Shear Force at the Free End — Cantilever with Uniformly Distributed Load A cantilever beam of length l carries a uniformly distributed load w per unit length over the entire span. The shear force at the free end is:

Introduction:
Shear force and bending moment diagrams for basic loading cases are core knowledge in strength of materials. For a cantilever with a uniformly distributed load (UDL), recognizing boundary values helps draw accurate diagrams quickly.

Given Data / Assumptions:

• Cantilever span length = l, fixed at one end and free at the other.
• Uniformly distributed load w acts over the entire length.
• Linearly elastic, small deflection assumptions.

Concept / Approach:
Shear force is the integral of load intensity, and the bending moment gradient equals shear. At the free end of a cantilever, there is no support reaction to carry shear; thus the internal shear at that section must be zero. Maximum shear occurs at the fixed support where reactions develop.

Step-by-Step Solution:
1) Resultant of UDL = w * l acting at midspan from the free end.2) Shear diagram for a cantilever with UDL starts at V = w * l at the fixed end and linearly decreases to V = 0 at the free end.3) Therefore, shear at the free end is zero.

Verification / Alternative check:
From boundary conditions, the free end cannot develop internal shear or moment; both must be zero at that free boundary.

Why Other Options Are Wrong:

• w l, w l / 2, w l / 4, 2 w l: These are nonzero values that contradict the cantilever free-end condition.

Common Pitfalls:
Confusing the fixed-end values (nonzero) with the free-end values (zero for both V and M).

Final Answer:
zero