WO2004018772A1

WO2004018772A1 - A method of designing a concrete railway sleeper

Info

Publication number: WO2004018772A1
Application number: PCT/AU2003/001074
Authority: WO
Inventors: Nicholas John Stevens; Peter Francis Dux
Original assignee: The University Of Queensland
Priority date: 2002-08-23
Filing date: 2003-08-22
Publication date: 2004-03-04
Also published as: GB2407607B; GB2407607A; AU2002951099A0; GB0503619D0; NZ538417A

Abstract

A method of designing a concrete sleeper, the method including the steps of determining a loading spectrum for a length of railway track; choosing a trial sleeper design having known structural properties including bending capacity at a rail seat and the tendon and concrete stresses for a range of bending moments; determining a load distribution for the railway track including calculating a bending moment in the sleeper for a predetermined load at a known distance from the sleeper; calculating an ultimate load based on the loading spectrum; comparing the ultimate load with the bending capacity at the rail seat for the sleeper; determining fatigue life of the sleeper based on the loading spectrum, load distribution, and tendon and concrete stresses; comparing the calculated fatigue life of the sleeper with predetermined safe fatigue life values.

Description

"A METHOD OF DESIGNING A CONCRETE RAILWAY SLEEPER" FIELD OF THE INVENTION This invention relates to a method of designing a concrete railway sleeper. In particular, the invention relates to a method of designing a concrete railway sleeper for replacing existing timber sleepers on an existing railway track. However, it should be appreciated that the sleepers to be replaced may be of other material such as steel. BACKGROUND OF THE INVENTION Many existing railway tracks utilise timber sleepers to support the rails of a railway track. Due to a number of factors including cost and life span, timber sleepers are being used less and less in the production of railway track. As the timber railway sleepers are deteriorating with age, they need to be replaced. It would be advantageous to replace these timber sleepers with concrete sleepers due to the cost and life span of concrete sleepers. Further, replacing timber sleepers with new timber sleepers is not environmentally friendly.

In Australia and other countries around the world, engineering codes have been developed that are used to design concrete sleepers. Concrete sleepers that have similar dimensions as timber sleepers cannot be designed to satisfy these codes. That is, it is not possible to achieve the required cracking strength specified by the codes with the reduced cross section necessary to replace the timber sleepers.

OBJECT OF THE INVENTION It is an object of the invention to overcome or alleviate the above disadvantages or provide the consumer with a useful or commercial choice.

SUMMARY OF THE INVENTION In one form the invention resides in a method of designing a concrete sleeper, the method including the steps of: determining a loading spectrum for a length of railway track; choosing a trial sleeper design having known structural properties including bending capacity at a rail seat and the tendon and concrete stresses for a range of bending moments; determining a load distribution for the railway track including calculating a bending moment in the sleeper for a predetermined load at a known distance from the sleeper; calculating an ultimate load based on the loading spectrum; comparing the ultimate load with the bending capacity at the rail seat for the sleeper; determining fatigue life of the sleeper based on the loading spectrum, load distribution, and tendon and concrete stresses; comparing the calculated fatigue life of the sleeper with predetermined safe fatigue life values.

The loading spectrum may be obtained by measuring a multiplicity of discrete loads at a typical location on the railway track.

Dynamic impact factors may be calculated from the measured discrete loads when comparing the measured loads with a predetermined notional load. Usually, the loads are wheel or axle loads.

The probability of exceedence of any load may be calculated from the measured discrete loads.

The loading spectrum may be obtained by plotting the probability of exceedence Vs the dynamic impact factors and drawing a curve which represents an upper boundary for the plot. The loading spectrum may be represented by a straight line.

The loading spectrum may also be obtained by taking previous measurements from another railway track and applying them to a similar railway track.

The choice of trial sleeper design is normally based on the structural properties of the sleeper. Usually, a cost efficient sleeper design with the high resistance to stress within the dimensional constraints is selected. The bending capacity at a rail seat and the tendon and concrete stresses for a range of bending moments may be calculated using standard engineering methods. Normally, the stress is calculated for bending moments at regular intervals from 0 to the ultimate bending capacity.

The load distribution may be obtained through the use of finite element analysis. Alternatively, the load distribution may be interpolated from previous finite element analyses. The ultimate load may be obtained by calculating an ultimate dynamic impact factor for a predetermined probability of exceedence over the life of the sleeper. The usual predetermined probability of exceedence for ultimate loads is 5% over the life of the sleeper.

