ME221 Statics
LECTURE # 11
Sections 3.6 – 3.7
ME221
Lecture 11
1
Homework #4
• Chapter 3 problems:
–
–
–
–
1, 4, 8, 11, 17, 25, 26, 28, 35 & 40
To be solved using hand calculations
May check work using MathCAD, etc.
Due Friday, September 26
Quiz #3
• Today
ME221
Lecture 11
2
Moment of a Force about an Axis
y ^
n
|Mn| =MA·n^
A
^
=n·(rB/A x F )
Same as the projection of MA
along n
rAB=rB/A
F
B
O
x
z
nx
r
|Mn|= B/Ax
Fx
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ny
r B/A y
Fy
nz
r B/Az
Fz
Lecture 11
3
Resolve the vector MA into MA
two vectors one parallel and
one perpendicular to n.
y Mp
Mn
A
Mn=|Mn|n^
n^
F
rAB=rB/A B
O
Mp = MA - Mn
x
z
^
^
=n x [(r B/A x F) x n]
ME221
Lecture 11
4
Moment of a Couple
Let F1 = -F2
B
y
|C|=|F1| d
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d
rAB=rB/A
F2
Mo=rA x F2+ rB x F1
=(rB - rA ) x F1
=rAB x F1= C
F1
A
rB
rA
O
x
The Moment of two equal
and opposite forces is called
a Couple
z
Lecture 11
5
Moment of a Couple (continued)
• The two equal and opposite forces form a couple
(no net force, pure moment)
• The moment depends only on the relative positions
of the two forces and not on their position with
respect to the origin of coordinates
ME221
Lecture 11
6
Moment of a Couple (continued)
• Since the moment is independent of the origin, it
can be treated as a free vector, meaning that it is the
same at any point in space
• The two parallel forces define a plane, and the
moment of the couple is perpendicular to that plane
ME221
Lecture 11
7
Example
ME221
Lecture 11
8