that adopted here as follows: 



0.91 



ct)bm/ OM - ^ 



1-1/2 (37) 



l-aF2 

 l-aF7 



In Figure 12, the pressure ratio Pc8^Pc6 ^^^ been plotted as a function of 

 the stress ratios, Equations (37) and (38). Thus, Equations (37) and (38) 

 can be used in conjunction with these curves and Equation (35) for p^^ to 

 determine values of the plastic-hinge pressure p^g for different geome- 

 tries. 



The formulas for predicting axisymmetric collapse precipitated by- 

 yielding, and given in this section, represent explicit expressions for 

 collapse pressure only for the special case of zero "beam column" effect, 

 i.e.,Y= 0, since in this case only are the F functions given by Equations 

 (23) through (26) independent of pressure. For the general case in which 

 Y i 0, the stresses become nonlinear functions of the pressure, and Equa- 

 tions (31), (32), (35), and (36) are transcendental in the pressure. How- 

 ever, a numerical iteration procedure can be used in which the collapse 

 pressures p^2>> Pc5' ^^^- ^.re first calculated for Y = 0, and these values 

 are then used as the first approximation in the last of Equations (27) to 

 determine a value of Y- Then, with this value of Y in each corresponding 

 case, new values of the pressures Pc3» Pc5> • • • ^'c. can be found. This 



36 