Usually, the fatigue life of the sleeper takes into consideration a group of axles. Typically, the group of axles consists of two axles on a bogie at one end of the vehicle followed by two axles on a bogie at the start of the next vehicle.

The fatigue life of the sleeper is usually determined using the loading spectrum. The entire range of dynamic impact factors is normally considered i.e. 1 to the ultimate. The dynamic impact factors may be divided into a number of intervals to calculate a fraction of the fatigue life for each of the intervals.

The fraction of the fatigue life also may be calculated differently between high loads and low loads. The high loads may be considered in the top 25% whilst the low loads may be in the bottom 75%.

BRIEF DESCRIPTION OF THE DRAWINGS An example of the method will be described with reference to the accompanying drawings in which:

FIG. 1 is a graph of the probability of exceedence Vs measured dynamic impact factors (DIF);

FIG. 2 is a graph showing the straight line representing the loading spectrum;

FIG. 3 is a table representing sleeper properties for a trial sleeper design designated as "Low Profile Sleeper, 260 Wide 866 Strand"; FIG. 4 is a diagram representing the bending moment in a sleeper as a single load passes over it;

FIG. 5 is a load distribution diagram showing the bending moments in a sleeper due to the passage of a group of adjacent axles; FIG. 6 shows the bending moments a sleeper might be subjected to for CASE A;

FIG. 7 shows the bending moments a sleeper might be subjected to for CASE B; FIG. 8 is a diagram of the stress ranges that might correspond to the bending moment ranges of FIG. 6;

FIG. 9 is a diagram of the moments used to calculate the stress ranges for the lower 75% of loads;

FIG. 10 is a diagram representing the fraction of a load carried by a sleeper, at a distance from the load; and

FIGS. 11A to 11F represent a table of fatigue results for the intervals between DIF = 1 and the DIF = ultimate.

DETAILED DESCRIPTION OF THE PREFFERED EMBODIMENT

An embodiment, by way of example only, of a method of designing a sleeper is described below.

The sleeper that is to be designed must cater for the following design criteria.

DESIGN CRITERIA

Rail Construction

Gauge: Broad

Sleeper Width: 260

Sleeper Depth: 130, 140 at rail seat

Rail Size: 50 kg

Sleeper Spacing: 670

Rollingstock:

Nominal Axle Load (PA): 128 kN

Axle spacing on bogie (b): 2.6m

Axle spacing over Coupler (c): 5.3m

Axles/Car: 4

Cars/Train: 5

Trains per year: 36000

Design life (years) 50

Total number of load cycles = 36000 x 5 x 4 x 50 = 36 x 10⁶ LOADING SPECTRUM

Measurements of actual wheel loads from trains were taken over a period of time at a typical location on the railway track for which the sleepers are to be designed. These measurements were then used to calculate a range of dynamic impact factors (DIF) using the follow formula:

DIF = Measured Wheel Load/Nominal Wheel Load

Hence, the dynamic impact factor (DIF) is applied to the nominal wheel or axle load to get the actual wheel or axle load. The probability of a measured dynamic impact factor exceeding any particular dynamic impact factor was also calculated from measured loads.

The probability of exceedence Vs the dynamic impact factors was then plotted on a graph show in FIG. 1. A line representing a conservative analysis of the probability of exceedence Vs the dynamic impact factors was then drawn to represent the loading spectrum.

Referring to FIG. 2 (a simplified version of the loading spectrum of FIG. 1), the loading spectrum is represented by, the straight line which approximates the test results. These are plotted as log (b) Vs DIF where b is the probability of exceedence and DIF is the Dynamic Impact Factor. The straight line is defined by the constant A and B which can be determined from DIFι which gives b of 1.0, and DIF.₀₀₁ which gives a b of 0.001.

Accordingly we have Log (b) = A.DIF + B

^ p = 10 ^{(A DIF + B)}

To find the number of cycles in a range from DIFi to DIFJ: ny = (tj(DIF_j) - p(DIFi)) x n_τ where n_τ is the total number of cycles. SLEEPER PROPERTIES

A sleeper design is then chosen that is thought to have suitable stress and bending moment properties. These properties are usually calculated using cross-section response software that is readily available to a person skilled in the art.

For this example, FIG. 3 shows a table indicating tendon stress and concrete stress at various bending moments of the trial concrete sleeper design (Low Profile Sleeper 260 wide, 866 Strands) that was thought to have suitable properties to satisfy the design requirements. In particular bending capacity at a rail seat of the sleeper and the maximum tendon stresses and concrete stresses for a range of bending moments between 0 and ultimate were determined. Also the reliable ultimate bending capacity (Φ M_u) was calculated to be 22.6 kNm. LOAD DISTRIBUTION

The rail construction controls the load distribution. That is, the bending moment each sleeper sees when an axle of a known load passes over it.

