metodo de kani final

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CONTENIDO INTRODUCCION.......................................................................................................3 METODO DE KANI...................................................................................................4 CASO ESTRUCTURA SIN DESPLAZAMIENTO....................................................6 VENTAJAS..............................................................................................................6 DESVENTAJAS.......................................................................................................6 PROCEDIMIENTO................................................................................................. 7 ESTRUCTURA CON DESPLAZAMIENTO: ..................................................7 ESTRUCTURA SIN DESPLZAMIENTO: ......................................................7 ESCUELA PROFESIONAL DE FACULTAD DE INGENIERIA, ARQUITECTU R A Y CICLO V  Fecha de entrega: 0 DE JULIO DEL 0!" ANALISIS ESTRUCTURAL  I  #REA INFORME METODO DE KANI ELA$ORADO POR LOS ALUMNOS: CONDOR TAPIA JOSÉ FERNANDO GALINDO ROJAS SET BELSASAR QUISPE S ANDOV AL JORGE EDIL BER TO SA A VEDRA VELA IRWIN P AL VIDAURRE VALDERA JOS É DANIEL DOCENTE ENCAR%ADO DEL CURSO I!". MARIN BARDALES NOE #UMBERTO

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CONTENIDO

INTRODUCCION.......................................................................................................3

METODO DE KANI...................................................................................................4

CASO ESTRUCTURA SIN DESPLAZAMIENTO....................................................6

VENTAJAS..............................................................................................................6

DESVENTAJAS.......................................................................................................6

PROCEDIMIENTO.................................................................................................7

• ESTRUCTURA CON DESPLAZAMIENTO:..................................................7

• ESTRUCTURA SIN DESPLZAMIENTO:......................................................7

ESCUELA PROFESIONAL DE

FACULTAD DE INGENIERIA,ARQUITECTURA Y

CICLO V

  Fecha de entrega:

0 DE JULIO DEL 0!"

ANALISISESTRUCTURAL

 I 

#REA

INFORMEMETODO DE KANI

ELA$ORADO POR LOS ALUMNOS:CONDOR TAPIA JOSÉ FERNANDOGALINDO ROJAS SET BELSASAR

QUISPE SANDOVAL JORGE EDILBERTOSAAVEDRA VELA IRWIN PAL

VIDAURRE VALDERA JOSÉ DANIEL

DOCENTE ENCAR%ADO DEL CURSO

I!". MARIN BARDALES NOE #UMBERTO

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PASO A PASO PARA DESARROLLAR PORTICOS POR EL METODO DE KANIEN ESTRUCTURAS SIN DESPLAZAMIENTO&......................................................$

PASO A PASO PARA DESARROLLAR PORTICOS POR EL METODO DE KANIEN ESTRUCTURAS CON DESPLAZAMIENTO......................................................%

COLUMNAS 'UE PERTENECEN A M#S DE UN PISO.........................................%

M(TODO DE %ASPAR KANI EN LA RESOLUCI)N DE VI%AS *IPEREST#TICASDE +N, CLAROS.................................................................................................&'

EJEMPLO N- !.....................................................................................................&&

EJEMPLO N- 0...................................................................................................&6

INTRODUCCION

E()* )+-/ -0(1 20++ 1/!/15*!)/ *! /( 5)/2/( 2* 8!,/-(*+9!2/ (0( :+/1*25*!)/(, (0( 9*!)( ; 2*(9*!)( :+ :/2*+ (< +*(/9*+ !=(( *()+01)0+ 1/!9*!1/! :+ *2>1/( 2* 9+/( :(/( -/100*+ 1/!21?! 2* 1+"( 22, -(2/( *! /( 5)/2/( 2*:+/@51/!*( (01*(9( ; 2()+-01?! 2* 5/5*!)/(.

E 5)/2/ *() -(2/ *! * 5)/2/ 2* ( :+/@51/!*( (01*(9( ; *! 2()+-01?! 2* 5/5*!)/( :+ *@:+*(+ * **1)/ 2* ( +/)1/!*( ;2*(:5*!)/( !/2*(

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METODO DE KANI

E()* 5)/2/ *()= -(2/ *! * 2*(++/2/ !15*!)* :/+ G(:+ K!0*! !1? *! /1)0-+* 2* &%&' *! F+!)), S*+-, 0* 0* :0-12/ *! *

2/5 *(:/  :/+ :+5*+ 9* *! &%6$, *! !"(  *! &%7 ; *! :+/:0*() 5*/+2 :/+ * I!"*!*+/ J:/!( F080* TK-*;, :0-12:/+ :+5*+ 9* *! * 2/5 *(:/ *! &%6%, (*!2/ (0 :+5*+ *21?! *!I!"( *! &%6. T5-! (* !10;*! "0!/( 1/!1*:)/( 2*(++/2/( :/+#+2< C+//( E! )/2( ( :0-11/!*( 5*!1/!2( (* !10< * !=((:+ :?+)1/( 1/! !/2/( 2*(:-*(.

E()/( :+/1*25*!)/( +*(0*9*! * (()*5 2* *101/!*( 2* +/)1?! :+0! *()+01)0+ / (()*5 *()+01)0+ 2* ):/ 0!25*!)5*!)* 52/P?+)1/ P!/, :/+ 5*2/ 2* :+/@51/!*( (01*(9( 0* (* 1/++"*!)5-! (01*(95*!)*. P/+ )!)/ *( 5:/+)!)* +*1/+2+ ( :?)*(( -/

( 10*( (* 2*201*! ( *101/!*( 2* +/)1?! 1/5/ (/!H E 5)*+ *( /5/"!*/, (?)+/:/ ; (* 1/5:/+) 1/5/ !*

*=()1/, *( 2*1+, )/2/ * 5)*+ *( 2* 5(5 !)0+*, )*!*2!)1( :+/:*22*( <(1( *! )/2( ( 2+*11/!*( ; (2*/+51/!*(, * , 0* (0+* (/! 2+*1)5*!)* :+/:/+1/!*( /(*(0*+/(, ( , 0* +*(()* ; * 1)/+ 2* :+/:/+1/!22 (* 55?20/ 2* *()122, E, *( 2*1+, ( E * L*; 2* #//8*H.

-H E :+!1:/ 2* ( 2*/+51/!*( :*0*( 0* (* 0* 0! 9*1+"2 *()+01)0+ ( 2*/+51/!*( / 2*(:5*!)/( !**( ;!"0+*( 2* ( 0!)( / !/2/( ; 2* 12 0!/ 2* /( :0!)/( 2* (0(

3

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5*5-+/( (/! -()!)*( :*0*/( 2* ) 5!*+ 0* /+5 2* *!/ 15- ! (* )*+ :+*1-*5*!)*.

1H E :+!1:/ 2* (0:*+:/(1?! 2* **1)/( 0* (0:/!* /(2*(:5*!)/( ; 0*+( !)*+!( )/)*( / >!*( 2* *()+01)0+(/5*)2 0! 1/!0!)/ / (()*5 2* 1+"( (* :0*2*! *!1/!)++ :/+ (05 2* /( **1)/( 2* 12 0! 2* ( 1+"( 1/!(2*+2((25*!)*.

2H S// (* :0*2*! )/5+ *! 10*!) /( **1)/( 2* :+5*+ /+2*! 1/5/(/! L( 2*/+51/!*( !)*+!( :/+ *@?! (*5:+*, 5*!)+( 0* (:/+ 0*+ @ ; )/+(?! (< 1/5/ *@()*!1 2* (*"5*!)/( +<"2/((* :0*2*! )/5+ *! 10*!) / !/.

E *!/0* 2* 8! *()= -(2/ *! * 5)/2/ 2* ( :+/@51/!*(

(01*(9( ; *! 2()+-01?! 2* 5/5*!)/( :+ *@:+*(+ * **1)/ 2* (+/)1/!*( ; 2*(:5*!)/( !/2*(. E 5)/2/ )*+)9/ 2* !=(( 2**()+01)0+( 2*(++/2/ :/+ G. K!, 9*!* (*+ *@)+*525*!)*()(1)/+/ :+ * !=(( 2* 100*+ *()+01)0+ 1/!9*!1/! :+*2>1/( 2* 9+/( :(/( -/ 100*+ 1/!21?! 2* 1+"( 22(. K!:+/:0(/ *@)*!2*+ *()* 5)/2/ ( *()+01)0+( 1/! 1/05!( 1/!)!0( )+9( 2* 9+/( :(/( 1/! (// "*+( 5/2>11/!*(.

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E( *++?!*/ (0:/!*+ 0* 0! 5)/2/ 2* :+/@51/!*( (01*(9( (* 0!5)/2/ :+/@52/. E(*!15*!)* 0! 5)/2/ :+/@52/, *( 0* 0*:+/:/+1/! 1/5/ (0 !/5-+* / !21, 9/+*( :+/@52/(, 5*!)+( 0*/( 5)/2/( 2* :+/@51/!*( (01*(9( ++/! +*(0)2/( 1/! :+*1(?!2*(*2 :/+ * 110()

E *!/0* 2* !=(( *()+01)0+ 1/! :11?! 2* 5)+1*( )09/ ( 5=("+!2*( 1/!)+-01/!*( 2* 4 :+/)"/!()( C/+, D0!1!, A+";+( ; T0+!*+.

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4

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"*!*+ ; 50; *>1*!)* 2* 5:*5*!)1?! 1/5:0)1/! 2* *!)/!1*(!1:*!)*, M)/2/ 2* /( E*5*!)/( F!)/(. L )*/+< 2* *()122 *(0! )*/+< 0* *()2/ 2(:/!-* :+ )/2/( /( 2*+*!)*( *!/0*(+*0*+2/( 2* !=(( *()+01)0+, :*+/ +*0*+* 2* 0! 1/!/15*!)/+*)95*!)* 9!2/ *! * =+* 2* ( 5)*5=)1(.

E *!/0* !*0+/! 2* 5)/2/ 2* 8! *( )/*+!)* (, :/+ (*+1/++*1)9/, *()/ :*+5)* 1>1+ 1/5/ 0! 5)/2/ 1/! *5!1?!0)/5=)1 2* *++/+*( 5*22 0* +*2 :+*!2*. L 1/5:+/-1?! 2* /(+*(0)2/( 0* (* /-)*!*! 2*(:0( 2* +*+ /( :+/201)/( ; (05( 2*0!/( :/1/( 9/+*( :0*2* 1*+(* 1/! >!22 *@)+*5 *! 100*+**5*!)/ 2* :+/1*(5*!)/ / !/2/ ; *! 100*+ 1: 2* !*0+/!(, (!0* :+ */ (* +*0*+ 2* (*+91/( 2* *@:*+)/( *! !"*!*+< *()+01)0+.

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CASO ESTRUCTURA SIN DESPLAZAMIENTO

L 2*2011?! 2* ( !/+5( -=(1( :+ * )+)5*!)/ 2* ( *()+01)0+((! 2*(:5*!)/ +*)9/ 2* (0( *@)+*5/( *( 1/5:*)5*!)* !=/" 9() !)*+/+5*!)* *! /( 5)/2/( 2* =!"0/( 2* "+/ ; 2* *@?! ; C+/(((/5*!)* *@()*! "*+/( 15-/( *! !/5*!1)0+.D* !0*9/ (* 1/!(2*+ 0* * *()2/ >! 2* **5*!)/ (* 1! 5*2!)* (0:*+:/(1?! 2* 3 **1)/( * 2* ( 1+"( 1/!(2*+!2/ *5:/)+5*!)/*! /( !02/(, * **1)/ 2* "+/ *! * !02/ H ; * **1)/ 2* "+/ *! * :0!)/H.VENTAJAS

• E 5)/2/ 2* 8! 5!* :+/@51/!*( (01*(9( ;, *! 1/!(*10*!1( +*(:0*()( (* :0*2*! /"++ 1/! *@1))02 0* (* 2*(** 5*!)+(( :?)*(( 0!25*!)*( ; /( 2)/( -=(1/( / :*+5)!.

• L !10(?! 2* /( **1)/( 2* 2*(:5*!)/ (* 1* *! /+5 50;(5:*.

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(* :0*2*! )*!*+ *! 10*!) 1/! 50; :/1/ *(0*+/ 21/!.•

N/ *( 2<1 2* :1+ *()+01)0+( 1/! 5*5-+/( 1+)*2/(.

