CURVAS VERTICALES
TOPOGRAFIA II
ANDRES GAROFALO MOYANO
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UNIVERSIDAD DE GUAYAQUIL FACULT FACUL TAD DE CIENCIAS MATEMAT MATEMATICAS ICAS Y FISICAS FIS ICAS ESCUELA DE INGENIERIA CIVIL
TOPOGRAFIA II
ANDRES GAROFALO MOYANO
ING GUSTAVO TOBAR
GRUPO 3ª
CURVAS CURV AS VERTICALES VERTICAL ES
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Índice INTRODUCCI INTRODUCCION...... ON..................... .............................. ............................. ............................. ............................. ............................. .............................. ............................. ..........................4 ............4 Objetivo Objetivos.......... s......................... ............................. ............................. .............................. ............................. ............................. .............................. ............................. ................................. ...................... ...55 Curvas Curvas verticaes verticaes.............. ............................ ............................. .............................. ............................. ............................. ............................. .................................................. .................................... ! Criterios Criterios de co"odidad... co"odidad................. ............................. .............................. ............................. ............................. ............................. ............................. ..................................# ...................# Criterios Criterios de o$eraci%n. o$eraci%n................ .............................. ............................. ............................. .............................. ............................. ............................. ............................. ...................... ........## Criterios Criterios de drenaje......... drenaje....................... ............................. ............................. ............................. .............................. ............................. ............................. .............................. ................... ....## Criterio Criterio de se&uridad. se&uridad................ ............................. ............................. .............................. ............................. ............................. ..................................................... ...................................... # Tan&en Tan&ente te vertica... vertica................. ............................. .............................. ............................. ............................. ............................. ............................. ............................................. ..................................## i$os de curvas verticaes.. verticaes................ ............................. ............................. ............................. .............................. ............................. ............................. .....................................' ......................' Curvas Curvas verticaes verticaes conv conve(as.... e(as................... ............................. ............................. .............................. ............................. ............................. .......................................)* ........................)* +on&itud ",ni"a de a curva vertica conve(a se&-n e criterio de se&uridad...........................................) Curvas Curvas verticaes verticaes c%ncavas..... c%ncavas.................... .............................. ............................. ............................. .............................. ............................. .........................................)4 ...........................)4 Curvas Curvas verticaes verticaes si"/tricas.. si"/tricas................. ............................. ............................. .............................. ............................. ............................. ................................ ............................ ........... )5 0e"entos 0e"entos de a curva vertica vertica si"/trica....... si"/trica...................... ............................. ............................. .............................. ......................................... .............................)! ...)! curvas verticaes asi"/tricas..................................................................................................................)! 0e"entos de a curva vertica asi"/trica..............................................................................................)1 CONC+UCION CONC+UCION02........ 02...................... ............................. .............................. ............................. ............................. .............................. ............................. ...................................... ........................ ) 3I3+IOGRAF 3I3+IOGRAFIA.... IA.................. ............................. .............................. ............................. ............................. ............................. ............................. .............................. .............................. ............... 3iobio& 3iobio&raia raia i"6&enes.... i"6&enes................... .............................. ............................. ............................. .............................. ............................. ............................. ....................................4 .....................4
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INTRODUCCION 0 tra7o de as curvas verticaes es de &ran i"$ortancia a "o"ento de e"$earas en a construcci%n de v,as8 carreteras etc. Pues bien esta sirve $ara conectar dos ,neas de dierente direcci%n es decir de dierentes $endientes. 0 uso de a $ar6boa es de &ran i"$ortancia a "o"ento de 9acer tra7os de curvas verticaes $ara eo 9e"os evado a cabo a si&uientes investi&aci%n $ara conocer "6s sobre e te"a : e verdadero a$rendi7aje de curvas verticaes en to$o&ra,a.
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Objetivo Uno de os objetivos $rinci$aes a evar a cabo esta investi&aci%n es conocer "6s sobre e te"a de curvas verticaes e"$eadas en To$o&ra,a II a$render a reconocer sus caracter,sticas : "/todos de c%"o eaborar una curva vertica : reai7ar os res$ectivos c6cuos.
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C!"v# ve"ti$#%e +as curvas verticaes son curvas ;ue se dise
A
Fi&.) curva vertica
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PIV
Punto de intersecci%n de as tan&entes verticaes PCV Punto en donde co"ien7a a curva vertica PTV Punto en donde ter"ina a curva vertica PSV Punto cua;uiera sobre a curva vertica &' Pendiente de a tan&ente de entrada8 en "?" &( Pendiente de a tan&ente de saida8 en "?" A Dierencia a&ebraica de $endientes L +on&itud de a curva vertica8 en "etros ) =ariaci%n =ariaci%n de on&itud $or
unidad de $endiente @$ar6"etro @ $ar6"etro
* Distancia de
PC= a un P2= P2 =8 e" "etros
& Pendiente en
un P2=8 en "?"
