If the support at B is removed, the reaction VB cannot occur, and the system becomes statically determinate (or isostatic). Note that the system is completely constrained here. The solution to the problem is
- ,
- ,
- .
If, in addition, the support at A is changed to a roller support, the number of reactions are reduced to three (without HA), but the beam can now be moved horizontally; the system becomes unstable or partially constrained. In order to distinguish between this and the situation when a system under equilibrium is perturbed and becomes unstable, it is preferable to use the phrase partially constrained here. In this case, the 2 unknowns VA and VC can be determined by resolving the vertical force equation and the moment equation simultaneously. The solution yields the same results as previously obtained. However, it is not possible to satisfy the horizontal force equation unless .
Statical indeterminacy is the existence of a non-trivial (non-zero) solution to the homogeneous system of equilibrium equations. It indicates the possibility of self-stress (stress in the absence of an external load) that may be induced by mechanical or thermal action.
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