Definition of a fixed beam: a beam that is rigidly fixed at both of its ends (no rotation and no translation at supports).

Introduction / Context:
Support conditions dictate bending moments and deflections in beams. A fixed (built-in) support restrains both rotation and translation, producing end moments even under uniform loading.

Given Data / Assumptions:

• Linear elastic, prismatic beam.
• Ideal fixed ends with zero slope and zero deflection at supports.
• Transverse loading.

Concept / Approach:
A fixed beam has both ends built-in. This contrasts with simply supported beams (pinned/roller) where rotations are free, and cantilevers where one end is fixed and the other is free.

Step-by-Step Solution:

Verification / Alternative check:
Compare slopes: in a fixed beam, slope at ends is zero; in simply supported beam, slope is generally non-zero.

Why Other Options Are Wrong:
One fixed end only defines a cantilever.Support type does not vary with loading for a given structural detail.

Common Pitfalls:
Confusing fixed with guided supports; assuming zero moment at ends when fixity exists.

Final Answer:

both