concrete sleepers and bearers Part 6: Design Applications ferroviaires - Voie - Traverses et supports en béton - Partie 6 : Conception

Bahnanwendungen - Oberbau - Gleis- und Weichenschwellen aus Beton - Teil 6: Entwurf

This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee CEN/TC 256. If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of which they are aware and to provide supporting documentation. Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without notice and shall not be referred to as a European Standard.

EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels

© 2014 CEN

All rights of exploitation in any form and by any means reserved worldwide for CEN national Members.

Ref. No. prEN 13230-6:2014 E

prEN 13230-6:2014 (E)

Contents

Page

Foreword.............................................................................................................................................................. 4 Introduction ......................................................................................................................................................... 5 1

Scope ...................................................................................................................................................... 6

2

Normative references ............................................................................................................................ 6

3

Terms and definitions ........................................................................................................................... 7

4 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2 4.2.3 4.3 4.4

General requirements ............................................................................................................................ 9 General process for determination of bending moments ................................................................. 9 General.................................................................................................................................................... 9 Empirical method ................................................................................................................................... 9 Theoretical method ..............................................................................................................................10 Combined method ...............................................................................................................................11 Cracks in concrete sleepers or bearers ............................................................................................11 Cracks under rail seat .........................................................................................................................11 Cracks at centre part (prestressed monoblock sleepers) ...............................................................12 Cracks for tests for negative bending under rail seat or positive bending at centre part ...........12 Section design of sleeper ...................................................................................................................12 Durability and expected life time .......................................................................................................12

5 5.1 5.1.1 5.1.2 5.1.3 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.3.7 5.3.8 5.4 5.4.1 5.4.2 5.4.3

Design parameters ..............................................................................................................................12 Maintenance .........................................................................................................................................12 Track and rolling stock quality ...........................................................................................................12 Distribution of longitudinal load ........................................................................................................13 Distribution of ballast reaction along the length of the sleeper .....................................................13 Track laying conditions.......................................................................................................................13 Mass of sleeper ....................................................................................................................................13 Length of sleeper .................................................................................................................................13 Depth of sleeper ...................................................................................................................................13 Track installation methods .................................................................................................................13 Track components design ..................................................................................................................14 Rail profile and sleeper spacing ........................................................................................................14 Fastening system ................................................................................................................................14 Attenuation of impact loads by fastening system ...........................................................................14 Vertical stiffness of fastening system ...............................................................................................14 Electrical insulation .............................................................................................................................14 Vertical load test for cast-in fastening components ........................................................................14 Lateral resistance of sleeper in ballast for continuous welded rails .............................................15 Longitudinal resistance of sleeper in ballast for continuous welded rails ...................................15 Traffic characteristics and track alignment design .........................................................................15 Axle load ...............................................................................................................................................15 Maximum speed and category of traffic ............................................................................................15 Curving load .........................................................................................................................................15

6 6.1 6.1.1 6.1.2 6.1.3 6.1.4

Design calculation ...............................................................................................................................16 Experience from railway use or manufacturing ...............................................................................16 Railway experience for exceptional or accidental impact loads ....................................................16 Tensile flexural strength of concrete .................................................................................................16 Losses of prestress .............................................................................................................................16 Experience for track work ...................................................................................................................16

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6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.2.7

Design calculation ............................................................................................................................... 16 General ................................................................................................................................................. 16 Calculation of normal dynamic rail seat load Pk .............................................................................. 17 Calculated characteristic bending moments for rail seat of sleepers ........................................... 17 Calculated characteristic bending moments for centre part of sleepers ...................................... 17 Calculated characteristic bending moments for bearers ................................................................ 18 Checking of stresses in concrete ...................................................................................................... 18 Determination of test bending moments for first crack formation ................................................ 18

Annex A (informative) Design methods and factors for sleepers ................................................................ 20 A.1 General ................................................................................................................................................. 20 A.1.1 Introduction .......................................................................................................................................... 20 A.1.2 Determination of characteristic bending moments ......................................................................... 20 A.1.3 Determination of test bending moments .......................................................................................... 21 A.2 Rail seat load ....................................................................................................................................... 22 A.2.1 Normal service increment for the dynamic wheel load ................................................................... 22 A.2.2 Distribution of longitudinal load ........................................................................................................ 23 A.2.3 Dynamic rail seat load......................................................................................................................... 25 A.3 Characteristic bending moments ...................................................................................................... 25 A.3.1 General ................................................................................................................................................. 25 A.3.2 Rail seat section .................................................................................................................................. 25 A.3.3 Sleeper centre section ........................................................................................................................ 27 A.4 Test bending moments ....................................................................................................................... 31 A.4.1 First crack test bending moment ....................................................................................................... 31 A.4.2 Test bending moments for exceptional and accidental loads ........................................................ 32 A.4.3 Calculation of test moments for the fatigue test .............................................................................. 32 A.5 Checking of stresses for Serviceability Limit State (for prestressed sleepers only) ................... 33 A.6 Design examples ................................................................................................................................. 33 A.6.1 Standard gauge sleeper ...................................................................................................................... 33 A.6.2 Broad gauge sleeper ........................................................................................................................... 40 Annex B (informative) Design methods and factors for bearers ................................................................. 43 Annex ZA (informative) Relationship between this European Standard and the Essential Requirements of Directive 2008/57/EC .............................................................................................. 45 Bibliography ...................................................................................................................................................... 48

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prEN 13230-6:2014 (E)

Foreword This document (prEN 13230-6:2014) has been prepared by Technical Committee CEN/TC 256 “Railway applications”, the secretariat of which is held by DIN. This document is currently submitted to the CEN Enquiry. This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association, and supports essential requirements of EU Directive(s). For relationship with EU Directive(s), see informative Annex ZA, which is an integral part of this document. This European Standard is one of the series EN 13230 "Railway applications – Track – Concrete sleepers and bearers", which consist of the following parts: 

Part 1: General requirements;



Part 2: Prestressed monoblock sleepers;



Part 3: Twin-block reinforced sleepers;



Part 4: Prestressed bearers for switches and crossings;



Part 5: Special elements;



Part 6: Design.

This European Standard is used as the technical basis for transaction between corresponding parties (purchaser – supplier). Annexes A and B are informative; they can be used as normative requirements by completion of a contract, if agreed by the contractors.

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Introduction This part of the standard covers the design of concrete sleepers and bearers and is used in conjunction with the following parts: 

Part 1: General requirements;



Part 2: Prestressed monoblock sleepers;



Part 3: Twin-block reinforced sleepers;



Part 4: Prestressed bearers for switches and crossings;



Part 5: Special elements.

Concrete sleepers and bearers are safety critical components for railway applications. They are not covered by any other standards. As safety critical components, an agreement is needed between purchaser and supplier to operate a factory Quality System.

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prEN 13230-6:2014 (E)

1

Scope

This part of EN 13230 provides particular design guidance in the following areas: 

derivation of characteristic loads and test loads;



calculation of characteristic and test bending moments.

The aim of this part of the standard is to give guidance for the preparation of all data to be given by the purchaser to the supplier in accordance with parts 1 to 5 of EN 13230. It applies to all gauges (standard, broad and narrow) as well as to all lengths of sleepers. This standard gives special criteria for the design of concrete sleepers and bearers as track components. The design methods in the Eurocode do not apply to these concrete elements. All track parameters to be taken into account for the design of sleepers and bearers are detailed in this standard. Information is given on these parameters so that they can be used as inputs for the design calculation process. It is the responsibility of the purchaser to calculate or determine all track parameters used in this standard. This standard gives guidance for the design calculation process. It explains how experience and calculation can be combined to use design parameters. This standard gives examples of numerical data that can be used when applying Clauses 4 to 6 according to the state of the art.

