Castigliano's theorem 2 falls under ______ method.

Explanation:

Castigliano’s first theorem: 

• It is a type of force method and it states that the first partial derivative of the total internal energy (strain energy) in a structure with respect to any particular deflection component at a point is equal to the force applied at that point and in the direction corresponding to that deflection component.
• This first theorem is applicable to linearly or non-linearly elastic structures in which the temperature is constant, and the supports are unyielding.

Castigliano’s second theorem: 

• The first partial derivative of the total internal energy in a structure with respect to the force applied at any point is equal to the deflection at the point of application of that force in the direction of its line of action.
• The second theorem of Castigliano is applicable to linearly elastic structures with constant temperature and unyielding supports.