For a beam, if fundamental equations of statics are not sufficient to determine all the reactive forces at the

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For a beam, if fundamental equations of statics are not sufficient to determine all the reactive forces at the supports, the structure is said to be

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Option C: Statically indeterminate

Explanation & Concepts:
A structure is statically indeterminate when the number of independent equilibrium equations ($\sum F_x = 0$, $\sum F_y = 0$, and $\sum M = 0$) is insufficient to solve for all unknown reactive forces. This occurs due to the presence of redundant constraints or supports that provide more reaction components than required for structural stability.

Working Principle: In a 2D beam, there are 3 basic equations of equilibrium. If the total number of unknown reaction components ($r$) exceeds the number of equilibrium equations ($n$), the structure is statically indeterminate to a degree ($D_s = r - n$). Additional equations based on compatibility conditions (deformations) are required to solve for the redundant reactions.

Key Formulas: $D_s = r - n$ — degree of static indeterminacy; $r > n$ — condition for static indeterminacy

Key Points: Equilibrium equations alone cannot find all support reactions.; Indeterminate structures are usually more rigid than determinate ones.; Requires compatibility of displacements to solve.; Also known as hyperstatic structures.

Advantages: Higher redundancy provides better safety factors.; Redistribution of internal forces occurs if one section reaches its plastic capacity.

Disadvantages: Internal stresses are induced by temperature changes or support settlements.; Complexity in manual analysis compared to determinate structures.

Applications: Continuous beams in bridge construction.; Building frames subjected to wind or seismic loads.; Fixed-ended beams used in aerospace structures.

Additional Info: Determinate structures rely solely on the laws of statics for solution.. A propped cantilever beam is a classic example of a statically indeterminate structure with $D_s = 1$.

Answer: C is correct — A structure is statically indeterminate if the unknowns exceed the number of independent equilibrium equations.

Exam Tip: Always verify if the number of unknown reactions ($r$) is greater than the number of equations of static equilibrium ($n=3$ for beams) before attempting a manual calculation.

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Option A: Determinate

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Option B: Statically determinate

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Option D: None of these

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