Basic definitions – cantilever support conditions:\nA cantilever beam is defined as a beam that is:

Introduction / Context:
Support conditions control the internal forces and deflections of beams. The cantilever is a fundamental boundary condition found in balconies, crane jibs, and shelf brackets. Recognizing its definition immediately sets the boundary values for shear, moment, slope, and deflection.

Given Data / Assumptions:

• One end of the beam is rigidly fixed (built-in), preventing translation and rotation.
• The other end is free, with no restraint to translation or rotation.
• Loads may act along the span or at the free end.

Concept / Approach:
At the fixed end, reactions include a vertical force and a fixing moment (and potentially a horizontal force in 2D). At the free end, both the shear force and bending moment are zero in the absence of applied end actions. These boundary conditions define the shape of shear and moment diagrams and the characteristic deflection curve of a cantilever.

Step-by-Step Solution:

Verification / Alternative check:
Compare with simply supported beams (pin and roller): both ends allow rotation and do not provide a fixing moment; that is not a cantilever. Continuous beams over multiple supports also differ.

Why Other Options Are Wrong:

• Fixed–fixed: both ends restrained, not a cantilever.
• Simply supported or multi-support beams: lack a fixed end; they admit rotations at supports.
• Overhang with simple supports is not a cantilever because the overhang end is not fixed.

Common Pitfalls:
Confusing overhanging simply supported beams with cantilevers; only a fixed connection qualifies the member as a cantilever.

Final Answer:
Fixed at one end and free at the other end