Bettie's law (Rayleigh theorem),What is Bettie's law? 2021

 Bettie's law (Rayleigh      theorem):-

When material is linearly elastic, supports are unyielding and temperature is constant Then the virtual work done by P-system of forces in going through displacement caused by Q-system of forces is equal to the virtual work done by Q-system of forces in going through displacement caused by P-system of forces.



Limitations:-

1.material is linearly elastic
2.temperature is constant
3.supports are unyielding


Example:-





Special cases for Bettie's law:-

Case -1 :-If theta-1 be the rotational displacement in the direction of M1 caused by  M2 and theta-2 be the rotational displacement in the direction of M1 caused by M1.


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