Track-Bridge Longitudinal Interaction of Continuous Welded Rails on Arch Bridge.pdf

8/10/2019 Track-Bridge Longitudinal Interaction of Continuous Welded Rails on Arch Bridge.pdf

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Hindawi Publishing CorporationMathematical Problems in EngineeringVolume , Article ID ,pageshttp://dx.doi.org/.//

Research ArticleTrack-Bridge Longitudinal Interaction of Continuous WeldedRails on Arch Bridge

Rong Chen, Ping Wang, and Xian-kui Wei

MOE Key Laboratory o High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu , China

Correspondence should be addressed to Ping Wang; [email protected]

Received November ; Revised March ; Accepted March

Academic Editor: Valentina E. Balas

Copyright Rong Chen et al. Tis is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

aking arch bridges, including deck, hal-through, and through arch bridges (short or DAB, HAB, and AB) as examples,mechanics analysis models o longitudinal interaction between continuously welded rails (short or CWRs) and arch bridges areestablished. Based on the nite element method (FEM), the longitudinal interaction calculation sofware o CWR on arch bridgeshas been developed. Focusing on an HAB, the tension, compression, and deection conditions are calculated and analyzed. Teresults show that the mechanics analysis models o three types o arch bridges can truly reect the real state o the structure; thecalculation sofware can be used or systematic research o theCWR on arch bridge; as or HAB, temperaturedifference o arch ribhas a small effect on rail tension/compression, and arch bridgecan be simplied as a continuous beam or rail tension/compressionadditional orce calculation; in calculation o deection conditions o HAB, it is suggested that train loads are arranged on hal

span and ullspan and take thedirection o load enteringbridge into account. Additionally, the deectionadditional orce variationo CFS basket handle arch bridge is different rom that o ordinary bridge.

1. Introduction

Over the years, continuous welded rail (CWR) was usuallylaid on common simply supported beams or continuousbeam bridge structure in China []. Nevertheless, in recentyears, with the continuous improvement o the bridge andCWR construction level, more and more railway bridges

applied a special type o bridge structure. Among them, themore typical cases are the ollowing three types o arch bridg-es (deck, hal-through, and through arch bridges, reerred toas DAB, HAB,and AB), cable-stayed steel truss bridge, andso orth. Compared with general simply supported beam andcontinuous beam bridge, these special orms o bridges canmore effectively meet the height requirements o larger spanand a smaller structure and better adapt to changes in therailway line terrain. Tereore, the special orms o bridgestructures play an important role when the clearance limitedor project investment increased due to the need o uplifingthe elevation o railway line, especially when there are somespecial requirementsin terms o aesthetics, art, andlandscape

coordination or the bridge structure, these special structureso bridges can give ull play to the role that ordinary bridge isdifficult to replace.

Up to now, the related technology o CWR on ordinarybridge structure is relatively mature. Many scholars havestarted researches on the mechanics problems o the railwaybridge under the load o moving vehicles and have obtained

a lot o valuable results, including the Greens unctionsmethod or both innite and nite elastic structures [,]and the modal analysis method [, ]. Some scholars havedeveloped a general-purpose computing sofware []. Tedesign and calculation method o CWR on ordinary bridgehave been specied in a specication []. However, it ofenrequires a separate establishment o the computational modelto conduct a special study o CWR on the special bridgestructures. It will cost a lot o efforts and slow downdesign progress, so it is necessary to analyze the mechanicalcharacteristics and establish a common computational modelor different special bridge structures. In this way, designercan get the calculation results o longitudinal interaction


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Mathematical Problems in Engineering

Rail axisLongitudinal nonlinear spring

Rigid girders

Neutral axis of deck

Pier axis

Rigid girders

Nodes at height of

upper face of arch rib

F M F F M F FM FM FM

F: xed bearing

M: movable bearing

F : Te mechanics model o track/girder/pier o DAB.

F M FM

F: xed bearing

M: movable bearing

Rail axisLongitudinal nonlinear spring

Rigid girders

Neutral axis of deck

Rigid girders

Suspender hanger center node

Arch axis nodes

F : Te mechanics model o track/girder/pier o HAB.

between CWR and special bridge through the modicationo some key parameters. Tis paper ocused on the lon-gitudinal interaction o CWR on arch bridge, establishedan integrated model o track/bridge/pier or CWR on thedeck, hal-through, and through arch bridges, programmedthe longitudinal interaction analysis sofware o CWR onarch bridge (LIACAB), and used this sofware to study thelongitudinal orce and deormation law to provide theoreticalguidance or the design o CWR on the arch bridge.

