Why use Castigliano's theorem

You can apply Castigliano's theorem if you should have some background with :

• Deflection of a beam/cylinder due to axial loading, bending, torsion.
• For calculating the normal moment of inertia.
• For calculating the polar moment of inertia.
• Deriving equations for linear changes in quantities.
• Using singularity functions but it is often used in conjunction with Castigliano’s Theorem.
• Determining the deflection of beams 
• Castigliano’s Theorem uses strain energies at the locations of forces to determine the deflections.
• For determining of deflections for objects with changing cross-sectional areas.