Post on 28-Feb-2018
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Torneamento (Complementar)
CENFIM Centro de Formao Profissional da Indstria Metalrgica e Metalomecnica 1
!
"#$
% "# & ' "# &( ( )
%"#
& ' "# &(( )
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Torneamento (Complementar)
CENFIM Centro de Formao Profissional da Indstria Metalrgica e Metalomecnica 2
NDICE
*+ &!,%-./, ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 01+ ,23&4, +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5
1+* ,67 8 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5
1+1 ,67 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 5
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Torneamento (Complementar)
CENFIM Centro de Formao Profissional da Indstria Metalrgica e Metalomecnica 3
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 > +
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Torneamento (Complementar)
CENFIM Centro de Formao Profissional da Indstria Metalrgica e Metalomecnica 4
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
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CENFIM 1
! " #
$ " %
%
&'()*+,-(. (*/0/123'4+. %
(.()5/15'6()*/ (67*'4/ 8
/&)(+6()*/ 2)'4/ 9
(:')',;/ 9
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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#?
%
%
%
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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+.
#
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CENFIM 4
$ %&'(
)*+,,-
(5(&7K
/)O(4'6()*/. L7.'4/. 0( 0(.()O/ *
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CENFIM 5
# ./ ( .0'
# ./ ( .0' 12
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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/)'*/&(.
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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=/.
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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@
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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
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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
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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
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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'+
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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-!" :
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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 #
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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)
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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+ =(&:>&+,;/
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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
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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(
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CENFIM 19
$M 8% $M 8# [ $M$$9
4/&&(.=/)0()*( + >6 (&&/ 0( 4(&4+ 0( %UM =&+*'4+6()*( 0(.=&(J75(1 K (&&/ N>( 1*&+=+..+ U
2 7:!" :!- 8;7
.*( =&/4(../ =(&6'*( / */&)(+6()*/ +>*/67*'4/M =(1/ 0(.1/4+6()*/ 0/ 4+&&/
1/)3'*>0')+1 ( / 0+ (E(4>,;/ 0( 4/)(. 0( &+J/75('. 4/6=&'6()*/.
(6M 4/6/ 0(.5+)*+3(6M */&)(+& 4/)(. (E*(&'/&(. 0( =/>4+ 4/)'4'0+0(M =/'. /
0(.+1')O+6()*/ 0/ 4+L(,/*( 625(1 );/ 5+'M 3(&+16()*(M +1P(',;/ 0+ =(,+ .(& 0(:('*>/.+ C0(5'0/ +/ 0(.+1')O+6()*/DM /. =/)*/.
42)'4/. 0( 4()*&+3(6M ./:&(6 0(:/&6+,-(.M / N>( '6=1'4+ 4/&&(4,-(. 4/).*+)*(.M )/
&(+=(&*/ 0/ 4+L(,/*( 625(1
+1 +/ .(6'
('E/ )/ 5
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CENFIM 20
0(.1/4+6()*/ M 0/ 4/)*&+=/)*/M 4+14>1+.( =(&=()0'4>1+&6()*( +
/ *&'R)3>1/ &(4*R)3>1/ []K
[ .() [ .()
6+.M =+&+ /. =(N>()/. R)3>1/. C+*< $IDM =/0(.( 4/):>)0'& + *+)3()*( 4/6 / .()/
0/ R)3>1/ C/>M / N>( < / 6(.6/M ( '3 DM 0( 6/0/ N>( K
x = L . tg
D d c
Ora, tg = = (frmulas conhecidas)2 l 2
'3
/& 4/).(3>')*(M .(&7 :74'1 4/)O(4(& / 0(.1/4+6()*/ + '6=&'6'& +/ 4/)*&+=/)*/M .(P+
N>+)0/ .( 0;/ +. 0'6().-(. 0/ 4/)(M .(P+ N>+)0/ < 0+0+ + 4/)'4'0+0( (M L(6
()*()0'0/M / 4/6=&'6()*/ */*+1 0+ =(,+
I +./ 4/)( < 0(:')'0/ =(1+. .>+. 0'6().-(.
D dFrmula 1 : x = x L
2 l
I +./ 4/)( < 0(:')'0/ =(1+ .>+ 4/)'4'0+0(
cFrmula 2 : x = x L
2
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CENFIM 21
=1'4+,-(.
I E(6=1/ +14>1+& / 0(.+1')O+6()*/ 0/ 4/)*&+=/)*/M =+&+ */&)(+& >6 4/)(
4/6 +. .(3>')*(. 0'6().-(.K
[ 9 66 0 [ # 66 [ $$ 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+
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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()*+
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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 #
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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+.(
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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)
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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
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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>'*/
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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
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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
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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
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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
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CENFIM 32
/ 4+./ 0( L'*/1+. 0'.=/.*+. ./L&( >6+ 0>=1+ .
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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
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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( =(&:('*+
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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
*'&+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/.M0( :/&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/)'*/&(.
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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
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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=/&*+)*(.
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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
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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+&
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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
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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
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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 %
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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
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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 ?
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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
=/0( (6=&(3+&.(M =+&+ + 5(&':'4+,;/M / 4/6=+&+0/& 0( .>=/&*( C'3 $D
'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('.
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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',;/
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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
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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&'*
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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/
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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/
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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/
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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
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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/
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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(
/)(.
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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/
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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&;/
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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( /&*(
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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/
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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/
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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
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# (%.'
4 (
/&)(+6()*/ 2)'4/ /&+6 :/4+0/. ( +L/&0+0/. /. 6+1 0( 7N>')+. ( (&&+6()*+.
M +)>+1 0/ /&)('&/ (4R)'4/ /1(4,;/ +)>+'.