Degree of Static Indeterminacy and Primary Structure

The degree of static indeterminacy is the number of independent force unknowns that cannot be determined from equilibrium alone. In the force method it also gives the number of redundants $X_i$ and the number of compatibility equations.

External and internal indeterminacy

Redundancy may arise from support reactions or from internal force connections within the structure. Counting support reactions alone is therefore sufficient only for simple cases; frames, closed loops, and combined systems may contain internal redundancies.

Selecting redundants

Choose reactions or internal force resultants whose release produces a convenient statically determinate structure. Different valid sets of redundants can produce different primary structures, but the final response of the original structure must be the same.

Requirements for the primary structure

After releasing the redundants, the primary structure must be statically determinate and geometrically stable. A release that creates a mechanism or leaves hidden static indeterminacy is not valid.

Replacing released restraints

Each released restraint is replaced by its corresponding unknown generalized force or moment $X_i$. The primary structure is then analyzed for the prescribed loading and separately for a unit value of each redundant.

Efficient choice

A good primary structure produces simple internal-force diagrams, few integration segments, and makes use of symmetry when available. The choice affects computational effort, not the physical solution.