Deflection Comparison – Point Load at Midspan vs Equivalent Uniform Load Two identical simply supported beams have span L and flexural rigidity E I. Beam A carries a point load W at midspan. Beam B carries a uniformly distributed load of intensity w = W / L so that the total load equals W. What is the ratio of maximum deflections delta_A : delta_B?

Introduction / Context:
Serviceability checks often compare deflections under different loading patterns for the same total load. Understanding how load distribution affects deflection is crucial for realistic performance predictions.

Given Data / Assumptions:

• Simply supported beams, identical L and E I.
• Beam A: central point load W.
• Beam B: uniform load with total W, so w = W / L.
• Linear elastic, small deflection, prismatic sections.

Concept / Approach:

Use standard closed-form deflection formulas and take the ratio. The maximum deflection occurs at midspan for both cases under the given loads.

Step-by-Step Solution:

Verification / Alternative check:

Energy methods or numerical integration give the same ratio because both deflections scale with W L^3 / (E I), and only coefficients differ.

Why Other Options Are Wrong:

5 / 8 is the reciprocal. 4 / 5 and 3 / 2 are not obtained from standard coefficients. 2 ignores the correct constants in the solution.

Common Pitfalls:

Confusing total load with intensity, applying W as w directly, or forgetting that the UDL deflection coefficient is 5/384.

Final Answer:

8 / 5