DISEÑO DE UNA CURVA VERTICAL PARA UN TRAMO DE CARRETERA PRIMARIA DE UNA CALZADA
ANDREA CAROLINA CUESTA BOHORQUEZ DAYANIS GUERRERO TEJADA HEIDIS PÉREZ SIERRA RUDY ANDREA SALAZAR CAMPO
ESP. YULIETH PEREZ HERNANDEZ
UNIVERSIDAD DE SUCRE FACULTAD DE INGENIERIAS PROGRAMA DE INGENIERIA CIVIL SINCELEJO-SUCRE 201
TABLA DE CONTENIDO INTRODUCCION............................................................................................................3 1. OBJETIVOS....................................................................................................................4 1.1 OBJETIVO GENERAL..............................................................................................4 1.2 OBJETIVOS ESPECIFICOS....................................................................................4 2. JUSTIFICACION.............................................................................................................5 3. MARCO DE REFERENCIAS..........................................................................................6 3.1 MARCO TEORICO.......................................................................................................6 4. PROCEDIMIENTO..........................................................................................................7 4.1 PROCEDIMIENTO EN OFICINA..............................................................................7 4.2 PROCEDIMIENTO EN CAMPO...............................................................................7 5. CÁLCULOS.....................................................................................................................8 6. ANALISIS DE RESULTADOS.........................................................................................9 7. PREGUNTAS FRECUENTES EN LA PRÁCTICA........................................................1 8. CONCLUSIONES..........................................................................................................14 9. ANE!OS........................................................................................................................15 1. BIBLIOGRAFIA..........................................................................................................16
2
INTRODUCCI!N
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
3
1. OBJETIVOS 1 OBJETIVO GENERAL D-,(/% #"/ )#%/ (%*-)/ +( #" *%/=& +( )/%%(*(%/ ' %(/-/% ,# %(,$()*-& $(%;-.
2
OBJETIVOS ESPECIFICOS I+("*-;-)/% ' +(*(%=-"/% &, /&%(, +( )/+/ #"& +( &, ((=("*&, )&%%(,$&"+-("*(, ' "()(,/%-&, $/%/ ( +-,(& +( #"/ )#%/ (%*-)/. F/=--/%-/%,( )&" / *(%=-"&&@/ ' &, )&")($*&, *&$&%<;-)&, #*--/+&, (" ( +-,(& +( )/%%(*(%/,. R(/-/% / )//-+/+ ( $%&)(+-=-("*& $/%/ +-,(/% #"/ )#%/ (%*-)/. C/)#/% /, )&%%())-&"(, $&% $("+-("*( ' /, )&*/, ,&%( / )#%/. E,*/()(% /, $("+-("*(, +( / )#%/ /?& $/%<=(*%&, (,*/()-+&, $&% ( -",*-*#*& +( @/, INVIAS ' /,@ )/)#/% ( $/%<=(*%& -.
2. JUSTIFICACI!N
4
E,*( $%&)(+-=-("*&0 ,( /)( )&" ( &?(*-& +( )%(/% +(,*%(/, (" ( (,*#+-/"*( (" *&+& & )&")(%"-("*( / +-,(& )#%/ (%*-)/0 $#(,*& :#( ,( /)( (,*%-)*/=("*( "()(,/%-& :#( ( (,*#+-/"*( $(%*("()-("*( / (,*( )#%,& )&"&)/ ' /&%+( &, ;#"+/=("*&, "()(,/%-&, $/%/ %(/-/% ( +-,(& +( #"/ )#%/ (%*-)/0 $/%/ :#( )#/"+& ,( (";%("*( / )/=$& /&%/ *("/ #" /=$-& )&"&)-=-("*& (" & :#( / (,*&, +-,(&, ,( %(;-(%( ' /,@ "& *("/ %/"+(, +-;-)#*/+(, / =&=("*& +( %(/-/% &, )<)#&, ' ( $%&)(+-=-("*& $(%*("()-("*( / +-,(& =(")-&"/+& $%(-/=("*(. D( =-,=& =&+&0 ,( #,)/ :#( ( (,*#+-/"*( +( )#%,& +( @/, I +( $%&%/=/ +( -"("-(%@/ )-- +( / U"-(%,-+/+ +( S#)%(0 /;-/")( ,#, )&"&)-=-("*&, /+:#-%-+&, (" ( /#/ +( )/,(, %(/-/"+& $%&)(+-=-("*&, :#( & %()*-;-:#(" ' ("(%(" +(,*%(/ (" ( )<)#& +( *&+&, &, $/%<=(*%&, "()(,/%-&, $/%/ (,*( +-,(&0 '/ :#( (" &)/,-&"(, &, %(/-/+&, (" ( /#/ +( )/,(, "& //,*()(" /, ;/(")-/, +( /#"&, (,*#+-/"*(,.
