Cantilever deflection comparison – point load at free end vs. uniformly distributed load (same total load) For a cantilever of length L and flexural rigidity EI, compare the maximum deflections when (i) a point load W acts at the free end and (ii) a uniformly distributed load of intensity w acts over the whole length such that total load W = wL. What is the ratio δ_point / δ_udl?

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:

• Cantilever length L, flexural rigidity EI.
• Case (i): point load W at the free end.
• Case (ii): UDL intensity w with total load W = wL (same total load as case i).

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:

• 3/8 inverts the ratio.
• 2 and 4/3 do not match the derived value.
• 1 would imply equal deflections, which is false.

Common Pitfalls:Comparing for equal intensities rather than equal total load; always align the basis of comparison.

Final Answer:8/3