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  • 7/25/2019 HormigonEstructural Y PRESFORZADO[1]

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    HORMIGN ARMADO Y PRETENSADO

    CONCRETO REFORZADO Y PREESFORZADO

    ENRIQUE HERNNDEZ MONTESLUISA MARA GIL MARTN

    HORMIGN ARMADO Y PRETENSADO

    CONCRETO REFORZADO Y PREESFORZADO

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    F+9(r '27' L",9+#(! !e #r,s*+s+-,Longituddetransmisin

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    $%,r e$ v$"r P se %","%e %"*" longitud de transmisin' L $",9+#(! !e#r,s*+s+-, se )(e!e %$%($r )r#+r !e $ EHE r#%($" 70 " !e$ EC2 " 3+e,s()",er .(e es >0 ve%es e$ !+*e#r" ,"*+,$ )r %"r!",es - ?00 !+*e#r"s )r$*3res *#"!" ACI'

    T,#" $ EHE %"*" e$ EC2 s()",e, (, #e,s+-, %",s#,#e 1pt $" $r9" !e $$",9+#(! !e #r,s*+s+-, lpt'

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    )r%#+%, (,s *(es%s e, 1r" e, $ ", !e ,%$5e4 re!(%+,!"se s $ $",9+#(!!e #r,s*+s+-,'

    '?0' RELAACIN

    HORMIGN ESTRUCTURAL Hernndez-Gil

    E, $ 1+9(r '?? se re)rese,#3, $"s 1e,-*e,"s !e 1$(e,%+ 6 re$5%+-,'C"*" 6 v+*"s4 $ re$5%+-, es $ )r!+! !e #e,s+-, 35" !e1"r*%+-, %",s#,#e1+9(r '2 s+e,!" es#e 1e,-*e," es)e%+$*e,#e +*)"r#,#e e, e$ %er" !e )re#e,s!"'L re$5%+-, !e)e,!e !e$ #+e*)"4 !e $ #e*)er#(r 6 !e$ ,+ve$ !e #e,s+-,' Pr v$"res!e #e,s+-, +,1er+"res (41p $ re$5%+-, se )(e!e %",s+!err !es)re%+3$e'

    %

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    P"r e1e%#" !e $ re$5%+-, e$ v$"r !e$ *-!($" !e !e1"r*%+-, $",9+#(!+,$

    Ep vr' E$ ,(ev" v$"r Ep,e1 1+9(r '2 se )(e!e !e!(%+r )r#+r !e $"s v$"res !e$ re$5%+-,'

    L re$5%+-, XX'Op/pi )r (, #e,s+-, +,+%+$ pi %"*)re,!+! e,#re 0'> 60' !e1mF 6 )r (, #+e*)" t se )(e!e es#+*r )r#+r !e $ e%(%+-, '2:

    = p log; < = log pi

    = K! + K + log;t s,mFU s,m0n 6 e$ ,*er" !e %+%$"s .(e !+%& %r9 es re)e#+! &s# %(sr e$9"#*+e,#" !e$ *#er+$' E, &"r*+9-, r*!" 6 )re#e,s!" $ 1#+9 !e$ %er" es,#er+"r $ !e &"r*+9-,' E, $ 1+9(r '0 se & re)rese,#!" $ re$%+-, e,#re r,9" !e#e,s+",es 6 %+%$"s !e %r9 ,e%esr+"s &s# $ r"#(r:

    $**

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    ds.sTM+sTMK

    ds

    SE=>N '.'

    %igura !"." 3=cleo de hormign efca/mente confnado para armaduratransversalcircular.

    PROPIEDADES DE LOS MATERIALES ;2

    n la fgura!"." se o$serva la variacin (en direccinlongitudinal) del n=cleo efca/mente coninado para unacolumna circular con cercos circulares separados a unadistancias.

    0ea 6con la presin lateral e9ercida por la armadurauniormemente repartida so$re la superfcie del n=cleo de laseccin, !c. n realidad, esta presin se e9erce so$re elexterior de !e (/ona eica/mente coninada) 2ue, como yase ha comentado, no tiene un valor constante y 2ue es

    menor 2ue !c (n=cleo de la seccin).arapoderoperarconel n=cleo de la seccin se defne una presin lateral efca/(6e,con) 2ue act=a en el exterior del n=cleo de la seccin (!c)

    y produce el mismo eecto. Lgicamente, al aumentar elrea de actuacin, la presin lateral efca/sermenor 2uelapresinlateraldeconfnamiento(6e,con ?6con )

    e,conf

    = conf

    ke

    k =AeAcc

    !"."

    Acc

    =Ac ;! cc neamediade loscercosesds.0esupone2ue

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    el arco de descarga orma una par$ola con una inclinacinde salida de B; grados. l rea confnada eica/ (a mediadistanciaentre loscercos)yelreadehormigndentrodeln=cleode laseccin son,respectivamente

    A

    e dssT ds !

    sT K +

    K +ds

    !".B

    A =A (!)= d + (! )cc ccc

    Ks cc

    y,enestecaso, elcoeicientedeconfnamientoeica/,ke esHORMIGN ESTRUCTURAL ;

    Hernndez-Gil

    sT !

    k = +d

    s e

    !

