Abstract
Upper and lower bounds are derived for the torsional rigidity and the maximum shear-stress magnitude. The values provided by Bredt's formulas are characterized as asymptotic approximations. Explicit results on error bounds are included.
Zusammenfassung
Obere und untere Schranken für die Torsionssteifigkeit und den maximalen Betrag der Schubspannung werden hergeleitet. Die von der Bredt-schen Formel gelieferten Werte werden als asymptotische Annäherungen charakterisiert. Die Arbeit enthält ausführliche Ergebnisse über Fehlerschranken.
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References
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Polya, George and Weinstein, Alexander, On the Torsional Rigidity of Multiply Connected Cross Sections, Annals of Mathematics, 52 (1950) 154–163
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Wheeler, L.T. Stress bounds for the torsion of tubes of uniform wall thickness. J Elasticity 4, 281–292 (1974). https://doi.org/10.1007/BF00048611
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DOI: https://doi.org/10.1007/BF00048611