Relatório TP2

8/18/2019 Relatório TP2

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RELATÓRIO DO TRABALHO II DA DISCIPLINA“ARQUITETURA NAVAL I”

TEMA: MODELOS DE EQUILÍBRIO

Lucas Calil Fessel DRE:1112212!

Be"#a"$% Cu#&a Bess%#e DRE:1112'(()*

Ce#+"% $e Tec#%l%,ia - Bl%c% C - Sala C2*./0 - Il&a $% Fu#$% - R2


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ÍNDICE

13 I#+"%$u4% 55533333333333333333333333333333333333333333333333333333333333333*!

23 O06e+i7% 55533555555555333333333333333333333333333333333333333 *!

'3 O0se"7a48es 3333333333333333333333333333333333333333333333333333333333333333333*!

!3 M%$el% $as Cu"7as Hi$"%s+9+icas333333333333333333333333333333333333 *..3 Cu"7as $e B%#6ea#;las%7 33335333333333333333333333333333333333333333

12


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INTRODUÇÃO

U=a e=0a"ca4% $e7e es+a" >"e>a"a$a >a"a as a$7e"si$a$es >a"a ?ual @%i>"%6e+a$a3 A?u= $as a$7e"si$a$es ?ue % =a" >%$e ,e"a" &9 %s i=>"e7is+%s e as%>e"a48es #%"=ais c%=% ca",a$esca",a ?ue al+e"a= as ca"ac+e"s+icas&i$"%s+9+icas e % e?uil0"i% $a e=0a"ca4%3

P"e7e" % es+a$% #al $essas ca"ac+e"s+icas >e"=i+e a%s e#,e#&ei"%s #a7ais>la#e6a" e eecu+a" =el&%"es ca""e,a=e#+%s ,a"a#+i#$% 7ia,e#s =ais se,u"as ec%= =e#%s i#cli#a4% l%#,i+u$i#al %u +"a#s7e"sal3 Pa"a iss% #ecessi+a=%s $e@e""a=e#+as se,u"as e >"9+icas >a"a calcula" a C%#$i4% $e E?uil0"i% Fi#al $% #a7i%a>s u=a %>e"a4% %u i=>"e7is+%3 Da su",e % M%$el% Ge"al $e E?uil0"i%3

N% e#+a#+% $e=a#$a$% =ui+% +e=>% >a"a e@e+ua" %s c9lcul%s >%" esse=%$el% ?ue a>esa" $e se" u= =+%$% si=>les +e%"ica=e#+e @ala#$% #e= se=>"e$e+e"=i#a a >%si4% $e e?uil0"i% $e @%"=a $i"e+a >%$e se" #ecess9"i% =ui+asi+e"a48es $e>e#$e#$% $a @%"=a $% casc% =es=% c%= =+%$%s $e c%#7e",#ciaJ3Al= $iss% a ,e%=e+"ia $% c%">% e= su0=e"s% >%$e se" c%=>lea e as c%#$i48es

$e #a7e,a4% e Ku+ua4% #% c%s+u=a= se,ui" as es+a0eleci$as e= >"%6e+%3 A#ecessi$a$e $e =+%$%s =ais >"9+ic%s e 9,eis @e c%= ?ue %u+"%s =+%$%s,a#&asse= $es+a?ue3

Esses =+%$%s se"% a>"ese#+a$%s e $iscu+i$%s #es+e "ela+"i%3 S% eles: AsCu"7as Hi$"%s+9+icas Cu"7as $e B%#6ea#;las%7 e %s Dia,"a=as $e Fi"s%73

OBJETIVO

O %06e+i7% $es+e +"a0al&% >"%>%"ci%#a" % e#+e#$i=e#+% $e c%#cei+%sli=i+a48es a>lica48es e a ca>aci$a$e $e a>lica"=%s % M%$el% Ge"al $e E?uil0"i%

1 T"a0al&% P"9+ic%J % M%$el% $e E?uil0"i% Pelas Cu"7as Hi$"%s+9+icas as Cu"7as$e B%#6ea# e ;las%7 e %s Dia,"a=as $e Fi"s%7 sa0e#$% esc%l&/l%s e e=>"e,9/l%sc%#7e#ie#+e=e#+e #a "es%lu4% $e >"%0le=as $e e?uil0"i% $e e=0a"ca48es e=es+a$% $e Ku+ua4% es+9+ica e e= 9,uas +"a#?uilas3

OBSERVAÇÕES

A %"i,e= $% sis+e=a $e c%%"$e#a$as $% #a7i% es+a"9 se=>"e #a se4% $e=eia #au #% e#c%#+"% $a Li#&a $e Base e $a Li#&a $e Ce#+"% c%= se#+i$% $% ei%l%#,i+u$i#al >%si+i7% >a"a a >%>a +"a#s7e"sal >%si+i7% a 0%=0%"$% e ei% 7e"+ical>%si+i7% >a"a ci=a3

As u#i$a$es $e ca$a c%=>%#e#+e usa$as $u"a#+e +%$% % "ela+"i% e "es%lu4%$e ee"cci%s a c%l%ca$a a0ai%:



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MODELOS DAS CURVAS HIDROSTÁTICAS

