TABLE 2 GEOMETRIC RATIOS, YIELD POINTS, EXPERIMENTAL AND THEORETICAL COLLAPSE PRESSURES FOR STEEL CYLINDERS 



• Numbers in parentha 

 t No distinction made i 

 In the above table. 



■ Calculated for median turfa 



(1) 



(3) 



(8) 



(4) 



(5) 



(6) 





(7) 



(8) (9) 





(10) 

 Pressure to 













Expt. 



Maximum 



Theoretical elastic buckling 



cause axinym- 





L 

 2« 



A 





Number of 

 stiffenera 



buckling 





staining 



pressure from Eq. [11] o! 

 Xablo 1 uai 



f 



metric yielding 

 of stiffened 



Model 



2~R 



(p«> 



p«i 



proosura, 

 p«i 



Simple supports Clamped 



ends 



50 



0.125 



0.0028 



39000 



2 internal 



175 



195 



(18, 19)» 



301 (17) 451.6 



(18) 



284 



83 



0.250 



0.0032 



81000 



2 internal 



183 



189 



(13, 14) 



192.5 (12) 262 



( >M 



226 



es 



0.600 



0.0048 



40000 





2351 



235 



(8,9) 



283 (8) 395 



SipS 





71 



0.500 



0.0085 



44000 





327 1 



327 



S T) 



686 (8) 804 



(9) 





42 



1.000 



0.0033 



48000 





68 



69 



8) 



61.2 (7) 73.4 



(8) 





61 



2..000 



0.0040 



39000 





48 <• 



48 



(6,6) 



41.1 (6) 60,2 



(6) 





BR-1 



0.184 



0.0024 



61700 



5 external 



80 



107 



(16) 



135 (16) 188 



vU 



322 



BR-4 



0.250 



0.0049 



50800 



6 external 



390 



390 



(10) 



613 (11) 848 



12) 



560 



BR- 6 



0.184 



0.0023 



54400 



5 external 



80 



95 



(14) 



120 (15) 186 



(17) 



284 



s of shell at mid-bay length using analysis of von Sanden and Gunther in conjunction with octahedral shear stress criterion 



TABLE 3 



U) 



BR-1 

 BR-4 

 BR-5 



MAXIMUM s/a-VALUES OBTAINED BY DIFFERENT METHODS FOR DETERMINING INITIAL OUT-OF-ROUNDNE8S 



(2) 



(8) 



(4) 



(6) 



(6) 













Method («) 





. Method (ci 





, (i) Outward . 



. (ii) Inward , 



, Max. of (i) and (ii) , 



C.E. S.S. 



C.E. 



8.S. 



Method (t>) 



C.E. 



S.S. 



C.E. 



S.S. 



0.186« 



0.140 



0.176 



0.016 



0.017 



0.074 



0.078 



0.074 0.078 



0.097 



0.104 



0.098 



0.067 



0.078 



0.085 



0.093 



0.085 0.093 



0.043 



0.047 



0.041 



0.041 



0.045 



0.082 



0.037 



0.041 0.045 



0.139 



0.148 



0.118 



0.008 



0.011 



0.090 



0.098 



0.090 0.098 



0.267 



0.272 



0.191 



0.080 



0.091 



0.114 



0.121 



0.114 0.121 



0.125 



0.180 



0.082 



0.027 



0.033 



0.022 



0.027 



0.027 0.083 



0.575(6)* 



0.815(8) 



0.554(2) 



0.819(6) 



0.375(6) 



0.287(8) 



0.802(6) 



0.819(8) 0.875(8) 



0.164(4) 



0.176(4) 



0.128(2) 



0.063(4) 



0.068(4) 



0.073(4) 



0.082(4) 



0.073 4) 0.082(4) 



0.741(4) 



0.758(4) 



0.502(4) 



0.236(10) 



0.286(10) 



0.210(4) 



0.247(4) 



0.238(10) 0.285(10) 



* Tabulated values accurate to approximately ±5 per cent. 



t Numbers in square brackets indicate the stations at which lobes first appeared i 

 tiona at which the maximum a/a-valuee occurred, according to the method used. 



. the multibay stiffened cylinders. Numbers in parentheses are the eta- 



(1) (2) 



Model --Method (o)^ 

 no. C.E. S.S. 



86 



278 



71 



332 



42 



56 



Gl 



56 



BR-1 



74 



BR-4 



804 



BR-5 



67 



— M< 



(3) 

 ithod (6)-- 



(4) 

 , — Method (c) . 



