Torsional Rigidities for Bars Under Fully Plastic Torsion

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Abstract
The completely plastic torsion of multiply connected cylindrical bars is formulated as a variational problem over a closed convex subset in a Hilbert space. The basic existence and uniqueness questions are answered and an explicit formula for the solution is derived. By using this formulation, a classification of all solid bars has been made according to their torsional rigidities. Finally, it is shown that under fully plastic torsion the circular pipe is the strongest one among all multiply connected bars with the same cross-sectional areas. The last assertion leads to an inequality which has also been generalized and proved here.

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