Statically Determinate vs Indeterminate structures

Statically indeterminate structures are over-restrained in the sense that there are more force unknowns than available equilibrium equations. This situation happens when:

• There are more supports than needed to prevent rigid body motion (e.g. multi-span continuous beams);
• Indeterminacy may also result when there is an excess of members in order to satisfy static stability (such as a truss with multiple diagonals).

In other words, Indeterminate structures have more members and/or support reactions than required for static stability.

The advantages of statically indeterminate structures over determinate structures include the following:

• Smaller Stresses: The maximum stresses in statically indeterminate structures are generally lower than those in comparable determinate structures.
• Greater Stiffnesses: Statically indeterminate structures generally have higher stiffnesses (i.e., smaller deformations), than those of comparable determinate structures;

• Redundancies: Statically indeterminate structures have the capacity for redistributing loads when certain structural portions become overstressed or collapse (plastic hinges develop). If a part (or member or support) of such a structure fails, the entire structure will not necessarily collapse, and the loads will be redistributed to the adjacent portions of the structure.

The main disadvantages of statically indeterminate structures, over determinate structures, are the following:

• More complex analysis is required (all three basic equation types of structural analysis, i.e. equilibrium equations, Compatibility conditions and force-deformation relation equations must be used to analyze an indeterminate structure; while for statically determinate structures only equilibrium equations are enough);
• Stresses Due to Support Settlements: Support settlements do not cause any stresses in determinate structures; they may, however, induce significant stresses in indeterminate structures;

• Stresses Due to Temperature Changes and Fabrication Errors: Like support settlements, these effects do not cause stresses in determinate structures but may induce significant stresses in indeterminate ones.