For a cantilever beam, the internal shear force and bending moment at the free end are zero. Considering the listed load cases, when is this statement true?

Introduction / Context:Cantilever beams are fixed at one end and free at the other. Understanding boundary conditions—especially that the free end cannot transmit moment or shear—is crucial for drawing correct shear-force and bending-moment diagrams.

Given Data / Assumptions:

• Cantilever of any prismatic or non-prismatic form.
• Loads may be a point load, uniformly distributed load, or other distributions.
• Linear elastic beam theory applies for internal force definitions.

Concept / Approach:By definition, at the free end of a cantilever, there is no support to develop a reaction shear or reaction moment. Therefore, the internal shear force V and bending moment M evaluated at the very free tip are zero for any applied loading configuration.

Step-by-Step Solution:

Verification / Alternative check:All standard shear and moment diagrams for cantilevers start at zero at the free end and grow towards the fixed end to meet boundary conditions at the built-in support.

Why Other Options Are Wrong:Options limiting the zero condition to particular loads (point load or UDL) are incorrect; the zero condition holds universally at the free end.“True only for no loading” is false; even with loads, the free-end values remain zero.

Common Pitfalls:Misreading internal shear/moment at a small distance from the tip (which may be nonzero) versus exactly at the tip where both are zero.

Final Answer:

None of the above (it is always true for the free end of a cantilever)