If the moment in the sleeper immediately below the load (M₀) is known, as well as what fraction of the total load is carried by that sleeper (DF₀), then the curve, shown in FIG. 4, can be approximated by assuming the curve shape is similar to that obtained from a classical beam on elastic foundation solution.

Hence, using finite element analysis for this rail construction, the following results were obtained for a nominal load of P₀ = 100 kN (wheel load):

Mo = 5.36 kNm

DFo = 0.469

The values for M₀ and DF₀ are determined by a finite element analysis. However, it should be appreciated that as solutions for more track configurations are obtained it will be possible to interpolate values for M₀ and DF₀ from previous solutions. CHECK ULTIMATE LOAD

The ultimate load is defined as having a probability of exceedence of 5% over the life of the sleeper.

Hence, if JD_Uι is the probability of exceedence of the ultimate load in one cycle (as yet unknown) and n is the number of cycles in the sleeper design life, then

0.05=1-(1 -t⁾ _u„)ⁿ which gives

|D_Uιt= 1.0- 0.95 ⁽¹ⁿ⁾ when p_U|_t is known, the load spectrum can be used to find the ultimate Dynamic Impact Factor (DIF_Uιt) which has a probability of exceedence of b_uι_t. This is applied to the nominal wheel load to give the ultimate wheel load.

For the above example: n = 36x10⁶

= 1.425 x10^"9

Load spectrum:

Log (p) = A.DIF + B log( „)-B ₌₆₁₆₀

DIF_U„ = A

Hence, ultimate axle load:

where

P ^: nominal wheel load

^: 0.5 P_A

= 64kN

Hence: urt = 6.16x64kN = 394 kN Ultimate bending moment at rail seat:

P..

M // ult = M₀x ^■ a

P₀ 394

= 5.36 x

100

M_uι_t =21.1 kNm Sleeper bending capacity at rail seat (from sleeper properties) = 22.6 kNm Therefore, the sleeper that has been chosen will withstand the theoretical ultimate bending moment. FATIGUE ASSESSMENT

The bending moment and stress ranges in a sleeper due to the passage of a group of axles (consisting of two axles on a bogie at the end of one vehicle followed by two axles on a bogie at the start of the next vehicle) is considered. This is because these axles are generally close enough together so that a sleeper receives load from more than one axle. A representation of this is shown in FIG. 5. The loads applied to a sleeper range vary widely according to the dynamic impact spectrum. The distribution of the very high loads among the lower loads will also affect the fatigue life. Consider the following two cases:

Each case has 4 axle groups (each with 4 axles), 4 very high loads, and 12 lower loads.

CASE A. One very high load/axle group as shown in FIG. 6

CASE B. Four very high loads in one group, and four lower loads in three more groups show in FIG. 7.

The fatigue damage due to a cycle of load stress is proportional to the load range raised to some power, i.e. Damage = KΔM^m m varies according to the material. As a minimum m = 3, but is often much higher. Hence a large load range can do much more damage than many smaller ranges. It is likely that Case A above will result in more fatigue damage than Case B. To investigate this, assume some relative magnitudes for the moment ranges shown in FIG. 6 and FIG. 7. Let Δ M_E = 2 Δ M_n

Δ MBE = 0.5 Δ ME, Δ MBN = .5 Δ MN Δ MCE = 0.6 Δ Mc, Δ M_CN = .6 Δ M_N The damage due to N_a cycles of Δ M_a, say, can be expressed as a number of cycles NE of M_a which will cause equivalent fatigue damage:

N_aΔM_a ^m = N_E Δ M_E ^m

For Case A, express the total damage as an equivalent number of cycles of ΔME- Use m=3.

Cycles Range Equiv. Cycles of Δ M_E

4 Δ M_E

8 Δ MEN .125 8 x ( .25)³ 4 Δ MCN .108 4 x (0.30)³

Total Equivalent Cycles: 4.233

Similarly for Case B

#Cycles Range Equiv. Cycles of Δ ME

1 Δ M_E 1.0

2 Δ MBN .25 2 X .5³

3 Δ M .375 3 X .5³

6 Δ MBN .094 6 X .25³

3 Δ MCN 0.81 3 X .3³

Total Equivalent Cycles: 2.016

Clearly, Case A results in more fatigue damage (4.23 cycles of ΔM_E) than Case B (2.02 cycles of ΔM_E).

