Calculo de Desalinhamento de Contraponto

7/25/2019 Calculo de Desalinhamento de Contraponto

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2/67

Torneamento (Complementar)

CENFIM Centro de Formao Profissional da Indstria Metalrgica e Metalomecnica 1

!

"#$

% "# & ' "# &( ( )

%"#

& ' "# &(( )


3/67



NDICE

*+ &!,%-./, ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 01+ ,23&4, +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5

1+* ,67 8 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5

1+1 ,67 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5


4/67



1. INTRODUO

"# 9": );< "# =?< @ )< @ < @

< @ ": =< ,

"#+

? 7< < A B

B ": ) =+

, 7# @ >

6 > @ # 7

+

7# 6@ >

7 7< # ><

6 6 @ " 6@+

%7 C ": )< ?

= > <

67< # < < 77

B +

=< B "#< = = < ><

B< > >< >

+, B # < < D < >> +

> =< B = < > >

6 6"# "+

%7 = @ B

D 7= 7< > =<

>> (7 > +


5/67



2. OBJECTIVOS

2.1 Objectivo Geral

&A E B< >

A > 7 +

= 7 C =< $< C B"#

6 B< 7 +

@ "#< A"#

> C B"# < 7= "#

D+

2.2 Objectivos especficos

>"# "< @ =< B"# ":

< 7 7


6/67


7/67

CENFIM 1

! " #

$ " %

%

&'()*+,-(. (*/0/123'4+. %

(.()5/15'6()*/ (67*'4/ 8

/&)(+6()*/ 2)'4/ 9

(:')',;/ 9


8/67

CENFIM 2

/&6+ '1B)0&'4+ 9

/&6+ 1B=*'4+ C=/& (,+ /0(1/D

(&':'4+,;/ 0+ E4()*&'4'0+0(

FG @ 8

@ H I 8

@ H I ?

@ H I #

@ H I #

@ H I ###

@ H I %#8

@ H I 8#?

%

%

%


9/67

CENFIM 3

/ :')+1 0(.*+ )'0+0( (0+323'4+ 0(5(&7 .(& 4+=+J 0(K

E(4>*+& +. =&')4'=+'. /=(&+,-(. 0( */&)(+6()*/ 42)'4/

/).>1*+& *+L(1+. ( 7L+4/.

/&)(+6()*/ 4/)5()4'/)+1 L7.'4/

/&)(+6()*/ 42)'4/

!"

>&+)*( / 0(.()5/15'6()*/ 0(.*+ )'0+0( (0+323'4+ .(&;/ +=&(.()*+0/. /. *(6+.

)(1+ :/4+0/.M (.41+&(4()0/ +. N>(.*-(. N>( '&;/ .>&3'& =+&+ N>( =/..+ :'4+& 4/6 >6+

5'.;/ 6+'. +1+&3+0+ 0/. ().')+6()*/. /L*'0/.

(6/).*&+,;/ 0/. 57&'/. *'=/. 0( /=(&+,-(. 0( */&)(+6()*/

/).>1*+ 0/. 7L+4/. ( *+L(1+. =+&+ + .(1(4,;/ 0( 5(1/4'0+0(. 0( 4/&*(M 0(

+5+),/ ( =()(*&+,;/ (6 .'*>+,-(. .'6>1+0+.

.4/1O+ 0/ 1>L&':'4+)*( 0( 4/&*(M =+&+ 0(*(&6')+0/ *&+L+1O/ .'6>1+0/

>P(',;/ 0+. :(&&+6()*+. 0( 4/&*( .'6>1+)0/ .'*>+,-(. =&7*'4+.

#


10/67

CENFIM 4

$ %&'(

)*+,,-

(5(&7K

/)O(4'6()*/. L7.'4/. 0( 0(.()O/ *


11/67

CENFIM 5

# ./ ( .0'

# ./ ( .0' 12


12/67

CENFIM 6

3 ( 0

4

4 ,5-!6 (-789,:

(5'0/ Q (.=(4':'4'0+0( 0( 4(&*/. .(4*/&(. 0+. 4/).*&>,-(. 6(*+1/6(4R)'4+.M */&)+.(

)(4(..7&'/ N>( 4+0+ >6 0/. +..>)*/. .(P+ *&+*+0/ 0( :/&6+ .'6=1(.M 6+. 6>'*/

/LP(4*'5+M 0( 6+)('&+ + );/ 4/):>)0'&M )(6 4/6=1'4+&M / 0(.()5/15'6()*/ 0( 4+0+

:+.( 0/. (E(&4B4'/. =&/=/.*/.

+ =&7*'4+M (6 4/)*(E*/ 0( :/&6+,;/M .(&7 )(4(..7&'/ &(=(*'&M :&(N>()*(6()*(M /.

(E(&4B4'/.M =+&+ N>( / :/&6+)0/ =/..+ 4/&&'3'& /. (&&/. 6+'. :&(N>()*(.M 4/6 N>( .(

0(:&/)*(M + :'6 0( :'4+& 0(5'0+6()*( (.41+&(4'0/

. (E(&4B4'/. .(&;/ 0(6/).*&+0/.M =&'6('&+6()*(M =(1/ :/&6+0/&6/)'*/& (M 0(=/'.M

*'&+0+. */0+. +. 0S5'0+.M N>( =/..+6 .>&3'& + N>+1N>(& 6/6()*/

(6=&( N>( )(4(..7&'/M / (E(&4B4'/ .(&7 &(=(*'0/M =+&+ N>( / :/&6+)0/ :'N>(

(.41+&(4'0/ ./L&( 4+0+ :+.( 0( (1+L/&+,;/ 0( >6+ =(,+

(5( .(& .(6=&( )(4(..7&'/ &(4/&&(& +/. 0(.()O/. +=&(.()*+0/. )/. (E(&4B4'/. ( /

:/&6+0/&6/)'*/& 0(5(&7 +=&(.()*+& +. 5'.*+.M N>( ()*()0(& )(4(..7&'/M 0( 6/0/ +

(.41+&(4(& N>+1N>(& 0S5'0+ N>( / :/&6+)0/ =/..+ *(&

&(*()0(.(M +..'6M ')*&/0>J'& / :/&6+)0/ )/. =&/4(../. *(4)/123'4/. 6+'. 4/6=1(E/.M

0( :/&6+ N>( =/..+ &(+1'J+& +. *+&(:+. N>( 6+'. *+&0( 5+' *(& 0( ():&()*+& )/ .('/ 0+

(6=&(.+

(.4/1O+ 0/. 6+*(&'+'. ( .>+ 6+)'=>1+,;/M + >*'1'J+,;/ 0+ :(&&+6()*+ ( 0/.

(N>'=+6()*/. 6+'. +=&/=&'+0/. Q (E(4>,;/ 0( 4+0+ *+&(:+M 0(5(&7 .(& =&(/4>=+,;/

=(&6+)()*( 0/. :/&6+0/&(.6/)'*/&(.


13/67

CENFIM 7

4$ 5;7;,5- Q. /=(&+,-(. + (E(4>*+&M +..'6 4/6/M 0/.

(N>'=+6()*/. ( +4(..2&'/.M 4/).*'*>' >6+ (*+=+ :>)0+6()*+1M =+&+ + &(+1'J+,;/ 0( >6

L/6 *&+L+1O/

&(6/.M 0( .(3>'0+M 0(:')'& / 6+*(&'+1 + 6+N>')+&M +. :(&&+6()*+. 0( 4/&*(M + >*'1'J+&M

+..'6 4/6/M /. (N>'=+6()*/. ( +4(..2&'/.

.*+. 0(:')',-(. =/0(&;/ .(& +1*(&+0+.M 0(.0( N>( *()O+6 + +=&/5+,;/ 0/ :/&6+0/&

6/)'*/&

(-,,

,/ T # /> T # +,/. +/ 4+&L/)/M 6+4'/.

5- :-

(5(6 .(& +0(N>+0+. +/. (E(&4B4'/. =&/=/.*/.M 0( +4/&0/ 4/6 +. /=(&+,-(. +&(+1'J+&

>=/&*(. 4/6 =1+N>(*(.M =+&+ 0(.L+.*( ( +4+L+6()*/

,- - =5- :-

. (&&+6()*+. =/0(&;/ .(& '6/L'1'J+0+.M 0'&(4*+6()*(M )+ */&&( =/&*+:(&&+6()*+.

/> (6 +4(..2&'/. C*/&&(*+.DM 6+'. 6/0(&)/.M 0( 6>0+),+ &7='0+M *'=/ 13&+ #$ />6(.*&+

/*+K &(4/6()0+.( >6+ &(5'.;/ 0/. 20>1/. +)*(&'/&(. C+)>+1 0( /&)(+6()*/

7.'4/D

,- - -,, *+,5

>4O+. >)'5(&.+'. 0( /> 3&+6=/.


14/67

CENFIM 8

&+*/ 0( 4+5+1')O/M =+&+ */&)(+6()*/ ()*&( =/)*/.

.+,=,:!" :-

+&+ + 6+N>')+3(6 0( +,/M &(4/6()0+.( + >*'1'J+,;/ 0( 21(/ ./1S5(1

*+,5-

+&+ + (E(4>,;/ 0/. (E(&4B4'/. N>( .(&;/ =&/=/.*/.M 6+'. Q :&()*(M 0(5(6 .(&

>*'1'J+0/. */&)/. 6(4R)'4/. =+&+1(1/.M =&(:(&()4'+16()*(M 4/6 L+&&+6()*/.

=&'.67*'4/.

7:, -!" ;5!

(4/6()0+.( + 4/).>1*+ 0+. &(.=(4*'5+. *+L(1+. ( 7L+4/.M N>( 4/).*+6 )/.

20>1/. +)*(&'/&(.

9+5! /,9,5 ,-

(5(6 .(& *'0+. (6 4/)*+M +. &(4/6()0+,-(. 0( (3>&+),+ ( !'3'()(M )+

6+)'=>1+,;/ ( 4/)0>,;/ 0( 67N>')+.:(&&+6()*+M +..'6 4/6/M 0(5(6 .(& >*'1'J+0/.