    !".;cc

    aradeducirlaexpresindelapresinlateraldeconinamientoseplantea

    ele2uili$riodemediocercocircular,fgura!".B

    +As,4*f/ ,4* = conf sds!".

    siendof,!" la tensin mxima de la armadura del cerco. 0i sedefne#s como lacuant>ageomtricadelaarmaduratransversalrespectodeln=cleodelaseccin

    =As,4*ds KAs,4*

    !".8 s d +s

    ds s

    Ks

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    con ds

    y,4*'s,4*

    %igura!".Bresindeconfnamiento.

    losvaloresdelapresinlateraldeconinamientoydelapresinlateralefca/de confnamientosepuedeno$tenerapartirdelasexpresiones!".",!".y!".8

    +

    =

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    conf

    =!

    f+

    s / ,4*

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    e,conf

    = kesf/ ,4*

    +Dnave/ conocida latensin efca/ de confnamiento sepueden calcular

    losvalores de resistencia mxima del hormign confnado (fcc)yla deormacin

    PROPIEDADES DE LOS MATERIALES ;Hernndez-Gil

    As+,4*f/,4* =conf,+ sdc

    As/,4* f/,4* =conf,/ sbc

    !".#

    donde

    +s*,!"y+s,!" son lasreasdelasarmadurastransversalesseg=nlasdirecciones

    *erespectivamenteconf,*yconf, son las presiones laterales de

    confnamiento seg=n * e , respectivamente.

    12cleoefica*mente /confinado [

    dc3s45"

    dc

    ' '+

    c

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    1 1

    Hormi&)n inefica*mente

    ,-.sT s

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    bc

    SE=>N '.'

    %igura !".; 3=cleo de hormign eica/mente confnado para

    armaduratransversal rectangular.

    Ie la expresin anterior se pueden deducir lapresin lateral de confnamientoylapresinlateraleica/deconfnamientoenlasdirecciones*e

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    conf ,+

    PROPIEDADES DE LOS MATERIALES ;J

    =A

    s+,4*f/ ,4*

    sdc

    e,conf ,+ =ke + f/ ,4*

    !".#"

    conf ,/

    =A

    s/ ,4*f/ ,4*

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    e,conf ,/

    =ke / f/ ,4*

    dondekevienedadoporlaexpresin!".##.

    Conocidos los valores de las tensiones eicaces deconfnamiento en am$as direcciones se puede recurrir a unmodelo tridimensionalderoturayo$teneruna expresin parafcc. &ander (#+--) propuso el grfco de la fgura !".para el clculodefcc.Conestevalordefcc sepuedeemplearelmodelotensin5deormacin parahormignconinadodadopor

    laexpresin!."..ara el caso de confnamiento circular o

    rectangular igual en las direcciones*e,sepuedeemplearlasiguienteexpresin(&ander#+--)

    0"4K = ++=

    e,conf=

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    fc

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    +"+$K ! fc+

    !".#B

    c HORMIGN ESTRUCTURAL ;7

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    elacin de resistencias fcc5fc

    6e7conf7!8 6e7conf7"

    =+ f/ ,4*

    =

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    Relaci)n de confinamiento menor 6e7conf7!5fc

    %igura!".Hncrementodelaresistenciaacompresinenseccionesrectangularesconfnadasportensionesortogonales.

    Ladeormacinunitaria=ltimadelhormign(c),verigura!".#,sede$e

    alaroturadelconfnamientoypuedeaproximarsepor(aulay#++)

    cu

    =*"**K+!"K sf/ ,4* sm

    fcc

    !".#;

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    PROPIEDADES DE LOS MATERIALES ;

    Re"erencias

    Klume, 1. !., 3emarM, 3. &., and Corning, L. 4. (#+#). -esi.n of/ltistor 0einforcedoncrete ildin.s for Eart34ake /otions, ortland Cement !ssociation,0MoMie, Hllinois.

    4ernnde/5&ontes, ., !schheim, & and Fil5&art>n, L.&. (B). NGheimpact o optimal longitudinal reinorcement on the curvature ductilitycapacity o reinorced concretecolumn sectionsO./a.azine of oncrete 0esearc3, ;, 3o. +, 3oviem$re,B++5;#.

    &ander 1. K., &.1.3. riestley and *. arM (#+--). PGheoretical 0tress50train &odel or

    Confned ConcreteP.5ornal of 6trctral En.ineerin.. Qol ##B, 3E -, !gosto#+--. !0C.

    aulay G., riestley &.1.3. 6eismic -esi.n of 0einforced oncrete and/asonr ildin.s. 1ohnRiley S 0ons. #++.

    0heiMh 0.0., Teh C.C. (#++). P!nalytical &oment5Curvature *elations orGied ConcreteColumnsP.5ornal of 6trctral En.ineerin.. Qol. ##-, 3o., %e$rero, #++.!0C.

    E#emlo$

    HORMIGN ESTRUCTURAL ;;Hernndez-Gil

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    hormignes4!5;yelaceroK5B50.Laarmaduralongitudinalestcompuesta por;Uencadacaraconuntotalde#U.

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    0ehandispuestocercosycrucesde U# cada - cent>metros (confnamiento propuesto paraesta seccin por la !CH5"#-5; para /onas de alto riesgos>smico). n la fgura !".8$ se ha representado eldiagrama momento5curvatura correspondiente a estaseccin solicitada por un axil de compresin constante de#; M3. ara el n=cleo de la seccin se ha considerado elmodelo de arcos de descargay para el exterior de la seccinunmodelodehormignnoconfnado. lpunto#correspondealaroturadela/onaexteriordesprendimientodelrecu$rimiento.lpunto

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    es v$+! !+%& &+)-#es+s !e3+!" $ e/+s#e,%+ !e (, !+s#r+3(%+-, !e !e1"r*%+",es%"*)$e56%$r*e,#e,"$+,e$'

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    HORMIGNESTRUCTURAL ?27Hernndez-Gil

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    HORMIGNESTRUCTURAL ?2;Hernndez-Gil

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