Beam types – identification by support conditions\nA beam that is fixed at one end and free at the other is called:

Introduction / Context:
Structural analysis begins with recognizing beam support conditions, since bending moments, shear forces, slopes, and deflections depend on how the beam is restrained.

Given Data / Assumptions:

• One end built-in (encastré: zero slope and zero deflection).
• Other end free (no support reactions).
• Linearly elastic, prismatic beam.

Concept / Approach:
Standard beam types include simply supported (pin–roller), fixed beam (both ends fixed), cantilever (one end fixed, other free), overhanging (span extends beyond a support), and continuous (more than two supports). Correct naming ensures correct use of formulas.

Step-by-Step Identification:
Check restraints: fixed at one end implies encastré support.Opposite end is free → no restraint → classic cantilever configuration.

Verification / Alternative check:
Moment and slope diagrams for standard loads (point load at free end, uniform load, etc.) match cantilever beam solutions: maximum moment at the fixed end, zero at the free end.

Why Other Options Are Wrong:
Simply supported has rotation allowed at both ends; fixed beam is fixed at both ends; overhanging beams have spans extending beyond supports; continuous beams have three or more supports.

Common Pitfalls:
Confusing cantilever with a propped cantilever (one end fixed, one end simply supported) or with an overhang case.

Final Answer:
Cantilever beam