Length effect on cantilever deflection – point load at free end For a cantilever beam carrying a point load W at its free end, if the length of the cantilever is doubled (other parameters unchanged), by what factor does the free-end deflection change?

Introduction / Context:Deflection sensitivity to span length is especially pronounced in cantilevers. Recognizing the power-law dependence helps engineers anticipate serviceability issues when spans change.

Given Data / Assumptions:

• Cantilever with end point load W.
• Original length L becomes 2L; material (E) and section (I) unchanged.

Concept / Approach:For a cantilever with an end point load, the free-end deflection is δ = W L^3 / (3 E I). Because δ ∝ L^3, a proportional change in length produces a cubic change in deflection.

Step-by-Step Solution:Original: δ_1 = W L^3 / (3 E I).New length 2L: δ_2 = W (2L)^3 / (3 E I) = W (8 L^3) / (3 E I) = 8 δ_1.Hence, the deflection increases eightfold.

Verification / Alternative check:Dimensional reasoning confirms cubic dependence on length for this loading condition; many design tables list the same relationship.

Why Other Options Are Wrong:

• 1/8 and 1/3 suggest decreases, which is incorrect.
• 2 and 3 underestimate the cubic effect.

Common Pitfalls:Assuming linear dependence on L; for beams under bending, deflections commonly scale with L^3 for simple cases.

Final Answer:8