Research Article Nonlinear Finite Element Modelling of ...

Research ArticleNonlinear Finite Element Modelling of Railway TurnoutSystem considering BearerSleeper-Ballast Interaction

James Sae Siew12 Olivia Mirza2 and Sakdirat Kaewunruen3

1 JKW Engineering Penrith NSW 2057 Australia2School of Civil Engineering University of Western Sydney Penrith NSW 2057 Australia3Birmingham Centre for Railway Research and Education School of Civil EngineeringThe University of Birmingham Edgbaston Birmingham B15 2TT UK

Correspondence should be addressed to Sakdirat Kaewunruen sakdirathotmailcom

Received 11 September 2014 Accepted 17 February 2015

Academic Editor Lucio Nobile

Copyright copy 2015 James Sae Siew et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Rail turnouts are built to enable flexibility in the rail network as they allow for vehicles to switch between various tracks thereforemaximizing the utilisation of existing rail infrastructure In general railway turnouts are a safety-critical and expensive feature toa rail system as they suffer aggressive operational loads in comparison to a plain rail track and thus require frequent monitoringand maintenance In practice great consideration is given to the dynamic interaction between the turnouts components as a failedcomponent may have adverse effects on the performance of neighbouring components This paper presents a nonlinear 3D finiteelement (FE)model taking into account the nonlinearities ofmaterials in order to evaluate the interaction and behaviour of turnoutcomponents Using ABAQUS the finite element model was developed to simulate standard concrete bearers with 60 kgm rail andwith a tangential turnout radius of 250mThe turnout structure is supported by a ballast layer which is represented by a nonlinearlydeformable tensionless solid The numerical studies firstly demonstrate the importance of load transfer mechanisms in the failuremodes of the turnout componentsThe outcome will lead to a better design andmaintenance of railway turnouts improving publicsafety and operational reliability

1 Introduction

Rail operators are considerably demanded by the public andother stakeholders to be more efficient than ever As a resultthe maximisation of utilisation and flexibility of rail networkis one of the key strategies in rail asset management Arailway turnout is a critical part of the railway where trackscross over one another at an angle to divert a train from theoriginal track It allows for train vehicles to cross over orswitch between various tracks and in turn maximising theutility of tracks and assets Its main components include railsswitches crossings steel plates bearers ballast and subgrade(as shown in Figure 1) The rail turnouts are an essential partof a rail system but at the same time they are a costly featureto a rail system as they suffer adverse operational loads incomparison to a plain rail track and require frequent mainte-nance Due to the particular geometry of wheel-rail contactand sudden variation of track flexibility severe impact loads

may occur during train passage over the turnout Turnoutcomponents are subjected to general wear rolling contactfatigue and accumulated irreversible (plastic) deformations[1 2]

Railway track structures experience static dynamic andoften impact loading conditions due to wheelrail interac-tions associated with the abnormalities in either a wheel ora rail over their life cycle [3 4] Specially at turnouts crossingthe wheel-rail interaction at the transfer zone often causesdetrimental impact forces and excessive dynamic actions [5ndash7] Many studies showed that it is very likely that railroadturnout bearers or crossties could be subjected to severeimpact loads resulting in a rapid deterioration in terms ofstructural integrity and durability track settlement and ridecomfort [8ndash10] Traditional turnouts generally impart highimpact forces on to structuralmembers because of their bluntgeometry and the gaps between mechanical connectionsbetween closure rails and switch rails (ie heel-block joints)

Hindawi Publishing CorporationJournal of StructuresVolume 2015 Article ID 598562 11 pageshttpdxdoiorg1011552015598562

2 Journal of Structures

Closure rails

Bearers

Heel block

Rail brace

Checkrail unit Crossing

Plates

Studsswitch stops

Stock rails

Switches

Figure 1 Typical components of a railway turnout

linear elastic range

Upper yield peak

Plastic plateau

Strain hardening portion

Actual behaviour

Elastic-perfectly plastic approximation

E

120590y

120576

120590

Figure 2 Stress-strain relationship of structural steel [30]

Although a new smoother method of geometrical analysisand tangential design to improve wheelrail navigations hasbeen adopted for turnouts the transfer zone at a crossing nosein any complex turnout system still generates high-intensityimpact forces to turnout components Generally the turnoutbearers for supporting points and crossing structures weredesigned using the beam on elastic foundation analysis or 2DFE grillage modelling [11 12] Kaewunruen [13 14] indicatedfrom recent work that some additional factors were oftenneglected from the grillage analyses although they must betaken into account in the design process including

(i) extra length of turnout bearers in comparison withstandard sleepers

(ii) centrifugal forces through curved pairs of rails

(iii) forces and bending moments induced from pointsmotors and other signaling equipment

(iv) impact forces induced by wheel-rail interaction

(v) mechanical rail joints

40

35

30

25

20

15

10

5

0

minus5

Stre

ss (N

mm

2)

minus0002 minus0001 0 0001 0002 0003 0004 0005

Strain

Figure 3 Stress-strain relationship of concrete [30]

