The solutions for torsional stress and torsional stiffness of circular shafts with flat sides which are presented in this paper have been obtained by means of the relaxation technique. The solutions for both shear stress and torsional stiffness are given for four ratios of flat side dimension to diameter of the shaft. The stress for a very small flat has been obtained by use of a hydrodynamic analogy to the torsion problem. A comparison of the results obtained is made with those given by Ōkubo.

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