The analysis of some equilibrium problems can be facilitated if one or
more of the members is subjected to only two or three forces. Knowing what structural members are two forces generally makes solving the problem easier.
Member BD is a Two-Force Member
Both Forces on Two-Force Members
Must Be Equal and Collinear
A two-force member is a rigid body with no force couples, acted upon by a system of forces composed of, or reducible to, two forces at different locations.
The most common example of the a two force member is a structural brace where each end is pinned to other members as shown at the left. In the diagram, notice that member BD is pinned at only two locations and thus only two forces will be acting on the member (not considering components, just the total force at the pinned joint).
Two-force members are special since the two forces must be co-linear and equal. This can be proven by taking a two force member with forces at arbitrary angles as shown at the left. If moments are summed at point B then force FD cannot not have any horizontal component. This requires FD to be vertical. Then the forces are summed in both directions, it shows FB must also be vertical. Furthermore, the two forces must be equal.
There are three criteria for a two-force member:
The forces are directed along a line that intersects their points of application.
A three-force member is a rigid body with no force couples, acted upon by a system of forces composed of, or reducible to, three forces at three different locations. Because all three forces act at different locations on the member, their direction and magnitude are not known.