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Lecture 2 : Castigliano’s Energy Theorems

Lecture 2 : Castigliano’s Energy Theorems. Hans Welleman. F a. F b. F c. F x. u a. u b. u x. u c. Castigliano. Use Maxwell’s notation :. Differentiate the Work to a specific force, e.g. F x :. Elaborate …. Maxwell :. Result:. Castigliano’s 2nd theorem. Castigliano.

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Lecture 2 : Castigliano’s Energy Theorems

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  1. Lecture 2 : Castigliano’sEnergy Theorems Hans Welleman

  2. Fa Fb Fc Fx ua ub ux uc Castigliano Work and Energy methods

  3. Use Maxwell’s notation : Differentiate the Work to a specific force, e.g. Fx: Work and Energy methods

  4. Elaborate … Work and Energy methods

  5. Maxwell : Result: Castigliano’s 2nd theorem Work and Energy methods

  6. 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 Work and Energy methods

  7. F EI wmax 0,5 l 0,5 l Example Work and Energy methods

  8. Strain Energy in terms of the load Work and Energy methods

  9. 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 ?? Work and Energy methods

  10. Smart help Work and Energy methods

  11. Castigliano • Second theorem • First theorem Work and Energy methods

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