TORSION OF CERTAIN FORMS OF SHAFTIXi;. 



TABLE of S./S,, 



13. Investigation of tlie Fail-Points other than the Points of Symmetry. 



The question now arises, are A and B really points of maximum slide, and therefore 

 shear ? Assuming that the fail-points do occur on the contour, are we sure that 

 there are not other points on the boundary where greater maxima occur, and may we 

 not be in presence of a case like that of SAINT-VENANT'S section en double spatule. 



To see whether this is so, it is necessary to go at some length into the equations 

 determining the maximum stress. 



Consider first the sides of the section vj = i ft. It is clear that the resultant 

 stress along this side will be simply the component parallel to the contour, since the 

 normal component must vanish in virtue of the boundary conditions. Calling S this 

 resultant stress, we find easily 



where 



Hence we have to make 



a maximum with regard to 

 We have therefore 



1 1 iat is 



J = (cosh 2 + cos 27?). 



8m 



dw 







8in * = 



Take now the second value of w as given by (17), and we get 