/. U. +0(N>+0/. CN>'=+6()*/. 0( &/*(4,;/ )0'5'0>+1D

(4/6()0+.(M 6+'. >6+ 5(JM N>( */0+. (.*+. /=(&+,-(. .(P+6 +4/6=+)O+0+. (

/&'()*+0+. =(1/ &(.=(4*'5/ :/&6+0/& 6/)'*/&M / N>+1 =/0(&7 +1*(&+& + .(N>V)4'+ (

0(.()5/15'6()*/ 0+. /=(&+,-(. +=&(.()*+0+.M .( *+1 .( P>.*':'4+&

4> 55- 85,:

4>4 =,5,!"

*/&)(+6()*/ 42)'4/M 4/).'.*( )+ (E(4>,;/ 0( .21'0/. 0( &(5/1>,;/M 4>P+. 3(&+*&'J(.

);/ .;/ =+&+1(1+.M 6+. N>( .( ()4/)*&+6 )>6 =/)*/M 4O+6+0/ 5,;/ 0( *&/)4/. 0( 4/)(M

N>(M (6 1')3>+3(6 /:'4')+1M .( 0(.'3)+6 +=()+. =/& ?:5@


15/67

CENFIM 9

/)( 0( &(5/1>,;/ 6 4/)( 0( &(5/1>,;/M < / .21'0/ 3(&+0/ =/& >6 *&'R)3>1/

&(4*R)3>1/M N>( &/0+ (6 */&)/ 0( >6 0/. 1+0/. 0/ R)3>1/ &(4*/ C4+*(*/DM / N>+1

4/).*'*>' / ('E/ @W 0/ 4/)(

X Y

&/)4/ 0( 4/)( 6 *&/)4/ 0( 4/)(M < / .21'0/ 3(&+0/ =(1+ &/*+,;/ 0( >6 *&+=' / ('E/ 0/ *&/)4/ 0( 4/)(

O

. 4/)(. 6+'. >.>+'.M (.*;/ )/&6+1'J+0/.M *()0/.( :'E+0/ +. 0(.'3)+,-(. 0(

X4/)'4'0+0(Y /> X4/)( K T XM 0( ')41')+,;/ /> 0(41'5( K @

..'6M )>6+ =(,+ 42)'4+M 0()/6')+.( 4/)'4'0+0(M +/ N>/4'()*( 0+ 0':(&(),+ 0/.

0'R6(*&/.M 6+'/& ( 6()/&M =(1/ 4/6=&'6()*/ 0/ 4/)(

.*( 5+1/& =/0( (E=&'6'&.( (6 =(&4()*+3(6M 6+. < 6+'. 5>13+& ')0'4+&.( + 3&+)0(J+

4/)( K TM ./L&( + 1')O+ 0( ('E/ =&')4'=+1M .'3)':'4+)0/ N>( / 0'R6(*&/ 0+ .(4,;/ 0/

4/)(M 5+&'+ 0( 66M =+&+ >6 4/6=&'6()*/ 0( T 66 C'3 D


16/67

CENFIM 10

'3 /)( /> /)'4'0+0(M KT

')41')+,;/ /> 0(41'5(M < / N>/4'()*( 0+ 0':(&(),+ 0/. &+'/.M 6+'/& ( 6()/&M =(1/

4/6=&'6()*/ /> +1*>&+ 0/ 4/)(

/&&(.=/)0(M (6 *&'3/)/6(*&'+M Q *+)3()*( C*3D 0/ R)3>1/ :/&6+0/ CD /> R)3>1/ 0(

')41')+,;/M N>( < '3>+1 + 6(*+0( 0/ R)3>1/ )/ 5+1 + 6(*+0( 0+ 4/)'4'0+0(

/0(.( (E=&'6'&M *+6L=(&'/& 0/ 0(.()O/M 4/6/ .( =/0( 5(& )+ '3 K

'3 )41')+,;/ /> 0(41'5( KE


17/67

CENFIM 11

(.*( 6/0/M + ')41')+,;/ K @ .'3)':'4+M N>( / &+'/ 0+ .(4,;/ 0/ 4/)(M 5+&'+ 0( 66M

=+&+ >6 4/6=&'6()*/ 4/&&(.=/)0()*( + @ 66

>=/)O+6/.M N>( =&(*()0(6/. 0(*(&6')+& + 4/)'4'0+0(M + ')41')+,;/ ( / R)3>1/ 0/5


18/67

CENFIM 12

4>4$ ()- -8,

E'.*(6 =&/4(../.M =+&+ + &(+1'J+,;/ 0/ */&)(+6()*/ 42)'4/K

/& /&'()*+,;/ 0/ 4+&&/ .>=(&'/& =/&*+:(&&+6()*+.

/& 0(.1/4+,;/ 0/ 4+L(,/*( 625(1

/6 + &+ ')41')75(1 ( 3&+0>+0+ C&+ 0( 4/)(.D

/& =(,+ +0&;/

F>+1N>(& N>( .(P+ / =&/4(../ 0( */&)(+6()*/ 42)'4/M >*'1'J+0/M / 3>6( 0+ :(&&+6()*+

0(5( ()4/)*&+&.(M &'3/&/.+6()*(M Q +1*>&+ 0/ ('E/ 0/. =/)*/.M 4+./ 4/)*&7&'/M / 4/)(

/L*'0/ );/ .(&7M (E+4*+6()*(M / 4/)( N>( .( =&(*()0(

.>=(&:B4'( */&)(+0+ *(&'+M 4/6/ 6(&'0'+)/M );/ >6+ &(4*+M 6+. >6+ 4>&5+

>&+)*( / =&/4(../ 0( 6+N>')+,;/M =/0(6/. =&(5(& / )S6(&/ 0( =+..+3(). +

(:(4*>+&M (6 N>+1N>(& 0/. =&/4(../.M 0+ .(3>')*( :/&6+ C'3 DK

'3

I +J(& >6+ =+..+3(6M 4/6 >6+ =&/:>)0'0+0( N>+1N>(& ( 6(0'& + 0'.*R)4'+


19/67

CENFIM 13

I /1/4+& / 1'6L/ 0/ *+6L/&M (6 J(&/M +)>1+)0/ +. :/13+.

I 5+),+& >6 )S6(&/ .'6=1(. 0( 0'5'.-(. $ ( (E(4>*+& >6+ =+..+3(6 (0'&

+ 0'.*R)4'+

I >L*&+'& 0( M + N>+)*'0+0( )4/)*&+.( + 6(0'0+ 0( %M9 66

#I (*(&6')+& / 4/6=&'6()*/ + */&)(+&M =+&+ +4+L+& / 4/)(

@ [ [ $M 66

%I .*+L(1(4(& >6+ &(3&+ 0( *&V. .'6=1(.

+ %M9 66 0( 4/6=&'6()*/ 0/ 4/)( 4/&&(.=/)0(6 $ 0'5'.-(.

+ $M 66 X X X X 4/&&(.=/)0(6 0'5'.-(.

10,2 x 10N = = 15 divises

6,8

8I \M =/&*+)*/M )(4(..7&'/ 0(.1/4+& + (.=(&+ *&+).5(&.+1M 0( 6+'. # 0'5'.-(.

2 55- :85,: ,5-!" :


20/67

CENFIM 14

>.*':'4+,;/ 0+ :2&6>1+ R)3>1/ CR)3>1/ 0( ')41')+,;/ 0+ 4/&&(0',+ 0/ 4+&&/

=/&*+:(&&+6()*+.DM < '3>+1 +/ R)3>1/ ] C.(6'R)3>1/ )/ 5)0/ + '3

D - d2 D - d

tg = =L 2 L

'3

E(6=1/ )>6*+&

/ 4/)( 0+ '3 #

'3 #


21/67

CENFIM 15

D d 60 - 25

tg = = = 0,875

2 L 2 x 20

e = 41 10 (ver tabela de tangentes)

/*+K .(3>)0/ /. 4+./.M + 4/&&(0',+ 0/ 4+&&/M +/ 3'&+&M =/0( */6+& 57&'+. /&'()*+,-(.

C'3. % ( 8D

'3 % '3 8

I +./ 4/)( < 0(:')'0/ =(1+ .>+ 4/)'4'0+0( 4M / 0'R6(*&/ ( / 4/6=&'6()*/

c

Frmula 2: tg = donde se tira 2

E(6=1/ )>61/ 0( ')41')+,;/ + 0+& Q 4/&&(0',+ 0/ 4+&&/ =/&*+:(&&+6()*+.M =+&+

*/&)(+& / 4/)( &(=&(.()*+0/ )+ '3 9

/)'4'0+0( $ Z [ $M$

c 0,10

tg = = = 0, 052 2

= 2 52 (tabela das tangentes)


22/67

CENFIM 16

42 5 *+5 :5,:,

+ 6+'/& =+&*( 0/. 4+./.M /. 4/)(. 0( +4/=1+6()*/M *V6 >6+ =(N>()+ 4/)'4'0+0(

(.*(. 4+./.M 0(5(6 +=1'4+&.( :2&6>1+. &7='0+.M N>( 0;/M 0'&(4*+6()*(M / R)3>1/ 0(

')41')+,;/M (6 3&+>. ( .>L0'5'.-(. 0(4'6+'. 0/ 3&+>M 4/6 >6+ +=&/E'6+,;/

.>:'4'()*(

;/ :2&6>1+. =&7*'4+.M N>( 0'.=().+6 / &(4>&./ + >6+ *+L(1+ 0( *+)3()*(.

.*+ =&7*'4+M .2 < +4('*75(1 =+&+ /. 4/)(. N>( );/ >1*&+=+..+6 % Z 0( 4/)'4'0+0(

CR)3>1/ )/ 56 R)3>1/ 0( ')41')+,;/

0+ 4/&&(0',+M 0( $I ^M )/ 67E'6/ C*+)3()*( 4/&&(.=/)0()*( [ $M9D

4'6+ 0(.*(. 5+1/&(.M / (&&/M N>( +>6()*+ 4/6 / R)3>1/M */&)+.( 6>'*/ '6=/&*+)*(

+&+ + .>+ (E(4>,;/M =/0(6 0+&.( 4+./.K

I +./ 4/)( < 0(:')'0/ =(1/. .(>. 0'R6(*&/. ( =(1/ .(> 4/6=&'6()*/

D - d

Frmula 1 = x 28,65 (- ngulo de inclinao)

L

=1'4+,;/ (*(&6')+& / R)3>1/ 0( ')41')+,;/ 0+ 4/&&(0',+ 0/ 4+&&/ =/&*+

:(&&+6()*+.M =+&+ (E(4>*+& / 4/)( ')*(&'/& 0+ '3 ?