&+ Pendiente de una cuerda8 en "?" E 0(terna8 en "etros F Fec9a8 en "etros T Desviaci%n de un P2= a a tan&ente de entrada8 en "etros ,o 0evaci%n de
PC=8 PC=8 en "etros
,*0evaci%n de un
P2=8 P2=8 en "etros
Nota 2i B : + se e($resan en estaciones de * " a eevaci%n de un P2= $uede cacuarse con cua;uiera de as e($resiones ( o E @* $) @)*AB?+B
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0 dise
2e a$ica a dise
2e a$ica a dise
2e a$ica a dise
2e a$ica a curvas c%ncavas : conve(as. +a on&itud de a curva debe ser ta8 ;ue en toda a curva a distancia de visibiidad sea "a:or o i&ua a a de $arada. 0n a&unos casos8 e nive de servicio deseado $uede obi&ar a dise
Tangente vertical Pe0ie0te .20i.#- +a $endiente ",ni"a on&itudina de a rasante debe &aranti7ar
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Fi& . taba de $endientes en a reacion de $eso?$otencia
ti&o e $!"v# ve"ti$#%e
+as curvas verticaes se $ueden casiicar $or su or"a co"o curvas verticaes c%ncavas : conve(as : de acuerdo con a $ro$orci%n entre sus ra"as ;ue as or"an co"o si"/tricas : asi"/tricas.
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C!"v# ve"ti$#%e $o0ve*#
A;ueos cu:o $unto "6s eevado se encuentra en e centro. 2e estudia $ara $er"itir ;ue e ve9,cuo ten&a sie"$re visibiidad de una distancia $or deante de / ;ue e $er"ita renar con se&uridad. 0n carreteras de &randes veocidades estos acuerdos deben $er"itir visuai7ar un obst6cuo a centenares de "etros
Fi&. 4 conve(a
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Fi& 5. +on&itudes : $ar6"etros ",ni"os curvas verticaes conve(as
0n t/r"inos &eneraes8 a on&itud de a curva vertica se deter"ina as,
Para a distancia de visibiidad de $arada8 to"ando co"o
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Lo01it! .20i.# e %# $!"v# ve"ti$#% $o0ve*# e140 e% $"ite"io e e1!"i#
De acuerdo con e criterio de se&uridad8 a on&itud ",ni"a se obtiene "ediante a a$icaci%n de a Distancia de =isibiidad de Parada @DP. 2e $resentan dos reaciones entre a distancia de visibiidad @DP : a +on&itud de a curva @+ Cuando DP K + : DP L +. +as ecuaciones ;ue se indican a continuaci%n $resentan a on&itud de a curva $ara cada reaci%n8 teniendo en cuenta a atura de ojo de conductor sobre a ca7ada @9)8 ;ue es i&ua a un "etro con oc9o cent,"etros @).*# "8 : a atura de obst6cuo @98 ;ue es i&ua a sesenta cent,"etros @*.!* "
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C!"v# ve"ti$#%e $/0$#v#
A;ueos con a cavidad en e centro.1 2us di"ensiones : caracter,sticas se estudian $ara ;ue $er"ita una correcta visibiidad en condiciones nocturnas.
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Fi&. 1. +on&itudes : $ar6"etros ",ni"os curvas verticaes verticaes c%ncavas
0n t/r"inos &eneraes8 a on&itud de a curva vertica se deter"ina as,8 $ara a distancia de visibiidad de $arada8 to"ado co"o D= D=P J *.!* " 9 *.)5 " TD tan )M *.**)15 entonces
C!"v# ve"ti$#%e i.5t"i$#
+a curva vertica si"/trica est6 conor"ada $or dos $ar6boas de i&ua on&itud8 ;ue se unen en a $ro:ecci%n vertica de P PI= I=.. +a curva vertica reco"endada es a$ar6boa cuadr6tica8 cu:os cu :os ee"entos $rinci$aes : e($resiones "ate"6ticas se incu:en a continuaci%n8 ta co"o se a$recia
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Fi&.# curvas verticaes verticaes si"etricas si"etricas
E%e.e0to e %# $!"v# ve"ti$#% i.5t"i$#
Donde
PC= Princi$io de a curva vertica. PI=
Punto de intersecci%n intersecci%n de as tan&entes tan&entes verticaes. verticaes. PT= PT=
Ter"inaci%n de a curva vertica.
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:
Ordenada vertica vertica en cua;uier cua;uier $unto8 ta"bi/n a"ada a"ada correcci%n correcci%n de a curva curva vertica8 vertica8 se cacua cacua
"ediante "ediante a
e($resi%n
$!"v# ve"ti$#%e #i.5t"i$#
+as curvas asi"/tricas a veces tienen tan&entes no i&uaes : se a"an $atas de $erro. 0 $roceso de resover un $robe"a $r obe"a de curvas asi"/tricas es casi e "is"o ;ue e usado usad o $ara resover e de una curva si"/trica. Pero debes usar una %r"ua dierente $ara e c6cuo de a
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2)
Pendiente de a tan&ente tan&ente de entrada8 en $orcentaje @. 2
Pendiente de a tan&ente de saida8 en $orcentaje @. +)
+on&i +on&itud tud de a $ri"e $ri"era ra ra"a8 ra"a8 "edid "edidaa $or $or su $ro:ec $ro:ecci ci%n %n 9ori7onta8 en "etros.
+
+on&i +on&itu tudd de a se&un se&unda da ra"a8 ra"a8 "edid "edidaa $or su $ro:ec $ro:ecci ci%n %n 9ori7onta8 en "etros.
+
+on&i +on&itu tudd de a curva curva verti vertica ca88 "edi "edida da $o $orr su $ro:ec $ro:ecci ci%n %n 9ori7onta8 en "etros8 se cu"$e + +) E + : +) +.
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