Design of One Span Concrete Railway Bridges: Design According to the Eurocodes and the Spanish National Annex

MASTER'S THESIS

Design of One Span Concrete Railway Bridges

Design According to the Eurocodes and the Spanish National Annex

Aida Garcia Rodriguez 2014

Master of Science in Engineering Technology Civil Engineering

Luleå University of Technology

Department of Civil, Environmental and Natural Resources Engineering

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LULEÅ

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TEKNISKA

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UNIVERSITET%

Design%of%One%Span%

Concrete%Railway%

Bridges ^!

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Design%according%to%the%Eurocodes%and%the%

Spanish%National%Annex%

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Aida!Garcia!Rodriguez!

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28!February!2014!

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Preface!

This!master!thesis!was!carried!out!at!the!Department)of)Civil,)Environmental)and)Natural)Resources) Engineering,)at!Luleå!University!of!Technology,!in!Luleå,!Sweden!under!the!supervision!of!Tekn.!Dr.!

Professor!emeritus!Lennart!Elfgren.

The!work!was!carried!out!in!collaboration!with!Trafikverket,!Luleå,!and!I!would!like!to!thank!Mr.!Magnus!

Edfast.!MSc.Eng,!for!his!support!and!collaboration!during!the!realization!of!this!thesis.!I!also!want!to!

thank!Dr!Anders!Carolin!for!his!assistance!especially!at!the!beginning!with!deciding!the!main!ideas!and!

its!relevance!and!interest!to!Trafikverket.

I!also!want!to!thank!Mr!Henrik!Bøgh!Friis,!MSc.Eng,!from!COWI!(Denmark)!for!all!his!valuable!comments!

on!the!design!and!calculation!according!to!the!new!Eurocodes.

The!thesis!will!be!part!of!the!European!MAINLINE!Project!on!Railway!Infrastructure.!My!stay!in!Sweden!

was!made!possible!through!the!European!Erasmus!project!and!through!a!grant!from!my!home!university!

of!Oviedo!and!my!supervisors!María!Jesús!Lamela!Rey!and!Manés!Fernández!Cabanas.

Finally,!I!would!like!to!thank!my!parents!for!their!support!and!effort!in!giving!me!the!chance!to!come!to!

Sweden!to!study!and!do!my!master!thesis,!and!my!friends!for!all!their!support.

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Luleå!in!March!2014 Aida!Garcia!Rodriguez!

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Abstract!

Not!long!ago,!national!codes!were!used!in!design!and!construction!of!bridges!and!buildings!in!Spain.!But!

in!the!last!years,!those!codes!are!being!replaced!by!new!common!European!design!standards:!the!

Eurocodes.

All!existing!bridges,!designed!according!to!the!earlier!standards!are!gradually!getting!older,!and!

eventually!they!have!to!be!either!repaired/strengthened!or!replaced.

The!aim!of!this!thesis!is!to!provide!useful!standard!designs!for!short!railway!concrete!bridges!and!to!

make!a!manual!for!their!design!without!getting!lost!in!the!huge!amount!of!information!that!the!

Eurocode!offer.!The!focus!is!on!the!most!important!parts!and!trying!to!make!the!design!process!fluent.!

In!this!thesis,!the!designed!bridges!have!lengths!between!3!and!9!meters!and!the!Spanish!National!

Annex!to!the!Eurocode.!There!will!be!some!limitations!in!the!calculations,!for!example,!the!bridges!are!

supposed!to!have!straight!tracks.

The!methods!followed!are!explained!covering!all!necessary!aspects!as!permanent!loads,!variable!loads,!

limit!states,!bending,!shear!and!torsion,!reinforcement,!anchorage,!crack!widths,!shrinkage!and!fatigue.

The!work!is!related!to!the!European!Project!MAINLINE!project!which!the!aim!to!help!to!improve!

management!of!the!European!railway!infrastructure.

The!results!show,!as!can!be!expected,!that!as!the!length!of!the!bridge!increases,!the!amount!of!

reinforcement!also!increases!and!so!does!the!thickness!of!the!walls.!In!Appendix!A,!the!calculations!for!a!

6!meters!bridge!is!given!in!detail,!as!an!example.!!A!table!with!reinforcement!distribution!and!

dimensions!is!given!for!each!length,!as!well!as!final!drawings.

When!the!results!obtained!are!compared!to!the!ones!obtained!using!the!Swedish!National!Annex!for!the!

Eurocode,!it!can!be!seen!that!the!two!designs!are!quite!similar.!The!differences!are!some!safety!factors!

and!coefficients,!but!they!don’t!make!a!big!change!when!all!the!calculations!are!done.!Moreover,!the!

possible!differences!in!the!designs!are!evened!out!after!a!fatigue!verification!for!120!years.!

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Sammanfattning!

För!inte!så!länge!sedan!användes!nationella!normer!vid!dimensionering!och!byggande!av!broar!i!Spanien.!

Under!senare!år!har!de!dock!ersatts!av!nya!internationella!regler:!Europakoderna

Alla!befintliga!broar,!som!dimensionerats!enligt!tidigare!normer,!blir!gradvis!allt!äldre!och!de!behöver!

med!tiden!repareras/förstärkas!eller!bytas!ut

Syftet!med!detta!examensarbete!är!att!ta!fram!användbara!standardritningar!för!korta!järnvägsbroar!av!

betongoch!att!ta!fram!en!vägledning!för!hur!en!bro!konstrueras!utan!att!gå!vilse!i!den!enorma!mängd!

information!som!finns!i!Eurokoderna.!Fokus!ligger!på!de!mest!viktiga!delarna!och!på!att!göra!

designprocessen!lättflytande.!Broarna!har!längder!mellan!3!och!9!meter.!Vissa!begränsningar!finns!i!

beräkningarna,!till!exempel!att!endast!bror!behandlas!med!raka!spår.

Metoderna!som!används!förklaras.!De!omfattar!permanenta!och!variabla!laster,!gränstillstånd,!

böjmoment,!tvärkraft!och!vridmoment,!förankring,!armeringsutformning,!sprickbredder,!krympning!och!

utmattning.

Arbetet!anknyter!till!det!europeiska!projektet!MAINLINE,!vars!mål!är!att!bidra!till!att!förbättra!underhåll!

och!skötsel!av!europeisk!järnvägsinfrastruktur.

Resultaten!visar,!som!man!kan!vänta!sig,!att!när!brolängden!ökar,!ökar!också!mängden!av!armering.!Så!

gör!också!erforderlig!väggtjocklek.!!I!bilaga!A!redovisas!beräkningarna!i!detalj!för!en!6!meter!lång!bro.!

Alla!huvudresultatredovisas!i!en!tabell!med!dimensioner!och!armeringsmängder,!såväl!som!d!ritningarna.

När!resultaten!från!beräkningar!enligt!den!spanska!nationella!bilaga!jämförs!med!de!som!erhållits!med!

den!svenska!nationella!bilagan,!kan!man!se!att!båda!ger!ganska!lika!resultat.!.!Skillnaden!är!några!

säkerhetsfaktorer!och!koefficienter,!men!de!ger!inga!så!stora!förändringar!när!alla!beräkningar!

genomförts.!!Dessa!skillnader!försvinner!dessutom!när!hänsyn!tas!till!att!broarna!skall!klara!utmattning!

under!120!år.!

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Abstracto!

No!hace!tanto!tiempo,!se!usaban!uno!códigos!nacionales!usados!en!el!diseño!y!construcción!de!puentes!

y!edificios!en!España.!Aunque!en!los!últimos!años,!esos!códigos!están!siendo!remplazados!por!unos!

nuevos!estándares!de!diseño!comunes!para!toda!Europa:!los!Eurocódigos.!