Hence, as a worst case, it is assumed that the highest 25% of the loads in the spectrum are distributed so that there is one in each axle group. The other 3 axles in each group are drawn from the lower 75% of the loads in the spectrum. This stress range is represented by FIG. 8.

Hence, for the upper 25% of the loads, the full stress cycle (Δf_fun) is considered. For the lower 75% of the loads the stress range between wheels on a bogie (Δf_D) is considered for 2/3 of the instances, and the stress range for wheels on either side of a coupler (Δf_c) for one- third of the instances.

Note, if the axle spacing on the bogie or across the coupler gets large, then these Δf_D and Δf_c become full cycles. In this case, a full cycle of load for each axle is effectively considered.

The bending moments in the sleeper are calculated as shown in FIG. 9. The stress range Δf is calculated from: Δf_b = f due to Mi - f due to M_b and Δf_c = f due to M₂ - f due to M_c

The load distribution (as defined by M₀, DF₀) and the wheel spacing allow this to be achieved. To achieve this the distribution factors at various distances from a load are calculated. These give the fraction of the entire load carried by a sleeper at a distance from the load. This is represented by FIG. 10.

Hence, the moment under the first axle Mi is

DF₀ + DF{b) P _nττ,

M = — °- — χ M_n χ — x DIF

DF₀ P₀ where DIF is the dynamic impact factor from the load spectrum. P is the nominal wheel load = 0.5 PA.

P₀ is wheel load used in the FEA. M₀ is the sleeper moment from the FEA.

Similarly,

(DF₀ +DF{b)+DF{c)\ p M₂ = -^ — -^ xM₀ x — x DIF

DF₀ P₀

2xDF{^cΔ p

M_c = — x M x — x DIF

DF P

For the fatigue assessment all load cycles with loads less than or equal to the ultimate load are considered. The range of dynamic impact factors considered is from 1.0 to DIFULT- The full range of DIF is subdivided into smaller ranges for assessment. The fatigue damage in each small range is calculated by assuming the mean DIF for the range applies to all of the cycles in the range. The fatigue damage for each small range is then summed together to get the total fatigue damage. FATIGUE ASSESSMENT FOR THIS SLEEPER

The results of the fatigue assessment for this sleeper is shown in FIG. 11 with a summary of the design criteria and results shown in FIG. 12. Examples of how these fatigue results were obtained are shown below. The results of the fatigue assessment shown in the FIG. 11 were obtained in the same manner.

The range of DIF was divided into intervals. Note that the lower 75% of cycles are treated differently from the upper 25% for the reasons stated above. DIF _min = 1

DIF _Ui_t = 6.16

_ log (0.25) -B

DIF 75%

A

= 1.3512 Divide the range from 1 to 1.3512 into 5 intervals. (This is the lower 75% of all cycles.)

(1 → 1.070, 1.070 → 1.140, 1.140 → 1.211 , 1.211 -» 1.281 , 1.281 →1.351)

Divide the range from 1.351 to 6.16 0 into 20 intervals. (This is the upper 25% of all cycles.) (1.351 → 1.592, 1.592 → 1.832 etc)

Calculate the fatigue damage for each interval. Example for lower 75% intervals: Consider the range:

DIF = 1.211 to 1.281 Avg DIF for this range = 1.246.

Assume this applies to all cycles in this interval. Number of cycles in this interval: n_y = (b(DIFj) - KDIFi)) x n_T

= (b(1.281) - b(1.211)) x n_τ = _{(1 0}(AX1.281 ₊ B) _ _{1 0} (A 1.211 ₊ B)_)nτ

3.794 x 10⁶ cycles Two-thirds of these cycles are subject to stress range Δf_D. The stress range between when the first axle of a group crosses the sleeper and when the bogie is centred over the sleeper. This is equal to the stress due to

less the stress due to M_b.

One-third of these cycles are subject to stress range Δf_c. The stress range between when the second axle of a group crosses the sleeper and when the coupler is centred over the sleeper. This is equal to the stress due to M₂ less the stress due to M_c.

