Equations (60) and (57) are of identical form; the only difference between 



the two is the factor 



\4 m 4 c 



which multiplies n in the denominator of Equation (60). The quantities 

 6jj^ and Sq appearing in Equation (60) can be determined from the stress 

 expressions given in an earlier section. It can be shown that using 

 Equations (16) and (18), respectively, 



C3. 

 > 



m V J^ 2 



„ .l.^L^F 



0=1 



o 



-(^-T) 



(61) 



Of particular interest is the fact that when "^AMf - "^u' ^hen rn = o = 1» 

 and this reduces Equation (60) exactly to (57); the assumption that the pre- 

 buckling stress _ pR 



C!, = Ci = - -r 



<t)Mf u h 



was used by Von Mises. For closely framed cylinders where the 

 stiffening effect is appreciable. Equation (60) may predict elastic buckling 

 pressures on the order of as much as 50 percent higher than those of 

 Equation (57). This suggests that the predictions from Equation (60) be 

 used in any comparison between theory and experiment but that some 

 conservatism in design of hulls can be introduced by the use of Equation 

 (57). 



A major contribution to the solution of shell-buckling problems was 

 made by the group at the Polytechnic Institute of Brooklyn working under 



51 



