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Which method is suitable for analyzing a beam when the degree of kinematic indeterminacy is less than a degree of static indeterminacy?

Which method is suitable for analyzing a beam when the degree of kinematic indeterminacy is less than a degree of static indeterminacy? Correct Answer Slope deflection method 

Explanation:

  • In the slope deflection method, the unknowns are slope and deflection (i.e. independent displacement). so if kinematic indeterminacy is less, then the slope deflection method is used to find the end moment quickly.
  • The number of simultaneous equations required in the slope deflection method to find unknown is equal to kinematic indeterminacy.


Important Points about Slope Deflection Method:

  1. The slope deflection equation will give the relationship between bending moment rotation and deflections.
  2. The number of simultaneous equations to be solved in the slope deflection method is equal to the number of joints in the structure.
  3. In the slope deflection equations, the deformations are caused by bending moment only.
  4. The slope deflection method of structural analysis is a method of displacement.

​Important Points

Force Methods

Displacement Methods

Types of indeterminacy:

Static Indeterminacy

Types of indeterminacy: Kinematic Indeterminacy

Governing equation: Compatibility Equations

Governing equations: Equilibrium Equations

Force displacement relations: Flexibility matrix

Force displacement relations: Stiffness matrix

Example:

1. Method of consistent deformation

2. Theorem of least work

3. Column analogy method

4. Flexibility matrix method

5. Castigliano’s Theorem- II

Example:

1. Slope deflection method

2. Moment distribution method

3. Kani’s method

4. Stiffness matrix method

5. Castigliano’s Theorem- I

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