38 



Art. 7. — K. Terazawa 



§'29. At the surface these expressions for the stress reduce to 

 simpler ones. 



(89) 



All the tractions acting on the boundary vanish, as they 

 ought to, under the conditions of our problem, except a uniform 

 pressure on the circle of radius a. The state of stress just below 

 the surface is made up of a simple and beautiful scheme of the 



pressure system with a radial tension equal to — ,-, o , ^ • ., inside 

 the circle, and -ötV^^ — ^- — ^ outside it; and a transverse tension 



lU-{- [X) Ttf ' 



2;>+/i 



// 



2(;.+/i) Ticv 



2" inside the circle, and 



/^ 



77 



2(/î + /^) ' nr'' 



equal to 



outside it. 



§30. Along the edge of the loaded circle there occurs 

 a singularity of stress. We have seen ah-eady that as a rule the 

 component stress zi^ vanishes at the Ijoundary surface. But this is 

 not always the case. If we put r=a in (88) and then proceed to 

 the limit z -^ o, we shall have 



{zr\ = — - 



77 



Tta- 



~ , (r = a). 



(90) 



Thus the tangential traction (£?')o does not vanish at the periphery 

 of the loaded area, which is contradictory to our assumed boundary 



