TORSION OF CERTAIN FORMS OF SHAFTINc. 

 TABLE of M'//*TC 4 . 





If we compare this with the preceding table, we see at once that although the 

 agreement is fairly good for the more compact sections, SAINT- VENANT'S empirical 

 formula utterly breaks down for deeply indented sections. That, indeed, might have 

 been expected, since it takes no account of slits cut into the material. One rather 

 noticeable feature in the comparison is that SAINT- VENANT'S formula always gives 

 too high a value for the torsional rigidity. 



10. Comparison with the Circle. "Relative" Torsional Riyidity. 



In order, however, to compare properly the efficiency or usefulness of these various 

 sections, it was found advisable to refer each of them to some kind of standard, or 

 unit. The most obvious standard, as I thought, was the circular section, this being 

 the one whose torsion obeys the most simple laws. I determined, therefore, to com- 

 pare every section with the circular section of the same area. 



Now if r be the radius of this circular section, its torsion moment M = 

 and the maximum stress S = p.rr. To find r, we have the equation : 



whence 



mi i ,. 



Ihe values ot 



= area of given section == c* ( sinh 2a + a sinh 2/J), 

 M, TT //3 sinh 2a + a sin 2\- 



1 T r "v- / 



S, _ _ /^ sinh 2a -I- a sin 2/S^ 

 HTC \ 



, //8sinh2o -f a sin 2N 

 \ 



) lor the various sections are easily found. 



VOL. cxcin. A. 



2 u 



