DETERMINANT, INDETERMINANT STRUCTURES AND INDETERMINACY OF STRUCTURE

DETERMINATE AND INDETERMINATE STRUCTURE DEFINITION

 In structural analysis our main motive is to find unknown forces or moments in different component of structures. 

If these unknown forces or moments can be determined only by the use of equation of statics, then the structure is said to be determinant structure and if not then it is said to be indeterminant structure. So, for a determinate structure ,no any additional equation is required for calculation of unknown while for the indeterminate structure some compatibility equations ( additional equations) which relates applied loads and reactions to the displacement known at some points in the structure are required.

So, the definition of determinate structure will be that- it is the type of structure in which the unknown forces and moments will be calculated by only using the statics equations. 

And the definition of indeterminate structure will be that- Indeterminate structure are the type of structure in which the unknown forces and moments are calculated by some compatibility equations in addition to those of equation of statics. 

INDETERMINACY OF STRUCTURE

For indeterminate structures, the difference between the total number of unknowns and the available number of static equilibrium equation is known as indeterminacy of structure (or static indeterminacy).

Ds = (total unknown forces in member or at support reactions)-(available equilibrium equation)

EXTERNAL AND INTERNAL INDETERMINACY

External indeterminacy is difference between total number of support reactions and the number of available static equilibrium equations.

∴ Dse = (total number of support reactions) - (available equilibrium equation)

Internal indeterminacy is indeterminacy in excess of external indeterminacy.

∴ Dsi = (total indeterminacy) - (external indeterminacy)

STATIC EQUILLIBRIUM EQUATION

• For PLANAR STRUCTURE i.e. 2D structure

1. ∑ Fx =0
2. ∑ Fy =0
3. ∑ M =0

• For SPACE STRUCTURE i.e. 3D structure 
  

1. ∑ Fx =0
2. ∑ Fy =0
3. ∑ Fz =0
4. ∑ Mx =0
5. ∑ My =0
6. ∑ Mz =0