esfuerzo simple de corte y de aplastamiento docx

8/19/2019 Esfuerzo Simple de Corte y de Aplastamiento Docx

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RESISTENCIA DE

MATERIALESUNIVERSIDAD TECNICA DE AMBATO

NG.

ERNANDO

URRUTIA.


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RESISTENCIA DE MATERIALES

ContenidoESFUERZO SIMPLE.............................................................................................. 2

103............................................................................................................... 3

104.-.............................................................................................................5

105............................................................................................................... 9

106.............................................................................................................12

107.............................................................................................................13

108.............................................................................................................14

109.............................................................................................................15

110.............................................................................................................17

111.............................................................................................................19

112.............................................................................................................21

113.............................................................................................................23

ESFUERZO CORTANTE....................................................................................... 25

114.............................................................................................................26

115.............................................................................................................29

116.............................................................................................................31

117.............................................................................................................34

118.............................................................................................................35119.............................................................................................................37

120.............................................................................................................39

121.............................................................................................................41

ESFUERZO DE CONTACTO O APLASTAMIENTO..................................................42

123.............................................................................................................43

124.............................................................................................................45

125.............................................................................................................47

126.............................................................................................................49127.............................................................................................................51

128.............................................................................................................53

129.............................................................................................................56

IN. FERNANDO URRUTIA P!"#$% 1


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ESFUERZOSIMPLE


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103.- Deterine e! "#io $e%o W &'e $'eden %o$ort(r !o% )(*!e%o%tr(do% en !( +,'r(. Lo% e%'ero% en !o% )(*!e% AB / AC no de*ene#)eder !o% 100 MP( / 50 MP( re%$e)ti(ente. L(% "re(%

tr(n%er%(!e% de (*o% %on2 400 mm2

P(r( e! )(*!e AB / 00 mm2

P(r( e! )(*!e AC.



5/87


DAOS.

&%'( 100 MP%

&%)( 50 MP%

AREA AB( 400 mm2

( 4 * 10−4

m2

AREA AC( 200 mm2

( 2 * 10−4

m2

SOLUCION.

• P+,)/, % %)%+ %,+ P +), % )%' AB )%' AC

%#)%$, % #"#$ ,+/% σ = P

A

R), % )%' AB.

100mpa= P

4∗10−4 m2

P 40 67.

R), % )%' AC.

σ = P

A

50mpa= P

2∗10−4 m2

P 10 67.

• E)%/, % /%,+#% +:% +), % ; #"%%/, % )+,%+% % /%$+% )/#+ ),$ % ),$#)#


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D

A

6/

4/

4/ 3/ 3/

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F

100N 200N

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EF

8

7ODO F

CE

00 67

ED

EF

7ODO E

7ODO B

9:

BA

BC

BD


S$45*10N ? S$30*40N @ ( 0

( 7.07N ? 20N

W ;.0; 67.

104.- C(!)'!e $(r( !( (r(d'r( de !( +,'r( !o% e%'ero% $rod')ido%en !o% e!eento% DF CE < BD. E! "re( tr(n%er%(! de )(d( e!eento e%

100 mm2

. Indi&'e !( ten%i=n >? o *ien !( )o$re%i=n >C?.



7/87


DAOS.

&(

&)(

&'(

AREA TRANSVERSAL( 1200 mm2

( 120 10−6

m2

SOLUCION.

• R%#:%/, % /%,+#% +:% $ A +), % ;. ; % /%,+#% /,/$, A.

>MA( 0

-4/100N @ 7/200N ? 10 R ( 0

-400 @ 1400 ( -10R*-1 M##)%/, ,+ -1 %+% G%+ , H+/#$,,##,.

1800 ( 10R

R ( 180 N.

>F.A( 0

R% ? R @ 100N @ 200N ( 0

R% ? R ( 300 N

R% ( 300 N @ 180N

R% ( 120 N

• E$),$+%/, !$", = '#)% $ +#!$", DEF.

T%$"$ ( 4J3

K( Tangente−1

4J3

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8/87


• E)%/, % /%,+#% +:% +), % $,, F )%)%/, +:, DF.

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R ? FD*S$53.13( 0

FD (− Rfy

Sen53.13

FD (−180knSen53.13

FD ( - 225 N.

>F.( 0

- EF @ FD*C,53.13( 0

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-EF ( 224*C,53.13

EF ( -134.40 N

&( FD

AREA .

