Ensayo de Resistencia a La Flexion en Vigas de Aluminio

8/17/2019 Ensayo de Resistencia a La Flexion en Vigas de Aluminio

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ENSAYO DE RESISTENCIA A LA FLEXION EN VIGAS DE ALUMINIO

ARANZA JIMENEZ GUZMAN 1102135

KAREN LIZETH DIAZ CASTIBLANCO 1102115LINA MARCELA AYALA BARBOSA 1102101

NESTOR JAVIER MOLINA RODRIGUEZ 1101428

UNIVERSIDAD MILITAR NUEVA GRANADA

ROGRAMA INGENIER!A CIVIL

BOGOT" DC

201#$1


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INDICE

INDICE................................................................................................................. 2

OBJETIVOS........................................................................................................... 3GENERAL..........................................................................................................3

ESEC!FICOS..................................................................................................... 3

INTRODUCCI%N....................................................................................................3

MARCO TE%RICO..................................................................................................4

N&'() *+(,-. '&+(/( /- ( /*(&*'*( /- (&('&*& 6107 &. - .&+- /- -.(9& /- --+-.'&( :-;*( 3) '*& /- +& /- -*'-.*( (( /*:--.'- -*&.- '(.-(-........................6F*,>( 4) C*>& /- +& (( -:>-=& 9 /-:&+(*&.-..................................................7F*,>( 5) E>(*&.- (( ( '(:&+(*


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F*,>( 11 D*(,(+( /- (,( /-:&+(*.*/( &. -+(- -. ( ->*.(12F*,>( 12 R---.'(*.*/(7 &. -+(- -. -.'&7 K(-. D(=.....13F*,>( 13 D*(,(+( /- (,( /-:&+(*.*/( &. -+(- -. - -.'&....14F*,>( 14 R---.'(*( 15 D*(,(+( /- (,( /-:&+(**.(............................11T(( # T(( /('& '&+(/& (( ( +*.( >.*/( &. -+(- -. ( ->*.( ..................11T(( C(('-'*( :*( /- ( +*.( >.*/( &. -+(- -. - -.'&.......................12

T(( 8 /('& '&+(/& (( ( +*.( >.*/( &. -+(- -. - -.'&...............................13T(( C(('-'*( :*( /- ( (( -. T................................................................14T(( 10 /('& '&+(/& (( ( (( -. :&+( /- T.........................................................14

OBJETIVOS

GENERAL

D-'-+*.( +-/*(.'- - -.(9& /- -*'-.*( ( ( :-;*+*.*&7 &. > /*:--.'- --*:*(*&.-?

ESEC!FICOS O-( - &+&'(+*-.'& /- ( /*:--.'- &-'( /- (>+*.*& &+-'*/( ( :-;**.( >.*-(?

C(>( - +& /- -('**/(/ 9 - &'(.'- >- - --.'( -. (/( (( /- (>+*.*&?

R-(*=( - ,:*& /- M&+-.'& F-'& -:>-=& &'(.'- /- (/( >.( /- ( ((?

A.(*=( 9 &.>* > /- ( /*:--.'- (( /- (>+*.*& - ( >- '*-.- +-&

-./*+*-.'& -,. & >& -(*=(/&?

INTRODUCCIÓN

E -*(/& /- >. +('-*( - ('>(+-.'- >.( /- ( ( + -,>( (( --'( - +-/*&(+*-.'- 9 -*'( >. (>& /-&.*/-(/& /- & ->& .('>(-? D-/- (- /(/( (&.*-.*(*/(/(.( -. '&.& ( -*(/& /- &/>'& >- >'**=(+& -. .>-'( */(&'*/*(.( ( */& -. (>+-.'&? T&/& >. &,&? D- '&/& & +('-*(- >- - -*(. -;*'- >.& -. -


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>- -'( ('**/(/ - (/( -= + -.'(- 9 > +'*- &*-/(/- & &.*-'-. -. >. +('-*(+&/-.& /- ,(. :>'>&) - (>+*.*&? R&,-

E. ( +(9&( /- ( *.,-.*-( - (>+*.*& - >'**=(/&7 & --+&7 -. ( *.,-.*-( ** ->'**=(/& (( :((/(7 (+(/>( & -(7 & > (& -& 9 > :* +(.-& ( (>*'-'>('(+*. & >'**=( (( > /*-P& -''*&?