Pa"a % c9lcul% $% e?uil0"i% $e u=a e=0a"ca4% >el% =%$el% ,e"al s%#ecess9"i%s =ui+%s >"%cess%s i+e"a+i7%s s 7ees =es=% c%= a a6u$a $e>"%cess%s $e c%#7e",#cia3 Da$a @al+a $e >"a+ici$a$e $% =%$el% su",e= asCu"7as Hi$"%s+9+icas c%= % %06e+i7% $e a>"ese#+a" $e @%"=a $i"e+a as >"%>"ie$a$es&i$"%s+9+icas $e u= #a7i% e= @u#4% $e seu cala$%3 A+"a7s $es+as cu"7as %0+=/se "a>i$a=e#+e as >"%>"ie$a$es &i$"%s+9+icas >a"a c%#$i48es $i@e"e#+es $e%>e"a4% "e$ui#$% % es@%"4% $e c9lcul% ei,i$% >el% M%$el% Ge"al3

NOTA: S% >"%>"ie$a$es &i$"%s+9+icas a?uelas ?ue $e>e#$e= eclusi7a=e#+e$a @%"=a $a >a"+e su0=e"sa $% casc% e $a ,e%=e+"ia $a 9"ea $% >la#% $e

Ku+ua4%3A a>lica4% $as cu"7as se li=i+a a c%#$i48es $e cala$% c%#s+a#+e >%$e#$%

se" usa$as >a"a >e?ue#as i#cli#a48es se @%"e= @ei+as c%""e48es e a>"%i=a48es#ecess9"ias3 E= #%ss% =%$el% usa"e=%s % Te%"e=a $e Eule" >a"a #,ul%s =ui+%>e?ue#%s $e i#cli#a4% e e= e=0a"ca48es $e c%">%s es0el+%s %u se6a ?ue>%ssue= $uas $i"e48es >"i#ci>ais $e $esl%ca=e#+% 0e= $e#i$as l%#,i+u$i#al e+"a#s7e"salJ3 S assi= >%$e=%s ,a"a#+i" a e?ui7%lu=e+"ia #ecess9"ia >a"aa>lica"=%s % Te%"e=a3 E+"a>%la$% % li=i+e $%s >e?ue#%s #,ul%s a >"ecis% $%M%$el% se "e$u 0as+a#+e >%"?ue a i#cli#a4% e?ui7%lu=+"ica se"9 >e"$i$a3

NOTA: N% usa"e=%s % M%$el% $e Cu"7as Hi$"%s+9+icas ?ua#$% &%u7e"

0a#$a3 S%=e#+e +"i=3 De7i$% a si=e+"ia $a e=0a"ca4% e= "ela4% li#&a $ece#+"% >%$e=%s @ae" u=a a>"%i=a4% sa+is@a+"ia >a"a >e?ue#%s #,ul%s se=?ue se >e"ca a e?ui7%lu=e+"ia3 O =es=% #% %c%""e ?ua#$% &9 0a#$a >%is #%eis+e si=e+"ia e= "ela4% se4% $e =eia #au3

C%=% >%$e=%s 7e" a>esa" $a @acili$a$e a$?ui"i$a #as Ta0elas e Cu"7asHi$"%s+9+icas &9 =ui+as c%#si$e"a48es ?ue $e7e= se" sa+is@ei+as % ?ue #% %c%""e?ua#$% usa=%s % M%$el% Ge"al3

CONCEITOS E CÁLCULOS DAS PROPRIEDADES HIDROSTÁTICAS

As >"%>"ie$a$es &i$"%s+9+icas $e"i7a= $i"e+a=e#+e $a @%"=a $% >la#% $eli#&a $9,ua e $a ,e%=e+"ia su0=e"sa $% casc% $e>e#$e#$% assi= $a c%#$i4%$e ca""e,a=e#+% $a e=0a"ca4%3

O Pla#% $e li#&a $9,ua a "e,i% @%"=a$a >ela i#+e"sec4% e#+"e u= >la#%#% #7el $a 9,ua e % casc% $% #a7i% #a c%#$i4% $e ca""e,a=e#+% a se" a#alisa$ac%#@%"=e ,u"a a0ai%:



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As >"i#ci>ais >"%>"ie$a$es &i$"%s+9+icas s%:

;%lu=e Su0=e"s% ;JO 7%lu=e su0=e"s% $e u=a e=0a"ca4% a+ $e+e"=i#a$% cala$% >%$e se"

calcula$% %u >%" i#+e,"a4% 7e"+ical $as 9"eas $as li#&as $9,ua %u >%" i#+e,"a4%l%#,i+u$i#al $as 9"eas $as 0alias a+"a7s $a cu"7a $e 9"eas secci%#ais $as0alias3 A 9"ea $e u=a 0alia $a$a >%":

Awl ( x )=2∫0

Ti

y ( x , z )dz

E= ?ue Al a 9"ea $a 0alia #a >%si4% * e T s% as c%%"$e#a$as7e"+icais cala$%sJ i#icial e #al e J a la",u"a $a 0alia3 C%=% a i#+e,"al

calcula =e+a$e $a 9"ea $ese6a$a =ul+i>lica=%s % "esul+a$% >%" 2 >a"a %0+e" a 9"ea+%+al3 Calcula"e=%s a 9"ea $e ca$a 0alia a+ % cala$% $e >"%6e+% e e#+%i#+e,"a"e=%s as 9"eas a% l%#,% $% c%=>"i=e#+%3 O 7%lu=e su0=e"s% $a$% >%":

