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									                     STANDARDS AND TESTS OF FASTENING SYSTEMS

                            Michael Steidl, Director Technical Services

 Vossloh Fastening Systems America Corporation, 233 S. Wacker Drive Suite 9730, Chicago, IL

                                             60606, USA

                                        Phone: 312.376.3205


The calculation method of Zimmermann, improved by Eisenmann, and based on Winkler

determines the forces and deflections which occur in a single supported track loaded by trains.

The idea of this method is to transform the single supported beam by converting the bearing area

into a continuously supported beam.

The tie is supported in the ballast on an area A at both ends of the tie. A support less center

section in the middle of the tie is shown with the length m (figure 1).

The bearing areas A = (l-m) x b1 / 2 are transformed by connecting the support areas of the

adjacent ties to achieve a theoretical continuously supported rail. The length of the transformed

area is following the tie spacing a. The new width of the bearing area is therefore b = A / a.

Figure 1: Principle of Zimmermann calculation
The stiffness of ballast is defined by the elastic modulus C with the unit lb/inch3. This means a

spring rate in lb/inch per support area in inch2. By using the above mentioned support area A the

spring rate can be calculated. Additionally the spring rate of rail pads c can be considered. The

over-all spring rate is calculated in following manner:

c=            , whereas c1, c2 … are the spring rates of the different components like ballast,
     1 1 1
       + +
     c1 c2 c3

tie and rail pad.

                                                                P⋅a                   4⋅E ⋅ I ⋅a
The deflection of the rail can then be calculated with    w=          , whereas L = 4
                                                               2⋅c⋅ L                    c

The force on the rail seat F is calculated with F = c ⋅ w .

The dynamic influences are included by increasing the static wheel load by following factors.

Based on a free centrifugal acceleration of aq = 0.85m/s2 the vertical loads in curves are modified

by an addition (high rail) or reduction (low rail) of 20% to the static wheel load.

This leads to effective P = P ± ∆P = (1 ± 0.2) * P

The track quality, type of train, speed and probability of failure are included by following formula:

Max P = effective P * (1 + s * n * ϕ), which gives the maximum dynamic wheel under

consideration of following parameters:

•    probability of failure:      16%:     factor s = 1.0

                                  2.5%:    factor s = 1.65

                                  0.15%: factor s = 3
•   factor for description of track quality: n = 0,10 to 0,25 for very good to bad

•   speed coefficient: ϕ

           Passenger train: ϕ = 1 + (v – 60) / 236

           Freight train: ϕ = 1 + (v – 60) / 99

For simplification only the forces and deflections under the wheel are considered for the

calculations here. It is done without showing the deflection curve along the whole rail which is

also possible


This method uses the same idea as the calculation according Zimmermann based on Winkler and

it was described by Kerr in “Fundamentals of Railway Track Engineering” (1). In North America a

k-value is used to describe the stiffness of the whole superstructure. This value is determined in

the track and mirrors the stiffness of the whole superstructure including rail, rail pad, tie and


The rail deflection w under the wheel is calculated with following formula:

           P⋅β   P 4  k                        k
wmax =         =   ⋅        , whereas β = 4
           2⋅k 2⋅k 4⋅ E ⋅ I                 4⋅ E ⋅ I

The load per rail seat is then: Fmax =         ⋅a
The dynamic effects are included by following formula:      Pdyn = (1+Θ) * Pstatic

                           Speed[mp / h]             v
Whereas      Θ = 0.33 ⋅                     = 0.33 ⋅
                          Wheeldiameter[in]          D

In comparison to the above mentioned calculation methods the determination of the force per rail

seat according AREMA (4) is done by using tables.

AREMA defines an impact factor IF which reflects dynamic influences and influences due to track

and rolling stock quality. The distribution factor DF mirrors the tie spacing having one of the most


                                                                              IF   DF
The load per rail seat is then calculated as follows: F = P ⋅ 1 +                ⋅
                                                                       ⎡          ⎛ ⎤         ⎞
                                                                                  ⎜ ⎥         ⎟
                                                                       ⎣     100 100
                                                                                  ⎝ ⎦         ⎠


To demonstrate the difference and the compliance of the North American method and the

European the following table 1 is given. The calculations are based on a 39ton axle load.

