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Chapter Four
Laith Batarseh
Statics
1. MOMENT SCALAR
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Statics
MOMENT SCALAR
Definition
Moment is defined as the tendency of a body lies under force to rotate about a point not on the line of the action of that force (i.e. there is a distance between the force and the rotation point )
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The acting force
Moment arm
Description
Moment depends on two variables:
Moment is a vector quantity
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Statics
MOMENT SCALAR
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Description
ForceArmTendency to rotate
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Statics
MOMENT SCALAR
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Tendency for rotation
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Statics
MOMENT SCALAR
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Magnitude
FD
Moment magnitude (M) = F.D
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Statics
MOMENT SCALAR
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Direction
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Statics
MOMENT SCALAR
Solving procedures
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1. Define the magnitudes of force (F) and arm (D)
2. Assume the positive direction (eg. Counter clock wise)
3. Find the magnitude of moment (M) as F.D
4. Give the moment the correct sign according to the tendency for rotation
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Statics
MOMENT SCALAR
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Example [1]
Find the moment caused by the following forces about point O
100 N
0.5m
2m
(b)
O
100 N
0.5m
2m
(a)
O
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Statics
MOMENT SCALAR
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Example [1]
Assume the CCW direction is the positive direction.
100 N
0.5m
2m
(b)
O
100 N
0.5m
2m
(a)
O
Branch (a) Mo = F.d = -(100N)(0.5m) Mo=-50 N.m=50N.m CWBranch (b) Mo=F.d = (100N)(2m) Mo=200 N.m CCW
+
+
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Statics
Principle Of Moments
Principle of Moments
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some times called Vrigonon’s theorem (Vrigonon is French
mathematician 1654-1722).
State that the moment of a force about a point equals the summation
of the moments created by the force components
In two dimensional problems: the magnitude is found as M = F.d and
the direction is found by the right hand rule
In three dimensional problems: the moment vector is found by M =rxf
and the direction is determined by the vector notation (ie. i,j and k
directions)
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Statics
Principle Of Moments
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Example [1]
Find the moment caused by the following forces about point O
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Statics
Principle Of Moments
Example [1]
Mo,1 = 100 sin(30) (10) = 500 N.m
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+
Mo,2 =- 100 cos(30) (5) =- 433N.m+
M = Mo,1+Mo,2=500-433=67N CCW
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Statics
Principle Of Moments
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Example [2]
1. Force analysis
100 cos(40)1.2 m
0.3 m
100 sin(40)
120 cos(60)
120 sin(60)
2. Moment calculations
∑ M = (100 cos(40))(1.5) –( 120 cos(60))(1.2) =43 N.m CCW +
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Statics
MOMENT SCALAR
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Moment resultant
F1
F2F3
d1
d2 d3
M1O
M2
M3
Mo = ∑Mo = M1 + M2 – M3 = F1d1+F2d2 – F3d3 +
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Statics
MOMENT SCALAR
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Example [2]
Find the moment caused by the following forces about point O
2m
3m
5m
1m30o
100 N
50 N
60 N
75 NO
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MOMENT SCALAR
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Example [2]
2m
3m
5m
1m30o
100 N
50 N
60 N
75 NO
CWmNmNM
M
o
o
.45.272.45.272
1)30cos(755)30sin(750503602100
+
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Statics
MOMENT SCALAR
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Exercise
Find the moment caused by the following forces about point O
100 N
300 N
5m
2m 45o
30oO 0.3m
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MOMENT SCALAR
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Exercise
CWmNmNM
M
o
o
.897.897
5)45sin(3003.0)45cos(3002)30sin(100
+
100 N
300 N
5m
2mO 0.3m
300 sin (45)N
300 cos (45)N
100sin (30)N
100cos (30)N
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Statics
MOMENT SCALAR
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Summary
Moment is the tendency to rotate produced by a force
Moment is vector quantity
The scalar magnitude of the moment equal to : F.d
The direction of the moment will be in a direction
perpendicular to the plane which contains the vectors of
the F and d