Statically Indeterminate

In statics, a structure is statically indeterminate (or hyperstatic) when the static equilibrium equations are insufficient 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

• : 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;

• : 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 V_A, V_B, V_C and H_A. The equilibrium equations are:

Σ V = 0:

V_A − F_v + V_B + V_C = 0

Σ H = 0:

H_A − F_h = 0

Σ M_A = 0:

F_v · a − V_B · (a + b) - V_C · (a + b + c) = 0.

Since there are four unknown forces (or variables) (V_A, V_B, V_C and H_A) but only three equilibrium equations, this system of simultaneous equations does not have a unique solution. The structure is therefore classified as statically indeterminate. Considerations in the material properties and compatibility in deformations are taken to solve statically indeterminate systems or structures.