Analysis of structure

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 itself are called as determinate structures.

Indeterminate Structures: These are the structures in which the unknown forces cannot be analyzed by using conditions of equilibrium only but instead it requires the additional equations to determine the unknowns which are called as compatibility equations.

Degree of indeterminacy

Degree of Indeterminacy is nothing but the number of redundants that has to be calculated .DOI is classified into two categories such 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 Indeterminancy is further classified into two categories

·        External Static Indeterminancy

·        Internal Static Indeterminancy

External Static Indeterminancy: It is the type of static Indeterminancy, 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 Indeterminancy: It refers to 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 geometric stability of structures sufficient members are requires 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 Indeterminancy

Degree of static Indeterminancy for different structures.

1. Plane Frame = 3m+r-3j
2. Space Frame = 6m+r-6j
3. Plane Truss = m+ r-3j
4. Space Truss = m+r-2j

Kinematic Indeterminancy

It is the number of free displacement 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 as kinematic Indeterminancy or it is also called as degree of freedom.