Statical determinacy

[Taken from the Wikipedia.org]

A structural engineer must understand the internal and external forces of a structural system consisting of structural elements and nodes at their intersections.

A statically determinate structure can be fully analysed using only consideration of equilibrium, from Newton’s Laws of Motion.

A statically indeterminate structure has more unknowns than equilibrium considerations can supply equations for (see simultaneous equations). Such a system can be solved using consideration of equations of compatibility between geometry and deflections in addition to equilibrium equations, or by using virtual work.

If a system is made up of b bars, j pin joints and r support reactions, then it cannot be statically determinate if the following relationship does not hold:

r + b = 2j

It should be noted that even if this relationship does hold, a structure can be arranged in such a way as to be statically indeterminate.