734 



löifj dip öifj ) ^ 



joy:, O.y^ d(/, ) ' 



O ' 



i 



(9) 



i dib öip pU' 



p. -q]^ '^os (iV.^•) + ^ cos (/V.v) + ^ ^«^ U^^) 



,/(i),<'k)/('S . 



) -] j -] = u 



o.v óy dz 



>m <<•£) >m 



Ox oy Oz 



If we now introduce the internal tensions Xx, Yy, Z~, Y., Z^, Xy, 

 usual in the Iheorv of elasticity, then hold for the components of 

 these tensions on an element of the surface: 



X,v = A', cos{Nx) 4- Xy cos (Ny) -|- X- cos {Nz) \ 



Y,w= Y,cos{Xx) + YyCos{Ny) 4- Y, cos {Nz) '• . . (10) 



Zy = Zjc cos {Nx) + Zy cos {Ny) H- Z, {cos {Nz) ] 



Further in case of equilibrium: 



p.,. + A\v -. py + Yx = p, + 2:,v — . . (11) 



From (8), (10), and (11) follows: 



d.% Oyy dz~ ' 



du» öil^ dtb , 



■' ^ di/, dzjc ^ iixy I 



The relations (12) introduced into (9) now yield the equations 



dX^. ÖX„ ÖX- 



ex dy dz 



,^^^^_^^ (13) 



OX oy oz 



^ dZ( dZy dZz 

 ox oy oz 



the known conditions of equilibrium for a deformed system. 



(12) 