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". MARCO DE REFERENCIAS ".1 MARCO TEORICO E +-,(& (&=*%-)& (%*-)/ +( #"/ )/%%(*(%/0 & /-"(/=-("*& (" $(%;-0 (, / $%&'())-" +( (?( %(/ & (,$/)-/ +( / @/ ,&%( #"/ ,#$(%;-)-( (%*-)/ $/%/(/ / =-,=&. D(-+& / (,*( $/%/(-,=&0 +-)/ $%&'())-" =&,*%/%< / &"-*#+ %(/ +( (?( +( / @/. A (,*( (?( */=-" ,( ( +("&=-"/ %/,/"*( & ,#%/,/"*(. E /-"(/=-("*& &%-&"*/ ' ( /-"(/=-("*& (%*-)/ +((" ,(% )&",-,*("*(, ' //")(/+&,0 (" ;&%=/ */ :#( &, $/%<=(*%&, +( $%-=(%& )&%%(,$&"+/" ' ,(/" )&"%#("*(, )&" &, +( ,(#"+&. P&% & */"*& (, "()(,/%-& :#( &, ((=("*&, +( +-,(& (%*-)/ *("/" / =-,=/ (&)-+/+ (,$()@;-)/ +( ,()*&% (" $/"*/ :#( )&-")-+( )&" ( ((=("*& (%*-)/ (" (,*#+-&. L& -+(/ (, / &*(")-" +( %/,/"*(, /%/, )&" #" /?#,*( $*-=& +( )#%/, (%*-)/(, ' )#%/, &%-&"*/(, / /, )&"+-)-&"(, +( *%<",-*& ' / -#/ :#( (" +-,(& (" $/"*/0 ( (?( +( /-"(/=-("*& (%*-)/ (,*< )&",*-*#-+& $&% T%/=&, %()*&, TANGENTES VERTICALES CURVAS VERTICALES
CURVA VERTICAL L/, )#%/, (%*-)/(, ,&" /, :#( ("//" +&, */"("*(, )&",()#*-/, +( /-"(/=-("*& (%*-)/0 $/%/ :#( (" ,# &"-*#+ ,( (;()*>( ( $/,& %/+#/ +( / $("+-("*( +( / */"("*( +( ("*%/+/ / / +( / */"("*( +( ,/-+/. D((" +/% $&% %(,#*/+& #"/ @/ +( &$(%/)-" ,(#%/ ' )&";&%*/(0 /$/%-(")-/ /%/+/( ' )&" )/%/)*(%@,*-)/, +( +%("/?( /+()#/+/,. T-$&, +( )#%/, (%*-)/(, L/, )#%/, (%*-)/(, ,( $#(+(" )/,-;-)/% $&% ,# ;&%=/ )&=& )#%/, (%*-)/(, )")//, ' )&"(/, ' +( /)#(%+& )&" / $%&$&%)-" ("*%( ,#, %/=/, :#( /, ;&%=/" )&=& ,-=*%-)/, ' /,-=*%-)/,. E" / F-#%/ 1 ,( -"+-)/" /, )#%/, (%*-)/(, )")//, ' )&"(/, ' (" / F-#%/ 2 /, )#%/, (%*-)/(, ,-=*%-)/, ' /,-=*%-)/,.
