Proyecto Final Vias

Proyecto final: Vías Presentado por:

Andrés Felipe Peláez A. 1 096 645 6! "efferson #alazar $%l%a&a. 1 15! 6'6 !99

PROYECTO FINAL “VÍAS” ANDRES FELIPE PELAEZ ARROYA ARROYAVE 1096645362 JEFFERSON SALAZAR ZULUAGA 115266299 REVISADO POR! "ARÍA ROSA GUZ"#N INGENIERA CIVIL TITULAR DE LA ASIGNATURA DE VÍAS PROGRA"A DE INGENIERÍA CIVIL

AR"ENIA "AYO 2013

Fac%ltad de (n&eniería FACULTAD DE DE INGENIERIA DE

Pro&ra)a de (n&eniería *i+il



Contenido

1. 2.

INTRODUCCI INTRODUCCIÓN... ÓN....... ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ ........ .......... ............ ........... ........3 ...3 OBJETIVOS................ OBJETIVOS........................ ................. .................. .................. .................. ................. ................. ...........................4 ..................4 2.1. OBJETIVO GENERAL:...........................................................................4 2.2. OBJETIVOS ESPECÍFICOS:............... ESPECÍFICOS:........................ .................. ................. ................................4 ........................4 3. JUSTIFICACIÓN.............. JUSTIFICACIÓN....................... ................. ................. .................. .................. .................. .................................5 ........................5 4. ALCANCE......................................................................................................6 5. MARCO TEÓRICO........................................................................................7 5.1 PALABRAS CLAVES  DEFINICIONES:................................................7 5.2 ASPECTOS GENERALES:................ GENERALES:......................... ................. ................. ..................................16 .........................16 6. DESCRIPCIÓN DEL PROECTO.................. PROECTO........................... .................. ..................................16 .........................16 7. METODOLOGÍA..........................................................................................17 !. PROCEDIMIENTO......................................................................................1" !.1 DISE#O DISE#O EN PLANTA PLANTA DL EJE DE DE LA CARRETERA.. CARRETERA...... ........ ........ ........ ......... .......24 ..24 !.2 DISE#O DISE#O EN EN PERFIL PERFIL DEL EJE DE LA LA CARR CARRETE ETERA.. RA..... ...... ...... ...... ....... ......... .....44 44 !.3 DISE#O DE LA SECCIÓN TRANSVERSAL DE LA CARRETERA......57 CARRETERA..... .57


Pro&ra)a de (n&eniería *i+il ,!,



1$ INTR INTROD ODUC UCCI CI%N %N E$ %&'( & )*' +*$*+,-,($*' *%($,/*' ($ () ('0/,* /(&))&/* /() M&$0&) /( /,'(* (*-,+* /( &' 288!9 /() INVIAS '( /,'(&; 0$& +&((& /( <,-( */($ +0-<),($/* +*$ )*' (=0,',*' > ('<(+,?,+&+,*$(' +*$(-<)&/&' ($ /,+@* -&$0&) @&+,($/* 0'* &-%,$ /( +*$*+,-,($*' %;',+*' > /( ;(&' +(+&$&' +*-* )& ,$($,(& /( ;$',*. E) /,'(* /( )& & /() +0&) '( &&; ($ ('( /*+0-($* +*('<*$/( & 0$& /( <,-( */($ > <&,($/* /( ('& +&&+(',+& '( ,$,+,& */* 0$ <*+('* =0( $*-&)-($( +*-<($/( )& *%($+,$ /( &)*(' ('<(+,?,+&/*' ($ )&' &%)&' /() -&$0&) +*-* )*' &/,*' -$,-*' <($/,($(' ()&,&' -$,-&' > -;,-&' ($ ($( **' &)*( *(' =0( +*$?,(($ ($ & )& & */& */&' ('& ('&' +&&+(',+&' ,/(&)(' /( ?0$+,*$&-,($* +*$ &)*' $,()(' /( '(0,/&/ > +*-*/,/&/. E) *%(,* /( ('( <*>(+* (' (&),& */* () /,'(* /( )& & '($ )*' &)+&$+(' /( )*' ('0/,&$(' ,$*)0+&$/* &-%,$ &)0$&' ;(&' +*-* )& @,/*)*& <&& (',-&+,$ /( +&0/&)(' -;,-*' > &' /,'(& )&' +0$(&'. T&-%,$ <0(/( <('($&'( *%&' &/,+,*$&)(' +*-* <0($(' >* &)0/(' =0( (=0,(($ 0$ $,() /( +&<&+,&+,$ &&$&/& <&& '0 /,'(* <* )* =0( $* '(;$ <0$*' & && +*$ -0+@* ,* ($ ('( /*+0-($*.


Pro&ra)a de (n&eniería *i+il ,,



2$ O&JETIVOS 2.1. OBJETIVO GENERAL: D,'(& 0$ &-* /( & +0-<),($/* +*$ )&' ('<(+,?,+&+,*$(' > &)*(' (+*-($/&/*' <* () M&$0&) /( /,'(* (*-,+* /( +&((&' 288!9 /() INVIAS. 2.2. OBJETIVOS ESPECÍFICOS: 

E',-& 0$ VD ($ 0$ @*,*$( /( 28 &*' <&& () /,'(* /( )& & $0(&.



D,'(& +0&' +,+0)&(' ',-<)(' > +0&' ('<,&)+0&('<,&)9.



D((-,$& )& ()*+,/&/ ('<(+?,+& /( +&/& ()(-($* /( )& &.



R(&),& () /,'(* ($ <)&$& <(?,) > &$'('&) /( )& &.



C&)+0)& )& +&(& /( <(&)(' +0-<),($/* +*$ )*' <(&)(' -;,-*' ('<(+,?,+&/*'.



C&)+0)& -*,-,($*' /( ,(&.



D,'(& *%&' &/,+,*$&)(' +*-* <0($(' =0( <0(/&$ ('0)& ($ () /,'(* (,+&).

Fac%ltad de (n&eniería FACULTAD DE DE INGENIERIA

Pro&ra)a de (n&eniería *i+il ,4,





3. JUSTIFICACIÓN

D(%,/* & )&' $(+(',/&/(' =0( (<('($& )& '*+,(/&/ ($ +0&$* & &$'<*( (('( ',($/* ($ $0('& (,$ () -;' +*$+0,/* /(%,/* & '0' %&* +*'*' /( *<(&+,$ (' $(+('&,* +*$*+( )*' <&;-(*' /( /,'(* (*-,+* /( &' <&& () ('0/,&$( /( ,$($,(& +,,) ($ ?*-&+,$ >& =0( '(; '( =0,($ ($ 0$ ?00* +*$ )&' +&<&+,/&/(' @&%,),/&/(' > /('(&' -($&)(' &/=0,,/&' /0&$( '0 <*+('* /( ?*-&+,$ > +*$ )*' +*$*+,-,($*' %;',+*' <(* %,($ ('0+0&/*' ('&; ($ )& +&<&+,/&/ /( &?*$& <*%)(-&' <;+,+*' ($ '0 ,/& <*?(',*$&) > +*$,%0, &' &) /('&*))* /( <*>(+*' /( ,$?&('0+0&) ,&) H+&'* <&,+0)& ($(&$/* /('&*))* &) <&'. E' <* ('* =0( (' $(+('&,* &%&& ($ <*>(+*' (&)(' /0&$( )& ?*-&+,$ &+&/-,+& <&& +*$,%0, ($ )& +&),/&/ /( (/0+&+,$ > )&' $*+,*$(' (/&/(&' '*%( )* =0( ,-<),+& (&)-($( 0$ <*>(+* /( ,$?&('0+0&.





4$ ALCANCE D( &+0(/* & )*' *%(,*' <)&$(&/*' &) ,$,+,* /( ('( /*+0-($* (' +)&* =0( () <*>(+* &( ,$*)0+&/* () /('&*))* +*$ ,* /() /,'(* (*-,+* /() &-* /( & > &-%,$ ($ %&'( & +*$*+,-,($*' <*<,*' /( ,$($,(& '( <0(/( @&%)& /( ('0/,*' /( ;$',* /,'(* /( +0$(&' 0'&$/* &$;),',' /( +&0/&)(' > +*$+(<*' %;',+*' =0( $* '( ($&; & @&%)& +*$ -0+@* /(&))( >& =0( () *%(,* <,$+,<&) (' /,'(& )& & +0-<),($/* +*$ )*' +,(,*' ('0/,&/*' /() -&$0&) /( /,'(* (*-,+* /( +&((&' /() INVIAS. L&' *%&' &/,+,*$&)(' +*-* <0($(' ('0/,*' /( '0()*' ('&%,),/&/ /( &)0/(' $()(' > /(-;' ('0/,*' * /,'(*' ('0+0&)(' $* '(;$ &&/&' +*$ -0+@& ()(&$+,& >& =0( +*-* '( -($+,*$ () <*>(+* (' <,$+,<&)-($( /,,,/* & /('&*))& () /,'(* (*-,+* /( )& &.





5$ "ARCO TE%RICO$ 5.1 PALABRAS CLAVES Y DEFINICIONES: 

CARRETERA! “,$?&('0+0& /() &$'<*( &+*$/,+,*$&/& /($* /( 0$& ?&$& /( (($* /($*-,$&/& /((+@* /( & +*$ () <*<',* /( <(-,, )& +,+0)&+,$ /( (@+0)*' +*$ $,()(' &)*' /( '(0,/&/ > +*-*/,/&/9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



PROECTO GEOMTRICO: +*$(-<)& )& ()&+,$ ($(K ()(-($*' ?',+*' /( )& & )&' +&&+(',+&' /( *<(&+,$ <(-,,/*' > )&' +&&+(',+&' /( )*' (@+0)*' * <(&*$('.



DISE#O GEOMTRICO: <*+('* /( +*()&+,*$& ()(-($*' ?',+*' H(*-(& /( )& &K &/,*' /( +0&0& <(&)( ($(&$($+,&' /( )& & +*$ )&' +*$/,+,*$(' /( *<(&+,$ /( )*' (@+0)*' H/,-($',*$(' ()*+,/&/ > +*$/0+* > )&' +&&+(',+&' ?',+&' /() (($* H<)&$* *$/0)&/* -*$&*'* * ('+&<&/*.



ALCANTARILLA. T,<* /( *%& /( +0+( * /( /($&( &$'('&) =0( ,($($ <* *%(* /& <&'* ;<,/* &) &0& =0( <* $* <*/( /(',&'( ($ *& ?*-& ($& =0( +0& /( 0$ )&/* & ** /() +&-,$*9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



BANCA: D,'&$+,& @*,*$&) -(/,/& $*-&)-($( &) (( ($( )*' ((-*' ((,*(' /( )&' +0$(&' * )*' %*/(' )&(&)('9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



BERMA: F&&' +*-<($/,/&' ($( )*' %*/(' /( )& +&)&/& > )&' +0$(&'. S,($ /( +*$?,$&-,($* )&(&) /( )& '0<(?,+,( /( */&/0& +*$*)&$ )& @0-(/&/ > )&' <*',%)(' (*',*$(' /( )& +&)&/&9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



BOMBEO: P($/,($( &$'('&) ($ )&' ($(&$($+,&' @*,*$&)(' /( )& & =0( ,($( <* *%(* ?&+,),& () ('+0,-,($* '0<(?,+,&) /(


Pro&ra)a de (n&eniería *i+il ,-,



&0&. '& <($/,($( & ($(&)-($( /() (( @&+,& )*' %*/('9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS. 

CALADA: *$& /( )& & /(',$&/& & )& +,+0)&+,$ /( (@+0)*'. G($(&)-($( <&,-($&/& * &+*$/,+,*$&/& +*$ &)$ ,<* /( -&(,&) /( &?,-&/*9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



CARRIL: P&( /( )& +&)&/& /(',$&/& &) ;$',* /( 0$& '*)& ?,)& /( (@+0)*'9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



CUNETA: &$&' ((',/&' * $* +*$'0,/&' <&&)()&-($( & )&' %(-&' /(',$&/&' & ?&+,),& () /($&( '0<(?,+,&) )*$,0/,$&) /( )& +&((&. S0 (*-(& <0(/( &,& '($ )&' +*$/,+,*$(' /( )& & > /() ;(& =0( /($&$9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



LÍNEA DE PENDIENTE: E' &=0())& )$(& =0( <&'&$/* <* )*' <0$*' *%),&/*' /() <*>(+* +*$'(& )& <($/,($( 0$,?*-( ('<(+,?,+&/& > =0( /( +*,$+,/, +*$ () (( /( )& & )*' +*(' > )*' (&<)($(' '(&$ -$,-*' &$ <* )& +0&) &-%,$ '( )( +*$*+( +*$ () $*-%( /( )$(& /( +(*'9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



LONGITUD DE APLANAMIENTO: L*$,0/ $(+('&,& <&& =0( () +&,) ((,* <,(/& '0 %*-%(* * '( &<)&$( +*$ ('<(+* &) (( /( *&+,$9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



PENDIENTE RELATIVA DE LA RAMPA DE PERALTES: M;,-& /,?(($+,& &)(%&,+& ($( )&' <($/,($(' )*$,0/,$&)(' /( )*' %*/(' /( )& +&)&/& > () (( /( )& -,'-&9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



PERALTE: I$+),$&+,$ /&/& &) <(?,) &$'('&) /( 0$& +&((& ($ )*' &-*' ($ +0& @*,*$&) <&& +*$&('& () (?(+* /( )& ?0(& +($?0& =0( &+& '*%( 0$ (@+0)* ($ -*,-,($*. T&-%,$


Pro&ra)a de (n&eniería *i+il ,',



+*$,%0>( &) ('+0,-,($* /() &0& ))0,&9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS. 