Hence, calculate Mi

DFo = 0.469

DF(b/2) = .0549

DF(b) = -.0167

DF(c/2 ) = -.0159

DF(c) = .00004 M₀ = 5.36kNm

Po = 100 kN

P 64 kN

DIF = DIF mean = 1.246

=> M = 4.122 kNm Interpolate, from the table shown in FIG 3, the structural response of sleeper to get tendon stress σ, and concrete stress at the top and bottom of the sleeper (fct_o , fcbtm) for this moment (Mi). We get σ , = 911.8 MPa fctopi = 14.39 MPa Similarly for M_b

M_b = 1.000 kNm σ_b = 903.7 MPa, f_cto_Pb = 10.62 Mpa Similarly for M₂

M₂ = 4.126 kNm σ₂ = 911.8 MPa, fc_to_P2= 14.39 MPa

Similarly for M_c

Mc = -0.289 kNm σ_c = 900.3 MPa, fdopc = 9.16 MPa

Calculate the stress ranges over the bogie (Δf_b) and over the coupler (Δf_c). Over the bogie: For tendons

Δ σ_b = σ ι - θb = 8.1 MPa For concrete

A simple stress range is not used in assessing concrete fatigue. Record maximum and minimum stresses. fcmax_b = 14.39 MPa,

= 10.62 MPa

Over the coupler: For tendons

Δ σ_c = σ₂ - σ_c = 11.5 MPa For concrete fcmaxc = 14.39 MPa, fcmmc = 9.06 MPa.

Calculate the fraction of the total fatigue life of the tendons that is used up by the cycles in this DIF interval. In this example this is done using the provisions of the European code, however other codes or recognised methods could be used. At a stress range of øΔσ*, 1 x 10⁶ cycles constitutes the full fatigue life.

Calculate the number of cycles øΔσ* which causes equivalent fatigue damage to: ^ of 3.794 x 10⁶ cycles at Δσ = 8.1 MPa

V. of 3.794 x 10⁶ cycles at Δσ = 11.5 MPa

'3

For Δσ < 0Δσ *, m = 9

N eq

= ²/ '3 x 3.794 x lO⁶ x

From the code use Δσ * = 120 for this design, and 0 = .79 Hence, N_eq = .00766 cycles

The full fatigue life at Δσ* is 1 x 10⁶ cycles. Therefore, the fraction of fatigue life used this DIF interval = 7.66 x 10 ^-9 Calculate the fraction of the total fatigue life for the concrete that is used up by the cycles in this interval.

Using the European code, concrete fatigue requirements: Over bogie: fcmax = 14.39 MPa, fcm_in = 10.62 MPa The code gives the full fatigue life for this stress range to be:

N_b = 8.1 x 10¹²² cycles Over coupler: fcmax = 14.39 MPa, fcmin = 9.06 MPa The code gives the full fatigue life for this stress range to be: N_c = 1.6 x 10¹⁵³ cycles

Fraction of fatigue life used in this interval is:

/ %3 x 3.794 x 10⁶ ₊ / 3 _xx 33.779944 _{x 1}1₀0⁶ _{χ 10}__U7

8.1 x lO¹²² 1.6 x lO¹⁵⁸

In summary, in this DIF interval 7.66 x 10^"9 of the tendon fatigue life was used and 3.1 x 10^"117 of the concrete fatigue life was used. Example for upper 25% intervals Consider the range:

DIF = 5.198 to 5.439 Avg DIF = 5.319

Number of cycles in interval = 1.400 The stress range considered for the upper 25% intervals is from the no load condition to the maximum load when the wheel is above the sleeper.

Sleeper moment when wheel above sleeper. Total moment under peak wheel

Mp = Mo x DIF x — + Mo x D\F₇₅ ^Q _B ^DF^ ^{+ DF{C)} X —

P₀ DF₀ P₀ = (5_C.3i1n9 , + _Λ 1.3_c5-1 x (0.0+.0004) -x 5 _.3.6,χ — 64

0.469 100

18.25 kNm Hence the stress ranges are between M = 0 and M = 18.25 kNm. Interpolate from structural response table in FIG. 3. M = 0 M = 18.25

Tendon σ 901.1 MPa 1011.5 MPa

Concrete f_dop 9.41 MPa 38.74 Mpa Hence,

Δ σ = 110.4 MPa Calculate faction of total fatigue life used up by cycles in this interval. Tendons

(110.4)"

N_eq = 1.4 χ - — ^'—^L- m = 5 since 110.4 > øΔ σ øΔσ^:

N_eq = 3.00

Fraction of total fatigue life = 3/(1 x 10°)= 3 x 10 Concrete fcmax = 38.74 fcmin = 9.41

Code gives total life for this range as 55.06 cycles Fraction of fatigue life for this interval is

— = 0.0254

55.6

Calculate the total fatigue damage.