2. Longitudinal Interaction Model

.. Basic Assumptions. Tree types o arch bridges and or-dinary bridge have common basic assumptions [], whichwill not be elaborated in this paper. Tere are some otherassumptions should be made or arch bridge. Tey are asollows:

() Te arch oot and the underlying connection o DABand HAB are ully constrained, without consideringunderlying displacements.

() Lateral stiffness o arch ring structure is not consid-ered, only considering vertical stiffness.

() For piers o DAB, only longitudinal stiffness is consid-ered; piers bottom and the upper arch ring are xedtogether.

() Hangers o HAB, AB, and arch ring connectednodes are on the arch axis.

.. Mechanics Model. Essentially, analysis o CWR longitu-dinal orce on bridgeis based on the rail/beam interaction [].It is necessary to build realistic computational model to trulyreect the structures stress state o special bridge structures.rack/girder/pier integrated computational model o threetypes o arch bridges is described below.

... Model o rack/Girder/Pier o DAB. Te mechanicsmodel o DAB is shown in Figure . Tis type o bridge

structure has the ollowing eatures: the rail longitudinallyinteracts with top ange o girder through longitudinalrailway track resistance; pier and lower ange o girder areconnected to transmit the longitudinal orce, vertical orce,or moment; pier is connected with the arch rib to transmitorce and bending moment. Mechanics model inFigure isthe true reection o bearing state o this structure.

... Model o rack/Girder/Pier o HAB. Te model otrack/girder/pier o HAB is shown inFigure . Features othis type o bridge structure are as ollows: the rail longitudi-nally interacts with top ange o girder through longitudinalrailway track resistance; the girder transmits longitudinal and


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M F M F

M: movable bearing

F: xed bearing

Rail axis

Longitudinal nonlinear spring

Rigid girders

Neutral axis of deckRigid girders

Suspender hanger center node

Arch axis nodes

F : Te mechanics model o track/girder/pier o AB.

vertical orces to the arch rib through pier or suspender; rail,girder, suspender, and arch rib orm a coupled system olongitudinal interaction. Under different calculation condi-tions, each section has a unique balance point o orce and

deormation, so the orces and displacements o various partscan be obtained i the balance points are ound.

... Model o rack/Girder/Pier o AB. AB is very com-mon in the construction o urban rail transit. It is usuallybuilt to meet the needs o urban landscape and large span,generally divided into simple supported beam arch or contin-uous beam arch. Now AB is ofen simplied into a normalsimple supported beam or continuous beam in calculation.Te calculation o longitudinal orce and the results canmeet the accuracy requirements. Te mechanics model otrack/girder/pier o AB is shown in Figure . Tis type obridge structure is similar to HAB, but the difference is thatthe arch oot and the girder are connected together to orm astructure o sel-equilibrium system.

In these mechanics models, arch span and both ends omain arch can be made up with any number and the span osimply supported beams, continuous beams, or rigid ramebridge. And the entire girder can be considered as uniormsection beam or beams with variable section. Te horizontalstiffness o piers has embodied the pier structure type and itsconnection with girder at both ends o the main arch span.Piers and suspenders stiffness are reected by their cross-section parameters. Te types o arch rib structures, such asreinorced concrete arch, concrete lled steel tubular arch,steel box arch and steel truss arch, can be simplied as beam

elements. Tree arch axis line orms, such as the arc line,quadratic parabola, and catenary, are considered in thesecalculation models. Moreover, structure parameters andresistance type o track components are variable in thecalculation model.

.. Element Selection. Te calculation models o CWR onarch bridge mentioned above are established and solved bymeans o secondary development based on a large niteelement sofware ANSYS. Reasonable element selection o thestructural parts is particularly important to the calculationresults, and the selections are as ollows.

(i)Rail: plane beam element BEAM is selected tosimulate the rail instead o bar element LINK; it mayconsider the inuence o deck vertical deormation onthe vertical deormation and orce o rail.

(ii)Longitudinal resistance: simulatedby nonlinear springelement COMBIN.

(iii)Stiffness o piers and rail bearing points at both endso main arch span: simulated by linear spring elementCOMBIN.

(iv) Girder, arch, and pier o arch bridge : simulated bytwo-dimensional elastic cone asymmetric plane beamelement BEAM. BEAM is single axle and ableto work under pressure and bending, degrees oreedom on each node (along the - and -axisdisplacement and rotation around the -axis). Teelement allows asymmetric end ace and end nodesto deviate rom the section centroid location (seeFigure ). Tis eature can be used to establish theelement nodes in the calculation model based on theactual bridge structure so as to accurately reect therealistic structural state.

