losas de cimentacion-cuerpo.docx

7/25/2019 Losas de cimentacion-cuerpo.docx

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UNIVERSIDAD TECNOLGICA DE PANAMASEDE EN CHIRIQU

FACULTAD DE INGENIERIA CIVILLICENCIATURA EN INGENIERIA CIVIL

INGENIERIA GEOTCNICA

PROF. ING. JORGE URETA

PROYECTO DE INVESTIGACINLOSAS DE CIMENTACION

GRUPO 2IC-25

INTEGRANTES!HECTOR ACOSTA "-#"5-2#$%ARI&A ESPINOSA -#2'-22("

CAROLINE SANTAMARIA )-#5*-"2

I SEMESTRE

2$'


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INDICEINTRODUCCION...................................................................................................2

MARCO TERICO................................................................................................. "

METODOS PARA CALCULAR LOSAS DE CIMENTACIN.........................................5

MTODO RGIDO CONVENCIONAL.................................................................'

EJEMPLO POR EL MTODO RGIDO...................................................................'

METODO FLE+I,LE..................................................................................."

DERIVACION DE ECUACIONES.....................................................................2#


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INTRODUCCION

E/01 341101/ 067/ 31 8910:871/ 6:: 8:3: /0;:8;101 0:?:@7 8796131 ;: 1/0>:8:;=7908:/ 918B8:/ K3B;=8:/ 8;:=;1 70: 67613:3 3101/.


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MARCO TERICO

U: =7/: 31 8910:8:/ 31= 1387 /7 0: 61/:3:/ 7 =: 61/:/ 87831 87 1= 810731 31 =: =7/: /1 87/31: ;1 =: 8:>: K:8::?: 1/ ;: 61/;:= : =: /;9: 31 =:/ 8:>:/ K:8: :?:@7 33:67 1= B1: 31 =: 676: =7/:. N7 /1 87/31: 1= 61/7 31 /0: 1 1= 6718071/0;80;:= 67;1 /1 /;671 ;1 =7 /7670: 3180:9101 1= /;1=7. C797 11/01 90737 31 :B=// 7 /1 87/31: =7/ 979107/ =:/ 4;1:/ 870:01/673;83:/ 67 =7/ :/10:9107/ 34118:=1/ /1 :87/0;9?: 147: =: =7/:9B/ ;1 =7 ;1 1;11 31 :8;137 87 1= :B=//.

L:/ =7/:/ 31 8910:88:01. C;:37 1/;=0: 96:808:?=1 K:81 ;:87961/:8: 1/ /;81019101 61;17 8797 6:: 673;8:/10:9107/ 07=1:?=1/.

S =:/ 8:>:/ 31 =:/ 87=;9:/ 7 1/0B 9B/ 7 917/ ;479191013/0?;3: 7 / 1= /;?/;1=7 1/ 0:= ;1 6;13: 673;8/1 >:31/:/10:9107/ 34118:=1/ =:/ =7/:/ >:31/ 6;131 147:/1 6:: 10:

31479:871/ 181/:/. E/0: 479: 31 14;17 /1 K:81 ;/:37 9;7/3/77/ 8797 1:3;:/ 3 >:/ T 87180:3:/ : =: 8910:8;7/ 8:/7/;0=:37 =: >31 31 ;: /;611/0;80;: 31 878107 147:37. C;:079:7 /1: =: =7/: 0:07 9B/ 87/07/7 1/;=0: 1/07/ 678139107/418;1019101 /7 6141?=1/ =:/ 8910:871/ 31 6=701/ 7 31 6=:/.


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METODOS PARA

CALCULAR LOSASDE CIMENTACIN


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MTODO RGIDO CONVENCIONAL

E 1/01 90737 31 3/17 =: =7/: /1 /;671 0:9101>3: =: 61/;101 >;:!

E= 90737 >37 87187:= 0:?:@: 87 9B/ 1:800;38;:37 =: =7/: 31 8910:83: 6190137 :/

;1 1/01 1=19107 0:?:@1 8797 ; 0737 8;:07 : =:/31479:871/ 31= 9/97. E/01 90737 3: 1/;=0:37/ ;1/1 :818: : =: 1:=3:3 8;:37 7 K: 9;8K: ::8: :6=8:37/ 87 =7 8;:= 1= 8107 31>:13:3 >179087 31 =: =7/: 31 8910:8


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87831 87 1= 8107 31 >:13:3 31 =: 1/;=0:01 31 =:8:>:.

