Most, but not all, two-force members are straight. Straight elements are subjected to either tension or compression. Those members of other geometries will have bending across their section in addition to tension or compression, but the two-force principle still applies. There are NO EXCEPTIONS!!!
Some common examples of two-force members are columns, struts, Hangers, Braces, and Truss Members.
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Let us examine the simple system shown. It could be the support for a canopy over a door. The load at point F could be a hanging lamp. All of the joints are considered to be pinned. If member BC is isolated, it can be seen that it has forces acting at only points C and B. This means that it is a two-force member. The line of action of the force at point C must also pass through point B; similarly, a force at point B must also pass through point C. If the force at B did not pass through point C (B' in the diagram), the force would cause a moment about point C and equilibrium would not be possible. Because the two forces are equal in magnitude, co-linear and opposite in sense, two-force members act only in pure tension or pure compression. Supports such as cables tend to work well as two force members.
If three non-parallel forces act on a body in equilibrium, it is known as a three-force member. This often refers to elements which have a single load and two reactions. If a three-force member is in equilibrium and the forces are not parallel, they must be concurrent. Therefore, the lines of action of all three forces acting on such a member must intersect at a common point; any single force is the equilibrant of the other two forces. These members usually have forces which cause bending and sometimes additional tension and compression.
The most common example of a three-force member is a beam.
If one isolates member AF in the pin connected frame to the right, one sees that it has forces acting at three points: A, C, and F. The free body diagram of the system can be seen in the diagram below. The magnitude and the line of action of the force at F, 10 Kips, is known. The line of action of the force at point C is known because it must be equal and opposite to the force C of the two-force member CB. The line of action of the forces at point F and point C intersect at X. The line of action of the force at point A must also go through points A and X. (Why is this?)
The lines of action of the reactions at points A and C have now been determined. The problem of establishing their sense and magnitude remains. The sense of these forces can be established intuitively in this example, but this is not always the case. The Three Force Principle, demonstrated in a step-by-step manner, will show how simple it is to establish both the sense and the magnitude of the reactions of a system of three forces:
Had it been assumed that the line of action of the reaction force going through point A had taken a direction other than through point X, the system would not be a concurrent force system. Although it could be in force equilibrium, it would not be in moment equilibrium because the summation of the moments about ANY point would no longer be zero. This can be seen below.
