ME 221 Statics
LECTURE # 12
Sections 3.8 – 3.9
ME221
Lecture 12
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Homework #4
• Chapter 3 problems:
– 1, 4, 8, 11, 17, 25, 26, 28, 35 & 40
– Due Today
Homework #5
• Chapter 3 problems:
– 48, 51, 55, 57, 61, 62, 65, 71, 72 & 75
– You may use MathCAD, etc. on any of the problems
– Due Friday, October 3
ME221
Lecture 12
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Equivalent Force Systems
• Learn how to replace a given set of forces
with an equivalent force-moment system
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Lecture 12
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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 12
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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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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
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+F
6
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
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A
rB/A
+F
+F
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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 12
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A parallel force system has the lines of action of all
forces acting parallel to a common line.
A concurrent force system has the lines of action of
all forces passing through a single point.
More on these later (Monday).
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Lecture 12
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Example Problem
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Lecture 12
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