Stability Assesment- Example: Assess the stability of the truss shown below.
Looking at the 9-bar truss, we see nothing but multiple closed triangular cells. Therefore, it is definitely a stable truss.
We can also verify its stability with the help of Eq. (1). The truss has 6 joints, therefore, 9 members are needed to assure its stability. The number of members present is also 9, thus, this is a stable truss.
If any member of this truss is removed, the truss becomes unstable and will collapse. For example, if we were to remove member 7, we will transform the triangles 3-5-6 and 3-4-5 into a single quadrilateral cell connecting joints 3-4-5-6. Thus, there is nothing to restrain the movement of joint 5 relative to joint 3, resulting in the collapse of the truss as shown below.