On this ground this numerical study was initiated bya recent number of reportedly broken concrete bearers ona mixed-traffic line in New South Wales (NSW) AustraliaDue to the complexity of the loadings and damage modesin railway turnouts this study aims to establish a three-dimensional (3D) finite-element (FE) model The 3D FEmodel adopts an elastoplastic region of bending and sheardeformation of materials The 3D FE model was developedbased upon a common tangential turnout used in AustraliaThis study indicates that the crossing panel is where turnoutbearers experience the greatest bending moment and shearforce and it provides the critical force envelopes for designimprovement of turnout bearers

2 Finite Element (FE) Modelling

Railway turnout systems have generally been analysed using agrillage beammethod (Manalo et al 2010) [12 15] Althoughthe simplification is useful such a method cannot adequatelyassist in the failure analyses of turnout components In somecases the results using the grillage beam method seem tohave discrepancies with the field observations where themaximum bending and shear forces were evident within thecrossing panel [16ndash19] A number of researches have beenconducted to locate the critical section within a turnout andmany of which conclude that the critical section is locatedspecifically at the crossing panel [20ndash23]

This paper presents a nonlinear 3D FE analysis usingABAQUS considering the whole turnout which comprisesbearers rail guard rails crossing nose rail pads baseplatesand guardrail support plates The benefits of modelling in3D space are to incorporate the effects of the neighbouringbearers and to take into consideration the longitudinal forcesof the continual rail The boundary conditions of the central3D model can be simulated enabling vibrations to radiatebeyond the model [24]

21 WheelRail Interface (W-R) A Practical Implication Ingeneral the surface conditions of the wheel and rail play acritical role in theW-R contact force in addition to geometricirregularities train speeds and type of track structure Thelarge contact force will accelerate the deterioration rate of

Journal of Structures 3

Vehicle Simulated locomotive

CouplerC

300kN 300kN 300kN 300kN

17m 17m 20m11m

360kN

(a) 300LA load case

Y

XZXZ

XZXZ

XZ

Y

ZX

XZ

Y

(b) Load steps 300LA coupled locomotive design loading on turnout (top) load step 2(middle) load step 36 and (bottom) load step 48

Figure 4 Railway traffic loads-axle loads

the turnout crossing Sun et al [25] provided an insightinto the potential sites for impact and fatigue damage asthe train wheel traverses through the nose of the crossingFirstly the wing rail fatigue damage is caused by contact fromthe far side of wheel Secondly the transition of the wheel

between the wing rail and nose causes a dipping movementThis is due to the tracking on the wing rail to an upwardmotion on the ramp of the nose resulting in fatigue damageGreater contact stress can be seen due to the acute contactarea in the crossing nose The British Railways Board [26]


X

Y

Z

(a) Tie constraint between rail and bearer

0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Sleeper

(b) Maximum recorded deflection at each bearer (midpoint)

Figure 5 Midpoint deflections of each bearer along the turnout

expressed that the permissible track forces in a low frequencyrange (or called 119875

2forces) for railway vehicles negotiating

a discontinuity in rail profile do not exceed 322 kN whilstoperating at their maximum design speed In Australia the1198752force is limited to 290 kN for locomotives on very good

track structure or otherwise must be less than 230 kNThe 1198752

force is calculated using the following formula

1198752= 119876 + (119860

119911sdot 119881119898sdot 119872 sdot 119862 sdot 119870) (1)

where

119872 = [119872V

119872V +119872119911]

05

119862 = [120587 sdot 119862119911

4 [119870119911(119872V +119872119911)]

05]

119870 = (119870119911sdot 119872V)05

(2)

the lesser of

119876 = 013119863 times 103

or 119876 = 125 times 103(3)

where 119863 is the wheel diameter (mm) 119876 is the maximumstatic wheel load (N) 119881

119898is the maximum normal operating

speed (ms) 119872V is the effective vertical unsprung mass perwheel (kg)119860

119911is total dip angle of vertical ramp discontinuity

(taken as 002 rad)119872119911is taken to be 245 kg as the effective

vertical rail mass per wheel 119862119911is taken to be 554 times 103Nm

as the effective vertical rail damping rate per wheel and 119870119911

is taken to be as 62 times 106Nm as the effective vertical railstiffness per wheel

In addition lateral resistance is usually designed toreinforce the structural integrity of the rail and turnoutConsiderations are only given to lateral force values sustainedfor distances of 2 metres or more Unless supported byappropriate technical justification vehicles attempting tonegotiate a lateral ramp discontinuity in track alignmentwhen travelling on a curve at maximum normal operating


X

Y

Z

X

Y

Z

XZ

(a) Bearer 47 (red) experiences the greatest deflection

0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Load stepminus00005

(b) Deflection response of bearer 47 at each load step

Figure 6 Displacement envelope of the bearer right underneath the crossing (number 47)

speed and at maximum cant deficiency without exceeding atotal lateral force level per axles of 71 kN should introducelateral action that can be calculated using the followingformula [26]