&(−225 KN

1200 x10−6

m2

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&d -1@;.5 $(

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>F.( 0

ED @ 200N( 0



9/87


ED(200N

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EF - CE(0

CE(134.40 N

&)(134.4 KN

1200 x10−6

m2

&)(112000 %

&e) 11.$(

C,$)#/, = +:, $#


10/87


AB( -144.239N

>F.%( 0

AC @ 144.239*C,56.3 ( 0

AC( 80.2N

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>F.'( 0

-AB*S$33.6 ? BD*S$56.31 ( 0

BD(

−144.239 KN ∗Sen33.6

Sen56.31

BD( - 95.93 N

&(BD

1200 x10−6

m2

&'(−95.93 KN

1200 x10−6m

2

&'( - 79943.67 %

&*d - ;.43 $(

C,$)#/, = +:, $ BD ! ),/+#/#$, % % +)+% ,+= $"%#,.



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F

B

40N

8/

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50N

C

D

A

8/

3/3/6/

B

P

E#

E/

E

EB

EB#

EB/

50 67

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EB#

40 67

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105.- Deterine $(r( !( (r(d'r( de !( +,'r( !(% "re(% tr(n%er%(!e%de !(% *(rr(% BE BF / CF de odo &'e !o% e%'ero% no e#)ed(n de

100 M7 m2

En ten%i=n ni de @0 M7 m2

En )o$re%i=n. P(r( eit(r

e! $e!i,ro de 'n $(ndeo %e e%$e)i+)( 'n( ten%i=n red')id( en !(

)o$re%i=n.



12/87


DAOS

&,+#,$( 100 MNJ m2

&),/+#,$( 80 MNJ m2

ABE(

ABF(

ACF(

SOLUCION.

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8J4

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>/( 0

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-150 ? 2.40*EB ( 0

EB(150

2.40

EB( 62.49 N ( P EB

R/%:%/, EB %+% %)%+ ),/,$$ $ Q ;.



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E' ( EB * S$

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FC ( 52.53 N ( P FC

• P%+% % ),/+#


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ACF 55 mm2

E !+% $ ),/+#


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B

8/

CA

10/

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10.- od(% !(% *(rr(% de !( e%tr')t'r( (rti)'!(d( de !( +,'r( tienen'n( %e))i=n de 30 $or 0 2 deterine !( "#i( )(r,( P &'e$'ede ($!i)(r%e %in &'e !o% e%'ero% e#)ed(n ( !o% +(do% en e!$ro*!e( 105.



16/87

B/#

AB/

AB

AC AB#A/

8

A

B

BC#

BA/

BC/

BA#

BA BC#

P

8 :


DAOS.

& T ( 100 MP%

&),+%$ ( 80 MP%

A ( 30 * 60 mm2

A ( 1800 mm2

A ( 1.8 * 10−3

m2

SOLUCIO7.

• A#)%$, % ),$, ,'#$ %#

64 ( 36 ? 100 @ 260C,

( cos−1

72

120

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( cos−1

128

160

( 36.87

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C, 36.87 ( x

8

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cos36.87

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18/87


-0.75BC *S$36.87 @ BC*S$53.13 ( P

BC-0.75BC*S$36.87 @ S$53.13 ( P

BC-1.25 ( P

BC ( -0.8P COMPRESION

• R/%:%/, BC $ ECUACIO7 .

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BA ( 0.75 * -0.8P

BA ( - 0.6P COMPRESION

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AC ( - AB*C,36.87

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&( P

A

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A

80 * 106

P% * 1.8 * 10−3 ¿ ( - 0.6P

P ( 240 N

&BC(BC

A

80 * 106

P% * 1.8 * 10−3 ¿ ( - 0.8P



19/87

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P 1@0 67 ES LA CARA MAIMA GUE SE DEBE APLCIAR SI SE APLICAMAS SE ROMPERA7 LOS SOPORES

&AC( AC

A

80 * 106

P% * 1.8 * 10−3 ¿ ( 0.48P

P ( 375 N

10;.- Un( )o!'n( de Hierro 'ndido >o F'ndi)i=n? %o$ort( 'n( )(r,((#i(! de )o$ren%i=n de 50 67. Deterine %' di"etro interior %i e!

e#terior e% de 00 / e! "#io e%'ero no de*e e#)eder de 50MP(.

DAOS.

&/%( 50 /%

P( 250 N

D#!/+, E+#,+( 200 // ( 0.2/ ( D

D#!/+, I$+#,+ ( D# (

SOLUCION.



