regardless of whether B is determined from Equation (86), (87), or (88). 

 The significance of this will now be demonstrated. 



Let us assume that the two values of B are different in Equation (93) 

 and designate them B^ and Bj-x for the numerator and denominator terms, 

 respectively. In the elastic buckling range, Equation (93) should reduce 

 to the pressure p^^, i.e., 



PjEPe = 



(^^/R)Bn 



1 + 



«yh/R\2--2 



(94) 



2PE 



This leads to a quadratic equation in p-^ which, when solved, yields 



i(!i!:Wi 



Pe - 2 \ E 



B_ ± 



N \ N 



B-.'-i:' 



D 



(95) 



where the lower of the double signs is to be considered. Now, taking the 

 partial derivative of Equation (93), with the appropriate N and D sub- 

 scripts on B, with respect to pp leads to the following expression for the 

 slope of the pj versus p„ curve: 



ifW^^i 





(96) 



pe^iit"; % 



Substituting the value of p^. given by Equation (95), with the minus sign in 



front of the radical, into Equation (96) leads to the following: 



apj 

 aPx 



%/V' 



V^-<\/V' 



(97) 



64 