∇ (T )=∫ x

i

xf

A wl ( x , z ) dx

i e @ s% %s li=i+es a " e a 7a#+e $a >%"4% su0=e"sa $% casc%J

Desl%ca=e#+% DJ

O $esl%ca=e#+% "e>"ese#+a % >es% $% 7%lu=e $e Kui$% $esl%ca$% >el% casc%3Seu 7al%" %0+i$% >ela =ul+i>lica4% $% 7%lu=e su0=e"s% (∇ (T )) >el% >es%es>ecc% $% Kui$% (γ ) :

∆ (T )=γ .∇(T )

Ce#+"% $e Ca"e#a BJ

% ce#+"% $e $is+"i0ui4% $e 7%lu=e $a >%"4% su0=e"sa $% casc%3 O ce#+"%$e ca"e#a i,ual a% ce#+"%i$e $% 7%lu=e $esl%ca$% $a e=0a"ca4% e $e>e#$eu#ica=e#+e $a ,e%=e+"ia $% casc% su0=e"s%3

Pela $e#i4% $% ce#+"% $e 7%lu=e calcula=%s a >%si4% l%#,i+u$i#al $%ce#+"% $e ca"e#a XB J >ela @"=ula a0ai%:



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2

Xb ( T )=∫ Xi

Xf

x . Aw ( x ,T ) . dx /∇(T )

1

'1 - "ea $a Balia $e >%si4% e cala$% T

2 - M%=e#+% $e "ea L%#,i+u$i#al

' - M%=e#+% $e ;%lu=e L%#,i+u$i#al

A >%si4% 7e"+ical $% ce#+"% $e ca"e#a V0J calcula$a $e @%"=a a#9l%,a a0:

Zb (T )=∫ xi

xf

Zw ( x , T ) . Awl ( x ,T ) . dx /∇(T )

Zw ( x ,T ) a c%%"$e#a$a $% ce#+"% $e 9"ea $a >a"+e su0=e"sa $% casc% ec%#si$e"a#$% ?ue #% &a6a 0a#$a %u se6a &a6a si=e+"ia +"a#s7e"sal #a >a"+esu0=e"sa $as 0alias c%#si$e"a$as +e"e=%s a se,ui#+e e>"ess%:

Zw=2.∫0

T

z . y ( x , z ) . dz / Aw( x , T )

Ce#+"% $e Flu+ua4% FJ

O ce#+"% $e Ku+ua4% % ce#+"% $e 9"ea $% >la#% $e Ku+ua4%3 Suac%%"$e#a$a l%#,i+u$i#al $a$a >%":

X F ( z )=2∫ X i

X f

x . Awl ( z )dx

Awl ( z)

∫ X i

X f

x . Awl ( z )dx #%s $9 % =%=e#+% $e 9"ea $a li#&a $9,ua $e al+u"a 3

Di7i$i#$% >%" Awl ( z ) ?ue a 9"ea $es+a li#&a $9,ua %0+e=%s a c%%"$e#a$a

$% ce#+"% $e 9"ea $es+a li#&a $9,ua3 N% cas% $e es+a li#&a $9,ua c%""es>%#$e" a%>la#% $e Ku+ua4% +e"e=%s @ c%=% "esul+a$% $%s c9lcul%s aci=a3

NOTA: E= #%ss%s ee"cci%s usa"e=%s as c%%"$e#a$as $e ce#+"% $e ,"a7i$a$eca"e#a e Ku+ua4% e= "ela4% se4% =es+"a $% #a7i% >ela @"=ula: SMJ WL>>2 - PRJ3 A =es=a @"=ula usa$a >a"a ?ual?ue" u=a $as c%%"$e#a$as0as+a +"%ca" a c%%"$e#a$a e= ?ues+%3

T%#ela$as >%" Ce#+=e+"% $e I=e"s% TPCJ

u= >a"=e+"% &i$"%s+9+ic% ?ue i#$ica ?ua#+as +%#ela$as $e ca",a s%#ecess9"ias >a"a a i=e"s% %u e=e"s% e= 1 c= $e cala$% >a"alel% e= "ela4% a%cala$% i#icial $a e=0a"ca4%3 Se a$ici%#a"=%s"e+i"a"=%s u=a ca",a $e >e?ue#%



7/26

7al%" p c%#si$e"a=%s assi= >e?ue#as 7a"ia48es $e cala$%3 L%,% >%$e=%sa>"%i=a" esse ac"sci=%$ec"sci=% $% 7%lu=e su0=e"s% $e u= >"is=a $e 1 c=e 9"ea $a 0ase i,ual a 9"ea $e li#&a $9,ua3 Te=%s u=a 7a"ia4% $e 7%lu=e>e?ue#a ?ue "e>"ese#+a$a >%":

δV = Peso ( p )

ρOu δV = Awl (T 0) δT

I,uala#$% as $uas e?ua48es %0+e=%s:

Peso

δT = Awl (T

0) ρ

C%=% ?ue"e=%s a 7a"ia4% $% $esl%ca=e#+% >a"a 1c= 11** =J e a @"=ulaaci=a es+9 e= =e+"%s a @"=ula #al $% TPC se"9:

TPC = Awl( z ) ρ

100

M%=e#+% >a"a T"i=a" u= Ce#+=e+"% MTCJ

a =e$i$a $% =%=e#+% #ecess9"i% >a"a al+e"a" $e u= ce#+=e+"% % +"i= a>a"+i" $a c%#$i4% i#icial es+a0eleci$a3 #ecess9"i% le=0"a" ?ue c%=% esse=%=e#+% 7a"ia c%= % 7%lu=e $esl%ca$% e se al+e"a c%#+i#ua=e#+e c%#@%"=e %casc% i#cli#a$% a =e$i$a se"9 u=a a>"%i=a4% c%= u= ce"+% ,"au $e e""%i#+"#sec%3

O =%=e#+% >a"a +"i=a" u= ce#+=e+"% calcula$% c%= 0ase e= ?ua#+%se"ia #ecess9"i% i#cli#a" l%#,i+u$i#al=e#+e % casc% >a"a ?ue % +"i= 7a"ie $e u=ce#+=e+"%3 Sa0e=%s ?ue % =%=e#+% ?ue a,e s%0"e % casc% $e7i$% a% 0i#9"i%>es%/e=>u% $a$% >%":

M =∆ . d se#$% $ % 0"a4% $esse 0i#9"i% $e#i$% >%":

d= ´GM L . sin

O#$e % #,ul% $e +"i= $% casc%3 C%#si$e"a#$% ?ue es+a=%s+"a0al&a#$% c%= a &i>+ese $e >e?ue#as i#cli#a48es >%$e=%s u+ilia" a se,ui#+ea>"%i=a4%:

sin=tan= !

L pp

Te"e=%s e#+%:

M =∆ . ´GM L . !

L pp

Que"e=%s c%=% "e@e"#cia % 7al%" >a"a +"i= $e 1 c= e#+%:



8/26

XFeqFeq

Teqm

v

dT

! = 1

100

E iss% le7a a:

MTC ( z )=∆ ( z ). ´GM L( z )

100 L pp

NOTA: As +a0elas &i$"%s+9+icas calcula= esses 7al%"es c%= 0ase e= BM #%lu,a" $e GM3 Pa"a %0+e" %s 7al%"es c%""e+%s >a"a GM e@e+ua=%s u=a c%""e4%:

MTC ¿= MTC −

∆ (ZG−ZB)100 L pp

Assi= %0+e=%s % 7al%" c%""e+% >a"a "e@e"#cia e= GM3

C%""e4% $% Desl%ca=e#+% >%" Ce#+=e+"% $e T"i= CDCTJ

Es+e u= @a+%" u+ilia$% >a"a c%""i,i" % $esl%ca=e#+% a >a"+i" $%$esl%ca=e#+% e#c%#+"a$% >a"a u= cala$% =$i%3 C%=% >%$e=%s i=a,i#a" % us%$% TPC $e7e a>a"ece" e= al,u= =%=e#+% $u"a#+e %s c9lcul%s 69 ?ue %$esl%ca=e#+% causa$% >%" u=a 7a"ia4% $e 1c=3

Pa"a c&e,a"=%s a% CDCT $e7e=%s a#+es $e#i" % @a+%" $e CDT C%""e4% $%Desl%ca=e#+% >%" T"i=J3 O0se"7e a ,u"a a0ai%:

C"T = ρ # X #=∫T$

Te%

Awl ( z ) dz≅ Awl (Te% ) . δ T

δ T =Te%−T$= XF (Te% ). ! & = XF (Te% ) . ! / Lpp

L%,%

# ≅ Awl (Te% ) . XF (Te% ) .!

Lpp

E

C"T = ρ. Awl (T ) . XF (T ). !

Lpp

Se c%#si$e"a"=%s + W 1c= W 11** =:

C"TC = ρ. Awl (Te% ) . XF (Te% ) .!

100. Lpp =TPC ( z ) .

XF ( z) Lpp

N%s ee"cci%s c%=% c%#si$e"a"e=%s ?ue % #,ul% @ =ui+% >e?ue#%>%$e=%s usa" % CDTC $a se,ui#+e =a#ei"a:

∆ (Te% )≅ ∆ (T$ )+100.! .C"CT (T$)%#$e



9/26

Te%=T$+ XF (T$ ) . ! / Lpp

NOTA: Na @%"=ula aci=a e=%s XF ( Te% )≅ XF (T$) >%is ?ua#$% '0 , XF (Te%)' XF (T$) 3

Al+u"a Me+ac#+"ica L%#,i+u$i#al e T"a#s7e"sal YML e YMVJ

/ Al+u"a Me+ac#+"ica L%#,i+u$i#al YMLJ:

Me+ace#+"% % >%#+% M #a ,u"a a0ai% % ce#+"% $e cu"7a+u"a i#s+a#+#e%$a +"a6e+"ia $% ce#+"% $e ca"e#a #% es>a4%3 Pa"a >e?ue#as i#cli#a48ese?ui7%lu=+"icas +"a#s7e"sais %u l%#,i+u$i#ais sua >%si4% a #% es>a4%3

