In structural engineering practice, how can the vertical deflection of a prismatic beam be most effectively reduced (keeping material and span otherwise similar)?

Introduction / Context:Beam deflection control is a core serviceability requirement in civil and structural engineering. Designers frequently tune member proportions to limit sag under working loads without excessive material use.

Given Data / Assumptions:

• Prismatic (constant cross-section) beam under typical service loads.
• Material and modulus of elasticity E unchanged.
• We compare the qualitative effect of changing section dimensions or span.

Concept / Approach:For a rectangular section, second moment of area I = b * d^3 / 12. Deflection Δ is inversely proportional to E * I for a given loading case (e.g., Δmax ∝ 1 / (E * I)). Because I scales with d^3, increasing depth produces a cubic gain in stiffness. Increasing width b helps only linearly and is therefore less effective for the same material.

Step-by-Step Solution:

Verification / Alternative check:Compare two sections of same area: making one deeper and narrower will typically reduce Δ more than making one wider and shallower, confirming the cubic sensitivity to depth.

Why Other Options Are Wrong:Increasing span raises deflection; decreasing depth reduces stiffness; increasing only width slightly gives limited benefit compared to depth for the same mass; “None” is incorrect because depth increase is effective.

Common Pitfalls:Focusing only on ultimate strength and neglecting serviceability; assuming width increase equals depth increase in impact; forgetting load case and support conditions also influence Δ.

Final Answer:Increasing the depth (overall height) of the beam section