Statically determinate beam with three reaction unknowns If a beam is supported such that there are exactly three independent reaction components, which equilibrium equations are sufficient to determine them?

Introduction / Context:A planar, statically determinate problem can be solved using only the equations of static equilibrium. For beams in the plane, there are three independent equations available.

Given Data / Assumptions:

• Planar system (2D), rigid body equilibrium.
• No additional redundants or internal releases.
• Supports provide exactly three independent reaction components in total.

Concept / Approach:The independent equilibrium equations in a plane are:∑H = 0∑V = 0∑M = 0These three equations can determine three unknown reaction components if the structure is statically determinate.

Step-by-Step Solution:

Verification / Alternative check:If more than three unknowns exist, the structure is statically indeterminate to that degree and requires compatibility (deformations) to solve.

Why Other Options Are Wrong:

• Options a, b: insufficient equations.
• Option c: duplicates ∑H and omits the others.
• Option e: omits ∑V = 0; system remains underdetermined.

Common Pitfalls:Counting dependent reaction components or missing the moment equation about a convenient point.

Final Answer:∑H = 0; ∑V = 0; ∑M = 0