SOBREANCO: A0-($* ($ )& '(++,$ &$'('&) /( 0$& +&)&/& ($ )&' +0&' +*$ )& ?,$&),/&/ /( -&$($( )& /,'&$+,& )&(&) ($( )*' (@+0)*' ($ -*,-,($*9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



SUBRASANTE: S0<(?,+,( ('<(+,&)-($( &+*$/,+,*$&/& '*%( )& +0&) '( &<*>& )& ('0+0& /() <&,-($*9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



TANGENTE VERTICAL: T&-*' (+*' /() (( /() &),$(&-,($* (,+&) )*' +0&)(' (';$ ($)&&/*' ($( ' <* +0&' (,+&)('9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



TRAMO OMOGNEO: L*$,0/ /() &&/* /( )& +&((& &) =0( <* )&' +&&+(',+&' *<*;?,+&' '( )( &',$& 0$& /((-,$&/& V()*+,/&/ /( D,'(* HVTR9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



TRANSICIÓN DEL PERALTE: T&-* /( )& & ($ )& =0( (' $(+('&,* (&),& 0$ +&-%,* /( ,$+),$&+,$ /( )& +&)&/& <&& <&'& /( 0$& '(++,$ &$'('&) +*$ %*-%(* $*-&) & *& +*$ <(&)(9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.



VELOCIDAD DE DISE#O: V()*+,/&/ 0& * /( (?(($+,& /( 0$ &-* @*-*$(* /( +&((& =0( <(-,( /(?,$, )&' +&&+(',+&' (*-,+&' -$,-&' /( */*' )*' ()(-($*' /() &&/* ($ +*$/,+,*$(' /( '(0,/&/ > +*-*/,/&/9. G)*'&,* /() -&$0&) /( /,'(* (*-,+* INVIAS.





CURVA ESPIRAL CLOTOIDE:

I-&($ 1. E)(-($*' /( 0$& +0& ('<,&) +)**,/(.

E' 0$& +0& &$($( &) (( /( )&' &%'+,'&' ($ () *,($ > +0>* &/,* /( +0&0& /,'-,$0>( /( -&$(& ,$('&-($( <*<*+,*$&) & )& /,'&$+,& (+*,/& '*%( ())& <*<*+,*$&$/* 0$& &>(+*,& $&0&) > ?;+,) /( '(0, <* )*' +*$/0+*(' H,-&($ 1. L*' +;)+0)*' /( '0' ()(-($*' (';$ /&/*' & +*$,$0&+,$. P&& () +;)+0)* /() <&;-(* -$,-* /( +)**,/( HA (,'($ (' -*/*' /( )*' +0&)(' <* <(?(($+,& <&,+0)& '( 0'& () '(0$/* () +0&) ,($( ($ +0($& )& ,$+),$&+,$ -;,-& <(-,,/& /( )& &-<& /( <(&)('.


Pro&ra)a de (n&eniería *i+il , 10 ,



L& )*$,0/ /( )& ('<,&) '( +&)+0)& 0$& ( '()(++,*$&/* 0$ &/,* /( +0& > () <&;-(* A /( )& ',0,($( ?*-& * &)($&,&-($( +*$ )& ?-0)& =0( /(<($/( &/(-;' /() ;$0)* /( /(?)(,$.

E) ;$0)* /( /(?)(,$ H ( (' () ;$0)* <,$+,<&) =0( '( ?*-& ($( 0$& )$(& <(<($/,+0)& & )& &$($( ($ () <0$* TE > () &/,* /( )& +0& +,+0)& HR+.

D,')*=0( /( )& ('<,&):

D(?)(,$ /() &-* +,+0)&:

D(?)(,$ ($ () PI:

L*$,0/ /() (-<&)-( +,+0)&:





CURVA CIRCULAR SIMPLE: <('($&$ 0$& +0&0& +*$'&$( )& +0&) (' ,$('&-($( <*<*+,*$&) &) &)* /() &/,*. E$ & ,-&($ 2 '( *%'(& )*' ()(-($*' > )0(* )&' ?-0)&' <&& () +;)+0)* /( '0' ()(-($*'.

I-&($ 2. E)(-($*' /( 0$& +0& +,+0)& ',-<)(.

P&& () /,'(* /( ('&' +0&' %;',+&-($( '( (=0,(($ )&' ',0,($(' (<(',*$(' (+*-($/&/&' ($ () -&$0&) /( /,'(* (*-,+* /( +&((&'.


Pro&ra)a de (n&eniería *i+il , 1! ,



C'()*+ ),(-./*,+! '*$ )&' =0( ($)&&$ /*' &$($(' +*$'(+0,&' /() &),$(&-,($* (,+&) <&& =0( ($ '0 *&),/&/ '( (?(+0 () <&'* &/0&) /( )&' <($/,($(' /( )& &$($( /( ($&/& & )& /( )& &$($( /( '&),/& C,(,*' <&& +0&' +$+&&'



C,(,* /( '(0,/&/: B&'&/* ($ )&' (',++,*$(' =0( '( <('($&$ /0&$( )& +,+0)&+,$ /( )*' (@+0)*' ($ )& $*+@(:

L-,$: L*$,0/ -$,-& /( )& +0& (,+&) A: D,?(($+,& &)(%&,+& /( <($/,($(' ($ <*+($&( D<: D,'&$+,& /( <&&/& C,(,* /( *<(&+,$: L& &<),+&+,$ /( ('( +,(,* (,& () +&-%,* '%,* /( <($/,($(:

C,(,*' <&& +0&' +*$(&' 

C,(,* /( '(0,/&/: R()&+,*$& )& &)0& /() ** /() +*$/0+* H@ 1 1.8! - > )& &)0& /() *%';+0)* H@ 2  8.68 - > )& /,'&$+,& /( ,',%,),/&/ /( <&&/&:

L-,$: L*$,0/ -$,-& /( )& +0& (,+&) A: D,?(($+,& &)(%&,+& /( <($/,($(' ($ <*+($&( D<: D,'&$+,& /( <&&/&


Pro&ra)a de (n&eniería *i+il , 1 ,





C,(,* /( /($&(: E$ <0$*' &)*' /( )& +('& /( )& +0& ,($( <($/,($( +(* )* +0&) *+&',*$& () /(<',* /( &0& ),-,&$/* () /($&( <&& ('* '( 0,),& () -,'-* <&;-(* H /( )&' +0&' +$+&&' :

D.+, ,-(./ -(*+),(+*! E) /,'(* (*-,+* &$'('&) /( 0$& +&((& +*$','( ($ )& /(?,$,+,$ /( )& 0%,+&+,$

>

/,-($',*$(' /( )*'

()(-($*' =0( ?*-&$ )& +&((& ($ 0$ <)&$* $*-&) & '0 (( > /( ('& -&$(& '( <*/; ?,& )& &'&$( > () &$+@* /( )& ?&& =0( *+0<&; )& ?00& +&((& > &' -,'-* (',-& )&' ;(&' > *)-($(' /( ,(& & -*(. L*' ',0,($(' '*$ ()(-($*' /( /,'(* (*-,+* &'('&): 

C&)&/&



B&$+&



A$+@* /( *$&



C@&?);$



B(-&'



T&)0/('



C**$&



C0$(&.



R&'&$(



L$(& /( +@&?)&$('



S0%&'&$(



C*& *&



C*& $(&



A)+&$&,))&



C0$(&





G;?,+& 1. E)(-($*' '(++,$ &$'('&)

 C'()*+ IDFHC0&' /( ,$($',/&//0&+,$?(+0($+,&: E' 0$& ()&+,$ (-<,+& ($( )& ($( )& ,$($',/&/ /( 0$& <(+,<,&+,$  '0 /0&+,$ > )& ?(+0($+,& +*$ )& =0( '( *%'(&.  P,(.7 7, (,-(! E) $-(* <*-(/,* /( &*' ($( )&' *+0($+,&' /( 0$ (($* @,/*),+* +*$ 0$& -&$,0/ ('<(+?,+& * -&>*. E$ () +&'* /( )& <(+,<,&+,$ /(%( ('<(+,?,+&'( )& +&$,/&/ /( <(+,<,&+,$ H-- > '0 /0&+,$.  R*7. 8.7('./! E' )& ()&+,$ ($( )& '(++,$ -*&/& > () <(-(* -*&/* /() ()(-($* /( /($&( HC0$(&





5.2 ASPECTOS GENERALES: L&' &' +*-* <,$+,<&)(' -**(' /( )& (+*$*-& /( 0$ <&' '*$ ($ ('($+,& 0$& ,$?&('0+0& /( )& ,$($,(& /( )& +0&) /(<($/(-*' >& =0( (' <* &)) /*$/( '( @&+( <*',%)( )& -*,),/&/ /( */* ,<* /( -(+&$+&' > &),-($*'. N* (' () $,+* -(/,* /( &$'<*( <(* ' () -;' +*$+0,/* ($ )& &+0&),/&/ > (' <* ('* =0( '( 0',?,+& <*$( ($ <;+,+& +*$*+,-,($*' > @&%,),/&/(' +*-* () /,'(* (*-,+* /( +&((&' <&& () ,$($,(* +,,) ($ ?*-&+,$ >& =0( '*$ )&' &' )*' <,$+,<&)(' ((' /( &$'<*( > /('&*))* /( 0$ <&'. A/(-;' /( (=0(, )&' &' +*-* &) (' $(+('&,* =0( ('&' +0($($ +*$ $,()(' &)*' /( '(0,/&/ > +*-*/,/&/ &) 0'0&,*. T*/* ('* +*$))(& & /,'(& +0-<),($/* +*$ )*' <&;-(*' /( )& $*-& > ($(&$/* &' 0$ /,'(* =0( <*<*+,*$( )&' +*$/,+,*$(' >& -($+,*$&/&' <&& &'(0&

/( &)0$& -&$(& 0$& & =0( &&$,+( (+()($('

/,'<*',+,*$(' /( %0($ '(,+,*.

6$ DESCRIPCI%N DEL PROYECTO

U$& & $0(& '( <*>(+& <* )& $(+(',/&/ =0( (<('($& 0$& (,$ * <&' <&& +*$,%0, &) /('&*))* (+*$-,+* '*+,&) > & 0$& -*,),/&/ +*$ $,()(' /( '(,+,* &)*' =0( &&$,+( ($ */* -*-($* 0$ ?;+,) &++('* & )&' (,*$(' > +,0/&/(' =0( '& +*$/0+( <*<*+,*$&$/* &' &) 0'0&,* 0$& &$ &,(/&/ /( &)($&,&' /( 0& <&& '0 /('<)&&-,($* +*$ &)*' $,()(' /( '(0,/&/ +*-*/,/&/ (+*$*-& > ($ &)0$*' +&'*' (/0+,($/* () ,(-<* /( (+*,/* ($( *,($ > /(',$*. E) &-* /( & $0(* =0( '( /,'(&; ('; ',0&/* ($ <(/,*' &)(/&*' & )& +,0/&/ /( A-($,& ($ () /(<&&-($* /() 0,$/* > ($( )*' )-,(' (*;?,+*' +*$ () -0$,+,<,* /( C&)&+;. L& & '( /,'(& +*$ () ?,$ /( Fac%ltad de (n&eniería FACULTAD DE DE INGENIERIA




+*$,%0, &) /('&*))* /( )& (,$ > /( +*$/0+, <* &)) */* () ;$',* /( (@+0)*' <('&/*' <&& =0( <* '0 <&'* $* ($&$ =0( ($& & )& +,0/&/ /( A-($,& ($(&$/* +&*' ($ )& -*,),/&/ (@,+0)& ',$* =0( <* )* +*$&,* @&+( =0( () ;$',* '(& -;' &$=0,)* ',$ ($( +*-* <&'* *%),&/* () -0$,+,<,* <&& =0( &' )*' (@+0)*' +*$,$($ +*$ '0 0&. E) <*>(+* /( /,'(* (*-,+* /( )& & > '0' ()(-($*' '( ,$,+,& +*$ )& *%($+,$ /( )*' <)&$*' *<*;?,+*' /( )& *$& > +*-* '( -($+,*$ ($ )*' *%(,*' > &)+&$+(' /( ('( <*>(+* +*-<($/( () /,'(* (*-,+* /() &-* /( )& & +*$ ,* ',0,($/* )*' <&;-(*' /() -&$0&) /( /,'(* (*-,+* /( +&((&' 288! /() INVIAS.