The fatigue damage to the tendons and concrete in each interval is summed:

The total fraction of tendon fatigue life used is 1.9 x 10^"5. Since this is less than 1.0 the tendons can be expected to not fail due to fatigue over the design life.

The total fraction of the concrete fatigue life used is 6.1 according to the provisions of the European code. Hence, according to this code, the concrete would fail from fatigue before reaching the end of the sleepers design life. Alternative methods to the European code can be used to assess that fatigue life of tendons and concrete subjected to known stress ranges.

The provisions in the European code for fatigue in concrete have been found to be over conservative for low numbers of cycles at very high stresses and hence, unsuitable in their current form to this application as stress cycles up to the ultimate moment are considered.

Modifications have been made to the equations in the European code to allow higher stress ranges at low numbers of cycles. Tests have been conducted to verify that the modified provisions are safe.

When assessed according to the modified provisions of total fraction of the concrete fatigue life used is 0.036. Hence, the concrete is not expected to fail in fatigue over the design life of the sleeper.

The above method of design of a concrete sleeper provides a rational design approach for low profile concrete sleepers than may be used to replace timber sleepers. The design method considers the entire load spectrum rather than a nominal design; considers local distribution; considers fatigue in concrete and in steel; considers ultimate capacity, and considers durability. In this manner, a concrete sleeper can be designed that is unlikely to fail but meets the physical constraints.

It should be appreciated that various other changes and modifications may be made to the example described without departing from the spirit or scope of the invention.

Claims

CLAIMS:

1. A method of designing a concrete sleeper, the method including the steps of: determining a loading spectrum for a length of railway track; choosing a trial sleeper design having known structural properties including bending capacity at a rail seat and the tendon and concrete stresses for a range of bending moments; determining a load distribution for the railway track including calculating a bending moment in the sleeper for a predetermined load at a known distance from the sleeper; calculating an ultimate load based on the loading spectrum; comparing the ultimate load with the bending capacity at the rail seat for the sleeper; determining fatigue life of the sleeper based on the loading spectrum, load distribution, and tendon and concrete stresses; comparing the calculated fatigue life of the sleeper with predetermined safe fatigue life values.

2 The method of claim 1 wherein the loading spectrum is obtained by measuring a multiplicity of discrete loads at a location on the railway track.

3. The method of claim 1 wherein the dynamic impact factors are calculated from the measured discrete loads when comparing the measured loads with a predetermined notional load.

4. The method of claim 1 wherein the probability of exceedence of any load is calculated from the measured discrete loads.

5. The method of claim 1 wherein the loading spectrum is obtained by plotting the probability of exceedence Vs the dynamic impact factors and drawing a curve which represents an upper boundary for the plot.

6. The method of claim 1 wherein the loading spectrum is obtained by taking previous measurements from another railway track and applying them to a similar railway track.

7. The method of claim 1 wherein the trial sleeper design is chosen based on the structural properties of the sleeper.

8. The method of claim 7 wherein the sleeper design is chosen with the high resistance to stress within the dimensional constraints.

9. The method of claim 1 wherein the bending capacity at a rail seat and the tendon and concrete stresses for a range of bending moments is calculated using standard engineering methods.

10. The method of claim 9 wherein the stress is calculated for bending moments at regular intervals from 0 to the ultimate bending capacity.

11. The method of claim 1 wherein the load distribution is obtained through the use of finite element analysis.

12. The method of claim 1 wherein the load distribution is interpolated from previous finite element analyses.

13. The method of claim 1 wherein the ultimate load is obtained by calculating an ultimate dynamic impact factor for a predetermined probability of exceedence over the life of the sleeper.

14. The method of claim 1 wherein the fatigue life of the sleeper takes into consideration a group of axles.

15. The method of claim 14 wherein the group of axles consists of two axles on a bogie at one end of the vehicle followed by two axles on a bogie at the start of the next vehicle.

16. The method of claim 1 wherein the fatigue life of the sleeper is determined using the loading spectrum.

17. The method of claim 1 wherein the entire range of dynamic impact factors is considered.

18. The method of claim 17 wherein the dynamic impact factors are divided into a number of intervals to calculate a fraction of the fatigue life for each of the intervals.

19. The method of claim 18 wherein the fraction of the fatigue life is calculated differently between high loads and low loads.

20. The method of claim 19 wherein the high loads are considered in the top 25% whilst the low loads are in the bottom 75%.