20/87


• E/%/, % ,+/% +:, %#)%$, % )%)#


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&( P

A

A (

P

σ E)%)#


22/87


• I"%%/, % )%)#


23/87

450//450//

R.ABR)/

R

B C


10.- En !( +,'r( %e 'e%tr( $(rte de! tren de (terri(e de 'n((ionet(. Deterine e! e%'ero de )o$re%i=n en e! torn($'nt( AB$rod')ido (! (terri(r $or 'n( re())i=n de! terreno R067 AB or('n "n,'!o de 53.1o )on BC.

DAOS.

&(

R ( 20 N

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D#!/+, E+$, ( D ( 40// ( 0.04/

SOLUCIO7.

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>M.) (0

0 ( -R650// ? AB*S$ 53.1450//

20N650// (AB*S$ 53.1*450//



24/87


AB= 20 KN (650mm)Sen53.1∗(450mm)

AB=¿ 36.125350N

AB=¿ 36125.350N

• E$),$+%/, !+% %#)%/, %


25/87

A(200

A(500

A(400

3P3

2PP

A/#$#,

A)+,

B+,$)

1/ 2/ 25/

A)ero.

-P

400

P M(#

A!'inio.

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P M(#

00

Bron)e.

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500

P M(#


110.- Un t'*o de ()ero %e en)'entr( rK,id(ente %'eto $or 'n $ernode (!'inio / $or otro de *ron)e t(! )oo %e 'e%tr( en !( +,'r(. L(%)(r,(% (#i(!e% %e ($!i)(n en !o% $'nto% indi)(do%. C(!)'!e e! "#io(!or de P &'e no e#)ed( 'n e%'ero de @0 MP( en e! (!'inio de150 MP( en e! ()ero 0 de 100 MP( en e! *ron)e.



26/87


DAOS.

&.% ( 80 MP%

&.A) ( 150 MP%

&.B+,$ ( 100 MP%

+%.%( 200 mm2=0.0002m2

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+%.B+,$( 500 mm2=0.0005m2

P.% (

P.A) (

P.B+,$ (

SOLUCIO7.

• A#)%$, % ,+/% +:, %)%/, %,+ P +), %%/#$#,.

&( P

A

P ( 80 /% * 0.0002m2

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• A#)%$, % ,+/% +:, %)%/, %,+ P +), %A)+,.

&( P

A



27/87


P ( 150 /% * 0.0004m2

P ( 0.06MN.

P ( 60 N.

R%#:%/, /%,+#% +:% +), % Q %+% ,'$+ %,+ /!#/, P $ % $#


28/87




29/87

AB

C

4/2/

3/

2N

D

3/

4

C 8BA

D

3

67 150 6,

3


111.- Un( *(rr( Hoo,Jne( A >de 1506,? %o$ort( 'n( 'er( de 67)oo $'ede er%e en !( +,'r(. L( *(rr( e%t( %o%tenid( $or 'n $erno>en B? / 'n )(*!e >CD? de 10 de di"etro. Deterine e! e%'eroeer)ido en e! )(*!e.

DAOS.

( 150 "

F( 2N

D#%/+, C%'( 10// ( 0.01 /



30/87


SOLUCIO7.

• P+,)/, % $),$+%+ !$", = $)$+% $ +#%$",BCD.

T%$"$ ( 4J3

K ( Tangente−1

4J3

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12$/ ? 4410N/ ( CD*S$53.13 *3/

1200N/ ? 4410N/ (CD*2.3999/

CD=16410 Nm

2.3999m

CD=6837.7849 N

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A( * r2

A( * (0.05m)2

A( 0.000078539 m2

• E/%$, % ,+/% +:, $),$+%/, %,+.

&( P

A

&(6837.7849 N

0.000078539m2

&( 87062286.25 P%.



31/87

8

A

C B:

8

:

W

P


&( @;.0 MP(

C,$)#/, = +:, = +%#:% )%' %+% ,$+ % % '%++% 87.062 MP%.

11.- C(!)'!e e! $e%o de! )i!indro (% $e%(do &'e %e $'ede )o!o)(r en!( $o%i)i=n &'e %e indi)( en !( +,'r( %in re*(%(r 'n e%'ero de50M7 en e! )(*!e BC2 De%$re)ie e! $e%o de !( *(rr( AB . E! "re(tr(n%er%(! de! )(*!e BC e% de 100.



32/87

6/

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R

BC

A;

AQ


DAOS.

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(

SOLUCIO7.

