The fixed support in a real beam becomes a free support in the conjugate beam. Let's understand this concept in detail.

Conjugate Beam Method:
The conjugate beam method is a structural analysis technique used to determine the bending moment and shear force in a beam. It is a mathematical tool that simplifies the analysis of complex beam problems by replacing the real beam with a hypothetical beam known as the conjugate beam.

Conversion of Supports in Conjugate Beam:
When converting a real beam to a conjugate beam, the supports undergo a transformation. Here is how the fixed support is converted to a free support in the conjugate beam:

1. Fixed Support:
A fixed support in a real beam provides both vertical and rotational restraints. It prevents any vertical movement and rotation at that particular support location. The fixed support generates bending moment and shear forces in the real beam.

2. Conjugate Beam:
In the conjugate beam, the vertical and rotational restraints provided by the fixed support are removed. The fixed support is transformed into a free support in the conjugate beam. This means that the conjugate beam can move vertically and rotate freely at the location corresponding to the fixed support in the real beam.

Explanation:
The conversion of a fixed support to a free support in the conjugate beam is based on the principle of virtual work. According to this principle, the deflection in a real beam due to external loads is equal to the deflection in the conjugate beam due to the bending moment caused by the same external loads.

By transforming the fixed support into a free support in the conjugate beam, we allow for vertical movement and rotation at that particular location. This enables the conjugate beam to develop the same deflection as the real beam, ensuring that the bending moment and shear force distributions are accurately represented.

Hence, the correct answer is option 'D' - Free support.