Table Of Content

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 ! LULEÅ%TEKNISKA%UNIVERSITET% Design%of%One%Span% Concrete%Railway% Bridges ! ! ! ! Design%according%to%the%Eurocodes%and%the% Spanish%National%Annex% ! ! ! Aida!Garcia!Rodriguez! ! 28!February!2014! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2! 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. ! Luleå!in!March!2014 Aida!Garcia!Rodriguez! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4! 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.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 5! 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.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 6! 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!.! ! ! ! ! ! ! ! ! ! ! ! ! ! 7! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 8! Symbols! Latin!upper!case!letters! A! Concrete!crossmsectional!area! c A ! ! Effective!area!of!concrete!in!tension! c,eff A ! ! Area!enclosed!by!the!centremlines!of!the!closed!transverse!torsional!reinforcements! k A ! ! Area!of!each!bar! ø A ! ! Reference!area! ref,x A! ! Total!reinforcement!area! s A' ! Area!of!pre!or!postmtensioned!tendons! ρ! ALS! !! Accidental!Limit!State! C ! Drag!coefficient! D C ! ! Allowance!in!design!for!deviation! dev C ! ! Directional!factor! dir C ! ! Reduction!of!minimum!cover!for!use!of!additional!protection! dur,add C ! ! Reduction!of!minimum!cover!for!use!of!stainless!steel! dur,st C ! ! Additive!safety!element! dur,γ C ! ! Minimum!concrete!cover! min C ! ! Minimum!cover!due!to!bond!requirements! min,b C ! ! Minimum!cover!due!to!environmental!conditions! min,dur C ! ! Season!factor! season E! ! Design!value!of!modulus!of!elasticity!of!concrete! c E! ! Design!value!of!modulus!of!elasticity!of!reinforcing!steel! s F! ! Forces!(kN/m)! FLS! !! Fatigue!Limit!State! G ! Characteristic!permanent!action! k I! ! Second!moment!of!inertia! L! ! Length!! M! ! Bending!moment! M ! ! Bending!moment!limit!for!cracking! crack M ! ! Maximum!design!moment! d M ! ! Design!value!of!the!applied!internal!bending!moment! Ed M ! ! Serviceability!Limit!State!bending!moment! SLS P! ! Point!load! Q! ! Point!load! ! ! 9!

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MASTER'S THESIS. Design of One Span Concrete Railway. Bridges. Design According to the Eurocodes and the Spanish National Annex.
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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 ! LULEÅ%TEKNISKA%UNIVERSITET% Design%of%One%Span% Concrete%Railway% Bridges ! ! ! ! Design%according%to%the%Eurocodes%and%the% Spanish%National%Annex% ! ! ! Aida!Garcia!Rodriguez! ! 28!February!2014! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2! 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. ! Luleå!in!March!2014 Aida!Garcia!Rodriguez! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 4! 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.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 5! 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.! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 6! 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!.! ! ! ! ! ! ! ! ! ! ! ! ! ! 7! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 8! Symbols! Latin!upper!case!letters! A! Concrete!crossmsectional!area! c A ! ! Effective!area!of!concrete!in!tension! c,eff A ! ! Area!enclosed!by!the!centremlines!of!the!closed!transverse!torsional!reinforcements! k A ! ! Area!of!each!bar! ø A ! ! Reference!area! ref,x A! ! Total!reinforcement!area! s A' ! Area!of!pre!or!postmtensioned!tendons! ρ! ALS! !! Accidental!Limit!State! C ! Drag!coefficient! D C ! ! Allowance!in!design!for!deviation! dev C ! ! Directional!factor! dir C ! ! Reduction!of!minimum!cover!for!use!of!additional!protection! dur,add C ! ! Reduction!of!minimum!cover!for!use!of!stainless!steel! dur,st C ! ! Additive!safety!element! dur,γ C ! ! Minimum!concrete!cover! min C ! ! Minimum!cover!due!to!bond!requirements! min,b C ! ! Minimum!cover!due!to!environmental!conditions! min,dur C ! ! Season!factor! season E! ! Design!value!of!modulus!of!elasticity!of!concrete! c E! ! Design!value!of!modulus!of!elasticity!of!reinforcing!steel! s F! ! Forces!(kN/m)! FLS! !! Fatigue!Limit!State! G ! Characteristic!permanent!action! k I! ! Second!moment!of!inertia! L! ! Length!! M! ! Bending!moment! M ! ! Bending!moment!limit!for!cracking! crack M ! ! Maximum!design!moment! d M ! ! Design!value!of!the!applied!internal!bending!moment! Ed M ! ! Serviceability!Limit!State!bending!moment! SLS P! ! Point!load! Q! ! Point!load! ! ! 9!

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MASTER'S THESIS. Design of One Span Concrete Railway. Bridges. Design According to the Eurocodes and the Spanish National Annex.
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