The elastic problem of a homogeneous circular ring acted upon by equally spaced concentrated twists of equal magnitude

Conclusions With the reservation and assumptions stated at the beginning of the preceding Section 8 the results derived in the present paper can be briefly formulated as follows:A homogeneous circular ring acted upon by equally spaced concentrated twists of equal magnitude is always free of torques. The bending moment B₀, represented by a vector normal to the original plane of the ring, vanishes, if one of the two cross sectional principal axes is situated in the plane just mentioned; the case that the two principal moments of inertia of the cross sectional area of the ring are equal to each other is a special case of the one just taken care of. If the angle t is essentially different from zero [cf. definition of case (I) in Section 8], which means that C₁ and C₂ are actually different from each other, then the bending moment B₀ is different from zero and given by our formula (64). This is basically the solution of our problem of a circular ring under concentrated twists, because the effects of the bending moments B, see formula (2), can be studied by means of elementary methods.The present paper is dedicated by its author to the memory of his teacher Professor Dr. Richard von Mises (April 19, 1883–July 14,1953).