Statics of Non-Concurrent Force Systems

Supporting a Rigid Body  |  Free-Body Diagram of a Rigid Body


Two-Force Members:

When only two forces are acting on a member, equilibrium dictates that the two forces be equal in magnitude, collinear, and opposite in direction, as shown in the figure. Otherwise, either the force equilibrium or the moment equilibrium would be violated. Such a member is referred to as a two-force member.

We identify two-force members in a built-up structure by the following characteristics:

    - Pin connection at two points.

    - No external force or couple moment at any point along its length.

 figure

Example 1

Example 2

Example 3
 

Three-Force Members:

When only three forces are acting on a member, equilibrium dictates that these forces must be either

    - parallel to each other or form a concurrent system as shown in the figure.
Notice that in both cases the forces point in different directions. Otherwise, the equilibrium of forces and moments would be violated. Such a member is called a three-force member.

We identify three-force members in a built-up structure by the following characteristics:

    - Pin or roller connection at two points.

    - Plus at least one force or couple moment at some point along its length.

Example 4

 figure

Supporting a Rigid Body  |  Free-Body Diagram of a Rigid Body