:$ "ETODOLOGÍA E) <*>(+* '( ,$,+,& +*$ 0$ %&)&$+( /( ;$',* (@,+0)& =0( <(-,& (',-& 0$ VD H*)0-($ @*&,* /( /,'(* /( &+0(/* & /&*' /( &?**' (@,+0)&(' ($ & &)(/&&' <&& +*-<&& )& +&<&+,/&/ ,/(&) /( )& & > () *)0-($ (@,+0)& <*>(+&/* & 28 &*' /( '(,+,* > +*$+)0, ('+*,($/* )&' /,-($',*$(' /( )& & +*-* &$+@* /( +&)&/& &$+@* /( %(-& (@+0)* /( /,'(* (+. &+,($/* (?(($+,& /( )* =0( ('&%)(+( () -&$0&) /( /,'(* (*-,+* /( &' '( +)&',?,+& )& & '($ '0 ?0$+,*$&),/&/ > ,<* /( (($* <&& &' *%($( 0$& ()*+,/&/ /( /,'(* ('<(+,?,+&/& HV   > /() -,'-* -&$0&) /( &+0(/* & )& +)&',?,+&+,$ *%($,/& '( '()(++,*$& )& <($/,($( -;,-& )*$,0/,$&) ($,($/* ($ +0($& () &)* /( )& V   =0( 0$& ( +*$ () <)&$* *<*;?,+* '( <0(/& && )& )$(& /( <($/,($(. L0(* '( (&),& () /,'(* /( +&/& 0$& /( )&' +0&' @*,*$&)(' > '( /(?)(+&$ '( +&)+0)& )& ()*+,/&/ ('<(+?,+& <&& +&/& +0& ($,($/* ($ +0($& )&' )*$,0/(' /( )*' &-*' ,$-(/,&&-($( &$(,*(' <&& )0(* (,?,+& =0( )&' ($( &$($+,&' Fac%ltad de (n&eniería FACULTAD DE DE INGENIERIA

Pro&ra)a de (n&eniería *i+il , 1- ,



('$ /($* /( )*' )-,(' &+(<&%)(' > &/(-;' =0( )*' &/,*' '(&$ -&>*(' & )*' -$,-*' &+(<&/*' <* )& $*-& <&& +&/& ()*+,/&/. U$& ( +*$+)0,/* () /,'(* ($ <)&$& /() (( /( )& & '( &?,+& () <(?,) $&0&) /() (($* H+*& $(& > '( && () &),$(&-,($* (,+&) +*$ 0$& <($/,($( -;' * -($*' +*$'&$( > ',$ (+(/( )& ('<(+,?,+&/& <* )& $*-& <&& /((-,$& +&/& 0$& /( )&' +0&' (,+&)(' =0( +*('<*$/($ & ('( &),$(&-,($* > /( ('& -&$(& <*/( *%($( )& +*& /( )& &'&$( /( )& & H+*& *& ($ +0&)=0,( <0$* <(-,,($/* &' (&),& )*' /,&&-&' /( <(&)( /( <&& +&/& +0& +*$ )&' +*&' +*('<*$/,($(' & +&/& %*/( > &) (( /( )& &. T($,($/* >& () &),$(&-,($* (,+&) <* /*$/( <&'&; )& & > () <(?,) /() (($* $&0&) '( <*+(/( & *%($( )&' '(++,*$(' &$'('&)(' /( 0$ &-* /( )& & <&& @&))& '0' *)-($(' /( +*( > /( ))($*. L&' ('<(+,?,+&+,*$(' /() /,'(* &&/* /( )& & @*,*$&) > (,+&) > /,&&-& /( <(&)(' &-%,$ '( (&),&$ -(/,&$( AUTOCAD <&& ($( 0$& <('($&+,$ -;' &/(+0&/& /() <*>(+* > <(-,,'( )& (,?,+&+,$ ($( )*' /,'(*' @(+@*' & -&$* > )*' &*&/*' ($ ('( '*?Q&(.


Pro&ra)a de (n&eniería *i+il , 1' ,



$ PROCEDI"IENTO$ E+-'7. 7, -(+.-! E) ('0/,* /( &$',* =0( '( (?(+0 <&& () $0(* &-* /( & A-($,&  P((,& 0* ($ +0($& )*' ',0,($(' &'<(+*':  

V*)-($(' /( &$',* +*$ <*>(++,$ & 28 &ños para el tramo de vía C*-<*',+,$ (@,+0)&.

D,+@& ,$?*-&+,$ '( *%0* -(/,&$( ('0/,*' >& (&),&/*' <* () ,$',0* $&+,*$&) /( &' <&& )& 0& +*('<*$/,($(. V*)0-($ (@,+0)&: L*' *)-($(' /( &$',* &+0&) /( )& & =0( +*$/0+( /( A-($,& A +&)&+; '( *-&*$ /( (,'*' /() ,$',0* $&+,*$&) /( &' &)) '( -0('& () TPDS H;$',* <*-(/,* /,&,* '(-&$&) -;' &+0&) /( &+0(/* & &?**' > () +0&) +*('<*$/( &) &* 288! +*$ 0$ TPDS: 73"4 H(@ /&.  -(/,&$( &?**' '( /((-,$ =0( () 65 /( (@+0)*' =0( &+0&)-($( &$',&$ <* /,+@* <0$* 0,),&;$ () $0(* &-* <(($(+,($( & )& & =0( '( +*$'0,; )* =0( (=0,&)( & 0$ TPDS: "681 H(@/,& +*$ 0$ VD: 488 H(@@. E$ ,'& =0( $* '( ,($( -0+@& ,$?*-&+,$ +*('<*$/,($( & ;$',* -($'0&) &$0&) (+. E' $(+('&,* +&)+0)& () ;$',* ?00* &&/* ($ () $0(* &-* <&& 0$ <(,*/* /( 28 &*' & ?00* <* )* =0( '( 0,),& )& ',0,($( (+0&+,$: S,($/*: T?  T&$',* ?00* T*  T&$',* &+0&) ,  T&'& /( +(+,-,($* $  N0-(* /( &*' D&*' /() &-* /( & $ 28 &*'





, 4 H+*('<*$/,($( & )& &'& /( ,$+(-($* /( )& +,0/&/ /( A-($,& *-&/* /() DANE  "681 (@+0)*' =0( 0,),&&$ )& $0(& +&)&/& ($ )& &+0&),/&/ P* )* &$*

TPDS ($ 28 &$*'

E) ;$',* <*-(/,* /,&,* '(-&$&) <*>(+&/* & 28 &*' '( *%,($( ((-<)&&$/* )*' &)*(' ($ )& (+0&+,$ &$(,* > '( *%,($( TPDS 21836H(@/& VD!77H(@@*&. A +*$,$0&+,$ '( <('($& )& /,',%0+,$ /( )& +*-<*',+,$ (@,+0)& &+0&) ($,($/* ($ +0($& )& $*-($+)&0& (+*-($/&/& <* () INVIAS ($ )& &%)& 2 /( ('( /*+0-($*.

Gráfica 2.C!"#ici$% V&'ic()ar a* 2+12.


Pro&ra)a de (n&eniería *i+il , !0 ,



T&%)& 2 . N*-($+)&0& <&& +*-<*',+,$ (@,+0)&.

D( &+0(/* & )&' +&(*&' /( (@+0)*' ('<(+,?,+&/&' ($ () ,$',0* $&+,*$&) /( &' >& '( ('+*, +*-* (@+0)* /( /,'(* )* =0( +*-$-($( '( +*$*+( +*-* &+* * +&-,$ &,+0)&/* > =0( +*('<*$/( & )& $*-($+)&0& C5. L& ()(++,$ /( ('( ,<* /( (@+0)* **& '(0,/&/ > +*-*/,/&/ &$* <&& ('( +*-* <&& (@+0)*' /( -($* ($(&/0& +*-* +&-,*$(' -;' <(=0(*' &0*-,)(' > -**+,+)(&' %,$/&$/* /,-($',*$(' *<,-&' /( )*' &$+@*' /( +&,) +&)&/& > %(-&.





C*;*/.7*7: E$ +0&$* &) ('0/,* /( +&<&+,/&/ <&& () &-* /( & '( ($/;$ ($ +0($& /,('*' ?&+*(' <&& @&+( ,/(&) () -;,-* $-(* /( (@+0)*' =0( <0(/($ &$',& <* 0$ <0$* * '(++,$ &$'('&) /( )& &: '( <&( ($,($/* 0$& +&<&+,/&/ ,/(&) /( C,  3288 &0*-,)('@*&&-%*' '($,/*' <(* +*-* )& & $* ?0$+,*$& ($ +*$/,+,*$(' ,/(&)(' '( ,($($ 0$*' ?&+*(' /( +*(++$ > )& +&<&+,/&/ (&) '( +&)+0)& +*-*: C  3288F<(F/F+%F<. D*$/(: C  C&<&+,/&/ ($ (@+0)*' -,*' <* @*& ',$ +*$',/(& &,&+,*$(' &)(&*,&'. F<(  F&+* /( +*(++,$ & )& +&<&+,/&/ <* <($/,($(.

C*+.<./*/.= 7, * /*((,-,(*! '($ '0 ?0$+,*$&),/&/ '( ('&%)(+( =0( '(; 0$& & /( <,-( H1 (  */($ =0( /( &+0(/* &) -&$0&) /( /,'(* (*-,+* /( +&((&' '*$ &=0())&' *$+&)(' &$'('&)(' > &++('*' & +&<,&)(' /( D(<&&-($* =0( +0-<)($ )& ?0$+,$ %;',+& /( ,$(&+,$ /( )&' <,$+,<&)(' *$&' /( <*/0++,$ > +*$'0-* /() <&' > /( '( +*$ )*' /(-;' <&'('9. S($ () ,<* /( (($* '( ('&%)(+( =0( (' (($* -*$&*'* +*$ <($/,($(' )*$,0/,$&)(' ($( 6  !9.

S,,//.= 7, * ),/.7*7 7, 7.+, >V-( ?! /( &+0(/* & )& &%)& 2.1 /() -&$0&) /( /,'(* (*-,+* /( &' > &%)& 2 ($ ('( /*+0-($* <&& 0$ (($* -*$&*'* > 0$& & /( <,-( H1 (  */($ )& ()*+,/&/ /( /,'(* ('; ($ () &$* ($( )*' 68 W-@ > "8 W-@. E$ ('( +&'* '( '()(++,*$& 0$& ()*+,/&/ /( 68 W-@ >& =0( () (($* ',($/* -*$&*'* ($ () &&/* /() (( <* )*' <0$*' <,$+,<&)(' /( )& & > )*' <0$*' /( +*$*) *%),&/*' '( <0(/($ *%($( /(?)(,*$(' -0> &$/(' )* +0&) (/0+( () &/,* > <&& $* (=0(, ($( &$($+,&' -0> &$/(' > +&0'& () +&-%,* /( &)*(' /( &)0$*' <&;-(*' )0(* /( /,'(& )&' ()*+,/&/(' ('<(+,?,+&'. Fac%ltad de (n&eniería FACULTAD DE DE INGENIERIA

Pro&ra)a de (n&eniería *i+il , !! ,



T&%)& 2. V&)*(' /( )& ()*+,/&/ /( /,'(* /( )*' &-*' @*-*$(*' HV   ($ ?0$+,$ /( )& +&(*& /( )& +&((& > () ,<* /( (($*.

S,,//.= 7, * ;,7.,-, ,7.* @.* 7, /((,7( 7, ('-* , <'/.= <&& )& '()( '()(++ ++, ,$ $ /( )& 7, * ), ),/ /.7 .7*7 *7 7, 7, -(* -(*    , ,  >V-( ?! ?! <&& <($/,($( =0( ('<(+?,+& () -&$0&) /( /,'(* (*-,+* /( &' ($ )& &%)& 4.1 > ($ ('( /*+0-($* /*+0-($* ($ )& &%)& 3 =0( '( <('($& & +*$,$0&+,$ +*$,$0&+,$ '( ( ($ )&' ()*+,/&/(' ($( )*' 68 W-@ > "8 W-@ <&& 0$& +&((& /( <,-( */($ =0( )&' <($/,($(' -(/,&' -;,-&' '*$: 7 ($ () &$* /( )&' ()*+,/&/(' ($( 68 -@ > 78 -@ > 6 ($( !8 -@ > "8 -@. E) +&'* +&'* <& <&,+ ,+0) 0)& & /( ('( ('( <*> <*>(+ (+* * ,-<) ,-<),+ ,+& & =0( =0( '( /(%( /(%(; ; &% &%& && & +*$ +*$ <($/,($(' -;,-&' )*$,0/,$&)(' /( 7 .

T&%)& 3: <($/,($(' H -(/,&' -;,-&' ($ ?0$+,$ /( )& ()*+,/&/ /() &-* @*-*$(*.


Pro&ra)a de (n&eniería *i+il , ! ,



,.1 DISE-O EN PLANTA PLANTA DL EJE DE LA CARRETERA

T(*B*7 (*B*7  7, *  , ,** 7, ;,7 ;,7., .,-,! ,! <&& () &&/* /( ('& '( @&))& )& )*$,0/ -$,-& /( +&/& &-* & && ($( +0&' /( $,() HD )&' +0&)(' (';$ &&/&' +&/& /*' H2 -(*' HDN /( /('$,() <&& ('* '( 0,),& )& ',0,($( ()&+,$ /( ,;$0)*.

T&%&&$/* +*$ )& <($/,($( /() 7 > () /('$,() /( 2 -(*' '( ,($( =0( )& /,'&$+,& @*,*$&) -$,-& HD (':

L0(*

L& (< (<(' ('($ ($& &+, +,$ $ /() /() ('0 ('0))&/ &/* * &$( &$(, ,* * '( (?) (?)( (& & ($ )& ,-& ,-&($ ($ 3 & +*$,$0&+,$. L& )$(& /( <($/,($( '( /(%( && <*+0&$/* -&$($( ',(-<( ',(-<( )& -,'-& /,'&$+,& @*,*$&) @*,*$&) * 0$& -&>* ($( +0&' &/>&+($(' &/>&+($(' <&& &&$,& =0( )& <($/,($( '( -&$($& +*-* )* ,$/,+& ($ )& ,-&($ 1 )& )$(& &0) ($ &)0$*' +&'*' '( /(%(; +&-%,& )& <($/,($( +0&$/* () (($* )* <**=0( <* 0$& <($/,($( -;' %&& * ', (' () +&'* 0$ <*+* -;' /( )& ('<(+,?,+&/&.