'3 ? >6( 0'&'3'0/ =+&+ L+'E/ +*+4+)0/ Q 0'&('*+ 0+ =(&:>&+,;/


23/67

CENFIM 17

28 - 23

= 28,65 x = 28,65 x 0,25 = 7, 16 (ler 7 e 16 centsimos do grau) ou20

16 x 607 + = 7 9

100

I +./ 4/)( < 0(:')'0/ =(1+ .>+ 4/)'4'0+0(

Frmula 2 : = c x 28,65 (- ngulo de inclinao)

=1'4+,;/ +0/ >6 4/)( 4/6 >6+ 4/)'4'0+0( 0( # Z C'3 $DM 0(*(&6')+& /

R)3>1/ 0( ')41')+,;/ 0+ 4/&&(0',+ 0/ 4+&&/

/)'4'0+0( # Z [ $M#

= c x 28,65 = 0,15 x 28,65 = 4,29 (4 e 29 centsimos do grau)

29 x 60

= 4 + = 4 17100

'3 $

>.*':'4+,;/ 0+ :2&6>1+ +&+ R)3>1/. =(N>()/.M +*< $IM =/0(.(M .(6 (&&/

+=&(4'75(1M 4/):>)0'& / 4/6=&'6()*/ 0/ +&4/ +LM 4/6 + *+)3()*( 0/ R)3>1/ C'3

D


24/67

CENFIM 18

(P+ >6+ 4'&4>):(&V)4'+ 0( &+'/ [

.(> 4/6=&'6()*/ 6(0(

'3

>6 R)3>1/ +/ 4()*&/M IM 4/&&(.=/)0( >6

+&4/ +L 0( 4/6=&'6()*/ E

2 R

x = x 360

360 x x 360 x x

= = ( por ser R = 1)

2 R 2

360

= x x = 57,29 x x2

M =/'. N>( +*< 4(&4+ 0( $IM .( =/0( 4/):>)0'& / +&4/ ( + *+)3()*( 0/ R)3>1/ M =/0(

(.4&(5(&.(K

D d c

= 57,29 x tg ou tg = =2L 2

D d D - d = 57,29 = 28,65 ou ainda

2 L L

c

= 57,29 = 28,65 c2

/*+K 4/6=&'6()*/ 0( >6 +&4/ 4/&&(.=/)0()*( + >6 R)3>1/ 0( $IM < '3>+1 +

$M8# C.>=/.*/ / [ D ( / 4/6=&'6()*/ 0+ *+)3()*( '3>+1 + $M8%M /> .(P+M >6+

0':(&(),+ 0(


25/67

CENFIM 19

$M 8% $M 8# [ $M$$9

4/&&(.=/)0()*( + >6 (&&/ 0( 4(&4+ 0( %UM =&+*'4+6()*( 0(.=&(J75(1 K (&&/ N>( 1*&+=+..+ U

2 7:!" :!- 8;7

.*( =&/4(../ =(&6'*( / */&)(+6()*/ +>*/67*'4/M =(1/ 0(.1/4+6()*/ 0/ 4+&&/

1/)3'*>0')+1 ( / 0+ (E(4>,;/ 0( 4/)(. 0( &+J/75('. 4/6=&'6()*/.

(6M 4/6/ 0(.5+)*+3(6M */&)(+& 4/)(. (E*(&'/&(. 0( =/>4+ 4/)'4'0+0(M =/'. /

0(.+1')O+6()*/ 0/ 4+L(,/*( 625(1 );/ 5+'M 3(&+16()*(M +1P(',;/ 0+ =(,+ .(& 0(:('*>/.+ C0(5'0/ +/ 0(.+1')O+6()*/DM /. =/)*/.

42)'4/. 0( 4()*&+3(6M ./:&(6 0(:/&6+,-(.M / N>( '6=1'4+ 4/&&(4,-(. 4/).*+)*(.M )/

&(+=(&*/ 0/ 4+L(,/*( 625(1

+1 +/ .(6'

('E/ )/ 5


26/67

CENFIM 20

0(.1/4+6()*/ M 0/ 4/)*&+=/)*/M 4+14>1+.( =(&=()0'4>1+&6()*( +

/ *&'R)3>1/ &(4*R)3>1/ []K

[ .() [ .()

6+.M =+&+ /. =(N>()/. R)3>1/. C+*< $IDM =/0(.( 4/):>)0'& + *+)3()*( 4/6 / .()/

0/ R)3>1/ C/>M / N>( < / 6(.6/M ( '3 DM 0( 6/0/ N>( K

x = L . tg

D d c

Ora, tg = = (frmulas conhecidas)2 l 2

'3

/& 4/).(3>')*(M .(&7 :74'1 4/)O(4(& / 0(.1/4+6()*/ + '6=&'6'& +/ 4/)*&+=/)*/M .(P+

N>+)0/ .( 0;/ +. 0'6().-(. 0/ 4/)(M .(P+ N>+)0/ < 0+0+ + 4/)'4'0+0( (M L(6

()*()0'0/M / 4/6=&'6()*/ */*+1 0+ =(,+

I +./ 4/)( < 0(:')'0/ =(1+. .>+. 0'6().-(.

D dFrmula 1 : x = x L

2 l

I +./ 4/)( < 0(:')'0/ =(1+ .>+ 4/)'4'0+0(

cFrmula 2 : x = x L

2


27/67

CENFIM 21

=1'4+,-(.

I E(6=1/ +14>1+& / 0(.+1')O+6()*/ 0/ 4/)*&+=/)*/M =+&+ */&)(+& >6 4/)(

4/6 +. .(3>')*(. 0'6().-(.K

[ 9 66 0 [ # 66 [ $$ 66 1 [ # 66

=1'4+)0/ + :2&6>1+ K

28 25x = x 300 = 0,012 x 300 = 3,6 mm

2 x 125

I E(6=1/ +0/ >6 4/)(M 4/6 + 4/)'4'0+0( 0( #Z C$M$#DM 4+14>1+& /

0(.+1')O+6()*/ 0/ 4/)*&+=/)*/M .+L()0/ N>( / 4/6=&'6()*/ */*+1 0+ =(,+ < 0( $$

66

=1'4+)0/ + :2&6>1+ K

0, 05x = x 200 = 0,025 x 200 = 5 mm

27,B!" ). 4+L(,/*(. 625('. (.*;/ 6>)'0/. 0>6+ 3&+0>+,;/ .'*>+0+ )+ L+.(M 4/6 )2)'/

=/& 4'6+ /> 0>6 6/.*&+0/& 4/6 =/)*('&/M 4/1/4+0/ ./L&( / ('E/ 0/ =+&+:>./ 0(

0(.+1')O+6()*/M =(&6'*')0/ 1(& + 6(0'0+M 0'&(4*+6()*(M (6 :&+4,;/ 0( 6'1B6(*&/

.*/ +>6()*+M 4(&*+6()*(M + =&(4'.;/ 0+ &(3>1+,;/

/ ()*+)*/M =/0(6 =_&.( +13>6+. &(.(&5+. K =+&+ &(+1'J+& / 0(.+1')O+6()*/M .+ 0+ =/..B5(1 :/13+M ()*&( +. 3>'+. 0/ L+&&+6()*/M + L+.( =/0( :'4+&

'6/L'1'J+0+M 4/6 >6+ 1'3('&+ /L1'N>'0+0( (6 &(1+,;/ Q .>+ =&'6('&+ =/.',;/

+N>' &(.>1*+ >6 0(.5'/ 0/ 4/)*&+=/)*/ (M =/& 4/).(3>')*(M >6 (&&/ )/ R)3>1/ 0/

4/)(

/)*>0/M (.*( 4/)*&+*(6=/ );/ < 0( &(4(+&M .( + 3>'+ 0/ +L(,/*( 625(1 :/&

=&'.67*'4+


28/67

CENFIM 22

2 , )9+ 5:7,5(

+4/6=+)O+ + 67N>')+

\ >*'1'J+0/ 0+ .(3>')*( :/&6+ C'3 DK

(=/'. 0( 0(.+=(&*+& / =+&+:>./ M N>( .>P('*+ + =/&4+ 0/ =+&+:>./ *&+).5(&.+1M +/

4+&&/ ! C=+&+ 1'L(&*+& / 4+&&/ < )(4(..7&'/M (6 4(&*/. 4+./.M 0(.6/)*+&

4/6=1(*+6()*(M / :>./ 0( 4/6+)0/DM :'E+.( / *'&+)*( 0( +4/=1+6()*/ M +/ 4+&&/ !

