Stability & Simple Trusses

There is an important characteristic of a useful truss: it must be stable, which is to say that it should not move freely in any direction. Below are some configurations of members joined at the ends. The first shown is the most basic triangular truss. The left support only allows connected members to rotate. The right support additionally allows horizontal movement. This configuration is stable, because there is no motion which can freely occur.

Two members connected at a joint form a hinged arch, as shown below. A hinged arch may be added to any stable truss to form another stable truss, as long as the angle of the arch is other than 180º. A truss which can be assembled in this manner is called a simple truss.

Shown next is a square configuration. This is unstable, because the side pieces will lean over freely as the top is pushed horizontally. How would this be stabilized?

Lastly, we see that a pentagonal configuration is also unstable, because as points A and B move apart, point C is free to move down. What is the smallest number of members required to make this stable? In a similar fashion, all but the triangle will be unstable, so the triangle is basic unit of any truss structure.