[Q] 



Vyl 



"^Vzl 



^5t1 



Vy2 



Qvz2 



Qt2 



Vyj 



Qv., 



QTi 



[28] 



Because the strain energy per unit length W is quadratic in q. and, therefore, in V , 

 V , Mjj (see page 48) we know that the form of the equations relating deformation to forces 

 and torques will be: 



z 



(9x 



N,, V + N,„ V + N., M 



11 y 12z 13x 



12 y 22 z 23 x 



13 y 23 z 33 x 



[29] 



where N.. is constant and N.. = N... 



To transform these equations into a more meaningful form, we can redefine quantities 

 with respect to a point s at y = y, z =1 instead of at the origin. This redefinition of quanti- 

 ties is given by: 



V = V 



y y 



V =V 



z z 



M =M -IV +fv 



X X V ■' 2 



U =U -z( 



y y 



z z -^ 



[30] 



It can be shown (see Equations [2a, b, c] and associated material in Appendix A.l) 

 that if we take y =-N23/N23 , "z = + N^^/Ngg , the transformed equations are of the form: 



d\}. 



d\ 



— + ol 



de 



X 



Nil Ni2 









' ^-y ^ 



-< 



V. - 





7'^ . 



[31] 



74 



