Variationsprobleme des achsial- und querbelasteten geraden Balkens

In der Theorie 2. Ordnung der Balkenbiegung lassen sich, ausgehend vom Variationsproblem des Extremums der potentiellen Energie, über das kanonische Variationsproblem eine Reihe neuer Variationsprobleme formulieren, u. a. ein Analogon zum Satz von Castigliano. Im Falle axialen Zugs können die Querverschiebungen des Balkens eingegrenzt werden.

Treated is the bending and buckling of a straight bar. The variational principle of extremal potential energy is transformed into the canonical variational problem for displacements and internal forces. This is the starting-point to win different new variational problems. Several instances are quoted, e.g. the analogon to Castigliano's principle and a variational problem for the displacements which leads to an integral equation. Maximum and minimum properties are investigated. In the case of axial traction there is the possibility to set limits to the deflections.


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