x and y defined by Eq. (14) of Z continue to hold generally. If we write (B) 



somewhat differently (by setting the expression in the parenthesis over a denomi- 

 nator and substituting partially for f> its value from Eq. (18) of Z), we get from 

 the foregoing expression: 



'-?T?TT(^'*;r7fc[ < °"-"' , '- 2 * '*4- 



(6) 



where 



ft = i [l + (1 + <V] [ 2 + (1 - F)f ] = 1 + 1.65/0 + 0.455/O' 

 f**= (1 - <v-)[l + (1 + 2 r)p - (1 - <T 2 )(1 + f-^ffV 2 ] 

 = 1 + 1.3/° - 1.39 f> 2 - 1.417/0 3 + 0.507/O 4 



Here as in Z 

 h a 



x = 



3a a ' 



y = p a/2h 



1 -o- 2 



*c a 



(°=n^T 



(6«) 



and E and (T are the elastic constants (<T = 0.3). The determination of y from 

 Eq. (6) is not particularly cumbersome once the two functions of p , II, and U v 

 have been computed, and placed in the form of tables or curves for in ( and u. z . 

 Fig. 3 contains the two curves for the entire range f> = to 1 sufficiently ade- 

 quate for all practical cases. 



[Translator's Note: The error noted in equation (B) of Z which was carried 

 through to the final formula (B) in Z has been corrected in the derivation of 

 formula (6). Hence, formula (6) is correct despite the error in the original 

 equation (B) in Zj 







Q 





Q£ 



0,3 



0,4 



0,5 



0,6 



°7 



0,8 



0,9 



I.0 













































\n 











































3,0 

















































































































































































r"S 











































-?,5 

















































































































































































?,n 





















£y 





















«?,0 















































































































































































I.S 











































is 































































































































































Jjg 





















10 











































1.0 

















































































































































































OS 











































0,5 

































































































































































































































c 



,l 



c 



4 







3 



6, 



4 



C 



),5 







6 







7 







S 







9 



I 



b p 



FIG. 3. Auxiliary Functions jti, and ju, for 

 Use in Computations by Formula (6). 



