2.2 Important Concepts

Stable/Unstable
A stable structure is one that will not collapse when disturbed. Stability is the capability for a structure to recover equilibrium. In general, there are many ways that a structure may become unstable, including buckling of compression members, yielding/rupture of members, or nonlinear geometric effects (P-Delta effects); however, for linear structural analysis, the main concern is instability caused by insufficient reaction points or poor layout of structural members.
Internally Stable
An internally stable structure is one that would maintain its shape if all the reactions supports were removed. A structure that is internally unstable may still be stable if it has sufficient external support reactions. An example is shown in Figure 2.1.
Figure 2.1: Internal Stability
External Determinacy
In an externally statically determinate structure, all of the external reaction component forces may be calculated using only static equilibrium. A structure for which the external reactions component forces cannot be calculated using only equilibrium is externally statically indeterminate.
Internal Determinacy
In an internally statically determinate structure, all of the external reaction component forces and internal forces may be calculated using only static equilibrium. A structure for which the internal forces cannot be calculated using only equilibrium is internally staticallyindeterminate.Typically if one talks about 'determinacy' (without specifying internal or external), then it is internal determinacy that is meant.
Redundant
Indeterminate structures effectively have more unknowns than can be solved using the three equilibrium equations (or six equilibrium equations in 3D). These extra unknowns are called redundants.
Degree of Indeterminacy
The degree of indeterminacy for a structure is equal to the number of redundants. An indeterminate structure with 2 redundants may be said to be statically indeterminate to the second degree or "$2^\circ$ S.I."