Method of superposition
The method of superposition is not used in the analysis of a fixed beam. This method is commonly used in the analysis of structures to determine the response of a structure to a combination of loads by considering the individual effects of each load separately and then summing them up.

Analysis of a fixed beam
When analyzing a fixed beam, there are several methods that can be used to determine the internal forces and moments in the beam. These methods include the area moment method, the double integration method, and the strain energy method.

Area moment method
The area moment method, also known as the moment distribution method, is a popular method for analyzing beams and frames. It involves breaking the beam into smaller sections and calculating the bending moments at each section using the principles of equilibrium. The total bending moment at any section is obtained by adding the moments contributed by the applied loads and the moments transferred from adjacent sections.

Double integration method
The double integration method is another commonly used method for analyzing beams. It involves integrating the equation of the curvature of the beam twice to obtain the equation of the deflected shape. From the deflection equation, the bending moment and shear force distributions can be determined.

Strain energy method
The strain energy method, also known as the Castigliano's method, is a powerful technique for analyzing structures. It is based on the principle of virtual work and involves calculating the strain energy stored in the structure due to the applied loads. By taking partial derivatives of the strain energy with respect to the applied loads, the displacements and internal forces can be determined.

Conclusion
In conclusion, the method of superposition is not used in the analysis of a fixed beam. Instead, the area moment method, double integration method, and strain energy method are commonly used to determine the internal forces and moments in a fixed beam.