Rai% Me+ac#+"ic% ´BM J a $is+a#cia e#+"e % ce#+"% $e ca"e#a BJ e %=e+ace#+"% MJ3

A,%"a ?ue +e=%s %s c%#cei+%s #ecess9"i%s >%$e=%s $e#i" al+u"a=e+ac#+"ica YMJ3 a al+u"a e= "ela4% a li#&a $e 0ase $% =e+ace#+"%l%#,i+u$i#al3

A e>"ess% >a"a a al+u"a =e+ac#+"ica l%#,i+u$i#al se"9:

(ML ( z )=ZB ( z)+B M L ( z)

O#$e

´BM L= ) L

V e ) L ( z )=∫

− L2

+ L2

y ( x , z )d x . x2 dx− A wl ( z ) X F 2( z )

NOTA: ) L ( z ) % =%=e#+% $e i#"cia l%#,i+u$i#al e VB a al+u"a $% ce#+"%$e ca"e#a e BML % "ai% =e+ac#+"ic% l%#,i+u$i#al3 Os li=i+es $e i#+e,"a4% s%$e+e"=i#a$%s +%=a#$% c%=% "e@e"#cia a se4% $e =eia/#au3



10/26

/ Al+u"a Me+ac#+"ica T"a#s7e"sal YMTJ:

A#9l%,a al+u"a =e+ac#+"ica l%#,i+u$i#al =as "e@e"e#+e a i#cli#a48es+"a#s7e"sais3 O c9lcul% @ei+% $% se,ui#+e =%$%:

(MT ( z )=ZB ( z )+B M ! ( z)

O#$e:

´BM ! = ) L

V e ) T ( z )=∫

− L2

+ L2

y ( x , z)3 dx

NOTA: VBJ a al+u"a $% ce#+"% $e ca"e#a e ) T ( z ) % =%=e#+% $e i#"cia+"a#s7e"sal e BM ! % "ai% =e+ac#+"ic% +"a#s7e"sal3 Os li=i+es $e i#+e,"a4%s% $e+e"=i#a$%s +%=a#$% c%=% "e@e"#cia a se4% $e =eia/#au3

M%=e#+% >a"a A$e"#a" u= G"au MAGJ

M%=e#+% >a"a a$e"#a" u= ,"au % =%=e#+% #ecess9"i% >a"a ,e"a" u=a7a"ia4% $a i#cli#a4% +"a#s7e"sal $e u= ,"au3

Es+a @%"=a $e =e$i" u+ilia$a >%"?ue c%=% a 0%ca =ui+% =e#%" $% ?ue %c%=>"i=e#+% $a e=0a"ca4% c%#@%"=e #ecess9"i% >a"a a a>lica4% $as cu"7as&i$"%s+9+icas a i#cli#a4% >a"a a$e"#a" u= ce#+=e+"% >%$e"ia se" =ui+% =ai%" $%?ue u= ,"au sai#$% $%s li=i+es $e >e?ue#as i#cli#a48es >a"a % ?ual sa0e=%s ?ue% =+%$% 79li$%3

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METODOLOGIA PARA BUSCA DE EQUILÍBRIO

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11/26

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12/26

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CURVAS DE BONJEAN/VLASOV

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CURVAS DE BONJEAN

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Pa"a ca$a 0alia a i#+e,"al a se "es%l7e" :



13/26

A w ( x , T ( x))=∫0

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14/26

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15/26

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16/26

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=ais +"s cu"7as "ela+i7as a% %u+"%0%"$% e#+"e+a#+% +a#+% e=si=e+"ia ?ua#+% e= assi=e+"ia



17/26

ca$a cu"7a "e>"ese#+a as>"%>"ie$a$es "ela+i7as a u= 0%"$%3

As =eias/9"eas secci%#ais s% calcula$as a+"a7s $as e>"ess8es:

A BB=∫0

T

+ BB( x , z)dze A B=∫0

T

+ B ( x , z ) dz , e= ?ue a 9"ea +%+al : A= ABB+ A B

E= cas% $e s%=e#+e &a7e" +"i= e % #a7i% se" si=+"ic% a e>"ess% se +%"#a:

A=2∫0

T

+ ( x , z )dz 3

A#al%,a=e#+e B%#6ea# se % #a7i% +i7e" +"i= >%$e/se calcula" % cala$% #%>la#% $ia=e+"al >a"a ?ue ele si"7a #%s c9lcul%s $as >"%>"ie$a$es usa#$%/se ae>"ess%:

T ( x )=T -− !

