trabajo de estructuras especiales-final 1

8/16/2019 Trabajo de Estructuras Especiales-final 1

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UNIVERSIDAD NACIONAL DANIEL ALCIDES CARRION FACULTAD DE INGENIERÍA

ESCUELA DE FORMACION PROFESIONAL DE INGENIERIA CIVIL

UNIVERSIDAD NACIONAL DANIEL ALCIDESCARRION-UNDAC

CONSIDERACIONES ESTRUCTURALES EN EL ANÁLISIS YDISEÑO DE PUENTE COLGANTE REFERENCIALES PARA

EL PUENTE COLGANTE-PROTOTIPO

DOCENTE: Ing. Earle TANGOA BERNARDO

ALUMNOS:

• Ger!n SANTIAGO ESPINO"A• Da#$% COTRINA PAUCAR • &$l're%! AMBROSIO PA(UELO• (e''er!n CORNELIO MUÑO"

Cerr! %e Pa)! * Per+,/

ESTRUCTURAS ESPECIALES : ANALISIS Y DISEÑO DE PUENTE Y CARACTERISTICAS DE PROTOTIPO 0


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ÍNDICE 1

RESUMEN 4

INTRODUCCIÓN 11

CAPÍTULO I. GENERALIDADES 12

1.1 OBJETIVO Y ALCANCES 12

1.2 ORGANIZACIÓN DEL DOCUMENTO 12

1.3 CARACTERÍSTICAS 12

1.4 RESEÑA HISTÓRICA 13

1.5 NORMATIVIDAD DE PUENTES 1

CAPÍTULO II. ELEMENTOS DE UN PUENTE COLGANTE 2!

2.1 LOS CABLES 2!

2.1.1 D"#$%$&$'% (" )*+,$%- 2!

2.1.2 P+-/$"(0(" ")+&)+0" (" - &0" 22

2.1.3 P+-)"&&$'% &-%)+0 0 &-++-$'% 24

2.2 LAS PNDOLAS 2

2.3 LA VIGA DE RIGIDEZ 2

2.4 TORRES DE PUENTES COLGANTES 32

CAPÍTULO III. ESTUDIO ANALÍTICO DE PUENTES COLGANTES 34

3.1 HIPÓTESIS Y RELACIONES B6SICAS PARA EL AN6LISIS 34

3.1.1 R"0&$'% "%)+" #"+70 "% " &0" 34

3.1.2 C0" &-% 0/-8- 0 ,$,- %$9": -,")$(- 0 %0 &0+;0

%$#-+,","%)" +"/0+)$(0 "% /+-8"&&$'%


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4.1 DESCRIPCIÓN GENERAL DEL PROYECTO 2

4.1.1 C0+0&)"+)$&0 (" /+-8"&)- 2

4.1.2 N-+,0 )*&%$&0 8 "/"&$#$&0&$-%" /0+0 " 0%@$$ 8 ($"-

E)+&)+0 24.1.3 M0)"+$0" 3

4.1.4 D"&+$/&$'% (" 0 ")+&)+0 8 ($,"%$-%0,$"%)- /+"$,$%0+ 3

4.2 AN6LISIS Y DISEÑO DE LA LOSA DEL PUENTE

4.3 AN6LISIS ESTRUCTURAL SEGN LA TERORÍA DE LAS

DE>LE?IONES !

4.3.1 M")+0(- (" &0+;0 1

4.3.2 C@&- (" 0 )"%$'% ,@$,0 "% " &0" /+$%&$/0 5

4.3.3 C@&- (" ,-,"%)- #"&)-+ "% 0 9$;0 (" +$;$("7 2

4.3.4 C@&- (" - &-+)0%)" )-)0" "% 0 9$;0 (" +$;$("7

CAPÍTULO V CARACTERISTICAS DEL PROTOTIPO 115

CAPÍTULO V CONCLUSIONES Y RECOMENDACIONES 115

5.1 CONCLUSIONES 115

5.2 RECOMENDACIONES 11

BIBLIOGRAFÍA 11

ANEXOS



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UNIVERSIDAD NACIONAL DANIEL ALCIDES CARRION

FACULTAD DE INGENIERÍA ESCUELA DE FORMACION PROFESIONAL DE INGENIERIA CIVIL

RESUMEN

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(" 0 A,"+$&0% S-&$")8 -# C$9$ E%;$%""+ KASCE. E% ($&


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INTRODUCCIÓN

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>IGURA N 11 P"%)" &-;0%)" -+" " +- A/+,0&



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CAPÍTULO I: GENERALIDADES

1.1 OBJETIVO Y ALCANCES

E% %")+- /0: " ("0++-- (" 0 $%#+0")+&)+0 9$0 " % +")- /"+,0%"%)"

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C!"#$%!& '()*&+!& A,-"$* %* )/,%!"$ S*--+0, %*" $"*&!

>IGURA N 1 D")0" (" P"%)" S"9"+%

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/0+0 ",/"0+ 0 T"-+0 (" ;+0%(" ("#"$-%": /-+ - " %- " F)$#$&0 ("F0+ ("

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S/"&$#$&0)$-% #-+ Z$%&C-0)"( S)"" S)+&)+0 $+" R-/".

CAPÍTULO II: ELEMENTOS DE UN PUENTE COLGANTE

2.1 LOS CABLES

L- &0" -% - "","%)- ,@ $,/-+)0%)" /0+0 +"$)$+ 0 &0+;0 ")"+%0

"% 0 ")+&)+0 (" % /"%)" &-;0%)". E &0" /"(" /+""%)0+ ($9"+0

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($/-%$" 90+$- )$/- (" &0" /0+0 " - "% /"%)" -/-+)0(- /-+ "-.

2.1.1 D*3+,+-+0, %* /&4+,!'

C$"*. C0$"+ ,$",+- #"$" 0 )"%$'% " &-%$)" "% %- - ,@ ;+/-

(" 00,+": )-+-%": &-+("" - 0++0.

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T!&0, *'&(-(&$" 5-!, *6-*)-+0, %*" !&0, %* $"$4&*' )$&$"*"!'7.

A0,+" "%+-0(-


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/+-(&$+ %0 "&&$'% $,*)+$&0 K>$;+0 N 22: /+-(&$(- "% - E)0(- U%$(-

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(" 0&"+(- &-% 0 %-+,0 ASTM A22 T$/- II K0(0 /0+0 )$+0%)0 (" &0"

>IGURA N 21 T$/- (" &0" 0(- /0+0 )$+0%)0



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>IGURA N 22 T$/- (" )-+-%"

>IGURA N 23 C-%#$;+0&$'% (" )-+'% 8 &0" ")+&)+0



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2.1.2 P&!)+*%$%*' *'&(-(&$"*' %* "!' -$"*'

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/-+ - ,"%- 1!W (" "#"+7- )$,- ")0"&$(- "% 0 %-+,0 - 0 ,@ (" =!W

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CUADRO N 22 M'(- ,%$,- (" "0)$&$(0( (" )-+-%" 8 &0"")+&)+0" /+"")$+0(-

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E% ")" &0- (" /*%(-0 #-+,0(0 /-+ % &-+('%: - /"+%- " /"+,$)"% 0F)0+

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>IGURA N 2 D$,"%$-%" (" 0%&0F" &-% /00(-+ KA,"+$&0% TIGER 1=45

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>IGURA N 2 T0"+- (" "&&$'% &0F'% KR80 MJ

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CAPÍTULO III: ESTUDIO ANALÍTICO DE PUENTES COLGANTES

9.1 IPÓTESIS Y RELACIONES BÁSICAS PARA EL ANÁLISIS

P0+0 /+""%)0+ - /+-&"($,$"%)- (" 0%@$$ (" /"%)" &-;0%)" " %"&"0+$-

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FIGURA N= 9>1: R"0&$-%" "%)+" #"+70 "% " &0"L0 "&0&$-%" (" "$$+$- (" "","%)- ($#"+"%&$0 (" -%;$)( $%($&0(- "% 0

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( )dx xqdT z −= K35

D" 0 #$;+0 3.1 " "%&"%)+0 "

dx

dz H Htg tg T T x z === φ φ

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R"",/070%(- K3 "% K3 " -)$"%"

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L0 #"&


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2

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L0 "&0&$'% (" 0 &+90 " )-,0 " &0" "% ")" &0- (" &0+;0 " ("%-,$%0

%0 &0)"%0+$0 8 &-++"/-%(" 0 &0+;0 ","F0%)" 0 /"- /+-/$- (" &0".

E -+$;"% (" &--+("%0(0 8 0 -+$"%)0&$'% (" - "F" " 0(-/)0% &-,- " $%($&0

"% 0 #$;+0 $;$"%)"

>IGURA N 3.2 C0" &-% 0/-8- 0 ,$,- %$9": -,")$(- 0 %0 &0+;0%$#-+,","%)" +"/0+)$(0 0 - 0+;- (" &0"

S$ " 0 -%;$)( (" &0" "%)+" D 8 P: " /"- (" ";,"%)- DP (" &0" " :

(-%(" " " /"- /-+ %$(0( (" -%;$)( (" &0". E "$$+$- (" #"+70 "% "

/%)- P (" 0 #$;+0 3.2: )"%$"%(- "% &"%)0 " +")0(- &0&0(- "% 0 "&0&$'%

K33: "

H T =φ cos qsTsen =φ

D"#$%$,- %0 &-%)0%)" C " "0 " &-&$"%)" (" 0 &-%)0%)" H "%)+" " /"-

: (" 90-+ &-%)0%)" /-+ %$(0( (" -%;$)( (" &0"

qC H q

H C =⇒= K322

C

s

qC

qs

H

qs

T

Tsentg ====

φ

φ φ

cos

L";-

( )φ tg C s = K323



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E)0 " 0 "&0&$'% (" 0 &0)"%0+$0 8 0 &-%)0%)" C: &8- 90-+ ")0 "% K322:

" 0,0(0 " /0+@,")+- (" 0 &0)"%0+$0. T+0%#-+,0,- ")0 "&0&$'% 0

&--+("%0(0 &0+)"$0%0

sdxdz C =

D"+$90%(- ")0 "&0&$'% +"/"&)- 0

2

2

2

1

+==dx

dz

dx

ds

dx

z d C

P0+0 /-("+ $%)";+0+ ")0 "&0&$'% ($#"+"%&$0: 0 ,-($#$&0,- (" 0 $;$"%)"

#-+,0

1

1

2=

+

dx

dz

dx

dz

dx

d

C K324

E% G+0%9$" 1=52: /0;. 521: " "%&"%)+0 " ")" &-&$"%)" " 0 ("+$90(0 ("

11 =

−dx

dz senh

dz

d C

D-%(": " ")@ ",/"0%(- 0 ("+$90(0 (" 0 #%&$'% $%9"+0 (" "%-


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P0+0 &0&0+ " 90-+ (" 0 &-%)0%)" A " &-%-&" " /0+0 ! 0 )0%;"%)" "


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P"+-

===C

xCsenh

dx

dz C Ctg s φ

2222222 1cosh C z C

xC C

x senhC s −=

−

=

=

R"",/070%(- ")" 90-+ "% K32 " )$"%"

( ) ( ) 2222222222 z qC C z qC sqT =+−=+=

L";-

( ) qC H T f C qT qz T ==⇒+=⇒= minmax

K32

22 C z C

xCsenh s −=

= K32=

S$ " &-,/0+0% - +")0(- -)"%$(- (" % &0" /0+0'$&- 8 %- &-% 0

"&0&$'% (" %0 &0)"%0+$0: &-% 0 ,$,0 7 L: #"&


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9.2.1. E-($-+0, ?'+-$ %* "$ @+#$ %* &+#+%*

L0 $;$"%)"


39/82

8 O+("%0(0 (" &0" 0F- 0 &0+;0 ,"+)0

8] 6%;- (" &0" 0F- 0 &0+;0 ,"+)0

8 ]] C+90)+0 (" &0" 0F- 0 &0+;0 ,"+)0

C-% 0 "+70 ($)+$$(0 "% 0 /*%(-0 9"+)$&0" ("$(- 0 0 &0+;0 9$90

D"#"$'% (" &0" 0F- &0+;0 9$90: $;0 0 0 ("#"$'% (" 0 9$;0 ("

0&"+(- 0 0


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K33

>IGURA N 34 C0+;0 "% " &0" 8 "% 0 9$;0K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;"

C-% 0 &0+;0 ,-)+0(0 "% 0 K#$;+0 3‐2 0 "&0&$'% ($#"+"%&$0 "

("&+$" 0 9$;0 (" +$;$("7 &-% %0 &-%)0%)" (" 0&"+(- 0 0


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0%0-;0 " $)+0(0 "% 0 K#$;+0 32=.

