A three-force member is in equilibrium when the forces are concurrent or parallel.

A three-force member is in equilibrium when the forces are concurrent or parallel.

• A. When the sum of the two forces is equal to the third force.
• B. When they are concurrent or parallel.
• C. When they are coplanar.
• D. All of the above

Answer: (B)

For a rigid body to be in static equilibrium, the sum of forces must be zero and the sum of moments about any point must be zero. For a system of exactly three forces, this leads to two geometric possibilities for their lines of action: they are either concurrent (all intersect at a single point) or parallel (all lie on parallel lines). If the three lines of action meet at one point, you can think of the forces as acting through that point. In this case, there’s no moment generated about that common point, and the three forces can be arranged (as a vector triangle) to balance so that the resultant force is zero. Hence the member can be in equilibrium. If the forces are parallel, they do not intersect, but equilibrium can still occur when their magnitudes are such that the resultant force is zero and the torques about any point cancel. In this parallel configuration, the force system can produce no net moment if the moments from the individual forces balance appropriately. If the lines of action are neither concurrent nor parallel, a nonzero moment will arise about some point, so the member cannot be in equilibrium.

For a rigid body to be in static equilibrium, the sum of forces must be zero and the sum of moments about any point must be zero. For a system of exactly three forces, this leads to two geometric possibilities for their lines of action: they are either concurrent (all intersect at a single point) or parallel (all lie on parallel lines).

If the three lines of action meet at one point, you can think of the forces as acting through that point. In this case, there’s no moment generated about that common point, and the three forces can be arranged (as a vector triangle) to balance so that the resultant force is zero. Hence the member can be in equilibrium.

If the forces are parallel, they do not intersect, but equilibrium can still occur when their magnitudes are such that the resultant force is zero and the torques about any point cancel. In this parallel configuration, the force system can produce no net moment if the moments from the individual forces balance appropriately.

If the lines of action are neither concurrent nor parallel, a nonzero moment will arise about some point, so the member cannot be in equilibrium.