Statics Moments4

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Statics (MET 2214)Prof. S. Nasseri

Forces and Moments MET 2214

http://wiki.spsu.edu/index.php/Image:HighRes-Horny.gif




Moments and ForcesPart 4





Moment of a Couple

A couple is defined as:

Two parallel forces

Same MagnitudeOpposite direction

Separated by a perpendicular distance d

-F

d

F





Couple Moment

A moment produced by a coupleis called a Couple Moment.

Fr M

r r -r But

Fr r -M

Fr F-r M

Fr F)(r M

AB

BA

BA

BA

So a couple moment is a free vector whichcan act at any point and depends only on r,not on rA and rB.












Couple MomentRemember:

Scalar Formulation:Magnitude: M = Fd

Direction and sense using right-hand rule

Vector Formulation:

Magnitude: M = r x F

Note: The moment of a couple does not

depend on the point one takes the momentabout. In other words, a moment of a coupleis the same about all points in space.





Example 1

Each person in this figure is exerting a 20N force onthe tube. If the distance between the two points is150mm, what is the moment due to the forces applied.

M = F.d= (20)(0.15) = 3N.m





Example 2

The crossbar wrench is used to remove a lug nut from the automobilewheel. The mechanic applies a moment couple to the wrench such that hishands are a constant distance apart.

Is it necessary that a = b in order toproduce the most effective turning ofthe nut? Explain.

Solution:Couple moment: Mc = F(a+b),

The couple moment depends on the totaldistance between grips. a = b is not anecessary condition to produce the mosteffective turning of the nut.

Also what is the effect of changing theshaft dimension c in this regard? Theforces act in the vertical plane.

Changing the dimension c has no effect on turning the nut.





Example 3

Determine the resultant couple moment of the two couples that act onthe pipe assembly. The distance from A to B is d = 400 mm. Expressthe result as a Cartesian vector.





Example 3

mk 0.2 j35.0r mk 0)(0.4sin30 j0)(-0.4cos30i0.350.35r

)sin30,0.40.4cos30-B(0.35,

0)0,A(0.35,

:Vector Position

AB

AB
















Example 3

N.m51710

0050-

0.23500

N.m2512

3500

0.23500

N}{-50 N;}{35

m0.2350

:MomentsCouple

2

k . j.

k ji

M

FrM

i..

k ji

M

FrM

iFk F

k j.r

2C

AB2C

1C

1AB1C

21

AB

N.m517102512

:MomentCoupleResultant

N.m51710

N.m2512

N}{-50 N;}{35

m0.2350

k . ji.MMM

ΣMM

k . jM

i.M

iFk F

k j.r

2C1CR

R

2C

1C

21

AB

Notice this is negative because we are taking moment about A !























Example 3

Come on!

There must

be an

easier

way!!





Example 3

Lets check three different views and see whatforces are causing moments about x, y and zaxes:

y

z

x

z

x

y

35N

35N

50N

50N

50N

50N

0.4cos30

0.4sin30

0.4cos30

X-viewGives moment about x

Y-viewGives moment about y

Z-viewGives moment about z

-

--





Example 3

N.m517102512

:vector CartesianaasMExpress

N.m517

304050

N.m10

304050

N.m2512

304035

axeszandy,about x,momentsSumming:AnalysisScalar

R

k . ji.M

.

)cos.(

)sin.(

.

)cos.(

R

z R

z z R

y R

y y R

x R

x x R

M

ΣM M

M

ΣM M

M

ΣM M





















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