Now, transforming to forces, moments, and locations measured with respect to point e (see 

 Figure 10) located at y =y, z =z, we define V , ivi , M to be forces and moments referred 

 to axes at point e: 



Also we define: 



v.. = V. 



M = M - z V 



y y X 



M^ =M, + yV, 



Yi = y +yei 



[3] 



where y ., z . locate node i relative to point e. 



Substitution of the definitions of Equations [3] into Equations [2] leads to: 



V = (B + Cy + Dz)SA. + Cly A+DXz A. 



x^ ^' '1 ^eii eii 



M =(B + Cy+Dz)Sz .A. + C Iy,,z^.A. + D X z .^A. 



y V '^ ' e 1 1 •^ e 1 ei 1 ei i 



M =-(B + Cy+Dz)Sy .A. - Cly 2A.-D2y .z A. 



z \ •' ' ■' e 1 1 •'ei 1 ei ei i , 



Now choose y and z by the following: 



Sy.A. Sz.A. 



•' 1 1 11 



2A. 



SA: 



[4] 



[5] 



Then 



Sy^.A. =S(y^-y)A. = ly.A. -y SA. =0 

 Iz .A. = 2(z. - z) A. = Sz. A. - z SA. = 



ei 1 ^1 '1 11 1 



and Equation [4j now becomes 



V^ = (B +Cy + Dz) 2A. 



M = 



y 



M = 



C Sy z A. + DXz .2A. 



•'eieii ei i 



-C 2y,,2A. - D Sy .z .A. 



[6] 



62 



