340 



MR. L. X. G. FILON ON THE KKSISTANTE TO 



e- 2 



w =0 







- 16/8 1 





i.e., 



tan 2/3 __ " (2m + l)ir - 2/3 (e-' 2 " 

 8 = .5, 2 



Tli is is the equation giving #. When we put in it /8 = ir/G 



TT = :;// + 1 



5)' 



-<0>l+l 



I find from this = '577 approximately, and the corresponding value of 

 S//UTT = '48984 cosh a. Referring to the value of S A //UTC given on p. 333, we see that 

 the real fail-point is on the broader side. 



The curve of true maximum stress S/S is shown also in fig. 9. It joins on to the 



Fig. 9. 







Showing the variation in the value of S/S as a increases, at the three points A, B, F, of Fig. 2. 



ft = const. = 7T/6. 



curve of S B /S at the point corresponding to the value a = 1 '225. It then remains 

 above the curve of S A /S , tending ultimately to a straight line parallel to the axis, at 

 a^height '8484 above it. 



17. Proof that there can be no other Maxima. 



It remains to show that the point yj = corresponds to a maximum along the side 

 f = a, and also that there is no maximum of the resultant stress inside the section. 

 The stress S along = a is given by 



/Sc\ 1 /dw 



= -p (- Arc 2 smh 2a 



V 



