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BENEMRITA UNIVERSIDADAUTNOMA DE

PUEBLA

FACULTAD DE INGENIERA QUMICAIngeniera el!"ri!a

Profesora: Dolores Garca Toral

#$er"a R%&ale& DalilaLara Delga'% Lilian

Pan%(a)a Ran!(% Angli!aVilla Gali!ia Selene

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TORSINLa "%r&i*n e& el e+e!"% ,r%'$!i'% ,%r a,li!ar +$er-a& ,aralela& 'e .agni"$' ,er% en &en"i'% %,$e&"% en el .i&.% &*li'%/

En ingeniera0 "%r&i*n e& la &%li!i"a!i*n 2$e &e ,re&en"a !$an'% &$n .%.en"% &%3re el e4e l%ngi"$'inal 'e $n ele.en"% !%n&"r,ri&.a .e!6ni!%0 !%.% ,$e'en &er e4e& %0 en general0 ele.en"%$na 'i.en&i*n ,re'%.ina &%3re la& %"ra& '%&0 a$n2$e e& en!%n"rarla en &i"$a!i%ne& '

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An6li&i& ,reli.inar 'e l%& e&+$er-%& 'e

Lla.an'%7 a la 'i&"an!ia ,er,en'i!$lar

'e la +$er-a 'F al !en"r% 'el e4e &e "iene,%r e&"6"i!a8

Mien"ra& 2$e la rela!i*n %3"eni'a e9,re&a $na !%n'i!i*n i.,%'e3en &a"i&+a!er l%& e&+$er-%& !%r"an"e& en !$al2$ier &e!!i*n "rane4e0 n% 'i!e !%.% &e 'i&"ri3$)en l%& e&+$er-%& !%r"an"e& en la &e!!%3&er5a 2$e la 'i&"ri3$!i*n real 'e l%& e&+$er-%& 3a4% $na !arge&"6"i!a.en"e in'e"er.ina'a/

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N% ,$e'e (a3er e&+$er-%& !%r"an"e& :ni!a.en"e en $n ,lan%/ Se &a"%r2$e a,li!a'% ,r%'$!e e&+$er-%& !%r"an"e& en la& !ara& ,er,en'ie4e/ Per% ,%r !%n&i'era!i%ne& 'e e2$ili3ri% &e re2$ieren e&+$er-%& ila& !ara& +%r.a'a& ,%r l%& ,lan%& 2$e !%n"ienen 'i

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C%n&i'eran'% $n e4e ela3%ra'% 'e '$ela& &e,ara'a& &$4e"a& !%n ,a&a.3%& e9"re.%& a 'i&!%& / Si &e ,in"an .ar!a& en '%& '$ela& a')a

%3&er5a 2$e la& '$ela& &e 'e&li-an $na !%n re&,e!"% a la %"ra a,li!an ,are& ig$ale& ) %,$e&"%& a l%& e9"re.%& 'el e4e/ A$n2$e n'e&li-a.ien"% en $n e4e 'e $n .a"erial (%.%gne% ) !%(e&i5%0 la "e'e&li-a.ien"% e9i&"ir60 l% !$al .$e&"ra 2$e %!$rren e&+$er-%& l%ngi"$'inale& a& !%.% en l%& ,lan%& ,er,en'i!$lare& al e4e/

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%r& n 0 e %r.a! %n e $n !ir!$larLa "%r&i*n &e re;ere a la 'e+%r.a!i*n 'e $na 3arra re!"a al &er !arga'a ,%r .%.en"%&

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De+%r.a!i*n 'e $na 3arra !i

C%n&i'ere.%& $n e4e !ir!$lar $ni'% a $n &%,%r"e;4% en $n e9"re.%

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Pr%,ie'a' i.,%r"an"e8C$an'% &e &%.e"e a "%r&i*n $n e4e !ir!$lar0 "%'a

&e!!i*n "ran&5er&al ,er.ane!e ,lana/Para en"en'er .e4%r e&"a ,r%,ie'a'

!%.,arare.%& $na 3arra !ir!$lar !%n $na 3arra!$a'ra'a0 .ien"ra& 2$e en la 3arra !ir!$lar"%'a& la& &e!!i%ne& ,er.ane!en ,lana& en la3arra !$a'ra'a &$& &e!!i%ne& "ran&5er&ale& &e!%.3an ) n% ,er.ane!en ,lana&/