EJEMPLO POR EL MTODO RGIDO

LOSAS DE CIMENTACIN (MTODO RGIDO)

P:: 1= 8B=8;=7 31 3/17 =: 1/;=0:01 31?1 1/0: 1 1= 8107 31>:13:3. S1> 1= 61/7 31 8:3: 87=;9: /1 K:81 ;: /;9:07: 311/0:

Xres=0

P:: 1= 1@1

yr= (27.80+51.80+48.80+51.80+27.80 )(27.30+71.30+92.60+71.30+27.30)(3.65)

yr=298.57

951.80=0.31m

CALCULO DE LAS DIMENSIONES DE LA LOSA:

Bmin=anchominimoque puedocolocar

C:=8;=7 31 =: 67/8:/L7/: /;6181 31= 0117 DF = 0

qa=0.75kg /m2

fc=210kg/m3

f y=4200kg /m3

QX=(27.30+62.70+27.80 ) (8.10 )+ (71.30+113.10+57.60 ) (4.05 )(71.30+113.10+51.60 ) (4.05 )

Xp=0,por ser simetrico en el eje x

,9 $." ".'5$.#5 2 *.D2# 9

E/87@7 :=7 019137, (9


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,9: .25".'5-$." 2 (.* 9

CALCULO DEL LADO SIN RESTRICCIONES DE LA LOSA

L=A losaB =145.54

9=16.17m

L L 3/67?=1

L9 7 L 3/67?=1 ).$5 ) $."5 '.55 9

L L 3/67?=1 NO OK

L ).$5 ) $.5) 2 #.2* 9

CALCULO DE LA NUEVA AREA DE LA LOSA

AL #.2* ( 55.52 92

CALCULO DE LA RESULTANTE MAYORADA

; .) D D9 "*$.#2

; .2 D .' D9 D 5#.$*

; .) 5#.$* #((.5 TON

; .2 5#.$* .' "*$.#2 2().)5 TON

CALCULO DE LA PRESION DE DISEO

Qu=q uA ln

=1294.45

155.52=8.32

TON

m

2

BUSCAMOS LA COLUMNA MS CARGADA:


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B22

!arga"i#a=67.86ton

!arga $uerta=67.86 ton

qu1=1.4 (67.86 )=95ton

qu2=1.2 (67.86 )+1.6 (45.24)=153.82ton

"u=quQu(Lado col+d )

2

4(0.35+d)d

"!=1.06fc=1.06 (0.85 )210=13.05x10=130.5 ton/m

2

C797 "c="u

130.5ton

m2=

153.82 ton8.32 ton/m2(0.35+d )2

4 (0.35+d )d

d=0.387=0.39m

C:=8;=7 31 =: :=0;: 31 =: =7/:!

h=d+rec+

2

=0.51.27 cm rec=7 cm

h=39cm+7 cm+

1.27cm

2 =46.63cm

ESPESOR PERMITIDO DE LOSA:

Lu% mayor10

=405 cm

10 =40.5cm


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Lu% mayor12

=405 cm

12 =33.75cm

C797 1= 1/61/7 7 8;96=1 K "5 89 1/09:37 18:97/ qne!(") = q"#q

$ERIFICO RIGIDE% DE LA LOSAT&'!'& *!n+! ,e -! -&!

?F ".'5 9

&=

' h3

12 =

(3.65 )(0.35)3

12 =0.0130m

4

(c=15200f c=220.2689x103 kg

cm2x 10 2.2026x10

6TON

m2

%/ 2$ : 0:6: 31= /;1=7 0792W

%/ 2$ $.#5 $ ($$TON

m2

X 4

)sAncho franja

4(c& =4

9003.65

42.20X1060.0130=0.4115

Verifcamos rigidez

)l=1.75

0.415=4.216 ).$5 OK KF "5 89


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Y /1 K:B B?:87/ 14;17 1 87=;9:/ 3731 /1 181/01 9:7

1/61/7 1 L: 87=;9:/ 3731 h>hf

S d: ;?8:8:3: 87 917 7=:37.