I-&($ 3. R(<('($&+,$ /( )& /,'&$+,& @*,*$&) <&& () &&/* /( )& )$(& /( <($/,($(

T(*B*7 7, *.,*.,- (.B-*! )& )$(& /( <($/,($( '( @&+( +*$ () ?,$ /( %0'+& () +&-,$* -;' &+(<&%)( <* () +0&) '( <0(/& && )& & ',$ '*%(<& '*%(<&'& '& )& <($/,( <($/,($( $( -;,-& -;,-& ('<(+, ('<(+,?,+ ?,+&/& &/& > <*+0&$ <*+0&$/* /* *%($( *%($( )*' -($*(' -($*(' -*,-,($*' -*,-,($*' /( ,(& <*',%)('. <*',%)('. D( &@ '( <&( <&& () &&/* /() &),$(&-,($ &),$(&-,($* * @*,*$&) () +0&) '( @&+( <*+0&$/* <*+0&$/* *%($( 0$& )$(& -;' * -($*' <&&)()& & )& )$(& /( <($/,($( > )* -;' +(+&$& <*',%)(. F,$&)-($( '( *%0,(*$ 7 &),$(&-,($*' )*' +*$ )*' +0&)(' '( &%&&; &%&&; & +*$,$0&+,$ <&& () +;)+0)* /( )&' +0&' ('<(+,&'. L&' +&&+(',+&' /( +&/& 0$* /( )*' &),$(&-,($*' '( <('($&$ & +*$,$0&+,$ ($ )& &%)& 3. Alineamiento 1 2 3 4 5 6 7

Longitud (m) Defexión (grados) 540 74 308 23 440 47 683 122 492 64 284 79 724

T&%)& 4. L*$,0/(' > /(?)(,*$(' /( )*' &),$(&-,($*'.





C/' 7, + ,,,-+ 7, /*7* '* 7, *+ /'()*+! & +*$,$0&+,$ '( <('($&$ )*' ()(-($*' /( +&/& 0$& /( )&' +0&' 1 > 3 ('<,&)+0& ('<,&) ('0-,/*' ($ )& &%)& 5 +&)+0)&/& ($ EXCEL. L*' /&*' ($ +()/&' &-&,))&' ,$/,+&$ () &)* ('+*,/* <&& +&/& 0$* /( )*' +;)+0)*' > ('*' & '0 ( '*$ +&)+0)&/*' +*$ )&' (<(',*$(' =0( (+*-,($/& () -&$0&) /( /,'(* (*-,+* /( +&((&' > '( <0(/($ *%'(& ($ () -&+* (,+*. L& '0'($&+,$ /( )&' ?-0)&' 0'&/&' > )*' +;)+0)*' +*('<*$/,($(' <&& +&/& ,<* /( +0& '( <0(/($ ( ($ )*' &$(*'. ∆S m"ximo m#nimo

espiral alineamientos Rc(m) defexin peralte ! 1 7$2 1 2 170 74 0$6 0$365 3 7$2 2 4 170 47 0$6 0$365 ta'la 3$2 ta'la 3$4 ta'la 3$6 Re%erencia en el man&al m#n con e con m#n * e con min * ∆Sm"x m#n con ∆Sm#n m"x ∆Sm"x ∆Smin

e max

86$29020802

110$6345335

187

43$8

72

205$7

86$29020802

110$6345335

187 p",$ 119

43$8

72

205$7

+",$ 118

+",$ 77

-e con (e.min.∆Smax) -e con (e.min.∆Smin) -e con (emax) -e con (e.min.∆Smax) (radianes) (radianes) (radianes) (,rados) 0$128823529

0$211764706

0$605

7$381044537

0$128823529

0$211764706 +",$ 77

0$605

7$381044537





-e con (e.min.∆Smin) (,rados)

-e con (emax) (,rados)

12$1332239

34$66394661

43$727 1$879

0$470 21$888 170$470

12$1332239

34$66394661

71$678 5$066

1$271 35$946 171$271 +",$ 78

xe

*e

∆R

+",$ 77

∆c (,rados)

∆c (radianes)

150$346

59$238

110$417

22$734

e

/m

m

c (empalme circ&lar)

cmin (m)

ericacin de empalme circ&lar

1$034

175$762

33$36

+

0$397

67$452 +",$ 79

33$36

+

T&%)& 5. C;)+0)* /( ()(-($*' /( )& ('<,&)+0&('<,&) 1 > 3.

L*' +;)+0)*' /( )*' ()(-($*' /( )& ('<,&)+0&('<,&) ?,$&)-($( =0(/&*$ +*-* -0('& )& &$(,* &%)& 5 > ($ ('0-($ */&' )&' +0&' '( <('($&$ ($ )& ',0,($( &%)& 5.1. NOTA: L& ),-& ?,)&K (?(($+,& ($ () -&$0&)9 ,$/,+& )& <;,$& ($ )& +0&) '( ($+0($& )& &%)& ?-0)& * +,(,* 0'&/* <&& () +;)+0)* /( +&/& &)* *-&/& /() -&$0&) /( /,'(* (*-,+* /( +&&(&'. L*' &)*(' <&& &$+@* /( +&)&/& > +&,) '*$ )*' ('&%)(+,/*' ($ )& &%)& 4 > '( *%0,(*$ /( )& &%)& ('<(+,?,+&/& &)) /() -&$0&) /( /,'(* (*-,+* /( +&&(&'. anco de calada (m)

7$3

anco de carril (m)

3$65

a'la 5$2

T&%)& 5.1. V&)* /( &$+@* /( +&)&/&.


Pro&ra)a de (n&eniería *i+il , !- ,

E$ ('0-($ () /,'(* /( +0&' @*,*$&)(' '( ('0-( ($ )& &%)& 5.2 & +*$,$0&+,$ +&)+0)&/& ($ EXCEL > '0' &)*(' '( '0'($&$ +*$ )&' (<(',*$(' /&/&' ($ )& (*&.

on,it&d :c =efexin Rc(m) (m) (;m<) (,rados)

&ra

an,ente

1

540

2

308

3

440

4

683

5

492

1(espiral)

60

2

60

3(espiral)

60

4

60

5 6 6

74 23 47 122

170 170 170 120

on,it&d de c&ra (m)

on,it&d espiral(m)

175$7624199

43$8

68$24237375 67$45180723 255$5162025

(m)

e(m)

+eralte max!

∆S &>liado !

150$35

7$2

0$6

34$59 72

7$2 110$42

216$5

7$2 8

real

:ericacin de entretan,encia

ramo recto anterior(m)

87$6

166$8667

+

123$066704

115$8

366$9963

+

294$996284

120$667 428$0974

+

356$097444

96$1167 194$2813

+

194$281254

96$1167 103$8466

+

103$846618

0$6 0$365 0$6

60

64

130

145$2113938

81$23

7$8

0$6

60

79

120

165$4572131

98$92

8

0$6

284

7 724 T&%)& 5.2. E)(-($*' /( )&' +0&' @*,*$&)('.

ntretan,encia(m) #nima

A+/.+*7 , + ;'-+ ;(./.;*,+! E' $(+('&,* /& 0$ &)* /( &%'+,'& ($ +&/& <0$* ,-<*&$( /() &&/* /( )& & H&%)& 6 <&& ,/($,?,+& +&/& 0$* /( )*' +&-%,*' =0( '& <('($& ($ '0 (+*,/*. E) &%'+,'&/* '( @&+( <&,($/* /('/( () 8 Y 88 @&'& ))(& &) <,-( ,$,+,* /( +0& > +*$ )& )*$,0/ /( ('<,&) * +0& ',-<)( '($ +*('<*$/& /((-,$& +&/& 0$& /( )&' &%'+,'&' +*('<*$/,($(' & +&/& 0$* /( )*' <0$*' <,$+,<&)(' /*$/( '( ,$,+,& (-,$& ( ,$(+(<&$ )&' +0&' +*$ )&' &$($('. L& &%)& 6 ')* ,$+)0>( )*' &)*(' <&& )&' &%'+,'&' ($ )*' <0$*' <,$+,<&)(' >& =0( -;' &/()&$( '( ($/;$ +&(&' +*$ &%'+,'&' +&/& 18-. c&ra

alineamiento 1

espiraliada

1 2

simple

2

2 3 3

espiraliada

3 4

simple

4

simple

5

simple

6

4 5 5 6 6 7

p&nto     + +     + + + + + +

T&%)& 6. A%'+,'&' ($ )*' <0$*' <,$+,<&)(' /( )&' +0&' @*,*$&)('.

a'scisa 389$6536 433$4536 609$2160 653$0160 776$0827 844$3251 1 139$3214 1 211$3214 1 278$7732 1 350$7732 1 706$8706 1 962$3868 2 156$6681 2 301$8795 2 405$7261 2 571$1833

D,<,@.= 7, *+ /'()*+! E' $(+('&,* /(?)(+& +&/& 0$& /( )&' +0&' <&& *%($( 0$& +&(& /( <0$*' =0( ($ &)$ -*-($* /( )& ((+0+,$ /() <*>(+* '( (=0,(($ <&& 0%,+& )&' +0&' ($ () +&-<*. A +*$,$0&+,$ ($ )& &%)& 7.1 > 7.2 '( <('($&$ )& /(?)(,$ /( )&' +0&' ('<,&)(' > ($ )&' &%)&' !.1 !.2 !.3 > !.4 )&' +,+0)&(' ',-<)('. S( @&+($ & <&( >& =0( (<('($&$ -*/*' /,?(($(' <&& /(?)(+&)&'. CURVA 1 (ESPIRAL) entre alineamientos 1 * 2 para espiral de entrada radio c&ra (m) a's  a's  defexin principal (,rados) ( defexin principal (radianes) lon,it&d de espiral (m) e (radianes) para c&ra de empalme a's  a's  radio c&ra (m) defexin principal (,rados) (c defexin principal (radianes) &erda (m) ?c (radianes) ?c (,rados) lon,it&d de la c&ra por c&erda ,rado(m) lon,it&d de la c&ra por arco ,rado (m) defexin (c) (,rados) defexin por metro (m) (,rados)

para espiral de entrada radio c&ra (m)

170 389$653595 433$453595 74 1$29154365 43$8 0$12882353 433$453595 609$216015 170 59$2379109 1$03389659 10 0$05883201 3$37082608 175$737073 175$76242 1$68541304 0$1685413

170

a's  a's  defexion principla (,rados) ( defexion principla (radianes) lon,it&d de espiral (m) e (radianes) p&nto a'scisas   389$653595 0 390 0$34640493 400 10$3464049 410 20$3464049 420 30$3464049 430 40$3464049  433$453595 43$8 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600  609$216015   653$016015 0 650 3$01601497 640 13$016015 630 23$016015 620 33$016015 610 43$016015  609$216015 43$8

609$216015 653$016015 74 1$29154365 43$8 0$12882353 /  0 0 0$34640493 9$30418@07 10$3463515 0$024790913 20$3448327 0$188523197 30$3348024 0$625358181 40$2982237 1$468823372 43$7273675 1$878595191



radianes)

,rados)

0 8$05777@06 0$007188295 0$027798563 0$061838859 0$109309186 0$128823529 1$103339624 2$788752664 4$474165704 6$159578744 7$844991785 9$530404825 11$21581787 12$90123091 14$58664395 16$27205699 17$95747003 19$64288307 21$32829611 23$01370915 24$69912219 26$38453523 28$06994827 29$62322745

0 0$000002685 0$002396097 0$009266127 0$020612286 0$036432709 0$042935141

0 0$00015389 0$13728627 0$53090996 1$18099698 2$08744043 2$46000238

,rados)

/





radianes)

0 3$01601486 13$0158465 23$0131028 32$9983298 42$9496507 43$7273675

0 0$000614082 0$049357803 0$272883237 0$805255066 1$779661003 1$878595191

0 0$000610821 0$011376353 0$035571914 0$073197505 0$124253125 0$128823529

0 0$000203607 0$003792113 0$011857178 0$024398062 0$041412293 0$042935141

T&%)& 7.1. D(?)(,$ /( )& +0& ('<,&) $-(* 1.

