-3- 



The shear forces N, and Ng that act in the w - direction cannot he ex- 

 pressed by means of displacements, but can be determined only through bending 

 equilibrium. 



From the previously considered resultant stresses, three different 

 stress moments, G]^, G2, and H^arise. The moment G]_ is due to the normal stresses 

 in the cross-section of which T-^ was the resultant. It causes in the first line 

 a curvature K^ of the cylinder-generator. Similarly, the normal stresses in the 

 longitudinal cross section give a bending moment 03, that changes the curvature i 

 of the line of intersection by an amount K^' We have then (See Love, p. 543) 



•^-fe' K,=i,(-0+|f) --(4) 



(Translator's note: In the text — is given in the place of -2) and considering 

 the cross contraction (Poisson's ratio) similar to eq.(5) (See Love,p.550,eq.37) 



Gi = -c ^ (Kj^ +(yK2), G2 = -c y- (Kg +0-%) (5) 



The factor w- in eq. (5) together with the 2h contained in c, eq. (2), 

 gives the moment of inertia of the rectangular cross-section of height 2h and 

 breadth unity. 



The shearing stresses whose resultant is Nq^, produce a moment H about 

 the X-axis that tends to make the rectangular element dx a dyof the tangential 

 plane into an oblique quadrilateral. The deformation in this sense is (See Love, 

 P.543) 



cx)=-LJ-(A^ + v) (6) 



^ dx \ay / 



and the moment H becomes (See Love, p.530» eq.37) 



H = c |!. (1 -0-) 00 (7) 



(Translator's note: In the text h* is given in place of h^). 



An equally large turning moment about the v-direction acts in the long- 

 itudinal section. 



2. The Conditions of Equilibrium. 



The equilibrium of the forces in the u- and v-directions requires (See 

 Love, p.535» eq.(45) ) 



dx ady acJy dX ^ (8) 



(Translator's note: See also Prescott's "Applied Elasticity", p.549f eq.i7.98, 

 and p. 550, eq. 17.102). 



