ME 221 Statics
LECTURE # 13
Section 3.9
ME221
Lecture 13
1
Homework #5
• Chapter 3 problems:
– 48, 51, 55, 57, 61, 62, 65, 71, 72 & 75
– May use MathCAD, etc. to solve
– Due Friday, February 14
ME221
Lecture 13
2
Last Lecture:
Equivalent Force Systems
• Learned how to replace a given set of forces
with an equivalent force-moment system
ME221
Lecture 13
3
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
ME221
Lecture 13
4
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
ME221
B
F
A
-F
Lecture 13
+F
5
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.
ME221
F
B
Lecture 13
A
rB/A
+F
+F
6
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
ME221
Lecture 13
7
Example Problems
ME221
Lecture 13
8