  North America (Kerr)                   AREMA                                Europe (Zimmermann, Eisenmann)

                                                 Wheel load P = 40,000lb

                                                       Rail section: 136RE

                                                       tie spacing a = 24”

Track stiffness k = 6,000   Impact Factor IF = 200%                Cballast ~ 340lb/inch3         Curve? = Yes

Speed n = 60 mph            Distribution Factor DF = 50.4          crail pad = 1,450kips/inch     Track quality = good

Wheel diameter D = 36”      Distance from neutral axis to          Support less area m = 16.9”    Speed = 60 mph

                            outer edge of base c = 3.4”            length = 8’-6”                 Type of train = freight

                                                                   Tie width = 11’                Confidence level = 95%

Fstatic, max = 12.9 kips    Fstatic, max = 20.0 kips               Fstatic, max = 12.9 kips
Fdyn, max = 20.0 kips      Fdyn, max = 60.0 kips           Fdyn, max = 20.5 kips

w = 0.14”                  w = not calculated              w = 0.14”

Table 1: Example calculations of the different methods

The comparison shows that the North American and the European methods provide almost the

same results. The determination according AREMA provides a much higher force than both other

methods. The dynamic force is here with 60.0 kips three times higher than the 20.5 kips

according the European method. AREMA requires higher safety values which is considered in the

very high impact factor. This is certainly due to the necessity of high and safe values for the

design of track components. The other two calculation method should more provide the actual

loads and deflections.

The North American method has the advantage that it requires only a few input values and

provides a quick calculation; however it does not offer the same flexibility as the European


The European method enables the engineer to consider the influence of different rail pad

stiffness, and consideration of dynamic stiffness can be observed.

Compression of the rail pad can be described which enables a better forecast of the clip life by

comparing the performance range or fatigue limit of the clip with the calculated rail pad deflection.

Therewith the possible use of elastic rail pads can be studied as elastic rail pads offer different

advantages like:

    •    reduced effects of the imperfections between wheel and rail (2)

    •    Protection of the ballast by damping the impacts on the ballast and balance of rail waves.

         Also by reducing the load per rail seat

    •    Protection of the rolling stock

    •    Reducing periodic stimulation (secondary deflection)

    •    A positive effect on the resistance against rail seat abrasion has to researched
The ratio between vertical deflection y and secondary deflection δ (figure 2), should be not more

than δ/y = 3-4%. (3) Otherwise it can lead to increasing of corrugation.

Figure 2: Secondary deflection

A stiffness of lower than 500kips/inch is here considered as an elastic rail pad.

The improvement and development of fastening system can be supported by using the more

comprehensive but also more flexible European method. But to emphasize again the North

American method is a quicker and handier method.


The fastening systems in North America have to be tested according AREMA Chapter 30 – Ties

(4). In Europe the fastening systems are tested according EN 13481-8 and EN 13146. EN 13481-

8 (5) describes the requirements and EN 13146 (6) how the different tests are performed.

In the following the repeated load test, longitudinal rail restraint and torsional resistance test,

determination of clamping force and stiffness of rail pad, insert test and test of electrical

resistance are described and compared.

Both standards require further tests, but these tests are not considered here for comparison as

they are not given in both standards or are anyway performed in a similar way. But for the test of

the torsional resistance an exception is made.

Repeated Load Test

The repeated load test is performed for both standards. The European standard draws here

distinctions regarding the stiffness of the rail pad whereas AREMA makes not this differentiation.
The European standard covers axle loads of 38.5tons whereas the test parameters are based on

axle loads of 33tons and 8.7° curves.

The following table 2 shows the comparison of the test parameters:

Table 2: Comparison of test paramaters of EN 13481-8 and AREMA Chapter 30 – Ties

Assuming a 33ton axle load the calculation according Zimmermann results in a dynamic vertical

load of 17.3 kips for medium soft rail pads. This corresponds well with the 17.2kips in the


The European standard considers higher lateral loads, whereas AREMA applies higher vertical

loads. The higher lateral forces are enforced by the demand that the rail section has to be cut

according figure 3 and accordingly loaded at this point.

Figure 3: Loading point according EN 13481-8

Another difference is that AREMA requires additionally an up-lift force between the load cycles.

This reflects the loading in the track as the rail can be pushed to both sides and following more

movement occurs on the rail seat.
The new additional repeated load test according AREMA detects the resistance against rail seat

abrasion. Both rail seats of one tie are loaded with a loading frame, which was originally

developed by the Technical University of Munich. A vertical load of 32.5 kips and lateral load of

16.9 kips are applied on every rail seat. Figure 4 shows the loading device with the spring

between the rails.

Figure 4: Test rig for repeated load test

The rails are pulled back in the original position after every loading by a spring between the two

rails. This higher movements and an applied sand water mixture enable to make forecasts about

the resistance against rail seat abrasion. The test is additionally performed at high and low


Longitudinal Load Restraint

The test of the longitudinal restraint is performed for both standards, whereas AREMA gives a

specific load at which the certain requirements have to be fulfilled. The European standard is

searching for the load at which the rail slips through fastening system.

AREMA demands that the fastening system is loaded with a force of 2.4 kip and hold for 15

minutes. The initial deflection must be lower than 0.2 inch. After the first 3 minutes further

deflections must be lower than 0.01 inch (figure 5).

