# Explanation Of The Castigliano’s Theorem

Strain energy is a very important term in classical engineering. And strain energy of bodies is used in many engineering calculations. One of these calculations is Castigliano’s theorem. Here we simply explain Castigliano’s theorem.

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## Types Of Strain Energy Storages In Engineering

First of all, the general sources of strain energy inducers must be known, to understand Castigliano’s theorem. These are;

## Castigliano’s Theorem

Castigliano’s theorem states that, if the total stored strain energy is known because of a load in a certain direction, the partial derivative of this stored strain energy with the deflection in the direction of the load, gives the load itself. And it has the equation like this;

Also, if the partial derivative of the total stored strain energy with the applied load in a certain direction is performed, it will give the total deflection in that direction because of the load. Also, this theorem has the equation like this;

## Conclusion

A simple explanation of Castigliano’s theorem can be made like above.