2

Normative references

The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 13146-3, Railway applications – Track – Test methods for fastening systems – Part 3: Determination of attenuation of impact loads EN 13146-5, Railway applications – Track – Test methods for fastening systems – Part 5: Determination of electrical resistance prEN 13230-1:2014, Railway applications – Track – Concrete sleepers and bearers – Part 1: General requirements prEN 13230-2:2014, Railway applications – Track – Concrete sleepers and bearers – Part 2: Prestressed monoblock sleepers prEN 13230-3:2014, Railway applications – Track – Concrete sleepers and bearers – Part 3: Twin-block reinforced sleepers prEN 13230-4:2014, Railway applications – Track – Concrete sleepers and bearers – Part 4: Prestressed bearers for switches and crossings prEN 13230-5:2014, Railway applications – Track – Concrete sleepers and bearers – Part 5: Special elements EN 13481-2, Railway applications – Track – Performance requirements for fastening systems – Part 2: Fastening systems for concrete sleepers EN 13848 (all parts), Railway applications – Track – Track geometry quality

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prEN 13230-6:2014 (E)

3

Terms and definitions

For the purposes of this document, the terms and definitions given in prEN 13230-1:2014 and the following apply. 3.1 nominal axle load

Anom nominal axle load from rolling stock 3.2 nominal wheel load

Qnom static vertical wheel load resulting from nominal axle load 3.3 factor kp factor to apply to nominal wheel load to allow for rail pad attenuation 3.4 factor kv factor to apply to nominal wheel load to allow for the effect of speed 3.5 factor kd factor used for longitudinal load distribution between sleepers 3.6 factor kr factor used for variations of the longitudinal load distribution between sleepers due to support faults 3.7 factor ki,r factor used for calculation of bending moments at rail seat due to irregularities in the support along the length of the sleeper 3.8 factor ki,c factor used for calculation of bending moments at centre section due to irregularities in the support along the length of the sleeper 3.9 internal lever arm

λ

internal lever arm of the forces and ballast reaction acting on the sleeper at the rail seat section 3.10 exceptional load load that occurs only few times in the life of sleeper 3.11 accidental load load that occurs only once in the life of sleeper

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3.12 factor kt factor used for calculation of testing bending moment Mt from characteristic bending moment Mk 3.13 dynamic rail seat load

Pk characteristic load on a rail seat of the sleeper for normal service dynamic loading 3.14 characteristic bending moments

Mk bending moments from dynamic rail seat load Pk 3.15 characteristic positive bending moment for rail seat section

Mk,r,pos positive bending moment at rail seat from dynamic rail seat load Pk 3.16 characteristic negative bending moment for rail seat section

Mk,r,neg negative bending moments at rail seat from dynamic rail seat load Pk 3.17 characteristic negative bending moment for centre section

Mk,c,neg negative bending moments at centre section from dynamic rail seat load Pk 3.18 characteristic positive bending moment for centre section

Mk,c,pos positive bending moment at centre section from dynamic rail seat load Pk 3.19 test bending moments

Mt test bending moments for first crack formation derived from characteristic bending moments 3.20 test positive bending moment for rail seat section

Mt,r,pos positive test bending moment for first crack formation at rail seat derived from characteristic bending moments 3.21 test negative bending moment for rail seat section

Mt,r,neg negative test bending moments for first crack formation at rail seat derived from characteristic bending moments 3.22 test negative bending moment for centre section

Mt,c,neg negative test bending moments for first crack formation at centre section derived from characteristic bending moments

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prEN 13230-6:2014 (E)

3.23 test positive bending moment for centre section

Mt,c,pos positive test bending moment for first crack formation at centre section derived from characteristic bending moments 3.24 factor k1 factor used for calculation of test bending moments due to exceptional and random impact load. This factor is applied to characteristic bending moments. This factor is k1d for dynamic test and k1s for static test 3.25 factor k2 factor used for calculation of test bending moments due to accidental impact load. This factor is applied to characteristic bending moments. This factor is k2d for dynamic test and k2s for static test 3.26 factor k3 factor used for calculation of fatigue test bending moments. This factor is applied to characteristic bending moments. It is used for the definition of Fr B at the end of fatigue test

4

General requirements

4.1 4.1.1

General process for determination of bending moments General

The track is an assembly of transverse concrete sleepers or bearers secured to the rails by means of a fastening system and supported by ballast or other support. It is characterised by the gauge of the track, the rail profile, the inclination of the rails and the spacing of the concrete sleepers and bearers. The assembly including the rail, the fastening system and concrete sleepers or bearers on ballast or other support may be considered as a beam on an elastic support The determination of bending moments in sleepers and bearers laid on ballast tracks for the service stage may be obtained using the three following different approaches. 4.1.2

Empirical method

In the empirical method appropriate sleepers or bearers are tested in track under service conditions. Deficiencies of the test elements may be excluded by stepwise improvements. The results shall be confirmed by permanent observation during at least five years. The characteristic bending moments shall be determined by measurements in track. The size of the sample shall be sufficient to give statistically reliable results. The characteristic bending moment may also be determined with the help of a bending test according to series EN 13230 using sleepers that have been in service for five years at least. The test bending moment which produces the first crack formation shall be in accordance with prEN 13230-1:2014, 7.2. Figure 1 details steps for the determination of characteristic bending moments.

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prEN 13230-6:2014 (E)

Figure 1 — Typical empirical method for determination of bending moments and coefficients 4.1.3

Theoretical method

The theoretical method shall be based on design procedures considering the dynamic load, the elastic behaviour of all track components including all types of elastic pads, the variable ballast-subsoil elasticity and the different ballast consolidation phases. Figure 2 details steps for the determination of bending moments.

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Figure 2 — Typical theoretical method for determination of bending moments and coefficients 4.1.4

Combined method

The combined method includes empirical and theoretical elements leading to a shorter product development time.

4.2 4.2.1

Cracks in concrete sleepers or bearers Cracks under rail seat

Wheel loads generate positive and negative bending moments under the rail seat. The bending resistance at the end of the required service life time under the rail seat is determined from the characteristic bending moment. When subjected to the static testing bending moment, there shall be no first crack at the tensile face of the prestressed concrete sleeper or bearer, see prEN 13230-1:2014, 7.2.

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prEN 13230-6:2014 (E)

The second stage of the bending moment to be defined is the exceptional loading bending moment due to exceptional and random impact loads and is calculated by multiplying the positive characteristic bending moment Mk,r,pos by coefficient k1. Any crack produced by this bending moment shall close (crack width below 0,05 mm) upon removal of the bending moment. Exceptional bending moments occur only a few times in the lifetime of a concrete sleeper and bearer. The third stage of the bending moment is the ultimate bending moment due to accidental impacts, calculated by multiplying the positive characteristic bending moment Mk,r,pos by coefficient k2. 4.2.2

Cracks at centre part (prestressed monoblock sleepers)

Wheel loads generate positive and negative bending over the central length of the sleeper. The required flexural strength over the central part of the sleeper is determined from the bending moment induced by the dynamic rail seat load and depends on the distribution of the ballast reaction. When subjected to the negative static test bending moment, there shall be no first crack at the tensile face of the concrete sleeper or bearer as required in prEN 13230-1:2014, 7.2. If permitted by the purchaser, controlled cracking can be accepted. In that case, residual crack opening and fatigue shall be checked according to method agreed by purchaser. 4.2.3

Cracks for tests for negative bending under rail seat or positive bending at centre part

Additional bending tests with crack measurement can be required to check the general design or manufacture of the sleeper or for specific loads imposed during track installation.

4.3

Section design of sleeper

The section design shall follow prescriptions of prEN 13230-1:2014.

4.4

Durability and expected life time

Requirements for providing durability are defined in prEN 13230-1:2014.

5

Design parameters

5.1

Maintenance

5.1.1

Track and rolling stock quality

The maintenance policy for both track and rolling stock will influence the loads imposed on the track. Track geometry quality should be according to series EN 13848 and rolling stock maintenance policies will define the maximum tolerance for wheel flats and their out of roundness. These criteria together with maximum train speed shall be taken into account by the purchaser to determine: 

the dynamic rail seat load;



the impact factor for exceptional loads;



the characteristic and test load bending moments.