0 0$01166582 0$2172721 0$67936624 1$39790595 2$37274962 2$46000238

C*-<*%&+,$: + c<2

29$6232274 29$6189555

?rados

CURVA  (ESPIRAL) entre alineamientos 3 * 4 para espiral de entrada radio c&ra (m) a's  a's  defexin principal (,rados) ( defexin principal (radianes) lon,it&d de espiral (m) e (radianes) para c&ra de empalme a's  a's  radio c&ra (m) defexin principal (,rados) (c defexin principal (radianes) &erda (m) ?c (radianes) ?c (,rados) lon,it&d de la c&ra por c&erda ,rado(m) lon,it&d de la c&ra por arco ,rado (m) defexin (c) (,rados) defexin por metro (m) (,rados)

para espiral de entrada radio c&ra a's  a's  defexin principal (,rados) ( defexin principal (radianes) lon,it&d de espiral

170 1139$321377 1211$321377 47 0$820304748 72 0$211764706 1211$321377 1278$773184 170 22$73355221 0$396775337 10 0$058832014 3$37082608 67$44207996 67$45180723 1$68541304 0$168541304

170 1278$773184 1350$773184 47 0$820304748 72

e (radianes)

p&nto a'scisas  1139$3214 1140 1150 1160 1170 1180 1190 1200 1210  1211$3214 1220 1230 1240 1250 1260 1270  1278$7732 



1350$7732 1350 1340 1330 1320 1310 1300 1290 1280 1278$7732

0 0$67862308 10$6786231 20$6786231 30$6786231 40$6786231 50$6786231 60$6786231 70$6786231 72

0$211764706 /  0 0 0$67862308 4$25553@06 10$6785999 0$016581065 20$6779922 0$120398955 30$6740886 0$393123557 40$6600401 0$916271799 50$6228686 1$770925465 60$541503 3$037195036 70$3848714 4$793354966 71$6777908 5$066096544



/



0 0$77318415 10$7731842 20$7731842 30$7731842 40$7731842 50$7731842 60$7731842 70$7731842 72

0 0$77318415 10$7731599 20$7725387 30$7685794 40$7543842 50$7169078 60$6349933 70$4774652 71$6777908



radianes)

,rados)

0 1$88125@05 0$00465821 0$017467543 0$03844681 0$067596012 0$104915149 0$15040422 0$204063226 0$211764706 1$462706451 3$148119491 4$833532531 6$518945572 8$204358612 9$889771652 11$36841555

0 6$27082@06 0$001552737 0$005822499 0$012815443 0$022531132 0$034968457 0$050125134 0$067997072 0$070561408

0 0$00035929 0$08896525 0$33360464 0$7342708 1$29093879 2$00354498 2$8719586 3$89594524 4$0428709





radianes)

,rados)

0 6$29385@06 0$017025461 0$122058184 0$396769442 0$92267372 1$780846585 3$051385785 4$81254305 5$066096544

0 2$44205@05 0$004741074 0$017627663 0$038684186 0$067910643 0$105307036 0$150873362 0$204609624 0$211764706

0 8$14017@06 0$001580358 0$005875872 0$012894565 0$022635997 0$035099049 0$050281424 0$068179011 0$070561408

T&%)& 7.2. D(?)(,$ /( )& +0& ('<,&) $-(* 3.

C*-<*%&+,$: + c<2

11$3684155 11$3667761

CURVA ! ("ir"ular sim#le) entre alineamientos 2 * 3 radio c&ra (m) a's pc a's pt defexin principal (,rados) ( defexin principal (radianes)

170 776$082719 844$325093 23 0$40142573

0 0$0004664 0$09054783 0$33666267 0$73880416 1$2969471 2$01102737 2$8809134 3$9063696 4$0428709

&erda (m) ?c (radianes) ?c (,rados) lon,it&d de la c&ra por c&erda ,rado(m) lon,it&d de la c&ra por arco ,rado (m) defexin (c) (,rados) defexin por metro (m) (,rados) p&nto a'scisas defexin + 776$082719 0 A 780 0$66022363 A 790 2$34563667 A 800 4$03104971 A 810 5$71646275 A 820 7$40187579 A 830 9$08728883 A 840 10$7727019 A + 844$325093 11$5016587 A ompro'acin + (,rados) 11$5016587 <2 (,rados) 11$5 T&%)& !.1. D(?)(,$ +0& +,+0)& 2.

10 0$05883201 3$37082608 68$2325325 68$2423738 1$68541304 0$1685413

CURVA $ ("ir"ular sim#le) entre alineamientos 4 * 5 radio c&ra (m) 120 a's pc 1706$87063 a's pt 1962$38683 defexin principal (,rados) (  122 defexin principal (radianes) 2$12930169 &erda (m) 10 ?c (radianes) 0$08335746 ?c (,rados) 4$77603093 lon,it&d de la c&ra por c&erda ,rado (m) 255$442232 lon,it&d de la c&ra por arco ,rado (m) 255$516202 defexin (c) (,rados) 2$38801546 defexin por metro (m) (,rados) 0$23880155 p&nto a'scisas defexion + 1706$87063 0 A 1710 0$74729876 A 1720 3$13531423 A 1730 5$52332969 A 1740 7$91134515 A 1750 10$2993606 A 1760 12$6873761 A 1770 15$0753915 A 1780 17$463407 A 1790 19$8514225 A 1800 22$2394379 A 1810 24$6274534 A 1820 27$0154689 A 1830 29$4034843 A 1840 31$7914998 A 1850 34$1795152 A 1860 36$5675307 A 1870 38$9555462 A 1880 41$3435616 A 1890 43$7315771 A 1900 46$1195926 A 1910 48$507608 A 1920 50$8956235 A 1930 53$283639 A

+

1940 1950 1960 1962$38683 ompro'acin + (,rados) 61$0176643 <2 (,rados) 61

55$6716544 58$0596699 60$4476853 61$0176643

A A A A

T&%)& !.2. D(?)(,$ +0& +,+0)& 4.

CURVA % ("ir"ular sim#le) entre alineamientos 5 * 6 radio c&ra (m) 130 a's pc 2156$66808 a's pt 2301$87948 defexin principal (,rados) (  64 defexin principal (radianes) 1$11701072 &erda (m) 10 ?c (radianes) 0$07694205 ?c (,rados) 4$40845501 lon,it&d de la c&ra por c&erda ,rado (m) 145$175577 lon,it&d de la c&ra por arco ,rado (m) 145$211394 defexin (c) (,rados) 2$2042275 defexin por metro (m) (,rados) 0$22042275 p&nto a'scisas defexin + 2156$66808 0 A 2160 0$73442996 A 2170 2$93865747 A 2180 5$14288497 A 2190 7$34711248 A 2200 9$55133998 A 2210 11$7555675 A 2220 13$959795 A 2230 16$1640225 A 2240 18$36825 A 2250 20$5724775 A 2260 22$776705 A 2270 24$9809325 A 2280 27$18516 A 2290 29$3893875 A 2300 31$593615 A

+

2301$87948 ompro'acin + (,rados) 32$0078948 <2 (,rados) 32

32$0078948 A

T&%)& !.3. D(?)(,$ +0& +,+0)& 5.

CURVA & entre alineamientos 6 * 7 radio c&ra (m) 120 a's pc 2405$7261 a's pt 2571$18331 defexin principal (,rados) (  79 defexin principal (radianes) 1$37881011 &erda (m) 10 ?c (radianes) 0$08335746 ?c (,rados) 4$77603093 lon,it&d de la c&ra por c&erda ,rado (m) 165$409314 lon,it&d de la c&ra por arco ,rado (m) 165$457213 defexin (c) (,rados) 2$38801546 defexin por metro (m) (,rados) 0$23880155 p&nto a'scisas defexin + 2405$7261 0 A 2410 1$02061482 A 2420 3$40863028 A 2430 5$79664574 A 2440 8$18466121 A 2450 10$5726767 A 2460 12$9606921 A 2470 15$3487076 A 2480 17$7367231 A 2490 20$1247385 A 2500 22$512754 A 2510 24$9007694 A 2520 27$2887849 A 2530 29$6768004 A 2540 32$0648158 A 2550 34$4528313 A 2560 36$8408468 A 2570 39$2288622 A + 2571$18331 39$5114383 A ompro'acin

+ (,rados) <2 (,rados)

39$5114383 39$5

T&%)& !.4. D(?)(,$ +0& +,+0)& 6.

D.*(** 7, ;,(*-,! '( '( @&+( & <&, /( )& +&(& /( )&' +*&' /() (( > '0' %*/(' <&& +&/& &%'+,'& +*('<*$/,($( ($ () &&/* /( )& & > ($,($/* ($ +0($& )&' <($/,($(' ()&,&' <(&)(' )*$,0/ /( &$',+,$ /( <(&)( ('<(+,?,+&/* <* () -&$0&) /( /,'(* (*-,+* /( +&((&'. T&-%,$ '( <0(/( @&+( ',$ */&& ($( )&' +*&' +*('<*$/,($(' &) (( %*/( ,=0,(/* > %*/( /((+@* <(* <&& (?(+*' <;+,+*' )& +&(& >; (' +*-<)(& +*$ '0' ('<(+,&' +*&' > <(&)(' <&& +&/& <0$* <,$+,<&). E'* ,-<),+ <,-(* *%($( () &&/* (,+&) > () /,'(* /( +0&' (,+&)(' >& =0( '( (=0,(($ )&' +*&' *&' <(* &+; '( ,$*/0+( >& =0( () /,&&-& /( <(&)( @&+( <&( /() /,'(* ($ <)&$& /() (( > '( &+)&& =0( &$(' '( @,+,(*$ )*' /,'(*' /( )&' +0&' (,+&)(' =0( -;' &/()&$( '( ('<(+,?,+&$. A +*$,$0&+,$ ($ )& &%)& " '( <('($& )& +&(& +*-<)(& +*$ )& +0&) '( *%0* () +*('<*$/,($( /,&&-& /( <(&)(' > '0 (,?,+&+,$ '( <0(/( @&+( (?(+,& ($ () <)&$* &$(* & ('( /*+0-($* ($ /*$/( '( &?,+ > &+* /(%,/&-($( /,+@* /,&&-&. E$ )& +&(& )*' &)*(' **' ,$/,+&$ <(&)( $(&,* > (/(' <(&)( <*',,*.

+BC DSES 0 14 20 80 98 134 174 178 194 304 377$4866  389$6536 401$8206  433$4536 436 455 498 545  609$216 610 640$849  653$016 660 665$183 672 720$1157 725 732$2827 735 744$4497 + 776$0827 + 844$3251 864

artera de peraltes C F C DE C D= 1478 1477$927 1477$927 1478$28 1478$207 1478$207 1478$4 1478$327 1478$327 1479$6 1479$527 1479$527 1479$96 1479$887 1479$887 1480$68 1480$607 1480$607 1481$48 1481$407 1481$407 1481$56 1481$487 1481$487 1481$88 1481$807 1481$807 1484$08 1484$007 1484$007 1485$54973 1485$47673 1485$47673 1485$79307 1485$72007 1485$79307 1486$03641 1485$96341 1486$10941 1486$66907 1486$40627 1486$93187 1486$72 1486$4572 1486$9828 1487$1 1486$8372 1487$3628 1487$96 1487$6972 1488$2228 1488$9 1488$6372 1489$1628 1490$18432 1489$92152 1490$44712 1490$2 1489$9419 1490$4581 1490$81698 1490$74398 1490$88998 1491$06032 1490$98732 1491$06032 1491$2 1491$127 1491$1581 1491$30366 1491$23066 1491$23066 1491$44 1491$367 1491$367 1492$40231 1492$32931 1492$32931 1492$5 1492$4563 1492$427 1492$64565 1492$64565 1492$57265 1492$7 1492$7163 1492$627 1492$88899 1492$962 1492$81599 1493$52165 1493$78445 1493$25885 1494$8865 1495$1493 1494$6237 1495$28 1495$42475 1495$13525

e EG ! 2 2 2 2 2 2 2 2 2 2 2 2 2 7$2 7$2 7$2 7$2 7$2 7$2 7$07112 2 2 2 2 2 2 1$19716 0 0$44668 2$00005 7$2 7$2 3$96577

e =er ! 2 2 2 2 2 2 2 2 2 2 2 0 2$00005 7$2 7$2 7$2 7$2 7$2 7$2 7$07112 2$00005 0 1$14805 2 2 2 2 2 2 2 7$2 7$2 3$96577 2

875$9581 1495$51916 1495$59216 1495$44616 2$00005 +BC DSES C F C DE C D= e EG ! e =er ! 888$1251 1495$7625 1495$7625 1495$6895 0 2 900 1496 1495$92875 1495$927 1$95204 2

900$2921 1496$00657 1495$93357 1495$93357 920 1496$45 1496$377 1496$377 925 1496$57813 1496$50513 1496$50513 965 1497$82813 1497$75513 1497$75513 970 1498$0125 1497$9395 1497$9395 1000 1499$25 1499$177 1499$177 1005 1499$46813 1499$39513 1499$39513 1015 1499$94313 1499$87013 1499$87013 1063 1502$57113 1502$49813 1502$49813 1066 1502$7545 1502$6815 1502$6815 1073 1503$19113 1503$11813 1503$11813 1080 1503$64 1503$567 1503$567 1084 1503$902 1503$829 1503$829 1100 1504$99 1504$917 1504$917 1110 1505$69 1505$617 1505$617 1119$3214 1506$3425 1506$2695 1506$2695  1139$3214 1507$7425 1507$6695 1507$7425 1144 1508$07 1507$997 1508$08708 1159$3214 1509$1425 1509$0695 1509$2155 1161 1509$26 1509$18087 1509$33913 1192 1511$43 1511$23772 1511$62228  1211$3214 1512$7825 1512$5197 1513$0453 1243 1515 1514$7372 1515$2628  1278$7732 1516$88167 1516$61887 1517$14447 1330 1519$5762 1519$50038 1519$65202 1330$7732 1519$60141 1519$52841 1519$67441 1343 1520 1519$927 1520$02837  1350$7732 1520$16013 1520$08713 1520$16013 1370$7732 1520$57213 1520$49913 1520$49913 1390 1520$9682 1520$8952 1520$8952 1404 1521$0858 1521$0128 1521$0128 1443 1521 1520$927 1520$927 1507 1520$36 1520$287 1520$287 1520 1520$23 1520$157 1520$157 1646$0336 1518$96966 1518$89666 1518$89666 +BC DSES C F C DE C D= 1658$2006 1518$84799 1518$77499 1518$84799 1670$3676 1518$72632 1518$65332 1518$79933 1690 1518$53 1518$3392 1518$7208 1705 1518$38 1518$0992 1518$6608 + 1706$8706 1518$36129 1518$06929 1518$65329

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2$16786 5$26786 7$2 7$2 7$2 2$07732 2 2 2 2 2 2 2 2 2 2 e EG ! 2 2 5$2273 7$69305 8

