Static equilibrium for support reactions: The reactions at the supports of a structure can be determined by enforcing which equilibrium conditions?

Introduction / Context:
Determining support reactions is the first step in analyzing statically determinate structures. Reactions follow directly from the equations of static equilibrium.

Given Data / Assumptions:

• Planar structure; loads and reactions lie in a plane.
• Body is rigid; supports are idealized as pins/rollers/fixed as appropriate.
• No acceleration (static case).

Concept / Approach:
For planar statics, three independent equilibrium equations are available: ΣF_x = 0, ΣF_y = 0, and ΣM_O = 0. Solving these yields the unknown reaction components and moments for determinate systems.

Step-by-Step Solution:
Write ΣF_x = 0 to relate horizontal reaction components and applied horizontal loads.Write ΣF_y = 0 to relate vertical reaction components and applied vertical loads.Write ΣM_O = 0 (about any convenient point) to eliminate one or more unknowns and solve.

Verification / Alternative check:
Choosing a different moment center gives the same reactions if calculations are correct, providing a natural check.

Why Other Options Are Wrong:
Each single equation alone is insufficient for a general 2D support-reaction problem; all three together are required for complete solution.

Common Pitfalls:
Incorrect sign conventions, neglecting couple moments, or forgetting inclined loads have both x and y components.

Final Answer:
All of the above.