119884 = 119882 sdot 119860119889+ 119860119910sdot 119881119898[119872119906

119872119906+119872119910

]

05

sdot [119870119910sdot 119872119906]05

(4)

where 119884 is the lateral force per axle (N) 119882 is the staticaxle load (N) 119860

119889is the maximum normal operating cant

deficiency angle (rad)119881119898is the maximum normal operating

speed (ms)119872119906is the effective lateral unsprungmass per axle

(kg)119860119910is taken to be 00038 rad which is the angle of lateral

ramp discontinuity119872119910is taken as 170 kg and is the effective

lateral rail mass per wheel and119870119910is taken to be 25 times 106Nm

as the effective lateral rail stiffness per wheel Based on theseformulas the dynamic forces can be estimated for the designof turnout components

22 Turnout Components The FE model comprises entirely3D deformable solids straight and curved rail bearers ofvarying length and a ballast layer as the track support Thisstudy focuses on the behaviour of the bearer and ballast

therefore a suitably accurate rail seat load within a tangentialconfiguration is required for the analysis Steel rails weremodelled in 3D space to account for their cross-sectionalproperties the width of the contact patch between the wheeland rail the width of the rail web and the width of therail footing The rail and switch rail profiles were validatedagainst rail authorityrsquos specifications [27ndash29] Table 1 showsthe engineering properties of turnout structural componentsConcrete bearers have been modelled as rectangular blockswith dimensions nominated according to the specificationsvarying lengths between 25m to 75m according to theturnout design

The elastic modulus of steel rails and crossing is definedby the initial slope of the stress-strain relationship to theextent of the upper yield threshold as illustrated in Figure 2For concretematerial it is assumed that its initial compressivestress behaviour is to be linear given that it does not exceed041198911015840

119888[30] Beyond the linear threshold nonlinear stress is

expressed as a function of strain according to (5) A graphicalrepresentation of the stress-strain relationship of concrete isdepicted in Figure 3 Consider

1198911015840

119888 (5)


Table 1 Design properties of materials

Materials Elastic modulus (MPa) Compressive strength (MPa) Tensile strength (MPa)Concrete 38000 36ndash55 40ndash630Prestressing tendon 200000 mdash 1700Steel rails 205000 mdash mdash

000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm

Figure 7 Effect of mesh sizes on the deflection of the bearerunderneath the crossing nose (number 47)

where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)

The ballast layer is simulated as a hardening-soil (HS)model [31] This method is an advanced method in analysingthe mechanical behaviour in soil as it considers the plasticitytheory along with the effect of viscosity on the shear strainand a yield cap In this study the evaluation takes upon theapproach of simplifying the ballasted track support usingelastoplastic solid elements [22 32] A track support modulusof 50MPa is adopted to comply with the design requirementsand field data [27 28]

23 Constraints and Boundary Conditions A sensitivity anal-ysis has been undertaken for mesh sizes for each rail compo-nent As themesh sizes and thematerial densities are differentbetween the two tied objects a tie constraint is generatedto allow for ABAQUS to automatically optimise and refinethe interface mesh Tie constraints are applied to the rail andthe concrete bearers to represent the rail fasteners Instead offrictional interaction and the effect of submersed bearers in a

ballast layer the bearers are tied onto the underlying ballastlayer to greatly reduce computational effort As all membersare tied translational and rotational degrees of freedom willbe distributed throughout All tie constraints were takenas surface to surface as opposed to a simplified node tosurface as this allowed for uniform distribution between thetied components The interface between bearer or sleeperand ballast has been treated with contact surface elementswhere the bearers can lift freely as ballast is modelled usingtensionless solid elements [24]

A fixed boundary condition is applied to the bottommostsurface of the subballast to idealise the substructure and asymmetrical constraint is applied to the ends of the rail toidealise a continuous rail within the relevant plane in thiscase the 119911-axis The bearers are attached to other memberswith boundary constraints and they can deform freely withthe ballast bed Note that this model is currently limited tothe investigations of ballast layer up to track structures Toevaluate soil formation behaviour the model can be furtherextended to accommodate contact support conditions andsoil foundation layers

24 Load Conditions Loading configuration is in accordancewith Standards Australia [33] The design loads are depictedin Figure 4(a) which simulate the worst case loading con-figuration that can be exerted onto a rail track The FEmodel predicts the behaviour of the turnout by consideringmultiwheel impacts which would simulate in-service andcyclic loading and have been adapted as a set of concentratedloads negotiating the turnout to represent a moving coupledlocomotive (in order to form the worst case scenario for thedesign) The coupled locomotive is then simulated with four300 kN axle loads and a single 360 kN axle load 2 metersahead of the group

