# Which of the following methods of structural analysis is true for compatibility governing equations?

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Which of the following methods of structural analysis is true for compatibility governing equations?
1. Theorem of least work
2. Slope deflection method
3. Stiffmess matrix method
4. Moment distribution method

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Correct Answer - Option 1 : Theorem of least work

Concept:

Compatibility governing equations are used in Force Methods.

In the force method of analysis:

Primary unknown forces in the members and compatibility equations are written for displacement and rotations (which are calculated by force-displacement equations) in this method.

Solving these equations, redundant forces are calculated. Once the redundant forces are calculated, the remaining reactions are evaluated by equations of equilibrium.

In the displacement method of analysis:

Primary unknowns are the displacements and initially, force-displacement relations are computed and subsequently, equations are written satisfying the equilibrium conditions of the structure in this method. After determining the unknown displacements, the other forces are calculated satisfying the compatibility conditions and force-displacement relations.

Difference between Force & Displacement Methods:

 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