Todos!los!puentes!existentes,!diseñados!de!acuerdo!con!los!estándares!anteriores,!están!envejeciéndose!

gradualmente,!y!!eventualmente!llegará!un!punto!en!el!que!será!necesario!reemplazarlos,!reforzarlos!o!

repararlos.!

El!objetivo!de!esta!tesis!es!proporcionar!diseños!estándares!útiles,!para!puentes!de!ferrocarril!cortos,!

hechos!de!hormigón!y!hacer!un!manual!para!su!diseño!,!sin!perderse!en!la!enorme!cantidad!de!

información!que!ofrecen!los!Eurocódigos.!El!foco!se!situa!en!las!partes!más!importantes!del!diseño,!y!en!

intentar!que!el!proceso!de!diseño!sea!lo!más!fluido!posible.!En!esta!tesis,!los!puentes!diseñados!tienen!

longitudes!comprendidas!entre!los!3!y!9!metros,!y!se!diseñan!de!acuerdo!a!los!Eurocódigos!y!al!anejo!

nacional!Español.!También!hay!que!tener!en!cuenta!que!se!tendrán!en!cuenta!ciertas!limitaciones!en!los!

cálculos,!como!por!ejemplo!la!suposición!de!que!los!puentes!tendrán!vías!rectas.!

Los!métodos!seguidos!se!explican!claramente!en!el!cuarto!capítulo!de!la!tesis,!que!cubre!todos!los!

aspectos!necesarios!(cargas!permanentes,!cargas!variables,!los!Estados!Límite!Últimos,!anclaje,!refuerzo,!

torsión,!los!anchos!de!fisura,!de!contracción!y!fatiga).!

Este!trabajo!está!fuertemente!relacionada!con!el!proyecto!europeo!MAINLINE,!cuyo!objetivo!es!ayudar!

a!mejorar!la!administración!de!la!infraestructura!de!ferrocarriles!europea.!!

Los!resultados!muestran,!como!es!de!esperar,!que!a!medida!que!la!longitud!del!puente!aumenta!,!

aumenta!la!cantidad!de!refuerzo,!así!como!el!espesor!de!las!paredes.!En!el!Apéndice!A,!los!cálculos!para!

el!puente!6!metros!están!expuestos!con!detalle,!a!modo!de!ejemplo.!En!el!capítulo!cinco,!todos!los!

resultados!están!expuestos!en!una!tabla,!con!la!distribución!y!el!diseño!de!refuerzos!para!cada!longitud,!

así!como!los!planos!finales.!

Cuando!los!resultados!obtenidos!en!esta!tesis!se!comparan!con!los!obtenidos!para!el!Anejo!Nacional!

Sueco!del!Eurocódigo,!se!observa!que!ambos!diseños!son!muy!similares!.!Las!únicas!diferencias!son!

ciertos!factores!de!seguridad!y!coeficientes,!pero!no!significan!una!gran!diferencia!una!vez!realizados!

todos!los!cálculos.!Por!otra!parte,!las!posibles!diferencias!en!los!diseños!quedan!eliminados!una!vez!que!

la!verificación!de!la!fatiga!se!realiza!para!120!años!.!

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Symbols!

Latin!upper!case!letters!

Ac!

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Concrete!crossmsectional!area!

Ac,eff!

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Effective!area!of!concrete!in!tension!

Ak!

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Area!enclosed!by!the!centremlines!of!the!closed!transverse!torsional!reinforcements!

Aø!

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Area!of!each!bar!

Aref,x!

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Reference!area!

As!

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Total!reinforcement!area!

A'ρ!

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Area!of!pre!or!postmtensioned!tendons!

ALS! ! Accidental!Limit!State!

CD!

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Drag!coefficient!

Cdev!

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Allowance!in!design!for!deviation!

Cdir!

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Directional!factor!

Cdur,add!

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Reduction!of!minimum!cover!for!use!of!additional!protection!

Cdur,st!

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Reduction!of!minimum!cover!for!use!of!stainless!steel!

Cdur,γ!

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Additive!safety!element!

Cmin!

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Minimum!concrete!cover!

Cmin,b!

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Minimum!cover!due!to!bond!requirements!

Cmin,dur!

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Minimum!cover!due!to!environmental!conditions!

Cseason!

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Season!factor!

Ec!

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Design!value!of!modulus!of!elasticity!of!concrete!

Es!

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Design!value!of!modulus!of!elasticity!of!reinforcing!steel!

F!

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Forces!(kN/m)!

FLS! ! Fatigue!Limit!State!

Gk!

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Characteristic!permanent!action!

I!

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Second!moment!of!inertia!

L!

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Length!!

M!

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Bending!moment!

Mcrack!

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Bending!moment!limit!for!cracking!

Md!

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Maximum!design!moment!

MEd!

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Design!value!of!the!applied!internal!bending!moment!

MSLS!

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Serviceability!Limit!State!bending!moment!

P!

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Point!load!

Q! Point!load!

Qlak!

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Traction!force!

Qlbk!

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Braking!force!

Sk!

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Characteristic!value!of!snow!on!the!ground!at!the!relevant!site!(kN/m2)!!

Sr,max!

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Maximum!crack!spacing!

SLS!

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Serviceavility!limit!state!

Te,max!

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Maximum!uniform!bridge!temperature!

Te,min!

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Minimum!uniform!bridge!temperature!

TEd!

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Design!value!of!the!applied!torsional!moment!

Tmax!

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Maximum!shade!temperature!

Tmin!

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Minimum!shade!temperature!

ULS!

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Ultimate!limit!state!

Vb!

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Basic!wind!velocity!

VEd!

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Shear!force!

Vref!

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Reference!value!of!wind!velocity!

We!

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Wind!force!(kN/m2)!

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Latin!lower!case!letters!

b!

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Width!

d!

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Depth!

f!

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Natural!frequency!

fcd!

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Design!value!of!concrete!compressive!strength!

fck!

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Characteristic!compressive!cylinder!strenth!of!concrete!at!28!days!

fctd!

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Design!value!of!concrete!tensile!strength!

fctk,!0,05!

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Characteristic!axial!tensile!strength!of!concrete!

fctm!

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Mean!value!of!axial!tensile!strenght!of!concrete!

fstd!

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Design!yield!strength!of!reinforcement!

fyd!

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Design!yield!strength!of!reinforcement!

fyk!

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Characteristic!yield!strength!of!reinforcement!

h!

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Height!

h0!

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Notional!size!

lb,rqd!

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Basic!anchorage!length!

lbd!

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Design!anchorage!length!

n!

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Number!of!reinforcement!bars!

q!

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Distributed!load!

s!

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Spacing!between!reinforcement!bars!

t!

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Age!of!the!concrete!at!the!moment!considered,!in!days!

u!

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Perimeter!of!that!part!of!the!crossmsection!which!is!exposed!to!drying!

wk!

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Crack!width!

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Greek!upper!case!letters!

Φ!!

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Dynamic!factor!according!to!EN!1991m2!

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Greek!lower!case!letters!

ø!

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Diameter!of!reinforcing!bars!

α!

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Classification!coefficient!

αc!

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Coefficient!taking!into!account!long!term!effects!on!the!copressive!strength!

γc!

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Partial!safety!factor!for!concrete!

γs!

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Partial!safety!factor!for!steel!

δ!

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Deflection!

εca!

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Autogenous!shrinkage!strain!

εcd!

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Drying!shrinkage!strain!

εcm!

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Mean!strain!in!the!concrete!between!cracks!

εcs!

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Total!shrinkage!strain!

εsm!

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Mean!strain!in!the!reinforcement!under!the!relevant!load!combination!

θ!

