Static Determinacy of Framed Structures

Static determinacy indicates whether equilibrium equations are sufficient to determine all reactions and internal force effects. This classification should be applied to a geometrically stable structure; an unstable mechanism should not be labeled statically determinate merely because the number of unknowns matches the number of equations.

Statically determinate structures

In a statically determinate structure, force unknowns can be obtained from equilibrium. A planar rigid body provides three independent equilibrium equations, while internal hinges and separation into structural parts can provide additional independent equilibrium conditions in compound structures.

Static indeterminacy

If the number of independent force unknowns exceeds the available independent static equations, the structure is statically indeterminate. The excess gives the degree of static indeterminacy when the structural topology has been counted correctly.

External and internal indeterminacy

External indeterminacy is associated with redundant support restraints, whereas internal indeterminacy results from redundant connections between structural parts. Both types may occur in the same structure.

Mechanical consequence

Equilibrium alone cannot solve an indeterminate structure. Member deformation and displacement compatibility must also be considered, leading to the force method, displacement method, and matrix stiffness method.