Which of the following is not a statically determinate beam?

Question

Examoogle · Accepted Answer

The correct answer is Option C: Continuous beam. A statically determinate structure is one where all reaction forces and internal member forces can be determined using only the equations of static equilibrium. A continuous beam, having more than two supports, results in more unknown reaction components than available equilibrium equations, making it statically indeterminate.

Step-by-Step Solution & Concepts:
A statically determinate structure is one where all reaction forces and internal member forces can be determined using only the equations of static equilibrium. A continuous beam, having more than two supports, results in more unknown reaction components than available equilibrium equations, making it statically indeterminate.

Working Principle: In a planar system, we have three fundamental equilibrium equations: $\sum F_x = 0$, $\sum F_y = 0$, and $\sum M = 0$. For a structure with $r$ reaction components, if $r > 3$, the structure is statically indeterminate. A continuous beam typically has four or more reaction components (at least three supports), requiring additional compatibility equations like the Theorem of Three Moments or Slope-Deflection method to solve.

Key Formulas: $D_s = r - 3$ — Static indeterminacy degree for planar beams; $\sum F_x = 0, \sum F_y = 0, \sum M_z = 0$ — Basic equations of static equilibrium

Key Points: A structure is determinate if the number of unknown reactions equals the number of independent equilibrium equations.; Simply supported, cantilever, and overhanging beams are basic statically determinate configurations.; Continuous beams are redundant structures because they have more supports than required for stability.; Degree of static indeterminacy ($D_s$) for a continuous beam over $n$ spans is $(n+1) - 3$.

Advantages: Determinate beams are independent of temperature changes or support settlements for stress calculations.; Easier to analyze manually without computational tools.

Disadvantages: Continuous beams (indeterminate) are more structurally efficient and offer better load redistribution.; Failure in one component of a determinate structure leads to total collapse (no redundancy).

Applications: Simple residential floor beams.; Temporary bridge structures.; Structural analysis education.

Additional Info: Continuous beams require the Principle of Superposition or methods like Moment Distribution to solve.. Option A, B, and D are statically determinate because their reaction forces can be found using the three basic equilibrium equations.

Answer: C is correct — Continuous beam is statically indeterminate because it possesses more reaction supports than the available equations of static equilibrium.

Exam Tip: Always check the number of constraints (supports) versus the degrees of freedom; if you can't solve it with just three equilibrium equations, it's statically indeterminate!

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Option A: Simply supported beam

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Option B: Cantilever beam

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Option D: Overhanging beam

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