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Structure Analysis

Structure Analysis

Theory of Structures
Due to the supplied external load, what is the force coming in individual members is the objective of Structural Analysis, along with the load we are also interested in the deflection of members.

Aim:
  • The main aim of structural analysis is to find out the forces/moments in various components of the structures.
  • If all these forces are found out with the help of the equation of static equilibrium, then the structure is said to be a Statically Determinate Structure.
Determinacy and Indeterminacy
  • In the structural analysis, we mostly adopt indeterminate structures because they are economical.

Advantages of Indeterminate Structure:
  • A sectional requirement is less because the maximum Bending Moment development is lesser.
  • Deflection is Less.
  • Multiple paths of load transfer are available.

Disadvantages of Indeterminate Structure:
  • Stronger support is required.
  • Temperature change and support settlement induce additional moments in the member.

There are two methods of analysis of indeterminate structures.
  1. Force method
  2. Displacement method.

1. Force Method
  • In the Force method of analysis, we find out the degree of static indeterminacy of the structure.
  • We then choose the Redundant.
  • The number of Redundant choose is equal to Ds(Degree of Static Indeterminacy).
  • Member Force or support Reaction are chosen as Redundant.
  • We write Force-Displacement relationship.
  • Redundant is found out using compatibility Equation.
  • The number of Compatibility Equation required is equal to Ds.

2. Displacement Method
  • In the Displacement method of analysis, joint displacements are taken as unknown.
  • No. of Joints displacement is called the Degree of Freedom or Degree of Kinematic Indeterminacy (Dk).
  • we write the Force-Displacement relationship and find out the unknown displacements using Equilibrium equations.
  • No. of equilibrium equations required is equal to the Degree of Kinematic Indeterminacy (Dk).
  • The Displacement once have known are put back into the force-displacement relationship to find out the Forces.

Degree of Static Indeterminacy (Ds):

Ds= [No. of member forces and support reactions present] - [No. of the equation of static equilibrium] 

No. of Equation of Static Equilibrium in 2D is 3.

                                       


No. of Equation of Static Equilibrium in 3D is 6.

                                




Ds= Dse + Dsi

Dse = Degree of external Indeterminacy.
Dsi = Degree of Internal Indeterminacy.
Dse = [No. of Support Reaction present] - [No. of equations of static equilibrium for the overall structure]

= [No. of Support Reaction present] - 3 for 2D

=[No. of Support Reaction present] - 6 for 3D

Dsi= Ds - Dse

1. Determinacy and Indeterminacy.
2. Force Method of Analysis.
3. Displacement Method
4. Trusses
5. Influence Lines
6. Matrix Method

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