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Lecture 2 : Castigliano’s Energy Theorems Hans Welleman

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Ir J.W. Welleman Work and Energy methods2 Castigliano uaua uxux FaFa FxFx FbFb ubub FcFc ucuc

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Ir J.W. Welleman Work and Energy methods3 Differentiate the Work to a specific force, e.g. F x : Use Maxwell’s notation :

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Ir J.W. Welleman Work and Energy methods4 Elaborate …

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Ir J.W. Welleman Work and Energy methods5 Castigliano’s 2nd theorem Maxwell : Result:

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Ir J.W. Welleman Work and Energy methods6 Castigliano Work done by external loads A ext is stored in the strain energy E v Differentiate the strain energy to a force at location x to find the displacement u at x

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Ir J.W. Welleman Work and Energy methods7 Example 0,5 l F w max EI

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Ir J.W. Welleman Work and Energy methods8 Strain Energy in terms of the load

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Ir J.W. Welleman Work and Energy methods9 Steps of the solution strategy Castigliano : differentiate E V to a force. E V is integral of the square of the moment distribution so …. differentiate after integration … IS THIS SMART TO DO ??

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Ir J.W. Welleman Work and Energy methods10 Smart help

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Ir J.W. Welleman Work and Energy methods11 Castigliano Second theorem First theorem

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