6 .(3>'0+M :'E+.( + *+L(1+ 3&+0>+0+ M +/ L+&&+6()*/ M =/& ')*(&6+1M .( 0(.1/4+ / ')0'4+0/&

M ./1'07&'/ 4/6 / *'&+)*(

')41')+,;/ 0+ &+ M =/0( 5+&'+& .(3>)0/ / R)3>1/ M + :/&6+& 4/6 + =(,+

'3

+15/ )/ 4+./ 0( >6 */&)/ 6>)'0/ 0( 0>=1/ 4+&&/M 4/6 3>'+. /&*/3/)+'.M '.*/ 1/ &(4*/M 4/6/ P7 );/ .( 0'.=-( 0/ 4+&&/ *&+).5(&.+1M =+&+ (:(4*>+& =+..+3(). (6

=&/:>)0'0+0(M 4/1/4+.( + 4/&&(0',+ =/&*+:(&&+6()*+.M =(&=()0'4>1+& +/ ('E/ 0/ */&)/

..'6M / 4+&&/ =&')4'=+1M 0(.1/4+)0/.(M +&&+.*+ 4/6 (1( / ')0'4+0/&

')0'4+0/& M =/& .>+ 5(JM .(3>')0/ / 4+6')O/ N>( 1O( '6=-( + &+ ')41')+0+ M

0(.1/4+M *&+).5(&.+16()*(M / 4+&&/ ! (M +/ 6(.6/ *(6=/M + :(&&+6()*+


29/67

CENFIM 23

0(.1/4+6()*/ +)3>1+&M 0+ &+ 0( .>*+6()*/ M < 1'6'*+0/ +M 4(&4+ 0( #IM =+&+

>6 1+0/ ( 0( $IM =+&+ / 1+0/ /=/.*/

1*&+=+..+& (.*(. 5+1/&(. +)3>1+&(.M =/0(&7 =&/5/4+& / (6=()+6()*/ 0/ ')0'4+0/& )+

3>'+

')41')+,;/ 0+ &+ 0( 3>'+M 4+14>1+.( =/& 6('/ 0+. :2&6>1+. ')0'4+0+. )/

*/&)(+6()*/ 42)'4/M =/& /&'()*+,;/ 0/ 4+&&/

Para x > 10 D d

tg =2 L

Para x < 10 D d

= x 28,65L

2 ! "

/0(6M *+6L*/6+*'4+6()*(M .>=(&:B4'(. 42)'4+. 0( 3&+)0(

4/6=&'6()*/M =/& 6('/ 0/ 0'.=/.'*'5/ &(=&(.()*+0/ )+ '3 #M N>( /L&'3+ + 4/).*&>'&M

=+&+ 4+0+ 4+./M >6 6/0(1/ C=+0&;/D (6 +,/ *(6=(&+0/M 4/6 / 0(41'5( 4/)5()'()*(

.*+ =(,+ =+0&;/ C&(=&/0>*/&DM (.*7 :'E+M )>6+ (E*&(6'0+0(M =/& >6 ('E/ +M

./L&( >6+ L&+,+0('&+ M '6/L'1'J+0+ )/ L+&&+6()*/ (6 :/&6+ 0( 1>)(*+

/>*&+ (E*&(6'0+0( (.*7 1'5&( ( +=/'+0+ )+ 4/&&(0',+ *&+).5(&.+1

'3 #


30/67

CENFIM 24

/6 / =+&+:>./M 0( +&&+.*/ 0/ 4+&&/ *&+).5(&.+1M 1(5+)*+0/M ')*&/0>J.( )+ .>+ &/.4+M

>6+ O+.*( :'1(*+0+M N>( +*&+5(..+ 1'5&(6()*(M / 4/&=/ M 0/ 4+&&/ =&')4'=+1

6+ =/&4+ M 6(*'0+ (6 M =(&6'*( &(3>1+& + &(+4,;/ 0>6+ 6/1+

=/'+)0/.( )/ 4+&&/ =&')4'=+1 M (.*+ 6/1+ '6=(1(M =+&+ *&7.M + =/&4+ M + O+.*(

(M =/& 4/).(3>')*(M + 4/&&(0',+ !M 4>P/ =/)*('&/ M 5(6 +=/'+&.( ./L&( / =1+)/

')41')+0/ 0/ &(=&/0>*/& C=+0&;/D

6 I =/)*('&/M M N>( =/..>' >6+ .+=+*+ M :'E+ )+ 3>'+ *&+).5(&.+1M 6+)**/&M =+&+1(1/ Q. 3>'+. 0/ L+&&+6()*/

6+ 1'3('&+ /5+1'J+,;/M 0/ :>&/ 0+ 4+5'1O+ +M :+4'1'*+ + &(+1'J+,;/ 0/ =+&+1(1'.6/

(.1/4+)0/.( / 4+&&/ =&')4'=+1M + :(&&+6()*+ &(=&/0>J )+ =(,+M / 0(41'5( 0/ 6/0(1/

&(=&/0>*/&

/0(6 .>L.*'*>'&.(M 4/6 5+)*+3(6M /. =/)*('&/.M =/& ')0'4+0/&(. &(4*+)3>1+&(. M

6/)*+0/. ./L&( / ('E/

C:+!"

/&)(+& >6 4/)(M 4/6 +. .(3>')*(. 0'6().-(.K

[ 8$ 66 0 [ #$ 66 [ $$ 66

/).*&>'& >6 &(=&/0>*/& 6+'. 4/6=&'0/ N>( M =/& (E(6=1/M 4/6 %$$ 66

0(41'5( 0+ 3(&+*&'JM ./L&( / ('E/M < 0(K

D d 70 - 50

2 2= = 0,025

L 400

F>(& 0'J(&M N>( )>6 4/6=&'6()*/ 0( 66M + 6(0'0+ 0+ ')41')+,;/ < 0( $M$# 66

/> 0( M# 66M )>6 4/6=&'6()*/ 0( $$ 66

:5

(41'5( < / 5+1/& 0+ ')41')+,;/ 0>6+ .>=(&:B4'( =1+)+M (6 &(1+,;/ + >6 =1+)/ 0(

L+.(


31/67

CENFIM 25

(*(&6')+.( =(1+ *+)3()*( 0/ R)3>1/ C'3 % +DM &(.>1*+)*( 0+ ')*(&4(=,;/M 0+

.>=(&:B4'( =1+)+M 4/6 / =1+)/ 0( L+.(

'3 %

/6+& >6+ =1+4+ 0( 0'6().-(. .>:'4'()*(.M 0(.L+.*+& 4>'0+0/.+6()*(M >6 1+0/ = N

C'3 %LD

( .(3>'0+M *&+,+&M 4/6 / (.N>+0&/ 0( ()4/.*/M 0/'. *&+,/. = 6 ( N ) M

=(&=()0'4>1+&(. + = N ( 0'.*+)*(. %$$ 66

(5+)*+& 0>6 1+0/M >6+ +1*>&+ 4/)5()'()*(M = 6 ( 0/ />*&/M >6+ +1*>&+ N )M *+1 N>(

N ) [ = 6 C = N E 0(41'5(D

N ) [ = 6 C%$$ E $M$#D [ = 6 # 66

+1*+M +=()+.M 4/).*&>'& / =1+)/ ')41')+0/ C&+6=+D 6 )

4D ,=,:!" 5-7

4D4 ,=,:!" 9+7!" 5:7,5!" ,!

/6 + =(,+ C/> 4/6 >6+ L+&&+ 0/ 6(.6/ 4/6=&'6()*/D ()*&( =/)*/.M */&)(+0+M

=(&:('*+6()*( 4'1B)0&'4+M 0(.1/4+.( + :(&&+6()*+ /> >6 4/6=+&+0/&M / N>( < 6+'.

4/&&(4*/M 0(=/'. 0( / *(& =/.*/ (6 4/)*+4*/ 4/6 + =(,+M )>6 4/6=&'6()*/ 7EM

&(3'.*+0/ )/ 6/.*&+0/& C'3 8D ( 5(&':'4+&.(7M =(1+. ')0'4+,-(. 0/ 6/.*&+0/& 0/

4+&&/ *&+).5(&.+1 C/> =(1+. N>( .;/ :/&)(4'0+. =(1/ 4/6=+&+0/&DM .( + :(&&+6()*+

(:(4*>/>M 0( :+4*/M / +5+),/ M 4+14>1+0/ =(1+ :2&6>1+K

e = l x sen (1)


32/67

CENFIM 26

(6 N>( M R)3>1/ 0( ')41')+,;/ 0+ 4/&&(0',+M < 0(*(&6')+0/ =/& >6+ 0+. :2&6>1+. P7

0(.4&'*+. +)*(&'/&6()*(

'3 8

0/=*+& =+&+ 7EM >6+ 4/*+ ')*('&+ C>6 6S1*'=1/ 0/ =+../ 0/ =+&+:>./DM *;/ 3&+)0(M

N>+)*/ =/..B5(1M =+&+ :+4'1'*+& ( */&)+& /. 4714>1/. 6+'. =&(4'./.

/& (.*+ &+J;/M *+6L+0/. .(&;/ 1(5+0/. + J(&/M +)*(. 0+.

6+)/L&+. 0( 4/)*&/1/ 0/ 0(.1/4+6()*/ 0+ :(&&+6()*+

/& (E(6=1/M 0(=/'. 0( .( *(& 1(5+0/ + :(&&+6()*+M +*< :'4+& *+)3()*( Q =(,+M )/ :'6

0/ =(&4>&./ 7E C'3 9DM /L.(&5+6.( $ 0'5'.-(. ./L&( / 6/.*&+0/& ')0'4+0/& 0/

0(.1/4+6()*/

( + &/*+,;/M 0( >6+ 0'5'.;/M 0'+)*( 0+ 6+&4+ :'E+ M 4/&&(.=/)0( + >6

0(.1/4+6()*/ 0( $M$# 66 C#$$ 0( 66DM 4/)41>'.(M N>( + :(&&+6()*+ .( 0(.1/4/>

F M N>( 0(5(&7 (.*+& 0( +4/&0/ 4/6 / 5+1/& 0( M /L*'0/ +*&+51+

CD

+./ .(P+ 0':(&()*(M 0(5(.( 4/&&'3'&M (6 4/):/&6'0+0(M + &(3>1+,;/ 0+ 4/&&(0',+ 0/

4+&&/ =/&*+ :(&&+6()*+

'3 9


33/67

CENFIM 27

4D4$ ,=,:!" 5,:,

\ ')0'.=().75(1 5(&':'4+& + 4/)'4'0+0( 0+ .>=(&:B4'( 42)'4+M +)*(. 0( +*')3'& + 4/*+

0(:')'*'5+ ( 0( 4/&&'3'&M .( :/& 4+./ 0'../M + ')41')+,;/ 0+ 4/&&(0',+ =/&*+ :(&&+6()*+

/> / 0(.+1')O+6()*/ 0/ 4+L(,/*( 625(1 /> /. 2&3;/. ')*(&(..+0/.

=+0&;/ >*'1'J+0/ 6 4+1'L&+0/& 42)'4/ &(4*':'4+0/M 6+4O/ />

:V6(+ C'3 ?D /> .(P+M >6+ =(,+ 6+4O/ /> :V6(+M P7 */&)(+0+M N>( .( +P>.*+ Q =(,+

(6 4>&./ 0( (E(4>,;/

'3 ?

