Two-Force Members
In some problems you will encounter a two-force member. This is a member that
only has a force applied at two different points. It can be straight, bent or curved. An
example of a two-force member is shown in the picture below. A force is applied at the
two points A and B.
FA
A
FB
B
Equilibrium requirements (net force is zero) dictate that the forces be equal and
opposite and thus have parallel lines of action (shown below).
F
A
-F
B
However there is a net moment since this now is a couple. In order to satisfy moment
equilibrium one must have a zero moment and the forces must then have the same line of
action. As seen below the two force member is now in force and moment equilibrium.
F
A
-F
B
A two-force member then has only equal and opposite forces directed along a line
joining the two points where the forces are applied. Thus the direction of the force is
known. There is only one unknown, which is the magnitude of the force. You must
recognize two-force members in order to solve problems that contain them. If you
don’t recognize the two force members, many problems are then unsolvable since there
are too many unknowns.
As a final point, a two-force member can not have a moment or couple applied to it.
In the picture below there are two forces and a moment applied to the member. Since
there is now a moment applied as well, the forces must be equal and opposite but have
parallel (but different) lines of action. In this case we generally just put x and y forces at
each point and treat it as any other problem.
FA
M
FB
B
A