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**Lecture 2 : Castigliano’s Energy Theorems**

Hans Welleman

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**Work and Energy methods**

Castigliano ua ux Fa Fx Fb ub Fc uc Ir J.W. Welleman Work and Energy methods

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**Differentiate the Work to a specific force, e.g. Fx:**

Use Maxwell’s notation : Ir J.W. Welleman Work and Energy methods

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**Work and Energy methods**

Elaborate … Ir J.W. Welleman Work and Energy methods

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**Castigliano’s 2nd theorem**

Result: Maxwell : Castigliano’s 2nd theorem Ir J.W. Welleman Work and Energy methods

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**Work and Energy methods**

Castigliano Work done by external loads Aext is stored in the strain energy Ev Differentiate the strain energy to a force at location x to find the displacement u at x Ir J.W. Welleman Work and Energy methods

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**Work and Energy methods**

Example 0,5 l F wmax EI Ir J.W. Welleman Work and Energy methods

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**Strain Energy in terms of the load**

Ir J.W. Welleman Work and Energy methods

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**Steps of the solution strategy**

Castigliano : differentiate EV to a force. EV is integral of the square of the moment distribution so …. differentiate after integration … IS THIS SMART TO DO ?? Ir J.W. Welleman Work and Energy methods

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**Work and Energy methods**

Smart help Ir J.W. Welleman Work and Energy methods

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**Work and Energy methods**

Castigliano Second theorem First theorem Ir J.W. Welleman Work and Energy methods

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