On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . it is clear that such aprocess must weaken the rigidity enormously, inasmuch as it tends to render the twohalves of the section independent of each other. When a •= w/G^ ft == w/6, the ratio MyMo is greatest. In this case the section doesnot deviate very much fi^om a square. (For very small values of a and ^ the sectionis, of course, a rectangle») This result shows us therefore that, so far as torsionalrigidity is concerned, the squa^re is a more efficient form of section than any one o
On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . it is clear that such aprocess must weaken the rigidity enormously, inasmuch as it tends to render the twohalves of the section independent of each other. When a •= w/G^ ft == w/6, the ratio MyMo is greatest. In this case the section doesnot deviate very much fi^om a square. (For very small values of a and ^ the sectionis, of course, a rectangle») This result shows us therefore that, so far as torsionalrigidity is concerned, the squa^re is a more efficient form of section than any one ofthose dealt with in the present paragraph. That the circle is a more efficient type of section for rigidity is quite evident fromthe table, since all the values in it are less than unity. It may be interesting to note what are the values of M/Mo for the full we use the values given by Saint-Venant in his memoir on torsion M M ^,—^7, and Mo ---- C(^ + ¥ 9 \(ib Mft (^ + & 0 tanh 2ct5 if hla = tanh a. TOESION OF CERTAIN FOEMS OF SHAFTING. 331 Hence we have, for the fall ellipse M/M(. a == 7r/2, Oi - 27r/3. •9963 •9995 If we compare this with the previous tahle, we see that for the flattest ellipse,a r:r: 7r/6, the ratio of the torsional rigidity to the torsional rigidity of the circularsection of equal area, which I projDOse to call for brevity the relative torsional rigidity,is greater for the truncated than for the full ellipse, except in the last case, j3 :^ last must necessarily be, since the strength of the section should be reduced bycutting two slits into it along the major axis. For the higher values of a we seethat the relative torsional rigidity is always greater for the full than, for thetruncated ellipse. § 11. Values of the Stresses at the Points of Symmetry. Passing now to the values of the stress, the values of Sb//xtc are given, for thesixteen symmetrical sections, in the table below. Table of SbZ/xtc. ft = tt/Q. ft = 7r/4. ft - 7
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