What are Indeterminate Structures?


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.
Continuous beam  Bridge ;
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Types of Indeterminacy
There are two types of indeterminacy:
  1. Static Indeterminacy
  2. Kinematic Indeterminacy

Static Indeterminacy

This is the degree of indeterminacy of the structure. It is of two types:
  1. External Indeterminacy
  2. 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 ΣFx = 0; ΣFy = 0 ; ΣMxy = 0;

For a 3D Structure:

The set of equilibrium equations are : ΣFx = 0; ΣFy = 0 ; ΣFz = 0; ΣMxy = 0;  ΣMyz = 0;  ΣMxz = 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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