K33=

D-%("

N T"%$'% 0$0

C0+;0 )+0%9"+0

>IGURA N 35 A%0-;0 (" %0 9$;0 0 T"%$'%K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;"

C-% &-%($&$-%" (" -+(" (0(0: K33= /"(" "+ +"")0 /0+0 0 ("#"$'% :

8 "&"%)","%)" /0+0 " @%;- X^: " ,-,"%)- MEI^^ 8 " &-+)0%)"

VEI^^̂ . E% 0 K#$;+0 33! " /+""%)0 0 -&$-%" /0+0 %0 9$;0

$,/","%)" 0/-80(0 &-% )"%$'% 0$0 8 /0+0 - &0- (" &0+;0 (" $%)"+* "%

" 0%@$$ (" /"%)" &-;0%)". L0 )00


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P0+0 "900+ 0 #'+,0 "% 0 K#$;+0 33!: 0 #"+70 "% " &0" H/

("" "+ &-%-&$(0. U%0 &-%($&$'% /0+0 (")"+,$%0+ ")0 #"+70 " (0(0 /-+ "

+""+$,$"%)- (" &-,/0)$$$(0( (" 0 /+-8"&&$'%


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/0+0 90-+" )/$&- (" ` 8 a: - +")0(- (" 0 "/+"$-%" "0&)0 8

0/+-$,0(0 -% &"+&0%0,"%)" $%($)$%;$". P-+ - )0%)-: " /"(" "&+$$+

/0+0 0 #'+,0 3‐430 8 3‐43.

K3430:

E$,$%0%(- a (" 0 3430 8 343 " ";0 0

K344

E &0" ")$+0(- ("$(- 0 0 &0+;0 9$90 8 &0,$- (" )",/"+0)+0 " (0(- /-+

K345

D-%("

EcAc: C0" (" +$;$("7

T: C0,$- (" )",/"+0)+0 "% " &0" (" /"%$'%

α t C-"#$&$"%)" "/0%$'% )*+,$&0

C-,$%0%(- K3‐41: K3‐44 8 K3‐45 8 &-% y’= dy/dx, w’ = dw/dx, y u’dx : "-)$"%".

. K34

E /+$,"+ )*+,$%- "% " $%)";+0%(- (" 0 #'+,0 K34 /"(" "+ 0/+-$,0(- /-+

K34

S)$)8"%(- "% "&. K331 /-+ 8^ 8 " ("0++-- (" 0 $%)";+0&$'% /+""%)0 0"&0&$'% (" &-,/0)$$$(0( /0+0 " &0".

K340

D-%("

K34

K34&


dydxd# ψ ε −= dxdydw ψ ε +=

dx

dydw

dx

dydxd# −+= ])(1[ 2ε

T dx

dy

A E

H T

A E

H T

cc

p

T

cc

pα α

θ ε ++=+= 2

12 ])(1[

cos

i" T

cc

pl

dx yw yT y A E

H δ δ α −=−+++∫ ]'')'1()'1([

223

2

0

...)'8

3'

2

31()'1( 422

32 +++≈+ y y

A E

H y

A E

H

cc

p

cc

p

i" l

T T c

cc

pwdx yTL L

A E

H δ δ α −=++ ∫ ''

]cos

1)(8[

3

2

α +=

l

f l Lc

]cos

1)(

3

16[

2

2

α +=

l

f l LT


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CUADRO N= 9>1 E&0&$-%" /0+0 0 9$;0 &-% )"%$'% 0$0 K0(0/)0&$'% ("P0)"0"% K1==3 8 R$'% 8 V-;" K1=2

K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;"



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>IGURA N 3 E&0&$-%" (" &-,/0)$$$(0( /0+0 " &0" K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;".

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>IGURA N 3 A/+-$,0&$'% /0+0 ((K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;"

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+$;$("7 0 0 #"$'% (" 0 )-++" " +"/+""%)0(0 /-+ +"-+)"


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D"$(- 0 0 +$;$("&" (" 0 )-++" 0 #"+70 IGURA N 3= I("0$70&$'% (" /"%)" /"%($(-K>"%)" P+"$,$%0+8 A%08$ -# S/"%$-% B+$(;"

K35!0

K35!


a

p

a"

H 1

=δ $

p p

$"

H H 12 −=δ

c

p p

c"

H H 23 −=δ d

p

d "