(5) 



(6) 

 .—Col. (2)/Col. (5)-> 



(7) 

 —Col. (3)/Col. (6)-> 



—Col. (4)/ 



Col. (6)— 



C.E. 





S.S. 



C.E. 



S.S. 



Expt. 



C.E. 



S.S. 



C.E. 



S.S. 



C.E. 



S.S. 



137 





125 



180 



160 



175 



0.863 



0.766 



0.784 



0.715 



1.03 



0.916 



128 





118 



135 



120 



133 



0.978 



0.866 



0.984 



0.873 



1.01 



0.903 



282 





234 



283 



230 



235 



1.18 



0.971 



1.20 



0.996 



1.20 



0.980 



352 





317 



384 



333 



327 



1.02 



0.910 



1.08 



0.970 



1.18 



1.02 



60 





44 



65 



48 



68 



0.985 



0.718 



1.03 



0.769 



1.12 



0.793 



66 





39 



59 



40.5 



48 



1.14 



0.793 



1.17 



0.813 



1.23 



0.845 



75 





67.5 



98 



80 



80 



0.922 



0.788 



0.938 



0.844 



1.22 



1.00 



331 





298 



390 



340 



890 



0.780 



0.686 



0.850 



0.765 



1.00 



0.872 



68 





61 



92.5 -, 



76 



80 



0.713 



0.825 



0.850 



0.783 



1.16 



0.950 



of the shell. The geometric ratios, yield points, experimental and 

 theoretical collapse pressures for these cylinders are given in 

 Table 2. The first six models in this table were tested some 20 

 years ago by Windenburg and Trilling (II), although they did 

 not investigate theoretically the effect of initial outr-of-roundness 

 on the collapse pressure. The last three models, which are multi- 

 bay cylinders, have been tested recently at the Taylor Model 

 Basin (13, 14). 



A comparison of columns 6 and 8 in Table 2 shows a consider- 

 able discrepancy between the experimental and theoretical 

 buckling pressures for even the simply supported cylinders. For 

 some models, it would also appear that axisymmetric yielding 

 rather than buckling was the controlling mode of failure. This 

 can be seen by comparing columns 8 and 10 in Table 2. However, 

 it will be seen later when out-of-roundness is taken into account 

 that the theoretical pressures for buckling-type failures are lower 

 than the axisymmetric yield pressures. It is also of interest to 

 note that Models 42 and 61 are the only models for which the ex- 

 perimental buckling pressures are higher than those predicted 

 theoretically for simply supported cylinders, although the same 

 supports were used for these two models as for the four models 

 preceding them. 



Using the geometric ratios and yield points shown in Table 2 

 aDd Equations [11] and [12] in Table 1, it is possible to construct 

 curves showing the relation between the pressure at which yielding 

 first occurs in the cylinder wall p v , and the ratio of the initial out- 

 of-roundness to the shell thickness e/h. Two such curves are 



shown in Fig. 2 for illustrative purposes. In constructing these 

 curves, the value of m used in Equation [12] was the value of 

 to which minimised Equation [11 ) in Table 1. These valueB of m 

 are listed in parentheses in columns 8 and 9 of Table 2. These 

 values of m do not actually give the minimum p„ for a given e/h. 

 This point will be discussed later. It also should be noted that 

 for e/h — some of the curves in Fig. 2 do not attain the elastio 

 buckling pressures tabulated in columns 8 and 9 of Table 2. 

 When this is found to occur it means that the pressure to cause 

 axisymmetric yielding of. the shell is lower than the elastic 

 buckling pressure. 



In Table 3 are tabulated the maximum e/A-values obtained 

 using the different methods for determining the initial out-of- 

 roundness described earlier. The e//i-values were determined at 

 mid-length for the unstiffened cylinders and at mid-length of the 

 bays for the multibay cylinders. Two values are listed for each 

 model under methods (a) and (e) because, in these methods, the 

 number of lobes into which the perfect cylinder would buckle is 

 used and bjis number is usually different for simply supported 

 and clamped endB. 



Now, selecting the experimental buckling pressures listed in 

 column 6 of Table 2 in conjunction with their corresponding ec- 

 centricities listed in columnB 2, 3, and 6 of Table 3, one can plot 

 points on curves similar to Fig. 2 which represent values deter- 

 mined experimentally. In Table 4 we also give a numerical com- 

 parison of the theoretical and experimental pressures at which 

 visible lobes first occur. The theoretical values in this table 