2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0$46786 2 2$16786 5$26786 7$2 7$2 7$2 2$07732 2 0$77732 0 2 2 2 2 2 2 2 e =er ! 0 2$00005 5$2273 7$69305 8

1710 1518$33 1518$038 1518$622 8 8 1712 1518$31 1518$018 1518$602 8 8 1720 1518$23 1517$938 1518$522 8 8 1730 1518$13 1517$838 1518$422 8 8 1731 1518$12 1517$828 1518$412 8 8 1740 1518$03 1517$738 1518$322 8 8 1750 1517$93 1517$638 1518$222 8 8 1755 1517$88 1517$588 1518$172 8 8 1760 1517$83 1517$538 1518$122 8 8 1770 1517$73 1517$438 1518$022 8 8 1772 1517$71 1517$418 1518$002 8 8 1778 1517$65 1517$358 1517$942 8 8 1780 1517$63 1517$338 1517$922 8 8 1782 1517$61 1517$318 1517$902 8 8 1788 1517$55 1517$258 1517$842 8 8 1790 1517$53 1517$238 1517$822 8 8 1795 1517$48 1517$188 1517$772 8 8 1800 1517$43 1517$138 1517$722 8 8 1802 1517$41 1517$118 1517$702 8 8 1808 1517$35 1517$058 1517$642 8 8 1810 1517$33 1517$038 1517$622 8 8 1812 1517$31 1517$018 1517$602 8 8 1816 1517$27 1516$978 1517$562 8 8 1820 1517$23 1516$938 1517$522 8 8 1830 1517$13 1516$838 1517$422 8 8 1840 1517$03 1516$738 1517$322 8 8 1845 1516$98 1516$688 1517$272 8 8 1850 1516$93 1516$638 1517$222 8 8 1853 1516$9 1516$608 1517$192 8 8 1855 1516$87933 1516$58733 1517$17133 8 8 1860 1516$81767 1516$52567 1517$10967 8 8 1865 1516$756 1516$464 1517$048 8 8 +BC DSES C F C DE C D= e EG ! e =er ! 1870 1516$68183 1516$38983 1516$97383 8 8 1880 1516$4385 1516$1465 1516$7305 8 8 1890 1516$19517 1515$90317 1516$48717 8 8 1900 1515$95183 1515$65983 1516$24383 8 8 1910 1515$7085 1515$4165 1516$0005 8 8 1920 1515$46517 1515$17317 1515$75717 8 8 1922 1515$4165 1515$1245 1515$7085 8 8 1930 1515$1245 1514$8325 1515$4165 8 8

1940 1514$7595 1514$4675 1515$0515 1943 1514$65 1514$358 1514$942 1950 1514$3436 1514$0516 1514$6356 1960 1513$9059 1513$6139 1514$1979 + 1962$3868 1513$80142 1513$50942 1514$09342 1970 1513$46819 1513$22185 1513$71453 1975 1513$24933 1513$03299 1513$46567 1980 1512$97517 1512$78883 1513$16151 1990 1512$42683 1512$30049 1512$55317 1998$8898 1511$93938 1511$86638 1512$01238 2000 1511$8785 1511$8055 1511$94484 2010 1511$25517 1511$18217 1511$26151 2011$0568 1511$18929 1511$11629 1511$18929 2020 1510$63183 1510$55883 1510$57817 2023$2238 1510$41315 1510$34015 1510$34015 2030 1509$9535 1509$8805 1509$8805 2033 1509$75 1509$677 1509$677 2038 1509$4 1509$327 1509$327 2040 1509$26 1509$187 1509$187 2050 1508$56 1508$487 1508$487 2060 1507$86 1507$787 1507$787 2067 1507$37 1507$297 1507$297 2070 1507$16 1507$087 1507$087 2080 1506$46 1506$387 1506$387 2090 1505$76 1505$687 1505$687 2097$0511 1505$26642 1505$19342 1505$19342 2100 1505$06 1505$012 1504$987 2108 1504$5 1504$49269 1504$427 2109$2181 1504$41473 1504$41473 1504$34173 +BC DSES C F C DE C D= 2121$3851 1503$56304 1503$63605 1503$49004 2150 1501$56 1501$80469 1501$31531 + 2156$6681 1501$09323 1501$37793 1500$80853 2200 1498$06 1498$3447 1497$7753 2208 1497$5 1497$7847 1497$2153 2224 1496$38 1496$6647 1496$0953 2245 1494$91 1495$1947 1494$6253 2262 1493$72 1494$0047 1493$4353 2270 1493$16 1493$4447 1492$8753 2275 1492$81 1493$0947 1492$5253 2282 1492$32 1492$6047 1492$0353

8 8 8 8 8 6$74906 5$92715 5$10523 3$46139 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1$31507 0$20024 0 e EG ! 2$00005 6$70387 7$8 7$8 7$8 7$8 7$8 7$8 7$8 7$8 7$8

8 8 8 8 8 6$74906 5$92715 5$10523 3$46139 2$00005 1$81756 0$17372 0 1$47012 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 e =er ! 2 6$70387 7$8 7$8 7$8 7$8 7$8 7$8 7$8 7$8 7$8

2290 1491$76 1492$0447 1491$4753 2298 1491$2 1491$4847 1490$9153 + 2301$8795 1490$92844 1491$21314 1490$64374 2308 1490$5 1490$75313 1490$24687 2340 1488$48187 1488$56988 1488$39386 2342$9066 1488$33634 1488$40934 1488$26334 2357$0561 1487$62792 1487$70092 1487$55492 2368 1487$08 1487$153 1487$007 2369$2261 1487$03083 1487$10383 1486$95783 2386 1486$3582 1486$53186 1486$18454 + 2405$7261 1485$78088 1486$07288 1485$48888 2418 1485$42167 1485$71367 1485$12967 2458 1484$875 1485$167 1484$583 2465 1484$85062 1485$14262 1484$55862 2495 1484$98662 1485$27862 1484$69462 2532 1485$69147 1485$98347 1485$39947 2538 1485$86167 1486$15367 1485$56967 + 2571$1833 1487$11212 1487$40412 1486$82012 2575 1487$25595 1487$52507 1486$98683 2605 1488$82195 1488$91107 1488$73283 2607$6863 1488$98138 1489$05438 1488$90838 2608 1489 1489$07112 1488$927 2619$8533 1489$7112 1489$7112 1489$6382 2630 1490$32 1490$25912 1490$247 2632$0203 1490$44122 1490$36822 1490$36822 2664 1492$36 1492$287 1492$287 +BC DSES C F C DE C D= 2680 1493$32 1493$247 1493$247 2717 1495$54 1495$467 1495$467 2745 1497$22 1497$147 1497$147 2785 1499$62 1499$547 1499$547 2823 1501$9 1501$827 1501$827 2862 1504$24 1504$167 1504$167 2905 1506$82 1506$747 1506$747 2955 1509$82 1509$747 1509$747 2998 1512$4 1512$327 1512$327 3040 1514$92 1514$847 1514$847 3085 1517$62 1517$547 1517$547 3130 1520$32 1520$247 1520$247 3158 1522 1521$927 1521$927

7$8 7$8 7$8 6$93505 2$41122 2 2 2 2 4$7579 8 8 8 8 8 8 8 8 7$37315 2$44164 2$00005 1$94849 0 1$66795 2 2 e EG ! 2 2 2 2 2 2 2 2 2 2 2 2 2

T&%)& ". C&(& /( <(&)(' +*$ +*&' +*('<*$/,($(' & %*/( /((+@* ,=0,(/* > ((.

7$8 7$8 7$8 6$93505 2$41122 2 2 2 2 4$7579 8 8 8 8 8 8 8 8 7$37315 2$44164 2 2 2 2 2 2 e =er ! 2 2 2 2 2 2 2 2 2 2 2 2 2

,.2 DISE-O EN PERFIL DEL EJE DE LA CARRETERA

T(*B*7 7, *.,*.,- ),(-./*! '( @&+( <&,($/* /() <(?,) /() (($* $&0&) &&$/* 0$& <*), )$(& +*$ <($/,($(' -($*(' & )&' ('<(+,?,+&/&' > <*+0&$/* <&'& )* -;' +(+& &) (($* $&0&) <&& (,& =0( @&>&$ &$/(' -*,-,($*' /( ,(& 0 *%&' &/,+,*$&)(' +*-* <0($(' $()(' (+. P&& ('( &),$(&-,($* '( *%0,(*$ 5 &$($(' (,+&)(' =0( )0(* '( <*+(/( & /,'(& +&/& 0$& /( )&' +0&' (,+&)(' +*('<*$/,($(' & )*' +&-%,*' /( <($/,($('. E) &),$(&-,($* > '0 &%'+,'&/* '( <('($&;$ -;' &/()&$( )0(* /() /,'(* (,+&).

D.+, 7, *+ /'()*+ ),(-./*,+! <&,($/* /() &),$(&-,($* (,+&) '( &$&),&$ +,(,*' +*-* )*$,0/ -$,-& <* +,(,*' /( '(0,/&/ > /( ,',%,),/&/ &0$=0( () +,(,* /( '(0,/&/ (' () -;' ,-<*&$( >& =0( ',(-<( '( *%,($( 0$& )*$,0/ -$,-& -&>* ($ ('( +,(,* > <* )* &$* (' () =0( ,(. T&-%,$ '( (),( 0$& )*$,0/ -;,-& =0( ,($( /&/& <* () +,(,* /( /($&( <&& (,& ('&$+&-,($* /( &0&' > &-%,$ <* )& )*$,0/ +,+& =0( ,-<),+& )& )*$,0/ ($ )& +0&) )*' (@+0)*' /,'-,$0>($ '0 ()*+,/&/ /( ;$',* ($ 25 W-@. A +*$,$0&+,$ ($ )& &%)& 18 '( <('($&$ )*' +;)+0)*' <&& +&/& 0$& /( )&' +0&' +*$ '0' ('<(+,& +*& /() ((' ($ +&/& <0$* @&))&/* & <&, /( )& ?-0)& /( +*(++,$. DS

C B?R (m)

0 10 14 20 30 40 50 60

1478 1478 1478 1478 1478J333 1478J667 1479 1479J333

+C

CS +E: C B?B +B=EB (m) (m)

2! 2! 2! 2! 2! 2! 2! 2!

1478 1478J2 1478J28 1478J4 1478J6 1478J8 1479 1479J2

+RHRC  (m)

$R: :RE(m)

CRREIB (m)

C RCF (m)

0 0 0 0 0 0 0 0

1478 1478J2 1478J28 1478J4 1478J6 1478J8 1479 1479J2

70 80 90 98 100 110 120 130 134 140 150 160 170 174 178 180 190 194 200 210

1479J667 1480 1481J111 1482 1482J111 1482J667 1483J222 1483J778 1484 1484J3 1484J8 1485J3 1485J8 1486 1486 1486 1486 1486 1486 1486

DS

C B?R (m)

220 230 240 250 260 270 280 290 300 304 310 320 330 340 350 360 370 380 390 400

1486 1486 1486 1486 1486 1486 1486 1486 1486 1486 1486J091 1486J242 1486J394 1486J545 1486J697 1486J848 1487 1487J152 1487J303 1487J455

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! +C

1479J4 1479J6 1479J8 1479J96 1480 1480J2 1480J4 1480J6 1480J68 1480J8 1481 1481J2 1481J4 1481J48 1481J56 1481J6 1481J8 1481J88 1482 1482J2

CS +E: C B?B +B=EB (m) (m)

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2!

1482J4 1482J6 1482J8 1483 1483J2 1483J4 1483J6 1483J8 1484 1484J08 1484J2 1484J4 1484J6 1484J8 1485 1485J2 1485J4 1485J6 1485J8 1486

+RHRC  (m)

$R: :RE(m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1479J4 1479J6 1479J8 1479J96 1480 1480J2 1480J4 1480J6 1480J68 1480J8 1481 1481J2 1481J4 1481J48 1481J56 1481J6 1481J8 1481J88 1482 1482J2


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1482J4 1482J6 1482J8 1483 1483J2 1483J4 1483J6 1483J8 1484 1484J08 1484J2 1484J4 1484J6 1484J8 1485 1485J2 1485J4 1485J6 1485J8 1486

410 420 430 436 440 450 455 460 470 480 490 498 500 510 520 530

1487J606 1487J758 1487J909 1488 1488 1488 1488 1488 1488 1488 1488 1488 1488J085 1488J511 1488J936 1489J362

DS

C B?R (m)

540 545 550 560 570 580 590 600 610 620 630 640 650 660 670 672 680 690 700 710 720 725 730 735

1489J787 1490 1490J154 1490J462 1490J769 1491J077 1491J385 1491J692 1492 1492J4 1492J8 1493J2 1493J6 1494 1494 1494 1494J302 1494J679 1495J057 1495J434 1495J811 1496 1496 1496

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! +C

1486J2 1486J4 1486J6 1486J72 1486J8 1487 1487J1 1487J2 1487J4 1487J6 1487J8 1487J96 1488 1488J2 1488J4 1488J6

CS +E: C B?B +B=EB (m) (m)

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2!