.. General-Purpose Computing Sofware. Most structureso the three types o arch bridges are similar, but the localstructure is slightly different. Tis paper used the combinedmethod o FORRAN language, the nite element sofwareANSYS, and Parametric Design Language (APDL) to pro-gram the general-purpose computing sofware o longitudi-nal interaction o CWR track on arch bridge (LICAB). Tis

sofware uses executable programs (by Fortran language) toread input parameters le and preprocess the data and usessource les compiled by APDL to read the relevant parame-ters o the arch bridge structure automatically. Afer that, itcalculates a variety o conditions (including the conditionso tension/compression orce, deection orce, the brakingorce, and the broken rail orce) in ANSYS environment andgenerates the corresponding calculation results le.Figure shows the three types o arch bridges established by LICAB.

LICABs calculation results were compared with theresults given in []. Te comparison shows that the mechan-ics analysis models o three types o arch bridges can trulyreect the real state o the structure; the calculation sofware


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1,4

Area 1

C.G.

111

2,3

1

1

1

12

3

4

1

2

3

4

1

2

2

F : BEAM element.

(a) Deck arch bridge

(b) Hal-through arch bridge

(c) Trough arch bridge

F : Mechanics model o three types o arch bridges.

can be used or systematic research o the CWR on archbridge.

3. Engineering Case 1

Here, taking the HAB as an example, tension/compressionand deection conditions (the rail intensity control condi-tions) are analyzed.

.. Overview o Bridge Structure. A new double-track railwaylarge span arch bridge: its main span is m, with a vectorheight o . m; the arch axis is quadratic parabola, and suspenderswithspacing o m are set. Te spano sidebeamis . m, and its arch rib has a structure o steel-concretecomposite truss basket arch structure; its main span adoptsthe prestressed concrete box girder. Bridge span arrangementis shown inFigure .

.. ension/Compression Condition. In calculation o ten-sion/compression condition, beam temperature difference isC, and temperature difference o arch rib in turn is ,, , and C. Rail tension/compression additional orcecalculation results are shown inFigure .

InFigure , temperature difference o arch rib only hasa small effect on rail tension/compression. Tis is primarilybecause the main girders longitudinal deormation is cen-trosymmetrical, and the deormation o arch rib has littleinuence on it. Based on this, the HAB can be simplied asa continuous beam model as shown in Figure . Te compar-ative results o the two were shown inFigure .

Figure shows the inuence o temperature difference othe arch rib on rail tension/compression additional orce issmall, mainly because the longitudinal tension/compressiondeormation o main span under temperature differenceeffect is almost centrosymmetric, andthe deormation o arch

rib has no inuence on the deormation o girder. Based onthis point, the arch bridge can be simplied as a continuousbeam whose xed bearing is set in the middle o span or thetension/compression orce condition.Figure shows the railtension/compression additional orce result o the simpliedmethod, which is almost identical to the results o accuratemodel. Te calculation result o simplied method is slightlylarger mainly because suspenders have some certain con-straints on the main beam. From the design perspective, thesimplied method is easible and saer.

.. Deection Condition. In calculation o deection con-ditions, the train loads (Chinese live load) are separately


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Sliding bearingFixed bearing

351

64.5

319.8

824.6 24.65 32 8 32

F : Span arrangement o bridge (unit: m).

0

100

200

300

200 0 200 400 600 800 1000

500

400

300

200

100Force

(kN)

Distance (m)

0C

15C

20C

25C

F : Rail tension/compression additional orce results.

arranged on /, /, /, and ull span o arch bridge romthe lef side to the other side. Rail deection orce calculationresults are shown inFigure .

Figure shows that the peak o tensile stress appearsat the lef junction pier o the mail span when the trainloads arranged on / span o arch bridge, and the peak ocompressive stress appears at the lef-side spans middle omain span. When the train loads are distributed uniormlyon ull span o bridge, rails maximum tensile stress occurs

near the right juncture pier, and the compressive stress peakappears at the middle o the right-side span. Te results areobtained in the case o train load entering into bridge romone direction. So, it is reasonable to arrange train loads on/ span and ull span and take the direction o load enteringbridge into account.

4. Engineering Case 2

A long span concrete lled steel tubular (CFS) baskethandlearch bridge is applied in newly constructed double-trackrailway. Te calculated span is m, and the vector heighto the bridges arch ring is m. Within the vault height o

0100

200

300

Simplied method

200 0 200 400 600 800 1000

500

400

300

200

100

Force

(kN)

Distance (m)

25

C

F : Result o simplied model.

m, concrete rigid rame with type is used; the beamon the arch outside the vault height m, m -type simplysupported girderis adopted; the column pier adoptssteeltubeconcrete rigid rame pier (seen inFigure ). On the bridge,the ballasted track with continuous welded rail is laid withnormal resistance asteners and without expansion rail joints.

