Analysis of structure
Based on the forces for analysis, structures are classified into two types
1. Determinate structures
2. Indeterminate structures
Determinate Structures: The structures whose unknown forces can be
determined by using the equilibrium conditions themselves are called
determinate structures.
Indeterminate Structures: These are the structures in which the unknown
forces cannot be analyzed by using conditions of equilibrium only instead it
requires additional equations to determine the unknowns which are called
compatibility equations.
Degree of indeterminacy
Degree of Indeterminacy is nothing but the number of redundant that has
to be calculated.DOI is classified into two categories as
1. Statically indeterminate structure
2. Kinematically indeterminate structure
Statically indeterminate structure: It is the number of additional equations
required apart from equilibrium conditions to solve the unknown reactions
of the structure.
Static Indeterminacy is further classified into two categories
· External Static Indeterminacy
· Internal Static Indeterminacy
External Static Indeterminacy: It is the type of static Indeterminacy,
caused due to the unknown reactions of the support itself.
De = R-3 (for 2D structures)
De =R-6 (for 3D structures, since for 3D structures, there will be 6 equilibrium conditions)
Where De = External Static Indeterminacy
R= Number of Support Reactions
De=R-3 = Externally Determinate Structure
De> R-3= Redundant structure
De< R-3=Unstable structure
Internal Static Indeterminacy:
It refers to the geometrical stability of the structure.
If the internal forces of the members cannot be determined by equilibrium
conditions itself then it is said to be internally indeterminate.
For the geometric stability of structures, sufficient members are required to
preserve the shape of the structure without causing excessive deformation.
Dsi =3C-Rr (Where C= No of closed loops
Dsi =6C-Rr Rr= Released reactions)
Therefore Static Indeterminancy= External + internal Indeterminacy
Degree of static Indeterminacy for different structures.
- Plane Frame = 3m+r-3j
- Space Frame = 6m+r-6j
- Plane Truss = m+ r-3j
- Space Truss = m+r-2j
Kinematic Indeterminacy
It is the number of free displacements of the structure which are unknown
in addition to the compatibility equations.
Hence the extra equations required to determine the additional unknown
displacements are called kinematic Indeterminancy or it is also called
as the degree of freedom.
Er. SP.ASWINPALANIAPPAN., M.E.,(Strut/.,)
Structural Engineer
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