A2! A;;1 7 1/ =: 87=;9: =:01:= 9B/ 8:>:3: 1/ =: 9B/31/4:7:?=1 67 1= 7=:37

C7=;9: A E/;:

Qu=1.4 (16.68 )=23.35 ton

Qu=1.2 (16.68 )+1.6(11.12)=31.78 ton

"u=31.788.32 ton/m2(0.35+d)2

2(0.54+(d+0.35

2 ))d

d=0.17m


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"u=139.268.32 ton /m2(0.35+d)2

4 (0.35+d)d

d=0.36 m>0.274

S1 181/0: A?:87

S1 31?1 K:81 ; B?:87 ?:@7 1/0: 87=;9: $."'-$.2# $.$ 89 311/61/7 ;: ?:/1 31 2$."5$.2#) .25 9

PERIMETRO RESISTENTE:

C7=;9: A2

Qu=1.4 (37.62 )=52.67ton

Qu=1.2 (32.67 )+1.6(25.08)=85.27 ton

C:=8;=:97/ / =: 87=;9: 7961 " 7 ) =:37/.

R1873:37 1= 019: 31 6;7:37.

S1 8796:: & 87 2 1= 917 /1 7961 10781/ / & 2 K: "=:37/ 31 619107.

2 7961 ) =:37/ 31 619107

x=0.54(0.35+0.274

2 )=0.228

%=c+d=0.35+0.274=0.644

C797 $.'2* 2$.22* 67 =7 0:07 7961 67 " =:37/.

"u=

85.278.32 tonm

2 (0.35+d )2

2(0.54+( d+0.352 )+(0.35+d ))d=130.6

d=0.271


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N7 /1 1;11 B?:87 1 =:/ 87=;9:/ =:01:=1/.

CALCULO DEL ACERO LONGITUDINAL

*=8.32x3.65=30.37ton

,"'5 89 E= :817 /1 87=78: 1037 1/ 318 1= 31 =7/ 0:97/ 67:?: 1= 31 =7/ :677/ 67 31?:@7.

CALCULO DEL ACERO TRAN$ERSAL.

, )$5 89


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METODO FLE+I,LE

M&,e-& ,e /n1-e*

E/01 90737 /;:=: 7 /;671 ;1 1= /;1=7 :80: 8797 ; >;67 311/701/ 6:1837 : ;: ?:/1 =;3: LUPACA 2$2 67 =7 ;1 =7/31/6=::9107/ /1 1=:87: =1:=9101 87 =:/ 61/71/ 31= /;1=7.L7/ 1/701/ /1 >1 67 =: =1 31 H77Z1 ;1 381 ;1 =: 4;1: 1/ >;:=: ;: 87/0:01 9;=06=8:3: 67 1= 31/6=::9107 1 1/01 8:/7!

q=ks +

D731!q C:>: :6=8:3:.

ks 931 Z[/

) ,s=)s rea!argada

D731!) ,s C7/0:01 31= 1/701 1;:=101.


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Y :/ /1 079: 8797 ;: >: :67:3: /7?1 ; 87@;07 31 1/701/ 87>;:= >31.E= 9731=7 31 \Z=1 871/6731 : ; 9731=7 918B87 ;1 073;81=: 1/6;1/0: 31= /;1=7 31 /76701 1 =: /7=;8


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P7 9137 31 =: 8;: 1/ 67/?=1 31019: 1= :=7 31= 9


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$ M79107 ]1807

(& R>31

y D1]1


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01:88: 1= /;1=7 31 4;3:8:318;:37 =: >31 31=: >: 1/ 9:7 ;1 =: 31= /;1=7 31 /76701 61;17 8;:37 =:>31 31= /;1=7 31/76701 1/ 9:7 ;1 =: 31 =: >:.

