Ductile Materials under Combined Stress. 



95 



or 



U^- e i-"th^^M^~%} 



n/2 



Q are £ 2 i? 2 &, 



or . it 



sin 



- + 2 cos 0, ; sin — -f 6> 2 sin 2 ; cos — ^ - 2 ; 



or 





To find L or x 2 y 2 z 2 , we have : — 

 (1) Since < LOP = <KOP, 



«*f 1 +#2*71 + 2 8 ?1 = £l* 1 + *7#i + &*1 



And (2), since LOPK is a plane, 



= . . 



0, 



3/2 



~2 



fi 



«h 



?1 



*! 



yi 



Z \ 



and 



0) 



(2) 

 (3) 



'rf+yi+tf=i 



Hence from (1) 



»,(i+»i- -| 2 - ^) +j,(i + w, +-- s (i-«, - f) 



or to the first order 



# 2 (l + 1 )+# 2 <£i + s 2 (I-0 1 )==l + 1 +«; . . (4a) 



.*. # 2 + 2 2 =l to first order (5) 



From (2) 



#2 



y 3 



i+ei- 4-i£, (i+^ 1-0,-^ 



2 



= 0; 



