# Statics/Resultants of Force Systems (contents)

A force system is a collection of forces acting at specified locations (may also include couples). Thus the set of forces shown on any free body diagram make up a force system. Force system is simply a term used to describe a group of forces.

## Resultants

When two or more forces or moments are combined, the combination is called a resultant. Any force system can be simplified about a point to a resultant consisting of one force and one couple (either or both of which may be zero). The force is applied to the point and is the vector sum of all of the forces in the system. The couple is the vector sum of all of the couples in the force system plus the vector sum of all of the moments about the point of all of the forces in the force system. One immediate consequence of this definition of resultant is that the resultant about any point of the external force system acting on any system in equilibrium must be zero. The statement that the sum of the external forces and the sum of the external moments acting on a system in equilibrium is zero is often replaced by the statement that the resultant acting on a system in equilibrium is zero. An important attribute of the resultant of a force system is that if you apply the resultant of a force system to a rigid body, the effect on that rigid body is exactly the same as the effect of the original force system. It is in this sense that the resultant is "equivalent" to the original force system. Thus as we study the behavior of rigid bodies under the action of forces, the resultant of the external force system will be of vital interest. Care must be taken in replacing force systems with their resultant when dealing with deformable bodies as the effects of the resultant acting on a non-rigid system will be different than the effects of the actual force system.

## Equipollence

The "equivalence" of effect on a rigid body of a force system and its resultant is the motivation for the term equipollence. Two force systems are said to be equipollent if they have the same resultant about a point. Thus two equipollent force systems have the same effect on a rigid body. Thus the precise way to state what we have learned about the toe is that the upper clamping surface exerts a force system on the toe that is equipollent to a force of 540 lb in the -Y direction acting at a point at the top, middle of the toe. Typically we are not this precise and merely state that the clamping surface is exerting a force of 540 lb in the -Y direction on the top, middle point of the toe. It is important for you to recognize that when you hear such statements, what they mean is that the force system acting on the object is equipollent to the specified force and that the particular distribution or combination of forces involved may be quite complicated.