Stiffness Method of Structural Analysis

The stiffness method is a widely used technique in structural analysis that allows us to analyze and determine the behavior of structures under various loading conditions. In this method, the unknowns to be determined are the displacements at each node or joint of the structure. These displacements can be determined by solving a system of linear equations derived from the equilibrium and compatibility equations.

Number of Unknowns

The number of unknowns to be determined in the stiffness method is equal to the number of displacements at each node or joint of the structure. These displacements are typically represented by the unknowns in the form of generalized displacements, such as axial displacements, bending rotations, or shear displacements.

Kinematic Indeterminacy

Kinematic indeterminacy refers to the number of independent displacements that cannot be determined solely from the equilibrium equations. It is related to the flexibility of the structure and represents the degrees of freedom in the system. Kinematic indeterminacy is typically denoted by the symbol "k".

Static Indeterminacy

Static indeterminacy, on the other hand, refers to the number of unknown internal forces or reactions that cannot be determined solely from the equilibrium equations. It is related to the stiffness of the structure and represents the number of redundant constraints in the system. Static indeterminacy is typically denoted by the symbol "s".

Relation between Unknowns and Indeterminacy

In the stiffness method, the number of unknowns to be determined is equal to the sum of the static and kinematic indeterminacy. Mathematically, it can be represented as:

Number of Unknowns = Static Indeterminacy + Kinematic Indeterminacy

Therefore, option 'C' - Kinematic indeterminacy is the correct answer. The number of unknowns in the stiffness method is equal to the kinematic indeterminacy of the structure.

Conclusion

In the stiffness method of structural analysis, the number of unknowns to be determined is equal to the kinematic indeterminacy of the structure. This represents the number of independent displacements that cannot be determined solely from the equilibrium equations. It is important to understand the concept of indeterminacy in order to accurately analyze and solve structural problems using the stiffness method.