torsion flexion y deflexion

7/25/2019 Torsion Flexion y Deflexion

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TORSION FLEX

DEFLEA

VA

UNIVERSIDAD DE EL SALVADOR.FACULTAD MULTIDISCI!LINARIA DE ORIENTE.

DE!ATARTAMENTO DE INGENIERIA Y AR#UITECTURA.


2/29

Torsion en elementos cerradopared delgada.

La $art%&'(ar%)a) *'n)a+enta( )e estas se&&%re(a&%-n &ara&terst%&a )e s's )%+ens%nes ge+/)e (as )%+ens%nes )e (a se&&%-n trans0ersa( 1e( e+'&3 +enr 4'e (a tra 1(a (ng%t') )e( &ntrn2


3/29

Formula de la torsin para tubpared delgada.

La *'er5a &rtante tta(

S

)s

* )s 7r

t

E( 8'9&rtante es

F-r+'(a )e trs%-n $ara t's )e $are) )e(ga)a

E( $ar )e trs%-n tta(


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Ejercicios.

Un $ar )e trs%-n T; < =N.+ se a$(%&a a'n e9et%ene (a se&&%-n trans0ersa( +stra)a en (a >g're( e*e&t )e (as &n&entra&%nes )e es*'er5s, ? es*'er5 &rtante en (s $'nts A ? B.

Ca(&'(an) e( es*'er5 &$'nt A@rea r)ea)a

A;L3A;1++2 1

A;


5/29

Cnt%n'an)

Ca(&'(an) e( es*'er5en e( $'nt B. @rea

r)ea)aA;L3

A;1++2 1


6/29

Torsion en elementos desecciones abiertas de par

delgada Ls e(e+ents )e $are) )e(ga)a )e se&&%-n a%erta

&erra)a &nst%t'?en 'na a$(%&a&%-n %+$rtante en e()e es*'er5s $(ans. $r4'e s's $are)es $nen $res%sten&%a a (a 8e%-n.


7/29

Torsion en elementos desecciones abiertas de par

delgada;

;

Coefcienterectangular


8/29

E9er&%&%.Un ng'( )e a&er )e + )e (ng%t') t%ene 'na se&&%-n traX


9/29

Cnt%n'an)

T+an) )e (a e&'a&%-n

Des$e9a+s T

A( s'st%t'%r )ats tene+s T =899.11!.mm

!ara e( ng'( )e trs%-n tene+s:

A( s'st%t'%r )ats en (a *r+'(a anter%r tene+s

Cn0%rt%en) a gra)s.


10/29

FLEXION DE VIGAS COM!UEST

La *r+a +as e>&%ente )e s$rtar &argas . La 0%ga 4'e se trans*r+a.

E( +%s+ a%+a s%&.


11/29

FLEXION DE VIGAS COM!UEST

Re(a&%-n M+entKC'r0at'ra

Es*'er5s nr+a(es 1*-r+'(as )e 8e%-n2

Ra5-n +)'(ar. M+ent )e Iner&%a )e

se&&%-n trans*r+a)a

A

&

B

9 % %


12/29

E9er&%&%.Una 0%ga )e +a)era s%+$(e+ente a$?a)a )e 7++ Hg'ra. Ca(&'(ar (a &arga &n&entra)a 4'e a$(%&arse en e( &entr )e( tra+ )e + (arg.Eacero=200GPay Emadera=10GPa, (s es*'er5s a)+%s%(es sn 77QM!a $ara e( a&er ? +a)era res$e&t%0a+ente


13/29

S('&%n.

E4'%(%r% Genera(

Crte K 7

Crte HKH

M


14/29

D%agra+as )e *'er5a&rtante ? ++ent8e&tr

"=1.#p

TRANFORMANDO ACERO A MADERA.

FIGUR

Ca(&'(an) &entr%)e )e (a se&&%-n


15/29

Ca(&'(an) Iner&%a 12

CALCULANDO !.

!ara (a +a)era

!ara e( a&er.

!rar en +a)era.

@NO CUM!LE

!rar en a&er

@SI CUM!LE

La &arga 4'e $'e)e a$(%&arse es:


16/29

Deexin: mtodo reamom

Este $r&e)%+%ent es$e&%a(%5a) es $art%&'(ar+ente&n0en%ente s% se re4'%ere s(a+ente (a )e8e%-n )e 'ns

$&s $'nts sre 'na 0%ga 'n +ar&.

!r ( genera( se 'sa e( +/t) $r )esarr((arse $aratener s( e( )es$(a5a+%ent ? (a rta&%-n en 'n s( $'ntsre 'na 0%ga.

Teorema reamomento.

Las &n)%&%nes )e *rnteras n entran en (a )e)'&&%-n )e (stere+as ?a 4'e ests se asan en (a %nter$reta&%-n )e%ntegra(es )e>n%)as.


17/29

Teorema reamomento.

T

E9er&%&%


18/29

E9er&%&%.

Ut%(%5an) (s tere+as )e reaKM+ent, tenga e( )es$rta&%-n en C, as &+ (a )e8e%-n +%+a en e( etre+ AB.

E4'%(%r% Genera(


19/29

D%agra+as )e *'er5a&rtante ? ++ent8e&tr C'r0a e(st%&a


20/29

Ca(&'(an)

Ns a$?are+s )e (s gr>&s )e ++ent ?&rtantes

Gra>& M1X2 Gra>& V1X2


21/29

Ca(&'(an)

Ca(&'(an) Ca(&'(an)


22/29

Ca(&'(an) Ca(&'(an)

Ca(&'(an)


23/29

Ca(&'(an) Crte K

Ca(&'(an) )%stan&%a X

1In&rre&t2

1In&rre&t

1Crr


24/29


25/29

Deexion: !todo desuperposicin.

En &n)%&%nes a)e&'a)as (a )e8e%-n )e 'na 0%ga $r)0ar%as &argas )%*erentes 4'e a&tan )e +anera s%+'(tnse $'e)e )eter+%nar s'$er$n%en) (as )e8e%nes $$r (as +%s+as &argas a( a&t'ar $r se$ara).

Cargas )%str%'%)as

En &as%nes en&ntra+s 'na &arga )%str%'%)a 4'e n %n&('%)a en 'na ta(a )e )e8e%-n )e 0%gas ? en ests &ares'(ta t%( e( +/t) )e s'$er$s%&%-n.


26/29

!r%n&%$% )e s'$er$s%&%-n

Este $r%n&%$% es 0(%) s%e+$re 4'e (a &ant%)a) $)eter+%nar sea 'na *'n&%-n (%nea( )e (a &arga a$(%

En estr'&t'ras r)%nar%as es 's'a( 4'e e( $r%n&%$%$ara es*'er5s, )e*r+a&%-n 'n%tar%a ? ++ents

8e%nantes, ? +'&3as tras &ant%)a)es a)e+s ))e8e%nes

Ejercicio


27/29

Ejercicio.

!ara (a 0%ga en 0(a)%5 ? (a &arga 4'e se +'estran e)eter+%ne (a $en)%ente ? )e8e%-n en e( $'nt B.

Use .

Ca(&'(an) I.

.


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!r e( +/t) )e s'$er$s%&%-n )esg(sa+s (as &arg

T+an) (s )ats )e (a ta(a &

Dn)e:

! ; H< ( L;7 $'(g X ; 7

Der%0an) 'na 0e5 tene+s

S'st%t'?en) 0a(res tene+s.


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T+an) (s )ats )e (a ta(a&as I.

Dn)e:

La $en)%ente es:

La )e8e%-n es:

torsion flexion y deflexion

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