1488J8 1488J9 1489 1489J2 1489J4 1489J6 1489J8 1490 1490J2 1490J4 1490J6 1490J8 1491 1491J2 1491J4 1491J44 1491J6 1491J8 1492 1492J2 1492J4 1492J5 1492J6 1492J7

+RHRC  (m)

$R: :RE(m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1486J2 1486J4 1486J6 1486J72 1486J8 1487 1487J1 1487J2 1487J4 1487J6 1487J8 1487J96 1488 1488J2 1488J4 1488J6


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1488J8 1488J9 1489 1489J2 1489J4 1489J6 1489J8 1490 1490J2 1490J4 1490J6 1490J8 1491 1491J2 1491J4 1491J44 1491J6 1491J8 1492 1492J2 1492J4 1492J5 1492J6 1492J7

740 750 760 770 780 790 800 810 820 830 840 850

1496J078 1496J233 1496J388 1496J543 1496J698 1496J853 1497J008 1497J163 1497J318 1497J473 1497J628 1497J783

DS

C B?R (m)

860 864 870 880 890 900 910 920 925 930 940 950 960 965 970 980 990 1000 1005 1010 1015 1020 1030 1040 1050 1060 1063 1066

1497J938 1498 1498J214 1498J571 1498J929 1499J286 1499J643 1500 1498 1498 1498 1498 1498 1498 1500 1500J571 1501J143 1501J714 1502 1503 1504 1504 1504 1504 1504 1504 1504 1506

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! +C

CS +E: C B?B +B=EB (m) (m)

2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2! 2!

+:1

+E:1

1492J8 1493 1493J2 1493J4 1493J6 1493J8 1494 1494J2 1494J4 1494J6 1494J8 1495

1498 7! 7! 7! 7! 7! 7! 7! 7! 7! 7!

1495J2 1495J28 1495J4 1495J6 1495J8 1496 1496J2 1496J4 1496J5 1496J6 1496J8 1497 1497J2 1497J3 1497J4 1497J6 1497J8 1498 1498J34 1498J69 1499J04 1499J39 1500J09 1500J79 1501J49 1502J19 1502J4 1502J61

+RHRC  (m)

$R: :RE(m)

200

5

0 0 0 0 0 0 0 0 0 0 0 0

1492J8 1493 1493J2 1493J4 1493J6 1493J8 1494 1494J2 1494J4 1494J6 1494J8 1495


C RCF (m)

0 0 0 0 0 0 0J0125 0J05 0J078125 0J1125 0J2 0J3125 0J45 0J528125 0J6125 0J8 1J0125 1J25 1J128125 1J0125 0J903125 0J8 0J6125 0J45 0J3125 0J2 0J171125 0J1445

1495J2 1495J28 1495J4 1495J6 1495J8 1496 1496J2125 1496J45 1496J578125 1496J7125 1497 1497J3125 1497J65 1497J828125 1498J0125 1498J4 1498J8125 1499J25 1499J468125 1499J7025 1499J943125 1500J19 1500J7025 1501J24 1501J8025 1502J39 1502J571125 1502J7545

1070 1073 1080 1084 1090 1100 1110 1120

1507J143 1508 1510 1512 1512J462 1513J231 1514 1514J588

DS

C B?R (m)

1130 1140 1144 1150 1160 1161 1170 1180 1190 1192 1200 1210 1220 1230 1240 1243 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1343 1350 1360 1370 1380 1390

1515J176 1515J765 1516 1516J706 1517J882 1518 1518J581 1519J226 1519J871 1520 1520J116 1520J261 1520J406 1520J551 1520J696 1520J739 1520J841 1520J986 1521J13 1521J275 1521J42 1521J565 1521J71 1521J855 1522 1522 1522 1522 1522 1522 1522 1522

7! 7! 7! 7! 7! 7! 7! 7!

+:1

+C

CS +E: C B?B +B=EB (m) (m)

7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7! 7!

+:2

+E:2

1502J89 1503J1 1503J59 1503J87 1504J29 1504J99 1505J69 1506J39

1522 @1! @1! @1! @1! @1!

1507J09 1507J79 1508J07 1508J49 1509J19 1509J26 1509J89 1510J59 1511J29 1511J43 1511J99 1512J69 1513J39 1514J09 1514J79 1515 1515J49 1516J19 1516J89 1517J59 1518J29 1518J99 1519J69 1520J39 1521J09 1521J79 1522 1521J93 1521J83 1521J73 1521J63 1521J53

0J1125 1503J0025 0J091125 1503J191125 0J05 1503J64 0J032 1503J902 0J0125 1504J3025 0 1504J99 0 1505J69 0 1506J39 +RHRC  (m)

$R: :RE(m)

200

8


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0J0098 0J0578 0J1458 0J2738 0J4418 0J6498 0J8978 1J1858 1J5138 1J8818 2 1J7298 1J3778 1J0658 0J7938 0J5618

1507J09 1507J79 1508J07 1508J49 1509J19 1509J26 1509J89 1510J59 1511J29 1511J43 1511J99 1512J69 1513J39 1514J09 1514J79 1515 1515J4802 1516J1322 1516J7442 1517J3162 1517J8482 1518J3402 1518J7922 1519J2042 1519J5762 1519J9082 1520 1520J2002 1520J4522 1520J6642 1520J8362 1520J9682

1400 1404 1410 1420

1522 1522 1522J117 1522J311

DS

C B?R (m)

1430 1440 1443 1450 1460 1470 1480 1490 1500 1507 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1705 1710 1712 1720 1730 1731

1522J505 1522J699 1522J757 1522J893 1523J087 1523J282 1523J476 1523J67 1523J864 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1524 1522J667 1522 1520J571 1520 1520 1520 1520

@1! @1! @1! @1! +C

+:2

1521J43 1521J39 1521J33 1521J23

CS +E: C B?B +B=EB (m) (m)

@1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1!

1521J13 1521J03 1521 1520J93 1520J83 1520J73 1520J63 1520J53 1520J43 1520J36 1520J33 1520J23 1520J13 1520J03 1519J93 1519J83 1519J73 1519J63 1519J53 1519J43 1519J33 1519J23 1519J13 1519J03 1518J93 1518J83 1518J73 1518J63 1518J53 1518J43 1518J38 1518J33 1518J31 1518J23 1518J13 1518J12

0J3698 0J3042 0J2178 0J1058 +RHRC  (m)


0J0338 0J0018 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1521J0602 1521J0858 1521J1122 1521J1242 C RCF (m)

1521J0962 1521J0282 1521 1520J93 1520J83 1520J73 1520J63 1520J53 1520J43 1520J36 1520J33 1520J23 1520J13 1520J03 1519J93 1519J83 1519J73 1519J63 1519J53 1519J43 1519J33 1519J23 1519J13 1519J03 1518J93 1518J83 1518J73 1518J63 1518J53 1518J43 1518J38 1518J33 1518J31 1518J23 1518J13 1518J12

DS

C B?R (m)

1740 1750 1755 1760 1770 1772 1778 1780 1782 1788 1790 1795 1800 1802 1808 1810 1812 1816 1820 1830 1840 1845 1850 1853 1855 1860 1865 1870 1880 1890 1900 1910 1920 1922 1930 1940 1943 1950 1960 1970

1520 1520 1520 1518 1516J333 1516 1514 1513 1512 1510 1510 1510 1511J429 1512 1514 1515 1516 1518 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1520 1519J698 1519J321 1519J208 1518J943 1518J566 1518J189

+C

CS +E: C B?B +B=EB (m) (m)

@1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1! @1!

+:3

+E:3

1516 @7! @7! @7!

1518J03 1517J93 1517J88 1517J83 1517J73 1517J71 1517J65 1517J63 1517J61 1517J55 1517J53 1517J48 1517J43 1517J41 1517J35 1517J33 1517J31 1517J27 1517J23 1517J13 1517J03 1516J98 1516J93 1516J9 1516J88 1516J83 1516J78 1516J73 1516J63 1516J53 1516J43 1516J33 1516J23 1516J21 1516J13 1516J03 1516 1515J56 1514J86 1514J16

+RHRC  (m)

$R: :RE(m)

180

6


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0J0006667 0J0081667 0J024 0J0481667 0J1215 0J2281667 0J3681667 0J5415 0J7481667 0J7935 0J9881667 1J2615 1J35 1J1481667 0J8881667 0J6615

1518J03 1517J93 1517J88 1517J83 1517J73 1517J71 1517J65 1517J63 1517J61 1517J55 1517J53 1517J48 1517J43 1517J41 1517J35 1517J33 1517J31 1517J27 1517J23 1517J13 1517J03 1516J98 1516J93 1516J9 1516J879333 1516J821833 1516J756 1516J681833 1516J5085 1516J301833 1516J061833 1515J7885 1515J481833 1515J4165 1515J141833 1514J7685 1514J65 1514J411833 1513J971833 1513J4985

1975 1980 1990 2000 2010 2020 2030 2033 2038 2040 2050 2060 2067 2070 2080 2090 2100 2108 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2208 2210 2220 2224 2230 2240

1518 1517J6 1516J8 1516 1515 1514 1512J889 1512J556 1512 1511J862 1511J172 1510J483 1510 1509J538 1508 1507J286 1506J571 1506 1505J905 1505J429 1504J952 1504J476 1504 1503J6 1503J2 1502J8 1502J4 1502 1502 1501J75 1500J5 1500 1500 1500

DS

C B?R (m)

2245 2250 2260 2262 2270

1500 1500 1500 1500 1498

+:3

+C

@7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7!

1513J81 1513J46 1512J76 1512J06 1511J36 1510J66 1509J96 1509J75 1509J4 1509J26 1508J56 1507J86 1507J37 1507J16 1506J46 1505J76 1505J06 1504J5 1504J36 1503J66 1502J96 1502J26 1501J56 1500J86 1500J16 1499J46 1498J76 1498J06 1497J5 1497J36 1496J66 1496J38 1495J96 1495J26

CS +E: C B?B +B=EB (m) (m)

@7! @7! @7! @7! @7!

1494J91 1494J56 1493J86 1493J72 1493J16

0J5606667 0J4681667 0J3081667 0J1815 0J0881667 0J0281667 0J0015 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +RHRC  (m)

$R: :RE(m)

1513J249333 1512J991833 1512J451833 1511J8785 1511J271833 1510J631833 1509J9585 1509J75 1509J4 1509J26 1508J56 1507J86 1507J37 1507J16 1506J46 1505J76 1505J06 1504J5 1504J36 1503J66 1502J96 1502J26 1501J56 1500J86 1500J16 1499J46 1498J76 1498J06 1497J5 1497J36 1496J66 1496J38 1495J96 1495J26


C RCF (m)

0 0 0 0 0

1494J91 1494J56 1493J86 1493J72 1493J16

2275 2280 2282 2290 2298 2300 2308 2310 2320 2330 2340 2350 2360 2368 2386 2370 2380 2390 2400 2410 2418 2420 2430 2440 2450 2458 2460 2465 2470 2480

1496 1494J571 1494 1492 1490 1489J905 1489J524 1489J429 1488J952 1488J476 1488 1487J286 1486J571 1486 1484 1485 1484J375 1483J75 1483J125 1482J5 1482 1482 1482 1482 1482 1482 1482 1482 1482J333 1483

DS

C B?R (m)

2490 2495 2500 2510 2520 2530 2532 2538 2540 2550

1483J667 1484 1484J27 1484J811 1485J351 1485J892 1486 1486 1486J108 1486J649

@7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7! @7!

+:4

+E:4

1480 6! 6! 6! 6!

+C

1492J81 1492J46 1492J32 1491J76 1491J2 1491J06 1490J5 1490J36 1489J66 1488J96 1488J26 1487J56 1486J86 1486J3 1485J04 1486J16 1485J46 1484J76 1484J06 1483J36 1482J8 1482J66 1481J96 1481J26 1480J56 1480 1480J12 1480J42 1480J72 1481J32

CS +E: C B?B +B=EB (m) (m)

6! 6! 6! 6! 6! 6! 6! 6! 6! 6!

1481J92 1482J22 1482J52 1483J12 1483J72 1484J32 1484J44 1484J8 1484J92 1485J52

300

13

+RHRC  (m)

0 0 0 0 0 0 0 0J0008667 0J0312 0J1048667 0J2218667 0J3822 0J5858667 0J78 1J3182 0J8328667 1J1232 1J4568667 1J8338667 2J2542 2J6216667 2J7178667 3J2248667 3J7752 4J3688667 4J875 4J7458667 4J4306167 4J1262 3J5498667

1492J81 1492J46 1492J32 1491J76 1491J2 1491J06 1490J5 1490J360867 1489J6912 1489J064867 1488J481867 1487J9422 1487J445867 1487J08 1486J3582 1486J992867 1486J5832 1486J216867 1485J893867 1485J6142 1485J421667 1485J377867 1485J184867 1485J0352 1484J928867 1484J875 1484J865867 1484J850617 1484J8462 1484J869867


C RCF (m)

3J0168667 2J7666167 2J5272 2J0808667 1J6778667 1J3182 1J2514667 1J0616667 1J0018667 0J7288667

1484J936867 1484J986617 1485J0472 1485J200867 1485J397867 1485J6382 1485J691467 1485J861667 1485J921867 1486J248867

2560 2570 2575 2580 2590 2600 2605 2608 2610 2620 2630 2640 2650 2660 2664 2670 2680 2690 2700 2710 2717 2720 2730 2740 2745 2750

1487J189 1487J73 1488 1488J333 1489 1489J667 1490 1490J24 1490J4 1491J2 1492 1492J588 1493J176 1493J765 1494 1494J75 1496 1496J541 1497J081 1497J622 1498 1498J214 1498J929 1499J643 1500 1500J25

DS

C B?R (m)

2760 2770 2780 2785 2790 2800 2810 2820 2823 2830 2840 2850 2860 2862

1500J75 1501J25 1501J75 1502 1502J263 1502J789 1503J316 1503J842 1504 1504J359 1504J872 1505J385 1505J897 1506

+:4

+C

6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6!