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5.1.2

Distribution of longitudinal load

The distribution of the wheel load between sleepers along the track depends on the vertical stiffness of the rail, sleeper spacing, rail pad stiffness and the stiffness of ballast or platform. Factor kd to determine for the longitudinal load distribution can be determined applying the “beam on elastic support "theory with a constant bedding modulus along the rail. In addition, factor kr. represents the variation of the sleeper reaction in the ballast due to longitudinal supports faults along the track. This factor should be evaluated by measurements in track. It is the responsibility of the purchaser to determine the coefficients kd and kr. See Annex A for recommendations for value of factors kr and kd. 5.1.3

Distribution of ballast reaction along the length of the sleeper

The length and the width of the sleeper can influence the average stiffness of the ballast and the longitudinal spreading of wheel load along length of sleeper. Moreover variation in ballast reaction can be caused by characteristic of sub grade under ballast, by variation of ballast stiffness due to tamping or freezing, or by ballast quality (size of ballast, stone characteristics and fouling of ballast layer). When uniform ballast reaction or bedding modulus are assumed, load distribution may be changed considerably in track due to the random formation of local load contact points within the ballast. The difference between the centre bending moments calculated with a simplified design model and the characteristic bending moments measured in track shall be taken into account by factors k at rail seat section or ki for bending

i,r

,c

moment increase at the centre. It is the responsibility of the purchaser to determine the coefficients ki,r and ki,c. See Annex A for recommendations concerning factors k

5.2 5.2.1

i,r

and k .

i,c

Track laying conditions Mass of sleeper

The mass of sleeper contributes to lateral resistance of track. Transportation to work site and track installation methods can determine the maximum mass. 5.2.2

Length of sleeper

The length of sleeper contributes to longitudinal and lateral distribution of ballast reaction. Transportation to work site and track installation methods can determine the maximum length. 5.2.3

Depth of sleeper

Depth of sleeper contributes to lateral resistance of track. Transportation to work site, track installation methods or ballast tamping methods can determine the depth. 5.2.4

Track installation methods

During track installation, different loadings may occur which are different from those that occur from the operation of commercial trains and care should be taken that there is no excessive central bending of the concrete sleeper.

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5.3

Track components design

5.3.1

Rail profile and sleeper spacing

An individual sleeper will only take a proportion of the wheel load as some will be shared with adjacent sleepers. The factor kd or load distribution between sleepers shall take into account the rail profile and the sleeper spacing, rail fastening assembly stiffness, foundation modulus (see 5.1.2). See Annex A for recommendations concerning the factor kd according to rail profile and sleeper spacing. 5.3.2

Fastening system

EN 13481-2 defines requirements for fastening system to be used for concrete sleepers 5.3.3

Attenuation of impact loads by fastening system

The type of rail pad shall be taken in account for choosing the impact attenuation factor kp. EN 13146-3 evaluates the impact attenuation of fastening systems by means of a test to measure the magnitude of impact bending strains in a concrete sleeper. Fastening systems, with their associated rail pads, can be classified according to the reduction of strain to a reference case as follows: 

low attenuation;



medium attenuation;



high attenuation.

These impact attenuation factors may be applied to design loads. However, it is recommended to reduce the attenuation value measured for the fastening system by 25 % in the normal case to allow for the service condition. In order to adopt the reductions that may be made in the design load by accounting for the use of resilient rail pads, the purchaser will need to ensure that maintenance standards ensure the continuous use of rail pads equivalent to or better than those assumed in the design. It is the responsibility of the purchaser to determine the coefficient kp. See Annex A for recommendations concerning the factor kp. 5.3.4

Vertical stiffness of fastening system

The vertical stiffness of fastening system contributes to track stiffness and shall be considered when choosing factors kd and kp. 5.3.5

Electrical insulation

EN 13146-5 defines method and arrangement for the determination of electrical resistance. 5.3.6

Vertical load test for cast-in fastening components

Annex A of EN 13481-2 defines requirements for load test for cast-in fastening components.

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5.3.7

Lateral resistance of sleeper in ballast for continuous welded rails

The lateral stability of track using continuous welded rails depends on dimensions of the sleeper (and in particular the mass) and the transverse ballast profiles. The design of the sleeper shall be in accordance with the purchaser’s rules for continuous welded rails. 5.3.8

Longitudinal resistance of sleeper in ballast for continuous welded rails

The dimensions of the sleeper (especially the mass) in relation with transverse ballast profiles influence the longitudinal resistance of sleeper and will require special consideration for transition zones at continuous welded rails ends, bridge ends or rail profile changes.

5.4

Traffic characteristics and track alignment design

5.4.1

Axle load

The static component of vertical wheel load can be determined directly from the static axle load (Anom) of trains (normally the sleeper design load will be expressed per wheel). At the design stage it should be borne in mind that sleepers are expected to last for 40 years or more. If future enhancements to axle load and speed are planned, this may be taken into account in the design. 5.4.2

Maximum speed and category of traffic

The maximum speed shall be taken into account for choosing the normal service dynamic factor kv. See Annex A for recommendations concerning the factor kv. 5.4.3

Curving load

The dynamic rail seat load shall take into account: 

the quasi-static increase of vertical wheel load on rails due to cant deficiency or excess;



the lateral force of wheel which can also induce an additional bending moment.

Both effects can be included in normal service dynamic factor kv. It is the responsibility of the purchaser to determine the coefficient kv. See Annex A for recommendations concerning the factor kv.

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6

Design calculation

6.1

Experience from railway use or manufacturing

6.1.1

Railway experience for exceptional or accidental impact loads

Exceptional impact loads (which can occur few time in a sleeper lifetime) from: 

wheel flats;



corrugated rail;



out of round wheels,

create bending moments higher than the characteristic bending moment. In order to take into account these exceptional impact loads, the characteristic bending moment shall be multiplied by a factor k1, taking into account rolling stock and track maintenance policy (see 4.2.1). Accidental impact loads occur only once in the life time of the sleeper and they generate very high bending moments. These accidental loads increase the characteristic bending moment by a factor k2 (see 4.2.1). The purchaser shall state the coefficient k1 and the coefficient k2 to be applied to the characteristic bending moment. See Annex A for recommendations concerning the factors k1and k2. 6.1.2

Tensile flexural strength of concrete

The tensile flexural strength of concrete shall be considered. See Annex A for recommendations concerning tensile flexural strength of concrete. 6.1.3

Losses of prestress

There is loss of prestress depending on time, service conditions and production method. Loss of prestress shall be taken into account for acceptance tests, routine tests and checking stresses in concrete. See Annex A for recommendations concerning loss of prestress. 6.1.4

Experience for track work

Track laying conditions and maintenance (tamping) can lead to various load distribution cases at the soffit of the sleeper.

6.2 6.2.1

Design calculation General

The analysis and design of the structural strength of the concrete sleeper shall be based upon the derivation of bending moments at least at the rail seat section and at the sleeper centre. The evaluation of calculated bending moments for the service stage is based on the elastic behaviour of the track.

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6.2.2 Calculation of normal dynamic rail seat load Pk The dynamic rail seat load, used to derive the basic characteristic bending moment, can therefore be calculated according to Formula (1):

Pk = 6.2.3

Anom (1 + k p × k v ) × k d × k r 2

(1)

Calculated characteristic bending moments for rail seat of sleepers

The bending moment at the rail seat is influenced by the ballast reaction, the width of the rail foot and the geometry of the sleeper. An example for calculation of characteristic bending moments is given in Annex A. The stages of the calculation and input data are described in the flow-chart bellow.

Figure 3 — Stages of the calculation and input data at rail seat section 6.2.4

Calculated characteristic bending moments for centre part of sleepers

Characteristic bending moments may be evaluated according to moment analysis of the reaction distribution. Two alternative methods are detailed in Annex A: 1) Reference method based on a complete elastic beam model; 2) A simplified method based on pre calculated curves. Stages of the calculation and input data for both methods are described in the flow-chart bellow.

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Figure 4 — Stages of the calculation and input data at centre section Example for calculation of characteristic bending moments is given in Annex A. 6.2.5

Calculated characteristic bending moments for bearers

Due to various length and position of rail seats, characteristic bending moments cannot be simply calculated. Positive and negative testing bending moments shall be defined by the purchaser (examples are given in Annex B). 6.2.6

Checking of stresses in concrete

The maximum bending tensile stress in concrete due to the characteristic bending moment shall be lower than the concrete tensile flexural fatigue strength fct,fl,fat. Maximum compressive stress shall be checked for fatigue life. See Annex A for recommendations concerning flexural strength of concrete. 6.2.7 6.2.7.1

Determination of test bending moments for first crack formation Prestressed sleepers

The flexural behaviour of a prestressed concrete section depends essentially on the prestressing force and the flexural concrete strength. Both parameters change during the life time of the structure.

