On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . position of the fail-points. They show us the connection between therectangular section and the section with a neck, and they give us the limiting cases^when the four fail-points coalesce into two, and vice versa. The four fixihpointsbeOTn to occur after the ratio of the lonff to the short axis of the section exceeds a o o certain value, which depends upon the angle of the bounding hyperbolas. As theindented appearance of the section becomes more obvious, that is, as ^ increases, thisli
On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . position of the fail-points. They show us the connection between therectangular section and the section with a neck, and they give us the limiting cases^when the four fail-points coalesce into two, and vice versa. The four fixihpointsbeOTn to occur after the ratio of the lonff to the short axis of the section exceeds a o o certain value, which depends upon the angle of the bounding hyperbolas. As theindented appearance of the section becomes more obvious, that is, as ^ increases, thislimiting value becomes greater and greater until, when the angle between theasymptotes is less than 73^ the fail-point is always at the vertex of the in no case are the fail-points on the convex; sides of the sections, unless the ellipsesare so flat that the points A are nearer to the centre than the points B. M. BoussiNESQ has given (^Journal de Mathematiques,^ Serie II., vol. 16, p. 200)a sketch of a proof that the fail-points must be sought for sur les petits diametres Fig, 10. Fig.
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