# Lecture 2 : Castigliano’s Energy Theorems

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Lecture 2 : Castigliano’s Energy Theorems
Hans Welleman

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

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

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

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

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

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

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

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

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

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