( );/ .( 5(&':'4+& )()O>6+ /.4'1+,;/M ()*&( >6+ ( />*&+ =(,+M +/ (:(4*>+&.( +=()(*&+,;/ C'3 $DM =/0( =+..+&.( Q /=(&+,;/ 0( &(+P>.*+6()*/

'3 $

6+&3(6 0( =()(*&+,;/M + &(.(&5+&M +)*(. 0/. ().+'/. 0( 4/6=&/5+,;/M 0(5( .(&

*+)*/ 6+'/&M N>+)*/ 6+'. =(N>()+ < + 4/)'4'0+0(M .()0/ + ')*&/0>,;/M )(.*( 4+./M

6>'*/


34/67

CENFIM 28

=&/)>)4'+0+ =+&+ >6+ =(N>()+ =&/:>)0'0+0( 0( =+..( K 66 =+&+ >6+ =&/:>)0'0+0(

0( =+..( 0( $M 66M )>6 4/)( 0( # Z 0( 4/)'4'0+0( C.(6'R)3>1/ )/ 54(..'5+.M .()0/ 4+0+

>6+ 0(1+. .(3>'0+ 0>6+ )/5+ 5(&':'4+,;/ )/ 4+1'L&(

+&+ (.*( (:('*/M *&+,+.( + 3'J /> 4/6 17='. 3&/../M 0/'. /> *&V. *&+,/. :')/.M .(3>)0/

/> 3(&+*&'J(. 0/ 4/)( 6+4O/

( .(3>'0+M ')*&/0>J.( (.*(M )+ =(&:>&+,;/ ( =&/4(0(.( +/ .(> 1()*/ */&)(+6()*/

( .( 4/).*+*+&M N>( /. *&+,/. );/ .( +=+3+&+6M + );/ .(& )>6+ 0+. (E*&(6'0+0(.M

+P>.*+.( 0(:')'*'5+6()*(M + =/.',;/ 0+ 4/&&(0',+ /> 0/ 4/)*&+=/)*/

(M =(1/ 4/)*&7&'/M /. *&+,/. :/&+6 +=+3+0/. /> +&&+.*+0/. + */0/ / 4/6=&'6()*/M /

+P>.*+6()*/ < 4/&&(4*/

(.*+ +=()+.M &(+1'J+& / *&+L+1O/ 0( +4+L+6()*/ )+ 4/*+ (E+4*+

-K ( /. *&+,/. .( +=+3+&+6M +/ 6(.6/ *(6=/M )+. (E*&(6'0+0(. 0/ 4/)( C'3

DM 0(5(.( 5(&':'4+& + &(3>1+,;/ 0/ :(&&/M (6 +1*>&+

'3


35/67

CENFIM 29

4D4> ,=,:!" 5-7 5

'57,

. .>=(&:B4'(. 42)'4+. 0( &(5/1>,;/M .;/ >*'1'J+0+. =+&+ /. ()4+L+0/>&/. 0( :(&&/. (

)/. 4/)P>)*/. 6(4R)'4/. 0(.6/)*75('.M =+&+ /. N>+'. .( (E'3( >6+ 4/)4()*&'4'0+0(

&'3/&/.+ 0/. (1(6()*/.

+ /:'4')+M + 6(0'0+ (E+4*+ 0+. =(,+. 42)'4+.M 4/).(3>(.( +*&+5 L'*/1+.D ( 4>)O+. =+0&;/M 0(

(E*&(6'0+0(. =+&+1(1+. C4O+6+0+. 4>)O+. 0( /O+)../)D

'3

6 3(&+1M 6(0(.( / 4/)( 6+4O/ ( +P>.*+.( (6 .(3>'0+M / 4/)( :V6(+M ./L&( /

6+4O/ 4/)O(4'0/

/. *&+L+1O/. (6 .

4+1'L&(. 6+4O/.M *(6=(&+0/. ( &(4*':'4+0/.

(E+6( 0'6().'/)+1M 0( >6 *&/)4/ 0( 4/)(M 4/6=/&*+ +. 0>+. /=(&+,-(. =&')4'=+'.

.(3>')*(.K

4/)*&/1/ 0+ 4/)'4'0+0( /> 0/ R)3>1/ `

6(0'0+ 0/ 0'R6(*&/ 0( =()(*&+,;/ 0>6+ .(4,;/ )/&6+1M 0( =/.',;/ 0(*(&6')+0+

(6 &(1+,;/ + >6+ 0+. L+.(.

(*(&6')+,;/ 0/ 0'R6(*&/ 6()/& 0( >6 4/)(M =/& 6(0'0+ ')0'&(4*+

+ '6=/..'L'1'0+0( 0( 6(0'& / 0'R6(*&/ 6()/& 0( >6 4/)(M ('. 4/6/ .( =/0( /=(&+&M

=+&+ 0(*(&6')+& .( (1( (.*7 )+ 6(0'0+ (E'3'0+K


36/67

CENFIM 30

=/'+& / 4/)( C'3 D ./L&( >6 4+1,/ C/> +=1'4+& >6+ +)'1O+ 4/)*&+ + :+4(

*(&6')+1 0+ L+.( 6()/&D

/& 6('/ 0>6+ 4&+5('&+M 4/6 +. (.=(&+. +=/'+0+. + 0'&('*/M ./L&( / 4+1,/ C/> 4/)*&+ +

+)'1O+DM 6+&4+& + 6(0'0+ 0UM 0/ 4/)(M +*()0()0/ Q (.=(..>&+ 0/. L'4/. 0/ 4+1'L&(M

4/6/ + :'3>&+ 6/.*&+

()0/ 4/)O(4'0/ 0 C5(& / 4714>1/ 0/. (1(6()*/. 0/ 4/)(M (6 :>),;/ 0( 5+1/&(.

4/)O(4'0/.D =/0(.(M 4/6 + :2&6>1+ .(3>')*(M .+L(& .( / 0'R6(*&/ 0+ L+.( 6()/&

(.*7M =&(4'.+6()*(M )+ 4/*+ =(0'0+M 4/).'0(&+)0/ 0U (6 :>),;/ 0( 0K

'3

0 (.*7 )+ 4/*+ .( 0U 6(0'&

(D d) x E (30 20) x 3,5d = d x = 20 + = 21, 09 mm

l 32

( / 4/)( < 0(:')'0/ =(1+ .>+ 4/)'4'0+0(

0U [ a C 1 D b

/> +')0+

0U [ 0 E C4 E D


37/67

CENFIM 31

,=,:!" ,H- + :5

(0'0+ =/& 6('/ 0( 4'1')0&/. *+)3()*(. C'3 D

6 4/)( (E*(&'/&M =/0( .(& 6(0'0/M >*'1'J+)0/ 0>+. L'*/1+. 4'1B)0&'4+.M =(&:('*+6()*(4+1'L&+0+.M 0( c 0U 0(:')'0/ ( 0>+. 4>)O+. C/O+)../)M 0( +1*>&+ OM +=&/=&'+0+D

'3

( .;/ +. 4/*+. + 1(& :/&+ 0+. L'*/1+. C'3 D

` [ .(6'R)3>1/ )/ 5


38/67

CENFIM 32

/ 4+./ 0( L'*/1+. 0'.=/.*+. ./L&( >6+ 0>=1+ .


39/67

CENFIM 33

5-7 :5,:,

.*( 4/)*&/1/ 0(5( =(&6'*'& 5(&':'4+& + 4/)'4'0+0( (6 4>&./ 0( :+L&'4+,;/M +)*(.

6(.6/ 0( /L*(& +. 4/*+. 0( &'3/&

/0(.(M )+ :+1*+ 0( =+0&;/M =+&+ 5(&':'4+,;/ 0+ 4/)'4'0+0(M >*'1'J+& >6 0/. 6')*(.K

(&':'4+,;/ =/& 6('/ 0( L'*/1+ ( 0( 4>)O+. C'3. # ( %D

(0(.( + 4/)'4'0+0( 4M 4/6 / 0'.=/.'*'5/ 0+. '3. # ( %M &(4/&&()0/ Q :2&6>1+

.(3>')*(K

X1 - X X1 - X

c = donde tg = c/2 =h1 - h 2 (h1 - h)

.()0/ ` / .(6'R)3>1/ )/ 5


40/67

CENFIM 34

,=,:!" + :5 5 -5 1,94 $I2

+&+ 4/)*&/1+& + 4/)'4'0+0( =/0(.(M 4/6 + =(,+ 4/1/4+0+ ()*&( =/)*/.M =&/4(0(& Q

5(&':'4+,;/ 4/6 :>)0+6()*/ )/ 66 4/6=+&+0/& )+ */&&( =/&*+:(&&+6()*+M 4/6 / =+1=+0/& &(3>1+0/M

(E+4*+6()*(M Q +1*>&+ 0/ ('E/ 0/. =/)*/.

(=/'. 0( *(& =/.*/ / =+1=+0/& (6 4/)*+4*/ 4/6 + =(,+M (6 ( *&+J'0/ / 0'.4/

3&+0>+0/ + J(&/M 0(.1/4+.( / 4+&&/ =&')4'=+1M Q 6;/M 0( >6 4/6=&'6()*/ M

1'3('&+6()*( '):(&'/& +/ 0/ 4/)( C4/6=&'6()*/ 4/)*&/1+0/ =/& 6('/ 0( >6+ 4>)O+ M

)+ 0'6().;/ 0(5'0+ /> 4/6 >6 ')0'4+0/& 0/. 4/6=&'6()*/.M .( / 4+&&/ =&')4'=+1 /

*'5(&D

'3 9

(&':'4+.(M ()*;/M =(1+. ')0'4+,-(. 0/ 4/6=+&+0/&M .( / =+1=+0/& (:(4*>/>M 0( :+4*/M

)/ 4/6=&'6()*/ M / 0(.1/4+6()*/ M 4/&&(.=/)0()*( Q 0':(&(),+ 0/. &+'/. 0/ 4/)(M

0(.1/4+6()*/ 4+14>1+0/ 4/6 >6+ 0+. :2&6>1+. .(3>')*(.K

D - d cx = x l ou x = x l

2 l 2

()0/ ( 0M / 0'R6(*&/ 0+ L+.( 6+'/& ( 0+ L+.( 6()/& 0/ 4/)( ( M 4/6=&'6()*/

/> +1*>&+ 0/ 4/)(

/*+ .*( 61+0/

(6 +1')O+6()*/M '.*/ 1+0/ + :'6 +..(3>&+& Q. .>=(&:B4'(. */&)(+0+.M >6+

4'1')0&'4'0+0( =(&:('*+


41/67

CENFIM 35

3$ ( JK

$4

$4 ,5-!6 (-789,:

(5'0/ Q (.=(4':'4'0+0( 0( 4(&*/. .(4*/&(. 0+. 4/).*&>,-(. 6(*+1/6(4R)'4+.M */&)+.(

)(4(..7&'/ N>( 4+0+ >6 0/. +..>)*/. .(P+ *&+*+0/ 0( :/&6+ .'6=1(.M 6+. 6>'*/

/LP(4*'5+M 0( 6+)('&+ + );/ 4/):>)0'&M )(6 4/6=1'4+&M / 0(.()5/15'6()*/ 0( 4+0+

:+.( 0/. (E(&4B4'/. =&/=/.*/.

