Explanation Of The Castigliano’s Theorem

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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. 

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.

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