Force Systems

By possessing an understanding of Newton’s Laws, following these three laws of
graphical solutions, and understanding vector algebra you can solve most
engineering static problems. Systems of Force Systems of force acting on objects
in equilibrium can be classified as either concurrent or nonconcurrent and as
either coplanar or noncoplanar. This gives us four general categories of
systems. The first category, concurrent-coplanar forces occur when the lines of
action of all forces lie in the same plane and pass through a common point.

Figure 1 illustrates a concurrent-coplanar force in such that F1, F2, and W all
lie in the same plane (the paper) and all their lines of action have point O in
common. To determine the resultant of concurrent force systems, you can use the
Pythagorean theorem, the law of sines, or the law of cosines as outlined in the
previous chapter. Nonconcurrent-coplanar force is when the lines of action of
all forces lie in the same plane but do not pass through a common point as
illustrated in figure 2. The magnitude and direction of the resultant force can
be determined by the rectangular component method using the first two equations
in figure 2, and the perpendicular distance of the line of action of R from the
axis of rotation of the body can be found using the third equation in figure 2.

Concurrent-noncoplanar forces are when Application the lines of action of all
forces pass through a common point and are not in the same plane. To find the
resultant of these forces it is best to resolve each force into components along
three axes that make angles of 90 degrees with each other.

Nonconcurrent-noncoplanar forces are when the lines of action of all forces do
not pass through a common point and the forces do not all lie in the same plane.

Stress When a restrained body is subject to external forces, there is a tendency
for the shape of the body.