Beam classification by end fixity\nA beam that is built-in (encastré) at both ends is referred to as which type?

Introduction / Context:
Beam behavior depends strongly on end restraints. Knowing the correct classification is essential for selecting bending moment and deflection formulas.

Given Data / Assumptions:

• Both ends are encastré (fully fixed: zero rotation and zero translation at supports).
• Linearly elastic, prismatic beam.

Concept / Approach:
A beam with both ends fixed is a fixed beam. By contrast, a simply supported beam has pin/roller supports allowing rotation; a cantilever is fixed at one end and free at the other; a continuous beam spans over more than two supports.

Step-by-Step Reasoning:
Identify boundary conditions: rotations at both ends are restrained.Thus, end moments develop even under symmetric loads, characteristic of a fixed beam.

Verification / Alternative check:
Deflection curves and moment diagrams of fixed beams show end negative moments compared to simply supported counterparts.

Why Other Options Are Wrong:
They do not match the described end fixity; continuous beams require three or more supports.

Common Pitfalls:
Confusing propped cantilever (fixed one end, simple support at the other) with a fully fixed beam.

Final Answer:
Fixed beam