;;K; Mi;. I.. X. C. FII.ON OX TIIK KKSISTAXCE TO 



The shears are given by the equations 



= (siuh cos i] " cosh sin 77 ' \ re sinh sin 77 (l -f sech 2a) 



1 / ... dn), . . , * tlia\ .. . 



= - - (cosh f sin 17 -rr -f smh f cos 77 -, j + TC cosh cos 17 (1 sech 2a) 



where J now stands for the quantity 



cosh 2 f sin 2 rj + sinlr f cos 2 17. 

 Tlio torsion moment M 



(27), 



= J [(* 



= fire* dr) dg {cosh 2 f cos 2 y (1 sech 2a) + sinlr f sin 2 17 (1 + s ech 2a)} J 



Jo J - * 



fa 



d (cosh 4 cos 477) sech 2a (cosh 2f cos 217) 



J-a 



sech 2a (cosh 4^cos 2rj cosh 2^ cos 477) 



ac 8 f r " B x* 6 * r a r ~Y 



+ - >i sin 2rt a-n -{ - u\ smh 2f f. 



^ Jo L _i- ^ J-a L J 



When this is integrated out and reduced as before, it is found that 

 M _ prr f ^ gjjjh 4 a ^_ a s j n 4^3) tanh 2 2a 



+ 2 sin 2/3 (2a sech 2 2a tanh 2a) (cosh 2a - cos 



- 204 8a 4 (cosh 2a - cos 2jS) 2 "/ 



tanh 



2n 



(28). 



(2n + 1) [TT* (2w + I) 8 + 16a ! ]' 



21. Alternative Solution for these Sections. 



For this type of section also we can find an alternative solution. 



Suppose we assume 



sinh 2 sin 2n , 

 M>= ire 2 - + v;,. 



cos 



These conditions (24) reduce to : 



,. 

 = ) f = a, 0<^ 



div t /dr) = i; = /3 a < < a 

 Also the condition of continuity requires that u>, must be odd in 



. . (29). 



