Cantilever with uniformly distributed load over the entire length – maximum fixed-end moment A cantilever of length L carries a uniformly distributed load over the whole span. If W denotes the total load on the cantilever, what is the maximum bending moment at the fixed end?

Introduction / Context:For a cantilever, the critical bending moment occurs at the fixed support. When the loading is a uniform load distributed along the span, the fixed-end moment can be expressed either in terms of intensity w (per unit length) or in terms of the total load W = wL.

Given Data / Assumptions:

• Cantilever length L.
• UDL over the entire length.
• W denotes the total load = wL.

Concept / Approach:Standard result: with intensity w, the fixed-end moment M_max = w L^2 / 2. Substitute w = W / L to express the moment in terms of W.

Step-by-Step Solution:M_max = (w L^2) / 2.Since W = wL, w = W / L.M_max = (W / L) × L^2 / 2 = (1/2) W L.

Verification / Alternative check:Dimensional check: bending moment has units of force × length; (1/2) W L is consistent.

Why Other Options Are Wrong:

• W L doubles the correct value.
• (1/3) W L is not the standard coefficient for this case.
• W L^2 has wrong dimensions if W is total load.

Common Pitfalls:Confusing W (total load) with w (load intensity). Always confirm symbols used in the question.

Final Answer:(1/2) W L