V1/8 1 (#" 1:=< 341101/ 1/0;37/ 1870:37 ;1 1= 9731=7 31\Z=1161/10: ?:/0:01 ?1 1= 879670:9107 31 >:/ /7?1 /;1=7D1=>:37 ((*. O07/1/0>:371/ K: 18:37 ;1 31613137 31 =: /1=188


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180: 1= 810731 31 =: 61/;: 5.(.E 1= 90737 ]1?=1 :679:37 31 3/17 1= /;1=7 /1 /;6711;:=101 : ; 917 07 31 1/701/ 1=B/087/ 8797 9;1/0: =:>;: 5.(? 3179:3: : 181/ 8797 =: 8910:80;3 0: 87979;1/0: =: >;: 5.(8. L: >: 1/0B /79103: : ;: /7=: 8:>:87810:3: Q. D1 =7/ 4;3:9107/ 31 =: 918B8: 31 9:01:=/


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FIGURA 5.9 (a) Principios del diseo por el mtodo rgido convencional;

(b) principios del mtodo flexible aproximado;

(c) obtencin de la ecuacion (5.4) para vigas sobre cimentacin el!stica.


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"a dimensin del trmino # como se defini en la ecuacin anterior es (longitud)$%&. 'ste

par!metro es mu importante en la determinacin si una losa de cimentacin debe ser diseada

por el mtodo rgido convencional o por el mtodo flexible aproximado. e acuerdo con el

*omit ++, (&-) del /merican *oncrete 0nstitute1 las losas deben disearse por el mtodo

rgido convencional si el espaciamiento de las columnas en una fran2a es menor 3ue &.5#. 6i

es maor 3ue &.5#1 deber! usarse el mtodo flexible aproximado.

Para efectuar el an!lisis para el diseo estructural de una losa flexible1 deben conocerse los

principios de la evaluacin del coeficiente1 71 de reaccin del subsuelo. /ntes de proceder con elestudio del mtodo flexible de diseo1 veamos este coeficiente con m!s detalle.

6i una cimentacin de anc8o 9 (figura 5.&:) est! sometida a una carga por !rea unitaria de 31

sta sufrir! un asentamiento1 'l coeficiente de mdulo1 71 del subsuelo se define como


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FIGURA 5.10 efinicin del coeficiente 7 de la reaccin del subsuelo.

L:/ ;3:31/ 31 Z /7 ZN9" 7 =?6;=>". E= :=7 31= 8718101 311:880;3 L 1= :8K7 , 31 _:8910:8K (55 K7 ; :96=7 1/0;37 31 =7/ 6:B9107/ ;1 ];11 1= 8718101 31 1:88:31/ ;1 93: , + , 31 =: />;1019:1:.

C910:871/ /7?1 /;1=7/ :17/7/!

C910:871/ /7?1 A8==:/!


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L: 18;:8


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E= 8718101 31 1:8837/ 31 8:101:/ 7 :176/0:/. E=6:9107 87 ;: /;6181 31 31/>:/01 31 878107 /1 ==:9:>11:=9101 6:9107 >37 87 ;: /;6181 31 31/>:/01

:/4B=08: /1 ==:9: 6:9107 ]1?=1. P:: ;: 8:>: 31 /;6181 ;1:80: /7?1 ; 6:9107 >37 1= 1/4;17 31 01/0;3 31= 1/4;17 31 01/37 /7/;9:9101 0=1/ =:/ /7=;871/ 1=B/08:/ 6:: =7/:/ /7?18910:871/ \Z=1. P:01 31 1/01 0:?:@7 8:= 4;1 K18K7 67\1/01>::3 (2' ("( ()#.

AK7: ;1 K197/ ::=:37 1= 8718101 31 1:8837 87187:=. N70:! J 1/ 1= 1/61/7 070:= 31 =:=7/:.

2. D10191 =: >31 67 ]1


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8:;/:37 67 ;: 8:>: 31 87=;9: >;: 5.:.

FIGURA 5. M0737 ]1?=1 :679:37 6:: 1= 3/17 31 =7/:/.


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E 1/;91Mtodo Flexible Aproximado

El mtodo flexible aproximado (ACI Comit 436 (1966)) requiere los siguientes pasos

1! Cal"ular la profundidad requerida para la losa de "imenta"i#n por el mtodo "on$en"ional

r%gido!

&! Cal"ular la rigide' de la pla"aDusando la e"ua"i#n mostrada en la ig! 1!*

3! Cal"ular el radio del alargamiento efe"ti$o L (n#tese que la 'ona aproximada de la

influen"ia de la "olumna es 4L) usando la e"ua"i#n mostrada en la figura 1*!

