The value of redundants will be such that the total strain energy is a minimum. The given statement is from which theorem?

Concept:

To find the slope and deflection of unsymmetric load Castigliano's theorem is used and the two theorems of Castigliano's for structural analysis are as follows:

Castigliano’s 1st theorem:

The partial derivative of the total strain energy of the system with respect to any particular deflection at a point is equal to the force applied at that point in the same direction as that of the deflection.The value of redundants will be such that the total strain energy is a minimum.

\(\frac{\partial U}{\partial \delta}\) = W

Castigliano’s 2nd theorem:

The partial derivative of strain energy of the system with respect to load at any point is equal to deflection at that point.

\(\frac{\partial U}{\partial w}\) = δ 

Also, the partial derivative of strain energy of the system with respect to the couple at any point is equal to the slope at that point.

\(\frac{\partial U}{\partial M}\) = θ 

Where U is the total strain energy of the system.