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Inclination!angle!of!stirrups!

μ!

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Relative!moment!

ρ!

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Density!

σs!

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Stress!in!tension!reinforcement!

τ!

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Torsional!shear!stress!

ψ!

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Factors!defining!representative!values!of!variable!actions!!

ψ0!

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combination!values!

ψ1!

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frequent!values!

ψ2!

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quasimpermanent!values!!

ω!

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Reinforcement!ratio!

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Table!of!Contents !

PREFACE! 3

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ABSTRACT! 5

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SAMMANFATTNING! 6

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ABSTRACTO! 7

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SYMBOLS! 9

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1.

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!INTRODUCTION! 15

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1.1!GENERAL!BACKGROUND! 15

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1.2!TRAFIKVERKET! 15

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1.3!AIMS!AND!SCOPE! 15

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1.4!MAINLINEm!A!EUROPEAN!RESEARCH!PROJECT! 16

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1.5!LIMITATIONS! 17

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1.6!STRUCTURE!OF!THE!THESIS! 17

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2.

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!RESEARCH!QUESTIONS! 19

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2.1!HOW!CAN!STANDARD!RAILWAY!BRIDGES!BE!DESIGNED!ACCORDING!TO!THE!NEW!EUROCODES?! 19

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2.2!HOW!DOES!THE!LENGTH!OF!A!BRIDGE!AFFECT!THE!CROSSmSECTION!GEOMETRY!AND!THE!!

!!!!!!!!AMOUNT!OF!REINFORCEMENT?! 19

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2.3!WHAT!ARE!THE!DIFFERENCES!BETWEEN!THE!DESIGN!IN!SOUTHERN!AND!NORTHERN!EUROPE?! 19

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3.

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!LITERATURE!STUDY! 21

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3.1!EUROCODES!(EUROCODE!0,!2005)! 21

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3.4!CONCRETE!BRIDGES! 22

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4.

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DESIGN!PRINCIPLES! 25

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4.1!BRIDGE!SPECIFICATIONS! 25

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4.2!DURABILITY!AND!COVER!TO!REINFORCEMENT! 28

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4.3!PERMANENT!LOADS! 29

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4.4!VARIABLE!LOADS! 31

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4.5!ULTIMATE!AND!SERVICEABILITY!LIMIT!STATES! 44

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4.6!ANCHORAGE! 50

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4.7!REINFORCEMENT! 52

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4.8!FATIGUE! 64

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5.

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SOLUTIONS!FOR!STANDARD!BRIDGES! 71

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5.1!THREE!METERS!LONG! 71

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5.2!FOUR!METERS!LONG! 74

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5.3!FIVE!METERS!LONG! 77

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5.4!SIX!METERS!LONG! 80

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5.5!SEVEN!METERS!LONG! 83

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5.6!EIGHT!METERS!LONG! 86

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5.7!NINE!METERS!LONG! 89

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5.8!SUMMARY! 92

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6.

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COMPARISON!WITH!OTHER!BRIDGES!IN!SWEDEN! 93

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7.

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CONCLUSIONS! 97

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8.

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REFERENCES! 99

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APPENDIX!A.!CALCULATIONS!FOR!6!METER!LENGTH! 101

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BRIDGE!SPECIFICATIONS! 101

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DURABILITY!AND!COVER!TO!REINFORCEMENT! 102

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PERMANENT!LOADS! 102

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VARIABLE!LOADS! 106

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ULTIMATE!AND!SERVICEABILITY!LIMIT!STATES! 110

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ANCHORAGE! 113

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REINFORCEMENT! 113

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FATIGUE! 123

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FINAL!DESIGN! 126

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APPENDIX!B.!!INTERESTING!MAPS!OF!SWEDEN! 127

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B.1!MAP!OF!SWEDEN!WITH!ITS!RIVERS!AND!LAKES! 127

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B.2!SCANDINAVIAN!RAILWAY!NETWORK! 128

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APPENDIX!C.!EXPOSURE!CLASSES! 129

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APPENDIX!D.!ULTIMATE!LIMIT!STATES!DESIGN!VALUES! 131

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APPENDIX!E.!DYNAMIC!ANALYSIS! 133

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APPENDIX!F.!THERMAL!ACTIONS! 135

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APPENDIX!G.!ANCHORAGE!LENGTHS! 137

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APPENDIX!H.!MATERIAL!PROPERTIES! 139

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APPENDIX!I.!FATIGUE! 141

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ABOUT!THE!AUTHOR! 145

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1.!!Introduction!

1.1!General!background!

Spain!has!an!extension!of!504,782!square!kilometres!of!which!about!5,24!square!kilometres!are!water.!

In!the!Spanish!geometry,!there!are!many!mountains,!which!means!that!the!roads!have!very!big!slopes.!

This!fact!presents!a!challenge!when!planning!a!proper!and!efficient!transport!network!to!allow!the!

communication!between!different!towns!and!cities.!!

Bridges!between!3!and!9!meters!long!are!quite!common!in!the!country!in!order!to!overcome!small!rivers,!

streams,!canals,!other!roads!and!valleys.!According!to!the!Mainline!Project!D3.1!"Benchmark!of!

production!and!replacement!of!railway!infrastructure",!in!Europe,!80%!of!the!bridges!are!short!bridges!

between!2!and!10!meters.!

In!highland!areas!where!there!may!be!snow!during!winters,!a!correct!and!proper!design!of!the!railway!

network!becomes!essential!to!maintain!communication!in!the!country.!!A!bridge!is!a!very!delicate!and!

important!stuff!on!a!transport!network!since!it!involves!a!lot!of!money!and!effort.!If!its!design!is!not!

correctly!done!or!if!there!is!any!error,!the!losses!will!be!really!important.!So!it!is!worth!spending!time,!

money!and!effort!on!optimizing!the!design!of!bridges!to!make!this!process!faster!and!easier!without!

losing!reliability!and!safety.!

To!have!designed!previously!some!kind!of!standard!bridges!is!really!useful!and!could!make!a!difference.!

Also,!it!will!be!interesting!to!compare!the!results!with!the!designs!used!in!the!northern!part!of!Europe,!in!

order!to!determine!the!possible!differences!between!northern!and!southern!Europe.!

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1.2!Trafikverket!

Trafikverket!(the!Swedish!Transport!Administration)!is!a!government!agency!which!is!responsible!for!

longmterm!planning!of!the!transport!system!for!all!kinds!of!transport!(road,!railway,!sea!and!flight)!and!it!

is!the!owner!and!maintainer!of!most!roads!and!railroads!in!Sweden.!It!is!responsible!for!the!construction,!

operation!and!maintenance!of!all!state!owned!roads.!

As!mentioned!above,!having!a!proper!railway!system!in!the!transport!network!of!a!country!like!Sweden!

is!crucial!and!it!is!important!to!have!a!competent!and!adequate!agency!as!Trafikverket!to!carry!out!this!

task.!The!Swedish!Transport!Administration!work!on!the!design!and!maintenance!of!the!railway!system!

is!essential,!and!the!amount!of!railway!bridges!that!compose!this!system!is!about!4000,!Trafikverket!

(2014).!

The!Swedish!Transport!Administration!is!also!responsible!for!administering!the!theoretical!and!driving!

tests!needed!to!receive!a!driving!licence!and!taxi!driver!badge,!as!well!as!the!theoretical!test!for!the!

professional!knowmhow!needed!for!a!transport!licence!and!certificate!of!professional!competence.!

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1.3!Aims!and!Scope!

