Castiglianos Theorem

Question 1

Castiglianos Theorem

Answer 1

‘If the strain energy of a linearly elastic structure is expressed in terms of the system of external loads, the partial derivative of the strain energy with respect to a concentrated external load is the deflection of the structure at the point of application and in the direction of that load.’

Question 2

Castigliano Procedure for Analysis

Answer 2

1. Write down strain energy, U, in terms of all applied loads
2. Differentiate U with respect to an applied load and the result is the displacement caused by that load in the direction of the load

Answer 3

Modified Castiglianos Theorem

Question 4

Castigliano’s theorem for angular movements (second theorem)

Answer 4