Deflection comparison: two simply supported beams of equal length l and breadth b carry the same central point load W. Beam B has double the depth (2d) compared to beam A (depth d). State whether the deflection of beam B is “double” that of beam A.

Introduction / Context:
The midspan deflection of a simply supported beam under a central point load depends on span, stiffness, and load. Changing the cross-section (depth) changes the second moment of area I and therefore the deflection. This question checks understanding of how deflection scales with depth.

Given Data / Assumptions:

• Both beams: simply supported, same length l and breadth b.
• Same central point load W and same material (same E).
• Beam B has depth 2d; beam A has depth d.

Concept / Approach:
The midspan deflection for a simply supported beam with a central point load is delta = W * l^3 / (48 * E * I). For a rectangle, I = b * d^3 / 12. Deflection is inversely proportional to I and thus to d^3 for constant b.

Step-by-Step Solution:

Verification / Alternative check:
Use section modulus or quick proportionality: deflection ∝ 1 / d^3 for rectangular sections; doubling depth reduces deflection by 2^3 = 8.

Why Other Options Are Wrong:
“Correct”: opposite of the actual scaling.Conditions about E or cantilevers are irrelevant; the stated comparison is for like-for-like beams and loading.

Common Pitfalls:
Thinking deflection scales with 1/d or 1/d^2 instead of 1/d^3; forgetting the cubic effect of depth on I.

Final Answer:

Incorrect