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The initial prestressing force decreases due to elastic shortening of the sleeper, steel relaxation, creep and shrinkage of the concrete, towards a final value. The total loss of prestress should be calculated according to the rules of EC 2 or estimated at 25 %. The flexural tensile strength increases within the first weeks after production. During the following service phase a continued loss of flexural strength may appear due to repeated wheel loads. Both effects, together, lead to the flexural strength varying with time. The first crack moments for sleepers and bearers after a short time are considerably higher than the required characteristic moments Mk. The characteristic bending moment Mk should therefore be increased by the coefficient kt for the calculation of static test bending moment Mt, taking into account the age of the sleeper during testing. The required increased test bending moment including the time depending losses is:

M t = kt × M k

(2)

It is the responsibility of the purchaser to determine the coefficient kt. See Annex A for recommendations concerning the factor kt. An example of calculation of static test bending moments is given in Annex A. 6.2.7.2

Reinforced concrete sleepers

First crack formation is not a design criterion for reinforced concrete sleepers.

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Annex A (informative) Design methods and factors for sleepers

A.1 General A.1.1 Introduction The design principle of using simple beam models combined with factors obtained by track measurements has already been established in ORE D71 and further on developed in ORE D170 and UIC 713. Methods and factors presented in this Annex follow the same rules. The designation of values such as loads, bending moments and factors however has been adapted to the actual state of art and use of symbols in Eurocodes and European Standards.

A.1.2 Determination of characteristic bending moments The determination of the characteristic bending moments in the rail seat and sleeper centre follows the vertical flow of forces starting with the nominal axle load within the wheel and ending with the bending moments in the sleeper or bearer. In Figure A.1, all relevant factors have been presented including the corresponding formula.

Figure A.1 — Load distribution for the determination of bending moments

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Figure A.1 points the effect of the wheel load on the different track components. For the determination of the longitudinal load distribution within the rail, the model of the beam on elastic foundation may be applied. The same method may be used for the determination of the bending moments in sleepers and bearers. The determination of bending moments as shown is limited to static and dynamic service loads. Exceptional and accidental loads are not taken into consideration. It should be noted, that the vertical load flow shown in Figure A.1 only depicts the chosen model with its different load phases. The dynamic interaction of wheel, rail and sleeper or bearer was omitted in order to simplify the figure.

A.1.3 Determination of test bending moments All test bending moments are directly related to the characteristic bending moments.

Key A B

accidental loads exceptional loads

C

service loads

The load levels presented in Figure A.2 indicate different levels of testing. 1 2 3 4

The accidental load level is limited by the ultimate load test. At the exceptional load level cracks may appear, but shall be closed after removal of the load. In the service load level test the time dependent factor kt determines the required bending resistance at which level there shall be no cracks. The initial reference characteristic moment determines the fatigue test for the prestressed tendons.

Figure A.2 — Load levels and bending moments for testing

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The three load levels presented in Figure A.2 indicate three different levels of testing. In the service load level, no cracks on prestressed elements shall appear due to bending moments. The test with time dependent factor kt secures the required bending resistance. In addition, the fatigue test controlling the dynamic strength of the prestressed tendons has to be performed under service load level conditions. In the exceptional load level cracks may appear, but it shall be closed after removal of the load. The accidental load level is limited by the ultimate load test.

A.2 Rail seat load A.2.1 Normal service increment for the dynamic wheel load The dynamic wheel load Q is calculated from the nominal axle load Anom using the factor kv for the influence of speed and track condition:

Q=

Anom × (1 + k v ) 2

Recommendation

(A.1)

For a track with usual vertical alignment defects and depressions the normal service dynamic increment factor kv may be taken from Figure A.3.

For 0 ≤ V ≤ 60 km/h

kv = 0,2 5

For 60 < V < 200 km/h

k v = 0,25 +

For V ≥ 200 km/h

kv = 0,75

V − 60 280

Figure A.3 — Factor kv

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The factor kv has been derived from measurement in track with usual levelling defects and depressions. It corresponds to the mean value plus two standard deviations of the dynamic wheel load. For a track with a high maintenance level (e.g. high speed lines) lower values of kv may occur.

A.2.2 Distribution of longitudinal load A.2.2.1

Theoretical distribution

The longitudinal distribution of the wheel loads by the rails between sleepers along the track may be calculated using the model of the "elastic beam on resilient support". The influence of all elastic track components may be taken into account. Attention should be paid regarding the stiffness ctot for one support of the rail. The formulae for the calculation of the load distribution factor kd are given here under. 

Stiffness c2 of ballast and subsoil for one support (half a sleeper):

c2 = 0,5 × AR × C 2 in N/mm

(A.2)

where 2

AR is the bearing area of the sleeper, in mm ;

C2 is the modulus of elasticity for ballast and subgrade, in N/mm3. 

Stiffness ctot for one support of the rail:

ctot

1 1  =  +   c1 c2 

−1

in N/mm

(A.3)

where

c1 is the stiffness of the rail pad for static loads, in N/mm; c2 is the stiffness of ballast and subsoil, in N/mm. 

Elastic length Lel of the Winkler beam:

Lel =

4 × ER × I R 4

c tot

in mm

(A.4)

a

where

ER is the modulus of elasticity of the rail, in N/mm2; 4

IR

is the moment of inertia of the rail, in mm ;

a

is the sleeper spacing, in mm.

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

Rail deflection y0 for a unit wheel load Q0 :

y0 =

Q0 × a in mm 2 × ctot × Lel

(A.5)

 Influence η of the axle positions xi:

ηi =

sin ξi + cos ξi

(A.6)

eξ i

where

ξi = 

xi Lel

(A.7)

Rail seat load P0 due to a unit wheel load Q0:

P0 = ctot × ∑ I ηi × y0 in N 

(A.8)

Load distribution factor:

kd =

P0 Q0

(A.9)

Measurement in track showed that kd corresponds to the mean value of longitudinal load distribution. Recommendations

a) A factor of k d = 0,5 may be used for normal cases. This value can be considered valid for rails ≥ 46 kg/m and a sleeper spacing ≤ 65 cm with typical formation conditions. b) For tracks with heavier rails and "low attenuation" rail pads, sleeper spacing of 0,6 m, sleeper 3 length from 2,3 to 2,6 m, bedding modulus of C = 0,1 N/mm , single wheel or bogies, calculation of kd using “beam on elastic foundation” theory leads to values as detailed in Table A.1.

Table A.1 – Typical values of kd

A.2.2.2

Rail type

Rail weight (kg/m)

kd

49 E1

49

0,41

54 E3

54

0,40

60 E1

60

0,38

Effect of support faults

The variation of the ballast reaction between sleepers due to ballast support faults is taken into account by the factor kr Measurement in track showed that the coefficient of variation leads to an increase rail seat load up to 35 %. It is recommended to use

24

k r = 1,35 .

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A.2.3 Dynamic rail seat load Attenuation effects of an elastic rail pad may be taken into account using a load decrease factor kp. The characteristic value of the rail seat load Pk may be calculated as follows:

Pk =

[ (

)]

Anom × 1 + k p × kv × kd × kr 2

Recommendation

(A.10)

The following values of kp may be used: 

for pads with low attenuation (< 15 %):

kp = 1,0



for pads with medium attenuation (15 % to 30 %):

kp = 0,89



for pads with high attenuation (> 30 %):

kp = 0,78

The factor kp shall be determined according to EN 13146-3 as the mean value of several tests.

A.3 Characteristic bending moments A.3.1 General For the calculation of the characteristic bending moments the uneven distribution of the ballast reaction under the sleeper and the elasticity of the sleeper should be taken into account. The following simplified design model may also be used.

A.3.2 Rail seat section The positive bending moment Mk,r,pos may be calculated from Pk using the beam on elastic foundation with a constant bedding modulus over the length 2 Lp. Irregularities of the ballast reaction are covered by ki,r. The simplified design model shown in Figure A.4 may also be used. A load distribution in the sleeper according to Figure A.4 and a constant ballast reaction over the length 2 Lp may be assumed. The uneven ballast reaction is taken into account by the factor ki,r. The characteristic bending moment Mk,r,pos is calculated using Formulae (A.11) to (A.14).

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Figure A.4 — Design model for Mk,r,pos Load distribution in the concrete under the rail foot:

2e = brail + (2 × z c.top )

(A.11)

where

brail

is the width of the rail foot;

zc,top is the distance to the axis of inertia from top surface of sleeper. The length of the ballast pressure is equal to Lp:

Lp =

L−c 2

(A.12)

where c

is the rail seat centre spacing;

L

is the sleeper length.

