The fixed support in a real beam becomes a free support in the conjugate beam. To understand why this is the case, let's first define what a real beam and a conjugate beam are.

Real Beam: A real beam is a structural member that is subjected to loads and supports reactions at its ends. It can be fixed, hinged, or simply supported, depending on the type of support it has at its ends.

Conjugate Beam: A conjugate beam is an imaginary beam that is used to determine the bending moments and shear forces in a real beam. It is obtained by replacing the supports of the real beam with certain types of supports depending on their nature.

Now, let's discuss why the fixed support in a real beam becomes a free support in the conjugate beam.

1. Definition of Fixed Support: A fixed support is one that prevents both translation and rotation of the beam at that point. It provides maximum resistance to bending moments and shear forces.

2. Definition of Free Support: A free support, also known as a simple support, allows both translation and rotation of the beam at that point. It provides no resistance to bending moments and shear forces.

3. Transformation of Supports: When we consider a real beam and its conjugate beam, we need to replace the supports in the conjugate beam in such a way that they accurately represent the bending moments and shear forces in the real beam.

4. Support Transformation Rules: The support transformation rules are as follows:
- A roller support in the real beam becomes a roller support in the conjugate beam.
- A hinged support in the real beam becomes a hinged support in the conjugate beam.
- A fixed support in the real beam becomes a free support in the conjugate beam.
- A free support in the real beam becomes a fixed support in the conjugate beam.

5. Explanation: In the case of a fixed support in a real beam, it provides maximum resistance to bending moments and shear forces. However, in the conjugate beam, the fixed support needs to be replaced by a support that provides no resistance to bending moments and shear forces. This is why the fixed support in a real beam becomes a free support in the conjugate beam.

In conclusion, the fixed support in a real beam becomes a free support in the conjugate beam because the support transformation rules dictate that a fixed support in the real beam should be replaced by a support that provides no resistance to bending moments and shear forces in the conjugate beam.