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BELL SYSTEM TECHNICAL JOURNAL 



The C matrix is 

 entirely analogous 



(8.21) 



Cubic System (^n Sn Sn ^ 



Xi, X2 and x^ Sn Su Su 



fourfold axes _ 5i2 Sn Sn 



3 moduli! ~ ^44 



544 



6*44 



Sn Sn SnO " 



Sn Sn Sn 



^12 ^12 SnO 



^-z 



5'2 



^2 

 6*2 = 2 (Sn ~~Sn) 



Several Elastic Ratios in common use are given here for reference: 

 Young's Modulus: A tension stress X divided by the component of 



X- 



strain in the direction of Z , Fj = — ^ . If the coordinate axes are chosen so 



Isotropic bodies 

 2 moduli! 



S = 



The C matrix is 

 analogous except 

 that 



Ci = 2 (^11 "^"12) 



(8.22) 



that the stress lies along Xi , Yi = -—- 



Sn 



To find the value of Y in an arbi- 



trary direction, (6, <p) find S' for a transformation that puts X' in the di- 

 rection (6, (f) 



S' = ac Sa 



Where a is taken as form (21.4). Whence we obtain: 



( y — I = ^152511 -1- 51^2522 + ^25*33 -\- 5i52C2544 + CiC2S2Sit + £15152^^66 



-{- 2C1S1C2S2S5& -{■ 2CiSiC2S2S^ + 2C1S1C2S2S56 + 2C1S1S2S26 

 + 2CiSiS2Sm + 2Ci52Ci5i5 -{• 2CiSiS2C2Su + 2ciC2525i3 



-+- 2ciSiS2Sn + 2S1C2S2S23 + 2^152^2534 + 2ciSiC2S2Sif, 



+ 2C1C2S2S35 + 2Ci5iC252526 + 25iC252524 (8.23) 



Rigidity Modulus: The shearing stress divided by the component of shear 

 about the axis of shearing stress. For shear about xi , 



Ni = 



1 



(8.24) 



Its value in another directions can be found as Ye^ was above. 



