Resultant of forces

(mechanics) 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 that body.

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 illustration 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.

parallelogram. (b, c) Hypotenuse of triangle.">
Resultant of two forces acting through a common center. (a) Diagonal of parallelogram. (b, c) Hypotenuse of triangle.

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. See also Calculus of vectors.

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 also Couple; Force; Statics.