Continuous beam is ________________.

Question

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The correct answer is Option C: Statically indeterminate. A continuous beam is a structural member supported by more than two supports, creating multiple spans. Because the number of reaction components at the supports exceeds the available number of independent equilibrium equations, it is classified as statically indeterminate.

Step-by-Step Solution & Concepts:
A continuous beam is a structural member supported by more than two supports, creating multiple spans. Because the number of reaction components at the supports exceeds the available number of independent equilibrium equations, it is classified as statically indeterminate.

Working Principle: In a continuous beam, the internal forces (bending moments and shear forces) cannot be determined by the equations of static equilibrium alone ($\sum F_x = 0, \sum F_y = 0, \sum M = 0$). Solving such a structure requires supplementary compatibility equations that account for material deformation, such as the Theorem of Three Moments or the Slope-Deflection Method.

Key Formulas: $D_s = R - 3$ — where $R$ is the total number of reaction components, representing degree of static indeterminacy for plane structures.; $M_a L_1 + 2M_b(L_1 + L_2) + M_c L_2 = -\frac{6A_1 \bar{x}_1}{L_1} - \frac{6A_2 \bar{x}_2}{L_2}$ — Clapeyron's Theorem of Three Moments.

Key Points: A beam with $n$ spans over $n+1$ supports is typically statically indeterminate of degree $(n-1)$.; Statically indeterminate structures redistribute stresses if one support settles or yields.; These structures are generally more rigid and economical in terms of material usage compared to simply supported beams.

Advantages: Higher structural stiffness and lower mid-span deflection; Economical as it allows for smaller section sizes due to moment redistribution

Disadvantages: Sensitive to support settlements which induce additional parasitic stresses; Temperature changes and fabrication errors cause secondary stresses

Applications: Bridge decks over multiple piers; Multi-span reinforced concrete floor beams; Continuous slab foundations

Additional Info: A beam with two supports is statically determinate; adding a third support makes it statically indeterminate of the 1st degree.. Option A and B are identical in technical meaning (both imply determinacy), whereas the continuous nature inherently introduces redundant reactions.

Answer: C is correct — Continuous beams possess more reaction components than static equilibrium equations, rendering them statically indeterminate.

Exam Tip: For competitive exams, always remember that 'continuous' implies $D_s > 0$. If you see a beam with $n$ supports and no internal hinges, the degree of indeterminacy is $R-3$.

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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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