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• E( 0!25*!)5*!)* 0! 5)/2/ 2* 2()+-01?! 2* 5/5*!)/(.•  T*!* 122 2* :+/"+51?! ; - *@"*!1 2* 5*5/+ 2*

1/5:0)2/+.

DESVENTAJAS

• S0 :11?! *()= 5)2 :?+)1/( /1)/"/!*( ; 0* !/ !10;* /(**1)/( 2* /( 1/+)5*!)/( @*(, 0* (* 1*! 12 9* 5(5:/+)!)*( !1+*5*!)+ * !5*+/ 2* :(/( /( !9**( 1/++*!)*(*! ( )/++*( 2* !0*()+/( 2<(.

• E()* ):/ 2* 5)/2/ *( "/ *@)*!(/ :+ *2>1/( 2* 501/( :(/( :/+(*+ 5)/2/ 5!0.

PROCEDIMIENTO

  ESTRUCTURA CON DESPLAZAMIENTO:

- S* 110 +"2*- S* 110 * 1/*>1*!)* 2* "+/- S* 110 * 1/*>1*!)* 2* 2*(:5*!)/- M/5*!)/ 2* *5:/)+5*!)/- M/5*!)/( 2* :(/( ; 5/5*!)/( >!*(

 

ESTRUCTURA SIN DESPLZAMIENTO:

- C10+ +"2*

- C10+ 1/*>1*!)* 2* "+/- M/5*!)/ 2* *5:/)+5*!)/

E()/( :+/1*25*!)/( +*(0*9*! * (()*5 2* *101/!*( 2* +/)1?! :+0! *()+01)0+ / (()*5 *()+01)0+ 2* ):/ 0!25*!)5*!)*52/ P?+)1/ P!/, :/+ 5*2/ 2* :+/@51/!*( (01*(9( 0* (*1/++"*! )5-! (01*(95*!)*. P/+ )!)/ *( 5:/+)!)* +*1/+2+( :?)*(( -/ ( 10*( (* 2*201*! ( *101/!*( 2* +/)1?!

E! *() 5*)/2//"< (* (* 0! :+/1*25*!)/ :+ )/5+ *! 10*!) ( (*2*(* "0! 2* ( )+*( / )/2( ( 1/!(2*+1/!*( ("0*!)*( (2*/+51/!*( 2*-2( 1/+)*, /( (*"5*!)/( +<"2/( *! /( *@)+*5/( 2*/( 5*5-+/(, (< 1/5/ )5-! 0* /( 5*5-+/( :0*2! (*+ 2* (*11?!9+-* / +"/ 2* (0 ** +*1)/. E()/ (* /"+ !)+/201*!2/ (0( **1)/( *! 2*)*+5!1?! 2* ( 1/!()!)*( *=()1( C, C ; C. O)+/( **1)/( 1/5/* 2* )/+(?! :0*2* !10+(* *! *()( 1/!()!)*( 2*!2/ *1)/+ )*()02/. L 1/!9*!1?! 2* ("!/( :+/:0*() :/+ K! ; -/ 10 (*2*201*! )/2( ( *@:+*(/!*( /-*)/ 2* 5!)*!*+ (0 :+/:0*() /+"!*( ("0*!)*

P+ 5/5*!)/( MH, "+/ 2* 0!)( H ; +/)1?! 2* 5*5-+/( H

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  P/()9/ (*!)2/ /++/ / 2* ( "0( 2* +*/ 

E()/ !/ 0*+* 2*1+ 0* !/ :/2*5/( 0(+ 1/!9*!1?! 2*(*!)2/ 1/!)++/ 1/5/ *( * 2* 1/!9*!1?! )+21/! 2*:/()9/( :+ 5/5*!)/(, "+/( 2* 0!)( ; +/)1/!*( 2*5*5-+/( * (*!)2/ !)/++/. E()/ !/ )*+ (*@:+*(/!*( 2*2012( ; 0* *()/ *092+< 1*+ * 5(5/:+/1*25*!)/ 1/! (*!)2/( 1/!)++/( /( !212/( *! (2*2011/!*(, *( 2*1+

P/+ / )!)/ :/2*5/( 0)+ 100*+ 2* /( 2/( (*!)2/( :+ 1/!9*!1?! 2* ("!/( ; (*+= 1/!9*!*!)* !21+ 0* (* 0)1* 12 9*0* :0*5/( *()* :+/1*25*!)/ 2* 1=10/.