6
F-. 1
F-. 2
7
#. PROCEDIMIENTO #.1P$%&'()*)'+,% E+ O)&)+
E,*( $%&)(+-=-("*&0 *-("( +&, $/%*(, / ,/(%. 1. D-,(& +( /, )#%/, (%*-)/(, S&%( ( $(%;- ,#=-"-,*%/+& ,( /%<" &, (",/'&, $/%/ +(*(%=-"/% /, */"("*(, (%*-)/(, ' ,#, %(,$()*-/, $("+-("*(,0 )&";&%=( )&" /, "&%=/, INVIAS0 /)-("+& ( %(,$()*-& )&"*%& +( / $("+-("*( )%@*-)/0 #(& ,( +(( )/)#/% / &"-*#+ +( )/+/ )#%/0 +( /)#(%+& )&" &, )%-*(%-&, +( +-,(&0 +(*(%=-"/% ,#, ((=("*&,0 /, )&*/, ,&%( / */"("*(0 / )&%%())-" $&% $("+-("*( ' /, )&*/, ,&%( / %/,/"*(. .
#.2P$%&'()*)'+,% E+ C*/% P/%/ (,*/ $%<)*-)/ ,( +()-+- &-/% ( $%&)(+-=-("*& %(/-/+& (" )/=$&0 $#(,*& :#( ,( $%(*("+( %(/-/% ,& ( +( &;-)-"/ $&% & :#( *-("+( / ,(% =#' +-,$("+-&,& ( *%//?& (" )/=$&.
8
. CLCULOS P$*',$% (' ()'3%4 C/%%(*(%/ $%-=/%-/ +( 2 )//+/, V( +( +-,(& (" *%/=& &=&"(& 8H=
D( $/"& *("(=&, :#( PUNTO 1 cota del perfl Abs del perfl
PIV
PUNTO 2
137,33 2900
123,7 3360
C/)#/=&, = ' "0 $/%/ //% / m=
137,33−123,7 2900−3360
=−2,96
m =−2,96 n=
133,95 −123,7 3900 −3360
=1,9
n =1,9 I =m −n i =−2,96 −1,9=−4,86
9
133,95 3900
i =−4,
N&, %(,#*/%@/ #"/ )#%/ (%*-)/ )")//.
L%+5),6( (' 7 &6$8 &9+&8 '5:+ 7% &$),'$)% C$),'$)% (' '56$)(( 3K=K3 2
0,695 Ve +
DP
Ve
87,18
h h 2 80 km /¿
¿ ¿
D$
87,18
¿ 80 km / ¿+¿ 0,695 ¿ Dp= 129,01 m
C% 1 D$ L 120 + 3,5 ( Dp )
¿ ¿
Lv =2 Dp −¿ 120 + 3,5 ( 129,01 )
¿ ¿
Lv =2 ( 129,01 )−¿ Lv =136,416 m 129,01 m > 136,416 m
E,*( ,#$#(,*& "& (, <-+&0 ("*&")(,
C%2 D$ ˂L
1
( Dp )2 i Lv = 120+ 3,5 Dp ( 129,01)2 × 4,86 Lv = 120+ 3,5 (129,01) Lv =141 , 53 m 129,01 m < 141 , 53 m
C$),'$)% (' %/'$&)9+ L 06V( L 0 68H=
L8 ; #<* C$),'$)% (' ($'+=' L 5L 540 86
L8 ; 2#"* L&, )<)#&, /"*(%-&%(, /%%&?/" #"/ L ("*%( 141053 ' 243 $&% & */"*& *&=/=&,
;> L8 ; 1<0*. C7&67% (' ?&) @ &%, | PIV |= K 3 + 360 CotaPIV =123,7
| PCV |=| PIV |−( Lv / 2)= K 3 + 270 | PTV |=| PIV |+( Lv / 2)= K 3 + 450 cota PCV =cota PIV + m ( Lv / 2 )=142,7
11
cota PTV = cota PIV + n
( )= Lv 2
294,7
C7&67% (' 7 E8 Ev =
i ∗ L v 800
E=1,0935 m
E" / ,-#-("*( *// ,( )/)#/" &, ' /, %(,$()*-/, )&*/, +( /, */"("*(, (%*-)/(, ' +( /, )#%/, (%*-)/(,0 )&=& (, ,-=*%-)/ ,( )/)#/ )&" / =-,=/ ()#/)-" Y =
i ( X 2 ) 2∗ Lv
+&"+( ! /%@/ +( /)#(%+& / $#"*&.