The European standard requires a load higher than 2 kips before the rail slips through the

fastening system. This load is read at the point D3 = D1 – D2 (figure 6). Additionally the difference

of the creep resistance before and after the repeated load test shall be lower than 20%.
Figure 5: longitudinal rail restraint according AREMA

Figure 6: longitudinal rail restraint according EN 13146-1

Torsional Resistance

The torsional resistance is important for resistance against track buckling. When the track panel

is moving horizontally the rail is rotating on the rail seat (figure 7). An increased resistance

against rotation leads to a higher moment of inertia of the track panel and following to a higher

resistance against track buckling.

The torsional resistance is performed only for the European standard. The rail is loaded to rotate

on the rail seat and the accordant resistance at a rotation of1.5° is recorded (figure 8)

Figure 7: Track buckling                            Figure 8: Principle of torsional resistance test
Determination Of Clamping Force

Both standards determine the force which is necessary to separate the rail from the rail pad in a

similar way.

The European standard requires that the change of the clamping force between before and after

the repeated load test is not higher than 20%

According AREMA the up-lift test is performed again after the repeated load test to ensure that

dynamic did not influence the toe load.

Testing Stiffness Of Rail Pad

According AREMA the pad is loaded with a force of 50kips and the stiffness is determined

between 24 and 44 kips. This test is performed two times with two different rail pads.

Following 3 requirements have to be fulfilled:

    •   The pad has to return to within 0.002” within 10seconds after load release

    •   The stiffness shall not vary more than 25% between the two rail pads

    •   The difference of stiffness between before and after the repeated load test shall be not

        more than 25%

According EN 13481-8 the fastened rail is loaded vertically with 19.1 kips 5 times. The stiffness is

determined between 1.1 and 18 kips. The change of stiffness between before and after the test

shall not be more than 25%

Insert Test

Both standards require similar performance of the test for cast in components

AREMA requires withstanding a pull out force of 12kips for 3 minutes. EN 13481-8 postulates to

withstand 13.5 kips again for 3 minutes without any cracking
Electrical resistance

The electrical resistance according AREMA is determined between two short lengths of rail. The

tie with the assembled fastener is watered for 6 h. Within the following hour a current of 10Volt

and 60 Hz is applied between the two rails for 15 minutes. The electrical resistance is recorded

and the lowest value shall be higher than 20 kW.

In contrast to AREMA the European standard attaches more importance to traceability and

following the conductivity of the water is checked. The electrical resistance is also measured

between two rails.

The tie has to be dry before starting the test. Detailed described spray nozzles spray water at a

rate of 7±1 l/min for each nozzle for 2 minutes onto the tie and fastener. During spraying and the

following 10 minutes a current supply of 30V and 50Hz is applied (figure 9).

The electrical resistance is determined considering the conductivity of the water. This shall be

between 20 and 80 mS/m. The measured electrical resistance is then converted to an electrical

resistance R33 based on a conductivity of 33mS/m. So it is possible to compare results of different

laboratories and of different fastening systems. This provides a better Traceability.

Figure 9: Test set-up electrical resistance test
Notation and Units

A      bearing area of a tie

l      length of tie

m      length if supportless bearing area of tie

b1     width of tie

c      stiffness (lb/inch)

w      vertical rail deflection (inch)

P      wheel load (kips)

a      tie spacing (inch)

E      elastic modulus rail (lb/inch2)
I      moment of inertia (inch )

L      elastic length of rail

n      factor for description of track quality

s      probability of failure factor

ϕ      speed coefficient

v      speed (mph)

D      wheel diameter (inch)

IF     impact factor

DF     distribution factor

α      loading angle

(1)    Kerr, Arnold D.; Fundamentals of Railway Track Engineering; Simmons-Boardman Book,

       Inc; November 3003

(2)    Leykauf, G. ; Stahl, W. : Anforderungen an moderne Schienenbefestigungen

       Prüfung nach DIN EN 13146 bzw. DIN EN 13481. Eisenbahningenieurkalender 2007, S.

       289 - 300

(3)    Josef Eisenmann, Stuetzpunktelastizitaet bei einer Festen Eisenbahn. ZEV + DET Glas.

       Ann. 123 (1999) 11/12 November/Dezember

(4)    AREMA – Chapter 30 – Ties

(5)    Railway applications – Track – Performance requirements for fastening systems

       EN 13481 – 8 Fastening systems for track with heavy axle loads

(6)    Railway applications – Track –Test methods for fastening systems

       EN13146-1 – Part 1 Determination of longitudinal rail restraint

       EN13146-2 – Part 2 Determination of torsional resistance

       EN13146-4 – Part 4 Effect of repeated load test

       EN13146-5 – Part 5 Determination of electrical resistance

       EN13146-7 – Part 7 Determination of clamping force

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