Machinery's Handbook, 31st Edition
162 Force Systems force. Then through the extreme end of this line, draw a line parallel to, and of the same length and direction as the third force, and continue this until all the forces have been thus represented. Then draw a line from the point of application of the forces (as A ) to the extreme point (as 5 1 ) of the line last drawn. This line ( A 5 1 ) is the resultant of the forces.
2 1
3 1
1
P
2
4 1
A
3
l Fig. 10.
4
5 1
A
B
5
Fig. 9.
Moment of a Force: The moment of a force with respect to a point is the magnitude of the force multiplied by the perpendicular distance from the given point to the direction of the force. In Fig. 10, the moment of the force P with relation to point A is P 3 AB . The perpendicular distance AB is called the lever-arm of the force. The moment is the measure of the tendency of the force to produce rotation about the given point, which is termed the center-of-moments. If the force is measured in pounds and the distance in inches, the moment is expressed in inch-pounds. In metric SI units, the moment is expressed in newton-meters (N·m), or newton-millimeters (N·mm). The moment of the resultant of any number of forces acting together in the same plane is equal to the algebraic sum of the moments of the separate forces. Couples.— Two parallel forces of equal magnitude acting parallel to one another in op- posite directions are a couple . The resultant force of a couple is zero; the resultant itself is a pure moment. In the first example of Fig. 11, forces AB and CD are a couple. A couple tends to produce rotation. The measure of this tendency is called the moment of the couple; it is the product of one of the forces multiplied by the distance between the two.
B
A
H
F
G
Fig. 11. Two Examples of Couples As a couple has zero resultant force, no single force can balance or counteract the ten- dency of the couple to produce rotation. To prevent the rotation of a body acted upon by a couple, two other forces are required, forming a second couple. In the second illustration of Fig. 11, E and F form one couple and G and H are the balancing couple. The body on which they act is in equilibrium if the moments of the two couples are equal and tend to rotate the body in opposite directions. A couple may also be represented by a vector in the direction of the axis about which the couple acts. The length of the vector, to some scale, represents the magnitude of the couple, and the direction of the vector is that in which a right-hand screw would advance if it were to be rotated by the couple. D C E
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