In this post, we'll explore the trusses' external and internal stability using different examples - a significant requirement in analyzing any structure.
Part of any structural analysis is to analyze its stability first. We have to ensure that the truss we're examining is indeed stable. It is only to be in that state if it is externally and internally stable.
External Stability
A truss is externally stable if these two criteria are satisfied, provided that the structure is a rigid body:
There is a proper arrangement of the truss's supports, and
The number of supports must be greater or equal to the number of equilibrium equations.
We can express the second criterion as:
\(r+m{\geq}2j\) for 2D-trusses
\(r+m{\geq}3j\) for 3D-trusses
Variables \(r\), \(m\), and \(j\) refer to the number of reaction components, members, and joints, respectively.
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This stability deals with properly arranging the truss's components. It is essential to have a sharp eye on member arrangements and the resulting movement when loads are applied.
To demonstrate, consider the truss shown. It is a structure with one rectangular panel \(BDEC\). That said panel has no diagonals whatsoever.
Let's first examine its external stability. From this example:
There is a proper arrangement of supports.
The number of supports equals the number of available equations (3=3).
The number of unknown components exceeds the number of known conditions (4>3).
Based on this, the truss is externally stable.
Now, let's say there is an earthquake that will cause the truss to sway side-to-side. The truss may deform too much or even collapse instantly. This event happens because no diagonal in panel \(BDEC\) would retain its general shape. From this example, you can see that the truss is unstable - a case of instability!
To avoid this, the arrangement of members must make the whole truss rigid. To make our example stable, we must add a diagonal member in panel \(BDEC\). That way, the structure has a better chance of resisting an earthquake. From this example, we can see why we use triangles to form most trusses.
Below are other situations wherein the truss is unstable:
Summary
A truss is said to be stable if it is both externally and internally stable.
External stability happens when these two criteria are satisfied: (1) supports are correctly arranged and (2) \(r+m{\geq}2j\) or \(r+m{\geq}3j\) is satisfied.
Internal stability happens when the arrangement of truss members makes it rigid.