L5 :+/0!25*!)* )*!1?!  :/1 20(?! 2* *()* 5)/2/, 0* :*(+ 2* )*5:/ )+!(10++2/ 2*(2* (0 :0-11?!, !/ ; (2/ 290"2/5:5*!)* :/+ 0)/+*( 5/2*+!/( *(:*1()( *! )*5=)1 2* A!=((E()+01)0+. E 0)/+ !/ 1/!(*"02/ () *1 0! 5)/2/ 2* A!=((E()+01)0+ 0* (0:*+* ( 9*!)( 0* /+*1*, !10(9* *! 1/5:+1?!1/! 0!/ 2* /( 5=( 1/!/12/( * 2* #+2; C+/((, 0*! !1? *! &$$V+"!, U.S.A., :0-12/ :/+ :+5*+ 9* *! !"( *! &%3, 2*(2* * :0!)/

2* 9() 2* / *@:*2)/ 2* :+/1*25*!)/, +=:2 1/!9*+"*!1, -0*!:+*1(?!, :+=1)1/, 0)/1/++*1)9/, **101?! 5!0 / 0)/5=)1. A2*5=(*5/( !102/ /( 2*!/5!2/( 1)/+*( 2* )+!(:/+)* 2*>!2/( *! *5)/2/ 2* C+/(( :+ +*1/!+/( 1/! *()* 5)/2/.

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L9*!(* *()/( 9/+*( 0! 2"+5 2*102/ ; 11*!(* /(5/5*!)/( 2* >1?! M   H2* 12 !02/.

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3. A2?:)*(* 0! (*10*!1 2* +*1/++2/ 2* /( !02/(, *5:*!2/ :/+ * 2*5;/+ 5/5*!)/ 2* >1?! :+ 1**++ 1/!9*+"*!1.

4. A:<0*(* 12 0!/ 2* /( **5*!)/( 0* 1/!10++*! 12 !02/

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:+5*+ !02/ ; /( MX (/! !0/( :+ )/2/( /( **5*!)/(H.

. U! 9* +*1/++2/( )/2/( /( !02/( (* 110! /( 5/5*!)/( 2* 2*2*(:5*!)/ MX

2* )/2( ( 1/05!( 5*2!)* ( *101/!*( MX

M:8M'M'

 H ? *101?!MX

M'M'

 H(*"! 1/++*(:/!2. E( 1/!9*!*!)* :+/1*2*+ :(/:/+ :(/. A 1/!10+ *()* :(/ (* -+= +*2/ 0! 11/.

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6. R*:<)(* /( :(/( 3 ; 4 0! ; /)+ 9* (). /-)*!*+ 1/!9*+"*!12*(*2, )!)/ *! /( 5/5*!)/( 2* "+/ 1/5/ *! /( 2*2*(:5*!)/.

7. C/! /( 9/+*( >!*( :<0*!(* 12 **5*!)/ ( *101/!*(MMF

M'M'

MX   ; M MF

 M' M'

MX  / (0 /+5 )*+!

MMFM'

M'M'

 MXH ; M MF

 M' M'

 M'MX

 H, 0* (+9*!:+ "+ * :+/1*(/ ; 1)+ (0 9*+>11?!.

COLUMNAS 'UE PERTENECEN A M#S DE UN PISO

H S *@()* 0! :1 +<"2 :/+ **5:/ !9* E() +"2* :+/201*0* )/2/( /( 2*(:5*!)/( /+/!)*( 2* :(/ (*! "0*( ;:/+ / )!)/ :/2*5/( (0:/!*+ 0! 9" >1)1 2* 25*!(/!*( !0(.

-H S !/ *@()* :1 / **5*!)/ (0>1*!)*5*!)* +<"2/ / 0! 91</ L

1/05! 1/-/+ *! ( !0*!1( MZZ: 2* /( :(/( 0*:*+)*!*1*. S* +*:+)* (0 !0*!1 :+/:/+1/!5*!)* ( MZZ 2*12 :(/, ; *! MZ 1/-/+! )/2( ( MZZ: 2* /( :(/( 0*:*+)*!*1* 1/05!.

