488 THE BELL SYSTEM TEfHXICAL JOURNAL, MARCH 1957 



We assume the ^-axis lies along the disc axis so t^z = —P and by sym- 

 metry Txi = Tyy. The condition of no lateral strain states e^ = Cyy = Q 

 which when combined with (4) gives 



_ cr 



'yy — 



Txx " Tui/ — :: I 



1 - a 

 Using the last result with (6) we obtain 



kP (I + (j\ 



and 



P ~ 1 dP~ ~pdP~ 3 Vl - o-y 



Combination of (2), (3), and (7) results in 



\_dC_ ^ \ {e- !)(£: + 2) 1 fc / l + a ' 



CdP L 3£ Js VI - (T, 



(7) 



(8) 



C. The Effect of a Hydrostatic Pressure Acting on a Disc 



Assume that conditions are similar to those considered in section B 

 except that e^x = eyy — is now replaced by 



I 



Txx Tyy T, 



The area is no longer independent of pressure so 



CdP~ EdP tdP^ AdP ^ ^ 



Hooke's law, (4), (5), (6), now becomes 



Thus 



= k (10) 



(11) 

 (12) 