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Se 'e.%&"r* 2$e en $n e4e !ir!$lar&%.e"i'% a "%r&i*n "%'a &e!!i*n "ra&5er&al,er.ane!e ,lana ) &in 'i&"%r&i*n> ,%r l%"an"% la 'e+%r.a!i*n !%r"an"e en $nele.en"% ,e2$e% !%n la'%& ,aralel%& )

,er,en'i!$lare& al e4e 'e la e!(a ) a $na'i&"an!ia 'el e4e8

D%n'e e& el 6ng$l% 'e gir% ,ara $nal%ngi"$'P%r %"ra ,ar"e &ig$ien'% e&"a e!$a!i*n

,%'e.%& 'e!ir 2$e la 'e+%r.a!i*n!%r"an"e e& .69i.a en la &$,er;!ie 'ele4e0 '%n'e !/ Se "iene8

Per% &i eli.ina.%& 'e la& '%& e!$a!i%ne&an"eri%re& "ene.%& la e!$a!i*n8

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C%n&i'eran'% l%& e&+$er-%& 'e !%r"e en $n e4e !ir!$lar3a4% el rang% el6&"i!% &e ,$e'e e&!ri3ir .e'ian"e laLe) 'e #%%

D%n'e G e& el .%'$l% 'e rigi'e- % .%'$l% !%r"an"e'el .a"erial e&+$er-% !%r"an"e ,%r 'e3a4% 'el li.i"e'e $en!ia/M$l"i,li!an'% a.3%& .ie.3r%& 'e la e!$a!i*n ,%r G

&$&"i"$)en'% en la e!$a!i*n an"eri%r n%& 2$e'a8

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T%.an'% en !$en"a la e!$a!i*n 'e "%r&i*n ) &$&"i"$)en'%n%& 2$e'a8

Per% la in"egral en el $l"i.% ele.en"% en el .%.en"% ,%lar 'einer!ia 'e la &e!!i*n "ran&5er&al !%n re&,e!"% al !en"r% O/ Re&$l"a8

D%n'e el .%.en"% ,%lar 'e iner!ia 'e $n !ir!$l% 'e ra'i% ! e&En !a&% 'e $n e4e ($e!% !ir!$lar 'e ra'i% in"eri%r ) e9"eri%r 0 el

.%.en"% ,%lar 'e iner!ia e&

T e&"ar6 en l3,$lg

! % 'a'a en ,$lg 'a'a en

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E4er!i!i%Un e4e !iln'ri!% ($e!% "iene H/ . 'e larg% )

'i6.e"r% in"ern% ) e9"ern% 'e JK ) K ..0re&,e!"i5a.en"e Q$ ,$e'e a,li!ar&e &i ele&+$er-% !%r"an"e n% ,$e'e ,a&ar 'e HK MPaTorque mximo admisible. E& el "%r2$e T

,ara el !$al / C%.% e&"e 5al%r e& .en%r 2$e ell.i"e 'e $en!ia0 ,$e'e $&ar&e la e!$a!i*n

re&%l5ien'% e&"a e!$a!i*n D%n'e

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ESFUERO DEFORMACIN EN EES ESTTICAMENTEINDETERMINADOS

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ESFUERO

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EJE ESTATICAMENTE INDETERMINADO

Un ele.en"% 'e !$al2$ier "i,% &e !la&i;!a !%.%e&"6"i!a.en"e in'e"er.ina'% &i el n:.er% 'erea!!i%ne& 'e&!%n%!i'a& e9!e'e el n:.er%'i&,%ni3le 'e e!$a!i%ne& 'e e2$ili3ri%/

La& rea!!i%ne& en l%& &%,%n% &%n ne!e&aria& ,ara e2$ili3ri% e&"a3le &e lla.ann$.er% 'e e&"a& re'$n'a!%.% el gra'% 'e in'e"er.i

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ESFUERO EN EES ESTTICAMENTE INDETERMINADOS

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EJEMPLO

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EJEMPLO

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Bi3li%gra+a

P/ Beer0 R$&&ell/ Me!6ni!a 'e .a"eriale&/ M! Gra ##i33eler0 R$&&ell C/ Me!6ni!a 'e .a"eriale&/ PEARSOEDUCACIN0 M9i!% KHH/