tqJ =[Q] 



^f ^ 



"vy2 Qvz2 Qt2 



'Vyj "^vzj "^Tj 



We have also determined (from Equation [39J) the term 



[27], [28J 



^•^-'^""''^"l^^ GSQ,.(y,,z,.-y,.z,.) 



[42] 



Now, to apply Castigliano's Theorem, note that the shear strain energy per unit 

 length in all the plates is (see pages 45, 53, 54 and 69): 



W 1 



W = — = 



Ax Ax 



^ (Vol.). = — y— — (t. As. Ax) 

 . 2G J AxZ_2G y ' ' 



[43] 



- 1 ^^^i 



W=— y— ^ q.2 

 2G^t. ^' 



Substituting from Equations [27]" and [28] yields: 



- 1 v-.^'j 

 W 



20 



i^E-T (Qvyi^ V/ . 2Q,^. Q,,. V^ V^ . 2Q,^. Q,. V^ M^ 



+ Qvzj'^z'-2Q^^.Q.j-jV.M, +Qt,.2m^2) 



Application of Castigliano's Theorem gives: 





dW 1 

 y 



As 



VyEr^Qv./^v^E 



^xE-r^QvviQTj 



As. 



^ QvyjQvzj 



[44] 



[45] 



77 



