On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . taken from Gudermanns Tables(^ Theorie der Potenzial ocler Cyklisch-hyperbolischen Ftmctionen^), and fromGlaishers and Neumans Tables of the Exponential Function ( Cambridge vol 13). § 9, Values of the Torsumal lUgidity. The first quantity calculated was the torsion moment. The values found areshown in the table below. 1ABn:K of ,M.,//xTO^ a ^ 7rl% CC = TT -J a V2 CC = JjT^ Z7r/3 [3 = 7r/Q, 7r/4. 3116 1 tt/B. -4055 7r/2, •1710 •4676 •8764 2-0317 3-2205 J 4-8117 3-8798 9*4161
On the Resistance to Torsion of Certain Forms of Shafting, with Special Reference to the Effect of Keyways . taken from Gudermanns Tables(^ Theorie der Potenzial ocler Cyklisch-hyperbolischen Ftmctionen^), and fromGlaishers and Neumans Tables of the Exponential Function ( Cambridge vol 13). § 9, Values of the Torsumal lUgidity. The first quantity calculated was the torsion moment. The values found areshown in the table below. 1ABn:K of ,M.,//xTO^ a ^ 7rl% CC = TT -J a V2 CC = JjT^ Z7r/3 [3 = 7r/Q, 7r/4. 3116 1 tt/B. -4055 7r/2, •1710 •4676 •8764 2-0317 3-2205 J 4-8117 3-8798 9*4161 16^442 ! 29-912 22*898 54-824 96-411 194-18 It is interesting to compare this table with the table of values of the torsionmoment, as given by de Saint-Venants empirical formula, viz., torsion moment fjLT A 40 l where A = area, I = moment of inertia of section about its M this value of the torsion moment, we have ^ (/3 siiih 2a + ^ sin 2^)^ /? si nil 4:ot — a sin 4/3 whence we obtain the following set of values : TORSION OF CERTAIN FORMS OF SHAFTING. ^ t/ -3 Table of MY/xrC*.. /^ = 7r/6. •1835 •9914 4-3368 23^289 ^/4. •32662-375912-195 71826 7r/3. 7r/2, •4152 •4723 3^8023 6-0121 23^260 51-500 152-96 420-95 If we compare this with the preceding table, we see at once that although theagreement is fairly good for the more compact sections, Saint-Venants empiricalformula utterly breaks down for deeply indented sections. That, indeed, might havebeen expected, since it takes no account of slits cut into the material. One rathernoticeable feature in the comparison is that Saint-Venants formula always givestoo high a value for the torsionpJ rigidity, § 10. Comparison ivith the Circle. Relative Torsional Rigidity, In order, however, to compare properly the efficiency or usefulness of these varioussections, it was found advisable to refer each of them to some kind of standard, orunit. The most obvious standard, as I thought, was the circular section,
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