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COE3001Deformablebodies

InternalForces

DiagramCOE3001Deformablebodies

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COE3001Deformablebodies

INTERNALFORCESDISTRIBUTIONS

Youneed

to

know

the

intensity

of

INTERNALFORCESateverysectionofa

beam

Todetermine

stress,

strain

and

deflection

Insuretheirvaluesarewithinallowables

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5EasySteps:1. Define

acoordinate

system;

2. Calculateallforcesappliedtothebeam

(reactionforces);

3. Identifynumber

of

sections

(cuts)

according

to

loaddistributionandbeamgeometry;

4. ImposeequilibriumforEACHsectionandsolve

for

axialresultant

N(x),

bending

moment

M(x)

andshearforceV(x);

5. Plotdiagramsaccordingtoresultsandsign

conventions.

INTERNALFORCESDISTRIBUTIONS

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COE3001Deformablebodies

Steps

Determinereactions

at

supports

using

equilibrium

02intpo@M

01intpo@M

0Fx

=

=

=

0Fy =

Anduseasacheck

INTERNALFORCESDISTRIBUTIONS

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Steps(cont.)

Dividethebeamintosectionaccordingto

Continuityofloadsandgeometry

Makeacut

in

each

section

showing

the

internalaxial,shearandbendingmoment

x

N(x)

V(x)

M(x)

q(x)HINT:drawunknowns

accordingtopositivesignconventions

INTERNALFORCESDISTRIBUTIONS

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Steps

Applyequilibrium

)x(M01intpo@M

)x(V0F

)x(N0F

y

x

=

=

=

x

N(x)

V(x)

M(x)q(x)

1

INTERNALFORCESDISTRIBUTIONS

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dx

q(x)

dx

)x(dN)x(N +

dx

)x(dV)x(V +

dx)x(dM)x(M +

)x(M

)x(N

)x(V

INTERNALFORCESDISTRIBUTIONS

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COE3001Deformablebodies

SHEARFORCE,BENDINGMOMENT,

LOAD

FromEquilibrium

0dx

)x(dN=

)()(

xqdx

xdV=

)x(Vdx

)x(dM

=

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COE3001Deformablebodies

SHEARFORCE,BENDINGMOMENT,

LOAD

ValueofShearandMoment Diagramsatends

Reactions

Concentratedload

Jump

in

Shear

Force

Diagram

Concentratedmoment

JumpinBendingMomentDiagram

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COE3001Deformablebodies

Examples

3/4/2009 11

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2001Broo

ks/C

ole

,a

divisiono

fThomson

Learn

ing

,In

c.

Thomson

Learn

ing

isatra

demarku

se

dhere

inun

der

license

.

Fig.47 Example41. Shear

forcesandbendingmomentsina

simplebeam.

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2001Broo

ks

/Co

le,

adivisiono

fThomson

Learnin

g,

Inc

.Thomson

Learn

ing

isatra

dem

arkuse

dhere

inun

der

license

.

Fig.48 Example42. Shear

forceandbendingmomentina

cantileverbeam.

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14/25

2001B

roo

ks

/Co

le,

adivisiono

fThomson

Lear

ning

,Inc

.Thomson

Learn

ing

isatrademarkuse

dhere

inun

der

license

.

Fig.49 Example43. Shear

forceandbendingmomentina

beamwith

an

overhang.

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15/25

2001Brooks

/Co

le,

adivisiono

fThomson

Learn

ing,

Inc

.Thomson

Learn

ing

isatra

demar

kuse

dhere

inun

der

license

.

Fig.411 Shearforceandbending

momentdiagrams

for

asimple

beam

withaconcentratedload.

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2001Broo

ks/

Cole

,a

divisiono

fThomson

Learn

ing

,Inc.

Thomson

Learn

ing

isatra

demarkuse

dhere

inun

der

license

.

Fig.412 Shearforceandbending

momentdiagramsforasimple

beamwith

auniform

load.

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2001Broo

ks/

Co

le,

adivisiono

fThomson

Learn

ing

,In

c.

Thomson

Learn

ing

isatra

demarku

se

dhere

inun

der

license

.

Fig.414 Example44.

Simplebeamwitha

uniformloadoverpartof

thespan.

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19/25

2001Bro

oks

/Co

le,

adivisiono

fThomson

Learning

,Inc

.Thomson

Learn

ing

isatra

dem

arkuse

dhere

inun

der

license

.

Fig.415 Example45.

Cantileverbeamwithtwo

concentratedloads.

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20/25

2001B

roo

ks

/Co

le,

adivisiono

fThomson

Learn

ing

,Inc

.Thomson

Learn

ing

isatrademarkuse

dhere

inun

der

license

.

Fig.416 Example46.

Cantileverbeamwitha

uniformload.

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2001Broo

ks/

Co

le,

adivisiono

fThomson

Learn

ing

,In

c.

Thomson

Learn

ing

isatra

demarku

se

dhere

inun

der

license

.

Fig.417 Example47.

Beamwith

an

overhang.

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COE3001Deformablebodies

BendingofBeams

AdvancedTopics

Chapter6

3/4/2009 22

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23/25

2001Broo

ks

/Co

le,a

divisionof

Thomson

Learn

ing

,Inc

.Thoms

on

Learn

ing

isa

tra

dema

rkuse

dhere

inun

der

licen

se

.

Examplesof

composite

beams:

(a)

bimetallicbeam,(b)plasticcoated

steelpipe,and(c)woodbeam

reinforcedwithasteelplate.

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Sandwichbeams

with:

(a)

plastic

core,(b)honeycombcore,and(c)

corrugatedcore.

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