1486J12 1486J72 1487J02 1487J32 1487J92 1488J52 1488J82 1489 1489J12 1489J72 1490J32 1490J92 1491J52 1492J12 1492J36 1492J72 1493J32 1493J92 1494J52 1495J12 1495J54 1495J72 1496J32 1496J92 1497J22 1497J52

CS +E: C B?B +B=EB (m) (m)

6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6!

1498J12 1498J72 1499J32 1499J62 1499J92 1500J52 1501J12 1501J72 1501J9 1502J32 1502J92 1503J52 1504J12 1504J24

0J4992 0J3128667 0J23595 0J1698667 0J0702 0J0138667 0J00195 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +RHRC  (m)

$R: :RE(m)

1486J6192 1487J032867 1487J25595 1487J489867 1487J9902 1488J533867 1488J82195 1489 1489J12 1489J72 1490J32 1490J92 1491J52 1492J12 1492J36 1492J72 1493J32 1493J92 1494J52 1495J12 1495J54 1495J72 1496J32 1496J92 1497J22 1497J52


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0

1498J12 1498J72 1499J32 1499J62 1499J92 1500J52 1501J12 1501J72 1501J9 1502J32 1502J92 1503J52 1504J12 1504J24

2870 2880 2890 2900 2905 2910 2920 2930 2940 2950 2955 2960 2970 2980 2990 2998 3000 3010 3020 3030 3040 3050

1506J372 1506J837 1507J302 1507J767 1508 1508J2 1508J6 1509 1509J4 1509J8 1510 1510J233 1510J698 1511J163 1511J628 1512 1512J095 1512J571 1513J048 1513J524 1514 1514J444

DS

C B?R (m)

3060 3070 3080 3085 3090 3100 3110 3120 3130 3140 3150 3158 3160 3164 3170 3180 3190 3196J2629

1514J889 1515J333 1515J778 1516 1516J222 1516J667 1517J111 1517J556 1518 1518J588 1519J176 1519J647 1519J765 1520 1520J372 1520J992 1521J612 1522

6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! +C

1504J72 1505J32 1505J92 1506J52 1506J82 1507J12 1507J72 1508J32 1508J92 1509J52 1509J82 1510J12 1510J72 1511J32 1511J92 1512J4 1512J52 1513J12 1513J72 1514J32 1514J92 1515J52

CS +E: C B?B +B=EB (m) (m)

6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6! 6!

1516J12 1516J72 1517J32 1517J62 1517J92 1518J52 1519J12 1519J72 1520J32 1520J92 1521J52 1522 1522J12 1522J36 1522J72 1523J32 1523J92 1524J295774

+RHRC  (m)

$R: :RE(m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1504J72 1505J32 1505J92 1506J52 1506J82 1507J12 1507J72 1508J32 1508J92 1509J52 1509J82 1510J12 1510J72 1511J32 1511J92 1512J4 1512J52 1513J12 1513J72 1514J32 1514J92 1515J52


C RCF (m)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1516J12 1516J72 1517J32 1517J62 1517J92 1518J52 1519J12 1519J72 1520J32 1520J92 1521J52 1522 1522J12 1522J36 1522J72 1523J32 1523J92 1524J295774

T&%)& 18. C&(& /( +0&' (,+&)(' +&/& 18 - ,$+)0,/&' +*& /( (( +*& /( &$($( > +*& $(&.

C(.-,(.+ 7, 7.+, 7, .-'7 7, /'()* ),(-./*! )*' +,(,*' & ($( ($ +0($& <&& )& ('+*($+,& /( )& )*$,0/ /( +0& (,+&) '*$ )*' $*-%&/*' ($ () -&+* (,+* =0( '*$ )*' (+*-($/&/*' <* () -&$0&) /( /,'(* (*-,+* /( +&((&' > )*' +;)+0)*' /( +&/& 0$& /( )&' )*$,0/(' '( '0'($&$ ($ )*' &$(*' & ('( /*+0-($* <&& &' 0',?,+& )& ('+*($+,& /( )& )*$,0/ +*('<*$/,($( & +&/& +0&. A +*$,$0&+,$ ($ )& &%)& 11 '( <('($& )& )*$,0/ -$,-& -;,-& > )& ()(,/&. Cur'a

L min (m)

L max

1 !  $

90 88 66 234

250 400 300 650

L elegida(m) 200 200 180 300

T&%)& 11. L*$,0/ /( +0& (,+&).

L.-'7 .* 7, * -*,-, ),(-./*! P&& '( +&'* <&,+0)& +*$ 0$ V ('<(+,?,+&/* /( 68 W-@ )& &%)& 4.3 /() -&$0&) /( /,'(* (*-,+* /( +&((&' ('<(+,?,+& 0$& )*$,0/ -$,-& /( &$($( (,+&) /( 178 -. (,?,+&$/* )&' /,'&$+,&' ($ )& +&(& &$(,* H&%)&18 ($( P, &/>&+($(' '( <0(/($ *%($( /,'&$+,&' -&>*(' & 178 - )* +0&) ,$/,+& =0( () /,'(* +0-<)( <&& ('( +,(,*. A) ,0&) =0( +0-<)( )& )*$,0/ -$,-& /( )& &$($( (,+&) )&' )*$,0/(' -,$,-&' <&& )& +0& (,+&) <* +,(,*' /( *<(&+,$ > '(0,/&/ > )& )*$,0/ -;,-& <* +,(,*' /( )*$,0/ +,,+& > /($&(. ,. DISE-O DE LA SECCI/N TRANSVERSAL DE LA CARRETERA

A/ 7, B*  7,(,/ 7, )*! '( &%&&; <&& 0$ &$+@* /( *$& /( 48 - +*$ () ?,$ /( +*$*+( )&' +*$/,+,*$(' /( <($/,($(' /() (($* ($ ('& ?&$& > /(?,$, &)0$*' <&;-(*' +*-* <($/,($(' /( &)0/('.

D.,+.,+ ;*(* + ,,,-+ 7, * +,//.= -(*+),(+*!



C*B*7*! /( &+0(/* & )*' &)*(' (+*-($/&/*' <* () -&$0&) /( /,'(* (*-,+* /( +&((&' ($ )& &%)& 5.2 <&& 0$& & <,-&,& /( 0$& +&)&/& +*$ V /( 68 W-@ > (($* -*$&*'* () &$+@* /( +&)&/& (' /( 7.3 -. E$ )*' <0$*' &$(,*(' >& '( @&%& &%&&/* +*$ ('( &)* <&& +&)+0)& > &+*& () /,&&-& /( <(&)( <(* '( ('<(+,?,+& ($ ('( <0$* <* <(($(+( & &)*(' ,$+)0,/*' ($ () -&$0&) ($ )* =0( +*('<*$/( &) /,'(* &$'('&).



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9rea 2#o de se""ión (m!) 79J5075 78J1075 77J8725 77J645 72J49 81J3125 80J6725 85J2025 80J85 71J975 "orte 29J425 ex"a'a"ión 43J1725 48J9 39J5925 36J485 35J5375 32J28 33J4325 18J555 20J8975 :ol&men total

Volumen (m) 788J075 777J5875 769J0125 829J375 764J125 362J9875 442J4625 360J1125 328J5625 197J2625 5619J5625

T&%)& 14. V*)-($(' ($( )&' &%'+,'&' W1Y"88 > W2Y8"8.

9$ DISEOS ADICIONALES DISEO DEL PUENTE E) <0($( '( /,'(&; <&& =0( +0-<)& +*$ ('<(+,?,+&+,*$(' > '( &+*<)( & )&' +&&+(',+&' =0( '( <('($&$ ($ () (($* /( )& & <*>(+&/& /('/(

)& &%'+,'& 1Y76712 @&'& )& &%'+,'& W1Y!1363. E' /(+, =0( () <0($( +*$&; +*$ 0$& )*$,0/ /( 4651 -(*'. A/(-;' )& <&( -;' &)& =0( /(%( ($( +*$ ('<(+* &) (($* $&0&) ('; ($ )& &%'+,'& W1Y7"16! +*$ !26 -(*' /( /('$,(). E) <0($( /(%( /,'(&'( +*$ +,(,*' /( '(0,/&/ +*-*/,/&/ (',+& > ,&%,),/&/ (+*$-,+&. E$ ('( +&'* &) &&'( /( 0$& )0 <(=0(& ($( &<*>*' <0(/( ,-<)(-($&'( 0$ <0($( ,<* ,& +*$ )*'&' (',%*' <,)&' > ,&' ($ +*$+(* (?*&/*. U$ <0($( ,<* ,& +0($& +*$ )&' ',0,($(' +&&+(',+&'

I-&($ 4.E)(-($*' /() <0($(.

L+* 7, //(,- (,<(B*7 / (,+.+-,/.* 7, V.*+ , //(,- (,<(B*7 / (,+.+-,/.* 7, E+;,+( 7, * +* E+;,+( 7, *+ ).*+ ;(./.;*,+

4000 ;+. 4000 ;+. 25 / :0 /

I-&($ 6. V,&' > /,-($',$ /( )& )*'&.

ESTRI&OS Y PILAS E+-(.+ >('0+0& ($ +*$+(* (?*&/* +*$ (','($+,& /( 4888 <', C&& '0<(,* (+&$0)&  18 -  5 C&& ,$?(,* &<&& (+&$0)&  12 -  18 L*$,0/ (',%* 1  33 &%'+,'&  1Y76712 L*$,0/ (',%* 2  27 &%'+,'&  W1Y!1363

P.* /,-(* >('0+0& ($ +*$+(* (?*&/* +*$ (','($+,& /( 4888 <', C&& '0<(,* (+&$0)&  18 -  5 C&& ,$?(,* &<&& (+&$0)&  18 -  5 L*$,0/ +*)0-$& /( )& <,)&  !77 &%'+,'& W1Y7"16!

/.,-*/.,+ ;*(* ,+-(.+: 13 &$+@*  12 ('<('*  2 &)*

;*(* ;.* /,-(*: 12 &$+@*  6 ('<('*  2 &)* )& ',0,($( &?,+& /('+,%( )& (*-(& > 0%,+&+,$ /( )*' ()(-($*' /() <0($(

I-&($ 5. V,'& ($ <(?,) /() <0($(. L& )$(& *& (<('($& () (($* $&0&).

D.+, 7, /*;* 7, (7*7'(*! S( <*<*$( <&& () /,'(* /( )& +&<& /( */&/0& 0,),& )& ;?,+& 6 (+*-($/&/& <* () +0(<* /( ,$($,(*' /( )*' E.U.A )& +0&) ,-<),+& )& *%($+,$ /() VRS H&)* ()&,* /( '*<*( /() '0()* '*%( () +0&) '( +*$'0,; )& &. P&& () '0()* /() <*>(+* '( ,($( 0$ VRS /( ! > ', '( ,($( 0$& +&& /( 7.25 *$ <*/0+,/& <* (@+0)*' '( /,'(&; +*$ 0$ ('<('* /( 45 +- &<*,-&/&-($( > &)($&,&-($( & ('( &)* '( <0(/( *%($( ** /( )& ;?,+& 7 /( &+0(/* & )&' +*$/,+,*$(' /( ;$',* /( )& &. C*-* '( <*>(+ ($ () ('0/,* /( ;$',* <&& 0$ VD /( !77 (@@ /( )& ;?,+& 7 '( *%,($( 0$ &)* -$,-* /( )& %&'( /( 12 +> 0$ ('<('* *%($,/* +*$ VRS ! > )& +0& III /( 38+- /( ('<('* /( )& '0%%&'( -;' )& %&'(.

G;?,+& 6. E'<('*(' (=0(,/*' /( <&,-($*.

G;?,+& 7. E'<('* (=0(,/* /( <&,-($*.

CONCLUSIONES 

S( /,'( () &-* /( & +*$ ($,($/* ($ +0($& +,(,*' /() -&$0&)



/( /,'(* (*-,+* /( +&((&' /() INVIAS. S( (&), () /,'(* (*-,+* (,+&) > &/,+,*$&) & ( ('0)



+*$($,($( /,'(& 0$ <0($( <&& (,& +*(' (+(',*' /( (($*. S( +&)+0) -*,-,($*' /( ,(& <&& () &-* ($( 1Y"88 > 2Y8"8 *%($,($/* <&& */* '( '(++,*$(' &$''&)(' =0(



,-<),+&$ ')* +*( /( (($*. S( /,'(&*$ )&' +0$(&' ($,($/* ($ +0($& )*' +&0/&)(' -;,-*'



*%($,/*' & <&, /() ('0/,* @,/*),+*. S( <*>(+ 0$ VD H*)0-($ @*&,* /( /,'(* +*$ 0$ @*,*$( /( 28 &*' /() +0&) '( *%0* 0$& <*>(++,$ /( !78 (@@ > /( &+0(/* & )& +&<&+,/&/ /( )& & '( '&,'?&+($ )&' +*$/,+,*$(' /( ;$',* <&



('( <(,*/* /( ,(-<*. S( (),, 0$& ()*+,/&/ ('<(+?,+& =0( &<),+& <&& */* () &-* /( )& & /( 68 W-@. REFERENCIAS

R,+* A. L& ,$($,(& /( '0()*' ($ )&' &' (('(' 2K +&((&' ?(*+&,)(' > &0*<,'&'. 1""5 M,+* D.F (/,*,&) LIMUSA.

Proyecto Final Vias

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