The above load set is applied to the model at 600mmincrement initially to coincide with turnout bearer spacingor referred to hereafter as load sets A total of 48 loadsteps (including model initiation) are modelled to generatethe overall movement of the locomotive negotiating theturnout When approaching the crossings the load step islater set at 50mm increment Figure 4(b) illustrates loadingconfigurations for particular steps

25 Validation The numerical model was previously cal-ibrated using the field measurement data [13 14 34 35]Alongwith an accurate resultant deflection the time requiredto compute the analysis is also significant in selecting anoptimum mesh size The typical aggregate size of ballastin practice is anywhere between 13mm and 65mm Aninitial analysis is carried out to determine the maximum


000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000

minus2000 Distance x (m)

(a) Shear force envelope of bearer 47 upon wheel impact

SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06

+2688e + 06minus2350e + 05minus3158e + 06minus6081e + 06minus9005e + 06minus1193e + 07

minus1485e + 07minus1777e + 07

X

Y

Z

(b) Shear stress distribution of bearer 47 (under load step 36)

Figure 8 Shear force envelope of the bearers upon wheel impact

Table 2 Resultant deflection of sleeper 47 and computational timewith varying ballast mesh size

Mesh size (mm) Deflection (mm) Computational time (s)60 times 60 254 2478470 times 70 232 1263880 times 80 228 1082490 times 90 259 5655100 times 100 254 5547

deflection under the said design train loading Figure 5 showsthe maximum vertical deflection taken at the midpoint ofeach bearer with a single pass of the coupled locomotiveload The deflection response is presented graphically inFigure 6 It can be seen that the bearer does not undergoany translations up until the 35th load step This is animportant step in dramatically reducing the computationaltime required to analyse the model with different mesh sizesAs we have located the critical bearer in the preliminarytest it is advantageous to exclude all previous steps betweenthe initial and 34th step from the analysis in determiningoptimum mesh size as this reduces the computational timeby almost 80 Table 2 lists the maximum deflection of thechosen bearer under train loading according to varied meshsizes [35] It can be seen from the results above that althoughthe 60mm and 100mm meshes yield similar precision andaccuracy of the numerical results the former takes almost 45times the amount of time to compute compared to the latterTo maximise the computing time efficiency the 100mm times100mmmesh is chosen for this study

3 Results and Discussion

In practice frequent maintenance of supporting bearers andfastening systems can often be observed in the field eventhough those components have been designed in accor-dance with engineering standards This study has thereforeinvestigated such an important issue It is found that thebearers which undergo the greatest deflection of a coupledlocomotive pass are the bearers underneath the crossing nose(maximum at bearer number 47) The sensitivity analysis

illustrates the maximum deflection in all bearers with thepassing of a moving couple train load 300LA [33] Fromthe sensitivity analysis it can be seen from Figure 7 that thebearer directly underneath the crossing (number 47) expe-riences the greatest deflection with a resultant of 254mmThe sharp spike in deflection clearly defines the moment atwhich each wheel axle impacts the above rail in this case thecrossing nose Any lateral sliding due to such vertical loadaction cannot be observed

The shear stress response of crossing bearer (number 47)at the most critical loading is illustrated Figure 8 It can bewitnessed that the large spike at the midpoint is obviously thepoint at which the wheel impacts the crossing nose Note thatthis shear response has not been considered in the componentdesign since it is often lower than the shear capacity ofprestressed concrete bearers Figure 9 represents both thebending stresses and moment envelopes given in the designspecification [28 29] and the bendingmoment obtained fromthe FE analysis by using the methodology recommended inthe specification Four reference points are chosen accordingto the given bending moment envelope which is gatheredfrom these reference points 0m 05m and total lengthminus05m and at the end span Figure 9(a) illustrates the bendingmoment envelope for 26 to 28m long turnout bearers Theblack line signifies the bending moment envelope whichis found in the design specification [29] and the blue linerepresents the shear envelope obtained from the FE analysisspecifically bearer 21 (the bearer under the closure rails) Itcan be seen that the computed results do not correlate wellwith the design allowable actions However this may be dueto the nature of the loading of the turnout as the train inthis particular instance is often modelled to travel along thediverging tangential path and the loading should not beexpected to be linear or symmetrical unlike what is depictedin the design specification Figure 9(b) demonstrates thecomparison of a chosen bearer with the suggested designenvelope The crossing bearer (critical bearer number 47)is chosen to validate the data sets and results As withthe former example the black line represents the bendingmoment envelope specified in the design standards [28 29]The bending moment envelope is intended to be used forturnout bearers between the lengths 28m and 52m Again


X

Y

Z

XZ

X

Y

Z

(a) Bearer 21 (red) in relation to load step 18 (yellow)

X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)

(b) Bending stress of bearer 21 under load step 18

0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10

(c) Bending moment envelope of bearer 21 with computed values (blue)against specifications (black)

X

Y

Z

X

Y

Z X

Y

Z

(d) Bearer 47 (red) in relation to load step 36 (yellow)

Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)

(e) Bending stress of bearer 47 under load step 36

0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10

(f) Bending moment envelope of bearer 47 with computed values (blue)against specifications (black)

Figure 9 Bending stresses and moment envelopes of turnout bearers

minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

Figure 10 Bendingmoment envelope of FEmodel bearer 47 (blue)and specifications (black)

the FE analysis has yielded resultant moments from thereference points

Due to the unchanging response of the modelled resultand the fact that the bearers under the crossings experiencecritical loading it is believed that the moment envelopeoverlooks the adverse loading configurations of a turnoutsystem and instead idealises the moment response to that ofstraight rail Figures 10 and 11 display the comparative bend-ing moment envelopes for the bearer at crossing (number

minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)

Figure 11 Bendingmoment envelope of bearer 21 Bendingmomentof FE model bearer 21 (blue) and specifications (black)

47) and the bearer at closure rail (number 21) Retaining thesame convention as earlier envelopes the blue line signifiesthe FE analysis There is an obvious spike approximately atthe midpoint of the bearer span It is logical to assume thatthe impact of the wheel onto the crossing nose will greatlyinfluence the shear and bending envelope Although theremay be a huge deviation between the specified value and thesimulated result it should be noted that the envelope withinSPC 233 [29] shows no deviation nor increased loadingwithin that particular location whatsoever


It is concerning the fact that the maximum bendingmoment simulated being 322 kNm is greater than that speci-fied by about 800 Also that no change in loading conditionor material property has been changed is noteworthy yet byinvolving a greater number of points in which to create anaccurate stress diagram the loadingmay be allowed to deviateso greatly As the increase in bendingmoment is concentratedwithin the midspan it can be deduced that the midspancould become more susceptible to permanent deformationsand cracking that was not designed to not be designed toaccommodate for the adverse loading

The resultant bending diagram depicted in Figure 11shows the much more comprehensive bending envelope incomparison to those given within specifications The enve-lope given in the specifications depicts a much more linearapproach to bendingmoment design and it is speculated thatthe diverse geometry of a rail turnout has been overlookedaltogetherThe significance of the bending moment envelopeobtained for the bearer under closure rail (number 21) is thatnot only does the larger bending moment occur at the pointof wheel impact but it also has the characteristic of unevenloading which is precisely when the train is diverting intothe tangential track

4 Conclusions

This paper firstly presents a development of three-dimensional finite element model of a tangential turnoutsystem for an investigation into the failure modes that werearisen from the field observations and measurements on amixed traffic rail line whereas broken concrete bearers andloose fasteners were reported routinely A 3D FE modelhas been established and validated for the analysis of acomplete turnout systemThe primary objective of this studyis to determine the critical location be able to realise thecritical deflection and validate shear force and bendingmoment envelopes of a turnout system To address thisABAQUS has been employed to carry out all modellingand postprocessing of a complete 3D turnout From thedetailed analysis turnout bearers right underneath crossingpanel experience the highest load actions resulting in thelargest deformations It is also found that the turnout sleeperor bearer underneath the closure rails or where there isa change in rail curvature is subjected to a high level ofvertical loading sometimes exceeding its design load limitsThese results are of significant importance to rail engineersand track designers in order to establish a safer and morereliable turnout system Future work will evaluate the effectsof ballast voids and pockets on the dynamic behaviour andlateral sliding of turnout systems

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful to University of Western Sydney andRailCorp for the support throughout this study Also thelast author wishes to thank Australian Government for hisEndeavour Executive Fellowships at Massachusetts Instituteof Technology Harvard University and Chalmers Universityof Technology

References

[1] E Kassa and J C O Nielsen ldquoDynamic interaction betweentrain and railway turnout full-scale field test and validation ofsimulation modelsrdquo Vehicle System Dynamics vol 46 no 1 pp521ndash534 2008

[2] S Kaewunruen and A M Remennikov ldquoOn the residualenergy toughness of prestressed concrete sleepers in railwaytrack structures subjected to repeated impact loadsrdquo ElectronicJournal of Structural Engineering vol 13 no 1 pp 31ndash47 2013

[3] A M Remennikov and S Kaewunruen ldquoA review of loadingconditions for railway track structures due to train and trackvertical interactionrdquo Structural Control and Health Monitoringvol 15 no 2 pp 207ndash234 2008

[4] B A Palsson ldquoOptimisation of railway crossing geometryconsidering a representative set of wheel profilesrdquo VehicleSystem Dynamics vol 53 no 2 pp 274ndash301 2015

[5] S Kaewunruen and A M Remennikov ldquoNonlinear transientanalysis of a railway concrete sleeper in a track systemrdquoInternational Journal of Structural Stability and Dynamics vol8 no 3 pp 505ndash520 2008

[6] S Kaewunruen and A M Remennikov ldquoProgressive impactbehaviours of prestressed concrete sleepers in railway trackenvironmentsrdquo Engineering Structures vol 31 no 10 pp 2460ndash2473 2009