+ =&7*'4+M (6 4/)*(E*/ 0( :/&6+,;/M .(&7 )(4(..7&'/ &(=(*'&M :&(N>()*(6()*(M /.

(E(&4B4'/.M =+&+ N>( / :/&6+)0/ =/..+ 4/&&'3'& /. (&&/. 6+'. :&(N>()*(.M 4/6 N>( .(

0(:&/)*(M + :'6 0( :'4+& 0(5'0+6()*( (.41+&(4'0/

. (E(&4B4'/. .(&;/ 0(6/).*&+0/.M =&'6('&+6()*(M =(1/ :/&6+0/&6/)'*/& (M 0(=/'.M

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(5( .(& .(6=&( )(4(..7&'/ &(4/&&(& +/. 0(.()O/. +=&(.()*+0/. )/. (E(&4B4'/. ( /

:/&6+0/&6/)'*/& 0(5(&7 +=&(.()*+& +. 5'.*+.M N>( ()*()0(& )(4(..7&'/M 0( 6/0/ +

(.41+&(4(& N>+1N>(& 0S5'0+ N>( / :/&6+)0/ =/..+ *(&

&(*()0(.(M +..'6M ')*&/0>J'& / :/&6+)0/ )/. =&/4(../. *(4)/123'4/. 6+'. 4/6=1(E/.M0( :/&6+ N>( =/..+ &(+1'J+& +. *+&(:+. N>( 6+'. *+&0( 5+' *(& 0( ():&()*+& )/ .('/ 0+

(6=&(.+

(.4/1O+ 0/. 6+*(&'+'. ( .>+ 6+)'=>1+,;/M + >*'1'J+,;/ 0+ :(&&+6()*+ ( 0/.

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=(&6+)()*( 0/. :/&6+0/&(.6/)'*/&(.


42/67

CENFIM 36

$4$ 5;7;,5- *+&M L(6 4/6/M 0/. (N>'=+6()*/. ( +4(..2&'/.M

4/).*'*>' >6+ (*+=+ :>)0+6()*+1M =+&+ + &(+1'J+,;/ 0( >6 L/6 *&+L+1O/

.*+. 0(:')',-(. =/0(&;/ .(& +1*(&+0+.M 0(.0( N>( *()O+6 + +=&/5+,;/ 0/ /&6+0/&

(-,,

,/ T # /> T # +,/. +/ 4+&L/)/M 6+4'/.

5- :-

(5(6 .(& +0(N>+0+. +/. (E(&4B4'/. =&/=/.*/.M 0( +4/&0/ 4/6 +. /=(&+,-(. +

&(+1'J+&

. .>=/&*(. 4/6 =1+N>(*(. +6/5B5('.M =+&+ 0(.L+.*( ( +4+L+6()*/M .;/ +.

:(&&+6()*+. 6+'. >*'1'J+0+.

,- - =5- -,, *+,5

)*&( =/)*/. 4/6 =&+*/ 0( 4+5+1')O/

>4O+. 0( 3&+6=/. ')0(=()0()*(.

/*+K &(4/6()0+.( >6+ &(5'.;/ 0/. 20>1/. +)*(&'/&(. C+)>+1 0( /&)(+6()*/

7.'4/D

,- - =5- :-

/&&(*+. :'E+. /> 0( 6>0+),+ &7='0+M *'=/ #$ />

.+,=,:!" :-

+&+ + 6+N>')+3(6 0( +,/M &(4/6()0+.( + >*'1'J+,;/ 0( 21(/ ./1S5(1


43/67

CENFIM 37

*+,5-

+&+ + (E(4>,;/ 0/. (E(&4B4'/. N>( .(&;/ =&/=/.*/.M 6+'. Q :&()*(M 0(5(6 .(&>*'1'J+0/. */&)/. 6(4R)'4/. =+&+1(1/.M =&(:(&()4'+16()*(M 4/6 L+&&+6()*/.

=&'.67*'4/.

7:, -!" ;5!

(4/6()0+.( + 4/).>1*+ 0+. &(.=(4*'5+. *+L(1+. ( 7L+4/.M N>( 4/).*+6 )/.

20>1/. +)*(&'/&(.

9+5! /,9,5 ,-

(5(6 .(& *'0+. (6 4/)*+M +. &(4/6()0+,-(. 0( (3>&+),+ ( !'3'()(M )+

6+)'=>1+,;/ ( 4/)0>,;/ 0( 67N>')+.:(&&+6()*+M +..'6 4/6/M 0(5(6 .(& >*'1'J+0/.

/. U. +0(N>+0/. CN>'=+6()*/. 0( &/*(4,;/ )0'5'0>+1D

(4/6()0+.(M 6+'. >6+ 5(JM N>( */0+. (.*+. /=(&+,-(. .(P+6 +4/6=+)O+0+. (

/&'()*+0+. =(1/ &(.=(4*'5/ :/&6+0/& 6/)'*/&M / N>+1 =/0(&7 +1*(&+& + .(N>V)4'+ (

0(.()5/15'6()*/ 0+. /=(&+,-(. +=&(.()*+0+.M .( *+1 .( P>.*':'4+&

$4> =,5,!6 8,:

*(&6/ X(E4V)*&'4/YM .'3)':'4+M X:/&+ 0/ 4()*&/Y

.*( 4/)4('*/M < L+.*+)*( '6=/&*+)*(M =/&N>( )/. 07 + =/..'L'1'0+0( 0( 4/).*&>,;/ 0(2&3;/. 6(4R)'4/.M N>( *&+).:/&6+6 / 6/5'6()*/ 0( &/*+,;/M (6 6/5'6()*/ 0( 5+'

5(6

+ '3 ?M 6/.*&+.( >6 (E(6=1/ 0+ +=1'4+,;/M 4/6 /. =/)*/. 0( &(:(&V)4'+ 6+'.

'6=/&*+)*(.


44/67

CENFIM 38

+D &+'/ 0( (E4()*&'4'0+0(

LD (.='3+. 0(.4()*&+0+.

4D 6/5'6()*/ 0( 5+'(5(6

'3 ? ('/ (E4V)*&'4/

.*( .'.*(6+ ()4/)*&+.(M );/ .2M )/. 6/*/&(. C4/)P>)*/ 4+6L/*+L'(1+DM =&().+.

6(4R)'4+.M 4/6/ )>6 .'6=1(. &(123'/ C6(4R)'4/D

$4D ()- -8,

$4D4 ,7L5,:

+D /& =/)*/. 0(.4()*&+0/.

LD /& +=(&*/ 0(.4()*&+0/

2 5- :5-

6+N>')+,;/ 0>6 5('/ (E4V)*&'4/M < :('*+ 0+ .(3>')*( 6+)('&+K

=(,+ < +=(&*+0+ )>6+ L>4O+ 0( *&V. 3&+6=/. ( */&)(+0+. +. :+4(. 0( */=/M

=/)0/+ )/ .(> 4/6=&'6()*/

(=/'. 0+ :>&+,;/M (6 +6L+. +. :+4(.M 0/. =/)*/. 0( 4()*&+3(6 4/&&(.=/)0()*(.M

0(.L+.*+.(M =&(5'+6()*(M / 0'R6(*&/ 6+'/&M =+&+ 4(&4+ 0( c

6 .(3>'0+M *&+,+6.( /. =/)*/. 0( 4()*&+3(6M =+&+ +. (.='3+. 0(.4()*&+0+. (

:>&+6.( (.*(. S1*'6/. C'3 D


45/67

CENFIM 39

M ! ,95!" ! M (-,7 (, +-

('/ (E4V)*&'4/ * c # E ##

'3 $ (.()O/ /:'4')+1

75 7A

-7A 5-

/&)(+& +. :+4(. :&/)*+'. =/)0/ + =(,+ )/ .(>

4/6=&'6()*/

(&&/ 0( :+4(P+&

'.=/& /. =/)*/. 0( 4()*&+3(6 =+&+ c &/4+ 0( 4()*&+& c66

(.L+.*+& ()*&( =/)*/. c (&&/ 0( 0(.L+.*+&

&+,+& ( :>&+& /. =/)*/. 0( 4()*&+3(6 =+&+ +.

(.='3+. 0(.4()*&+0+.

&+6')O/M 4/6=+../ 0(

&'.4+&M L&/4+ 0( 4()*&+&

# 4+L+6()*/ +/ */&)/ ()*&( =/)*/. (6 c (&&/ 0( */&)(+& 1'./

% (.L+.*+& ( +1'.+& +. (.='3+. (6 c $ (&&/. 0( 0(.L+.*+&M +1'.+&

( :+4(P+&


46/67

CENFIM 40

'3

*/&)(+6()*/ =&'0+M 0(.L+.*+6.( ( +1'.+6.(M >6+ +=2. + />*&+M +. 0>+. (.='3+.

'3 /)*/. 0( 4()*&+3(6 )/ 5('/ (E4V)*&'4/K

C+D &+'/ 0( (E4()*&'4'0+0(

CLD =/)*/ 0( 4()*&+3(6 =&')4'=+1

C4D =/)*/ 0( 4()*&+3(6 0+. (.='3+. 0(.1/4+0+.

(E4()*&'4+6()*(M (6 &(1+,;/ +/ =/)*/ 0( 4()*&+3(6

=&')4'=+1


47/67

CENFIM 41

F>+)0/ / &+'/ 0( (E4()*&'4'0+0( < .>:'4'()*(6()*( 3&+)0(M =/0(6 :+J(&.( +6L/. /.

=/)*/. 0( 4()*&+3(6 )(4(..7&'/. C'3 D

/&)('+.(M =&'6('&+6()*(M / 0'R6(*&/ 6+'/& ( (6 .(3>'0+ +. (.='3+. (E4V)*&'4+.

