Deflection of Beams MCQ with answer and solution

Concept

Maximum deflection of loaded cantilever beam

Formula

δ = WL³/(3EI)

Step-by-step solution

1. For a cantilever beam subjected to a point load at its free end, maximum deflection occurs at the free end. 2. Integrating the differential equation of the elastic curve twice with appropriate boundary conditions yields the deflection. 3. The resulting expression for maximum deflection is WL³/3EI, where W is load, L is length, E is modulus of elasticity, and I is moment of inertia. Answer: A

Explanation

For a cantilever beam carrying a single concentrated point load at its free end, maximum deflection occurs at the loaded free end. Using standard structural deflection equations derived from moment-area or double integration methods, this maximum displacement equals WL cubed divided by 3EI. Here E is the elasticity modulus and I is the moment of inertia.

Why the other options are wrong

B) WL³/8EI corresponds to a cantilever beam subjected to a uniformly distributed load over its entire length. C) WL³/16EI applies to specific simply supported beam deflection cases. D) WL³/48EI is the maximum deflection for a simply supported beam with a central point load.

Shortcut

Cantilever point load max deflection = WL³/3EI (3 in denominator for point load).

Common mistake

Confusing the maximum deflection formula for a point load on a cantilever beam with that of a central point load on a simply supported beam.