The geometric quantities R, h, Lf, A£, . . , etc. are defined at the begin- 

 ning of this report. The pressure Pj^ denotes the elastic buckling load 

 for a cylinder which buckles axisymmetrically in a shape defined by 



w(x)o_; cos 



inTTX 



Lf 



Furthermore, Reynolds uses the notation that internal pressure is posi- 

 tive and external pressure is negative; therefore, for the particular case 

 of external hydrostatic pressure loading which is of interest to us, it is 

 necessary to substitute negative numbers for p wherever it appears in 

 Equations (62) through (71). The multiplying factor (l-p/p^^) appearing in 

 Equation (69) reflects the "beam-column effect" introduced by Salerno and 

 Pulos into the basic eixisymmetric stress formulation. 



It becomes obvious upon examination of the buckling equation (62) 



27 

 that it is transcendental in the pressure. Reynolds suggests a graphi- 

 cal solution by which the left-hand side of Equation (62) is plotted against 



N+1 

 pressure. Such a plot will have zero - intercepts, one for each root 



of Equation (62), and an equal number of asymptotes corresponding to the 



vanishing of each of the denominators Dj. The first asymptote which 



results as a consequence of the denominator Di of Equation (62) vanishing 



corresponds to the buckling pressure for a single-wave simple support 



buckling configuration. The case D3 = corresponds to the buckling 



pressure for a three-wave simple support buckling configuration; and so 



on for D5 = 0, etc. The first "non- singular root" of Equation (62) which 



56 



