ME221 Statics
LECTURE # 6
Sections 3.6 – 3.9
ME221
Lecture 6
1
Homework #2
• Due today
Quiz #3
• Today
ME221
Lecture 6
2
Homework #3
• Chapter 3 problems:
– 48, 55, 57, 61, 62, 65 & 72
• Chapter 4 problems:
– 2, 4, 10, 11, 18, 24, 39 & 43
• Due Monday, June 7
ME221
Lecture 6
3
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 6
4
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
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Lecture 6
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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
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Lecture 6
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Equivalent Force Systems
• Replacing a given set of forces with an
equivalent force-moment system
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Lecture 6
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Equivalent Force Systems
The action of a force tends to translate the
body along the direction of the force and
rotate it about an axis not located along
the line of action of the force. The
External Effects remain the same if the
force is moved from one point to another
(from A to B ) if:
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Lecture 6
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1- Point B is on the line of action of the force
A force can be replaced by an equal magnitude
force provided it has the same line of action
and does not disturb equilibrium
B
A
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Lecture 6
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2- Point B is not on the line of action of the force
Start with a rigid body having force F applied to it.
Replace this force with
a force and couple at A.
Add “zero” to the body
in the form of adding
+F and -F
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B
F
A
-F
Lecture 6
+F
10
Next, group two forces to create couple C
Let rB/A be the relative position of B with respect to A.
Define couple with cross product
C
C = rB/A x F
In essence, the force F has
-F
been moved from point B to
A with the addition of couple C.
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F
B
Lecture 6
A
rB/A
+F
+F
11
For More Than One Force
A similar procedure is used when there are many
forces on the body:
R = S Fi
C = S ci = S ri x Fi
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Lecture 6
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Example Problems
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Lecture 6
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ME 221 Statics
Exam #1 Review
ME221
Lecture 6
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Exam 1
• Wednesday, June 2
• No class on Monday, May 31
ME221
Lecture 6
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Exam Format
• Similar to homework problems
• 5 or 6 (maybe 7) problems
• No new concepts
• Closed books and closed notes
• 25% of final grade
• Will need a calculator
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Lecture 6
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Exam 1 Helpful Hints
• Study by working homework problems
• Review the examples in the book
• Read the exam questions carefully
• Work the problems you know first
• Use a logical flow to show your knowledge
• Be complete – check your answers
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Lecture 6
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Exam 1 Pitfalls
• Vectors have both magnitude and direction
• Most answers will have units
• Calculated answers should be in decimal form
• Use 3 significant figures where appropriate
• Answers are generally worth ~1/3 of points
• Steps leading to answers are worth ~2/3
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Lecture 6
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Exam 1 Topics
• All of Chapters 1 & 2 except 2.11 Springs
• Up to 3.4 in Chapter 3
•
•
•
•
Newton’s Laws
Units
Scalars & vectors; defining, adding, etc.
Laws of sine and cosine
• Resolution of a vector into components
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Lecture 6
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Exam 1 Topics
• 3D coordinates & unit base vectors
• Directional cosines
• Non-orthogonal vector components
• Scalar & cross products of vectors
• 2D & 3D equilibrium problems
• Moments & couples
• Drawing good free-body diagrams
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Lecture 6
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