M(TODO DE %ASPAR KANI EN LA RESOLUCI)N DE VI%AS*IPEREST#TICAS DE +N, CLAROS

• E! *()* :+5*+ :(/ :+ (/01?! 2* 9"( :*+*()=)1( :/+

5*2/ 2* *()* 5)/2/ / :+5*+/ 0* :+/1*2*5/( +*+ *( *

1=10/ 2* /( 5/5*!)/( 2* *5:/)+5*!)/ :*+*1)/, *! /( )+5/(

*! 0* (* *!10*!)+ 9", )/5!2/ *! 10*!) /( :/;/( 0*

1/!)*!". A "0 0* )*!*5/( 0* )/5+ *! 10*!) 1+" ; 2*

1?5/ *()* 2()+-02 *! 9".

• C/5/ (*"0!2/ :(/ (* :+/1*2* 110+ ( +"2*1*( 0* *@()*!

*! 12 )+5/ 2* 9", ; 0* !/ (*5:+* (*+=! 2* 5(5/

5)*+, ; :+ */ (* 0) 0! /+50 *! 10 (* 2*(1+-*)!)/ * 5?20/ 2* *()122 ; * 5/5*!)/ 2* !*+1 *! /( )+5/(

110+ (0 +"2*. L ?+50 0)+ *! *()* :(/ *(

  R4 EI 

 L   D?!2* E M/20/ 2*

*()122L L/!")02 2*

)+5/

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  I M/5*!)/ 2*!*+1

• C/5/ )*+1*+ :(/ *! +*(/01?! 2* 9" (* *9 1-/ *

1=10/ 2* /( 1)/+*( 2* 2()+-01?! :+ 12 )+5/ / !02/ *! 0*

(* *()= 110!2/ 9", )/5!2/ /( 9/+*( /-)*!2/ *! * 110/

2* +"2*. P+ */ (* 0) ("0*!)* ?+50

 FDij=−1

2(  Ri

 Ri+ Rj)   D?!2* R R"2* !1 *! 0*

(* *!10*!)+R R"2*

0* *" !02/ *()022/

• E! *()* 10+)/ :(/ (* +* * 1=10/ 2* ( )*+1/!*( :+ :/2*+

/-)*!*+ /( 9/+*( 2* /( 5/5*!)/( +**( 2* /( !02/( ; (< (-*+

1?5/ (* 1/5:/+) 9" 1/! 1+" 1/! 0* (* *()= 110!2/. E!

*()* :(/ )*!*5/( 0* 2()+-0+ /( 9/+*( /-)*!2/( 2* /( :(/(

!)*+/+*( ; /( 10*( (/!- E 9/+ 2* *5:/)+5*!)/ :*+*1)/ *! 12 !02/ / )+5/.- L( 2*+*!1( 0* *@()*! *! 9/+*( 2* 5/5*!)/ 2*

*5:/)+5*!)/ :*+*1)/ *! * !02/.- L/( 1)/+*( 2* 2()+-01?! 2* 12 )+5/ 2* 9".- S* +=! )*+1/!*( () 0* ( 1!)22*( (* 11*!.

• E! *()* :(/ ; 1/! /( 9/+*( 2* /( 5/5*!)/( , (* :+/1*2*

*!+ )- :+ (< /-)*!*+ /( 9/+*( 2* /( 5/5*!)/( +**( 2*

9" ; (< :/2*+ (-*+ 1?5/ *()=! +*11/!!2/ *! 5(5. E

/+5)/ 2* )- *( ("0*!)*

 Y /-)*!2/( /( +*(0)2/( 1/! *() )- (* *"! /( 5/5*!)/( +**(; 1/5/ *()= +*11/!!2/ / )+-!2/ *! 9" ; (0 (*!)2/ 2* "+/.

E*5:/ 2* 1=10/ 2* 9" :/+ * 5)/2/ 2* 8!

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M./ent. 1 MEP M1 M1 T.ta2 

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EJEMPLO N- !

&&

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&

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&3

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&4

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&

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EJEMPLO N- 0

&6

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&7

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&$

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EJERCICIO 3&

&%

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'

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&

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3

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4

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