EXPERIMENTALLY DETERMINED «/h VALUES 

 j SIMPLE SUPPORTS^ 



300 



250 



200 



150 



a 100 



UJ 



cc 50 



if) 



in o 



UJ 



or 



°-300 

 o 



§250 



_i 



UJ 



£200 

 ll 150 



UJ 



S 100 



50 







■ CLAMPED ENDS 

 X METHOD (b) 

 O SIMPLE SUPPORTS' 

 • CLAMPED ENDS 



METHOD (0) 



METHOD (c) 



CLAMPED ENDS (m.|4) 

 SIMPLE SUPP0RTS(m.|2) 



MODEL 33 



CLAMPED ENDS(m.l8) 

 SIMPLE SUPPORTS (m. I?) 



MODEL. 50 



—Method («-> 

 C.E. S.S. 



-—Method (c)— - 

 C.E. S.S. 



1.12 0.89 

 0.88 0.79 



1.18 0.91 

 1.08 0.93 



14 15 16 17 18 19 20 



NUMBER OF CIRCUMFERENTIAL WAVES 



Fiq. 3 Initial Eccentricity-Shell Thickness Ratio Vebsub 



Number of Circumferential Waves for Model BR-1 (Assumed 



Simplt Supported) 



.05 .10 .15 .20 .25 



ECCENTRICITY- SHELL THICKNESS RATIO (e/h) 



Shell Yielding Pressure for Models 33 and 60 Versus 

 Eccentricity: Shell-Thickness Ratio 



Cylinder —Method (a)-, 



type C.E. S.S. 



TJnjtiffened 1.08 0.85 



Stiffened . 0.85 0.75 



were obtained from the e/A-values listed in Table 3 in conjunction 

 with the theoretical p„ versus e/h curveB similar to Fig. 2. The 

 last three columns in Table 4 show the ratios of theoretically pre- 

 dicted pressures for the occurrence of a visible lobe to those ob- 

 tained experimentally, according to the. various methods used for 

 determining the initial out-of-roundness. The average values of 

 these last three columns, classified according to whether the 

 cylinders were stiffened or not, are tabulated in Table 5. It can 

 be seen from Tables 4 and 5 that use of method (a), with the 

 assumption of Bimply supported ends, was the most conservative 

 in most cases and predicted pressures which were always below 

 those obtained experimentally. However, the best correlation 

 between the experimental results and the simplified theories 

 discussed in this paper appears to be obtained when method (r) is 

 used for determining the initial out-of-roundness and the cylinders 

 are assumed to be simply supported. 



It was mentioned earlier that for a given e/h the value of m that 

 would give the lowest p v was not necessarily the value of m which 

 minimized the expression for p or (Equations [11] in Table 1). It 

 was also noted at that time, however, that the error obtained by 

 assuming this to be so was not very great and also greatly re- 

 duced the computational labor. Some idea of the error involved 

 can be obtained by referring to Fig. 3. The curves in this figure 

 are plots of m which minimize e/h for a given p„. For a p v of 80 psi 

 it can be seen that the minimum value of e/h is 0.34 at m ■= 18, 

 while at m = 15 (the value which minimizes p or ) the value of 

 e/h is 0.4. However, if we now fix the value of e/h at 0.4, then 

 the minimum value of p v is 75 psi and occurs at m =■ 19. Similar 



180* 

 (MID-LENGTH OF CYLINDER) 



Fio. 4 Typical Initial Circularity Contours for Model 

 BR-i 



results are obtained with the other curveB and also with the m 

 versus e/h curves for clamped-end cylinders which we have not 

 included here. It is thus seen that assuming the value of m which 

 minimizes p or will also minimize p v for a given e/h is slightly on the 

 unsafe side, the magnitude of the error depending on the value of 

 e/h taken. However, owing to the fact that actual cylinders under 

 hydrostatic pressure collapse in substantially the same number of 

 lobes as is predicted by theory for the perfect cylinder, and also for 

 simplicity in calculations, we have ignored this discrepancy. 



It also will be remembered that in applying the analyses to 

 stiffened cylinders we made the assumption that the stiffening 

 rings were perfectly circular. This, of course, never occurs in 

 practice. Some idea of thg degree of circularity actually present 

 can be obtained by reference to Fig. 4. ThiB figure shows the 

 initial circularity contours of the stiffening rings bordering, and the 



