Difficulty: Medium
Correct Answer: 8/3
Explanation:
Introduction / Context:
Deflection formulas for common load cases are frequently compared to understand serviceability. For a cantilever, the end deflection depends strongly on how the load is distributed.
Given Data / Assumptions:
Concept / Approach:
Standard results: δ_point = W L^3 / (3 E I). For UDL with intensity w, δ_udl = w L^4 / (8 E I). With W = wL, substitute to compare.
Step-by-Step Solution:
δ_point = W L^3 / (3 E I).δ_udl = w L^4 / (8 E I) = (W/L) L^4 / (8 E I) = W L^3 / (8 E I).Ratio δ_point / δ_udl = (W L^3 / 3 E I) / (W L^3 / 8 E I) = 8/3.
Verification / Alternative check:
Since a point load is more severe than the same total UDL on a cantilever tip deflection, the ratio exceeding 1 (8/3 ≈ 2.67) is reasonable.
Why Other Options Are Wrong:
Common Pitfalls:
Comparing for equal intensities rather than equal total load; always align the basis of comparison.
Final Answer:
8/3
Discussion & Comments