'3

'3

/)*+3(6 0>6 5('/ (E4V)*&'4/M 4/6 3&+)0( (E4()*&'4'0+0(

C+D */&)(+6()*/ 0/ 0'R6(*&/ 6+'/&

CLD */&)(+6()*/ 0+. (.='3+. 0(.4()*&+0+.

F>+)0/ .( *&+*+ 0( &+'/. 0( (E4()*&'4'0+0( =(N>()/.M +4+L+.(M =&'6('&+6()*(M +/

*/&)/M / 0'R6(*&/ 6+'/&

6 .(3>'0+M (1'6')+6.( =/& :+4(P+6()*/M /. =/)*/. 0( 4()*&+3(6 >*'1'J+0/. (

0'.=-(6.( ./L&( +. 0>+. :+4(. :&/)*+'.M /. =/)*/. 0( 4()*&+3(6 (E4V)*&'4/. C'3

#D

=(,+ (6 L&>*/M 0(5( *(& / 4/6=&'6()*/ .>:'4'()*(M =+&+ *+1


48/67

CENFIM 42

'3 # /)*+3(6 0( >6 5('/ (E4V)*&'4/M 4/6 &+'/ 0( (E4()*&'4'0+0( &(0>J'0/

&+,+3(6 +J.( 4/6 / 4/6=+../ 0( =/)*+. .(4+.

&+,+6.(M (6 +6L+. +. :+4(. :&/)*+'.M +. 4'&4>):(&V)4'+. 0( (E4()*&'4'0+0(

&+'/ 0+ 4'&4>):(&V)4'+M < '3>+1 +/ &+'/ 0+ (E4()*&'4'0+0(

4'&4>):(&V)4'+ =/0(M *+6L XL/4+0(1/L/Y

/6 / &'.4+0/& 0/ 3&+6')O/M 4/1/4+0/M (E+4*+6()*(M )+ +1*>&+ 0/ 4()*&/M *&+,+.( (6

4+0+ >6+ 0+. :+4(. :&/)*+'.M >6+ 1')O+

. =/)*/. 0( ')*(&.(4,;/ 0+. 1')O+. 0+ *&+,+3(6M 4/6 +. 4'&4>):(&V)4'+. 0(

(E4()*&'4'0+0(M .;/ /. =/)*/. N>( .( =&/4>&+6 /> .(P+M /. =/)*/. 0( 4()*&+3(6

(5( *(&.( (6 +*(),;/M N>( +. 0>+. 1')O+. O/&'J/)*+'. 0+ *&+,+3(6 5()O+6 + :'4+&

)>6 6(.6/ =1+)/ C'3 %D

'3 %


49/67

CENFIM 43

'E/ 4 >6 (E4V)*&'4/ 'E/ 4 0/'. (E4V)*&'4/. 'E/ 4N>+*&/ (E4V)*&'4/.

C+D CLD C4D

=/)*/ =&')4'=+1 =/)*/ (E4V)*&'4/ E4()*&'4'0+0(

'3 8

2 - :5-

+&+ (.*( *'=/ 0( 6+N>')+,;/M */0/ / =&/4(../ < '3>+1 +/ +)*(&'/&M ')41>.'5(M +

*&+,+3(6

(:'&+.(M N>( )(.*( .'.*(6+M +. =(,+. .;/ '6/L'1'J+0+. (6 L>4O+. 4/)4V)*&'4+.

(E4V)*&'4+.M N>( *V6 3&+6=/. 0( +=(&*/ ')0(=()0()*(.

=/)*/ 0( (E4()*&'4'0+0(M 0(*(&6')+.( =/& *&+,+3(6 />M 4/6 6+'. =&(4'.;/M

>*'1'J+)0/ / 4/6=+&+0/&

(.*( 4+./M / &+'/ 0( (E4()*&'4'0+0( < '3>+1 + 6(*+0( 0+ 0':(&(),+ /L*'0+ ( 1'0+ )/

4/6=+&+0/&

$4D4$ 7L-,: 1 ! (72

+&+ + (E(4>,;/ 0(.*+ :/&6+M >*'1'J+.( >6 0'.=/.'*'5/ +=1'4+0/ )/ */&)/ C'3 9DM

4>P/ :>)4'/)+6()*/ .( 0(.4&(5(K

'3 9


50/67

CENFIM 44

(E4V)*&'4/ 6/0(1/

(E4V)*&'4/ + =(&:'1+&M 6/)*+0/ ./L&( >6 6+)0&'1

.>=/&*( (6 *+6L/&M :/&6+)0/ (.=(&+

=(,+ 4/6 =+&+:>./M =+&+ / +P>.*+6()*/ 0/ :(&&/ (6 =&/:>)0'0+0(

'L(&*+& / 4+&&/ *&+).5(&.+1M 0/ .(> =+&+:>./ ( 1'371/ + >6 4/)*&+=/)*/ M =/&

')*(&6( =+..+ ./L&( >6+ =/1'+ 0(

3+&3+)*+ M 6/)*+0+ ./L&( >6+ 4O+=+ M :'E+ )/ :>&/M N>( .(&5( 0( 4+.N>'1O/M )+

(E*&(6'0+0( 0/ :>./ 0/ 4+&&/ *&+).5(&.+1

4+&&/ *&+).5(&.+1 ')*(M Q +4,;/ 3'&+*2&'+ 0(.*( (E4V)*&'4/

L*/ ( 0( +5+),/M 0/ :(&&/M N>(

&(=&/0>JM ./L&( + =(,+ + 4/).*&>'&M / =(&:'1 0/ (E4V)*&'4/ 6/0(1/M )+ 4/)0',;/ 0(

4/1/4+& / ('E/ 0/ *+6L/& ( + +&(.*+ 0( 4/&*(M 0/ :(&&/M Q +1*>&+ 0/ ('E/ 0/. =/)*/.

&+L+1O+& + =(N>()+ 5(1/4'0+0(

$4D4> ,=,:!" C:5-,:,

(E4()*&'4'0+0( =/0( 5(&':'4+&.(M &(4/&&()0/ + 4+1'L&(. =+&+1(1/. /> 0( :+4(.

=+&+1(1+. /> +')0+M 0( /O+)../) C'3 ?D

'3 ?


51/67

CENFIM 45

/1/4+.( + =(,+ 4/6 / 4+L(0+1 (6 /> L/4+0(1/L/M ./L&( / =1+)/ 0( *&+,+&

('E/ *(6 0( :'4+& 5(&*'4+1 (M =+&+ / 0'.=/& +..'6M >*'1'J+.( / (.N>+0&/ 0( 4(=/ /> /

(.N>+0&/ &(4*/ 4/6 4+)*/)('&+

&'6('&+6()*(M +4O+.( + +1*>&+ M ')*&/0>J')0/ 4+1'L&(. =/& L+'E/ 0+ .(4,;/ 0( 6+'/&

0'R6(*&/

.*+ 0'6().;/ 0(=()0( 0+ +1*>&+ 0/ 4+L(0+1 (6 L/4+0(1/L/ (M )(.*( 4+./M .(&7 0(

$ 66

(M =/& (E(6=1/M / &+'/ 0( (E4()*&'4'0+0( *'5(& 0( .(& 0( # 66M 0(5(&;/ =/0(& 6(*(&

.( =/& L+'E/ 0+. (.='3+. /> L&+,/. 0/ 5('/M 4+1'L&(. =+&+1(1/.M 0+ .(3>')*( +1*>&+ (

.(6 0('E+& :/13+ +13>6+ C5(& '3 DK

[ # d % d $ $ [ 66

.*( =&/4(../ 0( 5(&':'4+,;/ < +0(N>+0/ =+&+ 3&+)0(. 0(.4()*&+3().

(5(M *+6L()/ ( .( 4/).(&5+6 /. =/)*/. 0( 4()*&+3(6M

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'3 $

7, 77N =: 77 + A55

. 4+1'L&(. =+&+1(1/. .;/ =(,+. N>( .(&5(6 =+&+ 6(0'& ( .;/ :('*/. 0( +,/ *(6=(&+0/

C'3 D

+&+ (:(4*>+& 6(0',-(. ( 5(&':'4+,-(.M =/0(6 4/6=/&.( (.*(. 4+1'L&(. ( ./L&(=/&.(M

+*< 4/6=&'6()*/. 5+&'75('.


52/67

CENFIM 46

0'.*R)4'+ 0/. =1+)/. 0( 6(0',;/ ( + .>+ 1'.>&+ ( =+&+1(1'.6/M .;/ 6>'*/ &'3/&/./.

+*< +/ =/)*/ 0( N>( + P>.*+=/.',;/ 0( # =(,+. 07)/. + 6(0'0+ 0(.(P+0+M 4/6 >6

(&&/ '):(&'/& + $$$ 66

. 4+1'L&(. =+&+1(1/. (.*;/ )/&6+1'J+0/. ( (E'.*(6 57&'/. 3&+>. 0( N>+1'0+0(

'3

'6().-(. ( 4+&+4*(&B.*'4+. 0/. 4+1'L&(. 0( :+4(. =+&+1(1+.K

+D .(4,;/ *&+).5(&.+1 0/. 4+1'L&(. 0( 6+'. 0( $ 66

LD ( 4D .(4,;/ *&+).5(&.+1 $M# + $ 66

0D .(4,;/ *&+).5(&.+1 +L+'E/ 0( $M# 66

. 4+1'L&(. '):(&'/&(. + % 66M *V6 + ').4&',;/ )/. =1+)/. 0( 6(0',;/


53/67

CENFIM 47

# OP J

J Q M

" C4/6 ')41')+,;/ 0/ 4+&&/ .>=(&'/&D

4 :-,;,

/&)(+6()*/ 42)'4/ =/& /&'()*+,;/ 0/ 4+&&/ .>=(&'/& =/&*+:(&&+6()*+.

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ + /=(&+,;/ 0( */&)(+6()*/ 0( 4/)(.M :+J()0/ >./ 0+.