4! Cal"ular los momentos radiales + tangen"iales, el "ortante + la deflexi#n usando las

siguientes e"ua"iones (a"torZi de -eten+i (1946))


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L7/ 979107/ 1 097/ 31 87731:3:/ 180:>;=:1/ 6;131 /18:=8;=:37/ 8797 /1 9;1/0: 1 =: >;: $-5.

C;:37 =7/ =901/ 31 =: =7/: 31 8910:87 67/07. C;:37 ::/87=;9:/ 8783: 87 =: 7: L :6=;1 /;6167/8


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F4"*! 607

8Z j 1/ 1=

4:807 6::8:=8;=: =:/

31]171/

979107/

870:01/ 1

;: 6=:8:

]1?=1. A401

H101

()'.

DERIVACION DE ECUACIONES

M9&,& ,e -! E2"!2n De*en2! ,e -! E-;2!

T79:37 =: /188: /16::3:/ 67 ; 3 /7?1=: ;1 :80;: ;: 8:>: 3/0?;3:


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P7 E;=?7

$0=0

$"dx+q (x ) dxdx2+ ($+d$)=0

"dx+d$=0

"=d$

dx

"=

d$

dx

L: F;1: C70:01 1 1= 1=19107 1/ >;:= : =: 31:3: 31= M79107F=1807

1y=0

""+d"+q (x ) dx=0

d"+q (x ) dx=0

d"dx=q(x )


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E= 1>:07 31 =: 8:>: :6=8:3: /7?1 ; 1=19107 /1B >;:= : =:31:3: 31 =: F;1: C70:01 7 : =: /1>;3: 31:3: 31= M79107

F=1807

R!,& ,e C"*

1

r=

$

(&

d y

dx

1+

1

r=

dy2

dx2

H:8137 =: >;:=:8


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dydx=tan2 617 8797 1= B>;=7 31 70:8:9107 ;1 K: /;437 =: ?: :? 3/0:8: 3

a'3dx

dx=a1'1

T:9?1

mn3dx


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mn=m1 n1

H:8137 70: 1=:8;:=:37 : =: D1479:8


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L:/ 01/71/ 79:=1/ 4x /7 676787:=1/ : /; 3/0:8: : =:

/;6181 1;0:.

F=1


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4x=$%y

&%

H:8137 =: >;:=:85e ,e ?*2@@&

E =7 ;1 />;1 1/0;3:197/ 1= 879670:9107 31 =B9:/ 8761;17/ 31/6=::9107/ 31 9737 ;1 /1 /;671 ;1 =7/

31/6=::9107/ /7 /;81019101 9171/ ;1 1= 1/61/7

u ih1

D731 ui /7 =:/ 87967101/ 31 31/6=::9107. L:/ ::?=1/ ;1

/1 1/8?: : 870;:8


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; 6;07 4;1: 31 =: /;6181 913: 0:= 8797 1= 6;07 P b 1 =:F>;: 2. 6;131 161/:/1 8797

u1=u1+x361

u2

=u2+x362

3731 u1 /7 =7/

31/6=::9107/ 31 =: /;6181913: 31= 6;07 P 1 =: >;: c /7 =:/ 70:871/ 31 =: 4?:180: : 87/18;18: 31 =:31479:8;: /1 /;671 ;1 1= /103767/07 31= 1@1 "79:= : =:

8B/8:: : K:8: :?:@7. D1 :8;137 : =:/ 18;:871/ 2.$ 1=

31/6=::9107 u1

31 ; 6;07 4;1: 31 =: /;6181 913: 1/

>;:= := 31/6=::9107 ; 31= 6;07 871/673101 ;?8:37 /7?1 =:/;61481 913: 9B/ =: 70:8


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H6


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D1 1/01 :7:9107 819B087 /1 878=;1 ;1 6:: =: 017:8=B/8: 31 6=:8:/ =: 31479:8:/. D1 >;:= 9:1: 1/;=0: ;=: =: 31479:8


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S /1 ;/: =: 18;:8


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N;: 2."! : E/4;17/ 919?::=1/. ? E/4;17/ 870:01/.

