320 



In figiire 2 the solutions are plotted in the r^ S, * -plane for several 

 fixed values of CCt). 



Let the symbol D denote the range of r in which the basic equa- 

 tions describe the behavior of the plate. If the boundary conditions are 

 such that D includes the point rs o , then, as one can easily see fxxjm 

 figure 2, the stress distribution must be given by the contour S » ) to 

 which corresponds also the contour S^ » * . If S, » S^ at any 

 point in D , then S, = 5^ at every point in D even though D 

 may not include the point r s o , The condition for the slmlarity of 

 Mohr circles in ccaijunction with the last statement implies (in the first 

 approximation, of course) that if the principal strains £,^ and c^ , are 

 equal anywhere in D > then they are equal everywhere in D , even thou^ 

 again D may not include r = o . If the boundary conditions are such that 

 D does not include fs o , and such that e,^e.^ or S^" -^ S^"^ for 

 any r in Q , the stress distribution will be given by one of the other 

 contours of figure 2 corresponding to the general solution of Eq, (25) with 

 CCt) finite. 



The prospective applications of the present theory are fortxinately 

 characterized by boundary conditions allovdng the range D to include rso» 

 in which case the stress distribution is S, = 5^ = I .In view of 

 the simplicity and wide range of applicability of the uniform stress distrl- 



/' Co) r Co) 



bution b, = O = 1 , the solution of the first approximation will be 

 resumed on that basis. 



Setting 5'"' and 5/**' equal to unity in Eos, (20) and (21) gives 



11 



i 



