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 forcedisplacement 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, forcedisplacement 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 forcedisplacement 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