[7] S Kaewunruen and A M Remennikov ldquoDynamic crackpropagations in prestressed concrete sleepers in railway tracksystems subjected to severe impact loadsrdquo Journal of StructuralEngineering vol 136 no 6 pp 749ndash754 2010

[8] C EsveldModern Railway Track MRT Press AmsterdamTheNetherlands 2001

[9] S Kaewunruen Experimental and numerical studies for evalu-ating dynamic behaviour of prestressed concrete sleepers subjectto severe impact loading [PhD thesis] School of Civil Miningand Environmental Engineering University of WollongongWollongong Australia 2007

[10] S Kaewunruen A M Remennikov A Aikawa and H SakaildquoFree vibrations of interspersed railway track systems in three-dimensional spacerdquoAcoustics Australia vol 42 no 1 pp 20ndash262014

[11] S Iwnicki Y Bezin G Xie and E Kassa ldquoAdvances in vehicle-track interaction toolsrdquo Railway Gazette International vol 165pp 47ndash49 51ndash52 2009

[12] A Manalo T Aravinthan W Karunasena and N StevensldquoAnalysis of a typical railway turnout sleeper system usinggrillage beamanalogyrdquoFinite Elements inAnalysisampDesign vol48 no 1 pp 1376ndash1391 2012

[13] S Kaewunruen ldquoMonitoring structural deterioration of railwayturnout systems via dynamic wheelrail interactionrdquo CaseStudies in Nondestructive Testing and Evaluation vol 1 pp 19ndash24 2014


[14] S Kaewunruen ldquoMonitoring in-service performance of fibre-reinforced foamed urethane sleepersbearers in railway urbanturnout systemsrdquo Structural Monitoring amp Maintenance vol 1no 1 pp 131ndash157 2014

[15] C Wan V L Markine and I Y Shevtsov ldquoAnalysis oftrainturnout vertical interaction using a fast numerical modeland validation of that modelrdquo Proceedings of the Institution ofMechanical Engineers F vol 228 no 7 pp 730ndash743 2014

[16] S Kaewunruen ldquoEffectiveness of using elastomeric pads tomitigate impact vibration at an urban turnout crossingrdquo inNoiseand Vibration Mitigation for Rail Transportation Systems TMaeda P-E Gautier C E Hanson B Hemsworth J T Nelsonand Burkhard Eds pp 357ndash365 Springer Berlin Germany2012

[17] B A Palsson Optimisation of railway switches and crossings[PhD thesis] ChalmersUniversity of Technology GothenburgSweden 2014

[18] C T Rapp RGKernes andMR Saat ldquoOverviewof issues andresearch related to special trackwork for shared high-speed-railpassenger and heavy-axle-load freight operationsrdquo Proceedingsof the Institution of Mechanical Engineers Part F Journal of Railand Rapid Transit vol 228 no 5 pp 557ndash565 2014

[19] C Wan V L Markine and I Y Shevtsov ldquoOptimisation of theelastic track properties of turnout crossingsrdquo Proceedings of theInstitution of Mechanical Engineers Part F Journal of Rail andRapid Transit 2014

[20] E Kassa and J C O Nielsen ldquoDynamic train-turnout interac-tion in an extended frequency range using a detailed model oftrack dynamicsrdquo Journal of Sound and Vibration vol 320 no4-5 pp 893ndash914 2009

[21] M Wiest W Daves F D Fischer and H Ossberger ldquoDefor-mation and damage of a crossing nose due to wheel passagesrdquoWear vol 265 no 9-10 pp 1431ndash1438 2008

[22] J Xiao F Zhang and L Qian ldquoNumerical simulation of stressand deformation in a railway crossingrdquo Engineering FailureAnalysis vol 18 no 8 pp 2296ndash2304 2011

[23] R Muller J C O Nielsen B Nelain and A Zemp ldquoGround-borne vibration mitigation measures for turnouts state-of-the-art and field testsrdquo in Noise and Vibration Mitigation for RailTransportation Systems vol 126 of Notes on Numerical FluidMechanics and Multidisciplinary Design pp 547ndash554 SpringerBerlin Germany 2015

[24] Karlsson and Sorensen ABAQUSCAE Userrsquos Manual ElementHibbitt Publication Pawtucket RI USA 2006

[25] Y Q Sun C Cole and M McClanachan ldquoThe calculation ofwheel impact force due to the interaction between vehicle and aturnoutrdquo Proceedings of the Institution of Mechanical EngineersPart F Journal of Rail and Rapid Transit vol 224 no 5 pp 391ndash403 2010

[26] U M Cherkashin S M Zakharov and A E Semechkin ldquoAnoverview of rolling stock and track monitoring systems andguidelines to provide safety of heavy and long train operationin the Russian Railwaysrdquo Proceedings of the Institution ofMechanical Engineers Part F Journal of Rail and Rapid Transitvol 223 no 2 pp 199ndash208 2009

[27] Rail Corporation of New South Wales ESC 240 Ballast RailCorporation of New South Wales Sydney Australia 2012

