What defines a statically determinate structure?

A statically determinate structure is one that can be mathematically solved using equilibrium equations without needing additional information from material properties or deformation characteristics. In essence, this means that the forces and moments at static equilibrium can be calculated using the basic principles of static mechanics. For such structures, the number of reactions and internal forces can be determined solely through the application of equations of equilibrium, making analysis straightforward.

The capability to solve for these forces is essential for engineers when designing structures to ensure they can support the loads they will encounter during their lifecycle. In contrast, structures that have more unknowns than available equations (often due to redundancy or additional constraints) are termed statically indeterminate, requiring more advanced analysis techniques.

While the ability to withstand external forces is important (as indicated in the first option), it does not specifically define a statically determinate structure. Similarly, rigidity and internal redundancy pertain to how structures respond to loads and their overall stability and performance under stress, rather than directly to the mathematical solvability of the structure’s forces. Hence, the most defining characteristic of a statically determinate structure is that it can be mathematically solved using static equilibrium principles.