Lever length of resulting internal forces

λ=

26

Lp − e 2

Pk is equal to λ: 2 (A.13)

prEN 13230-6:2014 (E)

Characteristic bending moment may be calculated as:

M k ,r , pos = k ir × λ × Recommendation 1

Pk 2

(A.14)

The simplified design model may be used for sleepers with 0,35 m ≤ Lp ≤ 0,55 m in combination with ki,r = 1,6. This value has been derived from measurement (mean value plus two standard deviations).

Recommendation 2

The characteristic negative bending moment at rail seat section may be assumed to be 50 % of Mk,r,pos for sleeper length between 2,5 m and 2,6 m and at least 70 % of Mk,r,pos for shorter sleepers.

A.3.3 Sleeper centre section A.3.3.1 A.3.3.1.1

Negative bending moment General

The negative bending moment Mk,neg in the centre section may be calculated from Pk using the beam on elastic foundation with constant bedding modulus over the entire length of the sleeper. Irregularities of the ballast reaction are covered by a factor ki,c. The following simplified method also may be used. A.3.3.1.2

Standard gauge sleeper

The characteristic value of the negative bending moment for sleepers with variable stiffness and different bottom width may be also calculated as:

M k ,c ,neg = kic × Pk × M c ,neg ,100 / 100

(A.15)

taking the values of Mc,neg,100 from Figure A.5 for the standard gauge. The sleeper to be calculated is defined by the values indicated in Figure A.5, Drawing A. The general pattern of Mc,neg,100 depending on the relations of sleeper stiffness and different bottom width has been summarized in Figure A.5, Drawing B. For standard gauge sleepers with different length L the bending moments Mc,neg,100 may be taken from Figure A.5. Recommendation

a) The bending moments Mc,neg,100 have been evaluated for a multiple rectangular soffit surface as indicated by x in Figure A.5, Drawing A. For a trapezoidal bottom transition as indicated by z in Figure A.5, Drawing A, the bending moment may be reduced by 10 %. For an intermediate transition as indicated by y in Figure A.5, Drawing A, the bending moment may be reduced by 5 %. b) The simplified method can be applied when the inertia moment Ir value indicated in 6 4 Figures A.5 and A.6 equal to 200 x 10 mm +- 20% for sleepers with 2,3 m ≤ L ≤ 2,6 m. c)

The standard rail gauge is assumed as 1,435 m and 1,668 m for broad gauge.

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Figure A.5 — Determination of centre bending moment Mc, neg,100 for standard gauge sleepers A.3.3.1.3

Broad gauge sleepers

Broad gauge sleepers' definition:

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Rail gauge = 1,688 m

Figure A.6 — Determination of centre bending moments Mc,neg,100 for broad gauge sleepers A.3.3.1.4

Narrow gauge sleepers

The negative bending moment Mc, neg for sleeper with a gauge ≥ 1 m, according to Figure A.7 may be determined in a simplified manner applying a constant bedding load: Mc, neg = - Pk (2S - L)/4

(A.16)

M k ,c ,neg = ki ,c × M k ,neg

(A.17)

Figure A.7 — Geometry for narrow gauge sleepers

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6

4

For these sleepers a constant bottom width Br and constant sleeper inertia Ir of app. 70∙10 mm have been assumed. A.3.3.1.5

Recommendations for ki c

The factor ki c may be chosen for standard gauge sleepers using the values recommended in Table A.2. 3 These values are valuable for a constant bedding modulus of C2 = 0,1 N/mm in the longitudinal and transversal direction of the track. Table A.2 – Recommended values for ki c for, narrow gauge, standard gauge and broad gauge Country

Narrow gauge Length

ki c

Standard gauge Length

ki c

Broad gauge Length

ki c

Austria

2,6

2,1 – 2,4

Belgium

2,5

1,1 – 2,2

France

2,26

0,9

2,4

1

2,5

1,1

2,6

2

2,4

1,5

Netherlands

2,5

1,13

Portugal

2,6

1,6

2,6

1

Spain

2,6

1,6

2,6

1

2,6

1,4

2,5

0,5 – 0,8

Germany

Switzerland

2,0

United Kingdom

1,6

This table shows the state of the art. Sleepers designed with these coefficients have shown satisfactory performance in track. For sleeper length outside these values, the purchaser shall determine the bending moment coefficient ki c. A.3.3.2

Positive bending moment

The characteristic positive bending moment for standard gauge sleepers with a length 2,20 m ≤ L ≤ 2,60 m may be assumed as:

M k ,c , pos = 0,7 × M k ,c ,neg

(A.18)

The characteristic positive bending moment for narrow gauge sleepers with a length 1,30 m ≤ L ≤ 2,00 m may be assumed as:

M k ,c , pos = 1,0 × M k ,c ,neg

30

(A.19)

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A.4 Test bending moments A.4.1 First crack test bending moment The bending moment M t = k t × M k for crack initiation depends on the age of the sleeper at moment of testing. The time dependent loss of the prestressing force and the difference between concrete flexural tensile strength under static load and fatigue load are taken into account by increasing the characteristic bending moment Mk appropriately. For the rail seat section of a 28 days old sleeper the positive testing bending moment Mt,r,pos may be calculated using Formula (A.20):

M t ,r , pos = M k ,r , pos + ( f ct , fl ,t =

28 days

− f ct , fl , fat ) += ( ∆σ c,c+ s+r ,t

− ∆σ

40 years = c , c + s + r ,t 28 days

) ×W = in kN.m

(A.20)

kt × M k,r,pos where

f ct , fl ,t = 28 days

is the concrete flexural tensile strength under static load at the age of 28 days, in N/mm

f ct , fl , fat

2

is the concrete flexural tensile strength after dynamic loads, in N/mm

∆σ c ,c + s + r ,t = 40 years

is the loss of prestress in concrete after 40 years, in N/mm

∆σ c ,c + s + r ,t = 28 days

is the loss of prestress in concrete after 28 days, in N/mm

W

is the modulus of the cross section, in mm

2

2

2

3

,

For the testing bending moments Mt,r,neg Mt,c,pos and Mt,c,neg the formula may be used accordingly. If the sleeper is older than 28 days at the moment of testing, this may be taken into account by adopting the loss of prestress. Recommendation 1

For concrete C50/60 the concrete flexural strength may be assumed to be

f ct , fl ,t =28

=

2

5,5 N/mm . Recommendation 2

The

flexural

f ct , fl , fat

strength

of

concrete

under

fatigue

loads

may

be

assumed

to

be

2

= 3,0 N/mm for concrete strength class C50/60.

Recommendation 3

The time dependent losses of prestress due to shrinkage creep and relaxation may be calculated according to EN 1992. If prestressing steel according to EN 10138 is used the total loss after 40 years may be assumed to be 25 % of the initial prestressing force.

Recommendation 4

The factor kt depends strongly on the production process and environmental conditions during service. It must be calculated based on the geometry of the cross section, the level of prestress and the factor of utilization of the bending resistance. For the testing of sleepers at the age of 28 days it can be in the range from 1,1 to 1,8.

Recommendation 5

At the age of testing (28 days) one third of total losses of prestress have occurred.

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A.4.2 Test bending moments for exceptional and accidental loads A.4.2.1

Exceptional loads

Exceptional loads occur due to wheel loads that are considerably higher than the characteristic wheel load, or due to extremely unfavourable support conditions. They may lead to the formation of cracks. However these cracks are closed by the effect of prestressing force or reinforcement after removal of the load. For a remaining crack width below 0,05 mm after removal of the load, the prestressing elements remain protected against corrosion by the concrete cover. Examples for exceptional loads are heavily overloaded freight wagons, wheel flats with a depth up to 2 mm, large voids under the ends of a sleeper (dancing sleepers). In order to cover these effects it is recommended to use at least the following coefficients in the design acceptance tests:

k1s = 1,8x 0,5 / k d k1d = 1,5x 0,5 / k d They shall be applied to the characteristic bending moments. A.4.2.2

Accidental loads

Accidental impact loads cause severe damage to the sleeper such as spalling of the concrete or gaping cracks. It is assumed that after accidental change the basic functions – such as guiding the vehicles, taking up the vehicle forces and transferring these loads to the ballast – are available at least for some time. Accidental loads are caused e.g. by big wheel flats (several millimetres of depth) or derailment of a single axle or bogie. In order to cover these effects it is recommended to use the following coefficients in the design acceptance tests:

k 2 s = 2 ,5 x0 ,5 /k d

k 2 d = 2 ,2 x0 ,5 /k d They shall be applied to the characteristic bending moments.