For this model, it is assumed that the arch oot pier inthe lef is the origin o coordinates. In order to reduce theinuence o boundary conditions, spans rom both sides othe arch ring center are taken as calculation sections accord-ing to the actual bridge arrangement.

.. ension/Compression Condition. Existing specicationonly species the conventionalbeam temperature differences,not involving temperature difference values o bridges withspecial types. In calculation o expansion orce, two con-ditions were considered, that is, the arch ring temperaturedifference and no arch ring temperature difference. Te tem-perature difference o concrete beam is taken as C.Te temperature difference o arch ring is considered asC.Figure shows the result o rail tension/compression


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Sliding bearingFixed bearing

319.824.6 24.65 32 8 32

F : Simplied model o HAB.

0

10

20

1/4 span

1/2 span3/4 spanFull span

Force

(kN)

200 0 200 400 600 800 1000

Distance (m)

50

40

30

20

10

F : Rail deection orce calculations.

F : Bridge structure diagram.

additional orce.Figure shows the relative displacements

between beam and rail.As shown in Figures and , when the temperaturedifference o the arch ring is considered, the maximumrail expansion additional orce is . kN/rail, and themaximal beam/rail relative displacement is . mm. I thetemperature difference o the arch ring is not considered, themaximum rail expansion additional orce is . kN/rail,and the maximal beam/rail relative displacement is . mm.

.. Deection Condition. China railway standard live load isused, and the load moves rom lef to right into the bridge.Te calculation considers two load distributions, that is, theull-span load and a hal-span load. Te deection additional

0

100

200

300

400

500

With arch ring temperature difference

No arch ring temperature difference

300 200 100 0 100 200 300 400 500 600 700500

400300

200

100

distance from the origin of the coordinate (m)

railtension/compression

additiona

lforce

(kN/rail)

F : Rail tension/compression additional orce.

0

1

2

3

45

6

7

With arch ring temperature difference

No arch ring temperature difference

distance from the origin of the coordinate (m)

100 50 0 50 100 150 200 250 300 350 400 450 500 550 6007

6

5

4

3

2

1

beam/railre

lative

displacement

(mm

)

F : Beam/rail relative displacements.

orce o rail resultis shown in Figure . Te beam/railrelativedisplacement is shown inFigure .

As seen rom Figures and , when there is ullspan load, the maximal deection additional tension is. kN/rail, and the maximaldeection additionalpressureis . kN/rail, maximal beam/rail relative displacement is


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is only set on hal span, the arch ring occurred approxima-tion anti-symmetric deormation, and the beam/rail relativedisplacement is big, which results in big deection additionalorce.

In braking condition, the beam/rail ast relative displace-ment is big when the braking load is distributed in ull span,

and the results can be used in the stability checking calcula-tion o ballast bed.

5. Conclusions

In summary, this paper analyzed the characteristics o CWRon arch bridges, created DAB, HAB, and AB mechanicsanalysis models, and developed the calculation sofware orlongitudinal interaction o CWR on arch bridges (LICABs).aking an HAB as an example, the results can be concludedas ollows:

() mechanics analysis models o three types o arch

bridges can truly reect the real state o the structure;() using the LICAB sofware, systematic research can be

realized orthe orce anddeormationlaw o theCWRon arch bridge;

() as or HAB, temperature difference o arch rib hasa small effect on rail tension/compression, and archbridge can be simplied as a continuous beam or railtension/compression calculation;

() it is suggestedthat train loads are arranged on / spanand ull span and take the direction o load enteringbridge into account in calculation o deection con-ditions o HAB;

() the deection additional orce variation o CFSbasket handle arch bridge is different rom that oordinary bridge. Te deormation o arch ring has biginuence on the deection additional orce o rail.Usually, when the load is set on hal o the span, thedeection additional orce is the worst. For ordinarybridge, its deection additional orce is much lessthan the tension/compression additional orce, so it isnot used as the controlling actor. But the deectionadditional orce o the basket handle arch bridge isbig, closeto the tension/compression additionalorce,so attention should be paid to its check calculation.

Acknowledgments

Tis work is nancially supported by the National NaturalScience Foundation o China under Grant no. andno. . And it was also supported by the ScienticResearch and Development Program o Chinese Ministry oRailways under Grant no. G.

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Track-Bridge Longitudinal Interaction of Continuous Welded Rails on Arch Bridge.pdf