Chapter Four
Laith Batarseh
Next
Previous
Home
End
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 )
Moment is a vector quantity
Description
Moment depends on two variables:
The acting force
Previous
Next
Moment arm
Home
End
Description
Force
Arm
Tendency to rotate
Next
Previous
Home
End
Tendency for rotation
Next
Previous
Home
End
Magnitude
D
F
Moment magnitude (M) = F.D
Next
Previous
Home
End
Direction
Next
Previous
Home
End
Solving procedures
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
Next
Previous
Home
End
Example [1]
Find the moment caused by the following forces about point O
2m
(a)
100 N
O
0.5m
100 N
(b)
Home
Previous
0.5m
Next
O
2m
End
Example [1]
Assume the CCW direction is the positive direction.
2m
2m
0.5m
0.5m
100 N
Branch (a)
+ Mo = F.d = -(100N)(0.5m)
Mo=-50 N.m=50N.m CW
Branch (b)
+ Mo=F.d = (100N)(2m)
Mo=200 N.m CCW
100 N
(b)
Home
Next
(a)
O
Previous
O
End
Principle Of Moments
Principle of Moments
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)
Next
Previous
Home
End
Principle Of Moments
Example [1]
Find the moment caused by the following forces about point O
Next
Previous
Home
End
Principle Of Moments
Example [1]
+
Mo,1 = 100 sin(30) (10) = 500 N.m
+
Mo,2 =- 100 cos(30) (5) =- 433N.m
M = Mo,1+Mo,2=500-433=67N CCW
Next
Previous
Home
End
Principle Of Moments
Example [2]
1. Force analysis
100 cos(40)
100 sin(40)
120 sin(60)
1.2 m
0.3 m 120 cos(60)
2. Moment calculations
+ ∑ M = (100 cos(40))(1.5) –( 120 cos(60))(1.2) =43 N.m CCW
Next
Previous
Home
End
Moment resultant
F1
d1
M1
O
M2
F2
M3
d3
F3
+ Mo = ∑Mo = M1 + M2 – M3 = F1d1+F2d2 – F3d3
Home
Next
Previous
d2
End
Example [2]
Find the moment caused by the following forces about point O
100 N
2m
50 N
O
1m
60 N
30o
5m
Previous
Home
Next
3m
75 N
End
Example [2]
100 N
2m
50 N
O
1m
3m
60 N
75 N
30o
5m
+  M o  1002  603  500  75 sin( 30) 5 75 cos(30) 1
 272.45 N .m  272.45 N .m CW
Home
Previous
o
Next
M
End
Exercise
Find the moment caused by the following forces about point O
100 N
5m
30o
O
0.3m
45o
300 N
Previous
Home
Next
2m
End
Exercise
100 N 100sin (30)N
5m
O 100cos (30)N
2m
300 sin (45)N
0.3m
300 cos (45)N
300 N
+  M o  100 sin( 30) 2  300 cos( 45) 0.3  300 sin( 45) 5
 897 N .m  897 N .m CW
Home
Previous
o
Next
M
End
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
Next
Previous
Home
End