MARCO TEÓRICO

L( :-;*.( &*-/(/ >- '*-.-. (,>.& +('-*(- /- - /&(/& & - >(/& -. --.'*/& &.,*'>/*.(7 *. &+--7 -& * - +('-*( '*-.- ( &*-/(/ /- -('**/(/ ->-( >:&+( &*,*.( /-> /- -'*(/( ( (,(Q (( - (-& 9 ( +(/-( '*-.-. ( &*-/(/ /- - +>9/'*- /- &-(( - +*'- -'*& *. ,-.-( >'>( /- +('-*( & >( & &.*-'- -. >.+('-*( &. >.( &*-/(/ /- >('>( '*? L( :-;*( '(((. ( :-;*-=( --./*>(- -. > --&.,*'>/*.(7 /- +&/& >- &&>-. - ,*& /- ( -*&.- '(.-(- &. --'& ( &*.+-/*('&? H*--7 R?2001??308?

DIAGRAMAS DE CORTANTE Y MOMENTO FLECTOR

E. >.( (( ,*/( ( ( >- - - (*(. (,( /- /*'*.'( +(,.*'>/-7 - ,-.-(. >.( :>-=(&'(.'- V 9 >. +&+-.'& :-'& M7 -'& - /-(&(. ( *.'-*& /- ( (( 9 -. (/( >.'&/- -- /- -:--.*( /- ( ((? (( '(=( & /*(,(+( /- V Y M - /--. (>( ( :>-=(&'(.'- +;*+( 9 '-+*.( -. -&7 9 /- ( +*+( +(.-( (( - +&+-.'& :-'&? H*--7R?2001??311?

Figura 1: Diagrama de cortante y momento flector

N&'() -. .-( *+(,-. -('(/( /-'')-?**-*'9?&,**&,(+(*&.I.,-.*-*(M-(.*(UB)G>&W016+-/*(F*-)D*(,(+(VM?,? E /( (/& 18 /- (* /- 2015 ( ( 8)00+

http://es.wikiversity.org/wiki/ProgramacionIngenieriaMecanicaUPB:Grupo_01#/media/File:DiagramaVM.jpghttp://es.wikiversity.org/wiki/ProgramacionIngenieriaMecanicaUPB:Grupo_01#/media/File:DiagramaVM.jpghttp://es.wikiversity.org/wiki/ProgramacionIngenieriaMecanicaUPB:Grupo_01#/media/File:DiagramaVM.jpghttp://es.wikiversity.org/wiki/ProgramacionIngenieriaMecanicaUPB:Grupo_01#/media/File:DiagramaVM.jpg


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MOMENTO FLEXIONANTE

E +&+-.'& :-;*&.(.'- & :-'& - ( >+('&*( /- & +&+-.'& /- ( :>-=( (*(/( -. (*,( --'& ( (.& --./*>(7 (/-+ - - -.(,(/& /- (- >( & :-;*&.( ( *,(?

(( /-'-+*.( - *,.& /- +&+-.'& :-'& - .--(*& /-:*.* ( /*-*. +&+-.'& &*'*& -& * ( (*( ((& - .-,('*&7 ( &.'*.>(*.( *,( &. +&+-.'& &*'*& 9 .-,('*&? M>P&7 E?2013??3?

Figura 2: tipos de flexión en una viga

N&'() -. .-( *+(,-. -('(/( /- '')-?*/-(-?.-'('(--9-:>-=&$.&+($9$&'(.'-? E /( (/& 1 /- (* /- 2015 ( ( 2)00+

ESFUERZO NORMAL

E'& -:>-=& - /(. & - +&+-.'& :-'& '(+*. - /-.&+*.(. -:>-=& /- :-;*(. ( ('* /- ( :( /- :-;*-=& .&+(- &. .>&? M>P&7 E?2013??4?

