Summary
Stability problems concerning thin rods and shafts subjected to torsion and thrust are usually treated under the assumption that during deflection the moment vectors of the external couples remain parallel to the axis. In consequence of this rather questionable assumption these problems are nonconservative; in some very simple buckling cases the critical load is found to be zero, and in numerous problems of critical speed every angular velocity results to be critical.
It seems more appropriate to assume that the vectors of the forces contributing to the external moments retain their directions. Then, as a rule, the moment vector is inclined, its slope, however, differing from that of the deflection curve and depending on the manner in which the forces are applied. Under this assumption the problem is conservative and yields new (in some cases even arbitrarily high) values for the critical load.
As a first application the buckling moments are recalculated for a prismatic rod with two equal flexural rigidities, subjected to torsion under various end conditions.
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Ziegler, H. Knickung gerader Stäbe unter Torsion. Journal of Applied Mathematics and Physics (ZAMP) 3, 96–119 (1952). https://doi.org/10.1007/BF02008450
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DOI: https://doi.org/10.1007/BF02008450