PUNTO
ABSCISA
PENDIENTE
COTA TANGENTE
CORRECCI ÓN (y)
PCV
2!""0 &2!"50
#1,5$% #1,5
%$13","9$ 13",3"
&2!"60
#1,5
%$13",1$2
&2!"70
#1,5
%$13",02"
0 0,01195$3 33 0,0"7$333 33 0,107625
&2!"$0
#1,5
%$133,$66
&2!"90
#1,5
%$133,70$
PIV
&2!500
133,55
&2!510
1,29%
133,679
&2!520
1,29%
133,$0$
&2!530
1,29%
133,937
&2!5"0
1,29%
13",066
12
COTA ROJA
13","9$ 13",351 95$ 13",229 $33 13",131 625 0,1913333 13",057 33 333 0,29$95$3 13",006 33 95$ 0,4305 133,9$0 5 0,29$95$3 133,977 33 95$ 0,1913333 133,999 33 333 0,107625 13",0"" 625 0,0"7$333 13",113
PTV
&2!550
1,29%
13",195
&2!560
1,29%
13",32"
33 0,01195$3 33 0
$33 13",206 95$ 13",32"
. ANLISIS DE RESULTADOS
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. PREGUNTAS FRECUENTES EN LA PRCTICA 1. Q6 ' 6+ &6$8 8'$,)&7 &9+&8 6+ &%+8' C9*% ' (','$*)+ C#/"+& ( %/+-& +( )#%/*#%/ ,( (")#("*%/ ;#(%/ +( <=-*& +( / *-(%%/ / )#%/ (%*-)/ (, )")//0 (" /, )#%/, )")//, ,-(=$%( *&=/ /&%(, "(/*-&,. E,*/ (, #"/ $/%<&/ :#( /%( /)-/ /%%-/. C#/"+& ( %/+-& +( )#%/*#%/ ,( (")#("*%/ +("*%& +( <=-*& +( / *-(%%/ / )#%/ (%*-)/ (, )&"(/0 (" (,*( *-$& +( )#%/, ( /&% +( - (, $&,-*-&. E,*/ $/%<&/ +( (,*( *-$& +( )#%/, /%( /)-/ //?&.
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
14
-#/ / / +( $/%/+/. E" /#"&, )/,&, ( "-( +( ,(%-)-& +(,(/+& $#(+( &-/% / +-,(/% )#%/, (%*-)/(, )&" / +-,*/")-/ +( -,---+/+ +( $/,&. L&"-*#+ +( /, C#%/, C&"(/,. L/ &"-*#+ +( /, )#%/, (%*-)/(, )&"(/,0 -("( +/+/ $&% /, ,-#-("*(, ($%(,-&"(, P/%/ )&"*/% )&" / -,---+/+ +( $/%/+/ D$ C#/"+& D$ K L
C#/"+& D$ L
D&"+(0 $/%/ *&+&, &, )/,&,. L L&"-*#+ +( / )#%/ (%*-)/ = D$ D-,*/")-/ +( -,---+/+ +( $/%/+/ = A D-;(%(")-/ /(%/-)/ +( $("+-("*(, 1 A*#%/ +( &?& ,&%( / %/,/"*( = 2 A*#%/ +( &?(*& ,&%( / %/,/"*( = P/%/ )&"*/% )&" / -,---+/+ +( P/,& D/. S( #*--/%<" /, =-,=/, ;%=#/, :#( (" / #*--<"+&,( )&=& 2 1.3 =0 )&",-+(%/"+& 1 1.7 = T("(=&,. D/ K L
D/ L
D/ D-,*/")-/ +( -,---+/+ +( P/,& = L ' A L&"-*#+ +( / )#%/ (%*-)/ = ' D-;(%(")-/ /(%/-)/ +( $("+-("*(, L&"-*#+ +( /, C#%/, C")//,. L/ &"-*#+ +( /, C#%/, (%*-)/(, )")//,0 -("( +/+/ $&% / ,-#-("*( ($%(,-" S- D K L
15
D L
