### Indeterminacy

If the number of unknown reactions is greater than the number of equilibrium equations in a structure, then the structure is called an**indeterminate structure.**

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**Types of Indeterminacy**

There are two types of indeterminacy:

- Static Indeterminacy
- Kinematic Indeterminacy

#### Static Indeterminacy

This is the degree of indeterminacy of the structure. It is of two types:

- External Indeterminacy
- Internal Indeterminacy

**External Indeterminacy**

It deals with the number of unknown support reactions in excess of available equilibrium equations.

**For a 2D Structure:**

The set of equilibrium equations are Î£Fx = 0; Î£Fy = 0 ; Î£Mxy = 0;

**For a 3D Structure:**

The set of equilibrium equations are : Î£Fx = 0; Î£Fy = 0 ; Î£Fz = 0; Î£Mxy = 0; Î£Myz = 0; Î£Mxz = 0;

E. I = Number of Unknown support reactions - No: of equilibrium equations

E.I = R - 3 [ For 2D Structure ];

E.I = R - 6 [ For 3D Structure ];

**Internal Indeterminacy**

It is the number of internal forces or reactions in excess of equilibrium equations. The number of equilibrium equations for 2D and 3D are mentioned above. The internal forces are:

**For 2D :**

Shear force = Fy

Axial Force = Fx

Bending Moment = Mxy

**For 3D:**

Shear Force = Fy and Fz

Axial Force = Fx

Bending Moment = Mxy, Myz and Mxz

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