The!aim!of!this!thesis!is!to!provide!some!useful!standard!drawings!and!create!a!handbook!of!bridge!

design!according!to!the!new!Eurocodes!in!order!to!have!some!standard!calculations!for!bridges!with!

spans!between!3!and!9!meters.!It!can!be!useful!in!order!to!save!time!and!money!where!a!replacement!

of!an!old!bridge!is!needed.!These!bridges!can!be!built!in!a!factory!and!transported!to!the!replacement!

site.!!

The!main!aspects!that!affect!the!design!of!a!bridge!are!the!following:!

- Ultimate!Limit!State!(ULS):!

• Bending!

• Shear!

• Torsion!

• Punching!(from!an!axle!load)!

- Fatigue!Limit!State!(FLS):!

• Fatigue!

- Serviceability!Limit!State!(SLS):!

• Cracks!

• Stresses!

• Natural!frequency!

• Deflection!(comfort!demands!and!clearance!under!bridge!

• Dynamic!analysis!

- Accidental!Limit!State!(ALS):!

• Derailment!

In!this!thesis,!most!of!these!aspects!will!be!covered!in!the!corresponding!sections.!!

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1.4!MAINLINEF!A!European!Research!Project!

Growth!in!demand!for!rail!transportation!across!Europe!is!predicted!to!continue.!Much!of!this!growth!

will!have!to!be!accommodated!on!existing!lines!that!contain!old!infrastructure.!This!demand!will!

increase!both!the!rate!of!deterioration!of!these!elderly!assets!and!the!need!for!shorter!line!closures!for!

maintenance!or!renewal!interventions.!The!impact!of!these!interventions!must!be!minimized!and!will!

also!need!to!take!into!account!the!need!for!lower!economic!and!environmental!impacts.!New!

interventions!will!need!to!be!developed!along!with!additional!tools!to!inform!decision!makers!about!the!

economic!and!environmental!consequences!of!different!intervention!options!being!considered.!!

The!questions!above!are!addressed!in!the!project!MAINLINE,!which!is!a!part!the!European!Framework!

Program!7,!see!Mainline!(2014).!The!questions!are!addressed!through!a!series!of!linked!work!packages!

that!target!a!reduced!environmental!footprint!in!terms!of!embodied!carbon!and!other!environmental!

benefits.!The!project:!!

- Applies!new!technologies!to!extend!the!life!of!elderly!infrastructure.!

- Improves!degradation!and!structural!models!to!develop!more!realistic!life!cycle!cost!and!safety!

models.!

- Investigates!new!construction!methods!for!the!replacement!of!obsolete!infrastructure.!

- Investigates!monitoring!techniques!to!complement!or!replace!existing!examination!techniques.!!

- Develops!management!tools!to!assess!whole!life!environmental!and!economic!impact.!

This!thesis!aims!to!fulfil!part!of!the!goals!for!WP3!above!by!providing!assistance!in!the!design!of!new!

bridges!when!there!is!a!need!to!exchange!existing!bridges.!!!

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1.5!Limitations!

In!order!to!simplify!the!calculations,!the!slab!is!assumed!to!have!a!constant!crossmsection!along!the!

bridge!and!to!have!a!linear!behaviour!in!the!Serviceability!and!Fatigue!Limit!States.!A!static!analysis!will!

be!used!in!the!Ultimate!and!Fatigue!Limit!State.!A!dynamic!analysis!is!not!needed!due!to!the!

characteristics!of!the!bridge!and!the!traffic.!Bending!moments!and!shear!forces!will!be!studied.!By!

choosing!a!specific!location,!it!is!possible!to!get!more!accurate!results!regarding!wind!and!snow.!

Rotation!requirements!are!not!going!to!be!taken!into!account.!

The!amount!of!reinforcement!could!be!optimized!with!a!3Dmmodel!but!it!will!not!be!performed!in!order!

to!keep!the!length!of!the!thesis!within!limits.!

It!is!necessary!to!check!if!the!concrete!is!cracked!or!unmcracked.!This!is!done!by!comparing!the!applied!

moment!and!the!“cracking!moment”!of!the!concrete!cross!section.!To!calculate!the!crack!moment!M!of!

a!concrete!cross!section!the!tensile!stress!σ has!to!be!calculated!with!Naviers!formula:!

σ = M

I ⋅ y ⇒ M = σ

I ⋅ y

_{! (1.1)}

M

_crack

=

f

_ctm

⋅ 1 12 ⋅ b ⋅ h

³

"

# $ %

&

' h

2

"

# $ %

&

'

= 1

6 ⋅ b ⋅ h

²

⋅ f

_ctm

! (1.2)

!

If!the!applied!moment!is!larger!than!the!cracking!moment,!the!concrete!is!cracked!and!the!crack!width!

should!be!calculated!according!to!EN1992m1m1!§7.3!(EN1992m2!§7.3)!

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1.6!Structure!of!the!thesis!

The!first!chapter!introduces!some!background!to!this!thesis,!as!well!as!some!information!about!

Trafikverket,!which!has!supported!the!work!with!information!about!similar!projects!using!the!old!

national!Swedish!codes.!Also,!the!aims!and!scope!of!the!thesis!is!outlined.!

The!second!chapter!describes!the!research!questions!that!have!motivated!the!thesis.!

The!third!chapter!includes!a!literature!study!made!to!get!the!information!needed!to!write!this!thesis.!

The!fourth!chapter!contains!the!calculations!performed!in!the!design.!

The!fifth!chapter!develops!the!solutions!for!design!and!distributions!for!all!the!different!lengths.!

The!sixth!chapter!includes!a!comparison!between!the!different!national!annexes!in!Europe.!

The!seventh!chapter!summarizes!the!results!and!contains!the!conclusions!that!were!reached!in!this!

thesis.!

Finally,!the!Appendices!provide!additional!data!and!results.!

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2.!!Research!questions!

With!this!thesis,!the!following!research!questions!will!be!answered:!

2.1!How!can!standard!railway!bridges!be!designed!according!to!the!

new!Eurocodes?!

In!the!new!Eurocodes,!there!is!a!part!that!refers!specifically!to!bridges,!EN1992m2.!This!second!part!of!

the!Eurocode!for!concrete!is!divided!into!several!sections:!

1. General!

2. Basis!of!design!

3. Materials!

4. Durability!and!cover!to!reinforcement!

5. Structural!analysis!

6. Ultimate!limit!states!

7. Serviceability!limit!states!

8. Detailing!of!reinforcement!and!premstressing!tendonsm!General!

9. Detailing!of!members!and!particular!rules!

10. Additional!rules!for!precast!concrete!elements!and!structures!

11. Lightweight!aggregate!concrete!structures!

12. Plain!and!lightly!reinforced!concrete!structures!

13. Design!of!the!execution!stages!

These!Eurocodes!determine!the!rules!to!follow!in!order!to!unify!the!design!for!all!Europe.!

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2.2!How!does!the!length!of!a!bridge!affect!the!crossFsection!

geometry!and!the!amount!of!reinforcement?!

In!this!thesis,!the!design!of!reinforced!concrete!bridges!with!lengths!between!3!and!9!meters!is!going!to!

be!carried!out.!The!amount!of!reinforcement!depends!on!the!bending!moments!and!shear!forces!that!

the!bridge!has!to!support.!As!the!length!of!the!bridge!increases,!the!moments!and!forces!also!will!

increase.!!

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2.3!What!are!the!differences!between!the!design!in!southern!and!

northern!Europe?!

The!final!results!are!going!to!be!compared!with!the!results!provided!using!the!Swedish!National!Annexes,!

Martínez!Díaz!(2014),!in!order!to!be!able!to!compare!the!differences!between!the!design!in!northern!

and!southern!Europe.!

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3.!!Literature!study!

There!are!quite!a!lot!of!studies!concerning!railway!bridge!design.!A!small!resume!of!the!used!literature!is!

presented!in!the!following!points.!

!!!!!!!!3.1!Eurocodes!(Eurocode!0,!2005)!

In!1975,!the!work!with!the!Eurocode!began.!This!was!done!in!order!to!unify!all!the!technical!aspects,!as!

well!as!to!minimize!the!obstacles!that!may!appear!in!the!trade!between!European!countries.!

Nowadays,!there!are!10!Eurocodes!and!58!parts.!!

- Eurocode!0!m!EN!1990!! Basis!of!Structural!design!

- Eurocode!1!m!EN!1991!!! Action!on!Structures!

- Eurocode!2!m!EN!1992!! Design!of!Concrete!Structures!

- Eurocode!3!m!EN!1993!! Design!of!Steel!Structures!

- Eurocode!4!m!EN!1994!! Design!of!Composite!Steel!And!Concrete!Structures!

- Eurocode!5!m!EN!1995!! Design!of!Timber!Structures!

- Eurocode!6!m!EN!1996!! Design!of!Masonry!Structures!

- Eurocode!7!m!EN!1997!! Geotechnical!Design!

- Eurocode!8!m!EN!1998!! Design!of!Structures!For!Earthquake!Resistance!

- Eurocode!9!m!EN!1999!! Design!of!Aluminium!Structures!

Eurocodes!EC0,!EC1,!EC7!and!EC8!would!have!no!application!if!they!weren’t!referred!to!in!the!other!

Eurocodes!EC2,!EC3,!EC4,!EC5,!EC6!and!EC9.!

This!implies!that!for!the!application!of!the!Eurocodes,!different!packages!of!norms!have!been!made.!

These!packages!are!made!in!order!to!group!the!norms!that!are!necessary!for!certain!calculations.!

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3.2!MAINLINE!!

The!project!consortium!includes!leading!railways,!contractors,!consultants!and!researchers!from!across!

Europe,!including!from!both!Eastern!Europe!and!the!emerging!economies.!Partners!also!bring!

experience!on!approaches!used!in!other!industry!sectors!which!have!relevance!to!the!rail!sector.!Project!

benefits!will!come!from!keeping!existing!infrastructure!in!service!through!the!application!of!

technologies!and!interventions!based!on!life!cycle!considerations.!Although!MAINLINE!will!focus!on!

certain!asset!types,!the!management!tools!developed!will!be!applicable!across!a!broader!asset!base.!

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The!project!is!led!by!UIC,!France,!with!Dr.!Björn!Paulsson!as!coordinator.!Luleå!University!of!Technology,!

Sweden,!acts!as!Scientific!and!Technical!Coordinator.!Other!partners!are:!Network!Rail!Infrastructure!

Limited,!United!Kingdom;!COWI,!Denmark;!SKM,!United!Kingdom;!University!of!Surrey,!United!Kingdom;!

TWI,!United!Kingdom;!University!of!Minho,!Portugal;!DB!Netz!AG,!Germany;!MÁV!Magyar!Államvasutak!

Zrt,!Hungary;!Universitat!Politècnica!de!Catalunya,!Spain;!Graz!University!of!Technology.!

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3.3!Bridge!design!

There!are!many!books!on!bridge!design!and!construction!as!e.g.!Chen!and!Duan!(2000),!Brühwiler!and!

Menn!(2003),!Reis!(2003),!Ryal!et!al!(2000),!Scheer!(2010),!Taly!(1998)!and!Xanthakos!(1994).!!

There!are!also!many!books!on!the!history!and!development!of!bridges!as!e.g.!Ahlberg!and!Spade!(2001),!

Brown!(1998),!Crickshank!(2010),!Fernández!Troyano!(2003)!and!Graf!(2002).!!

They!give!detailed!aspects!on!bridge!design!and!also!the!basic!principles!to!follow.!

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!!!!!!!3.4!Concrete!bridges!

As!it!is!well!known,!concrete!has!a!lot!of!benefits!in!comparison!with!other!materials!used!in!the!

construction!of!bridges,!such!as!steel!and!timber.!!Steel!has!a!much!better!tensile!strength!but!is!also!

more!expensive.!Timber!has!to!be!protected!in!order!not!to!deteriorate.!!

For!long!bridges,!the!best!option!is!to!combine!steel!and!concrete!into!composite!bridges!in!order!to!

reduce!costs!and!keep!a!good!resistance.!For!short!bridges,!as!in!our!case,!reinforced!concrete!will!give!

us!enough!capacity!to!carry!the!loads.!!

As!it!was!said,!concrete!also!has!more!benefits,!such!as:!

- Cost:!concrete!is!a!cheap!material!available!for!construction!and!it!also!has!a!low!maintenance!

cost!during!the!service!life!of!a!bridge.!

- Surface!Finish!variety:!the!use!of!concrete!in!building!gives!a!great!variety!of!surface!finishes!that!

can!be!applied!while!the!concrete!is!wet!or!once!it!is!dry.!!Concrete!is!versatile.!

- Shape!and!form!flexibility:!with!a!suitable!formwork,!concrete!can!be!made!into!any!shape,!and!

that!helps!out!so!that!no!extra!fixings!have!to!be!made!once!the!concrete!is!casted.!

- Specification!Variety:!with!different!proportions!in!the!composition!of!the!concrete,!it!can!be!

made!to!full!fill!the!requirements!needed!for!each!construction.!

- Durability:!concrete!bridges!can!have!a!very!long!life,!if!the!concrete!is!designed!in!order!to!

support!large!temperature!changes!and!other!external!attacks.!

- Environmentally!Friendly:!There!are!some!carbon!emissions!during!the!production!of!concrete,!

but!after!that!it!represents!no!harm!for!the!environment.!

- Resistance!to!Fire:!concrete!is!naturally!resistant!to!fire,!so!it!doesn't!need!any!extra!protection.!!

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There!are!many!different!types!of!concrete!bridges:!

- Arch!bridges:!Traditionally,!this!kind!of!bridges!were!made!of!stone,!brick!and!concrete,!which!are!

strong!materials,!able!to!cope!with!the!compressive!forces!that!appear!in!the!arch.!Nowadays,!

premstressing!and!reinforcing!are!used!for!this!kind!of!bridges.!Arch!bridges!are!strong!due!to!the!

capacity!to!generate!compressive!forces!in!the!arch!from!the!vertical!loads!acting!on!it.!These!

compressive!forces!translate!into!inclined!thrusts,!which!have!to!be!absorbed!by!the!supports.!!!

- Reinforced!slab!bridges:!For!short!spans,!the!simplest!design!of!this!kind!of!bridges!is!a!reinforced!

slab!cast!inmsitu.!These!are!simple!and!cheap!solutions,!due!to!the!simplicity!of!the!framework,!

formwork!and!reinforcement.!For!longer!spans,!the!solution!is!slightly!more!complicated.!The!

slab!has!to!be!thicker!in!order!to!cope!with!the!increased!loads,!this!also!increases!the!weight!of!

the!slab!and!it!may!become!a!problem.!In!order!to!solve!this,!either!premstressing!can!be!used!or!

the!deadweight!can!be!reduced.!!

- Beam!and!slab!bridges:!This!kind!of!bridges!is!very!simple,!cheap!and!quick!to!construct.!The!

construction!is!made!in!different!steps.!First,!precast!beams!can!be!placed!on!rubber!bearings!

that!don't!need!any!maintenance.!Then,!the!permanent!concrete!slab!can!be!casted!directly!on!

the!beams.!!

- Box!girder!bridges:!This!type!of!bridges!is!normally!used!for!long!spans!(longer!than!45!m).!The!

shape!of!the!box!isn't!fixed,!it!varies!between!bridges,!and!it!can!also!vary!along!the!same!bridge,!

being!deeper!at!the!abutments!and!shallower!in!the!spans.!To!build!this!type!of!bridges,!there!are!

different!construction!methods,!such!as:!

• Spanmbymspan!

• Balanced!cantilever!

- Integral!bridges:!Bridges!constructed!without!expansion!joints!and!bearings!are!called!integral!

bridges.!These!can!be!built!with!any!concrete!deck.!Where!to!locate!the!joints!is!a!difficult!step!of!

the!design!process.!These!are!useful!to!allow!the!movement!of!the!structure!as!it!expands!or!

contracts!due!to!temperature!variations.!On!the!other!hand,!these!joints!can!also!be!a!weak!point!

due!to!the!leaks!that!may!appear,!resulting!in!the!corrosion!of!the!metallic!components!of!the!

bridge!

- Cablemstayed!bridges:!In!this!type!of!bridge,!the!loads!are!carried!by!the!supporting!cables!that!

are!attached!from!the!sides!of!a!tower!(or!several!of!them)!to!the!sides!of!the!bridge.!They!are!

used!for!very!long!spans.!!

- Suspension!bridges:!These!bridges!usually!have!decks!made!of!concrete.!For!the!construction,!it!

is!very!important!to!have!huge!foundations!to!support!the!weight!of!the!whole!bridge,!as!well!as!

the!anchorages.!The!abutments!and!the!superstructure!can!also!made!in!concrete,!to!be!able!to!

support!all!the!forces!that!may!appear.!

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4.! Design!principles!

4.1!Bridge!specifications!!

According!to!Trafikverket,!the!optimum!design!for!very!short!span!bridges!(up!to!2m!length)!would!be!a!

thick!reinforced!slab,!which!copes!with!all!the!forces!acting!on!the!bridge,!and!nonmstructural!walls!

without!reinforcement,!see!Figure!4.1.!!

! Figure)4.1:)Standard)short)bridge)geometry)

)

For!bridges!with!lengths!over!10!m,!the!geometry!is!different.!In!these!cases!a!thinner!slab!is!used,!with!

reinforced!walls!acting!as!structural!beams,!see!Figure!4.2.!

! Figure)4.2:)Standard)long)bridge)geometry)

)

This!particular!case!is!somewhere!in!between,!the!lengths!taken!into!account!are!between!3!and!9!

metres.!A!good!study!case!would!be!to!find!an!optimized!design!for!these!intermediate!lengths.!In!this!

thesis,!the!focus!is!located!on!the!typical!design!for!longer!bridges,!with!slight!variations.!The!starting!

measures!for!the!standard!bridge!in!the!study!are!as!shown!in!Table)4.1.!

The!height!of!the!ballast!is!set!to!600!mm!in!the!National!Annex.!

In!the!following!many!references!are!made!to!the!formulae,!Figures!and!Tables!in!the!Eurocodes.!

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Length! L! meter!

Width! 5! meter!

Wall’s!height! 1,1! meter!

Slab!thickness! 0,3! meter!

Wall!thickness!top! 0,2! meter!

Wall!thickness!bottom! 0,4! meter!

Rail!width! 1,435! meter!

Ballast!height! 0,6! meter!

Table)4.1:)Bridge)dimensions)

) Figure)4.3:)Bridge)geometry)

For!all!the!different!lengths,!the!same!materials!will!be!used.!All!the!specific!characteristics!for!both!

materials!are!found!in!Appendix!H!in!this!thesis.!

- Concrete!C40/50!

The!design!compressive!strength!for!concrete!has!to!be!calculated!according!to!EN1992m2!

§3.1.6:!!

f

_cd

= α

_cc

⋅ f

_ck

γ

_c ^{! ! (4.1)!}

where:!

γ

c! ! partial!safety!factor!for!concrete!

!

α

_cc! ! !coefficient!taking!into!account!long!term!effects!on!the!

compressive!strength!!!(

0,8 ≤ α

cc

≤ 1, 00

^)!

where:!

α

_cc

=1, 00

! Spanish!national!annex!

The!design!tensile!strength!(also!according!to!EN1992m2!§3.1.6):!

f

_ctd

= α

_ct

⋅ f

_ctk,0,05

γ

_c ^{! ! (4.2)!}

where:!

γ

_c^! partial!safety!factor!for!concrete! !

! !

γ

c

= 1 , 5

!!from!1992m1m1!Table!2.1N!

!

α

ct! ! !coefficient!taking!into!account!long!term!effects!on!the!

compressive!strength!!!(

0,8 ≤ α

ct

≤ 1, 00

^)!

! ! !

α

ct

= 1 , 00

!for!Spanish!national!annex!

- Steel!B500B!

It!shall!have!adequate!ductility!as!defined!by!the!ratio!tensile!strengthmyield!stress!and!the!

elongation!at!maximum!force.!

The!design!tensile!strength!for!steel!according!to!EN1992m1m1!§Figure!3.8:!

s yk yd std

f f

f ^{= =} γ

^{!!!!!!!! ! (4.3)!}

where:!

γ

c! partial!safety!factor!for!concrete! !

! !

γ

_c

= 1 , 15

!!from!1992m1m1!Table!2.1N!

- Ballast!!

From!EN1991m1m1,!table!A.6,!the!density!for!ballast!can!be!obtained.!!

To!determine!the!upper!and!lower!characteristic!value!of!depth!of!ballast!on!railway!bridges,!a!

deviation!from!the!nominal!depth!of!+/m!30%!should!be!taken!into!account.!This!demand!can!be!

changed!by!the!National!Annexes!in!the!Eurocode.!

Material! Weight!(kN/m³)!

Concrete! 25,0!

Steel! 77,0!

Ballast! 20,0!

Table)4.2:)Materials)and)weights)

For!the!sidewalks,!pierced!steel!plates!will!be!used!with!the!following!characteristics:!!

Weight! 0,2943! kN/m²!

http://spanish.alibaba.com/productmgs/frpmmoldedmfloormmicromeshmgratingmlightweightm955102821.html!

Table)4.3:)Sidewalks) For!the!sleepers,!UIC!(Alm40)!are!going!to!be!used,!see!Table!4.4:!

Length! 2,6! meter!

Width! 0,3! meter!!

Height! 0,24! meter!

Weight! 320! kg!

Distance!in!between! 0,6! meter!

Table)4.4:)Sleepers)

And!for!the!rails,!UIC60!will!be!used,!see!Figure!4.4!and!Table!4.5:!

H! 172,00! mm!

B! 150,00! mm!

C! 72,00! mm!

D! 51,00! mm!

E! 16,50! mm!

Section! 76,70! cm²!!

Mass! 60,21! kg/m!

Table)4.5:)Rails)

! Figure)4.4:)Rails)geometry)

)

!!!!!!4.2!Durability!and!cover!to!reinforcement!

The!safety!class!for!this!type!of!construction!is!considered!Class!3,!with!!

γ

d

= 1,1

!for!Spain,!from!

EN1990.!!

We!assume!that!the!concrete!surface!is!subject!to!long!term!water!contact!and!that!corrosion!of!the!

reinforcement!can!be!induced!by!carbonation.!According!to!the!EN1992m1m1!§4.2!Table!4.1,!the!

exposure!class!to!use!in!this!case!is!XC2,!see!Appendix!C!in!this!thesis.!

In!EN1992m1m1!§4.4.1.1,!the!method!to!calculate!the!concrete!cover!can!be!found.!The!steps!to!follow!

are:!

C

_min

= max C {

_min,b

;C

_min,dur

+ ΔC

_dur,γ

− ΔC

_dur,st

− ΔC

_dur,add

;10 mm }

_{! ! (4.4)!}

where:!

