In statics "Statics (mechanical)"), a structure is hyperstatic or statically indeterminate when it is in equilibrium but the equations of statics are insufficient to determine all internal forces or reactions. There are various forms of hyperstaticity:

A structure is completely hyperstatic if it is internally and externally hyperstatic.

In the hyperstatic beam represented in the figure, there are four reactions to determine the forces that the beam transmits to its three supports, three vertical components V, V, V and a horizontal component H (F here represents the external force). Based on Newton's laws, the equilibrium equations of statics applicable to this plane structure in equilibrium are that the sum of vertical components must be zero, that the sum of horizontal forces must be zero and that the sum of moments with respect to any point on the plane must be zero:

Developing the previous equations:

Since there are only three linearly independent equations and four unknown forces or components (V, V, V and H) with only these equations it is impossible to calculate the reactions and therefore the structure is hyperstatic (in fact, externally hyperstatic).

Only when the elastic properties of the material are considered and the proper deformation compatibility equations are applied can the problem be solved (being statically indeterminate it is at the same time elastically determined). The reactions in the previous example can be determined, for example, by the three-moment theorem, which leads to:

Calculating the vertical reactions from the shear stress diagram leads to the expressions: