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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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