!

C

_min,b!! minimum!cover!due!to!bond!requirement![see!4.4.1.2(3)]!

!

C

_min,dur! minimum!cover!due!to!environmental!conditions![see!4.4.1.2(5)]!

!

ΔC

_dur,γ

! additive!safety!element![see!4.4.1.2(6)]!

!

ΔC

dur,st! reduction!of!minimum!cover!for!use!of!stainless!steel![§4.4.1.2(7)]!

!

ΔC

dur,add!reduction!of!minimum!cover!for!use!of!additional!protection![see!

4.4.1.2(8)]!

C

_min,b

= φ

reinf

C

_min,dur

= 20 mm

^!

- Exposure!class:!XC2!(No!salt!water!and!no!demicing!salt)!

- Table!4.3N:!Member!with!slab!geometry,!the!class!has!to!be!reduced!by!1!

- Table!4.4N:!The!initial!class!is!S4,!and!as!it!has!to!be!reduced!by!one,!the!

final!class!to!be!used!is!S3.!

ΔC

_dur,γ

= ΔC

_dur,st

= ΔC

_dur,add

= 0 mm

!(Recommended!value!by!the!Spanish!National!

Annex)!

C

_nom

= C

min

+ ΔC

dev! ! (4.5)!

where:!

Δ C

^dev_! allowance!in!design!for!deviation!(EN1992m1m1!§4.4.1.3)!

! ! !

ΔC

dev

= 10mm [National annex]

!!!!(National!Annex)!

!!!!!!4.3!Permanent!loads!

These!are!due!to!the!weight!of!the!different!elements!that!conform!a!bridge,!it!is!a!combination!of!the!

weight!and!the!dead!loads.!Its!values!are!deduced!from!the!dimensions!of!the!elements!specified!in!the!

plans,!and!from!the!corresponding!specific!weights.!

As!the!slab!is!supposed!to!be!premcasted!we!will!work!only!with!the!dry!concrete!for!the!dead!weight.!

- Own!weight:!the!weight!of!the!structural!elements!of!the!bridge.!

- Dead!loads:!these!correspond!to!the!nonmstructural!elements,!which!are!part!of!the!bridge,!such!

as!ballast,!sleepers,!sidewalks,…!If!it!is!not!very!clear!weather!a!load!is!acting!or!not!on!the!bridge!

during!its!life!cycle,!the!hypothesis!of!the!worst!possible!situation!will!be!taken!into!account.!!

Some!extra!permanent!loads!could!be!taken!into!account.!These!are:!

- Electrical!equipment!(1,0!kN/m)!

- Future!supplementary!dead!load!(2,0!kN/m)!

- Concrete!protection,!including!moisture!membrane!between!slab!and!ballast!(the!thickness!of!

the!concrete!protection!is!60!mm,!according!to!EN1991m1m1!Table!A.6)!

- 2!UIC60!rails!(1,2!kN/m,!from!EN1991m1m1!Table!A.6)!

Due!to!the!sleepers,!the!point!loads!are!distributed!through!the!ballast!and!act!as!a!distributed!load!on!

the!surface!of!the!slab.!This!characteristic!is!further!explained!later!in!the!traffic!load!distribution!section.!

This!load!is!not!uniformly!distributed!along!the!surface!because!there!is!a!sleeper!every!0.9!metres!in!

the!longitudinal!direction.!!

! Figure)4.5:)Sleeper)weight)distribution)

In!Figure)4.5,!it!is!allowed!to!smear!the!load!1:1!from!top!of!the!slab!to!the!centre!of!it.!

! Figure)4.6:)SelfKweight)distribution)(Longitudinal))

In!Figure)4.6,!load!q2!can!probably!be!smeared!as!q1!but!it!wont!be!done!in!order!to!get!more!accurate!

results.!

In!the!transversal!direction,!the!load!distribution!is!taken!as!follows:!

!

!

! Figure)4.7:)SelfKweight)distribution)(Transversal))

The!dead!load!of!every!component!of!the!bride!is!calculated!with!the!following!equation:!

q kN m

!

"

# $

% & = γ ^kN m

³

!

"

# $

% &⋅ A m ( )

²

! ! (4.6)!

And!the!final!value!of!the!permanent!load!is!obtained!by!adding!up!all!the!individual!loads!calculated!

above!(Table)D.1).!!

G

_k

= γ ( q

_concrete

+ q

_ballast

+ q

_rail

+ q

_sidewalks

+ q

_sleepers

)

!! ! (4.7)

!

!!

!!!!!!4.4!Variable!loads!

These!actions!consider!vertical,!horizontal!and!transverse!loads.!

- DYNAMIC!ANALYSIS!

From!EN1991m2!§6.4.4,!the!National!Annex!may!specify!the!requirements!for!determining!

whether!a!static!or!a!dynamic!analysis!is!required.!According!to!Figure!6.9![Figure!E.1,!Appendix!

E],!even!though!a!bridge!isn’t!a!continuous!bridge,!no!dynamic!analysis!is!required!if!the!natural!

frequency!of!the!bridge!is!within!the!limits!given!in!EN1991m2!§6.4.4,!Figure)6.10,!and!the!

maximum!speed!is!lower!than!200!km/h.!

The!natural!frequency!for!almost!all!lengths!is!within!the!limits!of!the!dynamic!analysis!

requirements.!Just!the!3!meters!bridge!is!out!of!the!limits,!so!the!dynamic!analysis!will!not!be!

done,!in!order!to!simplify!the!work.!

The!natural!frequency!for!the!bridge!is!calculated!by:!

f = π

2 ⋅ E ⋅ I

m ⋅ L

⁴ _{! ! (4.8)}^!

E

_c

= 32[GPa] = 32 ⋅10

⁹

[N / m

²

]

!

I = I

_slab

+ I

_beams

[m

⁴

]

_{! ! (4.9)!}

m = m

_slab

+ m

beams

+ m

ballast

[kg / m]

_{! ! (4.10)!}

L = length[m]

^!

The!Φ!factor!should!be!used!with!static!analysis!in!accordance!(EN1991m2!§6.4.5.2).!

Φ

₃

= 2,16

L

_Φ

− 0, 2 + 0, 3

! ! (4.11)!

where:!

L

_Φ

= L

^! Determinant!length!

- TRAFFIC!LOADS!

There!are!some!different!load!models!in!the!Eurocode!to!define!rail!traffic!actions:!

é!Load!Model!71!(and!Load!Model!SW/0!for!continuous!bridges)!representing!normal!rail!traffic!

on!mainline!railways.!

é!Load!Model!SW/2!for!heavy!loads!

é!Load!Model!HSLM!for!high!speed!passenger!trains!(over!200!km/h)!

é!Load!Model!“unloaded!train”!to!represent!the!effect!of!an!unloaded!train.!

This!thesis!is!going!to!be!focused!on!Load!Model!71!for!normal!rail!traffic!but!it!could!be!an!

interesting!study!case!to!check!the!differences!in!the!reinforcement!design!by!changing!the!Load!

Model.!

Load!model!71![EN!1991.2!§6.3.2]:!The!static!effect!caused!by!the!weight!of!the!railroad!vehicles!

on!a!rail,!shall!be!treated!as!a!train!from!the!Load!Model!71,!acting!on!the!axis!of!the!rail.!The!

specified!train!is!defined!by!the!following!actions,!occurring!simultaneously:!

• Four!axis!of!250!kN!each,!separated!1,6!meters,!located!in!the!least!favourable!position!for!

the!element!and!purpose!of!study.!!

• A!distributed!load!of!80!kN/m,!distributed!along!the!bridge,!at!both!sides!of!the!point!loads.!!!