M79107/ 1/;=0:01/


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A387:=9101 /1 311 979107/ 1/;=0:01/ 01>:37 1 1=1/61/7

!ij h /2

h /2

4ijx3dx3

L7/ 979107/ 6;131 :>;6:/1 8797 ;01/7

L7/ /1037/ 31 =7/ 979107/ 1/0B @:37/ 67 =7/ /1037/ 67/07/31 =:/ 01/71/ ;1 =1/ 3: 7>1 31 9737 ;1 1/;=0: 8797 1 =:F>;: 2.). L7/ 979107/ ]18071/ 67/07/ ! !22 673;81

01/71/ 67/0:/ 0:8871/ 1 =: 6:01 417 31 =: 6=:8: 87961/18:=1/ 1==7 873;81 : ;1 =:8;6=: 07/7: /7?1 =: 8:: 79:= :x 011 ; 979107 87 /10371807:= 10:01.

L7/ 18071/ 979107 ;/:37 =: 1>=: 31 =: 9:7 3118K: K:81 ;1=: 318 2.* >111 ! < $ !22 " $ !2 < $ !2 " $.

C:/7/ 6:08;=:1/

P:: =;/0: ;1 1/4;17/ 1/;=0:01/ /;>1 31 31019:3://0;:871/ 01/7:=1/ 87/31197/

:U 8:/7 31 01/71/ ij 87/0:01 1 1= 1/61/7 8797 1 =: F>;:2.5.:.L7/ 979107/ 1/;=0:


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F>;: 2.)! : M79107/ ]18071/ 07/71/. ? R161/10:871807:= 31 =7/ 979107/.

D1 9:1: ;1 ; 1/0:37 31 01/71/ 87/0:01/ 1 1= 1/61/7 7673;81 979107/.

?P7 70: 6:01 87/31197/ 1= 1/0:37 01/7:= 31 =: F>;: 2.5.? 87;:::8


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F>;: 2.5! : A88

D1?1 70:/1 ;1 u u2 u" 7 :: 6:: 341101/ :=71/ 31x".

D1/>:97/ =:/ 31479:871/ 1/6188:/ /7?1 =: /;6181 913:8797

A319B/ :679:97/ =7/ 8:9?7/ 31 8;:0;:#ij 31 =: /;6181913: 67

;1 6:: =: 017: 31 6=:8:/ 8=B/8: 18. 2. 1/;=0:

10781/ /1 6;131 1/8? =:/ 31479:871/ 31 ; 6;07 8;:=;1:31 =: 6=:8: 1 4;8


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R1=:871/ 87/00;0:/ 101 ::?=1/ 31 =: /;6181 913:

V97/ ;1 =: 8738


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(& d%

4

dx4=%) B

1

E8;:8: A67:3: E=B/08:9101!S;/00;97/

%=eBx

B4=

)B(&

C;:/ R:81/ S7!

B1=B3=4

B)4(& (1+i )=B(1+i)

B2=B4=4

B)4(&

(1+i )=B(1+i)

S7=;8::/ 67 9137 31 =:/ 18;:871/ 3E;=1 1/ 67/?=1 8710 1/07/ 097/ 1 4;871/ 31 /17/ 87/17/.

%=eBx [Acos (Bx )+Bsen(Bx)]+eBx [!cos (Bx )+sen(Bx )]

%=eBx [!cos ( Bx )+sen(Bx)]

E- ',"-& ,e Re!22n & C&e2ene ,e B!-!&/1 311 8797! La

relaci&n entre la tensi&n ca'a( de generar una 'enetraci&n de la 'laca


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en el terreno de ),)*+ que equiale a una deor.aci&n de ),1/0 c.,1/

318 ;1 1/01 8718101 1/ =: 613101 31 =: 180: ;1 ;1 1= 7>1

31 87731:3:/ 87 1= 6;07 31 =: 8;: 01/;: :3@;0:.

F4"*! N 6:E/:7 31 6=:07 31 8:>:


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L7/ 1/;=0:37/ 31 1/07/ 1/:7/ /1 161/: 87 =: =10: Z 3731 67

=7 >11:= /1 :/78: 1= /;?381 :37/:37 : =: =10: Z 6:: 38: ;1

1= :=7 871/6731 : ;: 6=:8: >3: 31 612Z.

D1/31 =: 9:/8:8


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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. . . . . . . .6)

3731 g 1/ 1= 8718101 31 P7//7 910:/ ;1 I 1/ ;

8718101/ ;1 011 1 8;10: =: 479: 31= B1: 8:>:3: =: >31

31 =: ?:/1.