A.4.3 Calculation of test moments for the fatigue test The fatigue test for steel tendons is assumed to simulate the behaviour of the cracked concrete section under service load. The upper dynamic bending moment corresponds to the characteristic bending moment. The recommended value for k3 to calculate the ultimate bending moment is:

k 3 = 2,5x 0,5 / k d It shall be applied to the characteristic bending moments.

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A.5 Checking of stresses for Serviceability Limit State (for prestressed sleepers only) Sleepers are normally designed for a minimum service life of 40 years. The load carrying capacity of the sleeper shall cover the characteristic bending moment Mk which takes account of static loading plus normal service dynamic increment and uneven ballast reaction. No cracking shall occur at this load level. This means that during the entire service life of the sleeper the maximum tensile stress

σ ct ,max

in the concrete

due to the bending moment Mk and the effects of prestressing shall not exceed the fatigue strength concrete under repeated loads.

f ct , fl , fat of

This requirement leads to Formula (A.21):

σ ct ,max =

N p (t = 40 years ) A

+

N p (t = 40 years ) × e p W

+

Mk < f ct , fl , fat in N/m² W

(A.21)

where

N p (t = 40 years ) is the remaining force of prestress after 40 years, in N; 2;

A

is the cross section of the sleeper, in mm

ep

is the eccentricity of the prestressing force, in mm;

W

is the moment of resistance, in mm ;

Mk

is the bending moment due to service load (characteristic value), in Nm.

3

Recommendation 1

The time dependent losses of prestress due to shrinkage creep and relaxation may be calculated according to EN 1992 If prestressing steel according to EN 10138 is used the total loss may be assumed to be 25 % of the initial prestressing force.

Recommendation 2

The

flexural

f ct , fl , fat

strength

of

concrete

under

fatigue

loads

may

be

estimated

with

2

= 3,0 N/mm for concrete strength class C50/60.

A.6 Design examples A.6.1 Standard gauge sleeper A.6.1.1

General

The following paragraphs presents an example of calculation for prestressed monoblock sleepers designed for standard gauge track. Input data are detailed in Table A.3.

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Table A.3 — Input data for standard gauge sleeper nominal axle load:

Anom = 225 kN

train speed:

V = 220 km/h

rail profile 60E1:

Irail = 3 038 cm

modulus of elasticity:

Erail = 210 000 N/mm

rail pads:

c1 = 600 kN/mm, low attenuation

sleeper spacing:

a = 600 mm

rail gauge:

1 435 mm

modulus of platform:

C2 = 0,1 N/mm

sleeper length:

L = 2,60 m

rail seat centre spacing:

c = 1,51 m

sleeper bottom surface:

AR = 6 800 cm

4 2

3

2

values for the rail seat section: 2

- cross section:

Ar = 505 cm

- second moment of area:

Ir = 18 320 cm

- modulus for bottom:

Wr,bottom = 1 850 cm

- modulus for top:

Wr,top = - 1 590 cm

- eccentricity of the prestressing force:

ep = 8 mm

4 3

3

values for the centre section: 2

- cross section:

Ac = 337 cm

- second moment of area:

Ic = 8 380 cm

- modulus for bottom:

Wc,bottom = 1 020 cm

- modulus for top:

Wc,top = - 900 cm

- eccentricity of the prestressing force:

ep = - 9 mm

4 3

3

prestressing force:

a

- initial prestressing force:

P0

- after transfer of the load:

Pm0 = 315 kN

- after four weeks (t1 = 28 days)

Pm,t1 = 297 kN

a

- after forty years (t2 = 40 years)

Pm,t2 = 260 kN

a

a

Calculated according to EC2.

A.6.1.2 Characteristic rail seat load Stiffness c2 of ballast and subsoil for one support (half a sleeper): -3

c2 = 0,5 x AR x C2 = 0,5 x 680 000 x 0,10 x 10 = 34,0 kN/mm

34

(A.22)

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Stiffness ctot for one support of the rail: −1

−1

1 1 1   1 ctot =  +  =  +  = 30,6 kN/mm c c 600 34 ,0   2   1

(A.23)

Elastic length of the Winkler beam:

Lel = 4

4 × E rail × I rail 4 4 × 210.000 × 3038 × 10 4 = = 841mm ctot / a 30600 / 600

(A.24)

Rail deflection y0 for a unit wheel load Q0 = 100 kN :

y0 =

Q0 × a 100 × 600 = = 1,17 mm 2 × ctot × Lel 2 × 30,6 × 841

(A.25)

Influence of the neighbouring axles, e.g. for three axles with spacing aA = 1,80 m:

ηi =

sin ξ i + cos ξ i e

for x1 = 0,00 m: for x2 = 1,800 m:

xi 841

with ξ i =

ξi

(A.26)

η1 = 1,00 η 2 = 0,036

(axle at the centre of the bogie)

Rail seat load for unit wheel load Q0 = 100 kN :

P0 = ctot × ∑l η i × y0 = 30,60 x (1 + 2 x 0,036) x 1,17 = 38,4 kN

(A.27)

Load distribution factor:

kd =

P0 38,4 = = 0,384 Q0 100

(A.28)

Characteristic rail seat load: 

speed increment factor:

kv

=

0,75



pad with low attenuation:

kp

=

1,00



ballast support faults:

kr

=

1,35

Pk =

for V = 220 km/h

Anom 225 × (1 + k p × k v ) × k d × k r = × (1 + 1,0 × 0,75) × 0,384 × 1,35 = 102kN 2 2

(A.29)

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A.6.1.3

Characteristic bending moments

A.6.1.3.1

Rail seat section

Positive bending moment (see Figure A.4): 2e = brail + (2 x zc,top) = 150 + (2 x 115) = 380 mm

Lp =

λ=

(A.30)

L − c 2600 − 1510 = = 545mm 2 2

Lp − e 2

=

(A.31)

545 − 380 / 2 = 178mm 2

M k ,r , pos = k i ,r × λ ×

(A.32)

Pk 102 = 1,6 × 0,178 × = 14,50kNm 2 2

(A.33)

Negative bending moment: sleeper length L = 2,60 m A.6.1.3.2

M k ,r ,neg = 0,5 × M k ,r , pos = 0,5 × 14,50 = 7,25kNm

(A.34)

Sleeper centre section

a) Calculation using the elastic beam as design model The sleeper is represented by an elastic beam as shown in Figure A.8. The stiffness ci of the springs shall be calculated taking the modulus of platform C2, the bottom width b and spring spacing Δx into account. The characteristic rail seat load Pk shall be transformed into a line load along the length 2e. 3

Figure A.8 shows the bending moment due to Pk = 102 kN for C2 = 0,1 N/mm and 2e = 380 mm. The negative bending moment at the sleeper centre Mc,neg = -5,36 kN.m shall be multiplied by the factor ki,c:

M k ,c ,neg = kic × Pk × M c,neg ,100 / 100 = 1,6 × 102 × 5,36 / 100 = −8,7 kNm

(A.35)

Positive bending moment: sleeper length L = 2,60 m

36

Mk,c,pos = 0,7 x Mk,c,neg = 0,7 x 8,7 = 6,1 kNm

(A.36)

prEN 13230-6:2014 (E)

Key A

bottom width

B C D

elastic beam spring elements bending moment Mk in [KNm]

E

deflection y in [mm]

Figure A.8 — Design model and results using the elastic beam on elastic foundation b) Calculation using the bending moment diagrams from Figure A.5 Initial values: L = 2,60 m

Bc 220 = = 0,73 Br 300

(A.37)

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Ic 8380 = = 0,46 I r 18320

(A.38)

Unit bending moment from Figure A.5 with 10 % reduction for bottom shape z: Mc,neg,100 = 0,9 x 6,3 = 5,7 kNm

(A.39)

Characteristic negative bending moment:

M k ,c ,neg = kic × Pk × M c ,neg

,100

/ 100 = 1,6 × 102 × 5,7 / 100 = −9,3kNm

(A.40)

Mc,pos = 0,7 x Mk,c,neg = 0,7 x 9,3 = +6,5 kNm

(A.41)

Positive bending moment: sleeper length L = 2,60 m A.6.1.3.3

Checking of tensile stress in the concrete for serviceability limit state

According to A.5 the maximum tensile stress in concrete σct,max due to the characteristic bending moment Mk must not exceed the concrete fatigue strength fct,fl,fat = 3,0 MPa during the entire service life of the sleeper. Positive bending moment at the rail seat section:

σ ct ,max =

Pm,t 2 Ar

Pm,t 2 e p

+

Wbottom

+

M k ,r , pos Wbottom

=

− 0,260 505 × 10 − 4

+

− 0,260 × 0,008 1850 × 10 −6

+

− 14,5 × 10 −3 1850 × 10 −6

= 1,57 MPa < 3,0MPa

(A.42)

= −1,90MPa < 3,0MPa

(A.43)

Negative bending moment at the rail seat section:

σ ct ,max =

Pm,t 2 Ar

Pm,t 2 e p

+

Wtop

+

M k ,r , pos Wtop

=

− 0,260 505 × 10 − 4

+

− 0,260 × 0,008 − 1590 × 10 −6

+

− 7,25 × 10 −3 1590 × 10 −6

Positive bending moment at the centre section, Mk,c,pos taken from A.6.1.3.2 a):

σ ct ,max =

Pm,t 2 Ac

Pm,t 2 e p

+

Wbottom

+

M k ,c , pos Wbottom

=

− 0,260 337 × 10 − 4

+

− 0,260 × (−0,009) 1020 × 10 −6

+

+ 6,0 × 10 −3 1020 × 10 −6

= 0,46MPa < 3,0MPa

(A.44)

Negative bending moment at the rail centre section, Mk,c,neg taken from A.6.1.3.2 a): σ ct ,max =

A.6.1.3.4

Pm,t 2 Ac

+

Pm,t 2 e p Wtop

+

M k ,c ,neg Wtop

=

− 0,260 337 × 10 − 4

+

− 0,260 × (−0,009) − 900 × 10 −6

+

− 8,7 × 10 −3 − 900 × 10 −6

= −0,76MPa < 3,0MPa

(A.45)

Calculation of test loads and acceptance criteria

a) Rail seat section The initial reference test load Fr0 is calculated according to EN 13230-2, 4.3: Lp = (L - c)/2 = (2,60 - 1,51) = 0,545 m Fr0 =

38

4 M k , r , pos Lr − 0,1

=

4 × 14,5 = 116kN 0,6 − 0,1

Lr = 0,60 m (A.46)

prEN 13230-6:2014 (E)

Calculation of the testing bending moment Mt,r,pos and coefficient kt for the formation of the first crack

[

]

M t , r , pos = M k , r , pos + ( f ct , fl ,t = 28 days − f ct , fl , fat ) + (∆σ c ,c + s + r ,t = 40 years − ∆σ c ,c + s + r ,t = 28 days ) × Wbottom = kt × M k,r,pos (A.47)

M t , r , pos = 14,5 + [(5,5 − 3,0 ) + 0,89]× 1850.10 −3 = 20,8kNm

kt =

20,8 = 1,43 14,5

(A.48)

As the longitudinal load distribution factor is kd = 0,382, calculation of coefficients k1s, k2s, k1d, k2d and k3 is performed as: k1s = 1,8 x 0,5/0,382 = 2,36 k2s = 2,5 x 0,5/0,382 = 3,27 k1d = 1,5 x 0,5/0,382 = 1,96 k2d = 2,2 x 0,5/0,382 = 2,88 k3 = 2,5 x 0,5/0,382 = 3,27 Calculation of the design acceptance criteria: a.1)

Static test • formation of the first crack: Frr > kt x Fr0 =

1,43 x 116 = 166 KN

• remaining crack width 0,05 mm Fr0.05 > k1s x Fr0 = • maximum test load: FrB > k2s x Fr0 = a.2)

2,36 x 116 = 274 KN

3,27 x 116 = 379 KN

Dynamic test • remaining crack width 0,05 mm: Fr0.05 > k1d x Fr0 =

1,96 x 116 = 227 KN

• remaining crack width 0,5 mm: Fr0.5 > k2d x Fr0 =

2,88 x 116 = 334 KN

• maximum test load: FrB > k2d x Fr0 = a.3)

2,88 x 116 = 334 KN

Fatigue test • maximum test load: FrB > k3 x Fr0 =

3,27 x 116 = 379 KN

39

prEN 13230-6:2014 (E)

b) Sleeper centre section The initial reference test load Fc0n is calculated according to prEN 13230-2:2014, 4.3: Fc0 n =

4 × M k ,c, pos Lc − 0,1

=

4 × 8,6 = 25kN 1,51 − 0,1

(A.49)

Calculation of the testing bending moment Mt,c,neg and coefficient kt for the formation of the first crack:

[(

)]

) (

M t , c , neg = M k , c , neg + f ct , fl ,t = 28days − f ct , fl , fat + ∆σ c , c + s + r ,t = 40 years − ∆σ c, c + s + r ,t = 28days × Wtop  1 ep ∆σ c ,c + s + r ,t =40 years − ∆σ c ,c + s + r ,t =28days = (Pm,t 2 − Pm,t1 )×  +  Ac Wtop 

(

 1 − 0,009  (A.50)  = (0,297 − 0,260 ) ×  +  = 1,47 MPa −4  − 900 × 10 −6   337 × 10 

)

M t ,c ,neg = −8,7 + [(5,5 − 3,0 ) + 1,47]× − 900 ⋅ 10 −3 = −12,3kNm kt =

− 12,3 = 1,42 − 8,7

Calculation of the design acceptance criterion: Static test: formation of the first crack:

A.6.2 Broad gauge sleeper A.6.2.1

General

Input data are detailed in Table A.4.

40

Fcrn > kt x Fc0n = 1,42 x 25 = 36 kN

prEN 13230-6:2014 (E)

Table A.4 — Input data for broad gauge sleeper nominal axle load:

Anom = 225 kN

train speed:

V = 220 km/h

rail profile 60E1:

Irail = 3 038 cm

modulus of elasticity:

Erail = 210 000 N/mm

rail pads:

c1 = 600 kN/mm, low attenuation

sleeper spacing:

a = 600 mm

modulus of platform:

c2 = 0,1 N/mm3

sleeper length:

L = 2,60 m

rail gauge:

1 668 mm

rail seat centre spacing:

c = 1,757 m

sleeper bottom surface:

AR= 6 800 cm

4 2

2

values for the rail seat section: Ir = 23 696 cm

- second moment of area:

4

values for the centre section: 2

- cross section:

Ac = 370 cm

- second moment of area:

Ic = 12 191 cm

- modulus for bottom:

Wc,bottom = 1 301 cm

- modulus for top:

Wc,top = - 1 146 cm

- eccentricity of the prestressing force:

ep = - 8,8 mm

4 3

3

prestressing force:

a

A.6.2.2

- initial prestressing force:

P0

- after transfer of the load:

Pm0 = 357 kN

- after four weeks (t1 = 28 days)

Pm,t1 = 340 kN

a

- after forty years (t2 = 40 years)

Pm,t2 = 297 kN

a

a

Calculated according to EC2.

Characteristic rail seat load

Calculation of characteristic rail seat load is performed using same methodology as in A.6.1.2 Pk = 225/2 x 0,5 x (1+0,75) x 1,35 = 132,9kN

with kd = 0,5

41

prEN 13230-6:2014 (E)

A.6.2.3 A.6.2.3.1

Characteristic bending moments Sleeper centre section

Calculation using the bending moment diagrams from Figure A.6 Initial values: L = 2,60 m Bc/Br = 220/280,2 = 0,785

br = 280,2 width at the rail section

Ic/Ir = 12 191 / 23 696 = 0,51 Unit bending moment from Figure A.6 with 5 % reduction for bottom shape: Mc,neg,100 = 0,95 x 10,67 = 10,13 kN.m A.6.2.3.2

Calculation of test loads and acceptance criteria

Characteristic negative bending moment at sleeper centre section is: For 2,6 m sleeper length and broad gauge kic=1 Mk,c,neg = ki,c x Mc,neg,100 x Pk /100 = 1 x 10,13 x 132,9/100 = - 13,46 kN.m Characteristic positive bending moment at sleepers centre section is: Mk,c,pos = 0,7 x Mk,c,neg = 0,7 x 13,46 = + 9,42 kN.m Calculation of the testing bending moment Mt,c,neg and coefficient kt for the formation of the first crack in static test

[(

)]

