statics moments4
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Statics (MET 2214)Prof. S. Nasseri
Forces and Moments MET 2214
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Statics (MET 2214)Prof. S. Nasseri
Moments and ForcesPart 4
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Statics (MET 2214)Prof. S. Nasseri
Moment of a Couple
A couple is defined as:
Two parallel forces
Same MagnitudeOpposite direction
Separated by a perpendicular distance d
-F
d
F
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Statics (MET 2214)Prof. S. Nasseri
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.
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Statics (MET 2214)Prof. S. Nasseri
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.
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Statics (MET 2214)Prof. S. Nasseri
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
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Statics (MET 2214)Prof. S. Nasseri
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.
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Statics (MET 2214)Prof. S. Nasseri
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.
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Statics (MET 2214)Prof. S. Nasseri
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
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Statics (MET 2214)Prof. S. Nasseri
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 !
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Statics (MET 2214)Prof. S. Nasseri
Example 3
Come on!
There must
be an
easier
way!!
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Statics (MET 2214)Prof. S. Nasseri
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
-
--
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Statics (MET 2214)Prof. S. Nasseri
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