Both!type!of!actions!will!be!multiplied!by!a!classification!coefficient,!in!this!case!of!study,!the!

value!to!be!used!is!α =1,21,!according!to!the!Spanish!Rail!Administration.!

α ∈!!0,75!–!0,83!–!0,91!–!1,00!–!1,10!–!1,21!–!1,33!–!1,46!![EN1991m2!§6.3.2(3)]!

The!following!actions!have!to!be!multiplied!by!the!α!factor:!

• Traffic!loads!

• Centrifugal!force!according!to!§6.5.1!

• Nosing!force!according!to!§6.5.2!

• Traction!and!braking!forces,!according!to!§6.5.3!

• Derailment!actions!for!accidental!design!situations,!according!to!§6.5.4!

! Figure)4.8:)Load)model)71)

Application!rules:!All!the!vertical!loads!exposed!may!act!combined!with!each!other!if!that!shows!

the!most!unfavourable!situation.!

• Local!distribution!of!the!loads![EN1991m2!§6.3.6.1]:!in!rails!located!over!ballast,!vertical!loads!

can!be!distributed!over!three!consecutive!sleepers.!The!medium!one!will!absorbs!50%!of!the!

load,!and!the!two!adjacent!ones!will!absorb!25%!each.!

The!load!on!each!sleeper!can!be!distributed!with!a!slope!of!4:1!through!the!ballast!height.!!

! Figure)4.9:)Longitudinal)distribution)of)a)point)load)on)the)sleepers)

)

! Figure)4.10:)Longitudinal)distribution)of)a)point)load)on)the)rail,)along)the)ballast)

P

_dim

= α ⋅ 250 ⋅ Φ

₃

q

_dim

= α ⋅80 ⋅ Φ

₃

#

$ %

&%

! ! (4.12)!

where:!

α = 1, 21

! Classification!coefficient!

!

!

!

!

!

!

!

- ENVIRONMENTAL!ACTIONS!

• Wind!loads![EN1991m1m4!§8]:!These!depend!on!the!mean!speed!and!the!terrain!category,!and!

they!can!vary!depending!on!the!country.!

Generally,!wind!loads!are!assimilated!to!a!static!equivalent!load.!In!order!to!calculate!the!

wind!force,!the!force!coefficients!on!the!bridge!and!on!the!train!have!to!be!calculated.!

! Figure)4.11:)Directions)of)wind)actions)on)bridges)

The!specifications!for!location,!type!of!terrain!and!elevation!are!the!recommended!values!

given!by!the!Eurocode.!

The!terrain!category!is!supposed!to!be!category!0!which!will!give!the!most!unfavourable!

exposure!factor![EN1991m1m4!Annex!A!A.1]:!Sea,!coastal!area!exposed!to!the!open!sea.!

The!altitude!of!the!bridge!is!taken!as!100!meters!to!give!the!most!unfavourable!coefficient.!

To!calculate!the!depth!to!be!used!for!the!reference!area!Aref,x!the!following!figure!is!used:!

! Figure)4.12:)Depth)to)be)used)for)Aref,x)

) ) ) )

Taking!into!account!the!road!restraint!system!in!the!bridge,!the!total!depth!is!obtained!as!

follows:!

ROAD!RESTRAINT!SYSTEM! On!one!side! On!both!sides!

Open!parapet!or!open!safety!barrier! d!+!0,3!m! d!+!0,6!m!

Solid!parapet!or!solid!safety!barrier! d!+!d1!m! d!+!2d1!m!

Open!parapet!and!open!safety!barrier! d!+!0,6!m! d!+!1,2!m!

Table)4.6:)Depth)dtot) )

Open!parapet!on!both!sides!are!assumed!for!this!thesis.!

! Figure)4.13:)Force)coefficient)for)bridges)Cfx,0)

! Figure)4.14:)Exposure)factor)for)bridges)Ce)

)

V

_b

= C

_dir

⋅ C

_season

⋅V

_ref

= 1, 00 ⋅1, 00 ⋅ 28 = 28[m / s]

! ! (4.13)!

where:!

!

V

_b! Basic!wind!velocity,!defined!as!the!function!of!wind!direction!and!time!of!

year!at!10m!above!ground!of!terrain!category!II!

V

_ref

! Reference!value!of!wind!velocity.!Taken!28!m/s!as!general!value!(most!

unfavourable)!

C

_dir!! It!is!the!directional!factor,!for!various!wind!directions.!The!recommended!

value!is!1,00!

C

_season!! It!is!the!season!factor,!for!various!wind!directions.!The!recommended!value!

is!1,00.!

!

W

_e1

= 1 2 ⋅ ρ ⋅V

b

2

⋅ C

D

⋅ A

ref ,x! ! (4.14)!

where:!

!

ρ

^! air!density!taken!as!

ρ = 1, 25 [kg / m

³

]

_!

!

C

_D! drag!coefficient!!

x

A

ref_, ! reference!area!given!in!8.3.1!

z W

_e

wind

= ⋅

F

_{! ! (4.15)!}

Wind!force!on!the!bridge:!

d = 1,1[m]

b = 5[m]

! "

# b d

_tot

= 5

1, 7 = 0, 98 → C

D

= 2, 0

!

V

_b

= 28[m / s]

^{! !}

ρ = 1, 25 [kg / m

³

]

_!

W

_e1

= 1

2 ⋅ ρ ⋅V

_b²

⋅ C

_D

⋅ A

_{ref ,x}

= 0, 59[kN / m

²

]

F

_wind,1

= W

_e1

⋅ z

₁

= 1, 00[kN / m]

_!

Wind!force!on!the!train:!

d = 1,1+ 4 = 5,1[m]

b = 5[m]

! "

# b

d

_tot

= 2, 94 → C

_D

= 1, 2

!

!

V

b

= 28[m / s]

^{! !}

ρ = 1, 25 [kg / m

³

]

_!

W

_e2

= 1

2 ⋅ ρ ⋅V

_b²

⋅ C

_D

⋅ A

_{ref ,x}

= 0, 98[kN / m

²

]

F

_wind,2

= W

_e2

⋅ z

₂

= 3, 33[kN / m]

_!

!

! Figure)4.15:)Wind)load)

!

In!longitudinal!direction!according!to!EN1991m1m4!§8.3.4,!the!National!Annex!may!give!the!

values!but,!for!Spain,!the!recommended!values!are!used:!

x wind x

wind y

wind

F F

F

_,

= 25 %

_,

= 0 , 25 ⋅

_, ^{! ! (4.16)!}

In!transversal!direction!(xmdirection)!the!results!are:!

Reaction!in!the!support:

F = 2, 44[kN / m]

! Maximum!moment:

M = 5, 97[kNm / m]

!

!

In!longitudinal!direction!(ymdirection)!the!results!are:!

Reaction!in!the!support:

F = 0, 51[kN / m]

! Maximum!moment:

M = 1, 50[kNm / m]

_!

!

• Snow!loads![EN1991m1m3]:!The!snow!load!will!only!be!considered!on!those!surfaces!that!

haven’t!been!acted!on!by!traffic!loads.!The!coefficients!that!determine!the!influence!of!the!

snow!on!the!different!regions!in!the!European!countries!is!found!in!the!national!annex!of!the!

Eurocodes.!

! Figure)4.16:)Snow)load)

)

k

k

S

q = 8 0 , ⋅

! ! (4.17)!

S

_k

= 1, 7 kN m

²

!

"

# $

% &(Spanish National Annex) q

_k

= 1, 36 kN

m

²

!

"

# $

% & = 6,8 kN m

!

"

# $

% &

2F = 6,8 kN m

!

"

# $

% & → F = 3, 4 kN m

!

"

# $

% &

!

!

!

!

! !