H 3−=δ

0'' 3212

22

2

2

=−

+−

+++ ∫ c

p p

$

p p

l T T c

cc

p

"

H H

%

H H wdx yTL L

A E

H α

0'' 323

33

3

3

=+−+++ ∫ d

p

c

p p

l T T c

cc

p

" H

% H H wdx yTL L

A E H α

0'' 211

11

1

1

=−

++++ ∫ $

p p

a

p

l T T c

cc

p

"

H H

%

H wdx yTL L

A E

H α


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K35!&

S$ 0 +$;$("7 (" 0 )-++" " ("/+"&$0(0 )"%",-

k b = k c = 0 H p1 = H p2 = H p3 = H p K351

P0+0 ")" &0- 0 "&0&$'% (" &-,/0)$$$(0( K340


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4 C0&0+ % %"9- 90-+ ,"F-+0(- /0+0 Hp 0%(- 354 8 352.

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D-%("

Hp,$ " $;0 0 90-+ 0&)0 /0+0 H/ 8

H p,$%1 I;0 0 %"9- 90-+ (" H/.

5 R"/$)0 - /0- 24


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• E/"&$#$&0&$-%" AASHTO 9"+$'% LR>D KA,"+$&0% A-&$0)$-% -# S)0)"

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P0+0 /-("+


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t T

T a

dise'o 82.551,1

45.0

32.698

45.0

===

C-%$("+0%(- &0" (" j 2 k &-% R%l&0"43!5 N 43. ) K9"+ 0%"-

N1: )"%",-

5.38.438

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===

ca$le (n

T ca$les !o dise'o

U0+",- 4 &0" (" j 2k /-+ %"0.

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"&&$-%" (" )$/- (-" &0%0 "% 0 +$(0: (-" )"" "% - ,-%)0%)" 8 9$;0

)+0%9"+0 8 (-" @%;- "% 0 ($0;-%0". S"


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>IGURA N 41 S"&&$'% )+0%9"+0 (" /"%)" &-;0%)" QE T+$%#-

>IGURA N 42 I("0$70&$'% (" /"%)"

L- "","%)- (" 0 9$;0 (" +$;$("7 8 0 9$;0 )+0%9"+0" (""+@% (" "+

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+"0$70+@ /0+0 " " &0" /"(0 ("#-+,0+" %$#-+,","%)" ,0%)"%$"%(-

#-+,0 /0+0'$&0.


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• L0 /*%(-0 ")@% ($)+$$(0 &-%)$%0,"%)" 0 - 0+;- (" 0

9$;0 8 -% $%")"%$".

• L0 /*%(-0 ")@% $%$&$0,"%)" 9"+)$&0" 8 /"+,0%"&"%

9"+)$&0" 0F- 0 &0+;0.

• L0 9$;0 (" +$;$("7 " &-%)0%)" /0+0 &0(0 )+0,-.

A$,$,-: "


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>IGURA N 430 S$)",0 c (" 0 -+"&0+;0 9"IGURA N 43 S$)",0 M (" 0 -+"&0+;0 9"IGURA N 44 U$&0&$'% (" 0 -+"&0+;0 9"


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P0+0 0 /-$&$'% 1: )"%",-S

@:p = 0.001

:p 8kN 58:p @:p :p#@:p 58:p#@:p :p8i#1

'3+%(&+ ".91+10 0.001 1"23.02 '.9/+09 1"23.02 0.000

♦# 3./9 ♦ A0.0 0."/9 0.'31

0.0 0.'00 0.'00♦A= 1.0 0.'31 0."/9

P0+0 0 /-$&$'% 2: )"%",-S

@:p = 0.001

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0.0 0.2'0 0.'00♦A= 1.0 0.'31 0."/9

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@:p = 0.001

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-+,(&$ 0.00+#00 0.001 2/.0' '.")+09 2/.0' 0.000

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&-++"&)-.

)&b'


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>IGURA N 45 E)+0&)- (" 0 >$;+0 N 31 E&0&$-%" /0+00 9$;0 &-% )"%$'% 0$0


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C0(+- N 41 D"#"$'% "% 0 9$;0 (" +$;$("7 " $%)";+0&$'% %,*+$&0KP-$&$'% (" &0+;0 1

C0(+- N 42 D"#"$'% "% 0 9$;0 (" +$;$("7 " $%)";+0&$'% %,*+$&0KP-$&$'% (" &0+;0 2

C0(+- N 43 D"#"$'% "% 0 9$;0 (" +$;$("7 " $%)";+0&$'% %,*+$&0KP-$&$'% (" &0+;0 3


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CUADRO N 44 D"#"$'% "% 0 9$;0 (" +$;$("7 " $%)";+0&$'% %,*+$&0


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)"%$'% 0$0


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CAPÍTULO V: PROTOTIPO DE PUENTE COLGANTE>CARACTERISTICAS:

E% " /+""%)" &0/$)- " /+""%)0+0 - ,0)"+$0" 0 0+: 0 "&00 8"/"&$#$&0&$-%" (" /"%)": 0 &0 " ,")+0 "% " $;$"%)" &0(+-.

UBICACIÓN REFERENCIAL: RIO MARAÑON EN EL DEPARTAMENTO DECAJAMARCA


77


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ANALISIS DE DISEÑO DE PUENTE REFERENCIAL Y LA PROPUESTA PARA

EL PROTOTIPOESTRUCTURAS ESPECIALES : ANALISIS Y DISEÑO DE PUENTE Y CARACTERISTICAS DE PROTOTIPO

78

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CAPÍTULO VI: CONCLUSIONES Y RECOMENDACIONES

.1 CONCLUSIONES

• S" ' 0 %-+,0 (" AASTHO /0+0 " /+" ($,"%$-%0,$"%)- (" /"%)"&-;0%)" 8 /-("+ ("0++-0+ 0 ($,"%$-%" /0+0 %")+- /+-)-)$/-: 8&-%-&"+ " ($"- ")+&)+0 '/)$,-.

• P0+0 /-("+ +"0$70+ " /+-)-)$/- " ("" (" )"%"+ (0)- +"#"+"%&$0" ("% /"%)" "% "&00 +"0.

•

L- ,0)"+$0" 0 0+ -% (" 0 >"++")"+0 (" C"++- (" P0&-• S" 0+0 " 0/ 2!!!: /0+0 " ($"- (" /+-)-)$/-.• S" )-,- /0+0 " /+" ($,"%$-%0,$"%)- - $%)"+90- /"+,$$" /0+0 "

($"- (" /"%)" &-;0%)"• E /"%)" " $&0+0 " R$- M0+0'%C0F0,0+&0.• S" )-,0+0 "% &"%)0 - ($9"+- &@&- /0+0 " ($"- )0,$*% ("

/+-)-)$/-• S" 0+0% 0 ($,"%$-%" ")@%(0+ (" ($"- "% "&00 /0+0 0

"0-+0&$'% (" %")+- /+-)-)$/-.• E% " /+-)-)$/- " (""+@ +$%(0+ &-% ,0)"+$0" " &"%)0 &-%

,0)"+$0" +"#"+"%)" 0$,$0(- "% /"- "/"&#$&-.

.2 RECOMENDACIONES

• L- /+$,-+($0 " &-%-&"+ " &-%&"/)- (" /"%)" &-;0%)"

• T"%"+ (0)- +"#"+"%&$0" (" % /+-8"&)-: /0+0 /-("+ +"0$70+- "% %

/+-)-)$/-.

• C-%-&"+ - ($9"+- &-,/-%"%)" " &"%)0 " /"%)" &-;0%)".

• C-%-&"+ - ($9"+- "","%)- " &-,/-+)0,$"%)- ")+&)+0.


79


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• P0+0 $("0$70+ % /+-)-)$/- " ("" )"%"+ "% &"%)0 " % ($"-

/+"$,$%0+ (" % /"%)" "$)"%)" - /+-&"- /+"$,$%0+: /0+0 /-("+ )"%"+

($,"%$-%" +"#"+"%&$0": /0+0 &+"0+ " /+-)-)$/-.

• P0+0 " ("0++-- (" % "% ($"- "% " /+-)-)$/-: - /+$,"+- "

&-%-&"+ " ,*)-(- (" 0%@$$ )$$70(- /0+0 % /"%)" &-;0%)"


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*+-E.A +A+A E +E+E.AA*TA E +E+E.A - .AA

BIBLIOGRAFÍA

1. A,"+$&0% A-&$0)$-% -# S)0)" H$;D B+$(;" D"$;% S/"&$#$&0)$-%: EE.UU:2!1!.

2. B+-&"%+-;

trabajo de estructuras especiales-final 1

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