This bachelor thesis at hand deals with the energy principles of
Castigliano and Menabrea, which are used in analytical mechanics. These
methods are applied to various examples from the field of mechanical
engineering. At the beginning of this work, the derivation of these
principles is reconstructed under the simplifying assumption that no
oblique bending occurs and that no shear is taken into account (because of
the consideration of long slender rods it can be neglected). First, the
relation between strain energy, forces, dispacements and tension are
inserted in the principles of Castigliano and Menabrea. Then, the formulas
are manipulated so that they can easily be applied to any problem. In order
to demonstrate the application of the principles, they are used to solve
increasingly complex tasks. In this process, typical procedures are
explained and frequent mistakes are examined. In the following, oblique
bending is incorporated to the formulas of the principles. The formulas are
extended with the necessary terms and the working principle is demonstrated
in problems. Summarizing, all previous experiences and advices are merged
into a detailed instruction plan to systematically solve problems using
Castigliano's and Menabrea's method. This plan is used as a basis for all
problems in the following. Finally, chosen parameter values are inserted
into some symbolic solutions, so that they can be compared and verified by
solutions governed by the commercial engineering simulation software
"Ansys".