D D-,*/")-/ ("*%( ( (@)#& ' ( $#"*& +&"+( )&" #" <"#& +( 10 &, %/'&, +( # +( &, ;/%&,0 -"*(%,()/ / / %/,/"*(. D( /+& +( / ,(#%-+/+ ,( *&=/ D D$. A+-)-&"/=("*(0 )&",-+(%/"+& :#( &, (;()*&, %/-*/)-&"/(, ' +( ;#(%/, )("*%@;#/, /;()*/" (" =/'&% $%&$&%)-" / /, )#%/, )")//,0 / ;-" +( )&",-+(%/% (,*( )%-*(%-&0 ,( *-("( :#(
V V(&)-+/+ D-%()*%- $ L ' A L&"-*#+ +( / )#%/ (%*-)/ = ' D-;(%(")-/ /(%/-)/ +( $("+-("*(, . 3. QQ6 ' 6+ &6$8 8'$,)&7 )*,$)& @ 6+ &6$8 8'$,)&7 )*,$)& E+
6 ' ()'$'+&)+ U"/ )#%/ (%*-)/ ,-=*%-)/ )#'/, %/=/, +( ("*%/+/ ' ,/-+/ *-("(" / =-,=/ &"-*#+0 (, =#' ;%()#("*( (,*/ )#%/ (" ( +-,(& (%*-)/ $(%& $#(+(" *("(% +-;(%("*(, $("+-("*(, ' ,( +-;(%(")-/ +( #"/ )#%/ (%*-)/ /,-=*%-)/ '/ :#( (,*/ /:#(/ )#'/, %/=/, +( ("*%/+/ ' ,/-+/ *-("(" +-;(%("*(, &"-*#+(, $&% & */"*& L L1 L2 ,&" )#%/, $/%/-)/, )&=$#(,*/,.
16
#. C6+(% ' +'&'$)% ()'3$ 6+ &6$8 8'$,)&7 )*,$)& P&% & ("(%/0 ,# #,& ,( /%/"*-/ ,& +&"+( "& $#(+( -"*%&+#)-%,( #"/ )#%/ ,-=*%-)/ $&% /, )&"+-)-&"(, -=$#(,*/, +( /-"(/=-("*&.
. C67 ' 7 )*/%$,+&) (' 7 '7'&&)9+ (' 7 /'+()'+,' 7%+5),6()+7' '+ '7 ()'3% (' 6+ &6$8 8'$,)&7 &%+ $'/'&,% 7 8'7%&)(( (' %/'$&)9+ (' 7% 8'&67% P("+-("*(, +( /,*/ 7 /;()*/" ,& =/%-"/=("*( / (&)-+/+ +( &$(%/)-" +( / %/" =/'&%@/ +( &, /#*&=-(,0 )#/:#-(%/ :#( ,(/ / &"-*#+ +( / $("+-("*(. E" ( )/,& +( &, )/=-&"(,0 $("+-("*(, ,&%( #" 3 )/#,/" %(+#))-&"(, )%()-("*(, +( ,# (&)-+/+ +( &$(%/)-"0 / =(+-+/ :#( / &"-*#+ (" $("+-("*( /#=("*/. E,*& /;()*/ / (&)-+/+ +( &$(%/)-" +( &, /#*&=-(,0 (" (,$()-/ (" )/=-"&, -+-%())-&"/(, )&" /*/ +(",-+/+ +( *%<",-*&. S( %()&=-("+/ (" )/,&, "&%=/(, "& ,#$(%/% &, 25 P +( )/@+/ +( (&)-+/+ $/%/ )/=-&"(, (" $("+-("*(.
<. CONCLUSIONES A ;-"/-/% / $%<)*-)/ ' ,# /"<-,-, $&+(=&, )&")#-% :#(
17
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
G%/)-/, / / %(/-/)-" +( (,*( *%//?& ,( &% )&"&)(% ' /;-/"/% / ;&"+& &, )&"&)-=-("*&, /$%("+-+&, ,&%( ( +-,(& (&=*%-)& (%*-)/ +( #"/ )/%%(*(%/.
18
K. BIBLIOGRAFA JAMES CÁRDENAS GRISALES0 D-,(& G(&=*%-)& +( C/%%(*(%/,0 E)& E+-)-&"(, L*+/.0 B&&*< 25. MINISTERIO DEL TRANSPORTE0 M/"#/ +( D-,(& G(&=*%-)&.
CIBERGRAFIA **$,+&(-/.&%+$%(,,.)&=27319)#%/,)-%)#/%(,,-=$(,
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