[28] Rail Corporation of New South Wales ESC 250 Turnouts andSpecial Trackwork Rail Corporation of New South Wales 2012

[29] Rail Corporation of New South Wales SPC 233mdashConcreteTurnout Bearers Rail Corporation of New South Wales 2012

[30] OMirza and BUy ldquoBehaviour of headed stud shear connectorsfor composite steel-concrete beams at elevated temperaturesrdquoJournal of Constructional Steel Research vol 65 no 3 pp 662ndash674 2009

[31] B Indraratna and S Nimbalkar ldquoImplications of ballast break-age on ballasted railway track based on numerical modelingrdquoin Proceedings of the 13th International Conference of theInternational Association for Computer Methods and Advancesin Geomechanics (IACMAG rsquo11) pp 1085ndash1092 May 2011

[32] L Montalban Domingo C Zamorano Martın C PalenzuelaAviles and J I Real Herraiz ldquoAnalysis of the influence ofcracked sleepers under static loading on ballasted railwaytracksrdquoTheScientificWorld Journal vol 2014 Article ID 36354710 pages 2014

[33] Standards Australia AS 51002 Bridge DesignmdashDesign LoadsStandards Australia 2004

[34] S Kaewunruen ldquoDiscussion of lsquomitigation of ground vibrationgenerated by high-speed trains on saturated poroelastic groundwith under-sleeper padsrsquo by Zhigang Cao Yuanqiang Cai andJie Hanrdquo Journal of Transportation Engineering vol 141 no 1Article ID 07014003 2015

[35] J Sae Siew O Mirza and S Kaewunruen ldquoTorsional effect ontrack support structures of rail turnouts crossing impactrdquoASCEJournal of Transportation Engineering Submitted

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Closure rails

Bearers

Heel block

Rail brace

Checkrail unit Crossing

Plates

Studsswitch stops

Stock rails

Switches

Figure 1 Typical components of a railway turnout

linear elastic range

Upper yield peak

Plastic plateau

Strain hardening portion

Actual behaviour

Elastic-perfectly plastic approximation

E

120590y

120576

120590

Figure 2 Stress-strain relationship of structural steel [30]

Although a new smoother method of geometrical analysisand tangential design to improve wheelrail navigations hasbeen adopted for turnouts the transfer zone at a crossing nosein any complex turnout system still generates high-intensityimpact forces to turnout components Generally the turnoutbearers for supporting points and crossing structures weredesigned using the beam on elastic foundation analysis or 2DFE grillage modelling [11 12] Kaewunruen [13 14] indicatedfrom recent work that some additional factors were oftenneglected from the grillage analyses although they must betaken into account in the design process including

(i) extra length of turnout bearers in comparison withstandard sleepers

(ii) centrifugal forces through curved pairs of rails

(iii) forces and bending moments induced from pointsmotors and other signaling equipment

(iv) impact forces induced by wheel-rail interaction

(v) mechanical rail joints

40

35

30

25

20

15

10

5

0

minus5

Stre

ss (N

mm

2)

minus0002 minus0001 0 0001 0002 0003 0004 0005

Strain

Figure 3 Stress-strain relationship of concrete [30]

On this ground this numerical study was initiated bya recent number of reportedly broken concrete bearers ona mixed-traffic line in New South Wales (NSW) AustraliaDue to the complexity of the loadings and damage modesin railway turnouts this study aims to establish a three-dimensional (3D) finite-element (FE) model The 3D FEmodel adopts an elastoplastic region of bending and sheardeformation of materials The 3D FE model was developedbased upon a common tangential turnout used in AustraliaThis study indicates that the crossing panel is where turnoutbearers experience the greatest bending moment and shearforce and it provides the critical force envelopes for designimprovement of turnout bearers

2 Finite Element (FE) Modelling

Railway turnout systems have generally been analysed using agrillage beammethod (Manalo et al 2010) [12 15] Althoughthe simplification is useful such a method cannot adequatelyassist in the failure analyses of turnout components In somecases the results using the grillage beam method seem tohave discrepancies with the field observations where themaximum bending and shear forces were evident within thecrossing panel [16ndash19] A number of researches have beenconducted to locate the critical section within a turnout andmany of which conclude that the critical section is locatedspecifically at the crossing panel [20ndash23]

This paper presents a nonlinear 3D FE analysis usingABAQUS considering the whole turnout which comprisesbearers rail guard rails crossing nose rail pads baseplatesand guardrail support plates The benefits of modelling in3D space are to incorporate the effects of the neighbouringbearers and to take into consideration the longitudinal forcesof the continual rail The boundary conditions of the central3D model can be simulated enabling vibrations to radiatebeyond the model [24]

21 WheelRail Interface (W-R) A Practical Implication Ingeneral the surface conditions of the wheel and rail play acritical role in theW-R contact force in addition to geometricirregularities train speeds and type of track structure Thelarge contact force will accelerate the deterioration rate of