Lpp x c%= ! =(T -−T -#)

C9lcul% $e ∇

E= cas% $e casc% si=+"ic% e s%=e#+e c%= +"i= >"%ce$e/se c%=% e= B%#6ea#:

∇ (T ( x ))=∫ x i

x f

Aw ( x , T ( x))dx

E= cas% $e &a7e" 0a#$a Fi,u"a) a i#cli#a4% +"a#s7e"sal ,e"a"99"eas $i@e"e#+es e= ca$a 0%"$% $ase4% u=a 7e ?ue %s cala$%s #%se"% % =es=%3 E#+% a e>"ess%

∫0

T ( x)

+ ( x , z)dz calcula"9 as 9"eas A1

a+ % cala$% TBB e A2 a+ TBE >%is %c9lcul% $a 9"ea $e ca$a 0%"$% >%ssuic%=% li=i+e u= cala$% u#i@%"=e3 A9"ea +%+al su0=e"sa s%=a $as9"eas: A1 [ A2 [ a' - a!3

E#+% a 9"ea +%+al su0=e"sa $a 0alia $a$a >%":

A ( x , T ( x ) )= A1+ A2+-3−-4


Aw(x,TB

BE

Cu"7as $e ;las%7

I#cli#a4% +"a#s7e"sal

"

TBE

TBB

A1 A

a3 a4


18/26

A ( x , T ( x ) )=∫0

T BB

+ ( x , z ) dz+∫0

T B

+ ( x , z ) dz++ B .+ B .!&∅

2 −+ BB. + BB .

!& ∅

2

Rea""a#6a#$%:

A w ( x , T ( x))= A ( T BB )+ A (T B)+ !&∅

2 (+ B2 −+ BB2 )

E= cas% $e #% &a7e" 0a#$a:

A ( x , T ( x ) )=2∫0

T

+ ( x , z ) dz

O #,ul% φ >%$e se" calcula$% >%":

∅=-0!& ( T BB−T B

+ ( x , T BB)++ ( x ,T B))

O 7%lu=e su0=e"s% $a$% >ela i#+e,"a4% $a cu"7a $e 9"eas secci%#ais:

∇ (T ( x ))=∫ x i

x f

Aw ( x , T ( x)) dx



19/26

C9lcul% $e CB

Pa"a calcula" CB se"9 usa$% % =%=e#+% es+9+ic% $e 7%lu=e a >a"+i" $a cu"7a$e 9"eas secci%#ais:

X CB=

∫ x i

x f

A w ( x , T ( x)) xdx

∇(T ( x ))

Pa"a ca$a 0alia % =%=e#+% es+9+ic% $e u= 0%"$% ?ual?ue" e= "ela4% li#&a $e 0ase calcula$% >a"a % cala$% u#i@%"=e $% 0%"$%3 Ele $a$% >%":

MLB ( x )=∫0

T

+ B ( x , z ) zdz

E= cas% $e 0a#$a a% se a>lica" a e>"ess% aci=a e= ca$a 0%"$% $e7e/se@ae" u=a c%""e4% >a"eci$a c%= a c%""e4% "ealia$a #% c9lcul% $e 9"ea $a 0aliaaci=a >%"?ue es+a e>"ess% se"7e >a"a % c9lcul% $% =%=e#+% a+ % cala$%

u#i@%"=e l%,% +e=%s ?ue "e+i"a" %u a$ici%#a" %s =%=e#+%s $%s +"i#,ul%s $aFi,u"a )3 O =%=e#+% +%+al MLBJ $a$% >ela s%=a $% =%=e#+% $a 9"ea A 2 =e#%s% =%=e#+% $a 9"ea $% +"i#,ul% a! =e#%s % =%=e#+% $a 9"ea A1 =e#%s %=%=e#+% $a 9"ea a' $% +"i#,ul%3

MLB ( x , T ( x))=∫0

T B

+ BB ( x , z ) zdz+∫0

T BB

+ B ( x , z ) zdz−+ BB . + BB . !&∅ . ´ zBB++ B .+ B . !&∅ . ́zB

́zBB e ´ zB s% as $is+#cias $%s ce#+"i$es $%s +"i#,ul%s $e 9"eas a' e a! e="ela4% a LB3 Da ,e%=e+"ia $%s +"i#,ul%s 7=:

́zBB=T ( x )+2

3+ BB( x , T BB )!& ∅ e ́zB=T ( x )−

2

3+ B ( x ,T B ) . !&∅

MLB ( x ,T ( x ) , )=∫0

T B

+ B ( x , z ) zdz+∫0

T BB

+ BB ( x , z ) zdz−+ BB

2.!& ∅

2 .[T ( x )+ 23 + BB ( x , T BB) !&∅]+¿

++ B2

.!&∅

2.

[T ( x )−

2

3+ B ( x ,T B )!& ∅]

Cas% se6a $a$% TBB e TBE =as #% φ e#+% a @"=ula aci=a ca"9 assi=:

MLB ( x ,T ( x ) )=∫0

T B

+ B ( x , z ) zdz+∫0

T BB

+ BB ( x , z ) zdz−+ BB ( x , T BB )

6 [T BB−T ( x ) ] [2T BB+T ( x ) ]+¿

++ B ( x , T B )6

[T ( x )−T B] [T ( x )+2T BB ]



20/26

P%" c%#7e#4% %s =%=e#+%s a 0%=0%"$% s% >%si+i7%s a 0%"es+e #e,a+i7%se %s si#ais #as >a"celas $e ca$a =%=e#+% ac%=%$a= a c%=0i#a4% $e =%=e#+%s$as >a"celas $%s +"i#,ul%s3

Pa"a casc% $ia=e+"al=e#+e si=+"ic% e e= cala$% u#i@%"=e \CB W *3 N% cas%

$e #a7i%s si=+"ic%s %u assi=+"ic%s e c%= 0a#$a $e7e/se c%=>%" % =%=e#+%es+9+ic% $e 9"ea $e ca$a 0%"$% e= "ela4% li#&a $e ce#+"% >a"a se calcula" \CB3E#+% $e7e/se "es%l7e" a i#+e,"al:

