Deflection of Beams MCQ with answer and solution

Concept

Analogy between actual beam and conjugate beam where loading is M/EI diagram.

Step-by-step solution

1. Understand the Mohr's theorems or conjugate beam analogies. 2. The load on the conjugate beam is the M/EI diagram of the actual beam. 3. Shear force in the conjugate beam = Slope of the actual beam. 4. Bending moment in the conjugate beam = Deflection of the actual beam.

Explanation

In the conjugate beam method, the shear force at any point in the conjugate beam corresponds to the slope at the corresponding point in the actual beam, and the bending moment at any point in the conjugate beam corresponds to the deflection of the actual beam.

Why the other options are wrong

A: Bending moment in conjugate beam gives deflection, not bending moment. B: Shear force in conjugate beam gives slope, not shear force. C: Slope is given by the shear force of the conjugate beam.

Shortcut

Remember 'Shear = Slope, Moment = Deflection' (SM-SD).

Common mistake

Confusing shear force with bending moment relation; remembering that shear gives deflection instead of slope.