# resultant of forces

## Resultant of forces

A system of at most a single force and a single couple whose external effects on a rigid body are identical with the effects of the several actual forces that act on the body. For analytic purposes, forces are grouped and replaced by their resultant. Forces can be added graphically (see illustration) or analytically. The sum of more than two vector forces can be found by extending the method of illus. *c* to *a* three-dimensional vector polygon in which one force is drawn from the tip of the previous one until all are laid out.

The resultant force is the force vector required to close the polygon directed from the tail of the first force vector to the tip of the last. A force system has a zero force resultant if its vector polygon closes.

Two force systems are equivalent if their resultant forces, as described above, are equal and if their total vector moments about the same point are also equal. Vector moments are combined in the same manner as forces, that is, by parallelograms, triangles, or polygons. A resultant is the equivalent force system having the fewest possible forces and couples. *See* Couple, Force, Statics