Z CB=∫ xi

X f MLB ( x , T ( x)) dx∇(T ( x))

O =%=e#+% es+9+ic% e= "ela4% li#&a $e ce#+"% +a=0= #ecessi+a $ec%""e48es3 Ele $a$% >ela e>"ess%:

MLC ( x ,T ( x ), )=+∫0

T BB

+ BB2

( x , z ) dz2

−∫0

T B

+ B2

( x , z )dz2

−+ BB . + BB . !&∅ . ́yBB−+ B. + B . !&∅ . ́yB

´ yBB e ´ y B s% as $is+#cias $%s ce#+"i$es $%s +"i#,ul%s $e 9"eas a' e a! li#&a$e ce#+"%3 Da ,e%=e+"ia $a ,u"a 7=:

´ yBB=+ BB( x , T BB )

3 e ´ yB=

+ B( x , T B)3

L%,%

MLC ( x ,T ( x ), )=∫0

T BB + BB2 ( x , z ) dz

2 −∫

0

T B + B2 ( x , z )dz

2 −

+ BB2 ( x ,T BB ) [T ( X )−T BB ]

6 −

+ B2 ( x , T B )[T B−T ( X ) ]

6

Assi=

+ CB=∫ x i

X f MLC ( x , T ( x)) dx∇

C%= as cu"7as $e ;las%7 es+% $e+e"=i#a$%s ∇ e CB e >%" e+e#s% CG?ual?ue" ?ue se6a a i#cli#a4% $% casc% %u sua @%"=a3

;e"ica4% $% E?uil0"i%

Usa#$%/se ;las%7 >%$e=/se a#alisa" e=0a"ca48es +"a#s7e"sal=e#+esi=+"icas assi=+"icas c%= +"i= %u c%= 0a#$a3 Es+9 $e#i$% CG CB e ∇3

Da ,e%=e+"ia a @%"4a "esul+a#+e 7ai a e"% ∇γ / ∆ ≤ ]1X % =%=e#+% $e +"i=l%#,i+u$i#al 7ai a e"% M TRIMLJ W ∆^CBc%sφ / VCBse#φJ / CGc%sφ / VCGse#φJ_ ≤ ] 2X e %



21/26

=%=e#+% $e +"i= +"a#s7e"sal 7ai a e"% M TRIMTJ W ∆^\CBc%sφ [ VCBse#φJ / CGc%sφ [VCGse#φJ_ ≤ ]2

Pa"a % e?uil0"i% l%#,i+u$i#al: !-12 = X&− XbZb−Z&

=T -−T -#

Lpp

Pa"a % e?uil0"i% +"a#s7e"sal: !-13=T B−T BB+ B−+ BB

=+ CG−+ CBZ CG−Z CB

O >"%cess% $e 0usca $% e?uil0"i% %c%""e e= suas e+a>as $a se,ui#+e @%"=a:

1J A+"a7s $% Pes% calcula/se % e=>u%3 O0+=/se $as Ta0elas Hi$"%s+9+icasu= 7%lu=e e?ui7ale#+e i,ual calcula$% >elas cu"7as $e B%#6ea# e ?ue ,e"e=e=>u% c%= $i@e"e#4a >a"a % Pes% =e#%" ?ue u=a +%le"#cia3 A +%le"#cia E1 es+a0eleci$a >a"a a $i@e"e#4a e#+"e %s =$ul%s $e P e E3 C%= CG e CB calcula/se+a=0= % 0"a4% $% =%=e#+% "esi$ual3 A +%le"#cia E2 es+a0eleci$a >a"a %+a=a#&% $% 0"a4% $% =%=e#+%3

2J E@e+ua/se i#cli#a4% $% #a7i% >el% +e%"e=a $e Eule" $e ac%"$% c%= %se#+i$% $% =%=e#+% "esi$ual a+ ?ue % =%=e#+% es+e6a c%= 7al%" =e#%" ?ue a+%le"#cia E23

'J ;e"ica/se % $esl%ca=e#+% #%7a=e#+e e cas% ele se6a =ai%" ?ue sua+%le"#cia i#icia/se % >"%cess% #%7a=e#+e $% >ass% 1 a+ se alca#4a" =%=e#+%a0ai% $a +%le"#cia e #%7a 7e"ica4% 3 Eecu+a/se +%$% esse >"%cess%sucessi7a=e#+e ?ue @%"4a e =%=e#+%s "esul+a#+es es+e6a= i,uais %u a0ai% $esuas +%le"#cias3

