Castigliano's method

The set of Castigliano (after Carlo Alberto Castigliano ) is the basis for various computational methods in engineering mechanics. It is based on an energy approach and allows the relatively simple calculation of selected sizes.

Set of Castigliano

The partial derivative of the data stored in a linear elastic body strain energy by the external force results in the displacement of the force application point in the direction of that force. Analogously, the partial derivative of the strain energy in accordance with a moment, the rotation of the beam at the point of this moment. In order to determine the deflection at points without force with the set of Castigliano, must be introduced at these sites assistants who are put at deriving zero.

= Strain energy ( strain energy )

= Number of regions

= Lengths of the areas

= Generalized force

= Generalized moment

= Transverse forces

= Longitudinal forces

= Bending moments

= torsional moment

= Shear factors in the cross section

= Generalized commuting

= Local coordinates with

Set of Menabrea

The set of Castigliano can also be used for the calculation of statically indeterminate sizes. In this particular form it will be referred to as a set of Menabrea. The set of Menabrea states that the partial derivative of the strain energy for a statically indeterminate bearing reaction is zero.

With

= Statically indeterminate variables ( whose working path must each be zero)

= Internal energy supplement