Question

What is the Castigliano's theorem to calculate the deflection and slope of the beam or frame.
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Answer 1

Answer:

Where δ is the deflection at the point of application of force P in the direction of P, θ is the rotation at the point of application of the couple ˉM in the direction of ˉM, and U is the strain energy. The strain energy of a beam was known to be U=∫L0M22EIdx .

Answer 2

Answer:

Castigliano's Theorem for Beam Deflection

For linearly elastic structures, the partial derivative of the strain energy with respect to an applied force (or couple) is equal to the displacement (or rotation) of the force (or couple) along its line of action.

Explanation:

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