TOltSiOX OF CKUTAIX FOfcMS OF SHAFTING. 

 We assume, therefore, 



But since 



wlii-iv 





"-" A . 2+l7rr, . . 

 ', = i A.SIM Slllh - 



MO -P -P 



. 7T 

 sin 20 = a, sin 



sin 



a "~ 



(- 1)" 16/9 coa 2/8 



(2n 



we tind easily from the first equation of (29), comparing coefficients 



( - 1) 1 6-1^)3* (cosh 2* - cos 2/9) 



2 n -f lira 



A.. = 



(2/i + l)ir[2w + 1 'TT* - 160*] cush 



and 



. sinli 2f sin 2i; 



M> = 



8111 



'/S 2 (cosh 2a- cos 2/8) 2 ( 1) 



. 2n+l-nrj . . 2n+1ir 



111 - Slllll 



y9 2/8 



(30). 



=o 



The stresses and torsion moment are deduced without difficulty. They are : 



(sinh f cos TJ - cosh f sin 17 ) ( - 1)" sin - "^ sinh "- 



x 2 i_ ^ 



,.-n 



2n + l|ir[2n+ 1 1*^-16)3*] cosh 



= rccosh f cos 77(1 - sec 20) + 





X 2 



d d\, 2n+l7n; . . - 



. (coshgsin^ + siuh gc,-)( - D-sin ^ ,!,- 



. (32). 



- 16/8 1 ] cosli - 



20 



'- (/8 sinh 4a - a sin 4)8) tan 2 2/8 



+ 2 sinh 2* (cosh 2a - cos 2)8) (2)8 sec 2 2)3 - tan 2/8) 



, 2n + ITT 

 tailh 2/8 

 2048 /8 4 (cosh 2a cos 2/8)' 2 , lir t., n+ i y _ 



2 Y 2 



(33). 