CouplerC

300kN 300kN 300kN 300kN

17m 17m 20m11m

360kN

(a) 300LA load case

Y

XZXZ

XZXZ

XZ

Y

ZX

XZ

Y






X

Y

Z


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Sleeper








1198752= 119876 + (119860


where

119872 = [119872V

119872V +119872119911]

05

119862 = [120587 sdot 119862119911

4 [119870119911(119872V +119872119911)]

05]

119870 = (119870119911sdot 119872V)05

(2)

the lesser of

119876 = 013119863 times 103

or 119876 = 125 times 103(3)











X

Y

Z

X

Y

Z

XZ


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Load stepminus00005




119884 = 119882 sdot 119860119889+ 119860119910sdot 119881119898[119872119906

119872119906+119872119910

]

05

sdot [119870119910sdot 119872119906]05

(4)














1198911015840

119888 (5)




000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm


where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)









000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











CouplerC

300kN 300kN 300kN 300kN

17m 17m 20m11m

360kN

(a) 300LA load case

Y

XZXZ

XZXZ

XZ

Y

ZX

XZ

Y






X

Y

Z


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Sleeper








1198752= 119876 + (119860


where

119872 = [119872V

119872V +119872119911]

05

119862 = [120587 sdot 119862119911

4 [119870119911(119872V +119872119911)]

05]

119870 = (119870119911sdot 119872V)05

(2)

the lesser of

119876 = 013119863 times 103

or 119876 = 125 times 103(3)











X

Y

Z

X

Y

Z

XZ


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Load stepminus00005




119884 = 119882 sdot 119860119889+ 119860119910sdot 119881119898[119872119906

119872119906+119872119910

]

05

sdot [119870119910sdot 119872119906]05

(4)














1198911015840

119888 (5)




000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm


where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)









000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Y

Z


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Sleeper








1198752= 119876 + (119860


where

119872 = [119872V

119872V +119872119911]

05

119862 = [120587 sdot 119862119911

4 [119870119911(119872V +119872119911)]

05]

119870 = (119870119911sdot 119872V)05

(2)

the lesser of

119876 = 013119863 times 103

or 119876 = 125 times 103(3)











X

Y

Z

X

Y

Z

XZ


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Load stepminus00005




119884 = 119882 sdot 119860119889+ 119860119910sdot 119881119898[119872119906

119872119906+119872119910

]

05

sdot [119870119910sdot 119872119906]05

(4)














1198911015840

119888 (5)




000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm


where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)









000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Y

Z

X

Y

Z

XZ


0

00005

0001

00015

0002

00025

0 10 20 30 40 50

Defl

ectio

n (m

)

Load stepminus00005




119884 = 119882 sdot 119860119889+ 119860119910sdot 119881119898[119872119906

119872119906+119872119910

]

05

sdot [119870119910sdot 119872119906]05

(4)














1198911015840

119888 (5)




000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm


where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)









000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












000

050

100

150

200

250

300

35 37 39 41 43 4745

minus050

60mm70mm80mm

90mm100mm


where

120574 =

100381610038161003816100381610038161003816100381610038161003816

1198911015840

119888

324

100381610038161003816100381610038161003816100381610038161003816

3

+ 155

1205761015840

119888= 0002

(6)









000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










000

2000

4000

6000

0 1 2 3 4 5

Shea

r for

ce (k

N)

minus6000

minus4000



SS12

(ave

rage

75

)

+1730e + 07+1438e + 07

+1146e + 07+8535e + 06+5611e + 06



X

Y

Z











X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Y

Z

XZ

X

Y

Z


X

Y

Z

+4974e + 06

+3714e + 06

+2454e + 06

+1194e + 06

minus6633e + 04

minus1326e + 06

minus2587e + 06

minus3847e + 06

minus5107e + 06

minus6367e + 06

minus7627e + 06

minus8887e + 06

minus1015e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

0 05 1 15 2 25 3

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus50

minus40

minus30

minus20

minus10


X

Y

Z

X

Y

Z X

Y

Z


Figure 9 Continued


X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










X

Y

Z

+1972e + 07

+1211e + 07

+4502e + 06

minus3108e + 06

minus1072e + 07

minus1833e + 07

minus2594e + 07

minus3355e + 07

minus4116e + 07

minus4877e + 07

minus5638e + 07

minus6399e + 07

minus7160e + 07

SS22

(ave

rage

75

)


0

10

20

30

40

50

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)

minus30

minus20

minus10



minus350

minus300

minus250

minus200

minus150

minus100

minus50

0

50

100

0 05 1 15 2 25 3 35 4 45

Bend

ing

mom

ent (

kNm

)

Distance x (m)




minus50

minus40

minus30

minus20

minus10

0

10

20

30

40

000E+00

500Eminus01

100E+00

150E+00

200E+00

250E+00

300E+00

350E+00

Bend

ing

mom

ent (

kNm

)

Distance x(m)






4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












4 Conclusions




Acknowledgments


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Nonlinear Finite Element Modelling of ...

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