Part of any structural analysis is to analyze its stability first. We have to ensure that the frame we're examining is indeed stable. It is only to be in that state if it is externally and internally stable.
External Stability
A frame is externally stable if these two criteria are satisfied, provided that the structure is a rigid body:
- There is a proper arrangement of the frame's supports, and
- The number of supports must be greater or equal to the number of equilibrium equations.
In the case of frames, we have to consider the possibility of structures with internal devices such as hinges and links. In this case, the second criterion becomes:
- \(r+3m{\geq}3j+e_c\) for 2D-frames
- \(r+6m{\geq}6j+e_c\) for 3D-frames
Variables \(r\), \(m\), \(j\), and \({e_c}\) refer to the number of reaction components, members, joints, and conditional equations, respectively.
Internal Stability
It deals with properly arranging a structure's members and other components. For frames, it is essential to have a keen eye on the arrangement of their members and resulting deflection when all sorts of loads are applied.
A good measure to see if a frame is unstable is to observe its behavior when applied with loads. If its arrangement fails to deliver its purpose, it is dangerous.
Summary
A frame 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) \(r+3m{\geq}3j+e_c\) or \(r+6m{\geq}6j+e_c\) is satisfied.
Internal stability happens when there is a proper arrangement of the components making up the frame.