σm = Mc

I -:>-=& +;*+& .&+(

σx = My

I -:>-=& .&+(

Dónde - σm - - -:>-=& +;*+& .&+(7 Mc - - +&+-.'& :-'& /-/- - -- -.'(7 I

- ( *.-*( /- ( -*'(! " e# σx - - -:>-=& .&+( (>(>*- /*'(.*( /- -- .->'(

ESFUERZO CORTANTE

S- '*-.- >- (( - -:>-=& &'(.'- -. & +&+-.'& ,-.-(/& & - -- 9 ( :>-=( *.'-.(

&'(.'- 9 >- ((. & - -- 9 &. .>( & '(.'& - '*-.- >-)

M90

R-(*=(./& /--- 9 >'*'>*&.- &. --'& ( +&+-.'& /- *.-*( /- (/( -*


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D-=& +;*+&7 I - - +& /- -*'-.*(9 -'- '(+*. - -*- &+& S? (/-+ -'( :( - +>9 >(/( -. ( *,( /- -*/ /- ( :>-=( &'(.'- - '*-.-)

D'&7 I +&+-.'& /- *.-*( /- '&/( - -( /- ( -*- ( '(.:&+(*&.- /- & -:>-=& 9 ( /-:&+(*&.- - ---.'(. & - >&/- +& 9( >- -'- +'&/& >-/- -;'-./-- ( ( '(.:&+(*&.- /- /-:&+(*'(/& >.

*'-+( /- ->(*&.- /- '- ->(*&.- &. '- *.


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Figura 4: Circulo de mohr para esfuerzos y deformaciones

N&'() *+(,-. '&+(/( /- ( /*(&*'*( /- (&('&*& 6107 &. - .&+- /- -.(9& /- --+-.'&( :-;*


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S- *.**< ( '*( &. >.( *.'&/>**? L>-,& - /-'-+*.(&. ( /*+-.*&.- :*(/- (/( >.( /- ( &-'(7 &+& - ( ('>(7 --&- 9 /-+?

S- -< (/( &-'( ( ( M>*.( U.*-( &**&../&( /- +(.-( >- ( (,( :>-- (*(/(

-. ( +*'(/ /- ( >= /- (/( &-'(7 >-,& -.'- - *'/*.( /- ( &-'( 9 ( *,(7 - >*< >. &/*& (( *.**( &. ( (*(*.( (- /- /('&7 (( > &'-*& &-(+*-.'&?

CALCULOS

A &.'*.>(* --'*& (&- /- (,( 9 /-:&+(*.*-(

BARRA MACIZA

Figura " #epresentación gr$fica de la %arra maciza& 'aren D(az

"REA DE LA SECCI%N TRANSVERSAL 1¿2

I.-*( 1/12¿4

Y 0?5 *.@ 0.5¿

3

)a%la 1 caracter(stica de la %arra maciza

CARGA E:>-=& Τ * DEFORMACION

0 0 10?3 ?4 21?48 1?48 35


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2?22 2?22 5038?# 38?# #048?0 48?0 0?1 ?1 88

)a%la 2 datos tomados en la %arra maciza

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

f(x) = 0.96x - 14.8

R² = 0.97

esfuerzo vs deformaco!

deformaco!

esfuerzo ("s)

Figura * Diagrama de carga vs deformación

(( (( - &'(.'-

ECUACI%N DESCRICI%N

Τ =VQ

It

V = I t Τ

Q

T-:>-=&V &'(.'-I *.-*(' (.& /- ( -*


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LAMIMAS SE7ARADAS

Figura + #epresentación gr$fica de la l$mina separada& 'aren D(az

"REA DE LA SECCI%N TRANSVERSAL 1¿2

Y 1/12¿4

@ 0?5 *.

0.5¿3

)a%la 3 Caracter(sticas de las l$minas separadas


0 0 0?3 ?4 451?48 1?48 1152?22 2?22 18038?# 38?# 24548?0 48?0 31558?43 58?43 410?1 ?1 515

)a%la 4 datos tomados para las l$minas separadas


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0 100 200 300 400 500 6000

10

20

30

40

50

60

70

80

90

f(x) = 0.15x # 2.22R² = 1


deformaco!

esfuerzo ("s)

Figura , Diagrama de carga vs deformación de las l$minas separadas

LAMINAS UNIDAS CON REMAC8ES EN LAS ES9UINAS

Figura 1- #epresentación gr$fica de las l$minas unidas& unidas con remaches en las es.uinas&

'aren D(az

"REA /- ( -*


12/17

D- 4 ( 5 0?0#8 +D- 5 ( # 0708 +D- # ( :*.( 07032 +Y 0?5 *.@ 0.5¿

3

)a%la Caracter(sticas f(sicas de las l$minas con remaches en las es.uinas


0 0 20?3 ?4 1001?48 1?48 1202?22 2?22 1#038?# 38?# 1548?0 48?0 22458?43 58?43 2#5?1 ?1 301

