In structural analysis of beams: If the static equilibrium equations alone are insufficient to determine all support reactions for a beam, what is such a structure called?

Introduction / Context:
Support reactions for beams are typically found using the three static equilibrium equations in a plane. When these equations are not enough to solve for all unknown reactions, the beam requires additional compatibility relations and is classified differently. This concept is fundamental in structural analysis and design.

Given Data / Assumptions:

• Planar beam problem.
• Standard static equilibrium equations available: sum of forces in x and y directions and sum of moments.
• Number of unknown support reactions exceeds the number of independent equilibrium equations.

Concept / Approach:
A structure is called statically determinate when all reaction components and internal forces can be found solely from static equilibrium. If not, the structure is statically indeterminate and needs additional deformation-compatibility conditions (and material/section properties) to find the unknowns.

Step-by-Step Solution:
Count unknown reactions.Compare with available independent equilibrium equations (in 2D, generally 3).If unknowns > equations, classification → statically indeterminate.

Verification / Alternative check:
Typical examples: A propped cantilever has four reaction components but only three equations, hence indeterminate to degree 1. A simply supported beam has two reactions, hence determinate.

Why Other Options Are Wrong:

• Determinate / Statically determinate: Require only equilibrium; contradicts the given condition.
• None of these / Partially determinate: Not standard classifications for this context.

Common Pitfalls:

• Ignoring internal redundants introduced by fixed or continuous supports.
• Counting equations incorrectly (e.g., dependent equations in some geometries).

Final Answer:
Statically indeterminate