) (

M t , c , neg = M k , c , neg + f ct , fl ,t = 28days − f ct , fl , fat + ∆σ c , c + s + r ,t = 40 years − ∆σ c, c + s + r ,t = 28days × Wtop

∆σ c ,c + s + r ,t = 40 years − ∆σ c ,c + s + r ,t = 28 days = ( Pm ,t 2 − Pm ,t1 ) × (

ep 1 ) + Ac Wtop

1 − 0,0088   ∆σ c ,c + s + r ,t = 40 years − ∆σ c ,c + s + r ,t = 28 days = (340 − 297) ×  +  = 1,49 MPa −4 − 1146 × 10 −6   370 × 10 M t ,c ,neg = −13,46 + [(5,5 − 3,0 ) + (1,49 )]× −1146 × 10 −3 = −18,04kN .m kt =

− 18,04 = 1,34 − 13,46

Checking of maximum concrete compression stress (compression concrete fatigue, 6.2.6) in bottom fibre:

42

Maximum stress in bottom fibre

1 0,0088  13,46  340 ×  + = 17,3MPa − −4 −6  1301 × 10  1301 × 10 −6  370 × 10

Assuming concrete C 50/60

17,3 < 0,5 × 50 = 25MPa

prEN 13230-6:2014 (E)

Annex B (informative) Design methods and factors for bearers

The bending moments for bearers have been calculated using the beam on elastic foundation for entire lay out. These results have applied in various railway companies. Experience from Railways Authorities show that bending moments comply with track conditions. The maximum bending moments have determined as

Mk.b.pos = Mk.b.neg. Range is within 22 to 30 kN.m.

As an example, following characteristic and testing bending moments are used:

43

prEN 13230-6:2014 (E)

Table B.1 – Characteristic and testing bending moments Country

Bearer type

Positive characteristic bending moment (kN.m)

Negative characteristic bending moment (kN.m)

Positive testing bending moment (kN.m)

Negative testing bending moment (kN.m)

AUSTRIA

All types

Width = 300 mm Depth = 220 mm

25

-25

25

-25

Bearer length ≤ 2,6 m

Width = 300 mm Depth = 200 mm

19,25

- 19,25

Bearer length > 2,6 m

Width = 300 mm Depth = 200 mm

25,20

- 25,20

Type KS

Width = 300 mm Depth = 220 mm

22,5

- 22,5

28

- 30

Type W

Width = 300 mm Depth = 220 mm

22,5

- 22,5

32

- 30

All types

Width = 300 mm Depth = 220 mm

22,5

- 22,5

28

- 30

Type R length ≤ 4,5 m

Depth = 186 mm Width = ?? Depth = 186 mm Width = ?? Depth = 205 mm Width = ??

FRANCE

GERMANY SPAIN

UNITED KINGDOM

Type R length > 4,5 m Type D

SWEDEN NETHERLANDS

44

Bearer Cross section

kb

kbn

1,30 to 1,40

31 34,5 34,5

All types All types

Depth = 200 mm Width = 300 mm

22,5

- 22,5

28

- 28

1,96

1,96

prEN 13230-6:2014 (E)

Annex ZA (informative) Relationship between this European Standard and the Essential Requirements of Directive 2008/57/EC

This European Standard has been prepared under a mandate given to CEN/CENELEC by the European Commission and the European Free Trade Association to provide a means of conforming to Essential Requirements of the New Approach 2008/57/EC 1). Once this standard is cited in the Official Journal of the European Union under that Directive and has been implemented as a national standard in at least one Member State, compliance with the clauses of this standard given in Tables ZA.1 for HS Infrastructure and ZA 2 for CR Infrastructure confers, within the limits of the scope of this standard, a presumption of conformity with the corresponding Essential Requirements of that Directive and associated EFTA regulations.

1)

This Directive 2008/57/EC adopted on 17th June 2008 is a recast of the previous Directives 96/48/EC ‘Interoperability of the trans-European high-speed rail system’ and 2001/16/EC ‘Interoperability of the trans-European conventional rail system’ and revisions thereof by 2004/50/EC ‘Corrigendum to Directive 2004/50/EC of the European Parliament and of the Council of 29 April 2004 amending Council Directive 96/48/EC on the interoperability of the trans-European high-speed rail system and Directive 2001/16/EC of the European Parliament and of the Council on the interoperability of the trans-European conventional rail system’

45

prEN 13230-6:2014 (E)

Table ZA.1 — Correspondence between this European Standard, the Infrastructure TSI for the trans-European high speed rail system dated 20 December 2007 (published in the Official Journal L77,19.03.2008, p.1) and Directive 2008/57/EC Clause(s)/ subclause(s) of this European Standard 4.General requirements 5.Design parameters 6.Design calculation

Chapter/§/annexes of the TSI

4. Description of the infrastructure domain 4.2. Functional and technical specifications of the domain § 4.2.2.Nominal track gauge §4.2.9.2.Equivalent conicity – Design values § 4.2.11 Rail inclination § 4.2.13.Track resistance §4.2.15 Global track stiffness §4.2.18 Electrical characteristics 5.3.3.Interoperability constituents – Constituents performances and specifications – Track sleepers and bearers - minimum mass - minimum length.

46

Corresponding text, articles/§/annexes of the Directive 2008/57/EC Annex III, Essential Requirements, 1.General Requirements

Comment

Concrete sleepers are safetycritical interoperability constituents and need an arrangement between the purchaser and the supplier to operate a factory quality system

1.1.1, 1.1.3. Safety 1.2. Reliability and availability. 1.4.5 Environmental protection 1.5 Technical compatibility.

Direct references to the HS INF TSI – overall length of the sleepers – mass of the sleepers For vibration levels the HS INF TSI refers to national rules (§4.2.19) This part of the standard EN 13230, which defines the design of concrete sleepers and bearers should be read in conjunction with EN 13230 Part 1 to 4 Annex H of HS INF TSI Global track stiffness remains an open point and is not assessed (§4.2.15)

prEN 13230-6:2014 (E)

Table ZA.2 — Correspondence between this European Standard, the ERA draft of Conventional Rail System TSI Infrastructure (IU-INF-0090902-TSI 4.0 dated 2009/09/18), and Directive 2008/57/EC Clause(s)/ subclause(s) of this European Standard 4.General requirements 5.Design parameters 6.Design calculation

Chapter/§/annexes of the TSI

4.Description of the infrastructure subsystem 4.2.Functional and technical specifications of subsystem 4.2.5 Track parameters § 4.2.5.1. Nominal track gauge § 4.2.5.5.1. Equivalent conicity – Design values for equivalent conicity §4.2.5.7.1. Rail inclination – Plain line §4.2.5.8 Track stiffness. 4.2.7. Track resistance to applied loads. 5.3.3.Interoperability constituents – Constituents performances and specifications – Track sleepers

Corresponding text, articles/§/annexes of the Directive 2008/57/EC Annex III, Essential Requirements, 1.General Requirements

Comment

Concrete sleepers and bearers are safety- critical interoperability constituents and need an arrangement between the purchaser and the supplier to operate a factory quality system

1.1.1, 1.1.3 Safety 1.2 Reliability and availability. 1.4.5 Environmental protection 1.5 Technical compatibility.

This part of the standard EN 13230, which defines the design of concrete sleepers and bearers should be read in conjunction with EN 13230 Part 1 to 4 Annex F of the draft ERA CR TSI -Requirements for controlling equivalent conicity in service remain an open point (§4.2.5.5.2). -Track stiffness remains an open point (§4.2.5.8) -Vibration limits remain an open point (§4.2.11.2)

6 Assessment of conformity of interoperability constituents and EC verification of the subsystems. §6.1.4.4.Interoperability constituents – EC declaration of conformity for interoperability constituents – EC declaration for track sleepers §6.2.4.4 Infrastructure subsystem – Particular assessment procedures for subsystem – Assessment of design values for equivalent conicity

WARNING — Other requirements and other EC Directives may be applicable to the product(s) falling within the scope of this standard.

47

prEN 13230-6:2014 (E)

Bibliography

EN 1992, Eurocode 2: Design of concrete structures. General rules and rules for buildings EN 10138, Prestressing steels EN 13146-3, Railway applications — Track - Test methods for fastening systems — Part 3: Determination of attenuation of impact loads ORE D71 (European Railway Research Institute) ORE D 170 RP4 (European Railway Research Institute) UIC 713, Design of monoblock concrete sleepers

48