:(&&+6()*+. ( +4(..2&'/. +0(N>+0/. +/ (E(&4B4'/

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I D

LD &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M / 4+&&/ .>=(&'/& =+&+ + &(+1'J+,;/

0/ R)3>1/ =&(*()0'0/

4D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #M =&(5'+6()*( 6+N>')+0+ /> );/ C4&'*,;/ 0/ 4/)(

(&&+6()*+. 0( 4/&*(

+1,/. =+0&;/

/1(*/. &(4*':'4+0/.

+N>B6(*&/

'4&26(*&/.

/6=+&+0/&

# J


54/67

CENFIM 48

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

:D (& (E(&4'*+0/M ./L&( + =/.*>&+ )/ =/.*/ 0( *&+L+1O/

D4 -

'4+&7 +/ 4&'*


55/67

CENFIM 49

J Q M $

" C=/& /&'()*+,;/ 0/ 4+&&/ .>=(&'/& C')*(&'/&DD

4 :-,;,

/&)(+6()*/ 2)'4/M =/& /&'()*+,;/ 0/ 4+&&/ .>=(&'/& C)*(&'/&D

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ + /=(&+,;/ 0( */&)(+6()*/ 0( 4/)(.M :+J()0/ >./ 0+.

:(&&+6()*+. ( +4(..2&'/. +0(N>+0/. +/ (E(&4B4'/

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I D

LD &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M / 4+&&/ .>=(&'/& =+&+ + &(+1'J+,;/

0/ R)3>1/ =&(*()0'0/

4D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #M =&(5'+6()*( 6+N>')+0+ /> );/ C4&'*,;/ 0/ 4/)(

(&&+6()*+. 0( 4/&*(

+1,/. =+0&;/

/1(*/. &(4*':'4+0/.

+N>B6(*&/

'4&26(*&/.

/6=+&+0/&

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/


56/67

CENFIM 50

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

:D (& (E(&4'*+0/M / )S6(&/ 0( 5(J(. )(4(..7&'/M ./L&( + =/.*>&+ )/ =/.*/ 0(

*&+L+1O/

D4 -

'4+&7 +/ 4&'**'1'J+0/ )/ (E(&4B4'/

I /)( 0/ =>)O/


57/67

CENFIM 51

J Q M >

" C=/& 0(.1/4+,;/ 0/ 4+L(,/*( 625(1D

4 :-,;,

/&)(+6()*/ 2)'4/M =/& 0(.1/4+,;/ 0/ 4+L(,/*( 625(1

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ + /=(&+,;/ 0( */&)(+6()*/ 0( 4/)(.M :+J()0/ >./ 0+.

:(&&+6()*+. ( +4(..2&'/. +0(N>+0/. +/ (E(&4B4'/

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I D

LD &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M / 0(.1/4+6()*/ 0/ 4+L(,/*(

625(1

4D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #M =&(5'+6()*( 6+N>')+0+ /> );/ C4&'*,;/ 0/ 4/)(

(&&+6()*+. 0( 4/&*(

+1,/. =+0&;/

/1(*/. &(4*':'4+0/.

+N>B6(*&/

'4&26(*&/.

/6=+&+0/&

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/


58/67

CENFIM 52

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

:D (& (E(&4'*+0/M / )S6(&/ 0( 5(J(. )(4(..7&'/M ./L&( + =/.*>&+ )/ =/.*/ 0(

*&+L+1O/

D4 -

'4+&7 +/ 4&'**'1'J+0/ )/ (E(&4B4'/

I /&)(+6()*/ 42)'4/ =/&

0(.1/4+,;/ 0/ 4+L(,/*( 625(1


59/67

CENFIM 53

J Q M D

" \ H C+ 0( /)(.D

4 :-,;,

/&)(+6()*/ 2)'4/M 4/6 + &+ ')41')75(1 ( 3&+0>+0+ C+ 0( /)(.D

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ + /=(&+,;/ 0( */&)(+6()*/ 0( 4/)(.M :+J()0/ >./ 0+.

:(&&+6()*+. ( +4(..2&'/. +0(N>+0/. +/ (E(&4B4'/

>4 : C:+!"

:/&6+)0/ 0(5(K

(D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I D

:D &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M + &+ 0( 4/)(.

3D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #M =&(5'+6()*( 6+N>')+0+ /> );/ C4&'*,;/ 0/ 4/)(

(&&+6()*+. 0( 4/&*(

+1,/. =+0&;/

/1(*/. &(4*':'4+0/.

+N>B6(*&/ '4&26(*&/.

/6=+&+0/&

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/


60/67

CENFIM 54

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

:D (& (E(&4'*+0/M / )S6(&/ 0( 5(J(. )(4(..7&'/M ./L&( + =/.*>&+ )/ =/.*/ 0(

*&+L+1O/

D4 -

'4+&7 +/ 4&'**'1'J+0/ )/ (E(&4B4'/

I /)( (E(4>*+0/ 4/6 + 0(

/)(.


61/67

CENFIM 55

J Q M R

"

4 :-,;,

/&)(+6()*/ 2)'4/M =/& 0(.1/4+,;/ 0/ 4+L(,/*( 625(1

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ + /=(&+,;/ 0( */&)(+6()*/ 0( 4/)(.M :+J()0/ >./ 0+.

:(&&+6()*+. ( +4(..2&'/. +0(N>+0/. +/ (E(&4B4'/

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I #D

LD &(=+&+& / */&)/ 6(4R)'4/ ( / .'.*(6+M =+&+ +=1'4+,;/ 0+ =(,+ =+0&;/ ( /

=+0&;/ + >*'1'J+& C/ =+0&;/ + >*'1'J+& ( + .>+ 4/).*&>,;/M 0(=()0(&7 0+(.*&+*')+0+ /> );/ C4&'*,;/ 0/ 4/)(

(&&+6()*+. 0( 4/&*(

+1,/. =+0&;/ /1(*/. &(4*':'4+0/.

+N>B6(*&/

'4&26(*&/.

/6=+&+0/&

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/


62/67

CENFIM 56

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

:D (& (E(&4'*+0/M / )S6(&/ 0( 5(J(. )(4(..7&'/M ./L&( + =/.*>&+ )/ =/.*/ 0(

*&+L+1O/

D4 -

'4+&7 +/ 4&'**'1'J+0/ )/ (E(&4B4'/

I # /)( (E(4>*+0/ =/& (,+

+0&;/


63/67

CENFIM 57

J Q M S

@A

4 :-,;,

55- ;, C:T5-,: 15- 5-2

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ +. /=(&+,-(. )(4(..7&'+. =+&+ + (E(4>,;/ 0/ 5('/

(E4V)*&'4/M )/ */&)/ 6(4R)'4/M 4/6 + =(,+ '6/L'1'J+0+ ()*&( =/)*/.

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I %D

LD &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M / 4+&&/ .>=(&'/& =+&+ + &(+1'J+,;/

0/ R)3>1/ =&(*()0'0/

4D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #

>=/&*(. 4/6 =1+N>(*(.

>4O+ 0( +=(&*/ &7='0/

&/4+. 0( =/)*/

+N>B6(*&/ '4&26(*&/

+*B6(*&/

/6=+&+0/&

1+)/ 0( *&+,+3(6M 4/6 4+L(0+'. (6 XY

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(


64/67

CENFIM 58

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

D4 -

'4+&7 +/ 4&'**'1'J+0/ )/ (E(&4B4'/

I % ('/ E4V)*&'4/


65/67

CENFIM 59

J Q M U

@A C4/6 =(,+ 6/0(1/D

4 :-,;,

/&)(+6()*/ 0( >6 5('/ 0( (E4V)*&'4/. 0( :/&6+ (1B=*'4+

$4 G:-,; :L=,:

&(=+&+& / :/&6+)0/ =+&+ +. /=(&+,-(. )(4(..7&'+. =+&+ + (E(4>,;/ 0/ 5('/

(E4V)*&'4/.M 0( :/&6+ (1B=*'4+M 4/6 + +P>0+ 0>6+ =(,+ 6/0(1/

>4 : C:+!"

:/&6+)0/ 0(5(K

+D (& ( ')*(&=&(*+& / 0(.()O/ +=&(.()*+0/ C I8D

LD &(=+&+& / */&)/ 6(4R)'4/ (M )/6(+0+6()*(M / 4+&&/ .>=(&'/& =+&+ +

&(+1'J+,;/ 0/ R)3>1/ =&(*()0'0/

4D &(=+&+& 6+*(&'+1M :(&&+6()*+. ( +=+&(1O/. 0( 6(0',;/ ( 4/)*&/1/K

=(,+ 0( +,/ T # /> T #

>=/&*(. 4/6 =1+N>(*(.

>4O+ 0( +=(&*/ &7='0/

&/4+. 0( =/)*/

+N>B6(*&/

'4&26(*&/

+*B6(*&/ /6=+&+0/&

(,+ 6/0(1/

1+)/ 0( *&+,+3(6M 4/6 4+L(0+'. (6 XY

0D =1'4+& /. 4/)O(4'6()*/. +0N>'&'0/. ./L&(K

'.*(6+. 0( =(&*/ ( (4)/1/3'+ 0( /&*(

&(=+&+,;/ 4/&&(4*+M )/ 0(4/&&(& 0/ *&+L+1O/

&(=+&+,;/ 0/ /.*/ 0( &+L+1O/


66/67

CENFIM 60

(3>&+),+ ( !'3'()(M )/ /.*/ 0( &+L+1O/

(D >&+)*( / =&/4(../ 0( (E(4>,;/ 0/ (E(&4B4'/M .(& (.41+&(4'0/ 0( :/&6+ .'6=1(.M

6+. /LP(4*'5+M ./L&( +. 0S5'0+. N>( =/..+6 .>&3'&

D4 -

'4+&7 +/ 4&'*

);/

R4 ;7,!"

+5+1'+,;/ 0/ (E(&4B4'/M < N>+1'*+*'5+ ( 0(5( *(& (6 4/).'0(&+,;/M 4/6/ =&')4'=+'.

:+4*/&(.K

+D /.*>&+ 4/&&(4*+ )/ =/.*/ 0( *&+L+1O/

LD


67/67

# (%.'

4 (

/&)(+6()*/ 2)'4/ /&+6 :/4+0/. ( +L/&0+0/. /. 6+1 0( 7N>')+. ( (&&+6()*+.

M +)>+1 0/ /&)('&/ (4R)'4/ /1(4,;/ +)>+'.

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