Diag de Fza Cortante y Mto Flexor

8/3/2019 Diag de Fza Cortante y Mto Flexor

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Diagramas de FuerzaDiagramas de Fuerzacortante y Momento Flexorcortante y Momento Flexor


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BeamsBeams areare usuallyusually long,long, straightstraight prismaticprismatic membersmembersdesigneddesigned toto supportsupport loadsloads appliedapplied atat variousvarious pointspoints alongalong

thethe membermember.. InIn general,general, thethe loadsloads areare perpendicularperpendicular toto

thethe axisaxis of of thethe beambeam andand produceproduce onlyonly shearshear andand

bendingbending inin thethe beambeam.. TheThe loadsloads maymay bebe either either

concentratedconcentrated atat specificspecific points,points, oror distributeddistributed alongalong

thethe entireentire lengthlength oror aa portionportion ofof thethe beambeam.. TheThe beambeam

itselfitself maymay bebe supportedsupported inin variousvarious waysways..

SinceSince onlyonly staticallystatically determinatedeterminate beamsbeams areare consideredconsideredinin thisthis text,text, wewe limitlimit ourour analysisanalysis toto thatthat of of simplysimply

supportedsupported beamsbeams,, overhangingoverhanging beamsbeams,, andand

cantileveredcantilevered beamsbeams..


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ToTo obtainobtain thethe shearshearVV andand bendingbending momentmomentMMatat aa givengiven pointpoint CC ofof aa beam,beam, wewe firstfirst determinedetermine

thethe reactionsreactions atat thethe supportssupports byby consideringconsidering thethe

entireentire beambeam asas aa freefree bodybody.. WeWe thenthen cutcut thethe

beambeam atat CCandand useuse thethe freefree--bodybody diagramdiagram ofof oneoneofof thethe twotwo portionsportions obtainedobtained inin thisthis fashionfashion toto

determinedetermine VVandand MM..

C

C


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TheThe signsign conventionconvention forfor positivepositive shearshear forceforce andand

bendingbending momentmoment isis asas shownshown.. OnceOnce thethe valuesvalues

ofof shearshear andand bendingbending momentmoment areare establishedestablished atat

severalseveral selectselect pointspoints alongalong thethe beam,beam, itit isisusuallyusually possiblepossible toto drawdraw thethe shearshear diagramdiagram andand

bendingbending--momentmoment diagramdiagram forfor thethe entireentire beambeam..

V

M

V

M


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Dibuje los diagramas de fuerza cortante yDibuje los diagramas de fuerza cortante y

momento flexor para la viga mostrada.momento flexor para la viga mostrada.

L

w0

3

2

0Lw

2

0Lw

L

w0

2/3L

2

0Lw


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x

3

3

0Lw

2

0Lw

2/3x

x

L

xwA

! 0

2

1

L

xww

0!

M

V

220

00

2

02

1

2

0

xL

L

wV

VxL

xwLw

Fy

!

!

!7

3230

00

2

0

326

03

1)(

2

1)(

23

0

xxLLL

wM

MxxL

xwx

LwLw

M

!

!

!7

Proponemos un nuevo

corte a una distancia x


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2202

xLL

wV !

3230 326

xxLLL

wM !

V

x

M

x

3

3

0Lw

2

0Lw0w

M

V

2

0Lw

3

3

0Lw

L


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EjemploEjemplo

Trace los diagramas de fuerzas cortantesTrace los diagramas de fuerzas cortantes

y de momentosy de momentos flexionantesflexionantes de las vigas yde las vigas y

la carga que se muestra.la carga que se muestra.

60 kN

2m1m2m

A B

C D

25 kN/m60 kN

2m1m2m

A B

C D

25 kN/m


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60 kN

2m1m2m

A B

C D

60 kN

2m1m2m

A B

C D

50 kN

Primero determinar las fuerzas exteriores don el DCL

MA=0 B(5m)-(60kN)(2m)-(50kN)(4m)=0

B=64kN

Fy=0 Ay+64kN-60kN-50kN=0

Ay=46kN


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Proponemos un corte:

x M

V46kN

J

De A a C

Fy=0 46kN -V=0V= 46kN

MJ=0 M-(46kN)(x)=0

M=46 x (kN m)


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M

De C a D

Fy=0 46kN 60kN -V=0V= -14kN

MJ=0 M-(46kN)(x)+60kN (x-2)=0

M=(120-14x) [kN m]

xV46kN

J

60kN

2m

Cuando x=2m MC = 92kN m

Cuando x=3m MD = 78 kN m


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u

V

64kN

(25)(u)u/2

De D a B

M

De D a B

Fy=0 V+64-25u=0V= (25u-64)kN

MJ=0 64u-(25u)(u/2)-M=0

M=(64u-12.5u2) [kN m]


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Para graficar:

AB

C D

-14

-64

46

92

V

M 78.0

x

x

Diag de Fza Cortante y Mto Flexor

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