)a%la " )a%la datos tomados para las l$minas unidas con remaches en las es.uinas

0 50 100 150 200 250 300 3500

10

20

3040

50

60

70

80

90

f(x) = 0.28x - 12.67

R² = 0.97


deformaco!

esfuerzo("s)

Figura 11 Diagrama de carga vs deformación de las l$minas unidas con remaches en las es.uinas


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LAMINAS UNIYDAS CON REMAC8ES EN EL CENTRO

Figura 12 #epresentación gr$fica de las l$minas unidas& con remaches en centro& 'aren D(az

"REA /- ( -*


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0 50 100 150 200 250 3000

10

20

30

40

50

60

70

80

90

f(x) = 0.31x # 2.22

R² = 0.99


deformaco!

esfuerzo("s)

Figura 13 Diagrama de carga vs deformación de las l$minas unidas con remaches en el centro

LAMINAS EN FORMA DE :T;

Figura 14 #epresentación gr$fica de la %arra en )& 'aren D(az

"REA /- ( -*


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0 0 5?3 ?4 231?48 1?48 512?22 2?22 83

38?# 38?# 1048?0 48?0 14558?43 58?43 180?1 ?1 248)a%la 1- datos tomados para la %arra en forma de )

0 50 100 150 200 250 3000

10

20

30

40

50

60

70

80

90

f(x) = 0.31x # 2.22

R² = 0.99


deformaco!

esfuerzo("s)

Figura 1 Diagrama de carga vs deformación de %arra en forma de )

COM7ARACION MODULOS DE LA ELASTICIDAD


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0 100 200 300 400 500 6000

100

200

300

400

500

600

700

$%&'R$%*

+,%R&$%*

,/,R%(')

S-*- 1) +(*=(

S-*- 2) &. -+(- -. ( ->*.(

S-*- 3) &. -+(- -. - -.'&

S-*- 4) -. :&+( /- T

S-*- 5) (+*.( -((/(

ANALISIS DE RESULTADOS

S- /-'-+*.< - +& /- -('**/(/ /- (/( >.& /- ( -*&.- /- (-& 9 ( -( /- - -+*+& +('-*(7 /-*/& ( ( :&+( (+*.(- &->-'(7 9 ( ( :&+( -. T 9 ( -( '(.-(/- (/( >.( /- -(7 - -.&.'< >- ( (( &+('( /- (-& --.'& >. +& /- -('**/(//- 0?# * *-./& >-*& ( (& /- +& /- -('**/(/ /- ( &-'( /- +*.( -((/(>- ->*(-.'- ( 07145 *?

T&/( ( &-'( ( -( /- - /- +*+& +('-*( - &+&'(. /- +(.-( /*:--.'-? L( &-'(>- +(9& -*'-.*( '*-.- - ( +(*=( 9( >- - ( >- '*-.- - +& /- -('**/(/ + ('&?

CONCLUSIONES

S* & >- - ->*-- &.'>* - >.( *,( >- -+*'( *-'( +&**/(/ - -( '(.-( (-+-( - - /- ( (( +(*=( 9( >- - - + (/->(/& (( -'( &./**(./& >. &>+-. +.*+& & &-'& - >'**=( >.( (( &.-*&7 >- - -( /- ( -*. :('& *+&'(.'- -. -


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+&+-.'& /- (- >&7 9( >- - >-/- (&( +('-*( 9 +-&( ( &./**.(-'>'>(

L( &**9- -. ( -('**/(/ /- --+-.'&7 /-*/& ( >- &/>- >.'& /-/-**/(/7 >- -(. ( >- - --+-.'& '-.,( >.( '(.**(7 & -./- - -:-*- -. >.( -'>'>( +-'*( (- ( +-.&-

-:&(*&.- &*- >- - ->*-(.7 (( /(- + -'(**/(/ ( ( *,( 9 (+*.&( & >.'&/- /-**/(/ 9 & &.*,>*-.'- >- > '(.**P&7 E? 2013? !sfuerzo normal y cortante en vigas? B(-&.(7 E(P() E/*'&*(

A:(&+-,(?

T&-/&7 M?A? 2010? ec$nica de materiales M;*&7 D?F) @>*.'( -/**

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Ensayo de Resistencia a La Flexion en Vigas de Aluminio