Deflection of Beams MCQ with answer and solution

Concept

Order of integration from load to deflection

Formula

q(x) -> V(x) = ∫ q dx -> M(x) = ∫ V dx -> θ(x) = ∫ (M/EI) dx -> y(x) = ∫ θ dx

Step-by-step solution

1. Distributed load intensity q(x) is related to shear force by V = int q dx. 2. Shear force is related to bending moment by M = int V dx. 3. Bending moment is related to beam slope by θ = int (M/EI) dx. 4. Beam slope is integrated to yield deflection: y = int θ dx. 5. Therefore, the successive order of integration is: Load -> Shear -> Moment -> Slope -> Deflection. Answer: A

Explanation

The governing differential equations of beam flexure follow a successive chain where integrating load intensity gives shear force, integrating shear gives bending moment, integrating moment divided by flexural rigidity gives slope, and integrating slope gives deflection.

Why the other options are wrong

B) Shear force must be evaluated before bending moment can be integrated. C) Moment cannot be integrated directly to obtain load. D) Curvature is directly proportional to moment, not integrated between moment and shear.

Shortcut

Downward derivatives (y -> θ -> M -> V -> q); upward integration (q -> V -> M -> θ -> y).

Common mistake

Reversing the order between shear force and bending moment during the integration sequence.