C7/31:37 =7 161/:37 :0179101 1= M


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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .()

P7 =7 0:07 6:: ;: :8==: /:0;:3: 3731 6B808:9101 7 /1

673;8B 31479:871/ 7=;908:/ 3;:01 =: :6=8:8:

;1 >11: 1= :/10:9107 /0:0B17 673197/ 318 ;1 =:

161/:;=:1/ 3731 1= 8718101 g 1/ 417 : $5$ /1

:679: : $) 7 $" 3731 67 =7 0:07 1/01 ;: 31479:8

*e!-,!, 2"!n,& -! 2&n!ne 6H e *ee'5-!3!,! 5&* 0HH e

,e2* 5!*!:

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . ( )


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P:: "e-& 2&@e


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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .(8)

D731 , /1 161/: 1 89 Z 161/10: 1= :=7 7?0137 87 ;

1/:7 31 6=:07 31 8:>: 31 "$ 89 31 =:37 ;1 0:9? 6;131 /1

8:=8;=:37 87 =: 18;:889"

E= :=7 31= 167101 :: 101 2 j j "

C;:37 =: ?:/1 /1 :67: : ;: 674;33:3 D /1 673B ;0=: =:/>;101 161/;=: 31 =:37/ , L 3731 L , 6::

87781 1= :=7 31= 8718101 31 ?:=:/07 013197/ ;1 31019: 1=

:=7 31 Z 6:: ;: ?:/1 8;:3:3: 31 =:37 , 87 =: :6=8:8


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C7/31:97/ :K7: ;1 01197/ ;: ?:/1 8;:3:3: 31 =:37 ,

:67:3: /7?1 ; '!n& 4*!n"-!*;1 4101 : ;: 01/11: ;: 31479:8:97/ :319B/ ;1 K:8197/ ;

1/:7 31 6=:07 31 8:>: 87 ; 6=:07 31 :8K7 ,6 013197/!

6:: 1= 6=:07 31 8:>: 6:: =: ?:/1 31 :8K7 ,;1

7/ 61901 K:8137 ;/7 31 =: 18;:8;101

R1=:8


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kl ).kP

C7 =7 8;:= 1= :=7 31 Z 6:: /0: 4;3:8


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#

*

( $A8K7 31 =: ,:/1 9


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.$$

.5$

2.$$

2.5$

".$$

".5$

).$$

A/120:9.1207?:/1VA/120:9.12076=:07

$

2

"

)

5

FIGURA N :R1=:8


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.B 6

. B

Tenn = 60 . q

F;3:910:=9101 /1 31?1B 87/31: =: 9:/: 31 /;1=7/ ;1 /1

7=;8: 3107 31= ?;=?7 31 61/71/ >11:37 0:07 67 =: 6=:8: 31

1/:7 31 , "$ 89 31 =:37 8797 67 =: ?:/1 31 :8K7 , 1/0:

/1>;7/ ;1 =7/ ?;=?7/ 31 01/71/ ;1 /1 31/:7==: /1 ;?8:

3107 31 9:/:/ 31 /;1=7/ 31 =:/ 9/9:/ 8::801/08:/ 918B8:/.

, ,

A 9737 31 14118: 31?197/ 079: 1 87/31:8;:= 01/: : ;: 674;33:3

31 37/ 181/ 1= :8K7 31 =: 9/9:.

S:?197/ ;1 1 =7/ /;1=7/ >:;=:1/ 1 =:/ :8==:/ ?=:3:/

79:=9101 87/7=3:3:/ 0:= 8797 =:/ ;1 /1 310180: 1 ;1/0:

7: 479:37 6:01 31 =: F79:81 3118K: 31= 0:97 417 31= R7 P::B 1 =07:= 31=

R7 31 L: P=:0: 1= 9


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D731 1/ =: 674;33:3 : =: 8;:= /1 =: 87/31:

E/07 7/ ==1: : 011 ;1 34118: =7/ :=71/ 1/;=0:01/ 31=

C718101 31 ,:=:/07 Z /1> =: 61/


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A1:/ /18:/ 7 K913:/ A1:/ /:0;:3:/

F4"*! N ! E/09:83:/


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