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Question
If the strain energy of a deformed elastic body is represented as a function of the displacements d1, d2, ..... a, partial derivative of that function with respect to any chosen displacement gives the corresponding force. This statement/principle is called as
A.
Principle of strain energy
B.
Maxwell's law of reciprocal deflections
C.
Conjugate beam/truss principle
D.
First theorem of Castigliano
Answer ( Option D)

First theorem of Castigliano

Solution

Castigliano's First Theorem: 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 i.e.
                       
Castigliano's Second Theorem: The first partial derivative of the total internal energy (strain 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 i.e.
                         

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