DIAGRAMAS DE FIRSOV

C%= c9lcul% >%" =ei% $as Cu"7as $e B%#6ea;las%7 e= c%#$i4% $e +"i= si=>les $e se %0+e" % 7%lu=e su0=e"s% e a >%si4% $% ce#+"% $e ca"e#a3 N%e#+a#+% =ui+% +"a0al&%s% =e$i$a ?ue >"ecisa=%s calcula" %s 7al%"es $as 9"ease $e seus =%=e#+%s >a"a %s cala$%s c%""es>%#$e#+es #as 0alias $e ca$a >la#%$e Ku+ua4%3 Ta=0= ei,e c%#si$e"97el es@%"4% $e+e"=i#a" %s >la#%s i#cli#a$%se?ui7%lu=+"ic%s $e7i$% c%=>lei$a$e ,e%=+"ica $% casc% % ?ue @a $a 0usca>el% >%#+% $e e?uil0"i% $e u=a c%#$i4% ?ual?ue" u= >"%cess% i+e"a+i7% >%" sua7e +% +"a0al&%s% ?ua#+% >el% =%$el% $e Cu"7as Hi$"%s+9+icas3

;ale "essal+a" +a=0= ?ue ?ua#$% +"a0al&a=%s c%= Cu"7as Hi$"%s+9+icases+a=%s assu=i#$% >%" &i>+ese ?ue &9 e?ui7%lu=e+"ia ?ua#$% i#cli#a=%s ae=0a"ca4% $es$e ?ue % ei% $e ,i"% c%#+e#&a % ce#+"%i$e $e 9"ea $% >la#% $e

Ku+ua4% $e=%#s+"a$% >el% Te%"e=a $e E`le"J3 P%"= ?ua#$% u+ilia=%s +aiscu"7as #% es+a=%s c%#si$e"a#$% >%ss7eis e""%s ?ue a>a"ece= >%" @ae"=%sessas a>"%i=a48es 69 ?ue as Cu"7as Hi$"%s+9+icas "e>"ese#+a= u=a =e+%$%l%,ia



22/26

?ue $e7e se" a>lica$a e= c%#$i48es $e cala$% u#i@%"=e3 L%,% ?ua#$% u+ilia=%sas cu"7as >a"a 0usca" >"%>"ie$a$es $e c%#$i48es i#cli#a$as $a e=0a"ca4%>%$e=%s es+a" $es>"ea#$% 7a"ia48es $e 7%lu=e ?ue #% s% #ecessa"ia=e#+e$es>"e7eis3

E= 7is+a $iss% >%$e"ia se" $e e+"e=a a6u$a $is>%" $e @%"=a $i"e+a $asi#@%"=a48es s%0"e a >%si4% $% ce#+"% $e ca"e#a >a"a >la#%s $e Ku+ua4% $e

=es=% 7%lu=e3 Ou =el&%" +e"=%s u= $ia,"a=a ?ue "elaci%#e % 7%lu=e e a>%si4% $% ce#+"% $e ca"e#a xB yB zB J >a"a >la#%s c%= +"i= >la#%s $eKu+ua4% i#cli#a$%s l%#,i+u$i#al=e#+eJ3 Da %s Dia,"a=as $e Fi"s%73

F%i 6us+a=e#+e 7isa#$% $i=i#ui" +ais >"%0le=as ?ue %s Dia,"a=as $e Fi"s%7@%"a= $ese#7%l7i$%s3 O >"%ce$i=e#+% $e 0usca >elas >"%>"ie$a$es ca =aissi=>les ?ua#$% c%=>a"a$% s Cu"7as Hi$"%s+9+icas >%is "elaci%#a=%s e= u= #ic%$ia,"a=a as >%si48es e V $% ce#+"% $e ca"e#a 7%lu=e su0=e"s% e cala$%s a7a#+e e a "3 A = $e +%"#a" a u+ilia4% =ais >"9+ica %s Dia,"a=as $e Fi"s%7 s+"a0al&a= c%= c%#$i48es $e i#cli#a4% l%#,i+u$i#al eclusi7a=e#+e e assu=i#$% a&i>+ese $e +e"=%s u=a e=0a"ca4% si=+"ica +"a#s7e"sal=e#+e3 Essasc%#si$e"a48es s% #ecess9"ias >%is cas% #% @%sse= "es>ei+a$as +%"#a"ia= %7%lu=e su0=e"s% assi=+"ic% @a+% ?ue i#$ui"ia u= +"i= e +%"#a"ia % >"%0le=aai#$a =ais c%=>le% >%is +e"a=%s ?ue ,e"a" #%7%s Dia,"a=as ?ue +"a+asse=$es+a c%#$i4%3

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23/26

Dia,"a=as 09sic%s $e Fi"s%7 >a"a X B

Dia,"a=as B9sic%s $e Fi"s%7 >a"a VB

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O0+e#4% $%s Dia,"a=as $e "s%7 >a"a X B e Z B :



24/26

Dia,"a=as $e Fi"s%7 >a"a B

Dia,"a=as $e Fi"s%7 >a"a VB

De7e/se le=0"a" $e ?ue %s Dia,"a=as $e Fi"s%7 s% li=i+a$%s a #,ul%s $e

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T - W * e T -# W D a+ T - W D e T -# W *3Essa a si+ua4% @a7%"97el #a7e,a4% ?ue #%s $a >%ssi0ili$a$e $e

,a"a#+i" c%= 0%a >"ecis% % e?uil0"i% $e @%"4as e $e =%=e#+%s3 Esse

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MODELO DE EQUILÍBRIOC%=% 7i=%s %s Dia,"a=as $e Fi"s%7 c%#se,ue= "elaci%#a" $i"e+a=e#+e % ;

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Documents

Relatório TP2