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>M.% (0

R * 4 ? BC* $ 53.14.10 ( 0

BC ( - R

2

BC ( - R

2



33/87

R1

R

370


D %


34/87

B

18/ 18/

C D

P

2/


113.- Un( *(rr( Hoo,Jne( AB >de 10006, de (%(? $ende de do%)(*!e% AC < BD )(d( 'no de !o% )'(!e% tiene 'n "re( tr(n%er%(! de400 )oo %e o*%er( en !( +,'r(. Deterine !( (,nit'd P. A%K )oo !( '*i)()i=n de !( 'er( (di)ion(! "#i( &'e %e $'ede ($!i)(r( !( *(rr(. Lo% e%'ero% en !o% )(*!e% AC / BD tiene 'n !iite de100MP( / 50 MP( re%$e)ti(ente.



35/87

BD

W

ACP

#

1


DAOS.

M ( 1000"

+% ( 400 //2 ( 0.0004 /2

P (

Q (

σ .AC ( 100 MP%

σ . BD ( 50 MP%

SOLUCIO7.

• A#)%$, % ,+/% +:, %)%/, , %,+ % $#,$%+% AC BD.

σ .AC ( P A

PAC ( 100 MP% * 0.0004 /2

PAC ( 0.004 MN.

PAC ( 40000 N



36/87


σ .BD ( P

A

PBD ( 50 MP% * 0.0004 /2

PBD ( 0.002 MN.

PBD ( 20000 N

• E)%/, % /%,+#% +:% $ ; %+% ,'$+ %,+ P

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TAC @ P @ 1000" * 9.8/J2 ? TBD ( 0

40000N @ P @ 9800N ?20000 ( 0

P ( 50200NP 50. 67.

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>M.% (0

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Q (9800 Nm−40000 Nm

−50200 N

Q (−30200 Nm−50200 N

0.0

L% '#)%)#


37/87



ESFUERZOCORA7

E


38/87


114.- Se de%e( $'non(r 'n( $!()( t(! )oo %e indi)( en !( +,'r( 1-10) &'e tiene 'n e%'ero )ort(nte '!tio de 300 MP(.

(? Si e! e%'ero de )o$re%i=n (di%i*!e en e! $'non e% 400

MP( deterine e! "#io e%$e%or de !( $!()( $(r( $oder$'non(r 'n ori+)io de 100 de di"etro.

*? Si !( $!()( tiene 'n e%$e%or de 10 )(!)'!e e! "#iodi"etro &'e $'ede $'non(r%e.



39/87


DAOS

(300 MP% % %'%+ $ +:, ),+%$ #/, ) = ,/!#/, = % %)% ,,+%+ ),+.

σ 400 $(.

>(?

( 01/

(

'

(001/

(

SOLUCIN7

%

Ʈ =V

A

V()%+"% ),+%$

R/%:%/, W $ % ,+/%.

3 X 108=

V

A

• A +/%:%+ %$ ,'#$$ , #$)


40/87


σ = P

A E %$!## , +%#:%/, $ $:


41/87


3 X 108=

3,14 x106

! ∗∗t

A $+ ),/, $#)% #$)


42/87


115.- L( +,'r( 'e%tr( !( 'ni=n de 'n tir(nte / !( *(%e de 'n((r(d'r( de (der(. De%$re)i(ndo e! ro(iento.

(? Deterine !( dien%i=n * %i e! e%'ero )ort(nte (di%i*!e e%

de 006P(.

*? C(!)'!e t(*iJn !( dien%i=n ) %i e! e%'ero de )ont()to node*e e#)eder de ; MP(.

DAOS

Ʈ =900 x103 P%

%

P( 50N

'

>( 7 x106

Pa

SOLUCIN7

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43/87

P(V(P),$

P

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P ( P X ? P" A $+ $ !$", ) = %

+:% % +%$ % /%,+#% ,+% , +:%

P X (V(P),$( P C,30\

P" ( P$30\

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Ʈ =V

A

A( ' 015/ !+% ' + %+%% % % +:% %+% = +,,= $ ),+.


'


44/87

C

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(P),$( P C,30\


R/%:%$, %,+ $ % *?

• D % /#/% /%$+% ' %$%#:%+ %$, % +:% ),/, !+% %+%% )% % %+ %,+ %, $ G+)#)#,.

&( P

A

A() 015/ ,/% $ !+% = % +$#)%+ % % )%+"% =

%/! ),/% ),$ % /#% ).

R/%:%/, $ %


45/87

450//200///

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A

C


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)ort(nte (di%i*!e e% de 50 M7 m2

.

DAOS

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.

^AB(531[

R067

SOLUCIO7


D% C.


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R

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A( 2/4

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P%+% AB.

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