Static equilibrium for support reactions: The reactions at the supports of a structure can be determined by enforcing which equilibrium conditions?
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ASum of horizontal forces equals zero
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BSum of vertical forces equals zero
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CSum of moments about any point equals zero
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DAll of the above
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ENone of the above
Answer
Correct Answer: All of the above
Explanation
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.