Statically Indeterminate

[From Wikipedia]

In statics, a structure is statically indeterminate when the static equilibrium equations are not sufficient for determining the internal forces and reactions on that structure.

Based on Newton’s laws of motion, the equilibrium equations available for a two-dimensional body are

* Σ F = 0 : the vectorial sum of the forces acting on the body equals zero. This translates to

Σ H = 0: the sum of the horizontal components of the forces equals zero;
Σ V = 0: the sum of the vertical components of forces equals zero;

* Σ M = 0 : the sum of the moments (about an arbitrary point) of all forces equals zero.

In the beam construction on the right, the four unknown reactions are VA, VB, VC and HA. The equilibrium equations are:

Σ V = 0:

VA − Fv + VB + VC = 0

Σ H = 0:

HA − Fh = 0

Σ MA = 0:

Fv · a − VB · (a + b) – VC · (a + b + c) = 0.

Since there are four unknown forces (or variables) (VA, VB, VC and HA) but only three equilibrium equations, this system of simultaneous equations cannot be solved. The structure is therefore classified statically indeterminate. Considerations in the material properties and compatibility in deformations are taken to solve statically indeterminate systems or structures.